/* origin: FreeBSD /usr/src/lib/msun/src/s_expm1f.c */
/*
 * Conversion to float by Ian Lance Taylor, Cygnus Support, ian@cygnus.com.
 */
/*
 * ====================================================
 * 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 o_threshold = 8.8721679688e+01, /* 0x42b17180 */
    ln2_hi = 6.9313812256e-01,                     /* 0x3f317180 */
    ln2_lo = 9.0580006145e-06,                     /* 0x3717f7d1 */
    invln2 = 1.4426950216e+00,                     /* 0x3fb8aa3b */
                                                   /*
                                                    * Domain [-0.34568, 0.34568], range ~[-6.694e-10, 6.696e-10]:
                                                    * |6 / x * (1 + 2 * (1 / (exp(x) - 1) - 1 / x)) - q(x)| < 2**-30.04
                                                    * Scaled coefficients: Qn_here = 2**n * Qn_for_q (see s_expm1.c):
                                                    */
    Q1 = -3.3333212137e-2,                         /* -0x888868.0p-28 */
    Q2 = 1.5807170421e-3;                          /*  0xcf3010.0p-33 */

float expm1f(float x) {
  float_t y, hi, lo, c, t, e, hxs, hfx, r1, twopk;
  union {
    float f;
    uint32_t i;
  } u = {x};
  uint32_t hx = u.i & 0x7fffffff;
  int k, sign = u.i >> 31;

  /* filter out huge and non-finite argument */
  if (hx >= 0x4195b844) { /* if |x|>=27*ln2 */
    if (hx > 0x7f800000)  /* NaN */
      return x;
    if (sign)
      return -1;
    if (x > o_threshold) {
      x *= 0x1p127f;
      return x;
    }
  }

  /* argument reduction */
  if (hx > 0x3eb17218) {   /* if  |x| > 0.5 ln2 */
    if (hx < 0x3F851592) { /* and |x| < 1.5 ln2 */
      if (!sign) {
        hi = x - ln2_hi;
        lo = ln2_lo;
        k = 1;
      } else {
        hi = x + ln2_hi;
        lo = -ln2_lo;
        k = -1;
      }
    } else {
      k = invln2 * x + (sign ? -0.5f : 0.5f);
      t = k;
      hi = x - t * ln2_hi; /* t*ln2_hi is exact here */
      lo = t * ln2_lo;
    }
    x = hi - lo;
    c = (hi - x) - lo;
  } else if (hx < 0x33000000) { /* when |x|<2**-25, return x */
    if (hx < 0x00800000)
      FORCE_EVAL(x * x);
    return x;
  } else
    k = 0;

  /* x is now in primary range */
  hfx = 0.5f * x;
  hxs = x * hfx;
  r1 = 1.0f + hxs * (Q1 + hxs * Q2);
  t = 3.0f - r1 * hfx;
  e = hxs * ((r1 - t) / (6.0f - x * t));
  if (k == 0) /* c is 0 */
    return x - (x * e - hxs);
  e = x * (e - c) - c;
  e -= hxs;
  /* exp(x) ~ 2^k (x_reduced - e + 1) */
  if (k == -1)
    return 0.5f * (x - e) - 0.5f;
  if (k == 1) {
    if (x < -0.25f)
      return -2.0f * (e - (x + 0.5f));
    return 1.0f + 2.0f * (x - e);
  }
  u.i = (0x7f + k) << 23; /* 2^k */
  twopk = u.f;
  if (k < 0 || k > 56) { /* suffice to return exp(x)-1 */
    y = x - e + 1.0f;
    if (k == 128)
      y = y * 2.0f * 0x1p127f;
    else
      y = y * twopk;
    return y - 1.0f;
  }
  u.i = (0x7f - k) << 23; /* 2^-k */
  if (k < 23)
    y = (x - e + (1 - u.f)) * twopk;
  else
    y = (x - (e + u.f) + 1) * twopk;
  return y;
}