/*  scfcabsH.cpp by K.Tsuru  */
// function ID = 9001
/***************************************
SN library
SComplex class reference
It returns the absolute value of z in high precision version.
****************************************/
#ifndef SN_H
#include "sn.h"
#endif
SDouble CabsH(const SComplex& z){
// z = x + iy
    SDouble x( z.Real() ), y( z.Imag() ), r;
// It takes absolute values.
    if(x.Sign()<0) x.ChangeSign();
    if(y.Sign()<0) y.ChangeSign();
// z = x+i*y
    if(x.Sign() == 0) return y; // |y|
    if(y.Sign() == 0) return x; // |x|

// |z| = sqrt(x*x+y*y) = |x|*sqrt(1+(y/x)^2) for |x| > |y|
    if(x > y){ // |x|>|y|
        r = y/x;
        r = 1.0 + r*r;
        r = x*Sqrt(r);
    } else {  // |x|<=|y|
        r = x/y;
        r = 1.0 + r*r;
        r = y*Sqrt(r);
    }
    return r;
}