1993-08-14 23:20:58 +04:00
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/*
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* Copyright (c) 1992 Regents of the University of California.
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* All rights reserved.
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*
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* Redistribution and use in source and binary forms, with or without
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* modification, are permitted provided that the following conditions
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* are met:
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* 1. Redistributions of source code must retain the above copyright
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* notice, this list of conditions and the following disclaimer.
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* 2. Redistributions in binary form must reproduce the above copyright
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* notice, this list of conditions and the following disclaimer in the
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* documentation and/or other materials provided with the distribution.
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* 3. All advertising materials mentioning features or use of this software
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* must display the following acknowledgement:
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* This product includes software developed by the University of
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* California, Berkeley and its contributors.
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* 4. Neither the name of the University nor the names of its contributors
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* may be used to endorse or promote products derived from this software
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* without specific prior written permission.
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*
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* THIS SOFTWARE IS PROVIDED BY THE REGENTS AND CONTRIBUTORS ``AS IS'' AND
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* ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE
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* IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE
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* ARE DISCLAIMED. IN NO EVENT SHALL THE REGENTS OR CONTRIBUTORS BE LIABLE
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* FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL
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* DAMAGES (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS
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* OR SERVICES; LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION)
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* HOWEVER CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT
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* LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY
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* OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF
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* SUCH DAMAGE.
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*/
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#ifndef lint
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/*static char sccsid[] = "from: @(#)log.c 5.10 (Berkeley) 1/10/93";*/
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1993-08-14 23:31:23 +04:00
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static char rcsid[] = "$Id: logtab.c,v 1.2 1993/08/14 19:31:28 mycroft Exp $";
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1993-08-14 23:20:58 +04:00
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#endif /* not lint */
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#include <math.h>
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#include <errno.h>
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#include "log.h"
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/* Table-driven natural logarithm.
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*
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* This code was derived, with minor modifications, from:
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* Peter Tang, "Table-Driven Implementation of the
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* Logarithm in IEEE Floating-Point arithmetic." ACM Trans.
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* Math Software, vol 16. no 4, pp 378-400, Dec 1990).
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*
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* Calculates log(2^m*F*(1+f/F)), |f/j| <= 1/256,
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* where F = j/128 for j an integer in [0, 128].
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*
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* log(2^m) = log2_hi*m + log2_tail*m
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* since m is an integer, the dominant term is exact.
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* m has at most 10 digits (for subnormal numbers),
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* and log2_hi has 11 trailing zero bits.
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*
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* log(F) = logF_hi[j] + logF_lo[j] is in tabular form in log_table.h
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* logF_hi[] + 512 is exact.
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*
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* log(1+f/F) = 2*f/(2*F + f) + 1/12 * (2*f/(2*F + f))**3 + ...
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* the leading term is calculated to extra precision in two
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* parts, the larger of which adds exactly to the dominant
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* m and F terms.
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* There are two cases:
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* 1. when m, j are non-zero (m | j), use absolute
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* precision for the leading term.
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* 2. when m = j = 0, |1-x| < 1/256, and log(x) ~= (x-1).
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* In this case, use a relative precision of 24 bits.
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* (This is done differently in the original paper)
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*
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* Special cases:
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* 0 return signalling -Inf
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* neg return signalling NaN
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* +Inf return +Inf
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*/
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/* Table of log(Fj) = logF_head[j] + logF_tail[j], for Fj = 1+j/128.
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* Used for generation of extend precision logarithms.
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* The constant 35184372088832 is 2^45, so the divide is exact.
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* It ensures correct reading of logF_head, even for inaccurate
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* decimal-to-binary conversion routines. (Everybody gets the
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* right answer for integers less than 2^53.)
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* Values for log(F) were generated using error < 10^-57 absolute
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* with the bc -l package.
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*/
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double __log_A1 = .08333333333333178827;
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double __log_A2 = .01250000000377174923;
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double __log_A3 = .002232139987919447809;
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double __log_A4 = .0004348877777076145742;
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double __logF_head[N+1] = {
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0.,
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.007782140442060381246,
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.015504186535963526694,
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.023167059281547608406,
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.030771658666765233647,
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.038318864302141264488,
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.045809536031242714670,
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.053244514518837604555,
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.060624621816486978786,
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.067950661908525944454,
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.075223421237524235039,
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.082443669210988446138,
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.089612158689760690322,
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.096729626458454731618,
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.103796793681567578460,
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.110814366340264314203,
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.117783035656430001836,
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.124703478501032805070,
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.131576357788617315236,
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.138402322859292326029,
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.145182009844575077295,
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.151916042025732167530,
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.158605030176659056451,
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.165249572895390883786,
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.171850256926518341060,
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.178407657472689606947,
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.184922338493834104156,
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.191394852999565046047,
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.197825743329758552135,
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.204215541428766300668,
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.210564769107350002741,
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.216873938300523150246,
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.223143551314024080056,
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.229374101064877322642,
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.235566071312860003672,
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.241719936886966024758,
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.247836163904594286577,
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.253915209980732470285,
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.259957524436686071567,
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.265963548496984003577,
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.271933715484010463114,
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.277868451003087102435,
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.283768173130738432519,
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.289633292582948342896,
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.295464212893421063199,
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.301261330578199704177,
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.307025035294827830512,
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.312755710004239517729,
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.318453731118097493890,
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.324119468654316733591,
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.329753286372579168528,
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.335355541920762334484,
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.340926586970454081892,
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.346466767346100823488,
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.351976423156884266063,
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.357455888922231679316,
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.362905493689140712376,
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.368325561158599157352,
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.373716409793814818840,
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.379078352934811846353,
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.384411698910298582632,
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.389716751140440464951,
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.394993808240542421117,
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.400243164127459749579,
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.405465108107819105498,
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.410659924985338875558,
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.415827895143593195825,
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.420969294644237379543,
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.426084395310681429691,
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.431173464818130014464,
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.436236766774527495726,
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.441274560805140936281,
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.446287102628048160113,
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.451274644139630254358,
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.456237433481874177232,
|
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.461175715122408291790,
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|
|
.466089729924533457960,
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.470979715219073113985,
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|
|
.475845904869856894947,
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.480688529345570714212,
|
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|
|
.485507815781602403149,
|
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|
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.490303988045525329653,
|
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|
|
.495077266798034543171,
|
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|
|
.499827869556611403822,
|
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|
|
.504556010751912253908,
|
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|
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.509261901790523552335,
|
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|
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.513945751101346104405,
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|
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.518607764208354637958,
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.523248143765158602036,
|
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.527867089620485785417,
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.532464798869114019908,
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.537041465897345915436,
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.541597282432121573947,
|
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.546132437597407260909,
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.550647117952394182793,
|
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.555141507540611200965,
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.559615787935399566777,
|
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.564070138285387656651,
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.568504735352689749561,
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.572919753562018740922,
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.577315365035246941260,
|
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.581691739635061821900,
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|
.586049045003164792433,
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|
.590387446602107957005,
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.594707107746216934174,
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|
.599008189645246602594,
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|
.603290851438941899687,
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|
|
.607555250224322662688,
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|
.611801541106615331955,
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|
.616029877215623855590,
|
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|
|
.620240409751204424537,
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|
|
.624433288012369303032,
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|
|
.628608659422752680256,
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|
|
.632766669570628437213,
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|
|
.636907462236194987781,
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.641031179420679109171,
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|
.645137961373620782978,
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.649227946625615004450,
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.653301272011958644725,
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|
|
.657358072709030238911,
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|
|
.661398482245203922502,
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|
|
.665422632544505177065,
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|
|
.669430653942981734871,
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|
|
.673422675212350441142,
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|
|
|
.677398823590920073911,
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|
|
.681359224807238206267,
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|
|
.685304003098281100392,
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.689233281238557538017,
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.693147180560117703862
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};
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double __logF_tail[N+1] = {
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0.,
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-.00000000000000543229938420049,
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|
|
|
.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,
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|
|
|
.00000000000036920375082080089,
|
|
|
|
|
-.00000000000009383417223663699,
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|
|
|
.00000000000009433398189512690,
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|
|
|
.00000000000041481318704258568,
|
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|
|
-.00000000000003792316480209314,
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|
|
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.00000000000008403156304792424,
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|
|
-.00000000000034262934348285429,
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|
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.00000000000043712191957429145,
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|
|
|
|
-.00000000000010475750058776541,
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|
|
-.00000000000011118671389559323,
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.00000000000037549577257259853,
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.00000000000013912841212197565,
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.00000000000010775743037572640,
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|
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.00000000000029391859187648000,
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|
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-.00000000000042790509060060774,
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|
|
.00000000000022774076114039555,
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|
|
|
.00000000000010849569622967912,
|
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|
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-.00000000000023073801945705758,
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|
|
.00000000000015761203773969435,
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|
|
.00000000000003345710269544082,
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|
|
|
-.00000000000041525158063436123,
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|
|
|
.00000000000032655698896907146,
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|
|
-.00000000000044704265010452446,
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|
|
|
.00000000000034527647952039772,
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-.00000000000007048962392109746,
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.00000000000011776978751369214,
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