Adding upstream version 86.0.1.upstream/86.0.1upstream

Signed-off-by: Daniel Baumann <daniel.baumann@progress-linux.org>

1 files changed, 100 insertions, 0 deletions

diff --git a/modules/fdlibm/src/k_log.h b/modules/fdlibm/src/k_log.h
new file mode 100644
index 0000000000..0efa020f63
--- /dev/null
+++ b/modules/fdlibm/src/k_log.h
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+
+/* @(#)e_log.c 1.3 95/01/18 */
+/*
+ * ====================================================
+ * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved.
+ *
+ * Developed at SunSoft, a Sun Microsystems, Inc. business.
+ * Permission to use, copy, modify, and distribute this
+ * software is freely granted, provided that this notice 
+ * is preserved.
+ * ====================================================
+ */
+
+//#include <sys/cdefs.h>
+//__FBSDID("$FreeBSD$");
+
+/*
+ * k_log1p(f):
+ * Return log(1+f) - f for 1+f in ~[sqrt(2)/2, sqrt(2)].
+ *
+ * The following describes the overall strategy for computing
+ * logarithms in base e.  The argument reduction and adding the final
+ * term of the polynomial are done by the caller for increased accuracy
+ * when different bases are used.
+ *
+ * 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.
+ */
+
+static const double
+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 */
+
+/*
+ * We always inline k_log1p(), since doing so produces a
+ * substantial performance improvement (~40% on amd64).
+ */
+static inline double
+k_log1p(double f)
+{
+	double hfsq,s,z,R,w,t1,t2;
+
+ 	s = f/(2.0+f);
+	z = s*s;
+	w = z*z;
+	t1= w*(Lg2+w*(Lg4+w*Lg6));
+	t2= z*(Lg1+w*(Lg3+w*(Lg5+w*Lg7)));
+	R = t2+t1;
+	hfsq=0.5*f*f;
+	return s*(hfsq+R);
+}