text: /* 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)
              {
                  uint32_t j2 = ly >> (52 - k);
                  if ((j2 << (52 - k)) == ly)
                      yisint = 2 - (j2 & 1);
              }
              else if (ly == 0)
              {
                  uint32_t j2 = iy >> (20 - k);
                  if ((j2 << (20 - k)) == (uint32_t)iy)
                      yisint = 2 - (j2 & 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;
  }
  