J.T. Conklin's latest version of the Sun math library.

-- Begin comments from J.T. Conklin:
The most significant improvement is the addition of "float" versions
of the math functions that take float arguments, return floats, and do
all operations in floating point.  This doesn't help (performance)
much on the i386, but they are still nice to have.

The float versions were orginally done by Cygnus' Ian Taylor when
fdlibm was integrated into the libm we support for embedded systems.
I gave Ian a copy of my libm as a starting point since I had already
fixed a lot of bugs & problems in Sun's original code.  After he was
done, I cleaned it up a bit and integrated the changes back into my
libm.
-- End comments

Reviewed by:	jkh
Submitted by:	jtc

1 files changed, 173 insertions, 0 deletions

diff --git a/lib/msun/src/s_log1p.c b/lib/msun/src/s_log1p.c
new file mode 100644
index 0000000..475c7ab
--- /dev/null
+++ b/lib/msun/src/s_log1p.c
@@ -0,0 +1,173 @@
+/* @(#)s_log1p.c 5.1 93/09/24 */
+/*
+ * ====================================================
+ * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved.
+ *
+ * Developed at SunPro, a Sun Microsystems, Inc. business.
+ * Permission to use, copy, modify, and distribute this
+ * software is freely granted, provided that this notice 
+ * is preserved.
+ * ====================================================
+ */
+
+#ifndef lint
+static char rcsid[] = "$Id: s_log1p.c,v 1.6 1994/08/18 23:06:59 jtc Exp $";
+#endif
+
+/* double log1p(double x)
+ *
+ * Method :                  
+ *   1. Argument Reduction: find k and f such that 
+ *			1+x = 2^k * (1+f), 
+ *	   where  sqrt(2)/2 < 1+f < sqrt(2) .
+ *
+ *      Note. If k=0, then f=x is exact. However, if k!=0, then f
+ *	may not be representable exactly. In that case, a correction
+ *	term is need. Let u=1+x rounded. Let c = (1+x)-u, then
+ *	log(1+x) - log(u) ~ c/u. Thus, we proceed to compute log(u),
+ *	and add back the correction term c/u.
+ *	(Note: when x > 2**53, one can simply return log(x))
+ *
+ *   2. Approximation of log1p(f).
+ *	Let s = f/(2+f) ; based on log(1+f) = log(1+s) - log(1-s)
+ *		 = 2s + 2/3 s**3 + 2/5 s**5 + .....,
+ *	     	 = 2s + s*R
+ *      We use a special Reme algorithm on [0,0.1716] to generate 
+ * 	a polynomial of degree 14 to approximate R The maximum error 
+ *	of this polynomial approximation is bounded by 2**-58.45. In
+ *	other words,
+ *		        2      4      6      8      10      12      14
+ *	    R(z) ~ Lp1*s +Lp2*s +Lp3*s +Lp4*s +Lp5*s  +Lp6*s  +Lp7*s
+ *  	(the values of Lp1 to Lp7 are listed in the program)
+ *	and
+ *	    |      2          14          |     -58.45
+ *	    | Lp1*s +...+Lp7*s    -  R(z) | <= 2 
+ *	    |                             |
+ *	Note that 2s = f - s*f = f - hfsq + s*hfsq, where hfsq = f*f/2.
+ *	In order to guarantee error in log below 1ulp, we compute log
+ *	by
+ *		log1p(f) = f - (hfsq - s*(hfsq+R)).
+ *	
+ *	3. Finally, log1p(x) = k*ln2 + log1p(f).  
+ *		 	     = k*ln2_hi+(f-(hfsq-(s*(hfsq+R)+k*ln2_lo)))
+ *	   Here ln2 is split into two floating point number: 
+ *			ln2_hi + ln2_lo,
+ *	   where n*ln2_hi is always exact for |n| < 2000.
+ *
+ * Special cases:
+ *	log1p(x) is NaN with signal if x < -1 (including -INF) ; 
+ *	log1p(+INF) is +INF; log1p(-1) is -INF with signal;
+ *	log1p(NaN) is that NaN with no signal.
+ *
+ * Accuracy:
+ *	according to an error analysis, the error is always less than
+ *	1 ulp (unit in the last place).
+ *
+ * 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.
+ *
+ * Note: Assuming log() return accurate answer, the following
+ * 	 algorithm can be used to compute log1p(x) to within a few ULP:
+ *	
+ *		u = 1+x;
+ *		if(u==1.0) return x ; else
+ *			   return log(u)*(x/(u-1.0));
+ *
+ *	 See HP-15C Advanced Functions Handbook, p.193.
+ */
+
+#include "math.h"
+#include "math_private.h"
+
+#ifdef __STDC__
+static const double
+#else
+static double
+#endif
+ln2_hi  =  6.93147180369123816490e-01,	/* 3fe62e42 fee00000 */
+ln2_lo  =  1.90821492927058770002e-10,	/* 3dea39ef 35793c76 */
+two54   =  1.80143985094819840000e+16,  /* 43500000 00000000 */
+Lp1 = 6.666666666666735130e-01,  /* 3FE55555 55555593 */
+Lp2 = 3.999999999940941908e-01,  /* 3FD99999 9997FA04 */
+Lp3 = 2.857142874366239149e-01,  /* 3FD24924 94229359 */
+Lp4 = 2.222219843214978396e-01,  /* 3FCC71C5 1D8E78AF */
+Lp5 = 1.818357216161805012e-01,  /* 3FC74664 96CB03DE */
+Lp6 = 1.531383769920937332e-01,  /* 3FC39A09 D078C69F */
+Lp7 = 1.479819860511658591e-01;  /* 3FC2F112 DF3E5244 */
+
+#ifdef __STDC__
+static const double zero = 0.0;
+#else
+static double zero = 0.0;
+#endif
+
+#ifdef __STDC__
+	double log1p(double x)
+#else
+	double log1p(x)
+	double x;
+#endif
+{
+	double hfsq,f,c,s,z,R,u;
+	int32_t k,hx,hu,ax;
+
+	GET_HIGH_WORD(hx,x);
+	ax = hx&0x7fffffff;
+
+	k = 1;
+	if (hx < 0x3FDA827A) {			/* x < 0.41422  */
+	    if(ax>=0x3ff00000) {		/* x <= -1.0 */
+		if(x==-1.0) return -two54/zero; /* log1p(-1)=+inf */
+		else return (x-x)/(x-x);	/* log1p(x<-1)=NaN */
+	    }
+	    if(ax<0x3e200000) {			/* |x| < 2**-29 */
+		if(two54+x>zero			/* raise inexact */
+	            &&ax<0x3c900000) 		/* |x| < 2**-54 */
+		    return x;
+		else
+		    return x - x*x*0.5;
+	    }
+	    if(hx>0||hx<=((int32_t)0xbfd2bec3)) {
+		k=0;f=x;hu=1;}	/* -0.2929<x<0.41422 */
+	} 
+	if (hx >= 0x7ff00000) return x+x;
+	if(k!=0) {
+	    if(hx<0x43400000) {
+		u  = 1.0+x; 
+		GET_HIGH_WORD(hu,u);
+	        k  = (hu>>20)-1023;
+	        c  = (k>0)? 1.0-(u-x):x-(u-1.0);/* correction term */
+		c /= u;
+	    } else {
+		u  = x;
+		GET_HIGH_WORD(hu,u);
+	        k  = (hu>>20)-1023;
+		c  = 0;
+	    }
+	    hu &= 0x000fffff;
+	    if(hu<0x6a09e) {
+	        SET_HIGH_WORD(u,hu|0x3ff00000);	/* normalize u */
+	    } else {
+	        k += 1; 
+		SET_HIGH_WORD(u,hu|0x3fe00000);	/* normalize u/2 */
+	        hu = (0x00100000-hu)>>2;
+	    }
+	    f = u-1.0;
+	}
+	hfsq=0.5*f*f;
+	if(hu==0) {	/* |f| < 2**-20 */
+	    if(f==zero) if(k==0) return zero;  
+			else {c += k*ln2_lo; return k*ln2_hi+c;}
+	    R = hfsq*(1.0-0.66666666666666666*f);
+	    if(k==0) return f-R; else
+	    	     return k*ln2_hi-((R-(k*ln2_lo+c))-f);
+	}
+ 	s = f/(2.0+f); 
+	z = s*s;
+	R = z*(Lp1+z*(Lp2+z*(Lp3+z*(Lp4+z*(Lp5+z*(Lp6+z*Lp7))))));
+	if(k==0) return f-(hfsq-s*(hfsq+R)); else
+		 return k*ln2_hi-((hfsq-(s*(hfsq+R)+(k*ln2_lo+c)))-f);
+}