is_zero() for floats does an exact comparison

[Mitchelldscott]

Should probably replace the is_zero() calls with something that supports relative eq/rounding errors. There is a comparison function for f32 and f64 in math::assert_f, should pull the logic out of the macro and use it in a custom Zero/One trait impl.

ChatGPT Explaination:

Great question — here's the core reason:

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❗ You should not use exact comparisons (like ==, or is_zero()) for f32 and f64 in most numerical code because floating-point arithmetic is inherently imprecise due to:

1. Rounding Errors

• Operations like addition, subtraction, multiplication, and division often result in small rounding differences that accumulate.

• For example:

  let x = 0.1 + 0.2;
  println!("{}", x == 0.3); // false!
  

2. Representation Limits

• Many decimal numbers cannot be exactly represented in binary floating-point. For example, 0.1 in f64 is actually:

  0.10000000000000000555...
  

3. is_zero() is an exact comparison

• num_traits::Float::is_zero() is implemented as self == T::zero(), which is an exact bitwise comparison — and that’s rarely what you want when checking results from computation.

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✅ What to Use Instead: Epsilon-based Approximate Comparison

This checks whether a number is close enough to zero (or another value), within a tolerance:

(x - y).abs() < EPSILON

Or use approx crate macros:

use approx::assert_relative_eq;
assert_relative_eq!(computed, expected, epsilon = 1e-12);

Or define a helper for near-zero:

fn is_near_zero(x: f64, tol: f64) -> bool {
    x.abs() < tol
}

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✅ When Exact Comparison Is Okay:

• You're comparing constants, not results of arithmetic:

  let a = 1.0f64;
  assert_eq!(a, 1.0); // fine
  

• You're working with types like u32, i32, or bool.

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Summary:

Comparison Type	Good Practice?	Use Instead
f64 == 0.0	❌ No	x.abs() < 1e-12 or approx crate
is_zero() on floats	❌ No	Custom is_near_zero(x, tol)
Comparing constants	✅ Yes	—

Let me know if you want a utility function or trait to handle approximate comparisons safely in your library.