math

Mathematical constants and functions. They take and return numbers. A result that is not a number, such as the square root of a negative number, is Undefined.

Constants

math.PI -> Numb
math.E -> Numb
math.INF -> Numb
math.INFINITY -> Numb

math.PI is π, math.E is Euler's number e, and math.INF and math.INFINITY are positive infinity. For negative infinity, write -(math.INF).

math.PI              # => 3.141592653589793
math.E               # => 2.718281828459045
-(math.INF)          # => -inf

Rounding

math.round x -> Numb
math.floor x -> Numb
math.ceil x -> Numb
math.trunc x -> Numb
math.abs x -> Numb

math.round rounds to the nearest whole number, and halfway cases away from zero. math.floor rounds down, math.ceil rounds up, and math.trunc drops the fraction. math.abs returns the absolute value.

math.round 2.5       # => 3
math.round (-2.5)    # => -3
math.floor (-1.5)    # => -2
math.ceil 1.2        # => 2
math.trunc (-1.7)    # => -1
math.abs (-3)        # => 3

To round to a number of decimals, scale first:

math.round (math.PI * 100) / 100         # => 3.14

Powers and logarithms

math.sqrt x -> Numb
math.exp x -> Numb
math.ln x -> Numb
math.log2 x -> Numb
math.log10 x -> Numb
math.pow exponent base -> Numb
math.log base x -> Numb

math.sqrt is the square root, math.exp x is e to the power x, and math.ln, math.log2 and math.log10 are the logarithms in base e, 2 and 10.

math.pow and math.log are curried, and take the fixed part first: math.pow exponent base is base ^ exponent, and math.log base x is the logarithm of x in base base.

math.sqrt 16         # => 4
math.sqrt (-1)       # => Undefined
math.log10 1000      # => 3
math.pow 2 5         # => 25
square = math.pow 2
(1, 2, 3) => square  # => (1, 4, 9)
math.log 2 8         # => 3

Trigonometry

math.sin x -> Numb
math.cos x -> Numb
math.tan x -> Numb
math.asin x -> Numb
math.acos x -> Numb
math.atan x -> Numb
math.atan2 x y -> Numb
math.hypot x y -> Numb

The trigonometric functions and their inverses work in radians. math.atan2 x y is the angle of the point (x, y) from the positive x axis, between -π and π. math.hypot x y is the distance of the point (x, y) from the origin.

math.sin 0           # => 0
math.cos math.PI     # => -1
math.atan2 1 1       # => 0.7853981633974483
math.hypot 3 4       # => 5

Hyperbolic functions

math.sinh x -> Numb
math.cosh x -> Numb
math.tanh x -> Numb
math.asinh x -> Numb
math.acosh x -> Numb
math.atanh x -> Numb

The hyperbolic functions and their inverses.

math.cosh 0          # => 1

math.max, math.min

math.max numbers -> Numb
math.min numbers -> Numb

Return the largest and the smallest item of the tuple numbers. They reduce the whole tuple to one value. Every item must be a number, and the tuple must not be empty; otherwise the result is Undefined.

math.max (1, 5, 2)   # => 5
math.min (1, 5, 2)   # => 1
math.max (list.enum [3, 9])    # => 9
math.max ()          # => Undefined