diff options
| author | drochner <drochner@NetBSD.org> | 2004-06-30 18:43:15 +0000 |
|---|---|---|
| committer | drochner <drochner@NetBSD.org> | 2004-06-30 18:43:15 +0000 |
| commit | a6d8e4cf79189e3aa249bf67cd2ac65bb8febb42 (patch) | |
| tree | 65ff0276085e10bd2b6fd2ab74503d451d78af12 /lib/libm/src | |
| parent | 8b477ad95537a5bea09e6d9a22678a2e30e10ab2 (diff) | |
-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.)
Diffstat (limited to 'lib/libm/src')
| -rw-r--r-- | lib/libm/src/e_pow.c | 41 |
1 files changed, 21 insertions, 20 deletions
diff --git a/lib/libm/src/e_pow.c b/lib/libm/src/e_pow.c index 53671cb66b5..c90efd6b9bd 100644 --- a/lib/libm/src/e_pow.c +++ b/lib/libm/src/e_pow.c @@ -12,7 +12,7 @@ #include <sys/cdefs.h> #if defined(LIBM_SCCS) && !defined(lint) -__RCSID("$NetBSD: e_pow.c,v 1.12 2002/05/26 22:01:51 wiz Exp $"); +__RCSID("$NetBSD: e_pow.c,v 1.13 2004/06/30 18:43:15 drochner Exp $"); #endif /* __ieee754_pow(x,y) return x**y @@ -22,7 +22,7 @@ __RCSID("$NetBSD: e_pow.c,v 1.12 2002/05/26 22:01:51 wiz 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) * @@ -173,8 +173,13 @@ __ieee754_pow(double x, double y) } } + 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 */ @@ -183,11 +188,11 @@ __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; + 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; @@ -195,7 +200,7 @@ __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) @@ -209,11 +214,11 @@ __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; @@ -221,33 +226,29 @@ __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 y1+y2 and compute (y1+y2)*(t1+t2) */ y1 = y; SET_LOW_WORD(y1,0); |
