API docs for Lua's math module.

math.random(m?, n?)

Returns a random number.

• random() returns a random float in range [0,1)
• random(m) returns a random integer in range [1,m]
• random(m,n) returns a random integer in range [m,n]

Example:

print(math.random())      -- prints: 0.123456789 (random float between 0 and 1)
print(math.random(10))    -- prints: 5 (random integer between 1 and 10)
print(math.random(5, 10)) -- prints: 7 (random integer between 5 and 10)

math.abs(x)

Returns the absolute value of x.

Example:

print(math.abs(-5))  -- prints: 5
print(math.abs(5))   -- prints: 5

math.ceil(x)

Returns the smallest integer greater than or equal to x.

Example:

print(math.ceil(4.2))   -- prints: 5
print(math.ceil(-4.2))  -- prints: -4

math.floor(x)

Returns the largest integer less than or equal to x.

Example:

print(math.floor(4.8))   -- prints: 4
print(math.floor(-4.8))  -- prints: -5

Note: math.floor(x + 0.5) rounds to closest integer, similar to round(x) function from other languages

math.max(...)

Returns the maximum value among its arguments.

Example:

print(math.max(1, 2, 3, 4, 5))  -- prints: 5
print(math.max(-10, -5, -1))    -- prints: -1

math.min(...)

Returns the minimum value among its arguments.

Example:

print(math.min(1, 2, 3, 4, 5))  -- prints: 1
print(math.min(-10, -5, -1))    -- prints: -10

math.fmod(x, y)

Returns the remainder of the division of x by y that rounds the quotient towards zero.

Example:

print(math.fmod(10, 3))    -- prints: 1
print(math.fmod(-10, 3))   -- prints: -1

math.modf(x)

Returns two numbers, the integral part of x and the fractional part of x.

Example:

local intPart, fracPart = math.modf(3.14)
print(intPart, fracPart)   -- prints: 3    0.14

math.exp(x)

Returns the value e^x (where e is the base of natural logarithms).

Example:

print(math.exp(0))    -- prints: 1
print(math.exp(1))    -- prints: 2.7182818284590455

math.log(x, base?)

Returns the logarithm of x in the given base. If base is not specified, returns the natural logarithm of x.

Example:

print(math.log(10))       -- prints: 2.302585092994046 (natural log)
print(math.log(100, 10))  -- prints: 2 (log base 10)

math.pow(x, y)

Returns x^y.

Example:

print(math.pow(2, 3))   -- prints: 8
print(math.pow(10, 2))  -- prints: 100

math.sqrt(x)

Returns the square root of x.

Example:

print(math.sqrt(16))   -- prints: 4
print(math.sqrt(2))    -- prints: 1.4142135623730951

math.cos(x)

Returns the cosine of x (in radians).

Example:

print(math.cos(0))          -- prints: 1
print(math.cos(math.pi))    -- prints: -1

math.sin(x)

Returns the sine of x (in radians).

Example:

print(math.sin(0))                  -- prints: 0
print(math.sin(math.pi / 2))        -- prints: 1

math.tan(x)

Returns the tangent of x (in radians).

Example:

print(math.tan(0))             -- prints: 0
print(math.tan(math.pi / 4))   -- prints: 1

math.acos(x)

Returns the arc cosine of x (in radians).

Example:

print(math.acos(1))    -- prints: 0
print(math.acos(0))    -- prints: 1.5707963267948966 (pi/2)

math.asin(x)

Returns the arc sine of x (in radians).

Example:

print(math.asin(0))    -- prints: 0
print(math.asin(1))    -- prints: 1.5707963267948966 (pi/2)

math.atan(y, x?)

Returns the arc tangent of y/x (in radians). If x is not provided, returns the arc tangent of y (in radians).

Example:

print(math.atan(1))        -- prints: 0.7853981633974483 (pi/4)
print(math.atan(1, 1))     -- prints: 0.7853981633974483 (pi/4)

math.cosh(x)

Returns the hyperbolic cosine of x.

Example:

print(math.cosh(0))   -- prints: 1

math.sinh(x)

Returns the hyperbolic sine of x.

Example:

print(math.sinh(0))   -- prints: 0

math.tanh(x)

Returns the hyperbolic tangent of x.

Example:

print(math.tanh(0))   -- prints: 0

math.deg(x)

Converts angle x from radians to degrees.

Example:

print(math.deg(math.pi))      -- prints: 180
print(math.deg(math.pi/2))    -- prints: 90

math.rad(x)

Converts angle x from degrees to radians.

Example:

print(math.rad(180))    -- prints: 3.141592653589793
print(math.rad(90))     -- prints: 1.5707963267948966

math.ult(m, n)

Returns a boolean, true if integer m is below integer n when they are compared as unsigned integers.

Example:

print(math.ult(2, 3))     -- prints: true
print(math.ult(-1, 1))    -- prints: false (as unsigned integers)

Non-standard Extensions

math.cosineSimilarity(vecA, vecB)

Returns the cosine similarity between two vectors.

Example:

local vec1 = {1, 2, 3}
local vec2 = {4, 5, 6}
print(math.cosineSimilarity(vec1, vec2))  -- prints: 0.9746318461970762