/*  scfacosh.cpp  by K.Tsuru  */
// function ID = 9118  since ver 2.18
// bug fix version 2.21
/*****************************************
SComplex class
It returns arcosh(z).
Cacosh(z) = Clog{z + Csqrt(z+1)*Csqrt(z-1)}.
 ={ i arccos(z) Im(z)>0
  { (-i)arccos(z) Im(z)<0
Gradshteyn and Ryzhik (2000, p. xxx) 
[reference]WolframMathWorld's page
Calculus and Analysis > Special Functions > Hyperbolic Functions >
Interactive Entries > webMathematica Examples >
Inverse Hyperbolic Cosine
ver 2.21
When z = x(pure real),let acosh(x) = p,
  x = cosh(p) >= 1 must be satisfied.
*****************************************/
#ifndef SN_H
#include "sn.h"
#endif

#if 0

SComplex Cacosh(const SComplex& z) {
//  SComplex y = Csqrt(z * z - ONE); cannot be used.
    if(z == 0.0) return SComplex(0.0, MPi2()); // log(i) = i*pi/2
    if(Im(z) == 0.0){ // pure real z = x
        if(Re(z) <= 1.0) z.Real().SetError(z.Real().DOMAIN_ERR, "Cacosh(z) with z = x(x < 1.0))", 9118);
        return SComplex(Acosh(Re(z)), 0.0);  // arcosh(x)
    }
    SComplex y = Csqrt(z + ONE) * Csqrt(z - ONE);
    return Clog(z + y);
}
#else /********************************/

SComplex Cacosh(const SComplex& z) {
    if(z == 0.0) return SComplex(0.0, MPi2()); // log(i) = i*pi/2
    if(Im(z) == 0.0){ // pure real z = x
        if(Re(z) <= 1.0) z.Real().SetError(z.Real().DOMAIN_ERR, "Cacosh(z) with z = x(x < 1.0))", 9116);
        return SComplex(Acosh(Re(z)), 0.0);  // arcosh(x)
    }
    
//if(z == 0.0) return Clog(I);
    if(Im(z) > 0.0) return IU * Cacos(z);// i*arccos(z) in the upper half of the complex plane
    return MI * Cacos(z);               // -i*arccos(z)
}
#endif