Lua Coding Docs: Library Methods ‐ Mathematical Methods

Mathematical Methods

math.min(multi:Float...):Float

Finds the minimum number by searching through each argument passed until it finds one.

• multi - An infinite parameter, The multiple number arguments to find the minimum number.

Examples:

debugPrint( math.min(43, 34, 19, 34)    )    --> 19
debugPrint( math.min(1.34, 0.37, 94.34) )    --> 0.37
debugPrint( math.min(0x83, 0x8a, 0xff)  )    --> 131

debugPrint( math.min(-43, -34, -19, -34)   ) --> -43
debugPrint( math.min(-1.34, -0.37, -94.34) ) --> -94.34
debugPrint( math.min(-0x83, -0x8a, -0xff)  ) --> -255

math.max(multi:Float...):Float

Finds the maximum number by searching through each argument passed until it finds one.

• multi - An infinite parameter, The multiple number arguments to find the maximum number.

Example:

debugPrint( math.max(43, 34, 19, 34)    )    --> 43
debugPrint( math.max(1.34, 0.37, 94.34) )    --> 94.34
debugPrint( math.max(0x83, 0x8a, 0xff)  )    --> 255

debugPrint( math.max(-43, -34, -19, -34)   ) --> -19
debugPrint( math.max(-1.34, -0.37, -94.34) ) --> -0.37
debugPrint( math.max(-0x83, -0x8a, -0xff)  ) --> -131

math.floor(num:Float):Float

Rounds down a floating-point number to its nearest integer value.

• num - The number to round down closest integer number.

Example:

debugPrint( math.floor(93.73) ) --> 93
debugPrint( math.floor(54.23) ) --> 54

math.ceil(num:Float):Float

Rounds up a floating-point number to its nearest integer value.

• num - The number to round up closest integer number.

Example:

debugPrint( math.floor(93.73) ) --> 94
debugPrint( math.floor(54.23) ) --> 55

math.abs(num:Float):Float

The absolute value from a given number, distance of the number from $0$.

• num - The number to returns its absolute number.

Example:

debugPrint( math.abs(-47) ) --> 47
debugPrint( math.abs(47)  ) --> 47

math.sqrt(rad:Float):Float

The square root of the given number.

• num - The radicand of the given number.

Example:

debugPrint( math.sqrt(4) ) --> 2
debugPrint( math.sqrt(2) ) --> 1.4142135623731

math.modf(num:Float):<Int, Float>

Returns the floating-point integral part (integer) and fractional part (decimal places).

• num - The floating-point to split into integral and fractional parts.

Example:

local int, frc = math.modf(364.36452)
debugPrint(int) --> 364
debugPrint(frc) --> 0.36452

math.log(num:Float, ?base:Float = 2):Float

The logarithmic of a number to the base, inverse (opposite) of exponential. Which makes the base number is the exponent must be raised to produced the number. For an example, since $\log_{2}(8)=3$, its inverse equivalent is $2^3=8$.

Caution

Logarithms cannot have negative numbers and the base must be above $1$. Remember it is the inverse of exponential, so if you're saying $\log_{2}(-8)=n$ then its inverse is $2^n=-8$, which is impossible to do. If we try using base one $1$ let's say $\log_{1}(5)=n$ its inverse is $1^5=n$, again impossible because $1^5$ is always equal to $1$.

• num - The logarithmic of the given number to its base.
• base - An optional parameter, The logarithmic base number; Default value: 2.

Example:

debugPrint( math.log(32, 2) ) --> 5.0
debugPrint( math.log(13, 2) ) --> 3.7004397181411

math.log10(num:Float):Float

The logarithmic of a number to the base of $10$, the common logarithm.

• num - The logarithmic of the given number to the base ten $10$.

Example:

debugPrint( math.log10(1000) ) --> 3.0
debugPrint( math.log10(567)  ) --> 2.7535830588929

math.random(?min:Int = 0, ?max:Int = 1):Float

Randomizes a number between the minimum to maximum numbers. It utilizes a Pseudo-Random Number Generator (PRNG), an mathematical algorithm that takes use of formulas. To produce a sequences of random numbers; utilizing a seed to initializing the PRNG.

Since it's not truly "random", due to computer limitations. It will always return the exact same number sequences, even if you try restarting it will still generate the exact same number sequences. That's because it uses the same seed that the PRNG utilizes within that script.

Tip

If you want to generate an "actually" random number, you can either both use. The getRandomInt() function for integer numbers and getRandomFloat() function for floating-point numbers. Or use the math.randomseed() method to change its current seed to generate different random number sequences.

• min - An optional parameter, the minimum number value range to start randomizing; Default value: 0.
• max - An optional parameter, the maximum number value range to end randomizing; Default value: 1.

Example:

debugPrint( math.random()     ) --> 0.84018771676347
debugPrint( math.random(1, 6) ) --> 5

math.randomseed(seed:Int):Int

Sets the seed of the pseudo-random number generator; equal seeds produce equal sequences of numbers.

Tip

Highly recommended to use os.time() method, this returns every second from the Unix Epoch Time, which initially starts at: 00:00:00 UTC on 1 January 1970. Making the seed change every second thus making it actually random.

• seed - The specified seed to generate a new random number sequence.

Examples:

math.randomseed(103)
debugPrint( math.random(4, 6)  ) --> 5
debugPrint( math.random(1, 40) ) --> 37

math.randomseed(os.time())
debugPrint( math.random(4, 6)  ) --> 4
debugPrint( math.random(1, 40) ) --> 23

Trigonometry Methods

math.rad(deg:Float):Float

Converts a radians to degrees.

• deg - The degree number to convert to radians.

Example:

debugPrint( math.rad(90)  ) --> 1.5707963267949 or (1/2)π
debugPrint( math.rad(180) ) --> 3.1415926535898 or π
debugPrint( math.rad(30)  ) --> 0.5235987755983 or (1/6)π

math.deg(rad:Float):Float

Converts a degrees to radians.

• rad - The radian number to convert to degrees.

Example:

debugPrint( math.deg( math.pi/2 )   ) --> 90.0
debugPrint( math.deg( 6*math.pi/6 ) ) --> 180.0
debugPrint( math.deg( 8*math.pi/6 ) ) --> 240.0

math.sin(rad:Float):Float

Returns the sine of the number, given in radians.

• rad - The radians to calculate the sine value.

Example:

debugPrint(math.sin(180))         --> -0.80115263573383
debugPrint(math.sin(360))         --> 0.95891572341431
debugPrint(math.sin(2 * math.pi)) --> -2.4492935982947e-16

math.cos(rad:Float):Float

Returns the cosine of the number, given in radians.

• rad - The radians to calculate the cosine value.

Example:

debugPrint(math.cos(180))         --> -0.59846006905786
debugPrint(math.cos(360))         --> -0.28369109148653
debugPrint(math.cos(2 * math.pi)) --> 1.0

math.tan(rad:Float):Float

Returns the tangent of the number, given in radians.

• rad - The radians to calculate the tangent value.

Example:

debugPrint(math.tan(180))         --> 1.3386902103512
debugPrint(math.tan(360))         --> -3.380140413961
debugPrint(math.tan(2 * math.pi)) --> -2.4492935982947e-16

math.asin(rad:Float):Float

Returns the arc (inverse) sine of the number, given in radians. Returns between $-\frac{\pi}{2}$ radians ($-90^\circ$ degrees) and $\frac{\pi}{2}$ radians ($90^\circ$ degrees).

• rad - The radians to calculate the inverse sine value; Goes from -1 to 1.

Example:

debugPrint( math.asin(-1) ) --> -1.5707963267949 or -(1/2)π
debugPrint( math.asin(0)  ) --> 0.0
debugPrint( math.asin(1)  ) --> 1.5707963267949  or (1/2)π

math.acos(rad:Float):Float

Returns the arc (inverse) cosine of the number, given in radians. Returns between $\pi$ radians ($180^\circ$ degrees) and $0$ radians ($0^\circ$ degrees).

• rad - The radians to calculate the inverse cosine value; Goes from -1 to 1.

Example:

debugPrint( math.acos(-1) ) --> 3.1415926535898 or π
debugPrint( math.acos(0)  ) --> 1.5707963267949 or π/2
debugPrint( math.acos(1)  ) --> 0.0

math.atan(rad:Float):Float

Returns the arc (inverse) tangent of the number, given in radians. Returns between $-\frac{\pi}{2}$ radians ($-90^\circ$ degrees) and $\frac{\pi}{2}$ radians ($90^\circ$ degrees).

• rad - The radians to calculate the inverse tangent value.

Example:

debugPrint( math.atan(-1) ) --> -0.78539816339745 or -(π/4)
debugPrint( math.atan(0)  ) --> 0.0
debugPrint( math.atan(1)  ) --> 0.78539816339745  or π/4

math.atan2(y:Float, x:Float):Float

Returns the calculated arc (inverse) tangent of x and y coordinate points, given in radians. Between the between the positive x-axis and the ray from the origin to the x and y coordinate points in the Cartesian plane.

• y - The given y position to calculate.
• x - The given x position to calculate.

Example:

Calculates the given x and y coordinate plane degrees.

local calcDeg = function() -- i stole this example
     return (math.atan2(y, x) * 180) / math.pi
end

debugPrint( calcDeg(10, 10)   ) --> 45.0
debugPrint( calcDeg(180, 0)   ) --> 90.0
debugPrint( calcDeg(270, 180) ) --> 56.30993247402

math.sinh(rad:Float):Float

Returns the hyperbolic sine of the number, given in radians.

• rad - The radians to calculate the hyperbolic sine value.

Example:

debugPrint( math.sinh(1)  ) --> 1.1752011936438
debugPrint( math.sinh(0.3)) --> 0.30452029344714
debugPrint( math.sinh(-5) ) --> -74.203210577789

math.cosh(rad:Float):Float

Returns the hyperbolic cosine of the number, given in radians.

• rad - The radians to calculate the hyperbolic cosine value.

Example:

debugPrint( math.cosh(1)   ) --> 1.5430806348152
debugPrint( math.cosh(0.3) ) --> 1.0453385141289
debugPrint( math.cosh(-5)  ) --> 74.209948524788

math.tanh(rad:Float):Float

Returns the hyperbolic tangent of the number, given in radians.

• rad - The radians to calculate the hyperbolic tangent value.

Example:

debugPrint( math.tanh(1)   ) --> 0.76159415595576
debugPrint( math.tanh(0.3) ) --> 0.29131261245159
debugPrint( math.tanh(-5)  ) --> -0.9999092042626

Constants

math.pi

The constant value of pi $\pi$ in $14$ fractional digits; Returns: 3.1415926535898.

math.huge

The constant value of "infinity", any number that is greater than or equal to $2^{1024}$; Returns inf.