From: martynas Date: Sun, 20 Jul 2008 13:07:27 +0000 (+0000) Subject: get in the bug fix for pow, from fdlibm 5.3. also adapt it for X-Git-Url: http://artulab.com/gitweb/?a=commitdiff_plain;h=17d217fa2eec87d6eb388749b37dc3d926685a4e;p=openbsd get in the bug fix for pow, from fdlibm 5.3. also adapt it for powf, the float version of it > 1. e_pow.c incorrect results when > x is very close to -1.0 and y is very large, e.g. > pow(-1.0000000000000002e+00,4.5035996273704970e+15) = 0 > pow(-9.9999999999999978e-01,4.5035996273704970e+15) = 0 > Correct results are close to -e and -1/e. while here merge more changes for pow, fixes sign in oflow/uflow cases ok millert@ --- diff --git a/lib/libm/src/e_pow.c b/lib/libm/src/e_pow.c index 9ee8279ea3a..4c4ad3bd112 100644 --- a/lib/libm/src/e_pow.c +++ b/lib/libm/src/e_pow.c @@ -5,7 +5,7 @@ * * Developed at SunPro, a Sun Microsystems, Inc. business. * Permission to use, copy, modify, and distribute this - * software is freely granted, provided that this notice + * software is freely granted, provided that this notice * is preserved. * ==================================================== */ @@ -21,7 +21,7 @@ static char rcsid[] = "$NetBSD: e_pow.c,v 1.9 1995/05/12 04:57:32 jtc Exp $"; * 1. Compute and return log2(x) in two pieces: * log2(x) = w1 + w2, * where w1 has 53-24 = 29 bit trailing zeros. - * 2. Perform y*log2(x) = n+y' by simulating muti-precision + * 2. Perform y*log2(x) = n+y' by simulating multi-precision * arithmetic, where |y'|<=0.5. * 3. Return x**y = 2**n*exp(y'*log2) * @@ -49,20 +49,20 @@ static char rcsid[] = "$NetBSD: e_pow.c,v 1.9 1995/05/12 04:57:32 jtc Exp $"; * Accuracy: * pow(x,y) returns x**y nearly rounded. In particular * pow(integer,integer) - * always returns the correct integer provided it is + * 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 + * 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" -static const double +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 */ @@ -109,12 +109,12 @@ __ieee754_pow(double x, double y) ix = hx&0x7fffffff; iy = hy&0x7fffffff; /* y==zero: x**0 = 1 */ - if((iy|ly)==0) return one; + 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; + 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 @@ -122,7 +122,7 @@ __ieee754_pow(double x, double y) * yisint = 2 ... y is an even int */ yisint = 0; - if(hx<0) { + if(hx<0) { if(iy>=0x43400000) yisint = 2; /* even integer y */ else if(iy>=0x3ff00000) { k = (iy>>20)-0x3ff; /* exponent */ @@ -133,11 +133,11 @@ __ieee754_pow(double x, double y) j = iy>>(20-k); if((j<<(20-k))==iy) yisint = 2-(j&1); } - } - } + } + } /* special value of y */ - if(ly==0) { + if(ly==0) { if (iy==0x7ff00000) { /* y is +-inf */ if(((ix-0x3ff00000)|lx)==0) return y - y; /* inf**+-1 is NaN */ @@ -145,14 +145,14 @@ __ieee754_pow(double x, double y) 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 __ieee754_sqrt(x); + return __ieee754_sqrt(x); } } @@ -165,15 +165,20 @@ __ieee754_pow(double x, double y) if(hx<0) { if(((ix-0x3ff00000)|yisint)==0) { z = (z-z)/(z-z); /* (-1)**non-int is NaN */ - } else if(yisint==1) + } else if(yisint==1) z = -z; /* (x<0)**odd = -(|x|**odd) */ } return z; } } - + + n = (hx>>31)+1; + /* (x<0)**(non-int) is NaN */ - if(((((u_int32_t)hx>>31)-1)|yisint)==0) return (x-x)/(x-x); + 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 */ @@ -182,11 +187,11 @@ __ieee754_pow(double x, double y) 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 + 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 = x-1; /* t has 20 trailing zeros */ + t = ax-one; /* 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; @@ -194,7 +199,7 @@ __ieee754_pow(double x, double y) SET_LOW_WORD(t1,0); t2 = v-(t1-u); } else { - double s2,s_h,s_l,t_h,t_l; + double ss,s2,s_h,s_l,t_h,t_l; n = 0; /* take care subnormal number */ if(ix<0x00100000) @@ -208,11 +213,11 @@ __ieee754_pow(double x, double y) 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) */ + /* 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]); - s = u*v; - s_h = s; + ss = u*v; + s_h = ss; SET_LOW_WORD(s_h,0); /* t_h=ax+bp[k] High */ t_h = zero; @@ -220,33 +225,29 @@ __ieee754_pow(double x, double y) 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; + s2 = ss*ss; r = s2*s2*(L1+s2*(L2+s2*(L3+s2*(L4+s2*(L5+s2*L6))))); - r += s_l*(s_h+s); + r += s_l*(s_h+ss); 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+v = ss*(1+...) */ u = s_h*t_h; - v = s_l*t_h+t_l*s; - /* 2/(3log2)*(s+...) */ + 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) = (s+..)*2/(3*log2) = n + dp_h + z_h + z_l */ + /* log2(ax) = (ss+..)*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 = 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 yy1+y2 and compute (yy1+y2)*(t1+t2) */ yy1 = y; SET_LOW_WORD(yy1,0); @@ -281,7 +282,7 @@ __ieee754_pow(double x, double y) 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; diff --git a/lib/libm/src/e_powf.c b/lib/libm/src/e_powf.c index 0555bf85b0c..ec93660cc3f 100644 --- a/lib/libm/src/e_powf.c +++ b/lib/libm/src/e_powf.c @@ -130,7 +130,7 @@ __ieee754_powf(float x, float y) 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 */ + t = ax-one; /* 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;