rational.h

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/*****************************************************************************/
/*!
 * \file rational.h
 * 
 * Author: Sergey Berezin
 * 
 * Created: Dec 12 22:00:18 GMT 2002
 *
 * <hr>
 * Copyright (C) 2003 by the Board of Trustees of Leland Stanford
 * Junior University and by New York University. 
 *
 * License to use, copy, modify, sell and/or distribute this software
 * and its documentation for any purpose is hereby granted without
 * royalty, subject to the terms and conditions defined in the \ref
 * LICENSE file provided with this distribution.  In particular:
 *
 * - The above copyright notice and this permission notice must appear
 * in all copies of the software and related documentation.
 *
 * - THE SOFTWARE IS PROVIDED "AS-IS", WITHOUT ANY WARRANTIES,
 * EXPRESSED OR IMPLIED.  USE IT AT YOUR OWN RISK.
 * 
 * <hr>
 * 
 */
/*****************************************************************************/
// Class: Rational
// Author: Sergey Berezin, 12/12/2002 (adapted from Bignum)
//
// Description: This is an abstration of a rational with arbitrary
// precision.  It provides a constructor from a pair of ints and
// strings, overloaded operator{+,-,*,/}, assignment, etc.  The
// current implementation uses GMP mpq_class.
///////////////////////////////////////////////////////////////////////////////

#ifndef _CVC_lite__rational_h_
#define _CVC_lite__rational_h_

// Do not include <gmpxx.h> here; it contains some depricated C++
// headers.  We only include it in the .cpp file.

#include <string>
#include <vector>
#include <iostream>
#include "debug.h"

// To be defined only in bignum.cpp
namespace CVCL {

  class Rational {
  private:
    class Impl;
    Impl *d_n;
    // Debugging
#ifdef _DEBUG_RATIONAL_
    // Encapsulate static values in a function to guarantee
    // initialization when we need it
    int& getCreated() {
      static int num_created = 0;
      return(num_created);
    }
      
    int& getDeleted() {
      static int num_deleted = 0;
      return(num_deleted);
    }
      
    void printStats();
#endif
    // Private constructor (for internal consumption only)
    Rational(const Impl& t);

  public:
    // Constructors
    Rational();
    // Copy constructor
    Rational(const Rational &n);
    Rational(int n, int d = 1);
    Rational(const char* n, int base = 10);
    Rational(const std::string& n, int base = 10);
    Rational(const char* n, const char* d, int base = 10);
    Rational(const std::string& n, const std::string& d, int base = 10);
    // Destructor
    ~Rational();

    // Assignment
    Rational& operator=(const Rational& n);

    std::string toString(int base = 10) const;

    // Compute hash value (for DAG expression representation)
    size_t hash() const;

    friend bool operator==(const Rational &n1, const Rational &n2);
    friend bool operator<(const Rational &n1, const Rational &n2);
    friend bool operator<=(const Rational &n1, const Rational &n2);
    friend bool operator>(const Rational &n1, const Rational &n2);
    friend bool operator>=(const Rational &n1, const Rational &n2);
    friend bool operator!=(const Rational &n1, const Rational &n2);
    friend Rational operator+(const Rational &n1, const Rational &n2);
    friend Rational operator-(const Rational &n1, const Rational &n2);
    friend Rational operator*(const Rational &n1, const Rational &n2);
    friend Rational operator/(const Rational &n1, const Rational &n2);
    // 'mod' operator, defined only for integer values of n1 and n2
    friend Rational operator%(const Rational &n1, const Rational &n2);

    // Unary minus
    Rational operator-() const;
    Rational &operator+=(const Rational &n2);
    Rational &operator-=(const Rational &n2);
    Rational &operator*=(const Rational &n2);
    Rational &operator/=(const Rational &n2);
    //! Prefix increment
    const Rational& operator++() { *this = (*this)+1; return *this; }
    //! Postfix increment
    Rational operator++(int) { Rational x(*this); *this = x+1; return x; }
    //! Prefix decrement
    const Rational& operator--() { *this = (*this)-1; return *this; }
    //! Postfix decrement
    Rational operator--(int) { Rational x(*this); *this = x-1; return x; }

    // Resust is integer
    Rational getNumerator() const;
    Rational getDenominator() const;

    // Equivalent to (getDenominator() == 1), but possibly more efficient
    bool isInteger() const;
    // Convert to int; defined only on integer values
    int getInt() const;
    // Equivalent to (*this >= 0 && isInteger())
    bool isUnsigned() const { return (isInteger() && (*this) >= 0); }
    // Convert to unsigned int; defined only on non-negative integer values
    unsigned int getUnsigned() const;

    friend std::ostream &operator<<(std::ostream &os, const Rational &n);

    /* Computes gcd and lcm on *integer* values. Result is always a
       positive integer. */

    friend Rational gcd(const Rational &x, const Rational &y);
    friend Rational gcd(const std::vector<Rational> &v);
    friend Rational lcm(const Rational &x, const Rational &y);
    friend Rational lcm(const std::vector<Rational> &v);

    friend Rational abs(const Rational &x);

    //! Compute the floor of x (result is an integer)
    friend Rational floor(const Rational &x);
    //! Compute the ceiling of x (result is an integer)
    friend Rational ceil(const Rational &x);
    //! Compute non-negative remainder for *integer* x,y.
    friend Rational mod(const Rational &x, const Rational &y);

    // For debugging, to be able to print in gdb
    void print() const;

  }; // Rational class

  //! Raise 'base' into the power of 'pow' (pow must be an integer)
  inline Rational pow(Rational pow, const Rational& base) {
    DebugAssert(pow.isInteger(), "pow("+pow.toString()
                +", "+base.toString()+")");
    bool neg(pow < 0);
    if(neg) pow = -pow;
    Rational res(1);
    for(; pow > 0; --pow) res *= base;
    if(neg) res = 1/res;
    return res;
  }

  
  // Methods creating new Rational values, similar to the
  // constructors, but can be nested
  inline Rational newRational(int n, int d = 1) { return Rational(n, d); }
  inline Rational newRational(const char* n, int base = 10)
    { return Rational(n, base); }
  inline Rational newRational(const std::string& n, int base = 10)
    { return Rational(n, base); }
  inline Rational newRational(const char* n, const char* d, int base = 10)
    { return Rational(n, d, base); }
  inline Rational newRational(const std::string& n, const std::string& d,
                              int base = 10)
    { return Rational(n, d, base); }
    
  // Debugging print
  void printRational(const Rational &x);

}; // end of namespace CVCL

#endif

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