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/*
* Scilab ( http://www.scilab.org/ ) - This file is part of Scilab
* Copyright (C) 2008-2008 - 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
*
*/
#include <stdio.h>
#include <math.h>
#include "sqrt.h"
#include "lapack.h"
#include "abs.h"
#include "sign.h"
#include "pythag.h"
#ifdef _MSC_VER
#include <float.h>
#define isnan(x) _isnan((double)x)
#endif
#define _sign(a, b) b >=0 ? a : -a
doubleComplex zsqrts(doubleComplex in) {
double RMax = getOverflowThreshold();
double BRMin = 2 * getUnderflowThreshold();
double RealIn = zreals(in);
double ImgIn = zimags(in);
double RealOut = 0;
double ImgOut = 0;
if(RealIn == 0)
{/* pure imaginary case */
if(dabss(ImgIn >= BRMin))
RealOut = dsqrts(0.5 * dabss(ImgIn));
else
RealOut = dsqrts(dabss(ImgIn)) * dsqrts(0.5);
ImgOut = _sign(1, ImgIn) * RealOut;
}
else if( dabss(RealIn) <= RMax && dabss(ImgIn) <= RMax)
{/* standard case : a (not zero) and b are finite */
double Temp = dsqrts(2 * (dabss(RealIn) + dpythags(RealIn, ImgIn)));
/* overflow test */
if(Temp > RMax)
{/* handle (spurious) overflow by scaling a and b */
double RealTemp = RealIn / 16;
double ImgTemp = ImgIn / 16;
Temp = dsqrts(2 * (dabss(RealIn) + dpythags(RealIn, ImgTemp)));
if(RealTemp >= 0)
{
RealOut = 2 * Temp;
ImgOut = 4 * ImgTemp / Temp;
}
else
{
RealOut = 4 * dabss(ImgIn) / Temp;
ImgOut = _sign(2, ImgIn) * Temp;
}
}
else if(RealIn >= 0) /* classic switch to get the stable formulas */
{
RealOut = 0.5 * Temp;
ImgOut = ImgIn / Temp;
}
else
{
RealOut = dabss(ImgIn) / Temp;
ImgOut = (_sign(0.5, ImgIn)) * Temp;
}
}
else
{
/*
//Here we treat the special cases where a and b are +- 00 or NaN.
//The following is the treatment recommended by the C99 standard
//with the simplification of returning NaN + i NaN if the
//the real part or the imaginary part is NaN (C99 recommends
//something more complicated)
*/
if(isnan(RealIn) == 1 || isnan(ImgIn) == 1)
{/* got NaN + i NaN */
RealOut = RealIn + ImgIn;
ImgOut = RealOut;
}
else if( dabss(ImgIn) > RMax)
{/* case a +- i oo -> result must be +oo +- i oo for all a (finite or not) */
RealOut = dabss(ImgIn);
ImgOut = ImgIn;
}
else if(RealIn < -RMax)
{/* here a is -Inf and b is finite */
RealOut = 0;
ImgOut = _sign(1, ImgIn) * dabss(RealIn);
}
else
{/* here a is +Inf and b is finite */
RealOut = RealIn;
ImgOut = 0;
}
}
return DoubleComplex(RealOut, ImgOut);
}
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