third_party/ulib/musl/third_party/math/log10f.c

/* origin: FreeBSD /usr/src/lib/msun/src/e_log10f.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.
 * ====================================================
 */
/*
 * See comments in log10.c.
 */

#include <math.h>
#include <stdint.h>

static const float ivln10hi = 4.3432617188e-01, /* 0x3ede6000 */
    ivln10lo = -3.1689971365e-05,               /* 0xb804ead9 */
    log10_2hi = 3.0102920532e-01,               /* 0x3e9a2080 */
    log10_2lo = 7.9034151668e-07,               /* 0x355427db */
    /* |(log(1+s)-log(1-s))/s - Lg(s)| < 2**-34.24 (~[-4.95e-11, 4.97e-11]). */
    Lg1 = 0xaaaaaa.0p-24, /* 0.66666662693 */
    Lg2 = 0xccce13.0p-25, /* 0.40000972152 */
    Lg3 = 0x91e9ee.0p-25, /* 0.28498786688 */
    Lg4 = 0xf89e26.0p-26; /* 0.24279078841 */

float log10f(float x) {
    union {
        float f;
        uint32_t i;
    } u = {x};
    float_t hfsq, f, s, z, R, w, t1, t2, dk, hi, lo;
    uint32_t ix;
    int k;

    ix = u.i;
    k = 0;
    if (ix < 0x00800000 || ix >> 31) { /* x < 2**-126  */
        if (ix << 1 == 0)
            return -1 / (x * x); /* log(+-0)=-inf */
        if (ix >> 31)
            return (x - x) / 0.0f; /* log(-#) = NaN */
        /* subnormal number, scale up x */
        k -= 25;
        x *= 0x1p25f;
        u.f = x;
        ix = u.i;
    } else if (ix >= 0x7f800000) {
        return x;
    } else if (ix == 0x3f800000)
        return 0;

    /* reduce x into [sqrt(2)/2, sqrt(2)] */
    ix += 0x3f800000 - 0x3f3504f3;
    k += (int)(ix >> 23) - 0x7f;
    ix = (ix & 0x007fffff) + 0x3f3504f3;
    u.i = ix;
    x = u.f;

    f = x - 1.0f;
    s = f / (2.0f + f);
    z = s * s;
    w = z * z;
    t1 = w * (Lg2 + w * Lg4);
    t2 = z * (Lg1 + w * Lg3);
    R = t2 + t1;
    hfsq = 0.5f * f * f;

    hi = f - hfsq;
    u.f = hi;
    u.i &= 0xfffff000;
    hi = u.f;
    lo = f - hi - hfsq + s * (hfsq + R);
    dk = k;
    return dk * log10_2lo + (lo + hi) * ivln10lo + lo * ivln10hi + hi * ivln10hi + dk * log10_2hi;
}