text: /* @(#)e_pow.c 1.5 04/04/22 SMI */
  /*
   * ====================================================
   * 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.
   * ====================================================
   */
  
  #include <sys/cdefs.h>
  
  /* __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 multi-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 except 1 ** NAN = 1
   *	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
   *	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 "math.h"
  #include "math_private.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 */
    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*/
  
  double __ieee754_pow(double x, double y) {
    double z, ax, z_h, z_l, p_h, p_l;
    double yy1, t1, t2, r, s, t, u, v, w;
    int32_t i, j, k, yisint, n;
    int32_t hx, hy, ix, iy;
    u_int32_t lx, ly;
  
    EXTRACT_WORDS(hx, lx, x);
    EXTRACT_WORDS(hy, ly, y);
    ix = hx & 0x7fffffff;
    iy = hy & 0x7fffffff;
  
    /* y==zero: x**0 = 1 */
    if ((iy | ly) == 0)
      return one;
  
    /* x==1: 1**y = 1, even if y is NaN */
    if (hx == 0x3ff00000 && lx == 0)
      return one;
  
    /* y!=zero: result is NaN if either arg is NaN */
    if (ix > 0x7ff00000 || ((ix == 0x7ff00000) && (lx != 0)) || iy > 0x7ff00000 ||
        ((iy == 0x7ff00000) && (ly != 0)))
      return (x + 0.0) + (y + 0.0);
  
    /* 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 ((uint32_t)(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)
          return one;              /* (-1)**+-inf is 1 */
        else if (ix >= 0x3ff00000) /* (|x|>1)**+-inf = inf,0 */
          return (hy >= 0) ? y : zero;
        else /* (|x|<1)**-,+inf = inf,0 */
          return (hy < 0) ? -y : zero;
      }
      if (iy == 0x3ff00000) { /* y is  +-1 */
        if (hy < 0)
          return one / x;
        else
          return x;
      }
      if (hy == 0x40000000)
        return x * x;         /* y is  2 */
      if (hy == 0x3fe00000) { /* y is  0.5 */
        if (hx >= 0)          /* x >= +0 */
          return __ieee754_sqrt(x);
      }
    }
  
    ax = fabs(x);
    /* 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) */
        }
        return z;
      }
    }
  
    /* CYGNUS LOCAL + fdlibm-5.3 fix: This used to be
        n = (hx>>31)+1;
       but ANSI C says a right shift of a signed negative quantity is
       implementation defined.  */
    n = ((u_int32_t)hx >> 31) - 1;
  
    /* (x<0)**(non-int) is NaN */
    if ((n | yisint) == 0)
      return (x - x) / (x - x);
  
    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)
          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 - 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;
      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)
        k = 0; /* |x|<sqrt(3/2) */
      else if (j < 0xBB67A)
        k = 1; /* |x|<sqrt(3)   */
      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 = one / (ax + bp[k]);
      ss = u * v;
      s_h = ss;
      SET_LOW_WORD(s_h, 0);
      /* t_h=ax+bp[k] High */
      t_h = zero;
      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 yy1+y2 and compute (yy1+y2)*(t1+t2) */
    yy1 = y;
    SET_LOW_WORD(yy1, 0);
    p_l = (y - yy1) * t1 + y * t2;
    p_h = yy1 * 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 */
      else {
        if (p_l + ovt > z - p_h)
          return s * huge * huge; /* overflow */
      }
    } else if ((j & 0x7fffffff) >= 0x4090cc00) { /* z <= -1075 */
      if (((j - 0xc090cc00) | i) != 0)           /* z < -1075 */
        return s * tiny * tiny;                  /* underflow */
      else {
        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 = zero;
      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 - two) - (w + z * w);
    z = one - (r - z);
    GET_HIGH_WORD(j, z);
    j += (n << 20);
    if ((j >> 20) <= 0)
      z = scalbn(z, n); /* subnormal output */
    else
      SET_HIGH_WORD(z, j);
    return s * z;
  }
  