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annotate libquadmath/math/log10q.c @ 158:494b0b89df80 default tip

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author Shinji KONO <kono@ie.u-ryukyu.ac.jp>
date Mon, 25 May 2020 18:13:55 +0900
parents 1830386684a0
children
Ignore whitespace changes - Everywhere: Within whitespace: At end of lines:
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1 /* log10l.c
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2 *
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3 * Common logarithm, 128-bit long double precision
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4 *
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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 * SYNOPSIS:
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8 *
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9 * long double x, y, log10l();
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10 *
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11 * y = log10l( x );
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12 *
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13 *
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14 *
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15 * DESCRIPTION:
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16 *
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17 * Returns the base 10 logarithm of x.
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18 *
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19 * The argument is separated into its exponent and fractional
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20 * parts. If the exponent is between -1 and +1, the logarithm
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21 * of the fraction is approximated by
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22 *
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23 * log(1+x) = x - 0.5 x^2 + x^3 P(x)/Q(x).
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24 *
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25 * Otherwise, setting z = 2(x-1)/x+1),
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26 *
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27 * log(x) = z + z^3 P(z)/Q(z).
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28 *
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29 *
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30 *
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31 * ACCURACY:
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32 *
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33 * Relative error:
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34 * arithmetic domain # trials peak rms
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35 * IEEE 0.5, 2.0 30000 2.3e-34 4.9e-35
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36 * IEEE exp(+-10000) 30000 1.0e-34 4.1e-35
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37 *
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38 * In the tests over the interval exp(+-10000), the logarithms
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39 * of the random arguments were uniformly distributed over
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40 * [-10000, +10000].
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41 *
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42 */
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43
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44 /*
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45 Cephes Math Library Release 2.2: January, 1991
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46 Copyright 1984, 1991 by Stephen L. Moshier
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47 Adapted for glibc November, 2001
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48
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Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
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49 This library is free software; you can redistribute it and/or
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50 modify it under the terms of the GNU Lesser General Public
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51 License as published by the Free Software Foundation; either
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52 version 2.1 of the License, or (at your option) any later version.
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53
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54 This library is distributed in the hope that it will be useful,
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55 but WITHOUT ANY WARRANTY; without even the implied warranty of
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56 MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU
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57 Lesser General Public License for more details.
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58
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59 You should have received a copy of the GNU Lesser General Public
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60 License along with this library; if not, see <http://www.gnu.org/licenses/>.
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61 */
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62
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63 #include "quadmath-imp.h"
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64
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65 /* Coefficients for ln(1+x) = x - x**2/2 + x**3 P(x)/Q(x)
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66 * 1/sqrt(2) <= x < sqrt(2)
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67 * Theoretical peak relative error = 5.3e-37,
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68 * relative peak error spread = 2.3e-14
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69 */
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70 static const __float128 P[13] =
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71 {
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72 1.313572404063446165910279910527789794488E4Q,
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73 7.771154681358524243729929227226708890930E4Q,
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74 2.014652742082537582487669938141683759923E5Q,
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75 3.007007295140399532324943111654767187848E5Q,
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76 2.854829159639697837788887080758954924001E5Q,
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77 1.797628303815655343403735250238293741397E5Q,
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78 7.594356839258970405033155585486712125861E4Q,
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79 2.128857716871515081352991964243375186031E4Q,
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80 3.824952356185897735160588078446136783779E3Q,
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81 4.114517881637811823002128927449878962058E2Q,
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82 2.321125933898420063925789532045674660756E1Q,
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83 4.998469661968096229986658302195402690910E-1Q,
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84 1.538612243596254322971797716843006400388E-6Q
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85 };
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86 static const __float128 Q[12] =
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87 {
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88 3.940717212190338497730839731583397586124E4Q,
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89 2.626900195321832660448791748036714883242E5Q,
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90 7.777690340007566932935753241556479363645E5Q,
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91 1.347518538384329112529391120390701166528E6Q,
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92 1.514882452993549494932585972882995548426E6Q,
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93 1.158019977462989115839826904108208787040E6Q,
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94 6.132189329546557743179177159925690841200E5Q,
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95 2.248234257620569139969141618556349415120E5Q,
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96 5.605842085972455027590989944010492125825E4Q,
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Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
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97 9.147150349299596453976674231612674085381E3Q,
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Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
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98 9.104928120962988414618126155557301584078E2Q,
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Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
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99 4.839208193348159620282142911143429644326E1Q
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100 /* 1.000000000000000000000000000000000000000E0L, */
68
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101 };
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102
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103 /* Coefficients for log(x) = z + z^3 P(z^2)/Q(z^2),
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104 * where z = 2(x-1)/(x+1)
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105 * 1/sqrt(2) <= x < sqrt(2)
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106 * Theoretical peak relative error = 1.1e-35,
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107 * relative peak error spread 1.1e-9
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108 */
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109 static const __float128 R[6] =
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110 {
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111 1.418134209872192732479751274970992665513E5Q,
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Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
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112 -8.977257995689735303686582344659576526998E4Q,
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113 2.048819892795278657810231591630928516206E4Q,
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114 -2.024301798136027039250415126250455056397E3Q,
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115 8.057002716646055371965756206836056074715E1Q,
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116 -8.828896441624934385266096344596648080902E-1Q
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117 };
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118 static const __float128 S[6] =
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119 {
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120 1.701761051846631278975701529965589676574E6Q,
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Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
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121 -1.332535117259762928288745111081235577029E6Q,
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parents:
diff changeset
122 4.001557694070773974936904547424676279307E5Q,
561a7518be6b update gcc-4.6
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff changeset
123 -5.748542087379434595104154610899551484314E4Q,
561a7518be6b update gcc-4.6
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff changeset
124 3.998526750980007367835804959888064681098E3Q,
561a7518be6b update gcc-4.6
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff changeset
125 -1.186359407982897997337150403816839480438E2Q
145
1830386684a0 gcc-9.2.0
anatofuz
parents: 111
diff changeset
126 /* 1.000000000000000000000000000000000000000E0L, */
68
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
561a7518be6b update gcc-4.6
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff changeset
129 static const __float128
561a7518be6b update gcc-4.6
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff changeset
130 /* log10(2) */
561a7518be6b update gcc-4.6
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff changeset
131 L102A = 0.3125Q,
561a7518be6b update gcc-4.6
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff changeset
132 L102B = -1.14700043360188047862611052755069732318101185E-2Q,
561a7518be6b update gcc-4.6
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff changeset
133 /* log10(e) */
561a7518be6b update gcc-4.6
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff changeset
134 L10EA = 0.5Q,
561a7518be6b update gcc-4.6
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff changeset
135 L10EB = -6.570551809674817234887108108339491770560299E-2Q,
561a7518be6b update gcc-4.6
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff changeset
136 /* sqrt(2)/2 */
561a7518be6b update gcc-4.6
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff changeset
137 SQRTH = 7.071067811865475244008443621048490392848359E-1Q;
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
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 /* Evaluate P[n] x^n + P[n-1] x^(n-1) + ... + P[0] */
561a7518be6b update gcc-4.6
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff changeset
142
561a7518be6b update gcc-4.6
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff changeset
143 static __float128
561a7518be6b update gcc-4.6
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff changeset
144 neval (__float128 x, const __float128 *p, int n)
561a7518be6b update gcc-4.6
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff changeset
145 {
561a7518be6b update gcc-4.6
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff changeset
146 __float128 y;
561a7518be6b update gcc-4.6
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff changeset
147
561a7518be6b update gcc-4.6
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff changeset
148 p += n;
561a7518be6b update gcc-4.6
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff changeset
149 y = *p--;
561a7518be6b update gcc-4.6
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff changeset
150 do
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 y = y * x + *p--;
561a7518be6b update gcc-4.6
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff changeset
153 }
561a7518be6b update gcc-4.6
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff changeset
154 while (--n > 0);
561a7518be6b update gcc-4.6
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff changeset
155 return y;
561a7518be6b update gcc-4.6
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff changeset
156 }
561a7518be6b update gcc-4.6
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff changeset
157
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 /* Evaluate x^n+1 + P[n] x^(n) + P[n-1] x^(n-1) + ... + P[0] */
561a7518be6b update gcc-4.6
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff changeset
160
561a7518be6b update gcc-4.6
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff changeset
161 static __float128
561a7518be6b update gcc-4.6
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff changeset
162 deval (__float128 x, const __float128 *p, int n)
561a7518be6b update gcc-4.6
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff changeset
163 {
561a7518be6b update gcc-4.6
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff changeset
164 __float128 y;
561a7518be6b update gcc-4.6
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff changeset
165
561a7518be6b update gcc-4.6
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff changeset
166 p += n;
561a7518be6b update gcc-4.6
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff changeset
167 y = x + *p--;
561a7518be6b update gcc-4.6
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff changeset
168 do
561a7518be6b update gcc-4.6
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff changeset
169 {
561a7518be6b update gcc-4.6
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff changeset
170 y = y * x + *p--;
561a7518be6b update gcc-4.6
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff changeset
171 }
561a7518be6b update gcc-4.6
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff changeset
172 while (--n > 0);
561a7518be6b update gcc-4.6
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff changeset
173 return y;
561a7518be6b update gcc-4.6
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff changeset
174 }
561a7518be6b update gcc-4.6
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff changeset
175
561a7518be6b update gcc-4.6
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff changeset
176
561a7518be6b update gcc-4.6
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff changeset
177
561a7518be6b update gcc-4.6
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff changeset
178 __float128
561a7518be6b update gcc-4.6
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff changeset
179 log10q (__float128 x)
561a7518be6b update gcc-4.6
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff changeset
180 {
561a7518be6b update gcc-4.6
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff changeset
181 __float128 z;
561a7518be6b update gcc-4.6
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff changeset
182 __float128 y;
561a7518be6b update gcc-4.6
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff changeset
183 int e;
561a7518be6b update gcc-4.6
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff changeset
184 int64_t hx, lx;
561a7518be6b update gcc-4.6
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff changeset
185
561a7518be6b update gcc-4.6
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff changeset
186 /* Test for domain */
561a7518be6b update gcc-4.6
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff changeset
187 GET_FLT128_WORDS64 (hx, lx, x);
561a7518be6b update gcc-4.6
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff changeset
188 if (((hx & 0x7fffffffffffffffLL) | lx) == 0)
145
1830386684a0 gcc-9.2.0
anatofuz
parents: 111
diff changeset
189 return (-1 / fabsq (x)); /* log10l(+-0)=-inf */
68
561a7518be6b update gcc-4.6
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff changeset
190 if (hx < 0)
561a7518be6b update gcc-4.6
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff changeset
191 return (x - x) / (x - x);
561a7518be6b update gcc-4.6
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff changeset
192 if (hx >= 0x7fff000000000000LL)
561a7518be6b update gcc-4.6
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff changeset
193 return (x + x);
561a7518be6b update gcc-4.6
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff changeset
194
145
1830386684a0 gcc-9.2.0
anatofuz
parents: 111
diff changeset
195 if (x == 1)
1830386684a0 gcc-9.2.0
anatofuz
parents: 111
diff changeset
196 return 0;
111
kono
parents: 68
diff changeset
197
68
561a7518be6b update gcc-4.6
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff changeset
198 /* separate mantissa from exponent */
561a7518be6b update gcc-4.6
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff changeset
199
561a7518be6b update gcc-4.6
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff changeset
200 /* Note, frexp is used so that denormal numbers
561a7518be6b update gcc-4.6
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff changeset
201 * will be handled properly.
561a7518be6b update gcc-4.6
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff changeset
202 */
561a7518be6b update gcc-4.6
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff changeset
203 x = frexpq (x, &e);
561a7518be6b update gcc-4.6
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff changeset
204
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 /* logarithm using log(x) = z + z**3 P(z)/Q(z),
561a7518be6b update gcc-4.6
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff changeset
207 * where z = 2(x-1)/x+1)
561a7518be6b update gcc-4.6
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff changeset
208 */
561a7518be6b update gcc-4.6
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff changeset
209 if ((e > 2) || (e < -2))
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 if (x < SQRTH)
561a7518be6b update gcc-4.6
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff changeset
212 { /* 2( 2x-1 )/( 2x+1 ) */
561a7518be6b update gcc-4.6
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff changeset
213 e -= 1;
561a7518be6b update gcc-4.6
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff changeset
214 z = x - 0.5Q;
561a7518be6b update gcc-4.6
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff changeset
215 y = 0.5Q * z + 0.5Q;
561a7518be6b update gcc-4.6
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff changeset
216 }
561a7518be6b update gcc-4.6
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff changeset
217 else
561a7518be6b update gcc-4.6
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff changeset
218 { /* 2 (x-1)/(x+1) */
561a7518be6b update gcc-4.6
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff changeset
219 z = x - 0.5Q;
561a7518be6b update gcc-4.6
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff changeset
220 z -= 0.5Q;
561a7518be6b update gcc-4.6
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff changeset
221 y = 0.5Q * x + 0.5Q;
561a7518be6b update gcc-4.6
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff changeset
222 }
561a7518be6b update gcc-4.6
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff changeset
223 x = z / y;
561a7518be6b update gcc-4.6
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff changeset
224 z = x * x;
561a7518be6b update gcc-4.6
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff changeset
225 y = x * (z * neval (z, R, 5) / deval (z, S, 5));
561a7518be6b update gcc-4.6
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff changeset
226 goto done;
561a7518be6b update gcc-4.6
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff changeset
227 }
561a7518be6b update gcc-4.6
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff changeset
228
561a7518be6b update gcc-4.6
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff changeset
229
561a7518be6b update gcc-4.6
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff changeset
230 /* 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
231
561a7518be6b update gcc-4.6
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff changeset
232 if (x < SQRTH)
561a7518be6b update gcc-4.6
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff changeset
233 {
561a7518be6b update gcc-4.6
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff changeset
234 e -= 1;
145
1830386684a0 gcc-9.2.0
anatofuz
parents: 111
diff changeset
235 x = 2.0 * x - 1; /* 2x - 1 */
68
561a7518be6b update gcc-4.6
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff changeset
236 }
561a7518be6b update gcc-4.6
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff changeset
237 else
561a7518be6b update gcc-4.6
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff changeset
238 {
145
1830386684a0 gcc-9.2.0
anatofuz
parents: 111
diff changeset
239 x = x - 1;
68
561a7518be6b update gcc-4.6
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff changeset
240 }
561a7518be6b update gcc-4.6
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff changeset
241 z = x * x;
561a7518be6b update gcc-4.6
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff changeset
242 y = x * (z * neval (x, P, 12) / deval (x, Q, 11));
561a7518be6b update gcc-4.6
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff changeset
243 y = y - 0.5 * z;
561a7518be6b update gcc-4.6
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff changeset
244
561a7518be6b update gcc-4.6
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff changeset
245 done:
561a7518be6b update gcc-4.6
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff changeset
246
561a7518be6b update gcc-4.6
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff changeset
247 /* Multiply log of fraction by log10(e)
561a7518be6b update gcc-4.6
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff changeset
248 * and base 2 exponent by log10(2).
561a7518be6b update gcc-4.6
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff changeset
249 */
561a7518be6b update gcc-4.6
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff changeset
250 z = y * L10EB;
561a7518be6b update gcc-4.6
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff changeset
251 z += x * L10EB;
561a7518be6b update gcc-4.6
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff changeset
252 z += e * L102B;
561a7518be6b update gcc-4.6
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff changeset
253 z += y * L10EA;
561a7518be6b update gcc-4.6
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff changeset
254 z += x * L10EA;
561a7518be6b update gcc-4.6
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff changeset
255 z += e * L102A;
561a7518be6b update gcc-4.6
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff changeset
256 return (z);
561a7518be6b update gcc-4.6
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff changeset
257 }