From 5f8de423f190bbb79a62f804151bc24824fa32d8 Mon Sep 17 00:00:00 2001
From: "Matt A. Tobin" <mattatobin@localhost.localdomain>
Date: Fri, 2 Feb 2018 04:16:08 -0500
Subject: Add m-esr52 at 52.6.0

---
 modules/fdlibm/src/e_log2.cpp | 112 ++++++++++++++++++++++++++++++++++++++++++
 1 file changed, 112 insertions(+)
 create mode 100644 modules/fdlibm/src/e_log2.cpp

(limited to 'modules/fdlibm/src/e_log2.cpp')

diff --git a/modules/fdlibm/src/e_log2.cpp b/modules/fdlibm/src/e_log2.cpp
new file mode 100644
index 000000000..5649fec44
--- /dev/null
+++ b/modules/fdlibm/src/e_log2.cpp
@@ -0,0 +1,112 @@
+
+/* @(#)e_log10.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("$FreeBSD$");
+
+/*
+ * Return the base 2 logarithm of x.  See e_log.c and k_log.h for most
+ * comments.
+ *
+ * This reduces x to {k, 1+f} exactly as in e_log.c, then calls the kernel,
+ * then does the combining and scaling steps
+ *    log2(x) = (f - 0.5*f*f + k_log1p(f)) / ln2 + k
+ * in not-quite-routine extra precision.
+ */
+
+#include <float.h>
+
+#include "math_private.h"
+#include "k_log.h"
+
+static const double
+two54      =  1.80143985094819840000e+16, /* 0x43500000, 0x00000000 */
+ivln2hi    =  1.44269504072144627571e+00, /* 0x3ff71547, 0x65200000 */
+ivln2lo    =  1.67517131648865118353e-10; /* 0x3de705fc, 0x2eefa200 */
+
+static const double zero   =  0.0;
+static volatile double vzero = 0.0;
+
+double
+__ieee754_log2(double x)
+{
+	double f,hfsq,hi,lo,r,val_hi,val_lo,w,y;
+	int32_t i,k,hx;
+	u_int32_t lx;
+
+	EXTRACT_WORDS(hx,lx,x);
+
+	k=0;
+	if (hx < 0x00100000) {			/* x < 2**-1022  */
+	    if (((hx&0x7fffffff)|lx)==0)
+		return -two54/vzero;		/* 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;
+	if (hx == 0x3ff00000 && lx == 0)
+	    return zero;			/* log(1) = +0 */
+	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);
+	y = (double)k;
+	f = x - 1.0;
+	hfsq = 0.5*f*f;
+	r = k_log1p(f);
+
+	/*
+	 * f-hfsq must (for args near 1) be evaluated in extra precision
+	 * to avoid a large cancellation when x is near sqrt(2) or 1/sqrt(2).
+	 * This is fairly efficient since f-hfsq only depends on f, so can
+	 * be evaluated in parallel with R.  Not combining hfsq with R also
+	 * keeps R small (though not as small as a true `lo' term would be),
+	 * so that extra precision is not needed for terms involving R.
+	 *
+	 * Compiler bugs involving extra precision used to break Dekker's
+	 * theorem for spitting f-hfsq as hi+lo, unless double_t was used
+	 * or the multi-precision calculations were avoided when double_t
+	 * has extra precision.  These problems are now automatically
+	 * avoided as a side effect of the optimization of combining the
+	 * Dekker splitting step with the clear-low-bits step.
+	 *
+	 * y must (for args near sqrt(2) and 1/sqrt(2)) be added in extra
+	 * precision to avoid a very large cancellation when x is very near
+	 * these values.  Unlike the above cancellations, this problem is
+	 * specific to base 2.  It is strange that adding +-1 is so much
+	 * harder than adding +-ln2 or +-log10_2.
+	 *
+	 * This uses Dekker's theorem to normalize y+val_hi, so the
+	 * compiler bugs are back in some configurations, sigh.  And I
+	 * don't want to used double_t to avoid them, since that gives a
+	 * pessimization and the support for avoiding the pessimization
+	 * is not yet available.
+	 *
+	 * The multi-precision calculations for the multiplications are
+	 * routine.
+	 */
+	hi = f - hfsq;
+	SET_LOW_WORD(hi,0);
+	lo = (f - hi) - hfsq + r;
+	val_hi = hi*ivln2hi;
+	val_lo = (lo+hi)*ivln2lo + lo*ivln2hi;
+
+	/* spadd(val_hi, val_lo, y), except for not using double_t: */
+	w = y + val_hi;
+	val_lo += (y - w) + val_hi;
+	val_hi = w;
+
+	return val_lo + val_hi;
+}
-- 
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