Lua Numbers
Numbers Tutorial
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Internal representation
Some languages support one or more of the following number types by default:
Integer
Unlimited precision integer
Single precision floating point
Double precision floating point
Complex fun
In the interest of simplicity Lua supports only one type of number: floating point numbers. By default these are double precision floating point numbers. However Lua can easily be recompiled to support single precision floating point numbers should you so desire. If you are unfamiliar with floating point it may be advantageous for you to read about FloatingPoint numbers.
The main thing to remember is that if you use numbers with fractional parts (or division), they may have a rounding error.
Also numbers which have infinitely repeating patterns in decimal will not have them in binary, so don’t assume that any fractional number is “safe”. The main thing to remember is don’t use the == operator with fractional numbers since it checks for perfect equality. The other thing to remember is to write your code so that rounding error can’t build up to large amounts over time.
If your numbers are integers (with no fractional part), and they don’t reach 2^53; then you won’t need to worry about these issues.
Using numbers
We can use the Lua interactive command line prompt as a calculator by prefixing an expression by =, e.g.,
Lua 5.1 Copyright (C) 1994-2006 Lua.org, PUC-Rio
> = 1
1
> = 1 + 2
3
> = 3.1415927
3.1415927
> = 5 / 6
0.83333333333333
We can enter numbers and evaluate simple calculations. Lua can also understand exponent types for expressing numbers in the form
> = 1.2345e6
1234500
> = 543.21E8
54321000000
> = 2.56e-4
0.000256
We can assign numbers to variables and do arithmetic:
> width = 7.5
> height = 12.7
> = width * height
95.25
> depth = 2.8
> area = width * height
> volume = area * depth
> print(area, volume)
95.25 266.7
The math library
Lua is equipped with a math library (see section 5.6 of the Reference Manual [1]). The functions provided are as follows:
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.ldexp math.log
math.log10 math.max math.min math.modf math.pow
math.rad math.random math.randomseed math.sin math.sinh
math.sqrt math.tan math.tanh
We’ll try a few of the functions and variables as an example.
> = math.sqrt(101)
10.049875621121
> = math.pi
3.1415926535898
> = math.sin( math.pi/3 )
0.86602540378444
Read the MathLibraryTutorial for more details.
Conversion
You can convert strings to numbers using the function tonumber(). This takes a string argument and returns a number.
> = tonumber("123") + 25
148
> x = tonumber("123.456e5")
> print(x)
12345600
Coercion
Lua will automatically convert string and number types to the correct format to perform calculations. For example: if you try to apply an arithmetic operation to a string Lua will try to convert that string to a number first. Otherwise the operation will not work. If the string cannot be converted to a number an error is raised. This automatic conversion of types is called coercion.
> = 100 + "7"
107
> = "1000" + 234
1234
> = "hello" + 234
stdin:1: attempt to perform arithmetic on a string value
stack traceback:
stdin:1: in main chunk
[C]: ?
> = 234 + "1000"
1234
You can see the calculation succeeds where a string was converted to number. The string “hello” cannot be converted to a number and so an error occurs. In statically typed languages (e.g. C) this would cause an error because you cannot assign a value to a variable of an incompatible type without a cast. This works in Lua because it is dynamically typed.
A notable exception: comparison operators (== ~= < > <= >=) do not coerce their arguments. The (in)equality operators consider a number to be not equal to its string representation (or any non-number type in fact). Ordered comparison operators throw an error when you feed them different types.
> = 100 == "100"
false
> = 100 ~= "hello"
true
> = 100 ~= {}
true
> = 100 == tonumber("100")
true
> = 100 <= "100"
stdin:1: attempt to compare number with string
stack traceback:
stdin:1: in main chunk
[C]: ?
For performance reasons you should avoid relying on automatic coercion too much. Make sure that all numbers in performance sensitive computations (especially in inner loops) are of the proper type. RecentChanges · preferences edit · history Last edited August 4, 2014 10:43 am GMT (diff)