/** @file time_lw_H.cpp
 *
 *  Test H from the paper "Comparison of Polynomial-Oriented CAS" by Robert H.
 *  Lewis and Michael Wester. */

/*
 *  GiNaC Copyright (C) 1999-2001 Johannes Gutenberg University Mainz, Germany
 *
 *  This program is free software; you can redistribute it and/or modify
 *  it under the terms of the GNU General Public License as published by
 *  the Free Software Foundation; either version 2 of the License, or
 *  (at your option) any later version.
 *
 *  This program is distributed in the hope that it will be useful,
 *  but WITHOUT ANY WARRANTY; without even the implied warranty of
 *  MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the
 *  GNU General Public License for more details.
 *
 *  You should have received a copy of the GNU General Public License
 *  along with this program; if not, write to the Free Software
 *  Foundation, Inc., 59 Temple Place, Suite 330, Boston, MA  02111-1307  USA
 */

#include "times.h"

static unsigned test(unsigned n)
{
	matrix hilbert(n,n);
	
	for (unsigned r=0; r<n; ++r)
		for (unsigned c=0; c<n; ++c)
			hilbert.set(r,c,numeric(1,r+c+1));
	ex det = hilbert.determinant();
	
	/*
	   The closed form of the determinant of n x n Hilbert matrices is:
	
	     n-1   /                      n-1                 \
	    ----- |                      -----                 |
	     | |  | pow(factorial(r),2)   | |    hilbert(r,c)  |
	     | |  |                       | |                  |   
	    r = 0  \                     c = 0                /
	*/
	
	ex hilbdet = 1;
	for (unsigned r=0; r<n; ++r) {
		hilbdet *= pow(factorial(numeric(r)),2);
		for (unsigned c=0; c<n; ++c)
			hilbdet *= hilbert(r,c);
	}
	
	if (det != hilbdet) {
		clog << "determinant of " << n << "x" << n << " erroneously returned " << det << endl;
		return 1;
	}
	return 0;
}

unsigned time_lw_H(void)
{
	unsigned result = 0;
	unsigned count = 0;
	timer rolex;
	double time = .0;
	
	cout << "timing Lewis-Wester test H (det of 80x80 Hilbert)" << flush;
	clog << "-------Lewis-Wester test H (det of 80x80 Hilbert)" << endl;
	
	rolex.start();
	// correct for very small times:
	do {
		result = test(80);
		++count;
	} while ((time=rolex.read())<0.1 && !result);
	cout << '.' << flush;
	
	if (!result) {
		cout << " passed ";
		clog << "(no output)" << endl;
	} else {
		cout << " failed ";
	}
	cout << int(1000*(time/count))*0.001 << 's' << endl;
	
	return result;
}