// TODO: Add licence
//
// This file is provided AS IS with NO WARRANTY OF ANY KIND, INCLUDING THE
// WARRANTY OF DESIGN, MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE.
//
// $URL:$
// $Id: $
// 
//
// Author(s)     :  
//
// ============================================================================

// TODO: The comments are all original EXACUS comments and aren't adapted. So
//         they may be wrong now.

#ifndef CGAL_POLYNOMIAL_UNIVARIATE_POLYNOMIAL_UTILS_H
#define CGAL_POLYNOMIAL_UNIVARIATE_POLYNOMIAL_UTILS_H

#include <CGAL/Polynomial.h>

CGAL_BEGIN_NAMESPACE

namespace INTERN_POLYNOMIAL {
    //! return an upper bound on the absolute value of all real roots of \c P.
    /*! The upper bound is a power of two. Only works for univariate polynomials.
     *  \pre \c NT must be \c RealComparable.
     *  \relates NiX::Polynomial
     */
    template <class NT>
    NT weak_upper_root_bound(const Polynomial<NT>& P) { 
        // code comes from Kurt Mehlhorn
        // see [Mignotte, 1992], p.144 for a proof
        CGAL_precondition(Polynomial_traits_d<NT>::d == 0);
        typename Real_embeddable_traits<NT>::Abs abs;
        const int n = P.degree();
        NT x(1); 
        NT val;
        for (;;) {
            val = -abs(P[n]);
            for (int i = n-1; i >= 0; i--) {
                val = val*x + abs(P[i]);
            }
            if (val < NT(0)) return x;
            x *= NT(2);
        }
    }
    
    //! return the number of sign variations in the coefficient sequence of \c P.
    /*! This is the number of sign changes (+ to - or - to +) in the
     *  coefficient sequence of the polynomial, ignoring zeroes.
     *  Only meaningful for univariate polynomials.
     *  \pre \c NT must be \c RealComparable.
     *  \relates NiX::Polynomial
     */
    template <class NT>
    int sign_variations(const Polynomial<NT>& P) { 
        typename Real_embeddable_traits<NT>::Sign sign;
        const int n = P.degree();
        int variations = 0;
        int old_sign = sign(P[n]); // never zero unless P is zero
        for (int i = n-1; i >= 0; i--) {
            int s = sign(P[i]);
            if (s == 0) continue;
            if (old_sign != s) {
                old_sign = s;
                variations++;
            }
        }
        return variations;
    }

} // namespace INTERN_POLYNOMIAL

CGAL_END_NAMESPACE


#endif // CGAL_POLYNOMIAL_UNIVARIATE_POLYNOMIAL_UTILS_H