Library

`math`

A library of math functions.

This library is an interface to the standard C math library, providing all of its functions inside the math table.

Properties 7#

e`number`	The value of Euler's number, e.
huge`number`	Returns a value larger than or equal to any other numerical value (about 2¹⁰²⁴).
nan`number`	A NaN value, as defined by the IEEE 754 standard.
phi`number`	The value of the golden ratio.
pi`number`	The value of pi.
sqrt2`number`	The value of the square root of 2.
tau`number`	The value of tau, which is defined as `2 * math.pi`.

`e`: `number`#

The value of Euler's number, e.

`huge`: `number`#

Returns a value larger than or equal to any other numerical value (about 2¹⁰²⁴). Dividing a positive number by zero yields this same value.

`nan`: `number`#

A NaN value, as defined by the IEEE 754 standard. Comparing directly to math.nan will always return false; use math.isnan() instead.

`phi`: `number`#

The value of the golden ratio.

`pi`: `number`#

The value of pi.

`sqrt2`: `number`#

The value of the square root of 2.

`tau`: `number`#

The value of tau, which is defined as 2 * math.pi.

Functions 37#

abs	Returns the absolute value of `x`.
acos	Returns the arc cosine of `x`.
asin	Returns the arc sine of `x`.
atan	Returns the arc tangent of `x` in radians.
atan2	Returns the arc tangent of `y`/`x` (in radians) while using the signs of both parameters to find the quadrant of the result.
ceil	Returns the smallest integer larger than or equal to `x`.
clamp	Returns a number between `min` and `max`, inclusive.
cos	Returns the cosine of `x`, assumed to be in radians.
cosh	Returns the hyperbolic cosine of `x`.
deg	Returns the angle `x` (given in radians) in degrees.
exp	Returns the value `e`^`x`.
floor	Returns the largest integer smaller than or equal to `x`.
fmod	Returns the remainder of the division of `x` by `y` that rounds the quotient towards zero.
frexp	Returns `m` and `e` such that `x` = `m`*`2`^`e`.
isfinite	Returns true if `x` is a finite number.
isinf	Returns true if `x` is positive or negative infinity and false otherwise.
isnan	Returns true if `x` is not a number (NaN) and false otherwise.
ldexp	Returns `x`*`2`^`e` (`e` should be an integer).
lerp	Returns the linear interpolation between `a` and `b`.
log	Returns the logarithm of `x` using the given base.
log10	Returns the base-10 logarithm of `x`.
map	Returns the value of `x` mapped from one range to another.
max	Returns the maximum value among the numbers passed to the function.
min	Returns the minimum value among the numbers passed to the function.
modf	Returns two numbers: the integral part of `x` and the fractional part of `x`.
noise	Returns a Perlin noise value.
pow	Returns `x`^`y`.
rad	Returns the angle `x` (given in degrees) in radians.
random	Returns a random number within the range provided.
randomseed	Sets `x` as the seed for the pseudo-random generator.
round	Returns the integer with the smallest difference between it and the given number.
sign	Returns `-1` if `x` is less than `0`, `0` if `x` equals `0`, or `1` if `x` is greater than `0`.
sin	Returns the sine of `x`, assumed to be in radians.
sinh	Returns the hyperbolic sine of `x`.
sqrt	Returns the square root of `x`.
tan	Returns the tangent of `x`, assumed to be in radians.
tanh	Returns the hyperbolic tangent of `x`.

`abs(x: number)`: number#

Returns the absolute value of x.

Name	Type	Default	Description
`x`	`number`		The number to return the absolute value of.

Returns

number — The absolute value of x.

`acos(x: number)`: number#

Returns the arc cosine of x.

Name	Type	Default	Description
`x`	`number`		The cosine value, between `-1` and `1`.

Returns

number — The angle in radians whose cosine is x, in the range [0, pi].

`asin(x: number)`: number#

Returns the arc sine of x.

Name	Type	Default	Description
`x`	`number`		The sine value, between `-1` and `1`.

Returns

number — The angle in radians whose sine is x, in the range [-pi/2, pi/2].

`atan(x: number)`: number#

Returns the arc tangent of x in radians.

Name	Type	Default	Description
`x`	`number`		The value to compute the arc tangent of.

Returns

number — The arc tangent of x in radians, in the range [-pi/2, pi/2].

`atan2(y: number, x: number)`: number#

Returns the arc tangent of y/x (in radians) while using the signs of both parameters to find the quadrant of the result. It also handles correctly the case of x being zero.

Name	Type	Default	Description
`y`	`number`		The Y coordinate.
`x`	`number`		The X coordinate.

Returns

number — The arc tangent of y/x in radians, in the range [-pi, pi].

`ceil(x: number)`: int#

Returns the smallest integer larger than or equal to x.

Name	Type	Default	Description
`x`	`number`		The number to round up.

Returns

int — The smallest integer greater than or equal to x.

`clamp(x: number, min: number, max: number)`: number#

Returns a number between min and max, inclusive.

Name	Type	Description
`x`	`number`	The number to clamp.
`min`	`number`	The minimum value of the range.
`max`	`number`	The maximum value of the range; must be greater than or equal to `min`.

Returns

number — x constrained to the range [min, max].

`cos(x: number)`: number#

Returns the cosine of x, assumed to be in radians.

Name	Type	Default	Description
`x`	`number`		The angle in radians.

Returns

number — The cosine of x.

`cosh(x: number)`: number#

Returns the hyperbolic cosine of x.

Name	Type	Default	Description
`x`	`number`		The number to compute the hyperbolic cosine of.

Returns

number — The hyperbolic cosine of x.

`deg(x: number)`: number#

Returns the angle x (given in radians) in degrees.

Name	Type	Default	Description
`x`	`number`		The angle in radians to convert.

Returns

number — The angle x converted to degrees.

`exp(x: number)`: number#

Returns the value e^x.

Name	Type	Default	Description
`x`	`number`		The exponent.

Returns

number — The value of e raised to the power x.

`floor(x: number)`: int#

Returns the largest integer smaller than or equal to x.

Name	Type	Default	Description
`x`	`number`		The number to round down.

Returns

int — The largest integer less than or equal to x.

`fmod(x: number, y: number)`: number#

Returns the remainder of the division of x by y that rounds the quotient towards zero.

Name	Type	Default	Description
`x`	`number`		The dividend.
`y`	`number`		The divisor.

Returns

number — The remainder of the division of x by y.

`frexp(x: number)`: number, int#

Returns m and e such that x = m*2^e. e is an integer and the absolute value of m is in the range of 0.5 to 1 (inclusive of 0.5 but exclusive of 1), or zero when x is zero.

Name	Type	Default	Description
`x`	`number`		The number to decompose into mantissa and exponent.

Returns

number — The mantissa m, a value whose absolute value is in [0.5, 1) or zero.
int — The exponent e such that x = m * 2^e.

`isfinite(x: number)`: boolean#

Returns true if x is a finite number, meaning it is neither NaN nor positive or negative infinity (±math.huge).

Name	Type	Default	Description
`x`	`number`		The number to test.

Returns

boolean — True if x is neither NaN nor infinity, false otherwise.

`isinf(x: number)`: boolean#

Returns true if x is positive or negative infinity (±math.huge) and false otherwise.

Name	Type	Default	Description
`x`	`number`		The number to test.

Returns

boolean — True if x is positive or negative infinity, false otherwise.

`isnan(x: number)`: boolean#

Returns true if x is not a number (NaN) and false otherwise.

Name	Type	Default	Description
`x`	`number`		The number to test.

Returns

boolean — True if x is NaN, false otherwise.

`ldexp(x: number, e: int)`: number#

Returns x*2^e (e should be an integer).

Name	Type	Default	Description
`x`	`number`		The mantissa value.
`e`	`int`		The integer exponent.

Returns

number — The value x * 2^e.

`lerp(a: number, b: number, t: number)`: number#

Returns the linear interpolation between a and b based on the factor t.

This function uses the formula a+(b-a)*t. t is typically between 0 and 1 but values outside this range are acceptable.

Name	Type	Description
`a`	`number`	The starting value.
`b`	`number`	The ending value.
`t`	`number`	The interpolation factor, typically between `0` and `1`.

Returns

number — The interpolated value between a and b.

`log(x: number, base: number = 2.7182818)`: number#

Returns the logarithm of x using the given base, or the mathematical constant e if no base is provided (natural logarithm).

Name	Type	Default	Description
`x`	`number`		The number to compute the logarithm of.
`base`	`number`	`2.7182818`	The base of the logarithm, the constant `e` by default.

Returns

number — The logarithm of x in the given base.

`log10(x: number)`: number#

Returns the base-10 logarithm of x.

Name	Type	Default	Description
`x`	`number`		The number to compute the base-10 logarithm of.

Returns

number — The base-10 logarithm of x.

`map(x: number, inmin: number, inmax: number, outmin: number, outmax: number)`: number#

Returns a value that represents x mapped linearly from the input range (inmin to inmax) to the output range (outmin to outmax). This is achieved by determining the relative position of x within the input range and applying that ratio to the output range.

Name	Type	Description
`x`	`number`	The number to be mapped.
`inmin`	`number`	The lower bound of the input range.
`inmax`	`number`	The upper bound of the input range.
`outmin`	`number`	The lower bound of the output range.
`outmax`	`number`	The upper bound of the output range.

Returns

number — The value of x mapped to the output range.

`max(x: number, ...: number)`: number#

Returns the maximum value among the numbers passed to the function.

Name	Type	Default	Description
`x`	`number`		The first number to compare.
`...`	`number`		Additional numbers to compare.

Returns

number — The largest value among all arguments.

`min(x: number, ...: number)`: number#

Returns the minimum value among the numbers passed to the function.

Name	Type	Default	Description
`x`	`number`		The first number to compare.
`...`	`number`		Additional numbers to compare.

Returns

number — The smallest value among all arguments.

`modf(x: number)`: number, number#

Returns two numbers: the integral part of x and the fractional part of x.

Name	Type	Default	Description
`x`	`number`		The number to split into integral and fractional parts.

Returns

number — The integral part of x.
number — The fractional part of x.

`noise(x: number, y: number = 0, z: number = 0)`: number#

Returns a Perlin noise value. The returned value is most often between the range of -1 to 1 (inclusive) but sometimes may be outside that range; if the interval is critical to you, use Library.math.clamp(noise, -1, 1) on the output.

If you leave arguments out, they will be interpreted as zero, so Library.math.noise(1.158) is equivalent to Library.math.noise(1.158, 0, 0) and Library.math.noise(1.158, 5.723) is equivalent to Library.math.noise(1.158, 5.723, 0).

Note that this function uses a Perlin noise algorithm to assign fixed values to coordinates. For example, Library.math.noise(1.158, 5.723) will always return 0.48397532105446 and Library.math.noise(1.158, 6) will always return 0.15315161645412.

If x, y, and z are all integers, the return value will be 0. For fractional values of x, y, and z, the return value will gradually fluctuate between -0.5 and 0.5. For coordinates that are close to each other, the return values will also be close to each other.

The noise repeats with a period of 256 on each axis, so Library.math.noise(x, y, z) and Library.math.noise(x + 256, y, z) return identical values.

Name	Type	Default	Description
`x`	`number`		The X coordinate of the sample point.
`y`	`number`	`0`	The Y coordinate of the sample point.
`z`	`number`	`0`	The Z coordinate of the sample point.

Returns

number — A Perlin noise value, typically between -1 and 1.

`pow(x: number, y: number)`: number#

Returns x^y (you can also use the expression x^y to compute this value).

Name	Type	Default	Description
`x`	`number`		The base value.
`y`	`number`		The exponent value.

Returns

number — The value x raised to the power y.

`rad(x: number)`: number#

Returns the angle x (given in degrees) in radians.

Name	Type	Default	Description
`x`	`number`		The angle in degrees to convert.

Returns

number — The angle x converted to radians.

`random(m: number = 0, n: number = 1)`: number#

When called without arguments, returns a uniform pseudo-random real number in the range of 0 to 1 (inclusive of 0 but exclusive of 1).

When called with an integer number m, returns a uniform pseudo-random integer in the range of 1 to m, inclusive.

When called with two integer numbers m and n, returns a uniform pseudo-random integer in the range of m to n, inclusive.

Internally, this uses a 32-bit PCG (Permuted Congruential Generator) which achieves excellent statistical performance and makes its output hard to predict.

Name	Type	Default	Description
`m`	`number`	`0`	When used alone, the upper bound of the integer range (lower bound is `1`). When used with `n`, the lower bound.
`n`	`number`	`1`	The upper bound of the integer range.

Returns

number — A pseudo-random number within the specified range.

`randomseed(x: number)`: ()#

Sets x as the seed for the pseudo-random generator: equal seeds produce equal sequences of numbers.

Name	Type	Default	Description
`x`	`number`		The seed value for the pseudo-random number generator.

Returns

()

`round(x: number)`: number#

Returns the integer with the smallest difference between it and the given number. For example, the value 5.8 returns 6.

For values like 0.5 that are equidistant to two integers, the value with the greater difference between it and zero is chosen. In other words, the function "rounds away from zero" such that 0.5 rounds to 1 and -0.5 rounds to -1.

Name	Type	Default	Description
`x`	`number`		The value to be rounded.

Returns

number — The nearest integer to x, rounding away from zero for midpoints.

`sign(x: number)`: int#

Returns -1 if x is less than 0, 0 if x equals 0, or 1 if x is greater than 0.

Name	Type	Default	Description
`x`	`number`		The number to determine the sign of.

Returns

int — -1 if x is negative, 0 if x is zero, or 1 if x is positive.

`sin(x: number)`: number#

Returns the sine of x, assumed to be in radians.

Name	Type	Default	Description
`x`	`number`		The angle in radians.

Returns

number — The sine of x.

`sinh(x: number)`: number#

Returns the hyperbolic sine of x.

Name	Type	Default	Description
`x`	`number`		The number to compute the hyperbolic sine of.

Returns

number — The hyperbolic sine of x.

`sqrt(x: number)`: number#

Returns the square root of x. You can also use the expression x^0.5 to compute this value.

Name	Type	Default	Description
`x`	`number`		The number to compute the square root of.

Returns

number — The square root of x.

`tan(x: number)`: number#

Returns the tangent of x, assumed to be in radians.

Name	Type	Default	Description
`x`	`number`		The angle in radians.

Returns

number — The tangent of x.

`tanh(x: number)`: number#

Returns the hyperbolic tangent of x.

Name	Type	Default	Description
`x`	`number`		The number to compute the hyperbolic tangent of.

Returns

number — The hyperbolic tangent of x.

Properties 7#

e: number#

huge: number#

nan: number#

phi: number#

pi: number#

sqrt2: number#

tau: number#

Functions 37#

abs(x: number): number#

Returns

acos(x: number): number#

Returns

asin(x: number): number#

Returns

atan(x: number): number#

Returns

atan2(y: number, x: number): number#

Returns

ceil(x: number): int#

Returns

clamp(x: number, min: number, max: number): number#

Returns

cos(x: number): number#

Returns

cosh(x: number): number#

Returns

deg(x: number): number#

Returns

exp(x: number): number#

Returns

floor(x: number): int#

Returns

fmod(x: number, y: number): number#

Returns

frexp(x: number): number, int#

Returns

isfinite(x: number): boolean#

Returns

isinf(x: number): boolean#

Returns

isnan(x: number): boolean#

Returns

ldexp(x: number, e: int): number#

Returns

lerp(a: number, b: number, t: number): number#

Returns

log(x: number, base: number = 2.7182818): number#

Returns

log10(x: number): number#

Returns

map(x: number, inmin: number, inmax: number, outmin: number, outmax: number): number#

Returns

max(x: number, ...: number): number#

Returns

min(x: number, ...: number): number#

Returns

modf(x: number): number, number#

Returns

noise(x: number, y: number = 0, z: number = 0): number#

Returns

pow(x: number, y: number): number#

Returns

rad(x: number): number#

Returns

random(m: number = 0, n: number = 1): number#

Returns

randomseed(x: number): ()#

Returns

round(x: number): number#

Returns

sign(x: number): int#

Returns

sin(x: number): number#

Returns

sinh(x: number): number#

Returns

sqrt(x: number): number#

Returns

tan(x: number): number#

`e`: `number`#

`huge`: `number`#

`nan`: `number`#

`phi`: `number`#

`pi`: `number`#

`sqrt2`: `number`#

`tau`: `number`#

`abs(x: number)`: number#

`acos(x: number)`: number#

`asin(x: number)`: number#

`atan(x: number)`: number#

`atan2(y: number, x: number)`: number#

`ceil(x: number)`: int#

`clamp(x: number, min: number, max: number)`: number#

`cos(x: number)`: number#

`cosh(x: number)`: number#

`deg(x: number)`: number#

`exp(x: number)`: number#

`floor(x: number)`: int#

`fmod(x: number, y: number)`: number#

`frexp(x: number)`: number, int#

`isfinite(x: number)`: boolean#

`isinf(x: number)`: boolean#

`isnan(x: number)`: boolean#

`ldexp(x: number, e: int)`: number#

`lerp(a: number, b: number, t: number)`: number#

`log(x: number, base: number = 2.7182818)`: number#

`log10(x: number)`: number#

`map(x: number, inmin: number, inmax: number, outmin: number, outmax: number)`: number#

`max(x: number, ...: number)`: number#

`min(x: number, ...: number)`: number#

`modf(x: number)`: number, number#

`noise(x: number, y: number = 0, z: number = 0)`: number#

`pow(x: number, y: number)`: number#

`rad(x: number)`: number#

`random(m: number = 0, n: number = 1)`: number#

`randomseed(x: number)`: ()#

`round(x: number)`: number#

`sign(x: number)`: int#

`sin(x: number)`: number#

`sinh(x: number)`: number#

`sqrt(x: number)`: number#

`tan(x: number)`: number#

`tanh(x: number)`: number#