# Math Library Tutorial  wiki

The math library is documented in section 6.7 of the Reference Manual. 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.ceil
math.cos
math.deg
math.exp
math.floor
math.fmod
math.huge
math.log
math.max
math.maxinteger
math.min
math.mininteger
math.modf
math.pi
math.random
math.randomseed
math.sin
math.sqrt
math.tan
math.tointeger
math.type
math.ult
```

### 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

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

Using two arguments should usually be preferred, particularly when converting rectangular co-ordinates to polar co-ordinates. It will use 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.atan(1, 0), math.atan(-1, 0), math.atan(0, 1), math.atan(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 (even for negatives).
```> = math.floor(0.5)
0
> = math.ceil(0.5)
1
> = math.floor(-0.5)
-1
> = math.ceil(-0.5)
-0
```

### 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
```

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

### 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()` with no arguments generates a real number between 0 and 1.
• `math.random(upper)` generates integer numbers between 1 and upper (both inclusive).
• `math.random(lower, upper)` generates integer numbers between lower and upper (both inclusive).
```> = 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  (note that Lua 5.1 actually casts to a signed int , 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
```

 : 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 A library for generating random numbers based on the Mersenne Twister.

### 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
```

```> = math.pi