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#include "variety.h"
#include <complex.h>
#include "cplx.h"

_WPRTLINK Complex asinh( const Complex &z ) {
/******************************************/
// Hyperbolic arcsin of a complex number.
// From "Complex Variables and Applications" (pg. 63).
//    asinh( z ) = log( z + sqrt( z*z + 1 ) )
//               = log( z + sqrt( 1 + (z.r + z.i)*(z.r - z.i) + 2*z.r*z.i*i ) )
    dcomplex    value;

    value = _IF_CDSQRT( 1.0 + (z.real()+z.imag())*(z.real()-z.imag()),
                    2.0 * z.real() * z.imag() );
    value = _IF_CDLOG( value.realpart + z.real(), value.imagpart + z.imag() );
    return Complex( value.realpart, value.imagpart );
}
