/*

 * ====================================================

 * 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 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_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,

half    =  0.5,

qrtr    =  0.25,

thrd    =  3.3333333333333331e-01, /* 0x3fd55555, 0x55555555 */

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 y1,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 nan_mix(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(((u_int32_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 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)*(half-t*(thrd-t*qrtr));

      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+s2+r;

      SET_LOW_WORD(t_h,0);

      t_l = r-((t_h-3)-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 = 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 */

      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 += (int32_t)((u_int32_t)n<<20);

  if((j>>20)<=0) z = s_scalbn(z,n);  /* subnormal output */

  else SET_HIGH_WORD(z,j);

  return s*z;

}