/* linbox/field/gmp-rational.h
 * Copyright (C) 2001, 2002 Bradford Hovinen
 *
 * Written by Bradford Hovinen <hovinen@cis.udel.edu>
 *
 * ----------------------------------------
 *
 * 
 * ========LICENCE========
 * This file is part of the library LinBox.
 * 
 * LinBox 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 2.1 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, write to the Free Software
 * Foundation, Inc., 51 Franklin Street, Fifth Floor, Boston, MA  02110-1301  USA
 * ========LICENCE========
 *
 */

#ifndef __LINBOX_field_gmp_rational_H
#define __LINBOX_field_gmp_rational_H

#include <iostream>
#include <cctype>

#include <gmp.h>

#include "linbox/integer.h"
#include "linbox/field/field-interface.h"
#include "linbox/element/gmp-rational.h"
#include "linbox/linbox-config.h"
#include "linbox/util/debug.h"
#include "linbox/field/field-traits.h"

// Namespace in which all LinBox library code resides
namespace LinBox
{

	// Forward declarations
	class GMPRationalRandIter ;

	/**
	 * \brief Field of rational numbers using GMP
	 \ingroup field
	 *
	 * This is a wrapper for the GMP rational number facility, built to the
	 * interface of the field archetype.
	 */

	template <class Ring>
	struct ClassifyRing;

	class GMPRationalField;

	template<>
	struct ClassifyRing<GMPRationalField> {
		typedef RingCategories::RationalTag categoryTag;
	};

	class GMPRationalField : public FieldInterface {
	private:

		const integer _cardinality;
		const integer _characteristic;

		const integer _zero;
		const integer _one;
		const integer _mOne;

	public:

		/** @name Common Object Interface for a LinBox Field.
		 * These methods are required of all \ref LinBox fields.
		 */
		//@{

		/// element type.
		typedef GMPRationalElement Element;

		/// Random iterator generator type.
		typedef GMPRationalRandIter RandIter;

		const Element zero;
		const Element one;
		const Element mOne;

		/** @name Object Management
		 * x <- convert (y)
		 */
		//@{

		/** Copy constructor.
		 *
		 * Vacuous, since this field is unparametric so there is no need to
		 * construct multiple field objects
		 */

		GMPRationalField (const GMPRationalField &) :
			_cardinality (0), _characteristic (0), _zero (0), _one (1), _mOne (-1),
			zero (_zero, _one), one (_one, _one), mOne (_mOne, _one)
		{}

		/** Destructor.
		 *
		 * Also vacuous, since there is no de-initialization system
		 */
		~GMPRationalField (void)
		{}

		/** Assignment operator.
		 *
		 * Also vacuous
		 */
		GMPRationalField &operator= (const GMPRationalField &)
		{
			return *this;
		}

		/** Initialization of field element from an integer.
		 * Behaves like C++ allocator construct.
		 * This function assumes the output field element x has already been
		 * constructed, but that it is not necessarily already initialized.
		 * In this implementation, this means the _elem_ptr of x exists, but
		 * that it may be the null pointer.
		 * @return reference to field element.
		 * @param x field element to contain output (reference returned).
		 * @param y constant reference to integer.
		 */
		Element &init (Element &x, const integer &y = 0) const
		{
			mpq_set_z (x. rep, SpyInteger::get_mpz(const_cast<integer&>(y)));
			//mpq_set_si (x.rep, (signed long) y, 1L);
			//mpq_canonicalize (x.rep);
			return x;
		}

		/*
		 * aniau@astronet.pl: 06/2009 Initialization of field element from numerator and denominator
		 * */
		Element &init (Element &x, const integer &num, const integer &den) const
		{
			init(x,num);
			Element y;
			init(y,den);
			divin(x,y);
			return x;
		}

		Element &init (Element &x, const Element &y) const
		{
			mpq_set (x.rep, y.rep);
			return x;
		}

		Element &init (Element &x, const int &y ) const
		{
			mpq_set_si (x. rep, (long)y,1L);
			//mpq_canonicalize (x.rep);
			return x;
		}

		Element &init (Element &x, const long int &y ) const
		{
			mpq_set_si (x. rep, (long)y,1L);
			//mpq_canonicalize (x.rep);
			return x;
		}

		Element &init (Element &x, const unsigned int &y ) const
		{
			mpq_set_ui (x. rep, (unsigned long)y,1L);
			//mpq_canonicalize (x.rep);
			return x;
		}

		Element &init (Element &x, const long unsigned int &y ) const
		{
			mpq_set_ui (x. rep, (long unsigned)y,1L);
			//mpq_canonicalize (x.rep);
			return x;
		}


		/** Conversion of field element to an integer.
		 * This function assumes the output field element x has already been
		 * constructed, but that it is not already initialized.
		 * In this implementation, this means the _elem_ptr of y exists, and
		 * that it is not the null pointer.
		 *
		 * Returns floor (numerator (y) / denominator (y))
		 *
		 * @return reference to integer.
		 * @param x reference to integer to contain output (reference returned).
		 * @param y constant reference to field element.
		 */
		integer &convert (integer &x, const Element &y = 0) const
		{
			mpz_t n, d;

			mpz_init (n);
			mpz_init (d);
			mpq_get_num (n, y.rep);
			mpq_get_den (d, y.rep);

			mpz_divexact (x.get_mpz(), n, d);

			mpz_clear (n);
			mpz_clear (d);

			/* Shouldn't there be something like this? We'll assume integer is gmp integers.
			   x.set_mpz(n);
			   */
#if 0
			x = integer::zero;

			// Really bad, but I know of no other general way to do this
			while (mpz_sgn (n) != 0) {
				// We need to be ready for multiple word sizes and so on here...
				x = (x << (sizeof (unsigned long) << 3)) + mpz_get_ui (n);
				mpz_tdiv_q_2exp (n, n, sizeof (unsigned long) << 3);
			}
#endif

			return x;
		}

		/** Assignment of one field element to another.
		 * This function assumes both field elements have already been
		 * constructed and initialized.
		 * In this implementation, this means for both x and y,
		 * _elem_ptr exists and does not point to null.
		 * @return reference to x
		 * @param  x field element (reference returned).
		 * @param  y field element.
		 *
		 * FIXME: Is this x := y? I am assuming so.
		 */
		Element &assign (Element &x, const Element &y) const
		{
			mpq_set (x.rep, y.rep);
			return x;
		}

		/// is infinite (signified by -1 here)
		integer &cardinality (integer &c) const
		{
			return c = _cardinality;
		}

		/// of the rationals is 0.
		integer &characteristic (integer &c) const
		{
			return c = _characteristic;
		}

		integer cardinality () const
		{
			return _cardinality ;
		}

		integer characteristic () const
		{
			return _characteristic ;
		}

		//@} Object Management

		/** @name Arithmetic Operations
		 * x <- y op z; x <- op y
		 * These operations require all elements, including x, to be initialized
		 * before the operation is called.  Uninitialized field elements will
		 * give undefined results.
		 */
		//@{

		/** Equality of two elements.
		 * This function assumes both field elements have already been
		 * constructed and initialized.
		 * In this implementation, this means for both x and y,
		 * _elem_ptr exists and does not point to null.
		 * @return boolean true if equal, false if not.
		 * @param  x field element
		 * @param  y field element
		 */
		bool areEqual (const Element &x, const Element &y) const
		{ return mpq_equal (x.rep, y.rep); }

		/** Addition.
		 * x = y + z
		 * This function assumes all the field elements have already been
		 * constructed and initialized.
		 * In this implementation, this means for x, y, and z,
		 * _elem_ptr exists and does not point to null.
		 * @return reference to x.
		 * @param  x field element (reference returned).
		 * @param  y field element.
		 * @param  z field element.
		 */
		Element &add (Element &x, const Element &y, const Element &z) const
		{
			mpq_add (x.rep, y.rep, z.rep);
			return x;
		}

		/** Subtraction.
		 * x = y - z
		 * This function assumes all the field elements have already been
		 * constructed and initialized.
		 * In this implementation, this means for x, y, and z,
		 * _elem_ptr exists and does not point to null.
		 * @return reference to x.
		 * @param  x field element (reference returned).
		 * @param  y field element.
		 * @param  z field element.
		 */
		Element &sub (Element &x, const Element &y, const Element &z) const
		{
			mpq_sub (x.rep, y.rep, z.rep);
			return x;
		}

		/** Multiplication.
		 * x = y * z
		 * This function assumes all the field elements have already been
		 * constructed and initialized.
		 * In this implementation, this means for x, y, and z,
		 * _elem_ptr exists and does not point to null.
		 * @return reference to x.
		 * @param  x field element (reference returned).
		 * @param  y field element.
		 * @param  z field element.
		 */
		Element &mul (Element &x, const Element &y, const Element &z) const
		{
			mpq_mul (x.rep, y.rep, z.rep);
			return x;
		}

		/** Division.
		 * x = y / z
		 * This function assumes all the field elements have already been
		 * constructed and initialized.
		 * In this implementation, this means for x, y, and z,
		 * _elem_ptr exists and does not point to null.
		 * @return reference to x.
		 * @param  x field element (reference returned).
		 * @param  y field element.
		 * @param  z field element.
		 */
		Element &div (Element &x, const Element &y, const Element &z) const
		{
			mpq_div (x.rep, y.rep, z.rep);
			return x;
		}

		/** Additive Inverse (Negation).
		 * x = - y
		 * This function assumes both field elements have already been
		 * constructed and initialized.
		 * In this implementation, this means for both x and y
		 * _elem_ptr exists and does not point to null.
		 * @return reference to x.
		 * @param  x field element (reference returned).
		 * @param  y field element.
		 */
		Element &neg (Element &x, const Element &y) const
		{
			mpq_neg (x.rep, y.rep);
			return x;
		}

		/** Multiplicative Inverse.
		 * x = 1 / y
		 * This function assumes both field elements have already been
		 * constructed and initialized.
		 * In this implementation, this means for both x and y
		 * _elem_ptr exists and does not point to null.
		 * @return reference to x.
		 * @param  x field element (reference returned).
		 * @param  y field element.
		 */
		Element &inv (Element &x, const Element &y) const
		{
			mpq_inv (x.rep, y.rep);
			return x;
		}

		//@} Arithmetic Operations

		/** @name Inplace Arithmetic Operations
		 * x <- x op y; x <- op x
		 * These operations require all elements, including x, to be initialized
		 * before the operation is called.  Uninitialized field elements will
		 * give undefined results.
		 */
		//@{

		/** Zero equality.
		 * Test if field element is equal to zero.
		 * This function assumes the field element has already been
		 * constructed and initialized.
		 * In this implementation, this means the _elem_ptr of x
		 * exists and does not point to null.
		 * @return boolean true if equals zero, false if not.
		 * @param  x field element.
		 */
		bool isZero (const Element &x) const
		{ return mpq_sgn (x.rep) == 0; }

		/** One equality.
		 * Test if field element is equal to one.
		 * This function assumes the field element has already been
		 * constructed and initialized.
		 * In this implementation, this means the _elem_ptr of x
		 * exists and does not point to null.
		 * @return boolean true if equals one, false if not.
		 * @param  x field element.
		 */
		bool isOne (const Element &x) const
		{ return mpq_cmp_ui (x.rep, 1L, 1L) == 0; }

		/** Inplace Addition.
		 * x += y
		 * This function assumes both field elements have already been
		 * constructed and initialized.
		 * In this implementation, this means for both x and y
		 * _elem_ptr exists and does not point to null.
		 * @return reference to x.
		 * @param  x field element (reference returned).
		 * @param  y field element.
		 */
		Element &addin (Element &x, const Element &y) const
		{
			mpq_add (x.rep, x.rep, y.rep);
			return x;
		}

		/** Inplace Subtraction.
		 * x -= y
		 * This function assumes both field elements have already been
		 * constructed and initialized.
		 * In this implementation, this means for both x and y
		 * _elem_ptr exists and does not point to null.
		 * @return reference to x.
		 * @param  x field element (reference returned).
		 * @param  y field element.
		 */
		Element &subin (Element &x, const Element &y) const
		{
			mpq_sub (x.rep, x.rep, y.rep);
			return x;
		}

		/** Inplace Multiplication.
		 * x *= y
		 * This function assumes both field elements have already been
		 * constructed and initialized.
		 * In this implementation, this means for both x and y
		 * _elem_ptr exists and does not point to null.
		 * @return reference to x.
		 * @param  x field element (reference returned).
		 * @param  y field element.
		 */
		Element &mulin (Element &x, const Element &y) const
		{
			mpq_mul (x.rep, x.rep, y.rep);
			return x;
		}

		/*! axpy.
		 * r = a*x + y
		 * @param r
		 * @param a
		 * @param x
		 * @param y
		 */
		Element &axpy (Element &r, const Element &a, const Element &x, const Element &y) const
		{
			mpq_mul (r.rep, a.rep, x.rep);
			mpq_add (r.rep, r.rep, y.rep);
			return r;
		}

		/*! axpyin.
		 * r += a*x
		 * @param r
		 * @param a
		 * @param x
		 */
		Element &axpyin (Element &r, const Element &a, const Element &x) const
		{
			Element tmp;
			mpq_mul (tmp.rep, a.rep, x.rep);
			mpq_add (r.rep, r.rep, tmp.rep);
			return r;
		}

		/** Inplace Division.
		 * x /= y
		 * This function assumes both field elements have already been
		 * constructed and initialized.
		 * In this implementation, this means for both x and y
		 * _elem_ptr exists and does not point to null.
		 * @return reference to x.
		 * @param  x field element (reference returned).
		 * @param  y field element.
		 */
		Element &divin (Element &x, const Element &y) const
		{
			mpq_div (x.rep, x.rep, y.rep);
			return x;
		}

		/** Inplace Additive Inverse (Inplace Negation).
		 * x = - x
		 * This function assumes the field element has already been
		 * constructed and initialized.
		 * In this implementation, this means the _elem_ptr of x
		 * exists and does not point to null.
		 * @return reference to x.
		 * @param  x field element (reference returned).
		 */
		Element &negin (Element &x) const
		{
			mpq_neg (x.rep, x.rep);
			return x;
		}

		/** Inplace Multiplicative Inverse.
		 * x = 1 / x
		 * This function assumes the field elementhas already been
		 * constructed and initialized.
		 * In this implementation, this means the _elem_ptr of x
		 * exists and does not point to null.
		 * @return reference to x.
		 * @param  x field element (reference returned).
		 */
		Element &invin (Element &x) const
		{
			mpq_inv (x.rep, x.rep);
			return x;
		}

		//@} Inplace Arithmetic Operations

		/** @name Input/Output Operations */
		//@{

		/** Print field.
		 * @return output stream to which field is written.
		 * @param  os  output stream to which field is written.
		 *
		 * This does not do much...
		 */
		std::ostream &write (std::ostream &os) const
		{
			os << "GMP rational numbers";
			return os;
		}

		/** Read field.
		 * @return input stream from which field is read.
		 * @param  is  input stream from which field is read.
		 *
		 * This does not do much either...
		 *
		 * FIXME: Read the same thing written above, and throw an exception if the
		 * strings do not match.
		 */
		std::istream &read (std::istream &is) { return is; }

		/** Print field element.
		 * This function assumes the field element has already been
		 * constructed and initialized.
		 * In this implementation, this means for the _elem_ptr for x
		 * exists and does not point to null.
		 * @return output stream to which field element is written.
		 * @param  os  output stream to which field element is written.
		 * @param  x   field element.
		 */
		std::ostream &write (std::ostream &os, const Element &x) const
		{
			char *str;

			str = new char[mpz_sizeinbase (mpq_numref (x.rep), 10) + 2];
			mpz_get_str (str, 10, mpq_numref (x.rep));
			os << str;
			delete[] str;

			if (mpz_cmp_ui (mpq_denref (x.rep), 1L) != 0) {
				str = new char[mpz_sizeinbase (mpq_denref (x.rep), 10) + 2];
				mpz_get_str (str, 10, mpq_denref (x.rep));
				os << '/' << str;
				delete[] str;
			}

			return os;
		}

		/** Read field element.
		 * This function assumes the field element has already been
		 * constructed and initialized.
		 * In this implementation, this means for the _elem_ptr for x
		 * exists and does not point to null.
		 * @return input stream from which field element is read.
		 * @param  is  input stream from which field element is read.
		 * @param  x   field element.
		 *
		 * FIXME: Avoid the magical limit on size here
		 * FIXME: Right now it skips over everything until it finds something that
		 * looks like a number. Is this really the correct policy?
		 *
		 * aniau@astronet.pl: 06/2009: supports scientific E/e notation for decimal fractions
		 */
		std::istream &read (std::istream &is, Element &x) const
		{
			char buffer[65535], endc;
			bool found_space = false;
			int i = 0;

			do {
				is.get (endc);
			} while (is && !isdigit (endc) && endc != '-' && endc != '.' &&  endc !='e' && endc != 'E');

			buffer[i]=endc;

			while ((buffer[i] == '-' || isdigit (buffer[i])) && i < 65535)  {
				i++;
				is.get (buffer[i]);
			}

			endc = buffer[i];
			buffer[i] = '\0';

			if (i > 0)
				mpz_set_str (mpq_numref (x.rep), buffer, 10);
			else
				mpq_set_si (x.rep, 0L, 1L);

			if (endc == ' ') {
				found_space = true;
				while (endc == ' ') is >> endc;
			}

			if (endc == '/') {
				i = 0;

				is.get (endc);
				while (isspace (endc)) is.get (endc);
				is.putback (endc);

				do {
					is.get (buffer[i++]);
				} while (isdigit (buffer[i - 1]) && i < 65536);

				is.putback (buffer[i - 1]);
				buffer[i - 1] = '\0';

				mpz_set_str (mpq_denref (x.rep), buffer, 10);
				mpq_canonicalize (x.rep);
				return is;
			}
			else {
				mpz_set_si (mpq_denref (x.rep), 1L);
			}

			if (endc == '.' && !found_space) {
				Element decimal_part;

				mpz_set_si (mpq_denref (x.rep), 1L);
				mpq_set_si (decimal_part.rep, 1L, 1L);
				mpz_set_si (mpq_denref (decimal_part.rep), 1L);

				i = 0;

				do {
					is.get (buffer[i++]);
					if (isdigit (buffer[i - 1]))
						mpz_mul_ui (mpq_denref (decimal_part.rep),
							    mpq_denref (decimal_part.rep), 10L);
				} while (isdigit (buffer[i - 1]) && i < 65536);

				is.putback (buffer[i - 1]);
				buffer[i - 1] = '\0';

				mpz_set_str (mpq_numref (decimal_part.rep), buffer, 10);
				mpq_canonicalize (decimal_part.rep);

				mpq_add (x.rep, x.rep, decimal_part.rep);

				do {
					is.get (endc);
				} while (is && endc == ' ') ;
			}

			if ((endc == 'e') || (endc == 'E')) {
				is.get(endc);
				bool minus = false;
				if (endc == '-') {
					minus = true;
				}
				else if (endc == '+') {
					minus = false;
				}
				else {
					is.putback(endc);
				}

				i=0;
				do {
					is.get (buffer[i++]);
				} while (isdigit (buffer[i-1]) && i < 65536);
				is.putback(buffer[i-1]);
				buffer[i-1] = '\0';

				integer pow(buffer), powten=1;

				for (integer it=0; it< pow; ++it) powten *=10;
				if (minus) {
					div(x,x,powten);
				}
				else {
					mul(x,x,powten);
				}
			}
			else {
				is.putback (endc);
				//	mpz_set_si (mpq_denref (x.rep), 1L);
			}

			mpq_canonicalize (x.rep);

			return is;
		}

		//@} Input/Output Operations


		//@} Common Object Interface

		GMPRationalField (int p = 0, int exp = 1) :
			_cardinality (0), _characteristic (0), _zero (0), _one (1), _mOne (-1),
			zero (_zero, _one), one (_one, _one), mOne (_mOne, _one)
		{
			if(p != 0) throw PreconditionFailed(__func__,__FILE__,__LINE__,"modulus must be 0 (no modulus)");
			if(exp != 1) throw PreconditionFailed(__func__,__FILE__,__LINE__,"exponent must be 1");
		}

		/// max modulus.
		static inline int getMaxModulus() { return 0; } // no modulus

		/*! get numerator.
		 * @param x  numerator of y
		 * @param y
		 */
		integer& get_num (integer& x, const Element& y)  const{
			mpq_get_num (SpyInteger::get_mpz(x), y. rep);
			return x;

		}

		/*! get denominator.
		 * @param x  denominator of y
		 * @param y
		 */
		integer& get_den (integer& x, const Element& y) const
		{
			mpq_get_den (SpyInteger::get_mpz(x), y. rep);
			return x;
		}

		/*! sign.
		 * @param x
		 * @return sign of \c x
		 */
		int sign (const Element& x) const
		{
			return mpq_sgn (x. rep);
		}

		/*!
		 * Bitsize as sum of bitsizes of numerator and denominator.
		 * @param bs
		 * @param q
		 * @return \c bs
		 */
		integer& bitsize(integer& bs, const Element q) const
		{
			integer y; get_den(y,q);
			integer x; get_num(x,q);
			bs = x.bitsize() + y.bitsize();
			return bs;
		}


	}; // class GMPRationalField


#if 0
	// use GMPRationalField::read() and GMPRationalField::write(), not these operators.
	std::ostream &operator << (std::ostream &os, GMPRationalElement &elt)
	{
		GMPRationalField field;

		field.write (os, elt);
		return os;
	}

	std::istream &operator >> (std::istream &is, GMPRationalElement &elt)
	{
		GMPRationalField field;

		field.read (is, elt);
		return is;
	}

#endif

} // namespace LinBox

#include "linbox/randiter/gmp-rational.h"

#endif // __LINBOX_field_gmp_rational_H



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