/*! \file
Copyright (c) 2003, The Regents of the University of California, through
Lawrence Berkeley National Laboratory (subject to receipt of any required 
approvals from U.S. Dept. of Energy) 

All rights reserved. 

The source code is distributed under BSD license, see the file License.txt
at the top-level directory.
*/

/*! @file scomplex.c
 * \brief Common arithmetic for complex type
 *
 * <pre>
 * -- SuperLU routine (version 2.0) --
 * Univ. of California Berkeley, Xerox Palo Alto Research Center,
 * and Lawrence Berkeley National Lab.
 * November 15, 1997
 *
 * This file defines common arithmetic operations for complex type.
 * </pre>
 */

#include <math.h>
#include <stdlib.h>
#include <stdio.h>
#include "slu_scomplex.h"


/*! \brief Complex Division c = a/b */
void c_div(complex *c, complex *a, complex *b)
{
    float ratio, den;
    float abr, abi, cr, ci;
  
    if( (abr = b->r) < 0.)
	abr = - abr;
    if( (abi = b->i) < 0.)
	abi = - abi;
    if( abr <= abi ) {
	if (abi == 0) {
	    fprintf(stderr, "z_div.c: division by zero\n");
            exit(-1);
	}	  
	ratio = b->r / b->i ;
	den = b->i * (1 + ratio*ratio);
	cr = (a->r*ratio + a->i) / den;
	ci = (a->i*ratio - a->r) / den;
    } else {
	ratio = b->i / b->r ;
	den = b->r * (1 + ratio*ratio);
	cr = (a->r + a->i*ratio) / den;
	ci = (a->i - a->r*ratio) / den;
    }
    c->r = cr;
    c->i = ci;
}


/*! \brief Returns sqrt(z.r^2 + z.i^2) */
double c_abs(complex *z)
{
    float temp;
    float real = z->r;
    float imag = z->i;

    if (real < 0) real = -real;
    if (imag < 0) imag = -imag;
    if (imag > real) {
	temp = real;
	real = imag;
	imag = temp;
    }
    if ((real+imag) == real) return(real);
  
    temp = imag/real;
    temp = real*sqrt(1.0 + temp*temp);  /*overflow!!*/
    return (temp);
}


/*! \brief Approximates the abs. Returns abs(z.r) + abs(z.i) */
double c_abs1(complex *z)
{
    float real = z->r;
    float imag = z->i;
  
    if (real < 0) real = -real;
    if (imag < 0) imag = -imag;

    return (real + imag);
}

/*! \brief Return the exponentiation */
void c_exp(complex *r, complex *z)
{
    float expx;

    expx = exp(z->r);
    r->r = expx * cos(z->i);
    r->i = expx * sin(z->i);
}

/*! \brief Return the complex conjugate */
void r_cnjg(complex *r, complex *z)
{
    r->r = z->r;
    r->i = -z->i;
}

/*! \brief Return the imaginary part */
double r_imag(complex *z)
{
    return (z->i);
}


/*! \brief SIGN functions for complex number. Returns z/abs(z) */
complex c_sgn(complex *z)
{
    register float t = c_abs(z);
    register complex retval;

    if (t == 0.0) {
	retval.r = 1.0, retval.i = 0.0;
    } else {
	retval.r = z->r / t, retval.i = z->i / t;
    }

    return retval;
}

/*! \brief Square-root of a complex number. */
complex c_sqrt(complex *z)
{
    complex retval;
    register float cr, ci, real, imag;

    real = z->r;
    imag = z->i;

    if ( imag == 0.0 ) {
        retval.r = sqrt(real);
        retval.i = 0.0;
    } else {
        ci = (sqrt(real*real + imag*imag) - real) / 2.0;
        ci = sqrt(ci);
        cr = imag / (2.0 * ci);
        retval.r = cr;
        retval.i = ci;
    }

    return retval;
}