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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 ? 1.0f : -1.0f)
floatComplex cacoss(floatComplex z) {
static float sfltPi = 3.1415926535897932384626433f;
static float sfltPi_2 = 1.5707963267948966192313216f;
static float sfltLn2 = 0.6931471805599453094172321f;
static float sfltAcross = 1.5f;
static float sfltBcross = 0.6417f;
float fltLsup = ssqrts((float) getOverflowThreshold())/8.0f;
float fltLinf = 4.0f * ssqrts((float) getUnderflowThreshold());
float fltEpsm = ssqrts((float) getRelativeMachinePrecision());
float fltAbsReal = sabss(creals(z));
float fltAbsImg = sabss(cimags(z));
float fltSignReal = localSign(creals(z));
float fltSignImg = localSign(cimags(z));
float fltR = 0, fltS = 0, fltA = 0, fltB = 0;
float fltTemp = 0;
float _pfltReal = 0;
float _pfltImg = 0;
if( min(fltAbsReal, fltAbsImg) > fltLinf && max(fltAbsReal, fltAbsImg) <= fltLsup)
{/* we are in the safe region */
fltR = ssqrts( (fltAbsReal + 1 )*(fltAbsReal + 1 ) + fltAbsImg*fltAbsImg);
fltS = ssqrts( (fltAbsReal - 1 )*(fltAbsReal - 1 ) + fltAbsImg*fltAbsImg);
fltA = 0.5f * ( fltR + fltS );
fltB = fltAbsReal / fltA;
/* compute the real part */
if(fltB <= sfltBcross)
_pfltReal = sacoss(fltB);
else if( fltAbsReal <= 1)
_pfltReal = satans(ssqrts(0.5f * (fltA + fltAbsReal) * (fltAbsImg*fltAbsImg / (fltR + (fltAbsReal + 1)) + (fltS + (1 - fltAbsReal)))) / fltAbsReal);
else
_pfltReal = satans((fltAbsImg * ssqrts(0.5f * ((fltA + fltAbsReal) / (fltR + (fltAbsReal + 1)) + (fltA + fltAbsReal) / (fltS + (fltAbsReal - 1))))) / fltAbsReal);
/* compute the imaginary part */
if(fltA <= sfltAcross)
{
float fltImg1 = 0;
if(fltAbsReal < 1)
/* Am1 = 0.5d0*((y**2)/(R+(x+1.d0))+(y**2)/(S+(1.d0-x))) */
fltImg1 = 0.5f * (fltAbsImg*fltAbsImg / (fltR + (fltAbsReal + 1)) + fltAbsImg*fltAbsImg / (fltS + (1 - fltAbsReal)));
else
/* Am1 = 0.5d0*((y**2)/(R+(x+1.d0))+(S+(x-1.d0))) */
fltImg1 = 0.5f * (fltAbsImg*fltAbsImg / (fltR + (fltAbsReal + 1)) + (fltS + (fltAbsReal - 1)));
/* ai = logp1(Am1 + sqrt(Am1*(A+1.d0))) */
fltTemp = fltImg1 + ssqrts(fltImg1 *( fltA + 1));
_pfltImg = slog1ps(fltTemp);
}
else
/* ai = log(A + sqrt(A**2 - 1.d0)) */
_pfltImg = slogs(fltA + ssqrts(fltA*fltA - 1));
}
else
{/* evaluation in the special regions ... */
if(fltAbsImg <= fltEpsm * sabss(fltAbsReal - 1))
{
if(fltAbsReal < 1)
{
_pfltReal = sacoss(fltAbsReal);
_pfltImg = fltAbsImg / ssqrts((1 + fltAbsReal) * (1 - fltAbsReal));
}
else
{
_pfltReal = 0;
if(fltAbsReal <= fltLsup)
{
fltTemp = (fltAbsReal - 1) + ssqrts((fltAbsReal - 1) * (fltAbsReal + 1));
_pfltImg = slog1ps(fltTemp);
}
else
_pfltImg = sfltLn2 + slogs(fltAbsReal);
}
}
else if(fltAbsImg < fltLinf)
{
_pfltReal = ssqrts(fltAbsImg);
_pfltImg = _pfltReal;
}
else if((fltEpsm * fltAbsImg - 1 >= fltAbsReal))
{
_pfltReal = sfltPi_2;
_pfltImg = sfltLn2 + slogs(fltAbsImg);
}
else if(fltAbsReal > 1)
{
_pfltReal = satans(fltAbsImg / fltAbsReal);
fltTemp = (fltAbsReal / fltAbsImg)*(fltAbsReal / fltAbsImg);
_pfltImg = sfltLn2 + slogs(fltAbsImg) + 0.5f * slog1ps(fltTemp);
}
else
{
float fltTemp2 = ssqrts(1 + fltAbsImg*fltAbsImg);
_pfltReal = sfltPi_2;
fltTemp = 2 * fltAbsImg * (fltAbsImg + fltTemp2);
_pfltImg = 0.5f * slog1ps(fltTemp);
}
}
if(fltSignReal < 0)
_pfltReal = sfltPi - _pfltReal;
if(fltAbsImg != 0 || fltSignReal < 0)
_pfltImg = - fltSignImg * _pfltImg;
return FloatComplex(_pfltReal, _pfltImg);
}
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