693 Opensource replacement of sunwlibm

Reviewed by: Igor Kozhukhov ikozhukhov@gmail.com
Reviewed by: Keith M Wesolowski <keith.wesolowski@joyent.com>
Reviewed by: Richard Lowe <richlowe@richlowe.net>
Approved by: Dan McDonald <danmcd@omniti.com>

1 files changed, 173 insertions, 0 deletions

diff --git a/usr/src/lib/libm/common/Q/logl.c b/usr/src/lib/libm/common/Q/logl.c
new file mode 100644
index 0000000000..1cdf224c07
--- /dev/null
+++ b/usr/src/lib/libm/common/Q/logl.c
@@ -0,0 +1,173 @@
+/*
+ * CDDL HEADER START
+ *
+ * The contents of this file are subject to the terms of the
+ * Common Development and Distribution License (the "License").
+ * You may not use this file except in compliance with the License.
+ *
+ * You can obtain a copy of the license at usr/src/OPENSOLARIS.LICENSE
+ * or http://www.opensolaris.org/os/licensing.
+ * See the License for the specific language governing permissions
+ * and limitations under the License.
+ *
+ * When distributing Covered Code, include this CDDL HEADER in each
+ * file and include the License file at usr/src/OPENSOLARIS.LICENSE.
+ * If applicable, add the following below this CDDL HEADER, with the
+ * fields enclosed by brackets "[]" replaced with your own identifying
+ * information: Portions Copyright [yyyy] [name of copyright owner]
+ *
+ * CDDL HEADER END
+ */
+
+/*
+ * Copyright 2011 Nexenta Systems, Inc.  All rights reserved.
+ */
+/*
+ * Copyright 2006 Sun Microsystems, Inc.  All rights reserved.
+ * Use is subject to license terms.
+ */
+
+#pragma weak logl = __logl
+
+/*
+ * logl(x)
+ * Table look-up algorithm
+ * By K.C. Ng, March 6, 1989
+ *
+ * (a). For x in [31/33,33/31], using a special approximation:
+ *	f = x - 1;
+ *	s = f/(2.0+f);	... here |s| <= 0.03125
+ *	z = s*s;
+ *	return f-s*(f-z*(B1+z*(B2+z*(B3+z*(B4+...+z*B9)...))));
+ *
+ * (b). Otherwise, normalize x = 2^n * 1.f.
+ *	Use a 6-bit table look-up: find a 6 bit g that match f to 6.5 bits,
+ *	then
+ *	    log(x) = n*ln2 + log(1.g) + log(1.f/1.g).
+ *	Here the leading and trailing values of log(1.g) are obtained from
+ *	a size-64 table.
+ *	For log(1.f/1.g), let s = (1.f-1.g)/(1.f+1.g), then
+ *	    log(1.f/1.g) = log((1+s)/(1-s)) = 2s + 2/3 s^3 + 2/5 s^5 +...
+ *	Note that |s|<2**-8=0.00390625. We use an odd s-polynomial
+ *	approximation to compute log(1.f/1.g):
+ *		s*(A1+s^2*(A2+s^2*(A3+s^2*(A4+s^2*(A5+s^2*(A6+s^2*A7))))))
+ *	(Precision is 2**-136.91 bits, absolute error)
+ *
+ * (c). The final result is computed by
+ *		(n*ln2_hi+_TBL_logl_hi[j]) +
+ *			( (n*ln2_lo+_TBL_logl_lo[j]) + s*(A1+...) )
+ *
+ * Note.
+ *	For ln2_hi and _TBL_logl_hi[j], we force their last 32 bit to be zero
+ *	so that n*ln2_hi + _TBL_logl_hi[j] is exact. Here
+ *	_TBL_logl_hi[j] + _TBL_logl_lo[j] match log(1+j*2**-6) to 194 bits
+ *
+ *
+ * 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.
+ *
+ * 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 "libm.h"
+
+extern const long double _TBL_logl_hi[], _TBL_logl_lo[];
+
+static const long double
+	zero	=   0.0L,
+	one	=   1.0L,
+	two	=   2.0L,
+	two113  =   10384593717069655257060992658440192.0L,
+	ln2hi	=   6.931471805599453094172319547495844850203e-0001L,
+	ln2lo	=   1.667085920830552208890449330400379754169e-0025L,
+	A1	=   2.000000000000000000000000000000000000024e+0000L,
+	A2	=   6.666666666666666666666666666666091393804e-0001L,
+	A3	=   4.000000000000000000000000407167070220671e-0001L,
+	A4	=   2.857142857142857142730077490612903681164e-0001L,
+	A5	=   2.222222222222242577702836920812882605099e-0001L,
+	A6	=   1.818181816435493395985912667105885828356e-0001L,
+	A7	=   1.538537835211839751112067512805496931725e-0001L,
+	B1	=   6.666666666666666666666666666666961498329e-0001L,
+	B2	=   3.999999999999999999999999990037655042358e-0001L,
+	B3	=   2.857142857142857142857273426428347457918e-0001L,
+	B4	=   2.222222222222222221353229049747910109566e-0001L,
+	B5	=   1.818181818181821503532559306309070138046e-0001L,
+	B6	=   1.538461538453809210486356084587356788556e-0001L,
+	B7	=   1.333333344463358756121456892645178795480e-0001L,
+	B8	=   1.176460904783899064854645174603360383792e-0001L,
+	B9	=   1.057293869956598995326368602518056990746e-0001L;
+
+long double
+logl(long double x) {
+	long double f, s, z, qn, h, t;
+	int *px = (int *) &x;
+	int *pz = (int *) &z;
+	int i, j, ix, i0, i1, n;
+
+	/* get long double precision word ordering */
+	if (*(int *) &one == 0) {
+		i0 = 3;
+		i1 = 0;
+	} else {
+		i0 = 0;
+		i1 = 3;
+	}
+
+	n = 0;
+	ix = px[i0];
+	if (ix > 0x3ffee0f8) {	/* if x >  31/33 */
+		if (ix < 0x3fff1084) {	/* if x < 33/31 */
+			f = x - one;
+			z = f * f;
+			if (((ix - 0x3fff0000) | px[i1] | px[2] | px[1]) == 0) {
+				return (zero);	/* log(1)= +0 */
+			}
+			s = f / (two + f);	/* |s|<2**-8 */
+			z = s * s;
+			return (f - s * (f - z * (B1 + z * (B2 + z * (B3 +
+				z * (B4 + z * (B5 + z * (B6 + z * (B7 +
+				z * (B8 + z * B9))))))))));
+		}
+		if (ix >= 0x7fff0000)
+			return (x + x);	/* x is +inf or NaN */
+		goto LARGE_N;
+	}
+	if (ix >= 0x00010000)
+		goto LARGE_N;
+	i = ix & 0x7fffffff;
+	if ((i | px[i1] | px[2] | px[1]) == 0) {
+		px[i0] |= 0x80000000;
+		return (one / x);	/* log(0.0) = -inf */
+	}
+	if (ix < 0) {
+		if ((unsigned) ix >= 0xffff0000)
+			return (x - x);	/* x is -inf or NaN */
+		return (zero / zero);	/* log(x<0) is NaN  */
+	}
+	/* subnormal x */
+	x *= two113;
+	n = -113;
+	ix = px[i0];
+LARGE_N:
+	n += ((ix + 0x200) >> 16) - 0x3fff;
+	ix = (ix & 0x0000ffff) | 0x3fff0000;	/* scale x to [1,2] */
+	px[i0] = ix;
+	i = ix + 0x200;
+	pz[i0] = i & 0xfffffc00;
+	pz[i1] = pz[1] = pz[2] = 0;
+	s = (x - z) / (x + z);
+	j = (i >> 10) & 0x3f;
+	z = s * s;
+	qn = (long double) n;
+	t = qn * ln2lo + _TBL_logl_lo[j];
+	h = qn * ln2hi + _TBL_logl_hi[j];
+	f = t + s * (A1 + z * (A2 + z * (A3 + z * (A4 + z * (A5 +
+		z * (A6 + z * A7))))));
+	return (h + f);
+}