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Diffstat (limited to 'sysdeps/generic/log.c')
| -rw-r--r-- | sysdeps/generic/log.c | 486 |
1 files changed, 0 insertions, 486 deletions
diff --git a/sysdeps/generic/log.c b/sysdeps/generic/log.c deleted file mode 100644 index ae186722f8..0000000000 --- a/sysdeps/generic/log.c +++ /dev/null @@ -1,486 +0,0 @@ -/* - * Copyright (c) 1992, 1993 - * The Regents of the University of California. All rights reserved. - * - * Redistribution and use in source and binary forms, with or without - * modification, are permitted provided that the following conditions - * are met: - * 1. Redistributions of source code must retain the above copyright - * notice, this list of conditions and the following disclaimer. - * 2. Redistributions in binary form must reproduce the above copyright - * notice, this list of conditions and the following disclaimer in the - * documentation and/or other materials provided with the distribution. - * 3. All advertising materials mentioning features or use of this software - * must display the following acknowledgement: - * This product includes software developed by the University of - * California, Berkeley and its contributors. - * 4. Neither the name of the University nor the names of its contributors - * may be used to endorse or promote products derived from this software - * without specific prior written permission. - * - * THIS SOFTWARE IS PROVIDED BY THE REGENTS AND CONTRIBUTORS ``AS IS'' AND - * ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE - * IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE - * ARE DISCLAIMED. IN NO EVENT SHALL THE REGENTS OR CONTRIBUTORS BE LIABLE - * FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL - * DAMAGES (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS - * OR SERVICES; LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION) - * HOWEVER CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT - * LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY - * OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF - * SUCH DAMAGE. - */ - -#ifndef lint -static char sccsid[] = "@(#)log.c 8.2 (Berkeley) 11/30/93"; -#endif /* not lint */ - -#include <math.h> -#include <errno.h> - -#include "mathimpl.h" - -/* Table-driven natural logarithm. - * - * This code was derived, with minor modifications, from: - * Peter Tang, "Table-Driven Implementation of the - * Logarithm in IEEE Floating-Point arithmetic." ACM Trans. - * Math Software, vol 16. no 4, pp 378-400, Dec 1990). - * - * Calculates log(2^m*F*(1+f/F)), |f/j| <= 1/256, - * where F = j/128 for j an integer in [0, 128]. - * - * log(2^m) = log2_hi*m + log2_tail*m - * since m is an integer, the dominant term is exact. - * m has at most 10 digits (for subnormal numbers), - * and log2_hi has 11 trailing zero bits. - * - * log(F) = logF_hi[j] + logF_lo[j] is in tabular form in log_table.h - * logF_hi[] + 512 is exact. - * - * log(1+f/F) = 2*f/(2*F + f) + 1/12 * (2*f/(2*F + f))**3 + ... - * the leading term is calculated to extra precision in two - * parts, the larger of which adds exactly to the dominant - * m and F terms. - * There are two cases: - * 1. when m, j are non-zero (m | j), use absolute - * precision for the leading term. - * 2. when m = j = 0, |1-x| < 1/256, and log(x) ~= (x-1). - * In this case, use a relative precision of 24 bits. - * (This is done differently in the original paper) - * - * Special cases: - * 0 return signalling -Inf - * neg return signalling NaN - * +Inf return +Inf -*/ - -#if defined(vax) || defined(tahoe) -#define _IEEE 0 -#define TRUNC(x) x = (double) (float) (x) -#else -#define _IEEE 1 -#define endian (((*(int *) &one)) ? 1 : 0) -#define TRUNC(x) *(((int *) &x) + endian) &= 0xf8000000 -#define infnan(x) 0.0 -#endif - -#define N 128 - -/* Table of log(Fj) = logF_head[j] + logF_tail[j], for Fj = 1+j/128. - * Used for generation of extend precision logarithms. - * The constant 35184372088832 is 2^45, so the divide is exact. - * It ensures correct reading of logF_head, even for inaccurate - * decimal-to-binary conversion routines. (Everybody gets the - * right answer for integers less than 2^53.) - * Values for log(F) were generated using error < 10^-57 absolute - * with the bc -l package. -*/ -static double A1 = .08333333333333178827; -static double A2 = .01250000000377174923; -static double A3 = .002232139987919447809; -static double A4 = .0004348877777076145742; - -static double logF_head[N+1] = { - 0., - .007782140442060381246, - .015504186535963526694, - .023167059281547608406, - .030771658666765233647, - .038318864302141264488, - .045809536031242714670, - .053244514518837604555, - .060624621816486978786, - .067950661908525944454, - .075223421237524235039, - .082443669210988446138, - .089612158689760690322, - .096729626458454731618, - .103796793681567578460, - .110814366340264314203, - .117783035656430001836, - .124703478501032805070, - .131576357788617315236, - .138402322859292326029, - .145182009844575077295, - .151916042025732167530, - .158605030176659056451, - .165249572895390883786, - .171850256926518341060, - .178407657472689606947, - .184922338493834104156, - .191394852999565046047, - .197825743329758552135, - .204215541428766300668, - .210564769107350002741, - .216873938300523150246, - .223143551314024080056, - .229374101064877322642, - .235566071312860003672, - .241719936886966024758, - .247836163904594286577, - .253915209980732470285, - .259957524436686071567, - .265963548496984003577, - .271933715484010463114, - .277868451003087102435, - .283768173130738432519, - .289633292582948342896, - .295464212893421063199, - .301261330578199704177, - .307025035294827830512, - .312755710004239517729, - .318453731118097493890, - .324119468654316733591, - .329753286372579168528, - .335355541920762334484, - .340926586970454081892, - .346466767346100823488, - .351976423156884266063, - .357455888922231679316, - .362905493689140712376, - .368325561158599157352, - .373716409793814818840, - .379078352934811846353, - .384411698910298582632, - .389716751140440464951, - .394993808240542421117, - .400243164127459749579, - .405465108107819105498, - .410659924985338875558, - .415827895143593195825, - .420969294644237379543, - .426084395310681429691, - .431173464818130014464, - .436236766774527495726, - .441274560805140936281, - .446287102628048160113, - .451274644139630254358, - .456237433481874177232, - .461175715122408291790, - .466089729924533457960, - .470979715219073113985, - .475845904869856894947, - .480688529345570714212, - .485507815781602403149, - .490303988045525329653, - .495077266798034543171, - .499827869556611403822, - .504556010751912253908, - .509261901790523552335, - .513945751101346104405, - .518607764208354637958, - .523248143765158602036, - .527867089620485785417, - .532464798869114019908, - .537041465897345915436, - .541597282432121573947, - .546132437597407260909, - .550647117952394182793, - .555141507540611200965, - .559615787935399566777, - .564070138285387656651, - .568504735352689749561, - .572919753562018740922, - .577315365035246941260, - .581691739635061821900, - .586049045003164792433, - .590387446602107957005, - .594707107746216934174, - .599008189645246602594, - .603290851438941899687, - .607555250224322662688, - .611801541106615331955, - .616029877215623855590, - .620240409751204424537, - .624433288012369303032, - .628608659422752680256, - .632766669570628437213, - .636907462236194987781, - .641031179420679109171, - .645137961373620782978, - .649227946625615004450, - .653301272011958644725, - .657358072709030238911, - .661398482245203922502, - .665422632544505177065, - .669430653942981734871, - .673422675212350441142, - .677398823590920073911, - .681359224807238206267, - .685304003098281100392, - .689233281238557538017, - .693147180560117703862 -}; - -static double logF_tail[N+1] = { - 0., - -.00000000000000543229938420049, - .00000000000000172745674997061, - -.00000000000001323017818229233, - -.00000000000001154527628289872, - -.00000000000000466529469958300, - .00000000000005148849572685810, - -.00000000000002532168943117445, - -.00000000000005213620639136504, - -.00000000000001819506003016881, - .00000000000006329065958724544, - .00000000000008614512936087814, - -.00000000000007355770219435028, - .00000000000009638067658552277, - .00000000000007598636597194141, - .00000000000002579999128306990, - -.00000000000004654729747598444, - -.00000000000007556920687451336, - .00000000000010195735223708472, - -.00000000000017319034406422306, - -.00000000000007718001336828098, - .00000000000010980754099855238, - -.00000000000002047235780046195, - -.00000000000008372091099235912, - .00000000000014088127937111135, - .00000000000012869017157588257, - .00000000000017788850778198106, - .00000000000006440856150696891, - .00000000000016132822667240822, - -.00000000000007540916511956188, - -.00000000000000036507188831790, - .00000000000009120937249914984, - .00000000000018567570959796010, - -.00000000000003149265065191483, - -.00000000000009309459495196889, - .00000000000017914338601329117, - -.00000000000001302979717330866, - .00000000000023097385217586939, - .00000000000023999540484211737, - .00000000000015393776174455408, - -.00000000000036870428315837678, - .00000000000036920375082080089, - -.00000000000009383417223663699, - .00000000000009433398189512690, - .00000000000041481318704258568, - -.00000000000003792316480209314, - .00000000000008403156304792424, - -.00000000000034262934348285429, - .00000000000043712191957429145, - -.00000000000010475750058776541, - -.00000000000011118671389559323, - .00000000000037549577257259853, - .00000000000013912841212197565, - .00000000000010775743037572640, - .00000000000029391859187648000, - -.00000000000042790509060060774, - .00000000000022774076114039555, - .00000000000010849569622967912, - -.00000000000023073801945705758, - .00000000000015761203773969435, - .00000000000003345710269544082, - -.00000000000041525158063436123, - .00000000000032655698896907146, - -.00000000000044704265010452446, - .00000000000034527647952039772, - -.00000000000007048962392109746, - .00000000000011776978751369214, - -.00000000000010774341461609578, - .00000000000021863343293215910, - .00000000000024132639491333131, - .00000000000039057462209830700, - -.00000000000026570679203560751, - .00000000000037135141919592021, - -.00000000000017166921336082431, - -.00000000000028658285157914353, - -.00000000000023812542263446809, - .00000000000006576659768580062, - -.00000000000028210143846181267, - .00000000000010701931762114254, - .00000000000018119346366441110, - .00000000000009840465278232627, - -.00000000000033149150282752542, - -.00000000000018302857356041668, - -.00000000000016207400156744949, - .00000000000048303314949553201, - -.00000000000071560553172382115, - .00000000000088821239518571855, - -.00000000000030900580513238244, - -.00000000000061076551972851496, - .00000000000035659969663347830, - .00000000000035782396591276383, - -.00000000000046226087001544578, - .00000000000062279762917225156, - .00000000000072838947272065741, - .00000000000026809646615211673, - -.00000000000010960825046059278, - .00000000000002311949383800537, - -.00000000000058469058005299247, - -.00000000000002103748251144494, - -.00000000000023323182945587408, - -.00000000000042333694288141916, - -.00000000000043933937969737844, - .00000000000041341647073835565, - .00000000000006841763641591466, - .00000000000047585534004430641, - .00000000000083679678674757695, - -.00000000000085763734646658640, - .00000000000021913281229340092, - -.00000000000062242842536431148, - -.00000000000010983594325438430, - .00000000000065310431377633651, - -.00000000000047580199021710769, - -.00000000000037854251265457040, - .00000000000040939233218678664, - .00000000000087424383914858291, - .00000000000025218188456842882, - -.00000000000003608131360422557, - -.00000000000050518555924280902, - .00000000000078699403323355317, - -.00000000000067020876961949060, - .00000000000016108575753932458, - .00000000000058527188436251509, - -.00000000000035246757297904791, - -.00000000000018372084495629058, - .00000000000088606689813494916, - .00000000000066486268071468700, - .00000000000063831615170646519, - .00000000000025144230728376072, - -.00000000000017239444525614834 -}; - -double -#ifdef _ANSI_SOURCE -log(double x) -#else -log(x) double x; -#endif -{ - int m, j; - double F, f, g, q, u, u2, v, zero = 0.0, one = 1.0; - volatile double u1; - - /* Catch special cases */ - if (x <= 0) - if (_IEEE && x == zero) /* log(0) = -Inf */ - return (-one/zero); - else if (_IEEE) /* log(neg) = NaN */ - return (zero/zero); - else if (x == zero) /* NOT REACHED IF _IEEE */ - return (infnan(-ERANGE)); - else - return (infnan(EDOM)); - else if (!finite(x)) - if (_IEEE) /* x = NaN, Inf */ - return (x+x); - else - return (infnan(ERANGE)); - - /* Argument reduction: 1 <= g < 2; x/2^m = g; */ - /* y = F*(1 + f/F) for |f| <= 2^-8 */ - - m = logb(x); - g = ldexp(x, -m); - if (_IEEE && m == -1022) { - j = logb(g), m += j; - g = ldexp(g, -j); - } - j = N*(g-1) + .5; - F = (1.0/N) * j + 1; /* F*128 is an integer in [128, 512] */ - f = g - F; - - /* Approximate expansion for log(1+f/F) ~= u + q */ - g = 1/(2*F+f); - u = 2*f*g; - v = u*u; - q = u*v*(A1 + v*(A2 + v*(A3 + v*A4))); - - /* case 1: u1 = u rounded to 2^-43 absolute. Since u < 2^-8, - * u1 has at most 35 bits, and F*u1 is exact, as F has < 8 bits. - * It also adds exactly to |m*log2_hi + log_F_head[j] | < 750 - */ - if (m | j) - u1 = u + 513, u1 -= 513; - - /* case 2: |1-x| < 1/256. The m- and j- dependent terms are zero; - * u1 = u to 24 bits. - */ - else - u1 = u, TRUNC(u1); - u2 = (2.0*(f - F*u1) - u1*f) * g; - /* u1 + u2 = 2f/(2F+f) to extra precision. */ - - /* log(x) = log(2^m*F*(1+f/F)) = */ - /* (m*log2_hi+logF_head[j]+u1) + (m*log2_lo+logF_tail[j]+q); */ - /* (exact) + (tiny) */ - - u1 += m*logF_head[N] + logF_head[j]; /* exact */ - u2 = (u2 + logF_tail[j]) + q; /* tiny */ - u2 += logF_tail[N]*m; - return (u1 + u2); -} - -/* - * Extra precision variant, returning struct {double a, b;}; - * log(x) = a+b to 63 bits, with a is rounded to 26 bits. - */ -struct Double -#ifdef _ANSI_SOURCE -__log__D(double x) -#else -__log__D(x) double x; -#endif -{ - int m, j; - double F, f, g, q, u, v, u2, one = 1.0; - volatile double u1; - struct Double r; - - /* Argument reduction: 1 <= g < 2; x/2^m = g; */ - /* y = F*(1 + f/F) for |f| <= 2^-8 */ - - m = logb(x); - g = ldexp(x, -m); - if (_IEEE && m == -1022) { - j = logb(g), m += j; - g = ldexp(g, -j); - } - j = N*(g-1) + .5; - F = (1.0/N) * j + 1; - f = g - F; - - g = 1/(2*F+f); - u = 2*f*g; - v = u*u; - q = u*v*(A1 + v*(A2 + v*(A3 + v*A4))); - if (m | j) - u1 = u + 513, u1 -= 513; - else - u1 = u, TRUNC(u1); - u2 = (2.0*(f - F*u1) - u1*f) * g; - - u1 += m*logF_head[N] + logF_head[j]; - - u2 += logF_tail[j]; u2 += q; - u2 += logF_tail[N]*m; - r.a = u1 + u2; /* Only difference is here */ - TRUNC(r.a); - r.b = (u1 - r.a) + u2; - return (r); -} |