Comment by Sharlin

For what it's worth, here's the Rust std implementation [1] of the total (as in, makes NaNs comparable) comparison algorithm given by IEE 751:

  let mut left = self.to_bits() as i32;
  let mut right = other.to_bits() as i32;

  // In case of negatives, flip all the bits except the sign
  // to achieve a similar layout as two's complement integers

  left ^= (((left >> 31) as u32) >> 1) as i32;
  right ^= (((right >> 31) as u32) >> 1) as i32;

  left.cmp(&right)

[1] https://doc.rust-lang.org/src/core/num/f32.rs.html#1348