/* origin: FreeBSD /usr/src/lib/msun/src/e_pow.c */
/*
 * ====================================================
 * Copyright (C) 2004 by Sun Microsystems, Inc. All rights reserved.
 *
 * Permission to use, copy, modify, and distribute this
 * software is freely granted, provided that this notice
 * is preserved.
 * ====================================================
 */
/* pow(x,y) return x**y
 *
 *                    n
 * Method:  Let x =  2   * (1+f)
 *      1. Compute and return log2(x) in two pieces:
 *              log2(x) = w1 + w2,
 *         where w1 has 53-24 = 29 bit trailing zeros.
 *      2. Perform y*log2(x) = n+y' by simulating muti-precision
 *         arithmetic, where |y'|<=0.5.
 *      3. Return x**y = 2**n*exp(y'*log2)
 *
 * Special cases:
 *      1.  (anything) ** 0  is 1
 *      2.  1 ** (anything)  is 1
 *      3.  (anything except 1) ** NAN is NAN
 *      4.  NAN ** (anything except 0) is NAN
 *      5.  +-(|x| > 1) **  +INF is +INF
 *      6.  +-(|x| > 1) **  -INF is +0
 *      7.  +-(|x| < 1) **  +INF is +0
 *      8.  +-(|x| < 1) **  -INF is +INF
 *      9.  -1          ** +-INF is 1
 *      10. +0 ** (+anything except 0, NAN)               is +0
 *      11. -0 ** (+anything except 0, NAN, odd integer)  is +0
 *      12. +0 ** (-anything except 0, NAN)               is +INF, raise
 * divbyzero
 *      13. -0 ** (-anything except 0, NAN, odd integer)  is +INF, raise
 * divbyzero
 *      14. -0 ** (+odd integer) is -0
 *      15. -0 ** (-odd integer) is -INF, raise divbyzero
 *      16. +INF ** (+anything except 0,NAN) is +INF
 *      17. +INF ** (-anything except 0,NAN) is +0
 *      18. -INF ** (+odd integer) is -INF
 *      19. -INF ** (anything) = -0 ** (-anything), (anything except odd
 * integer)
 *      20. (anything) ** 1 is (anything)
 *      21. (anything) ** -1 is 1/(anything)
 *      22. (-anything) ** (integer) is (-1)**(integer)*(+anything**integer)
 *      23. (-anything except 0 and inf) ** (non-integer) is NAN
 *
 * Accuracy:
 *      pow(x,y) returns x**y nearly rounded. In particular
 *                      pow(integer,integer)
 *      always returns the correct integer provided it is
 *      representable.
 *
 * Constants :
 * The hexadecimal values are the intended ones for the following
 * constants. The decimal values may be used, provided that the
 * compiler will convert from decimal to binary accurately enough
 * to produce the hexadecimal values shown.
 */

#include "libm.h"

static const double bp[] =
    {
        1.0, 1.5,
},
                    dp_h[] =
                        {
                            0.0, 5.84962487220764160156e-01,
}, /* 0x3FE2B803, 0x40000000 */
    dp_l[] =
        {
            0.0, 1.35003920212974897128e-08,
},                              /* 0x3E4CFDEB, 0x43CFD006 */
    two53 = 9007199254740992.0, /* 0x43400000, 0x00000000 */
    huge = 1.0e300,
                    tiny = 1.0e-300,
                    /* poly coefs for (3/2)*(log(x)-2s-2/3*s**3 */
    L1 = 5.99999999999994648725e-01,     /* 0x3FE33333, 0x33333303 */
    L2 = 4.28571428578550184252e-01,     /* 0x3FDB6DB6, 0xDB6FABFF */
    L3 = 3.33333329818377432918e-01,     /* 0x3FD55555, 0x518F264D */
    L4 = 2.72728123808534006489e-01,     /* 0x3FD17460, 0xA91D4101 */
    L5 = 2.30660745775561754067e-01,     /* 0x3FCD864A, 0x93C9DB65 */
    L6 = 2.06975017800338417784e-01,     /* 0x3FCA7E28, 0x4A454EEF */
    P1 = 1.66666666666666019037e-01,     /* 0x3FC55555, 0x5555553E */
    P2 = -2.77777777770155933842e-03,    /* 0xBF66C16C, 0x16BEBD93 */
    P3 = 6.61375632143793436117e-05,     /* 0x3F11566A, 0xAF25DE2C */
    P4 = -1.65339022054652515390e-06,    /* 0xBEBBBD41, 0xC5D26BF1 */
    P5 = 4.13813679705723846039e-08,     /* 0x3E663769, 0x72BEA4D0 */
    lg2 = 6.93147180559945286227e-01,    /* 0x3FE62E42, 0xFEFA39EF */
    lg2_h = 6.93147182464599609375e-01,  /* 0x3FE62E43, 0x00000000 */
    lg2_l = -1.90465429995776804525e-09, /* 0xBE205C61, 0x0CA86C39 */
    ovt = 8.0085662595372944372e-017,    /* -(1024-log2(ovfl+.5ulp)) */
    cp = 9.61796693925975554329e-01,     /* 0x3FEEC709, 0xDC3A03FD =2/(3ln2) */
    cp_h = 9.61796700954437255859e-01,   /* 0x3FEEC709, 0xE0000000 =(float)cp */
    cp_l =
        -7.02846165095275826516e-09, /* 0xBE3E2FE0, 0x145B01F5 =tail of cp_h*/
    ivln2 = 1.44269504088896338700e+00,   /* 0x3FF71547, 0x652B82FE =1/ln2 */
    ivln2_h = 1.44269502162933349609e+00, /* 0x3FF71547, 0x60000000 =24b 1/ln2*/
    ivln2_l =
        1.92596299112661746887e-08; /* 0x3E54AE0B, 0xF85DDF44 =1/ln2 tail*/

double pow(double x, double y) {
  double z, ax, z_h, z_l, p_h, p_l;
  double y1, t1, t2, r, s, t, u, v, w;
  int32_t i, j, k, yisint, n;
  int32_t hx, hy, ix, iy;
  uint32_t lx, ly;

  EXTRACT_WORDS(hx, lx, x);
  EXTRACT_WORDS(hy, ly, y);
  ix = hx & 0x7fffffff;
  iy = hy & 0x7fffffff;

  /* x**0 = 1, even if x is NaN */
  if ((iy | ly) == 0)
    return 1.0;
  /* 1**y = 1, even if y is NaN */
  if (hx == 0x3ff00000 && lx == 0)
    return 1.0;
  /* NaN if either arg is NaN */
  if (ix > 0x7ff00000 || (ix == 0x7ff00000 && lx != 0) || iy > 0x7ff00000 ||
      (iy == 0x7ff00000 && ly != 0))
    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 >= 0x43400000)
      yisint = 2; /* even integer y */
    else if (iy >= 0x3ff00000) {
      k = (iy >> 20) - 0x3ff; /* exponent */
      if (k > 20) {
        j = ly >> (52 - k);
        if ((j << (52 - k)) == ly)
          yisint = 2 - (j & 1);
      } else if (ly == 0) {
        j = iy >> (20 - k);
        if ((j << (20 - k)) == iy)
          yisint = 2 - (j & 1);
      }
    }
  }

  /* special value of y */
  if (ly == 0) {
    if (iy == 0x7ff00000) {              /* y is +-inf */
      if (((ix - 0x3ff00000) | lx) == 0) /* (-1)**+-inf is 1 */
        return 1.0;
      else if (ix >= 0x3ff00000) /* (|x|>1)**+-inf = inf,0 */
        return hy >= 0 ? y : 0.0;
      else /* (|x|<1)**+-inf = 0,inf */
        return hy >= 0 ? 0.0 : -y;
    }
    if (iy == 0x3ff00000) { /* y is +-1 */
      if (hy >= 0)
        return x;
      y = 1 / x;
#if FLT_EVAL_METHOD != 0
      {
        union {
          double f;
          uint64_t i;
        } u = {y};
        uint64_t i = u.i & -1ULL / 2;
        if (i >> 52 == 0 && (i & (i - 1)))
          FORCE_EVAL((float)y);
      }
#endif
      return y;
    }
    if (hy == 0x40000000) /* y is 2 */
      return x * x;
    if (hy == 0x3fe00000) { /* y is 0.5 */
      if (hx >= 0)          /* x >= +0 */
        return sqrt(x);
    }
  }

  ax = fabs(x);
  /* special value of x */
  if (lx == 0) {
    if (ix == 0x7ff00000 || ix == 0 ||
        ix == 0x3ff00000) { /* x is +-0,+-inf,+-1 */
      z = ax;
      if (hy < 0) /* z = (1/|x|) */
        z = 1.0 / z;
      if (hx < 0) {
        if (((ix - 0x3ff00000) | 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;
    }
  }

  s = 1.0; /* 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) */
      s = -1.0;
  }

  /* |y| is huge */
  if (iy > 0x41e00000) {   /* if |y| > 2**31 */
    if (iy > 0x43f00000) { /* if |y| > 2**64, must o/uflow */
      if (ix <= 0x3fefffff)
        return hy < 0 ? huge * huge : tiny * tiny;
      if (ix >= 0x3ff00000)
        return hy > 0 ? huge * huge : tiny * tiny;
    }
    /* over/underflow if x is not close to one */
    if (ix < 0x3fefffff)
      return hy < 0 ? s * huge * huge : s * tiny * tiny;
    if (ix > 0x3ff00000)
      return hy > 0 ? s * huge * huge : s * 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 - 1.0; /* t has 20 trailing zeros */
    w = (t * t) * (0.5 - t * (0.3333333333333333333333 - t * 0.25));
    u = ivln2_h * t; /* ivln2_h has 21 sig. bits */
    v = t * ivln2_l - w * ivln2;
    t1 = u + v;
    SET_LOW_WORD(t1, 0);
    t2 = v - (t1 - u);
  } else {
    double ss, s2, s_h, s_l, t_h, t_l;
    n = 0;
    /* take care subnormal number */
    if (ix < 0x00100000) {
      ax *= two53;
      n -= 53;
      GET_HIGH_WORD(ix, ax);
    }
    n += ((ix) >> 20) - 0x3ff;
    j = ix & 0x000fffff;
    /* determine interval */
    ix = j | 0x3ff00000; /* normalize ix */
    if (j <= 0x3988E)    /* |x|<sqrt(3/2) */
      k = 0;
    else if (j < 0xBB67A) /* |x|<sqrt(3)   */
      k = 1;
    else {
      k = 0;
      n += 1;
      ix -= 0x00100000;
    }
    SET_HIGH_WORD(ax, ix);

    /* compute ss = 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 = 1.0 / (ax + bp[k]);
    ss = u * v;
    s_h = ss;
    SET_LOW_WORD(s_h, 0);
    /* t_h=ax+bp[k] High */
    t_h = 0.0;
    SET_HIGH_WORD(t_h, ((ix >> 1) | 0x20000000) + 0x00080000 + (k << 18));
    t_l = ax - (t_h - bp[k]);
    s_l = v * ((u - s_h * t_h) - s_h * t_l);
    /* compute log(ax) */
    s2 = ss * ss;
    r = s2 * s2 *
        (L1 + s2 * (L2 + s2 * (L3 + s2 * (L4 + s2 * (L5 + s2 * L6)))));
    r += s_l * (s_h + ss);
    s2 = s_h * s_h;
    t_h = 3.0 + s2 + r;
    SET_LOW_WORD(t_h, 0);
    t_l = r - ((t_h - 3.0) - s2);
    /* u+v = ss*(1+...) */
    u = s_h * t_h;
    v = s_l * t_h + t_l * ss;
    /* 2/(3log2)*(ss+...) */
    p_h = u + v;
    SET_LOW_WORD(p_h, 0);
    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) = (ss+..)*2/(3*log2) = n + dp_h + z_h + z_l */
    t = (double)n;
    t1 = ((z_h + z_l) + dp_h[k]) + t;
    SET_LOW_WORD(t1, 0);
    t2 = z_l - (((t1 - t) - dp_h[k]) - z_h);
  }

  /* split up y into y1+y2 and compute (y1+y2)*(t1+t2) */
  y1 = y;
  SET_LOW_WORD(y1, 0);
  p_l = (y - y1) * t1 + y * t2;
  p_h = y1 * t1;
  z = p_l + p_h;
  EXTRACT_WORDS(j, i, z);
  if (j >= 0x40900000) {             /* z >= 1024 */
    if (((j - 0x40900000) | i) != 0) /* if z > 1024 */
      return s * huge * huge;        /* overflow */
    if (p_l + ovt > z - p_h)
      return s * huge * huge; /* overflow */
  } else if ((j & 0x7fffffff) >= 0x4090cc00) {
    /* z <= -1075 */                 // FIXME: instead of abs(j) use unsigned j
    if (((j - 0xc090cc00) | i) != 0) /* z < -1075 */
      return s * tiny * tiny;        /* underflow */
    if (p_l <= z - p_h)
      return s * tiny * tiny; /* underflow */
  }
  /*
   * compute 2**(p_h+p_l)
   */
  i = j & 0x7fffffff;
  k = (i >> 20) - 0x3ff;
  n = 0;
  if (i > 0x3fe00000) { /* if |z| > 0.5, set n = [z+0.5] */
    n = j + (0x00100000 >> (k + 1));
    k = ((n & 0x7fffffff) >> 20) - 0x3ff; /* new k for n */
    t = 0.0;
    SET_HIGH_WORD(t, n & ~(0x000fffff >> k));
    n = ((n & 0x000fffff) | 0x00100000) >> (20 - k);
    if (j < 0)
      n = -n;
    p_h -= t;
  }
  t = p_l + p_h;
  SET_LOW_WORD(t, 0);
  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 - 2.0) - (w + z * w);
  z = 1.0 - (r - z);
  GET_HIGH_WORD(j, z);
  j += n << 20;
  if ((j >> 20) <= 0) /* subnormal output */
    z = scalbn(z, n);
  else
    SET_HIGH_WORD(z, j);
  return s * z;
}