pxfm 0.1.29

Fast and accurate math
Documentation 
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/*
 * // Copyright (c) Radzivon Bartoshyk 9/2025. All rights reserved.
 * //
 * // Redistribution and use in source and binary forms, with or without modification,
 * // are permitted provided that the following conditions are met:
 * //
 * // 1.  Redistributions of source code must retain the above copyright notice, this
 * // list of conditions and the following disclaimer.
 * //
 * // 2.  Redistributions in binary form must reproduce the above copyright notice,
 * // this list of conditions and the following disclaimer in the documentation
 * // and/or other materials provided with the distribution.
 * //
 * // 3.  Neither the name of the copyright holder nor the names of its
 * // contributors may be used to endorse or promote products derived from
 * // this software without specific prior written permission.
 * //
 * // THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND CONTRIBUTORS "AS IS"
 * // AND ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE
 * // IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE ARE
 * // DISCLAIMED. IN NO EVENT SHALL THE COPYRIGHT HOLDER OR CONTRIBUTORS BE LIABLE
 * // FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL
 * // DAMAGES (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS OR
 * // SERVICES; LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION) HOWEVER
 * // CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT LIABILITY,
 * // OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY OUT OF THE USE
 * // OF THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF SUCH DAMAGE.
 */
use crate::common::EXP_MASK_F32;

/// Hypot function
///
/// Max ULP 0.5
#[inline]
pub fn f_hypotf(x: f32, y: f32) -> f32 {
    let x_abs = f32::from_bits(x.to_bits() & 0x7fff_ffffu32);
    let y_abs = f32::from_bits(y.to_bits() & 0x7fff_ffffu32);

    let a_bits = x_abs.to_bits().max(y_abs.to_bits());
    let b_bits = x_abs.to_bits().min(y_abs.to_bits());

    let a_u = a_bits;
    let b_u = b_bits;

    if a_u >= EXP_MASK_F32 {
        // x or y is inf or nan
        if f32::from_bits(a_bits).is_nan() || f32::from_bits(b_bits).is_nan() {
            return f32::NAN;
        }
        if f32::from_bits(a_bits).is_infinite() || f32::from_bits(b_bits).is_infinite() {
            return f32::INFINITY;
        }
        return f32::from_bits(a_bits);
    }

    if a_u.wrapping_sub(b_u) >= ((23u32 + 2) << 23) {
        return x_abs + y_abs;
    }

    #[cfg(any(
        all(
            any(target_arch = "x86", target_arch = "x86_64"),
            target_feature = "fma"
        ),
        target_arch = "aarch64"
    ))]
    {
        let ad = x as f64;
        let bd = y as f64;
        use crate::common::f_fmla;
        // for FMA environment we're using Kahan style summation which is short and reliable.
        let w = bd * bd; // RN(bc)
        let e = f_fmla(-bd, bd, w); // RN(w − bc)
        let f = f_fmla(ad, ad, w); // RN(ad + w)
        let r = e + f; // RN(f + e)
        let hyp = r.sqrt(); // sqrt(x^2 + y^2)
        hyp as f32
    }
    #[cfg(not(any(
        all(
            any(target_arch = "x86", target_arch = "x86_64"),
            target_feature = "fma"
        ),
        target_arch = "aarch64"
    )))]
    {
        let ad = f32::from_bits(a_bits) as f64;
        let bd = f32::from_bits(b_bits) as f64;
        use crate::double_double::DoubleDouble;
        let dy2 = DoubleDouble::from_exact_mult(bd, bd);
        let fdx = DoubleDouble::from_exact_mult(ad, ad);
        // elements are always sorted thus fdx.hi > dy2.hi, thus fasttwosum requirements is fulfilled
        let f = DoubleDouble::add_f64(fdx, dy2.hi).to_f64();
        let r = dy2.lo + f;
        let cath = r.sqrt();
        cath as f32
    }
}

#[cfg(test)]
mod tests {
    use super::*;

    #[test]
    fn test_hypotf() {
        assert_eq!(
            f_hypotf(
                0.000000000000000000000000000000000000000091771,
                0.000000000000000000000000000000000000011754585
            ),
            0.000000000000000000000000000000000000011754944
        );
        assert_eq!(
            f_hypotf(9.177e-41, 1.1754585e-38),
            0.000000000000000000000000000000000000011754944
        );
        let dx = (f_hypotf(1f32, 1f32) - (1f32 * 1f32 + 1f32 * 1f32).sqrt()).abs();
        assert!(dx < 1e-5);
        let dx = (f_hypotf(5f32, 5f32) - (5f32 * 5f32 + 5f32 * 5f32).sqrt()).abs();
        assert!(dx < 1e-5);
    }

    #[test]
    fn test_hypotf_edge_cases() {
        assert_eq!(f_hypotf(-1.0, -3.0), 3.1622777);
        assert_eq!(f_hypotf(0.0, 0.0), 0.0);
        assert_eq!(f_hypotf(f32::INFINITY, 0.0), f32::INFINITY);
        assert_eq!(f_hypotf(0.0, f32::INFINITY), f32::INFINITY);
        assert_eq!(f_hypotf(f32::INFINITY, f32::INFINITY), f32::INFINITY);
        assert_eq!(f_hypotf(f32::NEG_INFINITY, 0.0), f32::INFINITY);
        assert_eq!(f_hypotf(0.0, f32::NEG_INFINITY), f32::INFINITY);
        assert_eq!(
            f_hypotf(f32::NEG_INFINITY, f32::NEG_INFINITY),
            f32::INFINITY
        );
        assert!(f_hypotf(f32::NAN, 1.0).is_nan());
        assert!(f_hypotf(1.0, f32::NAN).is_nan());
    }
}