pxfm 0.1.29

Fast and accurate math
Documentation 
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/*
 * // Copyright (c) Radzivon Bartoshyk 8/2025. 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::f_fmla;
use crate::polyeval::f_polyeval5;
use crate::sin_cosf::sincosf_eval::sincosf_eval;

/// Computes sinc(x)
///
/// Max found ULP 0.5
pub fn f_sincf(x: f32) -> f32 {
    let x_abs = x.to_bits() & 0x7fff_ffffu32;
    let xd = x as f64;

    // |x| <= pi/16
    if x_abs <= 0x3e49_0fdbu32 {
        // |x| < 0.000443633
        if x_abs < 0x39e8_9769u32 {
            if x_abs == 0u32 {
                // For signed zeros.
                return 1.;
            }
            /*
            Generated by Sollya:
            f = sin(x) / x;

            d = [0.0; 0.000443633];
            pf = fpminimax(f, [|0, 2|], [|1, D...|], d, relative, floating);

            See ./notes/sincf.sollya
             */
            return f_fmla(
                xd * xd,
                f64::from_bits(0xbfc555555265f618),
                f64::from_bits(0x3ff0000000000000),
            ) as f32;
        }

        let xsqr = xd * xd;

        /*
        Generated by Sollya:
        f_sinpi_16 = sin(x)/x;
        Q = fpminimax(f_sinpi_16, [|0, 2, 4, 6, 8|], [|1, D...|], [0, pi/16]);

        See ./notes/sincosf.sollya
         */
        let p = f_polyeval5(
            xsqr,
            f64::from_bits(0x3ff0000000000000),
            f64::from_bits(0xbfc55555555554c6),
            f64::from_bits(0x3f81111111085e65),
            f64::from_bits(0xbf2a019f70fb4d4f),
            f64::from_bits(0x3ec718d179815e74),
        );
        return p as f32;
    }

    if x_abs >= 0x7f80_0000u32 {
        return x + f32::NAN;
    }

    // Formula:
    //   sin(x) = sin((k + y)*pi/32)
    //          = sin(y*pi/32) * cos(k*pi/32) + cos(y*pi/32) * sin(k*pi/32)
    // The values of sin(k*pi/32) and cos(k*pi/32) for k = 0..31 are precomputed
    // and stored using a vector of 32 doubles. Sin(y*pi/32) and cos(y*pi/32) are
    // computed using degree-7 and degree-6 minimax polynomials generated by
    // Sollya respectively.

    let rs = sincosf_eval(xd, x_abs);
    let v_sin = f_fmla(rs.sin_y, rs.cos_k, f_fmla(rs.cosm1_y, rs.sin_k, rs.sin_k));
    (v_sin / xd) as f32
}

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

    #[test]
    fn test_f_sincf() {
        assert_eq!(f_sincf(-7.991783e37), -1.1754942946874968e-38);
        assert_eq!(f_sincf(-8.04695e37), 1.1754942974913884e-38);
        assert_eq!(f_sincf(-0.00044236073), 0.9999999673861641);
        assert_eq!(f_sincf(0.0), 1.0);
        assert_eq!(f_sincf(0.2), 0.99334663);
        assert!(f_sincf(f32::INFINITY).is_nan());
        assert!(f_sincf(f32::NEG_INFINITY).is_nan());
    }
}