68
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff
changeset
|
1 /* lgammal
|
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff
changeset
|
2 *
|
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff
changeset
|
3 * Natural logarithm of gamma function
|
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff
changeset
|
4 *
|
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff
changeset
|
5 *
|
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff
changeset
|
6 *
|
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff
changeset
|
7 * SYNOPSIS:
|
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff
changeset
|
8 *
|
145
|
9 * long double x, y, lgammal();
|
68
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff
changeset
|
10 * extern int sgngam;
|
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff
changeset
|
11 *
|
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff
changeset
|
12 * y = lgammal(x);
|
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff
changeset
|
13 *
|
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff
changeset
|
14 *
|
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff
changeset
|
15 *
|
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff
changeset
|
16 * DESCRIPTION:
|
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff
changeset
|
17 *
|
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff
changeset
|
18 * Returns the base e (2.718...) logarithm of the absolute
|
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff
changeset
|
19 * value of the gamma function of the argument.
|
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff
changeset
|
20 * The sign (+1 or -1) of the gamma function is returned in a
|
145
|
21 * global (extern) variable named sgngam.
|
68
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff
changeset
|
22 *
|
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff
changeset
|
23 * The positive domain is partitioned into numerous segments for approximation.
|
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff
changeset
|
24 * For x > 10,
|
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff
changeset
|
25 * log gamma(x) = (x - 0.5) log(x) - x + log sqrt(2 pi) + 1/x R(1/x^2)
|
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff
changeset
|
26 * Near the minimum at x = x0 = 1.46... the approximation is
|
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff
changeset
|
27 * log gamma(x0 + z) = log gamma(x0) + z^2 P(z)/Q(z)
|
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff
changeset
|
28 * for small z.
|
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff
changeset
|
29 * Elsewhere between 0 and 10,
|
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff
changeset
|
30 * log gamma(n + z) = log gamma(n) + z P(z)/Q(z)
|
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff
changeset
|
31 * for various selected n and small z.
|
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff
changeset
|
32 *
|
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff
changeset
|
33 * The cosecant reflection formula is employed for negative arguments.
|
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff
changeset
|
34 *
|
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff
changeset
|
35 *
|
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff
changeset
|
36 *
|
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff
changeset
|
37 * ACCURACY:
|
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff
changeset
|
38 *
|
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff
changeset
|
39 *
|
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff
changeset
|
40 * arithmetic domain # trials peak rms
|
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff
changeset
|
41 * Relative error:
|
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff
changeset
|
42 * IEEE 10, 30 100000 3.9e-34 9.8e-35
|
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff
changeset
|
43 * IEEE 0, 10 100000 3.8e-34 5.3e-35
|
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff
changeset
|
44 * Absolute error:
|
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff
changeset
|
45 * IEEE -10, 0 100000 8.0e-34 8.0e-35
|
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff
changeset
|
46 * IEEE -30, -10 100000 4.4e-34 1.0e-34
|
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff
changeset
|
47 * IEEE -100, 100 100000 1.0e-34
|
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff
changeset
|
48 *
|
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff
changeset
|
49 * The absolute error criterion is the same as relative error
|
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff
changeset
|
50 * when the function magnitude is greater than one but it is absolute
|
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff
changeset
|
51 * when the magnitude is less than one.
|
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff
changeset
|
52 *
|
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff
changeset
|
53 */
|
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff
changeset
|
54
|
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff
changeset
|
55 /* Copyright 2001 by Stephen L. Moshier <moshier@na-net.ornl.gov>
|
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff
changeset
|
56
|
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff
changeset
|
57 This library is free software; you can redistribute it and/or
|
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff
changeset
|
58 modify it under the terms of the GNU Lesser General Public
|
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff
changeset
|
59 License as published by the Free Software Foundation; either
|
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff
changeset
|
60 version 2.1 of the License, or (at your option) any later version.
|
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff
changeset
|
61
|
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff
changeset
|
62 This library is distributed in the hope that it will be useful,
|
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff
changeset
|
63 but WITHOUT ANY WARRANTY; without even the implied warranty of
|
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff
changeset
|
64 MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU
|
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff
changeset
|
65 Lesser General Public License for more details.
|
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff
changeset
|
66
|
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff
changeset
|
67 You should have received a copy of the GNU Lesser General Public
|
145
|
68 License along with this library; if not, see
|
|
69 <http://www.gnu.org/licenses/>. */
|
68
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff
changeset
|
70
|
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff
changeset
|
71 #include "quadmath-imp.h"
|
111
|
72 #ifdef HAVE_MATH_H_SIGNGAM
|
145
|
73 # include <math.h>
|
111
|
74 #endif
|
145
|
75 __float128
|
|
76 lgammaq (__float128 x)
|
|
77 {
|
|
78 #ifndef HAVE_MATH_H_SIGNGAM
|
|
79 int signgam;
|
|
80 #endif
|
|
81 return __quadmath_lgammaq_r (x, &signgam);
|
|
82 }
|
111
|
83
|
145
|
84 static const __float128 PIL = 3.1415926535897932384626433832795028841972E0Q;
|
68
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff
changeset
|
85 static const __float128 MAXLGM = 1.0485738685148938358098967157129705071571E4928Q;
|
145
|
86 static const __float128 one = 1;
|
|
87 static const __float128 huge = FLT128_MAX;
|
68
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff
changeset
|
88
|
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff
changeset
|
89 /* log gamma(x) = ( x - 0.5 ) * log(x) - x + LS2PI + 1/x P(1/x^2)
|
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff
changeset
|
90 1/x <= 0.0741 (x >= 13.495...)
|
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff
changeset
|
91 Peak relative error 1.5e-36 */
|
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff
changeset
|
92 static const __float128 ls2pi = 9.1893853320467274178032973640561763986140E-1Q;
|
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff
changeset
|
93 #define NRASY 12
|
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff
changeset
|
94 static const __float128 RASY[NRASY + 1] =
|
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff
changeset
|
95 {
|
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff
changeset
|
96 8.333333333333333333333333333310437112111E-2Q,
|
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff
changeset
|
97 -2.777777777777777777777774789556228296902E-3Q,
|
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff
changeset
|
98 7.936507936507936507795933938448586499183E-4Q,
|
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff
changeset
|
99 -5.952380952380952041799269756378148574045E-4Q,
|
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff
changeset
|
100 8.417508417507928904209891117498524452523E-4Q,
|
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff
changeset
|
101 -1.917526917481263997778542329739806086290E-3Q,
|
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff
changeset
|
102 6.410256381217852504446848671499409919280E-3Q,
|
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff
changeset
|
103 -2.955064066900961649768101034477363301626E-2Q,
|
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff
changeset
|
104 1.796402955865634243663453415388336954675E-1Q,
|
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff
changeset
|
105 -1.391522089007758553455753477688592767741E0Q,
|
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff
changeset
|
106 1.326130089598399157988112385013829305510E1Q,
|
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff
changeset
|
107 -1.420412699593782497803472576479997819149E2Q,
|
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff
changeset
|
108 1.218058922427762808938869872528846787020E3Q
|
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff
changeset
|
109 };
|
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff
changeset
|
110
|
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff
changeset
|
111
|
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff
changeset
|
112 /* log gamma(x+13) = log gamma(13) + x P(x)/Q(x)
|
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff
changeset
|
113 -0.5 <= x <= 0.5
|
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff
changeset
|
114 12.5 <= x+13 <= 13.5
|
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff
changeset
|
115 Peak relative error 1.1e-36 */
|
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff
changeset
|
116 static const __float128 lgam13a = 1.9987213134765625E1Q;
|
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff
changeset
|
117 static const __float128 lgam13b = 1.3608962611495173623870550785125024484248E-6Q;
|
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff
changeset
|
118 #define NRN13 7
|
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff
changeset
|
119 static const __float128 RN13[NRN13 + 1] =
|
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff
changeset
|
120 {
|
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff
changeset
|
121 8.591478354823578150238226576156275285700E11Q,
|
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff
changeset
|
122 2.347931159756482741018258864137297157668E11Q,
|
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff
changeset
|
123 2.555408396679352028680662433943000804616E10Q,
|
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff
changeset
|
124 1.408581709264464345480765758902967123937E9Q,
|
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff
changeset
|
125 4.126759849752613822953004114044451046321E7Q,
|
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff
changeset
|
126 6.133298899622688505854211579222889943778E5Q,
|
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff
changeset
|
127 3.929248056293651597987893340755876578072E3Q,
|
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff
changeset
|
128 6.850783280018706668924952057996075215223E0Q
|
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff
changeset
|
129 };
|
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff
changeset
|
130 #define NRD13 6
|
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff
changeset
|
131 static const __float128 RD13[NRD13 + 1] =
|
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff
changeset
|
132 {
|
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff
changeset
|
133 3.401225382297342302296607039352935541669E11Q,
|
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff
changeset
|
134 8.756765276918037910363513243563234551784E10Q,
|
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff
changeset
|
135 8.873913342866613213078554180987647243903E9Q,
|
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff
changeset
|
136 4.483797255342763263361893016049310017973E8Q,
|
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff
changeset
|
137 1.178186288833066430952276702931512870676E7Q,
|
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff
changeset
|
138 1.519928623743264797939103740132278337476E5Q,
|
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff
changeset
|
139 7.989298844938119228411117593338850892311E2Q
|
145
|
140 /* 1.0E0L */
|
68
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff
changeset
|
141 };
|
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff
changeset
|
142
|
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff
changeset
|
143
|
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff
changeset
|
144 /* log gamma(x+12) = log gamma(12) + x P(x)/Q(x)
|
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff
changeset
|
145 -0.5 <= x <= 0.5
|
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff
changeset
|
146 11.5 <= x+12 <= 12.5
|
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff
changeset
|
147 Peak relative error 4.1e-36 */
|
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff
changeset
|
148 static const __float128 lgam12a = 1.75023040771484375E1Q;
|
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff
changeset
|
149 static const __float128 lgam12b = 3.7687254483392876529072161996717039575982E-6Q;
|
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff
changeset
|
150 #define NRN12 7
|
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff
changeset
|
151 static const __float128 RN12[NRN12 + 1] =
|
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff
changeset
|
152 {
|
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff
changeset
|
153 4.709859662695606986110997348630997559137E11Q,
|
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff
changeset
|
154 1.398713878079497115037857470168777995230E11Q,
|
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff
changeset
|
155 1.654654931821564315970930093932954900867E10Q,
|
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff
changeset
|
156 9.916279414876676861193649489207282144036E8Q,
|
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff
changeset
|
157 3.159604070526036074112008954113411389879E7Q,
|
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff
changeset
|
158 5.109099197547205212294747623977502492861E5Q,
|
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff
changeset
|
159 3.563054878276102790183396740969279826988E3Q,
|
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff
changeset
|
160 6.769610657004672719224614163196946862747E0Q
|
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff
changeset
|
161 };
|
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff
changeset
|
162 #define NRD12 6
|
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff
changeset
|
163 static const __float128 RD12[NRD12 + 1] =
|
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff
changeset
|
164 {
|
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff
changeset
|
165 1.928167007860968063912467318985802726613E11Q,
|
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff
changeset
|
166 5.383198282277806237247492369072266389233E10Q,
|
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff
changeset
|
167 5.915693215338294477444809323037871058363E9Q,
|
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff
changeset
|
168 3.241438287570196713148310560147925781342E8Q,
|
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff
changeset
|
169 9.236680081763754597872713592701048455890E6Q,
|
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff
changeset
|
170 1.292246897881650919242713651166596478850E5Q,
|
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff
changeset
|
171 7.366532445427159272584194816076600211171E2Q
|
145
|
172 /* 1.0E0L */
|
68
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff
changeset
|
173 };
|
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff
changeset
|
174
|
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff
changeset
|
175
|
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff
changeset
|
176 /* log gamma(x+11) = log gamma(11) + x P(x)/Q(x)
|
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff
changeset
|
177 -0.5 <= x <= 0.5
|
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff
changeset
|
178 10.5 <= x+11 <= 11.5
|
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff
changeset
|
179 Peak relative error 1.8e-35 */
|
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff
changeset
|
180 static const __float128 lgam11a = 1.5104400634765625E1Q;
|
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff
changeset
|
181 static const __float128 lgam11b = 1.1938309890295225709329251070371882250744E-5Q;
|
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff
changeset
|
182 #define NRN11 7
|
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff
changeset
|
183 static const __float128 RN11[NRN11 + 1] =
|
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff
changeset
|
184 {
|
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff
changeset
|
185 2.446960438029415837384622675816736622795E11Q,
|
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff
changeset
|
186 7.955444974446413315803799763901729640350E10Q,
|
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff
changeset
|
187 1.030555327949159293591618473447420338444E10Q,
|
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff
changeset
|
188 6.765022131195302709153994345470493334946E8Q,
|
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff
changeset
|
189 2.361892792609204855279723576041468347494E7Q,
|
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff
changeset
|
190 4.186623629779479136428005806072176490125E5Q,
|
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff
changeset
|
191 3.202506022088912768601325534149383594049E3Q,
|
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff
changeset
|
192 6.681356101133728289358838690666225691363E0Q
|
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff
changeset
|
193 };
|
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff
changeset
|
194 #define NRD11 6
|
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff
changeset
|
195 static const __float128 RD11[NRD11 + 1] =
|
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff
changeset
|
196 {
|
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff
changeset
|
197 1.040483786179428590683912396379079477432E11Q,
|
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff
changeset
|
198 3.172251138489229497223696648369823779729E10Q,
|
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff
changeset
|
199 3.806961885984850433709295832245848084614E9Q,
|
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff
changeset
|
200 2.278070344022934913730015420611609620171E8Q,
|
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff
changeset
|
201 7.089478198662651683977290023829391596481E6Q,
|
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff
changeset
|
202 1.083246385105903533237139380509590158658E5Q,
|
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff
changeset
|
203 6.744420991491385145885727942219463243597E2Q
|
145
|
204 /* 1.0E0L */
|
68
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff
changeset
|
205 };
|
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff
changeset
|
206
|
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff
changeset
|
207
|
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff
changeset
|
208 /* log gamma(x+10) = log gamma(10) + x P(x)/Q(x)
|
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff
changeset
|
209 -0.5 <= x <= 0.5
|
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff
changeset
|
210 9.5 <= x+10 <= 10.5
|
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff
changeset
|
211 Peak relative error 5.4e-37 */
|
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff
changeset
|
212 static const __float128 lgam10a = 1.280181884765625E1Q;
|
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff
changeset
|
213 static const __float128 lgam10b = 8.6324252196112077178745667061642811492557E-6Q;
|
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff
changeset
|
214 #define NRN10 7
|
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff
changeset
|
215 static const __float128 RN10[NRN10 + 1] =
|
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff
changeset
|
216 {
|
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff
changeset
|
217 -1.239059737177249934158597996648808363783E14Q,
|
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff
changeset
|
218 -4.725899566371458992365624673357356908719E13Q,
|
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff
changeset
|
219 -7.283906268647083312042059082837754850808E12Q,
|
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff
changeset
|
220 -5.802855515464011422171165179767478794637E11Q,
|
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff
changeset
|
221 -2.532349691157548788382820303182745897298E10Q,
|
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff
changeset
|
222 -5.884260178023777312587193693477072061820E8Q,
|
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff
changeset
|
223 -6.437774864512125749845840472131829114906E6Q,
|
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff
changeset
|
224 -2.350975266781548931856017239843273049384E4Q
|
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff
changeset
|
225 };
|
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff
changeset
|
226 #define NRD10 7
|
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff
changeset
|
227 static const __float128 RD10[NRD10 + 1] =
|
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff
changeset
|
228 {
|
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff
changeset
|
229 -5.502645997581822567468347817182347679552E13Q,
|
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff
changeset
|
230 -1.970266640239849804162284805400136473801E13Q,
|
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff
changeset
|
231 -2.819677689615038489384974042561531409392E12Q,
|
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff
changeset
|
232 -2.056105863694742752589691183194061265094E11Q,
|
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff
changeset
|
233 -8.053670086493258693186307810815819662078E9Q,
|
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff
changeset
|
234 -1.632090155573373286153427982504851867131E8Q,
|
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff
changeset
|
235 -1.483575879240631280658077826889223634921E6Q,
|
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff
changeset
|
236 -4.002806669713232271615885826373550502510E3Q
|
145
|
237 /* 1.0E0L */
|
68
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff
changeset
|
238 };
|
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff
changeset
|
239
|
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff
changeset
|
240
|
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff
changeset
|
241 /* log gamma(x+9) = log gamma(9) + x P(x)/Q(x)
|
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff
changeset
|
242 -0.5 <= x <= 0.5
|
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff
changeset
|
243 8.5 <= x+9 <= 9.5
|
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff
changeset
|
244 Peak relative error 3.6e-36 */
|
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff
changeset
|
245 static const __float128 lgam9a = 1.06045989990234375E1Q;
|
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff
changeset
|
246 static const __float128 lgam9b = 3.9037218127284172274007216547549861681400E-6Q;
|
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff
changeset
|
247 #define NRN9 7
|
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff
changeset
|
248 static const __float128 RN9[NRN9 + 1] =
|
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff
changeset
|
249 {
|
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff
changeset
|
250 -4.936332264202687973364500998984608306189E13Q,
|
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff
changeset
|
251 -2.101372682623700967335206138517766274855E13Q,
|
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff
changeset
|
252 -3.615893404644823888655732817505129444195E12Q,
|
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff
changeset
|
253 -3.217104993800878891194322691860075472926E11Q,
|
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff
changeset
|
254 -1.568465330337375725685439173603032921399E10Q,
|
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff
changeset
|
255 -4.073317518162025744377629219101510217761E8Q,
|
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff
changeset
|
256 -4.983232096406156139324846656819246974500E6Q,
|
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff
changeset
|
257 -2.036280038903695980912289722995505277253E4Q
|
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff
changeset
|
258 };
|
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff
changeset
|
259 #define NRD9 7
|
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff
changeset
|
260 static const __float128 RD9[NRD9 + 1] =
|
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff
changeset
|
261 {
|
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff
changeset
|
262 -2.306006080437656357167128541231915480393E13Q,
|
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff
changeset
|
263 -9.183606842453274924895648863832233799950E12Q,
|
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff
changeset
|
264 -1.461857965935942962087907301194381010380E12Q,
|
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff
changeset
|
265 -1.185728254682789754150068652663124298303E11Q,
|
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff
changeset
|
266 -5.166285094703468567389566085480783070037E9Q,
|
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff
changeset
|
267 -1.164573656694603024184768200787835094317E8Q,
|
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff
changeset
|
268 -1.177343939483908678474886454113163527909E6Q,
|
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff
changeset
|
269 -3.529391059783109732159524500029157638736E3Q
|
145
|
270 /* 1.0E0L */
|
68
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff
changeset
|
271 };
|
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff
changeset
|
272
|
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff
changeset
|
273
|
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff
changeset
|
274 /* log gamma(x+8) = log gamma(8) + x P(x)/Q(x)
|
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff
changeset
|
275 -0.5 <= x <= 0.5
|
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff
changeset
|
276 7.5 <= x+8 <= 8.5
|
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff
changeset
|
277 Peak relative error 2.4e-37 */
|
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff
changeset
|
278 static const __float128 lgam8a = 8.525146484375E0Q;
|
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff
changeset
|
279 static const __float128 lgam8b = 1.4876690414300165531036347125050759667737E-5Q;
|
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff
changeset
|
280 #define NRN8 8
|
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff
changeset
|
281 static const __float128 RN8[NRN8 + 1] =
|
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff
changeset
|
282 {
|
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff
changeset
|
283 6.600775438203423546565361176829139703289E11Q,
|
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff
changeset
|
284 3.406361267593790705240802723914281025800E11Q,
|
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff
changeset
|
285 7.222460928505293914746983300555538432830E10Q,
|
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff
changeset
|
286 8.102984106025088123058747466840656458342E9Q,
|
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff
changeset
|
287 5.157620015986282905232150979772409345927E8Q,
|
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff
changeset
|
288 1.851445288272645829028129389609068641517E7Q,
|
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff
changeset
|
289 3.489261702223124354745894067468953756656E5Q,
|
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff
changeset
|
290 2.892095396706665774434217489775617756014E3Q,
|
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff
changeset
|
291 6.596977510622195827183948478627058738034E0Q
|
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff
changeset
|
292 };
|
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff
changeset
|
293 #define NRD8 7
|
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff
changeset
|
294 static const __float128 RD8[NRD8 + 1] =
|
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff
changeset
|
295 {
|
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff
changeset
|
296 3.274776546520735414638114828622673016920E11Q,
|
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff
changeset
|
297 1.581811207929065544043963828487733970107E11Q,
|
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff
changeset
|
298 3.108725655667825188135393076860104546416E10Q,
|
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff
changeset
|
299 3.193055010502912617128480163681842165730E9Q,
|
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff
changeset
|
300 1.830871482669835106357529710116211541839E8Q,
|
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff
changeset
|
301 5.790862854275238129848491555068073485086E6Q,
|
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff
changeset
|
302 9.305213264307921522842678835618803553589E4Q,
|
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff
changeset
|
303 6.216974105861848386918949336819572333622E2Q
|
145
|
304 /* 1.0E0L */
|
68
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff
changeset
|
305 };
|
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff
changeset
|
306
|
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff
changeset
|
307
|
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff
changeset
|
308 /* log gamma(x+7) = log gamma(7) + x P(x)/Q(x)
|
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff
changeset
|
309 -0.5 <= x <= 0.5
|
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff
changeset
|
310 6.5 <= x+7 <= 7.5
|
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff
changeset
|
311 Peak relative error 3.2e-36 */
|
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff
changeset
|
312 static const __float128 lgam7a = 6.5792388916015625E0Q;
|
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff
changeset
|
313 static const __float128 lgam7b = 1.2320408538495060178292903945321122583007E-5Q;
|
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff
changeset
|
314 #define NRN7 8
|
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff
changeset
|
315 static const __float128 RN7[NRN7 + 1] =
|
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff
changeset
|
316 {
|
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff
changeset
|
317 2.065019306969459407636744543358209942213E11Q,
|
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff
changeset
|
318 1.226919919023736909889724951708796532847E11Q,
|
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff
changeset
|
319 2.996157990374348596472241776917953749106E10Q,
|
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff
changeset
|
320 3.873001919306801037344727168434909521030E9Q,
|
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff
changeset
|
321 2.841575255593761593270885753992732145094E8Q,
|
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff
changeset
|
322 1.176342515359431913664715324652399565551E7Q,
|
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff
changeset
|
323 2.558097039684188723597519300356028511547E5Q,
|
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff
changeset
|
324 2.448525238332609439023786244782810774702E3Q,
|
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff
changeset
|
325 6.460280377802030953041566617300902020435E0Q
|
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff
changeset
|
326 };
|
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff
changeset
|
327 #define NRD7 7
|
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff
changeset
|
328 static const __float128 RD7[NRD7 + 1] =
|
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff
changeset
|
329 {
|
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff
changeset
|
330 1.102646614598516998880874785339049304483E11Q,
|
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff
changeset
|
331 6.099297512712715445879759589407189290040E10Q,
|
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff
changeset
|
332 1.372898136289611312713283201112060238351E10Q,
|
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff
changeset
|
333 1.615306270420293159907951633566635172343E9Q,
|
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff
changeset
|
334 1.061114435798489135996614242842561967459E8Q,
|
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff
changeset
|
335 3.845638971184305248268608902030718674691E6Q,
|
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff
changeset
|
336 7.081730675423444975703917836972720495507E4Q,
|
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff
changeset
|
337 5.423122582741398226693137276201344096370E2Q
|
145
|
338 /* 1.0E0L */
|
68
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff
changeset
|
339 };
|
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff
changeset
|
340
|
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff
changeset
|
341
|
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff
changeset
|
342 /* log gamma(x+6) = log gamma(6) + x P(x)/Q(x)
|
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff
changeset
|
343 -0.5 <= x <= 0.5
|
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff
changeset
|
344 5.5 <= x+6 <= 6.5
|
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff
changeset
|
345 Peak relative error 6.2e-37 */
|
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff
changeset
|
346 static const __float128 lgam6a = 4.7874908447265625E0Q;
|
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff
changeset
|
347 static const __float128 lgam6b = 8.9805548349424770093452324304839959231517E-7Q;
|
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff
changeset
|
348 #define NRN6 8
|
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff
changeset
|
349 static const __float128 RN6[NRN6 + 1] =
|
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff
changeset
|
350 {
|
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff
changeset
|
351 -3.538412754670746879119162116819571823643E13Q,
|
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff
changeset
|
352 -2.613432593406849155765698121483394257148E13Q,
|
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff
changeset
|
353 -8.020670732770461579558867891923784753062E12Q,
|
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff
changeset
|
354 -1.322227822931250045347591780332435433420E12Q,
|
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff
changeset
|
355 -1.262809382777272476572558806855377129513E11Q,
|
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff
changeset
|
356 -7.015006277027660872284922325741197022467E9Q,
|
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff
changeset
|
357 -2.149320689089020841076532186783055727299E8Q,
|
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff
changeset
|
358 -3.167210585700002703820077565539658995316E6Q,
|
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff
changeset
|
359 -1.576834867378554185210279285358586385266E4Q
|
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff
changeset
|
360 };
|
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff
changeset
|
361 #define NRD6 8
|
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff
changeset
|
362 static const __float128 RD6[NRD6 + 1] =
|
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff
changeset
|
363 {
|
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff
changeset
|
364 -2.073955870771283609792355579558899389085E13Q,
|
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff
changeset
|
365 -1.421592856111673959642750863283919318175E13Q,
|
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff
changeset
|
366 -4.012134994918353924219048850264207074949E12Q,
|
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff
changeset
|
367 -6.013361045800992316498238470888523722431E11Q,
|
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff
changeset
|
368 -5.145382510136622274784240527039643430628E10Q,
|
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff
changeset
|
369 -2.510575820013409711678540476918249524123E9Q,
|
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff
changeset
|
370 -6.564058379709759600836745035871373240904E7Q,
|
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff
changeset
|
371 -7.861511116647120540275354855221373571536E5Q,
|
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff
changeset
|
372 -2.821943442729620524365661338459579270561E3Q
|
145
|
373 /* 1.0E0L */
|
68
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff
changeset
|
374 };
|
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff
changeset
|
375
|
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff
changeset
|
376
|
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff
changeset
|
377 /* log gamma(x+5) = log gamma(5) + x P(x)/Q(x)
|
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff
changeset
|
378 -0.5 <= x <= 0.5
|
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff
changeset
|
379 4.5 <= x+5 <= 5.5
|
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff
changeset
|
380 Peak relative error 3.4e-37 */
|
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff
changeset
|
381 static const __float128 lgam5a = 3.17803955078125E0Q;
|
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff
changeset
|
382 static const __float128 lgam5b = 1.4279566695619646941601297055408873990961E-5Q;
|
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff
changeset
|
383 #define NRN5 9
|
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff
changeset
|
384 static const __float128 RN5[NRN5 + 1] =
|
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff
changeset
|
385 {
|
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff
changeset
|
386 2.010952885441805899580403215533972172098E11Q,
|
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff
changeset
|
387 1.916132681242540921354921906708215338584E11Q,
|
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff
changeset
|
388 7.679102403710581712903937970163206882492E10Q,
|
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff
changeset
|
389 1.680514903671382470108010973615268125169E10Q,
|
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff
changeset
|
390 2.181011222911537259440775283277711588410E9Q,
|
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff
changeset
|
391 1.705361119398837808244780667539728356096E8Q,
|
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff
changeset
|
392 7.792391565652481864976147945997033946360E6Q,
|
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff
changeset
|
393 1.910741381027985291688667214472560023819E5Q,
|
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff
changeset
|
394 2.088138241893612679762260077783794329559E3Q,
|
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff
changeset
|
395 6.330318119566998299106803922739066556550E0Q
|
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff
changeset
|
396 };
|
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff
changeset
|
397 #define NRD5 8
|
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff
changeset
|
398 static const __float128 RD5[NRD5 + 1] =
|
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff
changeset
|
399 {
|
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff
changeset
|
400 1.335189758138651840605141370223112376176E11Q,
|
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff
changeset
|
401 1.174130445739492885895466097516530211283E11Q,
|
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff
changeset
|
402 4.308006619274572338118732154886328519910E10Q,
|
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff
changeset
|
403 8.547402888692578655814445003283720677468E9Q,
|
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff
changeset
|
404 9.934628078575618309542580800421370730906E8Q,
|
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff
changeset
|
405 6.847107420092173812998096295422311820672E7Q,
|
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff
changeset
|
406 2.698552646016599923609773122139463150403E6Q,
|
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff
changeset
|
407 5.526516251532464176412113632726150253215E4Q,
|
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff
changeset
|
408 4.772343321713697385780533022595450486932E2Q
|
145
|
409 /* 1.0E0L */
|
68
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff
changeset
|
410 };
|
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff
changeset
|
411
|
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff
changeset
|
412
|
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff
changeset
|
413 /* log gamma(x+4) = log gamma(4) + x P(x)/Q(x)
|
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff
changeset
|
414 -0.5 <= x <= 0.5
|
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff
changeset
|
415 3.5 <= x+4 <= 4.5
|
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff
changeset
|
416 Peak relative error 6.7e-37 */
|
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff
changeset
|
417 static const __float128 lgam4a = 1.791748046875E0Q;
|
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff
changeset
|
418 static const __float128 lgam4b = 1.1422353055000812477358380702272722990692E-5Q;
|
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff
changeset
|
419 #define NRN4 9
|
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff
changeset
|
420 static const __float128 RN4[NRN4 + 1] =
|
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff
changeset
|
421 {
|
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff
changeset
|
422 -1.026583408246155508572442242188887829208E13Q,
|
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff
changeset
|
423 -1.306476685384622809290193031208776258809E13Q,
|
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff
changeset
|
424 -7.051088602207062164232806511992978915508E12Q,
|
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff
changeset
|
425 -2.100849457735620004967624442027793656108E12Q,
|
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff
changeset
|
426 -3.767473790774546963588549871673843260569E11Q,
|
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff
changeset
|
427 -4.156387497364909963498394522336575984206E10Q,
|
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff
changeset
|
428 -2.764021460668011732047778992419118757746E9Q,
|
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff
changeset
|
429 -1.036617204107109779944986471142938641399E8Q,
|
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff
changeset
|
430 -1.895730886640349026257780896972598305443E6Q,
|
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff
changeset
|
431 -1.180509051468390914200720003907727988201E4Q
|
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff
changeset
|
432 };
|
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff
changeset
|
433 #define NRD4 9
|
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff
changeset
|
434 static const __float128 RD4[NRD4 + 1] =
|
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff
changeset
|
435 {
|
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff
changeset
|
436 -8.172669122056002077809119378047536240889E12Q,
|
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff
changeset
|
437 -9.477592426087986751343695251801814226960E12Q,
|
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff
changeset
|
438 -4.629448850139318158743900253637212801682E12Q,
|
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff
changeset
|
439 -1.237965465892012573255370078308035272942E12Q,
|
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff
changeset
|
440 -1.971624313506929845158062177061297598956E11Q,
|
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff
changeset
|
441 -1.905434843346570533229942397763361493610E10Q,
|
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff
changeset
|
442 -1.089409357680461419743730978512856675984E9Q,
|
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff
changeset
|
443 -3.416703082301143192939774401370222822430E7Q,
|
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff
changeset
|
444 -4.981791914177103793218433195857635265295E5Q,
|
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff
changeset
|
445 -2.192507743896742751483055798411231453733E3Q
|
145
|
446 /* 1.0E0L */
|
68
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff
changeset
|
447 };
|
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff
changeset
|
448
|
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff
changeset
|
449
|
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff
changeset
|
450 /* log gamma(x+3) = log gamma(3) + x P(x)/Q(x)
|
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff
changeset
|
451 -0.25 <= x <= 0.5
|
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff
changeset
|
452 2.75 <= x+3 <= 3.5
|
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff
changeset
|
453 Peak relative error 6.0e-37 */
|
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff
changeset
|
454 static const __float128 lgam3a = 6.93145751953125E-1Q;
|
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff
changeset
|
455 static const __float128 lgam3b = 1.4286068203094172321214581765680755001344E-6Q;
|
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff
changeset
|
456
|
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff
changeset
|
457 #define NRN3 9
|
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff
changeset
|
458 static const __float128 RN3[NRN3 + 1] =
|
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff
changeset
|
459 {
|
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff
changeset
|
460 -4.813901815114776281494823863935820876670E11Q,
|
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff
changeset
|
461 -8.425592975288250400493910291066881992620E11Q,
|
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff
changeset
|
462 -6.228685507402467503655405482985516909157E11Q,
|
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff
changeset
|
463 -2.531972054436786351403749276956707260499E11Q,
|
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff
changeset
|
464 -6.170200796658926701311867484296426831687E10Q,
|
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff
changeset
|
465 -9.211477458528156048231908798456365081135E9Q,
|
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff
changeset
|
466 -8.251806236175037114064561038908691305583E8Q,
|
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff
changeset
|
467 -4.147886355917831049939930101151160447495E7Q,
|
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff
changeset
|
468 -1.010851868928346082547075956946476932162E6Q,
|
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff
changeset
|
469 -8.333374463411801009783402800801201603736E3Q
|
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff
changeset
|
470 };
|
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff
changeset
|
471 #define NRD3 9
|
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff
changeset
|
472 static const __float128 RD3[NRD3 + 1] =
|
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff
changeset
|
473 {
|
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff
changeset
|
474 -5.216713843111675050627304523368029262450E11Q,
|
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff
changeset
|
475 -8.014292925418308759369583419234079164391E11Q,
|
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff
changeset
|
476 -5.180106858220030014546267824392678611990E11Q,
|
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff
changeset
|
477 -1.830406975497439003897734969120997840011E11Q,
|
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff
changeset
|
478 -3.845274631904879621945745960119924118925E10Q,
|
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff
changeset
|
479 -4.891033385370523863288908070309417710903E9Q,
|
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff
changeset
|
480 -3.670172254411328640353855768698287474282E8Q,
|
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff
changeset
|
481 -1.505316381525727713026364396635522516989E7Q,
|
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff
changeset
|
482 -2.856327162923716881454613540575964890347E5Q,
|
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff
changeset
|
483 -1.622140448015769906847567212766206894547E3Q
|
145
|
484 /* 1.0E0L */
|
68
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff
changeset
|
485 };
|
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff
changeset
|
486
|
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff
changeset
|
487
|
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff
changeset
|
488 /* log gamma(x+2.5) = log gamma(2.5) + x P(x)/Q(x)
|
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff
changeset
|
489 -0.125 <= x <= 0.25
|
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff
changeset
|
490 2.375 <= x+2.5 <= 2.75 */
|
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff
changeset
|
491 static const __float128 lgam2r5a = 2.8466796875E-1Q;
|
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff
changeset
|
492 static const __float128 lgam2r5b = 1.4901722919159632494669682701924320137696E-5Q;
|
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff
changeset
|
493 #define NRN2r5 8
|
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff
changeset
|
494 static const __float128 RN2r5[NRN2r5 + 1] =
|
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff
changeset
|
495 {
|
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff
changeset
|
496 -4.676454313888335499356699817678862233205E9Q,
|
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff
changeset
|
497 -9.361888347911187924389905984624216340639E9Q,
|
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff
changeset
|
498 -7.695353600835685037920815799526540237703E9Q,
|
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff
changeset
|
499 -3.364370100981509060441853085968900734521E9Q,
|
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff
changeset
|
500 -8.449902011848163568670361316804900559863E8Q,
|
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff
changeset
|
501 -1.225249050950801905108001246436783022179E8Q,
|
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff
changeset
|
502 -9.732972931077110161639900388121650470926E6Q,
|
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff
changeset
|
503 -3.695711763932153505623248207576425983573E5Q,
|
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff
changeset
|
504 -4.717341584067827676530426007495274711306E3Q
|
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff
changeset
|
505 };
|
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff
changeset
|
506 #define NRD2r5 8
|
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff
changeset
|
507 static const __float128 RD2r5[NRD2r5 + 1] =
|
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff
changeset
|
508 {
|
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff
changeset
|
509 -6.650657966618993679456019224416926875619E9Q,
|
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff
changeset
|
510 -1.099511409330635807899718829033488771623E10Q,
|
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff
changeset
|
511 -7.482546968307837168164311101447116903148E9Q,
|
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff
changeset
|
512 -2.702967190056506495988922973755870557217E9Q,
|
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff
changeset
|
513 -5.570008176482922704972943389590409280950E8Q,
|
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff
changeset
|
514 -6.536934032192792470926310043166993233231E7Q,
|
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff
changeset
|
515 -4.101991193844953082400035444146067511725E6Q,
|
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff
changeset
|
516 -1.174082735875715802334430481065526664020E5Q,
|
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff
changeset
|
517 -9.932840389994157592102947657277692978511E2Q
|
145
|
518 /* 1.0E0L */
|
68
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff
changeset
|
519 };
|
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff
changeset
|
520
|
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff
changeset
|
521
|
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff
changeset
|
522 /* log gamma(x+2) = x P(x)/Q(x)
|
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff
changeset
|
523 -0.125 <= x <= +0.375
|
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff
changeset
|
524 1.875 <= x+2 <= 2.375
|
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff
changeset
|
525 Peak relative error 4.6e-36 */
|
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff
changeset
|
526 #define NRN2 9
|
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff
changeset
|
527 static const __float128 RN2[NRN2 + 1] =
|
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff
changeset
|
528 {
|
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff
changeset
|
529 -3.716661929737318153526921358113793421524E9Q,
|
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff
changeset
|
530 -1.138816715030710406922819131397532331321E10Q,
|
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff
changeset
|
531 -1.421017419363526524544402598734013569950E10Q,
|
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff
changeset
|
532 -9.510432842542519665483662502132010331451E9Q,
|
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff
changeset
|
533 -3.747528562099410197957514973274474767329E9Q,
|
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff
changeset
|
534 -8.923565763363912474488712255317033616626E8Q,
|
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff
changeset
|
535 -1.261396653700237624185350402781338231697E8Q,
|
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff
changeset
|
536 -9.918402520255661797735331317081425749014E6Q,
|
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff
changeset
|
537 -3.753996255897143855113273724233104768831E5Q,
|
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff
changeset
|
538 -4.778761333044147141559311805999540765612E3Q
|
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff
changeset
|
539 };
|
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff
changeset
|
540 #define NRD2 9
|
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff
changeset
|
541 static const __float128 RD2[NRD2 + 1] =
|
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff
changeset
|
542 {
|
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff
changeset
|
543 -8.790916836764308497770359421351673950111E9Q,
|
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff
changeset
|
544 -2.023108608053212516399197678553737477486E10Q,
|
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff
changeset
|
545 -1.958067901852022239294231785363504458367E10Q,
|
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff
changeset
|
546 -1.035515043621003101254252481625188704529E10Q,
|
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff
changeset
|
547 -3.253884432621336737640841276619272224476E9Q,
|
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff
changeset
|
548 -6.186383531162456814954947669274235815544E8Q,
|
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff
changeset
|
549 -6.932557847749518463038934953605969951466E7Q,
|
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff
changeset
|
550 -4.240731768287359608773351626528479703758E6Q,
|
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff
changeset
|
551 -1.197343995089189188078944689846348116630E5Q,
|
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff
changeset
|
552 -1.004622911670588064824904487064114090920E3Q
|
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff
changeset
|
553 /* 1.0E0 */
|
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff
changeset
|
554 };
|
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff
changeset
|
555
|
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff
changeset
|
556
|
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff
changeset
|
557 /* log gamma(x+1.75) = log gamma(1.75) + x P(x)/Q(x)
|
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff
changeset
|
558 -0.125 <= x <= +0.125
|
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff
changeset
|
559 1.625 <= x+1.75 <= 1.875
|
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff
changeset
|
560 Peak relative error 9.2e-37 */
|
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff
changeset
|
561 static const __float128 lgam1r75a = -8.441162109375E-2Q;
|
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff
changeset
|
562 static const __float128 lgam1r75b = 1.0500073264444042213965868602268256157604E-5Q;
|
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff
changeset
|
563 #define NRN1r75 8
|
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff
changeset
|
564 static const __float128 RN1r75[NRN1r75 + 1] =
|
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff
changeset
|
565 {
|
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff
changeset
|
566 -5.221061693929833937710891646275798251513E7Q,
|
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff
changeset
|
567 -2.052466337474314812817883030472496436993E8Q,
|
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff
changeset
|
568 -2.952718275974940270675670705084125640069E8Q,
|
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff
changeset
|
569 -2.132294039648116684922965964126389017840E8Q,
|
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff
changeset
|
570 -8.554103077186505960591321962207519908489E7Q,
|
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff
changeset
|
571 -1.940250901348870867323943119132071960050E7Q,
|
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff
changeset
|
572 -2.379394147112756860769336400290402208435E6Q,
|
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff
changeset
|
573 -1.384060879999526222029386539622255797389E5Q,
|
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff
changeset
|
574 -2.698453601378319296159355612094598695530E3Q
|
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff
changeset
|
575 };
|
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff
changeset
|
576 #define NRD1r75 8
|
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff
changeset
|
577 static const __float128 RD1r75[NRD1r75 + 1] =
|
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff
changeset
|
578 {
|
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff
changeset
|
579 -2.109754689501705828789976311354395393605E8Q,
|
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff
changeset
|
580 -5.036651829232895725959911504899241062286E8Q,
|
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff
changeset
|
581 -4.954234699418689764943486770327295098084E8Q,
|
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff
changeset
|
582 -2.589558042412676610775157783898195339410E8Q,
|
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff
changeset
|
583 -7.731476117252958268044969614034776883031E7Q,
|
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff
changeset
|
584 -1.316721702252481296030801191240867486965E7Q,
|
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff
changeset
|
585 -1.201296501404876774861190604303728810836E6Q,
|
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff
changeset
|
586 -5.007966406976106636109459072523610273928E4Q,
|
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff
changeset
|
587 -6.155817990560743422008969155276229018209E2Q
|
145
|
588 /* 1.0E0L */
|
68
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff
changeset
|
589 };
|
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff
changeset
|
590
|
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff
changeset
|
591
|
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff
changeset
|
592 /* log gamma(x+x0) = y0 + x^2 P(x)/Q(x)
|
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff
changeset
|
593 -0.0867 <= x <= +0.1634
|
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff
changeset
|
594 1.374932... <= x+x0 <= 1.625032...
|
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff
changeset
|
595 Peak relative error 4.0e-36 */
|
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff
changeset
|
596 static const __float128 x0a = 1.4616241455078125Q;
|
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff
changeset
|
597 static const __float128 x0b = 7.9994605498412626595423257213002588621246E-6Q;
|
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff
changeset
|
598 static const __float128 y0a = -1.21490478515625E-1Q;
|
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff
changeset
|
599 static const __float128 y0b = 4.1879797753919044854428223084178486438269E-6Q;
|
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff
changeset
|
600 #define NRN1r5 8
|
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff
changeset
|
601 static const __float128 RN1r5[NRN1r5 + 1] =
|
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff
changeset
|
602 {
|
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff
changeset
|
603 6.827103657233705798067415468881313128066E5Q,
|
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff
changeset
|
604 1.910041815932269464714909706705242148108E6Q,
|
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff
changeset
|
605 2.194344176925978377083808566251427771951E6Q,
|
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff
changeset
|
606 1.332921400100891472195055269688876427962E6Q,
|
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff
changeset
|
607 4.589080973377307211815655093824787123508E5Q,
|
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff
changeset
|
608 8.900334161263456942727083580232613796141E4Q,
|
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff
changeset
|
609 9.053840838306019753209127312097612455236E3Q,
|
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff
changeset
|
610 4.053367147553353374151852319743594873771E2Q,
|
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff
changeset
|
611 5.040631576303952022968949605613514584950E0Q
|
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff
changeset
|
612 };
|
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff
changeset
|
613 #define NRD1r5 8
|
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff
changeset
|
614 static const __float128 RD1r5[NRD1r5 + 1] =
|
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff
changeset
|
615 {
|
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff
changeset
|
616 1.411036368843183477558773688484699813355E6Q,
|
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff
changeset
|
617 4.378121767236251950226362443134306184849E6Q,
|
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff
changeset
|
618 5.682322855631723455425929877581697918168E6Q,
|
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff
changeset
|
619 3.999065731556977782435009349967042222375E6Q,
|
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff
changeset
|
620 1.653651390456781293163585493620758410333E6Q,
|
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff
changeset
|
621 4.067774359067489605179546964969435858311E5Q,
|
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff
changeset
|
622 5.741463295366557346748361781768833633256E4Q,
|
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff
changeset
|
623 4.226404539738182992856094681115746692030E3Q,
|
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff
changeset
|
624 1.316980975410327975566999780608618774469E2Q,
|
145
|
625 /* 1.0E0L */
|
68
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff
changeset
|
626 };
|
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff
changeset
|
627
|
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff
changeset
|
628
|
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff
changeset
|
629 /* log gamma(x+1.25) = log gamma(1.25) + x P(x)/Q(x)
|
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff
changeset
|
630 -.125 <= x <= +.125
|
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff
changeset
|
631 1.125 <= x+1.25 <= 1.375
|
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff
changeset
|
632 Peak relative error = 4.9e-36 */
|
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff
changeset
|
633 static const __float128 lgam1r25a = -9.82818603515625E-2Q;
|
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff
changeset
|
634 static const __float128 lgam1r25b = 1.0023929749338536146197303364159774377296E-5Q;
|
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff
changeset
|
635 #define NRN1r25 9
|
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff
changeset
|
636 static const __float128 RN1r25[NRN1r25 + 1] =
|
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff
changeset
|
637 {
|
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff
changeset
|
638 -9.054787275312026472896002240379580536760E4Q,
|
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff
changeset
|
639 -8.685076892989927640126560802094680794471E4Q,
|
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff
changeset
|
640 2.797898965448019916967849727279076547109E5Q,
|
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff
changeset
|
641 6.175520827134342734546868356396008898299E5Q,
|
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff
changeset
|
642 5.179626599589134831538516906517372619641E5Q,
|
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff
changeset
|
643 2.253076616239043944538380039205558242161E5Q,
|
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff
changeset
|
644 5.312653119599957228630544772499197307195E4Q,
|
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff
changeset
|
645 6.434329437514083776052669599834938898255E3Q,
|
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff
changeset
|
646 3.385414416983114598582554037612347549220E2Q,
|
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff
changeset
|
647 4.907821957946273805080625052510832015792E0Q
|
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff
changeset
|
648 };
|
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff
changeset
|
649 #define NRD1r25 8
|
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff
changeset
|
650 static const __float128 RD1r25[NRD1r25 + 1] =
|
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff
changeset
|
651 {
|
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff
changeset
|
652 3.980939377333448005389084785896660309000E5Q,
|
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff
changeset
|
653 1.429634893085231519692365775184490465542E6Q,
|
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff
changeset
|
654 2.145438946455476062850151428438668234336E6Q,
|
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff
changeset
|
655 1.743786661358280837020848127465970357893E6Q,
|
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff
changeset
|
656 8.316364251289743923178092656080441655273E5Q,
|
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff
changeset
|
657 2.355732939106812496699621491135458324294E5Q,
|
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff
changeset
|
658 3.822267399625696880571810137601310855419E4Q,
|
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff
changeset
|
659 3.228463206479133236028576845538387620856E3Q,
|
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff
changeset
|
660 1.152133170470059555646301189220117965514E2Q
|
145
|
661 /* 1.0E0L */
|
68
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff
changeset
|
662 };
|
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff
changeset
|
663
|
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff
changeset
|
664
|
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff
changeset
|
665 /* log gamma(x + 1) = x P(x)/Q(x)
|
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff
changeset
|
666 0.0 <= x <= +0.125
|
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff
changeset
|
667 1.0 <= x+1 <= 1.125
|
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff
changeset
|
668 Peak relative error 1.1e-35 */
|
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff
changeset
|
669 #define NRN1 8
|
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff
changeset
|
670 static const __float128 RN1[NRN1 + 1] =
|
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff
changeset
|
671 {
|
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff
changeset
|
672 -9.987560186094800756471055681088744738818E3Q,
|
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff
changeset
|
673 -2.506039379419574361949680225279376329742E4Q,
|
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff
changeset
|
674 -1.386770737662176516403363873617457652991E4Q,
|
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff
changeset
|
675 1.439445846078103202928677244188837130744E4Q,
|
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff
changeset
|
676 2.159612048879650471489449668295139990693E4Q,
|
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff
changeset
|
677 1.047439813638144485276023138173676047079E4Q,
|
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff
changeset
|
678 2.250316398054332592560412486630769139961E3Q,
|
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff
changeset
|
679 1.958510425467720733041971651126443864041E2Q,
|
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff
changeset
|
680 4.516830313569454663374271993200291219855E0Q
|
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff
changeset
|
681 };
|
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff
changeset
|
682 #define NRD1 7
|
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff
changeset
|
683 static const __float128 RD1[NRD1 + 1] =
|
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff
changeset
|
684 {
|
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff
changeset
|
685 1.730299573175751778863269333703788214547E4Q,
|
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff
changeset
|
686 6.807080914851328611903744668028014678148E4Q,
|
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff
changeset
|
687 1.090071629101496938655806063184092302439E5Q,
|
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff
changeset
|
688 9.124354356415154289343303999616003884080E4Q,
|
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff
changeset
|
689 4.262071638655772404431164427024003253954E4Q,
|
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff
changeset
|
690 1.096981664067373953673982635805821283581E4Q,
|
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff
changeset
|
691 1.431229503796575892151252708527595787588E3Q,
|
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff
changeset
|
692 7.734110684303689320830401788262295992921E1Q
|
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff
changeset
|
693 /* 1.0E0 */
|
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff
changeset
|
694 };
|
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff
changeset
|
695
|
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff
changeset
|
696
|
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff
changeset
|
697 /* log gamma(x + 1) = x P(x)/Q(x)
|
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff
changeset
|
698 -0.125 <= x <= 0
|
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff
changeset
|
699 0.875 <= x+1 <= 1.0
|
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff
changeset
|
700 Peak relative error 7.0e-37 */
|
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff
changeset
|
701 #define NRNr9 8
|
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff
changeset
|
702 static const __float128 RNr9[NRNr9 + 1] =
|
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff
changeset
|
703 {
|
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff
changeset
|
704 4.441379198241760069548832023257571176884E5Q,
|
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff
changeset
|
705 1.273072988367176540909122090089580368732E6Q,
|
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff
changeset
|
706 9.732422305818501557502584486510048387724E5Q,
|
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff
changeset
|
707 -5.040539994443998275271644292272870348684E5Q,
|
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff
changeset
|
708 -1.208719055525609446357448132109723786736E6Q,
|
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff
changeset
|
709 -7.434275365370936547146540554419058907156E5Q,
|
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff
changeset
|
710 -2.075642969983377738209203358199008185741E5Q,
|
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff
changeset
|
711 -2.565534860781128618589288075109372218042E4Q,
|
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff
changeset
|
712 -1.032901669542994124131223797515913955938E3Q,
|
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff
changeset
|
713 };
|
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff
changeset
|
714 #define NRDr9 8
|
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff
changeset
|
715 static const __float128 RDr9[NRDr9 + 1] =
|
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff
changeset
|
716 {
|
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff
changeset
|
717 -7.694488331323118759486182246005193998007E5Q,
|
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff
changeset
|
718 -3.301918855321234414232308938454112213751E6Q,
|
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff
changeset
|
719 -5.856830900232338906742924836032279404702E6Q,
|
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff
changeset
|
720 -5.540672519616151584486240871424021377540E6Q,
|
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff
changeset
|
721 -3.006530901041386626148342989181721176919E6Q,
|
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff
changeset
|
722 -9.350378280513062139466966374330795935163E5Q,
|
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff
changeset
|
723 -1.566179100031063346901755685375732739511E5Q,
|
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff
changeset
|
724 -1.205016539620260779274902967231510804992E4Q,
|
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff
changeset
|
725 -2.724583156305709733221564484006088794284E2Q
|
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff
changeset
|
726 /* 1.0E0 */
|
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff
changeset
|
727 };
|
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff
changeset
|
728
|
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff
changeset
|
729
|
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff
changeset
|
730 /* Evaluate P[n] x^n + P[n-1] x^(n-1) + ... + P[0] */
|
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff
changeset
|
731
|
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff
changeset
|
732 static __float128
|
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff
changeset
|
733 neval (__float128 x, const __float128 *p, int n)
|
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff
changeset
|
734 {
|
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff
changeset
|
735 __float128 y;
|
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff
changeset
|
736
|
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff
changeset
|
737 p += n;
|
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff
changeset
|
738 y = *p--;
|
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff
changeset
|
739 do
|
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff
changeset
|
740 {
|
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff
changeset
|
741 y = y * x + *p--;
|
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff
changeset
|
742 }
|
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff
changeset
|
743 while (--n > 0);
|
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff
changeset
|
744 return y;
|
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff
changeset
|
745 }
|
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff
changeset
|
746
|
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff
changeset
|
747
|
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff
changeset
|
748 /* Evaluate x^n+1 + P[n] x^(n) + P[n-1] x^(n-1) + ... + P[0] */
|
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff
changeset
|
749
|
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff
changeset
|
750 static __float128
|
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff
changeset
|
751 deval (__float128 x, const __float128 *p, int n)
|
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff
changeset
|
752 {
|
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff
changeset
|
753 __float128 y;
|
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff
changeset
|
754
|
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff
changeset
|
755 p += n;
|
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff
changeset
|
756 y = x + *p--;
|
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff
changeset
|
757 do
|
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff
changeset
|
758 {
|
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff
changeset
|
759 y = y * x + *p--;
|
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff
changeset
|
760 }
|
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff
changeset
|
761 while (--n > 0);
|
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff
changeset
|
762 return y;
|
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff
changeset
|
763 }
|
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff
changeset
|
764
|
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff
changeset
|
765
|
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff
changeset
|
766 __float128
|
145
|
767 __quadmath_lgammaq_r (__float128 x, int *signgamp)
|
68
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff
changeset
|
768 {
|
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff
changeset
|
769 __float128 p, q, w, z, nx;
|
111
|
770 int i, nn;
|
68
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff
changeset
|
771
|
145
|
772 *signgamp = 1;
|
68
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff
changeset
|
773
|
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff
changeset
|
774 if (! finiteq (x))
|
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff
changeset
|
775 return x * x;
|
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff
changeset
|
776
|
145
|
777 if (x == 0)
|
68
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff
changeset
|
778 {
|
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff
changeset
|
779 if (signbitq (x))
|
145
|
780 *signgamp = -1;
|
68
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff
changeset
|
781 }
|
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff
changeset
|
782
|
145
|
783 if (x < 0)
|
68
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff
changeset
|
784 {
|
145
|
785 if (x < -2 && x > -50)
|
|
786 return __quadmath_lgamma_negq (x, signgamp);
|
68
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff
changeset
|
787 q = -x;
|
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff
changeset
|
788 p = floorq (q);
|
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff
changeset
|
789 if (p == q)
|
145
|
790 return (one / fabsq (p - p));
|
|
791 __float128 halfp = p * 0.5Q;
|
|
792 if (halfp == floorq (halfp))
|
|
793 *signgamp = -1;
|
68
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff
changeset
|
794 else
|
145
|
795 *signgamp = 1;
|
|
796 if (q < 0x1p-120Q)
|
|
797 return -logq (q);
|
68
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff
changeset
|
798 z = q - p;
|
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff
changeset
|
799 if (z > 0.5Q)
|
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff
changeset
|
800 {
|
145
|
801 p += 1;
|
68
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff
changeset
|
802 z = p - q;
|
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff
changeset
|
803 }
|
145
|
804 z = q * sinq (PIL * z);
|
|
805 w = __quadmath_lgammaq_r (q, &i);
|
|
806 z = logq (PIL / z) - w;
|
68
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff
changeset
|
807 return (z);
|
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff
changeset
|
808 }
|
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff
changeset
|
809
|
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff
changeset
|
810 if (x < 13.5Q)
|
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff
changeset
|
811 {
|
145
|
812 p = 0;
|
68
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff
changeset
|
813 nx = floorq (x + 0.5Q);
|
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff
changeset
|
814 nn = nx;
|
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff
changeset
|
815 switch (nn)
|
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff
changeset
|
816 {
|
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff
changeset
|
817 case 0:
|
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff
changeset
|
818 /* log gamma (x + 1) = log(x) + log gamma(x) */
|
145
|
819 if (x < 0x1p-120Q)
|
|
820 return -logq (x);
|
|
821 else if (x <= 0.125)
|
68
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff
changeset
|
822 {
|
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff
changeset
|
823 p = x * neval (x, RN1, NRN1) / deval (x, RD1, NRD1);
|
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff
changeset
|
824 }
|
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff
changeset
|
825 else if (x <= 0.375)
|
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff
changeset
|
826 {
|
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff
changeset
|
827 z = x - 0.25Q;
|
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff
changeset
|
828 p = z * neval (z, RN1r25, NRN1r25) / deval (z, RD1r25, NRD1r25);
|
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff
changeset
|
829 p += lgam1r25b;
|
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff
changeset
|
830 p += lgam1r25a;
|
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff
changeset
|
831 }
|
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff
changeset
|
832 else if (x <= 0.625)
|
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff
changeset
|
833 {
|
145
|
834 z = x + (1 - x0a);
|
68
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff
changeset
|
835 z = z - x0b;
|
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff
changeset
|
836 p = neval (z, RN1r5, NRN1r5) / deval (z, RD1r5, NRD1r5);
|
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff
changeset
|
837 p = p * z * z;
|
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff
changeset
|
838 p = p + y0b;
|
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff
changeset
|
839 p = p + y0a;
|
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff
changeset
|
840 }
|
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff
changeset
|
841 else if (x <= 0.875)
|
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff
changeset
|
842 {
|
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff
changeset
|
843 z = x - 0.75Q;
|
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff
changeset
|
844 p = z * neval (z, RN1r75, NRN1r75) / deval (z, RD1r75, NRD1r75);
|
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff
changeset
|
845 p += lgam1r75b;
|
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff
changeset
|
846 p += lgam1r75a;
|
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff
changeset
|
847 }
|
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff
changeset
|
848 else
|
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff
changeset
|
849 {
|
145
|
850 z = x - 1;
|
68
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff
changeset
|
851 p = z * neval (z, RN2, NRN2) / deval (z, RD2, NRD2);
|
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff
changeset
|
852 }
|
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff
changeset
|
853 p = p - logq (x);
|
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff
changeset
|
854 break;
|
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff
changeset
|
855
|
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff
changeset
|
856 case 1:
|
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff
changeset
|
857 if (x < 0.875Q)
|
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff
changeset
|
858 {
|
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff
changeset
|
859 if (x <= 0.625)
|
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff
changeset
|
860 {
|
145
|
861 z = x + (1 - x0a);
|
68
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff
changeset
|
862 z = z - x0b;
|
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff
changeset
|
863 p = neval (z, RN1r5, NRN1r5) / deval (z, RD1r5, NRD1r5);
|
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff
changeset
|
864 p = p * z * z;
|
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff
changeset
|
865 p = p + y0b;
|
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff
changeset
|
866 p = p + y0a;
|
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff
changeset
|
867 }
|
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff
changeset
|
868 else if (x <= 0.875)
|
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff
changeset
|
869 {
|
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff
changeset
|
870 z = x - 0.75Q;
|
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff
changeset
|
871 p = z * neval (z, RN1r75, NRN1r75)
|
111
|
872 / deval (z, RD1r75, NRD1r75);
|
68
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff
changeset
|
873 p += lgam1r75b;
|
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff
changeset
|
874 p += lgam1r75a;
|
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff
changeset
|
875 }
|
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff
changeset
|
876 else
|
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff
changeset
|
877 {
|
145
|
878 z = x - 1;
|
68
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff
changeset
|
879 p = z * neval (z, RN2, NRN2) / deval (z, RD2, NRD2);
|
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff
changeset
|
880 }
|
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff
changeset
|
881 p = p - logq (x);
|
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff
changeset
|
882 }
|
145
|
883 else if (x < 1)
|
68
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff
changeset
|
884 {
|
145
|
885 z = x - 1;
|
68
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff
changeset
|
886 p = z * neval (z, RNr9, NRNr9) / deval (z, RDr9, NRDr9);
|
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff
changeset
|
887 }
|
145
|
888 else if (x == 1)
|
|
889 p = 0;
|
68
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff
changeset
|
890 else if (x <= 1.125Q)
|
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff
changeset
|
891 {
|
145
|
892 z = x - 1;
|
68
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff
changeset
|
893 p = z * neval (z, RN1, NRN1) / deval (z, RD1, NRD1);
|
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff
changeset
|
894 }
|
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff
changeset
|
895 else if (x <= 1.375)
|
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff
changeset
|
896 {
|
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff
changeset
|
897 z = x - 1.25Q;
|
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff
changeset
|
898 p = z * neval (z, RN1r25, NRN1r25) / deval (z, RD1r25, NRD1r25);
|
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff
changeset
|
899 p += lgam1r25b;
|
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff
changeset
|
900 p += lgam1r25a;
|
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff
changeset
|
901 }
|
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff
changeset
|
902 else
|
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff
changeset
|
903 {
|
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff
changeset
|
904 /* 1.375 <= x+x0 <= 1.625 */
|
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff
changeset
|
905 z = x - x0a;
|
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff
changeset
|
906 z = z - x0b;
|
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff
changeset
|
907 p = neval (z, RN1r5, NRN1r5) / deval (z, RD1r5, NRD1r5);
|
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff
changeset
|
908 p = p * z * z;
|
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff
changeset
|
909 p = p + y0b;
|
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff
changeset
|
910 p = p + y0a;
|
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff
changeset
|
911 }
|
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff
changeset
|
912 break;
|
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff
changeset
|
913
|
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff
changeset
|
914 case 2:
|
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff
changeset
|
915 if (x < 1.625Q)
|
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff
changeset
|
916 {
|
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff
changeset
|
917 z = x - x0a;
|
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff
changeset
|
918 z = z - x0b;
|
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff
changeset
|
919 p = neval (z, RN1r5, NRN1r5) / deval (z, RD1r5, NRD1r5);
|
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff
changeset
|
920 p = p * z * z;
|
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff
changeset
|
921 p = p + y0b;
|
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff
changeset
|
922 p = p + y0a;
|
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff
changeset
|
923 }
|
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff
changeset
|
924 else if (x < 1.875Q)
|
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff
changeset
|
925 {
|
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff
changeset
|
926 z = x - 1.75Q;
|
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff
changeset
|
927 p = z * neval (z, RN1r75, NRN1r75) / deval (z, RD1r75, NRD1r75);
|
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff
changeset
|
928 p += lgam1r75b;
|
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff
changeset
|
929 p += lgam1r75a;
|
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff
changeset
|
930 }
|
145
|
931 else if (x == 2)
|
|
932 p = 0;
|
68
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff
changeset
|
933 else if (x < 2.375Q)
|
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff
changeset
|
934 {
|
145
|
935 z = x - 2;
|
68
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff
changeset
|
936 p = z * neval (z, RN2, NRN2) / deval (z, RD2, NRD2);
|
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff
changeset
|
937 }
|
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff
changeset
|
938 else
|
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff
changeset
|
939 {
|
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff
changeset
|
940 z = x - 2.5Q;
|
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff
changeset
|
941 p = z * neval (z, RN2r5, NRN2r5) / deval (z, RD2r5, NRD2r5);
|
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff
changeset
|
942 p += lgam2r5b;
|
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff
changeset
|
943 p += lgam2r5a;
|
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff
changeset
|
944 }
|
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff
changeset
|
945 break;
|
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff
changeset
|
946
|
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff
changeset
|
947 case 3:
|
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff
changeset
|
948 if (x < 2.75)
|
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff
changeset
|
949 {
|
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff
changeset
|
950 z = x - 2.5Q;
|
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff
changeset
|
951 p = z * neval (z, RN2r5, NRN2r5) / deval (z, RD2r5, NRD2r5);
|
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff
changeset
|
952 p += lgam2r5b;
|
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff
changeset
|
953 p += lgam2r5a;
|
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff
changeset
|
954 }
|
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff
changeset
|
955 else
|
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff
changeset
|
956 {
|
145
|
957 z = x - 3;
|
68
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff
changeset
|
958 p = z * neval (z, RN3, NRN3) / deval (z, RD3, NRD3);
|
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff
changeset
|
959 p += lgam3b;
|
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff
changeset
|
960 p += lgam3a;
|
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff
changeset
|
961 }
|
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff
changeset
|
962 break;
|
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff
changeset
|
963
|
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff
changeset
|
964 case 4:
|
145
|
965 z = x - 4;
|
68
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff
changeset
|
966 p = z * neval (z, RN4, NRN4) / deval (z, RD4, NRD4);
|
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff
changeset
|
967 p += lgam4b;
|
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff
changeset
|
968 p += lgam4a;
|
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff
changeset
|
969 break;
|
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff
changeset
|
970
|
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff
changeset
|
971 case 5:
|
145
|
972 z = x - 5;
|
68
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff
changeset
|
973 p = z * neval (z, RN5, NRN5) / deval (z, RD5, NRD5);
|
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff
changeset
|
974 p += lgam5b;
|
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff
changeset
|
975 p += lgam5a;
|
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff
changeset
|
976 break;
|
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff
changeset
|
977
|
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff
changeset
|
978 case 6:
|
145
|
979 z = x - 6;
|
68
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff
changeset
|
980 p = z * neval (z, RN6, NRN6) / deval (z, RD6, NRD6);
|
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff
changeset
|
981 p += lgam6b;
|
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff
changeset
|
982 p += lgam6a;
|
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff
changeset
|
983 break;
|
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff
changeset
|
984
|
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff
changeset
|
985 case 7:
|
145
|
986 z = x - 7;
|
68
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff
changeset
|
987 p = z * neval (z, RN7, NRN7) / deval (z, RD7, NRD7);
|
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff
changeset
|
988 p += lgam7b;
|
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff
changeset
|
989 p += lgam7a;
|
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff
changeset
|
990 break;
|
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff
changeset
|
991
|
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff
changeset
|
992 case 8:
|
145
|
993 z = x - 8;
|
68
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff
changeset
|
994 p = z * neval (z, RN8, NRN8) / deval (z, RD8, NRD8);
|
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff
changeset
|
995 p += lgam8b;
|
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff
changeset
|
996 p += lgam8a;
|
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff
changeset
|
997 break;
|
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff
changeset
|
998
|
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff
changeset
|
999 case 9:
|
145
|
1000 z = x - 9;
|
68
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff
changeset
|
1001 p = z * neval (z, RN9, NRN9) / deval (z, RD9, NRD9);
|
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff
changeset
|
1002 p += lgam9b;
|
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff
changeset
|
1003 p += lgam9a;
|
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff
changeset
|
1004 break;
|
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff
changeset
|
1005
|
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff
changeset
|
1006 case 10:
|
145
|
1007 z = x - 10;
|
68
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff
changeset
|
1008 p = z * neval (z, RN10, NRN10) / deval (z, RD10, NRD10);
|
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff
changeset
|
1009 p += lgam10b;
|
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff
changeset
|
1010 p += lgam10a;
|
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff
changeset
|
1011 break;
|
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff
changeset
|
1012
|
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff
changeset
|
1013 case 11:
|
145
|
1014 z = x - 11;
|
68
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff
changeset
|
1015 p = z * neval (z, RN11, NRN11) / deval (z, RD11, NRD11);
|
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff
changeset
|
1016 p += lgam11b;
|
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff
changeset
|
1017 p += lgam11a;
|
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff
changeset
|
1018 break;
|
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff
changeset
|
1019
|
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff
changeset
|
1020 case 12:
|
145
|
1021 z = x - 12;
|
68
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff
changeset
|
1022 p = z * neval (z, RN12, NRN12) / deval (z, RD12, NRD12);
|
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff
changeset
|
1023 p += lgam12b;
|
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff
changeset
|
1024 p += lgam12a;
|
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff
changeset
|
1025 break;
|
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff
changeset
|
1026
|
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff
changeset
|
1027 case 13:
|
145
|
1028 z = x - 13;
|
68
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff
changeset
|
1029 p = z * neval (z, RN13, NRN13) / deval (z, RD13, NRD13);
|
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff
changeset
|
1030 p += lgam13b;
|
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff
changeset
|
1031 p += lgam13a;
|
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff
changeset
|
1032 break;
|
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff
changeset
|
1033 }
|
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff
changeset
|
1034 return p;
|
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff
changeset
|
1035 }
|
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff
changeset
|
1036
|
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff
changeset
|
1037 if (x > MAXLGM)
|
145
|
1038 return (*signgamp * huge * huge);
|
68
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff
changeset
|
1039
|
145
|
1040 if (x > 0x1p120Q)
|
|
1041 return x * (logq (x) - 1);
|
68
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff
changeset
|
1042 q = ls2pi - x;
|
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff
changeset
|
1043 q = (x - 0.5Q) * logq (x) + q;
|
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff
changeset
|
1044 if (x > 1.0e18Q)
|
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff
changeset
|
1045 return (q);
|
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff
changeset
|
1046
|
145
|
1047 p = 1 / (x * x);
|
68
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff
changeset
|
1048 q += neval (p, RASY, NRASY) / x;
|
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff
changeset
|
1049 return (q);
|
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff
changeset
|
1050 }
|