Math Library Tutorial

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The math library is documented in section 5.6 of the Reference Manual.[1] Below is a summary of the functions and variables provided. Each is described, with an example, on this page.
math.abs   math.acos  math.asin  math.atan math.atan2 math.ceil
math.cos   math.cosh  math.deg   math.exp  math.floor math.fmod
math.frexp math.huge  math.ldexp math.log  math.log10 math.max
math.min   math.modf  math.pi    math.pow  math.rad   math.random
math.randomseed       math.sin   math.sinh math.sqrt  math.tanh
math.tan

math.abs

Return the absolute, or non-negative value, of a given value.
> = math.abs(-100)
100
> = math.abs(25.67)
25.67
> = math.abs(0)
0

math.acos , math.asin

Return the inverse cosine and sine in radians of the given value.
> = math.acos(1)
0
> = math.acos(0)
1.5707963267949
> = math.asin(0)
0
> = math.asin(1)
1.5707963267949

math.atan , math.atan2

Return the inverse tangent in radians. We can do this by supplying y/x ourselves using math.atan or we can pass y and x to math.atan2 to do this for us.
> c, s = math.cos(0.8), math.sin(0.8)
> = math.atan(s/c)
0.8
> = math.atan2(s,c)
0.8

math.atan2 should usually be preferred, particularly when converting rectangular co-ordinates to polar co-ordinates. math.atan2 uses the sign of both arguments to place the result into the correct quadrant, and also produces correct values when one of its arguments is 0 or very close to 0.

> = math.atan2(1, 0), math.atan2(-1, 0), math.atan2(0, 1), math.atan2(0, -1)
1.5707963267949 -1.5707963267949        0        3.1415926535898

math.ceil , math.floor

Return the integer no greater than or no less than the given value.
> = math.floor(0.5)
0
> = math.ceil(0.5)
1

math.cos , math.sin , math.tan

Return the cosine, sine and tangent value for a given value in radians.
> = math.cos(math.pi / 4)
0.70710678118655
> = math.sin(0.123)
0.12269009002432
> = math.tan(5/4)
3.0095696738628
> = math.tan(.77)
0.96966832796149

math.cosh , math.sinh , math.tanh

Return the hyperbolic cosine, hyperbolic sine, and hyperbolic tangent[2] value for a given value.

> = math.sinh(1)
1.1752011936438

math.deg , math.rad

Convert from radians to degrees and vice versa.
> = math.deg(math.pi)
180
> = math.deg(math.pi / 2)
90
> = math.rad(180)
3.1415926535898
> = math.rad(1)
0.017453292519943

math.exp , math.log

math.exp(myval) returns e (the base of natural logarithms) raised to the power myval. math.log() returns the inverse of this. math.exp(1) returns e.
> = math.exp(0)
1
> = math.exp(1)
2.718281828459
> = math.exp(27)
532048240601.8
> = math.log(532048240601)
26.999999999998
> = math.log(3)
1.0986122886681

math.log10

Return the base 10 logarithm of a given number. The number must be positive.
> = math.log10(100)
2
> = math.log10(256)
2.4082399653118
> = math.log10(-1)  -- can return -1.#INF on some Windows installs
nan

-- I get math.log10(-1) == -1.#IND and math.log10(0) == -1.#INF (MSVC2008), as I think it should be. --DavidManura

math.pow , x^y

math.pow() raises the first parameter to the power of the second parameter and returns the result. The binary ^ operator performs the same job as math.pow(), i.e. math.pow(x,y) == x^y.
> = math.pow(100,0)
1
> = math.pow(7,2)
49
> = math.pow(2,8)
256
> = math.pow(3,2.7)
19.419023519771
> = 5 ^ 2
25
> = 2^8
256

math.min , math.max

Return the minimum or maximum value from a variable length list of arguments.
> = math.min(1,2)
1
> = math.min(1.2, 7, 3)
1.2
> = math.min(1.2, -7, 3)
-7
> = math.max(1.2, -7, 3)
3
> = math.max(1.2, 7, 3)
7

math.modf

Return the integral and fractional parts of the given number.
> = math.modf(5)
5       0
> = math.modf(5.3)
5       0.3
> = math.modf(-5.3)
-5      -0.3

If you want the modulus (remainder), look for the modulo % operator instead.[3]

math.sqrt

Return the square root of a given number. Only non-negative arguments are allowed.
> = math.sqrt(100)
10
> = math.sqrt(1234)
35.128336140501
> = math.sqrt(-7)
-1.#IND

math.random , math.randomseed

math.random() generates pseudo-random numbers uniformly distributed. Supplying argument alters its behaviour:
> = math.random()
0.0012512588885159
> = math.random()
0.56358531449324
> = math.random(100)
20
> = math.random(100)
81
> = math.random(70,80)
76
> = math.random(70,80)
75
upper and lower must be integer. In other case Lua casts upper into an integer, sometimes giving math.floor(upper) and others math.ceil(upper), with unexpected results (the same for lower).

The math.randomseed() function sets a seed for the pseudo-random generator: Equal seeds produce equal sequences of numbers.

> math.randomseed(1234)
> = math.random(), math.random(), math.random()
0.12414929654836        0.0065004425183874      0.3894466994232
> math.randomseed(1234)
> = math.random(), math.random(), math.random()
0.12414929654836        0.0065004425183874      0.3894466994232

A good* 'seed' is os.time(), but wait a second before calling the function to obtain another sequence! To get nice random numbers use:

math.randomseed( os.time() )
If Lua could get milliseconds from os.time() the init could be better done. Another thing to be aware of is truncation of the seed provided. math.randomseed will call the underlying C function srand which takes an unsigned integer value. Lua will cast the value of the seed to this format. In case of an overflow the seed will actually become a bad seed, without warning [4] (note that Lua 5.1 actually casts to a signed int [5], which was corrected in 5.2).

Nevertheless, in some cases we need a controlled sequence, like the obtained with a known seed.

But beware! The first random number you get is not really 'randomized' (at least in Windows 2K and OS X). To get better pseudo-random number just pop some random number before using them for real:

-- Initialize the pseudo random number generator
math.randomseed( os.time() )
math.random(); math.random(); math.random()
-- done. :-)

-- This not exactly true. The first random number is as good (or bad) as the second one and the others. The goodness of the generator depends on other things. To improve somewhat the built-in generator we can use a table in the form:

-- improving the built-in pseudorandom generator
do
   local oldrandom = math.random
   local randomtable
   math.random = function ()
      if randomtable == nil then
         randomtable = {}
         for i = 1, 97 do
            randomtable[i] = oldrandom()
         end
      end
      local x = oldrandom()
      local i = 1 + math.floor(97*x)
      x, randomtable[i] = randomtable[i], x
      return x
   end
end

[6] : Why math.random() might give weird results on OSX and FreeBSD?

*...The problem seems to be that when the seeds differ very little the first value of generated by BSD rand() also differ very little. This difference is lost when Lua converts the integer returned by rand() into a real number, effectively preserving only the high bits in the result. When you call math.random(1,100) from Lua, the low-bit difference vanishes and you see the same integer result.

-- improve seeding on these platforms by throwing away the high part of time, 
-- then reversing the digits so the least significant part makes the biggest change
-- NOTE this should not be considered a replacement for using a stronger random function
-- ~ferrix
math.randomseed( tonumber(tostring(os.time()):reverse():sub(1,6)) )

There is also lrandom[7] A library for generating random numbers based on the Mersenne Twister.

math.frexp , math.ldexp

These are normalisation functions [8]. The math.frexp() function is used to split the number value into a normalized fraction and an exponent. Two values are returned: the first is a value always in the range 1/2 (inclusive) to 1 (exclusive) and the second is an exponent.The number value will be returned in the operation:
> = normalized_fraction * 2 ^ exponent
The math.ldexp() function takes a normalised number and returns the floating point representation. This is the value multiplied by 2 to the power of the exponent, i.e.:
> = math.ldexp(x, exp) == x * 2 ^ exp 
true

> = math.frexp(2)
0.5     2
> = math.frexp(3)
0.75    2
> = math.frexp(128)
0.5     8
> = math.frexp(3.1415927)
0.785398175     2
> = math.ldexp(0.785,2)
3.14
> = math.ldexp(0.5,8)
128

math.huge

math.huge is a constant. It represents +infinity.

> = math.huge
inf
> = math.huge / 2
inf
> = -math.huge
-inf
> = math.huge/math.huge   -- indeterminate
nan
> = math.huge * 0         -- indeterminate
nan
> = 1/0
inf
> = (math.huge == math.huge)
true
> = (1/0 == math.huge)
true

Note that some operations on math.huge return a special "not-a-number" value that displays as nan. This is a bit of a misnomer. nan is a number type, though it's different from other numbers:

> = type(math.huge * 0)
number

See also FloatingPoint.

math.pi

This is a part of the constant Pi.

> = math.pi
3.1415926535898

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Last edited November 16, 2014 10:06 pm GMT (diff)