// =================================================================== //
// Copyright(c)'1994-2009 by The Givaro group
// This file is part of Givaro.
// Givaro is governed by the CeCILL-B license under French law
// and abiding by the rules of distribution of free software.
// see the COPYRIGHT file for more details.
//
// Time-stamp: <30 Jun 04 10:59:26 Jean-Guillaume.Dumas@imag.fr>
// =================================================================== //

/*! @file givintnumtheo.h
 * @ingroup integers
 * @brief num theory.
 * - Euler's phi function
 * -  Primitive roots
 * - RSA scheme.
 * .
 */

#ifndef __GIVARO_numtheory_H
#define __GIVARO_numtheory_H

#include <iostream>
#include "givaro/givinteger.h"
#include "givaro/givintprime.h"
#include "givaro/givintfactor.h"
#include "givaro/givrandom.h"

namespace Givaro {
	//! Num theory Domain.
	template<class RandIter = GivRandom>
		class IntNumTheoDom : public IntFactorDom<RandIter> {
			public:
				typedef IntFactorDom<RandIter> Father_t;
				typedef typename IntFactorDom<RandIter>::Rep Rep;
				IntNumTheoDom(RandIter g = RandIter())
					:  IntFactorDom<RandIter>(g) {}

				// =================================================================== //
				//! Euler's phi function
				// =================================================================== //
				template <template <class, class> class Container, template<class> class Alloc>
					Rep& phi(Rep& res, const Container<Rep, Alloc<Rep> >& Lf, const Rep& n) const ;

				Rep& phi(Rep& r, const Rep& n) const ;

				// =================================================================== //
				//! Primitive Root
				// =================================================================== //
				Rep& prim_root(Rep&, const Rep&) const ;
				Rep& prim_root(Rep&, unsigned long&, const Rep&) const ;
				Rep& prim_root_of_prime(Rep&, const Rep&) const ;
				template<class Array> Rep& prim_root_of_prime(Rep& A, const Array& Lf, const Rep& phin, const Rep& n) const ;

				/**  Polynomial-time generation of primitive roots.
				*  L is number of loops of Pollard partial factorization of n-1
				*  10,000,000 gives at least 1-2^{-40} probability of success
				*  [Dubrois & Dumas, Industrial-strength primitive roots]
				*  Returns the probable primitive root and the probability of error.
				*/
				Rep& probable_prim_root(Rep&, double&, const Rep& n, const unsigned long L = 10000000) const;

				//!  Here L is computed so that the error is close to epsilon
				Rep& probable_prim_root(Rep&, double&, const Rep& n, const double epsilon) const;

				Rep& lowest_prim_root(Rep&, const Rep&) const ;
				bool is_prim_root(const Rep&, const Rep&) const ;
				Rep& order(Rep&, const Rep&, const Rep&) const ;
				bool isorder(const Rep&, const Rep&, const Rep&) const ;

				// =================================================================== //
				/** Generalization of primitive roots for any modulus
				 * Primitive means maximal order
				 *    Primitive Element, Primitive invertible
				 *    Both functions coïncides except for m=8
				 *
				 * Lambda Function : maximal orbit size
				 *    lambda : Order of a primitive Element
				 *    lambda_inv : Order of an invertible primitive Element
				 *    Both functions coïncides except for m=8
				 */
				// =================================================================== //
				Rep& prim_inv(Rep & , const Rep&) const ;
				Rep& prim_elem(Rep & , const Rep&) const ;
			private:
				Rep& prim_base(Rep & , const Rep&) const ;
				Rep& lambda_base(Rep & , const Rep&) const ;
			public:
				Rep& lambda_primpow(Rep & , const Rep&, unsigned long) const ;
				Rep& lambda_inv_primpow(Rep & , const Rep&, unsigned long) const ;
				Rep& lambda(Rep & , const Rep&) const ;
				Rep& lambda_inv(Rep & , const Rep&) const ;

				// =================================================================== //
				//! Möbius function
				// =================================================================== //
				template< template<class, class> class Container, template <class> class Alloc>
					short mobius(const Container<Rep, Alloc<Rep> >& lpow) const ;

				//! Möbius function
				short mobius(const Rep& a) const;
		};

} // givaro
#include "givaro/givintnumtheo.inl"

#endif // __GIVARO_numtheory_H

// vim:sts=8:sw=8:ts=8:noet:sr:cino=>s,f0,{0,g0,(0,\:0,t0,+0,=s
