/* origin: FreeBSD /usr/src/lib/msun/src/e_log2f.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 log2.c.
 */

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

static const float ivln2hi = 1.4428710938e+00, /* 0x3fb8b000 */
    ivln2lo = -1.7605285393e-04,               /* 0xb9389ad4 */
    /* |(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 log2f(float x) {
  union {
    float f;
    uint32_t i;
  } u = {x};
  float_t hfsq, f, s, z, R, w, t1, t2, 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);
  return (lo + hi) * ivln2lo + lo * ivln2hi + hi * ivln2hi + k;
}