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/* Copyright (C) 1994 DJ Delorie, see COPYING.DJ for details */

/* e_powf.c -- float version of e_pow.c.

 * Conversion to float by Ian Lance Taylor, Cygnus Support, ian@cygnus.com.

 */

/*

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

 * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved.

 *

 * Developed at SunPro, a Sun Microsystems, Inc. business.

 * Permission to use, copy, modify, and distribute this

 * software is freely granted, provided that this notice

 * is preserved.

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

 */

#if defined(LIBM_SCCS) && !defined(lint)

static char rcsid[] = "$Id: e_powf.c,v 1.2 1994/08/18 23:05:54 jtc Exp $";

#endif

#include "math.h"

#include "math_private.h"

#ifdef __STDC__

static const float

#else

static float

#endif

bp[] = {1.0, 1.5,},

dp_h[] = { 0.0, 5.84960938e-01,}, /* 0x3f15c000 */

dp_l[] = { 0.0, 1.56322085e-06,}, /* 0x35d1cfdc */

zero    =  0.0,

one	=  1.0,

two	=  2.0,

two24	=  16777216.0,	/* 0x4b800000 */

huge	=  1.0e30,

tiny    =  1.0e-30,

	/* poly coefs for (3/2)*(log(x)-2s-2/3*s**3 */

L1  =  6.0000002384e-01, /* 0x3f19999a */

L2  =  4.2857143283e-01, /* 0x3edb6db7 */

L3  =  3.3333334327e-01, /* 0x3eaaaaab */

L4  =  2.7272811532e-01, /* 0x3e8ba305 */

L5  =  2.3066075146e-01, /* 0x3e6c3255 */

L6  =  2.0697501302e-01, /* 0x3e53f142 */

P1   =  1.6666667163e-01, /* 0x3e2aaaab */

P2   = -2.7777778450e-03, /* 0xbb360b61 */

P3   =  6.6137559770e-05, /* 0x388ab355 */

P4   = -1.6533901999e-06, /* 0xb5ddea0e */

P5   =  4.1381369442e-08, /* 0x3331bb4c */

lg2  =  6.9314718246e-01, /* 0x3f317218 */

lg2_h  =  6.93145752e-01, /* 0x3f317200 */

lg2_l  =  1.42860654e-06, /* 0x35bfbe8c */

ovt =  4.2995665694e-08, /* -(128-log2(ovfl+.5ulp)) */

cp    =  9.6179670095e-01, /* 0x3f76384f =2/(3ln2) */

cp_h  =  9.6179199219e-01, /* 0x3f763800 =head of cp */

cp_l  =  4.7017383622e-06, /* 0x369dc3a0 =tail of cp_h */

ivln2    =  1.4426950216e+00, /* 0x3fb8aa3b =1/ln2 */

ivln2_h  =  1.4426879883e+00, /* 0x3fb8aa00 =16b 1/ln2*/

ivln2_l  =  7.0526075433e-06; /* 0x36eca570 =1/ln2 tail*/

#ifdef __STDC__

	float __ieee754_powf(float x, float y)

#else

	float __ieee754_powf(x,y)

	float x, y;

#endif

{

	float z,ax,z_h,z_l,p_h,p_l;

	float y1,t1,t2,r,s,t,u,v,w;

	int32_t i,j,k,yisint,n;

	int32_t hx,hy,ix,iy,is;

	GET_FLOAT_WORD(hx,x);

	GET_FLOAT_WORD(hy,y);

	ix = hx&0x7fffffff;  iy = hy&0x7fffffff;

    /* y==zero: x**0 = 1 */

	if(iy==0) return one;

    /* +-NaN return x+y */

	if(ix > 0x7f800000 ||

	   iy > 0x7f800000)

		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>=0x4b800000) yisint = 2; /* even integer y */

	    else if(iy>=0x3f800000) {

		k = (iy>>23)-0x7f;	   /* exponent */

		j = iy>>(23-k);

		if((j<<(23-k))==iy) yisint = 2-(j&1);

	    }

	}

    /* special value of y */

	if (iy==0x7f800000) {	/* y is +-inf */

	    if (ix==0x3f800000)

	        return  y - y;	/* inf**+-1 is NaN */

	    else if (ix > 0x3f800000)/* (|x|>1)**+-inf = inf,0 */

	        return (hy>=0)? y: zero;

	    else			/* (|x|<1)**-,+inf = inf,0 */

	        return (hy<0)?-y: zero;

	}

	if(iy==0x3f800000) {	/* y is  +-1 */

	    if(hy<0) return one/x; else return x;

	}

	if(hy==0x40000000) return x*x; /* y is  2 */

	if(hy==0x3f000000) {	/* y is  0.5 */

	    if(hx>=0)	/* x >= +0 */

	    return sqrtf(x);

	}

	ax   = fabsf(x);

    /* special value of x */

	if(ix==0x7f800000||ix==0||ix==0x3f800000){

	    z = ax;			/*x is +-0,+-inf,+-1*/

	    if(hy<0) z = one/z;	/* z = (1/|x|) */

	    if(hx<0) {

		if(((ix-0x3f800000)|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(((((u_int32_t)hx>>31)-1)|yisint)==0) return (x-x)/(x-x);

    /* |y| is huge */

	if(iy>0x4d000000) { /* if |y| > 2**27 */

	/* over/underflow if x is not close to one */

	    if(ix<0x3f7ffff8) return (hy<0)? huge*huge:tiny*tiny;

	    if(ix>0x3f800007) 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)*((float)0.5-t*((float)0.333333333333-t*(float)0.25));

	    u = ivln2_h*t;	/* ivln2_h has 16 sig. bits */

	    v = t*ivln2_l-w*ivln2;

	    t1 = u+v;

	    GET_FLOAT_WORD(is,t1);

	    SET_FLOAT_WORD(t1,is&0xfffff000);

	    t2 = v-(t1-u);

	} else {

	    float s2,s_h,s_l,t_h,t_l;

	    n = 0;

	/* take care subnormal number */

	    if(ix<0x00800000)

		{ax *= two24; n -= 24; GET_FLOAT_WORD(ix,ax); }

	    n  += ((ix)>>23)-0x7f;

	    j  = ix&0x007fffff;

	/* determine interval */

	    ix = j|0x3f800000;		/* normalize ix */

	    if(j<=0x1cc471) k=0;	/* |x|

	    else if(j<0x5db3d7) k=1;	/* |x|

	    else {k=0;n+=1;ix -= 0x00800000;}

	    SET_FLOAT_WORD(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;

	    GET_FLOAT_WORD(is,s_h);

	    SET_FLOAT_WORD(s_h,is&0xfffff000);

	/* t_h=ax+bp[k] High */

	    SET_FLOAT_WORD(t_h,((ix>>1)|0x20000000)+0x0040000+(k<<21));

	    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 = (float)3.0+s2+r;

	    GET_FLOAT_WORD(is,t_h);

	    SET_FLOAT_WORD(t_h,is&0xfffff000);

	    t_l = r-((t_h-(float)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;

	    GET_FLOAT_WORD(is,p_h);

	    SET_FLOAT_WORD(p_h,is&0xfffff000);

	    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 = (float)n;

	    t1 = (((z_h+z_l)+dp_h[k])+t);

	    GET_FLOAT_WORD(is,t1);

	    SET_FLOAT_WORD(t1,is&0xfffff000);

	    t2 = z_l-(((t1-t)-dp_h[k])-z_h);

	}

	s = one; /* s (sign of result -ve**odd) = -1 else = 1 */

	if(((((u_int32_t)hx>>31)-1)|(yisint-1))==0)

	    s = -one;	/* (-ve)**(odd int) */

    /* split up y into y1+y2 and compute (y1+y2)*(t1+t2) */

	GET_FLOAT_WORD(is,y);

	SET_FLOAT_WORD(y1,is&0xfffff000);

	p_l = (y-y1)*t1+y*t2;

	p_h = y1*t1;

	z = p_l+p_h;

	GET_FLOAT_WORD(j,z);

	if (j>0x43000000)				/* if z > 128 */

	    return s*huge*huge;				/* overflow */

	else if (j==0x43000000) {			/* if z == 128 */

	    if(p_l+ovt>z-p_h) return s*huge*huge;	/* overflow */

	}

	else if ((j&0x7fffffff)>0x43160000)		/* z <= -150 */

	    return s*tiny*tiny;				/* underflow */

	else if (j==0xc3160000){			/* z == -150 */

	    if(p_l<=z-p_h) return s*tiny*tiny;		/* underflow */

	}

    /*

     * compute 2**(p_h+p_l)

     */

	i = j&0x7fffffff;

	k = (i>>23)-0x7f;

	n = 0;

	if(i>0x3f000000) {		/* if |z| > 0.5, set n = [z+0.5] */

	    n = j+(0x00800000>>(k+1));

	    k = ((n&0x7fffffff)>>23)-0x7f;	/* new k for n */

	    SET_FLOAT_WORD(t,n&~(0x007fffff>>k));

	    n = ((n&0x007fffff)|0x00800000)>>(23-k);

	    if(j<0) n = -n;

	    p_h -= t;

	}

	t = p_l+p_h;

	GET_FLOAT_WORD(is,t);

	SET_FLOAT_WORD(t,is&0xfffff000);

	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_FLOAT_WORD(j,z);

	j += (n<<23);

	if((j>>23)<=0) z = scalbnf(z,n);	/* subnormal output */

	else SET_FLOAT_WORD(z,j);

	return s*z;

}