Math Module

The aivi.math module provides standard numeric functions and constants for Int and Float. It is intentionally small, predictable, and aligned with common math libraries across languages.

Overview

use aivi.math

area = pi * r * r
clamped = clamp 0.0 1.0 x

Constants

pi : Float
tau : Float
e : Float
inf : Float
nan : Float
phi : Float
sqrt2 : Float
ln2 : Float
ln10 : Float

Angles

Angles are represented by a dedicated domain so trigonometric functions are not called with raw Float values.

Angle = { radians: Float }

Function	Explanation
radians value Float -> Angle	Creates an Angle from a raw radians value.

Function	Explanation
degrees value Float -> Angle	Creates an Angle from a raw degrees value.

Function	Explanation
toRadians angle Angle -> Float	Extracts the radians value from an Angle.

Function	Explanation
toDegrees angle Angle -> Float	Extracts the degrees value from an Angle.

Basic helpers

Function	Explanation
abs value Int -> Int	Returns the absolute value of value.
abs value Float -> Float	Returns the absolute value of value.

Function	Explanation
sign x Float -> Float	Returns -1.0, 0.0, or 1.0 based on the sign of x.
copysign mag sign Float -> Float -> Float	Returns mag with the sign of sign.

Function	Explanation
min a b Float -> Float -> Float	Returns the smaller of a and b.
max a b Float -> Float -> Float	Returns the larger of a and b.
minAll values List Float -> Option Float	Returns the minimum of values or None when empty.
maxAll values List Float -> Option Float	Returns the maximum of values or None when empty.

Function	Explanation
clamp low high x Float -> Float -> Float -> Float	Limits x to the closed interval [low, high].
sum values List Float -> Float	Sums values (empty list yields 0.0).
sumInt values List Int -> Int	Sums values (empty list yields 0).

Rounding and decomposition

Function	Explanation
floor x Float -> Float	Rounds toward -inf.
ceil x Float -> Float	Rounds toward +inf.
trunc x Float -> Float	Rounds toward 0.
round x Float -> Float	Uses banker's rounding (ties to even).
fract x Float -> Float	Returns the fractional part with the same sign as x.

Function	Explanation
modf x Float -> (Float, Float)	Returns (intPart, fracPart) where x = intPart + fracPart.
frexp x Float -> (Float, Int)	Returns (mantissa, exponent) such that x = mantissa * 2^exponent.
ldexp mantissa exponent Float -> Int -> Float	Computes mantissa * 2^exponent.

Powers, roots, and logs

Function	Explanation
pow base exp Float -> Float -> Float	Raises base to exp.
sqrt x Float -> Float	Computes the square root.
cbrt x Float -> Float	Computes the cube root.
hypot x y Float -> Float -> Float	Computes sqrt(x*x + y*y) with reduced overflow/underflow.

Function	Explanation
exp x Float -> Float	Computes e^x.
exp2 x Float -> Float	Computes 2^x.
expm1 x Float -> Float	Computes e^x - 1 with improved precision near zero.

Function	Explanation
log x Float -> Float	Computes the natural log.
log10 x Float -> Float	Computes the base-10 log.
log2 x Float -> Float	Computes the base-2 log.
log1p x Float -> Float	Computes log(1 + x) with improved precision near zero.

Trigonometry

Function	Explanation
sin angle Angle -> Float	Computes the sine ratio for angle.
cos angle Angle -> Float	Computes the cosine ratio for angle.
tan angle Angle -> Float	Computes the tangent ratio for angle.

Function	Explanation
asin x Float -> Angle	Returns the angle whose sine is x.
acos x Float -> Angle	Returns the angle whose cosine is x.
atan x Float -> Angle	Returns the angle whose tangent is x.
atan2 y x Float -> Float -> Angle	Returns the angle of the vector (x, y) from the positive x-axis.

Hyperbolic functions

Function	Explanation
sinh x Float -> Float	Computes hyperbolic sine.
cosh x Float -> Float	Computes hyperbolic cosine.
tanh x Float -> Float	Computes hyperbolic tangent.
asinh x Float -> Float	Computes inverse hyperbolic sine.
acosh x Float -> Float	Computes inverse hyperbolic cosine.
atanh x Float -> Float	Computes inverse hyperbolic tangent.

Integer math

Function	Explanation
gcd a b Int -> Int -> Int	Computes the greatest common divisor.
lcm a b Int -> Int -> Int	Computes the least common multiple.
gcdAll values List Int -> Option Int	Returns the gcd of all values or None when empty.
lcmAll values List Int -> Option Int	Returns the lcm of all values or None when empty.

Function	Explanation
factorial n Int -> BigInt	Computes n!.
comb n k Int -> Int -> BigInt	Computes combinations ("n choose k").
perm n k Int -> Int -> BigInt	Computes permutations ("n P k").

Function	Explanation
divmod	Int -> Int -> (Int, Int)
modPow	Int -> Int -> Int -> Int

Notes:

• BigInt is from aivi.number.bigint and is re-exported by aivi.math.

Floating-point checks

Function	Explanation
isFinite x Float -> Bool	Returns whether x is finite.
isInf x Float -> Bool	Returns whether x is infinite.
isNaN x Float -> Bool	Returns whether x is NaN.
nextAfter from to Float -> Float -> Float	Returns the next representable float after from toward to.
ulp x Float -> Float	Returns the size of one unit-in-the-last-place at x.

Remainders

Function	Explanation
fmod a b Float -> Float -> Float	Returns the remainder using truncation toward zero.
remainder a b Float -> Float -> Float	Returns the IEEE-754 remainder (round-to-nearest quotient).

Usage Examples

use aivi.math

angle = degrees 90.0
unit = sin angle

digits = [1.0, 2.0, 3.0] |> sum