/* 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;
}