Math Module

Mathematical functions and constants.

The Math module provides standard mathematical operations. Many functions are polymorphic over numeric types using the number type variable, which accepts both Int and Float. Functions like sqrt and sin require Float arguments.

Common patterns

import Math

-- Basic arithmetic
Math.abs (-5)                  -- 5
Math.max 3 7                   -- 7
Math.clamp 0 100 150           -- 100

-- Rounding (Float -> Int)
Math.floor 3.7                 -- 3
Math.ceil 3.2                  -- 4
Math.round 3.5                 -- 4

-- Powers and roots
Math.sqrt 16.0                 -- 4.0
Math.pow 2.0 10.0              -- 1024.0

-- Trigonometry (radians)
Math.sin (Math.pi / 2.0)       -- 1.0
Math.atan2 1.0 1.0             -- 0.785... (pi/4)

-- Number theory (Int -> Int)
Math.gcd 12 8                  -- 4
Math.lcm 4 6                   -- 12

Type variables

number — Int or Float (e.g. abs : number -> number)
comparable — types that support ordering (e.g. min : comparable -> comparable -> comparable)

Rounding functions (floor, ceil, round, truncate) take Float and return Int. Use toFloat : Int -> Float to convert in the other direction.

Functions

Arithmetic

`Math.abs`

number -> number

Returns the absolute value of a number.

Example:

import Math

Math.abs (-5)

Notes: Works with both Int and Float.

See also: Math.negate, Math.sign

`Math.negate`

number -> number

Negate a number.

Example:

import Math

Math.negate 5

See also: Math.abs, Math.sign

`Math.sign`

number -> Int

Returns -1, 0, or 1 based on the sign of the number.

Example:

import Math

Math.sign 5

See also: Math.abs, Math.negate

`Math.rem`

Int -> Int -> Maybe Int

Returns the remainder of integer division (has the sign of the dividend). Returns Nothing when the divisor is 0.

Example:

import Math
import Maybe

Math.rem 7 3 |> Maybe.withDefault 0

Notes: Returns Nothing instead of erroring when the divisor is 0.

See also: Math.gcd

`Math.gcd`

Int -> Int -> Int

Returns the greatest common divisor of two integers.

Example:

import Math

Math.gcd 12 8

Notes: Always returns non-negative value.

See also: Math.lcm

`Math.lcm`

Int -> Int -> Int

Returns the least common multiple of two integers.

Example:

import Math

Math.lcm 4 6

Notes: Returns 0 if either input is 0.

See also: Math.gcd

Bounds

`Math.min`

number -> number -> number

Returns the smaller of two values.

Example:

import Math

Math.min 3 5

-- 3

Notes: Works with Int, Float, or mixed types.

See also: Math.max, Math.clamp, List.minimum

`Math.max`

number -> number -> number

Returns the larger of two values.

Example:

import Math

Math.max 3 5

-- 5

Notes: Works with Int, Float, or mixed types.

See also: Math.min, Math.clamp, List.maximum

`Math.clamp`

number -> number -> number -> number

Clamp a value to be within the range [min, max].

Example:

import Math

Math.clamp 0 10 15

See also: Math.min, Math.max

Rounding

`Math.floor`

Float -> Int

Rounds a float down to the nearest integer.

Example:

import Math

Math.floor 3.7

See also: Math.ceil, Math.round, Math.truncate

`Math.ceil`

Float -> Int

Rounds a float up to the nearest integer.

Example:

import Math

Math.ceil 3.2

See also: Math.floor, Math.round, Math.truncate

`Math.round`

Float -> Int

Rounds a float to the nearest integer.

Example:

import Math

Math.round 3.7

Notes: Rounds half away from zero (0.5 -> 1, -0.5 -> -1).

See also: Math.floor, Math.ceil, Math.truncate

`Math.truncate`

Float -> Int

Truncate a float towards zero.

Example:

import Math

Math.truncate 3.9

See also: Math.floor, Math.ceil, Math.round

Powers

`Math.sqrt`

Float -> Maybe Float

Returns the square root of a number, or Nothing if the input is negative.

Example:

import Math
import Maybe

Math.sqrt 4.0 |> Maybe.withDefault 0.0

See also: Math.pow

`Math.pow`

Float -> Float -> Maybe Float

Returns base raised to the power of exponent, or Nothing if the result is undefined (e.g. negative base with non-integer exponent).

Example:

import Math
import Maybe

Math.pow 2.0 3.0 |> Maybe.withDefault 0.0

-- 8.0

See also: Math.sqrt, Math.exp

`Math.exp`

Float -> Maybe Float

Returns e raised to the given power, or Nothing if the result overflows to infinity.

Example:

import Math
import Maybe

Math.exp 1.0 |> Maybe.withDefault 0.0

See also: Math.log, Math.e

`Math.log`

Float -> Maybe Float

Returns the natural logarithm of a number, or Nothing if the input is not positive.

Example:

import Math
import Maybe

Math.log Math.e |> Maybe.withDefault 0.0

See also: Math.log10, Math.log2, Math.exp

`Math.log2`

Float -> Maybe Float

Returns the base-2 logarithm of a number, or Nothing if the input is not positive.

Example:

import Math
import Maybe

Math.log2 8.0 |> Maybe.withDefault 0.0

-- 3.0

See also: Math.log, Math.log10

`Math.log10`

Float -> Maybe Float

Returns the base-10 logarithm of a number, or Nothing if the input is not positive.

Example:

import Math
import Maybe

Math.log10 100.0 |> Maybe.withDefault 0.0

-- 2.0

See also: Math.log, Math.log2

Trigonometry

`Math.sin`

Float -> Float

Returns the sine of an angle in radians.

Example:

import Math

Math.sin (Math.pi / 2.0)

See also: Math.cos, Math.tan, Math.asin

`Math.cos`

Float -> Float

Returns the cosine of an angle in radians.

Example:

import Math

Math.cos 0.0

-- 1.0

See also: Math.sin, Math.tan, Math.acos

`Math.tan`

Float -> Float

Returns the tangent of an angle in radians.

Example:

import Math

Math.tan 0.0

-- 0.0

See also: Math.sin, Math.cos, Math.atan

`Math.asin`

Float -> Maybe Float

Returns the arc sine in radians, or Nothing if the input is outside [-1, 1].

Example:

import Math
import Maybe

Math.asin 1.0 |> Maybe.withDefault 0.0

See also: Math.sin, Math.acos, Math.atan

`Math.acos`

Float -> Maybe Float

Returns the arc cosine in radians, or Nothing if the input is outside [-1, 1].

Example:

import Math
import Maybe

Math.acos 1.0 |> Maybe.withDefault 0.0

-- 0.0

See also: Math.cos, Math.asin, Math.atan

`Math.atan`

Float -> Float

Returns the arc tangent in radians.

Example:

import Math

Math.atan 1.0

See also: Math.tan, Math.atan2

`Math.atan2`

Float -> Float -> Float

Returns the arc tangent of y/x in radians, using signs to determine quadrant.

Example:

import Math

Math.atan2 1.0 1.0

-- 0.7853... (pi/4)

Notes: More robust than atan(y/x) for determining angle.

See also: Math.atan

Hyperbolic

`Math.sinh`

Float -> Maybe Float

Returns the hyperbolic sine, or Nothing if the result overflows to infinity.

Example:

import Math
import Maybe

Math.sinh 0.0 |> Maybe.withDefault 0.0

-- 0.0

See also: Math.cosh, Math.tanh

`Math.cosh`

Float -> Maybe Float

Returns the hyperbolic cosine, or Nothing if the result overflows to infinity.

Example:

import Math
import Maybe

Math.cosh 0.0 |> Maybe.withDefault 0.0

-- 1.0

See also: Math.sinh, Math.tanh

`Math.tanh`

Float -> Float

Returns the hyperbolic tangent.

Example:

import Math

Math.tanh 0.0

-- 0.0

See also: Math.sinh, Math.cosh

Constants

`Math.pi`

Float

The mathematical constant π (3.14159...).

Example:

import Math

Math.pi

See also: Math.e

`Math.e`

Float

Euler's number e (2.71828...).

Example:

import Math

Math.e

See also: Math.pi

Converting

`Math.toFloat`

Int -> Float

Convert an integer to a float.

Example:

import Math

Math.toFloat 42

-- 42.0

See also: Math.floor, Math.round

`Math.degrees`

Float -> Float

Convert radians to degrees.

Example:

import Math

Math.degrees Math.pi

See also: Math.radians

`Math.radians`

Float -> Float

Convert degrees to radians.

Example:

import Math

Math.radians 180.0

-- 3.14159... (pi)

See also: Math.degrees