Math Module

Mathematical functions and constants.

The Math module provides standard mathematical operations. 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 (any numeric -> 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

Trait constraints

abs, negate, and sign are constrained by the Numeric trait, accepting Int, Float, or Decimal (e.g. abs : Numeric a => a -> a). Passing a String or Bool is a compile-time error.

Ordering functions min, max, and clamp are constrained by Ord a (e.g. min : Ord a => a -> a -> a). See the Traits guide for details.

Rounding functions (floor, ceil, round, truncate) accept any numeric type (Int, Float, or Decimal) and return Int. For Int input, the result is the identity.

Functions

Arithmetic

`Math.abs`

number -> number

Returns the absolute value of a number.

Example:

import Math

Math.abs (-5)

Notes: Works with Int, Float, and Decimal.

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`

number -> Int

Rounds a number down to the nearest integer.

Example:

import Math

Math.floor 3.7

Notes: Accepts Int (identity), Float, or Decimal.

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

`Math.ceil`

number -> Int

Rounds a number up to the nearest integer.

Example:

import Math

Math.ceil 3.2

Notes: Accepts Int (identity), Float, or Decimal.

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

`Math.round`

number -> Int

Rounds a number to the nearest integer.

Example:

import Math

Math.round 3.7

Notes: Rounds half away from zero (0.5 -> 1, -0.5 -> -1). Accepts Int (identity), Float, or Decimal.

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

`Math.truncate`

number -> Int

Truncate a number toward zero.

Example:

import Math

Math.truncate 3.9

Notes: Accepts Int (identity), Float, or Decimal.

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

Powers

`Math.sqrt`

Real a => a -> Maybe a

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

Example:

import Math
import Maybe

Math.sqrt 4.0 |> Maybe.withDefault 0.0

See also: Math.pow

`Math.pow`

Real a => a -> a -> Maybe a

Returns base raised to the power of exponent, or Nothing if the result is undefined. Accepts Float or Decimal.

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`

Real a => a -> Maybe a

Returns e raised to the given power, or Nothing if the result overflows. Accepts Float or Decimal.

Example:

import Math
import Maybe

Math.exp 1.0 |> Maybe.withDefault 0.0

See also: Math.log, Math.e

`Math.log`

Real a => a -> Maybe a

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

Example:

import Math
import Maybe

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

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

`Math.log2`

Real a => a -> Maybe a

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

Example:

import Math
import Maybe

Math.log2 8.0 |> Maybe.withDefault 0.0

-- 3.0

See also: Math.log, Math.log10

`Math.log10`

Real a => a -> Maybe a

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

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