455b2ccda3
. Disconnect b_exp.c and b_log.c from the build.
* lib/msun/bsdsrc/b_exp.c:
. Replace scalb() usage with C99's ldexp().
. Replace finite(x) usage with C99's isfinite().
. Whitespace changes towards style(9).
. Remove include of "mathimpl.h". It is no longer needed.
. Remove #if 0 ... #endif code, which has been present since svn r93211
(2002-03-26).
. New minimax polynomial coefficients.
. Add comments to explain origins of some constants.
. Use ansi-C prototype. Remove K&R prototype. Add static to prototype.
* lib/msun/bsdsrc/b_log.c:
. Remove include of "mathimpl.h". It is no longer needed.
. Fix comments to actually describe the code.
. Reduce minimax polynomial from degree 4 to degree 3.
This uses newly computed coefficients.
. Use ansi-C prototype. Remove K&R prototype. Add static to prototype.
. Remove volatile in declaration of u1.
. Alphabetize decalaration list.
. Whitespace changes towards style(9).
. In argument reduction of x to g and m, replace use of logb() and
ldexp() with a single call to frexp(). Add code to get 1 <= g < 2.
. Remove #if 0 ... #endif code, which has been present since svn r93211
(2002-03-26).
. The special case m == -1022, replace logb() with ilogb().
* lib/msun/bsdsrc/b_tgamma.c:
. Update comments. Fix comments where needed.
. Add float.h to get LDBL_MANT_DIG for weak reference of tgammal to tgamma.
. Remove include of "mathimpl.h". It is no longer needed.
. Use "math.h" instead of <math.h>.
. Add '#include math_private.h"
. Add struct Double from mathimpl.h and include b_log.c and b_exp.c.
. Remove forward declarations of neg_gam(), small_gam(), smaller_gam,
large_gam() and ratfun_gam() by re-arranging the code to move these
function above their first reference.
. New minimax coefficients for polynomial in large_gam().
. New splitting of a0 into a0hi nd a0lo, which include additional
bits of precision.
. Use ansi-C prototype. Remove K&R prototype.
. Replace the TRUNC() macro with a simple cast of a double entities
to float before assignment (functional changes).
. Replace sin(M_PI*z) with sinpi(z) and cos(M_PI*(0.5-z)) with cospi(0.5-z).
Submitted by: Steve Kargl
Differential Revision: https://reviews.freebsd.org/D33444
Reviewed by: pfg
405 lines
12 KiB
C
405 lines
12 KiB
C
/*-
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* SPDX-License-Identifier: BSD-3-Clause
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*
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* Copyright (c) 1992, 1993
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* The Regents of the University of California. 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. 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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/* @(#)log.c 8.2 (Berkeley) 11/30/93 */
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#include <sys/cdefs.h>
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__FBSDID("$FreeBSD$");
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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/F| <= 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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* The leading term is exact, because m is an integer,
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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 table below.
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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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*
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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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*
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* There are two cases:
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* 1. When m and 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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#define N 128
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/*
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* Coefficients in the polynomial approximation of log(1+f/F).
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* Domain of x is [0,1./256] with 2**(-64.187) precision.
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*/
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static const double
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A1 = 8.3333333333333329e-02, /* 0x3fb55555, 0x55555555 */
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A2 = 1.2499999999943598e-02, /* 0x3f899999, 0x99991a98 */
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A3 = 2.2321527525957776e-03; /* 0x3f624929, 0xe24e70be */
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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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static 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,
|
|
.178407657472689606947,
|
|
.184922338493834104156,
|
|
.191394852999565046047,
|
|
.197825743329758552135,
|
|
.204215541428766300668,
|
|
.210564769107350002741,
|
|
.216873938300523150246,
|
|
.223143551314024080056,
|
|
.229374101064877322642,
|
|
.235566071312860003672,
|
|
.241719936886966024758,
|
|
.247836163904594286577,
|
|
.253915209980732470285,
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|
.259957524436686071567,
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.265963548496984003577,
|
|
.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,
|
|
.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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.490303988045525329653,
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.495077266798034543171,
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.499827869556611403822,
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.504556010751912253908,
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.509261901790523552335,
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.513945751101346104405,
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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,
|
|
.577315365035246941260,
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.581691739635061821900,
|
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.586049045003164792433,
|
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.590387446602107957005,
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.594707107746216934174,
|
|
.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,
|
|
.628608659422752680256,
|
|
.632766669570628437213,
|
|
.636907462236194987781,
|
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.641031179420679109171,
|
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.645137961373620782978,
|
|
.649227946625615004450,
|
|
.653301272011958644725,
|
|
.657358072709030238911,
|
|
.661398482245203922502,
|
|
.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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static double logF_tail[N+1] = {
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0.,
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-.00000000000000543229938420049,
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.00000000000000172745674997061,
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-.00000000000001323017818229233,
|
|
-.00000000000001154527628289872,
|
|
-.00000000000000466529469958300,
|
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.00000000000005148849572685810,
|
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-.00000000000002532168943117445,
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-.00000000000005213620639136504,
|
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-.00000000000001819506003016881,
|
|
.00000000000006329065958724544,
|
|
.00000000000008614512936087814,
|
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-.00000000000007355770219435028,
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.00000000000009638067658552277,
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.00000000000007598636597194141,
|
|
.00000000000002579999128306990,
|
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-.00000000000004654729747598444,
|
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-.00000000000007556920687451336,
|
|
.00000000000010195735223708472,
|
|
-.00000000000017319034406422306,
|
|
-.00000000000007718001336828098,
|
|
.00000000000010980754099855238,
|
|
-.00000000000002047235780046195,
|
|
-.00000000000008372091099235912,
|
|
.00000000000014088127937111135,
|
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.00000000000012869017157588257,
|
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.00000000000017788850778198106,
|
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.00000000000006440856150696891,
|
|
.00000000000016132822667240822,
|
|
-.00000000000007540916511956188,
|
|
-.00000000000000036507188831790,
|
|
.00000000000009120937249914984,
|
|
.00000000000018567570959796010,
|
|
-.00000000000003149265065191483,
|
|
-.00000000000009309459495196889,
|
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.00000000000017914338601329117,
|
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-.00000000000001302979717330866,
|
|
.00000000000023097385217586939,
|
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.00000000000023999540484211737,
|
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.00000000000015393776174455408,
|
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-.00000000000036870428315837678,
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.00000000000036920375082080089,
|
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-.00000000000009383417223663699,
|
|
.00000000000009433398189512690,
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.00000000000041481318704258568,
|
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-.00000000000003792316480209314,
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|
.00000000000008403156304792424,
|
|
-.00000000000034262934348285429,
|
|
.00000000000043712191957429145,
|
|
-.00000000000010475750058776541,
|
|
-.00000000000011118671389559323,
|
|
.00000000000037549577257259853,
|
|
.00000000000013912841212197565,
|
|
.00000000000010775743037572640,
|
|
.00000000000029391859187648000,
|
|
-.00000000000042790509060060774,
|
|
.00000000000022774076114039555,
|
|
.00000000000010849569622967912,
|
|
-.00000000000023073801945705758,
|
|
.00000000000015761203773969435,
|
|
.00000000000003345710269544082,
|
|
-.00000000000041525158063436123,
|
|
.00000000000032655698896907146,
|
|
-.00000000000044704265010452446,
|
|
.00000000000034527647952039772,
|
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-.00000000000007048962392109746,
|
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.00000000000011776978751369214,
|
|
-.00000000000010774341461609578,
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|
.00000000000021863343293215910,
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|
.00000000000024132639491333131,
|
|
.00000000000039057462209830700,
|
|
-.00000000000026570679203560751,
|
|
.00000000000037135141919592021,
|
|
-.00000000000017166921336082431,
|
|
-.00000000000028658285157914353,
|
|
-.00000000000023812542263446809,
|
|
.00000000000006576659768580062,
|
|
-.00000000000028210143846181267,
|
|
.00000000000010701931762114254,
|
|
.00000000000018119346366441110,
|
|
.00000000000009840465278232627,
|
|
-.00000000000033149150282752542,
|
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-.00000000000018302857356041668,
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-.00000000000016207400156744949,
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.00000000000048303314949553201,
|
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-.00000000000071560553172382115,
|
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.00000000000088821239518571855,
|
|
-.00000000000030900580513238244,
|
|
-.00000000000061076551972851496,
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|
.00000000000035659969663347830,
|
|
.00000000000035782396591276383,
|
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-.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,
|
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-.00000000000035246757297904791,
|
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-.00000000000018372084495629058,
|
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.00000000000088606689813494916,
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.00000000000066486268071468700,
|
|
.00000000000063831615170646519,
|
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.00000000000025144230728376072,
|
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-.00000000000017239444525614834
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};
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/*
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* Extra precision variant, returning struct {double a, b;};
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* log(x) = a+b to 63 bits, with 'a' rounded to 24 bits.
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*/
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static struct Double
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__log__D(double x)
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{
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int m, j;
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double F, f, g, q, u, v, u1, u2;
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struct Double r;
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/*
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* Argument reduction: 1 <= g < 2; x/2^m = g;
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* y = F*(1 + f/F) for |f| <= 2^-8
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*/
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g = frexp(x, &m);
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g *= 2;
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m--;
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if (m == -1022) {
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j = ilogb(g);
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m += j;
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g = ldexp(g, -j);
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}
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j = N * (g - 1) + 0.5;
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F = (1. / N) * j + 1;
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f = g - F;
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g = 1 / (2 * F + f);
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u = 2 * f * g;
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v = u * u;
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q = u * v * (A1 + v * (A2 + v * A3));
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if (m | j) {
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u1 = u + 513;
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u1 -= 513;
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} else {
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u1 = (float)u;
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}
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u2 = (2 * (f - F * u1) - u1 * f) * g;
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u1 += m * logF_head[N] + logF_head[j];
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u2 += logF_tail[j];
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u2 += q;
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u2 += logF_tail[N] * m;
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r.a = (float)(u1 + u2); /* Only difference is here. */
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r.b = (u1 - r.a) + u2;
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return (r);
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}
|