math.isnan, math.isinf and math.isfinite for Math Library

Summary

This RFC proposes a math.isnan, a math.isinf, and a math.isfinite function to be added to the math library. These functions will validate that numbers are not NaN and are “finite” (non-NaN non-inf valid numbers) respectively.

Motivation

Currently, determinating if a value is NaN requires non-obvious and non-semantic check x ~= x. Determining if a number is finite requires a verbose check that handles both NaN and Inf cases, typically like x == x & math.abs(x) ~= math.huge. Checking specifically for Infinity also requires a manual check like math.abs(x) == math.huge.

Adding explicit math.isnan(x), math.isinf(x) and math.isfinite(x) functions brings Luau’s math library in line with modern languages (such as C++, JavaScript, Python, etc), improving code clarity, robustness and safety for mathemetical applications. In networked environments, validating numbers received from the client is a must and applicable across most games.

Design

We propose adding three new functions to the global math table:

math.isnan(x: number): boolean

Returns true if x is Not-a-Number (NaN), and false otherwise.

Example:

local x = 0 / 0 -- produces NaN
local y = 10

print(math.isnan(x)) -- true
print(math.isnan(y)) -- false

math.isinf(x: number): boolean

Returns true if x is positive or negative infinity (Inf), and false otherwise.

Example:

local x = math.huge
local y = 10

print(math.isinf(x)) -- true
print(math.isinf(y)) -- false
print(math.isinf(0 / 0)) -- false (NaN)

math.isfinite(x: number): boolean

Returns true if x is a finite number, meaning it is neither NaN nor positive or negative infinity (math.huge).

Example:

local x = math.huge
local y = 0 / 0
local z = 123.45

print(math.isfinite(x)) -- false
print(math.isfinite(y)) -- false
print(math.isfinite(z)) -- true

Drawbacks

1. Increased API: This proposal adds three new functions to the global math library, increasing the overall size of the standard library.
2. Redundancy for experienced developers: Experienced developers familiary with these checks, may view these functions as unnecessary syntactic sugar for the already fast and idiomatic check x ~= x and math.abs(x) ~= math.huge.

Alternatives

Alternative 1: Status Quo

Proposal: Do not add new functions. Continue to rely on checks for both.

Rejection: This sacrifices clarity and developer experience for the sake of library minimalism. The lack of standard functions makes code more brittle and harder to read, especially for newcomes to Luau.

Alternative 2: Only add math.isfinite

Proposal: Only add the primary utility check, math.isfinite(x), as it covers the most common use case (checking if a number is safe). Users could rely on idioms (x ~= x) for NaN and (math.abs(x) == math.huge) for Inf.