rational.h

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/**
 *
 *   Copyright (c) 2005-2021 by Pierre-Henri WUILLEMIN(@LIP6) & Christophe GONZALES(@AMU)
 *   info_at_agrum_dot_org
 *
 *  This library is free software: 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.
 *
 *  This library 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 Lesser General Public License for more details.
 *
 *  You should have received a copy of the GNU Lesser General Public License
 *  along with this library.  If not, see <http://www.gnu.org/licenses/>.
 *
 */


/**
 * @file
 * @brief Class template used to approximate decimal numbers by rationals
 * @author Matthieu HOURBRACQ and Pierre-Henri WUILLEMIN(@LIP6)
 */

#ifndef GUM_RATIONAL_H
#define GUM_RATIONAL_H

#include <iomanip>
#include <iostream>
#include <sstream>
#include <stdlib.h>
#include <vector>
#include <agrum/tools/core/math/math_utils.h>

// 64 bits for windows (long is 32 bits)
#ifdef _MSC_VER
typedef __int64          int64_t;
typedef unsigned __int64 uint64_t;
#else
#  include <stdint.h>
#endif

namespace gum {

  /**
   * @class Rational
   * @headerfile rational.h <agrum/tools/core/math/rational.h>
   * @brief Class template used to approximate decimal numbers by rationals.
   * @ingroup math_group
   *
   * @tparam GUM_SCALAR The floating type ( float, double, long double ... ) of
   * the number.
   */
  template < typename GUM_SCALAR >
  class Rational {
    public:
    // ========================================================================
    /// @name Real approximation by rational
    // ========================================================================
    /// @{

    /**
     * @brief Find the rational close enough to a given ( decimal ) number in
     * [-1,1] and whose denominator is not higher than a given integer number.
     *
     * Because of the double constraint on precision and size of the
     * denominator, there is no guarantee on the precision of the approximation
     * if \c den_max is low and \c zero is high. Prefer the use of continued
     * fractions.
     *
     * @param numerator The numerator of the rational.
     * @param denominator The denominator of the rational.
     * @param number The constant number we want to approximate using rationals.
     * @param den_max The constant highest authorized denominator. 1000000 by
     * default.
     * @param zero The positive value below which a number is considered zero.
     * 1e-6 by default.
     */
    static void farey(int64_t&          numerator,
                      int64_t&          denominator,
                      const GUM_SCALAR& number,
                      const int64_t&    den_max = 1000000L,
                      const GUM_SCALAR& zero    = 1e-6);

    /**
     * @brief Find the first best rational approximation.
     *
     * The one with the smallest denominator such that no other rational with
     * smaller denominator is a better approx,  within precision zero to a
     * given ( decimal ) number ( ANY number).
     *
     * It gives the same answer than farey assuming \c zero is the same and
     * den_max is infinite. Use this functions because you are sure to get an
     * approx within \c zero of \c number.
     *
     * We look at the semi-convergents left of the last admissible convergent,
     * if any. They may be within the same precision and have a smaller
     * denominator.
     *
     * @param numerator The numerator of the rational.
     * @param denominator The denominator of the rational.
     * @param number The constant number we want to approximate using rationals.
     * @param zero The positive value below which a number is considered zero.
     * 1e-6 by default.
     */
    static void continuedFracFirst(int64_t&          numerator,
                                   int64_t&          denominator,
                                   const GUM_SCALAR& number,
                                   const double&     zero = 1e-6);

    /**
     * @brief Find the best rational approximation.
     *
     * Not the first, to a given ( decimal) number ( ANY number ) and whose
     * denominator is not higher than a given integer number.
     *
     * In this case, we look for semi-convergents at the right of the last
     * admissible convergent, if any. They are better approximations, but have
     * higher denominators.
     *
     * @param numerator The numerator of the rational.
     * @param denominator The denominator of the rational.
     * @param number The constant number we want to approximate using rationals.
     * @param den_max The constant highest authorized denominator. 1000000 by
     * default.
     */
    static void continuedFracBest(int64_t&          numerator,
                                  int64_t&          denominator,
                                  const GUM_SCALAR& number,
                                  const int64_t&    den_max = 1000000);

    /// @}
  };

}   // namespace gum


#ifndef GUM_NO_EXTERN_TEMPLATE_CLASS
#  ifndef GUM_NO_EXTERN_TEMPLATE_CLASS
extern template class gum::Rational< double >;
#  endif
#endif
#ifndef GUM_NO_EXTERN_TEMPLATE_CLASS
#  ifndef GUM_NO_EXTERN_TEMPLATE_CLASS
extern template class gum::Rational< long double >;
#  endif
#endif


// Always include template implementation in header file
#include <agrum/tools/core/math/rational_tpl.h>

#endif   // GUM_RATIONAL_H