kc3-lang/gnulib/lib/logl.c

• Show log

  Commit

• Hash : 57fdfd3f
  Author :
  Date : 2007-10-07T19:14:58
  

  Change copyright notice from GPLv2+ to GPLv3+.
  

Download

• lib/logl.c

• /* Copyright 2001 by Stephen L. Moshier <moshier@na-net.ornl.gov>
  
     This program is free software: you can redistribute it and/or modify
     it under the terms of the GNU General Public License as published by
     the Free Software Foundation; either version 3 of the License, or
     (at your option) any later version.
  
     This program is distributed in the hope that it will be useful,
     but WITHOUT ANY WARRANTY; without even the implied warranty of
     MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the
     GNU General Public License for more details.
  
     You should have received a copy of the GNU General Public License
     along with this program.  If not, see <http://www.gnu.org/licenses/>.  */
  
  #include <config.h>
  
  /* Specification.  */
  #include <math.h>
  
  /*							logll.c
   *
   * Natural logarithm for 128-bit long double precision.
   *
   *
   *
   * SYNOPSIS:
   *
   * long double x, y, logl();
   *
   * y = logl( x );
   *
   *
   *
   * DESCRIPTION:
   *
   * Returns the base e (2.718...) logarithm of x.
   *
   * The argument is separated into its exponent and fractional
   * parts.  Use of a lookup table increases the speed of the routine.
   * The program uses logarithms tabulated at intervals of 1/128 to
   * cover the domain from approximately 0.7 to 1.4.
   *
   * On the interval [-1/128, +1/128] the logarithm of 1+x is approximated by
   *     log(1+x) = x - 0.5 x^2 + x^3 P(x) .
   *
   *
   *
   * ACCURACY:
   *
   *                      Relative error:
   * arithmetic   domain     # trials      peak         rms
   *    IEEE   0.875, 1.125   100000      1.2e-34    4.1e-35
   *    IEEE   0.125, 8       100000      1.2e-34    4.1e-35
   *
   *
   * WARNING:
   *
   * This program uses integer operations on bit fields of floating-point
   * numbers.  It does not work with data structures other than the
   * structure assumed.
   *
   */
  
  #include "isnanl.h"
  
  /* log(1+x) = x - .5 x^2 + x^3 l(x)
     -.0078125 <= x <= +.0078125
     peak relative error 1.2e-37 */
  static const long double
  l3 =   3.333333333333333333333333333333336096926E-1L,
  l4 =  -2.499999999999999999999999999486853077002E-1L,
  l5 =   1.999999999999999999999999998515277861905E-1L,
  l6 =  -1.666666666666666666666798448356171665678E-1L,
  l7 =   1.428571428571428571428808945895490721564E-1L,
  l8 =  -1.249999999999999987884655626377588149000E-1L,
  l9 =   1.111111111111111093947834982832456459186E-1L,
  l10 = -1.000000000000532974938900317952530453248E-1L,
  l11 =  9.090909090915566247008015301349979892689E-2L,
  l12 = -8.333333211818065121250921925397567745734E-2L,
  l13 =  7.692307559897661630807048686258659316091E-2L,
  l14 = -7.144242754190814657241902218399056829264E-2L,
  l15 =  6.668057591071739754844678883223432347481E-2L;
  
  /* Lookup table of ln(t) - (t-1)
      t = 0.5 + (k+26)/128)
      k = 0, ..., 91   */
  static const long double logtbl[92] = {
  -5.5345593589352099112142921677820359632418E-2L,
  -5.2108257402767124761784665198737642086148E-2L,
  -4.8991686870576856279407775480686721935120E-2L,
  -4.5993270766361228596215288742353061431071E-2L,
  -4.3110481649613269682442058976885699556950E-2L,
  -4.0340872319076331310838085093194799765520E-2L,
  -3.7682072451780927439219005993827431503510E-2L,
  -3.5131785416234343803903228503274262719586E-2L,
  -3.2687785249045246292687241862699949178831E-2L,
  -3.0347913785027239068190798397055267411813E-2L,
  -2.8110077931525797884641940838507561326298E-2L,
  -2.5972247078357715036426583294246819637618E-2L,
  -2.3932450635346084858612873953407168217307E-2L,
  -2.1988775689981395152022535153795155900240E-2L,
  -2.0139364778244501615441044267387667496733E-2L,
  -1.8382413762093794819267536615342902718324E-2L,
  -1.6716169807550022358923589720001638093023E-2L,
  -1.5138929457710992616226033183958974965355E-2L,
  -1.3649036795397472900424896523305726435029E-2L,
  -1.2244881690473465543308397998034325468152E-2L,
  -1.0924898127200937840689817557742469105693E-2L,
  -9.6875626072830301572839422532631079809328E-3L,
  -8.5313926245226231463436209313499745894157E-3L,
  -7.4549452072765973384933565912143044991706E-3L,
  -6.4568155251217050991200599386801665681310E-3L,
  -5.5356355563671005131126851708522185605193E-3L,
  -4.6900728132525199028885749289712348829878E-3L,
  -3.9188291218610470766469347968659624282519E-3L,
  -3.2206394539524058873423550293617843896540E-3L,
  -2.5942708080877805657374888909297113032132E-3L,
  -2.0385211375711716729239156839929281289086E-3L,
  -1.5522183228760777967376942769773768850872E-3L,
  -1.1342191863606077520036253234446621373191E-3L,
  -7.8340854719967065861624024730268350459991E-4L,
  -4.9869831458030115699628274852562992756174E-4L,
  -2.7902661731604211834685052867305795169688E-4L,
  -1.2335696813916860754951146082826952093496E-4L,
  -3.0677461025892873184042490943581654591817E-5L,
  #define ZERO logtbl[38]
   0.0000000000000000000000000000000000000000E0L,
  -3.0359557945051052537099938863236321874198E-5L,
  -1.2081346403474584914595395755316412213151E-4L,
  -2.7044071846562177120083903771008342059094E-4L,
  -4.7834133324631162897179240322783590830326E-4L,
  -7.4363569786340080624467487620270965403695E-4L,
  -1.0654639687057968333207323853366578860679E-3L,
  -1.4429854811877171341298062134712230604279E-3L,
  -1.8753781835651574193938679595797367137975E-3L,
  -2.3618380914922506054347222273705859653658E-3L,
  -2.9015787624124743013946600163375853631299E-3L,
  -3.4938307889254087318399313316921940859043E-3L,
  -4.1378413103128673800485306215154712148146E-3L,
  -4.8328735414488877044289435125365629849599E-3L,
  -5.5782063183564351739381962360253116934243E-3L,
  -6.3731336597098858051938306767880719015261E-3L,
  -7.2169643436165454612058905294782949315193E-3L,
  -8.1090214990427641365934846191367315083867E-3L,
  -9.0486422112807274112838713105168375482480E-3L,
  -1.0035177140880864314674126398350812606841E-2L,
  -1.1067990155502102718064936259435676477423E-2L,
  -1.2146457974158024928196575103115488672416E-2L,
  -1.3269969823361415906628825374158424754308E-2L,
  -1.4437927104692837124388550722759686270765E-2L,
  -1.5649743073340777659901053944852735064621E-2L,
  -1.6904842527181702880599758489058031645317E-2L,
  -1.8202661505988007336096407340750378994209E-2L,
  -1.9542647000370545390701192438691126552961E-2L,
  -2.0924256670080119637427928803038530924742E-2L,
  -2.2346958571309108496179613803760727786257E-2L,
  -2.3810230892650362330447187267648486279460E-2L,
  -2.5313561699385640380910474255652501521033E-2L,
  -2.6856448685790244233704909690165496625399E-2L,
  -2.8438398935154170008519274953860128449036E-2L,
  -3.0058928687233090922411781058956589863039E-2L,
  -3.1717563112854831855692484086486099896614E-2L,
  -3.3413836095418743219397234253475252001090E-2L,
  -3.5147290019036555862676702093393332533702E-2L,
  -3.6917475563073933027920505457688955423688E-2L,
  -3.8723951502862058660874073462456610731178E-2L,
  -4.0566284516358241168330505467000838017425E-2L,
  -4.2444048996543693813649967076598766917965E-2L,
  -4.4356826869355401653098777649745233339196E-2L,
  -4.6304207416957323121106944474331029996141E-2L,
  -4.8285787106164123613318093945035804818364E-2L,
  -5.0301169421838218987124461766244507342648E-2L,
  -5.2349964705088137924875459464622098310997E-2L,
  -5.4431789996103111613753440311680967840214E-2L,
  -5.6546268881465384189752786409400404404794E-2L,
  -5.8693031345788023909329239565012647817664E-2L,
  -6.0871713627532018185577188079210189048340E-2L,
  -6.3081958078862169742820420185833800925568E-2L,
  -6.5323413029406789694910800219643791556918E-2L,
  -6.7595732653791419081537811574227049288168E-2L
  };
  
  /* ln(2) = ln2a + ln2b with extended precision. */
  static const long double
    ln2a = 6.93145751953125e-1L,
    ln2b = 1.4286068203094172321214581765680755001344E-6L;
  
  long double
  logl(long double x)
  {
    long double z, y, w;
    long double u, t;
    unsigned int m;
    int k, e;
  
    /* Check for IEEE special cases.  */
  
    /* log(NaN) = NaN. */
    if (isnanl (x))
      {
        return x;
      }
    /* log(0) = -infinity. */
    if (x == 0.0L)
      {
        return -0.5L / ZERO;
      }
    /* log ( x < 0 ) = NaN */
    if (x < 0.0L)
      {
        return (x - x) / ZERO;
      }
    /* log (infinity) */
    if (x + x == x)
      {
        return x + x;
      }
  
    /* Extract exponent and reduce domain to 0.703125 <= u < 1.40625  */
    x = frexpl(x, &e);
    if (x < 0.703125L)
      {
        x += x;
        e--;
      }
  
    /* On this interval the table is not used due to cancellation error.  */
    if ((x <= 1.0078125L) && (x >= 0.9921875L))
      {
        z = x - 1.0L;
        k = 64;
        t = 1.0L;
      }
    else
      {
        k = floorl ((x - 0.5L) * 128.0L);
        t = 0.5L + k / 128.0L;
        z = (x - t) / t;
      }
  
    /* Series expansion of log(1+z).  */
    w = z * z;
    y = ((((((((((((l15 * z
  		  + l14) * z
  		 + l13) * z
  		+ l12) * z
  	       + l11) * z
  	      + l10) * z
  	     + l9) * z
  	    + l8) * z
  	   + l7) * z
  	  + l6) * z
  	 + l5) * z
  	+ l4) * z
         + l3) * z * w;
    y -= 0.5 * w;
    y += e * ln2b;  /* Base 2 exponent offset times ln(2).  */
    y += z;
    y += logtbl[k-26]; /* log(t) - (t-1) */
    y += (t - 1.0L);
    y += e * ln2a;
    return y;
  }
  

Download