/* origin: FreeBSD /usr/src/lib/msun/src/e_log10.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.
 * ====================================================
 */
/*
 * Return the base 10 logarithm of x.  See log.c for most comments.
 *
 * Reduce x to 2^k (1+f) and calculate r = log(1+f) - f + f*f/2
 * as in log.c, then combine and scale in extra precision:
 *    log10(x) = (f - f*f/2 + r)/log(10) + k*log10(2)
 */

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

static const double ivln10hi = 4.34294481878168880939e-01, /* 0x3fdbcb7b, 0x15200000 */
    ivln10lo = 2.50829467116452752298e-11,                 /* 0x3dbb9438, 0xca9aadd5 */
    log10_2hi = 3.01029995663611771306e-01,                /* 0x3FD34413, 0x509F6000 */
    log10_2lo = 3.69423907715893078616e-13,                /* 0x3D59FEF3, 0x11F12B36 */
    Lg1 = 6.666666666666735130e-01,                        /* 3FE55555 55555593 */
    Lg2 = 3.999999999940941908e-01,                        /* 3FD99999 9997FA04 */
    Lg3 = 2.857142874366239149e-01,                        /* 3FD24924 94229359 */
    Lg4 = 2.222219843214978396e-01,                        /* 3FCC71C5 1D8E78AF */
    Lg5 = 1.818357216161805012e-01,                        /* 3FC74664 96CB03DE */
    Lg6 = 1.531383769920937332e-01,                        /* 3FC39A09 D078C69F */
    Lg7 = 1.479819860511658591e-01;                        /* 3FC2F112 DF3E5244 */

double log10(double x) {
    union {
        double f;
        uint64_t i;
    } u = {x};
    double_t hfsq, f, s, z, R, w, t1, t2, dk, y, hi, lo, val_hi, val_lo;
    uint32_t hx;
    int k;

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

    /* reduce x into [sqrt(2)/2, sqrt(2)] */
    hx += 0x3ff00000 - 0x3fe6a09e;
    k += (int)(hx >> 20) - 0x3ff;
    hx = (hx & 0x000fffff) + 0x3fe6a09e;
    u.i = (uint64_t)hx << 32 | (u.i & 0xffffffff);
    x = u.f;

    f = x - 1.0;
    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;

    /* See log2.c for details. */
    /* hi+lo = f - hfsq + s*(hfsq+R) ~ log(1+f) */
    hi = f - hfsq;
    u.f = hi;
    u.i &= (uint64_t)-1 << 32;
    hi = u.f;
    lo = f - hi - hfsq + s * (hfsq + R);

    /* val_hi+val_lo ~ log10(1+f) + k*log10(2) */
    val_hi = hi * ivln10hi;
    dk = k;
    y = dk * log10_2hi;
    val_lo = dk * log10_2lo + (lo + hi) * ivln10lo + lo * ivln10hi;

    /*
     * Extra precision in for adding y is not strictly needed
     * since there is no very large cancellation near x = sqrt(2) or
     * x = 1/sqrt(2), but we do it anyway since it costs little on CPUs
     * with some parallelism and it reduces the error for many args.
     */
    w = y + val_hi;
    val_lo += (y - w) + val_hi;
    val_hi = w;

    return val_lo + val_hi;
}