/usr/include/trigintegrals.h is in libalglib-dev 2.6.0-3.
This file is owned by root:root, with mode 0o644.
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Cephes Math Library Release 2.8: June, 2000
Copyright 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 _trigintegrals_h
#define _trigintegrals_h
#include "ap.h"
#include "ialglib.h"
/*************************************************************************
Sine and cosine integrals
Evaluates the integrals
x
-
| cos t - 1
Ci(x) = eul + ln x + | --------- dt,
| t
-
0
x
-
| sin t
Si(x) = | ----- dt
| t
-
0
where eul = 0.57721566490153286061 is Euler's constant.
The integrals are approximated by rational functions.
For x > 8 auxiliary functions f(x) and g(x) are employed
such that
Ci(x) = f(x) sin(x) - g(x) cos(x)
Si(x) = pi/2 - f(x) cos(x) - g(x) sin(x)
ACCURACY:
Test interval = [0,50].
Absolute error, except relative when > 1:
arithmetic function # trials peak rms
IEEE Si 30000 4.4e-16 7.3e-17
IEEE Ci 30000 6.9e-16 5.1e-17
Cephes Math Library Release 2.1: January, 1989
Copyright 1984, 1987, 1989 by Stephen L. Moshier
*************************************************************************/
void sinecosineintegrals(double x, double& si, double& ci);
/*************************************************************************
Hyperbolic sine and cosine integrals
Approximates the integrals
x
-
| | cosh t - 1
Chi(x) = eul + ln x + | ----------- dt,
| | t
-
0
x
-
| | sinh t
Shi(x) = | ------ dt
| | t
-
0
where eul = 0.57721566490153286061 is Euler's constant.
The integrals are evaluated by power series for x < 8
and by Chebyshev expansions for x between 8 and 88.
For large x, both functions approach exp(x)/2x.
Arguments greater than 88 in magnitude return MAXNUM.
ACCURACY:
Test interval 0 to 88.
Relative error:
arithmetic function # trials peak rms
IEEE Shi 30000 6.9e-16 1.6e-16
Absolute error, except relative when |Chi| > 1:
IEEE Chi 30000 8.4e-16 1.4e-16
Cephes Math Library Release 2.8: June, 2000
Copyright 1984, 1987, 2000 by Stephen L. Moshier
*************************************************************************/
void hyperbolicsinecosineintegrals(double x, double& shi, double& chi);
#endif
|