/* origin: FreeBSD /usr/src/lib/msun/src/s_log1pf.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.
 * ====================================================
 */

#include "libm.h"

static const float ln2_hi = 6.9313812256e-01, /* 0x3f317180 */
    ln2_lo = 9.0580006145e-06,                /* 0x3717f7d1 */
    /* |(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 log1pf(float x) {
  union {
    float f;
    uint32_t i;
  } u = {x};
  float_t hfsq, f, c, s, z, R, w, t1, t2, dk;
  uint32_t ix, iu;
  int k;

  ix = u.i;
  k = 1;
  if (ix < 0x3ed413d0 || ix >> 31) { /* 1+x < sqrt(2)+  */
    if (ix >= 0xbf800000) {          /* x <= -1.0 */
      if (x == -1)
        return x / 0.0f;     /* log1p(-1)=+inf */
      return (x - x) / 0.0f; /* log1p(x<-1)=NaN */
    }
    if (ix << 1 < 0x33800000 << 1) { /* |x| < 2**-24 */
      /* underflow if subnormal */
      if ((ix & 0x7f800000) == 0)
        FORCE_EVAL(x * x);
      return x;
    }
    if (ix <= 0xbe95f619) { /* sqrt(2)/2- <= 1+x < sqrt(2)+ */
      k = 0;
      c = 0;
      f = x;
    }
  } else if (ix >= 0x7f800000)
    return x;
  if (k) {
    u.f = 1 + x;
    iu = u.i;
    iu += 0x3f800000 - 0x3f3504f3;
    k = (int)(iu >> 23) - 0x7f;
    /* correction term ~ log(1+x)-log(u), avoid underflow in c/u */
    if (k < 25) {
      c = k >= 2 ? 1 - (u.f - x) : x - (u.f - 1);
      c /= u.f;
    } else
      c = 0;
    /* reduce u into [sqrt(2)/2, sqrt(2)] */
    iu = (iu & 0x007fffff) + 0x3f3504f3;
    u.i = iu;
    f = u.f - 1;
  }
  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;
  dk = k;
  return s * (hfsq + R) + (dk * ln2_lo + c) - hfsq + f + dk * ln2_hi;
}