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, 227 insertions, 0 deletions

diff --git a/usr/src/lib/libm/common/C/log2.c b/usr/src/lib/libm/common/C/log2.c
new file mode 100644
index 0000000000..6b588f17f4
--- /dev/null
+++ b/usr/src/lib/libm/common/C/log2.c
@@ -0,0 +1,227 @@
+/*
+ * 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 log2 = __log2
+
+/* INDENT OFF */
+/*
+ * log2(x) = log(x)/log2
+ *
+ * Base on Table look-up algorithm with product polynomial
+ * approximation for log(x).
+ *
+ * By K.C. Ng, Nov 29, 2004
+ *
+ * (a). For x in [1-0.125, 1+0.125], from log.c we have
+ *	log(x) =  f + ((a1*f^2) *
+ *		   ((a2 + (a3*f)*(a4+f)) + (f^3)*(a5+f))) *
+ *		   (((a6 + f*(a7+f)) + (f^3)*(a8+f)) *
+ *		   ((a9 + (a10*f)*(a11+f)) + (f^3)*(a12+f)))
+ *	where f = x - 1.
+ *	(i) modify a1 <- a1 / log2
+ *	(ii) 1/log2 = 1.4426950408889634...
+ *		    = 1.5 - 0.057304959... (4 bit shift)
+ *	     Let lv = 1.5 - 1/log2, then
+ *	     lv = 0.057304959111036592640075318998107956665325,
+ *	(iii) f*1.5 is exact because f has 3 trailing zero.
+ *	(iv) Thus, log2(x) = f*1.5 - (lv*f - PPoly)
+ *
+ * (b). For 0.09375 <= x < 24
+ *	Let j = (ix - 0x3fb80000) >> 15. Look up Y[j], 1/Y[j], and log(Y[j])
+ *	from _TBL_log.c. Then
+ *		log2(x)  = log2(Y[j]) + log2(1 + (x-Y[j])*(1/Y[j]))
+ *			  = log(Y[j])(1/log2) + log2(1 + s)
+ *	where
+ *		s = (x-Y[j])*(1/Y[j])
+ *	From log.c, we have log(1+s) =
+ *				  2              2                     2
+ *		(b s) (b + b s + s ) [b + b s + s (b + s)] (b + b s + s )
+ *		  1     2   3          4   5        6        7   8
+ *
+ *	By setting b1 <- b1/log2, we have
+ *		log2(x) = 1.5 * T - (lv * T - POLY(s))
+ *
+ * (c). Otherwise, get "n", the exponent of x, and then normalize x to
+ *	z in [1,2). Then similar to (b) find a Y[i] that matches z to 5.5
+ *	significant bits. Then
+ *	    log2(x) = n + log2(z).
+ *
+ * Special cases:
+ *	log2(x) is NaN with signal if x < 0 (including -INF) ;
+ *	log2(+INF) is +INF; log2(0) is -INF with signal;
+ *	log2(NaN) is that NaN with no signal.
+ *
+ * Maximum error observed: less than 0.84 ulp
+ *
+ * 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.
+ */
+/* INDENT ON */
+
+#include "libm.h"
+#include "libm_synonyms.h"
+#include "libm_protos.h"
+
+extern const double _TBL_log[];
+
+static const double P[] = {
+/* ONE   */  1.0,
+/* TWO52 */  4503599627370496.0,
+/* LN10V */  1.4426950408889634073599246810018920433347,   /* 1/log10 */
+/* ZERO  */  0.0,
+/* A1    */ -9.6809362455249638217841932228967194640116e-02,
+/* A2    */  1.99628461483039965074226529395673424005508422852e+0000,
+/* A3    */  2.26812367662950720159642514772713184356689453125e+0000,
+/* A4    */ -9.05030639084976384900471657601883634924888610840e-0001,
+/* A5    */ -1.48275767132434044270894446526654064655303955078e+0000,
+/* A6    */  1.88158320939722756293122074566781520843505859375e+0000,
+/* A7    */  1.83309386046986411145098827546462416648864746094e+0000,
+/* A8    */  1.24847063988317086291601754055591300129890441895e+0000,
+/* A9    */  1.98372421445537705508854742220137268304824829102e+0000,
+/* A10   */ -3.94711735767898475035764249696512706577777862549e-0001,
+/* A11   */  3.07890395362954372160402272129431366920471191406e+0000,
+/* A12   */ -9.60099585275022149311041630426188930869102478027e-0001,
+/* B1    */ -1.8039695622547469514898963204616532885451e-01,
+/* B2    */  1.87161713283355151891381127914642725337613123482e+0000,
+/* B3    */ -1.89082956295731507978530316904652863740921020508e+0000,
+/* B4    */ -2.50562891673640253387134180229622870683670043945e+0000,
+/* B5    */  1.64822828085258366037635369139024987816810607910e+0000,
+/* B6    */ -1.24409107065868340669112512841820716857910156250e+0000,
+/* B7    */  1.70534231658220414296067701798165217041969299316e+0000,
+/* B8    */  1.99196833784655646937267192697618156671524047852e+0000,
+/* LGH   */  1.5,
+/* LGL   */  0.057304959111036592640075318998107956665325,
+};
+
+#define	ONE   P[0]
+#define	TWO52 P[1]
+#define	LN10V P[2]
+#define	ZERO  P[3]
+#define	A1    P[4]
+#define	A2    P[5]
+#define	A3    P[6]
+#define	A4    P[7]
+#define	A5    P[8]
+#define	A6    P[9]
+#define	A7    P[10]
+#define	A8    P[11]
+#define	A9    P[12]
+#define	A10   P[13]
+#define	A11   P[14]
+#define	A12   P[15]
+#define	B1    P[16]
+#define	B2    P[17]
+#define	B3    P[18]
+#define	B4    P[19]
+#define	B5    P[20]
+#define	B6    P[21]
+#define	B7    P[22]
+#define	B8    P[23]
+#define	LGH   P[24]
+#define	LGL   P[25]
+
+double
+log2(double x) {
+	int i, hx, ix, n, lx;
+
+	n = 0;
+	hx = ((int *) &x)[HIWORD]; ix = hx & 0x7fffffff;
+	lx = ((int *) &x)[LOWORD];
+
+	/* subnormal,0,negative,inf,nan */
+	if ((hx + 0x100000) < 0x200000) {
+#if defined(FPADD_TRAPS_INCOMPLETE_ON_NAN)
+		if (ix >= 0x7ff80000)		/* assumes sparc-like QNaN */
+			return (x);		/* for Cheetah when x is QNaN */
+#endif
+		if (((hx << 1) | lx) == 0)	/* log(0.0) = -inf */
+			return (A5 / fabs(x));
+		if (hx < 0) {	/* x < 0 */
+			if (ix >= 0x7ff00000)
+				return (x - x);	/* x is -inf or NaN */
+			else
+				return (ZERO / (x - x));
+		}
+		if (((hx - 0x7ff00000) | lx) == 0)	/* log(inf) = inf */
+			return (x);
+		if (ix >= 0x7ff00000)		/* log(NaN) = NaN */
+			return (x - x);
+		x *= TWO52;
+		n = -52;
+		hx = ((int *) &x)[HIWORD]; ix = hx & 0x7fffffff;
+		lx = ((int *) &x)[LOWORD];
+	}
+
+	/* 0.09375 (0x3fb80000) <= x < 24 (0x40380000) */
+	i = ix >> 19;
+	if (i >= 0x7f7 && i <= 0x806) {
+		/* 0.875 <= x < 1.125 */
+		if (ix >= 0x3fec0000 && ix < 0x3ff20000) {
+			double s, z, r, w;
+			s = x - ONE; z = s * s; r = (A10 * s) * (A11 + s);
+			w = z * s;
+			if (((ix << 12) | lx) == 0)
+				return (z);
+			else
+				return (LGH * s - (LGL * s - ((A1 * z) *
+				((A2 + (A3 * s) * (A4 + s)) + w * (A5 + s))) *
+				(((A6 + s * (A7 + s)) + w * (A8 + s)) *
+				((A9 + r) + w * (A12 + s)))));
+		} else {
+			double *tb, s;
+			i = (ix - 0x3fb80000) >> 15;
+			tb = (double *) _TBL_log + (i + i + i);
+			if (((ix << 12) | lx) == 0)	/* 2's power */
+				return ((double) ((ix >> 20) - 0x3ff));
+			s = (x - tb[0]) * tb[1];
+			return (LGH * tb[2] - (LGL * tb[2] - ((B1 * s) *
+				(B2 + s * (B3 + s))) *
+				(((B4 + s * B5) + (s * s) * (B6 + s)) *
+				(B7 + s * (B8 + s)))));
+		}
+	} else {
+		double *tb, dn, s;
+		dn = (double) (n + ((ix >> 20) - 0x3ff));
+		ix <<= 12;
+		if ((ix | lx) == 0)
+			return (dn);
+		i = ((unsigned) ix >> 12) | 0x3ff00000;	/* scale x to [1,2) */
+		((int *) &x)[HIWORD] = i;
+		i = (i - 0x3fb80000) >> 15;
+		tb = (double *) _TBL_log + (i + i + i);
+		s = (x - tb[0]) * tb[1];
+		return (dn + (tb[2] * LN10V + ((B1 * s) *
+			(B2 + s * (B3 + s))) *
+			(((B4 + s * B5) + (s * s) * (B6 + s)) *
+			(B7 + s * (B8 + s)))));
+	}
+}