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```/* derived from /netlib/fdlibm */

/* @(#)e_pow.c 1.3 95/01/18 */
/*
* ====================================================
*
* Developed at SunSoft, a Sun Microsystems, Inc. business.
* 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"

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 y1,t1,t2,r,s,t,u,v,w;
int i,j,k,yisint,n;
int hx,hy,ix,iy;
unsigned lx,ly;

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) return one;

/* +-NaN return x+y */
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)
return  y - y;	/* inf**+-1 is NaN */
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;
}
}

/* (x<0)**(non-int) is NaN */
if((((hx>>31)+1)|yisint)==0) return (x-x)/(x-x);

/* |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)? Huge*Huge:tiny*tiny;
if(ix>0x3ff00000) return (hy>0)? Huge*Huge: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 = x-1;		/* 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 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 s = 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]);
s = u*v;
s_h = s;
__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 = s*s;
r = s2*s2*(L1+s2*(L2+s2*(L3+s2*(L4+s2*(L5+s2*L6)))));
r += s_l*(s_h+s);
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 = s*(1+...) */
u = s_h*t_h;
v = s_l*t_h+t_l*s;
/* 2/(3log2)*(s+...) */
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) = (s+..)*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);
}

s = one; /* s (sign of result -ve**odd) = -1 else = 1 */
if((((hx>>31)+1)|(yisint-1))==0) s = -one;/* (-ve)**(odd int) */

/* 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 */
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;
__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) z = scalbn(z,n);	/* subnormal output */
else __HI(z) += (n<<20);
return s*z;
}
```