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annotate libquadmath/math/log1pq.c @ 68:561a7518be6b

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update gcc-4.6
author Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
date Sun, 21 Aug 2011 07:07:55 +0900
parents
children 04ced10e8804
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rev   line source
68
561a7518be6b update gcc-4.6
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
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1 /* log1pl.c
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Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
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2 *
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Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
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3 * Relative error logarithm
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Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
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4 * Natural logarithm of 1+x, 128-bit long double precision
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Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
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5 *
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Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
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6 *
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Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
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7 *
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Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
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8 * SYNOPSIS:
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Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
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9 *
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Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
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10 * long double x, y, log1pl();
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Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
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11 *
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Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
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12 * y = log1pl( x );
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Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
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13 *
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Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
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14 *
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Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
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15 *
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Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
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16 * DESCRIPTION:
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Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
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17 *
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Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
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18 * Returns the base e (2.718...) logarithm of 1+x.
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Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
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19 *
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Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
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20 * The argument 1+x is separated into its exponent and fractional
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Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
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21 * parts. If the exponent is between -1 and +1, the logarithm
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Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
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22 * of the fraction is approximated by
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Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
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23 *
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Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
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24 * log(1+x) = x - 0.5 x^2 + x^3 P(x)/Q(x).
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Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
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25 *
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Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
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26 * Otherwise, setting z = 2(w-1)/(w+1),
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Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
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27 *
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Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
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28 * log(w) = z + z^3 P(z)/Q(z).
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Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
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29 *
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Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
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30 *
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Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
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31 *
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Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
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32 * ACCURACY:
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Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
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33 *
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Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
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34 * Relative error:
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Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
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35 * arithmetic domain # trials peak rms
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Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
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36 * IEEE -1, 8 100000 1.9e-34 4.3e-35
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Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
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37 */
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Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
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38
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Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
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39 /* Copyright 2001 by Stephen L. Moshier
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Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
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40
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Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
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41 This library is free software; you can redistribute it and/or
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Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
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42 modify it under the terms of the GNU Lesser General Public
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Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
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43 License as published by the Free Software Foundation; either
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Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
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44 version 2.1 of the License, or (at your option) any later version.
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Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
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45
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Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
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46 This library is distributed in the hope that it will be useful,
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Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
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47 but WITHOUT ANY WARRANTY; without even the implied warranty of
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Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
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48 MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU
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Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
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49 Lesser General Public License for more details.
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Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
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50
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Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
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51 You should have received a copy of the GNU Lesser General Public
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Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
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52 License along with this library; if not, write to the Free Software
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Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
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53 Foundation, Inc., 59 Temple Place, Suite 330, Boston, MA 02111-1307 USA */
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Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
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54
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Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
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55
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Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
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56 #include "quadmath-imp.h"
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Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
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57
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Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
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58 /* Coefficients for log(1+x) = x - x^2 / 2 + x^3 P(x)/Q(x)
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Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
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59 * 1/sqrt(2) <= 1+x < sqrt(2)
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Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
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60 * Theoretical peak relative error = 5.3e-37,
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Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
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61 * relative peak error spread = 2.3e-14
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Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
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62 */
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Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
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63 static const __float128
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Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
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64 P12 = 1.538612243596254322971797716843006400388E-6Q,
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Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
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65 P11 = 4.998469661968096229986658302195402690910E-1Q,
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Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
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66 P10 = 2.321125933898420063925789532045674660756E1Q,
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Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
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67 P9 = 4.114517881637811823002128927449878962058E2Q,
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Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
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68 P8 = 3.824952356185897735160588078446136783779E3Q,
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Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
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69 P7 = 2.128857716871515081352991964243375186031E4Q,
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Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
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70 P6 = 7.594356839258970405033155585486712125861E4Q,
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Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
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71 P5 = 1.797628303815655343403735250238293741397E5Q,
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Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
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72 P4 = 2.854829159639697837788887080758954924001E5Q,
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Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
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73 P3 = 3.007007295140399532324943111654767187848E5Q,
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Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
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74 P2 = 2.014652742082537582487669938141683759923E5Q,
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Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
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75 P1 = 7.771154681358524243729929227226708890930E4Q,
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Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
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76 P0 = 1.313572404063446165910279910527789794488E4Q,
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Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
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77 /* Q12 = 1.000000000000000000000000000000000000000E0Q, */
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Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
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78 Q11 = 4.839208193348159620282142911143429644326E1Q,
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Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
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79 Q10 = 9.104928120962988414618126155557301584078E2Q,
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Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
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80 Q9 = 9.147150349299596453976674231612674085381E3Q,
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Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
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81 Q8 = 5.605842085972455027590989944010492125825E4Q,
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Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
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82 Q7 = 2.248234257620569139969141618556349415120E5Q,
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Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
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83 Q6 = 6.132189329546557743179177159925690841200E5Q,
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Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
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84 Q5 = 1.158019977462989115839826904108208787040E6Q,
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Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
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85 Q4 = 1.514882452993549494932585972882995548426E6Q,
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Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
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86 Q3 = 1.347518538384329112529391120390701166528E6Q,
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Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
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87 Q2 = 7.777690340007566932935753241556479363645E5Q,
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Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
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88 Q1 = 2.626900195321832660448791748036714883242E5Q,
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Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
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89 Q0 = 3.940717212190338497730839731583397586124E4Q;
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Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
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90
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Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
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91 /* Coefficients for log(x) = z + z^3 P(z^2)/Q(z^2),
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Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
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92 * where z = 2(x-1)/(x+1)
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Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
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93 * 1/sqrt(2) <= x < sqrt(2)
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Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
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94 * Theoretical peak relative error = 1.1e-35,
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Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
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95 * relative peak error spread 1.1e-9
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Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
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96 */
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Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
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97 static const __float128
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Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
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98 R5 = -8.828896441624934385266096344596648080902E-1Q,
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Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
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99 R4 = 8.057002716646055371965756206836056074715E1Q,
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Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
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100 R3 = -2.024301798136027039250415126250455056397E3Q,
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Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
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101 R2 = 2.048819892795278657810231591630928516206E4Q,
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Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
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102 R1 = -8.977257995689735303686582344659576526998E4Q,
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Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
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103 R0 = 1.418134209872192732479751274970992665513E5Q,
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Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
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104 /* S6 = 1.000000000000000000000000000000000000000E0Q, */
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Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
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105 S5 = -1.186359407982897997337150403816839480438E2Q,
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Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
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106 S4 = 3.998526750980007367835804959888064681098E3Q,
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Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
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107 S3 = -5.748542087379434595104154610899551484314E4Q,
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Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
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108 S2 = 4.001557694070773974936904547424676279307E5Q,
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Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
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109 S1 = -1.332535117259762928288745111081235577029E6Q,
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Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
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110 S0 = 1.701761051846631278975701529965589676574E6Q;
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Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
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111
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Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
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112 /* C1 + C2 = ln 2 */
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Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
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113 static const __float128 C1 = 6.93145751953125E-1Q;
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Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
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114 static const __float128 C2 = 1.428606820309417232121458176568075500134E-6Q;
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Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
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115
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Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff changeset
116 static const __float128 sqrth = 0.7071067811865475244008443621048490392848Q;
561a7518be6b update gcc-4.6
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff changeset
117 static const __float128 zero = 0.0Q;
561a7518be6b update gcc-4.6
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff changeset
118
561a7518be6b update gcc-4.6
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff changeset
119
561a7518be6b update gcc-4.6
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff changeset
120 __float128
561a7518be6b update gcc-4.6
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff changeset
121 log1pq (__float128 xm1)
561a7518be6b update gcc-4.6
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff changeset
122 {
561a7518be6b update gcc-4.6
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff changeset
123 __float128 x, y, z, r, s;
561a7518be6b update gcc-4.6
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff changeset
124 ieee854_float128 u;
561a7518be6b update gcc-4.6
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff changeset
125 int32_t hx;
561a7518be6b update gcc-4.6
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff changeset
126 int e;
561a7518be6b update gcc-4.6
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff changeset
127
561a7518be6b update gcc-4.6
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff changeset
128 /* Test for NaN or infinity input. */
561a7518be6b update gcc-4.6
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff changeset
129 u.value = xm1;
561a7518be6b update gcc-4.6
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff changeset
130 hx = u.words32.w0;
561a7518be6b update gcc-4.6
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff changeset
131 if (hx >= 0x7fff0000)
561a7518be6b update gcc-4.6
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff changeset
132 return xm1;
561a7518be6b update gcc-4.6
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff changeset
133
561a7518be6b update gcc-4.6
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff changeset
134 /* log1p(+- 0) = +- 0. */
561a7518be6b update gcc-4.6
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff changeset
135 if (((hx & 0x7fffffff) == 0)
561a7518be6b update gcc-4.6
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff changeset
136 && (u.words32.w1 | u.words32.w2 | u.words32.w3) == 0)
561a7518be6b update gcc-4.6
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff changeset
137 return xm1;
561a7518be6b update gcc-4.6
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff changeset
138
561a7518be6b update gcc-4.6
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff changeset
139 x = xm1 + 1.0Q;
561a7518be6b update gcc-4.6
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff changeset
140
561a7518be6b update gcc-4.6
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff changeset
141 /* log1p(-1) = -inf */
561a7518be6b update gcc-4.6
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff changeset
142 if (x <= 0.0Q)
561a7518be6b update gcc-4.6
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff changeset
143 {
561a7518be6b update gcc-4.6
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff changeset
144 if (x == 0.0Q)
561a7518be6b update gcc-4.6
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff changeset
145 return (-1.0Q / (x - x));
561a7518be6b update gcc-4.6
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff changeset
146 else
561a7518be6b update gcc-4.6
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff changeset
147 return (zero / (x - x));
561a7518be6b update gcc-4.6
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff changeset
148 }
561a7518be6b update gcc-4.6
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff changeset
149
561a7518be6b update gcc-4.6
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff changeset
150 /* Separate mantissa from exponent. */
561a7518be6b update gcc-4.6
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff changeset
151
561a7518be6b update gcc-4.6
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff changeset
152 /* Use frexp used so that denormal numbers will be handled properly. */
561a7518be6b update gcc-4.6
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff changeset
153 x = frexpq (x, &e);
561a7518be6b update gcc-4.6
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff changeset
154
561a7518be6b update gcc-4.6
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff changeset
155 /* Logarithm using log(x) = z + z^3 P(z^2)/Q(z^2),
561a7518be6b update gcc-4.6
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff changeset
156 where z = 2(x-1)/x+1). */
561a7518be6b update gcc-4.6
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff changeset
157 if ((e > 2) || (e < -2))
561a7518be6b update gcc-4.6
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff changeset
158 {
561a7518be6b update gcc-4.6
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff changeset
159 if (x < sqrth)
561a7518be6b update gcc-4.6
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff changeset
160 { /* 2( 2x-1 )/( 2x+1 ) */
561a7518be6b update gcc-4.6
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff changeset
161 e -= 1;
561a7518be6b update gcc-4.6
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff changeset
162 z = x - 0.5Q;
561a7518be6b update gcc-4.6
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff changeset
163 y = 0.5Q * z + 0.5Q;
561a7518be6b update gcc-4.6
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff changeset
164 }
561a7518be6b update gcc-4.6
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff changeset
165 else
561a7518be6b update gcc-4.6
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff changeset
166 { /* 2 (x-1)/(x+1) */
561a7518be6b update gcc-4.6
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff changeset
167 z = x - 0.5Q;
561a7518be6b update gcc-4.6
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff changeset
168 z -= 0.5Q;
561a7518be6b update gcc-4.6
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff changeset
169 y = 0.5Q * x + 0.5Q;
561a7518be6b update gcc-4.6
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff changeset
170 }
561a7518be6b update gcc-4.6
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff changeset
171 x = z / y;
561a7518be6b update gcc-4.6
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff changeset
172 z = x * x;
561a7518be6b update gcc-4.6
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff changeset
173 r = ((((R5 * z
561a7518be6b update gcc-4.6
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff changeset
174 + R4) * z
561a7518be6b update gcc-4.6
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff changeset
175 + R3) * z
561a7518be6b update gcc-4.6
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff changeset
176 + R2) * z
561a7518be6b update gcc-4.6
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff changeset
177 + R1) * z
561a7518be6b update gcc-4.6
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff changeset
178 + R0;
561a7518be6b update gcc-4.6
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff changeset
179 s = (((((z
561a7518be6b update gcc-4.6
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff changeset
180 + S5) * z
561a7518be6b update gcc-4.6
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff changeset
181 + S4) * z
561a7518be6b update gcc-4.6
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff changeset
182 + S3) * z
561a7518be6b update gcc-4.6
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff changeset
183 + S2) * z
561a7518be6b update gcc-4.6
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff changeset
184 + S1) * z
561a7518be6b update gcc-4.6
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff changeset
185 + S0;
561a7518be6b update gcc-4.6
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff changeset
186 z = x * (z * r / s);
561a7518be6b update gcc-4.6
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff changeset
187 z = z + e * C2;
561a7518be6b update gcc-4.6
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff changeset
188 z = z + x;
561a7518be6b update gcc-4.6
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff changeset
189 z = z + e * C1;
561a7518be6b update gcc-4.6
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff changeset
190 return (z);
561a7518be6b update gcc-4.6
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff changeset
191 }
561a7518be6b update gcc-4.6
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff changeset
192
561a7518be6b update gcc-4.6
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff changeset
193
561a7518be6b update gcc-4.6
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff changeset
194 /* Logarithm using log(1+x) = x - .5x^2 + x^3 P(x)/Q(x). */
561a7518be6b update gcc-4.6
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff changeset
195
561a7518be6b update gcc-4.6
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff changeset
196 if (x < sqrth)
561a7518be6b update gcc-4.6
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff changeset
197 {
561a7518be6b update gcc-4.6
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff changeset
198 e -= 1;
561a7518be6b update gcc-4.6
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff changeset
199 if (e != 0)
561a7518be6b update gcc-4.6
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff changeset
200 x = 2.0Q * x - 1.0Q; /* 2x - 1 */
561a7518be6b update gcc-4.6
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff changeset
201 else
561a7518be6b update gcc-4.6
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff changeset
202 x = xm1;
561a7518be6b update gcc-4.6
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff changeset
203 }
561a7518be6b update gcc-4.6
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff changeset
204 else
561a7518be6b update gcc-4.6
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff changeset
205 {
561a7518be6b update gcc-4.6
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff changeset
206 if (e != 0)
561a7518be6b update gcc-4.6
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff changeset
207 x = x - 1.0Q;
561a7518be6b update gcc-4.6
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff changeset
208 else
561a7518be6b update gcc-4.6
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff changeset
209 x = xm1;
561a7518be6b update gcc-4.6
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff changeset
210 }
561a7518be6b update gcc-4.6
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff changeset
211 z = x * x;
561a7518be6b update gcc-4.6
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff changeset
212 r = (((((((((((P12 * x
561a7518be6b update gcc-4.6
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff changeset
213 + P11) * x
561a7518be6b update gcc-4.6
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff changeset
214 + P10) * x
561a7518be6b update gcc-4.6
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff changeset
215 + P9) * x
561a7518be6b update gcc-4.6
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff changeset
216 + P8) * x
561a7518be6b update gcc-4.6
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff changeset
217 + P7) * x
561a7518be6b update gcc-4.6
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff changeset
218 + P6) * x
561a7518be6b update gcc-4.6
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff changeset
219 + P5) * x
561a7518be6b update gcc-4.6
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff changeset
220 + P4) * x
561a7518be6b update gcc-4.6
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff changeset
221 + P3) * x
561a7518be6b update gcc-4.6
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff changeset
222 + P2) * x
561a7518be6b update gcc-4.6
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff changeset
223 + P1) * x
561a7518be6b update gcc-4.6
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff changeset
224 + P0;
561a7518be6b update gcc-4.6
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff changeset
225 s = (((((((((((x
561a7518be6b update gcc-4.6
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff changeset
226 + Q11) * x
561a7518be6b update gcc-4.6
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff changeset
227 + Q10) * x
561a7518be6b update gcc-4.6
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff changeset
228 + Q9) * x
561a7518be6b update gcc-4.6
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff changeset
229 + Q8) * x
561a7518be6b update gcc-4.6
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff changeset
230 + Q7) * x
561a7518be6b update gcc-4.6
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff changeset
231 + Q6) * x
561a7518be6b update gcc-4.6
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff changeset
232 + Q5) * x
561a7518be6b update gcc-4.6
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff changeset
233 + Q4) * x
561a7518be6b update gcc-4.6
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff changeset
234 + Q3) * x
561a7518be6b update gcc-4.6
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff changeset
235 + Q2) * x
561a7518be6b update gcc-4.6
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff changeset
236 + Q1) * x
561a7518be6b update gcc-4.6
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff changeset
237 + Q0;
561a7518be6b update gcc-4.6
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff changeset
238 y = x * (z * r / s);
561a7518be6b update gcc-4.6
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff changeset
239 y = y + e * C2;
561a7518be6b update gcc-4.6
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff changeset
240 z = y - 0.5Q * z;
561a7518be6b update gcc-4.6
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff changeset
241 z = z + x;
561a7518be6b update gcc-4.6
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff changeset
242 z = z + e * C1;
561a7518be6b update gcc-4.6
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff changeset
243 return (z);
561a7518be6b update gcc-4.6
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff changeset
244 }