How to compare floating-point numbers in Lua

In Lua, the number type represents real (double-precision floating-point) numbers. Lua does not have a separate integer type.

There’s a common misconception that floating-point numbers are unreliable even for simple operations like increments. However, when you use a double to represent integers (whole numbers), there is no rounding error—unless the number exceeds 253. In other words, Lua numbers can safely represent huge integers without rounding problems. Additionally, most modern CPUs handle floating-point arithmetic just as fast as integer ¹.

By default, Lua is compiled to use either single or double precision floating-point numbers. (You can check your configuration in luaconf.h). With double precision (64-bit floats), you are relatively safe. However, if Lua is compiled with single precision (32-bit floats), comparing numbers can become less reliable.

Consider the following example:

1/9 --> 0.11111111111111 (approximately 14 digits of 1)
1/9 == 1/9 --> true
0.11111111111111 == 0.11111111111111 --> true
1/9 == 0.11111111111111 --> false

This behavior occurs because of how floating-point numbers are represented internally in C and Lua using the IEEE 754² standard. When a number cannot be exactly represented, direct comparisons can produce unexpected results. This should always be in your head, there are very basics of programming.

Safer Float Comparison

This avoids hardly detected bugs, especially when doing math like money calculations, physics simulations, measurement, etc. Which might be critical in finance and game development.

It’s a good idea to use a helper function to safely compare two floating-point numbers:

---Compares two numbers for approximate equality, including edge cases.
---@param a number
---@param b number
---@param epsilon? number - Tolerance for precision (default: 0.000001)
---@return boolean
local function compareNumbers(a, b, epsilon)
    epsilon = epsilon or 1e-6
    return a == b or math.abs(a - b) < epsilon
end

When working with floats, using this function helps you avoid unexpected surprises when comparing values with floating-point.

print(compareNumbers(42, 42))                             -- true
print(compareNumbers(1/9, 1/9))                           -- true
print(compareNumbers(1/9, 0.11111111111111))              -- true
print(compareNumbers(0.11111111111111, 0.11111111111111)) -- true
print(compareNumbers(0, 0))                               -- true
print(compareNumbers(0, -0))                              -- true
print(compareNumbers(math.huge, math.huge))               -- true
print(compareNumbers(1e-6,  0.000001))                    -- true
print(compareNumbers(0.00001, 0.000001))                  -- false

References

Feedback

For feedback, please check the contacts section. Before writing, please specify where you came from and who you are. Sometimes spammers go insane. Thank you in advance for your understanding.