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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
*
*/
/*
* 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
* Thanks to Tom Fairgrieve
*/
#include "lapack.h"
#include "asin.h"
#include "atan.h"
#include "sqrt.h"
#include "abs.h"
#include "log.h"
#include "log1p.h"
#include "min.h"
#include "max.h"
doubleComplex zasins(doubleComplex z) {
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 * dsqrts(getUnderflowThreshold());
double dblEpsm = dsqrts(getRelativeMachinePrecision());
double _dblReal = zreals(z);
double _dblImg = zimags(z);
double dblAbsReal = dabss(_dblReal);
double dblAbsImg = dabss(_dblImg);
int iSignReal = _dblReal < 0 ? -1 : 1;
int iSignImg = _dblImg < 0 ? -1 : 1;
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 = dasins(dblB);
else if( dblAbsReal <= 1)
_pdblReal = datans(dblAbsReal / dsqrts( 0.5 * (dblA + dblAbsReal) * ( (dblAbsImg * dblAbsImg) / (dblR + (dblAbsReal + 1)) + (dblS + (1 - dblAbsReal)))));
else
_pdblReal = datans(dblAbsReal / (dblAbsImg * dsqrts(0.5 * ((dblA + dblAbsReal) / (dblR + (dblAbsReal + 1)) + (dblA + dblAbsReal) / (dblS + (dblAbsReal-1))))));
/* 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 = dasins(dblAbsReal);
_pdblImg = dblAbsImg / dsqrts((1 + dblAbsReal) * (1 - dblAbsReal));
}
else
{
_pdblReal = sdblPi_2;
if(dblAbsReal <= dblLsup)
{
dblTemp = (dblAbsReal - 1) + dsqrts((dblAbsReal - 1) * (dblAbsReal + 1));
_pdblImg = dlog1ps(dblTemp);
}
else
_pdblImg = sdblLn2 + dlogs(dblAbsReal);
}
}
else if(dblAbsImg < dblLinf)
{
_pdblReal = sdblPi_2 - dsqrts(dblAbsImg);
_pdblImg = dsqrts(dblAbsImg);
}
else if((dblEpsm * dblAbsImg - 1 >= dblAbsReal))
{
_pdblReal = dblAbsReal * dblAbsImg;
_pdblImg = sdblLn2 + dlogs(dblAbsReal);
}
else if(dblAbsReal > 1)
{
_pdblReal = datans(dblAbsReal / dblAbsImg);
dblTemp = (dblAbsReal / dblAbsImg) * (dblAbsReal / dblAbsImg);
_pdblImg = sdblLn2 + dlogs(dblAbsReal) + 0.5 * dlog1ps(dblTemp);
}
else
{
double dblTemp2 = dsqrts(1 + dblAbsImg * dblAbsImg);
_pdblReal = dblAbsReal / dblTemp2;
dblTemp = 2 * dblAbsImg * (dblAbsImg + dblTemp2);
_pdblImg = 0.5 * dlog1ps(dblTemp);
}
}
_pdblReal *= iSignReal;
_pdblImg *= iSignImg;
return (DoubleComplex(_pdblReal, _pdblImg));
}
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