Numbers Tutorial

wiki

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 numbers

In the interest of simplicity Lua supports only one type of number, floating point numbers. By default these are double precision floating point numbers, but 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.

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

> = 1.2345e6
1234500
> = 543.21E8
54321000000
> = 2.56e-4
0.000256

> 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

> = math.sqrt(101)
10.049875621121
> = math.pi
3.1415926535898
> = math.sin( math.pi/3 )
0.86602540378444

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 in order 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

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]: ?