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Date:      Mon, 17 Oct 2011 05:38:07 +0000 (UTC)
From:      David Schultz <das@FreeBSD.org>
To:        src-committers@freebsd.org, svn-src-all@freebsd.org, svn-src-stable@freebsd.org, svn-src-stable-8@freebsd.org
Subject:   svn commit: r226456 - in stable/8/lib/msun: man src
Message-ID:  <201110170538.p9H5c70h096723@svn.freebsd.org>

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Author: das
Date: Mon Oct 17 05:38:07 2011
New Revision: 226456
URL: http://svn.freebsd.org/changeset/base/226456

Log:
  MFC various log* improvements.
  
  r216247 - log2f style
  r216248 - log2f insignificant bug
  r219360 - log10 converted to use k_log
  r219361 - log10f converted to use k_log
  r226375 - log2/log10 style
  r226376 - log2/log10 bde's improvements; fix log(1) with FE_DOWNWARD rounding

Modified:
  stable/8/lib/msun/man/math.3
  stable/8/lib/msun/src/e_log10.c
  stable/8/lib/msun/src/e_log10f.c
  stable/8/lib/msun/src/e_log2.c
  stable/8/lib/msun/src/e_log2f.c
  stable/8/lib/msun/src/k_logf.h
Directory Properties:
  stable/8/lib/msun/   (props changed)

Modified: stable/8/lib/msun/man/math.3
==============================================================================
--- stable/8/lib/msun/man/math.3	Mon Oct 17 03:35:24 2011	(r226455)
+++ stable/8/lib/msun/man/math.3	Mon Oct 17 05:38:07 2011	(r226456)
@@ -198,7 +198,7 @@ yn	Bessel function of the second kind of
 .El
 .Pp
 The routines
-in this section may not produce a result that is correctly rounded,
+in this section might not produce a result that is correctly rounded,
 so reproducible results cannot be guaranteed across platforms.
 For most of these functions, however, incorrect rounding occurs
 rarely, and then only in very-close-to-halfway cases.
@@ -234,9 +234,8 @@ Many of the routines to compute transcen
 inaccurate results in other than the default rounding mode.
 .Pp
 On the i386 platform, trigonometric argument reduction is not
-performed accurately for very large arguments, resulting in errors
-greater than 1
-.Em ulp
+performed accurately for huge arguments, resulting in
+large errors
 for such arguments to
 .Fn cos ,
 .Fn sin ,

Modified: stable/8/lib/msun/src/e_log10.c
==============================================================================
--- stable/8/lib/msun/src/e_log10.c	Mon Oct 17 03:35:24 2011	(r226455)
+++ stable/8/lib/msun/src/e_log10.c	Mon Oct 17 05:38:07 2011	(r226456)
@@ -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;
 }

Modified: stable/8/lib/msun/src/e_log10f.c
==============================================================================
--- stable/8/lib/msun/src/e_log10f.c	Mon Oct 17 03:35:24 2011	(r226455)
+++ stable/8/lib/msun/src/e_log10f.c	Mon Oct 17 05:38:07 2011	(r226456)
@@ -1,7 +1,3 @@
-/* e_log10f.c -- float version of e_log10.c.
- * Conversion to float by Ian Lance Taylor, Cygnus Support, ian@cygnus.com.
- */
-
 /*
  * ====================================================
  * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved.
@@ -16,12 +12,18 @@
 #include <sys/cdefs.h>
 __FBSDID("$FreeBSD$");
 
+/*
+ * 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_logf.h"
 
 static const float
 two25      =  3.3554432000e+07, /* 0x4c000000 */
-ivln10     =  4.3429449201e-01, /* 0x3ede5bd9 */
+ivln10hi   =  4.3432617188e-01, /* 0x3ede6000 */
+ivln10lo   = -3.1689971365e-05, /* 0xb804ead9 */
 log10_2hi  =  3.0102920532e-01, /* 0x3e9a2080 */
 log10_2lo  =  7.9034151668e-07; /* 0x355427db */
 
@@ -30,7 +32,7 @@ static const float zero   =  0.0;
 float
 __ieee754_log10f(float x)
 {
-	float y,z;
+	float f,hi,lo,y,z;
 	int32_t i,k,hx;
 
 	GET_FLOAT_WORD(hx,x);
@@ -45,10 +47,16 @@ __ieee754_log10f(float x)
         }
 	if (hx >= 0x7f800000) return x+x;
 	k += (hx>>23)-127;
-	i  = ((u_int32_t)k&0x80000000)>>31;
-        hx = (hx&0x007fffff)|((0x7f-i)<<23);
-        y  = (float)(k+i);
-	SET_FLOAT_WORD(x,hx);
-	z  = y*log10_2lo + ivln10*__ieee754_logf(x);
+	hx &= 0x007fffff;
+	i = (hx+(0x4afb0d))&0x800000;
+	SET_FLOAT_WORD(x,hx|(i^0x3f800000));	/* normalize x or x/2 */
+	k += (i>>23);
+	y = (float)k;
+	f = __kernel_logf(x);
+	x = x - (float)1.0;
+	GET_FLOAT_WORD(hx,x);
+	SET_FLOAT_WORD(hi,hx&0xfffff000);
+	lo = x - hi;
+	z = y*log10_2lo + (x+f)*ivln10lo + (lo+f)*ivln10hi + hi*ivln10hi;
 	return  z+y*log10_2hi;
 }

Modified: stable/8/lib/msun/src/e_log2.c
==============================================================================
--- stable/8/lib/msun/src/e_log2.c	Mon Oct 17 03:35:24 2011	(r226455)
+++ stable/8/lib/msun/src/e_log2.c	Mon Oct 17 05:38:07 2011	(r226456)
@@ -14,8 +14,8 @@
 #include <sys/cdefs.h>
 __FBSDID("$FreeBSD$");
 
-/* log2(x)
- * Return the base 2 logarithm of x.
+/*
+ * Return the base 2 logarithm of x. See k_log.c for details on the algorithm.
  */
 
 #include "math.h"
@@ -24,8 +24,8 @@ __FBSDID("$FreeBSD$");
 
 static const double
 two54      =  1.80143985094819840000e+16, /* 0x43500000, 0x00000000 */
-ivln2hi    =  0x1.71547652000p+0,
-ivln2lo    =  0x1.705fc2eefa2p-33;
+ivln2hi    =  1.44269504072144627571e+00, /* 0x3ff71547, 0x65200000 */
+ivln2lo    =  1.67517131648865118353e-10; /* 0x3de705fc, 0x2eefa200 */
 
 static const double zero   =  0.0;
 

Modified: stable/8/lib/msun/src/e_log2f.c
==============================================================================
--- stable/8/lib/msun/src/e_log2f.c	Mon Oct 17 03:35:24 2011	(r226455)
+++ stable/8/lib/msun/src/e_log2f.c	Mon Oct 17 05:38:07 2011	(r226456)
@@ -12,14 +12,18 @@
 #include <sys/cdefs.h>
 __FBSDID("$FreeBSD$");
 
+/*
+ * Return the base 2 logarithm of x. See k_log.c for details on the algorithm.
+ */
+
 #include "math.h"
 #include "math_private.h"
 #include "k_logf.h"
 
 static const float
 two25      =  3.3554432000e+07, /* 0x4c000000 */
-ivln2hi    =  0x1.716p+0f,
-ivln2lo    = -0x1.7135a8fa03d11p-13;
+ivln2hi    =  1.4428710938e+00, /* 0x3fb8b000 */
+ivln2lo    = -1.7605285393e-04; /* 0xb9389ad4 */
 
 static const float zero   =  0.0;
 
@@ -46,7 +50,7 @@ __ieee754_log2f(float x)
 	SET_FLOAT_WORD(x,hx|(i^0x3f800000));	/* normalize x or x/2 */
 	k += (i>>23);
 	f = __kernel_logf(x);
-	x = x - 1;
+	x = x - (float)1.0;
 	GET_FLOAT_WORD(hx,x);
 	SET_FLOAT_WORD(hi,hx&0xfffff000);
 	lo = x - hi;

Modified: stable/8/lib/msun/src/k_logf.h
==============================================================================
--- stable/8/lib/msun/src/k_logf.h	Mon Oct 17 03:35:24 2011	(r226455)
+++ stable/8/lib/msun/src/k_logf.h	Mon Oct 17 05:38:07 2011	(r226456)
@@ -12,8 +12,8 @@
 #include <sys/cdefs.h>
 __FBSDID("$FreeBSD$");
 
-/* __kernel_logf(x)
- * Return log(x) - (x-1) for x in ~[sqrt(2)/2, sqrt(2)].
+/*
+ * float version of __kernel_log(x). See k_log.c for details.
  */
 
 static const float
@@ -33,7 +33,7 @@ __kernel_logf(float x)
 
 	f = x-(float)1.0;
 	if((0x007fffff&(0x8000+ix))<0xc000) {	/* -2**-9 <= f < 2**-9 */
-	    if(f==0.0) return 0.0;
+	    if(f==0.0f) return 0.0f;
 	    return f*f*((float)0.33333333333333333*f-(float)0.5);
 	}
  	s = f/((float)2.0+f);



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