Totally rework the math library, this time based on the MacOs X

math library (which is itself based on the math lib from FreeBSD).
 -Erik

1 files changed, 173 insertions, 0 deletions

diff --git a/libm/s_log1p.c b/libm/s_log1p.c
new file mode 100644
index 000000000..683026b54
--- /dev/null
+++ b/libm/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.
+ * ====================================================
+ */
+
+#if defined(LIBM_SCCS) && !defined(lint)
+static char rcsid[] = "$NetBSD: s_log1p.c,v 1.8 1995/05/10 20:47:46 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);
+}