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+/* @(#)e_pow.c 5.1 93/09/24 */
+/*
+ * ====================================================
+ * 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.
+ * ====================================================
+ */
+/* Modified by Naohiko Shimizu/Tokai University, Japan 1997/08/25,
+   for performance improvement on pipelined processors.
+*/
+
+#if defined(LIBM_SCCS) && !defined(lint)
+static char rcsid[] = "$NetBSD: e_pow.c,v 1.9 1995/05/12 04:57:32 jtc Exp $";
+#endif
+
+/* __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 "math.h"
+#include "math_private.h"
+#define zero      C[0]
+#define one	  C[1]
+#define two	  C[2]
+#define two53	  C[3]
+#define huge	  C[4]
+#define tiny      C[5]
+#define L1        C[6]
+#define L2        C[7]
+#define L3        C[8]
+#define L4        C[9]
+#define L5        C[10]
+#define L6        C[11]
+#define P1        C[12]
+#define P2        C[13]
+#define P3        C[14]
+#define P4        C[15]
+#define P5        C[16]
+#define lg2       C[17]
+#define lg2_h     C[18]
+#define lg2_l     C[19]
+#define ovt       C[20]
+#define cp        C[21]
+#define cp_h      C[22]
+#define cp_l      C[23]
+#define ivln2     C[24]
+#define ivln2_h   C[25]
+#define ivln2_l   C[26]
+
+#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 */
+C[] = {
+0.0,
+1.0,
+2.0,
+9007199254740992.0	,
+1.0e300,
+1.0e-300,
+5.99999999999994648725e-01 ,
+4.28571428578550184252e-01 ,
+3.33333329818377432918e-01 ,
+2.72728123808534006489e-01 ,
+2.30660745775561754067e-01 ,
+2.06975017800338417784e-01 ,
+1.66666666666666019037e-01 ,
+-2.77777777770155933842e-03 ,
+6.61375632143793436117e-05 ,
+-1.65339022054652515390e-06 ,
+4.13813679705723846039e-08 ,
+6.93147180559945286227e-01 ,
+6.93147182464599609375e-01 ,
+-1.90465429995776804525e-09 ,
+8.0085662595372944372e-0017 ,
+9.61796693925975554329e-01 ,
+9.61796700954437255859e-01 ,
+-7.02846165095275826516e-09 ,
+1.44269504088896338700e+00 ,
+1.44269502162933349609e+00 ,
+1.92596299112661746887e-08 };
+
+#ifdef __STDC__
+	double __ieee754_pow(double x, double y)
+#else
+	double __ieee754_pow(x,y)
+	double x, y;
+#endif
+{
+	double z,ax,z_h,z_l,p_h,p_l;
+	double y1,t1,t2,r,s,t,u,v,w, t12,t14,r_1,r_2,r_3;
+	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 C[1];
+
+    /* +-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((u_int32_t)(j<<(52-k))==ly) yisint = 2-(j&1);
+		} else if(ly==0) {
+		    j = iy>>(20-k);
+		    if((int32_t)(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: C[0];
+	        else			/* (|x|<1)**-,+inf = inf,0 */
+		    return (hy<0)?-y: C[0];
+	    }
+	    if(iy==0x3ff00000) {	/* y is  +-1 */
+		if(hy<0) return C[1]/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 = C[1]/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(((((u_int32_t)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)? C[4]*C[4]:C[5]*C[5];
+		if(ix>=0x3ff00000) return (hy>0)? C[4]*C[4]:C[5]*C[5];
+	    }
+	/* over/underflow if x is not close to one */
+	    if(ix<0x3fefffff) return (hy<0)? C[4]*C[4]:C[5]*C[5];
+	    if(ix>0x3ff00000) return (hy>0)? C[4]*C[4]:C[5]*C[5];
+	/* 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 = C[25]*t;	/* ivln2_h has 21 sig. bits */
+	    v = t*C[26]-w*C[24];
+	    t1 = u+v;
+	    SET_LOW_WORD(t1,0);
+	    t2 = v-(t1-u);
+	} else {
+	    double s2,s_h,s_l,t_h,t_l,s22,s24,s26,r1,r2,r3;
+	    n = 0;
+	/* take care subnormal number */
+	    if(ix<0x00100000)
+		{ax *= C[3]; 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 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 = C[1]/(ax+bp[k]);
+	    s = u*v;
+	    s_h = s;
+	    SET_LOW_WORD(s_h,0);
+	/* t_h=ax+bp[k] High */
+	    t_h = C[0];
+	    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 = s*s;
+#ifdef DO_NOT_USE_THIS
+	    r = s2*s2*(L1+s2*(L2+s2*(L3+s2*(L4+s2*(L5+s2*L6)))));
+#else
+	    r1 = C[10]+s2*C[11]; s22=s2*s2;
+	    r2 = C[8]+s2*C[9]; s24=s22*s22;
+	    r3 = C[6]+s2*C[7]; s26=s24*s22;
+            r = r3*s22 + r2*s24 + r1*s26;
+#endif
+	    r += s_l*(s_h+s);
+	    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 = s*(1+...) */
+	    u = s_h*t_h;
+	    v = s_l*t_h+t_l*s;
+	/* 2/(3log2)*(s+...) */
+	    p_h = u+v;
+	    SET_LOW_WORD(p_h,0);
+	    p_l = v-(p_h-u);
+	    z_h = C[22]*p_h;		/* cp_h+cp_l = 2/(3*log2) */
+	    z_l = C[23]*p_h+p_l*C[21]+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);
+	    SET_LOW_WORD(t1,0);
+	    t2 = z_l-(((t1-t)-dp_h[k])-z_h);
+	}
+
+	s = C[1]; /* s (sign of result -ve**odd) = -1 else = 1 */
+	if(((((u_int32_t)hx>>31)-1)|(yisint-1))==0)
+	    s = -C[1];/* (-ve)**(odd int) */
+
+    /* 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*C[4]*C[4];			/* overflow */
+	    else {
+		if(p_l+C[20]>z-p_h) return s*C[4]*C[4];	/* overflow */
+	    }
+	} else if((j&0x7fffffff)>=0x4090cc00 ) {	/* z <= -1075 */
+	    if(((j-0xc090cc00)|i)!=0) 		/* z < -1075 */
+		return s*C[5]*C[5];		/* underflow */
+	    else {
+		if(p_l<=z-p_h) return s*C[5]*C[5];	/* 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 = C[0];
+	    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*C[18];
+	v = (p_l-(t-p_h))*C[17]+t*C[19];
+	z = u+v;
+	w = v-(z-u);
+	t  = z*z;
+#ifdef DO_NOT_USE_THIS
+	t1  = z - t*(C[12]+t*(C[13]+t*(C[14]+t*(C[15]+t*C[16]))));
+#else
+	r_1 = C[15]+t*C[16]; t12 = t*t;
+	r_2 = C[13]+t*C[14]; t14 = t12*t12;
+	r_3 = t*C[12];
+	t1 = z - r_3 - t12*r_2 - t14*r_1;
+#endif
+	r  = (z*t1)/(t1-C[2])-(w+z*w);
+	z  = C[1]-(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;
+}