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annotate libquadmath/math/j0q.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
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rev   line source
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Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
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1 /* j0l.c
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2 *
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Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
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3 * Bessel function of order zero
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4 *
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5 *
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6 *
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7 * SYNOPSIS:
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8 *
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9 * long double x, y, j0l();
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10 *
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11 * y = j0l( 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 Bessel function of first kind, order zero of the argument.
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18 *
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19 * The domain is divided into two major intervals [0, 2] and
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20 * (2, infinity). In the first interval the rational approximation
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21 * is J0(x) = 1 - x^2 / 4 + x^4 R(x^2)
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22 * The second interval is further partitioned into eight equal segments
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23 * of 1/x.
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24 *
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25 * J0(x) = sqrt(2/(pi x)) (P0(x) cos(X) - Q0(x) sin(X)),
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26 * X = x - pi/4,
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27 *
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28 * and the auxiliary functions are given by
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29 *
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30 * J0(x)cos(X) + Y0(x)sin(X) = sqrt( 2/(pi x)) P0(x),
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31 * P0(x) = 1 + 1/x^2 R(1/x^2)
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32 *
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33 * Y0(x)cos(X) - J0(x)sin(X) = sqrt( 2/(pi x)) Q0(x),
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34 * Q0(x) = 1/x (-.125 + 1/x^2 R(1/x^2))
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35 *
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36 *
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37 *
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38 * ACCURACY:
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39 *
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40 * Absolute error:
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41 * arithmetic domain # trials peak rms
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42 * IEEE 0, 30 100000 1.7e-34 2.4e-35
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43 *
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44 *
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45 */
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46
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47 /* y0l.c
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48 *
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49 * Bessel function of the second kind, order zero
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50 *
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51 *
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52 *
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53 * SYNOPSIS:
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54 *
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55 * double x, y, y0l();
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56 *
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57 * y = y0l( x );
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58 *
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59 *
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60 *
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61 * DESCRIPTION:
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62 *
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63 * Returns Bessel function of the second kind, of order
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64 * zero, of the argument.
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65 *
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66 * The approximation is the same as for J0(x), and
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67 * Y0(x) = sqrt(2/(pi x)) (P0(x) sin(X) + Q0(x) cos(X)).
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68 *
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69 * ACCURACY:
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70 *
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71 * Absolute error, when y0(x) < 1; else relative error:
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72 *
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73 * arithmetic domain # trials peak rms
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74 * IEEE 0, 30 100000 3.0e-34 2.7e-35
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75 *
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76 */
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77
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78 /* Copyright 2001 by Stephen L. Moshier (moshier@na-net.ornl.gov).
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79
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80 This library is free software; you can redistribute it and/or
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81 modify it under the terms of the GNU Lesser General Public
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82 License as published by the Free Software Foundation; either
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83 version 2.1 of the License, or (at your option) any later version.
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84
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85 This library is distributed in the hope that it will be useful,
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86 but WITHOUT ANY WARRANTY; without even the implied warranty of
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87 MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU
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88 Lesser General Public License for more details.
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89
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90 You should have received a copy of the GNU Lesser General Public
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91 License along with this library; if not, see
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92 <http://www.gnu.org/licenses/>. */
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93
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94 #include "quadmath-imp.h"
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95
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96 /* 1 / sqrt(pi) */
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97 static const __float128 ONEOSQPI = 5.6418958354775628694807945156077258584405E-1Q;
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98 /* 2 / pi */
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99 static const __float128 TWOOPI = 6.3661977236758134307553505349005744813784E-1Q;
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100 static const __float128 zero = 0;
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101
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102 /* J0(x) = 1 - x^2/4 + x^2 x^2 R(x^2)
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103 Peak relative error 3.4e-37
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104 0 <= x <= 2 */
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105 #define NJ0_2N 6
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106 static const __float128 J0_2N[NJ0_2N + 1] = {
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107 3.133239376997663645548490085151484674892E16Q,
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108 -5.479944965767990821079467311839107722107E14Q,
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109 6.290828903904724265980249871997551894090E12Q,
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110 -3.633750176832769659849028554429106299915E10Q,
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111 1.207743757532429576399485415069244807022E8Q,
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112 -2.107485999925074577174305650549367415465E5Q,
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113 1.562826808020631846245296572935547005859E2Q,
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114 };
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115 #define NJ0_2D 6
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116 static const __float128 J0_2D[NJ0_2D + 1] = {
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117 2.005273201278504733151033654496928968261E18Q,
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118 2.063038558793221244373123294054149790864E16Q,
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119 1.053350447931127971406896594022010524994E14Q,
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120 3.496556557558702583143527876385508882310E11Q,
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121 8.249114511878616075860654484367133976306E8Q,
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122 1.402965782449571800199759247964242790589E6Q,
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123 1.619910762853439600957801751815074787351E3Q,
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124 /* 1.000000000000000000000000000000000000000E0 */
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125 };
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Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff changeset
126
561a7518be6b update gcc-4.6
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff changeset
127 /* J0(x)cosX + Y0(x)sinX = sqrt( 2/(pi x)) P0(x), P0(x) = 1 + 1/x^2 R(1/x^2),
561a7518be6b update gcc-4.6
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff changeset
128 0 <= 1/x <= .0625
561a7518be6b update gcc-4.6
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff changeset
129 Peak relative error 3.3e-36 */
561a7518be6b update gcc-4.6
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff changeset
130 #define NP16_IN 9
561a7518be6b update gcc-4.6
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff changeset
131 static const __float128 P16_IN[NP16_IN + 1] = {
561a7518be6b update gcc-4.6
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff changeset
132 -1.901689868258117463979611259731176301065E-16Q,
561a7518be6b update gcc-4.6
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff changeset
133 -1.798743043824071514483008340803573980931E-13Q,
561a7518be6b update gcc-4.6
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff changeset
134 -6.481746687115262291873324132944647438959E-11Q,
561a7518be6b update gcc-4.6
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff changeset
135 -1.150651553745409037257197798528294248012E-8Q,
561a7518be6b update gcc-4.6
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff changeset
136 -1.088408467297401082271185599507222695995E-6Q,
561a7518be6b update gcc-4.6
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff changeset
137 -5.551996725183495852661022587879817546508E-5Q,
561a7518be6b update gcc-4.6
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff changeset
138 -1.477286941214245433866838787454880214736E-3Q,
561a7518be6b update gcc-4.6
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff changeset
139 -1.882877976157714592017345347609200402472E-2Q,
561a7518be6b update gcc-4.6
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff changeset
140 -9.620983176855405325086530374317855880515E-2Q,
561a7518be6b update gcc-4.6
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff changeset
141 -1.271468546258855781530458854476627766233E-1Q,
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 #define NP16_ID 9
561a7518be6b update gcc-4.6
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff changeset
144 static const __float128 P16_ID[NP16_ID + 1] = {
561a7518be6b update gcc-4.6
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff changeset
145 2.704625590411544837659891569420764475007E-15Q,
561a7518be6b update gcc-4.6
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff changeset
146 2.562526347676857624104306349421985403573E-12Q,
561a7518be6b update gcc-4.6
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff changeset
147 9.259137589952741054108665570122085036246E-10Q,
561a7518be6b update gcc-4.6
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff changeset
148 1.651044705794378365237454962653430805272E-7Q,
561a7518be6b update gcc-4.6
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff changeset
149 1.573561544138733044977714063100859136660E-5Q,
561a7518be6b update gcc-4.6
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff changeset
150 8.134482112334882274688298469629884804056E-4Q,
561a7518be6b update gcc-4.6
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff changeset
151 2.219259239404080863919375103673593571689E-2Q,
561a7518be6b update gcc-4.6
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff changeset
152 2.976990606226596289580242451096393862792E-1Q,
561a7518be6b update gcc-4.6
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff changeset
153 1.713895630454693931742734911930937246254E0Q,
561a7518be6b update gcc-4.6
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff changeset
154 3.231552290717904041465898249160757368855E0Q,
561a7518be6b update gcc-4.6
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff changeset
155 /* 1.000000000000000000000000000000000000000E0 */
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 /* J0(x)cosX + Y0(x)sinX = sqrt( 2/(pi x)) P0(x), P0(x) = 1 + 1/x^2 R(1/x^2)
561a7518be6b update gcc-4.6
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff changeset
159 0.0625 <= 1/x <= 0.125
561a7518be6b update gcc-4.6
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff changeset
160 Peak relative error 2.4e-35 */
561a7518be6b update gcc-4.6
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff changeset
161 #define NP8_16N 10
561a7518be6b update gcc-4.6
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff changeset
162 static const __float128 P8_16N[NP8_16N + 1] = {
561a7518be6b update gcc-4.6
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff changeset
163 -2.335166846111159458466553806683579003632E-15Q,
561a7518be6b update gcc-4.6
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff changeset
164 -1.382763674252402720401020004169367089975E-12Q,
561a7518be6b update gcc-4.6
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff changeset
165 -3.192160804534716696058987967592784857907E-10Q,
561a7518be6b update gcc-4.6
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff changeset
166 -3.744199606283752333686144670572632116899E-8Q,
561a7518be6b update gcc-4.6
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff changeset
167 -2.439161236879511162078619292571922772224E-6Q,
561a7518be6b update gcc-4.6
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff changeset
168 -9.068436986859420951664151060267045346549E-5Q,
561a7518be6b update gcc-4.6
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff changeset
169 -1.905407090637058116299757292660002697359E-3Q,
561a7518be6b update gcc-4.6
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff changeset
170 -2.164456143936718388053842376884252978872E-2Q,
561a7518be6b update gcc-4.6
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff changeset
171 -1.212178415116411222341491717748696499966E-1Q,
561a7518be6b update gcc-4.6
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff changeset
172 -2.782433626588541494473277445959593334494E-1Q,
561a7518be6b update gcc-4.6
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff changeset
173 -1.670703190068873186016102289227646035035E-1Q,
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 #define NP8_16D 10
561a7518be6b update gcc-4.6
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff changeset
176 static const __float128 P8_16D[NP8_16D + 1] = {
561a7518be6b update gcc-4.6
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff changeset
177 3.321126181135871232648331450082662856743E-14Q,
561a7518be6b update gcc-4.6
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff changeset
178 1.971894594837650840586859228510007703641E-11Q,
561a7518be6b update gcc-4.6
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff changeset
179 4.571144364787008285981633719513897281690E-9Q,
561a7518be6b update gcc-4.6
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff changeset
180 5.396419143536287457142904742849052402103E-7Q,
561a7518be6b update gcc-4.6
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff changeset
181 3.551548222385845912370226756036899901549E-5Q,
561a7518be6b update gcc-4.6
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff changeset
182 1.342353874566932014705609788054598013516E-3Q,
561a7518be6b update gcc-4.6
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff changeset
183 2.899133293006771317589357444614157734385E-2Q,
561a7518be6b update gcc-4.6
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff changeset
184 3.455374978185770197704507681491574261545E-1Q,
561a7518be6b update gcc-4.6
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff changeset
185 2.116616964297512311314454834712634820514E0Q,
561a7518be6b update gcc-4.6
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff changeset
186 5.850768316827915470087758636881584174432E0Q,
561a7518be6b update gcc-4.6
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff changeset
187 5.655273858938766830855753983631132928968E0Q,
561a7518be6b update gcc-4.6
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff changeset
188 /* 1.000000000000000000000000000000000000000E0 */
561a7518be6b update gcc-4.6
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff changeset
189 };
561a7518be6b update gcc-4.6
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff changeset
190
561a7518be6b update gcc-4.6
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff changeset
191 /* J0(x)cosX + Y0(x)sinX = sqrt( 2/(pi x)) P0(x), P0(x) = 1 + 1/x^2 R(1/x^2)
561a7518be6b update gcc-4.6
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff changeset
192 0.125 <= 1/x <= 0.1875
561a7518be6b update gcc-4.6
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff changeset
193 Peak relative error 2.7e-35 */
561a7518be6b update gcc-4.6
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff changeset
194 #define NP5_8N 10
561a7518be6b update gcc-4.6
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff changeset
195 static const __float128 P5_8N[NP5_8N + 1] = {
561a7518be6b update gcc-4.6
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff changeset
196 -1.270478335089770355749591358934012019596E-12Q,
561a7518be6b update gcc-4.6
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff changeset
197 -4.007588712145412921057254992155810347245E-10Q,
561a7518be6b update gcc-4.6
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff changeset
198 -4.815187822989597568124520080486652009281E-8Q,
561a7518be6b update gcc-4.6
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff changeset
199 -2.867070063972764880024598300408284868021E-6Q,
561a7518be6b update gcc-4.6
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff changeset
200 -9.218742195161302204046454768106063638006E-5Q,
561a7518be6b update gcc-4.6
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff changeset
201 -1.635746821447052827526320629828043529997E-3Q,
561a7518be6b update gcc-4.6
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff changeset
202 -1.570376886640308408247709616497261011707E-2Q,
561a7518be6b update gcc-4.6
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff changeset
203 -7.656484795303305596941813361786219477807E-2Q,
561a7518be6b update gcc-4.6
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff changeset
204 -1.659371030767513274944805479908858628053E-1Q,
561a7518be6b update gcc-4.6
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff changeset
205 -1.185340550030955660015841796219919804915E-1Q,
561a7518be6b update gcc-4.6
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff changeset
206 -8.920026499909994671248893388013790366712E-3Q,
561a7518be6b update gcc-4.6
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff changeset
207 };
561a7518be6b update gcc-4.6
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff changeset
208 #define NP5_8D 9
561a7518be6b update gcc-4.6
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff changeset
209 static const __float128 P5_8D[NP5_8D + 1] = {
561a7518be6b update gcc-4.6
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff changeset
210 1.806902521016705225778045904631543990314E-11Q,
561a7518be6b update gcc-4.6
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff changeset
211 5.728502760243502431663549179135868966031E-9Q,
561a7518be6b update gcc-4.6
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff changeset
212 6.938168504826004255287618819550667978450E-7Q,
561a7518be6b update gcc-4.6
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff changeset
213 4.183769964807453250763325026573037785902E-5Q,
561a7518be6b update gcc-4.6
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff changeset
214 1.372660678476925468014882230851637878587E-3Q,
561a7518be6b update gcc-4.6
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff changeset
215 2.516452105242920335873286419212708961771E-2Q,
561a7518be6b update gcc-4.6
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff changeset
216 2.550502712902647803796267951846557316182E-1Q,
561a7518be6b update gcc-4.6
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff changeset
217 1.365861559418983216913629123778747617072E0Q,
561a7518be6b update gcc-4.6
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff changeset
218 3.523825618308783966723472468855042541407E0Q,
561a7518be6b update gcc-4.6
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff changeset
219 3.656365803506136165615111349150536282434E0Q,
561a7518be6b update gcc-4.6
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff changeset
220 /* 1.000000000000000000000000000000000000000E0 */
561a7518be6b update gcc-4.6
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff changeset
221 };
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 /* J0(x)cosX + Y0(x)sinX = sqrt( 2/(pi x)) P0(x), P0(x) = 1 + 1/x^2 R(1/x^2)
561a7518be6b update gcc-4.6
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff changeset
224 Peak relative error 3.5e-35
561a7518be6b update gcc-4.6
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff changeset
225 0.1875 <= 1/x <= 0.25 */
561a7518be6b update gcc-4.6
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff changeset
226 #define NP4_5N 9
561a7518be6b update gcc-4.6
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff changeset
227 static const __float128 P4_5N[NP4_5N + 1] = {
561a7518be6b update gcc-4.6
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff changeset
228 -9.791405771694098960254468859195175708252E-10Q,
561a7518be6b update gcc-4.6
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff changeset
229 -1.917193059944531970421626610188102836352E-7Q,
561a7518be6b update gcc-4.6
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff changeset
230 -1.393597539508855262243816152893982002084E-5Q,
561a7518be6b update gcc-4.6
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff changeset
231 -4.881863490846771259880606911667479860077E-4Q,
561a7518be6b update gcc-4.6
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff changeset
232 -8.946571245022470127331892085881699269853E-3Q,
561a7518be6b update gcc-4.6
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff changeset
233 -8.707474232568097513415336886103899434251E-2Q,
561a7518be6b update gcc-4.6
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff changeset
234 -4.362042697474650737898551272505525973766E-1Q,
561a7518be6b update gcc-4.6
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff changeset
235 -1.032712171267523975431451359962375617386E0Q,
561a7518be6b update gcc-4.6
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff changeset
236 -9.630502683169895107062182070514713702346E-1Q,
561a7518be6b update gcc-4.6
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff changeset
237 -2.251804386252969656586810309252357233320E-1Q,
561a7518be6b update gcc-4.6
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff changeset
238 };
561a7518be6b update gcc-4.6
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff changeset
239 #define NP4_5D 9
561a7518be6b update gcc-4.6
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff changeset
240 static const __float128 P4_5D[NP4_5D + 1] = {
561a7518be6b update gcc-4.6
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff changeset
241 1.392555487577717669739688337895791213139E-8Q,
561a7518be6b update gcc-4.6
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff changeset
242 2.748886559120659027172816051276451376854E-6Q,
561a7518be6b update gcc-4.6
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff changeset
243 2.024717710644378047477189849678576659290E-4Q,
561a7518be6b update gcc-4.6
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff changeset
244 7.244868609350416002930624752604670292469E-3Q,
561a7518be6b update gcc-4.6
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff changeset
245 1.373631762292244371102989739300382152416E-1Q,
561a7518be6b update gcc-4.6
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff changeset
246 1.412298581400224267910294815260613240668E0Q,
561a7518be6b update gcc-4.6
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff changeset
247 7.742495637843445079276397723849017617210E0Q,
561a7518be6b update gcc-4.6
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff changeset
248 2.138429269198406512028307045259503811861E1Q,
561a7518be6b update gcc-4.6
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff changeset
249 2.651547684548423476506826951831712762610E1Q,
561a7518be6b update gcc-4.6
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff changeset
250 1.167499382465291931571685222882909166935E1Q,
561a7518be6b update gcc-4.6
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff changeset
251 /* 1.000000000000000000000000000000000000000E0 */
561a7518be6b update gcc-4.6
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff changeset
252 };
561a7518be6b update gcc-4.6
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff changeset
253
561a7518be6b update gcc-4.6
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff changeset
254 /* J0(x)cosX + Y0(x)sinX = sqrt( 2/(pi x)) P0(x), P0(x) = 1 + 1/x^2 R(1/x^2)
561a7518be6b update gcc-4.6
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff changeset
255 Peak relative error 2.3e-36
561a7518be6b update gcc-4.6
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff changeset
256 0.25 <= 1/x <= 0.3125 */
561a7518be6b update gcc-4.6
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff changeset
257 #define NP3r2_4N 9
561a7518be6b update gcc-4.6
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff changeset
258 static const __float128 P3r2_4N[NP3r2_4N + 1] = {
561a7518be6b update gcc-4.6
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff changeset
259 -2.589155123706348361249809342508270121788E-8Q,
561a7518be6b update gcc-4.6
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff changeset
260 -3.746254369796115441118148490849195516593E-6Q,
561a7518be6b update gcc-4.6
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff changeset
261 -1.985595497390808544622893738135529701062E-4Q,
561a7518be6b update gcc-4.6
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff changeset
262 -5.008253705202932091290132760394976551426E-3Q,
561a7518be6b update gcc-4.6
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff changeset
263 -6.529469780539591572179155511840853077232E-2Q,
561a7518be6b update gcc-4.6
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff changeset
264 -4.468736064761814602927408833818990271514E-1Q,
561a7518be6b update gcc-4.6
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff changeset
265 -1.556391252586395038089729428444444823380E0Q,
561a7518be6b update gcc-4.6
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff changeset
266 -2.533135309840530224072920725976994981638E0Q,
561a7518be6b update gcc-4.6
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff changeset
267 -1.605509621731068453869408718565392869560E0Q,
561a7518be6b update gcc-4.6
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff changeset
268 -2.518966692256192789269859830255724429375E-1Q,
561a7518be6b update gcc-4.6
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff changeset
269 };
561a7518be6b update gcc-4.6
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff changeset
270 #define NP3r2_4D 9
561a7518be6b update gcc-4.6
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff changeset
271 static const __float128 P3r2_4D[NP3r2_4D + 1] = {
561a7518be6b update gcc-4.6
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff changeset
272 3.682353957237979993646169732962573930237E-7Q,
561a7518be6b update gcc-4.6
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff changeset
273 5.386741661883067824698973455566332102029E-5Q,
561a7518be6b update gcc-4.6
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff changeset
274 2.906881154171822780345134853794241037053E-3Q,
561a7518be6b update gcc-4.6
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff changeset
275 7.545832595801289519475806339863492074126E-2Q,
561a7518be6b update gcc-4.6
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff changeset
276 1.029405357245594877344360389469584526654E0Q,
561a7518be6b update gcc-4.6
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff changeset
277 7.565706120589873131187989560509757626725E0Q,
561a7518be6b update gcc-4.6
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff changeset
278 2.951172890699569545357692207898667665796E1Q,
561a7518be6b update gcc-4.6
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff changeset
279 5.785723537170311456298467310529815457536E1Q,
561a7518be6b update gcc-4.6
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff changeset
280 5.095621464598267889126015412522773474467E1Q,
561a7518be6b update gcc-4.6
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff changeset
281 1.602958484169953109437547474953308401442E1Q,
561a7518be6b update gcc-4.6
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff changeset
282 /* 1.000000000000000000000000000000000000000E0 */
561a7518be6b update gcc-4.6
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff changeset
283 };
561a7518be6b update gcc-4.6
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff changeset
284
561a7518be6b update gcc-4.6
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff changeset
285 /* J0(x)cosX + Y0(x)sinX = sqrt( 2/(pi x)) P0(x), P0(x) = 1 + 1/x^2 R(1/x^2)
561a7518be6b update gcc-4.6
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff changeset
286 Peak relative error 1.0e-35
561a7518be6b update gcc-4.6
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff changeset
287 0.3125 <= 1/x <= 0.375 */
561a7518be6b update gcc-4.6
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff changeset
288 #define NP2r7_3r2N 9
561a7518be6b update gcc-4.6
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff changeset
289 static const __float128 P2r7_3r2N[NP2r7_3r2N + 1] = {
561a7518be6b update gcc-4.6
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff changeset
290 -1.917322340814391131073820537027234322550E-7Q,
561a7518be6b update gcc-4.6
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff changeset
291 -1.966595744473227183846019639723259011906E-5Q,
561a7518be6b update gcc-4.6
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff changeset
292 -7.177081163619679403212623526632690465290E-4Q,
561a7518be6b update gcc-4.6
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff changeset
293 -1.206467373860974695661544653741899755695E-2Q,
561a7518be6b update gcc-4.6
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff changeset
294 -1.008656452188539812154551482286328107316E-1Q,
561a7518be6b update gcc-4.6
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff changeset
295 -4.216016116408810856620947307438823892707E-1Q,
561a7518be6b update gcc-4.6
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff changeset
296 -8.378631013025721741744285026537009814161E-1Q,
561a7518be6b update gcc-4.6
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff changeset
297 -6.973895635309960850033762745957946272579E-1Q,
561a7518be6b update gcc-4.6
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff changeset
298 -1.797864718878320770670740413285763554812E-1Q,
561a7518be6b update gcc-4.6
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff changeset
299 -4.098025357743657347681137871388402849581E-3Q,
561a7518be6b update gcc-4.6
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff changeset
300 };
561a7518be6b update gcc-4.6
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff changeset
301 #define NP2r7_3r2D 8
561a7518be6b update gcc-4.6
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff changeset
302 static const __float128 P2r7_3r2D[NP2r7_3r2D + 1] = {
561a7518be6b update gcc-4.6
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff changeset
303 2.726858489303036441686496086962545034018E-6Q,
561a7518be6b update gcc-4.6
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff changeset
304 2.840430827557109238386808968234848081424E-4Q,
561a7518be6b update gcc-4.6
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff changeset
305 1.063826772041781947891481054529454088832E-2Q,
561a7518be6b update gcc-4.6
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff changeset
306 1.864775537138364773178044431045514405468E-1Q,
561a7518be6b update gcc-4.6
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff changeset
307 1.665660052857205170440952607701728254211E0Q,
561a7518be6b update gcc-4.6
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff changeset
308 7.723745889544331153080842168958348568395E0Q,
561a7518be6b update gcc-4.6
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff changeset
309 1.810726427571829798856428548102077799835E1Q,
561a7518be6b update gcc-4.6
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff changeset
310 1.986460672157794440666187503833545388527E1Q,
561a7518be6b update gcc-4.6
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff changeset
311 8.645503204552282306364296517220055815488E0Q,
561a7518be6b update gcc-4.6
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff changeset
312 /* 1.000000000000000000000000000000000000000E0 */
561a7518be6b update gcc-4.6
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff changeset
313 };
561a7518be6b update gcc-4.6
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff changeset
314
561a7518be6b update gcc-4.6
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff changeset
315 /* J0(x)cosX + Y0(x)sinX = sqrt( 2/(pi x)) P0(x), P0(x) = 1 + 1/x^2 R(1/x^2)
561a7518be6b update gcc-4.6
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff changeset
316 Peak relative error 1.3e-36
561a7518be6b update gcc-4.6
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff changeset
317 0.3125 <= 1/x <= 0.4375 */
561a7518be6b update gcc-4.6
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff changeset
318 #define NP2r3_2r7N 9
561a7518be6b update gcc-4.6
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff changeset
319 static const __float128 P2r3_2r7N[NP2r3_2r7N + 1] = {
561a7518be6b update gcc-4.6
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff changeset
320 -1.594642785584856746358609622003310312622E-6Q,
561a7518be6b update gcc-4.6
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff changeset
321 -1.323238196302221554194031733595194539794E-4Q,
561a7518be6b update gcc-4.6
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff changeset
322 -3.856087818696874802689922536987100372345E-3Q,
561a7518be6b update gcc-4.6
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff changeset
323 -5.113241710697777193011470733601522047399E-2Q,
561a7518be6b update gcc-4.6
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff changeset
324 -3.334229537209911914449990372942022350558E-1Q,
561a7518be6b update gcc-4.6
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff changeset
325 -1.075703518198127096179198549659283422832E0Q,
561a7518be6b update gcc-4.6
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff changeset
326 -1.634174803414062725476343124267110981807E0Q,
561a7518be6b update gcc-4.6
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff changeset
327 -1.030133247434119595616826842367268304880E0Q,
561a7518be6b update gcc-4.6
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff changeset
328 -1.989811539080358501229347481000707289391E-1Q,
561a7518be6b update gcc-4.6
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff changeset
329 -3.246859189246653459359775001466924610236E-3Q,
561a7518be6b update gcc-4.6
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff changeset
330 };
561a7518be6b update gcc-4.6
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff changeset
331 #define NP2r3_2r7D 8
561a7518be6b update gcc-4.6
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff changeset
332 static const __float128 P2r3_2r7D[NP2r3_2r7D + 1] = {
561a7518be6b update gcc-4.6
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff changeset
333 2.267936634217251403663034189684284173018E-5Q,
561a7518be6b update gcc-4.6
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff changeset
334 1.918112982168673386858072491437971732237E-3Q,
561a7518be6b update gcc-4.6
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff changeset
335 5.771704085468423159125856786653868219522E-2Q,
561a7518be6b update gcc-4.6
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff changeset
336 8.056124451167969333717642810661498890507E-1Q,
561a7518be6b update gcc-4.6
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff changeset
337 5.687897967531010276788680634413789328776E0Q,
561a7518be6b update gcc-4.6
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff changeset
338 2.072596760717695491085444438270778394421E1Q,
561a7518be6b update gcc-4.6
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff changeset
339 3.801722099819929988585197088613160496684E1Q,
561a7518be6b update gcc-4.6
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff changeset
340 3.254620235902912339534998592085115836829E1Q,
561a7518be6b update gcc-4.6
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff changeset
341 1.104847772130720331801884344645060675036E1Q,
561a7518be6b update gcc-4.6
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff changeset
342 /* 1.000000000000000000000000000000000000000E0 */
561a7518be6b update gcc-4.6
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff changeset
343 };
561a7518be6b update gcc-4.6
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff changeset
344
561a7518be6b update gcc-4.6
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff changeset
345 /* J0(x)cosX + Y0(x)sinX = sqrt( 2/(pi x)) P0(x), P0(x) = 1 + 1/x^2 R(1/x^2)
561a7518be6b update gcc-4.6
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff changeset
346 Peak relative error 1.2e-35
561a7518be6b update gcc-4.6
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff changeset
347 0.4375 <= 1/x <= 0.5 */
561a7518be6b update gcc-4.6
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff changeset
348 #define NP2_2r3N 8
561a7518be6b update gcc-4.6
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff changeset
349 static const __float128 P2_2r3N[NP2_2r3N + 1] = {
561a7518be6b update gcc-4.6
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff changeset
350 -1.001042324337684297465071506097365389123E-4Q,
561a7518be6b update gcc-4.6
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff changeset
351 -6.289034524673365824853547252689991418981E-3Q,
561a7518be6b update gcc-4.6
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff changeset
352 -1.346527918018624234373664526930736205806E-1Q,
561a7518be6b update gcc-4.6
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff changeset
353 -1.268808313614288355444506172560463315102E0Q,
561a7518be6b update gcc-4.6
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff changeset
354 -5.654126123607146048354132115649177406163E0Q,
561a7518be6b update gcc-4.6
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff changeset
355 -1.186649511267312652171775803270911971693E1Q,
561a7518be6b update gcc-4.6
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff changeset
356 -1.094032424931998612551588246779200724257E1Q,
561a7518be6b update gcc-4.6
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff changeset
357 -3.728792136814520055025256353193674625267E0Q,
561a7518be6b update gcc-4.6
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff changeset
358 -3.000348318524471807839934764596331810608E-1Q,
561a7518be6b update gcc-4.6
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff changeset
359 };
561a7518be6b update gcc-4.6
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff changeset
360 #define NP2_2r3D 8
561a7518be6b update gcc-4.6
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff changeset
361 static const __float128 P2_2r3D[NP2_2r3D + 1] = {
561a7518be6b update gcc-4.6
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff changeset
362 1.423705538269770974803901422532055612980E-3Q,
561a7518be6b update gcc-4.6
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff changeset
363 9.171476630091439978533535167485230575894E-2Q,
561a7518be6b update gcc-4.6
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff changeset
364 2.049776318166637248868444600215942828537E0Q,
561a7518be6b update gcc-4.6
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff changeset
365 2.068970329743769804547326701946144899583E1Q,
561a7518be6b update gcc-4.6
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff changeset
366 1.025103500560831035592731539565060347709E2Q,
561a7518be6b update gcc-4.6
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff changeset
367 2.528088049697570728252145557167066708284E2Q,
561a7518be6b update gcc-4.6
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff changeset
368 2.992160327587558573740271294804830114205E2Q,
561a7518be6b update gcc-4.6
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff changeset
369 1.540193761146551025832707739468679973036E2Q,
561a7518be6b update gcc-4.6
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff changeset
370 2.779516701986912132637672140709452502650E1Q,
561a7518be6b update gcc-4.6
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff changeset
371 /* 1.000000000000000000000000000000000000000E0 */
561a7518be6b update gcc-4.6
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff changeset
372 };
561a7518be6b update gcc-4.6
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff changeset
373
561a7518be6b update gcc-4.6
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff changeset
374 /* Y0(x)cosX - J0(x)sinX = sqrt( 2/(pi x)) Q0(x),
561a7518be6b update gcc-4.6
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff changeset
375 Q0(x) = 1/x (-.125 + 1/x^2 R(1/x^2))
561a7518be6b update gcc-4.6
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff changeset
376 Peak relative error 2.2e-35
561a7518be6b update gcc-4.6
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff changeset
377 0 <= 1/x <= .0625 */
561a7518be6b update gcc-4.6
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff changeset
378 #define NQ16_IN 10
561a7518be6b update gcc-4.6
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff changeset
379 static const __float128 Q16_IN[NQ16_IN + 1] = {
561a7518be6b update gcc-4.6
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff changeset
380 2.343640834407975740545326632205999437469E-18Q,
561a7518be6b update gcc-4.6
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff changeset
381 2.667978112927811452221176781536278257448E-15Q,
561a7518be6b update gcc-4.6
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff changeset
382 1.178415018484555397390098879501969116536E-12Q,
561a7518be6b update gcc-4.6
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff changeset
383 2.622049767502719728905924701288614016597E-10Q,
561a7518be6b update gcc-4.6
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff changeset
384 3.196908059607618864801313380896308968673E-8Q,
561a7518be6b update gcc-4.6
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff changeset
385 2.179466154171673958770030655199434798494E-6Q,
561a7518be6b update gcc-4.6
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff changeset
386 8.139959091628545225221976413795645177291E-5Q,
561a7518be6b update gcc-4.6
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff changeset
387 1.563900725721039825236927137885747138654E-3Q,
561a7518be6b update gcc-4.6
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff changeset
388 1.355172364265825167113562519307194840307E-2Q,
561a7518be6b update gcc-4.6
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff changeset
389 3.928058355906967977269780046844768588532E-2Q,
561a7518be6b update gcc-4.6
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff changeset
390 1.107891967702173292405380993183694932208E-2Q,
561a7518be6b update gcc-4.6
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff changeset
391 };
561a7518be6b update gcc-4.6
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff changeset
392 #define NQ16_ID 9
561a7518be6b update gcc-4.6
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff changeset
393 static const __float128 Q16_ID[NQ16_ID + 1] = {
561a7518be6b update gcc-4.6
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff changeset
394 3.199850952578356211091219295199301766718E-17Q,
561a7518be6b update gcc-4.6
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff changeset
395 3.652601488020654842194486058637953363918E-14Q,
561a7518be6b update gcc-4.6
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff changeset
396 1.620179741394865258354608590461839031281E-11Q,
561a7518be6b update gcc-4.6
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff changeset
397 3.629359209474609630056463248923684371426E-9Q,
561a7518be6b update gcc-4.6
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff changeset
398 4.473680923894354600193264347733477363305E-7Q,
561a7518be6b update gcc-4.6
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff changeset
399 3.106368086644715743265603656011050476736E-5Q,
561a7518be6b update gcc-4.6
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff changeset
400 1.198239259946770604954664925153424252622E-3Q,
561a7518be6b update gcc-4.6
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff changeset
401 2.446041004004283102372887804475767568272E-2Q,
561a7518be6b update gcc-4.6
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff changeset
402 2.403235525011860603014707768815113698768E-1Q,
561a7518be6b update gcc-4.6
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff changeset
403 9.491006790682158612266270665136910927149E-1Q,
561a7518be6b update gcc-4.6
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff changeset
404 /* 1.000000000000000000000000000000000000000E0 */
561a7518be6b update gcc-4.6
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff changeset
405 };
561a7518be6b update gcc-4.6
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff changeset
406
561a7518be6b update gcc-4.6
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff changeset
407 /* Y0(x)cosX - J0(x)sinX = sqrt( 2/(pi x)) Q0(x),
561a7518be6b update gcc-4.6
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff changeset
408 Q0(x) = 1/x (-.125 + 1/x^2 R(1/x^2))
561a7518be6b update gcc-4.6
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff changeset
409 Peak relative error 5.1e-36
561a7518be6b update gcc-4.6
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff changeset
410 0.0625 <= 1/x <= 0.125 */
561a7518be6b update gcc-4.6
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff changeset
411 #define NQ8_16N 11
561a7518be6b update gcc-4.6
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff changeset
412 static const __float128 Q8_16N[NQ8_16N + 1] = {
561a7518be6b update gcc-4.6
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff changeset
413 1.001954266485599464105669390693597125904E-17Q,
561a7518be6b update gcc-4.6
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff changeset
414 7.545499865295034556206475956620160007849E-15Q,
561a7518be6b update gcc-4.6
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff changeset
415 2.267838684785673931024792538193202559922E-12Q,
561a7518be6b update gcc-4.6
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff changeset
416 3.561909705814420373609574999542459912419E-10Q,
561a7518be6b update gcc-4.6
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff changeset
417 3.216201422768092505214730633842924944671E-8Q,
561a7518be6b update gcc-4.6
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff changeset
418 1.731194793857907454569364622452058554314E-6Q,
561a7518be6b update gcc-4.6
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff changeset
419 5.576944613034537050396518509871004586039E-5Q,
561a7518be6b update gcc-4.6
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff changeset
420 1.051787760316848982655967052985391418146E-3Q,
561a7518be6b update gcc-4.6
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff changeset
421 1.102852974036687441600678598019883746959E-2Q,
561a7518be6b update gcc-4.6
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff changeset
422 5.834647019292460494254225988766702933571E-2Q,
561a7518be6b update gcc-4.6
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff changeset
423 1.290281921604364618912425380717127576529E-1Q,
561a7518be6b update gcc-4.6
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff changeset
424 7.598886310387075708640370806458926458301E-2Q,
561a7518be6b update gcc-4.6
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff changeset
425 };
561a7518be6b update gcc-4.6
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff changeset
426 #define NQ8_16D 11
561a7518be6b update gcc-4.6
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff changeset
427 static const __float128 Q8_16D[NQ8_16D + 1] = {
561a7518be6b update gcc-4.6
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff changeset
428 1.368001558508338469503329967729951830843E-16Q,
561a7518be6b update gcc-4.6
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff changeset
429 1.034454121857542147020549303317348297289E-13Q,
561a7518be6b update gcc-4.6
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff changeset
430 3.128109209247090744354764050629381674436E-11Q,
561a7518be6b update gcc-4.6
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff changeset
431 4.957795214328501986562102573522064468671E-9Q,
561a7518be6b update gcc-4.6
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff changeset
432 4.537872468606711261992676606899273588899E-7Q,
561a7518be6b update gcc-4.6
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff changeset
433 2.493639207101727713192687060517509774182E-5Q,
561a7518be6b update gcc-4.6
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff changeset
434 8.294957278145328349785532236663051405805E-4Q,
561a7518be6b update gcc-4.6
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff changeset
435 1.646471258966713577374948205279380115839E-2Q,
561a7518be6b update gcc-4.6
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff changeset
436 1.878910092770966718491814497982191447073E-1Q,
561a7518be6b update gcc-4.6
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff changeset
437 1.152641605706170353727903052525652504075E0Q,
561a7518be6b update gcc-4.6
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff changeset
438 3.383550240669773485412333679367792932235E0Q,
561a7518be6b update gcc-4.6
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff changeset
439 3.823875252882035706910024716609908473970E0Q,
561a7518be6b update gcc-4.6
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff changeset
440 /* 1.000000000000000000000000000000000000000E0 */
561a7518be6b update gcc-4.6
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff changeset
441 };
561a7518be6b update gcc-4.6
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff changeset
442
561a7518be6b update gcc-4.6
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff changeset
443 /* Y0(x)cosX - J0(x)sinX = sqrt( 2/(pi x)) Q0(x),
561a7518be6b update gcc-4.6
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff changeset
444 Q0(x) = 1/x (-.125 + 1/x^2 R(1/x^2))
561a7518be6b update gcc-4.6
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff changeset
445 Peak relative error 3.9e-35
561a7518be6b update gcc-4.6
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff changeset
446 0.125 <= 1/x <= 0.1875 */
561a7518be6b update gcc-4.6
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff changeset
447 #define NQ5_8N 10
561a7518be6b update gcc-4.6
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff changeset
448 static const __float128 Q5_8N[NQ5_8N + 1] = {
561a7518be6b update gcc-4.6
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff changeset
449 1.750399094021293722243426623211733898747E-13Q,
561a7518be6b update gcc-4.6
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff changeset
450 6.483426211748008735242909236490115050294E-11Q,
561a7518be6b update gcc-4.6
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff changeset
451 9.279430665656575457141747875716899958373E-9Q,
561a7518be6b update gcc-4.6
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff changeset
452 6.696634968526907231258534757736576340266E-7Q,
561a7518be6b update gcc-4.6
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff changeset
453 2.666560823798895649685231292142838188061E-5Q,
561a7518be6b update gcc-4.6
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff changeset
454 6.025087697259436271271562769707550594540E-4Q,
561a7518be6b update gcc-4.6
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff changeset
455 7.652807734168613251901945778921336353485E-3Q,
561a7518be6b update gcc-4.6
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff changeset
456 5.226269002589406461622551452343519078905E-2Q,
561a7518be6b update gcc-4.6
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff changeset
457 1.748390159751117658969324896330142895079E-1Q,
561a7518be6b update gcc-4.6
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff changeset
458 2.378188719097006494782174902213083589660E-1Q,
561a7518be6b update gcc-4.6
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff changeset
459 8.383984859679804095463699702165659216831E-2Q,
561a7518be6b update gcc-4.6
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff changeset
460 };
561a7518be6b update gcc-4.6
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff changeset
461 #define NQ5_8D 10
561a7518be6b update gcc-4.6
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff changeset
462 static const __float128 Q5_8D[NQ5_8D + 1] = {
561a7518be6b update gcc-4.6
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff changeset
463 2.389878229704327939008104855942987615715E-12Q,
561a7518be6b update gcc-4.6
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff changeset
464 8.926142817142546018703814194987786425099E-10Q,
561a7518be6b update gcc-4.6
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff changeset
465 1.294065862406745901206588525833274399038E-7Q,
561a7518be6b update gcc-4.6
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff changeset
466 9.524139899457666250828752185212769682191E-6Q,
561a7518be6b update gcc-4.6
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff changeset
467 3.908332488377770886091936221573123353489E-4Q,
561a7518be6b update gcc-4.6
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff changeset
468 9.250427033957236609624199884089916836748E-3Q,
561a7518be6b update gcc-4.6
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff changeset
469 1.263420066165922645975830877751588421451E-1Q,
561a7518be6b update gcc-4.6
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff changeset
470 9.692527053860420229711317379861733180654E-1Q,
561a7518be6b update gcc-4.6
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff changeset
471 3.937813834630430172221329298841520707954E0Q,
561a7518be6b update gcc-4.6
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff changeset
472 7.603126427436356534498908111445191312181E0Q,
561a7518be6b update gcc-4.6
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff changeset
473 5.670677653334105479259958485084550934305E0Q,
561a7518be6b update gcc-4.6
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff changeset
474 /* 1.000000000000000000000000000000000000000E0 */
561a7518be6b update gcc-4.6
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff changeset
475 };
561a7518be6b update gcc-4.6
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff changeset
476
561a7518be6b update gcc-4.6
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff changeset
477 /* Y0(x)cosX - J0(x)sinX = sqrt( 2/(pi x)) Q0(x),
561a7518be6b update gcc-4.6
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff changeset
478 Q0(x) = 1/x (-.125 + 1/x^2 R(1/x^2))
561a7518be6b update gcc-4.6
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff changeset
479 Peak relative error 3.2e-35
561a7518be6b update gcc-4.6
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff changeset
480 0.1875 <= 1/x <= 0.25 */
561a7518be6b update gcc-4.6
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff changeset
481 #define NQ4_5N 10
561a7518be6b update gcc-4.6
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff changeset
482 static const __float128 Q4_5N[NQ4_5N + 1] = {
561a7518be6b update gcc-4.6
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff changeset
483 2.233870042925895644234072357400122854086E-11Q,
561a7518be6b update gcc-4.6
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff changeset
484 5.146223225761993222808463878999151699792E-9Q,
561a7518be6b update gcc-4.6
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff changeset
485 4.459114531468296461688753521109797474523E-7Q,
561a7518be6b update gcc-4.6
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff changeset
486 1.891397692931537975547242165291668056276E-5Q,
561a7518be6b update gcc-4.6
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff changeset
487 4.279519145911541776938964806470674565504E-4Q,
561a7518be6b update gcc-4.6
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff changeset
488 5.275239415656560634702073291768904783989E-3Q,
561a7518be6b update gcc-4.6
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff changeset
489 3.468698403240744801278238473898432608887E-2Q,
561a7518be6b update gcc-4.6
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff changeset
490 1.138773146337708415188856882915457888274E-1Q,
561a7518be6b update gcc-4.6
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff changeset
491 1.622717518946443013587108598334636458955E-1Q,
561a7518be6b update gcc-4.6
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff changeset
492 7.249040006390586123760992346453034628227E-2Q,
561a7518be6b update gcc-4.6
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff changeset
493 1.941595365256460232175236758506411486667E-3Q,
561a7518be6b update gcc-4.6
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff changeset
494 };
561a7518be6b update gcc-4.6
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff changeset
495 #define NQ4_5D 9
561a7518be6b update gcc-4.6
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff changeset
496 static const __float128 Q4_5D[NQ4_5D + 1] = {
561a7518be6b update gcc-4.6
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff changeset
497 3.049977232266999249626430127217988047453E-10Q,
561a7518be6b update gcc-4.6
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff changeset
498 7.120883230531035857746096928889676144099E-8Q,
561a7518be6b update gcc-4.6
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff changeset
499 6.301786064753734446784637919554359588859E-6Q,
561a7518be6b update gcc-4.6
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff changeset
500 2.762010530095069598480766869426308077192E-4Q,
561a7518be6b update gcc-4.6
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff changeset
501 6.572163250572867859316828886203406361251E-3Q,
561a7518be6b update gcc-4.6
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff changeset
502 8.752566114841221958200215255461843397776E-2Q,
561a7518be6b update gcc-4.6
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff changeset
503 6.487654992874805093499285311075289932664E-1Q,
561a7518be6b update gcc-4.6
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff changeset
504 2.576550017826654579451615283022812801435E0Q,
561a7518be6b update gcc-4.6
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff changeset
505 5.056392229924022835364779562707348096036E0Q,
561a7518be6b update gcc-4.6
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff changeset
506 4.179770081068251464907531367859072157773E0Q,
561a7518be6b update gcc-4.6
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff changeset
507 /* 1.000000000000000000000000000000000000000E0 */
561a7518be6b update gcc-4.6
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff changeset
508 };
561a7518be6b update gcc-4.6
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff changeset
509
561a7518be6b update gcc-4.6
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff changeset
510 /* Y0(x)cosX - J0(x)sinX = sqrt( 2/(pi x)) Q0(x),
561a7518be6b update gcc-4.6
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff changeset
511 Q0(x) = 1/x (-.125 + 1/x^2 R(1/x^2))
561a7518be6b update gcc-4.6
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff changeset
512 Peak relative error 1.4e-36
561a7518be6b update gcc-4.6
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff changeset
513 0.25 <= 1/x <= 0.3125 */
561a7518be6b update gcc-4.6
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff changeset
514 #define NQ3r2_4N 10
561a7518be6b update gcc-4.6
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff changeset
515 static const __float128 Q3r2_4N[NQ3r2_4N + 1] = {
561a7518be6b update gcc-4.6
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff changeset
516 6.126167301024815034423262653066023684411E-10Q,
561a7518be6b update gcc-4.6
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff changeset
517 1.043969327113173261820028225053598975128E-7Q,
561a7518be6b update gcc-4.6
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff changeset
518 6.592927270288697027757438170153763220190E-6Q,
561a7518be6b update gcc-4.6
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff changeset
519 2.009103660938497963095652951912071336730E-4Q,
561a7518be6b update gcc-4.6
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff changeset
520 3.220543385492643525985862356352195896964E-3Q,
561a7518be6b update gcc-4.6
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff changeset
521 2.774405975730545157543417650436941650990E-2Q,
561a7518be6b update gcc-4.6
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff changeset
522 1.258114008023826384487378016636555041129E-1Q,
561a7518be6b update gcc-4.6
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff changeset
523 2.811724258266902502344701449984698323860E-1Q,
561a7518be6b update gcc-4.6
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff changeset
524 2.691837665193548059322831687432415014067E-1Q,
561a7518be6b update gcc-4.6
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff changeset
525 7.949087384900985370683770525312735605034E-2Q,
561a7518be6b update gcc-4.6
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff changeset
526 1.229509543620976530030153018986910810747E-3Q,
561a7518be6b update gcc-4.6
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff changeset
527 };
561a7518be6b update gcc-4.6
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff changeset
528 #define NQ3r2_4D 9
561a7518be6b update gcc-4.6
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff changeset
529 static const __float128 Q3r2_4D[NQ3r2_4D + 1] = {
561a7518be6b update gcc-4.6
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff changeset
530 8.364260446128475461539941389210166156568E-9Q,
561a7518be6b update gcc-4.6
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff changeset
531 1.451301850638956578622154585560759862764E-6Q,
561a7518be6b update gcc-4.6
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff changeset
532 9.431830010924603664244578867057141839463E-5Q,
561a7518be6b update gcc-4.6
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff changeset
533 3.004105101667433434196388593004526182741E-3Q,
561a7518be6b update gcc-4.6
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff changeset
534 5.148157397848271739710011717102773780221E-2Q,
561a7518be6b update gcc-4.6
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff changeset
535 4.901089301726939576055285374953887874895E-1Q,
561a7518be6b update gcc-4.6
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff changeset
536 2.581760991981709901216967665934142240346E0Q,
561a7518be6b update gcc-4.6
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff changeset
537 7.257105880775059281391729708630912791847E0Q,
561a7518be6b update gcc-4.6
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff changeset
538 1.006014717326362868007913423810737369312E1Q,
561a7518be6b update gcc-4.6
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff changeset
539 5.879416600465399514404064187445293212470E0Q,
561a7518be6b update gcc-4.6
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff changeset
540 /* 1.000000000000000000000000000000000000000E0*/
561a7518be6b update gcc-4.6
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff changeset
541 };
561a7518be6b update gcc-4.6
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff changeset
542
561a7518be6b update gcc-4.6
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff changeset
543 /* Y0(x)cosX - J0(x)sinX = sqrt( 2/(pi x)) Q0(x),
561a7518be6b update gcc-4.6
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff changeset
544 Q0(x) = 1/x (-.125 + 1/x^2 R(1/x^2))
561a7518be6b update gcc-4.6
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff changeset
545 Peak relative error 3.8e-36
561a7518be6b update gcc-4.6
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff changeset
546 0.3125 <= 1/x <= 0.375 */
561a7518be6b update gcc-4.6
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff changeset
547 #define NQ2r7_3r2N 9
561a7518be6b update gcc-4.6
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff changeset
548 static const __float128 Q2r7_3r2N[NQ2r7_3r2N + 1] = {
561a7518be6b update gcc-4.6
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff changeset
549 7.584861620402450302063691901886141875454E-8Q,
561a7518be6b update gcc-4.6
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff changeset
550 9.300939338814216296064659459966041794591E-6Q,
561a7518be6b update gcc-4.6
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff changeset
551 4.112108906197521696032158235392604947895E-4Q,
561a7518be6b update gcc-4.6
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff changeset
552 8.515168851578898791897038357239630654431E-3Q,
561a7518be6b update gcc-4.6
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff changeset
553 8.971286321017307400142720556749573229058E-2Q,
561a7518be6b update gcc-4.6
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff changeset
554 4.885856732902956303343015636331874194498E-1Q,
561a7518be6b update gcc-4.6
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff changeset
555 1.334506268733103291656253500506406045846E0Q,
561a7518be6b update gcc-4.6
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff changeset
556 1.681207956863028164179042145803851824654E0Q,
561a7518be6b update gcc-4.6
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff changeset
557 8.165042692571721959157677701625853772271E-1Q,
561a7518be6b update gcc-4.6
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff changeset
558 9.805848115375053300608712721986235900715E-2Q,
561a7518be6b update gcc-4.6
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff changeset
559 };
561a7518be6b update gcc-4.6
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff changeset
560 #define NQ2r7_3r2D 9
561a7518be6b update gcc-4.6
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff changeset
561 static const __float128 Q2r7_3r2D[NQ2r7_3r2D + 1] = {
561a7518be6b update gcc-4.6
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff changeset
562 1.035586492113036586458163971239438078160E-6Q,
561a7518be6b update gcc-4.6
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff changeset
563 1.301999337731768381683593636500979713689E-4Q,
561a7518be6b update gcc-4.6
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff changeset
564 5.993695702564527062553071126719088859654E-3Q,
561a7518be6b update gcc-4.6
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff changeset
565 1.321184892887881883489141186815457808785E-1Q,
561a7518be6b update gcc-4.6
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff changeset
566 1.528766555485015021144963194165165083312E0Q,
561a7518be6b update gcc-4.6
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff changeset
567 9.561463309176490874525827051566494939295E0Q,
561a7518be6b update gcc-4.6
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff changeset
568 3.203719484883967351729513662089163356911E1Q,
561a7518be6b update gcc-4.6
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff changeset
569 5.497294687660930446641539152123568668447E1Q,
561a7518be6b update gcc-4.6
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff changeset
570 4.391158169390578768508675452986948391118E1Q,
561a7518be6b update gcc-4.6
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff changeset
571 1.347836630730048077907818943625789418378E1Q,
561a7518be6b update gcc-4.6
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff changeset
572 /* 1.000000000000000000000000000000000000000E0 */
561a7518be6b update gcc-4.6
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff changeset
573 };
561a7518be6b update gcc-4.6
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff changeset
574
561a7518be6b update gcc-4.6
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff changeset
575 /* Y0(x)cosX - J0(x)sinX = sqrt( 2/(pi x)) Q0(x),
561a7518be6b update gcc-4.6
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff changeset
576 Q0(x) = 1/x (-.125 + 1/x^2 R(1/x^2))
561a7518be6b update gcc-4.6
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff changeset
577 Peak relative error 2.2e-35
561a7518be6b update gcc-4.6
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff changeset
578 0.375 <= 1/x <= 0.4375 */
561a7518be6b update gcc-4.6
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff changeset
579 #define NQ2r3_2r7N 9
561a7518be6b update gcc-4.6
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff changeset
580 static const __float128 Q2r3_2r7N[NQ2r3_2r7N + 1] = {
561a7518be6b update gcc-4.6
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff changeset
581 4.455027774980750211349941766420190722088E-7Q,
561a7518be6b update gcc-4.6
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff changeset
582 4.031998274578520170631601850866780366466E-5Q,
561a7518be6b update gcc-4.6
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff changeset
583 1.273987274325947007856695677491340636339E-3Q,
561a7518be6b update gcc-4.6
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff changeset
584 1.818754543377448509897226554179659122873E-2Q,
561a7518be6b update gcc-4.6
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff changeset
585 1.266748858326568264126353051352269875352E-1Q,
561a7518be6b update gcc-4.6
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff changeset
586 4.327578594728723821137731555139472880414E-1Q,
561a7518be6b update gcc-4.6
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff changeset
587 6.892532471436503074928194969154192615359E-1Q,
561a7518be6b update gcc-4.6
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff changeset
588 4.490775818438716873422163588640262036506E-1Q,
561a7518be6b update gcc-4.6
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff changeset
589 8.649615949297322440032000346117031581572E-2Q,
561a7518be6b update gcc-4.6
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff changeset
590 7.261345286655345047417257611469066147561E-4Q,
561a7518be6b update gcc-4.6
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff changeset
591 };
561a7518be6b update gcc-4.6
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff changeset
592 #define NQ2r3_2r7D 8
561a7518be6b update gcc-4.6
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff changeset
593 static const __float128 Q2r3_2r7D[NQ2r3_2r7D + 1] = {
561a7518be6b update gcc-4.6
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff changeset
594 6.082600739680555266312417978064954793142E-6Q,
561a7518be6b update gcc-4.6
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff changeset
595 5.693622538165494742945717226571441747567E-4Q,
561a7518be6b update gcc-4.6
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff changeset
596 1.901625907009092204458328768129666975975E-2Q,
561a7518be6b update gcc-4.6
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff changeset
597 2.958689532697857335456896889409923371570E-1Q,
561a7518be6b update gcc-4.6
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff changeset
598 2.343124711045660081603809437993368799568E0Q,
561a7518be6b update gcc-4.6
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff changeset
599 9.665894032187458293568704885528192804376E0Q,
561a7518be6b update gcc-4.6
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff changeset
600 2.035273104990617136065743426322454881353E1Q,
561a7518be6b update gcc-4.6
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff changeset
601 2.044102010478792896815088858740075165531E1Q,
561a7518be6b update gcc-4.6
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff changeset
602 8.445937177863155827844146643468706599304E0Q,
561a7518be6b update gcc-4.6
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff changeset
603 /* 1.000000000000000000000000000000000000000E0 */
561a7518be6b update gcc-4.6
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff changeset
604 };
561a7518be6b update gcc-4.6
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff changeset
605
561a7518be6b update gcc-4.6
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff changeset
606 /* Y0(x)cosX - J0(x)sinX = sqrt( 2/(pi x)) Q0(x),
561a7518be6b update gcc-4.6
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff changeset
607 Q0(x) = 1/x (-.125 + 1/x^2 R(1/x^2))
561a7518be6b update gcc-4.6
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff changeset
608 Peak relative error 3.1e-36
561a7518be6b update gcc-4.6
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff changeset
609 0.4375 <= 1/x <= 0.5 */
561a7518be6b update gcc-4.6
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff changeset
610 #define NQ2_2r3N 9
561a7518be6b update gcc-4.6
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff changeset
611 static const __float128 Q2_2r3N[NQ2_2r3N + 1] = {
561a7518be6b update gcc-4.6
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff changeset
612 2.817566786579768804844367382809101929314E-6Q,
561a7518be6b update gcc-4.6
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff changeset
613 2.122772176396691634147024348373539744935E-4Q,
561a7518be6b update gcc-4.6
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff changeset
614 5.501378031780457828919593905395747517585E-3Q,
561a7518be6b update gcc-4.6
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff changeset
615 6.355374424341762686099147452020466524659E-2Q,
561a7518be6b update gcc-4.6
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff changeset
616 3.539652320122661637429658698954748337223E-1Q,
561a7518be6b update gcc-4.6
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff changeset
617 9.571721066119617436343740541777014319695E-1Q,
561a7518be6b update gcc-4.6
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff changeset
618 1.196258777828426399432550698612171955305E0Q,
561a7518be6b update gcc-4.6
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff changeset
619 6.069388659458926158392384709893753793967E-1Q,
561a7518be6b update gcc-4.6
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff changeset
620 9.026746127269713176512359976978248763621E-2Q,
561a7518be6b update gcc-4.6
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff changeset
621 5.317668723070450235320878117210807236375E-4Q,
561a7518be6b update gcc-4.6
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff changeset
622 };
561a7518be6b update gcc-4.6
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff changeset
623 #define NQ2_2r3D 8
561a7518be6b update gcc-4.6
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff changeset
624 static const __float128 Q2_2r3D[NQ2_2r3D + 1] = {
561a7518be6b update gcc-4.6
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff changeset
625 3.846924354014260866793741072933159380158E-5Q,
561a7518be6b update gcc-4.6
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff changeset
626 3.017562820057704325510067178327449946763E-3Q,
561a7518be6b update gcc-4.6
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff changeset
627 8.356305620686867949798885808540444210935E-2Q,
561a7518be6b update gcc-4.6
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff changeset
628 1.068314930499906838814019619594424586273E0Q,
561a7518be6b update gcc-4.6
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff changeset
629 6.900279623894821067017966573640732685233E0Q,
561a7518be6b update gcc-4.6
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff changeset
630 2.307667390886377924509090271780839563141E1Q,
561a7518be6b update gcc-4.6
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff changeset
631 3.921043465412723970791036825401273528513E1Q,
561a7518be6b update gcc-4.6
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff changeset
632 3.167569478939719383241775717095729233436E1Q,
561a7518be6b update gcc-4.6
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff changeset
633 1.051023841699200920276198346301543665909E1Q,
561a7518be6b update gcc-4.6
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff changeset
634 /* 1.000000000000000000000000000000000000000E0*/
561a7518be6b update gcc-4.6
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff changeset
635 };
561a7518be6b update gcc-4.6
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff changeset
636
561a7518be6b update gcc-4.6
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff changeset
637
561a7518be6b update gcc-4.6
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff changeset
638 /* 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
639
561a7518be6b update gcc-4.6
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff changeset
640 static __float128
561a7518be6b update gcc-4.6
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff changeset
641 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
642 {
561a7518be6b update gcc-4.6
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff changeset
643 __float128 y;
561a7518be6b update gcc-4.6
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff changeset
644
561a7518be6b update gcc-4.6
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff changeset
645 p += n;
561a7518be6b update gcc-4.6
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff changeset
646 y = *p--;
561a7518be6b update gcc-4.6
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff changeset
647 do
561a7518be6b update gcc-4.6
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff changeset
648 {
561a7518be6b update gcc-4.6
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff changeset
649 y = y * x + *p--;
561a7518be6b update gcc-4.6
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff changeset
650 }
561a7518be6b update gcc-4.6
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff changeset
651 while (--n > 0);
561a7518be6b update gcc-4.6
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff changeset
652 return y;
561a7518be6b update gcc-4.6
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff changeset
653 }
561a7518be6b update gcc-4.6
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff changeset
654
561a7518be6b update gcc-4.6
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff changeset
655
561a7518be6b update gcc-4.6
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff changeset
656 /* 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
657
561a7518be6b update gcc-4.6
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff changeset
658 static __float128
561a7518be6b update gcc-4.6
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff changeset
659 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
660 {
561a7518be6b update gcc-4.6
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff changeset
661 __float128 y;
561a7518be6b update gcc-4.6
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff changeset
662
561a7518be6b update gcc-4.6
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff changeset
663 p += n;
561a7518be6b update gcc-4.6
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff changeset
664 y = x + *p--;
561a7518be6b update gcc-4.6
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff changeset
665 do
561a7518be6b update gcc-4.6
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff changeset
666 {
561a7518be6b update gcc-4.6
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff changeset
667 y = y * x + *p--;
561a7518be6b update gcc-4.6
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff changeset
668 }
561a7518be6b update gcc-4.6
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff changeset
669 while (--n > 0);
561a7518be6b update gcc-4.6
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff changeset
670 return y;
561a7518be6b update gcc-4.6
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff changeset
671 }
561a7518be6b update gcc-4.6
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff changeset
672
561a7518be6b update gcc-4.6
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff changeset
673
561a7518be6b update gcc-4.6
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff changeset
674 /* Bessel function of the first kind, order zero. */
561a7518be6b update gcc-4.6
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff changeset
675
561a7518be6b update gcc-4.6
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff changeset
676 __float128
561a7518be6b update gcc-4.6
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff changeset
677 j0q (__float128 x)
561a7518be6b update gcc-4.6
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff changeset
678 {
561a7518be6b update gcc-4.6
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff changeset
679 __float128 xx, xinv, z, p, q, c, s, cc, ss;
561a7518be6b update gcc-4.6
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff changeset
680
561a7518be6b update gcc-4.6
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff changeset
681 if (! finiteq (x))
561a7518be6b update gcc-4.6
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff changeset
682 {
561a7518be6b update gcc-4.6
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff changeset
683 if (x != x)
111
kono
parents: 68
diff changeset
684 return x + x;
68
561a7518be6b update gcc-4.6
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff changeset
685 else
145
1830386684a0 gcc-9.2.0
anatofuz
parents: 111
diff changeset
686 return 0;
68
561a7518be6b update gcc-4.6
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff changeset
687 }
145
1830386684a0 gcc-9.2.0
anatofuz
parents: 111
diff changeset
688 if (x == 0)
1830386684a0 gcc-9.2.0
anatofuz
parents: 111
diff changeset
689 return 1;
68
561a7518be6b update gcc-4.6
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff changeset
690
561a7518be6b update gcc-4.6
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff changeset
691 xx = fabsq (x);
145
1830386684a0 gcc-9.2.0
anatofuz
parents: 111
diff changeset
692 if (xx <= 2)
68
561a7518be6b update gcc-4.6
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff changeset
693 {
111
kono
parents: 68
diff changeset
694 if (xx < 0x1p-57Q)
145
1830386684a0 gcc-9.2.0
anatofuz
parents: 111
diff changeset
695 return 1;
68
561a7518be6b update gcc-4.6
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff changeset
696 /* 0 <= x <= 2 */
561a7518be6b update gcc-4.6
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff changeset
697 z = xx * xx;
561a7518be6b update gcc-4.6
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff changeset
698 p = z * z * neval (z, J0_2N, NJ0_2N) / deval (z, J0_2D, NJ0_2D);
561a7518be6b update gcc-4.6
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff changeset
699 p -= 0.25Q * z;
145
1830386684a0 gcc-9.2.0
anatofuz
parents: 111
diff changeset
700 p += 1;
68
561a7518be6b update gcc-4.6
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff changeset
701 return p;
561a7518be6b update gcc-4.6
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff changeset
702 }
561a7518be6b update gcc-4.6
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff changeset
703
111
kono
parents: 68
diff changeset
704 /* X = x - pi/4
kono
parents: 68
diff changeset
705 cos(X) = cos(x) cos(pi/4) + sin(x) sin(pi/4)
kono
parents: 68
diff changeset
706 = 1/sqrt(2) * (cos(x) + sin(x))
kono
parents: 68
diff changeset
707 sin(X) = sin(x) cos(pi/4) - cos(x) sin(pi/4)
kono
parents: 68
diff changeset
708 = 1/sqrt(2) * (sin(x) - cos(x))
kono
parents: 68
diff changeset
709 sin(x) +- cos(x) = -cos(2x)/(sin(x) -+ cos(x))
kono
parents: 68
diff changeset
710 cf. Fdlibm. */
kono
parents: 68
diff changeset
711 sincosq (xx, &s, &c);
kono
parents: 68
diff changeset
712 ss = s - c;
kono
parents: 68
diff changeset
713 cc = s + c;
145
1830386684a0 gcc-9.2.0
anatofuz
parents: 111
diff changeset
714 if (xx <= FLT128_MAX / 2)
111
kono
parents: 68
diff changeset
715 {
kono
parents: 68
diff changeset
716 z = -cosq (xx + xx);
kono
parents: 68
diff changeset
717 if ((s * c) < 0)
kono
parents: 68
diff changeset
718 cc = z / ss;
kono
parents: 68
diff changeset
719 else
kono
parents: 68
diff changeset
720 ss = z / cc;
kono
parents: 68
diff changeset
721 }
kono
parents: 68
diff changeset
722
kono
parents: 68
diff changeset
723 if (xx > 0x1p256Q)
kono
parents: 68
diff changeset
724 return ONEOSQPI * cc / sqrtq (xx);
kono
parents: 68
diff changeset
725
145
1830386684a0 gcc-9.2.0
anatofuz
parents: 111
diff changeset
726 xinv = 1 / xx;
68
561a7518be6b update gcc-4.6
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff changeset
727 z = xinv * xinv;
561a7518be6b update gcc-4.6
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff changeset
728 if (xinv <= 0.25)
561a7518be6b update gcc-4.6
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff changeset
729 {
561a7518be6b update gcc-4.6
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff changeset
730 if (xinv <= 0.125)
561a7518be6b update gcc-4.6
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff changeset
731 {
561a7518be6b update gcc-4.6
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff changeset
732 if (xinv <= 0.0625)
561a7518be6b update gcc-4.6
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff changeset
733 {
561a7518be6b update gcc-4.6
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff changeset
734 p = neval (z, P16_IN, NP16_IN) / deval (z, P16_ID, NP16_ID);
561a7518be6b update gcc-4.6
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff changeset
735 q = neval (z, Q16_IN, NQ16_IN) / deval (z, Q16_ID, NQ16_ID);
561a7518be6b update gcc-4.6
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff changeset
736 }
561a7518be6b update gcc-4.6
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff changeset
737 else
561a7518be6b update gcc-4.6
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff changeset
738 {
561a7518be6b update gcc-4.6
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff changeset
739 p = neval (z, P8_16N, NP8_16N) / deval (z, P8_16D, NP8_16D);
561a7518be6b update gcc-4.6
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff changeset
740 q = neval (z, Q8_16N, NQ8_16N) / deval (z, Q8_16D, NQ8_16D);
561a7518be6b update gcc-4.6
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff changeset
741 }
561a7518be6b update gcc-4.6
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff changeset
742 }
561a7518be6b update gcc-4.6
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff changeset
743 else if (xinv <= 0.1875)
561a7518be6b update gcc-4.6
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff changeset
744 {
561a7518be6b update gcc-4.6
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff changeset
745 p = neval (z, P5_8N, NP5_8N) / deval (z, P5_8D, NP5_8D);
561a7518be6b update gcc-4.6
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff changeset
746 q = neval (z, Q5_8N, NQ5_8N) / deval (z, Q5_8D, NQ5_8D);
561a7518be6b update gcc-4.6
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff changeset
747 }
561a7518be6b update gcc-4.6
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff changeset
748 else
561a7518be6b update gcc-4.6
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff changeset
749 {
561a7518be6b update gcc-4.6
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff changeset
750 p = neval (z, P4_5N, NP4_5N) / deval (z, P4_5D, NP4_5D);
561a7518be6b update gcc-4.6
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff changeset
751 q = neval (z, Q4_5N, NQ4_5N) / deval (z, Q4_5D, NQ4_5D);
561a7518be6b update gcc-4.6
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff changeset
752 }
561a7518be6b update gcc-4.6
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff changeset
753 } /* .25 */
561a7518be6b update gcc-4.6
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff changeset
754 else /* if (xinv <= 0.5) */
561a7518be6b update gcc-4.6
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff changeset
755 {
561a7518be6b update gcc-4.6
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff changeset
756 if (xinv <= 0.375)
561a7518be6b update gcc-4.6
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff changeset
757 {
561a7518be6b update gcc-4.6
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff changeset
758 if (xinv <= 0.3125)
561a7518be6b update gcc-4.6
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff changeset
759 {
561a7518be6b update gcc-4.6
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff changeset
760 p = neval (z, P3r2_4N, NP3r2_4N) / deval (z, P3r2_4D, NP3r2_4D);
561a7518be6b update gcc-4.6
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff changeset
761 q = neval (z, Q3r2_4N, NQ3r2_4N) / deval (z, Q3r2_4D, NQ3r2_4D);
561a7518be6b update gcc-4.6
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff changeset
762 }
561a7518be6b update gcc-4.6
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff changeset
763 else
561a7518be6b update gcc-4.6
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff changeset
764 {
561a7518be6b update gcc-4.6
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff changeset
765 p = neval (z, P2r7_3r2N, NP2r7_3r2N)
561a7518be6b update gcc-4.6
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff changeset
766 / deval (z, P2r7_3r2D, NP2r7_3r2D);
561a7518be6b update gcc-4.6
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff changeset
767 q = neval (z, Q2r7_3r2N, NQ2r7_3r2N)
561a7518be6b update gcc-4.6
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff changeset
768 / deval (z, Q2r7_3r2D, NQ2r7_3r2D);
561a7518be6b update gcc-4.6
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff changeset
769 }
561a7518be6b update gcc-4.6
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff changeset
770 }
561a7518be6b update gcc-4.6
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff changeset
771 else if (xinv <= 0.4375)
561a7518be6b update gcc-4.6
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff changeset
772 {
561a7518be6b update gcc-4.6
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff changeset
773 p = neval (z, P2r3_2r7N, NP2r3_2r7N)
561a7518be6b update gcc-4.6
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff changeset
774 / deval (z, P2r3_2r7D, NP2r3_2r7D);
561a7518be6b update gcc-4.6
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff changeset
775 q = neval (z, Q2r3_2r7N, NQ2r3_2r7N)
561a7518be6b update gcc-4.6
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff changeset
776 / deval (z, Q2r3_2r7D, NQ2r3_2r7D);
561a7518be6b update gcc-4.6
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff changeset
777 }
561a7518be6b update gcc-4.6
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff changeset
778 else
561a7518be6b update gcc-4.6
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff changeset
779 {
561a7518be6b update gcc-4.6
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff changeset
780 p = neval (z, P2_2r3N, NP2_2r3N) / deval (z, P2_2r3D, NP2_2r3D);
561a7518be6b update gcc-4.6
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff changeset
781 q = neval (z, Q2_2r3N, NQ2_2r3N) / deval (z, Q2_2r3D, NQ2_2r3D);
561a7518be6b update gcc-4.6
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff changeset
782 }
561a7518be6b update gcc-4.6
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff changeset
783 }
145
1830386684a0 gcc-9.2.0
anatofuz
parents: 111
diff changeset
784 p = 1 + z * p;
68
561a7518be6b update gcc-4.6
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff changeset
785 q = z * xinv * q;
561a7518be6b update gcc-4.6
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff changeset
786 q = q - 0.125Q * xinv;
561a7518be6b update gcc-4.6
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff changeset
787 z = ONEOSQPI * (p * cc - q * ss) / sqrtq (xx);
561a7518be6b update gcc-4.6
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff changeset
788 return z;
561a7518be6b update gcc-4.6
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff changeset
789 }
561a7518be6b update gcc-4.6
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff changeset
790
561a7518be6b update gcc-4.6
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff changeset
791
145
1830386684a0 gcc-9.2.0
anatofuz
parents: 111
diff changeset
792
68
561a7518be6b update gcc-4.6
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff changeset
793 /* Y0(x) = 2/pi * log(x) * J0(x) + R(x^2)
561a7518be6b update gcc-4.6
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff changeset
794 Peak absolute error 1.7e-36 (relative where Y0 > 1)
561a7518be6b update gcc-4.6
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff changeset
795 0 <= x <= 2 */
561a7518be6b update gcc-4.6
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff changeset
796 #define NY0_2N 7
145
1830386684a0 gcc-9.2.0
anatofuz
parents: 111
diff changeset
797 static const __float128 Y0_2N[NY0_2N + 1] = {
68
561a7518be6b update gcc-4.6
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff changeset
798 -1.062023609591350692692296993537002558155E19Q,
561a7518be6b update gcc-4.6
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff changeset
799 2.542000883190248639104127452714966858866E19Q,
561a7518be6b update gcc-4.6
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff changeset
800 -1.984190771278515324281415820316054696545E18Q,
561a7518be6b update gcc-4.6
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff changeset
801 4.982586044371592942465373274440222033891E16Q,
561a7518be6b update gcc-4.6
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff changeset
802 -5.529326354780295177243773419090123407550E14Q,
561a7518be6b update gcc-4.6
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff changeset
803 3.013431465522152289279088265336861140391E12Q,
561a7518be6b update gcc-4.6
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff changeset
804 -7.959436160727126750732203098982718347785E9Q,
561a7518be6b update gcc-4.6
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff changeset
805 8.230845651379566339707130644134372793322E6Q,
561a7518be6b update gcc-4.6
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff changeset
806 };
561a7518be6b update gcc-4.6
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff changeset
807 #define NY0_2D 7
145
1830386684a0 gcc-9.2.0
anatofuz
parents: 111
diff changeset
808 static const __float128 Y0_2D[NY0_2D + 1] = {
68
561a7518be6b update gcc-4.6
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff changeset
809 1.438972634353286978700329883122253752192E20Q,
561a7518be6b update gcc-4.6
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff changeset
810 1.856409101981569254247700169486907405500E18Q,
561a7518be6b update gcc-4.6
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff changeset
811 1.219693352678218589553725579802986255614E16Q,
561a7518be6b update gcc-4.6
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff changeset
812 5.389428943282838648918475915779958097958E13Q,
561a7518be6b update gcc-4.6
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff changeset
813 1.774125762108874864433872173544743051653E11Q,
561a7518be6b update gcc-4.6
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff changeset
814 4.522104832545149534808218252434693007036E8Q,
561a7518be6b update gcc-4.6
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff changeset
815 8.872187401232943927082914504125234454930E5Q,
561a7518be6b update gcc-4.6
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff changeset
816 1.251945613186787532055610876304669413955E3Q,
561a7518be6b update gcc-4.6
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff changeset
817 /* 1.000000000000000000000000000000000000000E0 */
561a7518be6b update gcc-4.6
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff changeset
818 };
561a7518be6b update gcc-4.6
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff changeset
819
111
kono
parents: 68
diff changeset
820 static const __float128 U0 = -7.3804295108687225274343927948483016310862e-02Q;
68
561a7518be6b update gcc-4.6
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff changeset
821
561a7518be6b update gcc-4.6
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff changeset
822 /* Bessel function of the second kind, order zero. */
561a7518be6b update gcc-4.6
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff changeset
823
561a7518be6b update gcc-4.6
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff changeset
824 __float128
145
1830386684a0 gcc-9.2.0
anatofuz
parents: 111
diff changeset
825 y0q(__float128 x)
68
561a7518be6b update gcc-4.6
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff changeset
826 {
561a7518be6b update gcc-4.6
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff changeset
827 __float128 xx, xinv, z, p, q, c, s, cc, ss;
561a7518be6b update gcc-4.6
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff changeset
828
561a7518be6b update gcc-4.6
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff changeset
829 if (! finiteq (x))
111
kono
parents: 68
diff changeset
830 return 1 / (x + x * x);
145
1830386684a0 gcc-9.2.0
anatofuz
parents: 111
diff changeset
831 if (x <= 0)
68
561a7518be6b update gcc-4.6
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff changeset
832 {
145
1830386684a0 gcc-9.2.0
anatofuz
parents: 111
diff changeset
833 if (x < 0)
68
561a7518be6b update gcc-4.6
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff changeset
834 return (zero / (zero * x));
111
kono
parents: 68
diff changeset
835 return -1 / zero; /* -inf and divide by zero exception. */
68
561a7518be6b update gcc-4.6
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff changeset
836 }
561a7518be6b update gcc-4.6
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff changeset
837 xx = fabsq (x);
111
kono
parents: 68
diff changeset
838 if (xx <= 0x1p-57)
kono
parents: 68
diff changeset
839 return U0 + TWOOPI * logq (x);
145
1830386684a0 gcc-9.2.0
anatofuz
parents: 111
diff changeset
840 if (xx <= 2)
68
561a7518be6b update gcc-4.6
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff changeset
841 {
561a7518be6b update gcc-4.6
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff changeset
842 /* 0 <= x <= 2 */
561a7518be6b update gcc-4.6
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff changeset
843 z = xx * xx;
561a7518be6b update gcc-4.6
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff changeset
844 p = neval (z, Y0_2N, NY0_2N) / deval (z, Y0_2D, NY0_2D);
561a7518be6b update gcc-4.6
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff changeset
845 p = TWOOPI * logq (x) * j0q (x) + p;
561a7518be6b update gcc-4.6
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff changeset
846 return p;
561a7518be6b update gcc-4.6
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff changeset
847 }
561a7518be6b update gcc-4.6
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff changeset
848
111
kono
parents: 68
diff changeset
849 /* X = x - pi/4
kono
parents: 68
diff changeset
850 cos(X) = cos(x) cos(pi/4) + sin(x) sin(pi/4)
kono
parents: 68
diff changeset
851 = 1/sqrt(2) * (cos(x) + sin(x))
kono
parents: 68
diff changeset
852 sin(X) = sin(x) cos(pi/4) - cos(x) sin(pi/4)
kono
parents: 68
diff changeset
853 = 1/sqrt(2) * (sin(x) - cos(x))
kono
parents: 68
diff changeset
854 sin(x) +- cos(x) = -cos(2x)/(sin(x) -+ cos(x))
kono
parents: 68
diff changeset
855 cf. Fdlibm. */
kono
parents: 68
diff changeset
856 sincosq (x, &s, &c);
kono
parents: 68
diff changeset
857 ss = s - c;
kono
parents: 68
diff changeset
858 cc = s + c;
145
1830386684a0 gcc-9.2.0
anatofuz
parents: 111
diff changeset
859 if (xx <= FLT128_MAX / 2)
111
kono
parents: 68
diff changeset
860 {
kono
parents: 68
diff changeset
861 z = -cosq (x + x);
kono
parents: 68
diff changeset
862 if ((s * c) < 0)
kono
parents: 68
diff changeset
863 cc = z / ss;
kono
parents: 68
diff changeset
864 else
kono
parents: 68
diff changeset
865 ss = z / cc;
kono
parents: 68
diff changeset
866 }
kono
parents: 68
diff changeset
867
kono
parents: 68
diff changeset
868 if (xx > 0x1p256Q)
kono
parents: 68
diff changeset
869 return ONEOSQPI * ss / sqrtq (x);
kono
parents: 68
diff changeset
870
145
1830386684a0 gcc-9.2.0
anatofuz
parents: 111
diff changeset
871 xinv = 1 / xx;
68
561a7518be6b update gcc-4.6
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff changeset
872 z = xinv * xinv;
561a7518be6b update gcc-4.6
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff changeset
873 if (xinv <= 0.25)
561a7518be6b update gcc-4.6
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff changeset
874 {
561a7518be6b update gcc-4.6
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff changeset
875 if (xinv <= 0.125)
561a7518be6b update gcc-4.6
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff changeset
876 {
561a7518be6b update gcc-4.6
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff changeset
877 if (xinv <= 0.0625)
561a7518be6b update gcc-4.6
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff changeset
878 {
561a7518be6b update gcc-4.6
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff changeset
879 p = neval (z, P16_IN, NP16_IN) / deval (z, P16_ID, NP16_ID);
561a7518be6b update gcc-4.6
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff changeset
880 q = neval (z, Q16_IN, NQ16_IN) / deval (z, Q16_ID, NQ16_ID);
561a7518be6b update gcc-4.6
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff changeset
881 }
561a7518be6b update gcc-4.6
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff changeset
882 else
561a7518be6b update gcc-4.6
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff changeset
883 {
561a7518be6b update gcc-4.6
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff changeset
884 p = neval (z, P8_16N, NP8_16N) / deval (z, P8_16D, NP8_16D);
561a7518be6b update gcc-4.6
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff changeset
885 q = neval (z, Q8_16N, NQ8_16N) / deval (z, Q8_16D, NQ8_16D);
561a7518be6b update gcc-4.6
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff changeset
886 }
561a7518be6b update gcc-4.6
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff changeset
887 }
561a7518be6b update gcc-4.6
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff changeset
888 else if (xinv <= 0.1875)
561a7518be6b update gcc-4.6
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff changeset
889 {
561a7518be6b update gcc-4.6
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff changeset
890 p = neval (z, P5_8N, NP5_8N) / deval (z, P5_8D, NP5_8D);
561a7518be6b update gcc-4.6
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff changeset
891 q = neval (z, Q5_8N, NQ5_8N) / deval (z, Q5_8D, NQ5_8D);
561a7518be6b update gcc-4.6
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff changeset
892 }
561a7518be6b update gcc-4.6
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff changeset
893 else
561a7518be6b update gcc-4.6
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff changeset
894 {
561a7518be6b update gcc-4.6
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff changeset
895 p = neval (z, P4_5N, NP4_5N) / deval (z, P4_5D, NP4_5D);
561a7518be6b update gcc-4.6
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff changeset
896 q = neval (z, Q4_5N, NQ4_5N) / deval (z, Q4_5D, NQ4_5D);
561a7518be6b update gcc-4.6
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff changeset
897 }
561a7518be6b update gcc-4.6
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff changeset
898 } /* .25 */
561a7518be6b update gcc-4.6
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff changeset
899 else /* if (xinv <= 0.5) */
561a7518be6b update gcc-4.6
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff changeset
900 {
561a7518be6b update gcc-4.6
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff changeset
901 if (xinv <= 0.375)
561a7518be6b update gcc-4.6
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff changeset
902 {
561a7518be6b update gcc-4.6
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff changeset
903 if (xinv <= 0.3125)
561a7518be6b update gcc-4.6
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff changeset
904 {
561a7518be6b update gcc-4.6
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff changeset
905 p = neval (z, P3r2_4N, NP3r2_4N) / deval (z, P3r2_4D, NP3r2_4D);
561a7518be6b update gcc-4.6
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff changeset
906 q = neval (z, Q3r2_4N, NQ3r2_4N) / deval (z, Q3r2_4D, NQ3r2_4D);
561a7518be6b update gcc-4.6
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff changeset
907 }
561a7518be6b update gcc-4.6
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff changeset
908 else
561a7518be6b update gcc-4.6
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff changeset
909 {
561a7518be6b update gcc-4.6
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff changeset
910 p = neval (z, P2r7_3r2N, NP2r7_3r2N)
561a7518be6b update gcc-4.6
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff changeset
911 / deval (z, P2r7_3r2D, NP2r7_3r2D);
561a7518be6b update gcc-4.6
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff changeset
912 q = neval (z, Q2r7_3r2N, NQ2r7_3r2N)
561a7518be6b update gcc-4.6
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff changeset
913 / deval (z, Q2r7_3r2D, NQ2r7_3r2D);
561a7518be6b update gcc-4.6
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff changeset
914 }
561a7518be6b update gcc-4.6
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff changeset
915 }
561a7518be6b update gcc-4.6
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff changeset
916 else if (xinv <= 0.4375)
561a7518be6b update gcc-4.6
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff changeset
917 {
561a7518be6b update gcc-4.6
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff changeset
918 p = neval (z, P2r3_2r7N, NP2r3_2r7N)
561a7518be6b update gcc-4.6
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff changeset
919 / deval (z, P2r3_2r7D, NP2r3_2r7D);
561a7518be6b update gcc-4.6
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff changeset
920 q = neval (z, Q2r3_2r7N, NQ2r3_2r7N)
561a7518be6b update gcc-4.6
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff changeset
921 / deval (z, Q2r3_2r7D, NQ2r3_2r7D);
561a7518be6b update gcc-4.6
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff changeset
922 }
561a7518be6b update gcc-4.6
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff changeset
923 else
561a7518be6b update gcc-4.6
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff changeset
924 {
561a7518be6b update gcc-4.6
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff changeset
925 p = neval (z, P2_2r3N, NP2_2r3N) / deval (z, P2_2r3D, NP2_2r3D);
561a7518be6b update gcc-4.6
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff changeset
926 q = neval (z, Q2_2r3N, NQ2_2r3N) / deval (z, Q2_2r3D, NQ2_2r3D);
561a7518be6b update gcc-4.6
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff changeset
927 }
561a7518be6b update gcc-4.6
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff changeset
928 }
145
1830386684a0 gcc-9.2.0
anatofuz
parents: 111
diff changeset
929 p = 1 + z * p;
68
561a7518be6b update gcc-4.6
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff changeset
930 q = z * xinv * q;
561a7518be6b update gcc-4.6
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff changeset
931 q = q - 0.125Q * xinv;
561a7518be6b update gcc-4.6
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff changeset
932 z = ONEOSQPI * (p * ss + q * cc) / sqrtq (x);
561a7518be6b update gcc-4.6
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff changeset
933 return z;
561a7518be6b update gcc-4.6
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff changeset
934 }