Built-in Reference¶

This page lists all dimensions, units, constants, and functions provided by the Graphcal prelude. These are available in every .gcl file without any import declarations.

Built-in Constants¶

Name	Type	Value
`PI`	`Dimensionless`	3.14159265358979...
`E`	`Dimensionless`	2.71828182845904...
`TAU`	`Dimensionless`	6.28318530717958... (2*PI)
`SQRT2`	`Dimensionless`	1.41421356237309...
`LN2`	`Dimensionless`	0.69314718055994...
`LN10`	`Dimensionless`	2.30258509299404...

Built-in Functions¶

Math Functions¶

Function	Signature	Description
`sqrt(x)`	`D -> D^(1/2)`	Square root (dimension halved)
`cbrt(x)`	`D -> D^(1/3)`	Cube root (dimension divided by 3)
`abs(x)`	`D -> D`	Absolute value
`sign(x)`	`D -> Dimensionless`	Sign of value (1.0, -1.0, or NaN)
`round(x)`	`D -> D`	Round to nearest integer
`trunc(x)`	`D -> D`	Truncate toward zero
`floor(x)`	`D -> D`	Round toward negative infinity
`ceil(x)`	`D -> D`	Round toward positive infinity
`clamp(x, min, max)`	`(D, D, D) -> D`	Clamp value to range
`hypot(a, b)`	`(D, D) -> D`	Hypotenuse (sqrt(a^2 + b^2))
`exp(x)`	`Dimensionless -> Dimensionless`	Exponential (e^x)
`expm1(x)`	`Dimensionless -> Dimensionless`	exp(x) - 1 (numerically stable for small x)
`ln(x)`	`Dimensionless -> Dimensionless`	Natural logarithm
`log1p(x)`	`Dimensionless -> Dimensionless`	ln(1 + x) (numerically stable for small x)
`log(x, base)`	`(Dimensionless, Dimensionless) -> Dimensionless`	Logarithm with arbitrary base
`log2(x)`	`Dimensionless -> Dimensionless`	Base-2 logarithm
`log10(x)`	`Dimensionless -> Dimensionless`	Base-10 logarithm

Trigonometric Functions¶

Function	Signature	Description
`sin(x)`	`Angle -> Dimensionless`	Sine
`cos(x)`	`Angle -> Dimensionless`	Cosine
`tan(x)`	`Angle -> Dimensionless`	Tangent
`asin(x)`	`Dimensionless -> Angle`	Inverse sine
`acos(x)`	`Dimensionless -> Angle`	Inverse cosine
`atan(x)`	`Dimensionless -> Angle`	Inverse tangent
`atan2(y, x)`	`(D, D) -> Angle`	Two-argument inverse tangent

Hyperbolic Functions¶

Function	Signature	Description
`sinh(x)`	`Dimensionless -> Dimensionless`	Hyperbolic sine
`cosh(x)`	`Dimensionless -> Dimensionless`	Hyperbolic cosine
`tanh(x)`	`Dimensionless -> Dimensionless`	Hyperbolic tangent
`asinh(x)`	`Dimensionless -> Dimensionless`	Inverse hyperbolic sine
`acosh(x)`	`Dimensionless -> Dimensionless`	Inverse hyperbolic cosine
`atanh(x)`	`Dimensionless -> Dimensionless`	Inverse hyperbolic tangent

Comparison Functions¶

Function	Signature	Description
`min(a, b)`	`(D, D) -> D`	Minimum of two values
`max(a, b)`	`(D, D) -> D`	Maximum of two values

Type Conversion Functions¶

Function	Signature	Description
`to_float(x)`	`Int -> Dimensionless`	Convert integer to float
`to_int(x)`	`Dimensionless -> Int`	Convert float to integer (truncates toward zero)

Datetime Functions¶

Constructors¶

Function	Signature	Description
`datetime("...")`	`String -> Datetime`	Parse ISO 8601/RFC 3339 datetime string (UTC)
`datetime("...", "tz")`	`(String, String) -> Datetime`	Parse civil datetime in a timezone (e.g., `"Asia/Tokyo"`)
`epoch("...", Scale)`	`(String, TimeScale) -> Datetime<Scale>`	Parse datetime in a specific time scale
`from_jd(x)`	`Dimensionless -> Datetime`	Construct from Julian Date (UTC)
`from_mjd(x)`	`Dimensionless -> Datetime`	Construct from Modified Julian Date (UTC)
`from_unix(x)`	`Dimensionless -> Datetime`	Construct from Unix timestamp in seconds

Time Scale Conversions¶

Function	Signature	Description
`to_utc(x)`	`Datetime(any) -> Datetime<UTC>`	Convert to UTC
`to_tai(x)`	`Datetime(any) -> Datetime<TAI>`	Convert to TAI
`to_tt(x)`	`Datetime(any) -> Datetime<TT>`	Convert to Terrestrial Time
`to_tdb(x)`	`Datetime(any) -> Datetime<TDB>`	Convert to Barycentric Dynamical Time
`to_et(x)`	`Datetime(any) -> Datetime<ET>`	Convert to Ephemeris Time
`to_gpst(x)`	`Datetime(any) -> Datetime<GPST>`	Convert to GPS Time
`to_gst(x)`	`Datetime(any) -> Datetime<GST>`	Convert to Galileo System Time
`to_bdt(x)`	`Datetime(any) -> Datetime<BDT>`	Convert to BeiDou Time
`to_qzsst(x)`	`Datetime(any) -> Datetime<QZSST>`	Convert to QZSS Time

Numeric Conversions¶

Function	Signature	Description
`to_jd(x)`	`Datetime -> Dimensionless`	Convert to Julian Date (UTC days)
`to_mjd(x)`	`Datetime -> Dimensionless`	Convert to Modified Julian Date (UTC days)
`to_unix(x)`	`Datetime -> Dimensionless`	Convert to Unix timestamp (seconds since 1970-01-01)

Extraction Functions¶

Function	Signature	Description
`year(x)`	`Datetime -> Int`	Extract year
`month(x)`	`Datetime -> Int`	Extract month (1-12)
`day(x)`	`Datetime -> Int`	Extract day of month (1-31)
`hour(x)`	`Datetime -> Int`	Extract hour (0-23)
`minute(x)`	`Datetime -> Int`	Extract minute (0-59)
`second(x)`	`Datetime -> Int`	Extract second (0-59)
`weekday(x)`	`Datetime -> Int`	Day of week (0=Monday, 6=Sunday)
`day_of_year(x)`	`Datetime -> Int`	Day of year (1-366)

Timezone Display¶

The -> operator can display a datetime in a specific timezone without changing the underlying value:

node meeting_ny: Datetime = @meeting -> "America/New_York";

Aggregation Functions (Indexed Values)¶

These functions operate on for comprehensions or indexed values:

Function	Signature	Description
`sum(...)`	`D[I] -> D`	Sum of all elements
`max(...)`	`D[I] -> D`	Maximum element
`min(...)`	`D[I] -> D`	Minimum element
`mean(...)`	`D[I] -> D`	Arithmetic mean
`count(...)`	`D[I] -> Dimensionless`	Number of elements

Prelude Base Dimensions¶

Dimension	Description
`Length`	Spatial distance
`Time`	Temporal duration
`Mass`	Mass
`Temperature`	Thermodynamic temperature
`ElectricCurrent`	Electric current
`Amount`	Amount of substance
`LuminousIntensity`	Luminous intensity
`Angle`	Plane angle
`Dimensionless`	No physical dimension

Prelude Derived Dimensions¶

Dimension	Definition
`Velocity`	`Length / Time`
`Acceleration`	`Length / Time^2`
`Force`	`Mass * Length / Time^2`
`Energy`	`Mass * Length^2 / Time^2`
`Power`	`Mass * Length^2 / Time^3`
`Pressure`	`Mass / (Length * Time^2)`
`Frequency`	`1 / Time`
`Area`	`Length^2`
`Volume`	`Length^3`

Prelude Units¶

Length¶

Unit	Definition
`m`	Base unit (meter)
`km`	1000 m
`cm`	0.01 m
`mm`	0.001 m

Time¶

Unit	Definition
`s`	Base unit (second)
`min`	60 s
`hour`	3600 s

Mass¶

Unit	Definition
`kg`	Base unit (kilogram)
`g`	0.001 kg

Temperature¶

Unit	Definition
`K`	Base unit (kelvin)

Electric Current¶

Unit	Definition
`A`	Base unit (ampere)

Amount of Substance¶

Unit	Definition
`mol`	Base unit (mole)

Luminous Intensity¶

Unit	Definition
`cd`	Base unit (candela)

Angle¶

Unit	Definition
`rad`	Base unit (radian)
`deg`	pi/180 rad

Force¶

Unit	Definition
`N`	1 kg*m/s^2
`kN`	1000 N

Energy¶

Unit	Definition
`J`	1 N*m
`kJ`	1000 J

Power¶

Unit	Definition
`W`	1 J/s
`kW`	1000 W

Pressure¶

Unit	Definition
`Pa`	1 N/m^2
`kPa`	1000 Pa
`MPa`	1000000 Pa

Frequency¶

Unit	Definition
`Hz`	1/s