// Copyright (c) 2009-2014 INRIA Sophia-Antipolis (France).
// All rights reserved.
//
// This file is part of CGAL (www.cgal.org); you can redistribute it and/or
// modify it under the terms of the GNU Lesser General Public License as
// published by the Free Software Foundation; either version 3 of the License,
// or (at your option) any later version.
//
// Licensees holding a valid commercial license may use this file in
// accordance with the commercial license agreement provided with the software.
//
// This file is provided AS IS with NO WARRANTY OF ANY KIND, INCLUDING THE
// WARRANTY OF DESIGN, MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE.
//
// $URL: https://github.com/CGAL/cgal/blob/releases/CGAL-4.14.3/Kernel_d/include/CGAL/Kernel_d/Interval_linear_algebra.h $
// $Id: Interval_linear_algebra.h 0698f79 2017-10-20T23:34:14+02:00 Sébastien Loriot
// SPDX-License-Identifier: LGPL-3.0+
//
// Author(s)    : Samuel Hornus, Olivier Devillers

#ifndef CGAL_INTERVAL_LINEAR_ALGEBRA_H
#define CGAL_INTERVAL_LINEAR_ALGEBRA_H

#include <CGAL/Interval_nt.h>
#include <CGAL/predicates/sign_of_determinant.h>

namespace CGAL {

namespace internal
{

template<class Matrix>
Sign // The matrix is row major: M[i] represents row i.
/*
FIXME : the function DOES MODIFY the matrix M, but calling functions
assume M is not modified --> BUGS. (e.g. Side_of_oriented_subsphere)
*/
sign_of_determinantDxD_with_interval_arithmetic(Matrix & M)
// attempts to compute the determinant using interval arithmetic
{
    typedef Interval_nt<false> NT; // Field number type
    int sign = 1;
    int curdim = M.dimension().first;
    for(int col = 0; col < curdim; ++col)
    {
	int pivot_line = -1;
	NT pivot = 0.0;
	for(int l = col; l < curdim; ++l)
	{
	    NT candidate = CGAL::abs(M[l][col]);
	    if( CGAL::certainly(0.0 < candidate) )
		if( pivot.inf() < candidate.inf() )
		{
		    pivot_line = l;
		    pivot = candidate;
		}
	}
	if( -1 == pivot_line )
	{
	    throw CGAL::Uncertain_conversion_exception("undecidable interval computation of determinant");
	}
	// if the pivot value is negative, invert the sign
	if( M[pivot_line][col] < 0.0 )
	    sign = - sign;
	// put the pivot cell on the diagonal
	if( pivot_line > col )
	{
	    std::swap(M[col], M[pivot_line]); // this takes constant time with std::vector<>
	    sign = - sign;
	}
	// using matrix-line operations, set zero in all cells below the pivot cell.
	// This costs roughly (curdim-col-1)^2 mults and adds, because we don't actually
	// compute the  zeros below the pivot cell
	NT denom = NT(1.0) / M[col][col];
	for(int line = col + 1; line < curdim; ++line)
	{
	    NT numer = M[line][col] * denom;
	    for (int c = col + 1; c < curdim; ++c)
		M[line][c] -= numer * M[col][c];
	}
    }
    return Sign(sign);
}

} // end of namespace internal

template<>
inline
Sign
Linear_algebraCd<Interval_nt_advanced>::sign_of_determinant(const Matrix & M)
{
    switch( M.dimension().first )
    {
	case 2:
	    return CGAL::sign_of_determinant( M(0,0), M(0,1),
		    M(1,0), M(1,1));
	    break;
	case 3:
	    return CGAL::sign_of_determinant( M(0,0), M(0,1), M(0,2),
		    M(1,0), M(1,1), M(1,2),
		    M(2,0), M(2,1), M(2,2));
	    break;
	case 4:
	    return CGAL::sign_of_determinant( M(0,0), M(0,1), M(0,2), M(0,3),
		    M(1,0), M(1,1), M(1,2), M(1,3),
		    M(2,0), M(2,1), M(2,2), M(2,3),
		    M(3,0), M(3,1), M(3,2), M(3,3));
	    break;
	default:
	    return internal::sign_of_determinantDxD_with_interval_arithmetic(const_cast<Matrix &>(M));
	    break;
    }
}

} //namespace CGAL

#endif // CGAL_INTERVAL_LINEAR_ALGEBRA_H
