/usr/include/jacobianelliptic.h is in libalglib-dev 2.6.0-3.
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Cephes Math Library Release 2.8: June, 2000
Copyright 1984, 1987, 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
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>>> END OF LICENSE >>>
*************************************************************************/
#ifndef _jacobianelliptic_h
#define _jacobianelliptic_h
#include "ap.h"
#include "ialglib.h"
/*************************************************************************
Jacobian Elliptic Functions
Evaluates the Jacobian elliptic functions sn(u|m), cn(u|m),
and dn(u|m) of parameter m between 0 and 1, and real
argument u.
These functions are periodic, with quarter-period on the
real axis equal to the complete elliptic integral
ellpk(1.0-m).
Relation to incomplete elliptic integral:
If u = ellik(phi,m), then sn(u|m) = sin(phi),
and cn(u|m) = cos(phi). Phi is called the amplitude of u.
Computation is by means of the arithmetic-geometric mean
algorithm, except when m is within 1e-9 of 0 or 1. In the
latter case with m close to 1, the approximation applies
only for phi < pi/2.
ACCURACY:
Tested at random points with u between 0 and 10, m between
0 and 1.
Absolute error (* = relative error):
arithmetic function # trials peak rms
IEEE phi 10000 9.2e-16* 1.4e-16*
IEEE sn 50000 4.1e-15 4.6e-16
IEEE cn 40000 3.6e-15 4.4e-16
IEEE dn 10000 1.3e-12 1.8e-14
Peak error observed in consistency check using addition
theorem for sn(u+v) was 4e-16 (absolute). Also tested by
the above relation to the incomplete elliptic integral.
Accuracy deteriorates when u is large.
Cephes Math Library Release 2.8: June, 2000
Copyright 1984, 1987, 2000 by Stephen L. Moshier
*************************************************************************/
void jacobianellipticfunctions(double u,
double m,
double& sn,
double& cn,
double& dn,
double& ph);
#endif
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