libm/upstream-freebsd/lib/msun/bsdsrc/b_log.c - android_bionic - Gitiles

 /*-
  * SPDX-License-Identifier: BSD-3-Clause
  *
  * 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.
  */

 /* 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/F| <= 1/256,
  * where F = j/128 for j an integer in [0, 128].
  *
  * log(2^m) = log2_hi*m + log2_tail*m
  * The leading term is exact, because m is an integer,
  * 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 table below.
  * 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 and 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
  */

 #define N 128

 /*
  * Coefficients in the polynomial approximation of log(1+f/F).
  * Domain of x is [0,1./256] with 2**(-64.187) precision.
  */
 static const double
     A1 =  8.3333333333333329e-02, /* 0x3fb55555, 0x55555555 */
     A2 =  1.2499999999943598e-02, /* 0x3f899999, 0x99991a98 */
     A3 =  2.2321527525957776e-03; /* 0x3f624929, 0xe24e70be */

 /*
  * 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 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
 };
 /*
  * Extra precision variant, returning struct {double a, b;};
  * log(x) = a+b to 63 bits, with 'a' rounded to 24 bits.
  */
 static struct Double
 __log__D(double x)
 {
 	int m, j;
 	double F, f, g, q, u, v, u1, u2;
 	struct Double r;

 	/*
 	 * Argument reduction: 1 <= g < 2; x/2^m = g;
 	 * y = F*(1 + f/F) for |f| <= 2^-8
 	 */
 	g = frexp(x, &m);
 	g *= 2;
 	m--;
 	if (m == -1022) {
 		j = ilogb(g);
 		m += j;
 		g = ldexp(g, -j);
 	}
 	j = N * (g - 1) + 0.5;
 	F = (1. / 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));
 	if (m | j) {
 		u1 = u + 513;
 		u1 -= 513;
 	} else {
 		u1 = (float)u;
 	}
 	u2 = (2 * (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 = (float)(u1 + u2);		/* Only difference is here. */
 	r.b = (u1 - r.a) + u2;
 	return (r);
 }
	/*-
	* SPDX-License-Identifier: BSD-3-Clause
	*
	* 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.
	*/

	/* 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^mF(1+f/F)), \|f/F\| <= 1/256,
	* where F = j/128 for j an integer in [0, 128].
	*
	* log(2^m) = log2_him + log2_tailm
	* The leading term is exact, because m is an integer,
	* 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 table below.
	* logF_hi[] + 512 is exact.
	*
	* log(1+f/F) = 2f/(2F + f) + 1/12 * (2f/(2F + 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 and 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
	*/

	#define N 128

	/*
	* Coefficients in the polynomial approximation of log(1+f/F).
	* Domain of x is [0,1./256] with 2**(-64.187) precision.
	*/
	static const double
	A1 = 8.3333333333333329e-02, /* 0x3fb55555, 0x55555555 */
	A2 = 1.2499999999943598e-02, /* 0x3f899999, 0x99991a98 */
	A3 = 2.2321527525957776e-03; /* 0x3f624929, 0xe24e70be */

	/*
	* 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 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
	};
	/*
	* Extra precision variant, returning struct {double a, b;};
	* log(x) = a+b to 63 bits, with 'a' rounded to 24 bits.
	*/
	static struct Double
	__log__D(double x)
	{
	int m, j;
	double F, f, g, q, u, v, u1, u2;
	struct Double r;

	/*
	* Argument reduction: 1 <= g < 2; x/2^m = g;
	* y = F*(1 + f/F) for \|f\| <= 2^-8
	*/
	g = frexp(x, &m);
	g *= 2;
	m--;
	if (m == -1022) {
	j = ilogb(g);
	m += j;
	g = ldexp(g, -j);
	}
	j = N * (g - 1) + 0.5;
	F = (1. / 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));
	if (m \| j) {
	u1 = u + 513;
	u1 -= 513;
	} else {
	u1 = (float)u;
	}
	u2 = (2 * (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 = (float)(u1 + u2); /* Only difference is here. */
	r.b = (u1 - r.a) + u2;
	return (r);
	}