145
|
1 /* log2l.c
|
|
2 * Base 2 logarithm, 128-bit long double precision
|
68
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff
changeset
|
3 *
|
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 * SYNOPSIS:
|
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff
changeset
|
7 *
|
145
|
8 * long double x, y, log2l();
|
68
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff
changeset
|
9 *
|
145
|
10 * y = log2l( x );
|
68
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 *
|
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 * DESCRIPTION:
|
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 * Returns the base 2 logarithm of x.
|
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 * The argument is separated into its exponent and fractional
|
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff
changeset
|
19 * parts. If the exponent is between -1 and +1, the (natural)
|
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff
changeset
|
20 * logarithm of the fraction is approximated by
|
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff
changeset
|
21 *
|
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff
changeset
|
22 * log(1+x) = x - 0.5 x^2 + x^3 P(x)/Q(x).
|
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff
changeset
|
23 *
|
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff
changeset
|
24 * Otherwise, setting z = 2(x-1)/x+1),
|
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff
changeset
|
25 *
|
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff
changeset
|
26 * log(x) = z + z^3 P(z)/Q(z).
|
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff
changeset
|
27 *
|
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff
changeset
|
28 *
|
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff
changeset
|
29 *
|
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff
changeset
|
30 * ACCURACY:
|
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff
changeset
|
31 *
|
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff
changeset
|
32 * Relative error:
|
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff
changeset
|
33 * arithmetic domain # trials peak rms
|
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff
changeset
|
34 * IEEE 0.5, 2.0 100,000 2.6e-34 4.9e-35
|
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff
changeset
|
35 * IEEE exp(+-10000) 100,000 9.6e-35 4.0e-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 * In the tests over the interval exp(+-10000), the logarithms
|
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff
changeset
|
38 * of the random arguments were uniformly distributed over
|
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff
changeset
|
39 * [-10000, +10000].
|
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff
changeset
|
40 *
|
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff
changeset
|
41 */
|
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff
changeset
|
42
|
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff
changeset
|
43 /*
|
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff
changeset
|
44 Cephes Math Library Release 2.2: January, 1991
|
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff
changeset
|
45 Copyright 1984, 1991 by Stephen L. Moshier
|
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff
changeset
|
46 Adapted for glibc November, 2001
|
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff
changeset
|
47
|
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff
changeset
|
48 This library is free software; you can redistribute it and/or
|
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff
changeset
|
49 modify it under the terms of the GNU Lesser General Public
|
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff
changeset
|
50 License as published by the Free Software Foundation; either
|
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff
changeset
|
51 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
|
52
|
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff
changeset
|
53 This library is distributed in the hope that it will be useful,
|
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff
changeset
|
54 but WITHOUT ANY WARRANTY; without even the implied warranty of
|
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff
changeset
|
55 MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU
|
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff
changeset
|
56 Lesser General Public License for more details.
|
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff
changeset
|
57
|
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff
changeset
|
58 You should have received a copy of the GNU Lesser General Public
|
145
|
59 License along with this library; if not, see <http://www.gnu.org/licenses/>.
|
68
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff
changeset
|
60 */
|
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 #include "quadmath-imp.h"
|
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff
changeset
|
63
|
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff
changeset
|
64 /* Coefficients for ln(1+x) = x - x**2/2 + x**3 P(x)/Q(x)
|
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff
changeset
|
65 * 1/sqrt(2) <= x < sqrt(2)
|
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff
changeset
|
66 * Theoretical peak relative error = 5.3e-37,
|
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff
changeset
|
67 * relative peak error spread = 2.3e-14
|
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff
changeset
|
68 */
|
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff
changeset
|
69 static const __float128 P[13] =
|
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 1.313572404063446165910279910527789794488E4Q,
|
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff
changeset
|
72 7.771154681358524243729929227226708890930E4Q,
|
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff
changeset
|
73 2.014652742082537582487669938141683759923E5Q,
|
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff
changeset
|
74 3.007007295140399532324943111654767187848E5Q,
|
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff
changeset
|
75 2.854829159639697837788887080758954924001E5Q,
|
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff
changeset
|
76 1.797628303815655343403735250238293741397E5Q,
|
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff
changeset
|
77 7.594356839258970405033155585486712125861E4Q,
|
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff
changeset
|
78 2.128857716871515081352991964243375186031E4Q,
|
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff
changeset
|
79 3.824952356185897735160588078446136783779E3Q,
|
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff
changeset
|
80 4.114517881637811823002128927449878962058E2Q,
|
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff
changeset
|
81 2.321125933898420063925789532045674660756E1Q,
|
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff
changeset
|
82 4.998469661968096229986658302195402690910E-1Q,
|
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff
changeset
|
83 1.538612243596254322971797716843006400388E-6Q
|
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff
changeset
|
84 };
|
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff
changeset
|
85 static const __float128 Q[12] =
|
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff
changeset
|
86 {
|
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff
changeset
|
87 3.940717212190338497730839731583397586124E4Q,
|
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff
changeset
|
88 2.626900195321832660448791748036714883242E5Q,
|
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff
changeset
|
89 7.777690340007566932935753241556479363645E5Q,
|
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff
changeset
|
90 1.347518538384329112529391120390701166528E6Q,
|
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff
changeset
|
91 1.514882452993549494932585972882995548426E6Q,
|
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff
changeset
|
92 1.158019977462989115839826904108208787040E6Q,
|
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff
changeset
|
93 6.132189329546557743179177159925690841200E5Q,
|
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff
changeset
|
94 2.248234257620569139969141618556349415120E5Q,
|
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff
changeset
|
95 5.605842085972455027590989944010492125825E4Q,
|
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff
changeset
|
96 9.147150349299596453976674231612674085381E3Q,
|
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff
changeset
|
97 9.104928120962988414618126155557301584078E2Q,
|
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff
changeset
|
98 4.839208193348159620282142911143429644326E1Q
|
145
|
99 /* 1.000000000000000000000000000000000000000E0L, */
|
68
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff
changeset
|
100 };
|
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff
changeset
|
101
|
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff
changeset
|
102 /* Coefficients for log(x) = z + z^3 P(z^2)/Q(z^2),
|
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff
changeset
|
103 * where z = 2(x-1)/(x+1)
|
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff
changeset
|
104 * 1/sqrt(2) <= x < sqrt(2)
|
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff
changeset
|
105 * Theoretical peak relative error = 1.1e-35,
|
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff
changeset
|
106 * relative peak error spread 1.1e-9
|
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff
changeset
|
107 */
|
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff
changeset
|
108 static const __float128 R[6] =
|
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 1.418134209872192732479751274970992665513E5Q,
|
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff
changeset
|
111 -8.977257995689735303686582344659576526998E4Q,
|
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff
changeset
|
112 2.048819892795278657810231591630928516206E4Q,
|
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff
changeset
|
113 -2.024301798136027039250415126250455056397E3Q,
|
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff
changeset
|
114 8.057002716646055371965756206836056074715E1Q,
|
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff
changeset
|
115 -8.828896441624934385266096344596648080902E-1Q
|
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff
changeset
|
116 };
|
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff
changeset
|
117 static const __float128 S[6] =
|
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff
changeset
|
118 {
|
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff
changeset
|
119 1.701761051846631278975701529965589676574E6Q,
|
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff
changeset
|
120 -1.332535117259762928288745111081235577029E6Q,
|
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff
changeset
|
121 4.001557694070773974936904547424676279307E5Q,
|
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff
changeset
|
122 -5.748542087379434595104154610899551484314E4Q,
|
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff
changeset
|
123 3.998526750980007367835804959888064681098E3Q,
|
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff
changeset
|
124 -1.186359407982897997337150403816839480438E2Q
|
145
|
125 /* 1.000000000000000000000000000000000000000E0L, */
|
68
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff
changeset
|
126 };
|
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff
changeset
|
127
|
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff
changeset
|
128 static const __float128
|
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff
changeset
|
129 /* log2(e) - 1 */
|
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff
changeset
|
130 LOG2EA = 4.4269504088896340735992468100189213742664595E-1Q,
|
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff
changeset
|
131 /* sqrt(2)/2 */
|
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff
changeset
|
132 SQRTH = 7.071067811865475244008443621048490392848359E-1Q;
|
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff
changeset
|
133
|
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff
changeset
|
134
|
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff
changeset
|
135 /* 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
|
136
|
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff
changeset
|
137 static __float128
|
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff
changeset
|
138 neval (__float128 x, const __float128 *p, int n)
|
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff
changeset
|
139 {
|
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff
changeset
|
140 __float128 y;
|
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 p += n;
|
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff
changeset
|
143 y = *p--;
|
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff
changeset
|
144 do
|
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff
changeset
|
145 {
|
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff
changeset
|
146 y = y * x + *p--;
|
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff
changeset
|
147 }
|
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff
changeset
|
148 while (--n > 0);
|
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff
changeset
|
149 return y;
|
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff
changeset
|
150 }
|
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff
changeset
|
151
|
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 /* 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
|
154
|
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff
changeset
|
155 static __float128
|
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff
changeset
|
156 deval (__float128 x, const __float128 *p, int n)
|
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff
changeset
|
157 {
|
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff
changeset
|
158 __float128 y;
|
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff
changeset
|
159
|
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff
changeset
|
160 p += n;
|
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff
changeset
|
161 y = x + *p--;
|
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff
changeset
|
162 do
|
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff
changeset
|
163 {
|
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff
changeset
|
164 y = y * x + *p--;
|
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff
changeset
|
165 }
|
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff
changeset
|
166 while (--n > 0);
|
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff
changeset
|
167 return y;
|
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff
changeset
|
168 }
|
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff
changeset
|
169
|
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff
changeset
|
170
|
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff
changeset
|
171
|
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff
changeset
|
172 __float128
|
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff
changeset
|
173 log2q (__float128 x)
|
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 __float128 z;
|
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff
changeset
|
176 __float128 y;
|
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff
changeset
|
177 int e;
|
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff
changeset
|
178 int64_t hx, lx;
|
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff
changeset
|
179
|
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff
changeset
|
180 /* Test for domain */
|
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff
changeset
|
181 GET_FLT128_WORDS64 (hx, lx, x);
|
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff
changeset
|
182 if (((hx & 0x7fffffffffffffffLL) | lx) == 0)
|
145
|
183 return (-1 / fabsq (x)); /* log2l(+-0)=-inf */
|
68
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff
changeset
|
184 if (hx < 0)
|
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff
changeset
|
185 return (x - x) / (x - x);
|
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff
changeset
|
186 if (hx >= 0x7fff000000000000LL)
|
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff
changeset
|
187 return (x + x);
|
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff
changeset
|
188
|
145
|
189 if (x == 1)
|
|
190 return 0;
|
111
|
191
|
68
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff
changeset
|
192 /* separate mantissa from exponent */
|
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 /* Note, frexp is used so that denormal numbers
|
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff
changeset
|
195 * will be handled properly.
|
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 x = frexpq (x, &e);
|
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff
changeset
|
198
|
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff
changeset
|
199
|
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff
changeset
|
200 /* logarithm using log(x) = z + z**3 P(z)/Q(z),
|
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff
changeset
|
201 * where z = 2(x-1)/x+1)
|
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff
changeset
|
202 */
|
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff
changeset
|
203 if ((e > 2) || (e < -2))
|
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff
changeset
|
204 {
|
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff
changeset
|
205 if (x < SQRTH)
|
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff
changeset
|
206 { /* 2( 2x-1 )/( 2x+1 ) */
|
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff
changeset
|
207 e -= 1;
|
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff
changeset
|
208 z = x - 0.5Q;
|
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff
changeset
|
209 y = 0.5Q * z + 0.5Q;
|
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff
changeset
|
210 }
|
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff
changeset
|
211 else
|
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff
changeset
|
212 { /* 2 (x-1)/(x+1) */
|
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff
changeset
|
213 z = x - 0.5Q;
|
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff
changeset
|
214 z -= 0.5Q;
|
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff
changeset
|
215 y = 0.5Q * x + 0.5Q;
|
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 x = z / y;
|
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff
changeset
|
218 z = x * x;
|
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff
changeset
|
219 y = x * (z * neval (z, R, 5) / deval (z, S, 5));
|
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff
changeset
|
220 goto done;
|
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff
changeset
|
221 }
|
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff
changeset
|
222
|
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff
changeset
|
223
|
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff
changeset
|
224 /* logarithm using log(1+x) = x - .5x**2 + x**3 P(x)/Q(x) */
|
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 if (x < SQRTH)
|
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff
changeset
|
227 {
|
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff
changeset
|
228 e -= 1;
|
145
|
229 x = 2.0 * x - 1; /* 2x - 1 */
|
68
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff
changeset
|
230 }
|
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff
changeset
|
231 else
|
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff
changeset
|
232 {
|
145
|
233 x = x - 1;
|
68
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff
changeset
|
234 }
|
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff
changeset
|
235 z = x * x;
|
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff
changeset
|
236 y = x * (z * neval (x, P, 12) / deval (x, Q, 11));
|
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff
changeset
|
237 y = y - 0.5 * z;
|
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 done:
|
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 /* Multiply log of fraction by log2(e)
|
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff
changeset
|
242 * and base 2 exponent by 1
|
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff
changeset
|
243 */
|
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff
changeset
|
244 z = y * LOG2EA;
|
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff
changeset
|
245 z += x * LOG2EA;
|
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff
changeset
|
246 z += y;
|
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff
changeset
|
247 z += x;
|
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff
changeset
|
248 z += e;
|
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff
changeset
|
249 return (z);
|
Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
diff
changeset
|
250 }
|