exp2f.rs - source
Description: Source of the Rust file `/Users/erlendbasso/.cargo/registry/src/github.com-1ecc6299db9ec823/libm-0.2.6/src/math/exp2f.rs`.
Keywords: rust, rustlang, rust-lang

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    // origin: FreeBSD /usr/src/lib/msun/src/s_exp2f.c
    //-
    // Copyright (c) 2005 David Schultz <das@FreeBSD.ORG>
    // 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.
    //
    // THIS SOFTWARE IS PROVIDED BY THE AUTHOR 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 AUTHOR 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.

    const TBLSIZE: usize = 16;

    static EXP2FT: [u64; TBLSIZE] = [
        0x3fe6a09e667f3bcd,
        0x3fe7a11473eb0187,
        0x3fe8ace5422aa0db,
        0x3fe9c49182a3f090,
        0x3feae89f995ad3ad,
        0x3fec199bdd85529c,
        0x3fed5818dcfba487,
        0x3feea4afa2a490da,
        0x3ff0000000000000,
        0x3ff0b5586cf9890f,
        0x3ff172b83c7d517b,
        0x3ff2387a6e756238,
        0x3ff306fe0a31b715,
        0x3ff3dea64c123422,
        0x3ff4bfdad5362a27,
        0x3ff5ab07dd485429,
    ];

    // exp2f(x): compute the base 2 exponential of x
    //
    // Accuracy: Peak error < 0.501 ulp; location of peak: -0.030110927.
    //
    // Method: (equally-spaced tables)
    //
    //   Reduce x:
    //     x = k + y, for integer k and |y| <= 1/2.
    //     Thus we have exp2f(x) = 2**k * exp2(y).
    //
    //   Reduce y:
    //     y = i/TBLSIZE + z for integer i near y * TBLSIZE.
    //     Thus we have exp2(y) = exp2(i/TBLSIZE) * exp2(z),
    //     with |z| <= 2**-(TBLSIZE+1).
    //
    //   We compute exp2(i/TBLSIZE) via table lookup and exp2(z) via a
    //   degree-4 minimax polynomial with maximum error under 1.4 * 2**-33.
    //   Using double precision for everything except the reduction makes
    //   roundoff error insignificant and simplifies the scaling step.
    //
    //   This method is due to Tang, but I do not use his suggested parameters:
    //
    //      Tang, P.  Table-driven Implementation of the Exponential Function
    //      in IEEE Floating-Point Arithmetic.  TOMS 15(2), 144-157 (1989).

    /// Exponential, base 2 (f32)
    ///
    /// Calculate `2^x`, that is, 2 raised to the power `x`.
    #[cfg_attr(all(test, assert_no_panic), no_panic::no_panic)]
    pub fn exp2f(mut x: f32) -> f32 {
        let redux = f32::from_bits(0x4b400000) / TBLSIZE as f32;
        let p1 = f32::from_bits(0x3f317218);
        let p2 = f32::from_bits(0x3e75fdf0);
        let p3 = f32::from_bits(0x3d6359a4);
        let p4 = f32::from_bits(0x3c1d964e);

        // double_t t, r, z;
        // uint32_t ix, i0, k;

        let x1p127 = f32::from_bits(0x7f000000);

        /* Filter out exceptional cases. */
        let ui = f32::to_bits(x);
        let ix = ui & 0x7fffffff;
        if ix > 0x42fc0000 {
            /* |x| > 126 */
            if ix > 0x7f800000 {
                /* NaN */
                return x;
            }
            if ui >= 0x43000000 && ui < 0x80000000 {
                /* x >= 128 */
                x *= x1p127;
                return x;
            }
            if ui >= 0x80000000 {
                /* x < -126 */
                if ui >= 0xc3160000 || (ui & 0x0000ffff != 0) {
                    force_eval!(f32::from_bits(0x80000001) / x);
                }
                if ui >= 0xc3160000 {
                    /* x <= -150 */
                    return 0.0;
                }
            }
        } else if ix <= 0x33000000 {
            /* |x| <= 0x1p-25 */
            return 1.0 + x;
        }

        /* Reduce x, computing z, i0, and k. */
        let ui = f32::to_bits(x + redux);
        let mut i0 = ui;
        i0 += TBLSIZE as u32 / 2;
        let k = i0 / TBLSIZE as u32;
        let ukf = f64::from_bits(((0x3ff + k) as u64) << 52);
        i0 &= TBLSIZE as u32 - 1;
        let mut uf = f32::from_bits(ui);
        uf -= redux;
        let z: f64 = (x - uf) as f64;
        /* Compute r = exp2(y) = exp2ft[i0] * p(z). */
        let r: f64 = f64::from_bits(i!(EXP2FT, i0 as usize));
        let t: f64 = r as f64 * z;
        let r: f64 = r + t * (p1 as f64 + z * p2 as f64) + t * (z * z) * (p3 as f64 + z * p4 as f64);

        /* Scale by 2**k */
        (r * ukf) as f32
    }