#include "FEATURE/uwin"

#if !_UWIN

void _STUB_log(){}

#else

/*

 * 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. 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

};

#if !_lib_log

extern 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);

}

#endif

/*

 * 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 = (int)logb(x);

	g = ldexp(x, -m);

	if (_IEEE && m == -1022) {

		j = (int)logb(g), m += j;

		g = ldexp(g, -j);

	}

	j = (int)(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);

}

#endif