97 lines
3.5 KiB
Rust
97 lines
3.5 KiB
Rust
/// Compute how different two floats are in ulps.
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///
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/// Notes:
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/// - Treats 0.0 and -0.0 as zero ulps apart, and extends the
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/// implications of that to the rest of the numbers. E.g. the numbers
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/// just before and after 0.0/-0.0 are only two ulps apart, not three.
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/// - Infinity is one ulp past float max, and converse for -infinity.
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/// - If either number is NaN, returns `u32::MAX`.
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#[inline(always)]
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pub fn ulp_diff(a: f32, b: f32) -> u32 {
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const TOP_BIT: u32 = 1 << 31;
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const NAN_THRESHOLD: u32 = 0x7f800000;
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let a = a.to_bits();
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let b = b.to_bits();
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let a_sign = a & TOP_BIT;
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let b_sign = b & TOP_BIT;
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let a_abs = a & !TOP_BIT;
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let b_abs = b & !TOP_BIT;
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if a_abs > NAN_THRESHOLD || b_abs > NAN_THRESHOLD {
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// NaNs always return maximum ulps apart.
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u32::MAX
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} else if a_sign == b_sign {
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a_abs.max(b_abs) - a_abs.min(b_abs)
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} else {
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a_abs + b_abs
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}
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}
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/// Checks if two floats are approximately equal, within `max_ulps`.
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#[inline(always)]
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pub fn ulps_eq(a: f32, b: f32, max_ulps: u32) -> bool {
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// The minimum ensures that NaNs never return true.
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ulp_diff(a, b) <= max_ulps.min(u32::MAX - 1)
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}
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#[cfg(test)]
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mod tests {
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use super::*;
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#[test]
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fn ulp_diff_test() {
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assert_eq!(ulp_diff(1.0, 1.0), 0);
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assert_eq!(ulp_diff(0.0, 0.0), 0);
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assert_eq!(ulp_diff(0.0, -0.0), 0);
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assert_eq!(ulp_diff(1.0, 2.0), 1 << 23);
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assert_eq!(ulp_diff(2.0, 4.0), 1 << 23);
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assert_eq!(ulp_diff(-1.0, -2.0), 1 << 23);
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assert_eq!(ulp_diff(-2.0, -4.0), 1 << 23);
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assert_eq!(ulp_diff(-1.0, 1.0), 0x7f000000);
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assert_eq!(ulp_diff(0.0, 1.0), 0x3f800000);
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assert_eq!(ulp_diff(-0.0, 1.0), 0x3f800000);
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assert_eq!(ulp_diff(0.0, -1.0), 0x3f800000);
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assert_eq!(ulp_diff(-0.0, -1.0), 0x3f800000);
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assert_eq!(ulp_diff(f32::INFINITY, -f32::INFINITY), 0xff000000);
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assert_eq!(ulp_diff(f32::NAN, f32::NAN), 0xffffffff);
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assert_eq!(ulp_diff(f32::NAN, 1.0), 0xffffffff);
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assert_eq!(ulp_diff(1.0, f32::NAN), 0xffffffff);
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assert_eq!(ulp_diff(-f32::NAN, 1.0), 0xffffffff);
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assert_eq!(ulp_diff(1.0, -f32::NAN), 0xffffffff);
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assert_eq!(ulp_diff(0.0, f32::from_bits(0.0f32.to_bits() + 1)), 1);
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assert_eq!(ulp_diff(-0.0, f32::from_bits(0.0f32.to_bits() + 1)), 1);
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}
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#[test]
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fn ulps_eq_test() {
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assert!(ulps_eq(1.0, 1.0, 0));
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assert!(ulps_eq(1.0, 1.0, 1));
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assert!(ulps_eq(0.0, 0.0, 0));
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assert!(ulps_eq(0.0, -0.0, 0));
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assert!(ulps_eq(1.0, 2.0, 1 << 23));
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assert!(!ulps_eq(1.0, 2.0, (1 << 23) - 1));
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assert!(ulps_eq(0.0, f32::from_bits(0.0f32.to_bits() + 1), 1));
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assert!(!ulps_eq(0.0, f32::from_bits(0.0f32.to_bits() + 1), 0));
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assert!(ulps_eq(-0.0, f32::from_bits(0.0f32.to_bits() + 1), 1));
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assert!(!ulps_eq(-0.0, f32::from_bits(0.0f32.to_bits() + 1), 0));
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assert!(ulps_eq(std::f32::INFINITY, -std::f32::INFINITY, 0xff000000));
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assert!(!ulps_eq(
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std::f32::INFINITY,
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-std::f32::INFINITY,
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0xff000000 - 1
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));
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assert!(!ulps_eq(std::f32::NAN, std::f32::NAN, 0));
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assert!(!ulps_eq(-std::f32::NAN, -std::f32::NAN, 0));
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assert!(!ulps_eq(std::f32::NAN, std::f32::NAN, u32::MAX));
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assert!(!ulps_eq(std::f32::NAN, std::f32::INFINITY, 1 << 31));
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assert!(!ulps_eq(std::f32::INFINITY, std::f32::NAN, 1 << 31));
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}
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}
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