log1p.rs - source
Description: Source of the Rust file `/Users/erlendbasso/.cargo/registry/src/github.com-1ecc6299db9ec823/libm-0.2.6/src/math/log1p.rs`.
Keywords: rust, rustlang, rust-lang

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    /* origin: FreeBSD /usr/src/lib/msun/src/s_log1p.c */
    /*
     * ====================================================
     * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved.
     *
     * Developed at SunPro, a Sun Microsystems, Inc. business.
     * Permission to use, copy, modify, and distribute this
     * software is freely granted, provided that this notice
     * is preserved.
     * ====================================================
     */
    /* double log1p(double x)
     * Return the natural logarithm of 1+x.
     *
     * Method :
     *   1. Argument Reduction: find k and f such that
     *                      1+x = 2^k * (1+f),
     *         where  sqrt(2)/2 < 1+f < sqrt(2) .
     *
     *      Note. If k=0, then f=x is exact. However, if k!=0, then f
     *      may not be representable exactly. In that case, a correction
     *      term is need. Let u=1+x rounded. Let c = (1+x)-u, then
     *      log(1+x) - log(u) ~ c/u. Thus, we proceed to compute log(u),
     *      and add back the correction term c/u.
     *      (Note: when x > 2**53, one can simply return log(x))
     *
     *   2. Approximation of log(1+f): See log.c
     *
     *   3. Finally, log1p(x) = k*ln2 + log(1+f) + c/u. See log.c
     *
     * Special cases:
     *      log1p(x) is NaN with signal if x < -1 (including -INF) ;
     *      log1p(+INF) is +INF; log1p(-1) is -INF with signal;
     *      log1p(NaN) is that NaN with no signal.
     *
     * Accuracy:
     *      according to an error analysis, the error is always less than
     *      1 ulp (unit in the last place).
     *
     * Constants:
     * The hexadecimal values are the intended ones for the following
     * constants. The decimal values may be used, provided that the
     * compiler will convert from decimal to binary accurately enough
     * to produce the hexadecimal values shown.
     *
     * Note: Assuming log() return accurate answer, the following
     *       algorithm can be used to compute log1p(x) to within a few ULP:
     *
     *              u = 1+x;
     *              if(u==1.0) return x ; else
     *                         return log(u)*(x/(u-1.0));
     *
     *       See HP-15C Advanced Functions Handbook, p.193.
     */

    use core::f64;

    const LN2_HI: f64 = 6.93147180369123816490e-01; /* 3fe62e42 fee00000 */
    const LN2_LO: f64 = 1.90821492927058770002e-10; /* 3dea39ef 35793c76 */
    const LG1: f64 = 6.666666666666735130e-01; /* 3FE55555 55555593 */
    const LG2: f64 = 3.999999999940941908e-01; /* 3FD99999 9997FA04 */
    const LG3: f64 = 2.857142874366239149e-01; /* 3FD24924 94229359 */
    const LG4: f64 = 2.222219843214978396e-01; /* 3FCC71C5 1D8E78AF */
    const LG5: f64 = 1.818357216161805012e-01; /* 3FC74664 96CB03DE */
    const LG6: f64 = 1.531383769920937332e-01; /* 3FC39A09 D078C69F */
    const LG7: f64 = 1.479819860511658591e-01; /* 3FC2F112 DF3E5244 */

    #[cfg_attr(all(test, assert_no_panic), no_panic::no_panic)]
    pub fn log1p(x: f64) -> f64 {
        let mut ui: u64 = x.to_bits();
        let hfsq: f64;
        let mut f: f64 = 0.;
        let mut c: f64 = 0.;
        let s: f64;
        let z: f64;
        let r: f64;
        let w: f64;
        let t1: f64;
        let t2: f64;
        let dk: f64;
        let hx: u32;
        let mut hu: u32;
        let mut k: i32;

        hx = (ui >> 32) as u32;
        k = 1;
        if hx < 0x3fda827a || (hx >> 31) > 0 {
            /* 1+x < sqrt(2)+ */
            if hx >= 0xbff00000 {
                /* x <= -1.0 */
                if x == -1. {
                    return x / 0.0; /* log1p(-1) = -inf */
                }
                return (x - x) / 0.0; /* log1p(x<-1) = NaN */
            }
            if hx << 1 < 0x3ca00000 << 1 {
                /* |x| < 2**-53 */
                /* underflow if subnormal */
                if (hx & 0x7ff00000) == 0 {
                    force_eval!(x as f32);
                }
                return x;
            }
            if hx <= 0xbfd2bec4 {
                /* sqrt(2)/2- <= 1+x < sqrt(2)+ */
                k = 0;
                c = 0.;
                f = x;
            }
        } else if hx >= 0x7ff00000 {
            return x;
        }
        if k > 0 {
            ui = (1. + x).to_bits();
            hu = (ui >> 32) as u32;
            hu += 0x3ff00000 - 0x3fe6a09e;
            k = (hu >> 20) as i32 - 0x3ff;
            /* correction term ~ log(1+x)-log(u), avoid underflow in c/u */
            if k < 54 {
                c = if k >= 2 {
                    1. - (f64::from_bits(ui) - x)
                } else {
                    x - (f64::from_bits(ui) - 1.)
                };
                c /= f64::from_bits(ui);
            } else {
                c = 0.;
            }
            /* reduce u into [sqrt(2)/2, sqrt(2)] */
            hu = (hu & 0x000fffff) + 0x3fe6a09e;
            ui = (hu as u64) << 32 | (ui & 0xffffffff);
            f = f64::from_bits(ui) - 1.;
        }
        hfsq = 0.5 * f * f;
        s = f / (2.0 + f);
        z = s * s;
        w = z * z;
        t1 = w * (LG2 + w * (LG4 + w * LG6));
        t2 = z * (LG1 + w * (LG3 + w * (LG5 + w * LG7)));
        r = t2 + t1;
        dk = k as f64;
        s * (hfsq + r) + (dk * LN2_LO + c) - hfsq + f + dk * LN2_HI
    }