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/*
* Scilab ( http://www.scilab.org/ ) - This file is part of Scilab
* Copyright (C) 2007-2008 - INRIA - Bruno JOFRET
* Copyright (C) Bruno Pincon
*
* 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
*
*/
/*
* This fonction is a translation of fortran wacos write by Bruno Pincon <Bruno.Pincon@iecn.u-nancy.fr>
* REFERENCE
* This is a Fortran-77 translation of an algorithm by
* T.E. Hull, T. F. Fairgrieve and P.T.P. Tang which
* appears in their article :
* "Implementing the Complex Arcsine and Arccosine
* Functions Using Exception Handling", ACM, TOMS,
* Vol 23, No. 3, Sept 1997, p. 299-335
*/
#include "acos.h"
#include "atan.h"
#include "log.h"
#include "log1p.h"
#include "sqrt.h"
#include "abs.h"
#include "lapack.h"
#include "min.h"
#include "max.h"
#define localSign(x) (x>0 ? 1 : -1)
doubleComplex zacoss(doubleComplex z) {
static double sdblPi = 3.1415926535897932384626433;
static double sdblPi_2 = 1.5707963267948966192313216;
static double sdblLn2 = 0.6931471805599453094172321;
static double sdblAcross = 1.5;
static double sdblBcross = 0.6417;
double dblLsup = dsqrts(getOverflowThreshold())/8.0;
double dblLinf = 4.0 * dsqrts(getUnderflowThreshold());
double dblEpsm = dsqrts(getRelativeMachinePrecision());
double dblAbsReal = dabss(zreals(z));
double dblAbsImg = dabss(zimags(z));
double dblSignReal = localSign(zreals(z));
double dblSignImg = localSign(zimags(z));
double dblR = 0, dblS = 0, dblA = 0, dblB = 0;
double dblTemp = 0;
double _pdblReal = 0;
double _pdblImg = 0;
if( min(dblAbsReal, dblAbsImg) > dblLinf && max(dblAbsReal, dblAbsImg) <= dblLsup)
{/* we are in the safe region */
dblR = dsqrts( (dblAbsReal + 1 )*(dblAbsReal + 1 ) + dblAbsImg*dblAbsImg);
dblS = dsqrts( (dblAbsReal - 1 )*(dblAbsReal - 1 ) + dblAbsImg*dblAbsImg);
dblA = 0.5 * ( dblR + dblS );
dblB = dblAbsReal / dblA;
/* compute the real part */
if(dblB <= sdblBcross)
_pdblReal = dacoss(dblB);
else if( dblAbsReal <= 1)
_pdblReal = datans(dsqrts(0.5 * (dblA + dblAbsReal) * (dblAbsImg*dblAbsImg / (dblR + (dblAbsReal + 1)) + (dblS + (1 - dblAbsReal)))) / dblAbsReal);
else
_pdblReal = datans((dblAbsImg * dsqrts(0.5 * ((dblA + dblAbsReal) / (dblR + (dblAbsReal + 1)) + (dblA + dblAbsReal) / (dblS + (dblAbsReal - 1))))) / dblAbsReal);
/* compute the imaginary part */
if(dblA <= sdblAcross)
{
double dblImg1 = 0;
if(dblAbsReal < 1)
/* Am1 = 0.5d0*((y**2)/(R+(x+1.d0))+(y**2)/(S+(1.d0-x))) */
dblImg1 = 0.5 * (dblAbsImg*dblAbsImg / (dblR + (dblAbsReal + 1)) + dblAbsImg*dblAbsImg / (dblS + (1 - dblAbsReal)));
else
/* Am1 = 0.5d0*((y**2)/(R+(x+1.d0))+(S+(x-1.d0))) */
dblImg1 = 0.5 * (dblAbsImg*dblAbsImg / (dblR + (dblAbsReal + 1)) + (dblS + (dblAbsReal - 1)));
/* ai = logp1(Am1 + sqrt(Am1*(A+1.d0))) */
dblTemp = dblImg1 + dsqrts(dblImg1 *( dblA + 1));
_pdblImg = dlog1ps(dblTemp);
}
else
/* ai = log(A + sqrt(A**2 - 1.d0)) */
_pdblImg = dlogs(dblA + dsqrts(dblA*dblA - 1));
}
else
{/* evaluation in the special regions ... */
if(dblAbsImg <= dblEpsm * dabss(dblAbsReal - 1))
{
if(dblAbsReal < 1)
{
_pdblReal = dacoss(dblAbsReal);
_pdblImg = dblAbsImg / dsqrts((1 + dblAbsReal) * (1 - dblAbsReal));
}
else
{
_pdblReal = 0;
if(dblAbsReal <= dblLsup)
{
dblTemp = (dblAbsReal - 1) + dsqrts((dblAbsReal - 1) * (dblAbsReal + 1));
_pdblImg = dlog1ps(dblTemp);
}
else
_pdblImg = sdblLn2 + dlogs(dblAbsReal);
}
}
else if(dblAbsImg < dblLinf)
{
_pdblReal = dsqrts(dblAbsImg);
_pdblImg = _pdblReal;
}
else if((dblEpsm * dblAbsImg - 1 >= dblAbsReal))
{
_pdblReal = sdblPi_2;
_pdblImg = sdblLn2 + dlogs(dblAbsImg);
}
else if(dblAbsReal > 1)
{
_pdblReal = datans(dblAbsImg / dblAbsReal);
dblTemp = (dblAbsReal / dblAbsImg)*(dblAbsReal / dblAbsImg);
_pdblImg = sdblLn2 + dlogs(dblAbsImg) + 0.5 * dlog1ps(dblTemp);
}
else
{
double dblTemp2 = dsqrts(1 + dblAbsImg*dblAbsImg);
_pdblReal = sdblPi_2;
dblTemp = 2 * dblAbsImg * (dblAbsImg + dblTemp2);
_pdblImg = 0.5 * dlog1ps(dblTemp);
}
}
if(dblSignReal < 0)
_pdblReal = sdblPi - _pdblReal;
if(dblAbsImg != 0 || dblSignReal < 0)
_pdblImg = - dblSignImg * _pdblImg;
return DoubleComplex(_pdblReal, _pdblImg);
}
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