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authorRoland McGrath <roland@gnu.org>1996-03-05 21:41:30 +0000
committerRoland McGrath <roland@gnu.org>1996-03-05 21:41:30 +0000
commitf7eac6eb504f4baf13dbb4d26717942df050ebe6 (patch)
tree95ff129c06c7f6f246a5e2bfa489ba6382659d19 /sysdeps/libm-ieee754/e_log.c
parent1521668f2afae1dc2ef5d7ffaeb84353b36874dd (diff)
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Mon Mar 4 20:54:40 1996 Andreas Schwab <schwab@issan.informatik.uni-dortmund.de>
	* Makeconfig ($(common-objpfx)config.make): Depend on config.h.in.


Mon Mar  4 17:35:09 1996  Roland McGrath  <roland@charlie-brown.gnu.ai.mit.edu>

	* hurd/catch-signal.c (hurd_safe_memmove): New function.
	(hurd_safe_copyin, hurd_safe_copyout): New functions.
	* hurd/hurd/sigpreempt.h: Declare them.

Sun Mar  3 08:43:44 1996  Roland McGrath  <roland@charlie-brown.gnu.ai.mit.edu>

	Replace math code with fdlibm from Sun as modified for netbsd by
	JT Conklin and Ian Taylor, including x86 FPU support.
	* sysdeps/libm-ieee754, sysdeps/libm-i387: New directories.
	* math/math_private.h: New file.
	* sysdeps/i386/fpu/Implies: New file.
	* sysdeps/ieee754/Implies: New file.
	* math/machine/asm.h, math/machine/endian.h: New files.
	* math/Makefile, math/math.h: Rewritten.
	* mathcalls.h, math/mathcalls.h: New file, broken out of math.h.
	* math/finite.c: File removed.
	* sysdeps/generic/Makefile [$(subdir)=math]: Frobnication removed.

	* math/test-math.c: Include errno.h and string.h.

	* sysdeps/unix/bsd/dirstream.h: File removed.
	* sysdeps/unix/bsd/readdir.c: File removed.
Diffstat (limited to 'sysdeps/libm-ieee754/e_log.c')
-rw-r--r--sysdeps/libm-ieee754/e_log.c146
1 files changed, 146 insertions, 0 deletions
diff --git a/sysdeps/libm-ieee754/e_log.c b/sysdeps/libm-ieee754/e_log.c
new file mode 100644
index 0000000000..c27e0a9d64
--- /dev/null
+++ b/sysdeps/libm-ieee754/e_log.c
@@ -0,0 +1,146 @@
+/* @(#)e_log.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: e_log.c,v 1.8 1995/05/10 20:45:49 jtc Exp $";
+#endif
+
+/* __ieee754_log(x)
+ * Return the logrithm of x
+ *
+ * Method :                  
+ *   1. Argument Reduction: find k and f such that 
+ *			x = 2^k * (1+f), 
+ *	   where  sqrt(2)/2 < 1+f < sqrt(2) .
+ *
+ *   2. Approximation of log(1+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) ~ Lg1*s +Lg2*s +Lg3*s +Lg4*s +Lg5*s  +Lg6*s  +Lg7*s
+ *  	(the values of Lg1 to Lg7 are listed in the program)
+ *	and
+ *	    |      2          14          |     -58.45
+ *	    | Lg1*s +...+Lg7*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
+ *		log(1+f) = f - s*(f - R)	(if f is not too large)
+ *		log(1+f) = f - (hfsq - s*(hfsq+R)).	(better accuracy)
+ *	
+ *	3. Finally,  log(x) = k*ln2 + log(1+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:
+ *	log(x) is NaN with signal if x < 0 (including -INF) ; 
+ *	log(+INF) is +INF; log(0) is -INF with signal;
+ *	log(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.
+ */
+
+#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 */
+Lg1 = 6.666666666666735130e-01,  /* 3FE55555 55555593 */
+Lg2 = 3.999999999940941908e-01,  /* 3FD99999 9997FA04 */
+Lg3 = 2.857142874366239149e-01,  /* 3FD24924 94229359 */
+Lg4 = 2.222219843214978396e-01,  /* 3FCC71C5 1D8E78AF */
+Lg5 = 1.818357216161805012e-01,  /* 3FC74664 96CB03DE */
+Lg6 = 1.531383769920937332e-01,  /* 3FC39A09 D078C69F */
+Lg7 = 1.479819860511658591e-01;  /* 3FC2F112 DF3E5244 */
+
+#ifdef __STDC__
+static const double zero   =  0.0;
+#else
+static double zero   =  0.0;
+#endif
+
+#ifdef __STDC__
+	double __ieee754_log(double x)
+#else
+	double __ieee754_log(x)
+	double x;
+#endif
+{
+	double hfsq,f,s,z,R,w,t1,t2,dk;
+	int32_t k,hx,i,j;
+	u_int32_t lx;
+
+	EXTRACT_WORDS(hx,lx,x);
+
+	k=0;
+	if (hx < 0x00100000) {			/* x < 2**-1022  */
+	    if (((hx&0x7fffffff)|lx)==0) 
+		return -two54/zero;		/* log(+-0)=-inf */
+	    if (hx<0) return (x-x)/zero;	/* log(-#) = NaN */
+	    k -= 54; x *= two54; /* subnormal number, scale up x */
+	    GET_HIGH_WORD(hx,x);
+	} 
+	if (hx >= 0x7ff00000) return x+x;
+	k += (hx>>20)-1023;
+	hx &= 0x000fffff;
+	i = (hx+0x95f64)&0x100000;
+	SET_HIGH_WORD(x,hx|(i^0x3ff00000));	/* normalize x or x/2 */
+	k += (i>>20);
+	f = x-1.0;
+	if((0x000fffff&(2+hx))<3) {	/* |f| < 2**-20 */
+	    if(f==zero) if(k==0) return zero;  else {dk=(double)k;
+				 return dk*ln2_hi+dk*ln2_lo;}
+	    R = f*f*(0.5-0.33333333333333333*f);
+	    if(k==0) return f-R; else {dk=(double)k;
+	    	     return dk*ln2_hi-((R-dk*ln2_lo)-f);}
+	}
+ 	s = f/(2.0+f); 
+	dk = (double)k;
+	z = s*s;
+	i = hx-0x6147a;
+	w = z*z;
+	j = 0x6b851-hx;
+	t1= w*(Lg2+w*(Lg4+w*Lg6)); 
+	t2= z*(Lg1+w*(Lg3+w*(Lg5+w*Lg7))); 
+	i |= j;
+	R = t2+t1;
+	if(i>0) {
+	    hfsq=0.5*f*f;
+	    if(k==0) return f-(hfsq-s*(hfsq+R)); else
+		     return dk*ln2_hi-((hfsq-(s*(hfsq+R)+dk*ln2_lo))-f);
+	} else {
+	    if(k==0) return f-s*(f-R); else
+		     return dk*ln2_hi-((s*(f-R)-dk*ln2_lo)-f);
+	}
+}