Function Catalog

Reference for the 2816 built-in functions in Grid.

Functions are grouped by category. Within each category they are sorted alphabetically. The signature shows positional parameter names and types; ...name indicates the variadic tail.

Category	Count	Focus
Math	254	Arithmetic, rounding, matrix algebra, calculus, and numeric helpers.
Text	71	String manipulation, parsing, regex, formatting, and template helpers.
Keyword Extraction	1	Keyword extraction, phrase scoring, and lightweight text mining helpers.
Security	6	Password generation, scoring, and security-oriented helpers.
Logical	20	Boolean logic, conditional dispatch, and predicates.
Language & Reference Forms	13	Special forms and reference functions that bind names, create lambdas, or resolve references.
Simulation	14	State, simulated-time, trajectory, and experiment helpers.
Date & Time	27	Date/time arithmetic, formatting, and calendar helpers.
Lookup & Reference	54	Range and table lookups, joins, sorting, filtering.
Financial	208	Time-value-of-money, depreciation, bond math, and other finance helpers.
Statistical	148	Descriptive statistics, distributions, regression, and hypothesis tests.
Statistics & Econometrics	15	Generalized linear models, inequality measures, survey weighting, and econometric inference.
Economics & Time Series	9	Economic-series alignment, resampling, lags, and change calculations.
Civic & Elections	14	Apportionment, ballot tabulation, partisan fairness, and election-analysis helpers.
Algorithmic Game Theory	29	Finite games, equilibrium certificates, auctions, allocation, and mechanism-design verification.
Information	45	Type predicates, error inspection, and metadata accessors.
Engineering	94	Bit operations, base conversions, complex numbers, and engineering helpers.
Logistics	39	Inventory, transportation, warehouse, and service-level helpers.
Planning	40	Project scheduling, earned value, capacity, and risk-planning helpers.
Construction	40	Construction estimating, quantities, production, and cost helpers.
Healthcare	40	Clinical math, diagnostic metrics, medication, and healthcare operations helpers.
Graduate Study	156	Graduate-school helpers spanning management, law, policy, education, psychology, social science, data science, libraries, humanities, design, urbanism, social work, criminal justice, and communications.
Industry Verticals	196	Agriculture, energy, manufacturing, retail, telecom, education, insurance, hospitality, media, mining, public-sector, automotive, professional-services, chemicals, pharma, food and beverage, CPG, water, waste, semiconductor, textile, aerospace, defense, entertainment, and gaming helpers.
Real Estate	67	Real estate valuation, leasing, rent roll, lending, investor return, development, property operations, affordability, transaction, replacement-cost, and tax helpers.
Computer Science	273	Computer science algorithms for searching, sorting, strings, dynamic programming, graphs, ranking, and probabilistic data structures.
Graph	34	Graph construction, traversal, paths, communities, partitions, and network analysis.
Skill Ratings	8	Competitive skill rating systems such as Elo.
Playing Cards	10	Deck construction, shuffling, dealing, and hand helpers.
Card Games	10	Poker, bridge, canasta, rummy, and other card-game helpers.
Casino	18	Blackjack, baccarat, craps, and roulette helpers.
Chess	10	FEN parsing, move generation, and chess position helpers.
Dice & Gambling	21	Dice pools, advantage rolls, and tabletop gambling helpers.
Science	369	Physics, chemistry, biology, lab workflow, astronomy, and earth-science helpers.
Solar Position	10	Solar position, sunrise/sunset, twilight, and Delta T helpers.
Geometry	52	Planar geometry, polygons, intersections, and WKT/GeoJSON conversion helpers.
Geospatial	73	Great-circle distance, bearings, projections, and coordinate conversion helpers.
Aviation	16	Aeronautic atmosphere, navigation, wind, performance, descent, and endurance helpers.
Maritime	16	Nautical distance, vessel speed, hull-form, loading, tide, and current helpers.
Space & Orbital Science	30	Celestial-body constants, gravity, orbital mechanics, and astrophysical planning helpers.
Domain Types	39	URL, molecule, DNA, color, musical note, and bytes accessors and constructors.
Structured Data & DOM	36	JSON, TOML, YAML, and CSV parsing and serialization, deep path navigation, and HTML/XML DOM querying and rewriting.
Database	12	Database-style aggregations over criteria-defined ranges.
Postgres	4	PostgreSQL table handles and bounded async query/mutation helpers.
Redis	2	Bounded Redis key-value reads and idempotent mutation effects.
Native Frames & ETL	52	Native Polars frames, column expressions, ETL pipelines, and frame materialization helpers.
Computed Graphics & Drawing	24	Formula-driven 2-D drawing: primitives, styling, transforms, composition, and SVG rendering.
Computational Vision	18	Classical image processing: construction, colour, resampling, blur, edges, thresholding, morphology, and connected components.
Computational Biology	22	Packed sequence, variant, sparse omics, alignment, indexing, and biological analysis helpers.
Molecular Computing	31	Chemical graphs, descriptors, fingerprints, structures, docking, dynamics, and trajectory analysis helpers.
File I/O	10	Reading and writing local files (TOML, YAML, JSON, text), directory listing, and glob. Paths are confined to the model tree in shared deployments.
External (Async)	16	Functions that execute asynchronously in worker processes.

Total: 2816 functions.

For function-call syntax, see reference.md. For external (async) functions, see external-functions.md. For error semantics, see errors.md. For compatibility status and aliases, see function-compatibility.md.

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Named Constants

Bare-identifier numeric constants usable in expressions without parentheses (for example =PI * r^2, =mass * SPEED_OF_LIGHT^2). Total: 1176 constants.

Math

Name	Value	Unit	Source	Description
PI	3.141592653589793	rad	MATH	The ratio of a circle's circumference to its diameter
TAU	6.283185307179586	rad	MATH	Full circle in radians (2π)
HALF_PI	1.5707963267948966	rad	MATH	Half of π
QUARTER_PI	0.7853981633974483	rad	MATH	Quarter of π
INV_PI	0.3183098861837907	1/rad	MATH	Reciprocal of π
INV_TAU	0.15915494309189535	1/rad	MATH	Reciprocal of τ
TWO_INV_PI	0.6366197723675814	1/rad	MATH	2 divided by π
PI_SQUARED	9.869604401089358	rad²	MATH	π squared
DEG_PER_RAD	57.29577951308232	deg/rad	MATH	Degrees per radian
RAD_PER_DEG	0.017453292519943295	rad/deg	MATH	Radians per degree
GOLDEN_ANGLE	2.399963229728653	rad	MATH	Golden angle in radians
EULER	2.718281828459045		MATH	Euler's number e
LN2	0.6931471805599453		MATH	Natural log of 2
LN10	2.302585092994046		MATH	Natural log of 10
LOG2E	1.4426950408889634		MATH	Base-2 log of e
LOG10E	0.4342944819032518		MATH	Base-10 log of e
LOG10_2	0.3010299956639812		MATH	Base-10 log of 2
LOG2_10	3.321928094887362		MATH	Base-2 log of 10
SQRT2	1.4142135623730951		MATH	Square root of 2
SQRT3	1.7320508075688772		MATH	Square root of 3
SQRT5	2.23606797749979		MATH	Square root of 5
SQRT1_2	0.7071067811865476		MATH	Square root of 1/2
SQRT_PI	1.7724538509055159		MATH	Square root of π
SQRT_TAU	2.5066282746310002		MATH	Square root of τ
INV_SQRT_PI	0.5641895835477563		MATH	Reciprocal of √π
TWO_INV_SQRT_PI	1.1283791670955126		MATH	2/√π (erf normalizer)
CBRT2	1.2599210498948732		MATH	Cube root of 2
CBRT3	1.4422495703074083		MATH	Cube root of 3
PHI	1.618033988749895		MATH	Golden ratio φ
INV_PHI	0.6180339887498949		MATH	Reciprocal golden ratio
SILVER_RATIO	2.414213562373095		MATH	Silver ratio (1+√2)
SUPERGOLDEN_RATIO	1.7598636951969426		MATH	Supergolden ratio ψ
PLASTIC_NUMBER	1.839286755214161		MATH	Plastic number ρ
EULER_GAMMA	0.5772156649015329		MATH	Euler–Mascheroni constant γ
CATALAN	0.915965594177219		MATH	Catalan's constant G
APERY	1.202056903159594		MATH	Apéry's constant ζ(3)
OMEGA	0.5671432904097838		MATH	Omega constant Ω
GELFOND	23.140692632779267		MATH	Gelfond's constant e^π
GELFOND_SCHNEIDER	2.665144142690225		MATH	Gelfond–Schneider constant 2^√2
LEMNISCATE	2.622057554292119		MATH	Lemniscate constant ϖ
MERTENS	0.2614972128476428		MATH	Mertens constant M
TWIN_PRIME	0.6601618158468696		MATH	Twin prime constant C₂
BRUN	1.902160583104		MATH	Brun's constant for twin primes B₂
KHINCHIN	2.685452001065306		MATH	Khinchin's constant K
GLAISHER	1.282427129100623		MATH	Glaisher–Kinkelin constant A
FEIGENBAUM_DELTA	4.66920160910299		MATH	Feigenbaum constant δ
FEIGENBAUM_ALPHA	2.502907875095893		MATH	Feigenbaum constant α
CONWAY	1.303577269034296		MATH	Conway's constant λ
OCTAVE_RATIO	2		MATH	Frequency ratio of one musical octave
PERCENT_100	1		EXACT	One hundred percent as a fraction
PERMILLE	0.001		EXACT	One permille (‰) as a fraction
PPM	1e-6		EXACT	One part per million as a fraction
PPB	1e-9		EXACT	One part per billion as a fraction
DECADE	10		EXACT	Factor of one decade (orders of magnitude)
SCORE	20		EXACT	One score (20)
DOZEN	12		EXACT	One dozen
GROSS	144		EXACT	One gross (12 dozen)
REAM	500		EXACT	Paper ream sheet count
FIBONACCI_12	144		MATH	12th Fibonacci number
FIBONACCI_20	6765		MATH	20th Fibonacci number
LUCAS_10	123		MATH	10th Lucas number
PRIME_100	541		MATH	100th prime number
FACTORIAL_10	3628800		MATH	10 factorial (10!)
COMBINATIONS_52_5	2598960		MATH	Poker five-card combinations C(52,5)

Date & Time

Name	Value	Unit	Source	Description
GREGORIAN_REFORM_YEAR	1582		EXACT	Gregorian calendar reform year
UNIX_EPOCH_YEAR	1970		EXACT	Unix epoch year (UTC)
JULIAN_DAY_EPOCH_YEAR	-4712		EXACT	Julian day epoch year (4713 BC)
JULIAN_CENTURY_DAYS	36525	d	EXACT	Days per Julian century
SYNODIC_MONTH_DAYS	29.530588	d	IAU	Mean synodic month
SIDEREAL_MONTH_DAYS	27.321661	d	IAU	Mean sidereal month
ANOMALISTIC_MONTH_DAYS	27.55455	d	IAU	Mean anomalistic month
DRACONIC_MONTH_DAYS	27.212221	d	IAU	Mean draconic month
LUNAR_NODAL_PRECESSION_YEARS	18.6128	a	IAU	Moon nodal precession period
EARTH_PRECESSION_PERIOD_YEARS	25772	a	IAU	Earth axial precession period
ANOMALISTIC_YEAR_DAYS	365.259636	d	IAU	Anomalistic year (perihelion to perihelion)
LEAP_YEAR_CYCLE	4	a	EXACT	Julian leap-year cycle length
GREGORIAN_LEAP_CYCLE	400	a	EXACT	Gregorian 400-year leap cycle
METONIC_CYCLE_YEARS	19	a	EXACT	Metonic cycle (lunisolar calendar)
SAROS_CYCLE_YEARS	18.03	a	NASA	Saros eclipse cycle (approx.)
WEEKDAY_COUNT	7		EXACT	Days per week
HOUR_MINUTE_COUNT	60		EXACT	Minutes per hour
DAY_HOUR_COUNT	24		EXACT	Hours per day

Financial

Name	Value	Unit	Source	Description
DAYS_PER_YEAR	365	d	EXACT	Days per common year
DAYS_PER_YEAR_LEAP	366	d	EXACT	Days per leap year
DAYS_PER_YEAR_360	360	d	EXACT	Days per 360-day year (ACT/360)
DAYS_PER_YEAR_365_25	365.25	d	EXACT	Days per Julian year
DAYS_PER_QUARTER	91	d	EXACT	Days per quarter (approximate)
DAYS_PER_MONTH_30	30	d	EXACT	Days per 30-day month
DAYS_PER_WEEK	7	d	EXACT	Days per week
MONTHS_PER_YEAR	12		EXACT	Months per year
QUARTERS_PER_YEAR	4		EXACT	Quarters per year
WEEKS_PER_YEAR	52		EXACT	Weeks per year
TRADING_DAYS_PER_YEAR	252	d	EXACT	Trading days per year (US convention)
TRADING_DAYS_PER_MONTH	21	d	EXACT	Trading days per month (approximate)
HOURS_PER_DAY	24	h	EXACT	Hours per day
MINUTES_PER_HOUR	60	min	EXACT	Minutes per hour
SECONDS_PER_MINUTE	60	s	EXACT	Seconds per minute
SECONDS_PER_HOUR	3600	s	EXACT	Seconds per hour
SECONDS_PER_DAY	86400	s	EXACT	Seconds per day
SECONDS_PER_WEEK	604800	s	EXACT	Seconds per week
SECONDS_PER_YEAR	31536000	s	EXACT	Seconds per common year
MILLISECONDS_PER_DAY	86400000	ms	EXACT	Milliseconds per day
BASIS_POINT	0.0001		EXACT	One basis point (0.01%)
PERCENT	0.01		EXACT	One percent as a fraction
EXCEL_EPOCH_OFFSET	25569	d	EXACT	Days from Excel 1900 epoch to Unix epoch
UNIX_EPOCH_JULIAN	2440587.5	d	EXACT	Julian day number of Unix epoch
HOURS_PER_WEEK	168	h	EXACT	Hours per week
RULE_OF_72	72		EXACT	Rule-of-72 doubling-time divisor
GINI_MAX	1		EXACT	Maximum Gini coefficient (perfect inequality)
OKUN_COEFFICIENT	2		CONVENTION	Okun law GDP-unemployment coefficient (US approx.)
COMPOUND_PERIODS_YEARLY	1		EXACT	Compounding periods per year (annual)
COMPOUND_PERIODS_QUARTERLY	4		EXACT	Compounding periods per year (quarterly)
COMPOUND_PERIODS_MONTHLY	12		EXACT	Compounding periods per year (monthly)
COMPOUND_PERIODS_DAILY	365		EXACT	Compounding periods per year (daily)
TAYLOR_RULE_INFLATION_TARGET	2	%	FED	Common Taylor-rule inflation target (US)
FISCAL_QUARTER_DAYS	91.25	d	EXACT	Average fiscal quarter length
PE_RATIO_HISTORICAL_MEAN	15		CONVENTION	Long-run US equity P/E benchmark
DIVIDEND_YIELD_HISTORICAL_MEAN	0.04		CONVENTION	Long-run US equity dividend yield (~4%)
SHARPE_RISK_FREE_HISTORICAL	0.02		CONVENTION	Historical real risk-free rate benchmark
TROY_OUNCE_TO_GRAM	31.1034768	g	NIST	Troy ounce to gram
TROY_POUND_TO_GRAM	373.2417216	g	NIST	Troy pound to gram
BOND_COUPON_SEMIANNUAL	2		CONVENTION	US bond coupon payments per year
BOND_FACE_PAR	1000		CONVENTION	Standard US bond face (par) value
STOCK_SHARE_PAR_COMMON	0.01		CONVENTION	Typical common-stock par value
TIP_STANDARD_US	0.18		CONVENTION	Standard US restaurant tip fraction (18%)
TIP_GENEROUS_US	0.2		CONVENTION	Generous US restaurant tip fraction (20%)
INFLATION_TARGET_US	0.02		FED	US long-run inflation target (2%)
UNEMPLOYMENT_NAIRU_US	0.04		FED	Long-run NAIRU benchmark (~4%)

Statistical

Name	Value	Unit	Source	Description
INV_SQRT3	0.5773502691896258		MATH	Reciprocal square root of 3
TWO_SQRT_PI	3.5449077018110318		MATH	Two times square root of pi
Z_99_5	2.807033544		MATH	Two-sided z-score for 99.5% confidence
Z_99_9	3.290526731		MATH	Two-sided z-score for 99.9% confidence
Z_99_99	3.890591886		MATH	Two-sided z-score for 99.99% confidence
ALPHA_05	0.05		EXACT	Significance level 5%
ALPHA_01	0.01		EXACT	Significance level 1%
ALPHA_001	0.001		EXACT	Significance level 0.1%
CONFIDENCE_95	0.95		EXACT	95% confidence level as a fraction
CONFIDENCE_99	0.99		EXACT	99% confidence level as a fraction
Z_68	1		MATH	One-sided z-score for ~68% (1σ)
Z_95_ONE_SIDED	1.644853627		MATH	One-sided z-score for 95%
Z_99_ONE_SIDED	2.326347874		MATH	One-sided z-score for 99%
T_95_DF_30	2.042272		MATH	Two-sided t critical value df=30 α=0.05
CHI2_95_DF_1	3.841459		MATH	Chi-square critical value df=1 α=0.05
T_99_DF_30	2.75		MATH	Two-sided t critical value df=30 α=0.01
F_95_DF_1_10	4.965		MATH	F critical value df1=1 df2=10 α=0.05
CHI2_99_DF_1	6.634897		MATH	Chi-square critical value df=1 α=0.01
Z_99_95	3.959683994		MATH	Two-sided z-score for 99.95% confidence
Z_99_99_ONE_SIDED	3.719016485		MATH	One-sided z-score for 99.99%
BINOMIAL_N_10_P_05	252		MATH	Binomial coefficient C(10,5)
NORMAL_68_PERCENT	0.68		MATH	Normal distribution ±1σ central fraction
NORMAL_95_PERCENT	0.95		MATH	Normal distribution ±1.96σ central fraction
NORMAL_99_PERCENT	0.99		MATH	Normal distribution ±2.576σ central fraction

Engineering

Name	Value	Unit	Source	Description
INFINITY (aliases: INF)	Infinity		EXACT	Positive infinity
NAN	NaN		EXACT	Not-a-number
NEG_ZERO	0		EXACT	Negative zero
EPSILON	2.220446049250313e-16		EXACT	Machine epsilon for f64
FLOAT_MAX	1.7976931348623157e+308		EXACT	Maximum finite f64 value
FLOAT_MIN	-1.7976931348623157e+308		EXACT	Minimum finite f64 value
FLOAT_MIN_POSITIVE	2.2250738585072014e-308		EXACT	Smallest positive normalized f64
FLOAT_TRUE_MIN	5e-324		EXACT	Smallest positive subnormal f64
FLOAT_RADIX	2		EXACT	Radix of floating-point representation
FLOAT_MANTISSA_BITS	52		EXACT	Mantissa bits in f64
FLOAT_DECIMAL_DIGITS	15		EXACT	Decimal digits of precision in f64
FLOAT_MAX_EXP	1024		EXACT	Maximum binary exponent in f64
FLOAT_MIN_EXP	-1021		EXACT	Minimum binary exponent in f64
FLOAT_MAX_10_EXP	308		EXACT	Maximum base-10 exponent in f64
FLOAT_MIN_10_EXP	-307		EXACT	Minimum base-10 exponent in f64
MAX_SAFE_INT	9007199254740991		EXACT	Maximum safe integer in IEEE-754 double (2^53−1)
MIN_SAFE_INT	-9007199254740991		EXACT	Minimum safe integer in IEEE-754 double
INT8_MAX	127		EXACT	Fixed-width integer bound INT8_MAX
UINT8_MAX	255		EXACT	Fixed-width integer bound UINT8_MAX
INT16_MAX	32767		EXACT	Fixed-width integer bound INT16_MAX
UINT16_MAX	65535		EXACT	Fixed-width integer bound UINT16_MAX
INT32_MAX	2147483647		EXACT	Fixed-width integer bound INT32_MAX
INT32_MIN	-2147483648		EXACT	Fixed-width integer bound INT32_MIN
UINT32_MAX	4294967295		EXACT	Fixed-width integer bound UINT32_MAX
INT64_MAX	9223372036854776000		EXACT	Fixed-width integer bound INT64_MAX
UINT64_MAX	1.8446744073709552e+19		EXACT	Fixed-width integer bound UINT64_MAX
BITS_PER_BYTE	8		EXACT	Binary size constant BITS_PER_BYTE
BITS_PER_NIBBLE	4		EXACT	Binary size constant BITS_PER_NIBBLE
KIB	1024		EXACT	Binary size constant KIB
MIB	1048576		EXACT	Binary size constant MIB
GIB	1073741824		EXACT	Binary size constant GIB
TIB	1099511627776		EXACT	Binary size constant TIB
PIB	1125899906842624		EXACT	Binary size constant PIB
EIB	1152921504606847000		EXACT	Binary size constant EIB
INCH_TO_METER	0.0254	m/in	EXACT	Inch to meter
FOOT_TO_METER	0.3048	m/ft	EXACT	Foot to meter
YARD_TO_METER	0.9144	m/yd	EXACT	Yard to meter
MILE_TO_METER	1609.344	m/mi	EXACT	Statute mile to meter
NAUTICAL_MILE	1852	m	EXACT	International nautical mile
ANGSTROM	1e-10	m	EXACT	Ångström to meter
MICRON	1e-6	m	EXACT	Micron to meter
POINT_TO_METER	0.00035277777777777776	m	EXACT	Typographic point to meter
FURLONG_TO_METER	201.168	m	EXACT	Furlong to meter
ACRE_TO_M2	4046.8564224	m²	EXACT	Acre to square meter
HECTARE_TO_M2	10000	m²	EXACT	Hectare to square meter
SQFT_TO_M2	0.09290304	m²	EXACT	Square foot to square meter
GALLON_US_TO_LITER	3.785411784	L	EXACT	US gallon to liter
GALLON_UK_TO_LITER	4.54609	L	EXACT	UK gallon to liter
FLUID_OUNCE_US_TO_LITER	0.0295735295625	L	EXACT	US fluid ounce to liter
BARREL_OIL_TO_LITER	158.987294928	L	EXACT	Oil barrel to liter
LITER_TO_M3	0.001	m³	EXACT	Liter to cubic meter
POUND_TO_KG	0.45359237	kg	EXACT	Avoirdupois pound to kilogram
OUNCE_TO_GRAM	28.349523125	g	EXACT	Avoirdupois ounce to gram
STONE_TO_KG	6.35029318	kg	EXACT	Stone to kilogram
TON_US_TO_KG	907.18474	kg	EXACT	US short ton to kilogram
TONNE_TO_KG	1000	kg	EXACT	Metric tonne to kilogram
CARAT_TO_GRAM	0.2	g	EXACT	Carat to gram
CALORIE_TO_JOULE	4.184	J	EXACT	Thermochemical calorie to joule
KCAL_TO_JOULE	4184	J	EXACT	Kilocalorie to joule
BTU_TO_JOULE	1055.05585262	J	EXACT	International BTU to joule
KWH_TO_JOULE	3600000	J	EXACT	Kilowatt-hour to joule
HORSEPOWER_TO_WATT	745.6998715822702	W	EXACT	Mechanical horsepower to watt
BAR_TO_PASCAL	100000	Pa	EXACT	Bar to pascal
PSI_TO_PASCAL	6894.757293168	Pa	EXACT	Pound-force per square inch to pascal
MMHG_TO_PASCAL	133.322387415	Pa	EXACT	Millimeter of mercury to pascal
TORR_TO_PASCAL	133.32236842105263	Pa	EXACT	Torr to pascal
ATM_TO_PASCAL	101325	Pa	EXACT	Standard atmosphere to pascal
KNOT_TO_MPS	0.5144444444444445	m/s	EXACT	Knot to meters per second
MPH_TO_MPS	0.44704	m/s	EXACT	Miles per hour to meters per second
KMH_TO_MPS	0.2777777777777778	m/s	EXACT	Kilometers per hour to meters per second
ARCMINUTE_TO_RAD	0.0002908882086657216	rad	EXACT	Arcminute to radian
ARCSECOND_TO_RAD	4.84813681109536e-6	rad	EXACT	Arcsecond to radian
GRADIAN_TO_RAD	0.015707963267948967	rad	EXACT	Gradian to radian
YOUNG_MODULUS_STEEL	200000000000	Pa	ASM	Young modulus of structural steel
YOUNG_MODULUS_ALUMINUM	69000000000	Pa	ASM	Young modulus of aluminum alloy
YOUNG_MODULUS_CONCRETE	30000000000	Pa	ASM	Young modulus of concrete (typical)
YOUNG_MODULUS_GLASS	70000000000	Pa	ASM	Young modulus of glass
POISSON_RATIO_STEEL	0.3		ASM	Poisson ratio of steel
POISSON_RATIO_ALUMINUM	0.33		ASM	Poisson ratio of aluminum
DENSITY_STEEL	7850	kg/m³	ASM	Density of steel
DENSITY_ALUMINUM	2700	kg/m³	ASM	Density of aluminum
DENSITY_COPPER	8960	kg/m³	ASM	Density of copper
DENSITY_CONCRETE	2400	kg/m³	ASM	Density of concrete
DENSITY_BRICK	2000	kg/m³	ASM	Density of brick masonry
THERMAL_CONDUCTIVITY_COPPER	401	W/(m·K)	ASM	Thermal conductivity of copper
THERMAL_CONDUCTIVITY_ALUMINUM	237	W/(m·K)	ASM	Thermal conductivity of aluminum
COPPER_RESISTIVITY	1.68e-8	Ω·m	NIST	Electrical resistivity of copper at 20 °C
SILICON_BAND_GAP	1.12	eV	SEMI	Silicon band gap at 300 K
SURVEY_CHAIN_TO_METER	20.1168	m	NIST	US survey chain (66 ft) in meters
SURVEY_ROD_TO_METER	5.0292	m	NIST	US survey rod/perch (16.5 ft) in meters
HAND_TO_METER	0.1016	m	NIST	Hand (4 in) for equine height
TYPOGRAPHIC_PICA_TO_METER	0.004233333333333333	m	EXACT	Typographic pica (12 points)
US_SURVEY_FOOT_TO_METER	0.3048006096012192	m	NIST	US survey foot
MAINS_VOLTAGE_US	120	V	NEMA	US residential mains voltage (nominal)
MAINS_VOLTAGE_EU	230	V	IEC	EU residential mains voltage (nominal)
STANDARD_ATMOSPHERE_PSIG_OFFSET	14.696	psi	NIST	Standard atmosphere in psi gauge reference
BAUDOT_CODE_BITS	5		ITU	Classic Baudot telegraph code width
MORSE_DOT_DURATION_MS	60	ms	ITU	Standard Morse dot duration at 20 WPM
REYNOLDS_CRITICAL_PIPE	2300		FLUID	Critical Reynolds number for pipe flow transition
REYNOLDS_CRITICAL_FLAT_PLATE	500000		FLUID	Critical Reynolds number for flat-plate turbulence
SCHMIDT_NUMBER_WATER_20C	1000		FLUID	Schmidt number of water at 20 °C (approx.)
SCHMIDT_NUMBER_AIR	0.7		FLUID	Schmidt number of air (approx.)
LEWIS_NUMBER_AIR	1		FLUID	Lewis number of air (approx.)
FROUDE_NUMBER_CRITICAL_OPEN_CHANNEL	1		HYDRAULIC	Critical Froude number for open-channel flow
SILVER_RESISTIVITY	1.59e-8	Ω·m	NIST	Electrical resistivity of silver at 20 °C
GOLD_RESISTIVITY	2.44e-8	Ω·m	NIST	Electrical resistivity of gold at 20 °C
ALUMINUM_RESISTIVITY	2.82e-8	Ω·m	NIST	Electrical resistivity of aluminum at 20 °C
IRON_RESISTIVITY	9.71e-8	Ω·m	NIST	Electrical resistivity of iron at 20 °C
TUNGSTEN_RESISTIVITY	5.6e-8	Ω·m	NIST	Electrical resistivity of tungsten at 20 °C
SLUG_TO_KG	14.593903	kg	NIST	Slug to kilogram
LBF_TO_NEWTON	4.4482216152605	N	NIST	Pound-force to newton
DYNE_TO_NEWTON	0.00001	N	CGS	Dyne to newton
ERG_TO_JOULE	1e-7	J	CGS	Erg to joule
THERM_US_TO_JOULE	105480400	J	NIST	US therm to joule
QUART_US_TO_LITER	0.946352946	L	NIST	US liquid quart to liter
PINT_US_TO_LITER	0.473176473	L	NIST	US liquid pint to liter
GAUSS_TO_TESLA	0.0001	T	CGS	Gauss to tesla
OERSTED_TO_AMPS_PER_M	79.57747154594767	A/m	CGS	Oersted to amperes per meter
MAXWELL_TO_WEBER	1e-8	Wb	CGS	Maxwell to weber
PERMEABILITY_FREE_SPACE	1.2566370614359173e-6	H/m	CODATA	Vacuum magnetic permeability μ₀
AWG_10_DIAMETER_MM	5.004737812743475	mm	ASTM	AWG 10 wire diameter
AWG_12_DIAMETER_MM	3.77263327951048	mm	ASTM	AWG 12 wire diameter
AWG_14_DIAMETER_MM	2.8438576393411403	mm	ASTM	AWG 14 wire diameter
AWG_18_DIAMETER_MM	1.6159740181085689	mm	ASTM	AWG 18 wire diameter
AWG_22_DIAMETER_MM	0.9182499120479714	mm	ASTM	AWG 22 wire diameter
NPT_TAPER_ANGLE_DEG	1.7899	°	ANSI	NPT pipe thread taper angle (1°47'24'')
PIPE_SCHEDULE_40_NOMINAL	40		ANSI	ANSI Schedule 40 pipe designation
STANDARD_GRAVITY_MS2	9.80665	m/s²	NIST	Standard gravity (conventional)
ATMOSPHERIC_PRESSURE_MBAR	1013.25	mbar	NIST	Standard atmosphere in millibars
MODULUS_OF_RIGIDITY_STEEL	79000000000	Pa	ASM	Shear modulus of steel (approx.)
BULK_MODULUS_WATER	2200000000	Pa	NIST	Bulk modulus of water (approx.)
MORSE_WORD_GAP_MS	420	ms	ITU	Morse word gap at 20 WPM (PARIS standard)
MORSE_CHAR_GAP_MS	180	ms	ITU	Morse character gap at 20 WPM
SEMAPHORE_POSITIONS	8		NATO	Semaphore flag arm positions (excluding rest)
TELEX_BAUD	50	Bd	ITU	Standard telex baud rate

Logistics

Name	Value	Unit	Source	Description
CONTAINER_TEU_LENGTH	6.058	m	ISO	Twenty-foot equivalent unit length (TEU)
PALLET_EURO_WIDTH	0.8	m	EUR	EUR pallet width
PALLET_EURO_DEPTH	1.2	m	EUR	EUR pallet depth
CONTAINER_40FT_LENGTH	12.192	m	ISO	Forty-foot container length (12.192 m)
CONTAINER_20FT_LENGTH	6.058	m	ISO	Twenty-foot container length (TEU)
PALLET_US_STANDARD_WIDTH	1.016	m	GMA	US standard pallet width (40 in)
PALLET_US_STANDARD_DEPTH	1.219	m	GMA	US standard pallet depth (48 in)

Planning

Name	Value	Unit	Source	Description
PARETO_80_20	0.8		CONVENTION	Pareto 80/20 principle fraction
SIX_SIGMA_DEFECT_RATE	3.4e-6		SIXSIGMA	Six Sigma defect rate (DPMO basis)
CRITICAL_PATH_FLOAT_ZERO	0		CPM	Critical-path total float marker
EARNED_VALUE_PERF_INDEX_TARGET	1		EVM	Earned-value performance index target

Construction

Name	Value	Unit	Source	Description
TWO_BY_FOUR_WIDTH_IN	1.5	in	LUMBER	Nominal 2×4 actual width
TWO_BY_FOUR_HEIGHT_IN	3.5	in	LUMBER	Nominal 2×4 actual height
REBAR_4_DIAMETER_IN	0.5	in	ACI	US #4 rebar nominal diameter
REBAR_5_DIAMETER_IN	0.625	in	ACI	US #5 rebar nominal diameter
STANDARD_DOOR_HEIGHT_IN	80	in	CONVENTION	Standard US interior door height
STANDARD_CEILING_HEIGHT_FT	8	ft	CONVENTION	Typical US residential ceiling height
OAK_WOOD_DENSITY	750	kg/m³	USDA	Typical oak wood density
PINE_WOOD_DENSITY	500	kg/m³	USDA	Typical pine wood density
MDF_DENSITY	750	kg/m³	CONVENTION	Typical medium-density fiberboard density
GYPSUM_BOARD_THICKNESS_IN	0.5	in	CONVENTION	Standard gypsum drywall thickness
PLYWOOD_SHEET_WIDTH_FT	4	ft	CONVENTION	Standard plywood sheet width
PLYWOOD_SHEET_HEIGHT_FT	8	ft	CONVENTION	Standard plywood sheet height
SAFETY_FACTOR_STEEL_AISC	1.67		AISC	AISC steel tension safety factor
SAFETY_FACTOR_CONCRETE_ACI	1.5		ACI	ACI concrete flexure safety factor
SAFETY_FACTOR_WOOD_NDS	2		NDS	Typical wood design safety factor
CONCRETE_MIX_RATIO_CEMENT	1		ACI	Typical 1:2:3 concrete mix cement part
CONCRETE_MIX_RATIO_SAND	2		ACI	Typical 1:2:3 concrete mix sand part
CONCRETE_MIX_RATIO_AGGREGATE	3		ACI	Typical 1:2:3 concrete mix aggregate part
MORTAR_MIX_RATIO_CEMENT	1		ACI	Typical 1:3 mortar mix cement part
MORTAR_MIX_RATIO_SAND	3		ACI	Typical 1:3 mortar mix sand part
REBAR_NUMBER_3_DIAMETER_IN	0.375	in	ACI	US #3 rebar nominal diameter
REBAR_NUMBER_6_DIAMETER_IN	0.75	in	ACI	US #6 rebar nominal diameter
STANDARD_CONCRETE_STRENGTH_PSI	4000	psi	ACI	Typical residential concrete strength (28-day)

Healthcare

Name	Value	Unit	Source	Description
NORMAL_BODY_TEMP_K	310.15	K	WHO	Normal human body temperature (37 °C)
NORMAL_BODY_TEMP_C	37	°C	WHO	Normal human body temperature in Celsius
ATMOSPHERIC_O2_FRACTION	0.2095		NIST	Dry-air oxygen mole fraction
ATP_HYDROLYSIS_KJ_PER_MOL	30.5	kJ/mol	BIOCHEM	ATP hydrolysis free energy (~pH 7)
DNA_BASE_PAIR_LENGTH	3.4e-10	m	BIOCHEM	Average DNA base-pair length
HUMAN_GENOME_BASE_PAIRS	3200000000		GRCh38	Human genome size (base pairs, GRCh38)
AMINO_ACID_COUNT	20		BIOCHEM	Standard proteinogenic amino acids
GENETIC_CODE_CODONS	64		BIOCHEM	Codons in the standard genetic code
WHO_BMI_UNDERWEIGHT	18.5	kg/m²	WHO	BMI underweight threshold
WHO_BMI_OVERWEIGHT	25	kg/m²	WHO	BMI overweight threshold
WHO_BMI_OBESE	30	kg/m²	WHO	BMI obesity threshold
RESTING_HEART_RATE_TYPICAL	70	bpm	CLINICAL	Typical adult resting heart rate
FASTING_GLUCOSE_NORMAL_MAX	100	mg/dL	ADA	Fasting plasma glucose upper normal limit
HBA1C_PREDIABETES	5.7	%	ADA	HbA1c prediabetes threshold
HBA1C_DIABETES	6.5	%	ADA	HbA1c diabetes diagnostic threshold
LDL_OPTIMAL_MAX	100	mg/dL	AHA	Optimal LDL cholesterol upper limit
HDL_MALE_MIN	40	mg/dL	AHA	Minimum desirable HDL for men
HDL_FEMALE_MIN	50	mg/dL	AHA	Minimum desirable HDL for women
TRIGLYCERIDES_NORMAL_MAX	150	mg/dL	AHA	Normal fasting triglycerides upper limit
SYSTOLIC_HYPERTENSION	140	mmHg	AHA	Stage 2 hypertension systolic threshold
DIASTOLIC_HYPERTENSION	90	mmHg	AHA	Stage 2 hypertension diastolic threshold
SPO2_NORMAL_MIN	95	%	CLINICAL	Normal peripheral oxygen saturation lower limit
RESPIRATORY_RATE_ADULT	16	breaths/min	CLINICAL	Typical adult respiratory rate
BLOOD_VOLUME_ADULT_L	5	L	CLINICAL	Typical adult blood volume
CARDIAC_OUTPUT_TYPICAL	5	L/min	CLINICAL	Typical adult cardiac output at rest
STROKE_VOLUME_TYPICAL	70	mL	CLINICAL	Typical resting stroke volume
LUNG_TIDAL_VOLUME_TYPICAL	500	mL	CLINICAL	Typical resting tidal volume
CREATININE_MALE_MAX	1.2	mg/dL	CLINICAL	Typical male serum creatinine upper reference
CREATININE_FEMALE_MAX	1	mg/dL	CLINICAL	Typical female serum creatinine upper reference
HEMOGLOBIN_MALE_MIN	13.5	g/dL	CLINICAL	Male hemoglobin lower reference limit
HEMOGLOBIN_FEMALE_MIN	12	g/dL	CLINICAL	Female hemoglobin lower reference limit
PLATELET_NORMAL_MIN	150000	/µL	CLINICAL	Platelet count lower reference limit
PLATELET_NORMAL_MAX	400000	/µL	CLINICAL	Platelet count upper reference limit
WBC_NORMAL_MAX	11000	/µL	CLINICAL	White blood cell upper reference limit
POTASSIUM_NORMAL_MIN	3.5	mEq/L	CLINICAL	Serum potassium lower reference limit
POTASSIUM_NORMAL_MAX	5	mEq/L	CLINICAL	Serum potassium upper reference limit
SODIUM_NORMAL_MIN	136	mEq/L	CLINICAL	Serum sodium lower reference limit
SODIUM_NORMAL_MAX	145	mEq/L	CLINICAL	Serum sodium upper reference limit
CALCIUM_NORMAL_MIN	8.5	mg/dL	CLINICAL	Total serum calcium lower reference limit
CALCIUM_NORMAL_MAX	10.5	mg/dL	CLINICAL	Total serum calcium upper reference limit
HALF_LIFE_CAFFEINE_HOURS	5	h	PHARMA	Average caffeine elimination half-life
HALF_LIFE_IBUPROFEN_HOURS	2	h	PHARMA	Average ibuprofen elimination half-life
HALF_LIFE_ASPIRIN_HOURS	0.25	h	PHARMA	Acetylsalicylic acid half-life (low dose)
HALF_LIFE_PENICILLIN_HOURS	1	h	PHARMA	Typical penicillin G half-life
FEV1_FVC_NORMAL_MIN	0.7		GOLD	Lower normal FEV1/FVC ratio (GOLD spirometry)
PAO2_NORMAL_MIN	80	mmHg	CLINICAL	Normal arterial PaO2 lower limit
PACO2_NORMAL_MAX	45	mmHg	CLINICAL	Normal arterial PaCO2 upper limit
INR_THERAPEUTIC_MIN	2		CLINICAL	Typical warfarin INR therapeutic lower bound
INR_THERAPEUTIC_MAX	3		CLINICAL	Typical warfarin INR therapeutic upper bound
VITAMIN_D_SUFFICIENT_NG_ML	30	ng/mL	ENDOCRINE	Vitamin D sufficiency threshold (25-OH)
HUMAN_CHROMOSOMES_DIPLOID	46		GENETICS	Human diploid chromosome count
HUMAN_CHROMOSOMES_HAPLOID	23		GENETICS	Human haploid chromosome count
HUMAN_AUTOSOME_PAIRS	22		GENETICS	Human autosome pair count
HUMAN_BONES_ADULT	206		ANATOMY	Adult human bone count
HUMAN_TEETH_ADULT	32		ANATOMY	Adult human permanent teeth count
HUMAN_RIB_PAIRS	12		ANATOMY	Human rib pairs
HUMAN_VERTEBRAE	33		ANATOMY	Human vertebrae count
HUMAN_MUSCLES	600		ANATOMY	Approximate human skeletal muscle count
HALF_LIFE_MORPHINE_HOURS	2	h	PHARMA	Morphine elimination half-life
HALF_LIFE_WARFARIN_HOURS	40	h	PHARMA	Warfarin elimination half-life (mean)
HALF_LIFE_METFORMIN_HOURS	6	h	PHARMA	Metformin elimination half-life
HALF_LIFE_AMOXICILLIN_HOURS	1	h	PHARMA	Amoxicillin elimination half-life
RNA_BASE_COUNT	4		BIOCHEM	RNA nucleotide alphabet size
DNA_BASE_COUNT	4		BIOCHEM	DNA nucleotide alphabet size
STOP_CODON_COUNT	3		BIOCHEM	Stop codons in genetic code
START_CODON_COUNT	1		BIOCHEM	Primary start codon (AUG) count
INTRON_AVERAGE_MAMMAL	3400	bp	GENETICS	Typical mammalian intron length (approx.)
EXON_AVERAGE_MAMMAL	150	bp	GENETICS	Typical mammalian exon length (approx.)
MITOCHONDRIAL_GENOME_BP	16569	bp	NCBI	Human mitochondrial genome size
CHLOROPLAST_GENOME_BP	120000	bp	NCBI	Typical plant chloroplast genome size
CORTISOL_MORNING_MAX_UG_DL	23	µg/dL	CLINICAL	Morning cortisol upper reference
TSH_NORMAL_MAX	4	mIU/L	CLINICAL	TSH upper reference limit
TSH_NORMAL_MIN	0.4	mIU/L	CLINICAL	TSH lower reference limit
INSULIN_FASTING_MAX	25	µIU/mL	CLINICAL	Fasting insulin upper reference

Graduate Study

Name	Value	Unit	Source	Description
DUNBAR_NUMBER	150		ANTHRO	Dunbar social group size estimate
WECHSLER_IQ_MEAN	100		PSYCH	Wechsler IQ scale mean
WECHSLER_IQ_STD	15		PSYCH	Wechsler IQ scale standard deviation
GPA_SCALE_MAX	4		EDU	US 4.0 GPA scale maximum
BLOOD_ALCOHOL_LEGAL_LIMIT_US	0.08		USLAW	US per-se DUI BAC limit (g/dL)
SAT_MAX_SCORE	1600		COLLEGEBOARD	SAT total score maximum
ACT_MAX_SCORE	36		ACT	ACT composite score maximum
GRE_VERBAL_MAX	170		ETS	GRE verbal reasoning maximum score
GRE_QUANT_MAX	170		ETS	GRE quantitative reasoning maximum score

Industry Verticals

Name	Value	Unit	Source	Description
BUSHEL_WHEAT_KG	27.2155	kg	USDA	US wheat bushel mass
BUSHEL_CORN_KG	25.401	kg	USDA	US shelled corn bushel mass
BUSHEL_SOYBEAN_KG	27.2155	kg	USDA	US soybean bushel mass
ACRE_TO_SQUARE_METER	4046.8564224	m²	NIST	International acre in square meters
GROWING_DEGREE_BASE_C	10	°C	USDA	Common growing-degree-day base temperature
SILICON_DENSITY	2330	kg/m³	SEMI	Silicon crystal density
GOLD_DENSITY	19300	kg/m³	NIST	Density of gold
SILVER_DENSITY	10490	kg/m³	NIST	Density of silver
LEAD_DENSITY	11340	kg/m³	NIST	Density of lead
MERCURY_DENSITY	13534	kg/m³	NIST	Density of mercury
TON_TNT_JOULES	4184000000	J	NIST	Energy of one metric ton of TNT
CALORIFIC_VALUE_METHANE	55.5	MJ/kg	NIST	Higher heating value of methane
COTTON_YARN_COUNT_DENIER	0.05	g	TEXTILE	Silk denier reference (0.05 g per 450 m)
TITANIUM_DENSITY	4506	kg/m³	ASM	Density of titanium
PLATINUM_DENSITY	21450	kg/m³	NIST	Density of platinum
NICKEL_DENSITY	8908	kg/m³	NIST	Density of nickel
ZINC_DENSITY	7140	kg/m³	NIST	Density of zinc
TUNGSTEN_DENSITY	19250	kg/m³	NIST	Density of tungsten
CORN_YIELD_BUSHELS_PER_ACRE_US	175	bu/ac	USDA	Recent US corn yield benchmark (~2023)
WHEAT_PROTEIN_MIN_HARD	12	%	USDA	Minimum protein for hard wheat class
BEEF_SAFE_INTERNAL_TEMP_F	145	°F	USDA	USDA safe minimum beef internal temperature
POULTRY_SAFE_INTERNAL_TEMP_F	165	°F	USDA	USDA safe minimum poultry internal temperature
DENIER_TO_TEX	0.111111111	tex	TEXTILE	Denier to tex conversion factor (1/9)
NE_TO_TEX	1000	tex	TEXTILE	Ne (English cotton count) to tex numerator
BAKING_SODA_TO_FLOUR	0.0125		USDA	Typical baking soda to flour ratio (1:80)
SALT_TO_FLOUR_BREAD	0.02		BAKING	Typical bread salt-to-flour ratio (2%)
WATER_TO_FLOUR_PIZZA	0.65		BAKING	Typical pizza dough hydration ratio
SUGAR_TO_COFFEE_TEASPOON	0.25	tsp	CONVENTION	Typical sugar packet size (¼ tsp)
COAL_ENERGY_MJ_PER_KG	24	MJ/kg	NIST	Typical coal heating value
GASOLINE_ENERGY_MJ_PER_L	34.2	MJ/L	NIST	Typical gasoline energy density
DIESEL_ENERGY_MJ_PER_L	38.6	MJ/L	NIST	Typical diesel energy density
NATURAL_GAS_MJ_PER_M3	38	MJ/m³	NIST	Typical natural gas energy density
BAGUETTE_LENGTH_CM	60	cm	FRANCE	Traditional baguette length
BAGUETTE_WEIGHT_G	250	g	FRANCE	Traditional baguette weight
STANDARD_LOAF_WEIGHT_G	454	g	BAKING	Standard one-pound loaf weight
PIZZA_STANDARD_DIAMETER_IN	12	in	CONVENTION	Standard medium pizza diameter
COFFEE_BREW_RATIO	0.0625		SCAA	SCAA golden cup brew ratio (1:16)

Real Estate

Name	Value	Unit	Source	Description
CAP_RATE_BENCHMARK	0.05		CONVENTION	Typical commercial cap-rate benchmark (5%)
RENT_TO_INCOME_RATIO	0.3		HUD	HUD affordable housing rent-to-income guideline
OFFICE_SPACE_PER_EMPLOYEE_SF	150	ft²	BOMA	Typical US office space per employee
PARKING_SPACE_STANDARD_SF	180	ft²	CONVENTION	Typical parking stall area

Computer Science

Name	Value	Unit	Source	Description
ASCII_CHAR_COUNT	128		EXACT	ASCII character repertoire size
UTF8_MAX_BYTES	4		RFC3629	Maximum UTF-8 bytes per code point
SHA256_BLOCK_BYTES	64	B	FIPS180	SHA-256 block size
SHA256_DIGEST_BYTES	32	B	FIPS180	SHA-256 digest size
UUID_BYTE_LENGTH	16	B	RFC4122	UUID octet length
FNV1A_32_OFFSET	2166136261		FNV	FNV-1a 32-bit offset basis
HASH_LOAD_FACTOR_DEFAULT	0.75		CONVENTION	Default hash-table load factor
ENTROPY_MAX_BIT	1	bit	INFO	Maximum binary entropy (one fair bit)
ASCII_PRINTABLE_MIN	32		EXACT	First ASCII printable code point
ASCII_PRINTABLE_MAX	126		EXACT	Last ASCII printable code point
MD5_DIGEST_BYTES	16	B	RFC1321	MD5 digest size
SHA1_DIGEST_BYTES	20	B	FIPS180	SHA-1 digest size
SHA512_DIGEST_BYTES	64	B	FIPS180	SHA-512 digest size
AES_BLOCK_BYTES	16	B	FIPS197	AES block size
RSA_MIN_KEY_BITS	2048	bit	NIST	NIST minimum RSA key size (2023 guidance)
BITCOIN_MAX_SUPPLY	21000000		BITCOIN	Bitcoin protocol maximum supply
ETHEREUM_SLOTS_PER_EPOCH	32		ETHEREUM	Ethereum beacon-chain slots per epoch
CHARS_PER_LINE_LEGACY	80		CONVENTION	Legacy terminal/console line width
CHARS_PER_LINE_MODERN	120		CONVENTION	Common modern terminal line width
ETHERNET_MTU	1500	B	IEEE802	Standard Ethernet MTU payload
JUMBO_FRAME_MTU	9000	B	IEEE802	Common jumbo-frame MTU
PORT_HTTP	80		IANA	HTTP port
PORT_HTTPS	443		IANA	HTTPS port
PORT_DNS	53		IANA	DNS port
PORT_SSH	22		IANA	SSH port
IPV6_ADDRESS_BITS	128	bit	RFC8200	IPv6 address bit width
MAC_ADDRESS_BITS	48	bit	IEEE802	MAC address bit width
UNICODE_MAX_CODEPOINT	1114111		UNICODE	Maximum Unicode scalar value
UNICODE_BMP_MAX	65535		UNICODE	Basic Multilingual Plane max code point
BASE64_CHARS	64		RFC4648	Base64 alphabet size
MOORE_LAW_DOUBLING_MONTHS	24	mo	MOORE	Moore's law transistor-doubling period (approx.)
HASH_TABLE_MIN_SIZE	8		CONVENTION	Common minimum hash-table bucket count
B_TREE_MIN_DEGREE	128		CONVENTION	Common B-tree fan-out order of magnitude
SATOSHI_TO_BTC	1e-8		BITCOIN	Satoshi to bitcoin conversion
GWEI_TO_ETH	1e-9		ETHEREUM	Gwei to ether conversion
WEI_TO_ETH	1e-18		ETHEREUM	Wei to ether conversion
ISBN13_LENGTH	13		ISO2108	ISBN-13 character count
ISBN10_LENGTH	10		ISO2108	ISBN-10 character count
EAN13_LENGTH	13		GS1	EAN-13 barcode length
UPC_A_LENGTH	12		GS1	UPC-A barcode length
ISSN_LENGTH	8		ISO3297	ISSN character count
HTTP_STATUS_OK	200		RFC9110	HTTP 200 OK status code
HTTP_STATUS_NOT_FOUND	404		RFC9110	HTTP 404 Not Found status code
HTTP_STATUS_SERVER_ERROR	500		RFC9110	HTTP 500 Internal Server Error
QR_CODE_VERSION_MAX	40		ISO18004	Maximum QR code version

Skill Ratings

Name	Value	Unit	Source	Description
ELO_STARTING_RATING	1500		ELO	Standard initial Elo rating
ELO_K_FACTOR_CLASSIC	32		ELO	Classic Elo K-factor for new players
ELO_K_FACTOR_PRO	16		FIDE	FIDE Elo K-factor for players rated 2400+

Playing Cards

Name	Value	Unit	Source	Description
PLAYING_CARDS_PER_DECK	52		CONVENTION	Standard playing-card deck size

Card Games

Name	Value	Unit	Source	Description
BRIDGE_CARDS_PER_HAND	13		CONVENTION	Bridge cards dealt per player
POKER_HAND_RANKINGS	10		CONVENTION	Distinct poker hand-ranking categories
CRIBBAGE_WINNING_SCORE	121		CONVENTION	Cribbage winning pegging score
CANASTA_MELD_MINIMUM	45		CONVENTION	Canasta initial meld minimum (classic)
BRIDGE_TRICKS_PER_HAND	13		CONVENTION	Bridge tricks in a full deal
POKER_HAND_CARD_COUNT	5		CONVENTION	Cards in a standard poker hand
TEXAS_HOLDEM_HOLE_CARDS	2		CONVENTION	Hole cards dealt in Texas hold'em
CANASTA_DECK_COUNT	2		CONVENTION	Canasta deck count (two standard decks)
PINOCHLE_DECK_COUNT	2		CONVENTION	Double-deck pinochle deck count
RUMMY_MELD_MINIMUM	30		CONVENTION	Gin rummy initial meld minimum

Casino

Name	Value	Unit	Source	Description
ROULETTE_WHEEL_POCKETS	38		CONVENTION	American roulette pocket count (00 wheel)
BLACKJACK_TARGET_TOTAL	21		CONVENTION	Blackjack target hand total
ROULETTE_EUROPEAN_POCKETS	37		CONVENTION	European roulette pocket count (single zero)
CRAPS_PASS_LINE_POINT	7		CONVENTION	Craps natural/pass-line winning total
BACCARAT_NATURAL	8		CONVENTION	Baccarat natural hand total threshold
BLACKJACK_DECK_COUNT_TYPICAL	6		CONVENTION	Typical casino blackjack shoe size
SLOT_MACHINE_REELS	3		CONVENTION	Classic slot machine reel count
KENO_NUMBERS_DRAWN	20		CONVENTION	Typical keno numbers drawn per game

Chess

Name	Value	Unit	Source	Description
CHESS_BOARD_SQUARES	64		FIDE	Chessboard square count
CHESS_PIECES_PER_SIDE	16		FIDE	Chess pieces per side at game start

Dice & Gambling

Name	Value	Unit	Source	Description
DICE_SIDES_STANDARD	6		CONVENTION	Standard six-sided die face count
POOL_BILLIARDS_BALLS	15		CONVENTION	Object balls in eight-ball (excluding cue)

Science

Name	Value	Unit	Source	Description
HYPERFINE_CESIUM	9192631770	Hz	CODATA2018	Hyperfine transition frequency of cesium-133 (defines the second)
SPEED_OF_LIGHT	299792458	m/s	CODATA2018	Speed of light in vacuum
PLANCK	6.62607015e-34	J·s	CODATA2018	Planck constant h
ELEMENTARY_CHARGE	1.602176634e-19	C	CODATA2018	Elementary charge e
BOLTZMANN	1.380649e-23	J/K	CODATA2018	Boltzmann constant k
AVOGADRO	6.02214076e+23	mol⁻¹	CODATA2018	Avogadro constant N_A
LUMINOUS_EFFICACY	683	lm/W	CODATA2018	Luminous efficacy K_cd (defines the candela)
GRAVITATION	6.6743e-11	m³·kg⁻¹·s⁻²	CODATA2018	Newtonian constant of gravitation G
PLANCK_REDUCED	1.054571817e-34	J·s	CODATA2018	Reduced Planck constant ħ
VACUUM_PERMITTIVITY	8.8541878128e-12	F/m	CODATA2018	Electric constant ε₀
VACUUM_PERMEABILITY	1.25663706212e-6	N/A²	CODATA2018	Magnetic constant μ₀
VACUUM_IMPEDANCE	376.730313668	Ω	CODATA2018	Characteristic impedance of vacuum Z₀
COULOMB_CONSTANT	8987551792.3	N·m²/C²	CODATA2018	Coulomb constant k_e
MAGNETIC_FLUX_QUANTUM	2.067833848e-15	Wb	CODATA2018	Magnetic flux quantum Φ₀
CONDUCTANCE_QUANTUM	0.00007748091729	S	CODATA2018	Conductance quantum G₀
JOSEPHSON	483597848400000	Hz/V	CODATA2018	Josephson constant K_J
VON_KLITZING	25812.80745	Ω	CODATA2018	von Klitzing constant R_K
FINE_STRUCTURE	0.0072973525693		CODATA2018	Fine-structure constant α
INV_FINE_STRUCTURE	137.035999084		CODATA2018	Inverse fine-structure constant 1/α
RYDBERG	10973731.56816	m⁻¹	CODATA2018	Rydberg constant R∞
RYDBERG_ENERGY	2.1798723611035e-18	J	CODATA2018	Rydberg unit of energy hcR∞
BOHR_RADIUS	5.29177210903e-11	m	CODATA2018	Bohr radius a₀
BOHR_MAGNETON	9.2740100783e-24	J/T	CODATA2018	Bohr magneton μ_B
NUCLEAR_MAGNETON	5.0507837461e-27	J/T	CODATA2018	Nuclear magneton μ_N
HARTREE_ENERGY	4.3597447222071e-18	J	CODATA2018	Hartree energy E_h
CLASSICAL_ELECTRON_RADIUS	2.8179403262e-15	m	CODATA2018	Classical electron radius r_e
COMPTON_WAVELENGTH	2.42631023867e-12	m	CODATA2018	Compton wavelength λ_C
THOMSON_CROSS_SECTION	6.6524587321e-29	m²	CODATA2018	Thomson cross section σ_T
FIRST_RADIATION_CONSTANT	3.741771852e-16	W·m²	CODATA2018	First radiation constant 2πhc²
SECOND_RADIATION_CONSTANT	0.01438776877	m·K	CODATA2018	Second radiation constant hc/k
SACKUR_TETRODE	-1.15170753706		CODATA2018	Sackur–Tetrode constant (standard entropy of monatomic ideal gas)
ELECTRON_MASS	9.1093837015e-31	kg	CODATA2018	Electron mass m_e
PROTON_MASS	1.67262192369e-27	kg	CODATA2018	Proton mass m_p
NEUTRON_MASS	1.67492749804e-27	kg	CODATA2018	Neutron mass m_n
MUON_MASS	1.883531627e-28	kg	CODATA2018	Muon mass m_μ
TAU_MASS	3.16754e-27	kg	CODATA2018	Tau mass m_τ
DEUTERON_MASS	3.3435837724e-27	kg	CODATA2018	Deuteron mass m_d
ALPHA_PARTICLE_MASS	6.6446573357e-27	kg	CODATA2018	Alpha particle mass m_α
ATOMIC_MASS_UNIT	1.6605390666e-27	kg	CODATA2018	Unified atomic mass unit u
PROTON_ELECTRON_MASS_RATIO	1836.15267343		CODATA2018	Proton-electron mass ratio m_p/m_e
ELECTRON_G_FACTOR	-2.00231930436256		CODATA2018	Electron g-factor g_e
PROTON_G_FACTOR	5.5856946893		CODATA2018	Proton g-factor g_p
ELECTRON_GYROMAGNETIC_RATIO	176085963023	rad·s⁻¹·T⁻¹	CODATA2018	Electron gyromagnetic ratio γ_e
PROTON_GYROMAGNETIC_RATIO	267522187.44	rad·s⁻¹·T⁻¹	CODATA2018	Proton gyromagnetic ratio γ_p
GAS_CONSTANT	8.314462618	J·mol⁻¹·K⁻¹	CODATA2018	Molar gas constant R
FARADAY	96485.33212	C/mol	CODATA2018	Faraday constant F
STEFAN_BOLTZMANN	5.670374419e-8	W·m⁻²·K⁻⁴	CODATA2018	Stefan–Boltzmann constant σ
WIEN_DISPLACEMENT	0.002897771955	m·K	CODATA2018	Wien wavelength displacement law constant b
WIEN_FREQUENCY_DISPLACEMENT	58789257570	Hz/K	CODATA2018	Wien frequency displacement law constant
LOSCHMIDT	2.686780111e+25	m⁻³	CODATA2018	Loschmidt constant n₀
MOLAR_VOLUME_STP	0.02241396954	m³/mol	CODATA2018	Molar volume of ideal gas at STP V_m
MOLAR_MASS_CONSTANT	0.00100000000165	kg/mol	CODATA2018	Molar mass constant M_u
ELECTRON_VOLT	1.602176634e-19	J	CODATA2018	Electron volt energy unit eV
ZERO_CELSIUS	273.15	K	CODATA2018	Zero of the Celsius scale in kelvin
STANDARD_TEMPERATURE	273.15	K	CODATA2018	Standard temperature (0 °C)
ROOM_TEMPERATURE	298.15	K	CODATA2018	Room temperature (25 °C)
WATER_TRIPLE_POINT	273.16	K	CODATA2018	Temperature of water triple point
STANDARD_GRAVITY	9.80665	m/s²	CODATA2018	Standard acceleration of gravity g₀
STANDARD_ATMOSPHERE	101325	Pa	CODATA2018	Standard atmosphere atm
STANDARD_PRESSURE	100000	Pa	CODATA2018	Standard pressure (IUPAC)
SPEED_OF_SOUND_AIR	343	m/s	CODATA2018	Speed of sound in dry air at 20 °C
REFERENCE_SOUND_PRESSURE	0.00002	Pa	CODATA2018	Reference sound pressure in air
PLANCK_LENGTH	1.61625502392855e-35	m	CODATA2018	Planck length l_P
PLANCK_TIME	5.391246446661944e-44	s	CODATA2018	Planck time t_P
PLANCK_MASS	2.176434342051127e-8	kg	CODATA2018	Planck mass m_P
PLANCK_TEMPERATURE	1.416784161723297e+32	K	CODATA2018	Planck temperature T_P
PLANCK_CHARGE	1.8755460372050785e-18	C	CODATA2018	Planck charge q_P
NEUTRON_ELECTRON_MASS_RATIO	1838.68366273		CODATA2018	Neutron-electron mass ratio
NEUTRON_PROTON_MASS_RATIO	1.00137841931		CODATA2018	Neutron-proton mass ratio
ELECTRON_MUON_MASS_RATIO	206.7682826		CODATA2018	Electron-muon mass ratio
ELECTRON_TAU_MASS_RATIO	3477.23		CODATA2018	Electron-tau mass ratio
MUON_ELECTRON_MASS_RATIO	206.7682826		CODATA2018	Muon-electron mass ratio
TAU_ELECTRON_MASS_RATIO	3477.23		CODATA2018	Tau-electron mass ratio
TAU_MUON_MASS_RATIO	16.8167		CODATA2018	Tau-muon mass ratio
PROTON_MUON_MASS_RATIO	8.88024337		CODATA2018	Proton-muon mass ratio
PROTON_TAU_MASS_RATIO	0.528063		CODATA2018	Proton-tau mass ratio
NEUTRON_MUON_MASS_RATIO	8.89248408		CODATA2018	Neutron-muon mass ratio
NEUTRON_TAU_MASS_RATIO	0.528791		CODATA2018	Neutron-tau mass ratio
DEUTERON_ELECTRON_MASS_RATIO	3670.48296788		CODATA2018	Deuteron-electron mass ratio
DEUTERON_PROTON_MASS_RATIO	1.99900750139		CODATA2018	Deuteron-proton mass ratio
TRITON_ELECTRON_MASS_RATIO	5496.92153551		CODATA2018	Triton-electron mass ratio
TRITON_PROTON_MASS_RATIO	2.99315267046		CODATA2018	Triton-proton mass ratio
HELIUM4_ATOM_MASS	6.646479073e-27	kg	CODATA2018	Helium-4 atom mass
ELECTRON_MASS_ENERGY_EQUIVALENT	8.1871057769e-14	J	CODATA2018	Electron mass energy equivalent m_e c²
PROTON_MASS_ENERGY_EQUIVALENT	1.50327761598e-10	J	CODATA2018	Proton mass energy equivalent m_p c²
NEUTRON_MASS_ENERGY_EQUIVALENT	1.50534963117e-10	J	CODATA2018	Neutron mass energy equivalent m_n c²
MUON_MASS_ENERGY_EQUIVALENT	1.692833804e-11	J	CODATA2018	Muon mass energy equivalent
TAU_MASS_ENERGY_EQUIVALENT	2.8467762768e-10	J	CODATA2018	Tau mass energy equivalent
DEUTERON_MASS_ENERGY_EQUIVALENT	3.00506323102e-10	J	CODATA2018	Deuteron mass energy equivalent
TRITON_MASS	5.00735674462e-27	kg	CODATA2018	Triton mass
HELION_MASS	5.00641277963e-27	kg	CODATA2018	Helion mass (³He nucleus)
NEUTRON_COMPTON_WAVELENGTH	1.31909090581e-15	m	CODATA2018	Neutron Compton wavelength
PROTON_COMPTON_WAVELENGTH	1.32140985539e-15	m	CODATA2018	Proton Compton wavelength
MUON_COMPTON_WAVELENGTH	1.17344411e-14	m	CODATA2018	Muon Compton wavelength
TAU_COMPTON_WAVELENGTH	6.97771e-16	m	CODATA2018	Tau Compton wavelength
NEUTRON_MAGNETIC_MOMENT	-9.6623651e-27	J/T	CODATA2018	Neutron magnetic moment
PROTON_MAGNETIC_MOMENT	1.41060679736e-26	J/T	CODATA2018	Proton magnetic moment
ELECTRON_MAGNETIC_MOMENT	-9.2847647043e-24	J/T	CODATA2018	Electron magnetic moment
MUON_MAGNETIC_MOMENT	-4.49044826e-26	J/T	CODATA2018	Muon magnetic moment
NEUTRON_G_FACTOR	-3.82608545		CODATA2018	Neutron g-factor
MUON_G_FACTOR	-2.0023318418		CODATA2018	Muon g-factor
ELECTRON_MUON_MAGNETIC_MOMENT_RATIO	206.7669883		CODATA2018	Electron-muon magnetic moment ratio
ELECTRON_PROTON_MAGNETIC_MOMENT_RATIO	-658.21068789		CODATA2018	Electron-proton magnetic moment ratio
ELECTRON_NEUTRON_MAGNETIC_MOMENT_RATIO	960.9205		CODATA2018	Electron-neutron magnetic moment ratio
PROTON_NEUTRON_MAGNETIC_MOMENT_RATIO	-1.45989805		CODATA2018	Proton-neutron magnetic moment ratio
ELECTRON_DEUTERON_MAGNETIC_MOMENT_RATIO	-2143.923491		CODATA2018	Electron-deuteron magnetic moment ratio
PROTON_ELECTRON_MAGNETIC_MOMENT_RATIO	-658.21068789		CODATA2018	Proton-electron magnetic moment ratio
NEUTRON_ELECTRON_MAGNETIC_MOMENT_RATIO	-960.9205		CODATA2018	Neutron-electron magnetic moment ratio
DEUTERON_ELECTRON_MAGNETIC_MOMENT_RATIO	-2143.923491		CODATA2018	Deuteron-electron magnetic moment ratio
DEUTERON_PROTON_MAGNETIC_MOMENT_RATIO	0.8574382311		CODATA2018	Deuteron-proton magnetic moment ratio
DEUTRON_G_FACTOR	-0.4669754556		CODATA2018	Deuteron g-factor
TRITON_G_FACTOR	5.957924931		CODATA2018	Triton g-factor
HELION_G_FACTOR	-4.255250616		CODATA2018	Helion g-factor
ALPHA_PARTICLE_G_FACTOR	0		CODATA2018	Alpha particle g-factor
ELECTRON_GYROMAGNETIC_RATIO_OVER_2PI	28024951424.2	Hz/T	CODATA2018	Electron gyromagnetic ratio over 2π
PROTON_GYROMAGNETIC_RATIO_OVER_2PI	42577478.518	Hz/T	CODATA2018	Proton gyromagnetic ratio over 2π
NEUTRON_GYROMAGNETIC_RATIO_OVER_2PI	29164693.1	Hz/T	CODATA2018	Neutron gyromagnetic ratio over 2π
MUON_GYROMAGNETIC_RATIO_OVER_2PI	135534990	Hz/T	CODATA2018	Muon gyromagnetic ratio over 2π
ELECTRON_GYROMAGNETIC_RATIO_IN_MHZ_PER_T	28024.9514242	MHz/T	CODATA2018	Electron gyromagnetic ratio in MHz/T
PROTON_GYROMAGNETIC_RATIO_IN_MHZ_PER_T	42.577478518	MHz/T	CODATA2018	Proton gyromagnetic ratio in MHz/T
NEUTRON_GYROMAGNETIC_RATIO_IN_MHZ_PER_T	29.1646931	MHz/T	CODATA2018	Neutron gyromagnetic ratio in MHz/T
SHIELDED_PROTON_GYROMAGNETIC_RATIO	42576385.11	Hz/T	CODATA2018	Shielded proton gyromagnetic ratio over 2π
SHIELDED_HELION_GYROMAGNETIC_RATIO	32434100.944	Hz/T	CODATA2018	Shielded helion gyromagnetic ratio over 2π
SHIELDED_PROTON_GYROMAGNETIC_RATIO_IN_MHZ_PER_T	42.57638511	MHz/T	CODATA2018	Shielded proton gyromagnetic ratio in MHz/T
ELECTRIC_CONSTANT	8.8541878128e-12	F/m	CODATA2018	Electric constant (alias for vacuum permittivity)
MAGNETIC_CONSTANT	1.25663706212e-6	N/A²	CODATA2018	Magnetic constant (alias for vacuum permeability)
ELECTRIC_DIPOLE_MOMENT	8.362693187e-20	C·m	CODATA2018	Deuteron electric dipole moment
ELECTRON_ELECTRIC_DIPOLE_MOMENT	0	C·m	CODATA2018	Electron electric dipole moment
NEUTRON_ELECTRIC_DIPOLE_MOMENT	0	C·m	CODATA2018	Neutron electric dipole moment
PROTON_ELECTRIC_DIPOLE_MOMENT	0	C·m	CODATA2018	Proton electric dipole moment
ELECTRON_ELECTRIC_QUADRUPOLE_MOMENT	0	C·m²	CODATA2018	Electron electric quadrupole moment
DEUTERON_ELECTRIC_QUADRUPOLE_MOMENT	2.875e-29	C·m²	CODATA2018	Deuteron electric quadrupole moment
ELECTRON_MAGNETIC_DIPOLE_MOMENT	-9.2847647043e-24	J/T	CODATA2018	Electron magnetic dipole moment
PROTON_MAGNETIC_DIPOLE_MOMENT	1.41060679736e-26	J/T	CODATA2018	Proton magnetic dipole moment
NEUTRON_MAGNETIC_DIPOLE_MOMENT	-9.6623651e-27	J/T	CODATA2018	Neutron magnetic dipole moment
MUON_MAGNETIC_DIPOLE_MOMENT	-4.49044826e-26	J/T	CODATA2018	Muon magnetic dipole moment
ATOMIC_UNIT_OF_CHARGE	1.602176634e-19	C	CODATA2018	Atomic unit of charge e
ATOMIC_UNIT_OF_CURRENT	0.0066236182375102	A	CODATA2018	Atomic unit of current
ATOMIC_UNIT_OF_ELECTRIC_DIPOLE_MOMENT	8.4783536251e-30	C·m	CODATA2018	Atomic unit of electric dipole moment
ATOMIC_UNIT_OF_ELECTRIC_FIELD	514220674763	V/m	CODATA2018	Atomic unit of electric field
ATOMIC_UNIT_OF_ELECTRIC_POTENTIAL	27.211386245988	V	CODATA2018	Atomic unit of electric potential
ATOMIC_UNIT_OF_ENERGY	4.3597447222071e-18	J	CODATA2018	Atomic unit of energy (Hartree)
ATOMIC_UNIT_OF_FORCE	8.23872336e-8	N	CODATA2018	Atomic unit of force
ATOMIC_UNIT_OF_LENGTH	5.29177210903e-11	m	CODATA2018	Atomic unit of length (Bohr radius)
ATOMIC_UNIT_OF_MAGNETIC_DIPOLE_MOMENT	1.85480201566e-23	J/T	CODATA2018	Atomic unit of magnetic dipole moment
ATOMIC_UNIT_OF_MAGNETIC_FLUX_DENSITY	235051.756758	T	CODATA2018	Atomic unit of magnetic flux density
ATOMIC_UNIT_OF_MAGNETIZABILITY	7.8910366008e-29	m³	CODATA2018	Atomic unit of magnetizability
ATOMIC_UNIT_OF_MASS	9.1093837015e-31	kg	CODATA2018	Atomic unit of mass (electron mass)
ATOMIC_UNIT_OF_MOMENTUM	1.9928519141e-24	kg·m/s	CODATA2018	Atomic unit of momentum
ATOMIC_UNIT_OF_PERMITTIVITY	1.11265005545e-10	F/m	CODATA2018	Atomic unit of permittivity
ATOMIC_UNIT_OF_TIME	2.4188843265857e-17	s	CODATA2018	Atomic unit of time
ATOMIC_UNIT_OF_VELOCITY	2187691.26364	m/s	CODATA2018	Atomic unit of velocity
ATOMIC_UNIT_OF_ACTION	1.054571817e-34	J·s	CODATA2018	Atomic unit of action (ħ)
ATOMIC_UNIT_OF_ACCELERATION	1.0977692476511e+21	m/s²	CODATA2018	Atomic unit of acceleration
ATOMIC_UNIT_OF_ANGULAR_MOMENTUM	1.054571817e-34	J·s	CODATA2018	Atomic unit of angular momentum
ATOMIC_UNIT_OF_ANGULAR_FREQUENCY	41341376622500000	rad/s	CODATA2018	Atomic unit of angular frequency
ATOMIC_UNIT_OF_DENSITY	8.487103425e+30	kg/m³	CODATA2018	Atomic unit of density
ATOMIC_UNIT_OF_ELECTRIC_POLARIZABILITY	1.64877727436e-41	C·m²/V	CODATA2018	Atomic unit of electric polarizability
ATOMIC_UNIT_OF_IMPEDANCE	0.00036143873276	Ω	CODATA2018	Atomic unit of impedance
ATOMIC_UNIT_OF_INDUCTANCE	1.811804566e-53	H	CODATA2018	Atomic unit of inductance
ATOMIC_UNIT_OF_POWER	8.2863886903e-9	W	CODATA2018	Atomic unit of power
ATOMIC_UNIT_OF_PRESSURE	29421013274948	Pa	CODATA2018	Atomic unit of pressure
ATOMIC_UNIT_OF_VISCOSITY	0.000017298842621	Pa·s	CODATA2018	Atomic unit of viscosity
ATOMIC_UNIT_OF_VOLUME	1.471521247251e-45	m³	CODATA2018	Atomic unit of volume
NATURAL_UNIT_OF_ACTION	1.054571817e-34	J·s	CODATA2018	Natural unit of action (ħ)
NATURAL_UNIT_OF_ENERGY	1.602176634e-10	J	CODATA2018	Natural unit of energy (GeV)
NATURAL_UNIT_OF_LENGTH	1.973269804e-16	m	CODATA2018	Natural unit of length (ħc)
NATURAL_UNIT_OF_MASS	1.782661921e-36	kg	CODATA2018	Natural unit of mass
NATURAL_UNIT_OF_MOMENTUM	5.347286763e-19	kg·m/s	CODATA2018	Natural unit of momentum
NATURAL_UNIT_OF_TIME	5.391247e-44	s	CODATA2018	Natural unit of time (ħ/m_e c²)
NATURAL_UNIT_OF_VELOCITY	299792458	m/s	CODATA2018	Natural unit of velocity (c)
NATURAL_UNIT_OF_ACTION_IN_EV_S	6.582119569e-16	eV·s	CODATA2018	Natural unit of action in eV·s
NATURAL_UNIT_OF_ENERGY_IN_MEV	0.51099895	MeV	CODATA2018	Natural unit of energy in MeV (electron mass)
NATURAL_UNIT_OF_MOMENTUM_IN_MEV_PER_C	0.51099895	MeV/c	CODATA2018	Natural unit of momentum in MeV/c
NATURAL_UNIT_OF_VELOCITY_IN_C	1		CODATA2018	Natural unit of velocity in units of c
ELECTRON_VOLT_ATOMIC_MASS_UNIT	931494.10242	eV/u	CODATA2018	Electron volt atomic mass unit relationship
MOLAR_MASS_OF_CARBON12	0.012	kg/mol	CODATA2018	Molar mass of carbon-12
MOLAR_PLANCK_CONSTANT	3.990312712e-10	J·s·mol⁻¹	CODATA2018	Molar Planck constant N_A h
MOLAR_GAS_CONSTANT	8.314462618	J·mol⁻¹·K⁻¹	CODATA2018	Molar gas constant (alias)
UNIFIED_ATOMIC_MASS_UNIT	1.6605390666e-27	kg	CODATA2018	Unified atomic mass unit (alias)
ATOMIC_MASS_CONSTANT	1.6605390666e-27	kg	CODATA2018	Atomic mass constant m_u
ATOMIC_MASS_CONSTANT_ENERGY_EQUIVALENT	1.4924180856e-10	J	CODATA2018	Atomic mass constant energy equivalent
ATOMIC_MASS_CONSTANT_ENERGY_EQUIVALENT_IN_MEV	931.49410242	MeV	CODATA2018	Atomic mass constant energy equivalent in MeV
ELECTRON_VOLT_IN_JOULES	1.602176634e-19	J	CODATA2018	Electron volt in joules
ELECTRON_VOLT_IN_HARTREE	0.036749322175665	E_h	CODATA2018	Electron volt in Hartree
ELECTRON_VOLT_IN_INVERSE_METERS	806554.5207	m⁻¹	CODATA2018	Electron volt in inverse meters
ELECTRON_VOLT_IN_INVERSE_CM	8065.545207	cm⁻¹	CODATA2018	Electron volt in inverse centimeters
ELECTRON_VOLT_IN_KELVIN	11604.51812	K	CODATA2018	Electron volt in kelvin
ELECTRON_VOLT_IN_KILOGRAMS	1.782661921e-36	kg	CODATA2018	Electron volt in kilograms
HARTREE_ENERGY_IN_EV	27.211386245988	eV	CODATA2018	Hartree energy in electron volts
HARTREE_ENERGY_IN_JOULES	4.3597447222071e-18	J	CODATA2018	Hartree energy in joules
HARTREE_ENERGY_IN_INVERSE_METERS	21947463.136308	m⁻¹	CODATA2018	Hartree energy in inverse meters
HARTREE_ENERGY_IN_INVERSE_CM	219474.63136308	cm⁻¹	CODATA2018	Hartree energy in inverse centimeters
HARTREE_ENERGY_IN_KELVIN	315775.02480407	K	CODATA2018	Hartree energy in kelvin
HARTREE_ENERGY_IN_KILOGRAMS	4.8508701299523e-35	kg	CODATA2018	Hartree energy in kilograms
RYDBERG_CONSTANT_TIMES_C_IN_HZ	3289841960250000	Hz	CODATA2018	Rydberg constant times c in Hz
RYDBERG_CONSTANT_TIMES_HC_IN_EV	13.605693122994	eV	CODATA2018	Rydberg constant times hc in eV
RYDBERG_CONSTANT_TIMES_HC_IN_J	2.1798723611035e-18	J	CODATA2018	Rydberg constant times hc in joules
FARADAY_CONSTANT_FOR_CONVENTIONAL_CURRENT	96485.3251	C/mol	CODATA2018	Faraday constant for conventional electric current
MOLAR_VOLUME_OF_IDEAL_GAS	0.02241396954	m³/mol	CODATA2018	Molar volume of ideal gas (273.15 K, 100 kPa)
MOLAR_VOLUME_OF_IDEAL_GAS_AT_STP	0.02241396954	m³/mol	CODATA2018	Molar volume of ideal gas at STP
MOLAR_VOLUME_OF_IDEAL_GAS_AT_SATP	0.024789570414	m³/mol	CODATA2018	Molar volume of ideal gas at SATP (298.15 K, 100 kPa)
FIRST_RADIATION_CONSTANT_FOR_SPECTRAL_RADIANCE	1.191042972e-16	W·m²·sr⁻¹	CODATA2018	First radiation constant for spectral radiance c₁L
SECOND_RADIATION_CONSTANT_FOR_SPECTRAL_RADIANCE	0.01438776877	m·K	CODATA2018	Second radiation constant for spectral radiance c₂
FINE_STRUCTURE_CONSTANT	0.0072973525693		CODATA2018	Fine-structure constant (alias)
ELECTRON_CHARGE_TO_MASS_RATIO	-175882001076	C/kg	CODATA2018	Electron charge to mass ratio -e/m_e
PROTON_CHARGE_TO_MASS_RATIO	95788331.56	C/kg	CODATA2018	Proton charge to mass ratio e/m_p
NEUTRON_PROTON_MAGNETIC_MOMENT_RATIO	-0.68497934		CODATA2018	Neutron-proton magnetic moment ratio
SHIELDED_HELION_GYROMAGNETIC_RATIO_IN_MHZ_PER_T	32.434100944	MHz/T	CODATA2018	Shielded helion gyromagnetic ratio in MHz/T
ELECTRON_MASS_IN_U	0.000548579909065	u	CODATA2018	Electron mass in unified atomic mass units
PROTON_MASS_IN_U	1.007276466621	u	CODATA2018	Proton mass in unified atomic mass units
NEUTRON_MASS_IN_U	1.00866491595	u	CODATA2018	Neutron mass in unified atomic mass units
MUON_MASS_IN_U	0.1134389259	u	CODATA2018	Muon mass in unified atomic mass units
TAU_MASS_IN_U	1.90754	u	CODATA2018	Tau mass in unified atomic mass units
DEUTERON_MASS_IN_U	2.013553212745	u	CODATA2018	Deuteron mass in unified atomic mass units
TRITON_MASS_IN_U	3.01550071632	u	CODATA2018	Triton mass in unified atomic mass units
HELION_MASS_IN_U	3.014932247175	u	CODATA2018	Helion mass in unified atomic mass units
ALPHA_PARTICLE_MASS_IN_U	4.00260325413	u	CODATA2018	Alpha particle mass in unified atomic mass units
HELIUM4_ATOM_MASS_IN_U	4.00260325413	u	CODATA2018	Helium-4 atom mass in unified atomic mass units
ELECTRON_MASS_IN_MEV	0.51099895	MeV/c²	CODATA2018	Electron mass in MeV/c²
PROTON_MASS_IN_MEV	938.27208816	MeV/c²	CODATA2018	Proton mass in MeV/c²
NEUTRON_MASS_IN_MEV	939.56542052	MeV/c²	CODATA2018	Neutron mass in MeV/c²
MUON_MASS_IN_MEV	105.6583755	MeV/c²	CODATA2018	Muon mass in MeV/c²
TAU_MASS_IN_MEV	1776.86	MeV/c²	CODATA2018	Tau mass in MeV/c²
DEUTERON_MASS_IN_MEV	1875.61294257	MeV/c²	CODATA2018	Deuteron mass in MeV/c²
TRITON_MASS_IN_MEV	2808.92113298	MeV/c²	CODATA2018	Triton mass in MeV/c²
HELION_MASS_IN_MEV	2808.39160743	MeV/c²	CODATA2018	Helion mass in MeV/c²
ALPHA_PARTICLE_MASS_IN_MEV	3727.3794066	MeV/c²	CODATA2018	Alpha particle mass in MeV/c²
HELIUM4_ATOM_MASS_IN_MEV	3727.3794066	MeV/c²	CODATA2018	Helium-4 atom mass in MeV/c²
ELECTRON_MASS_IN_AMU	0.000548579909065	u	CODATA2018	Electron mass in atomic mass units (alias)
PROTON_MASS_IN_AMU	1.007276466621	u	CODATA2018	Proton mass in atomic mass units (alias)
NEUTRON_MASS_IN_AMU	1.00866491595	u	CODATA2018	Neutron mass in atomic mass units (alias)
ELECTRON_MASS_IN_KG	9.1093837015e-31	kg	CODATA2018	Electron mass in kilograms (alias)
PROTON_MASS_IN_KG	1.67262192369e-27	kg	CODATA2018	Proton mass in kilograms (alias)
NEUTRON_MASS_IN_KG	1.67492749804e-27	kg	CODATA2018	Neutron mass in kilograms (alias)
ELECTRON_MASS_IN_JOULES	8.1871057769e-14	J	CODATA2018	Electron mass energy in joules (alias)
PROTON_MASS_IN_JOULES	1.50327761598e-10	J	CODATA2018	Proton mass energy in joules (alias)
NEUTRON_MASS_IN_JOULES	1.50534963117e-10	J	CODATA2018	Neutron mass energy in joules (alias)
ELECTRON_MASS_IN_HARTREE	1	E_h	CODATA2018	Electron mass in Hartree atomic units
PROTON_MASS_IN_HARTREE	1836.15267343	E_h	CODATA2018	Proton mass in Hartree atomic units
NEUTRON_MASS_IN_HARTREE	1838.68366273	E_h	CODATA2018	Neutron mass in Hartree atomic units
ELECTRON_MASS_IN_RYDBERG	2	R∞ hc	CODATA2018	Electron mass in Rydberg atomic units
PROTON_MASS_IN_RYDBERG	3672.305305304	R∞ hc	CODATA2018	Proton mass in Rydberg atomic units
NEUTRON_MASS_IN_RYDBERG	3677.36732546	R∞ hc	CODATA2018	Neutron mass in Rydberg atomic units
ELECTRON_MASS_IN_EV	510998.95	eV/c²	CODATA2018	Electron mass in eV/c²
PROTON_MASS_IN_EV	938272088.16	eV/c²	CODATA2018	Proton mass in eV/c²
NEUTRON_MASS_IN_EV	939565420.52	eV/c²	CODATA2018	Neutron mass in eV/c²
ELECTRON_MASS_IN_GEV	0.51099895	GeV/c²	CODATA2018	Electron mass in GeV/c²
PROTON_MASS_IN_GEV	0.93827208816	GeV/c²	CODATA2018	Proton mass in GeV/c²
NEUTRON_MASS_IN_GEV	0.93956542052	GeV/c²	CODATA2018	Neutron mass in GeV/c²
ELECTRON_MASS_IN_TEV	0.00051099895	TeV/c²	CODATA2018	Electron mass in TeV/c²
PROTON_MASS_IN_TEV	0.00093827208816	TeV/c²	CODATA2018	Proton mass in TeV/c²
NEUTRON_MASS_IN_TEV	0.00093956542052	TeV/c²	CODATA2018	Neutron mass in TeV/c²
ELECTRON_MASS_IN_KEV	510998950	keV/c²	CODATA2018	Electron mass in keV/c²
PROTON_MASS_IN_KEV	938272088160	keV/c²	CODATA2018	Proton mass in keV/c²
NEUTRON_MASS_IN_KEV	939565420520	keV/c²	CODATA2018	Neutron mass in keV/c²
ELECTRON_MASS_IN_MEV_PER_C_SQUARED	0.51099895	MeV/c²	CODATA2018	Electron mass in MeV/c² (alias)
PROTON_MASS_IN_MEV_PER_C_SQUARED	938.27208816	MeV/c²	CODATA2018	Proton mass in MeV/c² (alias)
NEUTRON_MASS_IN_MEV_PER_C_SQUARED	939.56542052	MeV/c²	CODATA2018	Neutron mass in MeV/c² (alias)
ELECTRON_MASS_IN_U_PER_C_SQUARED	0.000548579909065	u/c²	CODATA2018	Electron mass in u/c²
PROTON_MASS_IN_U_PER_C_SQUARED	1.007276466621	u/c²	CODATA2018	Proton mass in u/c²
NEUTRON_MASS_IN_U_PER_C_SQUARED	1.00866491595	u/c²	CODATA2018	Neutron mass in u/c²
ELECTRON_MASS_IN_AMU_PER_C_SQUARED	0.000548579909065	u/c²	CODATA2018	Electron mass in amu/c² (alias)
PROTON_MASS_IN_AMU_PER_C_SQUARED	1.007276466621	u/c²	CODATA2018	Proton mass in amu/c² (alias)
NEUTRON_MASS_IN_AMU_PER_C_SQUARED	1.00866491595	u/c²	CODATA2018	Neutron mass in amu/c² (alias)
A4_FREQUENCY	440	Hz	EXACT	Standard A4 musical pitch
SEMITONE_RATIO	1.0594630943592953		MATH	Semitone frequency ratio 2^(1/12)
CENTS_PER_OCTAVE	1200	cent	EXACT	Cents per octave in equal temperament
Z_80	1.2815515594		MATH	Two-sided z-score for 80% confidence
Z_90	1.644853627		MATH	Two-sided z-score for 90% confidence
Z_95	1.9599639845		MATH	Two-sided z-score for 95% confidence
Z_99	2.5758293035		MATH	Two-sided z-score for 99% confidence
WATER_DENSITY_25C	997	kg/m³	NIST	Liquid water density at 25 °C
WATER_DENSITY_4C	999.972	kg/m³	NIST	Maximum liquid water density at 4 °C
ICE_DENSITY	917	kg/m³	NIST	Ice density near 0 °C
SEAWATER_DENSITY	1025	kg/m³	NIST	Typical seawater density
WATER_SPECIFIC_HEAT	4186	J/(kg·K)	NIST	Specific heat of liquid water
WATER_HEAT_VAPORIZATION	2260000	J/kg	NIST	Latent heat of vaporization of water
BOILING_POINT_WATER_K	373.15	K	NIST	Boiling point of water at 1 atm
FREEZING_POINT_WATER_K	273.15	K	NIST	Freezing point of water
PKW_25C	14		NIST	Ion-product exponent pKw at 25 °C
PH_NEUTRAL	7		NIST	Neutral pH at 25 °C
WATER_ION_PRODUCT_25C	1e-14	mol²/L²	NIST	Water ion product Kw at 25 °C
REFRACTIVE_INDEX_AIR	1.000293		NIST	Refractive index of dry air (STP)
VISIBLE_WAVELENGTH_MIN	4e-7	m	CIE	Approximate visible spectrum short edge
VISIBLE_WAVELENGTH_MAX	7e-7	m	CIE	Approximate visible spectrum long edge
WAVELENGTH_RED	7e-7	m	CIE	Approximate red wavelength
WAVELENGTH_GREEN	5.5e-7	m	CIE	Approximate green wavelength
WAVELENGTH_BLUE	4.5e-7	m	CIE	Approximate blue wavelength
CARBON_14_HALF_LIFE_YEARS	5730	a	NIST	Carbon-14 half-life
CARBON_14_HALF_LIFE_SECONDS	180825048000	s	NIST	Carbon-14 half-life in seconds
URANIUM_238_HALF_LIFE_YEARS	4468000000	a	NIST	Uranium-238 half-life
EARTH_CRUST_THICKNESS_AVG	35000	m	GEOLOGY	Average continental crust thickness
GRANITE_DENSITY	2700	kg/m³	GEOLOGY	Typical granite density
LIMESTONE_DENSITY	2710	kg/m³	GEOLOGY	Typical limestone density
BASALT_DENSITY	3000	kg/m³	GEOLOGY	Typical basalt density
SANDSTONE_DENSITY	2400	kg/m³	GEOLOGY	Typical sandstone density
SOIL_BULK_DENSITY	1300	kg/m³	USDA	Typical agricultural soil bulk density
MOLAR_MASS_CARBON	12.011	g/mol	IUPAC	Molar mass of carbon
MOLAR_MASS_HYDROGEN	1.008	g/mol	IUPAC	Molar mass of hydrogen
MOLAR_MASS_OXYGEN	15.999	g/mol	IUPAC	Molar mass of oxygen
MOLAR_MASS_NITROGEN	14.007	g/mol	IUPAC	Molar mass of nitrogen
MOLAR_MASS_SODIUM	22.99	g/mol	IUPAC	Molar mass of sodium
MOLAR_MASS_CHLORINE	35.45	g/mol	IUPAC	Molar mass of chlorine
MOLAR_MASS_IRON	55.845	g/mol	IUPAC	Molar mass of iron
MOLAR_MASS_GOLD	196.967	g/mol	IUPAC	Molar mass of gold
REFRACTIVE_INDEX_WATER	1.333		NIST	Refractive index of water at 20 °C
DIELECTRIC_CONSTANT_WATER	80.1		NIST	Relative permittivity of water at 20 °C
DYNAMIC_VISCOSITY_WATER_20C	0.001002	Pa·s	NIST	Dynamic viscosity of water at 20 °C
PRANDTL_NUMBER_AIR	0.71		ENGINEERING	Prandtl number of air (~20 °C)
PRANDTL_NUMBER_WATER	7		ENGINEERING	Prandtl number of water (~20 °C)
POTASSIUM_40_HALF_LIFE_YEARS	1248000000	a	NIST	Potassium-40 half-life
URANIUM_235_HALF_LIFE_YEARS	703800000	a	NIST	Uranium-235 half-life
PLUTONIUM_239_HALF_LIFE_YEARS	24110	a	NIST	Plutonium-239 half-life
IODINE_131_HALF_LIFE_DAYS	8.02	d	NIST	Iodine-131 half-life
TRITIUM_HALF_LIFE_YEARS	12.32	a	NIST	Tritium half-life
RADON_222_HALF_LIFE_DAYS	3.8235	d	NIST	Radon-222 half-life
TECHNETIUM_99M_HALF_LIFE_HOURS	6.015	h	NIST	Technetium-99m half-life
COBALT_60_HALF_LIFE_YEARS	5.2713	a	NIST	Cobalt-60 half-life
STRONTIUM_90_HALF_LIFE_YEARS	28.79	a	NIST	Strontium-90 half-life
CESIUM_137_HALF_LIFE_YEARS	30.17	a	NIST	Cesium-137 half-life
AMERICIUM_241_HALF_LIFE_YEARS	432.2	a	NIST	Americium-241 half-life
RADIOCARBON_CALIBRATION_OFFSET	1950	a	RADIOCARBON	Radiocarbon BP reference year (1950 CE)
ATMOSPHERIC_N2_FRACTION	0.7808		NIST	Dry-air nitrogen mole fraction
ATMOSPHERIC_AR_FRACTION	0.00934		NIST	Dry-air argon mole fraction
OCEAN_SALINITY_PPT	35	ppt	OCEAN	Typical seawater salinity
OCEAN_PH_REFERENCE	8.1		OCEAN	Typical surface ocean pH (pre-anthropogenic ~8.2)
EARTH_SCALE_HEIGHT	8500	m	MET	Atmospheric scale height (approx.)
TROPOPAUSE_HEIGHT_ISA	11000	m	ICAO	ISA tropopause geopotential height
EARTH_MEAN_DENSITY	5514	kg/m³	NASA	Mean density of Earth
MOON_MEAN_DENSITY	3344	kg/m³	NASA	Mean density of the Moon
MOLAR_MASS_CALCIUM	40.078	g/mol	IUPAC	Molar mass of calcium
MOLAR_MASS_POTASSIUM	39.098	g/mol	IUPAC	Molar mass of potassium
MOLAR_MASS_PHOSPHORUS	30.974	g/mol	IUPAC	Molar mass of phosphorus
MOLAR_MASS_SULFUR	32.06	g/mol	IUPAC	Molar mass of sulfur
MOLAR_MASS_COPPER	63.546	g/mol	IUPAC	Molar mass of copper
MOLAR_MASS_SILVER	107.868	g/mol	IUPAC	Molar mass of silver
MOLAR_MASS_WATER	18.015	g/mol	IUPAC	Molar mass of water
MOLAR_MASS_CO2	44.009	g/mol	IUPAC	Molar mass of carbon dioxide
MOLAR_MASS_METHANE	16.043	g/mol	IUPAC	Molar mass of methane
MOLAR_MASS_ETHANOL	46.068	g/mol	IUPAC	Molar mass of ethanol
MOLAR_MASS_GLUCOSE	180.156	g/mol	IUPAC	Molar mass of glucose
STP_MOLAR_VOLUME	22.414	L/mol	IUPAC	Ideal molar volume at STP (0 °C, 1 atm)
YOCTO	1e-24		SI	SI prefix yocto (10⁻²⁴)
ZEPTO	1e-21		SI	SI prefix zepto (10⁻²¹)
ATTO	1e-18		SI	SI prefix atto (10⁻¹⁸)
FEMTO	1e-15		SI	SI prefix femto (10⁻¹⁵)
PICO	1e-12		SI	SI prefix pico (10⁻¹²)
NANO	1e-9		SI	SI prefix nano (10⁻⁹)
MICRO	1e-6		SI	SI prefix micro (10⁻⁶)
MILLI	0.001		SI	SI prefix milli (10⁻³)
CENTI	0.01		SI	SI prefix centi (10⁻²)
DECI	0.1		SI	SI prefix deci (10⁻¹)
DECA	10		SI	SI prefix deca (10¹)
HECTO	100		SI	SI prefix hecto (10²)
KILO	1000		SI	SI prefix kilo (10³)
MEGA	1000000		SI	SI prefix mega (10⁶)
GIGA	1000000000		SI	SI prefix giga (10⁹)
TERA	1000000000000		SI	SI prefix tera (10¹²)
PETA	1000000000000000		SI	SI prefix peta (10¹⁵)
EXA	1000000000000000000		SI	SI prefix exa (10¹⁸)
ZETTA	1e+21		SI	SI prefix zetta (10²¹)
YOTTA	1e+24		SI	SI prefix yotta (10²⁴)
RONNA	1e+27		SI	SI prefix ronna (10²⁷, 2022)
QUETTA	1e+30		SI	SI prefix quetta (10³⁰, 2022)
QUECTO	1e-30		SI	SI prefix quecto (10⁻³⁰, 2022)
RONTO	1e-30		SI	SI prefix ronto (10⁻³⁰, 2022)
EARTH_AGE_MA	4540	Ma	ICS	Approximate age of Earth
CAMBRIAN_BOUNDARY_MA	538.8	Ma	ICS	Cambrian period start (Precambrian-Phanerozoic)
ORDOVICIAN_BOUNDARY_MA	485.4	Ma	ICS	Ordovician period start
SILURIAN_BOUNDARY_MA	443.8	Ma	ICS	Silurian period start
DEVONIAN_BOUNDARY_MA	419.2	Ma	ICS	Devonian period start
CARBONIFEROUS_BOUNDARY_MA	358.9	Ma	ICS	Carboniferous period start
PERMIAN_BOUNDARY_MA	298.9	Ma	ICS	Permian period start
TRIASSIC_BOUNDARY_MA	251.902	Ma	ICS	Triassic period start
JURASSIC_BOUNDARY_MA	201.4	Ma	ICS	Jurassic period start
CRETACEOUS_BOUNDARY_MA	145	Ma	ICS	Cretaceous period start
PALEOGENE_BOUNDARY_MA	66	Ma	ICS	Paleogene period start (K-Pg boundary)
NEOGENE_BOUNDARY_MA	23.03	Ma	ICS	Neogene period start
QUATERNARY_BOUNDARY_MA	2.58	Ma	ICS	Quaternary period start
PLEISTOCENE_BOUNDARY_MA	2.58	Ma	ICS	Pleistocene epoch start
HOLOCENE_BOUNDARY_MA	0.0117	Ma	ICS	Holocene epoch start (11.7 ka)
PALEOZOIC_END_MA	251.902	Ma	ICS	End of Paleozoic era (Permian-Triassic)
MESOZOIC_END_MA	66	Ma	ICS	End of Mesozoic era (K-Pg)
CENOZOIC_START_MA	66	Ma	ICS	Cenozoic era start
DINOSAUR_EXTINCTION_MA	66	Ma	ICS	Cretaceous-Paleogene mass extinction
OLDEST_ROCKS_MA	4030	Ma	GEOLOGY	Approximate age of oldest known rocks
ARCHEAN_PROTEROZOIC_MA	2500	Ma	ICS	Archean-Proterozoic boundary
SAFFIR_SIMPSON_CAT5_WIND_MPH	157	mph	NHC	Saffir-Simpson category 5 wind threshold (1-min sustained)
UV_INDEX_EXTREME	11		WHO	UV index extreme threshold
AIR_QUALITY_AQI_HAZARDOUS	301		EPA	US AQI hazardous threshold
RICHter_SCALE_ENERGY_RATIO	10		USGS	Energy ratio per Richter magnitude unit
RANKINE_TO_KELVIN	0.5555555555555556		NIST	Rankine-to-kelvin scale factor (°R to K)
REAUMUR_TO_KELVIN	1.25		NIST	Réaumur ice-to-boil span ratio to kelvin
CELSIUS_TO_KELVIN_OFFSET	273.15	K	NIST	Celsius-to-kelvin offset (0 °C reference)
ATOMIC_NUMBER_HYDROGEN	1		IUPAC	Atomic number of hydrogen
ATOMIC_NUMBER_HELIUM	2		IUPAC	Atomic number of helium
ATOMIC_NUMBER_CARBON	6		IUPAC	Atomic number of carbon
ATOMIC_NUMBER_NITROGEN	7		IUPAC	Atomic number of nitrogen
ATOMIC_NUMBER_OXYGEN	8		IUPAC	Atomic number of oxygen
ATOMIC_NUMBER_SODIUM	11		IUPAC	Atomic number of sodium
ATOMIC_NUMBER_CHLORINE	17		IUPAC	Atomic number of chlorine
ATOMIC_NUMBER_IRON	26		IUPAC	Atomic number of iron
ATOMIC_NUMBER_COPPER	29		IUPAC	Atomic number of copper
ATOMIC_NUMBER_SILVER	47		IUPAC	Atomic number of silver
ATOMIC_NUMBER_GOLD	79		IUPAC	Atomic number of gold
ATOMIC_NUMBER_URANIUM	92		IUPAC	Atomic number of uranium
PERIODIC_TABLE_ELEMENTS	118		IUPAC	Recognized periodic-table elements
MOLAR_MASS_HELIUM	4.003	g/mol	IUPAC	Molar mass of helium
MOLAR_MASS_LITHIUM	6.941	g/mol	IUPAC	Molar mass of lithium
MOLAR_MASS_FLUORINE	18.998	g/mol	IUPAC	Molar mass of fluorine (F₂ reference)
MOLAR_MASS_NEON	20.18	g/mol	IUPAC	Molar mass of neon
MOLAR_MASS_ARGON	39.948	g/mol	IUPAC	Molar mass of argon
MOLAR_MASS_ZINC	65.38	g/mol	IUPAC	Molar mass of zinc
MOLAR_MASS_LEAD	207.2	g/mol	IUPAC	Molar mass of lead
MOLAR_MASS_URANIUM	238.029	g/mol	IUPAC	Molar mass of natural uranium
MOLAR_MASS_AMMONIA	17.031	g/mol	IUPAC	Molar mass of ammonia
MOLAR_MASS_SODIUM_CHLORIDE	58.44	g/mol	IUPAC	Molar mass of sodium chloride
PREINDUSTRIAL_CO2_PPM	280	ppm	IPCC	Pre-industrial atmospheric CO2 reference
CLIMATE_CO2_2X_FORCING_W_M2	3.7	W/m²	IPCC	Radiative forcing for CO2 doubling (approx.)
DECIBEL_POWER_FACTOR	10		IEEE	Decibel power ratio factor (10 log10)
DECIBEL_AMPLITUDE_FACTOR	20		IEEE	Decibel amplitude ratio factor (20 log10)
BEL_TO_DECIBEL	10		IEEE	Bels per decibel
LUMEN_PER_WATT_555NM	683	lm/W	CIE	Photopic luminous efficacy at 555 nm
FOOTCANDLE_TO_LUX	10.7639104167	lx	NIST	Foot-candle to lux
STERADIAN_FULL_SPHERE	12.566370614359172	sr	MATH	Solid angle of full sphere (4π sr)
BARN_TO_M2	1e-28	m²	NIST	Barn to square meter (nuclear cross section)
ARE_TO_M2	100	m²	SI	Are to square meter
MERCALLI_MAX	12		USGS	Maximum Modified Mercalli intensity
FUJITA_EF5_WIND_MPH	200	mph	NWS	Enhanced Fujita EF5 wind speed threshold
TORF_SCALE_MAX	5		NWS	TORRO tornado intensity scale maximum
BEAUFORT_FORCE_STORM	10		WMO	Beaufort force for storm winds
CH4_GWP100	28		IPCC	CH4 100-year global warming potential (AR5)
N2O_GWP100	265		IPCC	N2O 100-year global warming potential (AR5)
SF6_GWP100	23500		IPCC	SF6 100-year global warming potential (AR5)
ATOMIC_NUMBER_LITHIUM	3		IUPAC	Atomic number of lithium
ATOMIC_NUMBER_FLUORINE	9		IUPAC	Atomic number of fluorine
ATOMIC_NUMBER_PHOSPHORUS	15		IUPAC	Atomic number of phosphorus
ATOMIC_NUMBER_POTASSIUM	19		IUPAC	Atomic number of potassium
ATOMIC_NUMBER_CALCIUM	20		IUPAC	Atomic number of calcium
MOLAR_MASS_MAGNESIUM	24.305	g/mol	IUPAC	Molar mass of magnesium
MOLAR_MASS_ALUMINUM	26.982	g/mol	IUPAC	Molar mass of aluminum
MOLAR_MASS_SILICON	28.085	g/mol	IUPAC	Molar mass of silicon
MOLAR_MASS_MANGANESE	54.938	g/mol	IUPAC	Molar mass of manganese
MOLAR_MASS_BROMINE	79.904	g/mol	IUPAC	Molar mass of bromine (Br₂ reference)
MOLAR_MASS_IODINE	126.904	g/mol	IUPAC	Molar mass of iodine (I₂ reference)

Solar Position

Name	Value	Unit	Source	Description
SOLAR_ELEVATION_NOON_EQUINOX	90	°	ASTRON	Solar elevation at local noon on equator at equinox
EARTH_AXIAL_TILT	23.439281	°	IAU	Earth axial tilt (obliquity)
SOLAR_PANEL_STC_IRRADIANCE	1000	W/m²	IEC	Standard test condition solar irradiance

Geospatial

Name	Value	Unit	Source	Description
WGS84_SEMI_MAJOR	6378137	m	WGS84	WGS84 semi-major axis a
WGS84_SEMI_MINOR	6356752.314245	m	WGS84	WGS84 semi-minor axis b
WGS84_FLATTENING	0.0033528106647474805		WGS84	WGS84 flattening f
WGS84_INV_FLATTENING	298.257223563		WGS84	WGS84 inverse flattening 1/f
WGS84_ECCENTRICITY_SQ	0.0066943799901413165		WGS84	WGS84 eccentricity squared e²
WGS84_ECCENTRICITY	0.0818191908426		WGS84	WGS84 eccentricity e
WGS84_MEAN_RADIUS	6371008.7714	m	WGS84	WGS84 authalic mean radius
WGS84_GM	398600441800000	m³/s²	WGS84	WGS84 geocentric gravitational constant GM
WGS84_ANGULAR_VELOCITY	0.00007292115	rad/s	WGS84	WGS84 Earth rotation rate ω
EARTH_CIRCUMFERENCE_EQUATORIAL	40075016.686	m	WGS84	Earth equatorial circumference
EARTH_CIRCUMFERENCE_MERIDIONAL	40007863	m	WGS84	Earth meridional circumference
MOUNT_EVEREST_HEIGHT	8848.86	m	NGS	Mount Everest summit elevation (2020 survey)
MARIANA_TRENCH_DEPTH	10984	m	NOAA	Challenger Deep approximate depth
DEATH_VALLEY_ELEVATION	-86	m	USGS	Badwater Basin elevation
DEAD_SEA_ELEVATION	-430.5	m	SURVEY	Dead Sea surface elevation (approx.)
ANTARCTICA_AREA	14200000	km²	NSIDC	Antarctica surface area
SAHARA_AREA	9200000	km²	USGS	Sahara Desert approximate area
AMAZON_RIVER_LENGTH	6400	km	USGS	Amazon River approximate length
NILE_RIVER_LENGTH	6650	km	USGS	Nile River approximate length
UTM_ZONE_WIDTH_DEG	6	°	EPSG	UTM longitudinal zone width
MERCATOR_MAX_LATITUDE	85.0511287798	°	EPSG	Web Mercator latitude clipping limit
WGS84_EPSG_CODE	4326		EPSG	EPSG code for WGS 84 geographic CRS
WEB_MERCATOR_EPSG_CODE	3857		EPSG	EPSG code for Web Mercator projected CRS
DEGREES_IN_CIRCLE	360	°	EXACT	Degrees in a full circle
LATITUDE_MAX	90	°	EXACT	Maximum absolute latitude
LONGITUDE_MAX	180	°	EXACT	Maximum absolute longitude
RIGHT_ANGLE_DEG	90	°	EXACT	Right angle in degrees
STRAIGHT_ANGLE_DEG	180	°	EXACT	Straight angle in degrees
UTM_FALSE_EASTING	500000	m	EPSG	UTM false easting (meters)
UTM_SCALE_FACTOR	0.9996		EPSG	UTM central-meridian scale factor
COMPASS_BEARING_MAX	360	°	EXACT	Compass bearing wrap modulus
FATHOM_TO_METER	1.8288	m	NIST	International fathom to meter
CABLE_TO_METER	185.2	m	NIST	International cable (100 fathoms)
LEAGUE_NAUTICAL_TO_METER	5556	m	NIST	Nautical league (3 nautical miles)

Aviation

Name	Value	Unit	Source	Description
ISA_SEA_LEVEL_TEMP	288.15	K	ICAO	ISA sea-level temperature (15 °C)
ISA_LAPSE_RATE	0.0065	K/m	ICAO	ISA tropospheric temperature lapse rate
SPEED_OF_SOUND_ISA	340.29	m/s	ICAO	Speed of sound at ISA sea level
BEAUFORT_SCALE_MAX	12		WMO	Maximum Beaufort wind force number
MACH_CRUISE_JET	0.85		ICAO	Typical long-haul jet cruise Mach number
MACH_SUPERSONIC_THRESHOLD	1		ICAO	Supersonic Mach threshold
V1_DECISION_SPEED_RATIO	0.9		ICAO	Typical V1/VR ratio (approx.)
GLIDE_RATIO_LIGHT_JET	15		ICAO	Typical light-jet glide ratio (approx.)

Maritime

Name	Value	Unit	Source	Description
KNOTS_TO_KMH	1.852	km/h	EXACT	Knot expressed as km/h (1 nmi/h)
DRAFT_MARK_TOLERANCE_CM	2	cm	IMO	Typical draft-mark tolerance
BEAUFORT_FORCE_HURRICANE	12		WMO	Beaufort force for hurricane winds

Space & Orbital Science

Name	Value	Unit	Source	Description
ASTRONOMICAL_UNIT	149597870700	m	IAU	Astronomical unit
LIGHT_YEAR	9460730472580800	m	IAU	Light year
PARSEC	30856775814913670	m	IAU	Parsec
JANSKY	1e-26	W·m⁻²·Hz⁻¹	IAU	Jansky flux density unit
SOLAR_MASS	1.98892e+30	kg	IAU	Solar mass M☉
SOLAR_RADIUS	695700000	m	IAU	Solar radius R☉
SOLAR_LUMINOSITY	3.828e+26	W	IAU	Solar luminosity L☉
GM_SUN	1.32712440018e+20	m³/s²	IAU	Heliocentric gravitational parameter GM☉
SOLAR_CONSTANT	1361	W/m²	IAU	Solar constant at 1 AU
ESCAPE_VELOCITY_EARTH	11186	m/s	IAU	Earth escape velocity
EARTH_ORBITAL_VELOCITY	29780	m/s	IAU	Earth orbital velocity around the Sun
OBLIQUITY_ECLIPTIC	23.4392811	deg	IAU	Obliquity of the ecliptic J2000.0
HUBBLE_CONSTANT	67.4	(km/s)/Mpc	IAU	Hubble constant H₀
CMB_TEMPERATURE	2.72548	K	IAU	Cosmic microwave background temperature
CRITICAL_DENSITY	8.5e-27	kg/m³	IAU	Critical density of the universe
JULIAN_YEAR	31557600	s	IAU	Julian year (365.25 days)
SIDEREAL_YEAR	31558149.7635456	s	IAU	Sidereal year in seconds
TROPICAL_YEAR	31556925.216	s	IAU	Tropical year in seconds
SIDEREAL_DAY	86164.0905	s	IAU	Sidereal day
SYNODIC_MONTH	2551442.8032	s	IAU	Synodic month in seconds
EARTH_MOON_DISTANCE	384400000	m	IAU	Mean Earth-Moon distance
MERCURY_MASS	3.3011e+23	kg	IAU	Mercury mass
MERCURY_RADIUS	2439700	m	IAU	Mercury mean radius
GM_MERCURY	22032000000000	m³/s²	IAU	Mercury gravitational parameter GM
VENUS_MASS	4.8675e+24	kg	IAU	Venus mass
VENUS_RADIUS	6051800	m	IAU	Venus mean radius
GM_VENUS	324859000000000	m³/s²	IAU	Venus gravitational parameter GM
EARTH_MASS	5.972168e+24	kg	IAU	Earth mass
EARTH_RADIUS	6371000	m	IAU	Earth mean radius
GM_EARTH	398600441800000	m³/s²	IAU	Earth gravitational parameter GM
MARS_MASS	6.4171e+23	kg	IAU	Mars mass
MARS_RADIUS	3389500	m	IAU	Mars mean radius
GM_MARS	42828370000000	m³/s²	IAU	Mars gravitational parameter GM
JUPITER_MASS	1.89813e+27	kg	IAU	Jupiter mass
JUPITER_RADIUS	69911000	m	IAU	Jupiter mean radius
GM_JUPITER	126686534000000000	m³/s²	IAU	Jupiter gravitational parameter GM
SATURN_MASS	5.68319e+26	kg	IAU	Saturn mass
SATURN_RADIUS	58232000	m	IAU	Saturn mean radius
GM_SATURN	37931187000000000	m³/s²	IAU	Saturn gravitational parameter GM
URANUS_MASS	8.681e+25	kg	IAU	Uranus mass
URANUS_RADIUS	25362000	m	IAU	Uranus mean radius
GM_URANUS	5793939000000000	m³/s²	IAU	Uranus gravitational parameter GM
NEPTUNE_MASS	1.02413e+26	kg	IAU	Neptune mass
NEPTUNE_RADIUS	24622000	m	IAU	Neptune mean radius
GM_NEPTUNE	6836530000000000	m³/s²	IAU	Neptune gravitational parameter GM
PLUTO_MASS	1.303e+22	kg	IAU	Pluto mass
PLUTO_RADIUS	1188300	m	IAU	Pluto mean radius
GM_PLUTO	871000000000	m³/s²	IAU	Pluto gravitational parameter GM
MOON_MASS	7.342e+22	kg	IAU	Moon mass
MOON_RADIUS	1737400	m	IAU	Moon mean radius
GM_MOON	4902800000000	m³/s²	IAU	Moon gravitational parameter GM
EARTH_RADIUS_EQUATORIAL	6378137	m	IAU	Earth equatorial radius
EARTH_RADIUS_POLAR	6356752.3	m	IAU	Earth polar radius
LIGHT_MINUTE	17987547480	m	EXACT	Light-minute distance
LIGHT_HOUR	1079252848800	m	EXACT	Light-hour distance
LIGHT_DAY	25902068371200	m	EXACT	Light-day distance
LIGHT_WEEK	181314478598400	m	EXACT	Light-week distance
EARTH_PERIHELION_AU	0.9832899	au	IAU	Earth perihelion distance
EARTH_APHELION_AU	1.0167119	au	IAU	Earth aphelion distance
EARTH_ECCENTRICITY_ORBIT	0.01671123		IAU	Earth orbital eccentricity
J2000_EPOCH_YEAR	2000		IAU	J2000.0 equinox epoch year
LIGHT_YEAR_PARSECS	206264.80624709636	pc	IAU	Light-year in parsecs
SOLAR_EQUATORIAL_ROTATION_DAYS	25.05	d	NASA	Solar equatorial rotation period
MERCURY_ORBITAL_PERIOD_DAYS	87.969	d	NASA	Mercury orbital period
VENUS_ORBITAL_PERIOD_DAYS	224.701	d	NASA	Venus orbital period
MARS_ORBITAL_PERIOD_DAYS	686.98	d	NASA	Mars orbital period
JUPITER_ORBITAL_PERIOD_DAYS	4332.59	d	NASA	Jupiter orbital period
SATURN_ORBITAL_PERIOD_DAYS	10759.22	d	NASA	Saturn orbital period
UNIVERSE_AGE_GYR	13.787	Gyr	Planck2018	Cosmic microwave background universe age
CMB_REDSHIFT	1100		COSMO	CMB decoupling redshift (approx.)
CRITICAL_DENSITY_RATIO	1		COSMO	Flat-universe density parameter Ω=1 marker
NEPTUNE_ORBITAL_PERIOD_DAYS	60182	d	NASA	Neptune orbital period
URANUS_ORBITAL_PERIOD_DAYS	30688.5	d	NASA	Uranus orbital period
PLUTO_ORBITAL_PERIOD_DAYS	90560	d	NASA	Pluto orbital period

Domain Types

Name	Value	Unit	Source	Description
MARATHON_DISTANCE	42195	m	IAAF	Marathon race distance
OLYMPIC_POOL_LENGTH	50	m	FINA	Olympic swimming pool length
FIFA_GOAL_WIDTH	7.32	m	FIFA	Association football goal width
BASKETBALL_HOOP_HEIGHT	3.05	m	FIBA	Basketball rim height
TEASPOON_US_TO_ML	4.92892159375	mL	NIST	US teaspoon in milliliters
TABLESPOON_US_TO_ML	14.78676478125	mL	NIST	US tablespoon in milliliters
CUP_US_TO_ML	236.5882365	mL	NIST	US customary cup in milliliters
FLUID_OUNCE_US_TO_ML	29.5735295625	mL	NIST	US fluid ounce in milliliters
GOLD_KARAT_MAX	24		CONVENTION	Maximum gold karat fineness
DIAMOND_CARAT_TO_GRAM	0.2	g	EXACT	Diamond carat to gram
F_STOP_RATIO	1.4142135623730951		PHOTO	Adjacent f-stop ratio (√2)
A4_WIDTH	0.21	m	ISO216	ISO A4 paper width
A4_HEIGHT	0.297	m	ISO216	ISO A4 paper height
GOLDEN_RATIO_CONJUGATE	0.6180339887498948		MATH	Golden-ratio conjugate 1/φ
LETTER_WIDTH_IN	8.5	in	ANSI	US Letter paper width
LETTER_HEIGHT_IN	11	in	ANSI	US Letter paper height
LEGAL_HEIGHT_IN	14	in	ANSI	US Legal paper height
TABLOID_WIDTH_IN	11	in	ANSI	US Tabloid paper width
TABLOID_HEIGHT_IN	17	in	ANSI	US Tabloid paper height
BRAILLE_CELL_DOTS	6		ADA	Braille cell dot count
GO_BOARD_SIZE_19	19		CONVENTION	Standard Go board edge length (19×19)
BASEBALL_BASE_PATH_FT	90	ft	MLB	Baseball base path length
BASKETBALL_COURT_LENGTH	28.65	m	FIBA	FIBA basketball court length
SOCCER_PENALTY_SPOT	11	m	FIFA	Penalty mark distance from goal line
TENNIS_NET_HEIGHT_CENTER	0.914	m	ITF	Tennis net height at center
GOLF_HOLE_DIAMETER_IN	4.25	in	USGA	Golf hole diameter
OLYMPIC_TRACK_LANE_WIDTH	1.22	m	IAAF	Standard athletics lane width
TRIATHLON_IRONMAN_SWIM_M	3800	m	IRONMAN	Ironman swim distance
TRIATHLON_IRONMAN_BIKE_KM	180	km	IRONMAN	Ironman bike distance
TRIATHLON_IRONMAN_RUN_KM	42.195	km	IRONMAN	Ironman run distance (marathon)
ISO_A0_WIDTH	0.841	m	ISO216	ISO A0 paper width
ISO_A0_HEIGHT	1.189	m	ISO216	ISO A0 paper height
ISO_A1_WIDTH	0.594	m	ISO216	ISO A1 paper width
ISO_A1_HEIGHT	0.841	m	ISO216	ISO A1 paper height
ISO_A2_WIDTH	0.42	m	ISO216	ISO A2 paper width
ISO_A2_HEIGHT	0.594	m	ISO216	ISO A2 paper height
ISO_A3_WIDTH	0.297	m	ISO216	ISO A3 paper width
ISO_A3_HEIGHT	0.42	m	ISO216	ISO A3 paper height
ISO_A5_WIDTH	0.148	m	ISO216	ISO A5 paper width
ISO_A5_HEIGHT	0.21	m	ISO216	ISO A5 paper height
ISO_A6_WIDTH	0.105	m	ISO216	ISO A6 paper width
ISO_A6_HEIGHT	0.148	m	ISO216	ISO A6 paper height
ISO_B0_WIDTH	1	m	ISO216	ISO B0 paper width
ISO_B0_HEIGHT	1.4142135623730951	m	ISO216	ISO B0 paper height
ISO_B1_WIDTH	0.7071067811865475	m	ISO216	ISO B1 paper width
ISO_B1_HEIGHT	1	m	ISO216	ISO B1 paper height
ISO_B2_WIDTH	0.5	m	ISO216	ISO B2 paper width
ISO_B2_HEIGHT	0.7071067811865475	m	ISO216	ISO B2 paper height
ISO_B3_WIDTH	0.35355339059327373	m	ISO216	ISO B3 paper width
ISO_B3_HEIGHT	0.5	m	ISO216	ISO B3 paper height
ISO_B4_WIDTH	0.25	m	ISO216	ISO B4 paper width
ISO_B4_HEIGHT	0.35355339059327373	m	ISO216	ISO B4 paper height
ISO_B5_WIDTH	0.17677669529663687	m	ISO216	ISO B5 paper width
ISO_B5_HEIGHT	0.25	m	ISO216	ISO B5 paper height
ISO_B6_WIDTH	0.125	m	ISO216	ISO B6 paper width
ISO_B6_HEIGHT	0.17677669529663687	m	ISO216	ISO B6 paper height
ISO_B7_WIDTH	0.08838834764831843	m	ISO216	ISO B7 paper width
ISO_B7_HEIGHT	0.125	m	ISO216	ISO B7 paper height
ISO_B8_WIDTH	0.062	m	ISO216	ISO B8 paper width (62 mm)
ISO_B8_HEIGHT	0.08838834764831843	m	ISO216	ISO B8 paper height
ISO_B9_WIDTH	0.044	m	ISO216	ISO B9 paper width (44 mm)
ISO_B9_HEIGHT	0.062	m	ISO216	ISO B9 paper height
ISO_B10_WIDTH	0.031	m	ISO216	ISO B10 paper width (31 mm)
ISO_B10_HEIGHT	0.044	m	ISO216	ISO B10 paper height
LINES_PER_PAGE_SINGLE	66		CONVENTION	Traditional single-spaced typewritten lines per page
ISO_C0_WIDTH	0.917	m	ISO269	ISO C0 envelope width
ISO_C0_HEIGHT	1.297	m	ISO269	ISO C0 envelope height
ISO_C4_WIDTH	0.229	m	ISO269	ISO C4 envelope width
ISO_C4_HEIGHT	0.324	m	ISO269	ISO C4 envelope height
ISO_C5_WIDTH	0.162	m	ISO269	ISO C5 envelope width
ISO_C5_HEIGHT	0.229	m	ISO269	ISO C5 envelope height
ISO_C6_WIDTH	0.114	m	ISO269	ISO C6 envelope width
ISO_C6_HEIGHT	0.162	m	ISO269	ISO C6 envelope height
ISO_DL_WIDTH	0.11	m	ISO269	ISO DL envelope width
ISO_DL_HEIGHT	0.22	m	ISO269	ISO DL envelope height
PIANO_KEY_COUNT	88		CONVENTION	Standard piano key count
GUITAR_STRING_COUNT	6		CONVENTION	Standard guitar string count
MIDI_NOTE_MAX	127		MIDI	Maximum MIDI note number
MIDI_CHANNELS	16		MIDI	MIDI channel count
TEMPO_DEFAULT_BPM	120	BPM	CONVENTION	Common default tempo (120 BPM)
FRAME_RATE_CINEMA	24	fps	SMPTE	Standard cinema frame rate
FRAME_RATE_NTSC	29.97	fps	SMPTE	NTSC color frame rate
FRAME_RATE_PAL	25	fps	SMPTE	PAL frame rate
ASPECT_RATIO_16_9	1.7777777777777777		SMPTE	HD widescreen aspect ratio
ASPECT_RATIO_4_3	1.3333333333333333		SMPTE	Classic television aspect ratio
FILM_35MM_FRAME_WIDTH	0.036	m	ISO	35 mm still film frame width
FILM_35MM_FRAME_HEIGHT	0.024	m	ISO	35 mm still film frame height
CRICKET_PITCH_LENGTH	20.12	m	ICC	Cricket pitch length
RUGBY_GOALPOST_WIDTH	5.6	m	WorldRugby	Rugby goalpost width
ICE_HOCKEY_RINK_LENGTH	60.96	m	NHL	NHL hockey rink length
VOLLEYBALL_NET_HEIGHT_M	2.43	m	FIVB	Men's volleyball net height
SOFTBALL_BASE_PATH	60	ft	USA	Softball base path length (fastpitch)

---

Collection Constants

Bare-identifier collection constants that lower to string arrays (for example =PLANETS, =COUNT(ATOMS), ="Earth" IN PLANETS). Total: 150 collections.

Math

Name	Items	Count	Source	Description
GREEK_ALPHABET	Alpha, Beta, Gamma, Delta, Epsilon, …	24	EXACT	Greek alphabet letter names
ROMAN_NUMERALS	I, V, X, L, C, …	7	EXACT	Roman numeral symbols
MATRIX_TYPES	Diagonal, Identity, Symmetric, Triangular, Orthogonal, …	7	LINEAR_ALGEBRA	Matrix structural classifications
TRIG_FUNCTIONS	Sine, Cosine, Tangent, Cosecant, Secant, …	6	MATH	Trigonometric functions
NUMBER_SETS	Natural, Integer, Rational, Real, Complex	5	MATH	Standard number sets

Logical

Name	Items	Count	Source	Description
BOOLEAN_STRINGS	TRUE, FALSE	2	EXACT	Uppercase boolean string literals

Date & Time

Name	Items	Count	Source	Description
WEEKDAYS	Monday, Tuesday, Wednesday, Thursday, Friday, …	7	EXACT	Days of the week (ISO order)
MONTHS	January, February, March, April, May, …	12	EXACT	Gregorian calendar months
SEASONS	Spring, Summer, Autumn, Winter	4	EXACT	Meteorological seasons (Northern Hemisphere names)
QUARTERS	Q1, Q2, Q3, Q4	4	EXACT	Fiscal/calendar quarters
TIME_UNITS	Second, Minute, Hour, Day, Week, …	7	SI	Common civil time units
WEEKDAY_ABBR	Mon, Tue, Wed, Thu, Fri, …	7	ISO	Abbreviated weekday names (ISO order)
MONTH_ABBR	Jan, Feb, Mar, Apr, May, …	12	ISO	Abbreviated month names
TIME_ZONES_UTC	UTC-12, UTC-11, UTC-10, UTC-9, UTC-8, …	25	ISO8601	Whole-hour UTC offsets

Financial

Name	Items	Count	Source	Description
FINANCIAL_STATEMENTS	Balance Sheet, Income Statement, Cash Flow Statement, Statement of Equity	4	GAAP	Core financial statements
ACCOUNT_TYPES	Asset, Liability, Equity, Revenue, Expense	5	GAAP	Chart-of-accounts top-level types
ASSET_CLASSES	Equity, Fixed Income, Cash, Real Estate, Commodities, …	6	CFA	Broad portfolio asset classes
OPTION_GREEKS	Delta, Gamma, Theta, Vega, Rho	5	FINANCE	First-order option sensitivities
CREDIT_RATINGS	AAA, AA, A, BBB, BB, …	10	S&P	S&P-style long-term credit ratings (investment + speculative)
TRADE_ORDER_TYPES	Market, Limit, Stop, Stop Limit, Trailing Stop	5	FINANCE	Common exchange order types
INCOME_STATEMENT_LINES	Revenue, Cost of Goods Sold, Gross Profit, Operating Expenses, Operating Income, …	6	GAAP	High-level income-statement sections
MAJOR_CURRENCIES	USD, EUR, GBP, JPY, CHF, …	12	ISO4217	Major ISO 4217 currency codes
AUDIT_OPINIONS	Unqualified, Qualified, Adverse, Disclaimer	4	GAAP	External audit opinion types
BOND_TYPES	Treasury, Municipal, Corporate, Agency, Mortgage-Backed, …	7	FINANCE	Fixed-income instrument categories
DERIVATIVE_TYPES	Forward, Future, Option, Swap, Warrant, …	6	FINANCE	Common derivative contract types
ECONOMIC_INDICATORS	GDP, CPI, PPI, Unemployment, PMI, …	8	ECON	Macroeconomic indicator names

Statistical

Name	Items	Count	Source	Description
STATISTICAL_TESTS	t-test, z-test, chi-square, ANOVA, Mann-Whitney, …	8	STATISTICS	Common hypothesis-test names
PROBABILITY_DISTRIBUTIONS	Normal, Lognormal, Uniform, Exponential, Poisson, …	9	STATISTICS	Common probability distributions
REGRESSION_TYPES	Linear, Logistic, Polynomial, Ridge, Lasso, …	8	STATISTICS	Regression model families

Planning

Name	Items	Count	Source	Description
MOSCOW_PRIORITIES	Must, Should, Could, Wont	4	MANAGEMENT	MoSCoW prioritization categories
AGILE_CEREMONIES	Sprint Planning, Daily Standup, Sprint Review, Retrospective, Backlog Refinement	5	SCRUM	Scrum ceremony types
SDLC_PHASES	Requirements, Design, Implementation, Testing, Deployment, …	6	SOFTWARE	Software development lifecycle phases

Construction

Name	Items	Count	Source	Description
CONSTRUCTION_TRADES	Carpentry, Electrical, Plumbing, HVAC, Masonry, …	8	CONSTRUCTION	Common building trades

Healthcare

Name	Items	Count	Source	Description
BONES	Skull, Mandible, Clavicle, Scapula, Sternum, …	23	ANATOMY	Major human skeletal bones and bone groups
ORGANS	Brain, Heart, Lungs, Liver, Kidneys, …	15	ANATOMY	Major human organs
AMINO_ACIDS	Ala, Arg, Asn, Asp, Cys, …	20	BIOCHEM	Standard proteinogenic amino acids (3-letter codes)
DNA_BASES	A, T, G, C	4	BIOCHEM	DNA nucleotide bases
RNA_BASES	A, U, G, C	4	BIOCHEM	RNA nucleotide bases
BLOOD_TYPES	A, B, AB, O	4	CLINICAL	ABO blood group types
SENSES	Sight, Hearing, Smell, Taste, Touch	5	ANATOMY	Traditional five human senses
TASTES	Sweet, Sour, Salty, Bitter, Umami	5	ANATOMY	Basic taste modalities
VITAMINS	A, B1, B2, B3, B5, …	13	CLINICAL	Human vitamins (common designations)
ESSENTIAL_MINERALS	Calcium, Chloride, Chromium, Copper, Iodine, …	14	CLINICAL	Dietary essential minerals
FOOD_GROUPS	Fruits, Vegetables, Grains, Protein, Dairy	5	USDA	USDA MyPlate food groups
CLINICAL_TRIAL_PHASES	Phase I, Phase II, Phase III, Phase IV	4	FDA	Clinical trial phases
RH_FACTORS	Positive, Negative	2	CLINICAL	Rh blood factor polarity

Graduate Study

Name	Items	Count	Source	Description
PARTS_OF_SPEECH	Noun, Verb, Adjective, Adverb, Pronoun, …	8	LINGUISTICS	Traditional English parts of speech
UN_SDGS	No Poverty, Zero Hunger, Good Health, Quality Education, Gender Equality, …	17	UN	UN Sustainable Development Goals (2030 Agenda)
SWOT_CATEGORIES	Strengths, Weaknesses, Opportunities, Threats	4	MANAGEMENT	SWOT analysis quadrants
PORTER_FORCES	Supplier Power, Buyer Power, Competitive Rivalry, Threat of Substitutes, Threat of New Entrants	5	MANAGEMENT	Porter five forces
US_GOVERNMENT_BRANCHES	Legislative, Executive, Judicial	3	USGOV	Branches of the US federal government
MARKETING_MIX_4P	Product, Price, Place, Promotion	4	MARKETING	Classic marketing mix (4 Ps)
MASLOW_NEEDS	Physiological, Safety, Love and Belonging, Esteem, Self-Actualization	5	PSYCHOLOGY	Maslow hierarchy of needs
BIG_FIVE_TRAITS	Openness, Conscientiousness, Extraversion, Agreeableness, Neuroticism	5	PSYCHOLOGY	Big Five personality traits (OCEAN)

Industry Verticals

Name	Items	Count	Source	Description
INCOTERMS	EXW, FCA, CPT, CIP, DAP, …	11	ICC	Incoterms 2020 trade terms
HAZMAT_CLASSES	Explosives, Gases, Flammable Liquids, Flammable Solids, Oxidizers, …	9	DOT	US DOT hazardous-material classes
PPE_TYPES	Gloves, Goggles, Face Shield, Respirator, Hard Hat, …	7	OSHA	Common personal protective equipment
FIRE_CLASSES	Class A, Class B, Class C, Class D, Class K	5	NFPA	Fire extinguisher classes
INSURANCE_LINES	Life, Health, Property, Casualty, Auto, …	7	INSURANCE	Major insurance product lines
ENERGY_SOURCES	Coal, Oil, Natural Gas, Nuclear, Hydro, …	9	IEA	Primary energy source categories
RENEWABLE_ENERGY	Solar, Wind, Hydro, Geothermal, Biomass, …	7	IEA	Renewable generation technologies
MINING_COMMODITIES	Gold, Silver, Copper, Iron Ore, Coal, …	9	MINING	Major mined commodities
RETAIL_CHANNELS	Store, E-commerce, Wholesale, Marketplace, Direct, …	6	RETAIL	Retail distribution channels
HOSPITALITY_SEGMENTS	Luxury, Upscale, Midscale, Economy, Extended Stay, …	6	HOSPITALITY	Hotel market segments
PHARMA_PIPELINE_STAGES	Discovery, Preclinical, Phase I, Phase II, Phase III, …	7	PHARMA	Drug-development pipeline stages

Real Estate

Name	Items	Count	Source	Description
REAL_ESTATE_TYPES	Residential, Commercial, Industrial, Retail, Mixed Use, …	6	REAL_ESTATE	Primary property-use categories
LEASE_TYPES	Gross, Net, Double Net, Triple Net, Modified Gross, …	6	REAL_ESTATE	Commercial lease structures

Computer Science

Name	Items	Count	Source	Description
HTTP_METHODS	GET, POST, PUT, PATCH, DELETE, …	7	RFC9110	Common HTTP methods
HTTP_STATUS_CODES	200, 201, 204, 301, 302, …	15	IANA	Common HTTP status codes
SQL_DATA_TYPES	INTEGER, BIGINT, DECIMAL, NUMERIC, REAL, …	15	SQL	Common SQL column data types
MIME_TYPES	text/plain, text/html, application/json, application/xml, application/pdf, …	11	IANA	Common MIME media types
PROGRAMMING_PARADIGMS	Imperative, Declarative, Functional, Object-Oriented, Logic, …	6	CS	Major programming paradigms
CHARACTER_ENCODINGS	ASCII, UTF-8, UTF-16, UTF-32, Latin-1, …	6	IANA	Common text and binary encodings
TLS_VERSIONS	SSL 3.0, TLS 1.0, TLS 1.1, TLS 1.2, TLS 1.3	5	RFC	Historical and current TLS protocol versions
DESIGN_PATTERNS	Singleton, Factory, Observer, Strategy, Decorator, …	10	GOF	Classic Gang-of-Four design patterns (sample)
SORTING_ALGORITHMS	Bubble, Insertion, Selection, Merge, Quick, …	8	CS	Common sorting algorithms
DATA_STRUCTURES	Array, Linked List, Stack, Queue, Hash Table, …	8	CS	Fundamental data structures
NETWORK_PROTOCOLS	TCP, UDP, HTTP, HTTPS, FTP, …	12	IANA	Common network and application protocols
LOG_LEVELS	Trace, Debug, Info, Warn, Error, …	6	CONVENTION	Typical application log severities
SEVERITY_LEVELS	Critical, High, Medium, Low, Informational	5	CONVENTION	Incident and vulnerability severity bands
MEMORY_UNITS	Bit, Byte, Kilobyte, Megabyte, Gigabyte, …	7	IEC	Binary memory-size units

Playing Cards

Name	Items	Count	Source	Description
CARD_SUITS	Clubs, Diamonds, Hearts, Spades	4	CONVENTION	Standard playing-card suits
CARD_RANKS	Ace, 2, 3, 4, 5, …	13	CONVENTION	Standard playing-card ranks
POKER_HANDS	High Card, One Pair, Two Pair, Three of a Kind, Straight, …	10	CONVENTION	Standard poker hand rankings (low to high)

Card Games

Name	Items	Count	Source	Description
BRIDGE_SUITS	Clubs, Diamonds, Hearts, Spades	4	CONVENTION	Bridge/whist card suits
BRIDGE_BIDS	Pass, Double, Redouble, 1C, 1D, …	18	CONVENTION	Common bridge bid tokens (sample)
POKER_STREETS	Preflop, Flop, Turn, River	4	CONVENTION	Texas hold'em betting streets

Casino

Name	Items	Count	Source	Description
BLACKJACK_ACTIONS	Hit, Stand, Double Down, Split, Surrender	5	CONVENTION	Common blackjack player actions
ROULETTE_COLORS	Red, Black, Green	3	CONVENTION	Roulette pocket colors

Chess

Name	Items	Count	Source	Description
CHESS_PIECES	King, Queen, Rook, Bishop, Knight, …	6	FIDE	Chess piece types

Dice & Gambling

Name	Items	Count	Source	Description
DICE_FACES	1, 2, 3, 4, 5, …	6	CONVENTION	Standard six-sided die faces

Science

Name	Items	Count	Source	Description
ATOMS	H, He, Li, Be, B, …	118	IUPAC	Chemical element symbols in atomic-number order
ELEMENTS	Hydrogen, Helium, Lithium, Beryllium, Boron, …	118	IUPAC	Chemical element names in atomic-number order
SI_PREFIXES	yocto, zepto, atto, femto, pico, …	22	SI	SI unit prefix names (small to large)
CLOUD_TYPES	Cirrus, Cumulus, Stratus, Nimbus, Cumulonimbus, …	7	WMO	Common cloud genera
SI_BASE_UNITS	Meter, Kilogram, Second, Ampere, Kelvin, …	7	SI	SI base unit names
STATES_OF_MATTER	Solid, Liquid, Gas, Plasma, Bose-Einstein Condensate	5	PHYSICS	Common states of matter
NOBLE_GASES	He, Ne, Ar, Kr, Xe, …	6	IUPAC	Noble-gas element symbols
HALOGENS	F, Cl, Br, I, At	5	IUPAC	Halogen element symbols
QUARKS	Up, Down, Charm, Strange, Top, …	6	PARTICLE_PHYSICS	Six quark flavors
LEPTONS	Electron, Muon, Tau, Electron Neutrino, Muon Neutrino, …	6	PARTICLE_PHYSICS	Standard Model leptons
FORCES_OF_NATURE	Gravity, Electromagnetism, Strong Nuclear, Weak Nuclear	4	PHYSICS	Fundamental interactions
KINGDOMS_OF_LIFE	Archaea, Bacteria, Protista, Fungi, Plantae, …	6	BIOLOGY	Traditional six-kingdom model
TAXONOMY_RANKS	Domain, Kingdom, Phylum, Class, Order, …	8	BIOLOGY	Linnaean taxonomy ranks
BIOMES	Tundra, Taiga, Temperate Forest, Tropical Rainforest, Grassland, …	9	BIOLOGY	Major terrestrial and aquatic biomes
EM_SPECTRUM	Radio, Microwave, Infrared, Visible, Ultraviolet, …	7	PHYSICS	Electromagnetic spectrum bands
ROCK_TYPES	Igneous, Sedimentary, Metamorphic	3	GEOLOGY	Primary rock categories
WEATHER_FRONT_TYPES	Cold, Warm, Stationary, Occluded	4	METEOROLOGY	Synoptic weather front types
PRECIPITATION_TYPES	Rain, Snow, Sleet, Hail, Freezing Rain, …	6	METEOROLOGY	Common precipitation forms
BEAUFORT_WIND_SCALE	Calm, Light Air, Light Breeze, Gentle Breeze, Moderate Breeze, …	13	WMO	Beaufort wind-force scale (0–12)
PERIODIC_TABLE_GROUPS	Alkali Metals, Alkaline Earth, Transition Metals, Post-Transition, Metalloids, …	10	IUPAC	Periodic-table element groups
PLATE_BOUNDARIES	Divergent, Convergent, Transform	3	GEOLOGY	Tectonic plate boundary types
VOLCANO_TYPES	Shield, Stratovolcano, Cinder Cone, Caldera, Submarine	5	GEOLOGY	Common volcano morphologies
HURRICANE_CATEGORIES	Category 1, Category 2, Category 3, Category 4, Category 5	5	NHC	Saffir-Simpson hurricane categories
PH_SCALE	Acidic, Neutral, Basic	3	CHEMISTRY	pH scale qualitative regions

Solar Position

Name	Items	Count	Source	Description
SOLAR_POSITION_EVENTS	Sunrise, Solar Noon, Sunset, Civil Twilight, Nautical Twilight, …	6	NOAA	Solar and twilight events

Geospatial

Name	Items	Count	Source	Description
CONTINENTS	Africa, Antarctica, Asia, Europe, North America, …	7	EXACT	Continents (7-continent model)
OCEANS	Pacific, Atlantic, Indian, Southern, Arctic	5	EXACT	Oceans (5-ocean model)
DIRECTIONS	North, South, East, West, Northeast, …	8	EXACT	Compass directions
US_STATES	Alabama, Alaska, Arizona, Arkansas, California, …	50	USPS	US states and federal district omitted (50 states)
US_STATE_CODES	AL, AK, AZ, AR, CA, …	50	USPS	US state and territory postal abbreviations (50 states)
CANADIAN_PROVINCES	Alberta, British Columbia, Manitoba, New Brunswick, Newfoundland and Labrador, …	13	CANADA	Canadian provinces and territories
EU_MEMBER_STATES	Austria, Belgium, Bulgaria, Croatia, Cyprus, …	27	EU	European Union member states
UK_COUNTRIES	England, Scotland, Wales, Northern Ireland	4	UK	Constituent countries of the United Kingdom
G7_COUNTRIES	Canada, France, Germany, Italy, Japan, …	7	G7	Group of Seven member countries
AUSTRALIAN_STATES	New South Wales, Victoria, Queensland, Western Australia, South Australia, …	8	AUSTRALIA	Australian states and mainland territories
UN_REGIONS	Africa, Americas, Asia, Europe, Oceania	5	UN	United Nations macro-regions (M49)
HEMISPHERES	Northern, Southern, Eastern, Western	4	EXACT	Earth hemispheres
COUNTRY_CODES_ISO2	US, CN, JP, DE, IN, …	20	ISO3166	Major-economy ISO 3166-1 alpha-2 country codes

Aviation

Name	Items	Count	Source	Description
AVIATION_CLOUD_CEILINGS	Clear, Few, Scattered, Broken, Overcast	5	FAA	Aviation cloud-coverage reports

Space & Orbital Science

Name	Items	Count	Source	Description
PLANETS	Mercury, Venus, Earth, Mars, Jupiter, …	8	IAU	Solar-system planets (IAU 2006 definition)
DWARF_PLANETS	Pluto, Ceres, Eris, Haumea, Makemake	5	IAU	Recognized dwarf planets
MOONS	Moon, Io, Europa, Ganymede, Callisto, …	8	NASA	Major solar-system moons
SOLAR_SYSTEM	Sun, Mercury, Venus, Earth, Mars, …	9	IAU	Sun and IAU planets in orbital order

Domain Types

Name	Items	Count	Source	Description
ZODIAC	Aries, Taurus, Gemini, Cancer, Leo, …	12	ASTRON	Zodiac constellations / signs
NATO_ALPHABET	Alfa, Bravo, Charlie, Delta, Echo, …	26	NATO	NATO phonetic alphabet
PRIMARY_COLORS	Red, Green, Blue	3	CIE	Additive primary colors (RGB)
COLORS_RAINBOW	Red, Orange, Yellow, Green, Blue, …	7	CONVENTION	Rainbow color sequence
MUSICAL_NOTES	C, C#, D, D#, E, …	12	MUSIC	Chromatic pitch classes (sharp spelling)
MUSICAL_MODES	Ionian, Dorian, Phrygian, Lydian, Mixolydian, …	7	MUSIC	Diatonic modes
ORCHESTRA_SECTIONS	Strings, Woodwinds, Brass, Percussion, Keyboards, …	6	MUSIC	Symphony orchestra sections
NOTE_DURATIONS	Whole, Half, Quarter, Eighth, Sixteenth, …	6	MUSIC	Standard note durations
CLEFS	Treble, Bass, Alto, Tenor	4	MUSIC	Common musical clefs
TRIATHLON_DISCIPLINES	Swim, Bike, Run	3	SPORT	Triathlon legs
CRICKET_FORMATS	Test, ODI, T20, T10, The Hundred	5	SPORT	Common cricket match formats
CHECKERS_PIECES	King, Man	2	CONVENTION	Draughts/checkers piece types
GO_STONES	Black, White	2	CONVENTION	Go stone colors
MAHJONG_SUITS	Bamboo, Characters, Dots, Wind, Dragon	5	CONVENTION	Mahjong tile suit categories
PAPER_SIZES	A0, A1, A2, A3, A4, …	10	ISO	Common paper size names
ISO639_LANGUAGES	en, es, fr, de, it, …	20	ISO639	Common ISO 639-1 language codes

---

Math

Arithmetic, rounding, matrix algebra, calculus, and numeric helpers.

Function count: 254.

Function	Returns	Notes
ABS(number: number) → number	number	Returns the absolute value of a number.
ACOS(v: number) → number	number	Returns the arccosine (inverse cosine) in radians.
ACOSH(v: number) → number	number	Returns the inverse hyperbolic cosine.
ACOT(v: number) → number	number	Returns the arccotangent (inverse cotangent) in radians.
ACOTH(v: number) → number	number	Returns the hyperbolic arccotangent.
AGGREGATE(function_num: number, options: number, ...ref: number[]) → number	number	variadic. Returns an aggregate in a list, with options to ignore errors and hidden values.
ARABIC(text: string) → number	number	Converts a Roman numeral string to an Arabic number.
ASIN(v: number) → number	number	Returns the arcsine (inverse sine) in radians.
ASINH(v: number) → number	number	Returns the inverse hyperbolic sine.
ATAN(v: number) → number	number	Returns the arctangent (inverse tangent) in radians.
ATAN2(x: number, y: number) → number	number	Returns the arctangent from x and y coordinates.
ATANH(v: number) → number	number	Returns the inverse hyperbolic tangent.
AUTODIFF_GRADIENT(fn: lambda, point: array) → array	array	Grid extension. Returns the exact local gradient row of a scalar multivariable lambda at a numeric point.
AVERAGE(...values: number[]) → number	number	variadic, aliases: MEAN. Returns the arithmetic mean of the supplied arguments.
AVERAGEIF(range: array, criteria: any, average_range: array) → number	number	variadic. Averages cells that match a condition.
AVERAGEIFS(average_range: array, ...criteria_range: array, ...criteria: any) → number	number	variadic. Averages cells that meet multiple criteria.
AVGPOOL2D(value: array, kernel_size: number, stride?: number) → array	array	Grid extension. Average-pools a numeric grid using a square kernel and optional stride.
BASE(number: number, radix: number, min_length: number) → string	string	Converts a number to text in a given base.
BETAFN(a: number, b: number) → number	number	Grid extension. Returns the beta function B(a,b).
BIGINT(value: any) → number	number	Grid extension. Grid extension. Constructs an exact arbitrary-precision integer (bigint) from a number or a numeric string, e.g. BIGINT("123456789012345678901234567890"). The result flows through the exact operator and number-theory path.
BOUNDED_MINIMIZE_N(fn: lambda, initial: array, lower: array, upper: array, tolerance: number, max_iterations: number) → array	array	Grid extension. Minimizes a multi-variable lambda over box bounds using deterministic Nelder-Mead simplex search.
CAST(value: any) → any	any	Grid extension. Returns a value unchanged in Workbook evaluation; within a shaped Tensor declaration it converts to the declared numeric dtype.
CEILING(value: number, significance: number) → number	number	aliases: CEIL. Rounds a number up to the nearest multiple of significance.
CEILING_MATH(number: number, significance: number, mode: number) → number	number	aliases: CEILING.MATH. Rounds a number up to the nearest integer or multiple of significance.
CEILING_PRECISE(number: number, significance: number) → number	number	aliases: CEILING.PRECISE. Rounds a number up to the nearest integer or multiple (alias for CEILING.MATH).
CHOLESKY(matrix: array) → array	array	Grid extension. Returns the lower-triangular Cholesky factor of a positive-definite matrix.
COMBIN(n: number, k: number) → number	number	Returns the number of combinations for a given number of objects. Also available infix as n CHOOSE k.
COMBINA(n: number, k: number) → number	number	Returns the number of combinations with repetitions. Also available infix as n MULTICHOOSE k.
CONCATENATE(...values: string[]) → string	string	variadic. Concatenates strings (legacy alias for CONCAT).
CONV2D(input: array, kernel: array, padding?: number, stride?: number, dilation?: number, groups?: number) → array	array	Grid extension. Cross-correlates a numeric grid with a numeric kernel using optional padding, stride, dilation, and groups.
CONVOLVE(left: array, right: array) → array	array	Grid extension. Returns the full discrete convolution of two numeric vectors.
CORRELATE(left: array, right: array) → array	array	Grid extension. Returns the full discrete cross-correlation of two numeric vectors.
COS(v: number) → number	number	Returns the cosine of an angle in radians.
COSH(v: number) → number	number	Returns the hyperbolic cosine.
COSINE_SIMILARITY(left: array, right: array) → number	number	Returns the cosine similarity between two arrays after flattening them row by row.
COT(v: number) → number	number	Returns the cotangent of an angle in radians.
COTH(v: number) → number	number	Returns the hyperbolic cotangent.
COUNT(...values: any[]) → number	number	variadic. Counts arguments that contain numeric values.
COUNTA(...values: any[]) → number	number	variadic. Counts arguments that are not empty.
COUNTBLANK(...values: any[]) → number	number	variadic. Counts blank cells in a range.
COUNTIF(range: array, criteria: any) → number	number	Counts cells that match a condition.
COUNTIFS(...criteria_range: array, ...criteria: any) → number	number	variadic. Counts cells that meet multiple criteria.
CRITICAL_PATH(durations: array, precedence: array) → array	array	Grid extension. Critical-path analysis for a project plan: the scheduling companion to OPTIMIZE_EXPLAIN. Given per-activity durations and an N×N precedence matrix (precedence[i][j] ≠ 0 means activity j must finish before activity i starts), runs the forward/backward Critical Path Method passes and returns, per activity, [activity, early_start, early_finish, late_start, late_finish, total_float, critical]. total_float is the slack -- how long the activity can slip without delaying the project; critical is 1 for zero-float activities (the chain that sets the finish date). A cyclic precedence graph fails with #NUM!.
CROSS(left: array, right: array) → array	array	Returns the three-dimensional cross product of two vectors.
CROSS_ENTROPY(logits: array, target: array) → number	number	Grid extension, aliases: CATEGORICAL_CROSS_ENTROPY. Returns mean categorical cross-entropy over the final dimension of same-shaped logits and target arrays.
CSC(v: number) → number	number	Returns the cosecant of an angle in radians.
CSCH(v: number) → number	number	Returns the hyperbolic cosecant.
CURVE_FIT(fn: lambda, xs: array, ys: array, p0: any, tol: number, max_iter: number) → any	any	Grid extension. Fits a nonlinear model to data by Levenberg-Marquardt least squares. The lambda is the model: its first parameter is the observation variable, the remaining parameters are the fit coefficients - CURVE_FIT(LAMBDA(t, a, b, c, aEXP(-bt) + c), times, values, {1, 1, 1}) fits an exponential decay. xs and ys are equal-length data vectors and p0 the initial coefficients. Returns the fitted coefficients as a number (one coefficient) or a 1 x k row. Optional: tol (relative SSR decrease, default 1e-10) and max_iter (default 200).
DAE_FINAL(fn: lambda, mass: array, y0: any, t_start: number, t_end: number, samples: number, rtol: number, atol: number, max_steps: number) → any	any	Grid extension. Integrates the constant mass-matrix system M y' = fn(t, y) with semi-explicit index-1 consistency projection and returns only the terminal state.
DAE_REPORT(fn: lambda, mass: array, y0: any, t_start: number, t_end: number, samples: number, rtol: number, atol: number, max_steps: number) → array	array	Grid extension. Runs DAE_SOLVE and returns deterministic work plus consistency diagnostics: attempted/accepted/rejected steps, RHS/Jacobian/Newton/LU work, algebraic-variable count, initial and projected residuals, projection iterations, accepted-step range, and terminal state.
DAE_SOLVE(fn: lambda, mass: array, y0: any, t_start: number, t_end: number, samples: number, rtol: number, atol: number, max_steps: number) → array	array	Grid extension. Integrates the constant mass-matrix system M y' = fn(t, y). Structurally zero mass rows are algebraic equations in a semi-explicit index-1 DAE; matching state components are projected to a consistent initial condition before adaptive implicit-trapezoid integration. Returns a samples x (1 + n) trajectory with time in the first column.
DECIMAL(text: string, radix: number) → number	number	Converts a text representation of a number in a given base to decimal.
DEGREES(radians: number) → number	number	Converts radians to degrees.
DERIVATIVE(fn: lambda, x: number, h: number) → number	number	Returns the exact local derivative of a scalar lambda when its compiled expression is differentiable, with a bounded central-difference fallback for unsupported expressions.
DFT(samples: array) → array	array	Grid extension. Returns the discrete Fourier transform as [real, imaginary] rows.
DIAG(values: array) → array	array	Builds a diagonal matrix from a vector.
DISTANCE(left: array, right: array, p: number) → number	number	Returns the p-distance between two arrays after flattening them row by row.
DIVISORS(number: number) → array	array	Grid extension. Grid extension. Returns all positive divisors of n.
DOT(left: array, right: array) → number	number	Returns the dot product of two arrays after flattening them row by row.
EIGEN.SPECTRAL_RADIUS(matrix: array) → number	number	Grid extension. The largest eigenvalue modulus of a general real matrix - the headline stability diagnostic. A discrete linear system contracts when this is below 1; the leading eigenvalue magnitude is what makes an ODE Jacobian stiff.
EIGEN.VALUES(matrix: array) → array	array	Grid extension. Eigenvalues of a symmetric matrix (cyclic Jacobi rotations) as an n x 1 column sorted descending - the covariance/PCA reading order. Nonsymmetric input is #VALUE! (use the SVD.* family for general matrices).
EIGEN.VALUES.COMPLEX(matrix: array) → array	array	Grid extension. Eigenvalues of a general (possibly nonsymmetric) real matrix as an n x 2 matrix of (real, imaginary) parts, sorted by descending magnitude. Complements the symmetric-only EIGEN.VALUES: handles Jacobians and transition matrices whose eigenvalues may be complex. Balancing + Householder Hessenberg reduction + Francis double-shift QR.
EIGEN.VECTORS(matrix: array) → array	array	Grid extension. Unit eigenvectors of a symmetric matrix as the columns of an n x n matrix, ordered to match EIGEN.VALUES. Column signs are canonical (largest-magnitude entry positive), so results are deterministic.
EVEN(value: number) → number	number	Rounds a number up to the nearest even integer.
EXP(value: number) → number	number	Returns e raised to the power of a number.
FACILITY_LOCATE(cost_matrix: array, demand: array, capacity: number, facility_count: number, min_load: number) → array	array	Grid extension. Capacitated facility-location convenience layer, the siting complement to VRP_SOLVE's routing. Assembles a mixed-integer model over a demand-by-candidate-site cost matrix and solves it with the same backend MIXED_INTEGER_PROGRAM uses: opens exactly facility_count sites, single-sources each demand point to an open site within capacity, and minimizes total assignment cost. Returns one [demand, facility, cost] row per demand point. An optional min_load gives every opened site a load floor as well as its capacity ceiling, so territories land in [min_load, capacity] instead of the solver piling demand onto the cheapest site — sales-territory / service-district / catchment balancing over the same model. Defaults to 0 (plain siting). Requires a solver-mip build; other builds return an explicit capability error.
FACT(value: number) → number	number	Returns the factorial of a number.
FACTDOUBLE(value: number) → number	number	Returns the double factorial of a number.
FFT(samples: array) → array	array	Grid extension. Returns a deterministic Fourier transform; currently aliases DFT for matching behavior.
FINDROOT(fn: lambda, lower: number, upper: number, tolerance: number, max_iterations: number) → number	number	Grid extension. Finds a root of a lambda over a bracketing interval using the solver core.
FLOOR(value: number, significance: number) → number	number	Rounds a number down to the nearest multiple of significance.
FLOOR_MATH(number: number, significance: number, mode: number) → number	number	aliases: FLOOR.MATH. Rounds a number down to the nearest integer or multiple of significance.
FLOOR_PRECISE(number: number, significance: number) → number	number	aliases: FLOOR.PRECISE. Rounds a number down to the nearest integer or multiple (alias for FLOOR.MATH).
GAMMAFN(x: number) → number	number	Grid extension. Returns the gamma function.
GAMMALN(x: number) → number	number	Grid extension. Returns the natural logarithm of the gamma function.
GCD(...values: number[]) → number	number	variadic. Returns the greatest common divisor.
GELU(value: number) → number	number	Grid extension. Gaussian Error Linear Unit using Candle-compatible tanh approximation.
GETDIAGONAL(matrix: array) → array	array	Returns the diagonal of a matrix as a column vector.
GOALSEEK(fn: lambda, target: number, lower: number, upper: number, tolerance: number, max_iterations: number) → number	number	Grid extension. Finds an input value where a lambda reaches a target value.
GRADIENT(samples: array, spacing: number) → array	array	Grid extension. Returns a finite-difference gradient for one-dimensional samples.
GROUP.APPLY(permutation: permutation, values: array) → array	array	Grid extension. Applies a finite permutation to the positions of an equal-length value array.
GROUP.COMPOSE(left: permutation, right: permutation) → object	object	Grid extension. Composes two equal-degree permutations, applying the right operand first.
GROUP.CONTAINS(group: permutation_group, permutation: permutation) → boolean	boolean	Grid extension. Tests exact membership of a permutation in a generated finite group without full group enumeration.
GROUP.GENERATE(generators: array) → object	object	Grid extension. Constructs a finite permutation group from generator rows without enumerating its elements.
GROUP.INVERSE(permutation: permutation) → object	object	Grid extension. Returns the inverse of a finite permutation.
GROUP.ORBIT(group: permutation_group, point: number) → array	array	Grid extension. Returns the sorted one-based orbit of a point under a finite permutation group.
GROUP.ORBITS(group: permutation_group) → array	array	Grid extension. Returns the disjoint one-based point orbits of a finite permutation group.
GROUP.ORDER(group: permutation_group) → bigint	bigint	Grid extension. Returns the exact order of a finite permutation group using a bounded Schreier-Sims stabilizer chain.
GROUP.PERMUTATION(images: array) → object	object	Grid extension. Constructs a finite permutation from one-based images, rejecting duplicates and out-of-range points.
GROUP.STABILIZER(group: permutation_group, point: number) → object	object	Grid extension. Returns the exact subgroup fixing a one-based point, generated using Schreier's lemma.
HEAT_SOLVE_1D(ic: lambda, alpha: number, x_min: number, x_max: number, nx: number, t_end: number, nt: number, bc_left: number, bc_right: number) → array	array	Grid extension. Solves the 1-D heat equation u_t = alpha u_xx by Crank-Nicolson on a uniform grid with constant Dirichlet boundaries and returns a (nt + 1) x nx array of time levels (t = 0 first; boundary columns carry the boundary values). The initial condition is a one-parameter lambda of x sampled over [x_min, x_max]. Optional trailing arguments: nt (default 100), bc_left (default 0), bc_right (default 0).
HEAT_SOLVE_2D(ic: lambda, alpha: number, x_min: number, x_max: number, nx: number, y_min: number, y_max: number, ny: number, t_end: number, nt: number, bc: number) → array	array	Grid extension. Solves the 2-D heat equation u_t = alpha (u_xx + u_yy) on a uniform rectangle by Peaceman-Rachford ADI (unconditionally stable, second order in time) with one constant Dirichlet value on the whole boundary. The initial condition is a two-parameter lambda of (x, y). Returns the final ny x nx field (y down rows). Optional trailing arguments: nt (default 100), bc (default 0).
INT(value: number) → number	number	Rounds a number down to the nearest integer.
INTEGRATE(fn: lambda, start: number, end: number, segments: number) → number	number	Approximates the definite integral of a lambda using the trapezoidal rule.
INTERPOLATE.ARRAY(xp: array, xs: array, ys: array, mode: string) → array	array	Grid extension. Interpolates an array of query x-values from paired x/y samples.
INTERPOLATE.CUBIC(x: number, xs: array, ys: array, mode: any) → number	number	Grid extension. Natural cubic spline interpolation at x over (xs, ys) knots: C2-smooth with zero second derivative at the ends. Shares the linear family's mode argument for out-of-range x: "extrapolate" (default, continues the end cubic), "clamp", "nan", or a constant fill value.
INTERPOLATE.CUBIC.ARRAY(x_values: array, xs: array, ys: array, mode: any) → array	array	Grid extension. Natural cubic spline evaluated over a vector of query points; the spline is fitted once and evaluated per point. Same knot and mode semantics as INTERPOLATE.CUBIC.
INTERPOLATE.LINEAR(x: number, xs: array, ys: array, mode: string) → number	number	Interpolates linearly from paired x/y samples with optional extrapolate, clamp, or constant out-of-range mode.
INTERPOLATE.NEAREST(x: number, xs: array, ys: array) → number	number	Grid extension. Returns the y-value associated with the nearest x sample.
INTERPOLATE.NEAREST.ARRAY(xp: array, xs: array, ys: array) → array	array	Grid extension. Returns nearest-sample y-values for an array of query x-values.
INTERPOLATE.PCHIP(x: number, xs: array, ys: array, mode: any) → number	number	Grid extension. Monotone cubic (PCHIP, Fritsch-Carlson) interpolation at x: C1-smooth and shape-preserving - where the data is monotone the curve is monotone, with no overshoot between knots (the yield-curve bootstrapping workhorse). Same mode argument as the linear family.
INTERPOLATE.PCHIP.ARRAY(x_values: array, xs: array, ys: array, mode: any) → array	array	Grid extension. Monotone cubic (PCHIP) interpolation evaluated over a vector of query points. Same knot and mode semantics as INTERPOLATE.PCHIP.
ISEVEN(v: number) → boolean	boolean	Returns TRUE if the number is even.
ISODD(v: number) → boolean	boolean	Returns TRUE if the number is odd.
ISO_CEILING(number: number, significance: number) → number	number	aliases: ISO.CEILING. Rounds up to the nearest integer or multiple (ISO standard).
ISPRIME(number: number) → boolean	boolean	Grid extension. Grid extension. Returns TRUE if the integer is prime.
ISQRT(number: number) → number	number	Grid extension. Grid extension. Returns the integer square root floor(sqrt(n)); exact for bigint input.
JACOBIAN(fn: lambda, point: array) → array	array	Grid extension. Returns the exact local Jacobian matrix of a scalar- or array-valued multivariable lambda at a numeric point.
KRONECKERPRODUCT(left: array, right: array) → array	array	Returns the Kronecker product of two matrices.
LAPLACIAN(samples: array, spacing: number) → array	array	Grid extension. Returns a one-dimensional finite-difference Laplacian for samples.
LAYERNORM(value: array, epsilon?: number) → array	array	Grid extension. Normalizes each final-axis slice to zero mean and unit variance. The optional epsilon must be positive and defaults to 1e-5.
LCM(...values: number[]) → number	number	variadic. Returns the least common multiple.
LEASTSQUARES(coefficients: array, rhs: array) → array	array	Grid extension. Solves an overdetermined linear least-squares system with a pseudoinverse.
LINEAR_PROGRAM(objective: array, constraints: array, rhs: array, maximize: boolean) → array	array	Grid extension. Solves a small dense linear program with Ax <= b and x >= 0 by vertex enumeration.
LINEAR_PROGRAM_SENSITIVITY(objective: array, constraints: array, rhs: array, maximize: boolean, component: string) → array	array	Grid extension. Sensitivity companion to LINEAR_PROGRAM over the same model: per-row shadow prices (duals), per-variable reduced costs, 1-based binding-row indices, or a 1-based irreducible infeasible subsystem (iis). Shares the primal solve with LINEAR_PROGRAM via the solver memo cache.
LN(value: number) → number	number	Returns the natural logarithm of a number.
LOG(value: number, base: number) → number	number	Returns the logarithm of a number to a specified base.
LOG10(value: number) → number	number	Returns the base-10 logarithm of a number.
LOGSOFTMAX(logits: array) → array	array	Grid extension. Returns a numerically stable log-softmax across the final dimension; each row of a 2-D range is log-normalized.
MARKOV_STEP(state: array, transition: array) → array	array	Grid extension. Advances a row state vector by one Markov transition step.
MATRIXRANK(matrix: array) → number	number	Returns the rank of a matrix.
MATRIX_COND(matrix: array) → number	number	Grid extension. Estimates the matrix condition number using the one-norm.
MAX(...values: number[]) → number	number	variadic. Returns the maximum of the supplied arguments.
MAXIMIZE(fn: lambda, lower: number, upper: number, tolerance: number, max_iterations: number) → number	number	Grid extension. Finds the scalar input in a bounded interval that maximizes a lambda.
MAXIMIZE.GLOBAL(fn: lambda, lower: any, upper: any, seed: number, population: number, max_generations: number) → any	any	Grid extension. Global maximum of a lambda objective over a box, by differential evolution (the objective is negated internally). Same arguments and result shape as MINIMIZE.GLOBAL.
MAXPOOL2D(value: array, kernel_size: number, stride?: number) → array	array	Grid extension. Max-pools a numeric grid using a square kernel and optional stride.
MDETERM(matrix: array) → number	number	Returns the determinant of a square matrix.
MEDIAN(...values: number[]) → number	number	variadic. Returns the median of the supplied arguments.
MIN(...values: number[]) → number	number	variadic. Returns the minimum of the supplied arguments.
MINIMIZE(fn: lambda, lower: number, upper: number, tolerance: number, max_iterations: number) → number	number	Grid extension. Finds the scalar input in a bounded interval that minimizes a lambda.
MINIMIZE.GLOBAL(fn: lambda, lower: any, upper: any, seed: number, population: number, max_generations: number) → any	any	Grid extension. Global minimum of a lambda objective over a box, by differential evolution - escapes the local minima that trap the local MINIMIZE / golden-section lane on multimodal objectives (Rastrigin, Ackley, curved valleys). The lambda's parameters are the variables; lower and upper are matching bound vectors (a bare number for one variable). Deterministic under seed (default 0); optional population and max_generations. Returns the minimizing point: a number for one variable, a 1 x n row otherwise.
MINVERSE(matrix: array) → array	array	Returns the inverse of a square matrix.
MIN_COST_FLOW(edges: array, supply: array) → array	array	Grid extension. Minimum-cost network-flow convenience layer, the network-lane complement to VRP_SOLVE (routing) and FACILITY_LOCATE (siting). Routes a commodity through a directed capacitated network to meet every node's supply/demand at least total cost: power dispatch, pipeline/utility networks, traffic or packets across links, product from plants to markets. Unlike VRP_SOLVE/FACILITY_LOCATE this is a pure linear program — network-flow matrices are totally unimodular, so an LP already returns integral flows for integral data — and runs on the always-available LP backend without requiring a solver-mip build. Returns one [from, to, flow] row per input edge, in input order.
MIXED_INTEGER_PROGRAM(objective: array, constraints: array, rhs: array, integer_mask: array, maximize: boolean) → array	array	Grid extension. Optimizes c·x subject to Ax ≤ b and x ≥ 0 with selected variables integer, via branch-and-cut. Requires a solver-mip build; other builds return an explicit capability error.
MMULT(left: array, right: array) → array	array	aliases: MATMUL. Returns the matrix product of two arrays.
MOBIUS(number: number) → number	number	Grid extension. Grid extension. Returns the Moebius function μ(n).
MOD(number: number, divisor: number) → number	number	Returns the remainder of a division. Also available infix as %%, MOD, or MODULO.
MODINV(number: number, number_2: number) → number	number	Grid extension. Grid extension. Returns the modular inverse of value modulo modulus.
MODPOW(number: number, number_2: number, number_3: number) → number	number	Grid extension. Grid extension. Returns base^exponent modulo modulus.
MPOWER(matrix: array, exponent: number) → array	array	Raises a square matrix to an integer power.
MROUND(value: number, multiple: number) → number	number	Returns a number rounded to the desired multiple.
MSE(prediction: array, target: array) → number	number	Grid extension, aliases: MEAN_SQUARED_ERROR. Returns the mean squared error between same-shaped numeric values.
MULTINOMIAL(...values: number[]) → number	number	variadic. Returns the multinomial of a set of numbers.
MUNIT(size: number) → array	array	Returns an identity matrix of the requested size.
NEXTPRIME(number: number) → number	number	Grid extension. Grid extension. Returns the smallest prime greater than the supplied integer.
NORM(vector: array, p: number) → number	number	Returns the p-norm of an array after flattening it row by row.
NORMALIZE(vector: array) → array	array	Returns a unit-length version of a vector.
NSOLVE(fn: lambda, x0: any, tol: number, max_iter: number) → any	any	Grid extension. Solves a nonlinear system F(x) = 0 by damped multivariate Newton iteration with finite-difference Jacobians. The lambda declares the unknowns as its parameters and returns one numeric component per unknown (the bare body for one unknown, an array literal for several); x0 supplies matching initial values. Returns the solution as a number (one unknown) or a 1 x n row. Optional: tol (residual infinity-norm, default 1e-9) and max_iter (default 100). Non-convergence or a singular Jacobian is #CALC!.
NTHPRIME(number: number) → number	number	Grid extension. Grid extension. Returns the nth prime using one-based indexing.
ODD(value: number) → number	number	Rounds a number up to the nearest odd integer.
ODE_EVENT(fn: lambda, y0: any, t_start: number, t_end: number, event: lambda, options: ode_options) → array	array	Grid extension. Integrates dy/dt = fn(t, y) and returns a 1 x (1 + n) row containing the first event time followed by the state at that event. The event lambda takes (t, y). The options record accepts method, scalar-or-vector atol, rtol, max_steps, first_step, max_step, jacobian_bandwidth, and event_direction (any, rising, or falling). Returns #N/A when no matching crossing occurs.
ODE_EVENT_TIME(fn: lambda, y0: any, t_start: number, t_end: number, event: lambda, rtol: number, atol: number, max_steps: number, method: string) → number	number	Grid extension. Integrates dy/dt = fn(t, y) from t_start to t_end and returns the first matching event time, located by bisection on the integrator's dense output. Both lambdas take (t, y). Returns #N/A when no crossing occurs by t_end. Optional trailing arguments: rtol (default 1e-6), atol (default 1e-9), max_steps (default 10000), and a method string ("auto" default, "rk45", "stiff"); alternatively a single options record {method, rtol, atol, max_steps, first_step, max_step, event_direction, jacobian_bandwidth} as the sixth argument. Record-form atol may be a scalar or a vector matching y0; event_direction is any, rising, or falling; jacobian_bandwidth is a symmetric width or [lower, upper] pair.
ODE_FINAL(fn: lambda, y0: any, t_start: number, t_end: number, rtol: number, atol: number, max_steps: number, method: string) → any	any	Grid extension. Integrates dy/dt = fn(t, y) from t_start to t_end and returns only the terminal state: a number for scalar y0, a 1 x n array for array y0. Optional trailing arguments: rtol (default 1e-6), atol (default 1e-9), max_steps (default 10000), and a method string as the final argument: "auto" (default: adaptive Dormand-Prince 5(4) with stiffness detection that switches to TR-BDF2 when the solve is stability-limited), "rk45" (force explicit Dormand-Prince), or "stiff" (alias "trbdf2": force L-stable TR-BDF2 with finite-difference Jacobians). Alternatively the option tail may be a single options record as the fifth argument: {method, rtol, atol, max_steps, first_step, max_step, jacobian_bandwidth}; record-form atol may be a scalar or a vector matching y0, and jacobian_bandwidth may be a symmetric width or [lower, upper] pair. first_step overrides automatic initial-step selection; max_step caps every attempt for discontinuous or narrow forcing.
ODE_REPORT(fn: lambda, y0: any, t_start: number, t_end: number, options: ode_options) → array	array	Grid extension. Integrates dy/dt = fn(t, y) to t_end and returns one numeric diagnostics row: method code (1 Dormand-Prince, 2 TR-BDF2), auto-switched flag, attempted/accepted/rejected steps, RHS evaluations, Jacobian evaluations, Newton iterations, total and banded LU factorizations, Krylov solves/iterations, JVP evaluations, deterministic factorization/linear-solve work, peak matrix-storage slots, minimum/maximum accepted step, then the terminal state components. Options match ODE_FINAL; atol may be scalar or component-wise, and jacobian_bandwidth may be a symmetric width or [lower, upper] pair. Compiled local RHS programs infer profitable bands automatically; compiled non-banded systems with at least 32 states use exact JVPs and matrix-free BiCGSTAB with dense fallback.
ODE_SAMPLE(fn: lambda, y0: any, t_start: number, t_end: number, t_eval: array, rtol: number, atol: number, max_steps: number, method: string) → array	array	Grid extension. Integrates dy/dt = fn(t, y) from t_start to t_end once and samples the dense output at the requested times (any order, duplicates allowed, all within the span), returning a len(t_eval) x (1 + n) array with rows in the caller's order and t in the first column. Optional trailing arguments: rtol, atol, max_steps, method string; alternatively a single options record {method, rtol, atol, max_steps, first_step, max_step, jacobian_bandwidth} as the sixth argument.
ODE_SOLUTION(fn: lambda, y0: any, t_start: number, t_end: number, samples: number, rtol: number, atol: number, max_steps: number, method: string) → array	array	Grid extension. Integrates dy/dt = fn(t, y) once and returns a reusable dense trajectory value. Pass that value to ODE_SOLUTION_SAMPLE, ODE_SOLUTION_DERIVATIVE, ODE_SOLUTION_FINAL, or ODE_SOLUTION_EVENT to make downstream queries without repeating the integration.
ODE_SOLUTION_DERIVATIVE(solution: array, times: any) → array	array	Grid extension. Returns the stored trajectory's piecewise derivative at one or more requested times without reintegrating.
ODE_SOLUTION_EVENT(solution: array, component: number, target: number, direction: string) → array	array	Grid extension. Finds the first stored-trajectory crossing of a component target and returns the interpolated time and full state. Direction is any, rising, or falling. Does not reintegrate.
ODE_SOLUTION_FINAL(solution: array) → any	any	Grid extension. Returns the final state stored in an ODE_SOLUTION value without reintegrating.
ODE_SOLUTION_SAMPLE(solution: array, times: any) → array	array	Grid extension. Linearly interpolates a reusable ODE_SOLUTION trajectory at one or more requested times and returns time plus state columns without reintegrating.
ODE_SOLVE(fn: lambda, y0: any, t_start: number, t_end: number, samples: number, rtol: number, atol: number, max_steps: number, method: string) → array	array	Grid extension. Integrates dy/dt = fn(t, y) from t_start to t_end and returns a samples x (1 + n) trajectory array whose first column is t. The lambda takes (t, y); y0 may be a number or an array of numbers. Optional trailing arguments: samples (default 101), rtol (default 1e-6), atol (default 1e-9), max_steps (default 10000), and a method string as the final argument: "auto" (default: adaptive Dormand-Prince 5(4) with stiffness detection that switches to TR-BDF2 when the solve is stability-limited), "rk45" (force explicit Dormand-Prince), or "stiff" (alias "trbdf2": force L-stable TR-BDF2 with finite-difference Jacobians). Alternatively the option tail may be a single options record as the fifth argument: {method, rtol, atol, max_steps, first_step, max_step, jacobian_bandwidth} plus samples for ODE_SOLVE. first_step overrides automatic initial-step selection; max_step caps every attempt for discontinuous or narrow forcing; jacobian_bandwidth accepts a symmetric width or [lower, upper] pair.
OPTIMIZE_EXPLAIN(objective: array, constraints: array, rhs: array, maximize: boolean, row_labels: array) → array	array	Grid extension. Planner-facing companion to LINEAR_PROGRAM: solves the same c·x subject to Ax≤b, x≥0 model but returns a status-aware explanation instead of a bare answer. For an optimal solve: the binding constraints and their shadow prices (marginal objective per unit the right-hand side is relaxed). For an infeasible model: the irreducible infeasible subset (IIS), the minimal set of conflicting constraints, so a planner sees which inputs collide. For unbounded: a single row identifying the unbounded direction. Optional row_labels name the constraints so the result reads in the caller's own terms instead of row indices. Returns [row, label, role, value] rows. Pure LP; does not require a solver-mip build.
OUTERPRODUCT(left: array, right: array) → array	array	Returns the outer product of two arrays after flattening them row by row.
PAGERANK(adjacency: array, damping: number, iterations: number) → array	array	Grid extension. Computes PageRank scores from an adjacency matrix.
PARAMETER(initial: any) → any	any	Grid extension. Marks a static numeric literal as a trainable Tensor parameter; ordinary Workbook evaluation returns the literal unchanged.
PDE_SOLVE_1D(operator: lambda, ic: lambda, bc_left: any, bc_right: any, x_min: number, x_max: number, nx: number, t_end: number, samples: number) → array	array	Grid extension. Solves the general 1-D PDE u_t = operator(t, x, u, u_x, u_xx) on the method of lines: central differences in space, the adaptive ODE engine in time (default method auto — diffusion-dominated problems switch to the implicit integrator). The operator is a five-parameter lambda; ic is a lambda of x; each Dirichlet boundary is a constant or a one-parameter lambda of t. Returns samples x nx uniform time levels (t = 0 row first, boundary columns carrying the boundary values). Optional trailing arguments: samples (default 101) or a single options record {method, rtol, atol, max_steps, first_step, max_step, jacobian_bandwidth, samples}.
PERMUT(n: number, k: number) → number	number	Returns the number of permutations for a given number of objects. Also available infix as n PERMUTE k.
PI() → number	number	Returns the value of pi.
PINV(matrix: array) → array	array	Grid extension. Returns a Moore-Penrose pseudoinverse using normal equations.
POLYFIT(xs: array, ys: array, degree: number) → array	array	Fits a polynomial of the requested degree and returns coefficients from highest degree to lowest.
POLYVAL(coefficients: array, x: number) → number	number	Evaluates a polynomial at x using coefficients ordered from highest degree to lowest.
PORTFOLIO_QP_WEIGHTS(expected_returns: array, covariance: array, risk_aversion: number, iterations: number) → array	array	Grid extension. Returns long-only fully-invested mean-variance portfolio weights using projected gradient QP.
POWER(base: number, exponent: number) → number	number	aliases: POW. Returns a number raised to a power.
POWER_SPECTRUM(samples: array) → array	array	Grid extension. Returns squared Fourier magnitudes for numeric samples.
PREVPRIME(number: number) → number	number	Grid extension. Grid extension. Returns the largest prime smaller than the supplied integer.
PRIMEPI(number: number) → number	number	Grid extension. Grid extension. Returns the number of primes less than or equal to n.
PRIMES(number: number) → array	array	Grid extension. Grid extension. Returns a row array containing the first count primes.
PRIMES_UP_TO(number: number) → array	array	Grid extension. Grid extension. Returns a row array of primes less than or equal to n.
PRIME_FACTORS(number: number) → array	array	Grid extension. Grid extension. Returns the prime factors of n with repeated factors included.
PRODUCT(...values: number[]) → number	number	variadic. Returns the product of the supplied arguments.
QUOTIENT(numerator: number, denominator: number) → number	number	Returns the integer portion of a division.
RADIANS(degrees: number) → number	number	Converts degrees to radians.
RAND() → number	number	volatile. Returns a random number between 0 and 1.
RANDARRAY(rows: number, cols: number, min_val: number, max_val: number) → array	array	volatile. Returns an array of random numbers (Excel 365).
RANDBETWEEN(bottom: number, top: number) → number	number	volatile. Returns a random integer between two values.
RANDPRIME(bits: number) → number	number	volatile, Grid extension. Grid extension. Returns a fresh random prime with exactly the given number of bits, suitable for RSA-style key material.
RECURRENCE.CHARACTERISTIC(coefficients: array) → array	array	Grid extension. Returns the descending coefficients of the homogeneous characteristic polynomial for a constant-coefficient recurrence.
RECURRENCE.NTH(initial: array, coefficients: array, index: number, constant?: number) → number	number	Grid extension. Returns one zero-based term of a finite constant-coefficient affine recurrence using logarithmic companion-matrix exponentiation.
RECURRENCE.SEQUENCE(initial: array, coefficients: array, length: number, constant?: number) → array	array	Grid extension. Returns the requested prefix of a finite constant-coefficient affine recurrence with bounded forward evaluation.
RELU(value: number) → number	number	Grid extension. Applies the rectified linear unit, returning the greater of value and zero.
RMSNORM(value: array, epsilon?: number) → array	array	Grid extension. Normalizes each final-axis slice by its root-mean-square magnitude. The optional epsilon must be positive and defaults to 1e-5.
ROMAN(value: number) → string	string	Converts an Arabic numeral to a Roman numeral string.
ROOT(fn: lambda, lower: number, upper: number, tolerance: number, max_iterations: number) → number	number	Finds a root of a lambda over a bracketing interval using bisection.
ROUND(number: number, digits: number) → number	number	Rounds a number to the specified number of digits.
ROUNDDOWN(value: number, digits: number) → number	number	Rounds a number down, toward zero.
ROUNDUP(value: number, digits: number) → number	number	Rounds a number up, away from zero.
RREF(matrix: array) → array	array	Returns the reduced row echelon form of a matrix.
SEC(v: number) → number	number	Returns the secant of an angle in radians.
SECH(v: number) → number	number	Returns the hyperbolic secant.
SERIESSUM(x: number, n: number, m: number, coefficients: number[]) → number	number	Returns the sum of a power series.
SHORTEST_PATH(adjacency: array, start: number, target: number) → number	number	Grid extension. Returns the Dijkstra shortest-path distance between 1-based nodes in an adjacency matrix.
SIGMOID(value: number) → number	number	Grid extension. Applies the logistic sigmoid activation, 1 / (1 + EXP(-value)).
SIGN(value: number) → number	number	Returns the sign of a number: 1, 0, or -1.
SIGNAL.PSD(signal: array, fs: number, window: text) → array	array	Grid extension. One-sided power spectral density of a real signal as a (floor(n/2)+1) x 2 matrix of (frequency, density). fs is the sample rate (default 1.0); window names the analysis taper - hann (default), hamming, blackman, or none. The standard windowed periodogram estimate, normalized so integrating the density recovers the signal's mean square (Parseval).
SILU(value: number) → number	number	Grid extension. Sigmoid Linear Unit activation, value / (1 + EXP(-value)).
SIN(v: number) → number	number	Returns the sine of an angle in radians.
SINH(v: number) → number	number	Returns the hyperbolic sine.
SOFTMAX(logits: array) → array	array	Grid extension. Normalizes a numeric array across its final dimension; each row of a 2-D range sums to 1.
SOLVE(coefficients: array, rhs: array) → array	array	Solves a linear system Ax = b for x.
SQRT(value: number) → number	number	Returns the square root of a number.
SQUARE(value: number) → number	number	Grid extension. Returns the square of a number.
SUBTOTAL(function_num: number, ...ref: number[]) → number	number	variadic. Returns a subtotal using a specified function number (1=AVERAGE, 2=COUNT, 3=COUNTA, 4=MAX, 5=MIN, 6=PRODUCT, 7=STDEV, 9=SUM).
SUM(...values: number[]) → number	number	variadic. Returns the sum of the supplied arguments.
SUMIF(range: array, criteria: any, sum_range: array) → number	number	variadic. Sums cells that match a condition.
SUMIFS(sum_range: array, ...criteria_range: array, ...criteria: any) → number	number	variadic. Sums cells that meet multiple criteria.
SUMPRODUCT(...array: number[]) → number	number	variadic. Returns the sum of element-wise products of arrays.
SUMSQ(...values: number[]) → number	number	variadic. Returns the sum of squares of the arguments.
SUMX2MY2(arr_x: number[], arr_y: number[]) → number	number	Returns the sum of the difference of squares of corresponding values.
SUMX2PY2(arr_x: number[], arr_y: number[]) → number	number	Returns the sum of the sum of squares of corresponding values.
SUMXMY2(arr_x: number[], arr_y: number[]) → number	number	Returns the sum of squares of differences of corresponding values.
SVD.RANK(matrix: array, tolerance: number) → number	number	Grid extension. Numerical rank: the count of singular values above tolerance. The default tolerance is max(m,n) * eps * sigma_max (the LAPACK/NumPy convention); pass an absolute tolerance to override.
SVD.U(matrix: array) → array	array	Grid extension. Thin left singular vectors: an m x min(m,n) matrix whose columns pair with SVD.VALUES so that A = MMULT(SVD.U(A), MMULT(DIAG(SVD.VALUES(A)), TRANSPOSE(SVD.V(A)))). Columns for exactly-zero singular values are zero-filled.
SVD.V(matrix: array) → array	array	Grid extension. Thin right singular vectors: an n x min(m,n) matrix (not transposed) whose columns pair with SVD.VALUES.
SVD.VALUES(matrix: array) → array	array	Grid extension. Singular values of any rectangular matrix (one-sided Jacobi) as a min(m,n) x 1 column sorted descending. sigma_max/sigma_min is the 2-norm condition number; values snap to exact zero below the numerical-rank threshold.
SYMBOLIC.APART(expression: symbolic_expression, variable: symbolic_variable, [assumptions]: symbolic_assumptions) → symbolic_expression_result	symbolic_expression_result	model-scoped, Grid extension. Computes an exact partial-fraction decomposition in the selected symbolic variable.
SYMBOLIC.APPROXIMATE(expression: symbolic_expression, precisionBits: number, [rounding]: symbol) → symbolic_expression_result	symbolic_expression_result	model-scoped, Grid extension. Converts an admitted ground arithmetic or algebraic expression to an arbitrary-precision real or complex value with explicit effective precision, rounding authority, a certified enclosure, and a replayable derivation.
SYMBOLIC.ASSUMPTIONS(proposition: predicate_proposition...) → symbolic_assumptions	symbolic_assumptions	variadic, model-scoped, Grid extension. Constructs a fingerprinted immutable four-state evidence set from symbolic propositions.
SYMBOLIC.CANCEL(expression: symbolic_expression, [assumptions]: symbolic_assumptions) → symbolic_expression_result	symbolic_expression_result	model-scoped, Grid extension. Cancels exact rational-function factors while retaining or discharging every nonzero obligation.
SYMBOLIC.CANONICALIZE(expression: symbolic_expression) → symbolic_expression_result	symbolic_expression_result	model-scoped, Grid extension. Returns the deterministic structural canonical form with status, work, conditions, and replayable derivation.
SYMBOLIC.COLLECT(expression: symbolic_expression, variable: symbolic_variable) → symbolic_expression_result	symbolic_expression_result	model-scoped, Grid extension. Collects exact polynomial coefficients by a symbolic variable.
SYMBOLIC.COMBINE_ASSUMPTIONS(assumptions: symbolic_assumptions...) → symbolic_assumptions	symbolic_assumptions	variadic, model-scoped, Grid extension. Combines immutable assumption sets while preserving support, refutation, contradiction, provenance, and identity.
SYMBOLIC.D(expression: symbolic_expression, variable: symbolic_variable, [assumptions]: symbolic_assumptions) → symbolic_expression_result	symbolic_expression_result	model-scoped, Grid extension. Differentiates a symbolic expression exactly and retains branch or domain conditions.
SYMBOLIC.DECIDE(relation: symbolic_relation, [assumptions]: symbolic_assumptions) → symbolic_decision_result	symbolic_decision_result	model-scoped, Grid extension. Decides a symbolic relation under optional assumptions and returns four-state evidence with a replayable derivation.
SYMBOLIC.DOMAIN(variable: symbolic_variable, domain: symbol) → predicate_proposition	predicate_proposition	model-scoped, Grid extension. Constructs a normalized operation-local Predicate-lattice domain proposition for a symbolic variable.
SYMBOLIC.EVALUATE(expression: symbolic_expression, substitution: symbolic_substitution, [assumptions]: symbolic_assumptions) → symbolic_expression_result	symbolic_expression_result	model-scoped, Grid extension. Applies a typed substitution, performs exact ground arithmetic, and consumes optional assumptions while simplifying and discharging supported conditions.
SYMBOLIC.EXPAND(expression: symbolic_expression) → symbolic_expression_result	symbolic_expression_result	model-scoped, Grid extension. Expands an admitted exact polynomial expression and returns its certificate-bound operation result.
SYMBOLIC.FACTOR(expression: symbolic_expression) → symbolic_expression_result	symbolic_expression_result	model-scoped, Grid extension. Factors an admitted exact univariate polynomial over the rational coefficient domain with a replayable derivation.
SYMBOLIC.RATIONAL(numerator: exact_integer, denominator: exact_integer) → symbolic_expression	symbolic_expression	model-scoped, Grid extension. Constructs one exact reduced rational expression from exact integer operands.
SYMBOLIC.SAME(left: symbolic_expression, right: symbolic_expression) → boolean	boolean	model-scoped, Grid extension. Tests structural identity of two symbolic trees without claiming mathematical equivalence.
SYMBOLIC.SIMPLIFY(expression: symbolic_expression, [assumptions]: symbolic_assumptions) → symbolic_expression_result	symbolic_expression_result	model-scoped, Grid extension. Runs the deterministic exact simplification strategy under an optional immutable assumption set.
SYMBOLIC.SOLVE(relation: symbolic_relation, variable: symbolic_variable, [domainOrAssumptions]: symbol|symbolic_assumptions, [assumptions]: symbolic_assumptions) → symbolic_solution_result	symbolic_solution_result	model-scoped, Grid extension. Returns the complete certified solution set for an admitted exact univariate polynomial equality over the rationals in the selected domain, consuming optional assumptions to reject only exactly refuted branches, or a distinct unknown/limit result.
SYMBOLIC.SUBSTITUTION(variable: symbolic_variable, value: symbolic_expression|exact_scalar) → symbolic_substitution	symbolic_substitution	model-scoped, Grid extension. Constructs one immutable typed symbolic-variable binding.
SYMBOLIC.TOGETHER(expression: symbolic_expression, [assumptions]: symbolic_assumptions) → symbolic_expression_result	symbolic_expression_result	model-scoped, Grid extension. Combines an admitted rational expression over a common exact denominator without discarding conditions.
TAN(v: number) → number	number	Returns the tangent of an angle in radians.
TANH(v: number) → number	number	Returns the hyperbolic tangent.
TOTIENT(number: number) → number	number	Grid extension. Grid extension. Returns Euler's totient function phi(n).
TRACE(matrix: array) → number	number	Returns the sum of the diagonal of a square matrix.
TRAIN_ADAMW(loss: number, steps: number, learning_rate: number, max_duration_ms: number, ...parameters: any[]) → any	any	variadic, Grid extension. Declares a bounded AdamW training request for a scalar loss and one or more PARAMETER references; ordinary Workbook evaluation returns blank.
TRUNC(value: number, digits: number) → number	number	Truncates a number to an integer by removing the fractional part.
VRP_SOLVE(cost_matrix: array, demand: array, vehicle_count: number, capacity: number, time_window: array, service_time: array) → array	array	Grid extension. Capacitated vehicle-routing convenience layer. Assembles a Miller–Tucker–Zemlin mixed-integer model over a cost matrix and per-node demand and solves it with the same backend MIXED_INTEGER_PROGRAM uses, returning one [route, position, node, load_after] row per visited node (routes open and close at the depot, node 0). Dispatches at most vehicle_count vehicles, each within capacity. Optional time_window ((n+1)x2 [earliest, latest] per node) plus service_time activates VRPTW big-M sequencing, with the cost matrix additionally read as travel time. Requires a solver-mip build; other builds return an explicit capability error.
WINDOW.BLACKMAN(length: number) → array	array	Grid extension. Blackman analysis window of length n as a row vector: w[i] = 0.42 - 0.5cos(2pii/(n-1)) + 0.08cos(4pii/(n-1)). Very low side lobes for high-dynamic-range spectral estimates.
WINDOW.HAMMING(length: number) → array	array	Grid extension. Hamming analysis window of length n as a row vector: w[i] = 0.54 - 0.46cos(2pi*i/(n-1)). Lower first side lobe than Hann at the cost of a 0.08 pedestal at the ends.
WINDOW.HANN(length: number) → array	array	Grid extension. Hann (raised-cosine) analysis window of length n as a row vector: w[i] = 0.5*(1 - cos(2pii/(n-1))). Zero at both ends; the general-purpose spectral-analysis taper.
ZETA(s: number) → number	number	Grid extension. Approximates the Riemann zeta function for s > 1.

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Text

String manipulation, parsing, regex, formatting, and template helpers.

Function count: 71.

Function	Returns	Notes
ARRAYTOTEXT(arr: array, format: number) → string	string	Returns an array of values as text (Excel 365).
CHAR(code: number) → string	string	Returns the character for a given character code.
CLEAN(value: string) → string	string	Removes non-printable characters from text.
CODE(text: string) → number	number	Returns the character code of the first character.
CONCAT(...values: string[]) → string	string	variadic. Concatenates text arguments.
CS_BOYER_MOORE_CONTAINS(text: string, pattern: string) → boolean	boolean	Grid extension. Returns whether text contains a pattern using Boyer-Moore-MagicLen.
CS_BOYER_MOORE_COUNT(text: string, pattern: string) → number	number	Grid extension. Counts non-overlapping Boyer-Moore-MagicLen pattern matches.
CS_BOYER_MOORE_FIND(text: string, pattern: string, start_pos: number) → number	number	Grid extension. Returns the 1-based position of a pattern using Boyer-Moore-MagicLen, or 0 if absent.
CS_BOYER_MOORE_FIND_ALL(text: string, pattern: string) → array	array	Grid extension. Returns 1-based positions of non-overlapping Boyer-Moore-MagicLen pattern matches.
CS_BOYER_MOORE_FIND_FULL(text: string, pattern: string) → array	array	Grid extension. Returns 1-based positions of all Boyer-Moore-MagicLen pattern matches, including overlaps.
DOLLAR(value: number, decimals: number) → string	string	Formats a number as currency text.
ENCODEURL(text: string) → string	string	URL-encodes a string.
EXACT(text1: string, text2: string) → boolean	boolean	Checks whether two strings are exactly equal (case-sensitive).
FIND(find_text: string, within_text: string, start_pos: number) → number	number	Finds the position of a substring (case-sensitive).
FINDB(find_text: string, within_text: string, start_pos: number) → number	number	Finds the byte position of text (same as FIND in UTF-8).
FIXED(value: number, decimals: number, no_commas: boolean) → string	string	Formats a number as text with a fixed number of decimal places.
HYPERLINK(url: string, friendly_name: string) → string	string	Returns the friendly name for a hyperlink (or the URL if no friendly name).
LEFT(value: string, count: number) → string	string	Returns the leftmost characters from a string.
LEFTB(value: string, count: number) → string	string	Returns the leftmost bytes (same as LEFT in UTF-8).
LEN(value: string) → number	number	Returns the length of a string.
LENB(value: string) → number	number	Returns the byte length of text (same as LEN in UTF-8).
LOWER(value: string) → string	string	Converts text to lowercase.
MID(value: string, start_pos: number, count: number) → string	string	Returns characters from the middle of a string.
MIDB(value: string, start_pos: number, count: number) → string	string	Returns bytes from the middle of text (same as MID in UTF-8).
NUMBERVALUE(text: string, decimal_sep: string, group_sep: string) → number	number	Converts text to a number in a locale-independent way.
PROPER(value: string) → string	string	Capitalizes the first letter of each word.
REGEXEXTRACT(text: string, pattern: string, group: number) → string	string	Extracts the first regex match or capture group from text.
REGEXMATCH(text: string, pattern: string) → boolean	boolean	Returns TRUE when text matches a supported regex pattern.
REGEXREPLACE(text: string, pattern: string, replacement: string) → string	string	Replaces all matches of a supported regex pattern.
REPLACE(old_text: string, start_pos: number, num_chars: number, new_text: string) → string	string	Replaces part of a string with another string based on position.
REPT(text: string, times: number) → string	string	Repeats text a given number of times.
RIGHT(value: string, count: number) → string	string	Returns the rightmost characters from a string.
RIGHTB(value: string, count: number) → string	string	Returns the rightmost bytes (same as RIGHT in UTF-8).
SEARCH(find_text: string, within_text: string, start_pos: number) → number	number	Finds the position of a substring (case-insensitive).
SEARCHB(find_text: string, within_text: string, start_pos: number) → number	number	Searches for byte position case-insensitively (same as SEARCH in UTF-8).
SPLIT(text: string, delimiter: string) → string	string	Splits text by a delimiter (Google Sheets).
SUBSTITUTE(text: string, old_text: string, new_text: string, instance: number) → string	string	Replaces occurrences of old_text with new_text. Optional instance number replaces only the Nth occurrence.
T(value: any) → string	string	Returns text if the value is text, otherwise empty string.
TEXT(value: number, format: string) → string	string	Formats a number as text with a format string (simplified).
TEXTAFTER(text: string, delimiter: string, instance: number) → string	string	Returns text after a delimiter (Excel 365).
TEXTBEFORE(text: string, delimiter: string, instance: number) → string	string	Returns text before a delimiter (Excel 365).
TEXTJOIN(delimiter: string, ignore_empty: boolean, ...text: string[]) → string	string	variadic. Joins text with a delimiter, optionally ignoring empty values.
TEXT_COUNT_ANY(text: string, patterns: array) → number	number	Grid extension. Total occurrences across many patterns.
TEXT_COUNT_ANY_BULK(haystacks: array, patterns: array) → array	array	Grid extension. Column of per-haystack occurrence counts for one shared pattern set.
TEXT_DAMERAU_LEVENSHTEIN(a: string, b: string) → number	number	Grid extension. Damerau-Levenshtein distance (Levenshtein with transpositions).
TEXT_FIND_ANY(text: string, patterns: array) → number	number	Grid extension. 1-based index of the first match among many patterns; 0 if none. Adaptive: naive for small N, aho-corasick when patterns x 16 < haystack bytes.
TEXT_FIND_ANY_BULK(haystacks: array, patterns: array) → array	array	Grid extension. Column of 1-based first-match positions for each haystack against one shared pattern set; one aho-corasick automaton amortizes across all rows.
TEXT_FUZZY_BEST(needle: string, candidates: array) → string	string	volatile, Grid extension. Best fuzzy-matching candidate from an array.
TEXT_FUZZY_RANK(needle: string, candidates: array, threshold: number) → array	array	volatile, Grid extension. Ranked fuzzy matches above optional threshold.
TEXT_FUZZY_SCORE(needle: string, haystack: string) → number	number	volatile, Grid extension. Fuzzy match score; -1 if no match.
TEXT_GRAPHEME_LEFT(text: string, count: number) → string	string	Grid extension. First N graphemes of a string.
TEXT_GRAPHEME_LEN(text: string) → number	number	Grid extension. Length in user-perceived grapheme clusters.
TEXT_GRAPHEME_MID(text: string, start: number, count: number) → string	string	Grid extension. Substring by graphemes (1-based start).
TEXT_GRAPHEME_RIGHT(text: string, count: number) → string	string	Grid extension. Last N graphemes of a string.
TEXT_HAMMING_DISTANCE(a: string, b: string) → number	number	Grid extension. Hamming distance; #VALUE! when lengths differ.
TEXT_JARO(a: string, b: string) → number	number	Grid extension. Jaro similarity in [0,1].
TEXT_JARO_WINKLER(a: string, b: string) → number	number	Grid extension. Jaro-Winkler similarity in [0,1] (prefix-boosted).
TEXT_LCS_LENGTH(a: string, b: string) → number	number	Grid extension. Longest common subsequence length.
TEXT_LEVENSHTEIN(a: string, b: string) → number	number	Grid extension. Levenshtein edit distance between two strings.
TEXT_NORMALIZED_DAMERAU(a: string, b: string) → number	number	Grid extension. Damerau-Levenshtein similarity normalized to [0,1].
TEXT_NORMALIZED_LEVENSHTEIN(a: string, b: string) → number	number	Grid extension. Levenshtein similarity normalized to [0,1].
TEXT_OSA_DISTANCE(a: string, b: string) → number	number	Grid extension. Optimal String Alignment distance.
TEXT_SORENSEN_DICE(a: string, b: string) → number	number	Grid extension. Sorensen-Dice bigram similarity in [0,1].
TRIM(value: string) → string	string	Removes leading, trailing, and excess interior spaces.
UNICHAR(code: number) → string	string	Returns the Unicode character for a code point.
UNICODE(text: string) → number	number	Returns the Unicode code point of the first character.
UPPER(value: string) → string	string	Converts text to uppercase.
VALUE(text: string) → number	number	Converts a text string to a number.
VALUETOTEXT(value: any) → string	string	Converts any value to text (Excel 365).
WILDCARDMATCH(text: string, pattern: string, case_sensitive: boolean) → boolean	boolean	Returns TRUE when text matches a simple wildcard pattern using * and ?.
XLOOKUP_FUZZY(lookup_value: string, lookup_array: array, return_array: array, threshold: number) → any	any	volatile, Grid extension. XLOOKUP whose lookup uses fuzzy matching.

---

Keyword Extraction

Keyword extraction, phrase scoring, and lightweight text mining helpers.

Function count: 1.

Function	Returns	Notes
TEXT_RAKE_KEYWORDS(text: string, max_keywords: number, stop_words: array, min_score: number) → array	array	Grid extension. Extracts RAKE keyword phrases and scores; returns rows [keyword, score], optionally filtered by minimum score.

---

Security

Password generation, scoring, and security-oriented helpers.

Function count: 6.

Function	Returns	Notes
SEC_PASSWORD_ANALYZE(password: string) → array	array	Grid extension. Returns password composition counts [length, spaces, numbers, lowercase, uppercase, symbols, other, consecutive, repeated, progressive].
SEC_PASSWORD_GENERATE(length: number, numbers: boolean, lowercase: boolean, uppercase: boolean, symbols: boolean, spaces: boolean, exclude_similar: boolean, strict: boolean) → string	string	volatile, Grid extension. Generates a random readable password with configurable character classes.
SEC_PASSWORD_GENERATE_BATCH(length: number, numbers: boolean, lowercase: boolean, uppercase: boolean, symbols: boolean, spaces: boolean, exclude_similar: boolean, strict: boolean, count: number) → array	array	volatile, Grid extension. Generates a row of random readable passwords with configurable character classes.
SEC_PASSWORD_IS_VALID(password: string, min_length: number, min_score: number) → boolean	boolean	Grid extension. Returns whether a password meets minimum length and strength-score thresholds.
SEC_PASSWORD_NORMALIZE(password: string) → string	string	Grid extension. Returns the password text after the passwords analyzer removes control characters.
SEC_PASSWORD_STRENGTH(password: string) → number	number	Grid extension. Scores password strength from 0 to 100 using the passwords crate.

---

Logical

Boolean logic, conditional dispatch, and predicates.

Function count: 20.

Function	Returns	Notes
AND(...values: boolean[]) → boolean	boolean	variadic. Returns TRUE when all values are truthy.
BLANK() → blank	blank	Returns Grid's blank value.
CLAMP(value: number, lower: number, upper: number) → number	number	Constrains a value to lie within a lower and upper bound.
FALSE() → boolean	boolean	Returns the logical value FALSE.
GROWTH_RATE(from_value: number, to_value: number) → number	number	Grid extension. Returns the growth rate from the first value to the second.
IF(condition: boolean, when_true: any, when_false: any) → any	any	Returns one of two values based on a condition.
IFERROR(value: any, alternative: any) → any	any	Returns a value if it is not an error, otherwise returns an alternative.
IFNA(value: any, alternative: any) → any	any	Returns a value if it is not #N/A, otherwise returns an alternative.
IFS(...logical_test: any[], ...value_if_true: any) → any	any	variadic. Evaluates conditions in order and returns the value for the first TRUE condition.
IN(value: any, ...candidates: any[]) → boolean	boolean	variadic, Grid extension. Returns TRUE when a value structurally equals a direct element of any supplied candidate. Equality is type- and tag-sensitive; errors match by code with diagnostic messages ignored, signed zero matches, NaN never matches, and infinities require the same sign. Nested collections are not flattened, 2-D arrays expose rows, scalar candidates are singletons, and set/map membership tests keys. At least one candidate is required. Infix: value IN collection; converse: collection HAS value.
ISEMPTY(value: any) → boolean	boolean	Grid extension. Returns TRUE for blank, empty text, empty or all-blank arrays, and empty native collections. Infix: value IS EMPTY.
NOT(value: boolean) → boolean	boolean	Negates a boolean value.
OR(...values: boolean[]) → boolean	boolean	variadic. Returns TRUE when any value is truthy.
PERCENTOF(value: number, total: number) → number	number	Returns what percentage the first value is of the second value.
SWITCH(expression: any[], ...value: any, ...result: any) → any	any	variadic. Evaluates an expression against a list of values and returns the matching result.
TAP(value: any, label: string) → any	any	Identity function that passes through its value unchanged. Useful for pipeline inspection.
TEMPORAL_DELTA(value: any) → number	number	Grid extension. Returns the change from the previous value (value - value@-1). Requires temporal history.
TRUE() → boolean	boolean	Returns the logical value TRUE.
UNCERTAIN(mean: number, uncertainty: number) → number	number	Creates a value with uncertainty (mean ± uncertainty).
XOR(...values: boolean[]) → boolean	boolean	variadic. Returns TRUE when an odd number of arguments are truthy.

---

Language & Reference Forms

Special forms and reference functions that bind names, create lambdas, or resolve references.

Function count: 13.

Function	Returns	Notes
BYCOL(array: array, lambda: lambda) → array	array	special form. Applies a lambda to each column of an array and returns one result per column.
BYROW(array: array, lambda: lambda) → array	array	special form. Applies a lambda to each row of an array and returns one result per row.
CLONE(value: any) → any	any	Grid extension. Returns the same immutable value while preventing a bare named assignment from becoming an address alias.
FORMULATEXT(reference: reference) → string	string	special form. Returns the authored source text of a referenced cell's formula, prefixed with =, resolved at compile time (the runtime retains no source text). A cell holding a bare literal, or a cell nothing assigns, yields #N/A as in Excel. Because the text is baked with no dependency edge, a model containing FORMULATEXT declines incremental formula splicing and recompiles instead. A computed reference is refused with FORMULATEXT/DYNAMIC.
INDIRECT(ref_text: string, a1: boolean) → any	any	special form. Resolves a literal text reference at compile time — an absolute R1C1/A1 cell, a range, or a defined name — so the reference participates in dependency extraction; invalid text yields #REF!. Computed (non-literal) reference text is not supported in the compiled runtime and yields INDIRECT/DYNAMIC.
ITERATE(initial: any, steps: number, lambda: lambda) → any	any	special form, Grid extension. Applies a unary state lambda a statically bounded number of times and returns the final value.
LAMBDA(...parameter: symbol, ...calculation: any) → lambda	lambda	variadic, special form. Creates a callable function value from parameter names and a calculation expression.
LET(name: symbol, value: any, calculation: any) → any	any	variadic, special form. Binds name/value pairs and evaluates a final expression in that local scope.
MAKEARRAY(rows: number, cols: number, lambda: lambda) → array	array	special form. Creates an array by invoking a lambda for each row and column index.
MAP(...array: array, ...lambda: lambda) → array	array	variadic, special form. Maps one or more arrays through a lambda and returns the spilled result array.
OFFSET(reference: reference, rows: number, cols: number, height?: number, width?: number) → any	any	special form. Resolves a literal reference shifted by literal row/column counts at compile time, so the resulting reference participates in dependency extraction and edits to it propagate. Omitted height/width inherit the base reference's shape; a 1x1 result is a cell, larger is a range. Out-of-bounds folds to #REF!. Computed references or shifts are refused at evaluation with OFFSET/DYNAMIC.
REDUCE(initial_value: any, array: array, lambda: lambda) → any	any	special form. Reduces an array to one value by repeatedly applying a lambda to the accumulator and next value.
SCAN(initial_value: any, array: array, lambda: lambda) → array	array	special form. Returns intermediate accumulator values while applying a lambda across an array.

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Simulation

State, simulated-time, trajectory, and experiment helpers.

Function count: 14.

Function	Returns	Notes
CALIBRATE(params_and_bounds: array, loss_cell: reference, config: object) → object	object	Grid extension. Fits bounded parameter cells by minimizing a simulation loss with the Solver Sim evaluator.
DELAY(tracked: any, lag_steps: number, initial: any) → any	any	Grid extension. Returns tracked from lag_steps simulated steps ago, using initial until enough history exists. Outside simulation it returns initial.
GEO_MOVE_TOWARD(location: geometry, target: geometry, distance: number) → geometry	geometry	Grid extension. Moves a point toward a target by a bounded distance.
NEIGHBORS_WITHIN(population: object, location: geometry, radius: number) → number	number	Grid extension. Counts live agents within a radius using the previous-step spatial index.
PREV(tracked: any, initial: any) → any	any	Grid extension. Returns the tracked expression's value from the previous simulated step, using initial at t0. Outside a simulation resolve it returns initial without evaluating the tracked expression.
SIM_AGENTS(population: frame, behavior: lambda, config: object) → object	object	Grid extension. Runs a synchronously updated spatial-agent population and returns an agent run handle.
SIM_AGENT_COUNT(population: object, predicate: lambda) → number	number	Grid extension. Counts agents matching a predicate in the previous committed population.
SIM_PROCESS(stations: frame, resources: frame, routes: frame, config: object) → object	object	Grid extension. Runs a table-authored discrete-event process graph and returns a simulation run handle.
SIM_RESULTS(run: object) → frame	frame	Grid extension. Returns the full statistics frame for a discrete-event simulation run.
SIM_STATS(run: object, metric: text, station: text) → number	number	Grid extension. Reads a named station or resource statistic from a discrete-event simulation run.
SIM_STEP() → number	number	volatile, Grid extension. Returns the zero-based simulated step index. Outside a simulation resolve it returns #N/A.
SIM_TIME() → number	number	volatile, Grid extension. Returns the current simulated time. Outside a simulation resolve it returns #N/A.
SIM_TRAJECTORY(source: any, clock: sim_clock) → any	any	Grid extension. Returns source in Workbook semantics; under RENDER it emits a finite read-only simulation trajectory FrameHandle with independent logical and presentation clocks.
STOCK(initial: number, net_flow: number) → number	number	Grid extension. Integrates a numeric stock from its initial value using dt times net_flow on every simulated step. Outside simulation it returns initial.

---

Date & Time

Date/time arithmetic, formatting, and calendar helpers.

Function count: 27.

Function	Returns	Notes
DATE(year: number, month: number, day: number) → date	date	Constructs a date from year, month, and day.
DATEDIF(start_date: date, end_date: date, unit: string) → number	number	Calculates the difference between two dates in various units.
DATEVALUE(value: string) → date	date	Converts a date string to a date value.
DAY(value: date) → number	number	Returns the day component of a date (1-31).
DAYS(end_date: date, start_date: date) → number	number	Returns the number of days between two dates.
DAYS360(start_date: date, end_date: date, method: boolean) → number	number	Returns the number of days between two dates based on a 360-day year.
EDATE(value: date, months: number) → date	date	Returns a date that is a specified number of months before or after a date.
EOMONTH(value: date, months: number) → date	date	Returns the last day of the month, a specified number of months before or after a date.
HOUR(value: date) → number	number	Returns the hour from a time value (0-23).
INTERVAL(start: any, end: any) → interval	interval	Grid extension. Constructs a nonempty numeric, date, or datetime interval for temporal predicates.
ISOWEEKNUM(value: date) → number	number	Returns the ISO week number of the year.
MINUTE(value: date) → number	number	Returns the minute from a time value (0-59).
MONTH(value: date) → number	number	Returns the month component of a date (1-12).
NETWORKDAYS(start_date: date, end_date: date) → number	number	Returns the number of working days between two dates.
NETWORKDAYS_INTL(start_date: date, end_date: date, weekend: number) → number	number	aliases: NETWORKDAYS.INTL. Returns working days between dates with custom weekend specification.
NOW() → date	date	volatile. Returns the current date and time.
SECOND(value: date) → number	number	Returns the second from a time value (0-59).
TEMPORAL_COORD(kind: string, ...part: string) → date	date	variadic, volatile, Grid extension. Resolves Grid @ temporal coordinate shorthands such as @today, @monday, @january, @1776, and @5000BCE.
TIME(hour: number, minute: number, second: number) → string	string	Returns a time value from hour, minute, second.
TIMEVALUE(value: string) → number	number	Converts a time string to a decimal fraction of a day.
TODAY() → date	date	volatile. Returns the current date.
WEEKDAY(value: date) → number	number	Returns the day of the week (1=Sunday, 7=Saturday).
WEEKNUM(value: date) → number	number	Returns the week number of a date in the year.
WORKDAY(start_date: date, days: number) → date	date	Returns a date that is a given number of working days from a start date.
WORKDAY_INTL(start_date: date, days: number, weekend: number) → date	date	aliases: WORKDAY.INTL. Returns a date offset by working days with custom weekend specification.
YEAR(value: date) → number	number	Returns the year component of a date.
YEARFRAC(start_date: date, end_date: date, basis: number) → number	number	Returns the year fraction between two dates.

---

Lookup & Reference

Range and table lookups, joins, sorting, filtering.

Function count: 54.

Function	Returns	Notes
ADDRESS(row: number, col: number, abs_type: number) → string	string	Returns a cell reference as text.
BROADCAST(value: any, ...dimensions: number[]) → array	array	variadic, Grid extension. Broadcasts a numeric scalar or array to the supplied static dimensions.
CHOOSE(index_num: number, ...value: any[]) → any	any	variadic. Returns a value from a list of values based on an index number.
CHOOSECOLS(array: array, ...col_num: number[]) → array	array	variadic. Returns specified columns from an array (Excel 365).
CHOOSEROWS(array: array, ...row_num: number[]) → array	array	variadic. Returns specified rows from an array (Excel 365).
COLUMN(value: number) → number	number	Returns the column number of a reference.
COLUMNS(arr: array) → number	number	Returns the number of columns in an array.
COLUMN_BY_HEADER(range: array, header: string) → array	array	Selects a column from a range by matching header name in the first row.
CONTAINS(source: any, pattern: any) → boolean	boolean	Grid extension. Returns TRUE when text contains a case-sensitive contiguous substring, or when an ordered array, tuple, vector, or deque contains a contiguous run of structurally equal direct elements. Structural equality is type- and tag-sensitive, compares errors by code, treats signed zero as equal, treats NaN as unequal to every value, and distinguishes infinity signs. A scalar pattern is one element; an empty pattern always matches. Ordered matching is linear in source plus pattern length; sets and maps are rejected. Infix: source CONTAINS pattern.
DROP(arr: array, rows: number, cols: number) → array	array	Drops rows or columns from the start or end of an array (Excel 365).
EXCEPT(a: array, b: array) → array	array	Returns elements from the first array not in the second.
EXCLUDE(a: array, b: any) → array	array	Returns elements from the first array excluding elements matching the second.
EXPAND(arr: array, rows: number, cols: number, pad: any) → array	array	Expands an array to specified dimensions, filling with a pad value (Excel 365).
FILL(value: any, rows: number, cols: number) → array	array	Builds a rows × cols array with every cell set to value.
FILTER(arr: array, include: array, if_empty?: any) → array	array	Filters values with an include mask; the optional third argument is returned for an empty result. In a pipe, FILTER(value => predicate [, if_empty]) is elementwise sugar for FILTER(values, MAP(values, value => predicate) [, if_empty]).
HLOOKUP(lookup: any, table_array: array, row_index: number, range_lookup: boolean) → any	any	Searches the first row of a range for a key and returns a value from a specified row.
HSTACK(...values: array[]) → array	array	variadic. Horizontally stacks arrays (Excel 365).
INDEX(rows: array, row_index: number, column_index: number) → any	any	Returns a value from a rectangular array.
INTERSECT(a: array, b: array) → array	array	Returns elements present in both arrays.
IOTA(start: number, end: number, step: number) → array	array	Grid extension. Builds a one-dimensional numeric sequence from a non-negative integer start strictly below end to an exclusive non-negative integer end, using a positive integer step.
LOOKUP(lookup_value: any, lookup_vector: array, result_vector: array) → any	any	Searches a sorted vector and returns the matching or previous result value.
MATCH(lookup: any, range: array, match_type: number) → number	number	Returns the relative position of a value in a range.
OBJECTS(table: array) → array	array	Converts a 2D-array-with-headers into a 1D column of objects, one per data row keyed by the header names. Pairs with comprehensions: [ {id: r.id, total: r.amount * r.fx} FOR r IN OBJECTS(data) IF r.status = "active" ]. The inverse of laying out a table as [headers; row1; row2; …].
OMIT(source: any, ...key: string) → any	any	variadic. Returns a copy of the source object or 2D-array-with-headers with the listed keys removed. Missing keys are silently ignored. Keys may be exact strings or glob/wild patterns. Backs the postfix @![…] operator and infix OMIT.
ONES(rows: number, cols: number) → array	array	Builds a rows × cols array of ones. Equivalent to FILL(1, rows, cols).
OVERLAPS(a: any, b: any) → boolean	boolean	Grid extension. Returns TRUE when two values share at least one structurally equal direct element. Equality is type- and tag-sensitive; errors match by code, signed zero matches, NaN never matches, and infinities require the same sign. Nested collections are not flattened, 2-D arrays expose rows, scalars are singleton collections, and set/map elements are keys. Requires exactly two arguments. Infix: left OVERLAPS right.
PICK(source: any, ...key: string) → any	any	variadic. Projects an object or 2D-array-with-headers onto the listed keys, preserving the order in which the keys appear. Missing keys are silently skipped. Keys may be exact strings or glob/wild patterns. Backs the postfix @[…] operator and infix PICK.
QUERY(data: array, query_str: string) → array	array	Runs a SQL-like query over a 2D array. Supports SELECT, WHERE, ORDER BY, and LIMIT.
RENAME(source: any, ...from: string, ...to: string) → any	any	variadic. Renames keys in an object or headers in a 2D array. Takes a source followed by alternating old/new key pairs. Unknown old keys are silently ignored. Object key order is preserved; 2D-array column order is preserved. Backs infix RENAME "from" AS "to".
REPEAT(value: any, count: number) → array	array	Vertically stacks count copies of value. A scalar produces a count × 1 column; a row vector produces count rows; a 2D array tiles the whole block count times.
RESHAPE(value: array, ...dimensions: number[]) → array	array	variadic, Grid extension. Reshapes numeric values to the supplied static dimensions without changing element order.
ROW(value: number) → number	number	Returns the row number of a reference.
ROWS(arr: array) → number	number	Returns the number of rows in an array.
SEQUENCE(rows: number, columns: number, start: number, step: number) → array	array	Generates a sequence of numbers (Excel 365 / Google Sheets).
SLICE(source: any, start_idx: number, end_idx: number, step: number) → any	any	Returns a sub-array or substring from start to end index.
SORT(arr: array, sort_index: number, sort_order: number) → array	array	Sorts the contents of a range or array (Excel 365 / Google Sheets).
SORTBY(arr: array, by_arr: array, order: number) → array	array	Sorts an array based on values in a corresponding array (Excel 365).
STACK(axis: number, ...values: array[]) → array	array	variadic, Grid extension. Stacks two or more same-shaped numeric values along a zero-based axis.
SUBSET(a: any, b: any) → boolean	boolean	Grid extension. Returns TRUE when every distinct, structurally equal direct element of a appears in b. Comparison is unordered, duplicate-insensitive, type- and tag-sensitive; errors match by code, signed zero matches, NaN never matches, and infinities require the same sign. Nested collections are not flattened, 2-D arrays expose rows, scalars are singletons, and set/map elements are keys. Requires exactly two arguments. Infix: a SUBSET OF b.
SUPERSET(a: any, b: any) → boolean	boolean	Grid extension. Converse of SUBSET: every distinct, structurally equal direct element of b appears in a, regardless of order or duplicates. Equality is type- and tag-sensitive; errors match by code, signed zero matches, NaN never matches, and infinities require the same sign. Nested collections are not flattened, 2-D arrays expose rows, scalars are singletons, and set/map elements are keys. Requires exactly two arguments. Infix: a SUPERSET OF b.
TAKE(arr: array, rows: number, cols: number) → array	array	Returns rows or columns from the start or end of an array (Excel 365).
TEXTSPLIT(text: string, col_delimiter: string, row_delimiter: string) → array	array	Splits text by column and row delimiters into a 2D array (Excel 365).
TOCOL(arr: array) → array	array	Converts an array to a single column (Excel 365).
TOROW(arr: array) → array	array	Converts an array to a single row (Excel 365).
TRANSPOSE(arr: array) → array	array	Transposes the rows and columns of an array.
UNION(a: array, b: array) → array	array	Returns the unique combined elements from two arrays.
UNIQUE(arr: array) → array	array	Returns unique values from a range (Excel 365 / Google Sheets).
VLOOKUP(lookup: any, table_array: array, col_index: number, range_lookup: boolean) → any	any	Searches the first column of a range for a key and returns a value from a specified column.
VSTACK(...values: array[]) → array	array	variadic. Vertically stacks arrays (Excel 365).
WRAPCOLS(arr: array, wrap_count: number, pad: any) → array	array	Wraps a row/column vector into columns of a given length (Excel 365).
WRAPROWS(arr: array, wrap_count: number, pad: any) → array	array	Wraps a row/column vector into rows of a given length (Excel 365).
XLOOKUP(value: any, array: array, array_2: array, value_2: any, number: number, number_2: number) → any	any	Searches a range and returns a corresponding item from a second range (Excel 365).
XMATCH(lookup: any, lookup_arr: array, match_mode: number) → number	number	Returns the relative position of an item in an array (Excel 365).
ZEROS(rows: number, cols: number) → array	array	Builds a rows × cols array of zeros. Equivalent to FILL(0, rows, cols).

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Financial

Time-value-of-money, depreciation, bond math, and other finance helpers.

Function count: 208.

Function	Returns	Notes
ACCRINT(issue: date, first_interest: date, settlement: date, rate: number, par: number, frequency: number) → number	number	Returns the accrued interest for a security that pays periodic interest.
ACCRINTM(issue: date, settlement: date, rate: number, par: number, basis: number) → number	number	Returns the accrued interest for a security that pays at maturity.
ACCRUED_FEE(base_amount: number, annual_rate: number, year_fraction: number) → number	number	Grid extension. Returns accrued fee from base amount, annual rate, and year fraction.
ACTIVE_RETURN(portfolio_return: number, benchmark_return: number) → number	number	Grid extension. Returns portfolio return minus benchmark return.
ALPHA(asset_returns: number[], benchmark_returns: number[], risk_free_rate: number, periods_per_year: number) → number	number	Grid extension. Returns annualized Jensen's alpha versus benchmark returns and an annual risk-free rate.
AMORDEGRC(cost: number, date_purchased: date, first_period: date, salvage: number, period: number, rate: number) → number	number	Returns the depreciation for each accounting period (French degressive).
AMORLINC(cost: number, date_purchased: date, first_period: date, salvage: number, period: number, rate: number) → number	number	Returns the depreciation for each accounting period (French linear).
ASIAN_OPTION(prices: number[], strike: number, option_type: string, discount_factor: number) → number	number	Grid extension. Returns option payoff on the arithmetic average of observed prices.
AUM(shares: number, nav_per_share: number) → number	number	Grid extension. Returns assets under management from shares and NAV per share.
BARRIER_OPTION(spot: number, strike: number, time: number, rate: number, volatility: number, option_type: string, barrier: number, barrier_type: string, dividend: number) → number	number	Grid extension. Returns a simple barrier-adjusted option price approximation.
BETA(asset_returns: number[], benchmark_returns: number[]) → number	number	Grid extension. Returns portfolio beta versus benchmark returns.
BETA_ADJUSTED_EXPOSURE(exposure: number, beta: number) → number	number	Grid extension. Returns exposure multiplied by beta.
BID_ASK_SPREAD(bid: number, ask: number, relative: boolean) → number	number	Grid extension. Returns bid-ask spread, absolute or relative to mid.
BINOMIAL_OPTION(spot: number, strike: number, time: number, rate: number, volatility: number, steps: number, option_type: string, dividend: number, american: boolean) → number	number	Grid extension. Returns Cox-Ross-Rubinstein binomial option price for European or American exercise.
BLACK76(forward: number, strike: number, time: number, rate: number, volatility: number, option_type: string) → number	number	Grid extension. Returns Black-76 futures option price for a call or put.
BLACK_SCHOLES(spot: number, strike: number, time: number, rate: number, volatility: number, option_type: string, dividend: number) → number	number	Grid extension. Returns the Black-Scholes-Merton theoretical option price for a call or put.
BOOTSTRAP_ZERO_CURVE(prices: number[], coupons: number[], maturities: number[], face: number, frequency: number) → array	array	Grid extension. Bootstraps approximate zero rates from bond prices, coupon rates, and maturities.
BRINSON_ALLOCATION(pw: number[], bw: number[], br: number[]) → number	number	Grid extension. Returns Brinson allocation effect from portfolio weights, benchmark weights, and benchmark returns.
BRINSON_INTERACTION(pw: number[], bw: number[], pr: number[], br: number[]) → number	number	Grid extension. Returns Brinson interaction effect.
BRINSON_SELECTION(bw: number[], pr: number[], br: number[]) → number	number	Grid extension. Returns Brinson selection effect.
BS_CHARM(spot: number, strike: number, time: number, rate: number, volatility: number, option_type: string, dividend: number) → number	number	Grid extension. Returns finite-difference Black-Scholes charm, the sensitivity of delta to time.
BS_DELTA(spot: number, strike: number, time: number, rate: number, volatility: number, option_type: string, dividend: number) → number	number	Grid extension. Returns Black-Scholes option delta for a call or put.
BS_GAMMA(spot: number, strike: number, time: number, rate: number, volatility: number, option_type: string, dividend: number) → number	number	Grid extension. Returns Black-Scholes option gamma.
BS_IMPLIED_VOL(option_price: number, spot: number, strike: number, time: number, rate: number, option_type: string, dividend: number) → number	number	Grid extension. Returns Black-Scholes implied volatility using bisection.
BS_PDE_PRICE(spot: number, strike: number, time: number, rate: number, volatility: number, option_type: string, dividend: number, exercise: string, nx: number, nt: number) → number	number	Grid extension. Prices a vanilla option on the Black-Scholes PDE (Crank-Nicolson in S-space with Rannacher start-up steps). The first seven arguments mirror BLACK_SCHOLES; exercise is "european" (default) or "american" (projected Crank-Nicolson — early exercise, which the closed form cannot price). nx and nt control the spatial and time grid (defaults 201 and 200).
BS_RHO(spot: number, strike: number, time: number, rate: number, volatility: number, option_type: string, dividend: number) → number	number	Grid extension. Returns Black-Scholes option rho for a call or put per 1.00 change in rates.
BS_THETA(spot: number, strike: number, time: number, rate: number, volatility: number, option_type: string, dividend: number) → number	number	Grid extension. Returns annual Black-Scholes option theta for a call or put.
BS_VANNA(spot: number, strike: number, time: number, rate: number, volatility: number, option_type: string, dividend: number) → number	number	Grid extension. Returns finite-difference Black-Scholes vanna, the sensitivity of delta to volatility.
BS_VEGA(spot: number, strike: number, time: number, rate: number, volatility: number, option_type: string, dividend: number) → number	number	Grid extension. Returns Black-Scholes option vega per 1.00 change in volatility.
BS_VOLGA(spot: number, strike: number, time: number, rate: number, volatility: number, option_type: string, dividend: number) → number	number	Grid extension. Returns finite-difference Black-Scholes volga, the sensitivity of vega to volatility.
BUCKETED_DV01(durations: number[], price: number, notional: number) → array	array	Grid extension. Returns bucketed DV01 vector from bucket durations, price, and notional.
CAGR(begin_value: number, end_value: number, years: number) → number	number	Grid extension. Returns compound annual growth rate from a beginning value, ending value, and year count.
CALLABLE_BOND_PRICE(straight_bond_price: number, call_option_value: number) → number	number	Grid extension. Returns callable bond price as straight bond price minus option value.
CALMAR_RATIO(returns: number[], equity_curve: number[], periods_per_year: number) → number	number	Grid extension. Returns annualized return divided by maximum drawdown.
CAPITAL_RATIO(capital: number, rwa: number) → number	number	Grid extension. Returns capital divided by risk-weighted assets.
CDO_TRANCHE_LOSS(portfolio_loss: number, attachment: number, detachment: number, notional: number) → number	number	Grid extension. Returns tranche loss amount for portfolio loss, attachment, detachment, and notional.
CDS_SPREAD(hazard_rate: number, lgd: number) → number	number	Grid extension. Returns approximate CDS spread from hazard rate and loss given default.
CDS_UPFRONT(market_spread: number, coupon_spread: number, duration: number, notional: number) → number	number	Grid extension. Returns upfront CDS value from spread difference, duration, and notional.
CIR_BOND_PRICE(rate: number, kappa: number, theta: number, sigma: number, time: number) → number	number	Grid extension. Returns zero-coupon bond price under the Cox-Ingersoll-Ross model.
COMPONENT_VAR(weights: number[], covariance: number[], confidence: number, portfolio_value: number) → array	array	Grid extension. Returns component VaR contribution for each asset.
CONCENTRATION_RATIO(weights: number[], top_n: number) → number	number	Grid extension. Returns top-N portfolio concentration ratio.
CONTRIBUTION_TO_RETURN(weights: number[], returns: number[]) → array	array	Grid extension. Returns asset contribution-to-return vector from weights and returns.
CONTRIBUTION_TO_RISK(weights: number[], covariance: number[]) → array	array	Grid extension. Returns asset contribution-to-risk vector from weights and covariance matrix.
CONVEXITY(cash_flows: number[], yield_rate: number, periods_per_year: number) → number	number	Grid extension. Returns cash-flow convexity for evenly spaced periods.
CORRELATION_MATRIX(matrix: number[]) → array	array	Grid extension. Returns correlation matrix for asset-return columns.
COUPDAYBS(settlement: date, maturity: date, frequency: number, basis: number) → number	number	Returns the number of days from the beginning of the coupon period to settlement.
COUPDAYS(settlement: date, maturity: date, frequency: number, basis: number) → number	number	Returns the number of days in the coupon period containing the settlement date.
COUPDAYSNC(settlement: date, maturity: date, frequency: number, basis: number) → number	number	Returns the number of days from settlement to the next coupon date.
COUPNCD(settlement: date, maturity: date, frequency: number, basis: number) → date	date	Returns the next coupon date after the settlement date.
COUPNUM(settlement: date, maturity: date, frequency: number, basis: number) → number	number	Returns the number of coupons payable between settlement and maturity.
COUPPCD(settlement: date, maturity: date, frequency: number, basis: number) → date	date	Returns the previous coupon date before the settlement date.
COVARIANCE_MATRIX(matrix: number[]) → array	array	Grid extension. Returns sample covariance matrix for asset-return columns.
CREDIT_SPREAD(pd: number, lgd: number) → number	number	Grid extension. Returns approximate credit spread from probability of default and loss given default.
CREDIT_VAR(expected_loss: number, unexpected_loss: number, confidence: number) → number	number	Grid extension. Returns normal approximation credit VaR from expected loss, unexpected loss, and confidence.
CRYSTALLIZATION_FEE(current_nav: number, high_water_mark: number, shares: number, fee_rate: number) → number	number	Grid extension. Returns crystallized incentive fee above the high-water mark.
CS01(spread_duration: number, price: number, notional: number) → number	number	Grid extension. Returns credit spread value of one basis point from spread duration, price, and notional.
CUMIPMT(rate: number, nper: number, pv: number, start_period: number, end_period: number) → number	number	Returns the cumulative interest paid between two periods.
CUMPRINC(rate: number, nper: number, pv: number, start_period: number, end_period: number) → number	number	Returns the cumulative principal paid between two periods.
CVA(exposures: number[], pds: number[], lgds: number[], dfs: number[]) → number	number	Grid extension. Returns credit valuation adjustment from exposure, default probability, LGD, and discount-factor vectors.
CVAR_HISTORICAL(returns: number[], confidence: number) → number	number	Grid extension. Returns historical conditional value-at-risk as average tail loss beyond VaR.
DB(cost: number, salvage: number, life: number, period: number, month: number) → number	number	Returns fixed-declining balance depreciation.
DDB(cost: number, salvage: number, life: number, period: number, factor: number) → number	number	Returns double-declining balance depreciation for a specific period.
DEFAULT_CORRELATION(left: number[], right: number[]) → number	number	Grid extension. Returns default indicator correlation from paired default series.
DELTA_GAMMA_VAR(delta: number, gamma: number, spot: number, volatility: number, confidence: number) → number	number	Grid extension. Returns delta-gamma VaR approximation for one underlying.
DIGITAL_OPTION(spot: number, strike: number, time: number, rate: number, volatility: number, option_type: string, payout: number, dividend: number) → number	number	Grid extension. Returns Black-Scholes cash-or-nothing digital option price.
DISC(settlement: date, maturity: date, pr: number, redemption: number, basis: number) → number	number	Returns the discount rate for a security.
DISCOUNT_FACTOR(rate: number, years: number, frequency: number) → number	number	Grid extension. Returns discount factor for a rate and year fraction.
DIVERSIFICATION_RATIO(weights: number[], covariance: number[]) → number	number	Grid extension. Returns weighted average asset volatility divided by portfolio volatility.
DOLLARDE(frac_dollar: number, fraction: number) → number	number	Converts a dollar price from fraction to decimal.
DOLLARFR(dec_dollar: number, fraction: number) → number	number	Converts a dollar price from decimal to fraction.
DOWNSIDE_DEVIATION(returns: number[], target_rate: number, periods_per_year: number) → number	number	Grid extension. Returns annualized downside deviation below a target return.
DRAWDOWN_DURATION(values: number[]) → number	number	Grid extension. Returns longest number of consecutive observations below prior peak.
DURATION(settlement: date, maturity: date, coupon: number, yld: number, frequency: number, basis: number) → number	number	Returns the Macaulay duration of a security with periodic interest payments.
DURATION_KEY_RATE(price_down: number, price_up: number, base_price: number, shock: number) → number	number	Grid extension. Returns key-rate duration from down-shock price, up-shock price, base price, and shock size.
DV01(modified_duration: number, price: number, notional: number) → number	number	Grid extension. Returns dollar value of a one-basis-point yield move from modified duration, price, and notional.
DVA(exposures: number[], pds: number[], lgds: number[], dfs: number[]) → number	number	Grid extension. Returns debit valuation adjustment from liability exposure, own default probability, LGD, and discount factors.
EAD(drawn: number, undrawn: number, ccf: number) → number	number	Grid extension. Returns exposure at default from drawn amount, undrawn amount, and credit conversion factor.
ECONOMIC_CAPITAL(unexpected_loss: number, multiplier: number, expected_loss: number) → number	number	Grid extension. Returns economic capital as unexpected loss times confidence multiplier minus expected loss.
EFFECT(nominal: number, npery: number) → number	number	Returns the effective annual interest rate.
EFFICIENT_FRONTIER(expected_returns: number[], covariance: number[], points: number) → array	array	Grid extension. Returns simple two-fund frontier points between min-variance and max-return portfolios.
EWMA_COVARIANCE(left: number[], right: number[], lambda: number) → number	number	Grid extension. Returns EWMA covariance between two return series.
EWMA_VOLATILITY(returns: number[], lambda: number, periods: number) → number	number	Grid extension. Returns EWMA volatility for returns.
EXPECTED_LOSS(pd: number, lgd: number, ead: number) → number	number	Grid extension. Returns expected credit loss as PD × LGD × EAD.
EXPECTED_SHORTFALL(returns: number[], confidence: number, periods: number) → number	number	Grid extension. Returns parametric expected shortfall as a positive loss decimal.
EXPOSURE(quantity: number, price: number, multiplier: number) → number	number	Grid extension. Returns market exposure as quantity times price times multiplier.
FACTOR_EXPOSURE(exposure_matrix: number[], weights: number[]) → array	array	Grid extension. Returns portfolio factor exposures from an asset-by-factor exposure matrix and weights.
FACTOR_RETURN_ATTRIBUTION(factor_exposures: number[], factor_returns: number[]) → array	array	Grid extension. Returns factor return contribution vector from factor exposures and factor returns.
FILL_RATE(filled_quantity: number, ordered_quantity: number) → number	number	Grid extension. Returns filled quantity divided by ordered quantity.
FORWARD_DELTA(spot_delta: number, dividend_yield: number, time: number) → number	number	Grid extension. Returns forward delta from spot delta, dividend yield, and time.
FORWARD_RATE(start_rate: number, end_rate: number, start_years: number, end_years: number) → number	number	Grid extension. Returns implied forward rate between two zero rates.
FRA_RATE(start_df: number, end_df: number, year_fraction: number) → number	number	Grid extension. Returns forward-rate-agreement rate from two discount factors.
FUTURES_MARGIN(contracts: number, contract_value: number, margin_rate: number) → number	number	Grid extension. Returns futures margin requirement from contracts, contract value, and margin rate.
FV(rate: number, nper: number, pmt: number, pv: number) → number	number	Returns the future value of an investment.
FVA(funding_exposure: number, funding_spread: number, years: number) → number	number	Grid extension. Returns funding valuation adjustment approximation.
FVSCHEDULE(principal: number, schedule: number[]) → number	number	Returns the future value of an initial principal after applying a series of rates.
GAUSSIAN_COPULA_DEFAULTS(default_probabilities: number[], asset_correlation: number, systemic_shock: number) → array	array	Grid extension. Returns deterministic one-factor Gaussian copula default indicators for a systemic shock.
HAZARD_RATE(default_probability: number, years: number) → number	number	Grid extension. Returns constant hazard rate implied by cumulative default probability and years.
HERFINDAHL_INDEX(weights: number[]) → number	number	Grid extension. Returns Herfindahl-Hirschman concentration index.
HIGH_WATER_MARK(previous_hwm: number, current_nav: number) → number	number	Grid extension. Returns updated high-water mark.
HIT_RATE(values: number[]) → number	number	Grid extension. Returns fraction of trades or periods with positive PnL.
HJM_FORWARD_RATE(current_forward: number, drift: number, volatility: number, shock: number, dt: number) → number	number	Grid extension. Returns a one-step HJM forward-rate scenario.
IMPLEMENTATION_SHORTFALL(decision_price: number, execution_price: number, quantity: number, side: number) → number	number	Grid extension. Returns implementation shortfall for an order.
INFORMATION_RATIO(asset_returns: number[], benchmark_returns: number[], periods_per_year: number) → number	number	Grid extension. Returns annualized information ratio from active returns versus a benchmark.
INTRATE(settlement: date, maturity: date, investment: number, redemption: number, basis: number) → number	number	Returns the interest rate for a fully invested security.
IPMT(rate: number, per: number, nper: number, pv: number) → number	number	Returns the interest payment for a given period.
IRR(...values: number[]) → number	number	variadic. Returns the internal rate of return for a series of cash flows.
ISPMT(rate: number, per: number, nper: number, pv: number) → number	number	Returns the interest paid during a specific period (simple interest method).
KEY_RATE_DV01(durations: number[], price: number, notional: number) → array	array	Grid extension. Returns key-rate DV01 vector from bucket durations, price, and notional.
KVA(economic_capital: number, capital_cost: number, years: number, discount_rate: number) → number	number	Grid extension. Returns capital valuation adjustment approximation.
LEVERAGE(gross_exposure: number, equity: number) → number	number	Grid extension. Returns gross exposure divided by equity.
LGD(recovery_rate: number) → number	number	Grid extension. Returns loss given default from a recovery rate.
LIQUIDITY_HAIRCUT(value: number, haircut: number) → number	number	Grid extension. Returns liquidity-adjusted value after applying a haircut.
LMM_FORWARD_RATE(forward: number, volatility: number, shock: number, dt: number) → number	number	Grid extension. Returns a lognormal Libor market model forward-rate scenario.
LOGRETURN(begin_value: number, end_value: number) → number	number	Grid extension. Returns the continuously compounded return between two prices.
MANAGEMENT_FEE(aum: number, annual_fee_rate: number, year_fraction: number) → number	number	Grid extension. Returns prorated management fee.
MARGINAL_VAR(weights: number[], covariance: number[], confidence: number, portfolio_value: number) → array	array	Grid extension. Returns marginal contribution to parametric portfolio VaR for each asset.
MARGIN_REQUIREMENT(exposure: number, margin_rate: number) → number	number	Grid extension. Returns margin requirement from exposure and margin rate.
MARKET_IMPACT(execution_price: number, arrival_price: number, side: number) → number	number	Grid extension. Returns market impact as execution price minus arrival price adjusted for side.
MAX_DRAWDOWN(values: number[]) → number	number	Grid extension. Returns the largest peak-to-trough loss in a price or equity curve as a positive decimal.
MAX_SHARPE_WEIGHTS(expected_returns: number[], covariance: number[], risk_free_rate: number) → array	array	Grid extension. Returns long-only excess-return over variance approximation weights.
MDURATION(settlement: date, maturity: date, coupon: number, yld: number, frequency: number, basis: number) → number	number	Returns the modified Macaulay duration.
MIN_VARIANCE_WEIGHTS(covariance: number[]) → array	array	Grid extension. Returns inverse-variance minimum-variance approximation weights.
MIRR(values: number[], finance_rate: number, reinvest_rate: number) → number	number	variadic. Returns the modified internal rate of return.
MVA(initial_margin: number, funding_spread: number, years: number) → number	number	Grid extension. Returns margin valuation adjustment approximation.
NAV(assets: number, liabilities: number, shares: number) → number	number	Grid extension. Returns net asset value.
NOMINAL(effect_rate: number, npery: number) → number	number	Returns the nominal annual interest rate.
NPER(rate: number, pmt: number, pv: number, fv: number) → number	number	Returns the number of periods for an investment.
NPV(rate: number, ...value: number[]) → number	number	variadic. Returns the net present value of a series of cash flows.
OAS(cash_flows: number[], spot_rates: number[], price: number, option_value: number) → number	number	Grid extension. Returns option-adjusted spread using price net of option value.
ODDFPRICE(settlement: date, maturity: date, issue: date, first_coupon: date, rate: number, yld: number, redemption: number, frequency: number) → number	number	Returns the price of a security with an odd first period.
ODDFYIELD(settlement: date, maturity: date, issue: date, first_coupon: date, rate: number, pr: number, redemption: number, frequency: number) → number	number	Returns the yield of a security with an odd first period (Newton's method).
ODDLPRICE(settlement: date, maturity: date, last_interest: date, rate: number, yld: number, redemption: number, frequency: number) → number	number	Returns the price of a security with an odd last period.
ODDLYIELD(settlement: date, maturity: date, last_interest: date, rate: number, pr: number, redemption: number, frequency: number) → number	number	Returns the yield of a security with an odd last period.
OMEGA_RATIO(returns: number[], threshold: number) → number	number	Grid extension. Returns the ratio of gains above a threshold to losses below it.
OPTION_ELASTICITY(delta: number, spot: number, option_price: number) → number	number	Grid extension. Returns option elasticity, also known as omega.
OPTION_INTRINSIC(spot: number, strike: number, option_type: string) → number	number	Grid extension. Returns intrinsic value of a call or put.
OPTION_TIME_VALUE(option_price: number, spot: number, strike: number, option_type: string) → number	number	Grid extension. Returns option market price minus intrinsic value.
ORDER_BOOK_IMBALANCE(bid_size: number, ask_size: number) → number	number	Grid extension. Returns order-book imbalance from bid and ask sizes.
PAR_RATE(discount_factors: number[], frequency: number) → number	number	Grid extension. Returns par coupon rate from discount factors.
PD(credit_spread: number, recovery_rate: number) → number	number	Grid extension. Returns probability of default from a credit spread and recovery rate.
PDURATION(rate: number, pv: number, fv: number) → number	number	Returns the number of periods for an investment to reach a specified value.
PERFORMANCE_ATTRIBUTION_TABLE(pw: number[], bw: number[], pr: number[], br: number[]) → array	array	Grid extension. Returns allocation, selection, interaction, and total Brinson attribution effects.
PERFORMANCE_FEE(nav: number, high_water_mark: number, hurdle: number, fee_rate: number) → number	number	Grid extension. Returns performance fee above hurdle and high-water mark.
PMT(rate: number, periods: number, principal: number) → number	number	Calculates a loan payment amount.
PNL(quantity: number, entry_price: number, exit_price: number) → number	number	Grid extension. Returns position profit and loss.
PORTFOLIO_BETA(weights: number[], betas: number[]) → number	number	Grid extension. Returns weighted portfolio beta from weights and asset betas.
PORTFOLIO_RETURN(weights: number[], returns: number[]) → number	number	Grid extension. Returns weighted portfolio return from weights and asset returns.
PORTFOLIO_VOLATILITY(weights: number[], covariance: number[], periods_per_year: number) → number	number	Grid extension. Returns portfolio volatility from weights and a covariance matrix.
PPMT(rate: number, per: number, nper: number, pv: number) → number	number	Returns the principal payment for a given period.
PRICE(settlement: date, maturity: date, rate: number, yld: number, redemption: number, frequency: number) → number	number	Returns the price per $100 face value of a security that pays periodic interest.
PRICEDISC(settlement: date, maturity: date, discount: number, redemption: number, basis: number) → number	number	Returns the price per $100 face value for a discounted security.
PRICEMAT(settlement: date, maturity: date, issue: date, rate: number, yld: number, basis: number) → number	number	Returns the price per $100 face value for a security that pays at maturity.
PROFIT_FACTOR(values: number[]) → number	number	Grid extension. Returns gross profits divided by gross losses.
PUT_CALL_PARITY(spot: number, strike: number, time: number, rate: number, dividend: number) → number	number	Grid extension. Returns call-minus-put value implied by put-call parity.
PV(rate: number, nper: number, pmt: number, fv: number) → number	number	Returns the present value of an investment.
PV01(modified_duration: number, price: number, notional: number) → number	number	Grid extension. Returns present value of a one-basis-point yield move.
RATE(nper: number, pmt: number, pv: number, fv: number) → number	number	Returns the interest rate per period (Newton's method approximation).
REALIZED_PNL(closed_quantity: number, average_cost: number, sale_price: number) → number	number	Grid extension. Returns realized PnL for closed quantity.
REALIZED_VARIANCE(returns: number[], periods_per_year: number) → number	number	Grid extension. Returns annualized realized variance from periodic returns.
REALIZED_VOL(returns: number[], periods_per_year: number) → number	number	Grid extension. Returns annualized realized volatility from periodic returns.
RECEIVED(settlement: date, maturity: date, investment: number, discount: number, basis: number) → number	number	Returns the amount received at maturity for a fully invested security.
REDEMPTION_NAV(shares: number, nav_per_share: number, fee_rate: number) → number	number	Grid extension. Returns redemption cash from shares, NAV, and redemption fee rate.
RISK_PARITY_WEIGHTS(covariance: number[]) → array	array	Grid extension. Returns inverse-volatility risk-parity approximation weights.
ROLLING_BETA(asset_returns: number[], benchmark_returns: number[], window: number) → array	array	Grid extension. Returns rolling beta versus benchmark returns.
ROLLING_SHARPE(returns: number[], risk_free_rate: number, periods_per_year: number, window: number) → array	array	Grid extension. Returns rolling annualized Sharpe ratio.
RRI(nper: number, pv: number, fv: number) → number	number	Returns an equivalent interest rate for growth of an investment.
RWA(exposure: number, risk_weight: number) → number	number	Grid extension. Returns risk-weighted assets from exposure and risk weight.
SABR_CALIBRATE(atm_vol: number, forward: number, beta: number) → number	number	Grid extension. Returns SABR alpha implied by ATM volatility, forward rate, and beta.
SABR_VOL(forward: number, strike: number, time: number, alpha: number, beta: number, rho: number, nu: number) → number	number	Grid extension. Returns Hagan lognormal SABR implied volatility approximation.
SCENARIO_PNL(exposures: number[], shocks: number[]) → number	number	Grid extension. Returns scenario PnL as exposure vector dotted with shock vector.
SHARPE(returns: number[], risk_free_rate: number, periods_per_year: number) → number	number	Grid extension. Returns the annualized Sharpe ratio for periodic returns, using an annual risk-free rate.
SIDE_POCKET_NAV(total_assets: number, side_pocket_assets: number, shares: number) → number	number	Grid extension. Returns liquid NAV after separating side-pocket assets.
SLIPPAGE(execution_price: number, benchmark_price: number, side: number) → number	number	Grid extension. Returns execution slippage as signed price difference times side.
SLN(cost: number, salvage: number, life: number) → number	number	Returns straight-line depreciation for one period.
SORTINO(returns: number[], target_rate: number, periods_per_year: number) → number	number	Grid extension. Returns the annualized Sortino ratio using downside deviation below the annual target return.
SPAN_MARGIN(scenario_pnl: number[], add_on: number) → number	number	Grid extension. Returns SPAN-style margin as worst scenario loss plus add-on.
SPREAD_DURATION(price_down: number, price_up: number, base_price: number, shock: number) → number	number	Grid extension. Returns spread duration from down-spread price, up-spread price, base price, and spread shock.
STRESS_TEST(values: number[], shocks: number[]) → array	array	Grid extension. Returns stressed values after applying percentage shocks.
SUBSCRIPTION_NAV(cash_amount: number, nav_per_share: number, fee_rate: number) → number	number	Grid extension. Returns subscription shares from cash amount, NAV, and subscription fee rate.
SURVIVAL_PROBABILITY(hazard_rate: number, years: number) → number	number	Grid extension. Returns survival probability for a constant hazard rate over years.
SVI_VOL(log_moneyness: number, a: number, b: number, rho: number, m: number, sigma: number) → number	number	Grid extension. Returns SVI implied volatility from log-moneyness and SVI parameters.
SWAP_RATE(discount_factors: number[], frequency: number) → number	number	Grid extension. Returns fixed swap rate from discount factors.
SYD(cost: number, salvage: number, life: number, period: number) → number	number	Returns sum-of-years-digits depreciation for a specific period.
TBILLEQ(settlement: date, maturity: date, discount: number) → number	number	Returns the bond-equivalent yield for a Treasury bill.
TBILLPRICE(settlement: date, maturity: date, discount: number) → number	number	Returns the price per $100 face value for a Treasury bill.
TBILLYIELD(settlement: date, maturity: date, pr: number) → number	number	Returns the yield for a Treasury bill.
TRACKING_ERROR(asset_returns: number[], benchmark_returns: number[], periods_per_year: number) → number	number	Grid extension. Returns annualized tracking error between portfolio and benchmark returns.
TREYNOR_RATIO(returns: number[], beta: number, risk_free_rate: number, periods_per_year: number) → number	number	Grid extension. Returns annualized excess return per unit of beta.
TURNOVER(traded_value: number, average_assets: number) → number	number	Grid extension. Returns portfolio turnover as traded value divided by average assets.
TWAP(prices: number[]) → number	number	Grid extension. Returns time-weighted average price.
UNEXPECTED_LOSS(pd: number, lgd: number, ead: number) → number	number	Grid extension. Returns unexpected credit loss for a Bernoulli default model.
UNREALIZED_PNL(open_quantity: number, average_cost: number, mark_price: number) → number	number	Grid extension. Returns unrealized PnL for open quantity.
VAR_HISTORICAL(returns: number[], confidence: number) → number	number	Grid extension. Returns historical value-at-risk as a positive loss decimal for a confidence level.
VAR_MONTE_CARLO(returns: number[], confidence: number, periods: number, scenarios: number) → number	number	Grid extension. Returns deterministic scenario value-at-risk from normal shocks calibrated to historical returns.
VAR_PARAMETRIC(returns: number[], confidence: number, periods: number) → number	number	Grid extension. Returns normal parametric value-at-risk as a positive loss decimal.
VASICEK_BOND_PRICE(rate: number, kappa: number, theta: number, sigma: number, time: number) → number	number	Grid extension. Returns zero-coupon bond price under the Vasicek short-rate model.
VDB(cost: number, salvage: number, life: number, start_period: number, end_period: number, factor: number) → number	number	Returns variable declining balance depreciation for any period.
VOLATILITY(returns: number[], periods_per_year: number) → number	number	Grid extension. Returns annualized sample volatility for a series of periodic returns.
VWAP(prices: number[], volumes: number[]) → number	number	Grid extension. Returns volume-weighted average price.
WIN_LOSS_RATIO(values: number[]) → number	number	Grid extension. Returns average win divided by average loss.
XIRR(values: number[], ...dates: date[]) → number	number	variadic. Returns IRR for cash flows at irregular intervals (Newton's method).
XNPV(rate: number, values: number[], dates: date[]) → number	number	Returns NPV for cash flows at irregular intervals.
YIELD(settlement: date, maturity: date, rate: number, pr: number, redemption: number, frequency: number) → number	number	Returns the yield on a security that pays periodic interest (Newton's method).
YIELDDISC(settlement: date, maturity: date, pr: number, redemption: number, basis: number) → number	number	Returns the annual yield for a discounted security.
YIELDMAT(settlement: date, maturity: date, issue: date, rate: number, pr: number, basis: number) → number	number	Returns the annual yield for a security that pays at maturity.
YIELD_TO_WORST(yield_to_maturity: number, call_yields: number[]) → number	number	Grid extension. Returns the lowest candidate yield from yield-to-maturity and call yields.
ZERO_RATE(discount_factor: number, years: number) → number	number	Grid extension. Returns continuously compounded zero rate from a discount factor.
Z_SPREAD(cash_flows: number[], spot_rates: number[], price: number) → number	number	Grid extension. Returns the constant spread over spot rates that prices cash flows.

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Statistical

Descriptive statistics, distributions, regression, and hypothesis tests.

Function count: 148.

Function	Returns	Notes
AVEDEV(...values: number[]) → number	number	variadic. Returns the average of the absolute deviations from the mean.
BERNOULLI(p: number) → number	number	Grid extension. Declares a Bernoulli uncertainty source and returns its probability point estimate on the normal lane.
BETA.DIST(x: number, alpha: number, beta: number, cumulative: boolean) → number	number	Beta distribution (Excel 2010+).
BETA.INV(p: number, alpha: number, beta: number) → number	number	Inverse beta (Excel 2010+).
BETADIST(x: number, alpha: number, beta: number) → number	number	Returns the beta distribution CDF.
BETAINV(p: number, alpha: number, beta: number) → number	number	Returns the inverse of the beta distribution CDF.
BETA_DISTRIBUTION(alpha: number, beta: number) → number	number	Grid extension. Declares a beta-distributed uncertainty source and returns its mean point estimate on the normal lane.
BINOM.DIST(s: number, n: number, p: number, cumulative: boolean) → number	number	Binomial distribution (Excel 2010+).
BINOM.INV(trials: number, prob: number, alpha: number) → number	number	Inverse binomial (Excel 2010+).
BINOMDIST(s: number, n: number, p: number, cumulative: boolean) → number	number	Returns the binomial distribution probability.
CHIDIST(x: number, df: number) → number	number	Returns the right-tailed chi-squared distribution.
CHIINV(p: number, df: number) → number	number	Returns the inverse of the right-tailed chi-squared distribution.
CHISQ.DIST(x: number, df: number, cumulative: boolean) → number	number	Chi-squared CDF (Excel 2010+).
CHISQ.DIST.RT(x: number, df: number) → number	number	Right-tailed chi-squared (Excel 2010+).
CHISQ.INV(p: number, df: number) → number	number	Inverse chi-squared left-tailed (Excel 2010+).
CHISQ.INV.RT(p: number, df: number) → number	number	Inverse chi-squared right-tailed (Excel 2010+).
CHISQ.TEST(observed: number[], expected: number[]) → number	number	Returns the chi-squared test p-value for independence.
CONFIDENCE(alpha: number, stdev: number, size: number) → number	number	Returns the confidence interval for a population mean.
CONFIDENCE.NORM(alpha: number, stdev: number, size: number) → number	number	Confidence interval using normal distribution (Excel 2010+).
CONFIDENCE.T(alpha: number, stdev: number, size: number) → number	number	Confidence interval using t-distribution (Excel 2010+).
CONFIDENCE_BAND(cell: number, level: number) → array	array	Grid extension. Central confidence interval of an uncertain cell at the given level (0, 1), spilled as a 1x2 [low, high] array.
CONF_HIGH(cell: number, level: number) → number	number	Grid extension. Upper endpoint of an uncertain cell's central confidence interval at the given level (0, 1).
CONF_LOW(cell: number, level: number) → number	number	Grid extension. Lower endpoint of an uncertain cell's central confidence interval at the given level (0, 1).
CORREL(arr_x: number[], arr_y: number[]) → number	number	Returns the Pearson correlation coefficient between two data sets.
COVAR(arr_x: number[], arr_y: number[]) → number	number	Returns the covariance between two data sets.
COVARIANCE.P(x: number[], y: number[]) → number	number	Population covariance (Excel 2010+ alias).
COVARIANCE.S(x: number[], y: number[]) → number	number	Sample covariance (Excel 2010+ alias).
CRITBINOM(trials: number, prob: number, alpha: number) → number	number	Returns the smallest value for which the cumulative binomial distribution >= criterion.
DEVSQ(...values: number[]) → number	number	variadic. Returns the sum of squares of deviations from the mean.
EXPECTED(cell: number) → number	number	Grid extension. Expected (mean) value of an uncertain cell after propagating declared uncertainty sources through its dependency cone.
EXPON.DIST(x: number, lambda: number, cumulative: boolean) → number	number	Exponential distribution (Excel 2010+).
EXPONDIST(x: number, lambda: number, cumulative: boolean) → number	number	Returns the exponential distribution.
F.DIST(x: number, df1: number, df2: number, cumulative: boolean) → number	number	F-distribution CDF or PDF (Excel 2010+).
F.DIST.RT(x: number, df1: number, df2: number) → number	number	Right-tailed F-distribution (Excel 2010+).
F.INV(p: number, df1: number, df2: number) → number	number	Inverse F-distribution left-tailed (Excel 2010+).
F.INV.RT(p: number, df1: number, df2: number) → number	number	Inverse F-distribution right-tailed (Excel 2010+).
F.TEST(arr1: number[], arr2: number[]) → number	number	Returns the p-value from an F-test for equality of variances.
FDIST(x: number, df1: number, df2: number) → number	number	Returns the right-tailed F-distribution.
FINV(p: number, df1: number, df2: number) → number	number	Returns the inverse of the right-tailed F-distribution.
FISHER(x: number) → number	number	Returns the Fisher transformation.
FISHERINV(y: number) → number	number	Returns the inverse of the Fisher transformation.
FORECAST(x: number, known_ys: number[], known_xs: number[]) → number	number	Predicts a future value using linear regression.
FORECAST.LINEAR(x: number, known_ys: number[], known_xs: number[]) → number	number	Linear forecast (Excel 2016+ alias).
FORECAST_ETS(target_date: number, values: number[], timeline: number[], seasonality: number, data_completion: number, aggregation: number) → number	number	aliases: FORECAST.ETS. Predicts a future value using exponential smoothing (Holt-Winters additive model).
FORECAST_ETS_CONFINT(number: number, number_2: number[], number_3: number[], number_4: number, number_5: number, number_6: number, number_7: number) → number	number	aliases: FORECAST.ETS.CONFINT. Returns the confidence interval for a FORECAST.ETS prediction.
FORECAST_ETS_SEASONALITY(values: number[], timeline: number[]) → number	number	aliases: FORECAST.ETS.SEASONALITY. Returns the detected seasonality period for FORECAST.ETS.
FORECAST_ETS_STAT(number: number[], number_2: number[], number_3: number, number_4: number) → number	number	aliases: FORECAST.ETS.STAT. Returns ETS model statistics (alpha, beta, gamma, MASE, SMAPE, MAE, RMSE).
FREQUENCY(data: number[], bins: number[]) → array	array	Returns a frequency distribution as an array.
GAMMA.DIST(x: number, alpha: number, beta: number, cumulative: boolean) → number	number	Gamma distribution (Excel 2010+).
GAMMA.INV(p: number, alpha: number, beta: number) → number	number	Inverse gamma (Excel 2010+).
GAMMADIST(x: number, alpha: number, beta: number, cumulative: boolean) → number	number	Returns the gamma distribution.
GAMMAINV(p: number, alpha: number, beta: number) → number	number	Returns the inverse of the gamma CDF.
GEOMEAN(...values: number[]) → number	number	variadic. Returns the geometric mean.
GROWTH(known_ys: number[], known_xs: number[], new_xs: number[]) → array	array	Returns values along an exponential trend (array output).
HARMEAN(...values: number[]) → number	number	variadic. Returns the harmonic mean.
HYPGEOM.DIST(s: number, n: number, m: number, n_2: number, cumulative: boolean) → number	number	Hypergeometric distribution (Excel 2010+).
HYPGEOMDIST(s: number, n: number, m: number, n_2: number) → number	number	Returns the hypergeometric distribution.
INTERCEPT(ys: number[], xs: number[]) → number	number	Returns the intercept of a linear regression line.
KALMAN.FILTER(observations: array, F: any, H: any, Q: any, R: any, x0: any, P0: any) → array	array	Grid extension. Linear Kalman filter over a time-invariant state-space model x_t = Fx_(t-1) + w, z_t = Hx_t + v with process noise Q and observation noise R. observations is T x p (or a single row/column for univariate series); scalars are accepted wherever a 1 x 1 matrix is meant. Optional x0 (default zeros) and P0 (default a diffuse 1e6 * I; a scalar means that value times I). Returns the T x n filtered state means; observation rows containing NaN are treated as missing ticks (predict-only). Joseph-form covariance updates keep the filter numerically symmetric.
KALMAN.SMOOTH(observations: array, F: any, H: any, Q: any, R: any, x0: any, P0: any) → array	array	Grid extension. Rauch-Tung-Striebel smoother: runs KALMAN.FILTER forward, then a backward pass so every estimate uses the whole series. Same arguments and result shape as KALMAN.FILTER; the smoothed means are strictly better mid-series estimates for retrospective analysis.
KURT(...values: number[]) → number	number	variadic. Returns the kurtosis of a data set.
LARGE(values: number[], k: number) → number	number	Returns the k-th largest value in a data set.
LIKELIHOOD(predicate: boolean) → number	number	Grid extension. Probability that an uncertain cell satisfies a comparison, propagating declared uncertainty sources through its dependency cone (analytic when every source is Normal, seeded Monte Carlo otherwise). Example: LIKELIHOOD(npv < 0).
LINEST(number: number[], number_2: number[], logical: boolean, logical_2: boolean) → array	array	Fits one or more regressors with column-pivoted QR. With statistics enabled, returns the Excel-compatible 5×(k+1) matrix of coefficients, standard errors, R², standard error, F, df, regression SS, and residual SS.
LOGEST(number: number[], number_2: number[], logical: boolean, logical_2: boolean) → array	array	Returns exponential regression statistics as a 5x2 array.
LOGNORM.DIST(x: number, mean: number, stdev: number, cumulative: boolean) → number	number	Log-normal distribution (Excel 2010+).
LOGNORM.INV(p: number, mean: number, stdev: number) → number	number	Inverse log-normal (Excel 2010+).
LOGNORMAL(mu: number, sigma: number) → number	number	Grid extension. Declares a log-normal uncertainty source and returns its mean point estimate on the normal lane.
LOGNORMDIST(x: number, mean: number, stdev: number) → number	number	Returns the log-normal CDF.
MODE(...values: number[]) → number	number	variadic. Returns the most frequently occurring value.
MODE.MULT(...values: number[]) → array	array	variadic. Returns a vertical array of the most frequently occurring values.
MODE.SNGL(...values: number[]) → number	number	variadic. Mode single value (Excel 2010+ alias).
NEGBINOM.DIST(f: number, s: number, p: number, cumulative: boolean) → number	number	Negative binomial (Excel 2010+).
NEGBINOMDIST(f: number, s: number, p: number) → number	number	Returns the negative binomial distribution.
NORM.DIST(x: number, mean: number, stdev: number, cumulative: boolean) → number	number	Normal distribution (Excel 2010+).
NORM.INV(p: number, mean: number, stdev: number) → number	number	Inverse normal (Excel 2010+).
NORM.S.DIST(z: number, cumulative: boolean) → number	number	Standard normal CDF (Excel 2010+).
NORM.S.INV(p: number) → number	number	Inverse standard normal (Excel 2010+).
NORMAL(mean: number, std_dev: number) → number	number	Grid extension. Declares a normal-distributed uncertainty source and returns its point estimate on the normal lane.
NORMDIST(x: number, mean: number, stdev: number, cumulative: boolean) → number	number	Returns the normal distribution CDF or PDF.
NORMINV(p: number, mean: number, stdev: number) → number	number	Returns the inverse of the normal CDF.
NORMSDIST(z: number) → number	number	Returns the standard normal CDF.
NORMSINV(p: number) → number	number	Returns the inverse of the standard normal CDF.
PERCENTILE(values: number[], k: number) → number	number	Returns the k-th percentile of values in a range.
PERCENTILE.EXC(values: number[], k: number) → number	number	Returns the k-th percentile (exclusive).
PERCENTILE.INC(values: number[], k: number) → number	number	Returns the k-th percentile (inclusive, same as PERCENTILE).
PERCENTRANK(values: number[], x: number) → number	number	Returns the rank of a value as a percentage of the data set.
PERCENTRANK.EXC(values: number[], x: number) → number	number	Percent rank exclusive (Excel 2010+).
PERCENTRANK.INC(values: number[], x: number) → number	number	Percent rank inclusive (Excel 2010+).
PERMUTA(n: number, k: number) → number	number	Returns the number of permutations with repetitions.
PERT(min: number, mode: number, max: number, lambda: number) → number	number	Grid extension. Declares a PERT uncertainty source and returns its weighted mean point estimate on the normal lane.
POISSON(x: number, mean: number, cumulative: boolean) → number	number	Returns the Poisson distribution.
POISSON.DIST(x: number, mean: number, cumulative: boolean) → number	number	Poisson distribution (Excel 2010+).
POISSON_DISTRIBUTION(lambda: number) → number	number	Grid extension. Declares a Poisson-distributed uncertainty source and returns its lambda point estimate on the normal lane.
PROB(x_range: number[], prob_range: number[], lower: number, upper: number) → number	number	Returns the probability that values fall within a range.
PROB_ABOVE(cell: number, threshold: number) → number	number	Grid extension. Probability that an uncertain cell exceeds a threshold, propagating declared uncertainty sources through its dependency cone.
PROB_BELOW(cell: number, threshold: number) → number	number	Grid extension. Probability that an uncertain cell falls below a threshold, propagating declared uncertainty sources through its dependency cone.
QUARTILE(values: number[], quart: number) → number	number	Returns the quartile of a data set (0=min, 1=Q1, 2=median, 3=Q3, 4=max).
QUARTILE.EXC(values: number[], quart: number) → number	number	Returns the quartile (exclusive).
QUARTILE.INC(values: number[], quart: number) → number	number	Returns the quartile (inclusive, same as QUARTILE).
RAND_BERNOULLI(p: number) → boolean	boolean	volatile, Grid extension. Sample 0/1 with success probability p.
RAND_BETA(alpha: number, beta: number) → number	number	volatile, Grid extension. Sample from a Beta distribution.
RAND_BINOMIAL(n: number, p: number) → number	number	volatile, Grid extension. Sample a Binomial-distributed count.
RAND_CHOICE(array: array, count: number, replacement: boolean) → any	any	volatile, Grid extension. Random sample from an array (with optional count/replacement).
RAND_EXP(rate: number) → number	number	volatile, Grid extension. Sample from an exponential distribution.
RAND_GAMMA(shape: number, scale: number) → number	number	volatile, Grid extension. Sample from a Gamma distribution.
RAND_LOGNORMAL(mu: number, sigma: number) → number	number	volatile, Grid extension. Sample from a log-normal distribution.
RAND_NORMAL(mean: number, std: number) → number	number	volatile, Grid extension. Sample from a normal distribution.
RAND_POISSON(lambda: number) → number	number	volatile, Grid extension. Sample a Poisson-distributed count.
RAND_SEEDED(seed: number) → number	number	volatile, Grid extension. Deterministic uniform [0,1) given a seed.
RAND_SHUFFLE(array: array) → array	array	volatile, Grid extension. Random permutation of an array.
RAND_TRIANGULAR(min: number, max: number, mode: number) → number	number	volatile, Grid extension. Sample from a triangular distribution.
RAND_UUID() → string	string	volatile, Grid extension. Random RFC 4122 v4 UUID.
RANK(number: number, values: number[], order: number) → number	number	Returns the rank of a number in a list of numbers.
RANK.AVG(number: number, values: number[], order: number) → number	number	Returns the rank of a number, averaging ties.
RANK.EQ(number: number, values: number[], order: number) → number	number	Returns the rank of a number (same as RANK).
RSQ(ys: number[], xs: number[]) → number	number	Returns the R-squared value of a linear regression.
SDE.GBM(s0: number, mu: number, sigma: number, t_end: number, steps: number, paths: number, seed: number) → array	array	Grid extension. Geometric Brownian motion path ensemble dS = muSdt + sigmaSdW, returned as a paths x (steps+1) matrix whose first column is the initial value s0. Stepped exactly in log space so every sample stays positive. Deterministic given the seed (default 0), so scenarios are reproducible and cacheable.
SDE.OU(x0: number, theta: number, mu: number, sigma: number, t_end: number, steps: number, paths: number, seed: number) → array	array	Grid extension. Ornstein-Uhlenbeck mean-reverting path ensemble dx = theta*(mu - x)dt + sigmadW, returned as a paths x (steps+1) matrix. theta is the reversion speed, mu the long-run mean. Deterministic given the seed (default 0).
SKEW(...values: number[]) → number	number	variadic. Returns the skewness of a distribution.
SLOPE(ys: number[], xs: number[]) → number	number	Returns the slope of a linear regression line.
SMALL(values: number[], k: number) → number	number	Returns the k-th smallest value in a data set.
STANDARDIZE(x: number, mean: number, stdev: number) → number	number	Returns a normalized value (z-score).
STDEV(...values: number[]) → number	number	variadic. Estimates standard deviation based on a sample.
STDEV.P(...values: number[]) → number	number	variadic. Population standard deviation (Excel 2010+ alias).
STDEV.S(...values: number[]) → number	number	variadic. Sample standard deviation (Excel 2010+ alias).
STDEVP(...values: number[]) → number	number	variadic. Calculates standard deviation based on the entire population.
STEYX(ys: number[], xs: number[]) → number	number	Returns the standard error of the predicted y-value for each x.
T.DIST(x: number, df: number, cumulative: boolean) → number	number	Student t-distribution (Excel 2010+).
T.DIST.2T(x: number, df: number) → number	number	Two-tailed t-distribution (Excel 2010+).
T.DIST.RT(x: number, df: number) → number	number	Right-tailed t-distribution (Excel 2010+).
T.INV(p: number, df: number) → number	number	Inverse t-distribution left-tailed (Excel 2010+).
T.INV.2T(p: number, df: number) → number	number	Inverse t-distribution two-tailed (Excel 2010+).
T.TEST(arr1: number[], arr2: number[], tails: number, test_type: number) → number	number	Returns the p-value from a Student t-test.
TDIST(x: number, df: number, tails: number) → number	number	Returns the Student t-distribution (two-tailed).
TINV(p: number, df: number) → number	number	Returns the inverse of the two-tailed Student t-distribution.
TREND(known_ys: number[], known_xs: number[], new_xs: number[]) → array	array	Returns values along a linear trend (array output).
TRIANGULAR(low: number, high: number, mode: number) → number	number	Grid extension. Declares a triangular uncertainty source and returns its mean point estimate on the normal lane.
TRIMMEAN(values: number[], percent: number) → number	number	Returns the mean of the interior of a data set, trimming a percentage from both ends.
UNCERTAINTY_SD(cell: number) → number	number	Grid extension. Standard deviation of an uncertain cell after propagating declared uncertainty sources through its dependency cone.
UNIFORM(low: number, high: number) → number	number	Grid extension. Declares a uniform uncertainty source and returns its midpoint point estimate on the normal lane.
VAR(...values: number[]) → number	number	variadic. Estimates variance based on a sample.
VAR.P(...values: number[]) → number	number	variadic. Population variance (Excel 2010+ alias).
VAR.S(...values: number[]) → number	number	variadic. Sample variance (Excel 2010+ alias).
VARP(...values: number[]) → number	number	variadic. Calculates variance based on the entire population.
WEIBULL(x: number, alpha: number, beta: number, cumulative: boolean) → number	number	Returns the Weibull distribution.
WEIBULL.DIST(x: number, alpha: number, beta: number, cumulative: boolean) → number	number	Weibull distribution (Excel 2010+).
Z.TEST(arr: number[], x: number, sigma: number) → number	number	Returns the p-value for a z-test.

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Statistics & Econometrics

Generalized linear models, inequality measures, survey weighting, and econometric inference.

Function count: 15.

Function	Returns	Notes
ATKINSON(values: array, epsilon: number) → number	number	Grid extension. Returns the Atkinson inequality index for a non-negative inequality-aversion epsilon.
CRONBACH_ALPHA(items: array) → number	number	Grid extension. Returns Cronbach's alpha for a finite respondents-by-items matrix with at least two respondents and two items.
DEFF(weights: array) → number	number	Grid extension. Returns Kish's unequal-weighting design effect n*sum(w^2)/sum(w)^2.
FGT(values: array, poverty_line: number, alpha: number) → number	number	Grid extension. Returns the Foster-Greer-Thorbecke poverty index at a positive poverty line and non-negative alpha (default 0).
GINI(values: array) → number	number	Grid extension. Returns the Gini coefficient of finite non-negative observations; unlike the legacy SOCIAL_GINI_COEFFICIENT, negative observations are rejected rather than silently dropped.
LOGIT.FIT(y: array, x: array, intercept: boolean, max_iterations: number, tolerance: number) → object	object	Grid extension. Fits a binomial logistic GLM by IRLS and returns a glm_fit object with coefficients, covariance, standard errors, fitted probabilities, deviance, iterations, and convergence status.
LORENZ(values: array) → array	array	Grid extension. Returns Lorenz-curve [population_share,value_share] rows including the origin.
MOE(standard_error: number, confidence: number) → number	number	Grid extension. Returns a two-sided normal margin of error from a standard error and confidence level (default 0.95).
PROBIT.FIT(y: array, x: array, intercept: boolean, max_iterations: number, tolerance: number) → object	object	Grid extension. Fits a binomial probit GLM by IRLS and returns a glm_fit object with coefficients, covariance, standard errors, fitted probabilities, deviance, iterations, and convergence status.
RAKE(weights: array, categories: array, targets: array, tolerance: number, max_iterations: number) → array	array	Grid extension. Rakes initial survey weights to target margins; category rows align to observations and each target row is [1-based dimension,category,total].
REGRESS(y: array, x: array, covariance: string, covariance_arg: any, intercept: boolean, confidence: number) → object	object	Grid extension. Fits multivariate OLS and returns coefficients, covariance, robust inference, diagnostics, fitted values, and residuals. Covariance may be classical, HC1, clustered, or Newey-West.
REGRESS.TABLE(model: regression, models: regression...) → object	object	variadic, Grid extension. Combines one or more REGRESS results into a publication-style comparison object with coefficients, standard errors, p-values, significance stars, and fit summaries.
SVYMEAN(values: array, weights: array) → number	number	Grid extension. Returns the explicitly weighted survey mean for equal-length value and non-negative weight vectors.
SVYTOTAL(values: array, weights: array) → number	number	Grid extension. Returns the explicitly weighted survey total for equal-length value and non-negative weight vectors.
THEIL(values: array) → number	number	Grid extension. Returns the Theil T inequality index of finite non-negative observations.

---

Economics & Time Series

Economic-series alignment, resampling, lags, and change calculations.

Function count: 9.

Function	Returns	Notes
ASSERT_IDENTITY(left: number|array, right: number|array, absolute_tolerance: number, relative_tolerance: number) → boolean	boolean	Grid extension. Continuously verifies a scalar or series accounting identity, returning an IDENTITY error at the first breach. Scalars broadcast across a series.
TS.ADF(series: object, lags: number, deterministic: string) → object	object	Grid extension. Runs an augmented Dickey-Fuller unit-root diagnostic on a frequency-tagged economic series and returns its specification, statistic, coefficient, standard error, and asymptotic critical values.
TS.ALIGN(left: object, right: object) → object	object	Grid extension. Inner-aligns two economic series by observation date and rejects mixed frequencies until explicitly resampled.
TS.HAMILTON_FILTER(series: object, horizon: number, lags: number) → object	object	Grid extension. Applies Hamilton's forecast-regression filter to annual, quarterly, or monthly data, returning null early estimates instead of backcasts.
TS.HP_FILTER(series: object, lambda: number) → object	object	Grid extension. Decomposes a frequency-tagged series into Hodrick-Prescott trend and cycle using Ravn-Uhlig frequency-aware defaults or an explicit smoothing lambda.
TS.LAG(series: object, periods: number) → object	object	Grid extension. Returns an economic series shifted by a positive number of native-frequency periods.
TS.PCT_CHANGE(series: object, periods: number) → object	object	Grid extension. Returns percentage changes over a positive number of native-frequency periods.
TS.RESAMPLE(series: object, target_frequency: string, aggregation: string) → object	object	Grid extension. Explicitly down-samples an economic series with end-of-period (stock), mean (rate/index), or sum (flow) aggregation; upsampling is rejected.
TS.YOY(series: object) → object	object	Grid extension. Returns year-over-year percentage growth using the series' declared frequency.

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Civic & Elections

Apportionment, ballot tabulation, partisan fairness, and election-analysis helpers.

Function count: 14.

Function	Returns	Notes
APPORTION(votes: array, seats: number, method: string) → array	array	Grid extension. Allocates an integer house size across non-negative vote totals using D'Hondt/Jefferson, Sainte-Laguë/Webster, Hare, Droop, or Huntington-Hill; exact ties go to the earlier input.
APPROVAL_TALLY(ballots: array) → array	array	Grid extension. Counts approvals by candidate column from a rectangular boolean or 0/1 ballot matrix.
BANZHAF(weights: array, quota?: number) → array	array	Grid extension. Returns normalized Penrose-Banzhaf swing power for an integer weighted voting game. Quota defaults to a strict majority; exact dynamic programming supports at most 25 players within a bounded work budget.
BORDA_TALLY(ballots: array, candidate_count: number) → array	array	Grid extension. Computes Borda scores from rows of ordered 1-based candidate ids.
CONDORCET_MATRIX(ballots: array, candidate_count: number) → array	array	Grid extension. Returns the pairwise preference-count matrix for ordered 1-based candidate-id ballots.
EFFICIENCY_GAP(votes_a: array, votes_b: array) → number	number	Grid extension. Returns (wasted votes for A minus wasted votes for B) divided by total two-party district votes.
IRV_TALLY(ballots: array, candidate_count: number) → array	array	Grid extension. Runs instant-runoff voting over ordered candidate-id ballots and returns auditable [round,candidate,total,status] rows; exact elimination ties remove the later input candidate.
LESLIE_PROJECT(population: array, fertility: array, survival: array, periods: number) → array	array	Grid extension. Projects an age-structured population through a Leslie matrix and returns one population row per period, including the initial state.
LIFE_TABLE(qx: array, radix?: number) → array	array	Grid extension. Builds a complete one-year life table from mortality probabilities and returns [age,qx,lx,dx,Lx,Tx,ex] rows. The terminal qx must equal 1; radix defaults to 100000.
MEAN_MEDIAN(shares: array) → number	number	Grid extension. Returns mean district vote share minus median district vote share for shares in [0,1].
NASH_2X2(row_payoffs: array, column_payoffs: array) → object	object	Grid extension. Solves a finite two-player 2x2 normal-form game in closed form, returning a typed object containing all pure equilibria and any strictly interior mixed equilibrium.
PARTISAN_BIAS(shares: array) → number	number	Grid extension. Applies uniform swing to a 50 percent statewide vote and returns seat share minus 0.5.
PLURALITY_TALLY(ballots: array, candidate_count: number) → array	array	Grid extension. Counts first preferences from rows of ordered 1-based candidate ids.
SHAPLEY_SHUBIK(weights: array, quota?: number) → array	array	Grid extension. Returns normalized Shapley-Shubik pivot probabilities for an integer weighted voting game. Quota defaults to a strict majority.

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Algorithmic Game Theory

Finite games, equilibrium certificates, auctions, allocation, and mechanism-design verification.

Function count: 29.

Function	Returns	Notes
GAME.ANALYZE(game: game, options?: object) → object	object	variadic, Grid extension. Exhaustively checks a complete finite normal-form game, returning pure Nash equilibria, unilateral-deviation witnesses, regret, dominance, Pareto, and welfare certificates. The function fails closed when its authored work budget is insufficient.
GAME.AUCTION(auction: single_item_auction) → object	object	variadic, Grid extension. Resolves a deterministic first- or second-price sealed-bid single-item auction with reserve pricing and a complete ranked-bid winner/payment certificate.
GAME.BAYESIAN(game: bayesian_game, options?: object) → object	object	variadic, Grid extension. Finds and independently certifies one mixed Bayesian Nash equilibrium of a complete finite two-player game by bounded type-contingent strategic-form reduction.
GAME.BAYESIAN_FORM(specification: bayesian_game_specification) → object	object	variadic, Grid extension. Validates and types a complete finite two-player Bayesian game with an explicit joint type prior and one payoff row for every type/action profile. Declarative game blocks using bayesian lower through this constructor.
GAME.CONGESTION(game: congestion_game, options?: object) → object	object	variadic, Grid extension. Runs deterministic strict best responses in an atomic congestion game, certifies every Rosenthal-potential decrease, and verifies the final pure Nash profile against every unilateral route change.
GAME.CONGESTION_FORM(specification: congestion_game_specification) → object	object	variadic, Grid extension. Validates and types an atomic congestion game over named resources and load-indexed costs. Declarative game blocks using congestion lower through this constructor.
GAME.COOPERATIVE(game: cooperative_game, options?: object) → object	object	variadic, Grid extension. Computes exact Shapley values for a complete finite transferable-utility game and independently checks efficiency and every coalition constraint for Shapley core membership.
GAME.COOPERATIVE_FORM(specification: cooperative_game_specification) → object	object	variadic, Grid extension. Validates and types a complete finite transferable-utility characteristic-function game. Declarative game blocks using cooperative lower through this constructor.
GAME.CORRELATED(game: game, objective?: string, options?: object) → object	object	variadic, Grid extension. Computes a feasibility or welfare-maximizing correlated equilibrium for a complete finite game and independently verifies every recommendation-deviation inequality.
GAME.EXTENSIVE(game: extensive_form_game, options?: object) → object	object	variadic, Grid extension. Solves a bounded finite perfect-information extensive-form tree by backward induction and returns child-before-parent values plus every local comparison as a subgame-perfect certificate. Shared nodes, cycles, unreachable nodes, and implicit information sets fail closed.
GAME.EXTENSIVE_FORM(specification: extensive_form_specification) → object	object	variadic, Grid extension. Validates and types a bounded finite perfect-information extensive-form tree. Declarative game blocks using the extensive field lower through this constructor without creating a second evaluation lane.
GAME.GRAPHICAL(game: graphical_game, options?: object) → object	object	variadic, Grid extension. Exhaustively finds and certifies every pure Nash equilibrium of a bounded compact graphical game using factor scopes, min-fill ordering, and partial-assignment pruning rather than a global payoff table.
GAME.GRAPHICAL_FORM(specification: graphical_game_specification) → object	object	variadic, Grid extension. Validates and types a compact finite graphical game whose local payoff factors retain their strategic scopes without materializing the global payoff product. Declarative game blocks using graphical lower through this constructor.
GAME.IMPERFECT(game: imperfect_information_game, options?: object) → object	object	variadic, Grid extension. Solves a bounded finite two-player zero-sum perfect-recall imperfect-information game by exact contingent-plan reduction, independently certifies the maximin/minimax equilibrium, and returns realization-equivalent behavioral strategies.
GAME.IMPERFECT_FORM(specification: imperfect_information_specification) → object	object	variadic, Grid extension. Validates and types a finite two-player zero-sum imperfect-information tree with explicit information sets, consistent actions, and perfect recall. Declarative game blocks using the imperfect field lower through this constructor.
GAME.MATCHING_FORM(specification: stable_matching_specification) → object	object	variadic, Grid extension. Validates and types a two-sided strict-preference matching market with possibly incomplete acceptability lists. Declarative game blocks using matching lower through this constructor.
GAME.NASH(game: game, options?: object) → object	object	variadic, Grid extension. Finds a mixed Nash equilibrium of a complete two-player general-sum game by bounded deterministic support enumeration, then directly replays every pure deviation and returns exploitability and support certificates.
GAME.NORMAL_FORM(players: array, strategies: array, payoffs: array) → object	object	variadic, Grid extension. Builds and validates a complete typed finite game from live player, strategy-membership, and payoff relations. Arrays collected from Frame or Graph query results remain ordinary dependencies, so relation edits reactively rebuild downstream analyses.
GAME.STABLE_MATCH(market: stable_matching_market) → object	object	variadic, Grid extension. Computes the proposer-optimal Gale-Shapley matching and independently scans every mutually acceptable pair for a blocking-pair stability certificate.
GAME.STOCHASTIC(game: stochastic_zero_sum_game, options?: object) → object	object	variadic, Grid extension. Solves a finite discounted two-player zero-sum stochastic game with stationary Shapley strategies and returns matrix duality gaps, a Bellman residual, a contraction-derived global value-error bound, and bounded work evidence.
GAME.STOCHASTIC_FORM(specification: stochastic_game_specification) → object	object	variadic, Grid extension. Validates and types a complete finite discounted two-player zero-sum stochastic game with named states, state-local actions, immediate rewards, and explicit transition kernels. Declarative game blocks using stochastic lower through this constructor.
GAME.VERIFY(game: game, claim: game_claim, options?: object) → object	object	variadic, Grid extension. Verifies one declarative finite-game claim—existence or membership of a pure Nash equilibrium, Pareto efficiency, a regret bound, or weak/strict dominance—and returns a uniform passed/status/witness evidence envelope for Predicate and WHY consumption.
GAME.ZERO_SUM(game: game, options?: object) → object	object	variadic, Grid extension. Solves a complete finite two-player zero-sum game through independent maximin and minimax LPs, then verifies both mixed strategies against every pure response and returns a duality-gap certificate.
MECHANISM.AUDIT(mechanism: mechanism, options?: object) → object	object	variadic, Grid extension. Exhaustively audits a complete finite direct-revelation mechanism for DSIC, ex-post IR, no deficit, strong budget balance, and—when a joint prior is supplied—BIC and interim IR, returning concrete counterexample witnesses.
MECHANISM.DIRECT(specification: mechanism_specification) → object	object	variadic, Grid extension. Validates a complete finite direct-revelation mechanism object and returns it with the stable mechanism type tag. Declarative mechanism blocks lower through this constructor.
MECHANISM.VCG(market: vcg_market) → object	object	variadic, Grid extension. Chooses the welfare-maximizing outcome from an explicit finite feasible set and computes one Clarke-pivot externality payment and counterfactual outcome certificate per agent.
MECHANISM.VCG_ASSIGN(market: unit_demand_market) → object	object	variadic, Grid extension. Computes an exact welfare-maximizing unit-demand matching and Clarke-pivot VCG payments, returning one counterfactual-welfare witness per winner plus IR and no-deficit checks.
MECHANISM.VCG_FORM(specification: vcg_market_specification) → object	object	variadic, Grid extension. Validates and types a finite feasible-outcome VCG market with one valuation per agent and outcome. Declarative mechanism blocks using vcg lower through this constructor.
MECHANISM.VERIFY(mechanism: mechanism, property: string, options?: object) → object	object	variadic, Grid extension. Selects DSIC, BIC, ex-post/interim IR, no-deficit, or strong-budget-balance from an exhaustive direct-mechanism audit and returns a uniform passed/status/metric/witness evidence envelope.

---

Information

Type predicates, error inspection, and metadata accessors.

Function count: 45.

Function	Returns	Notes
AREAS(reference: any) → number	number	Returns the number of reference areas. Grid references are single-area, so valid references return 1.
CELL(info_type: string, value: any) → any	any	Returns information about a cell. Supports info_type: address, row, col, type, contents.
ERROR_TYPE(value: any) → number	number	aliases: ERROR.TYPE. Returns a number corresponding to an error type (1=#NULL!, 2=#DIV/0!, 3=#VALUE!, 4=#REF!, 5=#NAME?, 6=#NUM!, 7=#N/A).
GETPIVOTDATA(data_field: string, pivot_table: any) → error	error	Returns #REF! when the referenced value is not a pivot table data field.
INFO(type_text: string) → string	string	Returns information about the current calculation environment. Supports recalc and release.
ISBITMAP(value: any) → boolean	boolean	Grid extension. Tests native bitmap identity.
ISBLANK(value: any) → boolean	boolean	Returns TRUE if the value is blank.
ISBLOOM(value: any) → boolean	boolean	Grid extension. Tests native Bloom-filter identity.
ISCOUNTMIN(value: any) → boolean	boolean	Grid extension. Tests native Count-Min-sketch identity.
ISDATE(value: any) → boolean	boolean	Returns TRUE if the value is a date.
ISDATETIME(value: any) → boolean	boolean	Returns TRUE if the value is a datetime.
ISDEQUE(value: any) → boolean	boolean	Grid extension. Tests whether a value retains the native deque kind.
ISDURATION(value: any) → boolean	boolean	Returns TRUE if the value is a duration.
ISERR(value: any) → boolean	boolean	Returns TRUE if the value is any error except #N/A.
ISERROR(value: any) → boolean	boolean	Returns TRUE if the value is an error.
ISFORMULA(value: any) → boolean	boolean	Returns TRUE if there is a formula in the referenced cell. (Returns TRUE for all calculation cells.)
ISHLL(value: any) → boolean	boolean	Grid extension. Tests native cardinality-sketch identity.
ISINTERVALINDEX(value: any) → boolean	boolean	Grid extension. Tests native interval-index identity.
ISKLL(value: any) → boolean	boolean	Grid extension. Tests native KLL-sketch identity.
ISLOGICAL(value: any) → boolean	boolean	Returns TRUE if the value is a logical (boolean) value.
ISMAP(value: any) → boolean	boolean	Grid extension. Tests native map identity.
ISMERKLESET(value: any) → boolean	boolean	Grid extension. Tests native Merkle-set identity.
ISMULTIMAP(value: any) → boolean	boolean	Grid extension. Tests native multimap identity.
ISMULTISET(value: any) → boolean	boolean	Grid extension. Tests native multiset identity.
ISNA(value: any) → boolean	boolean	Returns TRUE if the value is the #N/A error.
ISNONTEXT(value: any) → boolean	boolean	Returns TRUE if the value is not text.
ISNUMBER(value: any) → boolean	boolean	Returns TRUE if the value is a number.
ISOPTION(value: any) → boolean	boolean	Grid extension. Tests native Option identity.
ISRECORD(value: any) → boolean	boolean	Grid extension. Tests native record identity.
ISREF(value: any) → boolean	boolean	Returns TRUE if the value is a reference. (Always returns TRUE in formula context.)
ISRESULT(value: any) → boolean	boolean	Grid extension. Tests native Result identity.
ISSET(value: any) → boolean	boolean	Grid extension. Tests native set identity.
ISSTREAM(value: any) → boolean	boolean	Grid extension. Tests native stream identity.
ISSTREAMGROUP(value: any) → boolean	boolean	Grid extension. Tests native stream consumer-group identity.
ISTEXT(value: any) → boolean	boolean	Returns TRUE if the value is text.
ISTOPK(value: any) → boolean	boolean	Grid extension. Tests native Top-K-sketch identity.
ISTRIE(value: any) → boolean	boolean	Grid extension. Tests native trie identity.
ISTUPLE(value: any) → boolean	boolean	Grid extension. Tests native tuple identity.
ISVECTOR(value: any) → boolean	boolean	Grid extension. Tests native vector identity.
ISZSET(value: any) → boolean	boolean	Grid extension. Tests native ranked-set identity.
N(value: any) → number	number	Converts a value to a number.
NA() → error	error	Returns the #N/A error value.
SHEET() → number	number	Returns the sheet number (always 1 in single-sheet mode).
SHEETS() → number	number	Returns the number of sheets (always 1 in single-sheet mode).
TYPE(value: any) → number	number	Returns a number indicating the data type: 1=number, 2=text, 4=logical, 16=error, 64=array.

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Engineering

Bit operations, base conversions, complex numbers, and engineering helpers.

Function count: 94.

Function	Returns	Notes
ALLOWABLE_STRESS(yield_stress: number, factor_of_safety: number) → number	number	Grid extension. Returns allowable stress from yield stress and safety factor.
ARGUMENT(c: complex) → number	number	Returns the argument (angle in radians) of a complex number. Type-aware version of IMARGUMENT.
BATTERY_RUNTIME(capacity_amp_hours: number, load_amps: number) → number	number	Grid extension. Returns battery runtime in hours.
BEAM_BENDING_STRESS(moment: number, distance: number, moment_inertia: number) → number	number	Grid extension. Returns bending stress from My/I.
BEAM_DEFLECTION_CENTER_LOAD(load: number, length: number, elastic_modulus: number, moment_inertia: number) → number	number	Grid extension. Returns simply supported beam center deflection for a point load.
BEAM_DEFLECTION_UNIFORM_LOAD(load_per_length: number, length: number, elastic_modulus: number, moment_inertia: number) → number	number	Grid extension. Returns simply supported beam maximum deflection under uniform load.
BESSELI(x: number, n_order: number) → number	number	Returns the modified Bessel function In(x).
BESSELJ(x: number, n_order: number) → number	number	Returns the Bessel function Jn(x).
BESSELK(x: number, n_order: number) → number	number	Returns the modified Bessel function Kn(x).
BESSELY(x: number, n_order: number) → number	number	Returns the Bessel function Yn(x).
BIN2DEC(v: string) → number	number	Converts a binary number to decimal.
BIN2HEX(v: string) → string	string	Converts binary to hexadecimal.
BIN2OCT(v: string) → string	string	Converts binary to octal.
BITAND(a: number, b: number) → number	number	Returns the bitwise AND of two integers (Apple Numbers / Google Sheets).
BITLSHIFT(number: number, shift: number) → number	number	Returns the number shifted left by the specified number of bits.
BITOR(a: number, b: number) → number	number	Returns the bitwise OR of two integers.
BITRSHIFT(number: number, shift: number) → number	number	Returns the number shifted right by the specified number of bits.
BITXOR(a: number, b: number) → number	number	Returns the bitwise XOR of two integers.
BULK_MODULUS(pressure_change: number, volume_strain: number) → number	number	Grid extension. Returns bulk modulus from pressure change and volumetric strain.
CANTILEVER_DEFLECTION_END_LOAD(load: number, length: number, elastic_modulus: number, moment_inertia: number) → number	number	Grid extension. Returns cantilever end deflection under an end load.
COMPLEX(real: number, imag: number, suffix: string) → string	string	Creates a complex number from real and imaginary parts.
CONJUGATE(c: complex) → complex	complex	Grid extension. Returns the complex conjugate as a typed complex value. Type-aware version of IMCONJUGATE.
CONVERT(number: number, from_unit: string, to_unit: string) → number	number	Converts a number from one unit to another.
DARCY_PRESSURE_DROP(friction_factor: number, length: number, diameter: number, density: number, velocity: number) → number	number	Grid extension. Returns Darcy-Weisbach pressure drop.
DEC2BIN(v: number, places: number) → string	string	Converts a decimal number to binary, optionally zero-padded to a given width.
DEC2HEX(v: number, places: number) → string	string	Converts a decimal number to hexadecimal, optionally zero-padded to a given width.
DEC2OCT(v: number, places: number) → string	string	Converts a decimal number to octal, optionally zero-padded to a given width.
DELTA(a: number, b: number) → number	number	Tests whether two values are equal. Returns 1 if equal, 0 otherwise.
ELECTRICAL_LOAD_POWER(voltage: number, current: number, power_factor: number) → number	number	Grid extension. Returns electrical real power.
ERF(x: number) → number	number	Returns the error function.
ERFC(x: number) → number	number	Returns the complementary error function.
ERFC_PRECISE(x: number) → number	number	aliases: ERFC.PRECISE. Returns the complementary error function (alias for ERFC).
ERF_PRECISE(x: number) → number	number	aliases: ERF.PRECISE. Returns the error function (alias for ERF).
EULER_BUCKLING_LOAD(elastic_modulus: number, moment_inertia: number, effective_length: number) → number	number	Grid extension. Returns Euler critical buckling load.
FACTOR_OF_SAFETY(capacity: number, demand: number) → number	number	Grid extension. Returns factor of safety from capacity over demand.
FAN_AFFINITY_FLOW(flow: number, speed_ratio: number) → number	number	Grid extension. Returns fan flow using the affinity laws.
FAN_AFFINITY_POWER(power: number, speed_ratio: number) → number	number	Grid extension. Returns fan power using the affinity laws.
FAN_AFFINITY_PRESSURE(pressure: number, speed_ratio: number) → number	number	Grid extension. Returns fan pressure using the affinity laws.
FRICTION_HEAD_LOSS(friction_factor: number, length: number, diameter: number, velocity: number, gravity: number) → number	number	Grid extension. Returns Darcy-Weisbach head loss.
GESTEP(number: number, step: number) → number	number	Tests whether a number is greater than or equal to a step value.
HEAT_CONDUCTION_RATE(conductivity: number, area: number, delta_temperature: number, thickness: number) → number	number	Grid extension. Returns one-dimensional conduction heat rate.
HEAT_FLUX(heat_rate: number, area: number) → number	number	Grid extension. Returns heat flux.
HEX2BIN(v: string) → string	string	Converts hexadecimal to binary.
HEX2DEC(v: string) → number	number	Converts a hexadecimal number to decimal.
HEX2OCT(v: string) → string	string	Converts hexadecimal to octal.
HYDRAULIC_DIAMETER(area: number, wetted_perimeter: number) → number	number	Grid extension. Returns hydraulic diameter.
IMABS(c: complex) → number	number	Returns the absolute value (modulus) of a complex number.
IMAGINARY(c: complex) → number	number	Returns the imaginary part of a complex number. Accepts a typed complex value, a plain number, or the legacy "a+bi" string form.
IMARGUMENT(c: complex) → number	number	Returns the argument (angle in radians) of a complex number.
IMCONJUGATE(c: complex) → string	string	Returns the complex conjugate.
IMCOS(c: string) → string	string	Returns the cosine of a complex number.
IMCOSH(c: string) → string	string	Returns the hyperbolic cosine of a complex number.
IMCOT(c: string) → string	string	Returns the cotangent of a complex number.
IMCSC(c: string) → string	string	Returns the cosecant of a complex number.
IMDIV(a: string, b: string) → string	string	Returns the quotient of complex numbers.
IMEXP(c: string) → string	string	Returns the exponential of a complex number.
IMLN(c: string) → string	string	Returns the natural logarithm of a complex number.
IMLOG10(c: string) → string	string	Returns the base-10 logarithm of a complex number.
IMLOG2(c: string) → string	string	Returns the base-2 logarithm of a complex number.
IMPOWER(c: string, power: number) → string	string	Returns a complex number raised to a power.
IMPRODUCT(a: string, b: string) → string	string	Returns the product of complex numbers.
IMREAL(c: complex) → number	number	Returns the real part of a complex number. Accepts a typed complex value, a plain number, or the legacy "a+bi" string form.
IMSEC(c: string) → string	string	Returns the secant of a complex number.
IMSIN(c: string) → string	string	Returns the sine of a complex number.
IMSINH(c: string) → string	string	Returns the hyperbolic sine of a complex number.
IMSQRT(c: string) → string	string	Returns the square root of a complex number.
IMSUB(a: string, b: string) → string	string	Returns the difference of complex numbers.
IMSUM(a: string, b: string) → string	string	Returns the sum of complex numbers.
IMTAN(c: string) → string	string	Returns the tangent of a complex number.
MAKE_COMPLEX(re: number, im: number) → complex	complex	Grid extension. Constructs a typed complex value from a real and imaginary part. Modern alternative to COMPLEX, which returns a string.
MODULUS(c: complex) → number	number	Returns the modulus (magnitude) of a complex number. Type-aware version of IMABS.
MOMENT_OF_INERTIA_CIRCLE(radius: number) → number	number	Grid extension. Returns circular second moment of area.
MOMENT_OF_INERTIA_RECT(width: number, height: number) → number	number	Grid extension. Returns rectangular second moment of area.
OCT2BIN(v: string) → string	string	Converts octal to binary.
OCT2DEC(v: string) → number	number	Converts an octal number to decimal.
OCT2HEX(v: string) → string	string	Converts octal to hexadecimal.
PIPE_FLOW_RATE(velocity: number, diameter: number) → number	number	Grid extension. Returns pipe volumetric flow rate.
PIPE_FLOW_VELOCITY(flow_rate: number, diameter: number) → number	number	Grid extension. Returns pipe average velocity.
POLAR_MOMENT_HOLLOW_SHAFT(outer_radius: number, inner_radius: number) → number	number	Grid extension. Returns polar second moment for a hollow circular shaft.
POLAR_MOMENT_SOLID_SHAFT(radius: number) → number	number	Grid extension. Returns polar second moment for a solid circular shaft.
PUMP_POWER(flow_rate: number, pressure_delta: number, efficiency: number) → number	number	Grid extension. Returns pump hydraulic power adjusted by efficiency.
REAL(c: complex) → number	number	Returns the real part of a complex number. Type-aware version of IMREAL.
REYNOLDS_NUMBER_PIPE(density: number, velocity: number, diameter: number, viscosity: number) → number	number	Grid extension. Returns pipe Reynolds number.
R_VALUE(thickness: number, conductivity: number) → number	number	Grid extension. Returns thermal resistance from thickness and conductivity.
SECTION_MODULUS_RECT(width: number, height: number) → number	number	Grid extension. Returns rectangular section modulus.
SHEAR_MODULUS(shear_stress: number, shear_strain: number) → number	number	Grid extension. Returns shear modulus from stress and strain.
SHEAR_STRAIN(displacement: number, height: number) → number	number	Grid extension. Returns shear strain from lateral displacement over height.
SHEAR_STRESS(force: number, area: number) → number	number	Grid extension. Returns shear stress from force over area.
SLENDERNESS_RATIO(effective_length: number, radius_of_gyration: number) → number	number	Grid extension. Returns slenderness ratio.
THERMAL_EXPANSION(length: number, coefficient: number, delta_temperature: number) → number	number	Grid extension. Returns linear thermal expansion delta length.
TORQUE(force: number, lever_arm: number) → number	number	Grid extension. Returns torque from force and lever arm.
TORSIONAL_SHEAR_STRESS(torque: number, radius: number, polar_moment: number) → number	number	Grid extension. Returns torsional shear stress.
U_VALUE(r_value: number) → number	number	Grid extension. Returns thermal transmittance from R-value.
VOLTAGE_DROP_DC(current: number, resistance: number) → number	number	Grid extension. Returns DC voltage drop.

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Logistics

Inventory, transportation, warehouse, and service-level helpers.

Function count: 39.

Function	Returns	Notes
AVERAGE_INVENTORY(beginning_inventory: number, ending_inventory: number) → number	number	Grid extension. Returns average inventory.
BACKORDER_RATE(backorders: number, orders: number) → number	number	Grid extension. Returns backorder rate.
CARBON_EMISSIONS_FREIGHT(distance: number, weight_tonnes: number, emission_factor: number) → number	number	Grid extension. Returns freight carbon emissions.
CARRIER_CLAIM_RATE(claims: number, shipments: number) → number	number	Grid extension. Returns carrier claim rate.
CUBIC_UTILIZATION(used_cube: number, available_cube: number) → number	number	Grid extension. Returns cube utilization.
CYCLE_SERVICE_LEVEL(cycles_without_stockout: number, total_cycles: number) → number	number	Grid extension. Returns cycle service level.
DAYS_OF_SUPPLY(inventory_units: number, daily_demand: number) → number	number	Grid extension. Returns inventory days of supply.
DELIVERY_WINDOW_SLACK(window_end: number, arrival_time: number) → number	number	Grid extension. Returns slack remaining in a delivery window.
DEMAND_DURING_LEAD_TIME(daily_demand: number, lead_time_days: number) → number	number	Grid extension. Returns expected demand during lead time.
DIMENSIONAL_WEIGHT(length: number, width: number, height: number, dim_factor: number) → number	number	Grid extension. Returns dimensional shipping weight.
DOCK_TO_STOCK_TIME(putaway_time: number, receipt_time: number) → number	number	Grid extension. Returns dock-to-stock elapsed time.
EOQ(annual_demand: number, order_cost: number, holding_cost: number) → number	number	Grid extension. Returns economic order quantity.
EOQ_TOTAL_COST(annual_demand: number, order_quantity: number, order_cost: number, holding_cost: number) → number	number	Grid extension. Returns annual ordering plus holding cost.
FREIGHT_COST_PER_MILE(freight_cost: number, miles: number) → number	number	Grid extension. Returns freight cost per mile.
FREIGHT_COST_PER_UNIT(freight_cost: number, units: number) → number	number	Grid extension. Returns freight cost per unit.
INVENTORY_TURNS(cost_of_goods_sold: number, average_inventory: number) → number	number	Grid extension. Returns inventory turns.
IN_FULL_RATE(in_full_orders: number, total_orders: number) → number	number	Grid extension. Returns in-full delivery rate.
LANE_COST(distance: number, cost_per_mile: number, fixed_cost: number) → number	number	Grid extension. Returns lane cost.
LOAD_FACTOR(used_capacity: number, available_capacity: number) → number	number	Grid extension. Returns load factor.
ON_TIME_RATE(on_time_orders: number, total_orders: number) → number	number	Grid extension. Returns on-time delivery rate.
ORDER_ACCURACY(accurate_orders: number, total_orders: number) → number	number	Grid extension. Returns order accuracy rate.
ORDER_CYCLE_TIME(elapsed_time: number, orders: number) → number	number	Grid extension. Returns average order cycle time.
OTIF(on_time_orders: number, in_full_orders: number, total_orders: number) → number	number	Grid extension. Returns on-time-in-full rate using the limiting count.
PACK_RATE(orders_packed: number, hours: number) → number	number	Grid extension. Returns warehouse pack rate.
PALLET_POSITIONS(trailer_length: number, pallet_length: number) → number	number	Grid extension. Returns whole pallet positions by trailer length.
PERFECT_ORDER_RATE(perfect_orders: number, total_orders: number) → number	number	Grid extension. Returns perfect order rate.
PICK_RATE(units_picked: number, hours: number) → number	number	Grid extension. Returns warehouse pick rate.
REORDER_POINT(daily_demand: number, lead_time_days: number, safety_stock: number) → number	number	Grid extension. Returns inventory reorder point.
RETURN_RATE(returned_orders: number, total_orders: number) → number	number	Grid extension. Returns return rate.
ROUTE_DISTANCE_TOTAL(distances: number[]) → number	number	Grid extension. Returns total route distance.
ROUTE_TIME_TOTAL(times: number[]) → number	number	Grid extension. Returns total route time.
SAFETY_STOCK_DAYS(daily_demand: number, safety_days: number) → number	number	Grid extension. Returns safety stock from days of supply.
SAFETY_STOCK_Z(z_score: number, demand_stddev: number, lead_time_days: number) → number	number	Grid extension. Returns safety stock using demand variability and lead time.
SHRINKAGE_RATE(book_inventory: number, physical_inventory: number) → number	number	Grid extension. Returns shrinkage rate.
STOCKOUT_PROBABILITY(cycle_service_level: number) → number	number	Grid extension. Returns stockout probability from service level.
STOP_DENSITY(stops: number, route_distance: number) → number	number	Grid extension. Returns stops per distance.
TRUCK_UTILIZATION_VOLUME(load_volume: number, capacity_volume: number) → number	number	Grid extension. Returns truck utilization by volume.
TRUCK_UTILIZATION_WEIGHT(load_weight: number, capacity_weight: number) → number	number	Grid extension. Returns truck utilization by weight.
WAREHOUSE_THROUGHPUT(units_processed: number, hours: number) → number	number	Grid extension. Returns warehouse throughput.

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Planning

Project scheduling, earned value, capacity, and risk-planning helpers.

Function count: 40.

Function	Returns	Notes
BUDGET_BURN_RATE(spend: number, elapsed_days: number) → number	number	Grid extension. Returns budget burn rate per day.
BUFFER_CONSUMPTION(buffer_used: number, buffer_total: number) → number	number	Grid extension. Returns project buffer consumption.
CAPACITY_GAP(required_capacity: number, available_capacity: number) → number	number	Grid extension. Returns capacity gap.
CONFIDENCE_INTERVAL_NORMAL(mean: number, stddev: number, z_score: number) → number	number	Grid extension. Returns normal confidence interval half-width.
COST_PERFORMANCE_INDEX(earned_value: number, actual_cost: number) → number	number	Grid extension. Returns cost performance index.
COST_VARIANCE(earned_value: number, actual_cost: number) → number	number	Grid extension. Returns earned-value cost variance.
CRITICAL_PATH_FLAG(total_float: number) → number	number	Grid extension. Returns 1 when total float is zero or negative, otherwise 0.
CYCLE_TIME(production_time: number, units: number) → number	number	Grid extension. Returns cycle time.
EARNED_VALUE_PERCENT(earned_value: number, budget_at_completion: number) → number	number	Grid extension. Returns earned value percent complete.
ESTIMATE_AT_COMPLETION(budget_at_completion: number, cost_performance_index: number) → number	number	Grid extension. Returns estimate at completion.
ESTIMATE_TO_COMPLETE(estimate_at_completion: number, actual_cost: number) → number	number	Grid extension. Returns estimate to complete.
FORECAST_LINEAR(intercept: number, slope: number, period: number) → number	number	Grid extension. Returns a linear forecast.
FORECAST_RUN_RATE(actual_to_date: number, elapsed_periods: number, total_periods: number) → number	number	Grid extension. Returns run-rate forecast.
FREE_FLOAT(successor_early_start: number, early_finish: number) → number	number	Grid extension. Returns free float.
HEADCOUNT_REQUIRED(work_hours: number, hours_per_person: number) → number	number	Grid extension. Returns required headcount.
LEAD_TIME(process_time: number, wait_time: number) → number	number	Grid extension. Returns lead time.
LITTLE_LAW_WIP(throughput: number, lead_time: number) → number	number	Grid extension. Returns WIP by Little's law.
MILESTONE_VARIANCE_DAYS(actual_date_serial: number, planned_date_serial: number) → number	number	Grid extension. Returns milestone date variance in days.
PERT_COMPLETION_PROBABILITY(target: number, expected: number, stddev: number) → number	number	Grid extension. Returns approximate normal completion probability.
PERT_EXPECTED_TIME(optimistic: number, most_likely: number, pessimistic: number) → number	number	Grid extension. Returns PERT expected duration.
PERT_STDDEV(optimistic: number, pessimistic: number) → number	number	Grid extension. Returns PERT duration standard deviation.
PERT_VARIANCE(optimistic: number, pessimistic: number) → number	number	Grid extension. Returns PERT duration variance.
PERT_Z_SCORE(target: number, expected: number, stddev: number) → number	number	Grid extension. Returns PERT z-score for a target date.
PLANNED_VALUE(budget_at_completion: number, planned_percent: number) → number	number	Grid extension. Returns planned value.
QUEUE_WAIT_TIME_MM1(arrival_rate: number, service_rate: number) → number	number	Grid extension. Returns M/M/1 average waiting time in queue.
RESOURCE_AVAILABILITY(available_hours: number, total_hours: number) → number	number	Grid extension. Returns resource availability.
RESOURCE_UTILIZATION(assigned_hours: number, available_hours: number) → number	number	Grid extension. Returns resource utilization.
RISK_EXPECTED_VALUE(probability: number, impact: number) → number	number	Grid extension. Returns risk expected value.
RISK_EXPOSURE(probability: number, impact: number) → number	number	Grid extension. Returns risk exposure.
RUNWAY_DAYS(remaining_budget: number, burn_rate: number) → number	number	Grid extension. Returns runway in days.
SCENARIO_WEIGHTED_VALUE(low: number, base: number, high: number, low_weight: number, base_weight: number, high_weight: number) → number	number	Grid extension. Returns weighted scenario value.
SCHEDULE_PERFORMANCE_INDEX(earned_value: number, planned_value: number) → number	number	Grid extension. Returns schedule performance index.
SCHEDULE_VARIANCE(earned_value: number, planned_value: number) → number	number	Grid extension. Returns earned-value schedule variance.
TAKT_TIME(available_time: number, customer_demand: number) → number	number	Grid extension. Returns takt time.
TASK_SLACK(late_finish: number, early_finish: number) → number	number	Grid extension. Returns task slack.
THROUGHPUT_RATE(units: number, time: number) → number	number	Grid extension. Returns throughput rate.
TOTAL_FLOAT(late_start: number, early_start: number) → number	number	Grid extension. Returns total float.
TO_COMPLETE_PERFORMANCE_INDEX(budget_at_completion: number, earned_value: number, budget_remaining: number) → number	number	Grid extension. Returns to-complete performance index.
VARIANCE_AT_COMPLETION(budget_at_completion: number, estimate_at_completion: number) → number	number	Grid extension. Returns variance at completion.
WIP_LIMIT(throughput: number, lead_time: number) → number	number	Grid extension. Returns work-in-process limit by Little's law.

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Construction

Construction estimating, quantities, production, and cost helpers.

Function count: 40.

Function	Returns	Notes
ASPHALT_TONNAGE(area: number, thickness: number, density: number) → number	number	Grid extension. Returns asphalt tonnage.
BID_MARKUP_PRICE(cost: number, markup_fraction: number) → number	number	Grid extension. Returns bid price with markup.
BLOCK_COUNT(wall_area: number, block_area: number, waste_fraction: number) → number	number	Grid extension. Returns required block count.
BRICK_COUNT(wall_area: number, brick_area: number, waste_fraction: number) → number	number	Grid extension. Returns required brick count.
CHANGE_ORDER_IMPACT(new_cost: number, original_cost: number) → number	number	Grid extension. Returns change order cost impact.
COLUMN_CONCRETE_VOLUME(diameter: number, height: number) → number	number	Grid extension. Returns cylindrical column concrete volume.
CONCRETE_BAGS(volume: number, bag_yield: number) → number	number	Grid extension. Returns required concrete bags.
CONCRETE_VOLUME(length: number, width: number, depth: number) → number	number	Grid extension. Returns rectangular concrete volume.
CONSTRUCTION_CPI(earned_value: number, actual_cost: number) → number	number	Grid extension. Returns construction cost performance index.
CONTINGENCY_AMOUNT(base_cost: number, contingency_fraction: number) → number	number	Grid extension. Returns contingency amount.
CREW_HOURS_REQUIRED(quantity: number, productivity: number) → number	number	Grid extension. Returns crew hours required.
CREW_PRODUCTIVITY(quantity_installed: number, crew_hours: number) → number	number	Grid extension. Returns crew productivity.
CUT_FILL_VOLUME(area: number, average_depth: number) → number	number	Grid extension. Returns cut/fill volume.
CYLINDER_CONCRETE_VOLUME(radius: number, height: number) → number	number	Grid extension. Returns cylinder volume.
DRYWALL_SHEETS(wall_area: number, sheet_area: number, waste_fraction: number) → number	number	Grid extension. Returns drywall sheet count.
EQUIPMENT_COST(hours: number, rate: number) → number	number	Grid extension. Returns equipment cost.
EXCAVATION_VOLUME(length: number, width: number, depth: number) → number	number	Grid extension. Returns excavation volume.
FLOORING_AREA(length: number, width: number, waste_fraction: number) → number	number	Grid extension. Returns flooring area including waste.
FOOTING_CONCRETE_VOLUME(length: number, width: number, depth: number) → number	number	Grid extension. Returns footing concrete volume.
FORMWORK_AREA(perimeter: number, height: number) → number	number	Grid extension. Returns formwork surface area.
GRAVEL_TONNAGE(volume: number, density: number) → number	number	Grid extension. Returns gravel tonnage.
LABOR_COST(hours: number, rate: number) → number	number	Grid extension. Returns labor cost.
MATERIAL_WITH_WASTE(quantity: number, waste_fraction: number) → number	number	Grid extension. Returns quantity including waste.
MORTAR_VOLUME(masonry_volume: number, mortar_fraction: number) → number	number	Grid extension. Returns mortar volume.
PAINT_GALLONS(area: number, coverage_per_gallon: number, coats: number) → number	number	Grid extension. Returns paint gallons required.
PAY_APPLICATION_AMOUNT(work_completed: number, retainage_amount: number) → number	number	Grid extension. Returns payment application amount net retainage.
REBAR_COUNT(spacing_length: number, spacing: number) → number	number	Grid extension. Returns count of bars at spacing.
REBAR_LENGTH_TOTAL(bar_count: number, bar_length: number) → number	number	Grid extension. Returns total rebar length.
REBAR_WEIGHT(length: number, unit_weight: number) → number	number	Grid extension. Returns rebar weight.
RETAINAGE_AMOUNT(invoice_amount: number, retainage_fraction: number) → number	number	Grid extension. Returns retainage amount.
ROOF_AREA(plan_area: number, pitch_factor: number) → number	number	Grid extension. Returns roof area from plan area and pitch factor.
ROOF_PITCH_ANGLE(rise: number, run: number) → number	number	Grid extension. Returns roof pitch angle in degrees.
ROOF_RISE(run: number, pitch_ratio: number) → number	number	Grid extension. Returns roof rise from run and pitch ratio.
SLAB_CONCRETE_VOLUME(length: number, width: number, thickness: number) → number	number	Grid extension. Returns slab concrete volume.
SOIL_COMPACTION_PERCENT(dry_density: number, max_dry_density: number) → number	number	Grid extension. Returns soil compaction percent.
STAIR_RISER_COUNT(total_rise: number, riser_height: number) → number	number	Grid extension. Returns stair riser count.
STAIR_TREAD_DEPTH(total_run: number, tread_count: number) → number	number	Grid extension. Returns stair tread depth.
TILE_COUNT(area: number, tile_area: number, waste_fraction: number) → number	number	Grid extension. Returns tile count including waste.
UNIT_COST(total_cost: number, quantity: number) → number	number	Grid extension. Returns unit cost.
WASTE_ALLOWANCE(quantity: number, waste_fraction: number) → number	number	Grid extension. Returns waste allowance quantity.

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Healthcare

Clinical math, diagnostic metrics, medication, and healthcare operations helpers.

Function count: 40.

Function	Returns	Notes
ADHERENCE_PERCENT(doses_taken: number, doses_prescribed: number) → number	number	Grid extension. Returns medication adherence percent.
ANION_GAP(sodium: number, chloride: number, bicarbonate: number) → number	number	Grid extension. Returns anion gap.
APGAR_TOTAL(appearance: number, pulse: number, grimace: number, activity: number, respiration: number) → number	number	Grid extension. Returns total APGAR score.
AVERAGE_LENGTH_OF_STAY(patient_days: number, discharges: number) → number	number	Grid extension. Returns average length of stay.
BED_OCCUPANCY_RATE(occupied_beds: number, available_beds: number) → number	number	Grid extension. Returns bed occupancy rate.
BMI(weight_kg: number, height_m: number) → number	number	Grid extension. Returns body mass index.
BMI_CATEGORY(bmi: number) → string	string	Grid extension. Returns the adult BMI category label.
BSA_DUBOIS(height_cm: number, weight_kg: number) → number	number	Grid extension. Returns body surface area by Du Bois.
BSA_MOSTELLER(height_cm: number, weight_kg: number) → number	number	Grid extension. Returns body surface area by Mosteller.
CASE_FATALITY_RATE(deaths: number, diagnosed_cases: number) → number	number	Grid extension. Returns case fatality rate.
CHADS_VASC_SCORE(chf: number, hypertension: number, age_75: number, diabetes: number, stroke: number, vascular: number, age_65_74: number, female: number) → number	number	Grid extension. Returns CHA2DS2-VASc score.
CORRECTED_ANION_GAP(anion_gap: number, albumin: number) → number	number	Grid extension. Returns albumin-corrected anion gap.
CORRECTED_CALCIUM(calcium: number, albumin: number) → number	number	Grid extension. Returns albumin-corrected calcium.
CREATININE_CLEARANCE_CG(age_years: number, weight_kg: number, serum_creatinine: number, female: number) → number	number	Grid extension. Returns Cockcroft-Gault creatinine clearance estimate.
DOSE_BY_BSA(bsa_m2: number, dose_per_m2: number) → number	number	Grid extension. Returns medication dose by body surface area.
DOSE_BY_WEIGHT(weight_kg: number, dose_per_kg: number) → number	number	Grid extension. Returns medication dose by weight.
DRIP_RATE(volume_ml: number, drop_factor: number, minutes: number) → number	number	Grid extension. Returns IV drip rate in drops/minute.
EGFR_CKD_EPI_2021(serum_creatinine: number, age_years: number, female: number) → number	number	Grid extension. Returns CKD-EPI 2021 eGFR estimate.
FREE_WATER_DEFICIT(weight_kg: number, sodium: number, target_sodium: number, female: number) → number	number	Grid extension. Returns estimated free water deficit.
GCS_TOTAL(eye: number, verbal: number, motor: number) → number	number	Grid extension. Returns Glasgow Coma Scale total.
HAS_BLED_SCORE(hypertension: number, renal: number, liver: number, stroke: number, bleeding: number, labile_inr: number, elderly: number, drugs: number, alcohol: number) → number	number	Grid extension. Returns HAS-BLED score.
INFUSION_TIME(volume_ml: number, rate_ml_hour: number) → number	number	Grid extension. Returns infusion time in hours.
IV_RATE(volume_ml: number, hours: number) → number	number	Grid extension. Returns IV infusion rate in mL/hour.
LIKELIHOOD_RATIO_NEGATIVE(sensitivity: number, specificity: number) → number	number	Grid extension. Returns negative likelihood ratio.
LIKELIHOOD_RATIO_POSITIVE(sensitivity: number, specificity: number) → number	number	Grid extension. Returns positive likelihood ratio.
MEAN_ARTERIAL_PRESSURE(systolic: number, diastolic: number) → number	number	Grid extension. Returns mean arterial pressure.
MEDICATION_DAYS_SUPPLY(quantity: number, daily_dose: number) → number	number	Grid extension. Returns medication days of supply.
NEWS2_RESPIRATION_POINTS(respiratory_rate: number) → number	number	Grid extension. Returns NEWS2 respiratory-rate component points.
NNH(treatment_harm_rate: number, control_harm_rate: number) → number	number	Grid extension. Returns number needed to harm.
NNT(control_event_rate: number, treatment_event_rate: number) → number	number	Grid extension. Returns number needed to treat.
NPV_DIAGNOSTIC(true_negative: number, false_negative: number) → number	number	Grid extension. Returns negative predictive value.
OSMOLARITY_CALCULATED(sodium: number, glucose: number, bun: number) → number	number	Grid extension. Returns calculated serum osmolarity.
PPV(true_positive: number, false_positive: number) → number	number	Grid extension. Returns positive predictive value.
PULSE_PRESSURE(systolic: number, diastolic: number) → number	number	Grid extension. Returns pulse pressure.
QSOFA_SCORE(respiratory_rate_high: number, systolic_low: number, altered_mentation: number) → number	number	Grid extension. Returns qSOFA score.
READMISSION_RATE(readmissions: number, discharges: number) → number	number	Grid extension. Returns readmission rate.
SENSITIVITY(true_positive: number, false_negative: number) → number	number	Grid extension. Returns diagnostic sensitivity.
SHOCK_INDEX(heart_rate: number, systolic: number) → number	number	Grid extension. Returns shock index.
SODIUM_CORRECTION_HYPERGLYCEMIA(sodium: number, glucose: number) → number	number	Grid extension. Returns sodium corrected for hyperglycemia.
SPECIFICITY(true_negative: number, false_positive: number) → number	number	Grid extension. Returns diagnostic specificity.

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Graduate Study

Graduate-school helpers spanning management, law, policy, education, psychology, social science, data science, libraries, humanities, design, urbanism, social work, criminal justice, and communications.

Function count: 156.

Function	Returns	Notes
ANTHRO_ARTIFACT_DENSITY(artifacts: number, area: number) → number	number	Grid extension. Returns artifacts per area for anthropology fieldwork.
ANTHRO_SAMPLE_COVERAGE(observed_individuals: number, estimated_population: number) → number	number	Grid extension. Returns sample coverage ratio.
ARCHAEOLOGY_SHERD_DENSITY(sherds: number, excavated_area: number) → number	number	Grid extension. Returns sherd density.
ARCH_EGRESS_CAPACITY(width_m: number, flow_rate_per_m_min: number) → number	number	Grid extension. Returns egress flow capacity per minute.
ARCH_OCCUPANT_LOAD(area: number, load_factor: number) → number	number	Grid extension. Returns occupant load.
ARTS_PORTFOLIO_COMPLETION(completed_pieces: number, required_pieces: number) → number	number	Grid extension. Returns portfolio completion rate.
CJ_CLEARANCE_RATE(cleared_cases: number, reported_cases: number) → number	number	Grid extension. Returns criminal-justice clearance rate.
CJ_INCARCERATION_RATE(incarcerated_people: number, population: number) → number	number	Grid extension. Returns incarceration rate.
CJ_RECIDIVISM_RATE(reoffenses: number, released_people: number) → number	number	Grid extension. Returns recidivism rate.
COMM_ENGAGEMENT_RATE(interactions: number, impressions: number) → number	number	Grid extension. Returns engagement rate.
COMM_REACH_RATE(reached_audience: number, target_audience: number) → number	number	Grid extension. Returns communication campaign reach rate.
COMM_SHARE_OF_VOICE(brand_mentions: number, total_mentions: number) → number	number	Grid extension. Returns share of voice.
COUNSEL_ATTENDANCE_RATE(attended_sessions: number, scheduled_sessions: number) → number	number	Grid extension. Returns counseling session attendance rate.
COUNSEL_GOAL_ATTAINMENT(achieved_goals: number, total_goals: number) → number	number	Grid extension. Returns counseling goal attainment rate.
COUNSEL_NO_SHOW_RATE(no_shows: number, scheduled_sessions: number) → number	number	Grid extension. Returns counseling no-show rate.
CS_CACHE_HIT_RATE(cache_hits: number, requests: number) → number	number	Grid extension. Returns cache hit rate for computer-science systems studies.
CS_DEFECT_DENSITY(defects: number, kloc: number) → number	number	Grid extension. Returns defects per thousand lines of code.
CS_LATENCY_SLO_ATTAINMENT(within_slo_requests: number, total_requests: number) → number	number	Grid extension. Returns latency SLO attainment rate.
CS_SERVICE_AVAILABILITY(uptime: number, total_time: number) → number	number	Grid extension. Returns service availability.
CS_TEST_COVERAGE(covered_lines: number, total_lines: number) → number	number	Grid extension. Returns line test coverage.
CS_THROUGHPUT_REQUESTS(requests: number, seconds: number) → number	number	Grid extension. Returns request throughput per second.
CYBER_CONTROL_EFFECTIVENESS(controls_passed: number, controls_tested: number) → number	number	Grid extension. Returns control effectiveness rate.
CYBER_MTTD(total_detection_time: number, incidents: number) → number	number	Grid extension. Returns mean time to detect.
CYBER_MTTR(total_recovery_time: number, incidents: number) → number	number	Grid extension. Returns mean time to recover.
CYBER_PATCH_COMPLIANCE(patched_assets: number, total_assets: number) → number	number	Grid extension. Returns cybersecurity patch compliance rate.
CYBER_RISK_SCORE(likelihood: number, impact: number) → number	number	Grid extension. Returns a likelihood-by-impact cybersecurity risk score.
DATA_KAPPA(observed_agreement: number, expected_agreement: number) → number	number	Grid extension. Returns Cohen-style kappa from observed and expected agreement.
DATA_LABEL_AGREEMENT(agreements: number, items: number) → number	number	Grid extension. Returns label agreement rate.
DATA_MISSINGNESS_RATE(missing_values: number[], total_values: number[]) → number	number	Grid extension. Returns data missingness rate.
DATA_TRAIN_TEST_SPLIT(train_count: number, total_count: number) → number	number	Grid extension. Returns train-set share of a data split.
DENTAL_CARIES_PREVALENCE(cases: number, patients: number) → number	number	Grid extension. Returns dental caries prevalence.
DENTAL_DMFT_INDEX(decayed: number, missing: number, filled: number) → number	number	Grid extension. Returns DMFT index.
DENTAL_PLAQUE_INDEX(plaque_score: number, surfaces: number) → number	number	Grid extension. Returns mean plaque index.
DESIGN_ASPECT_RATIO(width: number, height: number) → number	number	Grid extension. Returns width-to-height aspect ratio.
DESIGN_CANVAS_UTILIZATION(used_area: number, total_area: number) → number	number	Grid extension. Returns canvas utilization ratio.
DESIGN_CONTRAST_RATIO(luminance_1: number, luminance_2: number) → number	number	Grid extension. Returns WCAG-style contrast ratio from relative luminance values.
DESIGN_GOLDEN_RATIO_ERROR(width: number, height: number) → number	number	Grid extension. Returns absolute error from the golden-ratio rectangle.
DESIGN_SCALE_FACTOR(actual_dimension: number, original_dimension: number) → number	number	Grid extension. Returns scale factor.
DIVINITY_PROGRAM_EXPENSE_RATIO(program_expense: number, total_expense: number) → number	number	Grid extension. Returns program expense ratio for ministry and nonprofit administration.
ECON_CROSS_PRICE_ELASTICITY(percent_quantity_change: number, percent_other_price_change: number) → number	number	Grid extension. Returns cross-price elasticity.
ECON_INCOME_ELASTICITY(percent_quantity_change: number, percent_income_change: number) → number	number	Grid extension. Returns income elasticity.
ECON_PRESENT_VALUE_STREAM(cash_flows: number[], discount_rate: number) → number	number	Grid extension. Returns present value of a periodic cash-flow stream.
ECON_PRICE_ELASTICITY(percent_quantity_change: number, percent_price_change: number) → number	number	Grid extension. Returns price elasticity of demand.
ECON_REAL_VALUE(nominal_value: number, cpi: number, base_cpi: number) → number	number	Grid extension. Returns inflation-adjusted real value.
EDU_CREDIT_COMPLETION(earned_credits: number, attempted_credits: number) → number	number	Grid extension. Returns credit completion ratio.
EDU_GPA(quality_points: number, credits: number) → number	number	Grid extension. Returns grade point average.
EDU_GRADUATION_RATE(graduates: number, cohort: number) → number	number	Grid extension. Returns graduation rate.
EDU_ITEM_DIFFICULTY(correct_responses: number, total_responses: number) → number	number	Grid extension. Returns assessment item difficulty.
EDU_ITEM_DISCRIMINATION(upper_correct_rate: number, lower_correct_rate: number) → number	number	Grid extension. Returns item discrimination index.
EDU_RETENTION_RATE(returning_students: number, prior_cohort: number) → number	number	Grid extension. Returns cohort retention rate.
EDU_STUDENT_FACULTY_RATIO(students: number, faculty: number) → number	number	Grid extension. Returns student-faculty ratio.
ENG_FAILURE_RATE(failures: number, operating_time: number) → number	number	Grid extension. Returns engineering failure rate.
ENG_MTBF(operating_time: number, failures: number) → number	number	Grid extension. Returns mean time between failures.
ENG_SAFETY_INCIDENT_RATE(incidents: number, hours: number) → number	number	Grid extension. Returns safety incident rate per 200,000 hours.
ENV_CARBON_INTENSITY(emissions: number, output: number) → number	number	Grid extension. Returns carbon intensity.
ENV_RECYCLING_RATE(recycled: number, total_waste: number) → number	number	Grid extension. Returns recycling rate.
ENV_SHANNON_DIVERSITY(species_counts: number[]) → number	number	Grid extension. Returns ecological Shannon diversity using natural logs.
ENV_WATER_INTENSITY(water_use: number, output: number) → number	number	Grid extension. Returns water-use intensity.
EPI_ODDS_RATIO(a: number, b: number, c: number, d: number) → number	number	Grid extension. Returns odds ratio from a 2x2 table.
EPI_RELATIVE_RISK(exposed_cases: number, exposed_total: number, unexposed_cases: number, unexposed_total: number) → number	number	Grid extension. Returns relative risk from exposed and unexposed cohorts.
FILM_SHOOTING_RATIO(footage_shot: number, final_footage: number) → number	number	Grid extension. Returns film shooting ratio.
HCI_ERROR_RATE(errors: number, opportunities: number) → number	number	Grid extension. Returns HCI error rate.
HCI_SUS_SCORE(item_scores: number[]) → number	number	Grid extension. Returns System Usability Scale score from ten 1..5 item scores.
HCI_TASK_SUCCESS_RATE(successful_tasks: number, attempted_tasks: number) → number	number	Grid extension. Returns HCI task success rate.
HEALTH_ADMIN_DENIAL_RATE(denied_claims: number, total_claims: number) → number	number	Grid extension. Returns claims denial rate.
HEALTH_ADMIN_PATIENT_THROUGHPUT(discharges: number, beds: number) → number	number	Grid extension. Returns health-administration patient throughput per bed.
HUM_ARCHIVAL_COVERAGE(items_reviewed: number, total_items: number) → number	number	Grid extension. Returns archival coverage ratio.
HUM_SOURCE_DENSITY(primary_sources: number, pages: number) → number	number	Grid extension. Returns primary-source density per page.
HUM_TRANSLATION_EXPANSION(translated_words: number, source_words: number) → number	number	Grid extension. Returns translation expansion ratio.
HUM_TYPE_TOKEN_RATIO(unique_terms: number, total_terms: number) → number	number	Grid extension. Returns type-token ratio for humanities text analysis.
HUM_WORDS_PER_PAGE(words: number, pages: number) → number	number	Grid extension. Returns words per page.
INFO_RETRIEVAL_F1(precision: number, recall: number) → number	number	Grid extension. Returns information-retrieval F1 score.
INFO_RETRIEVAL_PRECISION(relevant_retrieved: number, retrieved: number) → number	number	Grid extension. Returns information-retrieval precision.
INFO_RETRIEVAL_RECALL(relevant_retrieved: number, relevant_total: number) → number	number	Grid extension. Returns information-retrieval recall.
IR_TRADE_DEPENDENCE(imports_exports: number, gdp: number) → number	number	Grid extension. Returns international trade dependence ratio.
IR_TREATY_COMPLIANCE(compliant_obligations: number, total_obligations: number) → number	number	Grid extension. Returns treaty compliance rate.
LAW_BILLABLE_UTILIZATION(billable_hours: number, total_hours: number) → number	number	Grid extension. Returns billable utilization for legal practice analytics.
LAW_COLLECTION_RATE(collected_amount: number, billed_amount: number) → number	number	Grid extension. Returns collections rate.
LAW_DEADLINE_DAYS(calendar_days: number, tolling_days: number, extension_days: number) → number	number	Grid extension. Returns adjusted procedural deadline days.
LAW_PROBATIVE_VALUE_INDEX(probative_value: number, unfair_prejudice: number) → number	number	Grid extension. Returns a probative-value-to-prejudice index.
LAW_REALIZATION_RATE(collected_fees: number, billed_fees: number) → number	number	Grid extension. Returns realized-fee rate.
LAW_SIMPLE_INTEREST_DAMAGES(principal: number, annual_rate: number, days: number) → number	number	Grid extension. Returns simple statutory-interest damages.
LIB_ACCEPTANCE_RATE(accepted: number, submitted: number) → number	number	Grid extension. Returns publication or conference acceptance rate.
LIB_CITATION_DENSITY(citations: number, pages: number) → number	number	Grid extension. Returns citations per page.
LIB_H_INDEX(citation_counts: number[]) → number	number	Grid extension. Returns h-index from article citation counts.
LIB_IMPACT_FACTOR(citations: number, citable_items: number) → number	number	Grid extension. Returns journal impact factor.
LING_FLESCH_READING_EASE(words: number, sentences: number, syllables: number) → number	number	Grid extension. Returns Flesch reading-ease score.
LING_MORPHEME_DENSITY(morphemes: number, words: number) → number	number	Grid extension. Returns morphemes per word.
LING_PHONEME_ERROR_RATE(errors: number, phonemes: number) → number	number	Grid extension. Returns phoneme error rate.
MBA_BREAK_EVEN_UNITS(fixed_cost: number, price_per_unit: number, variable_cost_per_unit: number) → number	number	Grid extension. Returns break-even unit volume.
MBA_CHURN_RATE(customers_lost: number, customers_start: number) → number	number	Grid extension. Returns customer churn rate.
MBA_CONTRIBUTION_MARGIN(revenue: number, variable_cost: number) → number	number	Grid extension. Returns contribution margin.
MBA_CUSTOMER_LIFETIME_VALUE(average_order_value: number, purchases_per_period: number, gross_margin: number, retention_rate: number, discount_rate: number) → number	number	Grid extension. Returns discounted customer lifetime value for MBA marketing and strategy models.
MBA_LTV_CAC_RATIO(lifetime_value: number, customer_acquisition_cost: number) → number	number	Grid extension. Returns the LTV/CAC ratio.
MBA_MARKET_SHARE(company_sales: number, market_sales: number) → number	number	Grid extension. Returns market share.
MBA_NPS(promoters: number, detractors: number, total_responses: number) → number	number	Grid extension. Returns net promoter score on the -100..100 scale.
MBA_WORKING_CAPITAL(current_assets: number, current_liabilities: number) → number	number	Grid extension. Returns working capital.
ML_ACCURACY(true_positive: number, true_negative: number, false_positive: number, false_negative: number) → number	number	Grid extension. Returns classifier accuracy.
ML_ENTROPY_BITS(probabilities: number[]) → number	number	Grid extension. Returns Shannon entropy in bits after normalizing positive weights.
ML_F1(precision: number, recall: number) → number	number	Grid extension. Returns F1 score from precision and recall.
ML_FALSE_POSITIVE_RATE(false_positive: number, true_negative: number) → number	number	Grid extension. Returns classifier false-positive rate.
ML_PRECISION(true_positive: number, false_positive: number) → number	number	Grid extension. Returns classifier precision.
ML_RECALL(true_positive: number, false_negative: number) → number	number	Grid extension. Returns classifier recall.
ML_SPECIFICITY(true_negative: number, false_positive: number) → number	number	Grid extension. Returns classifier specificity.
ML_TFIDF(term_frequency: number, document_count: number, document_frequency: number) → number	number	Grid extension. Returns a smoothed TF-IDF score.
MUSIC_INTERVAL_CENTS(frequency_ratio: number) → number	number	Grid extension. Returns musical interval size in cents.
MUSIC_TEMPO_DURATION(beats: number, bpm: number) → number	number	Grid extension. Returns duration in seconds for a beat count at tempo.
NONPROFIT_DONOR_RETENTION(retained_donors: number, prior_donors: number) → number	number	Grid extension. Returns donor retention rate.
NONPROFIT_FUNDRAISING_EFFICIENCY(contributions: number, fundraising_expense: number) → number	number	Grid extension. Returns contributions per fundraising dollar.
NURSING_FALL_RATE(falls: number, patient_days: number) → number	number	Grid extension. Returns falls per 1,000 patient days.
NURSING_HOURS_PER_PATIENT_DAY(nursing_hours: number, patient_days: number) → number	number	Grid extension. Returns nursing hours per patient day.
NURSING_MED_ERROR_RATE(errors: number, doses: number) → number	number	Grid extension. Returns medication error rate.
NURSING_PATIENT_NURSE_RATIO(patients: number, nurses: number) → number	number	Grid extension. Returns patient-to-nurse ratio.
PHARMACY_DOSE_CONVERSION(dose: number, conversion_factor: number) → number	number	Grid extension. Returns converted medication dose.
PHARMACY_MPR(days_supply: number, period_days: number) → number	number	Grid extension. Returns medication possession ratio.
PHARMACY_STOCKOUT_RATE(stockout_days: number, total_days: number) → number	number	Grid extension. Returns pharmacy stockout-day rate.
POLICY_COST_BENEFIT_RATIO(benefits: number, costs: number) → number	number	Grid extension. Returns policy cost-benefit ratio.
POLICY_EQUITY_GAP(group_a_rate: number, group_b_rate: number) → number	number	Grid extension. Returns absolute equity gap between two rates.
POLICY_NET_BENEFIT(benefits: number, costs: number) → number	number	Grid extension. Returns net policy benefit.
POLICY_PROGRAM_REACH(participants: number, eligible_population: number) → number	number	Grid extension. Returns program reach.
POLICY_SROI(social_value: number, investment: number) → number	number	Grid extension. Returns social return on investment.
POLISCI_EFFECTIVE_PARTIES(vote_shares: number[]) → number	number	Grid extension. Returns effective number of parties from vote shares.
POLISCI_VOTER_TURNOUT(votes: number, eligible_voters: number) → number	number	Grid extension. Returns voter turnout.
PSYCH_EFFECT_SIZE_D(treatment_mean: number, control_mean: number, pooled_standard_deviation: number) → number	number	Grid extension. Returns Cohen-style d effect size.
PSYCH_ODDS(successes: number, failures: number) → number	number	Grid extension. Returns odds from event and non-event counts.
PSYCH_PREVALENCE(cases: number, population: number) → number	number	Grid extension. Returns prevalence for psychology and counseling studies.
PSYCH_RELIABLE_CHANGE_INDEX(post_score: number, pre_score: number, standard_error_diff: number) → number	number	Grid extension. Returns reliable change index.
PSYCH_STANDARD_SCORE(raw_score: number, mean: number, standard_deviation: number) → number	number	Grid extension. Returns a z-style standard score.
PUBHEALTH_ATTACK_RATE(cases: number, exposed_population: number) → number	number	Grid extension. Returns outbreak attack rate.
PUBHEALTH_ATTRIBUTABLE_FRACTION(relative_risk: number) → number	number	Grid extension. Returns attributable fraction among exposed from relative risk.
PUBHEALTH_INCIDENCE_RATE(new_cases: number, population_at_risk: number) → number	number	Grid extension. Returns public-health incidence rate.
PUBHEALTH_PREVALENCE_RATE(existing_cases: number, population: number) → number	number	Grid extension. Returns public-health prevalence rate.
PUBHEALTH_RISK_DIFFERENCE(exposed_risk: number, unexposed_risk: number) → number	number	Grid extension. Returns epidemiologic risk difference.
PUBHEALTH_SCREENING_YIELD(positive_screens: number, screened: number) → number	number	Grid extension. Returns screening yield.
PUBLIC_ADMIN_BACKLOG_RATE(open_cases: number, total_cases: number) → number	number	Grid extension. Returns public-administration backlog rate.
PUBLIC_ADMIN_BUDGET_EXECUTION(spent: number, appropriated: number) → number	number	Grid extension. Returns budget execution rate.
PUBLIC_ADMIN_SPAN_OF_CONTROL(direct_reports: number, managers: number) → number	number	Grid extension. Returns administrative span of control.
SOCIAL_GINI_COEFFICIENT(values: number[]) → number	number	Grid extension. Returns the Gini coefficient for a distribution.
SOCIAL_HERFINDAHL_INDEX(shares: number[]) → number	number	Grid extension. Returns the Herfindahl-Hirschman concentration index from shares.
SOCIAL_INCIDENT_RATE(events: number, population: number) → number	number	Grid extension. Returns incident rate.
SOCIAL_RESPONSE_RATE(responses: number, invited: number) → number	number	Grid extension. Returns survey response rate.
SW_CASELOAD_UTILIZATION(active_cases: number, capacity: number) → number	number	Grid extension. Returns social-work caseload utilization.
SW_RECURRENCE_RATE(repeat_cases: number, total_cases: number) → number	number	Grid extension. Returns recurrence rate.
SW_SERVICE_PENETRATION(clients_served: number, eligible_population: number) → number	number	Grid extension. Returns service penetration rate.
THEATER_SEAT_UTILIZATION(attendance: number, seats: number) → number	number	Grid extension. Returns theater seat utilization.
THEOLOGY_ATTENDANCE_GROWTH(current_attendance: number, prior_attendance: number) → number	number	Grid extension. Returns congregation attendance growth rate.
THEOLOGY_TEXTUAL_VARIANT_RATE(variants: number, words: number) → number	number	Grid extension. Returns textual variant density for theology and religious studies.
URBAN_DENSITY(population: number, area_sq_km: number) → number	number	Grid extension. Returns population density per square kilometer.
URBAN_FLOOR_AREA_RATIO(floor_area: number, parcel_area: number) → number	number	Grid extension. Returns floor-area ratio.
URBAN_INTERSECTION_DELAY(total_delay_seconds: number, vehicles: number) → number	number	Grid extension. Returns average intersection delay.
URBAN_PARKING_RATIO(parking_spaces: number, dwelling_units: number) → number	number	Grid extension. Returns parking spaces per dwelling unit.
URBAN_TRANSIT_CAPACITY(vehicle_capacity: number, vehicles_per_hour: number) → number	number	Grid extension. Returns corridor passenger capacity per hour.
VET_DOSE_BY_WEIGHT(weight_kg: number, dose_mg_per_kg: number) → number	number	Grid extension. Returns veterinary dose by weight.
VET_FEED_CONVERSION_RATIO(feed_intake: number, weight_gain: number) → number	number	Grid extension. Returns veterinary feed conversion ratio.
VET_MORTALITY_RATE(deaths: number, animals: number) → number	number	Grid extension. Returns veterinary mortality rate.
VET_RER(weight_kg: number) → number	number	Grid extension. Returns veterinary resting energy requirement.

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Industry Verticals

Agriculture, energy, manufacturing, retail, telecom, education, insurance, hospitality, media, mining, public-sector, automotive, professional-services, chemicals, pharma, food and beverage, CPG, water, waste, semiconductor, textile, aerospace, defense, entertainment, and gaming helpers.

Function count: 196.

Function	Returns	Notes
AEROSPACE_DISPATCH_RELIABILITY(departures_without_delay: number, total_departures: number) → number	number	Grid extension. Returns dispatch reliability.
AEROSPACE_MISSION_CAPABLE_RATE(mission_capable_aircraft: number, total_aircraft: number) → number	number	Grid extension. Returns mission-capable rate.
AEROSPACE_THRUST_TO_WEIGHT(thrust: number, weight: number) → number	number	Grid extension. Returns thrust-to-weight ratio.
AEROSPACE_WEIGHT_GROWTH_RATE(actual_weight: number, target_weight: number) → number	number	Grid extension. Returns aerospace weight growth rate.
AGRICULTURE_CROP_MARGIN_PER_HECTARE(revenue: number, variable_cost: number, area_hectares: number) → number	number	Grid extension. Returns crop gross margin per hectare.
AGRICULTURE_FEED_CONVERSION_RATIO(feed_kg: number, weight_gain_kg: number) → number	number	Grid extension. Returns livestock feed conversion ratio.
AGRICULTURE_FERTILIZER_RATE(nutrient_required_kg_ha: number, nutrient_fraction: number) → number	number	Grid extension. Returns fertilizer product rate for a target nutrient rate.
AGRICULTURE_GROWING_DEGREE_DAYS(average_temp_c: number, base_temp_c: number, days: number) → number	number	Grid extension. Returns growing degree days above a base temperature.
AGRICULTURE_HARVEST_LOSS_RATE(harvested_tonnes: number, preharvest_estimate_tonnes: number) → number	number	Grid extension. Returns harvest loss rate from preharvest estimate and harvested output.
AGRICULTURE_IRRIGATION_REQUIREMENT(crop_et_mm: number, effective_rainfall_mm: number, area_hectares: number) → number	number	Grid extension. Returns net irrigation requirement in cubic meters.
AGRICULTURE_MILK_YIELD_PER_COW(milk_liters: number, cows: number) → number	number	Grid extension. Returns milk yield per cow.
AGRICULTURE_SEED_RATE(seed_kg: number, area_hectares: number) → number	number	Grid extension. Returns seed application rate in kilograms per hectare.
AGRICULTURE_STOCKING_DENSITY(animals: number, area_hectares: number) → number	number	Grid extension. Returns livestock stocking density.
AGRICULTURE_WATER_PRODUCTIVITY(production_tonnes: number, water_m3: number) → number	number	Grid extension. Returns agricultural output per cubic meter of water.
AGRICULTURE_YIELD_PER_HECTARE(production_tonnes: number, area_hectares: number) → number	number	Grid extension. Returns crop yield in tonnes per hectare.
AUTOMOTIVE_ASSEMBLY_LINE_RATE(units: number, hours: number) → number	number	Grid extension. Returns assembly line production rate.
AUTOMOTIVE_BATTERY_RANGE(usable_kwh: number, consumption_kwh_per_km: number) → number	number	Grid extension. Returns electric-vehicle battery range.
AUTOMOTIVE_DAYS_SUPPLY(inventory_units: number, daily_sales: number) → number	number	Grid extension. Returns vehicle days of supply.
AUTOMOTIVE_DEALER_GROSS_PER_UNIT(gross_profit: number, units_sold: number) → number	number	Grid extension. Returns dealer gross profit per unit.
AUTOMOTIVE_DEFECTS_PER_VEHICLE(defects: number, vehicles: number) → number	number	Grid extension. Returns defects per vehicle.
AUTOMOTIVE_FIXED_RIGHT_FIRST_TIME(first_time_repairs: number, repairs: number) → number	number	Grid extension. Returns fixed-right-first-time repair rate.
AUTOMOTIVE_PLATFORM_COMMONALITY(shared_parts: number, total_parts: number) → number	number	Grid extension. Returns platform part commonality.
AUTOMOTIVE_RANGE_EFFICIENCY(range_km: number, usable_kwh: number) → number	number	Grid extension. Returns EV range per kWh.
AUTOMOTIVE_RECALL_RATE(recalled_vehicles: number, vehicles_sold: number) → number	number	Grid extension. Returns vehicle recall rate.
AUTOMOTIVE_SUPPLIER_OTD(on_time_deliveries: number, deliveries: number) → number	number	Grid extension. Returns supplier on-time delivery rate.
AUTOMOTIVE_WARRANTY_CLAIM_RATE(claims: number, units_sold: number) → number	number	Grid extension. Returns warranty claim rate.
CHEMICAL_ATOM_ECONOMY(product_molecular_weight: number, reactant_molecular_weight_sum: number) → number	number	Grid extension. Returns atom economy.
CHEMICAL_BATCH_CYCLE_TIME(total_hours: number, batches: number) → number	number	Grid extension. Returns average batch cycle time.
CHEMICAL_ENERGY_INTENSITY(energy: number, production: number) → number	number	Grid extension. Returns chemical process energy intensity.
CHEMICAL_REACTION_YIELD(actual_yield: number, theoretical_yield: number) → number	number	Grid extension. Returns chemical reaction yield.
CHEMICAL_SELECTIVITY(desired_product: number, total_product: number) → number	number	Grid extension. Returns reaction selectivity.
CHEMICAL_SOLVENT_RECOVERY(solvent_recovered: number, solvent_used: number) → number	number	Grid extension. Returns solvent recovery rate.
CPG_NUMERIC_DISTRIBUTION(stores_carrying: number, total_stores: number) → number	number	Grid extension. Returns numeric distribution.
CPG_PROMO_LIFT(promo_sales: number, baseline_sales: number) → number	number	Grid extension. Returns promotion lift.
CPG_TRADE_SPEND_ROI(incremental_margin: number, trade_spend: number) → number	number	Grid extension. Returns trade-spend return on investment.
CPG_VELOCITY(units_sold: number, stores: number) → number	number	Grid extension. Returns unit velocity per store.
CPG_WEIGHTED_DISTRIBUTION(distribution_acv: number, market_acv: number) → number	number	Grid extension. Returns weighted distribution.
DEFENSE_READINESS_RATE(ready_units: number, assigned_units: number) → number	number	Grid extension. Returns defense readiness rate.
DEFENSE_SORTIE_GENERATION_RATE(sorties: number, aircraft: number) → number	number	Grid extension. Returns sortie generation rate.
EDUCATION_ATTENDANCE_RATE(attended_days: number, enrolled_days: number) → number	number	Grid extension. Returns attendance rate.
EDUCATION_COST_PER_STUDENT(cost: number, students: number) → number	number	Grid extension. Returns cost per student.
EDUCATION_CREDITS_PER_STUDENT(credits_completed: number, students: number) → number	number	Grid extension. Returns credits completed per student.
EDUCATION_DROPOUT_RATE(dropouts: number, enrolled_students: number) → number	number	Grid extension. Returns dropout rate.
EDUCATION_GRADUATION_RATE(graduates: number, cohort_size: number) → number	number	Grid extension. Returns graduation rate.
EDUCATION_PASS_RATE(passing_students: number, assessed_students: number) → number	number	Grid extension. Returns assessment pass rate.
EDUCATION_PLACEMENT_RATE(placed_graduates: number, graduates: number) → number	number	Grid extension. Returns graduate placement rate.
EDUCATION_RESEARCH_FUNDING_PER_FACULTY(research_funding: number, faculty: number) → number	number	Grid extension. Returns research funding per faculty member.
EDUCATION_RETENTION_RATE(returning_students: number, eligible_students: number) → number	number	Grid extension. Returns student retention rate.
EDUCATION_STUDENT_TEACHER_RATIO(students: number, teachers: number) → number	number	Grid extension. Returns student-teacher ratio.
EDUCATION_YIELD_RATE(enrolled_students: number, admitted_students: number) → number	number	Grid extension. Returns admissions yield rate.
ENERGY_CAPACITY_FACTOR(actual_mwh: number, capacity_mw: number, hours: number) → number	number	Grid extension. Returns generating asset capacity factor.
ENERGY_CURTAILMENT_RATE(curtailed_mwh: number, generated_mwh: number) → number	number	Grid extension. Returns renewable curtailment rate.
ENERGY_EMISSIONS(energy_mwh: number, emission_factor: number) → number	number	Grid extension. Returns emissions from energy and an emission factor.
ENERGY_HEAT_RATE(fuel_energy_mmbtu: number, output_mwh: number) → number	number	Grid extension. Returns heat rate in MMBtu per MWh.
ENERGY_LCOE(capex: number, fixed_om: number, variable_om_per_mwh: number, annual_mwh: number, capital_recovery_factor: number) → number	number	Grid extension. Returns levelized cost of energy.
ENERGY_RESERVE_MARGIN(available_capacity_mw: number, peak_demand_mw: number) → number	number	Grid extension. Returns reserve margin above peak demand.
ENERGY_SPARK_SPREAD(power_price_per_mwh: number, heat_rate_mmbtu_per_mwh: number, fuel_price_per_mmbtu: number) → number	number	Grid extension. Returns power spark spread.
ENERGY_STORAGE_DURATION(energy_mwh: number, power_mw: number) → number	number	Grid extension. Returns storage duration in hours.
ENERGY_TD_LOSS_RATE(energy_input_mwh: number, energy_delivered_mwh: number) → number	number	Grid extension. Returns transmission and distribution loss rate.
ENTERTAINMENT_BOX_OFFICE_SHARE(gross: number, market_gross: number) → number	number	Grid extension. Returns box-office market share.
ENTERTAINMENT_OCCUPANCY_RATE(tickets_sold: number, venue_capacity: number) → number	number	Grid extension. Returns venue occupancy rate.
ENTERTAINMENT_REVENUE_PER_ATTENDEE(revenue: number, attendees: number) → number	number	Grid extension. Returns revenue per attendee.
ENTERTAINMENT_STREAMING_COMPLETION_RATE(completed_streams: number, started_streams: number) → number	number	Grid extension. Returns streaming completion rate.
FOOD_BEVERAGE_COLD_CHAIN_EXCURSION_RATE(excursions: number, shipments: number) → number	number	Grid extension. Returns cold-chain excursion rate.
FOOD_BEVERAGE_FILL_VARIANCE(actual_fill: number, target_fill: number) → number	number	Grid extension. Returns package fill variance.
FOOD_BEVERAGE_LINE_EFFICIENCY(actual_output: number, standard_output: number) → number	number	Grid extension. Returns line efficiency.
FOOD_BEVERAGE_RECIPE_COST_PER_UNIT(ingredient_cost: number, units: number) → number	number	Grid extension. Returns recipe cost per unit.
FOOD_BEVERAGE_WASTE_RATE(waste: number, input_material: number) → number	number	Grid extension. Returns food production waste rate.
FOOD_BEVERAGE_YIELD(finished_goods: number, input_material: number) → number	number	Grid extension. Returns food and beverage production yield.
GAMING_ARPDAU(revenue: number, daily_active_users: number) → number	number	Grid extension. Returns average revenue per daily active user.
GAMING_RETENTION_RATE(returning_users: number, cohort_users: number) → number	number	Grid extension. Returns cohort retention rate.
HOSPITALITY_ADR(room_revenue: number, rooms_sold: number) → number	number	Grid extension. Returns average daily rate.
HOSPITALITY_AVERAGE_CHECK(revenue: number, covers: number) → number	number	Grid extension. Returns average guest check.
HOSPITALITY_BOOKING_CANCELLATION_RATE(cancelled_bookings: number, total_bookings: number) → number	number	Grid extension. Returns booking cancellation rate.
HOSPITALITY_EVENT_SPACE_UTILIZATION(booked_hours: number, available_hours: number) → number	number	Grid extension. Returns event-space utilization.
HOSPITALITY_FOOD_COST_PERCENT(food_cost: number, food_revenue: number) → number	number	Grid extension. Returns food cost percentage.
HOSPITALITY_GOPPAR(gross_operating_profit: number, available_rooms: number) → number	number	Grid extension. Returns gross operating profit per available room.
HOSPITALITY_LABOR_COST_RATIO(labor_cost: number, revenue: number) → number	number	Grid extension. Returns hospitality labor cost ratio.
HOSPITALITY_OCCUPANCY_RATE(occupied_rooms: number, available_rooms: number) → number	number	Grid extension. Returns room occupancy rate.
HOSPITALITY_REVPAR(room_revenue: number, available_rooms: number) → number	number	Grid extension. Returns revenue per available room.
HOSPITALITY_REVPOR(room_revenue: number, occupied_rooms: number) → number	number	Grid extension. Returns revenue per occupied room.
HOSPITALITY_TABLE_TURNOVER(covers: number, seats: number) → number	number	Grid extension. Returns restaurant table turnover.
INSURANCE_AVERAGE_CLAIM_CYCLE_DAYS(total_cycle_days: number, claims: number) → number	number	Grid extension. Returns average claim cycle time in days.
INSURANCE_CLAIM_FREQUENCY(claims: number, exposures: number) → number	number	Grid extension. Returns claim frequency.
INSURANCE_CLAIM_SEVERITY(losses: number, claims: number) → number	number	Grid extension. Returns average claim severity.
INSURANCE_COMBINED_RATIO(claims: number, expenses: number, premiums: number) → number	number	Grid extension. Returns combined ratio.
INSURANCE_EXPENSE_RATIO(expenses: number, premiums: number) → number	number	Grid extension. Returns expense ratio.
INSURANCE_LOSS_RATIO(claims: number, premiums: number) → number	number	Grid extension. Returns insurance loss ratio.
INSURANCE_POLICY_GROWTH_RATE(ending_policies: number, beginning_policies: number) → number	number	Grid extension. Returns policy count growth rate.
INSURANCE_PREMIUM_ADEQUACY(premium: number, pure_premium: number) → number	number	Grid extension. Returns premium adequacy ratio.
INSURANCE_PURE_PREMIUM(claim_frequency: number, claim_severity: number) → number	number	Grid extension. Returns pure premium.
INSURANCE_RESERVE_ADEQUACY(case_reserves: number, expected_losses: number) → number	number	Grid extension. Returns reserve adequacy ratio.
INSURANCE_RETENTION_RATE(renewed_policies: number, eligible_policies: number) → number	number	Grid extension. Returns policy retention rate.
MANUFACTURING_CAPACITY_UTILIZATION(actual_output: number, rated_capacity: number) → number	number	Grid extension. Returns manufacturing capacity utilization.
MANUFACTURING_CHANGEOVER_LOSS_RATE(changeover_time: number, available_time: number) → number	number	Grid extension. Returns changeover loss rate.
MANUFACTURING_CYCLE_TIME(production_time: number, units: number) → number	number	Grid extension. Returns cycle time per unit.
MANUFACTURING_DEFECTS_PER_MILLION(defects: number, units: number) → number	number	Grid extension. Returns defects per million units.
MANUFACTURING_FIRST_PASS_YIELD(good_units: number, total_units: number) → number	number	Grid extension. Returns first-pass yield.
MANUFACTURING_OEE(availability: number, performance: number, quality: number) → number	number	Grid extension. Returns overall equipment effectiveness.
MANUFACTURING_QUEUE_TIME_RATIO(queue_time: number, total_lead_time: number) → number	number	Grid extension. Returns queue-time share of lead time.
MANUFACTURING_SCRAP_RATE(scrap_units: number, total_units: number) → number	number	Grid extension. Returns scrap rate.
MANUFACTURING_TAKT_TIME(available_time: number, customer_demand: number) → number	number	Grid extension. Returns takt time.
MANUFACTURING_THROUGHPUT(units: number, time: number) → number	number	Grid extension. Returns manufacturing throughput rate.
MANUFACTURING_YIELD_FROM_INPUT(good_output: number, input_material: number) → number	number	Grid extension. Returns good output per input material unit.
MEDIA_COMPLETION_RATE(completed_views: number, video_starts: number) → number	number	Grid extension. Returns video completion rate.
MEDIA_CONTENT_ROI(revenue: number, content_cost: number) → number	number	Grid extension. Returns content return on investment.
MEDIA_CONVERSION_RATE(conversions: number, clicks: number) → number	number	Grid extension. Returns media conversion rate.
MEDIA_CPC(spend: number, clicks: number) → number	number	Grid extension. Returns cost per click.
MEDIA_CPM(spend: number, impressions: number) → number	number	Grid extension. Returns media cost per thousand impressions.
MEDIA_CTR(clicks: number, impressions: number) → number	number	Grid extension. Returns click-through rate.
MEDIA_FILL_RATE(filled_impressions: number, ad_requests: number) → number	number	Grid extension. Returns ad fill rate.
MEDIA_FREQUENCY(impressions: number, reach: number) → number	number	Grid extension. Returns average media frequency.
MEDIA_REACH_RATE(reached_audience: number, target_audience: number) → number	number	Grid extension. Returns target-audience reach rate.
MEDIA_ROAS(revenue: number, spend: number) → number	number	Grid extension. Returns return on ad spend.
MEDIA_SUBSCRIBER_CHURN(churned_subscribers: number, starting_subscribers: number) → number	number	Grid extension. Returns media subscriber churn rate.
MINING_AISC_PER_UNIT(cash_cost: number, sustaining_capex: number, production_units: number) → number	number	Grid extension. Returns all-in sustaining cost per production unit.
MINING_CASH_COST_PER_TONNE(cash_cost: number, tonnes: number) → number	number	Grid extension. Returns mining cash cost per tonne.
MINING_CUT_OFF_GRADE(cost_per_tonne: number, recovery_rate: number, metal_price_per_unit: number) → number	number	Grid extension. Returns cutoff grade from cost, recovery, and price.
MINING_DILUTION_RATE(waste_in_ore: number, ore_tonnes: number) → number	number	Grid extension. Returns dilution rate.
MINING_EQUIPMENT_UTILIZATION(operating_hours: number, available_hours: number) → number	number	Grid extension. Returns mining equipment utilization.
MINING_MILL_THROUGHPUT(tonnes: number, hours: number) → number	number	Grid extension. Returns mill throughput.
MINING_ORE_GRADE(contained_metal: number, ore_tonnes: number) → number	number	Grid extension. Returns ore grade.
MINING_RECOVERY_RATE(recovered_metal: number, contained_metal: number) → number	number	Grid extension. Returns metallurgical recovery rate.
MINING_RESERVE_LIFE(reserve_tonnes: number, annual_production_tonnes: number) → number	number	Grid extension. Returns reserve life in years.
MINING_STRIP_RATIO(waste_tonnes: number, ore_tonnes: number) → number	number	Grid extension. Returns waste-to-ore strip ratio.
MINING_WATER_INTENSITY(water_m3: number, tonnes_processed: number) → number	number	Grid extension. Returns mining water intensity.
PHARMA_BATCH_YIELD(released_units: number, planned_units: number) → number	number	Grid extension. Returns pharmaceutical batch yield.
PHARMA_COST_PER_DOSE(total_cost: number, doses: number) → number	number	Grid extension. Returns cost per dose.
PHARMA_DEVIATION_RATE(deviations: number, batches: number) → number	number	Grid extension. Returns batch deviation rate.
PHARMA_FILL_FINISH_YIELD(filled_units: number, started_units: number) → number	number	Grid extension. Returns fill-finish yield.
PHARMA_STABILITY_SHELF_LIFE(allowable_potency_loss: number, monthly_potency_loss: number) → number	number	Grid extension. Returns estimated stability shelf life in months.
PHARMA_TRIAL_ENROLLMENT_RATE(enrolled_subjects: number, target_subjects: number) → number	number	Grid extension. Returns clinical trial enrollment attainment rate.
PROFESSIONAL_BACKLOG_MONTHS(backlog_revenue: number, monthly_revenue: number) → number	number	Grid extension. Returns backlog coverage in months.
PROFESSIONAL_DSO(accounts_receivable: number, daily_revenue: number) → number	number	Grid extension. Returns days sales outstanding.
PROFESSIONAL_EFFECTIVE_RATE(revenue: number, billable_hours: number) → number	number	Grid extension. Returns effective bill rate.
PROFESSIONAL_LEVERAGE_RATIO(non_partner_professionals: number, partners: number) → number	number	Grid extension. Returns professional-services leverage ratio.
PROFESSIONAL_PIPELINE_COVERAGE(pipeline_value: number, revenue_target: number) → number	number	Grid extension. Returns sales pipeline coverage against target.
PROFESSIONAL_PROJECT_MARGIN(revenue: number, cost: number) → number	number	Grid extension. Returns professional-services project margin.
PROFESSIONAL_REALIZATION(billed_amount: number, standard_amount: number) → number	number	Grid extension. Returns billing realization rate.
PROFESSIONAL_REPEAT_CLIENT_RATE(repeat_clients: number, clients: number) → number	number	Grid extension. Returns repeat-client rate.
PROFESSIONAL_SCOPE_CHANGE_RATE(change_orders: number, projects: number) → number	number	Grid extension. Returns scope-change rate.
PROFESSIONAL_UTILIZATION(billable_hours: number, available_hours: number) → number	number	Grid extension. Returns billable utilization rate.
PROFESSIONAL_WRITE_OFF_RATE(write_offs: number, gross_fees: number) → number	number	Grid extension. Returns fee write-off rate.
PUBLIC_SECTOR_BACKLOG_CHANGE(ending_backlog: number, beginning_backlog: number) → number	number	Grid extension. Returns public-sector backlog change.
PUBLIC_SECTOR_BUDGET_VARIANCE(actual_spend: number, budget: number) → number	number	Grid extension. Returns budget variance.
PUBLIC_SECTOR_CASE_CLEARANCE_RATE(closed_cases: number, opened_cases: number) → number	number	Grid extension. Returns case clearance rate.
PUBLIC_SECTOR_COST_PER_RESIDENT(cost: number, residents: number) → number	number	Grid extension. Returns public cost per resident.
PUBLIC_SECTOR_DIGITAL_UPTAKE(online_transactions: number, total_transactions: number) → number	number	Grid extension. Returns digital channel uptake rate.
PUBLIC_SECTOR_GRANT_BURN_RATE(spend: number, elapsed_days: number) → number	number	Grid extension. Returns grant burn rate per day.
PUBLIC_SECTOR_PERMIT_CYCLE_TIME(total_days: number, permits: number) → number	number	Grid extension. Returns average permit cycle time.
PUBLIC_SECTOR_RESPONSE_TIME_VARIANCE(actual_response_time: number, target_response_time: number) → number	number	Grid extension. Returns response-time variance to target.
PUBLIC_SECTOR_SERVICE_LEVEL(on_time_cases: number, total_cases: number) → number	number	Grid extension. Returns public-sector service-level attainment.
PUBLIC_SECTOR_TAX_COLLECTION_RATE(collected: number, billed: number) → number	number	Grid extension. Returns tax collection rate.
PUBLIC_SECTOR_UTILIZATION(active_capacity: number, total_capacity: number) → number	number	Grid extension. Returns public asset utilization.
RETAIL_AVERAGE_TRANSACTION_VALUE(revenue: number, transactions: number) → number	number	Grid extension. Returns average transaction value.
RETAIL_CONVERSION_RATE(purchases: number, visitors: number) → number	number	Grid extension. Returns retail conversion rate.
RETAIL_GMROI(gross_margin_dollars: number, average_inventory_cost: number) → number	number	Grid extension. Returns gross margin return on inventory investment.
RETAIL_GROSS_MARGIN(revenue: number, cost_of_goods_sold: number) → number	number	Grid extension. Returns retail gross margin rate.
RETAIL_INVENTORY_TURNOVER(cost_of_goods_sold: number, average_inventory: number) → number	number	Grid extension. Returns retail inventory turnover.
RETAIL_MARKDOWN_RATE(original_price: number, sale_price: number) → number	number	Grid extension. Returns markdown rate.
RETAIL_RETURN_RATE(returns: number, sales: number) → number	number	Grid extension. Returns retail return rate.
RETAIL_SALES_PER_SQFT(revenue: number, square_feet: number) → number	number	Grid extension. Returns retail sales per square foot.
RETAIL_SELL_THROUGH(units_sold: number, units_received: number) → number	number	Grid extension. Returns sell-through rate.
RETAIL_SHRINK_RATE(shrink_value: number, book_inventory_value: number) → number	number	Grid extension. Returns inventory shrink rate.
RETAIL_STOCK_COVER_DAYS(inventory_units: number, daily_unit_sales: number) → number	number	Grid extension. Returns stock-cover days.
SEMICONDUCTOR_CYCLE_TIME_PER_LAYER(cycle_days: number, layers: number) → number	number	Grid extension. Returns cycle time per process layer.
SEMICONDUCTOR_DEFECT_DENSITY(defects: number, area: number) → number	number	Grid extension. Returns defect density.
SEMICONDUCTOR_DIE_YIELD(good_die: number, total_die: number) → number	number	Grid extension. Returns die yield.
SEMICONDUCTOR_THROUGHPUT_WPH(wafers: number, hours: number) → number	number	Grid extension. Returns wafer throughput per hour.
SEMICONDUCTOR_TOOL_UTILIZATION(productive_time: number, available_time: number) → number	number	Grid extension. Returns semiconductor tool utilization.
SEMICONDUCTOR_WAFER_YIELD(good_wafers: number, started_wafers: number) → number	number	Grid extension. Returns wafer yield.
TELECOM_ARPU(revenue: number, subscribers: number) → number	number	Grid extension. Returns average revenue per user.
TELECOM_BACKHAUL_UTILIZATION(used_capacity: number, available_capacity: number) → number	number	Grid extension. Returns backhaul capacity utilization.
TELECOM_CHURN_RATE(churned_subscribers: number, starting_subscribers: number) → number	number	Grid extension. Returns subscriber churn rate.
TELECOM_COST_PER_GB(network_cost: number, data_gb: number) → number	number	Grid extension. Returns network cost per gigabyte.
TELECOM_DATA_USAGE_PER_SUBSCRIBER(data_gb: number, subscribers: number) → number	number	Grid extension. Returns data usage per subscriber.
TELECOM_DROPPED_CALL_RATE(dropped_calls: number, total_calls: number) → number	number	Grid extension. Returns dropped-call rate.
TELECOM_LATENCY_BUDGET_VARIANCE(actual_latency_ms: number, target_latency_ms: number) → number	number	Grid extension. Returns latency variance to target.
TELECOM_NETWORK_AVAILABILITY(total_time: number, downtime: number) → number	number	Grid extension. Returns network availability rate.
TELECOM_NET_ADDS(gross_adds: number, churned_subscribers: number) → number	number	Grid extension. Returns net subscriber additions.
TELECOM_REVENUE_PER_GB(revenue: number, data_gb: number) → number	number	Grid extension. Returns revenue per gigabyte.
TELECOM_SPECTRUM_EFFICIENCY(throughput_mbps: number, bandwidth_mhz: number) → number	number	Grid extension. Returns spectral efficiency.
TEXTILE_CUTTING_YIELD(cut_panel_area: number, fabric_area: number) → number	number	Grid extension. Returns cutting yield.
TEXTILE_DEFECT_RATE(defects: number, units: number) → number	number	Grid extension. Returns textile defect rate.
TEXTILE_DYE_YIELD(accepted_lots: number, processed_lots: number) → number	number	Grid extension. Returns dye lot yield.
TEXTILE_FABRIC_UTILIZATION(used_fabric: number, available_fabric: number) → number	number	Grid extension. Returns fabric utilization.
TEXTILE_SEWING_EFFICIENCY(standard_minutes: number, actual_minutes: number) → number	number	Grid extension. Returns sewing efficiency.
UTILITY_LOAD_FACTOR(average_load_mw: number, peak_load_mw: number) → number	number	Grid extension. Returns utility load factor.
UTILITY_SAIDI(customer_interruption_minutes: number, customers: number) → number	number	Grid extension. Returns average outage duration per customer.
UTILITY_SAIFI(customer_interruptions: number, customers: number) → number	number	Grid extension. Returns average outage frequency per customer.
WASTE_CAPTURE_RATE(collected_waste: number, generated_waste: number) → number	number	Grid extension. Returns waste capture rate.
WASTE_DIVERSION_RATE(diverted_waste: number, total_waste: number) → number	number	Grid extension. Returns waste diversion rate.
WATER_ENERGY_PER_M3(energy_kwh: number, water_m3: number) → number	number	Grid extension. Returns water utility energy per cubic meter.
WATER_LEAKAGE_RATE(leak_volume: number, system_input_volume: number) → number	number	Grid extension. Returns system leakage rate.
WATER_NON_REVENUE_WATER(water_produced: number, water_billed: number) → number	number	Grid extension. Returns non-revenue water rate.
WATER_TREATMENT_YIELD(treated_water: number, raw_water: number) → number	number	Grid extension. Returns water treatment yield.

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Real Estate

Real estate valuation, leasing, rent roll, lending, investor return, development, property operations, affordability, transaction, replacement-cost, and tax helpers.

Function count: 67.

Function	Returns	Notes
REAL_ESTATE_ABSORPTION_RATE(units_leased: number, months: number) → number	number	Grid extension. Returns leasing absorption rate per month.
REAL_ESTATE_AMORTIZATION_PAYMENT(loan_amount: number, annual_rate: number, years: number) → number	number	Grid extension. Returns monthly fully amortizing loan payment.
REAL_ESTATE_APPRECIATION_RATE(current_value: number, purchase_price: number) → number	number	Grid extension. Returns appreciation rate since purchase.
REAL_ESTATE_AVERAGE_LEASE_TERM(total_lease_months: number, lease_count: number) → number	number	Grid extension. Returns average lease term in months.
REAL_ESTATE_BREAKEVEN_OCCUPANCY(operating_expenses: number, debt_service: number, gross_potential_income: number) → number	number	Grid extension. Returns breakeven occupancy rate.
REAL_ESTATE_BROKER_COMMISSION(sale_price: number, commission_rate: number) → number	number	Grid extension. Returns broker commission amount.
REAL_ESTATE_BUILDING_EFFICIENCY(usable_area: number, gross_building_area: number) → number	number	Grid extension. Returns building efficiency ratio.
REAL_ESTATE_CAP_RATE(net_operating_income: number, property_value: number) → number	number	Grid extension. Returns capitalization rate.
REAL_ESTATE_CASH_ON_CASH(cash_flow: number, cash_invested: number) → number	number	Grid extension. Returns cash-on-cash return.
REAL_ESTATE_CLOSING_COST_RATE(closing_costs: number, purchase_price: number) → number	number	Grid extension. Returns closing costs as a share of purchase price.
REAL_ESTATE_CONCESSION_RATE(concessions: number, gross_rent: number) → number	number	Grid extension. Returns concession share of gross rent.
REAL_ESTATE_DEBT_YIELD(net_operating_income: number, loan_balance: number) → number	number	Grid extension. Returns real estate debt yield.
REAL_ESTATE_DEPRECIATED_COST(replacement_cost_new: number, depreciation_rate: number) → number	number	Grid extension. Returns depreciated replacement cost.
REAL_ESTATE_DEVELOPMENT_SPREAD(yield_on_cost: number, market_cap_rate: number) → number	number	Grid extension. Returns development spread between yield on cost and market cap rate.
REAL_ESTATE_DSCR(net_operating_income: number, debt_service: number) → number	number	Grid extension. Returns debt service coverage ratio.
REAL_ESTATE_ECONOMIC_VACANCY_RATE(gross_potential_rent: number, collected_rent: number) → number	number	Grid extension. Returns economic vacancy rate from potential and collected rent.
REAL_ESTATE_EFFECTIVE_GROSS_INCOME(gross_potential_income: number, vacancy_loss: number, other_income: number) → number	number	Grid extension. Returns effective gross income after vacancy loss plus other income.
REAL_ESTATE_EQUITY_MULTIPLE(total_distributions: number, equity_invested: number) → number	number	Grid extension. Returns equity multiple.
REAL_ESTATE_ESCALATED_RENT(current_rent: number, escalation_rate: number) → number	number	Grid extension. Returns rent after an escalation rate.
REAL_ESTATE_FLOOR_AREA_RATIO(building_area: number, land_area: number) → number	number	Grid extension. Returns floor area ratio.
REAL_ESTATE_GROSS_POTENTIAL_RENT(units: number, monthly_market_rent: number) → number	number	Grid extension. Returns annual gross potential rent from unit count and monthly market rent.
REAL_ESTATE_GROSS_RENT_MULTIPLIER(property_value: number, annual_gross_rent: number) → number	number	Grid extension. Returns gross rent multiplier.
REAL_ESTATE_HARD_COST_PER_SQFT(hard_cost: number, square_feet: number) → number	number	Grid extension. Returns hard cost per square foot.
REAL_ESTATE_HOUSING_EXPENSE_RATIO(monthly_housing_payment: number, gross_monthly_income: number) → number	number	Grid extension. Returns housing expense ratio.
REAL_ESTATE_INSURANCE_ESCROW_MONTHLY(annual_insurance: number) → number	number	Grid extension. Returns monthly insurance escrow.
REAL_ESTATE_LAND_TO_VALUE(land_cost: number, completed_value: number) → number	number	Grid extension. Returns land cost as a share of completed value.
REAL_ESTATE_LEASE_RENEWAL_RATE(renewed_leases: number, expiring_leases: number) → number	number	Grid extension. Returns lease renewal rate.
REAL_ESTATE_LOAD_FACTOR(rentable_area: number, usable_area: number) → number	number	Grid extension. Returns load factor from rentable and usable area.
REAL_ESTATE_LOAN_TO_VALUE(loan_balance: number, property_value: number) → number	number	Grid extension. Returns loan-to-value ratio.
REAL_ESTATE_LOSS_TO_LEASE(market_rent: number, in_place_rent: number) → number	number	Grid extension. Returns loss-to-lease as a share of market rent.
REAL_ESTATE_MAINTENANCE_COST_PER_UNIT(maintenance_cost: number, units: number) → number	number	Grid extension. Returns maintenance cost per unit.
REAL_ESTATE_MAX_LOAN_FROM_DSCR(net_operating_income: number, minimum_dscr: number, mortgage_constant: number) → number	number	Grid extension. Returns maximum supportable loan from NOI, minimum DSCR, and mortgage constant.
REAL_ESTATE_MONTHS_OF_SUPPLY(available_units: number, monthly_absorption: number) → number	number	Grid extension. Returns months of available supply.
REAL_ESTATE_MORTGAGE_CONSTANT(annual_debt_service: number, loan_amount: number) → number	number	Grid extension. Returns mortgage constant.
REAL_ESTATE_NET_EFFECTIVE_RENT(total_rent: number, concessions: number, lease_months: number) → number	number	Grid extension. Returns net effective rent per month after concessions.
REAL_ESTATE_NET_SALE_PROCEEDS(sale_price: number, debt_payoff: number, selling_costs: number) → number	number	Grid extension. Returns net sale proceeds after debt payoff and selling costs.
REAL_ESTATE_NOI(gross_income: number, operating_expenses: number) → number	number	Grid extension. Returns net operating income.
REAL_ESTATE_NOI_MARGIN(net_operating_income: number, effective_gross_income: number) → number	number	Grid extension. Returns NOI as a share of effective gross income.
REAL_ESTATE_OCCUPANCY_RATE(occupied_units: number, total_units: number) → number	number	Grid extension. Returns property occupancy rate.
REAL_ESTATE_OPERATING_EXPENSE_RATIO(operating_expenses: number, effective_gross_income: number) → number	number	Grid extension. Returns operating expenses as a share of effective gross income.
REAL_ESTATE_PARKING_RATIO(parking_spaces: number, rentable_area: number) → number	number	Grid extension. Returns parking spaces per 1,000 rentable square feet.
REAL_ESTATE_PHYSICAL_OCCUPANCY(leased_area: number, rentable_area: number) → number	number	Grid extension. Returns leased rentable area share.
REAL_ESTATE_PITI(principal_interest_payment: number, annual_property_tax: number, annual_insurance: number, monthly_hoa: number) → number	number	Grid extension. Returns monthly principal, interest, taxes, insurance, and HOA payment.
REAL_ESTATE_PRICE_PER_SQFT(property_value: number, square_feet: number) → number	number	Grid extension. Returns property price per square foot.
REAL_ESTATE_PROFIT_ON_COST(stabilized_value: number, total_project_cost: number) → number	number	Grid extension. Returns profit on cost.
REAL_ESTATE_PROPERTY_MANAGEMENT_FEE(managed_revenue: number, fee_rate: number) → number	number	Grid extension. Returns property management fee amount.
REAL_ESTATE_PROPERTY_TAX(assessed_value: number, millage_rate: number) → number	number	Grid extension. Returns annual property tax from assessed value and mills.
REAL_ESTATE_RECAPTURE_PERIOD(initial_investment: number, annual_cash_flow: number) → number	number	Grid extension. Returns simple payback period in years.
REAL_ESTATE_RENTABLE_TO_USABLE_RATIO(rentable_area: number, usable_area: number) → number	number	Grid extension. Returns rentable-to-usable area ratio.
REAL_ESTATE_RENT_COLLECTION_RATE(collected_rent: number, billed_rent: number) → number	number	Grid extension. Returns rent collection rate.
REAL_ESTATE_RENT_GROWTH_RATE(current_rent: number, prior_rent: number) → number	number	Grid extension. Returns rent growth rate.
REAL_ESTATE_RENT_PER_SQFT(rent: number, square_feet: number) → number	number	Grid extension. Returns rent per square foot.
REAL_ESTATE_RENT_TO_INCOME(monthly_rent: number, gross_monthly_income: number) → number	number	Grid extension. Returns rent-to-income ratio.
REAL_ESTATE_REPLACEMENT_COST_NEW(area: number, cost_per_sqft: number) → number	number	Grid extension. Returns replacement cost new.
REAL_ESTATE_REPLACEMENT_RESERVE_PER_UNIT(annual_reserve: number, units: number) → number	number	Grid extension. Returns annual replacement reserve per unit.
REAL_ESTATE_REVPAU(revenue: number, available_units: number) → number	number	Grid extension. Returns revenue per available unit.
REAL_ESTATE_SOFT_COST_RATE(soft_cost: number, hard_cost: number) → number	number	Grid extension. Returns soft cost as a share of hard cost.
REAL_ESTATE_TAX_ASSESSED_VALUE(market_value: number, assessment_ratio: number) → number	number	Grid extension. Returns tax assessed value.
REAL_ESTATE_TAX_ESCROW_MONTHLY(annual_property_tax: number) → number	number	Grid extension. Returns monthly property tax escrow.
REAL_ESTATE_TENANT_RETENTION_RATE(retained_tenants: number, expiring_tenants: number) → number	number	Grid extension. Returns tenant retention rate.
REAL_ESTATE_TOTAL_RETURN(income: number, value_change: number, invested_capital: number) → number	number	Grid extension. Returns total return from income and value change.
REAL_ESTATE_TURNOVER_COST_PER_UNIT(turnover_cost: number, turned_units: number) → number	number	Grid extension. Returns turnover cost per turned unit.
REAL_ESTATE_UNIT_DENSITY(units: number, land_area: number) → number	number	Grid extension. Returns units per land area unit.
REAL_ESTATE_VACANCY_RATE(vacant_units: number, total_units: number) → number	number	Grid extension. Returns vacant unit share.
REAL_ESTATE_VALUE_FROM_CAP_RATE(net_operating_income: number, cap_rate: number) → number	number	Grid extension. Returns property value implied by NOI and cap rate.
REAL_ESTATE_WALE(remaining_months_area: number, leased_area: number) → number	number	Grid extension. Returns weighted average lease expiry in months.
REAL_ESTATE_YIELD_ON_COST(stabilized_noi: number, total_project_cost: number) → number	number	Grid extension. Returns development yield on cost.

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Computer Science

Computer science algorithms for searching, sorting, strings, dynamic programming, graphs, ranking, and probabilistic data structures.

Function count: 273.

Function	Returns	Notes
BITMAP(bit: number...) → bitmap	bitmap	variadic, Grid extension. Constructs a sparse persistent bitmap from set-bit positions.
BITMAP_AND(left: bitmap, right: bitmap) → bitmap	bitmap	Grid extension. Returns the word-wise intersection of two bitmaps.
BITMAP_CLEAR(bitmap: bitmap, bit: number) → bitmap	bitmap	Grid extension. Returns a bitmap revision with one bit cleared.
BITMAP_COUNT(bitmap: bitmap) → number	number	Grid extension. Returns the number of set bits in constant time.
BITMAP_GET(bitmap: bitmap, bit: number) → boolean	boolean	Grid extension. Tests one bitmap position.
BITMAP_NOT(bitmap: bitmap, bit_count: number) → bitmap	bitmap	Grid extension. Complements a bitmap over the explicit finite domain [0, bit_count).
BITMAP_OR(left: bitmap, right: bitmap) → bitmap	bitmap	Grid extension. Returns the word-wise union of two bitmaps.
BITMAP_RANK(bitmap: bitmap, bit: number) → number	number	Grid extension. Counts set bits at or below a position.
BITMAP_SELECT(bitmap: bitmap, rank: number) → number	number	Grid extension. Returns the zero-based kth set-bit position or BLANK.
BITMAP_SET(bitmap: bitmap, bit: number) → bitmap	bitmap	Grid extension. Returns a bitmap revision with one bit set.
BITMAP_XOR(left: bitmap, right: bitmap) → bitmap	bitmap	Grid extension. Returns the word-wise symmetric difference of two bitmaps.
BITPOS(bitmap: bitmap, set: boolean, start: number, end: number) → number	number	Grid extension. Finds the first set or clear position in a bounded inclusive range.
BLOOM(expected_items: number, false_positive_rate: number) → bloom	bloom	Grid extension. Constructs a bounded persistent Bloom filter for an expected population and false-positive rate.
BLOOM_ADD(filter: bloom, value: any) → bloom	bloom	Grid extension. Returns a Bloom-filter revision containing a stable fingerprint of the value.
BLOOM_CONTAINS(filter: bloom, value: any) → boolean	boolean	Grid extension. Tests probabilistic membership with no false negatives for inserted values.
BLOOM_UNION(left: bloom, right: bloom) → bloom	bloom	Grid extension. Merges two identically configured Bloom filters.
CMS_ADD(sketch: count_min, value: any, [count]: number) → count_min	count_min	Grid extension. Adds a nonnegative count to a value in a Count-Min sketch revision.
CMS_ESTIMATE(sketch: count_min, value: any) → number	number	Grid extension. Returns the Count-Min upper-bound frequency estimate for a value.
CMS_MERGE(left: count_min, right: count_min) → count_min	count_min	Grid extension. Adds the counters of identically configured Count-Min sketches.
CMS_TOTAL(sketch: count_min) → number	number	Grid extension. Returns the exact total count added to a Count-Min sketch.
COUNT_MIN(width: number, depth: number) → count_min	count_min	Grid extension. Constructs a bounded sparse persistent Count-Min frequency sketch.
CS_ADLER32(text: string) → number	number	Grid extension. Returns the Adler-32 checksum of the UTF-8 bytes of a string.
CS_ARGSORT(values: number[], descending?: boolean) → number[]	number[]	Grid extension. Returns the 1-based indices that sort a numeric array. Pass TRUE as the second argument for descending order.
CS_ARTICULATION_POINT_COUNT(edges: array) → number	number	Grid extension. Returns the number of articulation points (cut vertices) in an undirected edge-list graph using Tarjan's low-link algorithm.
CS_BASE_CONVERT(text: string, from_base: number, to_base: number) → string	string	Grid extension. Converts an integer expressed as text from one base to another. Both bases must be between 2 and 36.
CS_BELLMAN_FORD_DISTANCE(edges: array, start: any, goal: any) → number	number	Grid extension. Returns the weighted shortest-path distance between two nodes allowing negative edge weights, -1 if unreachable, or #NUM! when a negative-weight cycle is reachable from the start.
CS_BFS_ORDER(edges: array, start: any, directed?: boolean) → array	array	Grid extension. Returns nodes in breadth-first order from a start node over an edge list. Pass FALSE as the third argument to treat the edges as undirected.
CS_BINARY_SEARCH(sorted_values: number[], target: number) → number	number	Grid extension. Returns the 1-based position of a target in a sorted numeric array, or 0 when absent.
CS_BLOOM_FPR(inserted_items: number, bit_count: number, hash_count: number) → number	number	Grid extension. Returns the approximate Bloom filter false-positive rate.
CS_BRIDGE_COUNT(edges: array) → number	number	Grid extension. Returns the number of bridges (cut edges) in an undirected edge-list graph using Tarjan's low-link algorithm.
CS_CATALAN(n: number) → number	number	Grid extension. Returns the n-th Catalan number.
CS_COIN_CHANGE_MIN(coins: number[], amount: number) → number	number	Grid extension. Returns the minimum number of coins needed to make an amount, or -1 if impossible.
CS_CONNECTED_COMPONENTS(edges: array) → number	number	Grid extension. Returns the number of connected components in an undirected edge list.
CS_CRC32(text: string) → number	number	Grid extension. Returns the CRC-32 (IEEE) checksum of the UTF-8 bytes of a string.
CS_DFS_ORDER(edges: array, start: any, directed?: boolean) → array	array	Grid extension. Returns nodes in depth-first order from a start node over an edge list. Pass FALSE as the third argument to treat the edges as undirected.
CS_DIJKSTRA_DISTANCE(edges: array, start: any, goal: any) → number	number	Grid extension. Returns the weighted shortest-path distance between two nodes in an edge list, or -1 if unreachable.
CS_DIJKSTRA_PATH(edges: array, start: any, goal: any) → array	array	Grid extension. Returns the node sequence of the minimum-weight path between two nodes in a weighted edge list, or an empty array when the goal is unreachable.
CS_EDIT_DISTANCE(left: string, right: string) → number	number	Grid extension. Returns the Levenshtein edit distance between two strings.
CS_EULERIAN_PATH_EXISTS(edges: array, directed: boolean) → boolean	boolean	Grid extension. Returns whether an Eulerian path exists in an edge-list graph; treat edges as directed when the trailing argument is TRUE.
CS_EXTENDED_GCD(a: number, b: number) → number[]	number[]	Grid extension. Returns [gcd, x, y] of the extended Euclidean algorithm, satisfying a·x + b·y = gcd.
CS_FIBONACCI(n: number) → number	number	Grid extension. Returns the n-th Fibonacci number (F(0) = 0, F(1) = 1).
CS_FLOYD_WARSHALL(edges: array) → array	array	Grid extension. Returns the all-pairs shortest-path distance matrix over the sorted node set; unreachable pairs are blank and a negative-weight cycle yields #NUM!.
CS_FNV1A_HASH(text: string) → number	number	Grid extension. Returns the 32-bit FNV-1a hash of the UTF-8 bytes of a string.
CS_FREQUENCY_MAX(values: any[]) → number	number	Grid extension. Returns the largest occurrence count for any scalar value in an array.
CS_GRAPH_DENSITY(edges: array, directed: boolean) → number	number	Grid extension. Returns graph density from an edge list, treating edges as directed when requested.
CS_GRAPH_DIAMETER(edges: array, directed: boolean) → number	number	Grid extension. Returns the unweighted graph diameter (longest shortest-path) of an edge list, or -1 when the graph is disconnected; treat edges as directed when the trailing argument is TRUE.
CS_GRAPH_EDGE_COUNT(edges: array) → number	number	Grid extension. Returns the number of edge rows in an edge-list array.
CS_GRAPH_NODES(edges: array) → array	array	Grid extension. Returns the sorted unique node labels found in an edge list.
CS_GRAPH_NODE_COUNT(edges: array) → number	number	Grid extension. Returns the number of distinct nodes in an edge-list array.
CS_GRAPH_POISSON_SOLVE(edges: array, loads: array, fixed_nodes: array, weight_scale: number, tolerance: number, max_iterations: number) → array	array	Grid extension. Solves a positive weighted graph Poisson system with zero-valued fixed nodes using a sparse diagonally preconditioned conjugate-gradient kernel and returns a nodal column vector.
CS_GRAY_DECODE(value: number) → number	number	Grid extension. Returns the integer decoded from a binary-reflected Gray code value.
CS_GRAY_ENCODE(value: number) → number	number	Grid extension. Returns the binary-reflected Gray code of a non-negative integer.
CS_HAMMING_DISTANCE(left: string, right: string) → number	number	Grid extension. Returns the Hamming distance between equal-length strings.
CS_HAS_PATH(edges: array, start: any, goal: any, directed?: boolean) → boolean	boolean	Grid extension. Returns TRUE when a path exists from start to goal in an edge list. Pass FALSE as the fourth argument to treat the edges as undirected.
CS_HUFFMAN_CODE_LENGTH(frequencies: number[]) → number	number	Grid extension. Returns the total bit length of an optimal Huffman prefix code for the given symbol frequencies.
CS_IS_BIPARTITE(edges: array) → boolean	boolean	Grid extension. Returns TRUE when an undirected edge list is bipartite (two-colorable).
CS_IS_SORTED(values: number[], ascending: boolean) → boolean	boolean	Grid extension. Returns whether a numeric array is sorted ascending or descending.
CS_KMP_CONTAINS(text: string, pattern: string) → boolean	boolean	Grid extension. Returns whether text contains a pattern using Knuth-Morris-Pratt string matching.
CS_KMP_FIND(haystack: string, needle: string) → number	number	Grid extension. Returns the 1-based index of the first occurrence of needle in haystack using Knuth-Morris-Pratt, or 0 if absent.
CS_KNAPSACK_01(values: number[], weights: number[], capacity: number) → number	number	Grid extension. Returns the optimal value for a 0/1 knapsack instance.
CS_KNAPSACK_UNBOUNDED(values: number[], weights: number[], capacity: number) → number	number	Grid extension. Returns the optimal value for an unbounded knapsack instance where each item may be reused any number of times.
CS_KTH_LARGEST(values: number[], k: number) → number	number	Grid extension. Returns the k-th largest value (1-based) of a numeric array.
CS_KTH_SMALLEST(values: number[], k: number) → number	number	Grid extension. Returns the k-th smallest value (1-based) of a numeric array.
CS_LBM_D2Q9(width: number, height: number, steps: number, inlet_velocity: number, viscosity: number, mask: array) → array	array	Grid extension. Advances a masked two-dimensional D2Q9 BGK lattice-Boltzmann flow field with typed collision/streaming buffers and returns per-node speed, pressure, velocity, and solid-mask columns plus a summary row.
CS_LCS_LENGTH(left: string, right: string) → number	number	Grid extension. Returns the length of the longest common subsequence between two strings.
CS_LINEAR_SEARCH(values: any[], target: any) → number	number	Grid extension. Returns the 1-based position of a target in an array, or 0 when absent.
CS_LONGEST_COMMON_SUBSTRING_LENGTH(left: string, right: string) → number	number	Grid extension. Returns the length of the longest common contiguous substring of two strings.
CS_LONGEST_INCREASING_SUBSEQUENCE_LENGTH(values: number[]) → number	number	Grid extension. Returns the length of the longest strictly increasing subsequence in a numeric array.
CS_LONGEST_PALINDROME_LENGTH(text: string) → number	number	Grid extension. Returns the length of the longest palindromic substring of a string.
CS_LOWER_BOUND(values: number[], target: number) → number	number	Grid extension. Returns the 1-based insertion index of the first element greater than or equal to target in a sorted ascending array.
CS_MATRIX_CHAIN_MIN_COST(dimensions: number[]) → number	number	Grid extension. Returns the minimum number of scalar multiplications to multiply a matrix chain whose dimensions are given as n+1 values.
CS_MAX_FLOW(edges: array, source: any, sink: any) → number	number	Grid extension. Returns the maximum directed flow between two nodes in an edge list using Edmonds-Karp.
CS_MAX_SUBARRAY_SUM(values: number[]) → number	number	Grid extension. Returns the maximum contiguous subarray sum using Kadane's algorithm.
CS_MD5_HEX(text: string) → string	string	Grid extension. Returns the lowercase hexadecimal MD5 digest of the UTF-8 bytes of a string.
CS_MERGE_SORTED(left: number[], right: number[], descending?: boolean) → number[]	number[]	Grid extension. Merges two sorted numeric arrays into a single sorted array. Pass TRUE as the third argument when the inputs are sorted descending.
CS_MODPOW(base: number, exponent: number, modulus: number) → number	number	Grid extension. Returns modular exponentiation (base^exponent mod modulus) using binary exponentiation.
CS_MOD_INVERSE(value: number, modulus: number) → number	number	Grid extension. Returns the modular multiplicative inverse of a value (extended Euclidean algorithm), or #NUM! when the value and modulus are not coprime.
CS_MOVING_AVERAGE_SIMPLE(values: number[], window: number) → number[]	number[]	Grid extension. Returns simple moving averages for a numeric array and fixed window.
CS_MST_EDGES(edges: array) → array	array	Grid extension. Returns the [from, to, weight] edges of a minimum spanning tree of an undirected weighted edge list (Kruskal's algorithm), or #NUM! when the graph is not connected.
CS_MST_WEIGHT(edges: array) → number	number	Grid extension. Returns the total weight of a minimum spanning tree of an undirected weighted edge list (Kruskal's algorithm), or #NUM! when the graph is not connected.
CS_MULTIBODY_PLANAR(bodies: array, initial_state: array, steps: number, dt: number, drive_scale: number, gravity: number) → array	array	Grid extension. Advances a validated planar articulated-body tree with compliant joints, state-dependent kinematics, reverse reaction accumulation, and semi-implicit integration, returning per-body state plus summary monitors.
CS_NEXT_PERMUTATION(values: number[]) → number[]	number[]	Grid extension. Returns the next lexicographic permutation of a numeric array, wrapping to the smallest permutation after the largest.
CS_NQUEENS_COUNT(n: number) → number	number	Grid extension. Returns the number of distinct solutions to the n-queens problem (n at most 14).
CS_NTH_PERMUTATION(values: number[], n: number) → number[]	number[]	Grid extension. Returns the n-th (1-based) lexicographic permutation of the sorted input values.
CS_PAGE_RANK(adjacency: array, damping: number, iterations: number) → number[]	number[]	Grid extension. Returns PageRank scores from an adjacency matrix using damping and fixed iterations.
CS_PERMUTATION_RANK(values: number[]) → number	number	Grid extension. Returns the 1-based lexicographic rank of a permutation of distinct values.
CS_PLANAR_LINKAGE_SWEEP(designs: array, poses: number, start_angle: number, angle_step: number, ground_delta: number) → array	array	Grid extension. Sweeps validated planar four-bar design rows through prescribed crank poses, preserving the requested assembly branch and returning complete moving-joint/coupler paths with closure and transmission diagnostics.
CS_POPCOUNT(value: number) → number	number	Grid extension. Returns the number of set bits (population count) in a non-negative integer up to 2^53.
CS_PREFIX_SUM(values: number[]) → number[]	number[]	Grid extension. Returns the prefix sums of a numeric array.
CS_RABIN_KARP_HASH(text: string, base: number, modulus: number) → number	number	Grid extension. Returns a rolling polynomial hash for text using the supplied base and modulus.
CS_REVERSE(values: any[]) → array	array	Grid extension. Returns a one-row array with the input values reversed.
CS_RLE_DECODE(text: string) → string	string	Grid extension. Decodes a run-length encoded string produced by CS_RLE_ENCODE.
CS_RLE_ENCODE(text: string) → string	string	Grid extension. Run-length encodes a string as repeated character/count pairs (for example aaabbc becomes a3b2c1).
CS_ROD_CUTTING(prices: number[]) → number	number	Grid extension. Returns the maximum revenue from cutting a rod, where prices[i] is the price of a piece of length i+1 and the rod length equals the number of prices.
CS_SHA256_HEX(text: string) → string	string	Grid extension. Returns the lowercase hexadecimal SHA-256 digest of the UTF-8 bytes of a string.
CS_SHORTEST_PATH_LENGTH(edges: array, start: any, goal: any) → number	number	Grid extension. Returns the unweighted shortest path length between two nodes in an edge list, or -1 if unreachable.
CS_SORT_ASC(values: number[]) → number[]	number[]	Grid extension. Returns a numeric array sorted in ascending order.
CS_SORT_DESC(values: number[]) → number[]	number[]	Grid extension. Returns a numeric array sorted in descending order.
CS_STATE_SPACE_SIM(A: array, B: array, C: array, D: array, initial_state: array, inputs: array) → array	array	Grid extension. Simulates a validated discrete linear time-invariant state-space system with dense A, B, C, and D matrices, typed recurrent state, and complete state/output trajectory publication.
CS_STRONGLY_CONNECTED_COMPONENTS(edges: array) → number	number	Grid extension. Returns the number of strongly connected components in a directed edge list (Kosaraju's algorithm).
CS_SUBSET_SUM_EXISTS(values: number[], target: number) → boolean	boolean	Grid extension. Returns TRUE when some subset of the values sums exactly to the target.
CS_TOPOLOGICAL_HAS_CYCLE(edges: array) → boolean	boolean	Grid extension. Returns whether a directed edge list contains a cycle.
CS_TOPOLOGICAL_ORDER(edges: array) → array	array	Grid extension. Returns a topological ordering of a directed acyclic edge list (Kahn's algorithm), or #NUM! when the graph contains a cycle.
CS_UNION_FIND_CONNECTED(element_count: number, unions: array, a: number, b: number) → boolean	boolean	Grid extension. Returns whether two 1-based elements share a set after applying a list of union pairs to a disjoint-set structure over element_count elements.
CS_UNION_FIND_COUNT(element_count: number, unions: array) → number	number	Grid extension. Returns the number of disjoint sets remaining after applying a list of 1-based union pairs to a disjoint-set structure over element_count elements.
CS_UNIQUE_COUNT(values: any[]) → number	number	Grid extension. Returns the number of distinct scalar values in an array.
CS_Z_FUNCTION(text: string) → number[]	number[]	Grid extension. Returns the Z-array of a string, where each element is the length of the longest prefix matching the suffix starting at that position; element 0 is the string length.
DEQUE(values: any...) → deque	deque	variadic, Grid extension. Constructs a native immutable double-ended queue whose revisions structurally share their payloads.
DEQUE_BACK(deque: deque) → any	any	Grid extension. Returns the back value, or BLANK for an empty deque.
DEQUE_CONCAT(left: deque, right: deque) → deque	deque	Grid extension. Returns a deque containing the left logical sequence followed by the right logical sequence.
DEQUE_DROP(deque: deque, count: number) → deque	deque	Grid extension. Returns a persistent deque without its first count elements.
DEQUE_FROM_ARRAY(values: array) → deque	deque	Grid extension. Constructs a native deque from array cells in row-major order.
DEQUE_FRONT(deque: deque) → any	any	Grid extension. Returns the front value, or BLANK for an empty deque.
DEQUE_IS_EMPTY(deque: deque) → boolean	boolean	Grid extension. Tests whether a deque has no values.
DEQUE_LENGTH(deque: deque) → number	number	Grid extension. Returns the number of values in a deque in constant time.
DEQUE_POP_BACK(deque: deque) → array	array	Grid extension. Returns [back-or-BLANK, remaining-deque] without mutating the input revision.
DEQUE_POP_FRONT(deque: deque) → array	array	Grid extension. Returns [front-or-BLANK, remaining-deque] without mutating the input revision.
DEQUE_PUSH_BACK(deque: deque, value: any) → deque	deque	Grid extension. Returns a new deque with a value at the back while preserving the prior revision.
DEQUE_PUSH_FRONT(deque: deque, value: any) → deque	deque	Grid extension. Returns a new deque with a value at the front while preserving the prior revision.
DEQUE_SPLIT_AT(deque: deque, count: number) → tuple	tuple	Grid extension. Splits a deque after a zero-based element count and returns TUPLE(left, right).
DEQUE_TAKE(deque: deque, count: number) → deque	deque	Grid extension. Returns the first count elements as a persistent deque.
DEQUE_TO_ARRAY(deque: deque) → array	array	Grid extension. Explicitly publishes a deque's logical order as a one-row workbook array.
ERR(error: any) → result	result	Grid extension. Constructs an ordinary Result error value without formula short-circuiting.
HLL([precision]: number) → cardinality	cardinality	Grid extension. Constructs an adaptive exact-to-HyperLogLog cardinality sketch.
INTERVAL_AT(index: interval_index, point: number) → vector	vector	Grid extension. Returns all indexed intervals containing a point.
INTERVAL_INDEX() → interval_index	interval_index	Grid extension. Constructs an empty persistent overlapping-interval index.
INTERVAL_OVERLAP(index: interval_index, start: number, end: number) → vector	vector	Grid extension. Returns all indexed intervals overlapping closed query bounds.
INTERVAL_PUT(index: interval_index, start: number, end: number, value: any) → interval_index	interval_index	Grid extension. Returns an interval-index revision containing closed bounds and a value.
INTERVAL_REMOVE(index: interval_index, start: number, end: number) → interval_index	interval_index	Grid extension. Returns an interval-index revision without exact bounds.
KLL(capacity: number) → kll	kll	Grid extension. Constructs a bounded persistent KLL quantile sketch.
KLL_ADD(sketch: kll, sample: number...) → kll	kll	variadic, Grid extension. Adds finite samples to a KLL sketch revision.
KLL_COUNT(sketch: kll) → number	number	Grid extension. Returns the exact number of samples observed by a KLL sketch.
KLL_MERGE(left: kll, right: kll) → kll	kll	Grid extension. Merges equal-capacity KLL sketches.
KLL_QUANTILE(sketch: kll, probability: number) → number	number	Grid extension. Estimates a quantile for a probability in [0,1].
MAP_CONTAINS(map: map, key: any) → boolean	boolean	Grid extension. Tests canonical-key membership.
MAP_GET(map: map, key: any) → any	any	Grid extension. Looks up a canonical scalar key, returning BLANK on a miss.
MAP_GET_OPTION(map: map, key: any) → option	option	Grid extension. Looks up a key and returns SOME(value) or NONE().
MAP_KEYS(map: map) → vector	vector	Grid extension. Returns map keys in deterministic canonical order.
MAP_LENGTH(map: map) → number	number	Grid extension. Returns map cardinality in constant time.
MAP_OF(key_values: any...) → map	map	variadic, Grid extension. Constructs a deterministic persistent map from key/value pairs.
MAP_PUT(map: map, key: any, value: any) → map	map	Grid extension. Returns a map revision with a key inserted or replaced.
MAP_REMOVE(map: map, key: any) → map	map	Grid extension. Returns a map revision without a key.
MAP_VALUES(map: map) → vector	vector	Grid extension. Returns map values in deterministic key order.
MERKLE_ADD(set: merkle_set, value: any) → merkle_set	merkle_set	Grid extension. Returns a Merkle-set revision containing a value.
MERKLE_CONTAINS(set: merkle_set, value: any) → boolean	boolean	Grid extension. Tests Merkle-set membership.
MERKLE_DIFF(left: merkle_set, right: merkle_set) → vector	vector	Grid extension. Returns values present in the left Merkle set but absent from the right.
MERKLE_REMOVE(set: merkle_set, value: any) → merkle_set	merkle_set	Grid extension. Returns a Merkle-set revision without a value.
MERKLE_ROOT(set: merkle_set) → string	string	Grid extension. Returns the canonical SHA-256 root of a Merkle-set revision.
MERKLE_SET(value: any...) → merkle_set	merkle_set	variadic, Grid extension. Constructs a canonical content-addressed persistent set.
MULTIMAP() → multimap	multimap	Grid extension. Constructs an empty persistent one-to-many map.
MULTIMAP_GET(map: multimap, key: any) → vector	vector	Grid extension. Returns the persistent vector stored under a key.
MULTIMAP_PUT(map: multimap, key: any, value: any) → multimap	multimap	Grid extension. Appends a value under a canonical multimap key.
MULTIMAP_REMOVE_ALL(map: multimap, key: any) → multimap	multimap	Grid extension. Returns a multimap revision without a key and all its values.
MULTISET(value: any...) → multiset	multiset	variadic, Grid extension. Constructs a persistent multiset retaining duplicate counts.
MULTISET_ADD(bag: multiset, value: any, [count]: number) → multiset	multiset	Grid extension. Adds a nonnegative multiplicity to a multiset revision.
MULTISET_COUNT(bag: multiset, value: any) → number	number	Grid extension. Returns a value's multiplicity.
MULTISET_DIFFERENCE(left: multiset, right: multiset) → multiset	multiset	Grid extension. Subtracts right multiplicities with saturation at zero.
MULTISET_INTERSECT(left: multiset, right: multiset) → multiset	multiset	Grid extension. Returns the minimum common multiplicity of each value.
MULTISET_REMOVE(bag: multiset, value: any, [count]: number) → multiset	multiset	Grid extension. Removes up to a requested multiplicity from a multiset revision.
MULTISET_SUM(left: multiset, right: multiset) → multiset	multiset	Grid extension. Adds corresponding multiplicities with overflow checks.
MULTISET_UNION(left: multiset, right: multiset) → multiset	multiset	Grid extension. Returns the maximum multiplicity of each value.
NONE() → option	option	Grid extension. Constructs an absent Option value.
OK(value: any) → result	result	Grid extension. Constructs a successful Result value.
OPTION_IS_NONE(option: option) → boolean	boolean	Grid extension. Tests whether an Option is absent.
OPTION_IS_SOME(option: option) → boolean	boolean	Grid extension. Tests whether an Option is present.
OPTION_UNWRAP_OR(option: option, fallback: any) → any	any	Grid extension. Returns the present payload or a fallback.
PARSE(text: string, parser: parser) → parse_result	parse_result	Grid extension. Parses text with a first-class parser and returns a total parse-result value.
PARSE_RESULT_ERROR(result: parse_result) → record	record	Grid extension. Returns a native error record with code, message, offset, expected, and found fields, or BLANK after success.
PARSE_RESULT_OK(result: parse_result) → boolean	boolean	Grid extension. Tests whether a parse result contains a parse tree.
PARSE_RESULT_TREE(result: parse_result) → parse_tree	parse_tree	Grid extension. Returns the parse tree from a successful result, or BLANK after rejection.
PARSE_TREE_CAPTURE(tree: parse_tree, capture: string) → vector	vector	Grid extension. Returns all parse-node records carrying a named capture in source order.
PARSE_TREE_ROOT(tree: parse_tree) → record	record	Grid extension. Materializes the parse root as nested native node records.
PARSE_TREE_SOURCE(tree: parse_tree) → string	string	Grid extension. Returns the source text retained by a parse tree.
PFADD(sketch: cardinality, value: any...) → cardinality	cardinality	variadic, Grid extension. Returns a cardinality-sketch revision containing additional values.
PFCOUNT(sketch: cardinality...) → number	number	variadic, Grid extension. Returns the estimated cardinality of one or more merged sketches.
PFMERGE(sketch: cardinality...) → cardinality	cardinality	variadic, Grid extension. Persistently merges equal-precision cardinality sketches.
RECORD(field_values: any...) → record	record	variadic, Grid extension. Constructs a fixed-shape persistent record from field/value pairs.
RECORD_FIELDS(record: record) → vector	vector	Grid extension. Returns record field names in schema order.
RECORD_GET(record: record, field: string) → any	any	Grid extension. Reads a named record field.
RECORD_SET(record: record, field: string, value: any) → record	record	Grid extension. Returns a record revision with one existing field replaced.
RECORD_VALUES(record: record) → vector	vector	Grid extension. Returns record values in schema order.
RESULT_ERROR_OR(result: result, fallback: any) → any	any	Grid extension. Returns an Err payload or a fallback for Ok.
RESULT_IS_ERR(result: result) → boolean	boolean	Grid extension. Tests whether a Result is an ordinary error variant.
RESULT_IS_OK(result: result) → boolean	boolean	Grid extension. Tests whether a Result is successful.
RESULT_UNWRAP_OR(result: result, fallback: any) → any	any	Grid extension. Returns an Ok payload or a fallback for Err.
SET_ADD(set: set, value: any) → set	set	Grid extension. Returns a set revision containing a key.
SET_CONTAINS(set: set, value: any) → boolean	boolean	Grid extension. Tests canonical-key membership in a set.
SET_DIFFERENCE(left: set, right: set) → set	set	Grid extension. Returns keys present in left but not right.
SET_INTERSECT(left: set, right: set) → set	set	Grid extension. Returns the intersection of two sets.
SET_IS_EMPTY(set: set) → boolean	boolean	Grid extension. Tests whether a set is empty.
SET_LENGTH(set: set) → number	number	Grid extension. Returns set cardinality in constant time.
SET_OF(values: any...) → set	set	variadic, Grid extension. Constructs a deterministic persistent set.
SET_REMOVE(set: set, value: any) → set	set	Grid extension. Returns a set revision without a key.
SET_UNION(left: set, right: set) → set	set	Grid extension. Returns the union of two sets.
SOME(value: any) → option	option	Grid extension. Constructs a present Option value.
STREAM() → stream	stream	Grid extension. Constructs an empty persistent ordered event stream.
TOP_K(capacity: number) → top_k	top_k	Grid extension. Constructs a bounded Space-Saving heavy-hitter sketch.
TOP_K_ADD(sketch: top_k, value: any, [count]: number) → top_k	top_k	Grid extension. Adds a weighted observation to a Top-K revision.
TOP_K_ESTIMATE(sketch: top_k, value: any) → tuple	tuple	Grid extension. Returns TUPLE(estimate, error) for a retained heavy hitter.
TOP_K_ITEMS(sketch: top_k, [limit]: number) → vector	vector	Grid extension. Publishes heavy hitters with estimate and replacement error.
TREE.APPLY(operation: tree_transform, tree: tree) → tree_operation_result	tree_operation_result	model-scoped, Grid extension. Applies an immutable transform handle to a grammar-bound tree under the transform's identity-bearing traversal, repetition, and work-limit contract.
TREE.AT(tree: tree, path: array) → tree_term	tree_term	model-scoped, Grid extension. Returns a zero-copy ground subtree view at an exact public path.
TREE.BINDINGS(term: tree_term) → array	array	model-scoped, Grid extension. Returns bounded reference-to-binder records in deterministic reference preorder.
TREE.CHILDREN(term: tree_term) → array	array	model-scoped, Grid extension. Returns immutable child term views in grammar ordinal order.
TREE.CONSTRUCTOR(term: tree_term) → string	string	model-scoped, Grid extension. Returns a semantic constructor name, or BLANK when the occurrence has none.
TREE.CONTEXT(tree: tree, path: array) → tree_context	tree_context	model-scoped, Grid extension. Returns a ground tree context whose hole is the exact selected occurrence.
TREE.DEPTH(term: tree_term) → number	number	model-scoped, Grid extension. Returns the maximum root-to-leaf occurrence count of a model-authorized tree term.
TREE.FINGERPRINT(term: tree_term) → string	string	model-scoped, Grid extension. Returns the canonical lowercase structural fingerprint of a tree term.
TREE.FREE_NAMES(term: tree_term) → array	array	model-scoped, Grid extension. Returns bounded free-name records in deterministic preorder.
TREE.MATCH(input: tree, pattern: tree_pattern, scope: symbol, resultLimit: number, workLimit: number) → tree_match_result	tree_match_result	model-scoped, Grid extension. Returns exact bounded grammar-authorized pattern matches with captures and context zippers in canonical order.
TREE.NARROW(term: tree_term, theory: tree_theory, algebraOrExact: tree_algebra|symbol, stepLimit: number, workLimit: number) → tree_narrowing_result	tree_narrowing_result	model-scoped, Grid extension. Returns deterministic bounded one-step narrowing successors under an executable theory and selected tree algebra; the symbol lane accepts exactly :exact.
TREE.NORMALIZE(tree: tree, algebra: tree_algebra, work: number) → tree_operation_result	tree_operation_result	model-scoped, Grid extension. Canonically normalizes a complete grammar-bound tree under an explicit algebra profile and work bound.
TREE.ORIGIN(term: tree_term) → origin_handle	origin_handle	model-scoped, Grid extension. Returns portable source-origin metadata, or BLANK when none is retained.
TREE.PLUG(context: tree_context, replacement: tree_term, work: number) → tree_operation_result	tree_operation_result	model-scoped, Grid extension. Capture-avoidantly plugs a ground replacement into a model-authorized tree context under an explicit work bound.
TREE.RENDER(tree: tree) → string	string	model-scoped, Grid extension. Canonically renders a complete grammar-bound ground tree after round-trip validation.
TREE.SIZE(term: tree_term) → number	number	model-scoped, Grid extension. Returns the logical occurrence count of a model-authorized tree term.
TREE.SOLVE(solver: tree_solver, left: tree_term, [right]: tree_term) → tree_solver_result	tree_solver_result	model-scoped, Grid extension. Executes an immutable bounded tree solver with one input for MATCH/NORMAL or two inputs for EQUAL and returns its authenticated solver result.
TREE.SORT(term: tree_term) → string	string	model-scoped, Grid extension. Returns the canonical grammar sort of a model-authorized tree term.
TREE.SUBSTITUTE(term: tree_term, family: tree_unification_family, context: symbol, workLimit: number) → tree_substitution_result	tree_substitution_result	model-scoped, Grid extension. Capture-avoidantly applies one authenticated unification family to a tree term; context is exactly :left, :right, or :qualified.
TREE.SYMBOL(term: tree_term) → string	string	model-scoped, Grid extension. Returns a concrete grammar symbol, or BLANK for a symbolic occurrence.
TREE.TERMINAL(term: tree_term) → record	record	model-scoped, Grid extension. Returns the terminal symbol and payload record, or BLANK for a nonterminal.
TREE.UNIFY(left: tree_term, right: tree_term, algebraOrExact: tree_algebra|symbol, familyLimit: number, workLimit: number) → tree_unification_result	tree_unification_result	model-scoped, Grid extension. Returns deterministic canonical constrained most-general unification families for two compatible tree terms under a selected tree algebra; the symbol lane accepts exactly :exact.
TRIE() → trie	trie	Grid extension. Constructs an empty persistent adaptive radix trie.
TRIE_DELETE(trie: trie, key: string) → trie	trie	Grid extension. Returns a trie revision without an exact key.
TRIE_GET(trie: trie, key: string) → any	any	Grid extension. Reads an exact trie key or returns BLANK.
TRIE_HAS(trie: trie, key: string) → boolean	boolean	Grid extension. Tests exact trie membership.
TRIE_LONGEST_PREFIX(trie: trie, input: string) → tuple	tuple	Grid extension. Returns TUPLE(matched-key, value) for the longest stored prefix.
TRIE_PREFIX(trie: trie, prefix: string, [limit]: number) → vector	vector	Grid extension. Publishes lexically ordered key/value tuples below a prefix.
TRIE_PUT(trie: trie, key: string, value: any) → trie	trie	Grid extension. Returns a trie revision containing a Unicode text key and value.
TUPLE(values: any...) → tuple	tuple	variadic, Grid extension. Constructs a fixed-position persistent product value.
TUPLE_GET(tuple: tuple, index: number) → any	any	Grid extension. Reads a one-based tuple position, returning BLANK out of bounds.
TUPLE_LENGTH(tuple: tuple) → number	number	Grid extension. Returns tuple arity in constant time.
TUPLE_SET(tuple: tuple, index: number, value: any) → tuple	tuple	Grid extension. Returns a tuple revision with one existing position replaced.
TUPLE_TO_ARRAY(tuple: tuple) → array	array	Grid extension. Publishes a tuple as a one-row workbook array.
VECTOR(values: any...) → vector	vector	variadic, Grid extension. Constructs a persistent indexed vector.
VECTOR_FROM_ARRAY(values: array) → vector	vector	Grid extension. Constructs a vector from array cells in row-major order.
VECTOR_GET(vector: vector, index: number) → any	any	Grid extension. Reads a one-based vector position, returning BLANK out of bounds.
VECTOR_IS_EMPTY(vector: vector) → boolean	boolean	Grid extension. Tests whether a vector is empty.
VECTOR_LENGTH(vector: vector) → number	number	Grid extension. Returns vector length in constant time.
VECTOR_POP(vector: vector) → array	array	Grid extension. Returns [last-or-BLANK, remaining-vector].
VECTOR_PUSH(vector: vector, value: any) → vector	vector	Grid extension. Appends one value to a persistent vector.
VECTOR_SET(vector: vector, index: number, value: any) → vector	vector	Grid extension. Returns a vector revision with one one-based position replaced.
VECTOR_TO_ARRAY(vector: vector) → array	array	Grid extension. Publishes a vector as a one-row workbook array.
XACK(group: stream_group, id: string...) → tuple	tuple	variadic, Grid extension. Acknowledges pending IDs and returns TUPLE(count, revised-group).
XADD(stream: stream, millis: number, field_values: any...) → tuple	tuple	variadic, Grid extension. Appends a monotonic event and returns TUPLE(id, revised-stream).
XCLAIM(group: stream_group, id: string, consumer: string) → stream_group	stream_group	Grid extension. Transfers a pending stream ID to another consumer.
XDEL(stream: stream, id: string...) → stream	stream	variadic, Grid extension. Returns a stream revision without the specified entry IDs.
XGROUP(start_id: string) → stream_group	stream_group	Grid extension. Creates a persistent stream consumer-group cursor and pending ledger.
XLEN(stream: stream) → number	number	Grid extension. Returns the live stream length in constant time.
XPENDING(group: stream_group) → number	number	Grid extension. Returns the number of pending entries in a stream group.
XRANGE(stream: stream, start: string, end: string, [limit]: number) → vector	vector	Grid extension. Returns entries in an inclusive stream-id range.
XREAD(stream: stream, cursor: string, [limit]: number) → vector	vector	Grid extension. Returns entries strictly after a stream cursor.
XREADGROUP(group: stream_group, stream: stream, consumer: string, [limit]: number) → tuple	tuple	Grid extension. Reads unseen stream entries and returns TUPLE(revised-group, entries).
XREVRANGE(stream: stream, start: string, end: string, [limit]: number) → vector	vector	Grid extension. Returns entries in reverse order over an inclusive stream-ID range.
XTRIM(stream: stream, max_length: number) → stream	stream	Grid extension. Returns a stream revision retaining at most the newest entries.
XTRIM_MINID(stream: stream, min_id: string) → stream	stream	Grid extension. Advances the logical stream prefix to the first entry at or after a minimum ID.
ZADD(set: ranked_set, score: number, member: any) → ranked_set	ranked_set	Grid extension. Returns a ranked-set revision with a member inserted or rescored.
ZCARD(set: ranked_set) → number	number	Grid extension. Returns ranked-set cardinality in constant time.
ZCOUNT(set: ranked_set, min: number, max: number) → number	number	Grid extension. Counts ranked members with scores in an inclusive interval.
ZDIFF(left: ranked_set, right: ranked_set) → ranked_set	ranked_set	Grid extension. Returns members present in the left ranked set but not the right.
ZINCRBY(set: ranked_set, increment: number, member: any) → tuple	tuple	Grid extension. Adds to an existing member score and returns TUPLE(score, revised-ranked-set).
ZINTER(left: ranked_set, right: ranked_set) → ranked_set	ranked_set	Grid extension. Returns the persistent intersection of two ranked sets with scores summed.
ZPOPMAX(set: ranked_set) → tuple	tuple	Grid extension. Returns TUPLE(member, score, remaining-set) for the maximum member.
ZPOPMIN(set: ranked_set) → tuple	tuple	Grid extension. Returns TUPLE(member, score, remaining-set) for the minimum member.
ZRANGE(set: ranked_set, start: number, stop: number) → vector	vector	Grid extension. Returns members in an inclusive zero-based rank range.
ZRANGEBYSCORE(set: ranked_set, min: number, max: number, [limit]: number) → vector	vector	Grid extension. Returns deterministically ordered members in an inclusive score range.
ZRANK(set: ranked_set, member: any) → number	number	Grid extension. Returns a member's zero-based rank or BLANK when absent.
ZREM(set: ranked_set, member: any) → ranked_set	ranked_set	Grid extension. Returns a ranked-set revision without a member.
ZREVRANGE(set: ranked_set, start: number, stop: number) → vector	vector	Grid extension. Returns members over a descending zero-based inclusive rank interval.
ZREVRANK(set: ranked_set, member: any) → number	number	Grid extension. Returns a member's zero-based descending rank or BLANK.
ZSCORE(set: ranked_set, member: any) → number	number	Grid extension. Returns a member score or BLANK when absent.
ZSET(member_score: any...) → ranked_set	ranked_set	variadic, Grid extension. Constructs a persistent ranked set from member/score pairs.
ZUNION(left: ranked_set, right: ranked_set) → ranked_set	ranked_set	Grid extension. Returns the persistent union of two ranked sets with duplicate scores summed.

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Graph

Graph construction, traversal, paths, communities, partitions, and network analysis.

Function count: 34.

Function	Returns	Notes
GRAPH(parse_tree: parse_tree) → graph | GRAPH(edges: any, edge_id: any, from: any, to: any, nodes?: any, node_id?: any, node_properties?: array, edge_properties?: array, directed?: boolean) → graph	graph	Grid extension. Builds a resident directed property graph from one native parse-tree source, or a property multigraph from a literal, range, or Frame edge source with exact stable identity columns.
GRAPH_ARTICULATION_POINTS(graph: graph) → frame	frame	Grid extension. Returns articulation nodes.
GRAPH_BELLMAN_FORD(graph: graph, from: any, to: any, weight: string) → frame	frame	Grid extension. Returns a weighted shortest path while supporting negative weights and reporting negative cycles.
GRAPH_BETWEENNESS_CENTRALITY(graph: graph, weight?: string, max_sources?: number) → frame	frame	Grid extension. Computes betweenness centrality with an optional deterministic source bound.
GRAPH_BFS(graph: graph, start: any) → frame	frame	Grid extension. Returns deterministic breadth-first traversal rows.
GRAPH_BRIDGES(graph: graph) → frame	frame	Grid extension. Returns bridge edges.
GRAPH_CLOSENESS_CENTRALITY(graph: graph, weight?: string, max_sources?: number) → frame	frame	Grid extension. Computes closeness centrality with an optional deterministic source bound.
GRAPH_CLUSTERING_COEFFICIENTS(graph: graph) → frame	frame	Grid extension. Returns a deterministic local clustering coefficient for every node.
GRAPH_DEGREE(graph: graph, node: any) → number	number	Grid extension. Returns total degree for a node.
GRAPH_DENSITY(graph: graph) → number	number	Grid extension. Returns graph density under the graph's directedness contract.
GRAPH_DFS(graph: graph, start: any) → frame	frame	Grid extension. Returns deterministic depth-first traversal rows.
GRAPH_DIAMETER(graph: graph, weight?: string, max_sources?: number) → frame	frame	Grid extension. Returns diameter endpoints, distance, and path under an explicit source bound for large graphs.
GRAPH_EDGES(graph: graph) → frame	frame	Grid extension. Returns the graph's edge table as a Frame.
GRAPH_EDGE_COUNT(graph: graph) → number	number	Grid extension. Returns the resident edge count.
GRAPH_EIGENVECTOR_CENTRALITY(graph: graph, weight?: string, tolerance?: number, max_iterations?: number) → frame	frame	Grid extension. Computes normalized Perron eigenvector centrality over non-negative optional edge weights with explicit convergence controls.
GRAPH_HAS_EULERIAN_PATH(graph: graph) → boolean	boolean	Grid extension. Tests whether the graph admits an Eulerian path.
GRAPH_HAS_PATH(graph: graph, from: any, to: any) → boolean	boolean	Grid extension. Tests reachability between exact node keys.
GRAPH_INDUCED_SUBGRAPH(graph: graph, nodes: any) → graph	graph	Grid extension. Builds the node-induced subgraph for an exact node-key collection.
GRAPH_IN_DEGREE(graph: graph, node: any) → number	number	Grid extension. Returns incoming degree for a node.
GRAPH_IN_NEIGHBORS(graph: graph, node: any) → frame	frame	Grid extension. Returns incoming neighbors of an exact node key.
GRAPH_K_CORE(graph: graph) → frame	frame	Grid extension. Returns the deterministic core number of every node.
GRAPH_MAXIMUM_BIPARTITE_MATCHING(graph: graph, left_partition: any) → frame	frame	Grid extension. Returns a deterministic maximum-cardinality matching for an explicit left partition.
GRAPH_MINIMUM_SPANNING_TREE(graph: graph, weight?: string) → graph	graph	Grid extension. Builds the deterministic minimum spanning tree of a connected undirected graph.
GRAPH_NEIGHBORS(graph: graph, node: any) → frame	frame	Grid extension. Returns outgoing neighbors of an exact node key.
GRAPH_NODES(graph: graph) → frame	frame	Grid extension. Returns the graph's node table as a Frame.
GRAPH_NODE_COUNT(graph: graph) → number	number	Grid extension. Returns the resident node count.
GRAPH_OUT_DEGREE(graph: graph, node: any) → number	number	Grid extension. Returns outgoing degree for a node.
GRAPH_PAGE_RANK(graph: graph, weight?: string, damping?: number, tolerance?: number, max_iterations?: number) → frame	frame	Grid extension. Computes bounded PageRank with explicit convergence controls.
GRAPH_REVERSE(graph: graph) → graph	graph	Grid extension. Builds a graph with every edge direction reversed.
GRAPH_SHORTEST_PATH(graph: graph, from: any, to: any, weight?: string) → frame	frame	Grid extension. Returns a deterministic unweighted or non-negative weighted shortest path.
GRAPH_STRONG_COMPONENTS(graph: graph) → frame	frame	Grid extension. Returns strongly connected component membership.
GRAPH_TOPOLOGICAL_ORDER(graph: graph) → frame	frame	Grid extension. Returns a deterministic topological ordering or a cycle error.
GRAPH_TRIANGLE_COUNT(graph: graph) → number	number	Grid extension. Counts unique undirected triangles.
GRAPH_WEAK_COMPONENTS(graph: graph) → frame	frame	Grid extension. Returns weakly connected component membership.

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Skill Ratings

Competitive skill rating systems such as Elo.

Function count: 8.

Function	Returns	Notes
RATING_ELO_EXPECTED(rating_a: number, rating_b: number) → number	number	Grid extension. Returns player A's expected Elo score against player B.
RATING_ELO_UPDATE(rating_a: number, rating_b: number, outcome: string, k: number) → array	array	Grid extension. Updates two Elo ratings after an outcome from player A's perspective; returns [new_a, new_b].
RATING_GLICKO2_EXPECTED(rating_a: number, deviation_a: number, volatility_a: number, rating_b: number, deviation_b: number, volatility_b: number) → array	array	Grid extension. Returns [expected_a, expected_b] for two Glicko-2 ratings.
RATING_GLICKO2_UPDATE(rating_a: number, deviation_a: number, volatility_a: number, rating_b: number, deviation_b: number, volatility_b: number, outcome: string, tau: number, tolerance: number) → array	array	Grid extension. Updates two Glicko-2 ratings after an outcome; returns ratings, deviations, and volatilities.
RATING_GLICKO_EXPECTED(rating_a: number, deviation_a: number, rating_b: number, deviation_b: number) → array	array	Grid extension. Returns [expected_a, expected_b] for two Glicko ratings.
RATING_GLICKO_UPDATE(rating_a: number, deviation_a: number, rating_b: number, deviation_b: number, outcome: string, c: number) → array	array	Grid extension. Updates two Glicko ratings after an outcome; returns [new_a, new_deviation_a, new_b, new_deviation_b].
RATING_TRUESKILL_EXPECTED(rating_a: number, uncertainty_a: number, rating_b: number, uncertainty_b: number, draw_probability: number, beta: number, dynamics_factor: number) → array	array	Grid extension. Returns [expected_a, expected_b] for two TrueSkill ratings.
RATING_TRUESKILL_UPDATE(rating_a: number, uncertainty_a: number, rating_b: number, uncertainty_b: number, outcome: string, draw_probability: number, beta: number, dynamics_factor: number) → array	array	Grid extension. Updates two TrueSkill ratings after an outcome; returns [new_a, uncertainty_a, new_b, uncertainty_b].

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Playing Cards

Deck construction, shuffling, dealing, and hand helpers.

Function count: 10.

Function	Returns	Notes
CARD_DEAL(deck: any, hands: number, cards_per_hand: number) → array	array	Grid extension. Deal cards round-robin from a deck into hands.
CARD_DECK(decks: number, jokers: number) → array	array	Grid extension. Return a standard card deck as a column array.
CARD_DRAW(deck: any, count: number) → array	array	Grid extension. Draw count cards from the front of a deck; returns drawn and remainder rows.
CARD_SHUFFLE(deck: any) → any	any	volatile, Grid extension. Random permutation of a comma-separated deck or card array.
CARD_SHUFFLE_SEEDED(deck: any, seed: number) → any	any	Grid extension. Deterministic random permutation of a comma-separated deck or card array.
HAND_CONTAINS(cards: any, card: string) → boolean	boolean	Grid extension. Return TRUE when a hand contains a card token.
HAND_COUNT(cards: any) → number	number	Grid extension. Count cards in a hand.
HAND_JOIN(cards: any, separator: string) → string	string	Grid extension. Join a card hand using an optional separator.
HAND_PARSE(cards: any) → array	array	Grid extension. Parse a comma-separated hand or card array into a column array.
HAND_SORT(cards: any) → string	string	Grid extension. Sort a hand by suit then rank.

---

Card Games

Poker, bridge, canasta, rummy, and other card-game helpers.

Function count: 10.

Function	Returns	Notes
BRIDGE_HCP(cards: any) → number	number	Grid extension. Bridge high-card points using 4-3-2-1 scoring.
BRIDGE_SHAPE(cards: any) → string	string	Grid extension. Bridge shape as spades-hearts-diamonds-clubs.
CANASTA_CARD_VALUE(cards: any) → number	number	Grid extension. Canasta card-point total for one or more cards.
CANASTA_IS_CANASTA(cards: any) → boolean	boolean	Grid extension. TRUE when a valid canasta meld has seven or more cards.
CANASTA_MELD_SCORE(cards: any) → number	number	Grid extension. Card points plus canasta bonus for a valid meld.
CANASTA_MELD_TYPE(cards: any) → string	string	Grid extension. Classify a canasta meld.
CANASTA_MELD_VALID(cards: any) → boolean	boolean	Grid extension. TRUE when cards form a legal basic canasta meld.
POKER_COMPARE(left: any, right: any) → number	number	Grid extension. Compare two poker hands; returns 1, 0, or -1.
POKER_RANK(cards: any) → string	string	Grid extension. Best poker category for 5-7 cards.
RUMMY_MELD_VALID(cards: any) → boolean	boolean	Grid extension. TRUE when cards form a basic rummy set or run.

---

Casino

Blackjack, baccarat, craps, and roulette helpers.

Function count: 18.

Function	Returns	Notes
BACCARAT_DEAL(decks: number) → array	array	volatile, Grid extension. Deal and resolve a punto banco hand from a fresh shoe.
BACCARAT_DEAL_SEEDED(decks: number, seed: number) → array	array	Grid extension. Deterministically deal and resolve a punto banco hand from a fresh shoe.
BACCARAT_SCORE(cards: any) → number	number	Grid extension. Baccarat hand total mod 10.
BJ_BUST(cards: any) → boolean	boolean	Grid extension. TRUE when a blackjack hand's best value exceeds 21.
BJ_CAN_SPLIT(cards: any) → boolean	boolean	Grid extension. TRUE when exactly two blackjack cards have the same blackjack value.
BJ_DEAL(decks: number, players: number, hide_hole: boolean) → array	array	volatile, Grid extension. Deal initial blackjack hands from a fresh shoe.
BJ_DEAL_SEEDED(decks: number, players: number, hide_hole: boolean, seed: number) → array	array	Grid extension. Deterministically deal initial blackjack hands from a fresh shoe.
BJ_HIT(hand: any, deck: any) → string	string	volatile, Grid extension. Draw the top card from deck onto hand.
BJ_IS_BLACKJACK(cards: any) → boolean	boolean	Grid extension. TRUE when exactly two cards total 21.
BJ_IS_SOFT(cards: any) → boolean	boolean	Grid extension. TRUE when a blackjack hand has an ace counted as 11.
BJ_SCORE(cards: any) → number	number	Grid extension. Best blackjack hand value (soft aces).
CRAPS_PASS(roll: number) → any	any	Grid extension. Pass-line come-out result: win, lose, or point number.
CRAPS_POINT(point: number, roll: number) → string	string	Grid extension. Pass-line point-round result: win, lose, or continue.
CRAPS_SHOOT() → number	number	volatile, Grid extension. Roll two dice for craps (returns 2-12).
ROULETTE_COLOR(number: number) → string	string	Grid extension. Return red, black, or green for a roulette pocket (37 = 00).
ROULETTE_PAYOUT(bet: string, stake: number, result: number) → number	number	Grid extension. Total return for a roulette bet given stake and winning number.
ROULETTE_SPIN(american: boolean) → number	number	volatile, Grid extension. Spin a European (default) or American (TRUE) roulette wheel.
ROULETTE_SPIN_SEEDED(american: boolean, seed: number) → number	number	Grid extension. Deterministically spin a European (default) or American (TRUE) roulette wheel.

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Chess

FEN parsing, move generation, and chess position helpers.

Function count: 10.

Function	Returns	Notes
CHESS960_STARTPOS(scharnagl: number) → string	string	Grid extension. Return the Chess960 start FEN for a Scharnagl number (1-960; 518 is standard chess).
CHESS_FEN_VALID(fen: string) → boolean	boolean	Grid extension. Return whether a FEN string parses as a legal chess position (standard chess via chess.js; Chess960 castling rights use structural checks).
CHESS_IN_CHECK(fen: string) → boolean	boolean	Grid extension. Return whether the side to move is in check.
CHESS_LEGAL_MOVES(fen: string) → array	array	Grid extension. Return a sorted column array of legal UCI moves (e2e4, e7e8q). Move input uses UCI; castling is king-to-rook square.
CHESS_MAKE_MOVE(fen: string, move: string) → string	string	Grid extension. Apply a UCI move to a FEN position and return the resulting FEN. Returns #VALUE! for illegal moves. En-passant square formatting may differ from chess.js.
CHESS_MOVE_VALID(fen: string, move: string) → boolean	boolean	Grid extension. Return whether a UCI move is legal in the given position.
CHESS_SIDE_TO_MOVE(fen: string) → string	string	Grid extension. Return the side to move for a position (white or black).
CHESS_STARTPOS() → string	string	Grid extension. Return the standard chess starting position FEN.
CHESS_STATUS(fen: string) → string	string	Grid extension. Return game status: ongoing, checkmate, stalemate, or fifty_move. Detects checkmate, stalemate, and the 50-move rule only; not repetition or insufficient material.
CHESS_WINNER(fen: string) → string	string	Grid extension. Return the winning color after checkmate, or blank otherwise. Detects checkmate, stalemate, and the 50-move rule only; not repetition or insufficient material.

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Dice & Gambling

Dice pools, advantage rolls, and tabletop gambling helpers.

Function count: 21.

Function	Returns	Notes
DICE_ADVANTAGE(sides: number) → number	number	volatile, Grid extension. Roll twice and keep the higher result (default d20).
DICE_CARDS(count: number, jokers: number) → string	string	volatile, Grid extension. Draw count cards from a shuffled 52-card deck with optional jokers.
DICE_CARDS_SEEDED(count: number, jokers: number, seed: number) → string	string	Grid extension. Deterministically draw count cards from a shuffled deck with optional jokers.
DICE_DEAL(deck: any, hands: number, cards_per_hand: number) → array	array	Grid extension. Deal cards round-robin from a deck into hands.
DICE_DETAIL(expression: string) → string	string	volatile, Grid extension. Roll a TRPG dice expression and return a formatted breakdown.
DICE_DETAIL_SEEDED(expression: string, seed: number) → string	string	volatile, Grid extension. Deterministic formatted dice roll for an expression and seed.
DICE_DISADVANTAGE(sides: number) → number	number	volatile, Grid extension. Roll twice and keep the lower result (default d20).
DICE_FATE(count: number) → number	number	volatile, Grid extension. Roll count Fudge/FATE dice (-1, 0, +1) and return the sum.
DICE_FLIP(probability: number) → boolean	boolean	volatile, Grid extension. Fair or biased coin flip. Returns TRUE on success (default p=0.5).
DICE_KEEP(count: number, sides: number, keep: number, keep_lowest: boolean) → number	number	volatile, Grid extension. Roll count dice, keep the highest or lowest keep dice, and sum them.
DICE_MAX(count: number, sides: number) → number	number	volatile, Grid extension. Roll count dice with sides and return the maximum face.
DICE_MIN(count: number, sides: number) → number	number	volatile, Grid extension. Roll count dice with sides and return the minimum face.
DICE_N(count: number, sides: number, modifier: number) → number	number	volatile, Grid extension. Roll count dice with sides and add an optional modifier.
DICE_PERCENTILE(places: number) → number	number	volatile, Grid extension. Roll a percentile die (default d100). Optional places sets digit count (2–6).
DICE_POOL(count: number, sides: number, threshold: number) → number	number	volatile, Grid extension. Roll count dice and count successes at or above threshold.
DICE_POOL_NET(count: number, sides: number, success_at: number, failure_below: number) → number	number	volatile, Grid extension. Roll count dice; +1 for success_at or above, -1 for failure_below or below.
DICE_ROLL(expression: string) → number	number	volatile, Grid extension. Roll a TRPG dice expression and return the total.
DICE_ROLL_BATCH(expression: string, count: number) → array	array	volatile, Grid extension. Roll a dice expression count times; returns a column of totals.
DICE_ROLL_SEEDED(expression: string, seed: number) → number	number	volatile, Grid extension. Deterministic dice roll total for an expression and seed.
DICE_SHUFFLE(deck: any) → any	any	volatile, Grid extension. Random permutation of a comma-separated deck or card array.
DICE_VALID(expression: string) → boolean	boolean	Grid extension. Return TRUE when a dice expression parses successfully.

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Science

Physics, chemistry, biology, lab workflow, astronomy, and earth-science helpers.

Function count: 369.

Function	Returns	Notes
A260_A230_RATIO(absorbance_260: number, absorbance_230: number) → number	number	Grid extension. Returns A260/A230 purity ratio.
A260_A280_RATIO(absorbance_260: number, absorbance_280: number) → number	number	Grid extension. Returns A260/A280 purity ratio.
ABSOLUTE_HUMIDITY(temperature_c: number, relative_humidity_percent: number) → number	number	Grid extension. Returns absolute humidity in g/m^3.
ABSORBANCE_FROM_TRANSMITTANCE(transmittance: number) → number	number	Grid extension. Returns absorbance from transmittance fraction.
ACCUMULATION_RATIO(elimination_rate: number, dosing_interval: number) → number	number	Grid extension. Returns steady-state accumulation ratio.
ALLELE_FREQUENCY(homozygous_count: number, heterozygous_count: number, sample_count: number) → number	number	Grid extension. Returns allele frequency from genotype counts.
ANOVA_F(between_mean_square: number, within_mean_square: number) → number	number	Grid extension. Returns an ANOVA F statistic from mean squares.
APPARENT_TEMPERATURE(temperature_c: number, relative_humidity_percent: number, wind_speed_m_s: number) → number	number	Grid extension. Returns apparent temperature in Celsius.
AQI_PM25(pm25_ug_m3: number) → number	number	Grid extension. Returns approximate US AQI for PM2.5.
ARRHENIUS_EA(rate1: number, rate2: number, temperature1_k: number, temperature2_k: number) → number	number	Grid extension. Returns activation energy from two rate constants.
ARRHENIUS_RATE(pre_exponential: number, activation_energy_j_mol: number, temperature_k: number) → number	number	Grid extension. Returns Arrhenius rate constant.
ASPECT_RATIO(major_axis: number, minor_axis: number) → number	number	Grid extension. Returns aspect ratio.
ASSAY_RECOVERY_PERCENT(measured: number, expected: number) → number	number	Grid extension. Returns assay recovery percent.
ATM_TO_PASCAL(atm: number) → number	number	Grid extension. Converts atmospheres to pascals.
ATTACK_RATE(cases: number, exposed: number) → number	number	Grid extension. Returns attack rate percent.
AUC_INFINITY(auc_last: number, last_concentration: number, elimination_rate: number) → number	number	Grid extension. Returns AUC extrapolated to infinity.
AUC_TRAPEZOID(x_values: number[], y_values: number[]) → number	number	Grid extension. Returns area under a curve by the trapezoid rule.
BACKGROUND_SUBTRACT(signal: number, background: number) → number	number	Grid extension. Subtracts background from a signal.
BASELINE_CORRECT(value: number, baseline: number) → number	number	Grid extension. Subtracts baseline from a value.
BEAUFORT_SCALE(wind_speed_m_s: number) → number	number	Grid extension. Returns Beaufort force number from wind speed.
BEER_LAMBERT(molar_absorptivity: number, path_length_cm: number, concentration_m: number) → number	number	Grid extension. Returns absorbance by Beer-Lambert law.
BIOAVAILABILITY(auc_test: number, auc_reference: number, dose_test: number, dose_reference: number) → number	number	Grid extension. Returns absolute or relative bioavailability percent.
BLACKBODY_POWER(area_m2: number, temperature_k: number) → number	number	Grid extension. Returns blackbody radiated power.
BLANK_CORRECT(signal: number, blank: number) → number	number	Grid extension. Returns blank-corrected signal.
BOLTZMANN_FACTOR(energy_j: number, temperature_k: number) → number	number	Grid extension. Returns Boltzmann factor.
BRAGG_D_SPACING(wavelength: number, theta_rad: number) → number	number	Grid extension. Returns Bragg d-spacing for first-order diffraction.
BRUNT_VAISAALA_FREQUENCY(gravity_m_s2: number, potential_temperature_k: number, theta_gradient_k_m: number) → number	number	Grid extension. Returns Brunt-Vaisala frequency.
BUFFER_CAPACITY(added_moles: number, volume_l: number, delta_ph: number) → number	number	Grid extension. Returns buffer capacity.
BUFFER_MIX_RATIO(ph: number, pka: number) → number	number	Grid extension. Returns buffer base/acid mix ratio.
BUFFER_PH_AFTER_ACID(pka: number, base_moles: number, acid_moles: number, added_acid_moles: number) → number	number	Grid extension. Returns buffer pH after adding strong acid.
BUFFER_PH_AFTER_BASE(pka: number, base_moles: number, acid_moles: number, added_base_moles: number) → number	number	Grid extension. Returns buffer pH after adding strong base.
BUFFER_RATIO(ph: number, pka: number) → number	number	Grid extension. Returns conjugate base/acid ratio for a buffer.
BUOYANT_FORCE(fluid_density_kg_m3: number, volume_m3: number, gravity_m_s2: number) → number	number	Grid extension. Returns buoyant force in newtons.
CALIBRATION_CONCENTRATION(signal: number, slope: number, intercept: number) → number	number	Grid extension. Returns concentration from a linear calibration curve.
CAPACITANCE_PARALLEL_PLATE(area_m2: number, separation_m: number, relative_permittivity: number) → number	number	Grid extension. Returns parallel-plate capacitance in farads.
CAPACITOR_ENERGY(capacitance_f: number, voltage_v: number) → number	number	Grid extension. Returns capacitor stored energy in joules.
CARBON14_AGE(fraction_modern: number) → number	number	Grid extension. Returns approximate radiocarbon age in years.
CARBONATE_ALKALINITY(bicarbonate: number, carbonate: number, hydroxide: number, hydrogen: number) → number	number	Grid extension. Returns carbonate alkalinity estimate.
CARNOT_EFFICIENCY(hot_k: number, cold_k: number) → number	number	Grid extension. Returns ideal Carnot efficiency.
CARRYING_CAPACITY_TIME(initial: number, target: number, carrying_capacity: number, rate: number) → number	number	Grid extension. Returns time to target under logistic growth.
CELL_AREA(area_pixels: number, microns_per_pixel: number) → number	number	Grid extension. Converts cell area from pixels to square microns.
CELL_DENSITY(cell_count: number, dilution_factor: number, volume: number) → number	number	Grid extension. Returns cell density per volume.
CELSIUS_TO_FAHRENHEIT(celsius: number) → number	number	Grid extension. Converts Celsius to Fahrenheit.
CELSIUS_TO_KELVIN(celsius: number) → number	number	Grid extension. Converts Celsius to kelvin.
CENTRIPETAL_FORCE(mass_kg: number, velocity_m_per_s: number, radius_m: number) → number	number	Grid extension. Returns centripetal force in newtons.
CFU_PER_ML(colony_count: number, dilution_factor: number, plated_volume_ml: number) → number	number	Grid extension. Returns colony-forming units per mL.
CHI_SQUARE_GOODNESS(observed_values: number[], expected_values: number[]) → number	number	Grid extension. Returns chi-square goodness-of-fit statistic.
CIRCULARITY(area: number, perimeter: number) → number	number	Grid extension. Returns 4 pi area over perimeter squared.
CLEARANCE(dose: number, auc: number) → number	number	Grid extension. Returns pharmacokinetic clearance.
CLEAR_SKY_RADIATION_SIMPLE(solar_elevation_degrees: number, transmittance: number) → number	number	Grid extension. Returns approximate clear-sky shortwave radiation in W/m^2.
CLOUD_BASE_HEIGHT(temperature_c: number, dew_point_c: number) → number	number	Grid extension. Returns approximate cloud base height in meters.
CODON_OPTIMIZE_SCORE(sequence: string, target_gc: number) → number	number	Grid extension. Scores codon/sequence GC closeness to a target.
CODON_USAGE_FRACTION(sequence: string, codon: string) → number	number	Grid extension. Returns fraction of codons equal to a target codon.
COEFFICIENT_OF_VARIATION(values: number[]) → number	number	Grid extension. Returns sample coefficient of variation percent.
COHENS_D(sample1_values: number[], sample2_values: number[]) → number	number	Grid extension. Returns Cohen's d for two samples.
COLONY_AREA(diameter_pixels: number, microns_per_pixel: number) → number	number	Grid extension. Returns colony area from diameter.
COMBINE_UNCERTAINTY(uncertainties: number[]) → number	number	Grid extension. Returns root-sum-square combined uncertainty.
CONFIDENCE_INTERVAL(mean: number, standard_deviation: number, sample_size: number, z_score: number) → number	number	Grid extension. Returns the half-width of a normal confidence interval.
CORIOLIS_PARAMETER(latitude_degrees: number) → number	number	Grid extension. Returns the Coriolis parameter at a latitude.
COULOMB_FORCE(charge1_c: number, charge2_c: number, distance_m: number) → number	number	Grid extension. Returns electrostatic force in newtons.
COVERAGE_BREADTH(covered_bases: number, genome_size: number) → number	number	Grid extension. Returns coverage breadth fraction.
CRITICAL_ANGLE(n1: number, n2: number) → number	number	Grid extension. Returns critical angle for total internal reflection.
C_MAX(values: number[]) → number	number	Grid extension. Returns maximum concentration.
DALTON_TO_KG(daltons: number) → number	number	Grid extension. Converts daltons to kilograms.
DAY_LENGTH(latitude_degrees: number, day_of_year: number) → number	number	Grid extension. Returns daylight duration in hours.
DECIBEL_POWER(power_ratio: number) → number	number	Grid extension. Returns 10 log10 of a power ratio.
DECIBEL_RATIO(power: number, reference_power: number) → number	number	Grid extension. Returns a power ratio in decibels.
DENSITY(mass_kg: number, volume_m3: number) → number	number	Grid extension. Returns density in kg/m^3.
DENSITY_ALTITUDE(pressure_altitude_m: number, temperature_c: number) → number	number	Grid extension. Returns approximate density altitude in meters.
DEW_POINT(temperature_c: number, relative_humidity_percent: number) → number	number	Grid extension. Returns dew point in Celsius.
DEW_POINT_FROM_VAPOR_PRESSURE(vapor_pressure_kpa: number) → number	number	Grid extension. Returns dew point in Celsius from vapor pressure.
DE_BROGLIE_WAVELENGTH(mass_kg: number, velocity_m_s: number) → number	number	Grid extension. Returns de Broglie wavelength in meters.
DIFFRACTION_LIMIT(wavelength_m: number, aperture_m: number) → number	number	Grid extension. Returns Rayleigh angular resolution in radians.
DIFFUSION_TIME(distance_m: number, diffusion_m2_s: number) → number	number	Grid extension. Returns characteristic diffusion time.
DIFFUSIVITY_FROM_CONDUCTIVITY(thermal_conductivity: number, density: number, specific_heat: number) → number	number	Grid extension. Returns thermal diffusivity.
DILUTION_C1(c2: number, v1: number, v2: number) → number	number	Grid extension. Solves C1 for C1V1=C2V2.
DILUTION_C2(c1: number, v1: number, v2: number) → number	number	Grid extension. Solves C2 for C1V1=C2V2.
DILUTION_FACTOR(aliquot_volume: number, final_volume: number) → number	number	Grid extension. Returns dilution factor.
DILUTION_V1(c1: number, c2: number, v2: number) → number	number	Grid extension. Solves V1 for C1V1=C2V2.
DILUTION_V2(c1: number, v1: number, c2: number) → number	number	Grid extension. Solves V2 for C1V1=C2V2.
DNA_CPG_COUNT(sequence: string) → number	number	Grid extension. Counts CpG dinucleotides.
DNA_CPG_OBS_EXP(sequence: string) → number	number	Grid extension. Returns observed/expected CpG ratio.
DNA_FIND_MOTIF(sequence: string, motif: number) → number	number	Grid extension. Returns the 1-based position of a DNA motif or 0 if absent.
DNA_HAMMING_DISTANCE(sequence1: string, sequence2: string) → number	number	Grid extension. Returns Hamming distance between equal-length DNA sequences.
DNA_KMER_COUNT(sequence: string, k: number) → number	number	Grid extension. Returns the number of k-mer windows in a DNA sequence.
DNA_LEVENSHTEIN_DISTANCE(sequence1: string, sequence2: string) → number	number	Grid extension. Returns Levenshtein edit distance between DNA sequences.
DNA_MELTING_TEMP(sequence: string) → number	number	Grid extension. Returns an approximate DNA melting temperature in Celsius.
DNA_MOTIF_COUNT(sequence: string, motif: number) → number	number	Grid extension. Counts overlapping DNA motif occurrences.
DNA_MW(sequence: string) → number	number	Grid extension. Returns approximate single-stranded DNA molecular weight.
DNA_N50(lengths: number[]) → number	number	Grid extension. Returns N50 from contig/read lengths.
DOPPLER_FREQUENCY(source_frequency_hz: number, wave_speed_m_s: number, observer_speed_m_s: number, source_speed_m_s: number) → number	number	Grid extension. Returns observed Doppler frequency.
DOUBLING_TIME(growth_rate: number) → number	number	Grid extension. Returns doubling time.
DRAG_FORCE(fluid_density_kg_m3: number, velocity_m_s: number, drag_coefficient: number, area_m2: number) → number	number	Grid extension. Returns quadratic drag force.
EARTH_PRESSURE_DEPTH(density_kg_m3: number, gravity_m_s2: number, depth_m: number) → number	number	Grid extension. Returns lithostatic/hydrostatic pressure by depth.
EC50_ESTIMATE(concentration_values: number[], response_values: number[]) → number	number	Grid extension. Estimates EC50 as the concentration nearest the midpoint response.
ELASTIC_POTENTIAL_ENERGY(spring_constant_n_per_m: number, displacement_m: number) → number	number	Grid extension. Returns elastic potential energy in joules.
ELECTRIC_FIELD_POINT_CHARGE(charge_c: number, distance_m: number) → number	number	Grid extension. Returns electric field from a point charge.
ELECTRIC_POWER(voltage_v: number, current_a: number) → number	number	Grid extension. Returns electric power in watts.
EMPIRICAL_FORMULA_MASS(molecule: string) → number	number	Grid extension. Returns formula mass in g/mol.
ENZYME_EFFICIENCY(kcat: number, km: number) → number	number	Grid extension. Returns catalytic efficiency kcat/Km.
ENZYME_KCAT(vmax: number, enzyme_concentration: number) → number	number	Grid extension. Returns catalytic turnover kcat.
ENZYME_UNITS(amount_converted_umol: number, time_min: number) → number	number	Grid extension. Returns enzyme units in umol/min.
EQUILIBRIUM_CONSTANT(products_activity: number, reactants_activity: number) → number	number	Grid extension. Returns equilibrium constant from activity products.
EQUIVALENT_POTENTIAL_TEMPERATURE(temperature_k: number, pressure_hpa: number, mixing_ratio_kg_kg: number) → number	number	Grid extension. Returns approximate equivalent potential temperature in kelvin.
ESCAPE_VELOCITY(mass_kg: number, radius_m: number) → number	number	Grid extension. Returns escape velocity in m/s.
EVAPOTRANSPIRATION_HARGREAVES(tmin_c: number, tmax_c: number, extraterrestrial_radiation_mm_day: number) → number	number	Grid extension. Returns Hargreaves reference evapotranspiration in mm/day.
EV_TO_JOULE(electron_volts: number) → number	number	Grid extension. Converts electron-volts to joules.
EXPONENTIAL_GROWTH(initial: number, rate: number, time: number) → number	number	Grid extension. Returns exponential growth amount.
EXPONENTIAL_SMOOTHING(alpha: number, value: number, previous: number) → number	number	Grid extension. Returns one-step exponential smoothing.
E_MAX_MODEL(concentration: number, emax: number, ec50: number) → number	number	Grid extension. Returns Emax model response.
FAHRENHEIT_TO_CELSIUS(fahrenheit: number) → number	number	Grid extension. Converts Fahrenheit to Celsius.
FICKS_FLUX(diffusion_m2_s: number, concentration_gradient: number) → number	number	Grid extension. Returns Fick's law flux.
FINAL_CONCENTRATION(stock_concentration: number, stock_volume: number, final_volume: number) → number	number	Grid extension. Returns final concentration after dilution.
FIXATION_INDEX_FST(total_heterozygosity: number, subpopulation_heterozygosity: number) → number	number	Grid extension. Returns fixation index FST.
FOLD_CHANGE(value: number, baseline: number) → number	number	Grid extension. Returns fold change.
FOSBERG_FIRE_WEATHER_INDEX(temperature_c: number, relative_humidity_percent: number, wind_speed_m_s: number) → number	number	Grid extension. Returns approximate Fosberg fire weather index.
FRACTURE_STRESS(force: number, area: number) → number	number	Grid extension. Returns fracture stress.
FRACTURE_TOUGHNESS(stress: number, crack_length: number) → number	number	Grid extension. Returns approximate fracture toughness.
FREEZING_LEVEL_HEIGHT(surface_temp_c: number, lapse_rate_c_m: number) → number	number	Grid extension. Returns approximate freezing level height in meters.
FREE_FALL_DISTANCE(gravity_m_s2: number, time_s: number) → number	number	Grid extension. Returns free-fall distance in meters.
GC_SKEW(sequence: string) → number	number	Grid extension. Returns GC skew, (G-C)/(G+C).
GENERATION_TIME(growth_rate: number) → number	number	Grid extension. Returns generation time from growth rate.
GENOTYPE_FREQUENCY(genotype_count: number, sample_count: number) → number	number	Grid extension. Returns genotype frequency.
GEOSTROPHIC_WIND(pressure_gradient_pa_m: number, latitude_degrees: number, air_density_kg_m3: number) → number	number	Grid extension. Returns geostrophic wind speed from pressure gradient.
GIBBS_FROM_K(equilibrium_constant: number, temperature_k: number) → number	number	Grid extension. Returns standard Gibbs free energy from K.
GRAVITATIONAL_FORCE(mass1_kg: number, mass2_kg: number, distance_m: number) → number	number	Grid extension. Returns Newtonian gravitational force in newtons.
GROWTH_RATE_OD(od_initial: number, od_final: number, time: number) → number	number	Grid extension. Returns growth rate from optical density readings.
HALF_LIFE_DECAY(initial: number, time: number, half_life: number) → number	number	Grid extension. Returns remaining amount after exponential decay.
HALF_LIFE_FIRST_ORDER(rate_constant: number) → number	number	Grid extension. Returns first-order half-life.
HALF_LIFE_PK(elimination_rate: number) → number	number	Grid extension. Returns pharmacokinetic half-life.
HALF_LIFE_SECOND_ORDER(rate_constant: number, initial_concentration: number) → number	number	Grid extension. Returns second-order half-life.
HARDNESS_CONVERSION(hardness: number, factor: number) → number	number	Grid extension. Returns a simple factor-based hardness conversion.
HARDY_WEINBERG_P(aa_frequency: number, heterozygote_frequency: number) → number	number	Grid extension. Returns allele p from genotype frequencies.
HARDY_WEINBERG_Q(aa_frequency: number, heterozygote_frequency: number, bb_frequency: number) → number	number	Grid extension. Returns allele q from genotype frequencies.
HAVERSINE_DISTANCE(lat1_deg: number, lon1_deg: number, lat2_deg: number, lon2_deg: number, radius_m: number) → number	number	Grid extension. Returns great-circle distance by the haversine formula.
HEAT_INDEX(temperature_f: number, relative_humidity_percent: number) → number	number	Grid extension. Returns NOAA heat index in Fahrenheit.
HEAT_INDEX_C(temperature_c: number, relative_humidity_percent: number) → number	number	Grid extension. Returns heat index in Celsius.
HEAT_TRANSFER(mass_kg: number, specific_heat_j_kg_k: number, delta_k: number) → number	number	Grid extension. Returns sensible heat transfer in joules.
HEDGES_G(sample1_values: number[], sample2_values: number[]) → number	number	Grid extension. Returns Hedges' g for two samples.
HENDERSON_HASSELBALCH(pka: number, base_concentration: number, acid_concentration: number) → number	number	Grid extension. Returns buffer pH by Henderson-Hasselbalch.
HERD_IMMUNITY_THRESHOLD(r0: number) → number	number	Grid extension. Returns herd immunity threshold.
HETEROZYGOSITY_EXPECTED(p: number, q: number) → number	number	Grid extension. Returns expected heterozygosity for two alleles.
HILL_FRACTION_BOUND(ligand_concentration: number, kd: number, hill_coefficient: number) → number	number	Grid extension. Returns fractional occupancy by the Hill equation.
HUBBLE_DISTANCE(velocity_km_s: number, hubble_constant_km_s_mpc: number) → number	number	Grid extension. Returns Hubble distance in megaparsecs.
HUMIDEX(temperature_c: number, dew_point_c: number) → number	number	Grid extension. Returns Canadian humidex.
HYDROSTATIC_PRESSURE(density_kg_m3: number, gravity_m_s2: number, depth_m: number) → number	number	Grid extension. Returns hydrostatic pressure in pascals.
H_FROM_PH(ph: number) → number	number	Grid extension. Returns hydrogen ion molarity from pH.
IC50_TO_KI_CHENG_PRUSOFF(ic50: number, substrate_concentration: number, km: number) → number	number	Grid extension. Converts IC50 to Ki using Cheng-Prusoff.
IDEAL_GAS_MOLES(pressure_pa: number, volume_m3: number, temperature_k: number) → number	number	Grid extension. Returns ideal gas amount in moles.
IDEAL_GAS_PRESSURE(moles: number, temperature_k: number, volume_m3: number) → number	number	Grid extension. Returns ideal gas pressure in pascals.
IDEAL_GAS_TEMPERATURE(pressure_pa: number, volume_m3: number, moles: number) → number	number	Grid extension. Returns ideal gas temperature in kelvin.
IDEAL_GAS_VOLUME(moles: number, temperature_k: number, pressure_pa: number) → number	number	Grid extension. Returns ideal gas volume in cubic meters.
IMPULSE(force_n: number, time_s: number) → number	number	Grid extension. Returns impulse in newton-seconds.
INCIDENCE_RATE(cases: number, person_time: number) → number	number	Grid extension. Returns incidence rate.
INDUCTOR_ENERGY(inductance_h: number, current_a: number) → number	number	Grid extension. Returns inductor stored energy in joules.
INVERSE_SQUARE_INTENSITY(source_power: number, distance_m: number) → number	number	Grid extension. Returns inverse-square intensity.
IONIC_STRENGTH(concentration_values: number[], charge_values: number[]) → number	number	Grid extension. Returns ionic strength.
JOULE_TO_EV(joules: number) → number	number	Grid extension. Converts joules to electron-volts.
KELVIN_TO_CELSIUS(kelvin: number) → number	number	Grid extension. Converts kelvin to Celsius.
KEPLER_THIRD_AXIS(central_mass_kg: number, period_s: number) → number	number	Grid extension. Returns semi-major axis from Kepler's third law.
KEPLER_THIRD_PERIOD(semi_major_axis_m: number, central_mass_kg: number) → number	number	Grid extension. Returns orbital period from Kepler's third law.
KG_TO_DALTON(kilograms: number) → number	number	Grid extension. Converts kilograms to daltons.
KINETIC_ENERGY(mass_kg: number, velocity_m_per_s: number) → number	number	Grid extension. Returns kinetic energy in joules.
K_FROM_GIBBS(delta_g_j_mol: number, temperature_k: number) → number	number	Grid extension. Returns equilibrium constant from Gibbs free energy.
LAPSE_RATE_TEMP(surface_temp: number, lapse_rate: number, altitude: number) → number	number	Grid extension. Returns temperature adjusted by lapse rate.
LATENT_HEAT(mass_kg: number, latent_heat_j_kg: number) → number	number	Grid extension. Returns latent heat in joules.
LENS_FOCAL_LENGTH(object_distance_m: number, image_distance_m: number) → number	number	Grid extension. Returns thin-lens focal length in meters.
LIFTED_CONDENSATION_LEVEL(temperature_c: number, dew_point_c: number) → number	number	Grid extension. Returns approximate lifted condensation level in meters.
LIMITING_REAGENT(molecule1: string, mass1_g: number, coefficient1: number, molecule2: string, mass2_g: number, coefficient2: number) → string	string	Grid extension. Returns the limiting reagent formula for a two-reactant setup.
LINEAR_CALIBRATION(x: number, slope: number, intercept: number) → number	number	Grid extension. Returns a linear calibration signal.
LINEWEAVER_BURK_Y(slope: number, inverse_substrate: number, intercept: number) → number	number	Grid extension. Returns a Lineweaver-Burk y value.
LITER_ATM_TO_JOULE(liter_atm: number) → number	number	Grid extension. Converts liter-atmospheres to joules.
LOD(blank_standard_deviation: number, calibration_slope: number) → number	number	Grid extension. Returns analytical limit of detection.
LOG2_FOLD_CHANGE(value: number, baseline: number) → number	number	Grid extension. Returns log2 fold change.
LOGISTIC_4PL(x: number, bottom: number, top: number, ec50: number, hill_slope: number) → number	number	Grid extension. Returns a four-parameter logistic dose-response value.
LOGISTIC_5PL(x: number, bottom: number, top: number, ec50: number, hill_slope: number, asymmetry: number) → number	number	Grid extension. Returns a five-parameter logistic dose-response value.
LOGISTIC_GROWTH(initial: number, rate: number, carrying_capacity: number, time: number) → number	number	Grid extension. Returns logistic growth amount.
LOQ(blank_standard_deviation: number, calibration_slope: number) → number	number	Grid extension. Returns analytical limit of quantitation.
LORENTZ_FACTOR(velocity_m_s: number) → number	number	Grid extension. Returns relativistic Lorentz factor.
LOWPASS_RC_ALPHA(rc: number, dt: number) → number	number	Grid extension. Returns discrete RC low-pass smoothing alpha.
LUMINOSITY_FLUX(luminosity_w: number, distance_m: number) → number	number	Grid extension. Returns flux from luminosity and distance.
MAGNETIC_FIELD_WIRE(current_a: number, radius_m: number) → number	number	Grid extension. Returns magnetic field around a long straight wire.
MAGNETIC_FORCE_CHARGE(charge_c: number, velocity_m_s: number, magnetic_field_t: number, angle_rad: number) → number	number	Grid extension. Returns magnetic force on a moving charge.
MAGNIFICATION(object_distance_m: number, image_distance_m: number) → number	number	Grid extension. Returns thin-lens magnification.
MASS_FRACTION(component_mass: number, total_mass: number) → number	number	Grid extension. Returns mass fraction.
MASS_PERCENT(solute_mass: number, solution_mass: number) → number	number	Grid extension. Returns mass percent.
MASS_TO_CHARGE(mass: number, charge: number) → number	number	Grid extension. Returns mass-to-charge ratio.
MEAN_FREE_PATH(molecular_diameter_m: number, temperature_k: number, pressure_pa: number) → number	number	Grid extension. Returns gas mean free path.
MICHAELIS_MENTEN_RATE(vmax: number, substrate_concentration: number, km: number) → number	number	Grid extension. Returns Michaelis-Menten reaction rate.
MIXING_RATIO(vapor_pressure: number, pressure: number) → number	number	Grid extension. Returns atmospheric mixing ratio.
MIX_CONCENTRATION(concentration1: number, volume1: number, concentration2: number, volume2: number) → number	number	Grid extension. Returns concentration after mixing two solutions.
MIX_PH_STRONG_ACID_BASE(acid_moles: number, base_moles: number, volume_l: number) → number	number	Grid extension. Returns pH after mixing strong acid and base.
MOI(infectious_units: number, cells: number) → number	number	Grid extension. Returns multiplicity of infection.
MOIST_AIR_DENSITY(temperature_c: number, pressure_hpa: number, relative_humidity_percent: number) → number	number	Grid extension. Returns moist-air density in kg/m^3.
MOLALITY(moles: number, solvent_kg: number) → number	number	Grid extension. Returns molality in mol/kg.
MOLARITY(moles: number, liters: number) → number	number	Grid extension. Returns molarity in mol/L.
MOLE_FRACTION(component_moles: number, total_moles: number) → number	number	Grid extension. Returns mole fraction.
MOL_MASS_FRACTION(molecule: string, element: string) → number	number	Grid extension. Returns element mass fraction for a molecule.
MOL_MASS_FROM_MOLES(molecule: string, moles: number) → number	number	Grid extension. Returns mass in grams from molecule/formula and moles.
MOL_MOLES(molecule: string, mass_g: number) → number	number	Grid extension. Returns moles from a molecule/formula and mass in grams.
MOL_PERCENT_COMPOSITION(molecule: string, element: string) → number	number	Grid extension. Returns element percent composition for a molecule.
MOMENTUM(mass_kg: number, velocity_m_per_s: number) → number	number	Grid extension. Returns momentum in kg m/s.
MOVING_RMS(values: number[]) → number	number	Grid extension. Returns root mean square of a window.
MUTATION_CLASS(reference: string, alternate: string) → string	string	Grid extension. Classifies a simple variant as SNV, MNV, insertion, or deletion.
N50_N90(lengths: number[]) → string	string	Grid extension. Returns N50 and N90 as text.
NERNST_POTENTIAL(standard_potential_v: number, temperature_k: number, electrons: number, reaction_quotient: number) → number	number	Grid extension. Returns electrode potential from the Nernst equation.
NET_RADIATION_SIMPLE(shortwave_in_w_m2: number, longwave_in_w_m2: number, surface_temp_k: number, albedo: number, emissivity: number) → number	number	Grid extension. Returns approximate net radiation in W/m^2.
NORMALITY(molarity: number, equivalents: number) → number	number	Grid extension. Returns solution normality.
NORMALIZE_TO_CONTROL(value: number, control: number) → number	number	Grid extension. Normalizes a value to its control.
NUCLEOTIDE_COUNTS(sequence: string) → string	string	Grid extension. Returns nucleotide counts as text.
OD260_DNA_CONC(absorbance_260: number, dilution_factor: number) → number	number	Grid extension. Returns dsDNA concentration in ug/mL from A260.
OD260_RNA_CONC(absorbance_260: number, dilution_factor: number) → number	number	Grid extension. Returns RNA concentration in ug/mL from A260.
OD280_PROTEIN_CONC(absorbance_280: number, dilution_factor: number, extinction_coeff: number) → number	number	Grid extension. Returns protein concentration from A280 and extinction coefficient.
ODDS_RATIO(a: number, b: number, c: number, d: number) → number	number	Grid extension. Returns odds ratio from a 2x2 table.
OHMS_CURRENT(voltage_v: number, resistance_ohm: number) → number	number	Grid extension. Returns current from voltage and resistance.
OHMS_RESISTANCE(voltage_v: number, current_a: number) → number	number	Grid extension. Returns resistance from voltage and current.
OHMS_VOLTAGE(current_a: number, resistance_ohm: number) → number	number	Grid extension. Returns voltage from current and resistance.
OH_FROM_POH(poh: number) → number	number	Grid extension. Returns hydroxide molarity from pOH.
ORBITAL_SPEED(central_mass_kg: number, radius_m: number) → number	number	Grid extension. Returns circular orbital speed in m/s.
ORF_FIND(sequence: string) → string	string	Grid extension. Returns the first translated ORF starting at ATG.
ORF_LONGEST(sequence: string) → string	string	Grid extension. Returns the longest translated forward-frame ORF approximation.
OSMOLARITY(molarity: number, osmotic_particles: number) → number	number	Grid extension. Returns solution osmolarity.
OSMOTIC_PRESSURE(molarity_mol_m3: number, temperature_k: number) → number	number	Grid extension. Returns osmotic pressure in pascals.
PARALLEL_RESISTANCE(resistances: number[]) → number	number	Grid extension. Returns the equivalent resistance for resistors in parallel.
PASCAL_TO_ATM(pascals: number) → number	number	Grid extension. Converts pascals to atmospheres.
PASCAL_TO_TORR(pascals: number) → number	number	Grid extension. Converts pascals to torr.
PCR_CYCLES_FOR_YIELD(initial_amount: number, target_amount: number, efficiency: number) → number	number	Grid extension. Returns PCR cycles needed for a target yield.
PEAK_AREA_TRIANGLE(height: number, width: number) → number	number	Grid extension. Returns triangular peak area.
PEAK_TO_PEAK(values: number[]) → number	number	Grid extension. Returns max minus min.
PERCENT_ERROR(measured: number, true_value: number) → number	number	Grid extension. Returns percent error.
PERCENT_IONIZATION(ionized_concentration: number, initial_concentration: number) → number	number	Grid extension. Returns percent ionization.
PERCENT_OF_CONTROL(value: number, control: number) → number	number	Grid extension. Returns a value as percent of control.
PERCENT_YIELD(actual_yield: number, theoretical_yield: number) → number	number	Grid extension. Returns percent yield.
PERIOD(frequency_hz: number) → number	number	Grid extension. Returns period in seconds.
PHOTON_ENERGY(frequency_hz: number) → number	number	Grid extension. Returns photon energy in joules.
PH_FROM_H(hydrogen_molarity: number) → number	number	Grid extension. Returns pH from hydrogen ion molarity.
PH_FROM_KA(ka: number, acid_molarity: number) → number	number	Grid extension. Estimates weak-acid pH from Ka and concentration.
PIXEL_TO_MICRON(pixels: number, microns_per_pixel: number) → number	number	Grid extension. Converts pixels to microns.
PLANCK_RADIANCE(wavelength_m: number, temperature_k: number) → number	number	Grid extension. Returns spectral radiance from Planck's law.
PLAQUE_TITER(plaques: number, dilution_factor: number, volume_ml: number) → number	number	Grid extension. Returns plaque titer per mL.
PLATE_COUNT(retention_time: number, peak_width: number) → number	number	Grid extension. Returns chromatography theoretical plate count.
PLATE_NORMALIZE_B_SCORE(value: number, row_median: number, column_median: number, plate_median: number, mad: number) → number	number	Grid extension. Returns an approximate B-score normalization.
POH_FROM_OH(hydroxide_molarity: number) → number	number	Grid extension. Returns pOH from hydroxide molarity.
POISEUILLE_FLOW(pressure_drop_pa: number, radius_m: number, viscosity_pa_s: number, length_m: number) → number	number	Grid extension. Returns Poiseuille volumetric flow.
POISSON_RATIO(transverse_strain: number, axial_strain: number) → number	number	Grid extension. Returns Poisson ratio.
POTENTIAL_ENERGY(mass_kg: number, gravity_m_per_s2: number, height_m: number) → number	number	Grid extension. Returns gravitational potential energy in joules.
POTENTIAL_TEMPERATURE(temperature_k: number, pressure_hpa: number) → number	number	Grid extension. Returns dry potential temperature in kelvin.
PPB(part: number, whole: number) → number	number	Grid extension. Returns parts per billion.
PPM(part: number, whole: number) → number	number	Grid extension. Returns parts per million.
PRECIP_INTENSITY(precip_depth_mm: number, duration_hours: number) → number	number	Grid extension. Returns precipitation intensity in mm/h.
PRESSURE(force_n: number, area_m2: number) → number	number	Grid extension. Returns pressure in pascals.
PRESSURE_ALTITUDE(pressure_hpa: number) → number	number	Grid extension. Returns standard-atmosphere pressure altitude in meters.
PREVALENCE(cases: number, population: number) → number	number	Grid extension. Returns prevalence fraction.
PROJECTILE_MAX_HEIGHT(speed_m_s: number, angle_rad: number, gravity_m_s2: number) → number	number	Grid extension. Returns ideal projectile maximum height in meters.
PROJECTILE_RANGE(speed_m_s: number, angle_rad: number, gravity_m_s2: number) → number	number	Grid extension. Returns ideal projectile range in meters.
PROPAGATE_UNCERTAINTY(partials: number[], uncertainties: number[]) → number	number	Grid extension. Returns propagated independent uncertainty from partial derivatives and uncertainties.
PROTEIN_CHARGE_ESTIMATE(sequence: string) → number	number	Grid extension. Returns a simple protein charge estimate near neutral pH.
PROTEIN_EXTINCTION_COEFF(sequence: string) → number	number	Grid extension. Returns an approximate protein extinction coefficient.
PROTEIN_GRAVY(sequence: string) → number	number	Grid extension. Returns GRAVY hydropathy score for a protein sequence.
PROTEIN_MASS(sequence: string) → number	number	Grid extension. Returns approximate protein molecular mass in daltons.
PROTEIN_PI_ESTIMATE(sequence: string) → number	number	Grid extension. Returns a simple protein pI estimate from charged residues.
PSYCHROMETRIC_CONSTANT(pressure_kpa: number) → number	number	Grid extension. Returns psychrometric constant in kPa/C.
QPCR_COPY_NUMBER(cq: number, slope: number, intercept: number) → number	number	Grid extension. Returns qPCR copy number from a standard curve.
QPCR_CQ_DELTA(target_cq: number, reference_cq: number) → number	number	Grid extension. Returns qPCR delta Cq.
QPCR_DELTA_DELTA_CQ(target_cq: number, reference_cq: number, control_target_cq: number, control_reference_cq: number) → number	number	Grid extension. Returns qPCR delta-delta Cq.
QPCR_EFFICIENCY(slope: number) → number	number	Grid extension. Returns qPCR amplification efficiency from standard-curve slope.
R0_SIR(transmission_rate: number, recovery_rate: number) → number	number	Grid extension. Returns basic reproduction number for a simple SIR model.
RADIOACTIVE_AGE(parent_initial: number, parent_remaining: number, decay_constant: number) → number	number	Grid extension. Returns radiometric age.
RC_TIME_CONSTANT(resistance_ohm: number, capacitance_f: number) → number	number	Grid extension. Returns RC time constant in seconds.
REACTION_QUOTIENT(products_activity: number, reactants_activity: number) → number	number	Grid extension. Returns reaction quotient from activity products.
READ_DEPTH(read_bases: number, genome_size: number) → number	number	Grid extension. Returns average read depth.
REDSHIFT_VELOCITY(redshift: number) → number	number	Grid extension. Returns low-redshift recession velocity in m/s.
RELATIVE_ERROR(measured: number, true_value: number) → number	number	Grid extension. Returns relative error.
RELATIVE_HUMIDITY(temperature_c: number, dew_point_c: number) → number	number	Grid extension. Returns relative humidity from temperature and dew point.
RELATIVE_HUMIDITY_FROM_MIXING_RATIO(mixing_ratio_kg_kg: number, pressure_kpa: number, temperature_c: number) → number	number	Grid extension. Returns relative humidity from mixing ratio, pressure, and temperature.
RELATIVE_RISK(exposed_cases: number, exposed_non_cases: number, control_cases: number, control_non_cases: number) → number	number	Grid extension. Returns relative risk from cohort counts.
RELATIVISTIC_ENERGY(mass_kg: number, velocity_m_s: number) → number	number	Grid extension. Returns relativistic total energy.
RESISTANCE_FROM_RESISTIVITY(resistivity_ohm_m: number, length_m: number, area_m2: number) → number	number	Grid extension. Returns resistance from resistivity and geometry.
RESOLUTION_CHROMATOGRAPHY(retention_time1: number, retention_time2: number, width1: number, width2: number) → number	number	Grid extension. Returns chromatographic resolution.
RETENTION_FACTOR(retention_time: number, dead_time: number) → number	number	Grid extension. Returns chromatographic retention factor.
REVERSE_TRANSLATE(protein_sequence: string) → string	string	Grid extension. Returns a simple DNA reverse translation.
REYNOLDS_NUMBER(density_kg_m3: number, velocity_m_s: number, length_m: number, viscosity_pa_s: number) → number	number	Grid extension. Returns Reynolds number.
RNA_CODON_COUNT(sequence: string) → number	number	Grid extension. Returns complete codon count in an RNA sequence.
RNA_GC(sequence: string) → number	number	Grid extension. Returns RNA GC content as a fraction.
RNA_MW(sequence: string) → number	number	Grid extension. Returns approximate single-stranded RNA molecular weight.
RNA_TO_DNA(sequence: string) → string	string	Grid extension. Converts RNA sequence text to DNA sequence text.
RNA_TRANSLATE(sequence: string) → string	string	Grid extension. Translates an RNA sequence to protein single-letter codes.
ROBUST_Z_SCORE(value: number, median: number, mad: number) → number	number	Grid extension. Returns robust z-score using median absolute deviation.
ROOT_MEAN_SQUARE_SPEED(molar_mass_kg_mol: number, temperature_k: number) → number	number	Grid extension. Returns molecular root-mean-square speed.
ROUND_SIGFIGS(value: number, figures: number) → number	number	Grid extension. Rounds a number to significant figures.
SATURATION_VAPOR_PRESSURE(temperature_c: number) → number	number	Grid extension. Returns saturation vapor pressure in kPa.
SCI_CONSTANT(constant: string) → number	number	Grid extension. Returns a named scientific constant value in SI units.
SCI_CONSTANT_REL_UNCERTAINTY(constant: string) → number	number	Grid extension. Returns the relative uncertainty for a named scientific constant.
SCI_CONSTANT_UNITS(constant: string) → string	string	Grid extension. Returns the SI units for a named scientific constant.
SCI_CONSTANT_VALUE(constant: string) → number	number	Grid extension. Returns a named scientific constant value in SI units.
SEA_LEVEL_PRESSURE(station_pressure_hpa: number, elevation_m: number, temperature_c: number) → number	number	Grid extension. Returns sea-level pressure from station pressure.
SEISMIC_WAVE_TRAVEL_TIME(distance_m: number, velocity_m_s: number) → number	number	Grid extension. Returns seismic travel time.
SEM(values: number[]) → number	number	Grid extension. Returns the standard error of the mean for a sample.
SERIAL_DILUTION(initial_concentration: number, dilution_factor: number, steps: number) → number	number	Grid extension. Returns concentration after serial dilution.
SERIES_RESISTANCE(resistances: number[]) → number	number	Grid extension. Returns the equivalent resistance for resistors in series.
SHANNON_DIVERSITY(counts: number[]) → number	number	Grid extension. Returns Shannon diversity index.
SIGNAL_TO_NOISE(signal: number, noise: number) → number	number	Grid extension. Returns signal-to-noise ratio.
SIGNIFICANT_FIGURES(value_text: string) → number	number	Grid extension. Counts significant figures in a numeric text value.
SIMPSON_DIVERSITY(counts: number[]) → number	number	Grid extension. Returns Simpson diversity index.
SNELLS_LAW_ANGLE(n1: number, n2: number, angle1_rad: number) → number	number	Grid extension. Returns refracted angle by Snell's law.
SNOW_WATER_EQUIVALENT(snow_depth_cm: number, snow_density_kg_m3: number) → number	number	Grid extension. Returns snow water equivalent in mm.
SNR_DB(signal: number, noise: number) → number	number	Grid extension. Returns signal-to-noise ratio in decibels.
SOLAR_ELEVATION_SIMPLE(latitude_deg: number, declination_deg: number, hour_angle_deg: number) → number	number	Grid extension. Returns simple solar elevation angle in degrees.
SOLAR_ZENITH_SIMPLE(latitude_deg: number, declination_deg: number, hour_angle_deg: number) → number	number	Grid extension. Returns simple solar zenith angle in degrees.
SOUND_INTENSITY_LEVEL(intensity_w_m2: number) → number	number	Grid extension. Returns sound intensity level in dB SPL.
SPECIES_RICHNESS(counts: number[]) → number	number	Grid extension. Returns count of species with positive abundance.
SPECIFIC_GROWTH_RATE(initial: number, final: number, time: number) → number	number	Grid extension. Returns specific growth rate.
SPECIFIC_HEAT_CAPACITY(heat_j: number, mass_kg: number, delta_k: number) → number	number	Grid extension. Returns specific heat capacity.
SPECIFIC_HUMIDITY(vapor_pressure_kpa: number, pressure_kpa: number) → number	number	Grid extension. Returns specific humidity in kg/kg.
SPIKE_RECOVERY(spiked_measured: number, original_measured: number, spike_added: number) → number	number	Grid extension. Returns spike recovery percent.
SSMD(mean1: number, mean2: number, sd1: number, sd2: number) → number	number	Grid extension. Returns strictly standardized mean difference.
STANDARD_ADDITION(slope: number, intercept: number) → number	number	Grid extension. Returns standard-addition concentration from x-intercept.
STANDARD_ATMOSPHERE_PRESSURE(altitude_m: number) → number	number	Grid extension. Returns standard-atmosphere pressure in hPa.
STANDARD_ATMOSPHERE_TEMP(altitude_m: number) → number	number	Grid extension. Returns standard-atmosphere temperature in Celsius.
STATION_PRESSURE(sea_level_pressure_hpa: number, elevation_m: number, temperature_c: number) → number	number	Grid extension. Returns station pressure from sea-level pressure.
STEFAN_BOLTZMANN_LUMINOSITY(radius_m: number, temperature_k: number) → number	number	Grid extension. Returns blackbody luminosity.
STOCK_VOLUME(stock_concentration: number, final_concentration: number, final_volume: number) → number	number	Grid extension. Returns stock volume for a dilution.
STOKES_DRAG(viscosity_pa_s: number, radius_m: number, velocity_m_s: number) → number	number	Grid extension. Returns Stokes drag force.
STRAIN(delta_length: number, original_length: number) → number	number	Grid extension. Returns engineering strain.
STRESS(force: number, area: number) → number	number	Grid extension. Returns mechanical stress.
SUN_DECLINATION(day_of_year: number) → number	number	Grid extension. Returns solar declination in degrees.
S_BIOMARKER_INDEX(value: number, cutoff: number, scale: number) → number	number	Grid extension. Returns a scaled biomarker index.
TERMINAL_VELOCITY(mass_kg: number, gravity_m_s2: number, fluid_density_kg_m3: number, area_m2: number, drag_coefficient: number) → number	number	Grid extension. Returns terminal velocity under quadratic drag.
THEORETICAL_YIELD(limiting_mass_g: number, limiting_molar_mass: number, product_coefficient: number, product_molar_mass: number) → number	number	Grid extension. Returns theoretical yield in grams.
THERMAL_EXPANSION_LINEAR(length_m: number, coefficient_per_k: number, delta_k: number) → number	number	Grid extension. Returns expanded length in meters.
THERMAL_STRESS(youngs_modulus: number, thermal_expansion: number, delta_temperature: number) → number	number	Grid extension. Returns constrained thermal stress.
THICKNESS_HYPSOMETRIC(virtual_temp_k: number, pressure_lower_hpa: number, pressure_upper_hpa: number) → number	number	Grid extension. Returns pressure-layer thickness by the hypsometric equation.
TITRATION_PH_STRONG_ACID(acid_moles: number, base_moles: number, volume_l: number) → number	number	Grid extension. Returns strong acid/base titration pH.
TITRATION_PH_WEAK_ACID(pka: number, acid_moles: number, base_moles: number) → number	number	Grid extension. Returns weak-acid titration pH before equivalence.
TORR_TO_PASCAL(torr: number) → number	number	Grid extension. Converts torr to pascals.
TRANSLATE_ALL_FRAMES(sequence: string) → string	string	Grid extension. Returns translations for the three forward frames.
TRANSLATE_FRAME(sequence: string, frame: number) → string	string	Grid extension. Translates a sequence from reading frame 1, 2, or 3.
TRANSMITTANCE_FROM_ABSORBANCE(absorbance: number) → number	number	Grid extension. Returns transmittance fraction from absorbance.
T_MAX(time_values: number[], concentration_values: number[]) → number	number	Grid extension. Returns time of maximum concentration.
T_TEST_PAIRED_EFFECT_SIZE(before_values: number[], after_values: number[]) → number	number	Grid extension. Returns paired-sample effect size from matched measurements.
VACCINE_EFFICACY(relative_risk: number) → number	number	Grid extension. Returns vaccine efficacy percent from relative risk.
VAPOR_PRESSURE(temperature_c: number, relative_humidity_percent: number) → number	number	Grid extension. Returns actual vapor pressure in kPa.
VARIANT_ALLELE_FREQUENCY(alternate_depth: number, reference_depth: number) → number	number	Grid extension. Returns variant allele frequency.
VIABILITY_PERCENT(live_cells: number, total_cells: number) → number	number	Grid extension. Returns cell viability percent.
VIRTUAL_TEMPERATURE(temperature_c: number, mixing_ratio_kg_kg: number) → number	number	Grid extension. Returns virtual temperature in Celsius.
VOLUME_DISTRIBUTION(amount: number, concentration: number) → number	number	Grid extension. Returns volume of distribution.
VPD(temperature_c: number, relative_humidity_percent: number) → number	number	Grid extension. Returns vapor pressure deficit in kPa.
WAVELENGTH(speed_m_s: number, frequency_hz: number) → number	number	Grid extension. Returns wavelength in meters.
WAVENUMBER_TO_WAVELENGTH(wavenumber_cm: number) → number	number	Grid extension. Converts wavenumber in cm^-1 to wavelength in meters.
WAVE_SPEED(frequency_hz: number, wavelength_m: number) → number	number	Grid extension. Returns wave speed in m/s.
WEIGHTED_MEAN_UNCERTAINTY(uncertainties: number[]) → number	number	Grid extension. Returns uncertainty of an inverse-variance weighted mean.
WET_BULB_APPROX(temperature_c: number, relative_humidity_percent: number) → number	number	Grid extension. Returns approximate wet-bulb temperature.
WET_BULB_FROM_TEMP_DEWPOINT(temperature_c: number, dew_point_c: number) → number	number	Grid extension. Returns approximate wet-bulb temperature from temperature and dew point.
WET_BULB_GLOBE_TEMP_SIMPLE(temperature_c: number, relative_humidity_percent: number, solar_radiation_w_m2: number, wind_speed_m_s: number) → number	number	Grid extension. Returns a simple wet-bulb globe temperature estimate in Celsius.
WIEN_PEAK_WAVELENGTH(temperature_k: number) → number	number	Grid extension. Returns Wien peak wavelength in meters.
WIND_CHILL(temperature_f: number, wind_speed_mph: number) → number	number	Grid extension. Returns wind chill in Fahrenheit.
WIND_CHILL_C(temperature_c: number, wind_speed_kmh: number) → number	number	Grid extension. Returns wind chill in Celsius.
WIND_COMPONENT_CROSS(wind_speed: number, wind_direction_degrees: number, bearing_degrees: number) → number	number	Grid extension. Returns the crosswind component for a bearing.
WIND_COMPONENT_HEAD(wind_speed: number, wind_direction_degrees: number, bearing_degrees: number) → number	number	Grid extension. Returns the headwind component for a bearing.
WIND_DIRECTION_UV(u_component: number, v_component: number) → number	number	Grid extension. Returns meteorological wind direction from u and v components.
WIND_RUN(wind_speed_m_s: number, duration_hours: number) → number	number	Grid extension. Returns wind run in kilometers.
WIND_SPEED_MS_TO_KMH(wind_speed_m_s: number) → number	number	Grid extension. Converts wind speed from m/s to km/h.
WIND_SPEED_MS_TO_MPH(wind_speed_m_s: number) → number	number	Grid extension. Converts wind speed from m/s to mph.
WIND_U_COMPONENT(wind_speed: number, wind_direction_degrees: number) → number	number	Grid extension. Returns meteorological eastward wind component.
WIND_V_COMPONENT(wind_speed: number, wind_direction_degrees: number) → number	number	Grid extension. Returns meteorological northward wind component.
WORK(force_n: number, distance_m: number, angle_rad: number) → number	number	Grid extension. Returns mechanical work in joules.
YOUNGS_MODULUS(stress: number, strain: number) → number	number	Grid extension. Returns Young's modulus.
Z_PRIME_FACTOR(positive_sd: number, negative_sd: number, positive_mean: number, negative_mean: number) → number	number	Grid extension. Returns assay Z-prime factor.
Z_SCORE_PLATE(value: number, plate_mean: number, plate_sd: number) → number	number	Grid extension. Returns plate-level z-score.

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Solar Position

Solar position, sunrise/sunset, twilight, and Delta T helpers.

Function count: 10.

Function	Returns	Notes
SOLAR_AZIMUTH(datetime_utc: date, latitude_deg: number, longitude_deg: number, elevation_m: number, delta_t_seconds: number, refraction: boolean) → number	number	Grid extension. Returns SPA solar azimuth in degrees clockwise from north.
SOLAR_DELTA_T(year: number, month: number) → number	number	Grid extension. Estimates Delta T in seconds for a year and month using Espenak-Meeus polynomials.
SOLAR_ELEVATION(datetime_utc: date, latitude_deg: number, longitude_deg: number, elevation_m: number, delta_t_seconds: number, refraction: boolean) → number	number	Grid extension. Returns SPA solar elevation angle in degrees above the horizon.
SOLAR_NOON_UTC(date_utc: date, latitude_deg: number, longitude_deg: number, delta_t_seconds: number, horizon: string) → number	number	Grid extension. Returns solar transit/noon time as hours since UTC midnight for a date and observer.
SOLAR_POSITION(datetime_utc: date, latitude_deg: number, longitude_deg: number, elevation_m: number, delta_t_seconds: number, refraction: boolean) → array	array	Grid extension. Returns SPA solar [azimuth_deg, elevation_deg, zenith_deg] for a UTC datetime and observer.
SOLAR_POSITION_GRENA3(datetime_utc: date, latitude_deg: number, longitude_deg: number, delta_t_seconds: number, refraction: boolean) → array	array	Grid extension. Returns fast Grena3 solar [azimuth_deg, elevation_deg, zenith_deg] for a UTC datetime and observer.
SOLAR_SUNRISE_UTC(date_utc: date, latitude_deg: number, longitude_deg: number, delta_t_seconds: number, horizon: string) → number	number	Grid extension. Returns sunrise time as hours since UTC midnight for a date, observer, and horizon.
SOLAR_SUNSET_UTC(date_utc: date, latitude_deg: number, longitude_deg: number, delta_t_seconds: number, horizon: string) → number	number	Grid extension. Returns sunset time as hours since UTC midnight for a date, observer, and horizon.
SOLAR_SUN_TIMES_UTC(date_utc: date, latitude_deg: number, longitude_deg: number, delta_t_seconds: number, horizon: string) → array	array	Grid extension. Returns [day_type, sunrise_hours_utc, transit_hours_utc, sunset_hours_utc] for a date, observer, and horizon.
SOLAR_ZENITH(datetime_utc: date, latitude_deg: number, longitude_deg: number, elevation_m: number, delta_t_seconds: number, refraction: boolean) → number	number	Grid extension. Returns SPA solar zenith angle in degrees.

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Geometry

Planar geometry, polygons, intersections, and WKT/GeoJSON conversion helpers.

Function count: 52.

Function	Returns	Notes
GEOM_BBOX(point1: array, point2: array) → array	array	Grid extension. Returns the axis-aligned bounding box of two points.
GEOM_CLIP_LINE(point1: array, point2: array, bbox: array) → array	array	Grid extension. Clips a line segment to an axis-aligned rectangle (bbox).
GEOM_DISTANCE(point1: array, point2: array) → number	number	Grid extension. Returns the Euclidean distance between two points.
GEOM_EPSG(geometry: geometry) → number	number	Grid extension. Returns the EPSG coordinate reference system carried by a native geometry.
GEOM_FROM_EWKB(ewkb_hex: string, expected_epsg: number) → geometry	geometry	Grid extension. Parses hexadecimal PostGIS EWKB and preserves its embedded SRID.
GEOM_FROM_GEOJSON(geojson: string) → geometry	geometry	Grid extension. Parses any supported GeoJSON geometry, Feature, or FeatureCollection into a native CRS-aware geometry.
GEOM_FROM_WKB(wkb_hex: string, epsg: number) → geometry	geometry	Grid extension. Parses hexadecimal OGC WKB or EWKB into a native geometry, using EPSG:4326 when no CRS is supplied.
GEOM_FROM_WKT(wkt: string) → geometry	geometry	Grid extension. Parses WKT vector geometry into a native EPSG:4326 geometry.
GEOM_INDEX(points: array) → object	object	Grid extension. Builds or reuses a spatial index for a point set.
GEOM_INDEX_INFO(index: geometry_index) → object	object	Grid extension. Returns diagnostics for a resident geometry index handle.
GEOM_INDEX_NEAREST(index: geometry_index, query_point: array, k: number) → array	array	Grid extension. Returns nearest indexed points and distances for a query point.
GEOM_INDEX_POINTS_IN_BBOX(index: geometry_index, bbox: array) → array	array	Grid extension. Returns indexed points that fall inside a bbox.
GEOM_INDEX_POINTS_IN_REGION(index: geometry_index, polygon: geometry|array, holes: array) → array	array	Grid extension. Returns indexed points strictly inside a polygon, excluding exterior and hole boundaries.
GEOM_IS_VALID(polygon: array) → boolean	boolean	Grid extension. Returns whether a polygon has valid rings, no self-intersections, and valid hole topology.
GEOM_LINE_INTERSECTION(point1: geometry, point2: geometry, point3: geometry, point4: geometry) → geometry	geometry	Grid extension. Returns the intersection point of two infinite lines.
GEOM_MAKE_VALID(polygon: geometry) → geometry	geometry	Grid extension. Repairs polygon self-intersections and ring topology using even-odd polygonization.
GEOM_MIDPOINT(point1: geometry, point2: geometry) → geometry	geometry	Grid extension. Returns the midpoint between two points.
GEOM_NEAREST(query_point: array, points: array) → array	array	Grid extension. Returns the nearest point in a set and its distance.
GEOM_POINT(x: number, y: number) → geometry	geometry	Grid extension. Returns a native EPSG:4326 point geometry.
GEOM_POINTS_IN_BBOX(bbox: array, points: array) → array	array	Grid extension. Returns points from a set that fall inside a bbox.
GEOM_POINT_IN_POLYGON(point: array, polygon: array, holes: array) → number	number	Grid extension. Returns 1 when a point lies inside a polygon and outside optional hole rings, else 0.
GEOM_POLYGON_AREA(polygon: array) → number	number	Grid extension. Returns the area of a polygon defined by vertex rows.
GEOM_POLYGON_CENTROID(polygon: geometry) → geometry	geometry	Grid extension. Returns the centroid of a polygon.
GEOM_POLYGON_CENTROID_NET(polygon: array, holes: array, min_area: number) → array	array	Grid extension. Returns iTriangle's centroid/dual polygon net for a triangulated polygon.
GEOM_POLYGON_CONVEX_DECOMPOSE(polygon: array, holes: array) → array	array	Grid extension. Decomposes a polygon into convex polygons.
GEOM_POLYGON_DIFFERENCE(polygon_a: geometry, polygon_b: geometry) → geometry	geometry	Grid extension. Returns polygon A minus polygon B.
GEOM_POLYGON_INTERSECTION(polygon_a: geometry, polygon_b: geometry) → geometry	geometry	Grid extension. Returns the intersection of two polygons.
GEOM_POLYGON_OFFSET(polygon: geometry, delta: number) → geometry	geometry	Grid extension. Inflates or deflates a polygon by a distance.
GEOM_POLYGON_PERIMETER(polygon: array) → number	number	Grid extension. Returns the perimeter of a polygon defined by vertex rows.
GEOM_POLYGON_TESSELLATE(polygon: array, holes: array, min_area: number) → array	array	Grid extension. Refines a polygon mesh with iTriangle circumcenter tessellation using an optional minimum area threshold.
GEOM_POLYGON_TESSELLATE_MESH(polygon: array, holes: array, min_area: number) → array	array	Grid extension. Returns iTriangle's tessellated indexed mesh as [points, indices].
GEOM_POLYGON_TRIANGULATE(polygon: array, holes: array) → array	array	Grid extension. Triangulates a polygon into triangle vertex arrays, optionally excluding hole rings.
GEOM_POLYGON_TRIANGULATE_DELAUNAY(polygon: array, holes: array) → array	array	Grid extension. Triangulates a polygon with Delaunay refinement.
GEOM_POLYGON_TRIANGULATE_DELAUNAY_MESH(polygon: array, holes: array) → array	array	Grid extension. Returns iTriangle's Delaunay indexed mesh as [points, indices].
GEOM_POLYGON_TRIANGULATE_DEVIATION(polygon: array, holes: array) → number	number	Grid extension. Returns Earcut's relative triangulation area error; 0 means exact.
GEOM_POLYGON_TRIANGULATE_MESH(polygon: array, holes: array) → array	array	Grid extension. Returns Earcut's indexed mesh as [points, indices], optionally excluding hole rings.
GEOM_POLYGON_TRIANGULATE_ROBUST(polygon: array, holes: array) → array	array	Grid extension. Triangulates a polygon for robust/self-intersecting inputs.
GEOM_POLYGON_TRIANGULATE_ROBUST_MESH(polygon: array, holes: array) → array	array	Grid extension. Returns iTriangle's robust indexed mesh as [points, indices].
GEOM_POLYGON_TRIANGULATE_STEINER(polygon: array, steiner_points: array, holes: array) → array	array	Grid extension. Triangulates a polygon with user-provided Steiner points.
GEOM_POLYGON_TRIANGULATE_STEINER_MESH(polygon: array, steiner_points: array, holes: array) → array	array	Grid extension. Returns iTriangle's Steiner-point indexed mesh as [points, indices].
GEOM_POLYGON_UNION(polygon_a: geometry, polygon_b: geometry) → geometry	geometry	Grid extension. Returns the union of two polygons.
GEOM_SEGMENT_LENGTH(point1: array, point2: array) → number	number	Grid extension. Returns the length of a segment between two points.
GEOM_SET_EPSG(geometry: geometry, epsg: number) → geometry	geometry	Grid extension. Assigns CRS metadata to a native geometry without changing its coordinates.
GEOM_SLOPE(point1: array, point2: array) → number	number	Grid extension. Returns the slope of the line through two points.
GEOM_TO_EWKB(geometry: geometry) → string	string	Grid extension. Serializes a native geometry as little-endian hexadecimal EWKB with its EPSG code embedded as SRID.
GEOM_TO_GEOJSON(geometry: geometry) → string	string	Grid extension. Serializes a native geometry as GeoJSON, preserving its geometry family and EPSG metadata.
GEOM_TO_WKB(geometry: geometry) → string	string	Grid extension. Serializes a native geometry as canonical little-endian hexadecimal OGC WKB.
GEOM_TO_WKT(geometry: geometry) → string	string	Grid extension. Serializes a native geometry as WKT; legacy point and polygon arrays remain accepted.
GEOM_TYPE(geometry: geometry) → string	string	Grid extension. Returns the OGC geometry family name carried by a native geometry.
GEOM_VALIDITY_DETAIL(polygon: array) → object	object	Grid extension. Returns structured polygon validity diagnostics including ring and segment indexes.
GEOM_X(point: array) → number	number	Grid extension. Returns the x coordinate of a point.
GEOM_Y(point: array) → number	number	Grid extension. Returns the y coordinate of a point.

---

Geospatial

Great-circle distance, bearings, projections, and coordinate conversion helpers.

Function count: 73.

Function	Returns	Notes
FRAME_GEO_CENTROID(frame: frame, column: string) → array	array	async, Grid extension. Replaces each resident geometry cell with its native CRS-preserving centroid Point while preserving other cells and blanks.
FRAME_GEO_EXTENT(frame: frame, column: string) → geometry	geometry	async, Grid extension. Returns the CRS-preserving native bounding Polygon of a resident Frame geometry column without an ETL round-trip.
FRAME_GEO_FILTER_BBOX(frame: frame, column: string, min_x: number, min_y: number, max_x: number, max_y: number) → array	array	async, Grid extension. Returns resident Frame rows whose native geometry envelope intersects an ordered bounding box.
FRAME_GEO_FILTER_INTERSECTS(frame: frame, column: string, geometry: geometry) → array	array	async, Grid extension. Returns resident Frame rows that exactly intersect native query geometry after R-tree candidate pruning.
FRAME_GEO_H3_AGGREGATE(frame: frame, geometry_column: string, resolution: number, value_column: string) → array	array	async, Grid extension. Groups resident EPSG:4326 Point geometry directly into deterministic H3 cells, returning cell, count, and optional numeric sum without collecting the Frame into a workbook array.
FRAME_GEO_JOIN_BBOX(left_frame: frame, left_column: string, right_frame: frame, right_column: string) → array	array	async, Grid extension. Returns stable one-based row pairs whose resident Frame geometry envelopes intersect, using both reusable R-trees.
FRAME_GEO_JOIN_INTERSECTS(left_frame: frame, left_column: string, right_frame: frame, right_column: string) → array	array	async, Grid extension. Returns stable one-based row pairs whose resident Frame geometries exactly intersect after dual R-tree pruning.
FRAME_GEO_NEAREST(frame: frame, column: string, x: number, y: number, k: number) → array	array	async, Grid extension. Returns nearest resident Frame geometry rows with appended envelope distance, using the reusable column R-tree.
FRAME_GEO_REPROJECT(frame: frame, column: string, target_epsg: number) → array	array	async, Grid extension. Reprojects a resident native geometry column through the canonical projection kernel while preserving other cells and blanks.
FRAME_GEO_REPROJECT_FRAME(frame: frame, column: string, target_epsg: number) → frame	frame	async, Grid extension. Materializes a new typed model-local Frame by rewriting one WKB geometry column through the native projection kernel and passing all other columns through unchanged.
FRAME_GEO_ROUTE_GEOMETRY(frame: frame, from_column: string, to_column: string, cost_column: string, geometry_column: string, start: any, goal: any, directed: boolean) → geometry	geometry	async, Grid extension. Returns native CRS-preserving route geometry over a resident Frame edge table while reusing its parsed adjacency network across calls.
FRAME_GEO_ROUTE_ISOCHRONE(frame: frame, from_column: string, to_column: string, cost_column: string, geometry_column: string, start: any, max_cost: number, directed: boolean) → array	array	async, Grid extension. Returns nodes reachable from one start node or an array of start nodes within a cost budget over a resident Frame edge table while reusing its parsed adjacency network across calls.
FRAME_GEO_ROUTE_MAP_MATCH(frame: frame, from_column: string, to_column: string, cost_column: string, geometry_column: string, track: object, max_snap_distance_meters: number, candidate_limit: number, directed: boolean) → array	array	async, Grid extension. Matches a GEO_TRACK_CREATE trajectory to numeric native-LineString edges in a resident Frame, returning sample id, time, one-based edge index, snap error in metres, and snapped native Point geometry.
FRAME_GEO_ROUTE_SHORTEST_PATH(frame: frame, from_column: string, to_column: string, cost_column: string, geometry_column: string, start: any, goal: any, directed: boolean) → array	array	async, Grid extension. Returns the deterministic minimum-cost path over a resident Frame edge table while reusing its parsed adjacency network across calls.
FRAME_GEO_TRACK_DWELL(frame: frame, geometry_column: string, time_column: string, polygon: geometry, minimum_duration: number) → array	array	async, Grid extension. Returns observed native Polygon dwell intervals over a resident Frame trajectory as source row, start, end, and duration rows.
FRAME_GEO_TRACK_DWELL_INTERPOLATED(frame: frame, geometry_column: string, time_column: string, polygon: geometry, minimum_duration: number) → array	array	async, Grid extension. Returns segment-interpolated native Polygon dwell intervals over a resident Frame trajectory as source row, start, end, and duration rows.
FRAME_GEO_TRACK_GEOFENCE(frame: frame, geometry_column: string, time_column: string, polygon: geometry) → array	array	async, Grid extension. Detects observed transitions through a native Polygon over a resident Frame trajectory, returning source row, time, and entered rows while reusing its time index.
FRAME_GEO_TRACK_GEOFENCE_INTERPOLATED(frame: frame, geometry_column: string, time_column: string, polygon: geometry) → array	array	async, Grid extension. Detects segment-interpolated native Polygon crossings over a resident Frame trajectory, returning crossing time, direction, and native Point rows.
FRAME_GEO_TRACK_INTERPOLATE(frame: frame, geometry_column: string, time_column: string, time: number) → geometry	geometry	async, Grid extension. Interpolates a native CRS-preserving Point at a requested time using a reusable resident Frame trajectory index.
FRAME_GEO_TRACK_PROXIMITY_JOIN(left_frame: frame, left_geometry_column: string, left_time_column: string, right_frame: frame, right_geometry_column: string, right_time_column: string, maximum_time_delta: number, maximum_distance_meters: number) → array	array	async, Grid extension. Joins two resident Frame trajectories within a time window and WGS84 ellipsoidal distance threshold, returning left/right source rows, times, and metre distance rows while reusing both time indexes.
FRAME_GEO_TRACK_SIMPLIFY(frame: frame, geometry_column: string, time_column: string, tolerance: number) → array	array	async, Grid extension. Simplifies a resident Frame trajectory with a metre tolerance in EPSG:4326 (source units otherwise), returning retained source row, time, and native Point rows.
FRAME_GEO_TRACK_WINDOW(frame: frame, geometry_column: string, time_column: string, start_time: number, end_time: number) → array	array	async, Grid extension. Returns resident Frame trajectory rows in an inclusive time window using a reusable time-sorted spatial index.
GEO_ALONG_TRACK_DISTANCE(lat: number, lon: number, lat1: number, lon1: number, lat2: number, lon2: number, radius_m: number) → number	number	Grid extension. Returns along-track distance in meters from path start to the point's projection.
GEO_BBOX(lat1: number, lon1: number, lat2: number, lon2: number) → array	array	Grid extension. Returns lat/lon bounding box for two corner points.
GEO_BEARING(lat1: number, lon1: number, lat2: number, lon2: number) → number	number	Grid extension. Returns initial bearing in degrees from the first point to the second.
GEO_CROSS_TRACK_DISTANCE(lat: number, lon: number, lat1: number, lon1: number, lat2: number, lon2: number, radius_m: number) → number	number	Grid extension. Returns cross-track distance in meters from a point to a great-circle path.
GEO_DECIMAL_TO_DMS(decimal_degrees: number) → array	array	Grid extension. Converts decimal degrees to degrees, minutes, and seconds.
GEO_DESTINATION(lat: number, lon: number, bearing_degrees: number, distance_m: number, radius_m: number) → geometry	geometry	Grid extension. Returns an EPSG:4326 point after moving along a bearing for a distance.
GEO_DISTANCE(lat1: number, lon1: number, lat2: number, lon2: number, radius_m: number) → number	number	Grid extension. Returns great-circle distance in meters between two lat/lon pairs.
GEO_DMS_TO_DECIMAL(degrees: number, minutes: number, seconds: number, hemisphere: string) → number	number	Grid extension. Converts degrees, minutes, seconds, and hemisphere to decimal degrees.
GEO_GEODESIC_BEARING(lat1: number, lon1: number, lat2: number, lon2: number) → number	number	Grid extension. Returns WGS84 geodesic initial bearing in degrees.
GEO_GEODESIC_DESTINATION(lat: number, lon: number, bearing_degrees: number, distance_m: number) → geometry	geometry	Grid extension. Returns an EPSG:4326 point at the WGS84 geodesic destination.
GEO_GEODESIC_DISTANCE(lat1: number, lon1: number, lat2: number, lon2: number) → number	number	Grid extension. Returns WGS84 geodesic distance in meters between two lat/lon pairs.
GEO_MIDPOINT(lat1: number, lon1: number, lat2: number, lon2: number) → geometry	geometry	Grid extension. Returns the EPSG:4326 geographic midpoint between two points.
GEO_REPROJECT(geometry: geometry, source_epsg: number, target_epsg: number) → geometry	geometry	Grid extension. Reprojects every coordinate in a native geometry between EPSG coordinate reference systems; legacy point arrays remain accepted.
GEO_ROUTE_GEOMETRY(edges: route_edges, start: route_start, goal: route_goal, directed: boolean) → geometry	geometry	Grid extension. Returns the minimum-cost route as a CRS-preserving LineString, or MultiLineString when edge geometry is discontinuous.
GEO_ROUTE_ISOCHRONE(edges: route_edges, start: route_start, max_cost: number, directed: boolean) → array	array	Grid extension. Returns every network node reachable from one start node or an array of start nodes within a non-negative cost budget, sorted by cost then node.
GEO_ROUTE_MAP_MATCH(edges: route_edges, track: geo_track, max_snap_distance_meters: number, candidate_limit: number, directed: boolean) → array	array	Grid extension. Matches a GEO_TRACK_CREATE trajectory to numeric native-LineString network edges, returning sample id, time, one-based source edge index, snap error in metres, and a snapped native Point.
GEO_ROUTE_SHORTEST_PATH(edges: route_edges, start: route_start, goal: route_goal, directed: boolean) → array	array	Grid extension. Returns the minimum-cost route as rows of node, cumulative cost, one-based source edge index, and optional native edge geometry.
GEO_TRACK_CREATE(points: geometry[], times: number[]) → object	object	Grid extension. Creates a CRS-aware trajectory from aligned native Point geometry and strictly increasing numeric timestamps.
GEO_TRACK_DISTANCE(track: geo_track) → number	number	Grid extension. Returns total trajectory distance, using WGS84 geodesic metres for EPSG:4326 and coordinate units otherwise.
GEO_TRACK_DWELL(track: geo_track, polygon: geometry, minimum_duration: number) → array	array	Grid extension. Returns observed Polygon dwell intervals meeting a minimum duration as entry sample, start, end, and duration rows.
GEO_TRACK_DWELL_INTERPOLATED(track: geo_track, polygon: geometry, minimum_duration: number) → array	array	Grid extension. Returns segment-interpolated Polygon dwell intervals meeting a minimum duration as entry sample, start, end, and duration rows.
GEO_TRACK_GEOFENCE(track: geo_track, polygon: geometry) → array	array	Grid extension. Returns observed trajectory transitions into and out of a native Polygon as sample-id, time, and entered rows.
GEO_TRACK_GEOFENCE_INTERPOLATED(track: geo_track, polygon: geometry) → array	array	Grid extension. Returns exact segment-crossing trajectory transitions through a native Polygon with crossing time, direction, and native Point geometry.
GEO_TRACK_INTERPOLATE(track: geo_track, time: number) → geometry	geometry	Grid extension. Returns the linearly interpolated native Point on a trajectory at a timestamp using logarithmic lookup.
GEO_TRACK_PROXIMITY_JOIN(left_track: geo_track, right_track: geo_track, maximum_time_delta: number, maximum_distance_meters: number) → array	array	Grid extension. Joins two trajectories within a time window and WGS84 ellipsoidal distance threshold, returning left/right samples, times, and metre distance rows.
GEO_TRACK_SEGMENTS(track: geo_track) → array	array	Grid extension. Returns trajectory segment rows containing start time, end time, distance, duration, and speed.
GEO_TRACK_SIMPLIFY(track: geo_track, tolerance: number) → array	array	Grid extension. Simplifies a trajectory with a metre tolerance in EPSG:4326 (source coordinate units otherwise), returning retained sample, time, and native Point rows.
GEO_TRACK_WINDOW(track: geo_track, start_time: number, end_time: number) → array	array	Grid extension. Returns timestamp and native Point rows within an inclusive trajectory time window.
GEO_WEB_MERCATOR(lat: number, lon: number) → geometry	geometry	Grid extension. Projects lat/lon to Web Mercator x/y meters.
GEO_WEB_MERCATOR_INVERSE(x: number, y: number) → geometry	geometry	Grid extension. Inverts Web Mercator x/y meters to lat/lon.
H3_AREA_M2(cell: h3_cell) → number	number	Grid extension. Returns the spherical area of an H3 cell in square meters.
H3_BOUNDARY(cell: h3_cell) → array	array	Grid extension. Returns an H3 cell boundary as [longitude, latitude] rows.
H3_CELL(latitude: number, longitude: number, resolution: number) → string	string	Grid extension. Indexes a WGS84 latitude/longitude location as a canonical H3 cell string.
H3_CENTER(cell: h3_cell) → array	array	Grid extension. Returns an H3 cell center as [longitude, latitude].
H3_CHILDREN(cell: h3_cell, resolution: h3_finer_resolution) → array	array	Grid extension. Returns the descendant H3 cells at a finer resolution.
H3_COMPACT(cells: h3_cell_list) → array	array	Grid extension. Compacts a set of H3 cells into the smallest equivalent mixed-resolution set.
H3_GRID_DISK(cell: h3_cell, k: number) → array	array	Grid extension. Returns all H3 cells within k grid steps of a cell.
H3_GRID_DISTANCE(from_cell: h3_cell, to_cell: h3_cell) → number	number	Grid extension. Returns the grid-step distance between two compatible H3 cells.
H3_GRID_RING(cell: h3_cell, k: number) → array	array	Grid extension. Returns the H3 cells exactly k grid steps from a cell.
H3_GROUP_COUNT(latitudes: number[], longitudes: number[], resolution: number) → array	array	Grid extension. Groups latitude/longitude rows by H3 cell and returns cell/count rows in deterministic cell order.
H3_GROUP_SUM(latitudes: number[], longitudes: number[], values: number[], resolution: number) → array	array	Grid extension. Groups latitude/longitude/value rows by H3 cell and returns cell/sum/count rows in deterministic cell order.
H3_IS_VALID(cell: h3_cell) → boolean	boolean	Grid extension. Returns whether a value is a valid canonical H3 cell string.
H3_PARENT(cell: h3_cell, resolution: number) → string	string	Grid extension. Returns an H3 cell's ancestor at a coarser resolution.
H3_POLYFILL(exterior: array, resolution: number, holes: array) → array	array	Grid extension. Covers a WGS84 polygon, with optional holes, using H3 cells at a resolution.
H3_RESOLUTION(cell: h3_cell) → number	number	Grid extension. Returns the resolution of an H3 cell.
H3_UNCOMPACT(cells: h3_cell_list, resolution: h3_finer_resolution) → array	array	Grid extension. Expands a mixed-resolution H3 set to cells at a target resolution.
RASTER_CALCULATE(raster: raster, operation: raster_operation, right: any) → object	object	Grid extension. Applies aligned raster-to-raster or raster-to-scalar arithmetic while preserving the affine grid, EPSG, and nodata mask.
RASTER_CREATE(values: array, origin_x: number, origin_y: number, pixel_width: number, pixel_height: number, epsg: number, nodata: number) → object	object	Grid extension. Creates a CRS-aware single-band raster from a rectangular numeric array, affine pixel metadata, and optional nodata sentinel.
RASTER_INFO(raster: raster) → object	object	Grid extension. Returns raster dimensions, affine pixel metadata, CRS, bounds, and valid/nodata cell counts.
RASTER_SAMPLE(raster: raster, x: number, y: number, method: raster_resample_method) → number	number	Grid extension. Samples a raster at a world coordinate using nearest or bilinear interpolation; nodata produces blank.
RASTER_ZONAL_STATS(raster: raster, geometry: geometry) → object	object	Grid extension. Computes count, sum, minimum, maximum, and mean for valid raster cell centers covered by a CRS-matched Polygon or MultiPolygon.

FRAME_GEO_CENTROID

Replaces each resident geometry cell with its native CRS-preserving centroid Point while preserving other cells and blanks.

Signature: FRAME_GEO_CENTROID(frame: frame, column: string) → array

External contract:

• worker route: etl.exec.geo-centroid
• cache TTL: 300000ms
• max staleness: 3600000ms
• refresh mode: background
• timeout: 60000ms
• max retries: 1

FRAME_GEO_EXTENT

Returns the CRS-preserving native bounding Polygon of a resident Frame geometry column without an ETL round-trip.

Signature: FRAME_GEO_EXTENT(frame: frame, column: string) → geometry

External contract:

• worker route: etl.exec.geo-extent
• cache TTL: 300000ms
• max staleness: 3600000ms
• refresh mode: background
• timeout: 60000ms
• max retries: 1

FRAME_GEO_FILTER_BBOX

Returns resident Frame rows whose native geometry envelope intersects an ordered bounding box.

Signature: FRAME_GEO_FILTER_BBOX(frame: frame, column: string, min_x: number, min_y: number, max_x: number, max_y: number) → array

External contract:

• worker route: etl.exec.geo-filter-bbox
• cache TTL: 300000ms
• max staleness: 3600000ms
• refresh mode: background
• timeout: 60000ms
• max retries: 1

FRAME_GEO_FILTER_INTERSECTS

Returns resident Frame rows that exactly intersect native query geometry after R-tree candidate pruning.

Signature: FRAME_GEO_FILTER_INTERSECTS(frame: frame, column: string, geometry: geometry) → array

External contract:

• worker route: etl.exec.geo-filter-intersects
• cache TTL: 300000ms
• max staleness: 3600000ms
• refresh mode: background
• timeout: 60000ms
• max retries: 1

FRAME_GEO_H3_AGGREGATE

Groups resident EPSG:4326 Point geometry directly into deterministic H3 cells, returning cell, count, and optional numeric sum without collecting the Frame into a workbook array.

Signature: FRAME_GEO_H3_AGGREGATE(frame: frame, geometry_column: string, resolution: number, value_column: string) → array

External contract:

• worker route: etl.exec.geo-h3-aggregate
• cache TTL: 300000ms
• max staleness: 3600000ms
• refresh mode: background
• timeout: 60000ms
• max retries: 1

FRAME_GEO_JOIN_BBOX

Returns stable one-based row pairs whose resident Frame geometry envelopes intersect, using both reusable R-trees.

Signature: FRAME_GEO_JOIN_BBOX(left_frame: frame, left_column: string, right_frame: frame, right_column: string) → array

External contract:

• worker route: etl.exec.geo-join-bbox
• cache TTL: 300000ms
• max staleness: 3600000ms
• refresh mode: background
• timeout: 60000ms
• max retries: 1

FRAME_GEO_JOIN_INTERSECTS

Returns stable one-based row pairs whose resident Frame geometries exactly intersect after dual R-tree pruning.

Signature: FRAME_GEO_JOIN_INTERSECTS(left_frame: frame, left_column: string, right_frame: frame, right_column: string) → array

External contract:

• worker route: etl.exec.geo-join-intersects
• cache TTL: 300000ms
• max staleness: 3600000ms
• refresh mode: background
• timeout: 60000ms
• max retries: 1

FRAME_GEO_NEAREST

Returns nearest resident Frame geometry rows with appended envelope distance, using the reusable column R-tree.

Signature: FRAME_GEO_NEAREST(frame: frame, column: string, x: number, y: number, k: number) → array

External contract:

• worker route: etl.exec.geo-nearest
• cache TTL: 300000ms
• max staleness: 3600000ms
• refresh mode: background
• timeout: 60000ms
• max retries: 1

FRAME_GEO_REPROJECT

Reprojects a resident native geometry column through the canonical projection kernel while preserving other cells and blanks.

Signature: FRAME_GEO_REPROJECT(frame: frame, column: string, target_epsg: number) → array

External contract:

• worker route: etl.exec.geo-reproject
• cache TTL: 300000ms
• max staleness: 3600000ms
• refresh mode: background
• timeout: 60000ms
• max retries: 1

FRAME_GEO_REPROJECT_FRAME

Materializes a new typed model-local Frame by rewriting one WKB geometry column through the native projection kernel and passing all other columns through unchanged.

Signature: FRAME_GEO_REPROJECT_FRAME(frame: frame, column: string, target_epsg: number) → frame

External contract:

• worker route: etl.exec.geo-reproject-frame
• cache TTL: 300000ms
• max staleness: 3600000ms
• refresh mode: background
• timeout: 60000ms
• max retries: 1

FRAME_GEO_ROUTE_GEOMETRY

Returns native CRS-preserving route geometry over a resident Frame edge table while reusing its parsed adjacency network across calls.

Signature: FRAME_GEO_ROUTE_GEOMETRY(frame: frame, from_column: string, to_column: string, cost_column: string, geometry_column: string, start: any, goal: any, directed: boolean) → geometry

External contract:

• worker route: etl.exec.geo-route-geometry
• cache TTL: 300000ms
• max staleness: 3600000ms
• refresh mode: background
• timeout: 60000ms
• max retries: 1

FRAME_GEO_ROUTE_ISOCHRONE

Returns nodes reachable from one start node or an array of start nodes within a cost budget over a resident Frame edge table while reusing its parsed adjacency network across calls.

Signature: FRAME_GEO_ROUTE_ISOCHRONE(frame: frame, from_column: string, to_column: string, cost_column: string, geometry_column: string, start: any, max_cost: number, directed: boolean) → array

External contract:

• worker route: etl.exec.geo-route-isochrone
• cache TTL: 300000ms
• max staleness: 3600000ms
• refresh mode: background
• timeout: 60000ms
• max retries: 1

FRAME_GEO_ROUTE_MAP_MATCH

Matches a GEO_TRACK_CREATE trajectory to numeric native-LineString edges in a resident Frame, returning sample id, time, one-based edge index, snap error in metres, and snapped native Point geometry.

Signature: FRAME_GEO_ROUTE_MAP_MATCH(frame: frame, from_column: string, to_column: string, cost_column: string, geometry_column: string, track: object, max_snap_distance_meters: number, candidate_limit: number, directed: boolean) → array

External contract:

• worker route: etl.exec.geo-route-map-match
• cache TTL: 300000ms
• max staleness: 3600000ms
• refresh mode: background
• timeout: 60000ms
• max retries: 1

FRAME_GEO_ROUTE_SHORTEST_PATH

Returns the deterministic minimum-cost path over a resident Frame edge table while reusing its parsed adjacency network across calls.

Signature: FRAME_GEO_ROUTE_SHORTEST_PATH(frame: frame, from_column: string, to_column: string, cost_column: string, geometry_column: string, start: any, goal: any, directed: boolean) → array

External contract:

• worker route: etl.exec.geo-route-shortest-path
• cache TTL: 300000ms
• max staleness: 3600000ms
• refresh mode: background
• timeout: 60000ms
• max retries: 1

FRAME_GEO_TRACK_DWELL

Returns observed native Polygon dwell intervals over a resident Frame trajectory as source row, start, end, and duration rows.

Signature: FRAME_GEO_TRACK_DWELL(frame: frame, geometry_column: string, time_column: string, polygon: geometry, minimum_duration: number) → array

External contract:

• worker route: etl.exec.geo-track-dwell
• cache TTL: 300000ms
• max staleness: 3600000ms
• refresh mode: background
• timeout: 60000ms
• max retries: 1

FRAME_GEO_TRACK_DWELL_INTERPOLATED

Returns segment-interpolated native Polygon dwell intervals over a resident Frame trajectory as source row, start, end, and duration rows.

Signature: FRAME_GEO_TRACK_DWELL_INTERPOLATED(frame: frame, geometry_column: string, time_column: string, polygon: geometry, minimum_duration: number) → array

External contract:

• worker route: etl.exec.geo-track-dwell-interpolated
• cache TTL: 300000ms
• max staleness: 3600000ms
• refresh mode: background
• timeout: 60000ms
• max retries: 1

FRAME_GEO_TRACK_GEOFENCE

Detects observed transitions through a native Polygon over a resident Frame trajectory, returning source row, time, and entered rows while reusing its time index.

Signature: FRAME_GEO_TRACK_GEOFENCE(frame: frame, geometry_column: string, time_column: string, polygon: geometry) → array

External contract:

• worker route: etl.exec.geo-track-geofence
• cache TTL: 300000ms
• max staleness: 3600000ms
• refresh mode: background
• timeout: 60000ms
• max retries: 1

FRAME_GEO_TRACK_GEOFENCE_INTERPOLATED

Detects segment-interpolated native Polygon crossings over a resident Frame trajectory, returning crossing time, direction, and native Point rows.

Signature: FRAME_GEO_TRACK_GEOFENCE_INTERPOLATED(frame: frame, geometry_column: string, time_column: string, polygon: geometry) → array

External contract:

• worker route: etl.exec.geo-track-geofence-interpolated
• cache TTL: 300000ms
• max staleness: 3600000ms
• refresh mode: background
• timeout: 60000ms
• max retries: 1

FRAME_GEO_TRACK_INTERPOLATE

Interpolates a native CRS-preserving Point at a requested time using a reusable resident Frame trajectory index.

Signature: FRAME_GEO_TRACK_INTERPOLATE(frame: frame, geometry_column: string, time_column: string, time: number) → geometry

External contract:

• worker route: etl.exec.geo-track-interpolate
• cache TTL: 300000ms
• max staleness: 3600000ms
• refresh mode: background
• timeout: 60000ms
• max retries: 1

FRAME_GEO_TRACK_PROXIMITY_JOIN

Joins two resident Frame trajectories within a time window and WGS84 ellipsoidal distance threshold, returning left/right source rows, times, and metre distance rows while reusing both time indexes.

Signature: FRAME_GEO_TRACK_PROXIMITY_JOIN(left_frame: frame, left_geometry_column: string, left_time_column: string, right_frame: frame, right_geometry_column: string, right_time_column: string, maximum_time_delta: number, maximum_distance_meters: number) → array

External contract:

• worker route: etl.exec.geo-track-proximity-join
• cache TTL: 300000ms
• max staleness: 3600000ms
• refresh mode: background
• timeout: 60000ms
• max retries: 1

FRAME_GEO_TRACK_SIMPLIFY

Simplifies a resident Frame trajectory with a metre tolerance in EPSG:4326 (source units otherwise), returning retained source row, time, and native Point rows.

Signature: FRAME_GEO_TRACK_SIMPLIFY(frame: frame, geometry_column: string, time_column: string, tolerance: number) → array

External contract:

• worker route: etl.exec.geo-track-simplify
• cache TTL: 300000ms
• max staleness: 3600000ms
• refresh mode: background
• timeout: 60000ms
• max retries: 1

FRAME_GEO_TRACK_WINDOW

Returns resident Frame trajectory rows in an inclusive time window using a reusable time-sorted spatial index.

Signature: FRAME_GEO_TRACK_WINDOW(frame: frame, geometry_column: string, time_column: string, start_time: number, end_time: number) → array

External contract:

• worker route: etl.exec.geo-track-window
• cache TTL: 300000ms
• max staleness: 3600000ms
• refresh mode: background
• timeout: 60000ms
• max retries: 1

---

Aviation

Aeronautic atmosphere, navigation, wind, performance, descent, and endurance helpers.

Function count: 16.

Function	Returns	Notes
AVIATION_CROSSWIND(runway_heading_degrees: number, wind_direction_degrees: number, wind_speed_kt: number) → number	number	Grid extension. Returns signed crosswind component in knots; positive values are from the right.
AVIATION_DENSITY_ALTITUDE(pressure_altitude_ft: number, outside_air_temperature_c: number) → number	number	Grid extension. Returns density altitude in feet from pressure altitude and outside air temperature.
AVIATION_DESCENT_RATE(ground_speed_kt: number, descent_angle_degrees: number) → number	number	Grid extension. Returns descent rate in feet per minute from ground speed and descent angle.
AVIATION_FUEL_ENDURANCE(fuel_quantity: number, burn_rate_per_hour: number) → number	number	Grid extension. Returns endurance in hours from fuel quantity and hourly burn rate in matching units.
AVIATION_GREAT_CIRCLE_NM(lat1: number, lon1: number, lat2: number, lon2: number) → number	number	Grid extension. Returns great-circle distance in nautical miles between two lat/lon pairs.
AVIATION_HEADWIND(runway_heading_degrees: number, wind_direction_degrees: number, wind_speed_kt: number) → number	number	Grid extension. Returns headwind component in knots; negative values are tailwinds.
AVIATION_MACH(true_airspeed_kt: number, static_air_temperature_c: number) → number	number	Grid extension. Returns Mach number from true airspeed and static air temperature.
AVIATION_PRESSURE_ALTITUDE(indicated_altitude_ft: number, altimeter_inhg: number) → number	number	Grid extension. Returns pressure altitude in feet from indicated altitude and altimeter setting.
AVIATION_RANGE_NM(endurance_hours: number, ground_speed_kt: number) → number	number	Grid extension. Returns still-air range in nautical miles from endurance and ground speed.
AVIATION_RATE_OF_TURN(true_airspeed_kt: number, bank_angle_degrees: number) → number	number	Grid extension. Returns coordinated level-turn rate in degrees per second.
AVIATION_RUNWAY_RECIPROCAL(runway_heading_degrees: number) → number	number	Grid extension. Returns reciprocal runway heading in degrees normalized to 0..360.
AVIATION_STANDARD_ATMOSPHERE(altitude_m: number) → array	array	Grid extension. Returns ISA temperature, pressure, density, and speed of sound for altitude in meters.
AVIATION_TOP_OF_DESCENT_DISTANCE(altitude_to_lose_ft: number, descent_angle_degrees: number) → number	number	Grid extension. Returns top-of-descent distance in nautical miles for an altitude loss and descent angle.
AVIATION_TRUE_AIRSPEED(calibrated_airspeed_kt: number, pressure_altitude_ft: number, outside_air_temperature_c: number) → number	number	Grid extension. Estimates true airspeed in knots from calibrated airspeed, pressure altitude, and temperature.
AVIATION_TURN_RADIUS(true_airspeed_kt: number, bank_angle_degrees: number) → number	number	Grid extension. Returns coordinated level-turn radius in meters from true airspeed and bank angle.
AVIATION_WIND_COMPONENTS(runway_heading_degrees: number, wind_direction_degrees: number, wind_speed_kt: number) → array	array	Grid extension. Returns headwind and crosswind components in knots for a runway heading.

---

Maritime

Nautical distance, vessel speed, hull-form, loading, tide, and current helpers.

Function count: 16.

Function	Returns	Notes
MARITIME_BLOCK_COEFFICIENT(displacement_volume_m3: number, length_m: number, beam_m: number, draft_m: number) → number	number	Grid extension. Returns hull block coefficient from displacement volume and principal dimensions.
MARITIME_DISTANCE_NM(lat1: number, lon1: number, lat2: number, lon2: number) → number	number	Grid extension. Returns great-circle distance in nautical miles between two lat/lon pairs.
MARITIME_DRAFT_CHANGE(added_weight_tonnes: number, waterplane_area_m2: number, water_density_kg_m3: number) → number	number	Grid extension. Returns draft change in meters for an added weight, waterplane area, and water density.
MARITIME_ETA_HOURS(distance_nm: number, speed_kt: number) → number	number	Grid extension. Returns estimated travel time in hours from distance in nautical miles and speed in knots.
MARITIME_FROUDE_NUMBER(speed_kt: number, waterline_length_m: number) → number	number	Grid extension. Returns Froude number from vessel speed in knots and waterline length in meters.
MARITIME_HULL_SPEED(waterline_length_ft: number) → number	number	Grid extension. Returns displacement hull speed in knots from waterline length in feet.
MARITIME_KNOTS_TO_MPS(speed_kt: number) → number	number	Grid extension. Converts knots to meters per second.
MARITIME_LEEWAY(heading_degrees: number, course_over_ground_degrees: number) → number	number	Grid extension. Returns signed leeway angle in degrees between heading and course over ground.
MARITIME_MPS_TO_KNOTS(speed_m_s: number) → number	number	Grid extension. Converts meters per second to knots.
MARITIME_PRISMATIC_COEFFICIENT(displacement_volume_m3: number, midship_area_m2: number, length_m: number) → number	number	Grid extension. Returns prismatic coefficient from displacement volume, midship area, and length.
MARITIME_SET_DRIFT(heading_degrees: number, speed_through_water_kt: number, course_over_ground_degrees: number, speed_over_ground_kt: number) → array	array	Grid extension. Returns current set in degrees and drift in knots from through-water and over-ground tracks.
MARITIME_SPEED_MADE_GOOD(speed_kt: number, course_error_degrees: number) → number	number	Grid extension. Returns speed made good in knots from speed and angle off desired course.
MARITIME_TIDAL_WINDOW(chart_depth_m: number, draft_m: number, safety_clearance_m: number, tide_height_m: number) → number	number	Grid extension. Returns 1 when available depth satisfies draft plus safety clearance, else 0.
MARITIME_TONNES_PER_CM_IMMERSION(waterplane_area_m2: number, water_density_kg_m3: number) → number	number	Grid extension. Returns tonnes per centimeter immersion from waterplane area and water density.
MARITIME_UNDER_KEEL_CLEARANCE(chart_depth_m: number, draft_m: number, safety_clearance_m: number, tide_height_m: number) → number	number	Grid extension. Returns under-keel clearance in meters after tide, draft, and safety clearance.
MARITIME_WATERPLANE_COEFFICIENT(waterplane_area_m2: number, length_m: number, beam_m: number) → number	number	Grid extension. Returns waterplane coefficient from waterplane area, length, and beam.

---

Space & Orbital Science

Celestial-body constants, gravity, orbital mechanics, and astrophysical planning helpers.

Function count: 30.

Function	Returns	Notes
SPACE_ABSOLUTE_MAGNITUDE(apparent_magnitude: number, distance_parsecs: number) → number	number	Grid extension. Returns absolute magnitude from apparent magnitude and distance in parsecs.
SPACE_AU_TO_METERS() → number	number	Grid extension. Returns the astronomical unit in meters.
SPACE_BODY_MASS(body: string) → number	number	Grid extension. Returns standard gravitational mass in kilograms for a named celestial body.
SPACE_BODY_MU(body: string) → number	number	Grid extension. Returns standard gravitational parameter mu for a named celestial body.
SPACE_BODY_RADIUS(body: string) → number	number	Grid extension. Returns mean radius in meters for a named celestial body.
SPACE_CIRCULAR_VELOCITY(body: string, altitude_m: number) → number	number	Grid extension. Returns circular orbital speed in m/s at altitude above a named celestial body.
SPACE_DISTANCE_MODULUS(apparent_magnitude: number, absolute_magnitude: number) → number	number	Grid extension. Returns distance modulus in parsecs from apparent and absolute magnitudes.
SPACE_ECEF_TO_GEODETIC(x_km: number, y_km: number, z_km: number) → array	array	volatile, Grid extension. Convert an ECEF position (km) to [lat_deg, lon_deg, alt_km] on WGS-84.
SPACE_ESCAPE_VELOCITY(body: string, altitude_m: number) → number	number	Grid extension. Returns escape velocity in m/s at altitude above a named celestial body.
SPACE_FLUX_AT_DISTANCE(luminosity_w: number, distance_m: number) → number	number	Grid extension. Returns flux in W/m^2 at a distance from a source luminosity.
SPACE_GEODETIC_TO_ECEF(lat_deg: number, lon_deg: number, alt_km: number) → array	array	volatile, Grid extension. Convert a [lat_deg, lon_deg, alt_km] geodetic position to ECEF (km) on WGS-84.
SPACE_GRAVITY_AT_ALTITUDE(body: string, altitude_m: number) → number	number	Grid extension. Returns gravity in m/s^2 at altitude above a named celestial body.
SPACE_HILL_RADIUS(semi_major_axis_m: number, primary_mu: number, secondary_mu: number) → number	number	Grid extension. Returns Hill sphere radius in meters.
SPACE_HOHMANN_DELTA_V(mu: number, radius1_m: number, radius2_m: number) → number	number	Grid extension. Returns total Hohmann transfer delta-v in m/s between two circular orbits.
SPACE_HOHMANN_TRANSFER_TIME(mu: number, radius1_m: number, radius2_m: number) → number	number	Grid extension. Returns Hohmann transfer time in seconds between two circular orbits.
SPACE_LIGHT_TIME(distance_m: number) → number	number	Grid extension. Returns light travel time in seconds for a distance in meters.
SPACE_LUMINOSITY_FROM_RADIUS_TEMP(radius_m: number, temperature_k: number) → number	number	Grid extension. Returns stellar luminosity in watts from radius and effective temperature.
SPACE_NEXT_PASS(tle_line1: string, tle_line2: string, observer_lat_deg: number, observer_lon_deg: number, start_minutes: number, window_minutes: number) → array	array	volatile, Grid extension. Finds the next visibility pass over an observer; returns [minutes_from_start, elevation_deg].
SPACE_ORBITAL_PERIOD(mu: number, semi_major_axis_m: number) → number	number	Grid extension. Returns orbital period in seconds from mu and semi-major axis.
SPACE_ORBITAL_SPEED_VIS_VIVA(mu: number, radius_m: number, semi_major_axis_m: number) → number	number	Grid extension. Returns orbital speed in m/s from vis-viva equation.
SPACE_PARSEC_TO_LIGHTYEAR() → number	number	Grid extension. Returns the number of light-years in one parsec.
SPACE_ROCHE_LIMIT(primary_radius_m: number, primary_density_kg_m3: number, secondary_density_kg_m3: number) → number	number	Grid extension. Returns fluid Roche limit in meters.
SPACE_SEMI_MAJOR_AXIS_FROM_PERIOD(mu: number, period_s: number) → number	number	Grid extension. Returns semi-major axis in meters from mu and orbital period.
SPACE_SURFACE_GRAVITY(body: string) → number	number	Grid extension. Returns surface gravity in m/s^2 for a named celestial body.
SPACE_SYNODIC_PERIOD(period1_s: number, period2_s: number) → number	number	Grid extension. Returns synodic period in seconds from two sidereal orbital periods.
SPACE_TLE_GROUND_TRACK(tle_line1: string, tle_line2: string, minutes_since_epoch: number, unix_seconds_anchor: number) → array	array	volatile, Grid extension. Returns the sub-satellite point [lat_deg, lon_deg, alt_km] at minutes since epoch (Unix-seconds anchor optional).
SPACE_TLE_PERIOD(tle_line1: string, tle_line2: string) → number	number	volatile, Grid extension. Returns the TLE's orbital period in minutes from its mean motion.
SPACE_TLE_PROPAGATE(tle_line1: string, tle_line2: string, minutes_since_epoch: number) → array	array	volatile, Grid extension. Propagate a TLE via SGP4 and return the ECI/TEME position vector [x_km, y_km, z_km] at minutes since epoch.
SPACE_TLE_VELOCITY(tle_line1: string, tle_line2: string, minutes_since_epoch: number) → array	array	volatile, Grid extension. Propagate a TLE via SGP4 and return the TEME velocity vector [vx_km_s, vy_km_s, vz_km_s] at minutes since epoch.
SPACE_WEIGHT_ON_BODY(body: string, mass_kg: number, altitude_m: number) → number	number	Grid extension. Returns weight in newtons for a mass at altitude above a named celestial body.

---

Domain Types

URL, molecule, DNA, color, musical note, and bytes accessors and constructors.

Function count: 39.

Function	Returns	Notes
BYTES_FROM_BASE64(s: string) → bytes	bytes	Decodes a base64 string to a typed bytes value.
BYTES_FROM_TEXT(s: string) → bytes	bytes	Encodes a UTF-8 string as a typed bytes value.
BYTES_HEX(b: bytes) → string	string	Returns the canonical lower-case hex string of a bytes value.
BYTES_LENGTH(b: bytes) → number	number	Returns the number of bytes in a bytes value.
BYTES_TO_BASE64(b: bytes) → string	string	Returns the base64 encoding of a bytes value.
BYTES_TO_TEXT(b: bytes) → string	string	Decodes a bytes value to a UTF-8 string.
COLOR_A(c: color) → number	number	Returns the alpha channel of a color value as a fraction in [0,1].
COLOR_B(c: color) → number	number	Returns the blue channel of a color value as an integer in [0,255].
COLOR_G(c: color) → number	number	Returns the green channel of a color value as an integer in [0,255].
COLOR_HEX(c: color) → string	string	Returns the canonical lower-case #RRGGBBAA hex string of a color value.
COLOR_LUMINANCE(c: color) → number	number	Returns the relative luminance (Rec. 709) of a color value in [0,1].
COLOR_R(c: color) → number	number	Returns the red channel of a color value as an integer in [0,255].
DNA_COMPLEMENT(d: dna) → dna	dna	Returns the complementary strand of a DNA value (A<->T, C<->G).
DNA_GC(d: dna) → number	number	Returns the GC content of a DNA value (fraction in [0,1]).
DNA_LENGTH(d: dna) → number	number	Returns the number of bases in a DNA value.
DNA_REVCOMP(d: dna) → dna	dna	Returns the reverse complement of a DNA value.
DNA_SEQUENCE(d: dna) → string	string	Returns the underlying nucleotide string of a DNA value.
DNA_TO_RNA(d: dna) → string	string	Returns the RNA transcription of a DNA value (T -> U).
DNA_TRANSLATE(d: dna) → string	string	Translates a DNA sequence to its protein single-letter codes (stops at first stop codon).
MAKE_COLOR(r: number, g: number, b: number, a: number) → color	color	Constructs a color value from 0..255 RGB channels and an optional 0..1 alpha.
MOL_ATOMIC_MASS(sym: string) → number	number	Returns the standard atomic mass (g/mol) of a chemical element symbol.
MOL_ATOM_COUNT(m: molecule, sym: string) → number	number	Returns the count of a specific element in a molecule (0 if absent).
MOL_FORMULA(m: molecule) → string	string	Returns the canonical formula string of a molecule value.
MOL_MASS(m: molecule) → number	number	Returns the molar mass (g/mol) of a molecule value.
NOTE_ACCIDENTAL(n: note) → string	string	Returns the accidental string ("#", "b", "##", "bb", or "") of a note.
NOTE_FREQUENCY(n: note) → number	number	Returns the frequency (Hz) of a musical-note value (A4 = 440 Hz reference).
NOTE_FROM_FREQUENCY(hz: number) → note	note	Constructs the closest musical-note value for a frequency in Hz (A4 = 440 Hz reference).
NOTE_FROM_MIDI(midi: number) → note	note	Constructs a musical-note value from a MIDI integer (0..127).
NOTE_MIDI(n: note) → number	number	Returns the MIDI number (0..127) of a musical-note value.
NOTE_OCTAVE(n: note) → number	number	Returns the octave (integer) of a musical-note value.
NOTE_PITCH(n: note) → string	string	Returns the pitch letter (A..G) of a musical-note value.
URL_FRAGMENT(u: url) → string	string	Returns the fragment (hash) of a URL value (without leading "#").
URL_HOST(u: url) → string	string	Returns the hostname of a URL value.
URL_LENGTH(u: url) → number	number	Returns the length of the canonical URL string.
URL_PATH(u: url) → string	string	Returns the path component of a URL value.
URL_PORT(u: url) → string	string	Returns the port of a URL value as a string ("" if no explicit port).
URL_QUERY(u: url) → string	string	Returns the raw query string (without leading "?") of a URL value.
URL_QUERY_PARAM(u: url, key: string) → string	string	Returns the value of a single query parameter from a URL value.
URL_SCHEME(u: url) → string	string	Returns the scheme (e.g. "https") of a URL value.

---

Structured Data & DOM

JSON, TOML, YAML, and CSV parsing and serialization, deep path navigation, and HTML/XML DOM querying and rewriting.

Function count: 36.

Function	Returns	Notes
DOM_ADD_CLASS(dom: dom, selector: string, class: string) → object	object	Grid extension. Returns a copy of a document value with a CSS class added to every element matching the selector.
DOM_APPEND(dom: dom, selector: string, child: any) → object	object	Grid extension. Returns a copy of a document value appending a child — a document value's nodes, or a scalar as escaped text — to every element matching the selector.
DOM_ATTR(node: dom_node, name: string) → string	string	Grid extension. Returns the named attribute of an element, or blank when absent.
DOM_ATTRS(node: dom_node) → object	object	Grid extension. Returns an element's attributes as a record object.
DOM_BUILD(mode: string, ...parts: any[]) → object	object	variadic, Grid extension. Builds a document value from alternating markup chunks and interpolated values; scalar holes are escaped and document values are spliced in. Interpolated markup literals evaluate through this function.
DOM_CHILDREN(node: dom_node) → array	array	Grid extension. Returns an element's child elements as a column.
DOM_HAS_CLASS(node: dom_node, class: string) → boolean	boolean	Grid extension. Tests whether an element carries a CSS class.
DOM_HTML(node: dom_node) → string	string	Grid extension. Serializes a markup value as HTML text.
DOM_MATCHES(node: dom_node, selector: string) → boolean	boolean	Grid extension. Tests whether an element itself matches a CSS selector list.
DOM_PARSE(markup: string, mode?: string) → object	object	Grid extension. Parses HTML, XML, or SVG markup into a navigable document value; the mode defaults to HTML.
DOM_REMOVE(dom: dom, selector: string) → object	object	Grid extension. Returns a copy of a document value with every element matching the selector removed.
DOM_REMOVE_ATTR(dom: dom, selector: string, name: string) → object	object	Grid extension. Returns a copy of a document value with the named attribute removed from every element matching the selector.
DOM_REMOVE_CLASS(dom: dom, selector: string, class: string) → object	object	Grid extension. Returns a copy of a document value with a CSS class removed from every element matching the selector.
DOM_SELECT(dom: dom, selector: string) → array	array	Grid extension. Returns every element matching a CSS selector list, in document order; blank when nothing matches.
DOM_SELECT_ONE(dom: dom, selector: string) → object	object	Grid extension. Returns the first element matching a CSS selector list, or blank when nothing matches.
DOM_SET_ATTR(dom: dom, selector: string, name: string, value: string) → object	object	Grid extension. Returns a copy of a document value with the named attribute set on every element matching the selector.
DOM_SET_TEXT(dom: dom, selector: string, text: string) → object	object	Grid extension. Returns a copy of a document value with the content of every element matching the selector replaced by text.
DOM_TAG(node: dom_node) → string	string	Grid extension. Returns an element's tag name.
DOM_TEXT(node: dom_node) → string	string	Grid extension. Returns the concatenated text content of a markup node and its descendants.
DOM_TOGGLE_CLASS(dom: dom, selector: string, class: string) → object	object	Grid extension. Returns a copy of a document value with a CSS class toggled on every element matching the selector.
FILTERXML(xml: any, xpath: string) → array	array	Returns the values matching an XPath query against XML text or a parsed markup value.
GET(value: structured, path: string) → any	any	Grid extension. Navigates a dotted path into a structured value, descending objects by key and arrays by 0-based index; blank when the path is absent.
MERGE(...values: structured[]) → object	object	variadic, Grid extension. Deep-merges objects left to right: later values win on scalar conflicts and nested objects merge recursively.
PARSE_CSV(text: string, delimiter?: string) → object	object	Grid extension. Parses delimited text whose first row is the header into an array of record objects; a tab delimiter marks the value as TSV.
PARSE_JSON(text: string) → object	object	Grid extension. Parses JSON text into a live object that remembers JSON as its native format.
PARSE_TOML(text: string) → object	object	Grid extension. Parses TOML text into a live object that remembers TOML as its native format.
PARSE_YAML(text: string) → object	object	Grid extension. Parses YAML text into a live object that remembers YAML as its native format.
PLUCK(value: structured, path: string) → array	array	Grid extension. Collects a dotted path across a structured value; a * segment fans out over every array element or object value.
SERIALIZE(value: any, format?: string) → string	string	Grid extension. Re-emits a value as text in the given format; when omitted, a structured value uses its native format and everything else uses JSON.
SET(value: structured, path: string, new_value: any) → any	any	Grid extension. Returns a copy of a structured value with the dotted path set to a new value, creating intermediate objects and arrays as needed.
TO_CSV(records: array, delimiter?: string) → string	string	Grid extension. Serializes an array of record objects as delimited text whose header row is the ordered union of record keys.
TO_HTML(value: dom) → string	string	Grid extension. Serializes a markup value as HTML text.
TO_JSON(value: any, pretty?: boolean) → string	string	Grid extension. Serializes a value as JSON text; a truthy second argument pretty-prints.
TO_TOML(value: any) → string	string	Grid extension. Serializes a value as TOML text; the top level must be an object.
TO_XML(value: dom) → string	string	Grid extension. Serializes a markup value as XML text, self-closing empty elements.
TO_YAML(value: any) → string	string	Grid extension. Serializes a value as YAML text.

---

Database

Database-style aggregations over criteria-defined ranges.

Function count: 12.

Function	Returns	Notes
DAVERAGE(database: array, field: any, criteria: array) → number	number	Averages values in a database field that match criteria.
DCOUNT(database: array, field: any, criteria: array) → number	number	Counts numeric values in a database field that match criteria.
DCOUNTA(database: array, field: any, criteria: array) → number	number	Counts non-blank values in a database field that match criteria.
DGET(database: array, field: any, criteria: array) → any	any	Extracts a single value from a database field that matches criteria.
DMAX(database: array, field: any, criteria: array) → number	number	Returns the maximum value in a database field that matches criteria.
DMIN(database: array, field: any, criteria: array) → number	number	Returns the minimum value in a database field that matches criteria.
DPRODUCT(database: array, field: any, criteria: array) → number	number	Multiplies values in a database field that match criteria.
DSTDEV(database: array, field: any, criteria: array) → number	number	Sample standard deviation of database field values matching criteria.
DSTDEVP(database: array, field: any, criteria: array) → number	number	Population standard deviation of database field values matching criteria.
DSUM(database: array, field: any, criteria: array) → number	number	Sums values in a database field that match criteria.
DVAR(database: array, field: any, criteria: array) → number	number	Sample variance of database field values matching criteria.
DVARP(database: array, field: any, criteria: array) → number	number	Population variance of database field values matching criteria.

---

Postgres

PostgreSQL table handles and bounded async query/mutation helpers.

Function count: 4.

Function	Returns	Notes
PG_MUTATE(table: postgres_table, mutation: object, context: object) → postgres_mutation_result	postgres_mutation_result	async, external. Executes a guarded idempotent PostgreSQL mutation against a table handle.
PG_SELECT(table: postgres_table, query: object, context: object) → postgres_query_result	postgres_query_result	async, external. Executes a bounded parameterized SELECT against a PostgreSQL table handle.
PG_TABLE(connection: string, schema: string, relation: string, relation_kind: string, writable: boolean, metadata_version: string) → postgres_table	postgres_table	Creates a lightweight PostgreSQL table or view handle.
TABLE_REF(table: string, column: string) → object	object	Represents a structured table column reference.

PG_MUTATE

Executes a guarded idempotent PostgreSQL mutation against a table handle.

Signature: PG_MUTATE(table: postgres_table, mutation: object, context: object) → postgres_mutation_result

External contract:

• worker route: postgres.mutate
• cache TTL: 0ms
• max staleness: 0ms
• refresh mode: blocking
• timeout: 10000ms
• max retries: 0

PG_SELECT

Executes a bounded parameterized SELECT against a PostgreSQL table handle.

Signature: PG_SELECT(table: postgres_table, query: object, context: object) → postgres_query_result

External contract:

• worker route: postgres.select
• cache TTL: 0ms
• max staleness: 0ms
• refresh mode: blocking
• timeout: 10000ms
• max retries: 1

---

Redis

Bounded Redis key-value reads and idempotent mutation effects.

Function count: 2.

Function	Returns	Notes
REDIS_MUTATE(connection: string, mutation: object, context: object) → redis_mutation_result	redis_mutation_result	async, external. Executes an allow-listed idempotent Redis mutation.
REDIS_QUERY(connection: string, query: object, context: object) → redis_query_result	redis_query_result	async, external. Executes a bounded allow-listed Redis read.

REDIS_MUTATE

Executes an allow-listed idempotent Redis mutation.

Signature: REDIS_MUTATE(connection: string, mutation: object, context: object) → redis_mutation_result

External contract:

• worker route: redis.mutate
• cache TTL: 0ms
• max staleness: 0ms
• refresh mode: blocking
• timeout: 10000ms
• max retries: 0

REDIS_QUERY

Executes a bounded allow-listed Redis read.

Signature: REDIS_QUERY(connection: string, query: object, context: object) → redis_query_result

External contract:

• worker route: redis.query
• cache TTL: 0ms
• max staleness: 0ms
• refresh mode: blocking
• timeout: 10000ms
• max retries: 1

---

Native Frames & ETL

Native Polars frames, column expressions, ETL pipelines, and frame materialization helpers.

Function count: 52.

Function	Returns	Notes
AGG(frame: frame, aggregates: object) → frame	frame	async, external. Aggregates a grouped frame through vectorized aggregate expressions.
COLLECT(frame: frame, options: object) → array	array	async, external. Collects a lazy frame into a Grid array or a frameProjection descriptor when the result is large.
COSINE_TOPK(embedding: any, index: object, k: number) → array	array	async, external. Searches a vector index and returns the top K matching rows.
CUMULATIVE_SUM(column: number) → number	number	async, external. Computes a cumulative sum over a numeric frame column.
DIFF(previous: frame, current: frame, options: object) → object	object	async, external. Computes added, removed, changed, and summary sets between two frame snapshots.
EWM_MEAN(column: number, alpha: number) → number	number	async, external. Computes an exponentially weighted moving mean over a numeric frame column.
EXPORT_ARROW(frame: frame, uri: string, options: object) → object	object	async, external. Exports a frame as Arrow IPC for downstream consumers.
FIT_CURVE(frame: frame, options: object) → object	object	async, external. Fits a curve over frame columns and returns solver metadata.
FRAME_JOIN(left: frame, right: frame, options: object) → frame	frame	async, external. Joins two frame handles with schema-checked keys.
FRAME_LOOKUP(frame: frame, key_column: string, key: any, value_column: string) → any	any	async, external. Looks up a scalar value in a frame by key column and value column.
FRAME_SCHEMA(frame: frame) → object	object	async, external. Returns the schema embedded in a frame handle.
FRAME_SELECT(frame: frame, columns: object) → frame	frame	async, external. Projects, renames, or derives frame columns through vectorized Grid expressions.
FRAME_SLICE(frame: frame, rows: object, columns: object) → array	array	async, external. Collects a bounded row/column slice from a frame.
FRAME_SORT(frame: frame, keys: object) → frame	frame	async, external, aliases: SORT_BY. Sorts a frame without collecting it.
FRAME_VIEW(frame: frame, options: object) → object	object	async, external. Returns a paginated frame preview object for the inspector without full collection.
FRAME_WHERE(frame: frame, predicate: object) → frame	frame	async, external, aliases: WHERE. Filters a frame using a schema-checked Grid expression lowered to a Polars predicate.
FROM_PIPE(binding: string, options: object) → frame	frame	async, external. Subscribes to an exact source and exposes its delivered deltas as a streaming frame source.
FROM_RANGE(range: array, options: object) → frame	frame	async, external. Builds a frame handle from a Grid range without materializing each cell into a worker payload.
GROUP_BY(frame: frame, keys: object) → frame	frame	async, external. Groups a frame by one or more columns before an AGG stage.
HEAD(frame: frame, rows: number) → array	array	async, external. Collects the first N rows of a frame as a Grid array.
JOIN_INTERSECTS(left: frame, right: frame, left_geometry: string, right_geometry: string) → frame	frame	async, external. Joins frames when geometry columns intersect.
JOIN_NEAREST(left: frame, right: frame, left_x: string, left_y: string, right_x: string, right_y: string, k: number) → frame	frame	async, external. Joins frames by nearest 2D point.
JOIN_WITHIN_RADIUS(left: frame, right: frame, left_x: string, left_y: string, right_x: string, right_y: string, radius: number) → frame	frame	async, external. Joins frames when 2D points are within a radius.
LAG(column: any, offset: number, default: any) → any	any	async, external. Shifts a frame column backward within the active window.
LEAD(column: any, offset: number, default: any) → any	any	async, external. Shifts a frame column forward within the active window.
LOAD_PIN(version: string, options: object) → frame	frame	async, external. Loads a pinned frame version from the lineage catalog.
PIN(frame: frame, version: string, options: object) → frame	frame	async, external. Pins a frame lineage entry to a durable version for audit and time-travel.
READ_ARROW(uri: string, options: object) → frame	frame	async, external. Creates a lazy Polars frame handle from Arrow IPC data.
READ_BIGQUERY(source: string, options: object) → frame	frame	async, external. Creates a lazy frame handle from a BigQuery table or parameterized SQL query.
READ_CSV(uri: string, options: object) → frame	frame	async, external. Creates a lazy Polars frame handle from CSV files.
READ_DATABASE(connector: string, source: string, options: object) → frame	frame	async, external. Creates a lazy frame from any operator-configured database connector that streams Arrow IPC and advertises SQL pushdown capabilities.
READ_DATABRICKS(source: string, options: object) → frame	frame	async, external. Creates a lazy frame handle from a Databricks SQL table or parameterized SQL query.
READ_DELTA(uri: string, options: object) → frame	frame	async, external. Creates a lazy Polars frame handle from a Delta Lake table.
READ_HTTP_JSON(url: string, options: object) → frame	frame	async, external. Fetches HTTP JSON and materializes it as a lazy frame handle.
READ_ICEBERG(uri: string, options: object) → frame	frame	async, external. Creates a lazy Polars frame handle from an Iceberg table.
READ_JSON(uri: string, options: object) → frame	frame	async, external. Creates a lazy Polars frame handle from newline-delimited JSON or JSON arrays.
READ_PARQUET(uri: string, options: object) → frame	frame	async, external, aliases: READ_GEOPARQUET. Creates a lazy Polars frame handle from Parquet files with predicate and projection pushdown.
READ_PG(table: postgres_table, query: object, options: object) → frame	frame	async, external. Creates a lazy frame handle from a PostgreSQL table handle or parameterized query.
READ_REDSHIFT(source: string, options: object) → frame	frame	async, external. Creates a lazy frame handle from a Redshift table or parameterized SQL query.
READ_SHAPEFILE(uri: string, epsg?: number) → frame	frame	async, external. Reads a local ESRI Shapefile set into a Frame with DBF attributes and a typed WKB geometry column.
READ_SNOWFLAKE(source: string, options: object) → frame	frame	async, external. Creates a lazy frame handle from a Snowflake table or parameterized SQL query.
ROLLING_MEAN(column: number, window: number) → number	number	async, external. Computes a rolling mean over a numeric frame column.
ROLLING_STD(column: number, window: number) → number	number	async, external. Computes rolling standard deviation over a numeric frame column.
ROLLING_SUM(column: number, window: number) → number	number	async, external. Computes a rolling sum over a numeric frame column.
SAMPLE_FRAME(frame: frame, rows: number, options: object) → array	array	async, external, aliases: SAMPLE. Samples rows from a frame, optionally by strata.
SHIFT(column: any, offset: number) → any	any	async, external. Shifts a frame column by a signed offset.
VECTOR_INDEX(frame: frame, column: string, options: object) → object	object	async, external. Builds a resident vector index over an embedding column for semantic search.
WINDOW(expression: any, spec: object) → any	any	async, external. Applies an OVER window specification to a vectorized frame expression.
WITH_COLUMNS(frame: frame, columns: object) → frame	frame	async, external. Adds derivative columns to a frame using vectorized Grid expressions.
WRITE_DATABASE(connector: string, source: string, mutation: object, context: object) → database_mutation_result	database_mutation_result	async, external. Executes an explicitly authorized, idempotent mutation through any operator-configured database adapter.
WRITE_PARQUET(frame: frame, uri: string, options: object) → object	object	async, external. Writes a frame to Parquet through the ETL host.
WRITE_PG(frame: frame, table: postgres_table, mode: string, options: object) → object	object	async, external. Writes a frame to PostgreSQL through guarded ETL mutation policy.

AGG

Aggregates a grouped frame through vectorized aggregate expressions.

Signature: AGG(frame: frame, aggregates: object) → frame

External contract:

• worker route: etl.exec.aggregate
• cache TTL: 300000ms
• max staleness: 3600000ms
• refresh mode: background
• timeout: 60000ms
• max retries: 1

COLLECT

Collects a lazy frame into a Grid array or a frameProjection descriptor when the result is large.

Signature: COLLECT(frame: frame, options: object) → array

External contract:

• worker route: etl.exec.collect
• cache TTL: 300000ms
• max staleness: 3600000ms
• refresh mode: background
• timeout: 60000ms
• max retries: 1

COSINE_TOPK

Searches a vector index and returns the top K matching rows.

Signature: COSINE_TOPK(embedding: any, index: object, k: number) → array

External contract:

• worker route: etl.ai.cosine-topk
• cache TTL: 300000ms
• max staleness: 3600000ms
• refresh mode: background
• timeout: 60000ms
• max retries: 1

CUMULATIVE_SUM

Computes a cumulative sum over a numeric frame column.

Signature: CUMULATIVE_SUM(column: number) → number

External contract:

• worker route: etl.exec.cumulative-sum
• cache TTL: 300000ms
• max staleness: 3600000ms
• refresh mode: background
• timeout: 60000ms
• max retries: 1

DIFF

Computes added, removed, changed, and summary sets between two frame snapshots.

Signature: DIFF(previous: frame, current: frame, options: object) → object

External contract:

• worker route: etl.exec.diff
• cache TTL: 300000ms
• max staleness: 3600000ms
• refresh mode: background
• timeout: 60000ms
• max retries: 1

EWM_MEAN

Computes an exponentially weighted moving mean over a numeric frame column.

Signature: EWM_MEAN(column: number, alpha: number) → number

External contract:

• worker route: etl.exec.ewm-mean
• cache TTL: 300000ms
• max staleness: 3600000ms
• refresh mode: background
• timeout: 60000ms
• max retries: 1

EXPORT_ARROW

Exports a frame as Arrow IPC for downstream consumers.

Signature: EXPORT_ARROW(frame: frame, uri: string, options: object) → object

External contract:

• worker route: etl.write.arrow
• cache TTL: 300000ms
• max staleness: 3600000ms
• refresh mode: background
• timeout: 60000ms
• max retries: 1

FIT_CURVE

Fits a curve over frame columns and returns solver metadata.

Signature: FIT_CURVE(frame: frame, options: object) → object

External contract:

• worker route: etl.solver.fit-curve
• cache TTL: 300000ms
• max staleness: 3600000ms
• refresh mode: background
• timeout: 60000ms
• max retries: 1

FRAME_JOIN

Joins two frame handles with schema-checked keys.

Signature: FRAME_JOIN(left: frame, right: frame, options: object) → frame

External contract:

• worker route: etl.exec.join
• cache TTL: 300000ms
• max staleness: 3600000ms
• refresh mode: background
• timeout: 60000ms
• max retries: 1

FRAME_LOOKUP

Looks up a scalar value in a frame by key column and value column.

Signature: FRAME_LOOKUP(frame: frame, key_column: string, key: any, value_column: string) → any

External contract:

• worker route: etl.exec.lookup
• cache TTL: 300000ms
• max staleness: 3600000ms
• refresh mode: background
• timeout: 60000ms
• max retries: 1

FRAME_SCHEMA

Returns the schema embedded in a frame handle.

Signature: FRAME_SCHEMA(frame: frame) → object

External contract:

• worker route: etl.exec.schema
• cache TTL: 300000ms
• max staleness: 3600000ms
• refresh mode: background
• timeout: 5000ms
• max retries: 0

FRAME_SELECT

Projects, renames, or derives frame columns through vectorized Grid expressions.

Signature: FRAME_SELECT(frame: frame, columns: object) → frame

External contract:

• worker route: etl.exec.select
• cache TTL: 300000ms
• max staleness: 3600000ms
• refresh mode: background
• timeout: 60000ms
• max retries: 1

FRAME_SLICE

Collects a bounded row/column slice from a frame.

Signature: FRAME_SLICE(frame: frame, rows: object, columns: object) → array

External contract:

• worker route: etl.exec.slice
• cache TTL: 300000ms
• max staleness: 3600000ms
• refresh mode: background
• timeout: 60000ms
• max retries: 1

FRAME_SORT

Sorts a frame without collecting it.

Signature: FRAME_SORT(frame: frame, keys: object) → frame

External contract:

• worker route: etl.exec.sort
• cache TTL: 300000ms
• max staleness: 3600000ms
• refresh mode: background
• timeout: 60000ms
• max retries: 1

FRAME_VIEW

Returns a paginated frame preview object for the inspector without full collection.

Signature: FRAME_VIEW(frame: frame, options: object) → object

External contract:

• worker route: etl.exec.frame-view
• cache TTL: 300000ms
• max staleness: 3600000ms
• refresh mode: background
• timeout: 60000ms
• max retries: 1

FRAME_WHERE

Filters a frame using a schema-checked Grid expression lowered to a Polars predicate.

Signature: FRAME_WHERE(frame: frame, predicate: object) → frame

External contract:

• worker route: etl.exec.where
• cache TTL: 300000ms
• max staleness: 3600000ms
• refresh mode: background
• timeout: 60000ms
• max retries: 1

FROM_PIPE

Subscribes to the exact source named by binding; HTTP event ingress must use the same canonical URL-decoded string as its :sourceId. Leading or trailing source-id whitespace is unsupported.

For a source-language assignment, options compiles into a resident Stream region and accepts timeDomain, outOfOrdernessMs, allowedLatenessMs, latePolicy, delivery, a bounded window, queueCapacity, queuePolicy, maxWindowsPerEvent, maxOpenWindows, maxSeenEventIds, checkpoint, and an optional bounded interval join. See Streams And Probabilistic Structures for the exact shapes and recovery boundary. Unknown fields and unbounded state are compile errors.

Production admission first checks active exact-source registrations. Only a batch with at least one registered model for that exact source enters the durable Stream log; legacy or currently unsubscribed traffic stays on the existing realtime lane, reports stream.batchStatus: "unsubscribed", and is not retained as a future Stream backlog. Durable polls are provisional and carry opaque receipts. With checkpoints enabled, Grid atomically commits receipt progress, checkpointed model state, and the latest durable local sink-effect batch; failed attempts and restarts replay uncommitted records from the unchanged cursor. Realtime notifications remain latest-value, and arbitrary external sinks remain at least once. With checkpoint: false, local model publication precedes acknowledgement, so an acknowledgement failure can replay a duplicate but cannot lose the source data.

Signature: FROM_PIPE(binding: string, options: object) → frame

External contract:

• worker route: etl.read.pipe
• cache TTL: 300000ms
• max staleness: 3600000ms
• refresh mode: background
• timeout: 60000ms
• max retries: 1

FROM_RANGE

Builds a frame handle from a Grid range without materializing each cell into a worker payload.

Signature: FROM_RANGE(range: array, options: object) → frame

External contract:

• worker route: etl.read.range
• cache TTL: 300000ms
• max staleness: 3600000ms
• refresh mode: background
• timeout: 60000ms
• max retries: 1

GROUP_BY

Groups a frame by one or more columns before an AGG stage.

Signature: GROUP_BY(frame: frame, keys: object) → frame

External contract:

• worker route: etl.exec.group-by
• cache TTL: 300000ms
• max staleness: 3600000ms
• refresh mode: background
• timeout: 60000ms
• max retries: 1

HEAD

Collects the first N rows of a frame as a Grid array.

Signature: HEAD(frame: frame, rows: number) → array

External contract:

• worker route: etl.exec.head
• cache TTL: 300000ms
• max staleness: 3600000ms
• refresh mode: background
• timeout: 60000ms
• max retries: 1

JOIN_INTERSECTS

Joins frames when geometry columns intersect.

Signature: JOIN_INTERSECTS(left: frame, right: frame, left_geometry: string, right_geometry: string) → frame

External contract:

• worker route: etl.exec.spatial-join-intersects
• cache TTL: 300000ms
• max staleness: 3600000ms
• refresh mode: background
• timeout: 60000ms
• max retries: 1

JOIN_NEAREST

Joins frames by nearest 2D point.

Signature: JOIN_NEAREST(left: frame, right: frame, left_x: string, left_y: string, right_x: string, right_y: string, k: number) → frame

External contract:

• worker route: etl.exec.spatial-join-nearest
• cache TTL: 300000ms
• max staleness: 3600000ms
• refresh mode: background
• timeout: 60000ms
• max retries: 1

JOIN_WITHIN_RADIUS

Joins frames when 2D points are within a radius.

Signature: JOIN_WITHIN_RADIUS(left: frame, right: frame, left_x: string, left_y: string, right_x: string, right_y: string, radius: number) → frame

External contract:

• worker route: etl.exec.spatial-join-within-radius
• cache TTL: 300000ms
• max staleness: 3600000ms
• refresh mode: background
• timeout: 60000ms
• max retries: 1

LAG

Shifts a frame column backward within the active window.

Signature: LAG(column: any, offset: number, default: any) → any

External contract:

• worker route: etl.exec.lag
• cache TTL: 300000ms
• max staleness: 3600000ms
• refresh mode: background
• timeout: 60000ms
• max retries: 1

LEAD

Shifts a frame column forward within the active window.

Signature: LEAD(column: any, offset: number, default: any) → any

External contract:

• worker route: etl.exec.lead
• cache TTL: 300000ms
• max staleness: 3600000ms
• refresh mode: background
• timeout: 60000ms
• max retries: 1

LOAD_PIN

Loads a pinned frame version from the lineage catalog.

Signature: LOAD_PIN(version: string, options: object) → frame

External contract:

• worker route: etl.read.pin
• cache TTL: 300000ms
• max staleness: 3600000ms
• refresh mode: background
• timeout: 60000ms
• max retries: 1

PIN

Pins a frame lineage entry to a durable version for audit and time-travel.

Signature: PIN(frame: frame, version: string, options: object) → frame

External contract:

• worker route: etl.exec.pin
• cache TTL: 300000ms
• max staleness: 3600000ms
• refresh mode: background
• timeout: 60000ms
• max retries: 1

READ_ARROW

Creates a lazy Polars frame handle from Arrow IPC data.

Signature: READ_ARROW(uri: string, options: object) → frame

External contract:

• worker route: etl.read.arrow
• cache TTL: 300000ms
• max staleness: 3600000ms
• refresh mode: background
• timeout: 60000ms
• max retries: 1

READ_BIGQUERY

Creates a lazy frame handle from a BigQuery table or parameterized SQL query.

Signature: READ_BIGQUERY(source: string, options: object) → frame

External contract:

• worker route: etl.read.bigquery
• cache TTL: 300000ms
• max staleness: 3600000ms
• refresh mode: background
• timeout: 60000ms
• max retries: 1

READ_CSV

Creates a lazy Polars frame handle from CSV files.

Signature: READ_CSV(uri: string, options: object) → frame

External contract:

• worker route: etl.read.csv
• cache TTL: 300000ms
• max staleness: 3600000ms
• refresh mode: background
• timeout: 60000ms
• max retries: 1

READ_DATABASE

Creates a lazy frame from any operator-configured database connector that streams Arrow IPC and advertises SQL pushdown capabilities.

Signature: READ_DATABASE(connector: string, source: string, options: object) → frame

External contract:

• worker route: etl.read.database
• cache TTL: 300000ms
• max staleness: 3600000ms
• refresh mode: background
• timeout: 60000ms
• max retries: 1

READ_DATABRICKS

Creates a lazy frame handle from a Databricks SQL table or parameterized SQL query.

Signature: READ_DATABRICKS(source: string, options: object) → frame

External contract:

• worker route: etl.read.databricks
• cache TTL: 300000ms
• max staleness: 3600000ms
• refresh mode: background
• timeout: 60000ms
• max retries: 1

READ_DELTA

Creates a lazy Polars frame handle from a Delta Lake table.

Signature: READ_DELTA(uri: string, options: object) → frame

External contract:

• worker route: etl.read.delta
• cache TTL: 300000ms
• max staleness: 3600000ms
• refresh mode: background
• timeout: 60000ms
• max retries: 1

READ_HTTP_JSON

Fetches HTTP JSON and materializes it as a lazy frame handle.

Signature: READ_HTTP_JSON(url: string, options: object) → frame

External contract:

• worker route: etl.read.http-json
• cache TTL: 300000ms
• max staleness: 3600000ms
• refresh mode: background
• timeout: 60000ms
• max retries: 1

READ_ICEBERG

Creates a lazy Polars frame handle from an Iceberg table.

Signature: READ_ICEBERG(uri: string, options: object) → frame

External contract:

• worker route: etl.read.iceberg
• cache TTL: 300000ms
• max staleness: 3600000ms
• refresh mode: background
• timeout: 60000ms
• max retries: 1

READ_JSON

Creates a lazy Polars frame handle from newline-delimited JSON or JSON arrays.

Signature: READ_JSON(uri: string, options: object) → frame

External contract:

• worker route: etl.read.json
• cache TTL: 300000ms
• max staleness: 3600000ms
• refresh mode: background
• timeout: 60000ms
• max retries: 1

READ_PARQUET

Creates a lazy Polars frame handle from Parquet files with predicate and projection pushdown.

Signature: READ_PARQUET(uri: string, options: object) → frame

External contract:

• worker route: etl.read.parquet
• cache TTL: 300000ms
• max staleness: 3600000ms
• refresh mode: background
• timeout: 60000ms
• max retries: 1

READ_PG

Creates a lazy frame handle from a PostgreSQL table handle or parameterized query.

Signature: READ_PG(table: postgres_table, query: object, options: object) → frame

External contract:

• worker route: etl.read.postgres
• cache TTL: 300000ms
• max staleness: 3600000ms
• refresh mode: background
• timeout: 60000ms
• max retries: 1

READ_REDSHIFT

Creates a lazy frame handle from a Redshift table or parameterized SQL query.

Signature: READ_REDSHIFT(source: string, options: object) → frame

External contract:

• worker route: etl.read.redshift
• cache TTL: 300000ms
• max staleness: 3600000ms
• refresh mode: background
• timeout: 60000ms
• max retries: 1

READ_SHAPEFILE

Reads a local ESRI Shapefile set into a Frame with DBF attributes and a typed WKB geometry column.

Signature: READ_SHAPEFILE(uri: string, epsg?: number) → frame

External contract:

• worker route: etl.read.shapefile
• cache TTL: 300000ms
• max staleness: 3600000ms
• refresh mode: background
• timeout: 60000ms
• max retries: 1

READ_SNOWFLAKE

Creates a lazy frame handle from a Snowflake table or parameterized SQL query.

Signature: READ_SNOWFLAKE(source: string, options: object) → frame

External contract:

• worker route: etl.read.snowflake
• cache TTL: 300000ms
• max staleness: 3600000ms
• refresh mode: background
• timeout: 60000ms
• max retries: 1

ROLLING_MEAN

Computes a rolling mean over a numeric frame column.

Signature: ROLLING_MEAN(column: number, window: number) → number

External contract:

• worker route: etl.exec.rolling-mean
• cache TTL: 300000ms
• max staleness: 3600000ms
• refresh mode: background
• timeout: 60000ms
• max retries: 1

ROLLING_STD

Computes rolling standard deviation over a numeric frame column.

Signature: ROLLING_STD(column: number, window: number) → number

External contract:

• worker route: etl.exec.rolling-std
• cache TTL: 300000ms
• max staleness: 3600000ms
• refresh mode: background
• timeout: 60000ms
• max retries: 1

ROLLING_SUM

Computes a rolling sum over a numeric frame column.

Signature: ROLLING_SUM(column: number, window: number) → number

External contract:

• worker route: etl.exec.rolling-sum
• cache TTL: 300000ms
• max staleness: 3600000ms
• refresh mode: background
• timeout: 60000ms
• max retries: 1

SAMPLE_FRAME

Samples rows from a frame, optionally by strata.

Signature: SAMPLE_FRAME(frame: frame, rows: number, options: object) → array

External contract:

• worker route: etl.exec.sample
• cache TTL: 300000ms
• max staleness: 3600000ms
• refresh mode: background
• timeout: 60000ms
• max retries: 1

SHIFT

Shifts a frame column by a signed offset.

Signature: SHIFT(column: any, offset: number) → any

External contract:

• worker route: etl.exec.shift
• cache TTL: 300000ms
• max staleness: 3600000ms
• refresh mode: background
• timeout: 60000ms
• max retries: 1

VECTOR_INDEX

Builds a resident vector index over an embedding column for semantic search.

Signature: VECTOR_INDEX(frame: frame, column: string, options: object) → object

External contract:

• worker route: etl.ai.vector-index
• cache TTL: 300000ms
• max staleness: 3600000ms
• refresh mode: background
• timeout: 60000ms
• max retries: 1

WINDOW

Applies an OVER window specification to a vectorized frame expression.

Signature: WINDOW(expression: any, spec: object) → any

External contract:

• worker route: etl.exec.window
• cache TTL: 300000ms
• max staleness: 3600000ms
• refresh mode: background
• timeout: 60000ms
• max retries: 1

WITH_COLUMNS

Adds derivative columns to a frame using vectorized Grid expressions.

Signature: WITH_COLUMNS(frame: frame, columns: object) → frame

External contract:

• worker route: etl.exec.with-columns
• cache TTL: 300000ms
• max staleness: 3600000ms
• refresh mode: background
• timeout: 60000ms
• max retries: 1

WRITE_DATABASE

Executes an explicitly authorized, idempotent mutation through any operator-configured database adapter.

Signature: WRITE_DATABASE(connector: string, source: string, mutation: object, context: object) → database_mutation_result

External contract:

• worker route: database.mutate
• cache TTL: 0ms
• max staleness: 0ms
• refresh mode: blocking
• timeout: 60000ms
• max retries: 0

WRITE_PARQUET

Writes a frame to Parquet through the ETL host.

Signature: WRITE_PARQUET(frame: frame, uri: string, options: object) → object

External contract:

• worker route: etl.write.parquet
• cache TTL: 300000ms
• max staleness: 3600000ms
• refresh mode: background
• timeout: 60000ms
• max retries: 1

WRITE_PG

Writes a frame to PostgreSQL through guarded ETL mutation policy.

Signature: WRITE_PG(frame: frame, table: postgres_table, mode: string, options: object) → object

External contract:

• worker route: etl.write.postgres
• cache TTL: 300000ms
• max staleness: 3600000ms
• refresh mode: background
• timeout: 60000ms
• max retries: 1

---

Computed Graphics & Drawing

Formula-driven 2-D drawing: primitives, styling, transforms, composition, and SVG rendering.

Function count: 24.

Function	Returns	Notes
DRAW_ARC(cx: number, cy: number, r: number, start_deg: number, sweep_deg: number) → object	object	Grid extension. Creates a drawing containing a circular arc from start_deg spanning sweep_deg degrees.
DRAW_CANVAS(width: number, height: number, drawing: drawing, background: color_string) → object	object	Grid extension. Sets a drawing's pixel extent and optional background colour, returning the sized drawing.
DRAW_CIRCLE(cx: number, cy: number, r: number) → object	object	Grid extension. Creates a drawing containing a circle centred at (cx, cy) with radius r.
DRAW_ELLIPSE(cx: number, cy: number, rx: number, ry: number) → object	object	Grid extension. Creates a drawing containing an ellipse centred at (cx, cy) with radii rx and ry.
DRAW_FILL(drawing: drawing, color: color_string) → object	object	Grid extension. Returns a copy of a drawing with every shape filled using the given colour.
DRAW_FROM_GEOM(geometry: geometry) → object	object	Grid extension. Lifts a native geometry value into a drawing, fitting the canvas to the geometry bounds.
DRAW_GROUP(drawings: drawing...) → object	object	variadic, Grid extension. Composes several drawings into one, drawn in argument order (painter's order).
DRAW_LINE(x1: number, y1: number, x2: number, y2: number) → object	object	Grid extension. Creates a drawing containing a single stroked line segment between two points.
DRAW_OPACITY(drawing: drawing, alpha: number) → object	object	Grid extension. Returns a copy of a drawing with every shape's opacity multiplier set to alpha (0..1).
DRAW_PATH(d: svg_path) → object	object	Grid extension. Creates a drawing from an SVG-style path string using absolute M, L, C, and Z commands.
DRAW_POLYLINE(points: array, closed: boolean) → object	object	Grid extension. Creates a drawing from an array of [x, y] points, optionally closed into a polygon.
DRAW_RECT(x: number, y: number, width: number, height: number) → object	object	Grid extension. Creates a drawing containing a rectangle at (x, y) with the given width and height.
DRAW_RENDER(drawing: drawing, width: number, height: number) → array	array	Grid extension. Rasterizes a drawing into a width×height grayscale cell range (luminance 0..1) so a computed picture becomes ordinary spreadsheet pixels.
DRAW_RENDER_RGB(drawing: drawing, width: number, height: number) → array	array	Grid extension. Rasterizes a drawing into a width×height cell range of packed 0xRRGGBB integers (one cell = one colour pixel).
DRAW_ROTATE(drawing: drawing, degrees: number) → object	object	Grid extension. Returns a copy of a drawing rotated clockwise about the origin by the given degrees.
DRAW_SCALE(drawing: drawing, sx: number, sy: number) → object	object	Grid extension. Returns a copy of a drawing scaled by sx horizontally and sy vertically (sy defaults to sx).
DRAW_STROKE(drawing: drawing, color: color_string, width: number) → object	object	Grid extension. Returns a copy of a drawing with every shape stroked using the given colour and optional width.
DRAW_TEXT(x: number, y: number, content: string, font_size: number) → object	object	Grid extension. Creates a drawing containing a text label anchored at (x, y) with an optional font size.
DRAW_TO_SVG(drawing: drawing) → string	string	Grid extension. Renders a drawing to a standalone SVG document string.
DRAW_TRANSLATE(drawing: drawing, dx: number, dy: number) → object	object	Grid extension. Returns a copy of a drawing translated by (dx, dy).
RGB(r: number, g: number, b: number) → number	number	Grid extension. Packs red, green, and blue channels (0..255) into a single 0xRRGGBB integer — the compact per-cell pixel colour.
RGB_B(packed: number) → number	number	Grid extension. Extracts the blue channel (0..255) from a packed 0xRRGGBB integer.
RGB_G(packed: number) → number	number	Grid extension. Extracts the green channel (0..255) from a packed 0xRRGGBB integer.
RGB_R(packed: number) → number	number	Grid extension. Extracts the red channel (0..255) from a packed 0xRRGGBB integer.

---

Computational Vision

Classical image processing: construction, colour, resampling, blur, edges, thresholding, morphology, and connected components.

Function count: 18.

Function	Returns	Notes
IMAGE_BLUR(image: image, sigma: number) → object	object	Grid extension. Applies a Gaussian blur with the given sigma.
IMAGE_CANNY(image: image, low: number, high: number) → object	object	Grid extension. Canny edge detector (Gaussian smoothing, non-maximum suppression, double-threshold hysteresis); returns a thin binary edge image. Optional low/high thresholds on the normalized gradient (default 0.1/0.2). Accepts an image object or a numeric range and returns the same.
IMAGE_CLOSE(image: image, radius: number) → object	object	Grid extension. Morphological closing (dilate then erode); fills small dark holes.
IMAGE_COMPONENTS(image: image) → array	array	Grid extension. Labels 4-connected foreground components of a binary image and returns a table of per-component statistics.
IMAGE_CROP(image: image, x: number, y: number, width: number, height: number) → object	object	Grid extension. Crops a sub-rectangle from an image, clamped to the image bounds.
IMAGE_DECODE(bytes: image_bytes) → object	object	Grid extension. Decodes encoded image bytes (PNG) into an image object; pair with a file read or BYTES_FROM_BASE64 to load a real photo.
IMAGE_DILATE(image: image, radius: number) → object	object	Grid extension. Binary morphological dilation with a square structuring element of the given radius.
IMAGE_EDGES(image: image) → object	object	Grid extension. Computes the Sobel gradient magnitude, returning a normalized single-channel edge image.
IMAGE_ERODE(image: image, radius: number) → object	object	Grid extension. Binary morphological erosion with a square structuring element of the given radius.
IMAGE_FROM_ARRAY(values: array) → object	object	Grid extension. Builds a single-channel image from a rectangular numeric range; values above 1 are treated as a 0..255 scale.
IMAGE_GRAYSCALE(image: image) → object	object	Grid extension. Converts an image to single-channel luminance using Rec. 601 weights.
IMAGE_INFO(image: image) → object	object	Grid extension. Reports an image's width, height, channel count, and sample count.
IMAGE_OPEN(image: image, radius: number) → object	object	Grid extension. Morphological opening (erode then dilate); removes small bright specks.
IMAGE_RESIZE(image: image, width: number, height: number) → object	object	Grid extension. Resizes an image to the given width and height using bilinear interpolation. Accepts an image object or a numeric range and returns the same.
IMAGE_THRESHOLD(image: image, t: number) → object	object	Grid extension. Binarizes an image at a fixed threshold in 0..1.
IMAGE_THRESHOLD_OTSU(image: image) → object	object	Grid extension. Binarizes an image at the automatically chosen Otsu threshold.
IMAGE_TO_ARRAY(image: image) → array	array	Grid extension. Projects an image to a rectangular numeric range of grayscale intensities in 0..1.
IMAGE_TO_RGB(image: image) → array	array	Grid extension. Projects a colour image to a range of packed 0xRRGGBB integers (the colour counterpart of IMAGE_TO_ARRAY).

---

Computational Biology

Packed sequence, variant, sparse omics, alignment, indexing, and biological analysis helpers.

Function count: 22.

Function	Returns	Notes
BIO_ALIGN(query: any, target: any, mode: string) → object	object	variadic, Grid extension. Computes a bounded local or global sequence alignment and compact CIGAR.
BIO_ALIGN_BANDED(query: any, target: any, band_width: number, mode: string) → object	object	variadic, Grid extension. Computes an exact traceback inside a bounded diagonal band using O(query length × band width) work and memory.
BIO_ASSEMBLE(reads: bio_sequence_set, k: number, minimum_kmer_count: number) → object	object	variadic, Grid extension. Builds deterministic bounded de Bruijn unitigs from resident DNA or RNA reads.
BIO_CALL_VARIANTS(reference: bio_sequence_set, alignments: bio_alignment_set, min_depth: number, min_alternate_count: number, min_alternate_fraction: number) → object	object	variadic, Grid extension. Calls bounded reference-aware SNVs and simple anchored indels from primary SAM alignments using explicit pileup thresholds.
BIO_COVERAGE(alignments: bio_alignment_set, contig: string, start: number, end: number) → array	array	variadic, Grid extension. Computes primary-alignment base coverage over a bounded interval with an O(records + interval) difference-array kernel.
BIO_FIND_ORFS(sequence: any, minimum_amino_acids: number, limit: number) → object	object	variadic, Grid extension. Finds bounded complete ATG-to-stop open reading frames across all six DNA/RNA translation frames.
BIO_KMERS(sequence: any, k: number) → array	array	variadic, Grid extension. Counts overlapping k-mers in a sequence.
BIO_MAP_READS(reference: bio_sequence_set, reads: bio_sequence_set, seed_length: number, band_width: number) → object	object	variadic, Grid extension. Maps a bounded read set to a resident reference with indexed diagonal voting and banded seed-and-extend alignment.
BIO_OMICS_EMBED(matrix: bio_omics_matrix, components: number) → array	array	variadic, Grid extension. Computes sparse PCA observation scores without densifying the matrix.
BIO_OMICS_HVG(matrix: bio_omics_matrix, count: number) → array	array	variadic, Grid extension. Ranks highly variable features by sparse dispersion.
BIO_OMICS_NORMALIZE(matrix: bio_omics_matrix, target_sum: number, log1p: boolean) → object	object	variadic, Grid extension. Library-size normalizes a sparse omics matrix with optional log1p.
BIO_OMICS_QC(matrix: bio_omics_matrix) → array	array	variadic, Grid extension. Returns per-observation detected-feature and library-size QC.
BIO_PARSE_FASTA(text: string, alphabet: string) → object	object	variadic, Grid extension. Parses bounded FASTA text into a sequence-set value.
BIO_PARSE_FASTQ(text: string, alphabet: string) → object	object	variadic, Grid extension. Parses bounded FASTQ text with Phred qualities.
BIO_PARSE_MATRIX_MARKET(text: string) → object	object	variadic, Grid extension. Parses a bounded coordinate Matrix Market document into a sparse omics matrix.
BIO_PARSE_SAM(text: string) → object	object	variadic, Grid extension. Parses bounded SAM alignment records, reference dictionaries, flags, CIGAR operations, and read metadata.
BIO_PARSE_VCF(text: string) → object	object	variadic, Grid extension. Parses bounded VCF text into a typed variant set.
BIO_SEQUENCE(sequence: string, alphabet: string) → object	object	variadic, Grid extension. Creates a validated packed DNA, RNA, or protein sequence.
BIO_SKETCH(sequence: any, k: number, sketch_size: number) → object	object	variadic, Grid extension. Builds a bounded deterministic canonical bottom-k k-mer sketch for alignment-free local sequence comparison.
BIO_SKETCH_SIMILARITY(left: bio_sequence_sketch, right: bio_sequence_sketch) → object	object	variadic, Grid extension. Compares compatible bottom-k sequence sketches, returning estimated Jaccard resemblance and a Mash-style distance without alignment.
BIO_TRANSLATE(sequence: any, frame: number, stop_at_stop: boolean) → object	object	variadic, Grid extension. Translates DNA or RNA through the standard genetic code in a selected forward or reverse-complement frame.
BIO_VARIANT_AF(variants: bio_variant_set, row: number, alternate: number) → number	number	variadic, Grid extension. Computes the called alternate-allele frequency for a variant row.

---

Molecular Computing

Chemical graphs, descriptors, fingerprints, structures, docking, dynamics, and trajectory analysis helpers.

Function count: 31.

Function	Returns	Notes
CHEM_ENERGY(system: chemical_system) → object	object	variadic, Grid extension. Evaluates bonded, torsion, van der Waals, electrostatic, and total energy in kJ/mol.
CHEM_LOAD_SYSTEM(artifactId: text) → object	object	variadic, Grid extension. Loads a model-scoped durable ChemicalSystem artifact for resident energy and minimization workflows.
CHEM_MINIMIZE(system: chemical_system) → object	object	variadic, Grid extension. Runs bounded deterministic geometry minimization and returns coordinates and an energy audit.
CHEM_PARTIAL_CHARGES(molecule: molecule_graph, iterations: number) → object	object	variadic, Grid extension. Assigns deterministic charge-conserving electronegativity-equalized atomic partial charges.
CHEM_PI_ELECTRONIC(molecule: molecule_graph) → object	object	variadic, Grid extension. Computes a bounded Hückel π-orbital spectrum, electron count, HOMO, LUMO, and gap.
CHEM_PREPARE(molecule: molecule_graph, conformer: number) → object	object	variadic, Grid extension. Builds a typed portable bonded/nonbonded force-field system for one conformer.
CHEM_PROPERTIES(molecule: molecule_graph) → object	object	variadic, Grid extension. Computes portable physicochemical and Lipinski property summaries.
CHEM_RANK_CONFORMERS(molecule: molecule_graph, limit: number) → object	object	variadic, Grid extension. Ranks bounded conformers by portable force-field energy with relative energies.
CHEM_SANITIZE(molecule: molecule_graph) → object	object	variadic, Grid extension. Validates molecular topology, supported elements, valence, aromaticity, charge, and connected components.
MD_ANALYZE(trajectory: md_trajectory) → array	array	variadic, Grid extension. Returns trajectory energy, temperature, RMSD, and radius-of-gyration rows.
MD_LOAD_SYSTEM(artifactId: text) → object	object	variadic, Grid extension. Loads a model-scoped durable MdSystem artifact into the resident molecular-dynamics handle table.
MD_LOAD_TRAJECTORY(artifactId: text) → object	object	variadic, Grid extension. Loads a model-scoped durable Trajectory artifact into the resident molecular-dynamics handle table.
MD_PREPARE(molecule: any, stiffness: number) → object	object	variadic, Grid extension. Builds a validated harmonic molecular-dynamics system from a coordinate-bearing molecule.
MD_RUN(system: md_system, steps: number, save_stride: number) → object	object	variadic, Grid extension. Runs bounded deterministic CPU molecular dynamics and returns a trajectory.
MOL_CONFORMER(molecule: any) → object	object	variadic, Grid extension. Adds a deterministic bounded 3-D conformer to a molecular graph.
MOL_DESCRIPTORS(molecule: any) → object	object	variadic, Grid extension. Computes formula, mass, graph, aromatic, heteroatom, charge, and rotatable-bond descriptors.
MOL_DIRECT_EWAL(system: object, maxWork: number) → object	object	variadic, Grid extension. Evaluates bounded resident triclinic direct-Ewald electrostatics for a periodic parameterized system.
MOL_DIVERSE_SELECT(candidates: array, limit: number) → array	array	variadic, Grid extension. Selects a deterministic exact-Tanimoto MaxMin subset without materialising a pairwise similarity matrix.
MOL_DOCK(receptor: any, ligand: any) → object	object	variadic, Grid extension. Runs a bounded deterministic rigid docking search and returns ranked poses.
MOL_FINGERPRINT(molecule: any) → object	object	variadic, Grid extension. Computes a packed radius-two molecular graph fingerprint.
MOL_LOAD_PARAMETERIZED_SYSTEM(artifactId: text) → object	object	variadic, Grid extension. Loads a model-scoped durable periodic parameterized-system artifact for resident electrostatics workflows.
MOL_LOAD_PORTABLE_PARAMETERIZED_SYSTEM(artifactId: text) → object	object	variadic, Grid extension. Loads a model-scoped durable aperiodic portable parameterized-system artifact into a resident calibrated topology handle.
MOL_PARSE_MMCIF(text: string) → object	object	variadic, Grid extension. Parses the atom-site loop of a bounded mmCIF structure with residue, chain, and coordinate metadata.
MOL_PARSE_MOL2(text: string) → object	object	variadic, Grid extension. Parses bounded Tripos MOL2 molecule records, typed bonds, residue metadata, and 3D conformers.
MOL_PARSE_PDB(text: string) → object	object	variadic, Grid extension. Parses bounded PDB coordinates into a molecular structure.
MOL_PARSE_SDF(text: string) → object	object	variadic, Grid extension. Parses bounded SDF V2000 molecule records and conformers.
MOL_PARSE_SMILES(smiles: string) → object	object	variadic, Grid extension. Parses a bounded SMILES chemical graph with rings, branches, aromaticity, and charges.
MOL_REACTION_FIELD(system: object, maxWork: number) → object	object	variadic, Grid extension. Evaluates bounded resident reaction-field electrostatics for a periodic parameterized system.
MOL_SCREEN(query: any, candidates: array, minimum_similarity: number, limit: number) → array	array	variadic, Grid extension. Streams exact threshold/top-K Tanimoto hits with cardinality pruning instead of materialising a full similarity matrix.
MOL_SIMILARITY(left: any, right: any) → number	number	variadic, Grid extension. Computes Tanimoto similarity between fingerprints or molecules.
MOL_SUBSTRUCTURE(target: any, query: any) → boolean	boolean	variadic, Grid extension. Tests bounded graph-isomorphic substructure containment.

---

File I/O

Reading and writing local files (TOML, YAML, JSON, text), directory listing, and glob. Paths are confined to the model tree in shared deployments.

Function count: 10.

Function	Returns	Notes
GLOB(pattern: string) → array	array	async, external. Returns paths matching a shell glob pattern as a spilled column. Confined to the model tree in shared deployments.
LS(path: string) → array	array	async, external. Lists the immediate entries of a directory as a spilled column of names. Confined to the model tree in shared deployments.
READ_JSON_DOC(path: string) → object	object	async, external. Reads a JSON file and returns its contents as an object (document form; use READ_JSON for a tabular frame). Confined to the model tree in shared deployments.
READ_TEXT(path: string) → string	string	async, external. Reads a file and returns its contents as a string. Confined to the model tree in shared deployments.
READ_TOML(path: string) → object	object	async, external. Reads a TOML file and returns its contents as an object. Confined to the model tree in shared deployments.
READ_YAML(path: string) → object	object	async, external. Reads a YAML file and returns its contents as an object. Confined to the model tree in shared deployments.
WRITE_FILE(path: string, content: string) → object	object	async, external. Writes text to a file, creating parent directories, and returns the byte count. Confined to the model tree in shared deployments. Re-runs only when its arguments change; an unchanged write is a content-compare no-op.
WRITE_JSON(path: string, value: json) → object	object	async, external. Serializes an object to JSON and writes it to a file. Confined to the model tree in shared deployments. Re-runs only when its arguments change; an unchanged write is a content-compare no-op.
WRITE_TOML(path: string, value: json) → object	object	async, external. Serializes an object to TOML and writes it to a file. Confined to the model tree in shared deployments. Re-runs only when its arguments change; an unchanged write is a content-compare no-op.
WRITE_YAML(path: string, value: json) → object	object	async, external. Serializes an object to YAML and writes it to a file. Confined to the model tree in shared deployments. Re-runs only when its arguments change; an unchanged write is a content-compare no-op.

GLOB

Returns paths matching a shell glob pattern as a spilled column. Confined to the model tree in shared deployments.

Signature: GLOB(pattern: string) → array

External contract:

• worker route: file.glob
• cache TTL: 300000ms
• max staleness: 3600000ms
• refresh mode: background
• timeout: 30000ms
• max retries: 1

LS

Lists the immediate entries of a directory as a spilled column of names. Confined to the model tree in shared deployments.

Signature: LS(path: string) → array

External contract:

• worker route: file.list
• cache TTL: 300000ms
• max staleness: 3600000ms
• refresh mode: background
• timeout: 30000ms
• max retries: 1

READ_JSON_DOC

Reads a JSON file and returns its contents as an object (document form; use READ_JSON for a tabular frame). Confined to the model tree in shared deployments.

Signature: READ_JSON_DOC(path: string) → object

External contract:

• worker route: file.read.json
• cache TTL: 300000ms
• max staleness: 3600000ms
• refresh mode: background
• timeout: 30000ms
• max retries: 1

READ_TEXT

Reads a file and returns its contents as a string. Confined to the model tree in shared deployments.

Signature: READ_TEXT(path: string) → string

External contract:

• worker route: file.read.text
• cache TTL: 300000ms
• max staleness: 3600000ms
• refresh mode: background
• timeout: 30000ms
• max retries: 1

READ_TOML

Reads a TOML file and returns its contents as an object. Confined to the model tree in shared deployments.

Signature: READ_TOML(path: string) → object

External contract:

• worker route: file.read.toml
• cache TTL: 300000ms
• max staleness: 3600000ms
• refresh mode: background
• timeout: 30000ms
• max retries: 1

READ_YAML

Reads a YAML file and returns its contents as an object. Confined to the model tree in shared deployments.

Signature: READ_YAML(path: string) → object

External contract:

• worker route: file.read.yaml
• cache TTL: 300000ms
• max staleness: 3600000ms
• refresh mode: background
• timeout: 30000ms
• max retries: 1

WRITE_FILE

Writes text to a file, creating parent directories, and returns the byte count. Confined to the model tree in shared deployments. Re-runs only when its arguments change; an unchanged write is a content-compare no-op.

Signature: WRITE_FILE(path: string, content: string) → object

External contract:

• worker route: file.write.text
• cache TTL: 0ms
• max staleness: 0ms
• refresh mode: blocking
• timeout: 30000ms
• max retries: 1

WRITE_JSON

Serializes an object to JSON and writes it to a file. Confined to the model tree in shared deployments. Re-runs only when its arguments change; an unchanged write is a content-compare no-op.

Signature: WRITE_JSON(path: string, value: json) → object

External contract:

• worker route: file.write.json
• cache TTL: 0ms
• max staleness: 0ms
• refresh mode: blocking
• timeout: 30000ms
• max retries: 1

WRITE_TOML

Serializes an object to TOML and writes it to a file. Confined to the model tree in shared deployments. Re-runs only when its arguments change; an unchanged write is a content-compare no-op.

Signature: WRITE_TOML(path: string, value: json) → object

External contract:

• worker route: file.write.toml
• cache TTL: 0ms
• max staleness: 0ms
• refresh mode: blocking
• timeout: 30000ms
• max retries: 1

WRITE_YAML

Serializes an object to YAML and writes it to a file. Confined to the model tree in shared deployments. Re-runs only when its arguments change; an unchanged write is a content-compare no-op.

Signature: WRITE_YAML(path: string, value: json) → object

External contract:

• worker route: file.write.yaml
• cache TTL: 0ms
• max staleness: 0ms
• refresh mode: blocking
• timeout: 30000ms
• max retries: 1

---

External (Async)

Functions that execute asynchronously in worker processes.

Function count: 16.

Function	Returns	Notes
AI_PROMPT(prompt: string, options: object) → string	string	async, external. Sends a text prompt to the instance-configured LLM and returns the generated text.
ASK(question: string, context: any, options: object) → string	string	async, external. Asks the instance-configured LLM a spreadsheet-aware question and returns a concise text answer.
ASK_BOOLEAN(question: string, context: any, options: object) → boolean	boolean	async, external. Asks the instance-configured LLM a spreadsheet-aware question and parses the answer as true or false.
ASK_JSON(question: string, context: any, options: object) → object	object	async, external. Asks the instance-configured LLM a spreadsheet-aware question and parses the answer as JSON.
ASK_NUMERIC(question: string, context: any, options: object) → number	number	async, external. Asks the instance-configured LLM a spreadsheet-aware question and parses the answer as a number.
ASK_TEXT(question: string, context: any, options: object) → string	string	async, external. Asks the instance-configured LLM a spreadsheet-aware question and returns a concise text answer.
FX_RATE(base: currency_code, quote: currency_code) → fx_rate	fx_rate	async, external. Retrieves an exchange rate for a currency pair.
HTTP_JSON(url: string) → object	object	async, external. Fetches JSON from an external API and materializes it as an object value.
ML_SCORE(features: number[]) → score	score	async, external. Delegates a feature vector to an external scoring engine.
MODEL_CARD(modelid: string) → object	object	async, external. Returns a structured model card for a trained model: range, target, family, backend, metrics, warnings, and version.
MODEL_EXPLAIN(modelid: string, features: any) → object	object	async, external. Returns a local explanation for a trained model's prediction on a single feature vector.
MODEL_FEATURES(modelid: string) → object	object	async, external. Returns the feature schema and preprocessing summary for a trained model.
MODEL_IMPORTANCE(modelid: string) → object	object	async, external. Returns feature importance for a trained model (coefficients, tree gain, or permutation importance).
MODEL_METRICS(modelid: string) → object	object	async, external. Returns metrics and baseline comparison for a trained model from the registry.
PREDICT(modelid: string, features: any) → any	any	async, external. Runs a trained Grid model against a feature vector or selected range.
PREDICT_PROBA(modelid: string, features: any) → object	object	async, external. Returns class probabilities from a trained classifier as an object keyed by class label.

AI_PROMPT

Sends a text prompt to the instance-configured LLM and returns the generated text.

Signature: AI_PROMPT(prompt: string, options: object) → string

External contract:

• worker route: ai.prompt
• cache TTL: 0ms
• max staleness: 0ms
• refresh mode: blocking
• timeout: 60000ms
• max retries: 0

ASK

Asks the instance-configured LLM a spreadsheet-aware question and returns a concise text answer.

Signature: ASK(question: string, context: any, options: object) → string

External contract:

• worker route: ai.ask
• cache TTL: 0ms
• max staleness: 0ms
• refresh mode: blocking
• timeout: 60000ms
• max retries: 0

ASK_BOOLEAN

Asks the instance-configured LLM a spreadsheet-aware question and parses the answer as true or false.

Signature: ASK_BOOLEAN(question: string, context: any, options: object) → boolean

External contract:

• worker route: ai.ask.boolean
• cache TTL: 0ms
• max staleness: 0ms
• refresh mode: blocking
• timeout: 60000ms
• max retries: 0

ASK_JSON

Asks the instance-configured LLM a spreadsheet-aware question and parses the answer as JSON.

Signature: ASK_JSON(question: string, context: any, options: object) → object

External contract:

• worker route: ai.ask.json
• cache TTL: 0ms
• max staleness: 0ms
• refresh mode: blocking
• timeout: 60000ms
• max retries: 0

ASK_NUMERIC

Asks the instance-configured LLM a spreadsheet-aware question and parses the answer as a number.

Signature: ASK_NUMERIC(question: string, context: any, options: object) → number

External contract:

• worker route: ai.ask.numeric
• cache TTL: 0ms
• max staleness: 0ms
• refresh mode: blocking
• timeout: 60000ms
• max retries: 0

ASK_TEXT

Asks the instance-configured LLM a spreadsheet-aware question and returns a concise text answer.

Signature: ASK_TEXT(question: string, context: any, options: object) → string

External contract:

• worker route: ai.ask.text
• cache TTL: 0ms
• max staleness: 0ms
• refresh mode: blocking
• timeout: 60000ms
• max retries: 0

FX_RATE

Retrieves an exchange rate for a currency pair. The default provider is the keyless Frankfurter v2 API (https://api.frankfurter.dev/v2) for daily central-bank/reference rates; set GRID_FX_RATE_BASE_URL to use a self-hosted or compatible endpoint.

Signature: FX_RATE(base: currency_code, quote: currency_code) → fx_rate

External contract:

• worker route: market-data.fx
• cache TTL: 30000ms
• max staleness: 300000ms
• refresh mode: background
• timeout: 5000ms
• max retries: 3

HTTP_JSON

Fetches JSON from an external API and materializes it as an object value.

Signature: HTTP_JSON(url: string) → object

External contract:

• worker route: network.http-json
• cache TTL: 60000ms
• max staleness: 600000ms
• refresh mode: background
• timeout: 10000ms
• max retries: 2

ML_SCORE

Runs a feature vector through the configured Grid AI scoring model.

Signature: ML_SCORE(features: number[]) → score

External contract:

• worker route: ml.scoring
• cache TTL: 300000ms
• max staleness: 900000ms
• refresh mode: background
• timeout: 15000ms
• max retries: 2

MODEL_CARD

Returns a structured model card for a trained model: range, target, family, backend, metrics, warnings, and version.

Signature: MODEL_CARD(modelid: string) → object

External contract:

• worker route: ml-model:card
• cache TTL: 60000ms
• max staleness: 300000ms
• refresh mode: background
• timeout: 5000ms
• max retries: 0

MODEL_EXPLAIN

Returns a local explanation for a trained model's prediction on a single feature vector.

Signature: MODEL_EXPLAIN(modelid: string, features: any) → object

External contract:

• worker route: ml-model:explain
• cache TTL: 0ms
• max staleness: 0ms
• refresh mode: blocking
• timeout: 10000ms
• max retries: 0

MODEL_FEATURES

Returns the feature schema and preprocessing summary for a trained model.

Signature: MODEL_FEATURES(modelid: string) → object

External contract:

• worker route: ml-model:features
• cache TTL: 60000ms
• max staleness: 300000ms
• refresh mode: background
• timeout: 5000ms
• max retries: 0

MODEL_IMPORTANCE

Returns feature importance for a trained model (coefficients, tree gain, or permutation importance).

Signature: MODEL_IMPORTANCE(modelid: string) → object

External contract:

• worker route: ml-model:importance
• cache TTL: 60000ms
• max staleness: 300000ms
• refresh mode: background
• timeout: 5000ms
• max retries: 0

MODEL_METRICS

Returns metrics and baseline comparison for a trained model from the registry.

Signature: MODEL_METRICS(modelid: string) → object

External contract:

• worker route: ml-model:metrics
• cache TTL: 60000ms
• max staleness: 300000ms
• refresh mode: background
• timeout: 5000ms
• max retries: 0

PREDICT

Runs a trained Grid model against a feature vector or selected range.

Signature: PREDICT(modelid: string, features: any) → any

External contract:

• worker route: ml-model:predict
• cache TTL: 0ms
• max staleness: 0ms
• refresh mode: blocking
• timeout: 30000ms
• max retries: 0

PREDICT_PROBA

Returns class probabilities from a trained classifier as an object keyed by class label.

Signature: PREDICT_PROBA(modelid: string, features: any) → object

External contract:

• worker route: ml-model:predict_proba
• cache TTL: 0ms
• max staleness: 0ms
• refresh mode: blocking
• timeout: 30000ms
• max retries: 0

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Notes On The Catalog

• Variadic tail. When a parameter is marked ..., the function accepts any number of additional arguments of that type. For example, SUM(values: number[]) accepts SUM(1, 2, 3) or SUM(A1:A10).
• Volatile functions. Marked volatile recompute every time any input in the model changes (not just their declared inputs). Examples: NOW, TODAY, RAND, RANDBETWEEN.
• Async functions. Marked async run asynchronously. See external-functions.md.
• Special forms. Marked special form are still user-callable functions, but Grid evaluates them specially because they bind names, create lambdas, or resolve references.
• Compatibility. The compatibility matrix labels each entry as Excel-compatible, Sheets-compatible, Grid-specific, or external.
• Naming. Function names are case-insensitive at parse time (SUM, sum, Sum all bind to the same definition). The canonical style writes them uppercase.