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/* Copyright (C) 2017 - IIT Bombay - FOSSEE
This file must be used under the terms of the CeCILL.
This source file is licensed as described in the file COPYING, which
you should have received as part of this distribution. The terms
are also available at
http://www.cecill.info/licences/Licence_CeCILL_V2-en.txt
Author: Ankit Raj
Organization: FOSSEE, IIT Bombay
Email: toolbox@scilab.in
Reference:- Abramowitz, Milton and Stegun, Irene A
Handbook of Mathematical Functions, Dover, 1965
Chapter 16 (Sections 16.4, 16.13 and 16.15)
Link for FORTRAN code:-http://www.aip.de/groups/soe/local/numres/bookfpdf/f6-11.pdf
*/
#include<stdio.h>
#include<math.h>
#include "modsn.h"
#include "doubleComplex.h"
#define CA 0.0003
doubleComplex zmodsns(doubleComplex uu,double emmc)
{
doubleComplex ans;
double uur,uui;
uur=zreals(uu);
uui=zimags(uu);
double sr,cr,dr;
//Performing Elliptic Function operation for the real values
double a1,b1,c1,d1,emc1,u1;
double em1[14],en1[14];
int i1,ii1,l1,bo1;
emc1=1-emmc;
u1=uur;
if(emc1)
{
bo1=(emc1<0.0);
if(bo1)
{
d1=1.0-emc1;
emc1/=-1.0/d1;
u1*=(d1=sqrt(d1));
}
a1=1.0;
dr=1.0;
for(i1=1;i1<=13;i1++)
{
l1=i1;
em1[i1]=a1;
en1[i1]=(emc1=sqrt(emc1));
c1=0.5*(a1+emc1);
if(fabs(a1-emc1)<=CA*a1)break;
emc1*=a1;
a1=c1;
}
u1*=c1;
sr=sin(u1);
cr=cos(u1);
if(sr)
{
a1=cr/sr;
c1*=a1;
for(ii1=l1;ii1>=1;ii1--)
{
b1=em1[ii1];
a1*=c1;
c1*=dr;
dr=(en1[ii1]+a1)/(b1+a1);
a1=c1/b1;
}
a1=1.0/sqrt(c1*c1+1.0);
sr=(sr>=0.0?a1:-a1);
cr=c1*(sr);
}
if(bo1)
{
a1=dr;
dr=cr;
cr=a1;
sr/=d1;
}
}
else
{
cr=1.0/cosh(u1);
dr=cr;
sr=tanh(u1);
}
////////////////////////////////////////////////////////////////
double si,ci,di;
//Performing Elleptic Function operation for the imaginary values
double a,b,c,d,emc,u;
double em[14],en[14];
int i,ii,l,bo;
//double s1,c1,d1;
emc=emmc;
u=uui;
if(emc)
{
bo=(emc<0.0);
if(bo)
{
d=1.0-emc;
emc/=-1.0/d;
u*=(d=sqrt(d));
}
a=1.0;
di=1.0;
for(i=1;i<=13;i++)
{
l=i;
em[i]=a;
en[i]=(emc=sqrt(emc));
c=0.5*(a+emc);
if(fabs(a-emc)<=CA*a)break;
emc*=a;
a=c;
}
u*=c;
si=sin(u);
ci=cos(u);
if(si)
{
a=ci/si;
c*=a;
for(ii=l;ii>=1;ii--)
{
b=em[ii];
a*=c;
c*=di;
di=(en[ii]+a)/(b+a);
a=c/b;
}
a=1.0/sqrt(c*c+1.0);
si=(si>=0.0?a:-a);
ci=c*(si);
}
if(bo)
{
a=di;
di=ci;
ci=a;
si/=d;
}
}
else
{
ci=1.0/cosh(u);
di=ci;
si=tanh(u);
}
/////////////////////////////////////////////////////////
double delta;
delta=ci*ci + emmc*sr*sr*si*si;
double snir,snii;
snir=(sr*di)/delta;
snii=(cr*dr*si*ci)/delta;
ans=DoubleComplex(snir,snii);
return ans;
}
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