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authordrochner <drochner@NetBSD.org>2004-06-30 18:43:15 +0000
committerdrochner <drochner@NetBSD.org>2004-06-30 18:43:15 +0000
commita6d8e4cf79189e3aa249bf67cd2ac65bb8febb42 (patch)
tree65ff0276085e10bd2b6fd2ab74503d451d78af12 /lib/libm/src
parent8b477ad95537a5bea09e6d9a22678a2e30e10ab2 (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.c41
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);