svn commit: r219360 - head/lib/msun/src

[David Schultz]

Author: das
Date: Mon Mar  7 03:11:27 2011
New Revision: 219360
URL: http://svn.freebsd.org/changeset/base/219360

Log:
  Convert log10() to use __kernel_log(), which is more accurate and simpler.

Modified:
  head/lib/msun/src/e_log10.c

Modified: head/lib/msun/src/e_log10.c
==============================================================================
--- head/lib/msun/src/e_log10.c	Mon Mar  7 03:09:24 2011	(r219359)
+++ head/lib/msun/src/e_log10.c	Mon Mar  7 03:11:27 2011	(r219360)
@@ -14,45 +14,18 @@
 #include <sys/cdefs.h>
 __FBSDID("$FreeBSD$");
 
-/* __ieee754_log10(x)
- * Return the base 10 logarithm of x
- * 
- * Method :
- *	Let log10_2hi = leading 40 bits of log10(2) and
- *	    log10_2lo = log10(2) - log10_2hi,
- *	    ivln10   = 1/log(10) rounded.
- *	Then
- *		n = ilogb(x), 
- *		if(n<0)  n = n+1;
- *		x = scalbn(x,-n);
- *		log10(x) := n*log10_2hi + (n*log10_2lo + ivln10*log(x))
- *
- * Note 1:
- *	To guarantee log10(10**n)=n, where 10**n is normal, the rounding 
- *	mode must set to Round-to-Nearest.
- * Note 2:
- *	[1/log(10)] rounded to 53 bits has error  .198   ulps;
- *	log10 is monotonic at all binary break points.
- *
- * Special cases:
- *	log10(x) is NaN with signal if x < 0; 
- *	log10(+INF) is +INF with no signal; log10(0) is -INF with signal;
- *	log10(NaN) is that NaN with no signal;
- *	log10(10**N) = N  for N=0,1,...,22.
- *
- * 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 to produce the hexadecimal values
- * shown.
+/*
+ * Return the base 10 logarithm of x. See k_log.c for details on the algorithm.
  */
 
 #include "math.h"
 #include "math_private.h"
+#include "k_log.h"
 
 static const double
 two54      =  1.80143985094819840000e+16, /* 0x43500000, 0x00000000 */
-ivln10     =  4.34294481903251816668e-01, /* 0x3FDBCB7B, 0x1526E50E */
+ivln10hi   =  4.34294481878168880939e-01, /* 0x3fdbcb7b, 0x15200000 */
+ivln10lo   =  2.50829467116452752298e-11, /* 0x3dbb9438, 0xca9aadd5 */
 log10_2hi  =  3.01029995663611771306e-01, /* 0x3FD34413, 0x509F6000 */
 log10_2lo  =  3.69423907715893078616e-13; /* 0x3D59FEF3, 0x11F12B36 */
 
@@ -61,7 +34,7 @@ static const double zero   =  0.0;
 double
 __ieee754_log10(double x)
 {
-	double y,z;
+	double f,hi,lo,y,z;
 	int32_t i,k,hx;
 	u_int32_t lx;
 
@@ -77,10 +50,15 @@ __ieee754_log10(double x)
         }
 	if (hx >= 0x7ff00000) return x+x;
 	k += (hx>>20)-1023;
-	i  = ((u_int32_t)k&0x80000000)>>31;
-        hx = (hx&0x000fffff)|((0x3ff-i)<<20);
-        y  = (double)(k+i);
-	SET_HIGH_WORD(x,hx);
-	z  = y*log10_2lo + ivln10*__ieee754_log(x);
+	hx &= 0x000fffff;
+	i = (hx+0x95f64)&0x100000;
+	SET_HIGH_WORD(x,hx|(i^0x3ff00000));	/* normalize x or x/2 */
+	k += (i>>20);
+	y = (double)k;
+	f = __kernel_log(x);
+	hi = x = x - 1;
+	SET_LOW_WORD(hi,0);
+	lo = x - hi;
+	z = y*log10_2lo + (x+f)*ivln10lo + (lo+f)*ivln10hi + hi*ivln10hi;
 	return  z+y*log10_2hi;
 }