1 files changed, 486 insertions, 0 deletions

diff --git a/lib/libm/common_source/log.c b/lib/libm/common_source/log.c
new file mode 100644
index 000000000000..ae186722f8df
--- /dev/null
+++ b/lib/libm/common_source/log.c
@@ -0,0 +1,486 @@
+/*
+ * Copyright (c) 1992, 1993
+ *	The Regents of the University of California.  All rights reserved.
+ *
+ * Redistribution and use in source and binary forms, with or without
+ * modification, are permitted provided that the following conditions
+ * are met:
+ * 1. Redistributions of source code must retain the above copyright
+ *    notice, this list of conditions and the following disclaimer.
+ * 2. Redistributions in binary form must reproduce the above copyright
+ *    notice, this list of conditions and the following disclaimer in the
+ *    documentation and/or other materials provided with the distribution.
+ * 3. All advertising materials mentioning features or use of this software
+ *    must display the following acknowledgement:
+ *	This product includes software developed by the University of
+ *	California, Berkeley and its contributors.
+ * 4. Neither the name of the University nor the names of its contributors
+ *    may be used to endorse or promote products derived from this software
+ *    without specific prior written permission.
+ *
+ * THIS SOFTWARE IS PROVIDED BY THE REGENTS AND CONTRIBUTORS ``AS IS'' AND
+ * ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE
+ * IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE
+ * ARE DISCLAIMED.  IN NO EVENT SHALL THE REGENTS OR CONTRIBUTORS BE LIABLE
+ * FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL
+ * DAMAGES (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS
+ * OR SERVICES; LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION)
+ * HOWEVER CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT
+ * LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY
+ * OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF
+ * SUCH DAMAGE.
+ */
+
+#ifndef lint
+static char sccsid[] = "@(#)log.c	8.2 (Berkeley) 11/30/93";
+#endif /* not lint */
+
+#include <math.h>
+#include <errno.h>
+
+#include "mathimpl.h"
+
+/* Table-driven natural logarithm.
+ *
+ * This code was derived, with minor modifications, from:
+ *	Peter Tang, "Table-Driven Implementation of the
+ *	Logarithm in IEEE Floating-Point arithmetic." ACM Trans.
+ *	Math Software, vol 16. no 4, pp 378-400, Dec 1990).
+ *
+ * Calculates log(2^m*F*(1+f/F)), |f/j| <= 1/256,
+ * where F = j/128 for j an integer in [0, 128].
+ *
+ * log(2^m) = log2_hi*m + log2_tail*m
+ * since m is an integer, the dominant term is exact.
+ * m has at most 10 digits (for subnormal numbers),
+ * and log2_hi has 11 trailing zero bits.
+ *
+ * log(F) = logF_hi[j] + logF_lo[j] is in tabular form in log_table.h
+ * logF_hi[] + 512 is exact.
+ *
+ * log(1+f/F) = 2*f/(2*F + f) + 1/12 * (2*f/(2*F + f))**3 + ...
+ * the leading term is calculated to extra precision in two
+ * parts, the larger of which adds exactly to the dominant
+ * m and F terms.
+ * There are two cases:
+ *	1. when m, j are non-zero (m | j), use absolute
+ *	   precision for the leading term.
+ *	2. when m = j = 0, |1-x| < 1/256, and log(x) ~= (x-1).
+ *	   In this case, use a relative precision of 24 bits.
+ * (This is done differently in the original paper)
+ *
+ * Special cases:
+ *	0	return signalling -Inf
+ *	neg	return signalling NaN
+ *	+Inf	return +Inf
+*/
+
+#if defined(vax) || defined(tahoe)
+#define _IEEE		0
+#define TRUNC(x)	x = (double) (float) (x)
+#else
+#define _IEEE		1
+#define endian		(((*(int *) &one)) ? 1 : 0)
+#define TRUNC(x)	*(((int *) &x) + endian) &= 0xf8000000
+#define infnan(x)	0.0
+#endif
+
+#define N 128
+
+/* Table of log(Fj) = logF_head[j] + logF_tail[j], for Fj = 1+j/128.
+ * Used for generation of extend precision logarithms.
+ * The constant 35184372088832 is 2^45, so the divide is exact.
+ * It ensures correct reading of logF_head, even for inaccurate
+ * decimal-to-binary conversion routines.  (Everybody gets the
+ * right answer for integers less than 2^53.)
+ * Values for log(F) were generated using error < 10^-57 absolute
+ * with the bc -l package.
+*/
+static double	A1 = 	  .08333333333333178827;
+static double	A2 = 	  .01250000000377174923;
+static double	A3 =	 .002232139987919447809;
+static double	A4 =	.0004348877777076145742;
+
+static double logF_head[N+1] = {
+	0.,
+	.007782140442060381246,
+	.015504186535963526694,
+	.023167059281547608406,
+	.030771658666765233647,
+	.038318864302141264488,
+	.045809536031242714670,
+	.053244514518837604555,
+	.060624621816486978786,
+	.067950661908525944454,
+	.075223421237524235039,
+	.082443669210988446138,
+	.089612158689760690322,
+	.096729626458454731618,
+	.103796793681567578460,
+	.110814366340264314203,
+	.117783035656430001836,
+	.124703478501032805070,
+	.131576357788617315236,
+	.138402322859292326029,
+	.145182009844575077295,
+	.151916042025732167530,
+	.158605030176659056451,
+	.165249572895390883786,
+	.171850256926518341060,
+	.178407657472689606947,
+	.184922338493834104156,
+	.191394852999565046047,
+	.197825743329758552135,
+	.204215541428766300668,
+	.210564769107350002741,
+	.216873938300523150246,
+	.223143551314024080056,
+	.229374101064877322642,
+	.235566071312860003672,
+	.241719936886966024758,
+	.247836163904594286577,
+	.253915209980732470285,
+	.259957524436686071567,
+	.265963548496984003577,
+	.271933715484010463114,
+	.277868451003087102435,
+	.283768173130738432519,
+	.289633292582948342896,
+	.295464212893421063199,
+	.301261330578199704177,
+	.307025035294827830512,
+	.312755710004239517729,
+	.318453731118097493890,
+	.324119468654316733591,
+	.329753286372579168528,
+	.335355541920762334484,
+	.340926586970454081892,
+	.346466767346100823488,
+	.351976423156884266063,
+	.357455888922231679316,
+	.362905493689140712376,
+	.368325561158599157352,
+	.373716409793814818840,
+	.379078352934811846353,
+	.384411698910298582632,
+	.389716751140440464951,
+	.394993808240542421117,
+	.400243164127459749579,
+	.405465108107819105498,
+	.410659924985338875558,
+	.415827895143593195825,
+	.420969294644237379543,
+	.426084395310681429691,
+	.431173464818130014464,
+	.436236766774527495726,
+	.441274560805140936281,
+	.446287102628048160113,
+	.451274644139630254358,
+	.456237433481874177232,
+	.461175715122408291790,
+	.466089729924533457960,
+	.470979715219073113985,
+	.475845904869856894947,
+	.480688529345570714212,
+	.485507815781602403149,
+	.490303988045525329653,
+	.495077266798034543171,
+	.499827869556611403822,
+	.504556010751912253908,
+	.509261901790523552335,
+	.513945751101346104405,
+	.518607764208354637958,
+	.523248143765158602036,
+	.527867089620485785417,
+	.532464798869114019908,
+	.537041465897345915436,
+	.541597282432121573947,
+	.546132437597407260909,
+	.550647117952394182793,
+	.555141507540611200965,
+	.559615787935399566777,
+	.564070138285387656651,
+	.568504735352689749561,
+	.572919753562018740922,
+	.577315365035246941260,
+	.581691739635061821900,
+	.586049045003164792433,
+	.590387446602107957005,
+	.594707107746216934174,
+	.599008189645246602594,
+	.603290851438941899687,
+	.607555250224322662688,
+	.611801541106615331955,
+	.616029877215623855590,
+	.620240409751204424537,
+	.624433288012369303032,
+	.628608659422752680256,
+	.632766669570628437213,
+	.636907462236194987781,
+	.641031179420679109171,
+	.645137961373620782978,
+	.649227946625615004450,
+	.653301272011958644725,
+	.657358072709030238911,
+	.661398482245203922502,
+	.665422632544505177065,
+	.669430653942981734871,
+	.673422675212350441142,
+	.677398823590920073911,
+	.681359224807238206267,
+	.685304003098281100392,
+	.689233281238557538017,
+	.693147180560117703862
+};
+
+static double logF_tail[N+1] = {
+	0.,
+	-.00000000000000543229938420049,
+	 .00000000000000172745674997061,
+	-.00000000000001323017818229233,
+	-.00000000000001154527628289872,
+	-.00000000000000466529469958300,
+	 .00000000000005148849572685810,
+	-.00000000000002532168943117445,
+	-.00000000000005213620639136504,
+	-.00000000000001819506003016881,
+	 .00000000000006329065958724544,
+	 .00000000000008614512936087814,
+	-.00000000000007355770219435028,
+	 .00000000000009638067658552277,
+	 .00000000000007598636597194141,
+	 .00000000000002579999128306990,
+	-.00000000000004654729747598444,
+	-.00000000000007556920687451336,
+	 .00000000000010195735223708472,
+	-.00000000000017319034406422306,
+	-.00000000000007718001336828098,
+	 .00000000000010980754099855238,
+	-.00000000000002047235780046195,
+	-.00000000000008372091099235912,
+	 .00000000000014088127937111135,
+	 .00000000000012869017157588257,
+	 .00000000000017788850778198106,
+	 .00000000000006440856150696891,
+	 .00000000000016132822667240822,
+	-.00000000000007540916511956188,
+	-.00000000000000036507188831790,
+	 .00000000000009120937249914984,
+	 .00000000000018567570959796010,
+	-.00000000000003149265065191483,
+	-.00000000000009309459495196889,
+	 .00000000000017914338601329117,
+	-.00000000000001302979717330866,
+	 .00000000000023097385217586939,
+	 .00000000000023999540484211737,
+	 .00000000000015393776174455408,
+	-.00000000000036870428315837678,
+	 .00000000000036920375082080089,
+	-.00000000000009383417223663699,
+	 .00000000000009433398189512690,
+	 .00000000000041481318704258568,
+	-.00000000000003792316480209314,
+	 .00000000000008403156304792424,
+	-.00000000000034262934348285429,
+	 .00000000000043712191957429145,
+	-.00000000000010475750058776541,
+	-.00000000000011118671389559323,
+	 .00000000000037549577257259853,
+	 .00000000000013912841212197565,
+	 .00000000000010775743037572640,
+	 .00000000000029391859187648000,
+	-.00000000000042790509060060774,
+	 .00000000000022774076114039555,
+	 .00000000000010849569622967912,
+	-.00000000000023073801945705758,
+	 .00000000000015761203773969435,
+	 .00000000000003345710269544082,
+	-.00000000000041525158063436123,
+	 .00000000000032655698896907146,
+	-.00000000000044704265010452446,
+	 .00000000000034527647952039772,
+	-.00000000000007048962392109746,
+	 .00000000000011776978751369214,
+	-.00000000000010774341461609578,
+	 .00000000000021863343293215910,
+	 .00000000000024132639491333131,
+	 .00000000000039057462209830700,
+	-.00000000000026570679203560751,
+	 .00000000000037135141919592021,
+	-.00000000000017166921336082431,
+	-.00000000000028658285157914353,
+	-.00000000000023812542263446809,
+	 .00000000000006576659768580062,
+	-.00000000000028210143846181267,
+	 .00000000000010701931762114254,
+	 .00000000000018119346366441110,
+	 .00000000000009840465278232627,
+	-.00000000000033149150282752542,
+	-.00000000000018302857356041668,
+	-.00000000000016207400156744949,
+	 .00000000000048303314949553201,
+	-.00000000000071560553172382115,
+	 .00000000000088821239518571855,
+	-.00000000000030900580513238244,
+	-.00000000000061076551972851496,
+	 .00000000000035659969663347830,
+	 .00000000000035782396591276383,
+	-.00000000000046226087001544578,
+	 .00000000000062279762917225156,
+	 .00000000000072838947272065741,
+	 .00000000000026809646615211673,
+	-.00000000000010960825046059278,
+	 .00000000000002311949383800537,
+	-.00000000000058469058005299247,
+	-.00000000000002103748251144494,
+	-.00000000000023323182945587408,
+	-.00000000000042333694288141916,
+	-.00000000000043933937969737844,
+	 .00000000000041341647073835565,
+	 .00000000000006841763641591466,
+	 .00000000000047585534004430641,
+	 .00000000000083679678674757695,
+	-.00000000000085763734646658640,
+	 .00000000000021913281229340092,
+	-.00000000000062242842536431148,
+	-.00000000000010983594325438430,
+	 .00000000000065310431377633651,
+	-.00000000000047580199021710769,
+	-.00000000000037854251265457040,
+	 .00000000000040939233218678664,
+	 .00000000000087424383914858291,
+	 .00000000000025218188456842882,
+	-.00000000000003608131360422557,
+	-.00000000000050518555924280902,
+	 .00000000000078699403323355317,
+	-.00000000000067020876961949060,
+	 .00000000000016108575753932458,
+	 .00000000000058527188436251509,
+	-.00000000000035246757297904791,
+	-.00000000000018372084495629058,
+	 .00000000000088606689813494916,
+	 .00000000000066486268071468700,
+	 .00000000000063831615170646519,
+	 .00000000000025144230728376072,
+	-.00000000000017239444525614834
+};
+
+double
+#ifdef _ANSI_SOURCE
+log(double x)
+#else
+log(x) double x;
+#endif
+{
+	int m, j;
+	double F, f, g, q, u, u2, v, zero = 0.0, one = 1.0;
+	volatile double u1;
+
+	/* Catch special cases */
+	if (x <= 0)
+		if (_IEEE && x == zero)	/* log(0) = -Inf */
+			return (-one/zero);
+		else if (_IEEE)		/* log(neg) = NaN */
+			return (zero/zero);
+		else if (x == zero)	/* NOT REACHED IF _IEEE */
+			return (infnan(-ERANGE));
+		else
+			return (infnan(EDOM));
+	else if (!finite(x))
+		if (_IEEE)		/* x = NaN, Inf */
+			return (x+x);
+		else
+			return (infnan(ERANGE));
+	
+	/* Argument reduction: 1 <= g < 2; x/2^m = g;	*/
+	/* y = F*(1 + f/F) for |f| <= 2^-8		*/
+
+	m = logb(x);
+	g = ldexp(x, -m);
+	if (_IEEE && m == -1022) {
+		j = logb(g), m += j;
+		g = ldexp(g, -j);
+	}
+	j = N*(g-1) + .5;
+	F = (1.0/N) * j + 1;	/* F*128 is an integer in [128, 512] */
+	f = g - F;
+
+	/* Approximate expansion for log(1+f/F) ~= u + q */
+	g = 1/(2*F+f);
+	u = 2*f*g;
+	v = u*u;
+	q = u*v*(A1 + v*(A2 + v*(A3 + v*A4)));
+
+    /* case 1: u1 = u rounded to 2^-43 absolute.  Since u < 2^-8,
+     * 	       u1 has at most 35 bits, and F*u1 is exact, as F has < 8 bits.
+     *         It also adds exactly to |m*log2_hi + log_F_head[j] | < 750
+    */
+	if (m | j)
+		u1 = u + 513, u1 -= 513;
+
+    /* case 2:	|1-x| < 1/256. The m- and j- dependent terms are zero;
+     * 		u1 = u to 24 bits.
+    */
+	else
+		u1 = u, TRUNC(u1);
+	u2 = (2.0*(f - F*u1) - u1*f) * g;
+			/* u1 + u2 = 2f/(2F+f) to extra precision.	*/
+
+	/* log(x) = log(2^m*F*(1+f/F)) =				*/
+	/* (m*log2_hi+logF_head[j]+u1) + (m*log2_lo+logF_tail[j]+q);	*/
+	/* (exact) + (tiny)						*/
+
+	u1 += m*logF_head[N] + logF_head[j];		/* exact */
+	u2 = (u2 + logF_tail[j]) + q;			/* tiny */
+	u2 += logF_tail[N]*m;
+	return (u1 + u2);
+}
+
+/*
+ * Extra precision variant, returning struct {double a, b;};
+ * log(x) = a+b to 63 bits, with a is rounded to 26 bits.
+ */
+struct Double
+#ifdef _ANSI_SOURCE
+__log__D(double x)
+#else
+__log__D(x) double x;
+#endif
+{
+	int m, j;
+	double F, f, g, q, u, v, u2, one = 1.0;
+	volatile double u1;
+	struct Double r;
+
+	/* Argument reduction: 1 <= g < 2; x/2^m = g;	*/
+	/* y = F*(1 + f/F) for |f| <= 2^-8		*/
+
+	m = logb(x);
+	g = ldexp(x, -m);
+	if (_IEEE && m == -1022) {
+		j = logb(g), m += j;
+		g = ldexp(g, -j);
+	}
+	j = N*(g-1) + .5;
+	F = (1.0/N) * j + 1;
+	f = g - F;
+
+	g = 1/(2*F+f);
+	u = 2*f*g;
+	v = u*u;
+	q = u*v*(A1 + v*(A2 + v*(A3 + v*A4)));
+	if (m | j)
+		u1 = u + 513, u1 -= 513;
+	else
+		u1 = u, TRUNC(u1);
+	u2 = (2.0*(f - F*u1) - u1*f) * g;
+
+	u1 += m*logF_head[N] + logF_head[j];
+
+	u2 +=  logF_tail[j]; u2 += q;
+	u2 += logF_tail[N]*m;
+	r.a = u1 + u2;			/* Only difference is here */
+	TRUNC(r.a);
+	r.b = (u1 - r.a) + u2;
+	return (r);
+}