~zooko/cryptopp/trunk

#ifndef CRYPTOPP_POLYNOMI_H

#define CRYPTOPP_POLYNOMI_H

/*! \file */

#include "cryptlib.h"

#include "misc.h"

#include "algebra.h"

#include <iosfwd>

#include <vector>

NAMESPACE_BEGIN(CryptoPP)

//! represents single-variable polynomials over arbitrary rings

/*!	\nosubgrouping */

template <class T> class PolynomialOver

{

public:

	//! \name ENUMS, EXCEPTIONS, and TYPEDEFS

	//@{

		//! division by zero exception

		class DivideByZero : public Exception 

		{

		public: 

			DivideByZero() : Exception(OTHER_ERROR, "PolynomialOver<T>: division by zero") {}

		};

		//! specify the distribution for randomization functions

		class RandomizationParameter

		{

		public:

			RandomizationParameter(unsigned int coefficientCount, const typename T::RandomizationParameter &coefficientParameter )

				: m_coefficientCount(coefficientCount), m_coefficientParameter(coefficientParameter) {}

		private:

			unsigned int m_coefficientCount;

			typename T::RandomizationParameter m_coefficientParameter;

			friend class PolynomialOver<T>;

		};

		typedef T Ring;

		typedef typename T::Element CoefficientType;

	//@}

	//! \name CREATORS

	//@{

		//! creates the zero polynomial

		PolynomialOver() {}

		//!

		PolynomialOver(const Ring &ring, unsigned int count)

			: m_coefficients((size_t)count, ring.Identity()) {}

		//! copy constructor

		PolynomialOver(const PolynomialOver<Ring> &t)

			: m_coefficients(t.m_coefficients.size()) {*this = t;}

		//! construct constant polynomial

		PolynomialOver(const CoefficientType &element)

			: m_coefficients(1, element) {}

		//! construct polynomial with specified coefficients, starting from coefficient of x^0

		template <typename Iterator> PolynomialOver(Iterator begin, Iterator end)

			: m_coefficients(begin, end) {}

		//! convert from string

		PolynomialOver(const char *str, const Ring &ring) {FromStr(str, ring);}

		//! convert from big-endian byte array

		PolynomialOver(const byte *encodedPolynomialOver, unsigned int byteCount);

		//! convert from Basic Encoding Rules encoded byte array

		explicit PolynomialOver(const byte *BEREncodedPolynomialOver);

		//! convert from BER encoded byte array stored in a BufferedTransformation object

		explicit PolynomialOver(BufferedTransformation &bt);

		//! create a random PolynomialOver<T>

		PolynomialOver(RandomNumberGenerator &rng, const RandomizationParameter &parameter, const Ring &ring)

			{Randomize(rng, parameter, ring);}

	//@}

	//! \name ACCESSORS

	//@{

		//! the zero polynomial will return a degree of -1

		int Degree(const Ring &ring) const {return int(CoefficientCount(ring))-1;}

		//!

		unsigned int CoefficientCount(const Ring &ring) const;

		//! return coefficient for x^i

		CoefficientType GetCoefficient(unsigned int i, const Ring &ring) const;

	//@}

	//! \name MANIPULATORS

	//@{

		//!

		PolynomialOver<Ring>&  operator=(const PolynomialOver<Ring>& t);

		//!

		void Randomize(RandomNumberGenerator &rng, const RandomizationParameter &parameter, const Ring &ring);

		//! set the coefficient for x^i to value

		void SetCoefficient(unsigned int i, const CoefficientType &value, const Ring &ring);

		//!

		void Negate(const Ring &ring);

		//!

		void swap(PolynomialOver<Ring> &t);

	//@}

	//! \name BASIC ARITHMETIC ON POLYNOMIALS

	//@{

		bool Equals(const PolynomialOver<Ring> &t, const Ring &ring) const;

		bool IsZero(const Ring &ring) const {return CoefficientCount(ring)==0;}

		PolynomialOver<Ring> Plus(const PolynomialOver<Ring>& t, const Ring &ring) const;

		PolynomialOver<Ring> Minus(const PolynomialOver<Ring>& t, const Ring &ring) const;

		PolynomialOver<Ring> Inverse(const Ring &ring) const;

		PolynomialOver<Ring> Times(const PolynomialOver<Ring>& t, const Ring &ring) const;

		PolynomialOver<Ring> DividedBy(const PolynomialOver<Ring>& t, const Ring &ring) const;

		PolynomialOver<Ring> Modulo(const PolynomialOver<Ring>& t, const Ring &ring) const;

		PolynomialOver<Ring> MultiplicativeInverse(const Ring &ring) const;

		bool IsUnit(const Ring &ring) const;

		PolynomialOver<Ring>& Accumulate(const PolynomialOver<Ring>& t, const Ring &ring);

		PolynomialOver<Ring>& Reduce(const PolynomialOver<Ring>& t, const Ring &ring);

		//!

		PolynomialOver<Ring> Doubled(const Ring &ring) const {return Plus(*this, ring);}

		//!

		PolynomialOver<Ring> Squared(const Ring &ring) const {return Times(*this, ring);}

		CoefficientType EvaluateAt(const CoefficientType &x, const Ring &ring) const;

		PolynomialOver<Ring>& ShiftLeft(unsigned int n, const Ring &ring);

		PolynomialOver<Ring>& ShiftRight(unsigned int n, const Ring &ring);

		//! calculate r and q such that (a == d*q + r) && (0 <= degree of r < degree of d)

		static void Divide(PolynomialOver<Ring> &r, PolynomialOver<Ring> &q, const PolynomialOver<Ring> &a, const PolynomialOver<Ring> &d, const Ring &ring);

	//@}

	//! \name INPUT/OUTPUT

	//@{

		std::istream& Input(std::istream &in, const Ring &ring);

		std::ostream& Output(std::ostream &out, const Ring &ring) const;

	//@}

private:

	void FromStr(const char *str, const Ring &ring);

	std::vector<CoefficientType> m_coefficients;

};

//! Polynomials over a fixed ring

/*! Having a fixed ring allows overloaded operators */

template <class T, int instance> class PolynomialOverFixedRing : private PolynomialOver<T>

{

	typedef PolynomialOver<T> B;

	typedef PolynomialOverFixedRing<T, instance> ThisType;

public:

	typedef T Ring;

	typedef typename T::Element CoefficientType;

	typedef typename B::DivideByZero DivideByZero;

	typedef typename B::RandomizationParameter RandomizationParameter;

	//! \name CREATORS

	//@{

		//! creates the zero polynomial

		PolynomialOverFixedRing(unsigned int count = 0) : B(ms_fixedRing, count) {}

		//! copy constructor

		PolynomialOverFixedRing(const ThisType &t) : B(t) {}

		explicit PolynomialOverFixedRing(const B &t) : B(t) {}

		//! construct constant polynomial

		PolynomialOverFixedRing(const CoefficientType &element) : B(element) {}

		//! construct polynomial with specified coefficients, starting from coefficient of x^0

		template <typename Iterator> PolynomialOverFixedRing(Iterator first, Iterator last)

			: B(first, last) {}

		//! convert from string

		explicit PolynomialOverFixedRing(const char *str) : B(str, ms_fixedRing) {}

		//! convert from big-endian byte array

		PolynomialOverFixedRing(const byte *encodedPoly, unsigned int byteCount) : B(encodedPoly, byteCount) {}

		//! convert from Basic Encoding Rules encoded byte array

		explicit PolynomialOverFixedRing(const byte *BEREncodedPoly) : B(BEREncodedPoly) {}

		//! convert from BER encoded byte array stored in a BufferedTransformation object

		explicit PolynomialOverFixedRing(BufferedTransformation &bt) : B(bt) {}

		//! create a random PolynomialOverFixedRing

		PolynomialOverFixedRing(RandomNumberGenerator &rng, const RandomizationParameter &parameter) : B(rng, parameter, ms_fixedRing) {}

		static const ThisType &Zero();

		static const ThisType &One();

	//@}

	//! \name ACCESSORS

	//@{

		//! the zero polynomial will return a degree of -1

		int Degree() const {return B::Degree(ms_fixedRing);}

		//! degree + 1

		unsigned int CoefficientCount() const {return B::CoefficientCount(ms_fixedRing);}

		//! return coefficient for x^i

		CoefficientType GetCoefficient(unsigned int i) const {return B::GetCoefficient(i, ms_fixedRing);}

		//! return coefficient for x^i

		CoefficientType operator[](unsigned int i) const {return B::GetCoefficient(i, ms_fixedRing);}

	//@}

	//! \name MANIPULATORS

	//@{

		//!

		ThisType&  operator=(const ThisType& t) {B::operator=(t); return *this;}

		//!

		ThisType&  operator+=(const ThisType& t) {Accumulate(t, ms_fixedRing); return *this;}

		//!

		ThisType&  operator-=(const ThisType& t) {Reduce(t, ms_fixedRing); return *this;}

		//!

		ThisType&  operator*=(const ThisType& t) {return *this = *this*t;}

		//!

		ThisType&  operator/=(const ThisType& t) {return *this = *this/t;}

		//!

		ThisType&  operator%=(const ThisType& t) {return *this = *this%t;}

		//!

		ThisType&  operator<<=(unsigned int n) {ShiftLeft(n, ms_fixedRing); return *this;}

		//!

		ThisType&  operator>>=(unsigned int n) {ShiftRight(n, ms_fixedRing); return *this;}

		//! set the coefficient for x^i to value

		void SetCoefficient(unsigned int i, const CoefficientType &value) {B::SetCoefficient(i, value, ms_fixedRing);}

		//!

		void Randomize(RandomNumberGenerator &rng, const RandomizationParameter &parameter) {B::Randomize(rng, parameter, ms_fixedRing);}

		//!

		void Negate() {B::Negate(ms_fixedRing);}

		void swap(ThisType &t) {B::swap(t);}

	//@}

	//! \name UNARY OPERATORS

	//@{

		//!

		bool operator!() const {return CoefficientCount()==0;}

		//!

		ThisType operator+() const {return *this;}

		//!

		ThisType operator-() const {return ThisType(Inverse(ms_fixedRing));}

	//@}

	//! \name BINARY OPERATORS

	//@{

		//!

		friend ThisType operator>>(ThisType a, unsigned int n)	{return ThisType(a>>=n);}

		//!

		friend ThisType operator<<(ThisType a, unsigned int n)	{return ThisType(a<<=n);}

	//@}

	//! \name OTHER ARITHMETIC FUNCTIONS

	//@{

		//!

		ThisType MultiplicativeInverse() const {return ThisType(B::MultiplicativeInverse(ms_fixedRing));}

		//!

		bool IsUnit() const {return B::IsUnit(ms_fixedRing);}

		//!

		ThisType Doubled() const {return ThisType(B::Doubled(ms_fixedRing));}

		//!

		ThisType Squared() const {return ThisType(B::Squared(ms_fixedRing));}

		CoefficientType EvaluateAt(const CoefficientType &x) const {return B::EvaluateAt(x, ms_fixedRing);}

		//! calculate r and q such that (a == d*q + r) && (0 <= r < abs(d))

		static void Divide(ThisType &r, ThisType &q, const ThisType &a, const ThisType &d)

			{B::Divide(r, q, a, d, ms_fixedRing);}

	//@}

	//! \name INPUT/OUTPUT

	//@{

		//!

		friend std::istream& operator>>(std::istream& in, ThisType &a)

			{return a.Input(in, ms_fixedRing);}

		//!

		friend std::ostream& operator<<(std::ostream& out, const ThisType &a)

			{return a.Output(out, ms_fixedRing);}

	//@}

private:

	struct NewOnePolynomial

	{

		ThisType * operator()() const

		{

			return new ThisType(ms_fixedRing.MultiplicativeIdentity());

		}

	};

	static const Ring ms_fixedRing;

};

//! Ring of polynomials over another ring

template <class T> class RingOfPolynomialsOver : public AbstractEuclideanDomain<PolynomialOver<T> >

{

public:

	typedef T CoefficientRing;

	typedef PolynomialOver<T> Element;

	typedef typename Element::CoefficientType CoefficientType;

	typedef typename Element::RandomizationParameter RandomizationParameter;

	RingOfPolynomialsOver(const CoefficientRing &ring) : m_ring(ring) {}

	Element RandomElement(RandomNumberGenerator &rng, const RandomizationParameter &parameter)

		{return Element(rng, parameter, m_ring);}

	bool Equal(const Element &a, const Element &b) const

		{return a.Equals(b, m_ring);}

	const Element& Identity() const

		{return this->result = m_ring.Identity();}

	const Element& Add(const Element &a, const Element &b) const

		{return this->result = a.Plus(b, m_ring);}

	Element& Accumulate(Element &a, const Element &b) const

		{a.Accumulate(b, m_ring); return a;}

	const Element& Inverse(const Element &a) const

		{return this->result = a.Inverse(m_ring);}

	const Element& Subtract(const Element &a, const Element &b) const

		{return this->result = a.Minus(b, m_ring);}

	Element& Reduce(Element &a, const Element &b) const

		{return a.Reduce(b, m_ring);}

	const Element& Double(const Element &a) const

		{return this->result = a.Doubled(m_ring);}

	const Element& MultiplicativeIdentity() const

		{return this->result = m_ring.MultiplicativeIdentity();}

	const Element& Multiply(const Element &a, const Element &b) const

		{return this->result = a.Times(b, m_ring);}

	const Element& Square(const Element &a) const

		{return this->result = a.Squared(m_ring);}

	bool IsUnit(const Element &a) const

		{return a.IsUnit(m_ring);}

	const Element& MultiplicativeInverse(const Element &a) const

		{return this->result = a.MultiplicativeInverse(m_ring);}

	const Element& Divide(const Element &a, const Element &b) const

		{return this->result = a.DividedBy(b, m_ring);}

	const Element& Mod(const Element &a, const Element &b) const

		{return this->result = a.Modulo(b, m_ring);}

	void DivisionAlgorithm(Element &r, Element &q, const Element &a, const Element &d) const

		{Element::Divide(r, q, a, d, m_ring);}

	class InterpolationFailed : public Exception

	{

	public:

		InterpolationFailed() : Exception(OTHER_ERROR, "RingOfPolynomialsOver<T>: interpolation failed") {}

	};

	Element Interpolate(const CoefficientType x[], const CoefficientType y[], unsigned int n) const;

	// a faster version of Interpolate(x, y, n).EvaluateAt(position)

	CoefficientType InterpolateAt(const CoefficientType &position, const CoefficientType x[], const CoefficientType y[], unsigned int n) const;

/*

	void PrepareBulkInterpolation(CoefficientType *w, const CoefficientType x[], unsigned int n) const;

	void PrepareBulkInterpolationAt(CoefficientType *v, const CoefficientType &position, const CoefficientType x[], const CoefficientType w[], unsigned int n) const;

	CoefficientType BulkInterpolateAt(const CoefficientType y[], const CoefficientType v[], unsigned int n) const;

*/

protected:

	void CalculateAlpha(std::vector<CoefficientType> &alpha, const CoefficientType x[], const CoefficientType y[], unsigned int n) const;

	CoefficientRing m_ring;

};

template <class Ring, class Element>

void PrepareBulkPolynomialInterpolation(const Ring &ring, Element *w, const Element x[], unsigned int n);

template <class Ring, class Element>

void PrepareBulkPolynomialInterpolationAt(const Ring &ring, Element *v, const Element &position, const Element x[], const Element w[], unsigned int n);

template <class Ring, class Element>

Element BulkPolynomialInterpolateAt(const Ring &ring, const Element y[], const Element v[], unsigned int n);

//!

template <class T, int instance>

inline bool operator==(const CryptoPP::PolynomialOverFixedRing<T, instance> &a, const CryptoPP::PolynomialOverFixedRing<T, instance> &b)

	{return a.Equals(b, a.ms_fixedRing);}

//!

template <class T, int instance>

inline bool operator!=(const CryptoPP::PolynomialOverFixedRing<T, instance> &a, const CryptoPP::PolynomialOverFixedRing<T, instance> &b)

	{return !(a==b);}

//!

template <class T, int instance>

inline bool operator> (const CryptoPP::PolynomialOverFixedRing<T, instance> &a, const CryptoPP::PolynomialOverFixedRing<T, instance> &b)

	{return a.Degree() > b.Degree();}

//!

template <class T, int instance>

inline bool operator>=(const CryptoPP::PolynomialOverFixedRing<T, instance> &a, const CryptoPP::PolynomialOverFixedRing<T, instance> &b)

	{return a.Degree() >= b.Degree();}

//!

template <class T, int instance>

inline bool operator< (const CryptoPP::PolynomialOverFixedRing<T, instance> &a, const CryptoPP::PolynomialOverFixedRing<T, instance> &b)

	{return a.Degree() < b.Degree();}

//!

template <class T, int instance>

inline bool operator<=(const CryptoPP::PolynomialOverFixedRing<T, instance> &a, const CryptoPP::PolynomialOverFixedRing<T, instance> &b)

	{return a.Degree() <= b.Degree();}

//!

template <class T, int instance>

inline CryptoPP::PolynomialOverFixedRing<T, instance> operator+(const CryptoPP::PolynomialOverFixedRing<T, instance> &a, const CryptoPP::PolynomialOverFixedRing<T, instance> &b)

	{return CryptoPP::PolynomialOverFixedRing<T, instance>(a.Plus(b, a.ms_fixedRing));}

//!

template <class T, int instance>

inline CryptoPP::PolynomialOverFixedRing<T, instance> operator-(const CryptoPP::PolynomialOverFixedRing<T, instance> &a, const CryptoPP::PolynomialOverFixedRing<T, instance> &b)

	{return CryptoPP::PolynomialOverFixedRing<T, instance>(a.Minus(b, a.ms_fixedRing));}

//!

template <class T, int instance>

inline CryptoPP::PolynomialOverFixedRing<T, instance> operator*(const CryptoPP::PolynomialOverFixedRing<T, instance> &a, const CryptoPP::PolynomialOverFixedRing<T, instance> &b)

	{return CryptoPP::PolynomialOverFixedRing<T, instance>(a.Times(b, a.ms_fixedRing));}

//!

template <class T, int instance>

inline CryptoPP::PolynomialOverFixedRing<T, instance> operator/(const CryptoPP::PolynomialOverFixedRing<T, instance> &a, const CryptoPP::PolynomialOverFixedRing<T, instance> &b)

	{return CryptoPP::PolynomialOverFixedRing<T, instance>(a.DividedBy(b, a.ms_fixedRing));}

//!

template <class T, int instance>

inline CryptoPP::PolynomialOverFixedRing<T, instance> operator%(const CryptoPP::PolynomialOverFixedRing<T, instance> &a, const CryptoPP::PolynomialOverFixedRing<T, instance> &b)

	{return CryptoPP::PolynomialOverFixedRing<T, instance>(a.Modulo(b, a.ms_fixedRing));}

NAMESPACE_END

NAMESPACE_BEGIN(std)

template<class T> inline void swap(CryptoPP::PolynomialOver<T> &a, CryptoPP::PolynomialOver<T> &b)

{

	a.swap(b);

}

template<class T, int i> inline void swap(CryptoPP::PolynomialOverFixedRing<T,i> &a, CryptoPP::PolynomialOverFixedRing<T,i> &b)

{

	a.swap(b);

}

NAMESPACE_END

#endif