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 9ee8279..4c4ad3b 100644 (file)
--- 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 0555bf8..ec93660 100644 (file)
--- 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;