text: #ifndef lint
  static char sccsid[] = "@(#)e_pow.c 1.5 04/04/22 SMI";
  #endif
  
  /*
   * ====================================================
   * 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.
   * ====================================================
   */
  
  /* __ieee754_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.  (anything) ** 1  is itself
   *	3.  (anything) ** 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 NAN
   *	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
   *	13. -0 ** (-anything except 0, NAN, odd integer)  is +INF
   *	14. -0 ** (odd integer) = -( +0 ** (odd integer) )
   *	15. +INF ** (+anything except 0,NAN) is +INF
   *	16. +INF ** (-anything except 0,NAN) is +0
   *	17. -INF ** (anything)  = -0 ** (-anything)
   *	18. (-anything) ** (integer) is (-1)**(integer)*(+anything**integer)
   *	19. (-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 "fdlibm.h"
  
  #ifdef __STDC__
  static const double
  #else
  static double
  #endif
          bp[] = {1.0, 1.5,},
          dp_h[] = {0.0, 5.84962487220764160156e-01,}, /* 0x3FE2B803, 0x40000000 */
          dp_l[] = {0.0, 1.35003920212974897128e-08,}, /* 0x3E4CFDEB, 0x43CFD006 */
          zero = 0.0,
          one = 1.0,
          two = 2.0,
          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-0017, /* -(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*/
  
  #ifdef __STDC__
  void __ieee754_pow(double x, double y, double* result)
  #else
  void __ieee754_pow(x, y, result)
          double x, y; double* result;
  #endif
  {
      double z, ax, z_h, z_l, p_h, p_l;
      double y1, t1, t2, r, s, t, u, v, w;
      int i0, i1, i, j, k, yisint, n;
      int hx, hy, ix, iy;
      unsigned lx, ly;
  
      i0 = ((*(int*) &one) >> 29) ^ 1;
      i1 = 1 - i0;
      hx = __HI(x);
      lx = __LO(x);
      hy = __HI(y);
      ly = __LO(y);
      ix = hx & 0x7fffffff;
      iy = hy & 0x7fffffff;
  
      /* y==zero: x**0 = 1 */
      if ((iy | ly) == 0) {
          *result = one;
          return;
      }
  
      /* +-NaN return x+y */
      if (ix > 0x7ff00000 || ((ix == 0x7ff00000) && (lx != 0)) ||
          iy > 0x7ff00000 || ((iy == 0x7ff00000) && (ly != 0))) {
          *result = x + y;
          return;
      }
  
      /* 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) {
                  *result = y - y;    /* inf**+-1 is NaN */
                  return;
              }
              else if (ix >= 0x3ff00000) {/* (|x|>1)**+-inf = inf,0 */
                  *result = (hy >= 0) ? y : zero;
                  return;
              }
              else {            /* (|x|<1)**-,+inf = inf,0 */
                  *result = (hy < 0) ? -y : zero;
                  return;
              }
          }
          if (iy == 0x3ff00000) {    /* y is  +-1 */
              if (hy < 0) {
                  *result = one / x;
                  return;
              }
              else {
                  *result = x;
                  return;
              }
          }
          if (hy == 0x40000000) {
              *result = x * x;
              return;
          } /* y is  2 */
          if (hy == 0x3fe00000) {    /* y is  0.5 */
              if (hx >= 0) {    /* x >= +0 */
                  sqrt(x, result);
                  return;
              }
          }
      }
  
      fabs(x, &ax);
      /* special value of x */
      if (lx == 0) {
          if (ix == 0x7ff00000 || ix == 0 || ix == 0x3ff00000) {
              z = ax;            /*x is +-0,+-inf,+-1*/
              if (hy < 0) {
                  z = one / z;
              }    /* z = (1/|x|) */
              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) */
              }
              *result = z;
              return;
          }
      }
  
      n = (hx >> 31) + 1;
  
      /* (x<0)**(non-int) is NaN */
      if ((n | yisint) == 0) {
          *result = (x - x) / (x - x);
          return;
      }
  
      s = one; /* s (sign of result -ve**odd) = -1 else = 1 */
      if ((n | (yisint - 1)) == 0) {
          s = -one;
      }/* (-ve)**(odd int) */
  
      /* |y| is huge */
      if (iy > 0x41e00000) { /* if |y| > 2**31 */
          if (iy > 0x43f00000) {    /* if |y| > 2**64, must o/uflow */
              if (ix <= 0x3fefffff) {
                  *result = (hy < 0) ? huge * huge : tiny * tiny;
                  return;
              }
              if (ix >= 0x3ff00000) {
                  *result = (hy > 0) ? huge * huge : tiny * tiny;
                  return;
              }
          }
          /* over/underflow if x is not close to one */
          if (ix < 0x3fefffff) {
              *result = (hy < 0) ? s * huge * huge : s * tiny * tiny;
              return;
          }
          if (ix > 0x3ff00000) {
              *result = (hy > 0) ? s * huge * huge : s * tiny * tiny;
              return;
          }
          /* 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 - one;        /* 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;
          __LO(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;
              ix = __HI(ax);
          }
          n += ((ix) >> 20) - 0x3ff;
          j = ix & 0x000fffff;
          /* determine interval */
          ix = j | 0x3ff00000;        /* normalize ix */
          if (j <= 0x3988E) {
              k = 0;        /* |x|<sqrt(3/2) */
          }
          else if (j < 0xBB67A) {
              k = 1;    /* |x|<sqrt(3)   */
          }
          else {
              k = 0;
              n += 1;
              ix -= 0x00100000;
          }
          __HI(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 = one / (ax + bp[k]);
          ss = u * v;
          s_h = ss;
          __LO(s_h) = 0;
          /* t_h=ax+bp[k] High */
          t_h = zero;
          __HI(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;
          __LO(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;
          __LO(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);
          __LO(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;
      __LO(y1) = 0;
      p_l = (y - y1) * t1 + y * t2;
      p_h = y1 * t1;
      z = p_l + p_h;
      j = __HI(z);
      i = __LO(z);
      if (j >= 0x40900000) {                /* z >= 1024 */
          if (((j - 0x40900000) | i) != 0) {            /* if z > 1024 */
              *result = s * huge * huge;            /* overflow */
              return;
          }
          else {
              if (p_l + ovt > z - p_h) {
                  *result = s * huge * huge;
                  return;
              }    /* overflow */
          }
      }
      else if ((j & 0x7fffffff) >= 0x4090cc00) {    /* z <= -1075 */
          if (((j - 0xc090cc00) | i) != 0) {        /* z < -1075 */
              *result = s * tiny * tiny;        /* underflow */
              return;
          }
          else {
              if (p_l <= z - p_h) {
                  *result = s * tiny * tiny;
                  return;
              }    /* 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 = zero;
          __HI(t) = (n & ~(0x000fffff >> k));
          n = ((n & 0x000fffff) | 0x00100000) >> (20 - k);
          if (j < 0) {
              n = -n;
          }
          p_h -= t;
      }
      t = p_l + p_h;
      __LO(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 - two) - (w + z * w);
      z = one - (r - z);
      j = __HI(z);
      j += (n << 20);
      if ((j >> 20) <= 0) {
          scalbn(z, n, &z);    /* subnormal output */
      }
      else
          __HI(z) += (n << 20);
      *result = s * z;
      return;
  }
  