/* origin: FreeBSD /usr/src/lib/msun/src/e_powf.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 bp[] =
    {
        1.0, 1.5,
},
                   dp_h[] =
                       {
                           0.0, 5.84960938e-01,
}, /* 0x3f15c000 */
    dp_l[] =
        {
            0.0, 1.56322085e-06,
},                      /* 0x35d1cfdc */
    two24 = 16777216.0, /* 0x4b800000 */
    huge = 1.0e30,
                   tiny = 1.0e-30,
                   /* poly coefs for (3/2)*(log(x)-2s-2/3*s**3 */
    L1 = 6.0000002384e-01,      /* 0x3f19999a */
    L2 = 4.2857143283e-01,      /* 0x3edb6db7 */
    L3 = 3.3333334327e-01,      /* 0x3eaaaaab */
    L4 = 2.7272811532e-01,      /* 0x3e8ba305 */
    L5 = 2.3066075146e-01,      /* 0x3e6c3255 */
    L6 = 2.0697501302e-01,      /* 0x3e53f142 */
    P1 = 1.6666667163e-01,      /* 0x3e2aaaab */
    P2 = -2.7777778450e-03,     /* 0xbb360b61 */
    P3 = 6.6137559770e-05,      /* 0x388ab355 */
    P4 = -1.6533901999e-06,     /* 0xb5ddea0e */
    P5 = 4.1381369442e-08,      /* 0x3331bb4c */
    lg2 = 6.9314718246e-01,     /* 0x3f317218 */
    lg2_h = 6.93145752e-01,     /* 0x3f317200 */
    lg2_l = 1.42860654e-06,     /* 0x35bfbe8c */
    ovt = 4.2995665694e-08,     /* -(128-log2(ovfl+.5ulp)) */
    cp = 9.6179670095e-01,      /* 0x3f76384f =2/(3ln2) */
    cp_h = 9.6191406250e-01,    /* 0x3f764000 =12b cp */
    cp_l = -1.1736857402e-04,   /* 0xb8f623c6 =tail of cp_h */
    ivln2 = 1.4426950216e+00,   /* 0x3fb8aa3b =1/ln2 */
    ivln2_h = 1.4426879883e+00, /* 0x3fb8aa00 =16b 1/ln2*/
    ivln2_l = 7.0526075433e-06; /* 0x36eca570 =1/ln2 tail*/

float powf(float x, float y) {
  float z, ax, z_h, z_l, p_h, p_l;
  float y1, t1, t2, r, s, sn, t, u, v, w;
  int32_t i, j, k, yisint, n;
  int32_t hx, hy, ix, iy, is;

  GET_FLOAT_WORD(hx, x);
  GET_FLOAT_WORD(hy, y);
  ix = hx & 0x7fffffff;
  iy = hy & 0x7fffffff;

  /* x**0 = 1, even if x is NaN */
  if (iy == 0)
    return 1.0f;
  /* 1**y = 1, even if y is NaN */
  if (hx == 0x3f800000)
    return 1.0f;
  /* NaN if either arg is NaN */
  if (ix > 0x7f800000 || iy > 0x7f800000)
    return x + y;

  /* determine if y is an odd int when x < 0
   * yisint = 0       ... y is not an integer
   * yisint = 1       ... y is an odd int
   * yisint = 2       ... y is an even int
   */
  yisint = 0;
  if (hx < 0) {
    if (iy >= 0x4b800000)
      yisint = 2; /* even integer y */
    else if (iy >= 0x3f800000) {
      k = (iy >> 23) - 0x7f; /* exponent */
      j = iy >> (23 - k);
      if ((j << (23 - k)) == iy)
        yisint = 2 - (j & 1);
    }
  }

  /* special value of y */
  if (iy == 0x7f800000) { /* y is +-inf */
    if (ix == 0x3f800000) /* (-1)**+-inf is 1 */
      return 1.0f;
    else if (ix > 0x3f800000) /* (|x|>1)**+-inf = inf,0 */
      return hy >= 0 ? y : 0.0f;
    else /* (|x|<1)**+-inf = 0,inf */
      return hy >= 0 ? 0.0f : -y;
  }
  if (iy == 0x3f800000) /* y is +-1 */
    return hy >= 0 ? x : 1.0f / x;
  if (hy == 0x40000000) /* y is 2 */
    return x * x;
  if (hy == 0x3f000000) { /* y is  0.5 */
    if (hx >= 0)          /* x >= +0 */
      return sqrtf(x);
  }

  ax = fabsf(x);
  /* special value of x */
  if (ix == 0x7f800000 || ix == 0 ||
      ix == 0x3f800000) { /* x is +-0,+-inf,+-1 */
    z = ax;
    if (hy < 0) /* z = (1/|x|) */
      z = 1.0f / z;
    if (hx < 0) {
      if (((ix - 0x3f800000) | yisint) == 0) {
        z = (z - z) / (z - z); /* (-1)**non-int is NaN */
      } else if (yisint == 1)
        z = -z; /* (x<0)**odd = -(|x|**odd) */
    }
    return z;
  }

  sn = 1.0f; /* sign of result */
  if (hx < 0) {
    if (yisint == 0) /* (x<0)**(non-int) is NaN */
      return (x - x) / (x - x);
    if (yisint == 1) /* (x<0)**(odd int) */
      sn = -1.0f;
  }

  /* |y| is huge */
  if (iy > 0x4d000000) { /* if |y| > 2**27 */
    /* over/underflow if x is not close to one */
    if (ix < 0x3f7ffff8)
      return hy < 0 ? sn * huge * huge : sn * tiny * tiny;
    if (ix > 0x3f800007)
      return hy > 0 ? sn * huge * huge : sn * tiny * tiny;
    /* now |1-x| is tiny <= 2**-20, suffice to compute
       log(x) by x-x^2/2+x^3/3-x^4/4 */
    t = ax - 1; /* t has 20 trailing zeros */
    w = (t * t) * (0.5f - t * (0.333333333333f - t * 0.25f));
    u = ivln2_h * t; /* ivln2_h has 16 sig. bits */
    v = t * ivln2_l - w * ivln2;
    t1 = u + v;
    GET_FLOAT_WORD(is, t1);
    SET_FLOAT_WORD(t1, is & 0xfffff000);
    t2 = v - (t1 - u);
  } else {
    float s2, s_h, s_l, t_h, t_l;
    n = 0;
    /* take care subnormal number */
    if (ix < 0x00800000) {
      ax *= two24;
      n -= 24;
      GET_FLOAT_WORD(ix, ax);
    }
    n += ((ix) >> 23) - 0x7f;
    j = ix & 0x007fffff;
    /* determine interval */
    ix = j | 0x3f800000; /* normalize ix */
    if (j <= 0x1cc471)   /* |x|<sqrt(3/2) */
      k = 0;
    else if (j < 0x5db3d7) /* |x|<sqrt(3)   */
      k = 1;
    else {
      k = 0;
      n += 1;
      ix -= 0x00800000;
    }
    SET_FLOAT_WORD(ax, ix);

    /* compute s = s_h+s_l = (x-1)/(x+1) or (x-1.5)/(x+1.5) */
    u = ax - bp[k]; /* bp[0]=1.0, bp[1]=1.5 */
    v = 1.0f / (ax + bp[k]);
    s = u * v;
    s_h = s;
    GET_FLOAT_WORD(is, s_h);
    SET_FLOAT_WORD(s_h, is & 0xfffff000);
    /* t_h=ax+bp[k] High */
    is = ((ix >> 1) & 0xfffff000) | 0x20000000;
    SET_FLOAT_WORD(t_h, is + 0x00400000 + (k << 21));
    t_l = ax - (t_h - bp[k]);
    s_l = v * ((u - s_h * t_h) - s_h * t_l);
    /* compute log(ax) */
    s2 = s * s;
    r = s2 * s2 *
        (L1 + s2 * (L2 + s2 * (L3 + s2 * (L4 + s2 * (L5 + s2 * L6)))));
    r += s_l * (s_h + s);
    s2 = s_h * s_h;
    t_h = 3.0f + s2 + r;
    GET_FLOAT_WORD(is, t_h);
    SET_FLOAT_WORD(t_h, is & 0xfffff000);
    t_l = r - ((t_h - 3.0f) - s2);
    /* u+v = s*(1+...) */
    u = s_h * t_h;
    v = s_l * t_h + t_l * s;
    /* 2/(3log2)*(s+...) */
    p_h = u + v;
    GET_FLOAT_WORD(is, p_h);
    SET_FLOAT_WORD(p_h, is & 0xfffff000);
    p_l = v - (p_h - u);
    z_h = cp_h * p_h; /* cp_h+cp_l = 2/(3*log2) */
    z_l = cp_l * p_h + p_l * cp + dp_l[k];
    /* log2(ax) = (s+..)*2/(3*log2) = n + dp_h + z_h + z_l */
    t = (float)n;
    t1 = (((z_h + z_l) + dp_h[k]) + t);
    GET_FLOAT_WORD(is, t1);
    SET_FLOAT_WORD(t1, is & 0xfffff000);
    t2 = z_l - (((t1 - t) - dp_h[k]) - z_h);
  }

  /* split up y into y1+y2 and compute (y1+y2)*(t1+t2) */
  GET_FLOAT_WORD(is, y);
  SET_FLOAT_WORD(y1, is & 0xfffff000);
  p_l = (y - y1) * t1 + y * t2;
  p_h = y1 * t1;
  z = p_l + p_h;
  GET_FLOAT_WORD(j, z);
  if (j > 0x43000000)         /* if z > 128 */
    return sn * huge * huge;  /* overflow */
  else if (j == 0x43000000) { /* if z == 128 */
    if (p_l + ovt > z - p_h)
      return sn * huge * huge;                              /* overflow */
  } else if ((j & 0x7fffffff) > 0x43160000) /* z < -150 */  // FIXME: check
                                                            // should be
                                                            // (uint32_t)j >
                                                            // 0xc3160000
    return sn * tiny * tiny;                                /* underflow */
  else if (j == 0xc3160000) {                               /* z == -150 */
    if (p_l <= z - p_h)
      return sn * tiny * tiny; /* underflow */
  }
  /*
   * compute 2**(p_h+p_l)
   */
  i = j & 0x7fffffff;
  k = (i >> 23) - 0x7f;
  n = 0;
  if (i > 0x3f000000) { /* if |z| > 0.5, set n = [z+0.5] */
    n = j + (0x00800000 >> (k + 1));
    k = ((n & 0x7fffffff) >> 23) - 0x7f; /* new k for n */
    SET_FLOAT_WORD(t, n & ~(0x007fffff >> k));
    n = ((n & 0x007fffff) | 0x00800000) >> (23 - k);
    if (j < 0)
      n = -n;
    p_h -= t;
  }
  t = p_l + p_h;
  GET_FLOAT_WORD(is, t);
  SET_FLOAT_WORD(t, is & 0xffff8000);
  u = t * lg2_h;
  v = (p_l - (t - p_h)) * lg2 + t * lg2_l;
  z = u + v;
  w = v - (z - u);
  t = z * z;
  t1 = z - t * (P1 + t * (P2 + t * (P3 + t * (P4 + t * P5))));
  r = (z * t1) / (t1 - 2.0f) - (w + z * w);
  z = 1.0f - (r - z);
  GET_FLOAT_WORD(j, z);
  j += n << 23;
  if ((j >> 23) <= 0) /* subnormal output */
    z = scalbnf(z, n);
  else
    SET_FLOAT_WORD(z, j);
  return sn * z;
}