-fix a long-standing bug which affects the <close-to-1>^<huge number> case
(fixed in fdlibm-5.3) -being here, sync with -5.3 as far as possible (There is another bugfix - sign in overflow/underflow cases -; this doesn't change anything for us because the wrapper (w_pow.c) fixes this up. Keep things in sync anyway to ease further maintainance.)
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@ -12,7 +12,7 @@
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#include <sys/cdefs.h>
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#if defined(LIBM_SCCS) && !defined(lint)
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__RCSID("$NetBSD: e_pow.c,v 1.12 2002/05/26 22:01:51 wiz Exp $");
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__RCSID("$NetBSD: e_pow.c,v 1.13 2004/06/30 18:43:15 drochner Exp $");
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#endif
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/* __ieee754_pow(x,y) return x**y
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@ -22,7 +22,7 @@ __RCSID("$NetBSD: e_pow.c,v 1.12 2002/05/26 22:01:51 wiz Exp $");
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* 1. Compute and return log2(x) in two pieces:
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* log2(x) = w1 + w2,
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* where w1 has 53-24 = 29 bit trailing zeros.
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* 2. Perform y*log2(x) = n+y' by simulating muti-precision
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* 2. Perform y*log2(x) = n+y' by simulating multi-precision
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* arithmetic, where |y'|<=0.5.
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* 3. Return x**y = 2**n*exp(y'*log2)
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*
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@ -173,8 +173,13 @@ __ieee754_pow(double x, double y)
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}
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}
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n = (hx>>31)+1;
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/* (x<0)**(non-int) is NaN */
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if(((((u_int32_t)hx>>31)-1)|yisint)==0) return (x-x)/(x-x);
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if((n|yisint)==0) return (x-x)/(x-x);
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s = one; /* s (sign of result -ve**odd) = -1 else = 1 */
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if((n|(yisint-1))==0) s = -one;/* (-ve)**(odd int) */
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/* |y| is huge */
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if(iy>0x41e00000) { /* if |y| > 2**31 */
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@ -183,11 +188,11 @@ __ieee754_pow(double x, double y)
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if(ix>=0x3ff00000) return (hy>0)? huge*huge:tiny*tiny;
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}
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/* over/underflow if x is not close to one */
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if(ix<0x3fefffff) return (hy<0)? huge*huge:tiny*tiny;
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if(ix>0x3ff00000) return (hy>0)? huge*huge:tiny*tiny;
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if(ix<0x3fefffff) return (hy<0)? s*huge*huge:s*tiny*tiny;
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if(ix>0x3ff00000) return (hy>0)? s*huge*huge:s*tiny*tiny;
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/* now |1-x| is tiny <= 2**-20, suffice to compute
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log(x) by x-x^2/2+x^3/3-x^4/4 */
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t = x-1; /* t has 20 trailing zeros */
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t = ax-one; /* t has 20 trailing zeros */
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w = (t*t)*(0.5-t*(0.3333333333333333333333-t*0.25));
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u = ivln2_h*t; /* ivln2_h has 21 sig. bits */
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v = t*ivln2_l-w*ivln2;
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@ -195,7 +200,7 @@ __ieee754_pow(double x, double y)
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SET_LOW_WORD(t1,0);
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t2 = v-(t1-u);
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} else {
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double s2,s_h,s_l,t_h,t_l;
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double ss,s2,s_h,s_l,t_h,t_l;
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n = 0;
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/* take care subnormal number */
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if(ix<0x00100000)
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@ -209,11 +214,11 @@ __ieee754_pow(double x, double y)
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else {k=0;n+=1;ix -= 0x00100000;}
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SET_HIGH_WORD(ax,ix);
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/* compute s = s_h+s_l = (x-1)/(x+1) or (x-1.5)/(x+1.5) */
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/* compute ss = s_h+s_l = (x-1)/(x+1) or (x-1.5)/(x+1.5) */
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u = ax-bp[k]; /* bp[0]=1.0, bp[1]=1.5 */
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v = one/(ax+bp[k]);
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s = u*v;
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s_h = s;
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ss = u*v;
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s_h = ss;
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SET_LOW_WORD(s_h,0);
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/* t_h=ax+bp[k] High */
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t_h = zero;
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@ -221,33 +226,29 @@ __ieee754_pow(double x, double y)
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t_l = ax - (t_h-bp[k]);
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s_l = v*((u-s_h*t_h)-s_h*t_l);
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/* compute log(ax) */
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s2 = s*s;
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s2 = ss*ss;
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r = s2*s2*(L1+s2*(L2+s2*(L3+s2*(L4+s2*(L5+s2*L6)))));
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r += s_l*(s_h+s);
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r += s_l*(s_h+ss);
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s2 = s_h*s_h;
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t_h = 3.0+s2+r;
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SET_LOW_WORD(t_h,0);
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t_l = r-((t_h-3.0)-s2);
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/* u+v = s*(1+...) */
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/* u+v = ss*(1+...) */
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u = s_h*t_h;
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v = s_l*t_h+t_l*s;
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/* 2/(3log2)*(s+...) */
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v = s_l*t_h+t_l*ss;
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/* 2/(3log2)*(ss+...) */
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p_h = u+v;
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SET_LOW_WORD(p_h,0);
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p_l = v-(p_h-u);
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z_h = cp_h*p_h; /* cp_h+cp_l = 2/(3*log2) */
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z_l = cp_l*p_h+p_l*cp+dp_l[k];
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/* log2(ax) = (s+..)*2/(3*log2) = n + dp_h + z_h + z_l */
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/* log2(ax) = (ss+..)*2/(3*log2) = n + dp_h + z_h + z_l */
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t = (double)n;
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t1 = (((z_h+z_l)+dp_h[k])+t);
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SET_LOW_WORD(t1,0);
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t2 = z_l-(((t1-t)-dp_h[k])-z_h);
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}
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s = one; /* s (sign of result -ve**odd) = -1 else = 1 */
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if(((((u_int32_t)hx>>31)-1)|(yisint-1))==0)
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s = -one;/* (-ve)**(odd int) */
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/* split up y into y1+y2 and compute (y1+y2)*(t1+t2) */
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y1 = y;
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SET_LOW_WORD(y1,0);
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