/usr/include/elliptic.h is in libalglib-dev 2.6.0-3.
This file is owned by root:root, with mode 0o644.
The actual contents of the file can be viewed below.
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70 71 72 73 74 75 76 77 78 79 80 81 82 83 84 85 86 87 88 89 90 91 92 93 94 95 96 97 98 99 100 101 102 103 104 105 106 107 108 109 110 111 112 113 114 115 116 117 118 119 120 121 122 123 124 125 126 127 128 129 130 131 132 133 134 135 136 137 138 139 140 141 142 143 144 145 146 147 148 149 150 151 152 153 154 155 156 157 158 159 160 161 162 163 164 165 166 167 168 169 170 171 172 173 174 175 176 177 178 179 180 181 182 183 184 185 186 187 188 189 190 191 192 193 194 195 196 197 198 199 200 201 202 203 204 205 | /*************************************************************************
Cephes Math Library Release 2.8: June, 2000
Copyright 1984, 1987, 1995, 2000 by Stephen L. Moshier
Contributors:
* Sergey Bochkanov (ALGLIB project). Translation from C to
pseudocode.
See subroutines comments for additional copyrights.
>>> SOURCE LICENSE >>>
This program is free software; you can redistribute it and/or modify
it under the terms of the GNU General Public License as published by
the Free Software Foundation (www.fsf.org); either version 2 of the
License, or (at your option) any later version.
This program is distributed in the hope that it will be useful,
but WITHOUT ANY WARRANTY; without even the implied warranty of
MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
GNU General Public License for more details.
A copy of the GNU General Public License is available at
http://www.fsf.org/licensing/licenses
>>> END OF LICENSE >>>
*************************************************************************/
#ifndef _elliptic_h
#define _elliptic_h
#include "ap.h"
#include "ialglib.h"
/*************************************************************************
Complete elliptic integral of the first kind
Approximates the integral
pi/2
-
| |
| dt
K(m) = | ------------------
| 2
| | sqrt( 1 - m sin t )
-
0
using the approximation
P(x) - log x Q(x).
ACCURACY:
Relative error:
arithmetic domain # trials peak rms
IEEE 0,1 30000 2.5e-16 6.8e-17
Cephes Math Library, Release 2.8: June, 2000
Copyright 1984, 1987, 2000 by Stephen L. Moshier
*************************************************************************/
double ellipticintegralk(double m);
/*************************************************************************
Complete elliptic integral of the first kind
Approximates the integral
pi/2
-
| |
| dt
K(m) = | ------------------
| 2
| | sqrt( 1 - m sin t )
-
0
where m = 1 - m1, using the approximation
P(x) - log x Q(x).
The argument m1 is used rather than m so that the logarithmic
singularity at m = 1 will be shifted to the origin; this
preserves maximum accuracy.
K(0) = pi/2.
ACCURACY:
Relative error:
arithmetic domain # trials peak rms
IEEE 0,1 30000 2.5e-16 6.8e-17
Àëãîðèòì âçÿò èç áèáëèîòåêè Cephes
*************************************************************************/
double ellipticintegralkhighprecision(double m1);
/*************************************************************************
Incomplete elliptic integral of the first kind F(phi|m)
Approximates the integral
phi
-
| |
| dt
F(phi_\m) = | ------------------
| 2
| | sqrt( 1 - m sin t )
-
0
of amplitude phi and modulus m, using the arithmetic -
geometric mean algorithm.
ACCURACY:
Tested at random points with m in [0, 1] and phi as indicated.
Relative error:
arithmetic domain # trials peak rms
IEEE -10,10 200000 7.4e-16 1.0e-16
Cephes Math Library Release 2.8: June, 2000
Copyright 1984, 1987, 2000 by Stephen L. Moshier
*************************************************************************/
double incompleteellipticintegralk(double phi, double m);
/*************************************************************************
Complete elliptic integral of the second kind
Approximates the integral
pi/2
-
| | 2
E(m) = | sqrt( 1 - m sin t ) dt
| |
-
0
using the approximation
P(x) - x log x Q(x).
ACCURACY:
Relative error:
arithmetic domain # trials peak rms
IEEE 0, 1 10000 2.1e-16 7.3e-17
Cephes Math Library, Release 2.8: June, 2000
Copyright 1984, 1987, 1989, 2000 by Stephen L. Moshier
*************************************************************************/
double ellipticintegrale(double m);
/*************************************************************************
Incomplete elliptic integral of the second kind
Approximates the integral
phi
-
| |
| 2
E(phi_\m) = | sqrt( 1 - m sin t ) dt
|
| |
-
0
of amplitude phi and modulus m, using the arithmetic -
geometric mean algorithm.
ACCURACY:
Tested at random arguments with phi in [-10, 10] and m in
[0, 1].
Relative error:
arithmetic domain # trials peak rms
IEEE -10,10 150000 3.3e-15 1.4e-16
Cephes Math Library Release 2.8: June, 2000
Copyright 1984, 1987, 1993, 2000 by Stephen L. Moshier
*************************************************************************/
double incompleteellipticintegrale(double phi, double m);
#endif
|