Floating-point Comparison
0.1 + 0.2 ≠ 0.3
See also this article for a detailed discussion on comparing floating-point numbers.
Comparing floating-point numbers are tricky because they often fail miserably and unexpectedly.
Take the infamous 0.1 + 0.2 ≠ 0.3 example from most languages:
// JavaScript example
let x = 0.3; // 0.3
let y = 0.1 + 0.2; // 0.3?
console.log(x == y); // false!
console.log(x); // 0.3
console.log(y); // 0.30000000000000004
Epsilon-Based Implementation
If the unchecked feature is enabled, then all floating-point comparisons are done as per IEEE 754 standard.
The IEEE 754 standard for floating-point arithmetic provides an epsilon value that can be used to compare floating-point numbers.
With max_diff = max(|x|, |y|) × epsilon, Rhai compares floating-point numbers based on the following:
| operator | operands | algorithm |
|---|---|---|
x == y | has zero | |x - y| < epsilon |
x == y | both non-zero | |x - y| < |
x != y | has zero | |x - y| ≥ epsilon |
x != y | both non-zero | |x - y| ≥ max_diff |
x > y | has zero | x - y ≥ epsilon |
x > y | both non-zero | x - y ≥ max_diff |
x >= y | has zero | x - y ≥ –epsilon |
x >= y | both non-zero | x - y ≥ –max_diff |
x < y | has zero | y - x ≥ epsilon |
x < y | both non-zero | y - x ≥ max_diff |
x <= y | has zero | y - x ≥ –epsilon |
x <= y | both non-zero | y - x ≥ –max_diff |
Casual Scripting Usage
For most scripts that casually compare floating-point numbers, the default behavior is sufficient to cover all bases:
let x = 1e-16; // 0.0000000000000001
x > 0 == false; // comparing with zero Just Works when value is very small
x == 0 == true;
let x = 1e-15; // 0.000000000000001
x > 0 == true; // comparing with zero when value above epsilon
x == 0 == false;
let x = 1e-28; // 0.0000000000000000000000000001
let y = 1e-29; // 0.00000000000000000000000000001, 10x smaller than 'x'
x > y == true; // comparing very small numbers actually wide apart!
let x = 0.00000000000000000001;
let y = 0.000000000000000000010000000000000001;
x < y == false; // difference is small enough for 'x' == 'y'
let y = 0.00000000000000000001000000000000001;
x < y = true; // difference is not small enough for 'x' == 'y'