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

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    /* origin: FreeBSD /usr/src/lib/msun/src/e_log.c */
    /*
     * ====================================================
     * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved.
     *
     * Developed at SunSoft, a Sun Microsystems, Inc. business.
     * Permission to use, copy, modify, and distribute this
     * software is freely granted, provided that this notice
     * is preserved.
     * ====================================================
     */
    /* log(x)
     * Return the logarithm of x
     *
     * Method :
     *   1. Argument Reduction: find k and f such that
     *                      x = 2^k * (1+f),
     *         where  sqrt(2)/2 < 1+f < sqrt(2) .
     *
     *   2. Approximation of log(1+f).
     *      Let s = f/(2+f) ; based on log(1+f) = log(1+s) - log(1-s)
     *               = 2s + 2/3 s**3 + 2/5 s**5 + .....,
     *               = 2s + s*R
     *      We use a special Remez algorithm on [0,0.1716] to generate
     *      a polynomial of degree 14 to approximate R The maximum error
     *      of this polynomial approximation is bounded by 2**-58.45. In
     *      other words,
     *                      2      4      6      8      10      12      14
     *          R(z) ~ Lg1*s +Lg2*s +Lg3*s +Lg4*s +Lg5*s  +Lg6*s  +Lg7*s
     *      (the values of Lg1 to Lg7 are listed in the program)
     *      and
     *          |      2          14          |     -58.45
     *          | Lg1*s +...+Lg7*s    -  R(z) | <= 2
     *          |                             |
     *      Note that 2s = f - s*f = f - hfsq + s*hfsq, where hfsq = f*f/2.
     *      In order to guarantee error in log below 1ulp, we compute log
     *      by
     *              log(1+f) = f - s*(f - R)        (if f is not too large)
     *              log(1+f) = f - (hfsq - s*(hfsq+R)).     (better accuracy)
     *
     *      3. Finally,  log(x) = k*ln2 + log(1+f).
     *                          = k*ln2_hi+(f-(hfsq-(s*(hfsq+R)+k*ln2_lo)))
     *         Here ln2 is split into two floating point number:
     *                      ln2_hi + ln2_lo,
     *         where n*ln2_hi is always exact for |n| < 2000.
     *
     * Special cases:
     *      log(x) is NaN with signal if x < 0 (including -INF) ;
     *      log(+INF) is +INF; log(0) is -INF with signal;
     *      log(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.
     */

    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 log(mut x: f64) -> f64 {
        let x1p54 = f64::from_bits(0x4350000000000000); // 0x1p54 === 2 ^ 54

        let mut ui = x.to_bits();
        let mut hx: u32 = (ui >> 32) as u32;
        let mut k: i32 = 0;

        if (hx < 0x00100000) || ((hx >> 31) != 0) {
            /* x < 2**-126  */
            if ui << 1 == 0 {
                return -1. / (x * x); /* log(+-0)=-inf */
            }
            if hx >> 31 != 0 {
                return (x - x) / 0.0; /* log(-#) = NaN */
            }
            /* subnormal number, scale x up */
            k -= 54;
            x *= x1p54;
            ui = x.to_bits();
            hx = (ui >> 32) as u32;
        } else if hx >= 0x7ff00000 {
            return x;
        } else if hx == 0x3ff00000 && ui << 32 == 0 {
            return 0.;
        }

        /* reduce x into [sqrt(2)/2, sqrt(2)] */
        hx += 0x3ff00000 - 0x3fe6a09e;
        k += ((hx >> 20) as i32) - 0x3ff;
        hx = (hx & 0x000fffff) + 0x3fe6a09e;
        ui = ((hx as u64) << 32) | (ui & 0xffffffff);
        x = f64::from_bits(ui);

        let f: f64 = x - 1.0;
        let hfsq: f64 = 0.5 * f * f;
        let s: f64 = f / (2.0 + f);
        let z: f64 = s * s;
        let w: f64 = z * z;
        let t1: f64 = w * (LG2 + w * (LG4 + w * LG6));
        let t2: f64 = z * (LG1 + w * (LG3 + w * (LG5 + w * LG7)));
        let r: f64 = t2 + t1;
        let dk: f64 = k as f64;
        s * (hfsq + r) + dk * LN2_LO - hfsq + f + dk * LN2_HI
    }