Math

Standard constants and functions related to mathematics and numerical computation are assigned the namespace of Math:.

Constants

The type is all num.

Name	Description	Rough Value
`Math:Infinity`	Positive infinity	N/A
`Math:E`	Napier number $e$	`2.718281828459045`
`Math:LN2`	Natural logarithm of 2	`0.6931471805599453`
`Math:LN10`	Natural logarithm of 10	`2.302585092994046`
`Math:LOG2E`	Logarithm of $e$ with base 2	`1.4426950408889634`
`Math:LOG10E`	Logarithm of $e$ with base 10	`0.4342944819032518`
`Math:PI`	Pi $π$	`3.141592653589793`
`Math:SQRT1_2`	$\sqrt{\frac{1}{2}}$	`0.7071067811865476`
`Math:SQRT2`	$\sqrt{2}$	`1.4142135623730951`

Basic Functions

@Math:abs(x: num): num

Calculate absolute value. $| x |$

@Math:sign(x: num): num

Returns 1 if $x$ is positive, -1 if it is negative, and the same value if it is 0 or -0.
Returns NaN if $x$ is neither.

@Math:round(x: num): num

Returns the nearest integer, rounded to the nearest whole number.

@Math:ceil(x: num): num

Returns the smallest integer greater than or equal to the argument.

@Math:floor(x: num): num

Returns the largest integer less than or equal to the argument.

@Math:trunc(x: num): num

Truncates the decimal portion of the argument and returns the integer portion. $[x]$

@Math:min(a: num, b: num): num

Returns the smaller value.

@Math:max(a: num, b: num): num

Returns the larger value.

@Math:sqrt(x: num): num

Computes the positive square root. $\sqrt{x}$

@Math:cbrt(x: num): num

Calculate the cubic root. $\sqrt[3]{x}$

@Math:hypot(vs: arr): num

Returns the positive square root of the sum of the elements of vs after squaring each of them. $\sqrt{v_{1}^{2} + v_{2}^{2} + \dots + v_{n}^{2}}$

Trigonometric Functions

Hereafter, all angles are in radians.

@Math:sin(rad: num): num

Returns sine.

@Math:cos(rad: num): num

Returns cosine.

@Math:tan(rad: num): num

Returns tangent.

@Math:asin(x: num): num

Returns arcsine.

@Math:acos(x: num): num

Returns arccosine.

@Math:atan(x: num): num

Returns arctangent.

@Math:atan2(y: num, x: num): num

Returns the tangent of $\frac{y}{x}$ , but if $x$ is negative, returns a value off by $π$ .

Hyperbolic Functions

@Math:sinh(x: num): num

Returns hyperbolic sine.

@Math:cosh(x: num): num

Returns hyperbolic cosine.

@Math:tanh(x: num): num

Returns hyperbolic tangent.

@Math:asinh(x: num): num

Returns hyperbolic arcsine.

@Math:acosh(x: num): num

Returns hyperbolic arccosine.

@Math:atanh(x: num): num

Returns hyperbolic arctangent.

Exponential / Logarithmic Functions

@Math:pow(x: num, y: num): num

Returns the y power of x. Almost identical to Core:pow except that it internally uses the Math.pow function instead of Javascript's ** operator.

@Math:exp(x: num): num

Returns the x power of $e$ .

@Math:expm1(x: num): num

Returns the x power of $e$ minus 1.

@Math:log(x: num): num

Returns the natural logarithm. Use Math:log10 for the ordinary logarithm.

@Math:log1p(x: num): num

Returns the natural logarithm of x + 1.

@Math:log10(x: num): num

Returns the logarithm with 10 as the base (ordinary logarithm).

@Math:log2(x: num): num

Returns the logarithm with 2 as the base.

Random Generators

@Math:rnd(min?: num, max?: num): num

Generates random numbers.
If min and max are passed, integers with min <= x and x <= max are returned, otherwise decimals with 0 <= x and x < 1 are returned.

@Math:gen_rng(seed: num | str, options?: obj): @(min?: num, max?: num)

Generates a random number generator from the seed.
The generated random number generator returns an integer with min <= x, x <= max if min and max are passed,
If not passed, it returns a floating point number with 0 <= x, x < 1.
You can specify the internal behavior through the object passed to options.
The change in behavior by specifying options.algorithm is shown below:

`options.algorithm`	Internal randomize algorhythm	Range-specified integer generation algorithm
`rc4`	RC4	Rejection Sampling
`rc4_legacy`	RC4	Range limitation by floating-point arithmetic (pre-0.19.0 algorithm)
Not specified, or `chacha20`	ChaCha20	Rejection Sampling

aiscript

let rng = Math:gen_rng('AICHAN')

// Seed value is fixed, so under the same conditions,
// the same generation pattern will be generated each time.
<: rng(0, 10)
<: rng(0, 10)
<: rng(0, 10)

WARNING

Range-specified integer generation algorithms with floating-point arithmetic, such as rc4_legacy, may generate values larger than the specified max value due to rounding errors during arithmetic.

Misc.

@Math:clz32(x: num): num

Returns the number of leading zeros when x is represented in 32-bit binary.

@Math:fround(x: num): num

Returns the value when x is converted to a 32-bit floating-point number.

@Math:imul(x: num, y: num): num

Returns the result of a C-like 32-bit multiplication of x and y.

Math ​

Constants ​

Basic Functions ​

@Math:abs(x: num): num ​

@Math:sign(x: num): num ​

@Math:round(x: num): num ​

@Math:ceil(x: num): num ​

@Math:floor(x: num): num ​

@Math:trunc(x: num): num ​

@Math:min(a: num, b: num): num ​

@Math:max(a: num, b: num): num ​

@Math:sqrt(x: num): num ​

@Math:cbrt(x: num): num ​

@Math:hypot(vs: arr): num ​

Trigonometric Functions ​

@Math:sin(rad: num): num ​

@Math:cos(rad: num): num ​

@Math:tan(rad: num): num ​

@Math:asin(x: num): num ​

@Math:acos(x: num): num ​

@Math:atan(x: num): num ​

@Math:atan2(y: num, x: num): num ​

Hyperbolic Functions ​

@Math:sinh(x: num): num ​

@Math:cosh(x: num): num ​

@Math:tanh(x: num): num ​

@Math:asinh(x: num): num ​

@Math:acosh(x: num): num ​

@Math:atanh(x: num): num ​

Exponential / Logarithmic Functions ​

@Math:pow(x: num, y: num): num ​

@Math:exp(x: num): num ​

@Math:expm1(x: num): num ​

@Math:log(x: num): num ​

@Math:log1p(x: num): num ​

@Math:log10(x: num): num ​

@Math:log2(x: num): num ​

Random Generators ​

@Math:rnd(min?: num, max?: num): num ​

@Math:gen_rng(seed: num | str, options?: obj): @(min?: num, max?: num) ​

Misc. ​

@Math:clz32(x: num): num ​

@Math:fround(x: num): num ​

@Math:imul(x: num, y: num): num ​