// integer.cpp - written and placed in the public domain by Wei Dai
// contains public domain code contributed by Alister Lee and Leonard Janke

#include "pch.h"

#ifndef CRYPTOPP_IMPORTS

#include "integer.h"
#include "modarith.h"
#include "nbtheory.h"
#include "asn.h"
#include "oids.h"
#include "words.h"
#include "algparam.h"
#include "pubkey.h"		// for P1363_KDF2
#include "sha.h"

#include <iostream>

#ifdef SSE2_INTRINSICS_AVAILABLE
	#ifdef __GNUC__
		#include <xmmintrin.h>
		#include <malloc.h>
	#else
		#include <emmintrin.h>
	#endif
#elif defined(_MSC_VER) && defined(_M_IX86)
	#pragma message("You do no seem to have the Visual C++ Processor Pack installed, so use of SSE2 intrinsics will be disabled.")
#elif defined(__GNUC__) && defined(__i386__)
	#warning "You do not have GCC 3.3 or later, or did not specify -msse2 compiler option, so use of SSE2 intrinsics will be disabled."
#endif

NAMESPACE_BEGIN(CryptoPP)

bool FunctionAssignIntToInteger(const std::type_info &valueType, void *pInteger, const void *pInt)
{
	if (valueType != typeid(Integer))
		return false;
	*reinterpret_cast<Integer *>(pInteger) = *reinterpret_cast<const int *>(pInt);
	return true;
}

static const char s_RunAtStartup = (AssignIntToInteger = FunctionAssignIntToInteger, 0);

#if defined(SSE2_INTRINSICS_AVAILABLE) || defined(_MSC_VER)
template <class T>
CPP_TYPENAME AllocatorBase<T>::pointer AlignedAllocator<T>::allocate(size_type n, const void *)
{
	CheckSize(n);
	if (n == 0)
		return NULL;
#ifdef SSE2_INTRINSICS_AVAILABLE
	if (n >= 4)
	{
		void *p;
	#ifdef __GNUC__
		while (!(p = memalign(16, sizeof(T)*n)))
	#else
		while (!(p = _mm_malloc(sizeof(T)*n, 16)))
	#endif
			CallNewHandler();
		return (T*)p;
	}
#endif
	return new T[n];
}

template <class T>
void AlignedAllocator<T>::deallocate(void *p, size_type n)
{
	memset(p, 0, n*sizeof(T));
#ifdef SSE2_INTRINSICS_AVAILABLE
	if (n >= 4)
		#ifdef __GNUC__
			free(p);
		#else
			_mm_free(p);
		#endif
	else
#endif
		delete [] (T *)p;
}
#endif

static int Compare(const word *A, const word *B, unsigned int N)
{
	while (N--)
		if (A[N] > B[N])
			return 1;
		else if (A[N] < B[N])
			return -1;

	return 0;
}

static word Increment(word *A, unsigned int N, word B=1)
{
	assert(N);
	word t = A[0];
	A[0] = t+B;
	if (A[0] >= t)
		return 0;
	for (unsigned i=1; i<N; i++)
		if (++A[i])
			return 0;
	return 1;
}

static word Decrement(word *A, unsigned int N, word B=1)
{
	assert(N);
	word t = A[0];
	A[0] = t-B;
	if (A[0] <= t)
		return 0;
	for (unsigned i=1; i<N; i++)
		if (A[i]--)
			return 0;
	return 1;
}

static void TwosComplement(word *A, unsigned int N)
{
	Decrement(A, N);
	for (unsigned i=0; i<N; i++)
		A[i] = ~A[i];
}

static word AtomicInverseModPower2(word A)
{
	assert(A%2==1);

	word R=A%8;

	for (unsigned i=3; i<WORD_BITS; i*=2)
		R = R*(2-R*A);

	assert(R*A==1);
	return R;
}

// ********************************************************

class DWord
{
public:
	DWord() {}

#ifdef CRYPTOPP_NATIVE_DWORD_AVAILABLE
	explicit DWord(word low)
	{
		m_whole = low;
	}
#else
	explicit DWord(word low)
	{
		m_halfs.low = low;
		m_halfs.high = 0;
	}
#endif

	DWord(word low, word high)
	{
		m_halfs.low = low;
		m_halfs.high = high;
	}

	static DWord Multiply(word a, word b)
	{
		DWord r;
		#ifdef CRYPTOPP_NATIVE_DWORD_AVAILABLE
			r.m_whole = (dword)a * b;
		#elif defined(__alpha__)
			r.m_halfs.low = a*b; __asm__("umulh %1,%2,%0" : "=r" (r.m_halfs.high) : "r" (a), "r" (b));
		#elif defined(__ia64__)
			r.m_halfs.low = a*b; __asm__("xmpy.hu %0=%1,%2" : "=f" (r.m_halfs.high) : "f" (a), "f" (b));
		#elif defined(_ARCH_PPC64)
			r.m_halfs.low = a*b; __asm__("mulhdu %0,%1,%2" : "=r" (r.m_halfs.high) : "r" (a), "r" (b) : "cc");
		#elif defined(__x86_64__)
			__asm__("mulq %3" : "=d" (r.m_halfs.high), "=a" (r.m_halfs.low) : "a" (a), "rm" (b) : "cc");
		#elif defined(__mips64)
			__asm__("dmultu %2,%3" : "=h" (r.m_halfs.high), "=l" (r.m_halfs.low) : "r" (a), "r" (b));
		#elif defined(_M_IX86)
			// for testing
			word64 t = (word64)a * b;
			r.m_halfs.high = ((word32 *)(&t))[1];
			r.m_halfs.low = (word32)t;
		#else
			#error can not implement DWord
		#endif
		return r;
	}

	static DWord MultiplyAndAdd(word a, word b, word c)
	{
		DWord r = Multiply(a, b);
		return r += c;
	}

	DWord & operator+=(word a)
	{
		#ifdef CRYPTOPP_NATIVE_DWORD_AVAILABLE
			m_whole = m_whole + a;
		#else
			m_halfs.low += a;
			m_halfs.high += (m_halfs.low < a);
		#endif
		return *this;
	}

	DWord operator+(word a)
	{
		DWord r;
		#ifdef CRYPTOPP_NATIVE_DWORD_AVAILABLE
			r.m_whole = m_whole + a;
		#else
			r.m_halfs.low = m_halfs.low + a;
			r.m_halfs.high = m_halfs.high + (r.m_halfs.low < a);
		#endif
		return r;
	}

	DWord operator-(DWord a)
	{
		DWord r;
		#ifdef CRYPTOPP_NATIVE_DWORD_AVAILABLE
			r.m_whole = m_whole - a.m_whole;
		#else
			r.m_halfs.low = m_halfs.low - a.m_halfs.low;
			r.m_halfs.high = m_halfs.high - a.m_halfs.high - (r.m_halfs.low > m_halfs.low);
		#endif
		return r;
	}

	DWord operator-(word a)
	{
		DWord r;
		#ifdef CRYPTOPP_NATIVE_DWORD_AVAILABLE
			r.m_whole = m_whole - a;
		#else
			r.m_halfs.low = m_halfs.low - a;
			r.m_halfs.high = m_halfs.high - (r.m_halfs.low > m_halfs.low);
		#endif
		return r;
	}

	// returns quotient, which must fit in a word
	word operator/(word divisor);

	word operator%(word a);

	bool operator!() const
	{
	#ifdef CRYPTOPP_NATIVE_DWORD_AVAILABLE
		return !m_whole;
	#else
		return !m_halfs.high && !m_halfs.low;
	#endif
	}

	word GetLowHalf() const {return m_halfs.low;}
	word GetHighHalf() const {return m_halfs.high;}
	word GetHighHalfAsBorrow() const {return 0-m_halfs.high;}

private:
	union
	{
	#ifdef CRYPTOPP_NATIVE_DWORD_AVAILABLE
		dword m_whole;
	#endif
		struct
		{
		#ifdef IS_LITTLE_ENDIAN
			word low;
			word high;
		#else
			word high;
			word low;
		#endif
		} m_halfs;
	};
};

class Word
{
public:
	Word() {}

	Word(word value)
	{
		m_whole = value;
	}

	Word(hword low, hword high)
	{
		m_whole = low | (word(high) << (WORD_BITS/2));
	}

	static Word Multiply(hword a, hword b)
	{
		Word r;
		r.m_whole = (word)a * b;
		return r;
	}

	Word operator-(Word a)
	{
		Word r;
		r.m_whole = m_whole - a.m_whole;
		return r;
	}

	Word operator-(hword a)
	{
		Word r;
		r.m_whole = m_whole - a;
		return r;
	}

	// returns quotient, which must fit in a word
	hword operator/(hword divisor)
	{
		return hword(m_whole / divisor);
	}

	bool operator!() const
	{
		return !m_whole;
	}

	word GetWhole() const {return m_whole;}
	hword GetLowHalf() const {return hword(m_whole);}
	hword GetHighHalf() const {return hword(m_whole>>(WORD_BITS/2));}
	hword GetHighHalfAsBorrow() const {return 0-hword(m_whole>>(WORD_BITS/2));}
	
private:
	word m_whole;
};

// do a 3 word by 2 word divide, returns quotient and leaves remainder in A
template <class S, class D>
S DivideThreeWordsByTwo(S *A, S B0, S B1, D *dummy=NULL)
{
	// assert {A[2],A[1]} < {B1,B0}, so quotient can fit in a S
	assert(A[2] < B1 || (A[2]==B1 && A[1] < B0));

	// estimate the quotient: do a 2 S by 1 S divide
	S Q;
	if (S(B1+1) == 0)
		Q = A[2];
	else
		Q = D(A[1], A[2]) / S(B1+1);

	// now subtract Q*B from A
	D p = D::Multiply(B0, Q);
	D u = (D) A[0] - p.GetLowHalf();
	A[0] = u.GetLowHalf();
	u = (D) A[1] - p.GetHighHalf() - u.GetHighHalfAsBorrow() - D::Multiply(B1, Q);
	A[1] = u.GetLowHalf();
	A[2] += u.GetHighHalf();

	// Q <= actual quotient, so fix it
	while (A[2] || A[1] > B1 || (A[1]==B1 && A[0]>=B0))
	{
		u = (D) A[0] - B0;
		A[0] = u.GetLowHalf();
		u = (D) A[1] - B1 - u.GetHighHalfAsBorrow();
		A[1] = u.GetLowHalf();
		A[2] += u.GetHighHalf();
		Q++;
		assert(Q);	// shouldn't overflow
	}

	return Q;
}

// do a 4 word by 2 word divide, returns 2 word quotient in Q0 and Q1
template <class S, class D>
inline D DivideFourWordsByTwo(S *T, const D &Al, const D &Ah, const D &B)
{
	if (!B) // if divisor is 0, we assume divisor==2**(2*WORD_BITS)
		return D(Ah.GetLowHalf(), Ah.GetHighHalf());
	else
	{
		S Q[2];
		T[0] = Al.GetLowHalf();
		T[1] = Al.GetHighHalf(); 
		T[2] = Ah.GetLowHalf();
		T[3] = Ah.GetHighHalf();
		Q[1] = DivideThreeWordsByTwo<S, D>(T+1, B.GetLowHalf(), B.GetHighHalf());
		Q[0] = DivideThreeWordsByTwo<S, D>(T, B.GetLowHalf(), B.GetHighHalf());
		return D(Q[0], Q[1]);
	}
}

// returns quotient, which must fit in a word
inline word DWord::operator/(word a)
{
	#ifdef CRYPTOPP_NATIVE_DWORD_AVAILABLE
		return word(m_whole / a);
	#else
		hword r[4];
		return DivideFourWordsByTwo<hword, Word>(r, m_halfs.low, m_halfs.high, a).GetWhole();
	#endif
}

inline word DWord::operator%(word a)
{
	#ifdef CRYPTOPP_NATIVE_DWORD_AVAILABLE
		return word(m_whole % a);
	#else
		if (a < (word(1) << (WORD_BITS/2)))
		{
			hword h = hword(a);
			word r = m_halfs.high % h;
			r = ((m_halfs.low >> (WORD_BITS/2)) + (r << (WORD_BITS/2))) % h;
			return hword((hword(m_halfs.low) + (r << (WORD_BITS/2))) % h);
		}
		else
		{
			hword r[4];
			DivideFourWordsByTwo<hword, Word>(r, m_halfs.low, m_halfs.high, a);
			return Word(r[0], r[1]).GetWhole();
		}
	#endif
}

// ********************************************************

class Portable
{
public:
	static word Add(word *C, const word *A, const word *B, unsigned int N);
	static word Subtract(word *C, const word *A, const word *B, unsigned int N);

	static inline void Multiply2(word *C, const word *A, const word *B);
	static inline word Multiply2Add(word *C, const word *A, const word *B);
	static void Multiply4(word *C, const word *A, const word *B);
	static void Multiply8(word *C, const word *A, const word *B);
	static inline unsigned int MultiplyRecursionLimit() {return 8;}

	static inline void Multiply2Bottom(word *C, const word *A, const word *B);
	static void Multiply4Bottom(word *C, const word *A, const word *B);
	static void Multiply8Bottom(word *C, const word *A, const word *B);
	static inline unsigned int MultiplyBottomRecursionLimit() {return 8;}

	static void Square2(word *R, const word *A);
	static void Square4(word *R, const word *A);
	static void Square8(word *R, const word *A) {assert(false);}
	static inline unsigned int SquareRecursionLimit() {return 4;}
};

word Portable::Add(word *C, const word *A, const word *B, unsigned int N)
{
	assert (N%2 == 0);

	DWord u(0, 0);
	for (unsigned int i = 0; i < N; i+=2)
	{
		u = DWord(A[i]) + B[i] + u.GetHighHalf();
		C[i] = u.GetLowHalf();
		u = DWord(A[i+1]) + B[i+1] + u.GetHighHalf();
		C[i+1] = u.GetLowHalf();
	}
	return u.GetHighHalf();
}

word Portable::Subtract(word *C, const word *A, const word *B, unsigned int N)
{
	assert (N%2 == 0);

	DWord u(0, 0);
	for (unsigned int i = 0; i < N; i+=2)
	{
		u = (DWord) A[i] - B[i] - u.GetHighHalfAsBorrow();
		C[i] = u.GetLowHalf();
		u = (DWord) A[i+1] - B[i+1] - u.GetHighHalfAsBorrow();
		C[i+1] = u.GetLowHalf();
	}
	return 0-u.GetHighHalf();
}

void Portable::Multiply2(word *C, const word *A, const word *B)
{
/*
	word s;
	dword d;

	if (A1 >= A0)
		if (B0 >= B1)
		{
			s = 0;
			d = (dword)(A1-A0)*(B0-B1);
		}
		else
		{
			s = (A1-A0);
			d = (dword)s*(word)(B0-B1);
		}
	else
		if (B0 > B1)
		{
			s = (B0-B1);
			d = (word)(A1-A0)*(dword)s;
		}
		else
		{
			s = 0;
			d = (dword)(A0-A1)*(B1-B0);
		}
*/
	// this segment is the branchless equivalent of above
	word D[4] = {A[1]-A[0], A[0]-A[1], B[0]-B[1], B[1]-B[0]};
	unsigned int ai = A[1] < A[0];
	unsigned int bi = B[0] < B[1];
	unsigned int di = ai & bi;
	DWord d = DWord::Multiply(D[di], D[di+2]);
	D[1] = D[3] = 0;
	unsigned int si = ai + !bi;
	word s = D[si];

	DWord A0B0 = DWord::Multiply(A[0], B[0]);
	C[0] = A0B0.GetLowHalf();

	DWord A1B1 = DWord::Multiply(A[1], B[1]);
	DWord t = (DWord) A0B0.GetHighHalf() + A0B0.GetLowHalf() + d.GetLowHalf() + A1B1.GetLowHalf();
	C[1] = t.GetLowHalf();

	t = A1B1 + t.GetHighHalf() + A0B0.GetHighHalf() + d.GetHighHalf() + A1B1.GetHighHalf() - s;
	C[2] = t.GetLowHalf();
	C[3] = t.GetHighHalf();
}

inline void Portable::Multiply2Bottom(word *C, const word *A, const word *B)
{
	DWord t = DWord::Multiply(A[0], B[0]);
	C[0] = t.GetLowHalf();
	C[1] = t.GetHighHalf() + A[0]*B[1] + A[1]*B[0];
}

word Portable::Multiply2Add(word *C, const word *A, const word *B)
{
	word D[4] = {A[1]-A[0], A[0]-A[1], B[0]-B[1], B[1]-B[0]};
	unsigned int ai = A[1] < A[0];
	unsigned int bi = B[0] < B[1];
	unsigned int di = ai & bi;
	DWord d = DWord::Multiply(D[di], D[di+2]);
	D[1] = D[3] = 0;
	unsigned int si = ai + !bi;
	word s = D[si];

	DWord A0B0 = DWord::Multiply(A[0], B[0]);
	DWord t = A0B0 + C[0];
	C[0] = t.GetLowHalf();

	DWord A1B1 = DWord::Multiply(A[1], B[1]);
	t = (DWord) t.GetHighHalf() + A0B0.GetLowHalf() + d.GetLowHalf() + A1B1.GetLowHalf() + C[1];
	C[1] = t.GetLowHalf();

	t = (DWord) t.GetHighHalf() + A1B1.GetLowHalf() + A0B0.GetHighHalf() + d.GetHighHalf() + A1B1.GetHighHalf() - s + C[2];
	C[2] = t.GetLowHalf();

	t = (DWord) t.GetHighHalf() + A1B1.GetHighHalf() + C[3];
	C[3] = t.GetLowHalf();
	return t.GetHighHalf();
}

#define MulAcc(x, y)								\
	p = DWord::MultiplyAndAdd(A[x], B[y], c);		\
	c = p.GetLowHalf();								\
	p = (DWord) d + p.GetHighHalf();					\
	d = p.GetLowHalf();								\
	e += p.GetHighHalf();

#define SaveMulAcc(s, x, y) 						\
	R[s] = c;										\
	p = DWord::MultiplyAndAdd(A[x], B[y], d);				\
	c = p.GetLowHalf();								\
	p = (DWord) e + p.GetHighHalf();					\
	d = p.GetLowHalf();								\
	e = p.GetHighHalf();

#define SquAcc(x, y)								\
	q = DWord::Multiply(A[x], A[y]);	\
	p = q + c; 					\
	c = p.GetLowHalf();								\
	p = (DWord) d + p.GetHighHalf();					\
	d = p.GetLowHalf();								\
	e += p.GetHighHalf();			\
	p = q + c; 					\
	c = p.GetLowHalf();								\
	p = (DWord) d + p.GetHighHalf();					\
	d = p.GetLowHalf();								\
	e += p.GetHighHalf();

#define SaveSquAcc(s, x, y) 						\
	R[s] = c;										\
	q = DWord::Multiply(A[x], A[y]);	\
	p = q + d; 					\
	c = p.GetLowHalf();								\
	p = (DWord) e + p.GetHighHalf();					\
	d = p.GetLowHalf();								\
	e = p.GetHighHalf();			\
	p = q + c; 					\
	c = p.GetLowHalf();								\
	p = (DWord) d + p.GetHighHalf();					\
	d = p.GetLowHalf();								\
	e += p.GetHighHalf();

void Portable::Multiply4(word *R, const word *A, const word *B)
{
	DWord p;
	word c, d, e;

	p = DWord::Multiply(A[0], B[0]);
	R[0] = p.GetLowHalf();
	c = p.GetHighHalf();
	d = e = 0;

	MulAcc(0, 1);
	MulAcc(1, 0);

	SaveMulAcc(1, 2, 0);
	MulAcc(1, 1);
	MulAcc(0, 2);

	SaveMulAcc(2, 0, 3);
	MulAcc(1, 2);
	MulAcc(2, 1);
	MulAcc(3, 0);

	SaveMulAcc(3, 3, 1);
	MulAcc(2, 2);
	MulAcc(1, 3);

	SaveMulAcc(4, 2, 3);
	MulAcc(3, 2);

	R[5] = c;
	p = DWord::MultiplyAndAdd(A[3], B[3], d);
	R[6] = p.GetLowHalf();
	R[7] = e + p.GetHighHalf();
}

void Portable::Square2(word *R, const word *A)
{
	DWord p, q;
	word c, d, e;

	p = DWord::Multiply(A[0], A[0]);
	R[0] = p.GetLowHalf();
	c = p.GetHighHalf();
	d = e = 0;

	SquAcc(0, 1);

	R[1] = c;
	p = DWord::MultiplyAndAdd(A[1], A[1], d);
	R[2] = p.GetLowHalf();
	R[3] = e + p.GetHighHalf();
}

void Portable::Square4(word *R, const word *A)
{
#ifdef _MSC_VER
	// VC60 workaround: MSVC 6.0 has an optimization bug that makes
	// (dword)A*B where either A or B has been cast to a dword before
	// very expensive. Revisit this function when this
	// bug is fixed.
	Multiply4(R, A, A);
#else
	const word *B = A;
	DWord p, q;
	word c, d, e;

	p = DWord::Multiply(A[0], A[0]);
	R[0] = p.GetLowHalf();
	c = p.GetHighHalf();
	d = e = 0;

	SquAcc(0, 1);

	SaveSquAcc(1, 2, 0);
	MulAcc(1, 1);

	SaveSquAcc(2, 0, 3);
	SquAcc(1, 2);

	SaveSquAcc(3, 3, 1);
	MulAcc(2, 2);

	SaveSquAcc(4, 2, 3);

	R[5] = c;
	p = DWord::MultiplyAndAdd(A[3], A[3], d);
	R[6] = p.GetLowHalf();
	R[7] = e + p.GetHighHalf();
#endif
}

void Portable::Multiply8(word *R, const word *A, const word *B)
{
	DWord p;
	word c, d, e;

	p = DWord::Multiply(A[0], B[0]);
	R[0] = p.GetLowHalf();
	c = p.GetHighHalf();
	d = e = 0;

	MulAcc(0, 1);
	MulAcc(1, 0);

	SaveMulAcc(1, 2, 0);
	MulAcc(1, 1);
	MulAcc(0, 2);

	SaveMulAcc(2, 0, 3);
	MulAcc(1, 2);
	MulAcc(2, 1);
	MulAcc(3, 0);

	SaveMulAcc(3, 0, 4);
	MulAcc(1, 3);
	MulAcc(2, 2);
	MulAcc(3, 1);
	MulAcc(4, 0);

	SaveMulAcc(4, 0, 5);
	MulAcc(1, 4);
	MulAcc(2, 3);
	MulAcc(3, 2);
	MulAcc(4, 1);
	MulAcc(5, 0);

	SaveMulAcc(5, 0, 6);
	MulAcc(1, 5);
	MulAcc(2, 4);
	MulAcc(3, 3);
	MulAcc(4, 2);
	MulAcc(5, 1);
	MulAcc(6, 0);

	SaveMulAcc(6, 0, 7);
	MulAcc(1, 6);
	MulAcc(2, 5);
	MulAcc(3, 4);
	MulAcc(4, 3);
	MulAcc(5, 2);
	MulAcc(6, 1);
	MulAcc(7, 0);

	SaveMulAcc(7, 1, 7);
	MulAcc(2, 6);
	MulAcc(3, 5);
	MulAcc(4, 4);
	MulAcc(5, 3);
	MulAcc(6, 2);
	MulAcc(7, 1);

	SaveMulAcc(8, 2, 7);
	MulAcc(3, 6);
	MulAcc(4, 5);
	MulAcc(5, 4);
	MulAcc(6, 3);
	MulAcc(7, 2);

	SaveMulAcc(9, 3, 7);
	MulAcc(4, 6);
	MulAcc(5, 5);
	MulAcc(6, 4);
	MulAcc(7, 3);

	SaveMulAcc(10, 4, 7);
	MulAcc(5, 6);
	MulAcc(6, 5);
	MulAcc(7, 4);

	SaveMulAcc(11, 5, 7);
	MulAcc(6, 6);
	MulAcc(7, 5);

	SaveMulAcc(12, 6, 7);
	MulAcc(7, 6);

	R[13] = c;
	p = DWord::MultiplyAndAdd(A[7], B[7], d);
	R[14] = p.GetLowHalf();
	R[15] = e + p.GetHighHalf();
}

void Portable::Multiply4Bottom(word *R, const word *A, const word *B)
{
	DWord p;
	word c, d, e;

	p = DWord::Multiply(A[0], B[0]);
	R[0] = p.GetLowHalf();
	c = p.GetHighHalf();
	d = e = 0;

	MulAcc(0, 1);
	MulAcc(1, 0);

	SaveMulAcc(1, 2, 0);
	MulAcc(1, 1);
	MulAcc(0, 2);

	R[2] = c;
	R[3] = d + A[0] * B[3] + A[1] * B[2] + A[2] * B[1] + A[3] * B[0];
}

void Portable::Multiply8Bottom(word *R, const word *A, const word *B)
{
	DWord p;
	word c, d, e;

	p = DWord::Multiply(A[0], B[0]);
	R[0] = p.GetLowHalf();
	c = p.GetHighHalf();
	d = e = 0;

	MulAcc(0, 1);
	MulAcc(1, 0);

	SaveMulAcc(1, 2, 0);
	MulAcc(1, 1);
	MulAcc(0, 2);

	SaveMulAcc(2, 0, 3);
	MulAcc(1, 2);
	MulAcc(2, 1);
	MulAcc(3, 0);

	SaveMulAcc(3, 0, 4);
	MulAcc(1, 3);
	MulAcc(2, 2);
	MulAcc(3, 1);
	MulAcc(4, 0);

	SaveMulAcc(4, 0, 5);
	MulAcc(1, 4);
	MulAcc(2, 3);
	MulAcc(3, 2);
	MulAcc(4, 1);
	MulAcc(5, 0);

	SaveMulAcc(5, 0, 6);
	MulAcc(1, 5);
	MulAcc(2, 4);
	MulAcc(3, 3);
	MulAcc(4, 2);
	MulAcc(5, 1);
	MulAcc(6, 0);

	R[6] = c;
	R[7] = d + A[0] * B[7] + A[1] * B[6] + A[2] * B[5] + A[3] * B[4] +
				A[4] * B[3] + A[5] * B[2] + A[6] * B[1] + A[7] * B[0];
}

#undef MulAcc
#undef SaveMulAcc
#undef SquAcc
#undef SaveSquAcc

// CodeWarrior defines _MSC_VER
#if (defined(_MSC_VER) && !defined(__MWERKS__) && defined(_M_IX86)) || (defined(__GNUC__) && defined(__i386__))

// ************** x86 feature detection ***************

static bool s_sse2Enabled = true;

static void CpuId(word32 input, word32 *output)
{
#ifdef __GNUC__
	__asm__
	(
		"cpuid"
		: "=a" (output[0]), "=b" (output[1]), "=c" (output[2]), "=d" (output[3])
		: "a" (input)
	);
#else
	__asm
	{
		mov eax, input
		cpuid
		mov edi, output
		mov [edi], eax
		mov [edi+4], ebx
		mov [edi+8], ecx
		mov [edi+12], edx
	}
#endif
}

static bool HasSSE2()
{
	if (!s_sse2Enabled)
		return false;

	word32 cpuid[4];
	CpuId(1, cpuid);
	return (cpuid[3] & (1 << 26)) != 0;
}

static bool IsP4()
{
	word32 cpuid[4];

	CpuId(0, cpuid);
	std::swap(cpuid[2], cpuid[3]);
	if (memcmp(cpuid+1, "GenuineIntel", 12) != 0)
		return false;

	CpuId(1, cpuid);
	return ((cpuid[0] >> 8) & 0xf) == 0xf;
}

// ************** Pentium/P4 optimizations ***************

class PentiumOptimized : public Portable
{
public:
	static word CRYPTOPP_CDECL Add(word *C, const word *A, const word *B, unsigned int N);
	static word CRYPTOPP_CDECL Subtract(word *C, const word *A, const word *B, unsigned int N);
	static void CRYPTOPP_CDECL Multiply4(word *C, const word *A, const word *B);
	static void CRYPTOPP_CDECL Multiply8(word *C, const word *A, const word *B);
	static void CRYPTOPP_CDECL Multiply8Bottom(word *C, const word *A, const word *B);
};

class P4Optimized
{
public:
	static word CRYPTOPP_CDECL Add(word *C, const word *A, const word *B, unsigned int N);
	static word CRYPTOPP_CDECL Subtract(word *C, const word *A, const word *B, unsigned int N);
#ifdef SSE2_INTRINSICS_AVAILABLE
	static void CRYPTOPP_CDECL Multiply4(word *C, const word *A, const word *B);
	static void CRYPTOPP_CDECL Multiply8(word *C, const word *A, const word *B);
	static void CRYPTOPP_CDECL Multiply8Bottom(word *C, const word *A, const word *B);
#endif
};

typedef word (CRYPTOPP_CDECL * PAddSub)(word *C, const word *A, const word *B, unsigned int N);
typedef void (CRYPTOPP_CDECL * PMul)(word *C, const word *A, const word *B);

static PAddSub s_pAdd, s_pSub;
#ifdef SSE2_INTRINSICS_AVAILABLE
static PMul s_pMul4, s_pMul8, s_pMul8B;
#endif

static void SetPentiumFunctionPointers()
{
	if (IsP4())
	{
		s_pAdd = &P4Optimized::Add;
		s_pSub = &P4Optimized::Subtract;
	}
	else
	{
		s_pAdd = &PentiumOptimized::Add;
		s_pSub = &PentiumOptimized::Subtract;
	}

#ifdef SSE2_INTRINSICS_AVAILABLE
	if (HasSSE2())
	{
		s_pMul4 = &P4Optimized::Multiply4;
		s_pMul8 = &P4Optimized::Multiply8;
		s_pMul8B = &P4Optimized::Multiply8Bottom;
	}
	else
	{
		s_pMul4 = &PentiumOptimized::Multiply4;
		s_pMul8 = &PentiumOptimized::Multiply8;
		s_pMul8B = &PentiumOptimized::Multiply8Bottom;
	}
#endif
}

static const char s_RunAtStartupSetPentiumFunctionPointers = (SetPentiumFunctionPointers(), 0);

void DisableSSE2()
{
	s_sse2Enabled = false;
	SetPentiumFunctionPointers();
}

class LowLevel : public PentiumOptimized
{
public:
	inline static word Add(word *C, const word *A, const word *B, unsigned int N)
		{return s_pAdd(C, A, B, N);}
	inline static word Subtract(word *C, const word *A, const word *B, unsigned int N)
		{return s_pSub(C, A, B, N);}
	inline static void Square4(word *R, const word *A)
		{Multiply4(R, A, A);}
#ifdef SSE2_INTRINSICS_AVAILABLE
	inline static void Multiply4(word *C, const word *A, const word *B)
		{s_pMul4(C, A, B);}
	inline static void Multiply8(word *C, const word *A, const word *B)
		{s_pMul8(C, A, B);}
	inline static void Multiply8Bottom(word *C, const word *A, const word *B)
		{s_pMul8B(C, A, B);}
#endif
};

// use some tricks to share assembly code between MSVC and GCC
#ifdef _MSC_VER
	#define CRYPTOPP_NAKED __declspec(naked)
	#define AS1(x) __asm x
	#define AS2(x, y) __asm x, y
	#define AddPrologue \
		__asm	push ebp \
		__asm	push ebx \
		__asm	push esi \
		__asm	push edi \
		__asm	mov		ecx, [esp+20] \
		__asm	mov		edx, [esp+24] \
		__asm	mov		ebx, [esp+28] \
		__asm	mov		esi, [esp+32]
	#define AddEpilogue \
		__asm	pop edi \
		__asm	pop esi \
		__asm	pop ebx \
		__asm	pop ebp \
		__asm	ret
	#define MulPrologue \
		__asm	push ebp \
		__asm	push ebx \
		__asm	push esi \
		__asm	push edi \
		__asm	mov ecx, [esp+28] \
		__asm	mov esi, [esp+24] \
		__asm	push [esp+20]
	#define MulEpilogue \
		__asm	add esp, 4 \
		__asm	pop edi \
		__asm	pop esi \
		__asm	pop ebx \
		__asm	pop ebp \
		__asm	ret
#else
	#define CRYPTOPP_NAKED
	#define AS1(x) #x ";"
	#define AS2(x, y) #x ", " #y ";"
	#define AddPrologue \
		__asm__ __volatile__ \
		( \
			"push %%ebx;"	/* save this manually, in case of -fPIC */ \
			"mov %2, %%ebx;" \
			".intel_syntax noprefix;" \
			"push ebp;"
	#define AddEpilogue \
			"pop ebp;" \
			".att_syntax prefix;" \
			"pop %%ebx;" \
					: \
					: "c" (C), "d" (A), "m" (B), "S" (N) \
					: "%edi", "memory", "cc" \
		);
	#define MulPrologue \
		__asm__ __volatile__ \
		( \
			"push %%ebx;"	/* save this manually, in case of -fPIC */ \
			"push %%ebp;" \
			"push %0;" \
			".intel_syntax noprefix;"
	#define MulEpilogue \
			"add esp, 4;" \
			"pop ebp;" \
			"pop ebx;" \
			".att_syntax prefix;" \
			: \
			: "rm" (Z), "S" (X), "c" (Y) \
			: "%eax", "%edx", "%edi", "memory", "cc" \
		);
#endif

CRYPTOPP_NAKED word PentiumOptimized::Add(word *C, const word *A, const word *B, unsigned int N)
{
	AddPrologue

	// now: ebx = B, ecx = C, edx = A, esi = N
	AS2(	sub ecx, edx)	// hold the distance between C & A so we can add this to A to get C
	AS2(	xor eax, eax)	// clear eax

	AS2(	sub eax, esi)	// eax is a negative index from end of B
	AS2(	lea ebx, [ebx+4*esi])	// ebx is end of B

	AS2(	sar eax, 1)		// unit of eax is now dwords; this also clears the carry flag
	AS1(	jz	loopendAdd)		// if no dwords then nothing to do

	AS1(loopstartAdd:)
	AS2(	mov    esi,[edx])			// load lower word of A
	AS2(	mov    ebp,[edx+4])			// load higher word of A

	AS2(	mov    edi,[ebx+8*eax])		// load lower word of B
	AS2(	lea    edx,[edx+8])			// advance A and C

	AS2(	adc    esi,edi)				// add lower words
	AS2(	mov    edi,[ebx+8*eax+4])	// load higher word of B

	AS2(	adc    ebp,edi)				// add higher words
	AS1(	inc    eax)					// advance B

	AS2(	mov    [edx+ecx-8],esi)		// store lower word result
	AS2(	mov    [edx+ecx-4],ebp)		// store higher word result

	AS1(	jnz    loopstartAdd)			// loop until eax overflows and becomes zero

	AS1(loopendAdd:)
	AS2(	adc eax, 0)		// store carry into eax (return result register)

	AddEpilogue
}

CRYPTOPP_NAKED word PentiumOptimized::Subtract(word *C, const word *A, const word *B, unsigned int N)
{
	AddPrologue

	// now: ebx = B, ecx = C, edx = A, esi = N
	AS2(	sub ecx, edx)	// hold the distance between C & A so we can add this to A to get C
	AS2(	xor eax, eax)	// clear eax

	AS2(	sub eax, esi)	// eax is a negative index from end of B
	AS2(	lea ebx, [ebx+4*esi])	// ebx is end of B

	AS2(	sar eax, 1)		// unit of eax is now dwords; this also clears the carry flag
	AS1(	jz	loopendSub)		// if no dwords then nothing to do

	AS1(loopstartSub:)
	AS2(	mov    esi,[edx])			// load lower word of A
	AS2(	mov    ebp,[edx+4])			// load higher word of A

	AS2(	mov    edi,[ebx+8*eax])		// load lower word of B
	AS2(	lea    edx,[edx+8])			// advance A and C

	AS2(	sbb    esi,edi)				// subtract lower words
	AS2(	mov    edi,[ebx+8*eax+4])	// load higher word of B

	AS2(	sbb    ebp,edi)				// subtract higher words
	AS1(	inc    eax)					// advance B

	AS2(	mov    [edx+ecx-8],esi)		// store lower word result
	AS2(	mov    [edx+ecx-4],ebp)		// store higher word result

	AS1(	jnz    loopstartSub)			// loop until eax overflows and becomes zero

	AS1(loopendSub:)
	AS2(	adc eax, 0)		// store carry into eax (return result register)

	AddEpilogue
}

// On Pentium 4, the adc and sbb instructions are very expensive, so avoid them.

CRYPTOPP_NAKED word P4Optimized::Add(word *C, const word *A, const word *B, unsigned int N)
{
	AddPrologue

	// now: ebx = B, ecx = C, edx = A, esi = N
	AS2(	xor		eax, eax)
	AS1(	neg		esi)
	AS1(	jz		loopendAddP4)		// if no dwords then nothing to do

	AS2(	mov		edi, [edx])
	AS2(	mov		ebp, [ebx])

	AS1(loopstartAddP4:)
	AS2(	add		edi, eax)
	AS1(	jc		carry1AddP4)

	AS2(	xor		eax, eax)

	AS1(carry1continueAddP4:)
	AS2(	add		edi, ebp)
	AS2(	mov		ebp, 1)
	AS2(	mov		[ecx], edi)
	AS2(	mov		edi, [edx+4])
	AS2(	cmovc	eax, ebp)
	AS2(	mov		ebp, [ebx+4])
	AS2(	lea		ebx, [ebx+8])
	AS2(	add		edi, eax)
	AS1(	jc		carry2AddP4)

	AS2(	xor		eax, eax)

	AS1(carry2continueAddP4:)
	AS2(	add		edi, ebp)
	AS2(	mov		ebp, 1)
	AS2(	cmovc	eax, ebp)
	AS2(	mov		[ecx+4], edi)
	AS2(	add		ecx, 8)
	AS2(	mov		edi, [edx+8])
	AS2(	add		edx, 8)
	AS2(	add		esi, 2)
	AS2(	mov		ebp, [ebx])
	AS1(	jnz		loopstartAddP4)
	AS1(	jmp		loopendAddP4)

	AS1(carry1AddP4:)
	AS2(	mov		eax, 1)
	AS1(	jmp		carry1continueAddP4)

	AS1(carry2AddP4:)
	AS2(	mov		eax, 1)
	AS1(	jmp		carry2continueAddP4)

	AS1(loopendAddP4:)

	AddEpilogue
}

CRYPTOPP_NAKED word P4Optimized::Subtract(word *C, const word *A, const word *B, unsigned int N)
{
	AddPrologue

	// now: ebx = B, ecx = C, edx = A, esi = N
	AS2(	xor		eax, eax)
	AS1(	neg		esi)
	AS1(	jz		loopendSubP4)		// if no dwords then nothing to do

	AS2(	mov		edi, [edx])
	AS2(	mov		ebp, [ebx])

	AS1(loopstartSubP4:)
	AS2(	sub		edi, eax)
	AS1(	jc		carry1SubP4)

	AS2(	xor		eax, eax)

	AS1(carry1continueSubP4:)
	AS2(	sub		edi, ebp)
	AS2(	mov		ebp, 1)
	AS2(	mov		[ecx], edi)
	AS2(	mov		edi, [edx+4])
	AS2(	cmovc	eax, ebp)
	AS2(	mov		ebp, [ebx+4])
	AS2(	lea		ebx, [ebx+8])
	AS2(	sub		edi, eax)
	AS1(	jc		carry2SubP4)

	AS2(	xor		eax, eax)

	AS1(carry2continueSubP4:)
	AS2(	sub		edi, ebp)
	AS2(	mov		ebp, 1)
	AS2(	cmovc	eax, ebp)
	AS2(	mov		[ecx+4], edi)
	AS2(	add		ecx, 8)
	AS2(	mov		edi, [edx+8])
	AS2(	add		edx, 8)
	AS2(	add		esi, 2)
	AS2(	mov		ebp, [ebx])
	AS1(	jnz		loopstartSubP4)
	AS1(	jmp		loopendSubP4)

	AS1(carry1SubP4:)
	AS2(	mov		eax, 1)
	AS1(	jmp		carry1continueSubP4)

	AS1(carry2SubP4:)
	AS2(	mov		eax, 1)
	AS1(	jmp		carry2continueSubP4)

	AS1(loopendSubP4:)

	AddEpilogue
}

// multiply assembly code originally contributed by Leonard Janke

#define MulStartup \
	AS2(xor ebp, ebp) \
	AS2(xor edi, edi) \
	AS2(xor ebx, ebx) 

#define MulShiftCarry \
	AS2(mov ebp, edx) \
	AS2(mov edi, ebx) \
	AS2(xor ebx, ebx)

#define MulAccumulateBottom(i,j) \
	AS2(mov eax, [ecx+4*j]) \
	AS2(imul eax, dword ptr [esi+4*i]) \
	AS2(add ebp, eax)

#define MulAccumulate(i,j) \
	AS2(mov eax, [ecx+4*j]) \
	AS1(mul dword ptr [esi+4*i]) \
	AS2(add ebp, eax) \
	AS2(adc edi, edx) \
	AS2(adc bl, bh)

#define MulStoreDigit(i)  \
	AS2(mov edx, edi) \
	AS2(mov edi, [esp]) \
	AS2(mov [edi+4*i], ebp)

#define MulLastDiagonal(digits) \
	AS2(mov eax, [ecx+4*(digits-1)]) \
	AS1(mul dword ptr [esi+4*(digits-1)]) \
	AS2(add ebp, eax) \
	AS2(adc edx, edi) \
	AS2(mov edi, [esp]) \
	AS2(mov [edi+4*(2*digits-2)], ebp) \
	AS2(mov [edi+4*(2*digits-1)], edx)

CRYPTOPP_NAKED void PentiumOptimized::Multiply4(word* Z, const word* X, const word* Y)
{
	MulPrologue
	// now: [esp] = Z, esi = X, ecx = Y
	MulStartup
	MulAccumulate(0,0)
	MulStoreDigit(0)
	MulShiftCarry

	MulAccumulate(1,0)
	MulAccumulate(0,1)
	MulStoreDigit(1)
	MulShiftCarry

	MulAccumulate(2,0)
	MulAccumulate(1,1)
	MulAccumulate(0,2)
	MulStoreDigit(2)
	MulShiftCarry

	MulAccumulate(3,0)
	MulAccumulate(2,1)
	MulAccumulate(1,2)
	MulAccumulate(0,3)
	MulStoreDigit(3)
	MulShiftCarry

	MulAccumulate(3,1)
	MulAccumulate(2,2)
	MulAccumulate(1,3)
	MulStoreDigit(4)
	MulShiftCarry

	MulAccumulate(3,2)
	MulAccumulate(2,3)
	MulStoreDigit(5)
	MulShiftCarry

	MulLastDiagonal(4)
	MulEpilogue
}

CRYPTOPP_NAKED void PentiumOptimized::Multiply8(word* Z, const word* X, const word* Y)
{
	MulPrologue
	// now: [esp] = Z, esi = X, ecx = Y
	MulStartup
	MulAccumulate(0,0)
	MulStoreDigit(0)
	MulShiftCarry

	MulAccumulate(1,0)
	MulAccumulate(0,1)
	MulStoreDigit(1)
	MulShiftCarry

	MulAccumulate(2,0)
	MulAccumulate(1,1)
	MulAccumulate(0,2)
	MulStoreDigit(2)
	MulShiftCarry

	MulAccumulate(3,0)
	MulAccumulate(2,1)
	MulAccumulate(1,2)
	MulAccumulate(0,3)
	MulStoreDigit(3)
	MulShiftCarry

	MulAccumulate(4,0)
	MulAccumulate(3,1)
	MulAccumulate(2,2)
	MulAccumulate(1,3)
	MulAccumulate(0,4)
	MulStoreDigit(4)
	MulShiftCarry

	MulAccumulate(5,0)
	MulAccumulate(4,1)
	MulAccumulate(3,2)
	MulAccumulate(2,3)
	MulAccumulate(1,4)
	MulAccumulate(0,5)
	MulStoreDigit(5)
	MulShiftCarry

	MulAccumulate(6,0)
	MulAccumulate(5,1)
	MulAccumulate(4,2)
	MulAccumulate(3,3)
	MulAccumulate(2,4)
	MulAccumulate(1,5)
	MulAccumulate(0,6)
	MulStoreDigit(6)
	MulShiftCarry

	MulAccumulate(7,0)
	MulAccumulate(6,1)
	MulAccumulate(5,2)
	MulAccumulate(4,3)
	MulAccumulate(3,4)
	MulAccumulate(2,5)
	MulAccumulate(1,6)
	MulAccumulate(0,7)
	MulStoreDigit(7)
	MulShiftCarry

	MulAccumulate(7,1)
	MulAccumulate(6,2)
	MulAccumulate(5,3)
	MulAccumulate(4,4)
	MulAccumulate(3,5)
	MulAccumulate(2,6)
	MulAccumulate(1,7)
	MulStoreDigit(8)
	MulShiftCarry

	MulAccumulate(7,2)
	MulAccumulate(6,3)
	MulAccumulate(5,4)
	MulAccumulate(4,5)
	MulAccumulate(3,6)
	MulAccumulate(2,7)
	MulStoreDigit(9)
	MulShiftCarry

	MulAccumulate(7,3)
	MulAccumulate(6,4)
	MulAccumulate(5,5)
	MulAccumulate(4,6)
	MulAccumulate(3,7)
	MulStoreDigit(10)
	MulShiftCarry

	MulAccumulate(7,4)
	MulAccumulate(6,5)
	MulAccumulate(5,6)
	MulAccumulate(4,7)
	MulStoreDigit(11)
	MulShiftCarry

	MulAccumulate(7,5)
	MulAccumulate(6,6)
	MulAccumulate(5,7)
	MulStoreDigit(12)
	MulShiftCarry

	MulAccumulate(7,6)
	MulAccumulate(6,7)
	MulStoreDigit(13)
	MulShiftCarry

	MulLastDiagonal(8)
	MulEpilogue
}

CRYPTOPP_NAKED void PentiumOptimized::Multiply8Bottom(word* Z, const word* X, const word* Y)
{
	MulPrologue
	// now: [esp] = Z, esi = X, ecx = Y
	MulStartup
	MulAccumulate(0,0)
	MulStoreDigit(0)
	MulShiftCarry

	MulAccumulate(1,0)
	MulAccumulate(0,1)
	MulStoreDigit(1)
	MulShiftCarry

	MulAccumulate(2,0)
	MulAccumulate(1,1)
	MulAccumulate(0,2)
	MulStoreDigit(2)
	MulShiftCarry

	MulAccumulate(3,0)
	MulAccumulate(2,1)
	MulAccumulate(1,2)
	MulAccumulate(0,3)
	MulStoreDigit(3)
	MulShiftCarry

	MulAccumulate(4,0)
	MulAccumulate(3,1)
	MulAccumulate(2,2)
	MulAccumulate(1,3)
	MulAccumulate(0,4)
	MulStoreDigit(4)
	MulShiftCarry

	MulAccumulate(5,0)
	MulAccumulate(4,1)
	MulAccumulate(3,2)
	MulAccumulate(2,3)
	MulAccumulate(1,4)
	MulAccumulate(0,5)
	MulStoreDigit(5)
	MulShiftCarry

	MulAccumulate(6,0)
	MulAccumulate(5,1)
	MulAccumulate(4,2)
	MulAccumulate(3,3)
	MulAccumulate(2,4)
	MulAccumulate(1,5)
	MulAccumulate(0,6)
	MulStoreDigit(6)
	MulShiftCarry

	MulAccumulateBottom(7,0)
	MulAccumulateBottom(6,1)
	MulAccumulateBottom(5,2)
	MulAccumulateBottom(4,3)
	MulAccumulateBottom(3,4)
	MulAccumulateBottom(2,5)
	MulAccumulateBottom(1,6)
	MulAccumulateBottom(0,7)
	MulStoreDigit(7)
	MulEpilogue
}

#undef AS1
#undef AS2

#else	// not x86 - no processor specific code at this layer

typedef Portable LowLevel;

#endif

#ifdef SSE2_INTRINSICS_AVAILABLE

#ifdef __GNUC__
#define __fastcall
#endif

static void __fastcall P4_Mul(__m128i *C, const __m128i *A, const __m128i *B)
{
	__m128i a3210 = _mm_load_si128(A);
	__m128i b3210 = _mm_load_si128(B);

	__m128i sum;

	__m128i z = _mm_setzero_si128();
	__m128i a2b2_a0b0 = _mm_mul_epu32(a3210, b3210);
	C[0] = a2b2_a0b0;

	__m128i a3120 = _mm_shuffle_epi32(a3210, _MM_SHUFFLE(3, 1, 2, 0));
	__m128i b3021 = _mm_shuffle_epi32(b3210, _MM_SHUFFLE(3, 0, 2, 1));
	__m128i a1b0_a0b1 = _mm_mul_epu32(a3120, b3021);
	__m128i a1b0 = _mm_unpackhi_epi32(a1b0_a0b1, z);
	__m128i a0b1 = _mm_unpacklo_epi32(a1b0_a0b1, z);
	C[1] = _mm_add_epi64(a1b0, a0b1);

	__m128i a31 = _mm_srli_epi64(a3210, 32);
	__m128i b31 = _mm_srli_epi64(b3210, 32);
	__m128i a3b3_a1b1 = _mm_mul_epu32(a31, b31);
	C[6] = a3b3_a1b1;

	__m128i a1b1 = _mm_unpacklo_epi32(a3b3_a1b1, z);
	__m128i b3012 = _mm_shuffle_epi32(b3210, _MM_SHUFFLE(3, 0, 1, 2));
	__m128i a2b0_a0b2 = _mm_mul_epu32(a3210, b3012);
	__m128i a0b2 = _mm_unpacklo_epi32(a2b0_a0b2, z);
	__m128i a2b0 = _mm_unpackhi_epi32(a2b0_a0b2, z);
	sum = _mm_add_epi64(a1b1, a0b2);
	C[2] = _mm_add_epi64(sum, a2b0);

	__m128i a2301 = _mm_shuffle_epi32(a3210, _MM_SHUFFLE(2, 3, 0, 1));
	__m128i b2103 = _mm_shuffle_epi32(b3210, _MM_SHUFFLE(2, 1, 0, 3));
	__m128i a3b0_a1b2 = _mm_mul_epu32(a2301, b3012);
	__m128i a2b1_a0b3 = _mm_mul_epu32(a3210, b2103);
	__m128i a3b0 = _mm_unpackhi_epi32(a3b0_a1b2, z);
	__m128i a1b2 = _mm_unpacklo_epi32(a3b0_a1b2, z);
	__m128i a2b1 = _mm_unpackhi_epi32(a2b1_a0b3, z);
	__m128i a0b3 = _mm_unpacklo_epi32(a2b1_a0b3, z);
	__m128i sum1 = _mm_add_epi64(a3b0, a1b2);
	sum = _mm_add_epi64(a2b1, a0b3);
	C[3] = _mm_add_epi64(sum, sum1);

	__m128i	a3b1_a1b3 = _mm_mul_epu32(a2301, b2103);
	__m128i a2b2 = _mm_unpackhi_epi32(a2b2_a0b0, z);
	__m128i a3b1 = _mm_unpackhi_epi32(a3b1_a1b3, z);
	__m128i a1b3 = _mm_unpacklo_epi32(a3b1_a1b3, z);
	sum = _mm_add_epi64(a2b2, a3b1);
	C[4] = _mm_add_epi64(sum, a1b3);

	__m128i a1302 = _mm_shuffle_epi32(a3210, _MM_SHUFFLE(1, 3, 0, 2));
	__m128i b1203 = _mm_shuffle_epi32(b3210, _MM_SHUFFLE(1, 2, 0, 3));
	__m128i a3b2_a2b3 = _mm_mul_epu32(a1302, b1203);
	__m128i a3b2 = _mm_unpackhi_epi32(a3b2_a2b3, z);
	__m128i a2b3 = _mm_unpacklo_epi32(a3b2_a2b3, z);
	C[5] = _mm_add_epi64(a3b2, a2b3);
}

void P4Optimized::Multiply4(word *C, const word *A, const word *B)
{
	__m128i temp[7];
	const word *w = (word *)temp;
	const __m64 *mw = (__m64 *)w;

	P4_Mul(temp, (__m128i *)A, (__m128i *)B);

	C[0] = w[0];

	__m64 s1, s2;

	__m64 w1 = _mm_cvtsi32_si64(w[1]);
	__m64 w4 = mw[2];
	__m64 w6 = mw[3];
	__m64 w8 = mw[4];
	__m64 w10 = mw[5];
	__m64 w12 = mw[6];
	__m64 w14 = mw[7];
	__m64 w16 = mw[8];
	__m64 w18 = mw[9];
	__m64 w20 = mw[10];
	__m64 w22 = mw[11];
	__m64 w26 = _mm_cvtsi32_si64(w[26]);

	s1 = _mm_add_si64(w1, w4);
	C[1] = _mm_cvtsi64_si32(s1);
	s1 = _mm_srli_si64(s1, 32);

	s2 = _mm_add_si64(w6, w8);
	s1 = _mm_add_si64(s1, s2);
	C[2] = _mm_cvtsi64_si32(s1);
	s1 = _mm_srli_si64(s1, 32);

	s2 = _mm_add_si64(w10, w12);
	s1 = _mm_add_si64(s1, s2);
	C[3] = _mm_cvtsi64_si32(s1);
	s1 = _mm_srli_si64(s1, 32);

	s2 = _mm_add_si64(w14, w16);
	s1 = _mm_add_si64(s1, s2);
	C[4] = _mm_cvtsi64_si32(s1);
	s1 = _mm_srli_si64(s1, 32);

	s2 = _mm_add_si64(w18, w20);
	s1 = _mm_add_si64(s1, s2);
	C[5] = _mm_cvtsi64_si32(s1);
	s1 = _mm_srli_si64(s1, 32);

	s2 = _mm_add_si64(w22, w26);
	s1 = _mm_add_si64(s1, s2);
	C[6] = _mm_cvtsi64_si32(s1);
	s1 = _mm_srli_si64(s1, 32);

	C[7] = _mm_cvtsi64_si32(s1) + w[27];
	_mm_empty();
}

void P4Optimized::Multiply8(word *C, const word *A, const word *B)
{
	__m128i temp[28];
	const word *w = (word *)temp;
	const __m64 *mw = (__m64 *)w;
	const word *x = (word *)temp+7*4;
	const __m64 *mx = (__m64 *)x;
	const word *y = (word *)temp+7*4*2;
	const __m64 *my = (__m64 *)y;
	const word *z = (word *)temp+7*4*3;
	const __m64 *mz = (__m64 *)z;

	P4_Mul(temp, (__m128i *)A, (__m128i *)B);

	P4_Mul(temp+7, (__m128i *)A+1, (__m128i *)B);

	P4_Mul(temp+14, (__m128i *)A, (__m128i *)B+1);

	P4_Mul(temp+21, (__m128i *)A+1, (__m128i *)B+1);

	C[0] = w[0];

	__m64 s1, s2, s3, s4;

	__m64 w1 = _mm_cvtsi32_si64(w[1]);
	__m64 w4 = mw[2];
	__m64 w6 = mw[3];
	__m64 w8 = mw[4];
	__m64 w10 = mw[5];
	__m64 w12 = mw[6];
	__m64 w14 = mw[7];
	__m64 w16 = mw[8];
	__m64 w18 = mw[9];
	__m64 w20 = mw[10];
	__m64 w22 = mw[11];
	__m64 w26 = _mm_cvtsi32_si64(w[26]);
	__m64 w27 = _mm_cvtsi32_si64(w[27]);

	__m64 x0 = _mm_cvtsi32_si64(x[0]);
	__m64 x1 = _mm_cvtsi32_si64(x[1]);
	__m64 x4 = mx[2];
	__m64 x6 = mx[3];
	__m64 x8 = mx[4];
	__m64 x10 = mx[5];
	__m64 x12 = mx[6];
	__m64 x14 = mx[7];
	__m64 x16 = mx[8];
	__m64 x18 = mx[9];
	__m64 x20 = mx[10];
	__m64 x22 = mx[11];
	__m64 x26 = _mm_cvtsi32_si64(x[26]);
	__m64 x27 = _mm_cvtsi32_si64(x[27]);

	__m64 y0 = _mm_cvtsi32_si64(y[0]);
	__m64 y1 = _mm_cvtsi32_si64(y[1]);
	__m64 y4 = my[2];
	__m64 y6 = my[3];
	__m64 y8 = my[4];
	__m64 y10 = my[5];
	__m64 y12 = my[6];
	__m64 y14 = my[7];
	__m64 y16 = my[8];
	__m64 y18 = my[9];
	__m64 y20 = my[10];
	__m64 y22 = my[11];
	__m64 y26 = _mm_cvtsi32_si64(y[26]);
	__m64 y27 = _mm_cvtsi32_si64(y[27]);

	__m64 z0 = _mm_cvtsi32_si64(z[0]);
	__m64 z1 = _mm_cvtsi32_si64(z[1]);
	__m64 z4 = mz[2];
	__m64 z6 = mz[3];
	__m64 z8 = mz[4];
	__m64 z10 = mz[5];
	__m64 z12 = mz[6];
	__m64 z14 = mz[7];
	__m64 z16 = mz[8];
	__m64 z18 = mz[9];
	__m64 z20 = mz[10];
	__m64 z22 = mz[11];
	__m64 z26 = _mm_cvtsi32_si64(z[26]);

	s1 = _mm_add_si64(w1, w4);
	C[1] = _mm_cvtsi64_si32(s1);
	s1 = _mm_srli_si64(s1, 32);

	s2 = _mm_add_si64(w6, w8);
	s1 = _mm_add_si64(s1, s2);
	C[2] = _mm_cvtsi64_si32(s1);
	s1 = _mm_srli_si64(s1, 32);

	s2 = _mm_add_si64(w10, w12);
	s1 = _mm_add_si64(s1, s2);
	C[3] = _mm_cvtsi64_si32(s1);
	s1 = _mm_srli_si64(s1, 32);

	s3 = _mm_add_si64(x0, y0);
	s2 = _mm_add_si64(w14, w16);
	s1 = _mm_add_si64(s1, s3);
	s1 = _mm_add_si64(s1, s2);
	C[4] = _mm_cvtsi64_si32(s1);
	s1 = _mm_srli_si64(s1, 32);

	s3 = _mm_add_si64(x1, y1);
	s4 = _mm_add_si64(x4, y4);
	s1 = _mm_add_si64(s1, w18);
	s3 = _mm_add_si64(s3, s4);
	s1 = _mm_add_si64(s1, w20);
	s1 = _mm_add_si64(s1, s3);
	C[5] = _mm_cvtsi64_si32(s1);
	s1 = _mm_srli_si64(s1, 32);

	s3 = _mm_add_si64(x6, y6);
	s4 = _mm_add_si64(x8, y8);
	s1 = _mm_add_si64(s1, w22);
	s3 = _mm_add_si64(s3, s4);
	s1 = _mm_add_si64(s1, w26);
	s1 = _mm_add_si64(s1, s3);
	C[6] = _mm_cvtsi64_si32(s1);
	s1 = _mm_srli_si64(s1, 32);

	s3 = _mm_add_si64(x10, y10);
	s4 = _mm_add_si64(x12, y12);
	s1 = _mm_add_si64(s1, w27);
	s3 = _mm_add_si64(s3, s4);
	s1 = _mm_add_si64(s1, s3);
	C[7] = _mm_cvtsi64_si32(s1);
	s1 = _mm_srli_si64(s1, 32);

	s3 = _mm_add_si64(x14, y14);
	s4 = _mm_add_si64(x16, y16);
	s1 = _mm_add_si64(s1, z0);
	s3 = _mm_add_si64(s3, s4);
	s1 = _mm_add_si64(s1, s3);
	C[8] = _mm_cvtsi64_si32(s1);
	s1 = _mm_srli_si64(s1, 32);

	s3 = _mm_add_si64(x18, y18);
	s4 = _mm_add_si64(x20, y20);
	s1 = _mm_add_si64(s1, z1);
	s3 = _mm_add_si64(s3, s4);
	s1 = _mm_add_si64(s1, z4);
	s1 = _mm_add_si64(s1, s3);
	C[9] = _mm_cvtsi64_si32(s1);
	s1 = _mm_srli_si64(s1, 32);

	s3 = _mm_add_si64(x22, y22);
	s4 = _mm_add_si64(x26, y26);
	s1 = _mm_add_si64(s1, z6);
	s3 = _mm_add_si64(s3, s4);
	s1 = _mm_add_si64(s1, z8);
	s1 = _mm_add_si64(s1, s3);
	C[10] = _mm_cvtsi64_si32(s1);
	s1 = _mm_srli_si64(s1, 32);

	s3 = _mm_add_si64(x27, y27);
	s1 = _mm_add_si64(s1, z10);
	s1 = _mm_add_si64(s1, z12);
	s1 = _mm_add_si64(s1, s3);
	C[11] = _mm_cvtsi64_si32(s1);
	s1 = _mm_srli_si64(s1, 32);

	s3 = _mm_add_si64(z14, z16);
	s1 = _mm_add_si64(s1, s3);
	C[12] = _mm_cvtsi64_si32(s1);
	s1 = _mm_srli_si64(s1, 32);

	s3 = _mm_add_si64(z18, z20);
	s1 = _mm_add_si64(s1, s3);
	C[13] = _mm_cvtsi64_si32(s1);
	s1 = _mm_srli_si64(s1, 32);

	s3 = _mm_add_si64(z22, z26);
	s1 = _mm_add_si64(s1, s3);
	C[14] = _mm_cvtsi64_si32(s1);
	s1 = _mm_srli_si64(s1, 32);

	C[15] = z[27] + _mm_cvtsi64_si32(s1);
	_mm_empty();
}

void P4Optimized::Multiply8Bottom(word *C, const word *A, const word *B)
{
	__m128i temp[21];
	const word *w = (word *)temp;
	const __m64 *mw = (__m64 *)w;
	const word *x = (word *)temp+7*4;
	const __m64 *mx = (__m64 *)x;
	const word *y = (word *)temp+7*4*2;
	const __m64 *my = (__m64 *)y;

	P4_Mul(temp, (__m128i *)A, (__m128i *)B);

	P4_Mul(temp+7, (__m128i *)A+1, (__m128i *)B);

	P4_Mul(temp+14, (__m128i *)A, (__m128i *)B+1);

	C[0] = w[0];

	__m64 s1, s2, s3, s4;

	__m64 w1 = _mm_cvtsi32_si64(w[1]);
	__m64 w4 = mw[2];
	__m64 w6 = mw[3];
	__m64 w8 = mw[4];
	__m64 w10 = mw[5];
	__m64 w12 = mw[6];
	__m64 w14 = mw[7];
	__m64 w16 = mw[8];
	__m64 w18 = mw[9];
	__m64 w20 = mw[10];
	__m64 w22 = mw[11];
	__m64 w26 = _mm_cvtsi32_si64(w[26]);

	__m64 x0 = _mm_cvtsi32_si64(x[0]);
	__m64 x1 = _mm_cvtsi32_si64(x[1]);
	__m64 x4 = mx[2];
	__m64 x6 = mx[3];
	__m64 x8 = mx[4];

	__m64 y0 = _mm_cvtsi32_si64(y[0]);
	__m64 y1 = _mm_cvtsi32_si64(y[1]);
	__m64 y4 = my[2];
	__m64 y6 = my[3];
	__m64 y8 = my[4];

	s1 = _mm_add_si64(w1, w4);
	C[1] = _mm_cvtsi64_si32(s1);
	s1 = _mm_srli_si64(s1, 32);

	s2 = _mm_add_si64(w6, w8);
	s1 = _mm_add_si64(s1, s2);
	C[2] = _mm_cvtsi64_si32(s1);
	s1 = _mm_srli_si64(s1, 32);

	s2 = _mm_add_si64(w10, w12);
	s1 = _mm_add_si64(s1, s2);
	C[3] = _mm_cvtsi64_si32(s1);
	s1 = _mm_srli_si64(s1, 32);

	s3 = _mm_add_si64(x0, y0);
	s2 = _mm_add_si64(w14, w16);
	s1 = _mm_add_si64(s1, s3);
	s1 = _mm_add_si64(s1, s2);
	C[4] = _mm_cvtsi64_si32(s1);
	s1 = _mm_srli_si64(s1, 32);

	s3 = _mm_add_si64(x1, y1);
	s4 = _mm_add_si64(x4, y4);
	s1 = _mm_add_si64(s1, w18);
	s3 = _mm_add_si64(s3, s4);
	s1 = _mm_add_si64(s1, w20);
	s1 = _mm_add_si64(s1, s3);
	C[5] = _mm_cvtsi64_si32(s1);
	s1 = _mm_srli_si64(s1, 32);

	s3 = _mm_add_si64(x6, y6);
	s4 = _mm_add_si64(x8, y8);
	s1 = _mm_add_si64(s1, w22);
	s3 = _mm_add_si64(s3, s4);
	s1 = _mm_add_si64(s1, w26);
	s1 = _mm_add_si64(s1, s3);
	C[6] = _mm_cvtsi64_si32(s1);
	s1 = _mm_srli_si64(s1, 32);

	C[7] = _mm_cvtsi64_si32(s1) + w[27] + x[10] + y[10] + x[12] + y[12];
	_mm_empty();
}

#endif	// #ifdef SSE2_INTRINSICS_AVAILABLE

// ********************************************************

#define A0		A
#define A1		(A+N2)
#define B0		B
#define B1		(B+N2)

#define T0		T
#define T1		(T+N2)
#define T2		(T+N)
#define T3		(T+N+N2)

#define R0		R
#define R1		(R+N2)
#define R2		(R+N)
#define R3		(R+N+N2)

// R[2*N] - result = A*B
// T[2*N] - temporary work space
// A[N] --- multiplier
// B[N] --- multiplicant

void RecursiveMultiply(word *R, word *T, const word *A, const word *B, unsigned int N)
{
	assert(N>=2 && N%2==0);

	if (LowLevel::MultiplyRecursionLimit() >= 8 && N==8)
		LowLevel::Multiply8(R, A, B);
	else if (LowLevel::MultiplyRecursionLimit() >= 4 && N==4)
		LowLevel::Multiply4(R, A, B);
	else if (N==2)
		LowLevel::Multiply2(R, A, B);
	else
	{
		const unsigned int N2 = N/2;
		int carry;

		int aComp = Compare(A0, A1, N2);
		int bComp = Compare(B0, B1, N2);

		switch (2*aComp + aComp + bComp)
		{
		case -4:
			LowLevel::Subtract(R0, A1, A0, N2);
			LowLevel::Subtract(R1, B0, B1, N2);
			RecursiveMultiply(T0, T2, R0, R1, N2);
			LowLevel::Subtract(T1, T1, R0, N2);
			carry = -1;
			break;
		case -2:
			LowLevel::Subtract(R0, A1, A0, N2);
			LowLevel::Subtract(R1, B0, B1, N2);
			RecursiveMultiply(T0, T2, R0, R1, N2);
			carry = 0;
			break;
		case 2:
			LowLevel::Subtract(R0, A0, A1, N2);
			LowLevel::Subtract(R1, B1, B0, N2);
			RecursiveMultiply(T0, T2, R0, R1, N2);
			carry = 0;
			break;
		case 4:
			LowLevel::Subtract(R0, A1, A0, N2);
			LowLevel::Subtract(R1, B0, B1, N2);
			RecursiveMultiply(T0, T2, R0, R1, N2);
			LowLevel::Subtract(T1, T1, R1, N2);
			carry = -1;
			break;
		default:
			SetWords(T0, 0, N);
			carry = 0;
		}

		RecursiveMultiply(R0, T2, A0, B0, N2);
		RecursiveMultiply(R2, T2, A1, B1, N2);

		// now T[01] holds (A1-A0)*(B0-B1), R[01] holds A0*B0, R[23] holds A1*B1

		carry += LowLevel::Add(T0, T0, R0, N);
		carry += LowLevel::Add(T0, T0, R2, N);
		carry += LowLevel::Add(R1, R1, T0, N);

		assert (carry >= 0 && carry <= 2);
		Increment(R3, N2, carry);
	}
}

// R[2*N] - result = A*A
// T[2*N] - temporary work space
// A[N] --- number to be squared

void RecursiveSquare(word *R, word *T, const word *A, unsigned int N)
{
	assert(N && N%2==0);
	if (LowLevel::SquareRecursionLimit() >= 8 && N==8)
		LowLevel::Square8(R, A);
	if (LowLevel::SquareRecursionLimit() >= 4 && N==4)
		LowLevel::Square4(R, A);
	else if (N==2)
		LowLevel::Square2(R, A);
	else
	{
		const unsigned int N2 = N/2;

		RecursiveSquare(R0, T2, A0, N2);
		RecursiveSquare(R2, T2, A1, N2);
		RecursiveMultiply(T0, T2, A0, A1, N2);

		word carry = LowLevel::Add(R1, R1, T0, N);
		carry += LowLevel::Add(R1, R1, T0, N);
		Increment(R3, N2, carry);
	}
}

// R[N] - bottom half of A*B
// T[N] - temporary work space
// A[N] - multiplier
// B[N] - multiplicant

void RecursiveMultiplyBottom(word *R, word *T, const word *A, const word *B, unsigned int N)
{
	assert(N>=2 && N%2==0);
	if (LowLevel::MultiplyBottomRecursionLimit() >= 8 && N==8)
		LowLevel::Multiply8Bottom(R, A, B);
	else if (LowLevel::MultiplyBottomRecursionLimit() >= 4 && N==4)
		LowLevel::Multiply4Bottom(R, A, B);
	else if (N==2)
		LowLevel::Multiply2Bottom(R, A, B);
	else
	{
		const unsigned int N2 = N/2;

		RecursiveMultiply(R, T, A0, B0, N2);
		RecursiveMultiplyBottom(T0, T1, A1, B0, N2);
		LowLevel::Add(R1, R1, T0, N2);
		RecursiveMultiplyBottom(T0, T1, A0, B1, N2);
		LowLevel::Add(R1, R1, T0, N2);
	}
}

// R[N] --- upper half of A*B
// T[2*N] - temporary work space
// L[N] --- lower half of A*B
// A[N] --- multiplier
// B[N] --- multiplicant

void RecursiveMultiplyTop(word *R, word *T, const word *L, const word *A, const word *B, unsigned int N)
{
	assert(N>=2 && N%2==0);

	if (N==4)
	{
		LowLevel::Multiply4(T, A, B);
		memcpy(R, T+4, 4*WORD_SIZE);
	}
	else if (N==2)
	{
		LowLevel::Multiply2(T, A, B);
		memcpy(R, T+2, 2*WORD_SIZE);
	}
	else
	{
		const unsigned int N2 = N/2;
		int carry;

		int aComp = Compare(A0, A1, N2);
		int bComp = Compare(B0, B1, N2);

		switch (2*aComp + aComp + bComp)
		{
		case -4:
			LowLevel::Subtract(R0, A1, A0, N2);
			LowLevel::Subtract(R1, B0, B1, N2);
			RecursiveMultiply(T0, T2, R0, R1, N2);
			LowLevel::Subtract(T1, T1, R0, N2);
			carry = -1;
			break;
		case -2:
			LowLevel::Subtract(R0, A1, A0, N2);
			LowLevel::Subtract(R1, B0, B1, N2);
			RecursiveMultiply(T0, T2, R0, R1, N2);
			carry = 0;
			break;
		case 2:
			LowLevel::Subtract(R0, A0, A1, N2);
			LowLevel::Subtract(R1, B1, B0, N2);
			RecursiveMultiply(T0, T2, R0, R1, N2);
			carry = 0;
			break;
		case 4:
			LowLevel::Subtract(R0, A1, A0, N2);
			LowLevel::Subtract(R1, B0, B1, N2);
			RecursiveMultiply(T0, T2, R0, R1, N2);
			LowLevel::Subtract(T1, T1, R1, N2);
			carry = -1;
			break;
		default:
			SetWords(T0, 0, N);
			carry = 0;
		}

		RecursiveMultiply(T2, R0, A1, B1, N2);

		// now T[01] holds (A1-A0)*(B0-B1), T[23] holds A1*B1

		word c2 = LowLevel::Subtract(R0, L+N2, L, N2);
		c2 += LowLevel::Subtract(R0, R0, T0, N2);
		word t = (Compare(R0, T2, N2) == -1);

		carry += t;
		carry += Increment(R0, N2, c2+t);
		carry += LowLevel::Add(R0, R0, T1, N2);
		carry += LowLevel::Add(R0, R0, T3, N2);
		assert (carry >= 0 && carry <= 2);

		CopyWords(R1, T3, N2);
		Increment(R1, N2, carry);
	}
}

inline word Add(word *C, const word *A, const word *B, unsigned int N)
{
	return LowLevel::Add(C, A, B, N);
}

inline word Subtract(word *C, const word *A, const word *B, unsigned int N)
{
	return LowLevel::Subtract(C, A, B, N);
}

inline void Multiply(word *R, word *T, const word *A, const word *B, unsigned int N)
{
	RecursiveMultiply(R, T, A, B, N);
}

inline void Square(word *R, word *T, const word *A, unsigned int N)
{
	RecursiveSquare(R, T, A, N);
}

inline void MultiplyBottom(word *R, word *T, const word *A, const word *B, unsigned int N)
{
	RecursiveMultiplyBottom(R, T, A, B, N);
}

inline void MultiplyTop(word *R, word *T, const word *L, const word *A, const word *B, unsigned int N)
{
	RecursiveMultiplyTop(R, T, L, A, B, N);
}

static word LinearMultiply(word *C, const word *A, word B, unsigned int N)
{
	word carry=0;
	for(unsigned i=0; i<N; i++)
	{
		DWord p = DWord::MultiplyAndAdd(A[i], B, carry);
		C[i] = p.GetLowHalf();
		carry = p.GetHighHalf();
	}
	return carry;
}

// R[NA+NB] - result = A*B
// T[NA+NB] - temporary work space
// A[NA] ---- multiplier
// B[NB] ---- multiplicant

void AsymmetricMultiply(word *R, word *T, const word *A, unsigned int NA, const word *B, unsigned int NB)
{
	if (NA == NB)
	{
		if (A == B)
			Square(R, T, A, NA);
		else
			Multiply(R, T, A, B, NA);

		return;
	}

	if (NA > NB)
	{
		std::swap(A, B);
		std::swap(NA, NB);
	}

	assert(NB % NA == 0);
	assert((NB/NA)%2 == 0); 	// NB is an even multiple of NA

	if (NA==2 && !A[1])
	{
		switch (A[0])
		{
		case 0:
			SetWords(R, 0, NB+2);
			return;
		case 1:
			CopyWords(R, B, NB);
			R[NB] = R[NB+1] = 0;
			return;
		default:
			R[NB] = LinearMultiply(R, B, A[0], NB);
			R[NB+1] = 0;
			return;
		}
	}

	Multiply(R, T, A, B, NA);
	CopyWords(T+2*NA, R+NA, NA);

	unsigned i;

	for (i=2*NA; i<NB; i+=2*NA)
		Multiply(T+NA+i, T, A, B+i, NA);
	for (i=NA; i<NB; i+=2*NA)
		Multiply(R+i, T, A, B+i, NA);

	if (Add(R+NA, R+NA, T+2*NA, NB-NA))
		Increment(R+NB, NA);
}

// R[N] ----- result = A inverse mod 2**(WORD_BITS*N)
// T[3*N/2] - temporary work space
// A[N] ----- an odd number as input

void RecursiveInverseModPower2(word *R, word *T, const word *A, unsigned int N)
{
	if (N==2)
	{
		T[0] = AtomicInverseModPower2(A[0]);
		T[1] = 0;
		LowLevel::Multiply2Bottom(T+2, T, A);
		TwosComplement(T+2, 2);
		Increment(T+2, 2, 2);
		LowLevel::Multiply2Bottom(R, T, T+2);
	}
	else
	{
		const unsigned int N2 = N/2;
		RecursiveInverseModPower2(R0, T0, A0, N2);
		T0[0] = 1;
		SetWords(T0+1, 0, N2-1);
		MultiplyTop(R1, T1, T0, R0, A0, N2);
		MultiplyBottom(T0, T1, R0, A1, N2);
		Add(T0, R1, T0, N2);
		TwosComplement(T0, N2);
		MultiplyBottom(R1, T1, R0, T0, N2);
	}
}

// R[N] --- result = X/(2**(WORD_BITS*N)) mod M
// T[3*N] - temporary work space
// X[2*N] - number to be reduced
// M[N] --- modulus
// U[N] --- multiplicative inverse of M mod 2**(WORD_BITS*N)

void MontgomeryReduce(word *R, word *T, const word *X, const word *M, const word *U, unsigned int N)
{
	MultiplyBottom(R, T, X, U, N);
	MultiplyTop(T, T+N, X, R, M, N);
	word borrow = Subtract(T, X+N, T, N);
	// defend against timing attack by doing this Add even when not needed
	word carry = Add(T+N, T, M, N);
	assert(carry || !borrow);
	CopyWords(R, T + (borrow ? N : 0), N);
}

// R[N] --- result = X/(2**(WORD_BITS*N/2)) mod M
// T[2*N] - temporary work space
// X[2*N] - number to be reduced
// M[N] --- modulus
// U[N/2] - multiplicative inverse of M mod 2**(WORD_BITS*N/2)
// V[N] --- 2**(WORD_BITS*3*N/2) mod M

void HalfMontgomeryReduce(word *R, word *T, const word *X, const word *M, const word *U, const word *V, unsigned int N)
{
	assert(N%2==0 && N>=4);

#define M0		M
#define M1		(M+N2)
#define V0		V
#define V1		(V+N2)

#define X0		X
#define X1		(X+N2)
#define X2		(X+N)
#define X3		(X+N+N2)

	const unsigned int N2 = N/2;
	Multiply(T0, T2, V0, X3, N2);
	int c2 = Add(T0, T0, X0, N);
	MultiplyBottom(T3, T2, T0, U, N2);
	MultiplyTop(T2, R, T0, T3, M0, N2);
	c2 -= Subtract(T2, T1, T2, N2);
	Multiply(T0, R, T3, M1, N2);
	c2 -= Subtract(T0, T2, T0, N2);
	int c3 = -(int)Subtract(T1, X2, T1, N2);
	Multiply(R0, T2, V1, X3, N2);
	c3 += Add(R, R, T, N);

	if (c2>0)
		c3 += Increment(R1, N2);
	else if (c2<0)
		c3 -= Decrement(R1, N2, -c2);

	assert(c3>=-1 && c3<=1);
	if (c3>0)
		Subtract(R, R, M, N);
	else if (c3<0)
		Add(R, R, M, N);

#undef M0
#undef M1
#undef V0
#undef V1

#undef X0
#undef X1
#undef X2
#undef X3
}

#undef A0
#undef A1
#undef B0
#undef B1

#undef T0
#undef T1
#undef T2
#undef T3

#undef R0
#undef R1
#undef R2
#undef R3

/*
// do a 3 word by 2 word divide, returns quotient and leaves remainder in A
static word SubatomicDivide(word *A, word B0, word B1)
{
	// assert {A[2],A[1]} < {B1,B0}, so quotient can fit in a word
	assert(A[2] < B1 || (A[2]==B1 && A[1] < B0));

	// estimate the quotient: do a 2 word by 1 word divide
	word Q;
	if (B1+1 == 0)
		Q = A[2];
	else
		Q = DWord(A[1], A[2]).DividedBy(B1+1);

	// now subtract Q*B from A
	DWord p = DWord::Multiply(B0, Q);
	DWord u = (DWord) A[0] - p.GetLowHalf();
	A[0] = u.GetLowHalf();
	u = (DWord) A[1] - p.GetHighHalf() - u.GetHighHalfAsBorrow() - DWord::Multiply(B1, Q);
	A[1] = u.GetLowHalf();
	A[2] += u.GetHighHalf();

	// Q <= actual quotient, so fix it
	while (A[2] || A[1] > B1 || (A[1]==B1 && A[0]>=B0))
	{
		u = (DWord) A[0] - B0;
		A[0] = u.GetLowHalf();
		u = (DWord) A[1] - B1 - u.GetHighHalfAsBorrow();
		A[1] = u.GetLowHalf();
		A[2] += u.GetHighHalf();
		Q++;
		assert(Q);	// shouldn't overflow
	}

	return Q;
}

// do a 4 word by 2 word divide, returns 2 word quotient in Q0 and Q1
static inline void AtomicDivide(word *Q, const word *A, const word *B)
{
	if (!B[0] && !B[1]) // if divisor is 0, we assume divisor==2**(2*WORD_BITS)
	{
		Q[0] = A[2];
		Q[1] = A[3];
	}
	else
	{
		word T[4];
		T[0] = A[0]; T[1] = A[1]; T[2] = A[2]; T[3] = A[3];
		Q[1] = SubatomicDivide(T+1, B[0], B[1]);
		Q[0] = SubatomicDivide(T, B[0], B[1]);

#ifndef NDEBUG
		// multiply quotient and divisor and add remainder, make sure it equals dividend
		assert(!T[2] && !T[3] && (T[1] < B[1] || (T[1]==B[1] && T[0]<B[0])));
		word P[4];
		LowLevel::Multiply2(P, Q, B);
		Add(P, P, T, 4);
		assert(memcmp(P, A, 4*WORD_SIZE)==0);
#endif
	}
}
*/

static inline void AtomicDivide(word *Q, const word *A, const word *B)
{
	word T[4];
	DWord q = DivideFourWordsByTwo<word, DWord>(T, DWord(A[0], A[1]), DWord(A[2], A[3]), DWord(B[0], B[1]));
	Q[0] = q.GetLowHalf();
	Q[1] = q.GetHighHalf();

#ifndef NDEBUG
	if (B[0] || B[1])
	{
		// multiply quotient and divisor and add remainder, make sure it equals dividend
		assert(!T[2] && !T[3] && (T[1] < B[1] || (T[1]==B[1] && T[0]<B[0])));
		word P[4];
		Portable::Multiply2(P, Q, B);
		Add(P, P, T, 4);
		assert(memcmp(P, A, 4*WORD_SIZE)==0);
	}
#endif
}

// for use by Divide(), corrects the underestimated quotient {Q1,Q0}
static void CorrectQuotientEstimate(word *R, word *T, word *Q, const word *B, unsigned int N)
{
	assert(N && N%2==0);

	if (Q[1])
	{
		T[N] = T[N+1] = 0;
		unsigned i;
		for (i=0; i<N; i+=4)
			LowLevel::Multiply2(T+i, Q, B+i);
		for (i=2; i<N; i+=4)
			if (LowLevel::Multiply2Add(T+i, Q, B+i))
				T[i+5] += (++T[i+4]==0);
	}
	else
	{
		T[N] = LinearMultiply(T, B, Q[0], N);
		T[N+1] = 0;
	}

	word borrow = Subtract(R, R, T, N+2);
	assert(!borrow && !R[N+1]);

	while (R[N] || Compare(R, B, N) >= 0)
	{
		R[N] -= Subtract(R, R, B, N);
		Q[1] += (++Q[0]==0);
		assert(Q[0] || Q[1]); // no overflow
	}
}

// R[NB] -------- remainder = A%B
// Q[NA-NB+2] --- quotient	= A/B
// T[NA+2*NB+4] - temp work space
// A[NA] -------- dividend
// B[NB] -------- divisor

void Divide(word *R, word *Q, word *T, const word *A, unsigned int NA, const word *B, unsigned int NB)
{
	assert(NA && NB && NA%2==0 && NB%2==0);
	assert(B[NB-1] || B[NB-2]);
	assert(NB <= NA);

	// set up temporary work space
	word *const TA=T;
	word *const TB=T+NA+2;
	word *const TP=T+NA+2+NB;

	// copy B into TB and normalize it so that TB has highest bit set to 1
	unsigned shiftWords = (B[NB-1]==0);
	TB[0] = TB[NB-1] = 0;
	CopyWords(TB+shiftWords, B, NB-shiftWords);
	unsigned shiftBits = WORD_BITS - BitPrecision(TB[NB-1]);
	assert(shiftBits < WORD_BITS);
	ShiftWordsLeftByBits(TB, NB, shiftBits);

	// copy A into TA and normalize it
	TA[0] = TA[NA] = TA[NA+1] = 0;
	CopyWords(TA+shiftWords, A, NA);
	ShiftWordsLeftByBits(TA, NA+2, shiftBits);

	if (TA[NA+1]==0 && TA[NA] <= 1)
	{
		Q[NA-NB+1] = Q[NA-NB] = 0;
		while (TA[NA] || Compare(TA+NA-NB, TB, NB) >= 0)
		{
			TA[NA] -= Subtract(TA+NA-NB, TA+NA-NB, TB, NB);
			++Q[NA-NB];
		}
	}
	else
	{
		NA+=2;
		assert(Compare(TA+NA-NB, TB, NB) < 0);
	}

	word BT[2];
	BT[0] = TB[NB-2] + 1;
	BT[1] = TB[NB-1] + (BT[0]==0);

	// start reducing TA mod TB, 2 words at a time
	for (unsigned i=NA-2; i>=NB; i-=2)
	{
		AtomicDivide(Q+i-NB, TA+i-2, BT);
		CorrectQuotientEstimate(TA+i-NB, TP, Q+i-NB, TB, NB);
	}

	// copy TA into R, and denormalize it
	CopyWords(R, TA+shiftWords, NB);
	ShiftWordsRightByBits(R, NB, shiftBits);
}

static inline unsigned int EvenWordCount(const word *X, unsigned int N)
{
	while (N && X[N-2]==0 && X[N-1]==0)
		N-=2;
	return N;
}

// return k
// R[N] --- result = A^(-1) * 2^k mod M
// T[4*N] - temporary work space
// A[NA] -- number to take inverse of
// M[N] --- modulus

unsigned int AlmostInverse(word *R, word *T, const word *A, unsigned int NA, const word *M, unsigned int N)
{
	assert(NA<=N && N && N%2==0);

	word *b = T;
	word *c = T+N;
	word *f = T+2*N;
	word *g = T+3*N;
	unsigned int bcLen=2, fgLen=EvenWordCount(M, N);
	unsigned int k=0, s=0;

	SetWords(T, 0, 3*N);
	b[0]=1;
	CopyWords(f, A, NA);
	CopyWords(g, M, N);

	while (1)
	{
		word t=f[0];
		while (!t)
		{
			if (EvenWordCount(f, fgLen)==0)
			{
				SetWords(R, 0, N);
				return 0;
			}

			ShiftWordsRightByWords(f, fgLen, 1);
			if (c[bcLen-1]) bcLen+=2;
			assert(bcLen <= N);
			ShiftWordsLeftByWords(c, bcLen, 1);
			k+=WORD_BITS;
			t=f[0];
		}

		unsigned int i=0;
		while (t%2 == 0)
		{
			t>>=1;
			i++;
		}
		k+=i;

		if (t==1 && f[1]==0 && EvenWordCount(f, fgLen)==2)
		{
			if (s%2==0)
				CopyWords(R, b, N);
			else
				Subtract(R, M, b, N);
			return k;
		}

		ShiftWordsRightByBits(f, fgLen, i);
		t=ShiftWordsLeftByBits(c, bcLen, i);
		if (t)
		{
			c[bcLen] = t;
			bcLen+=2;
			assert(bcLen <= N);
		}

		if (f[fgLen-2]==0 && g[fgLen-2]==0 && f[fgLen-1]==0 && g[fgLen-1]==0)
			fgLen-=2;

		if (Compare(f, g, fgLen)==-1)
		{
			std::swap(f, g);
			std::swap(b, c);
			s++;
		}

		Subtract(f, f, g, fgLen);

		if (Add(b, b, c, bcLen))
		{
			b[bcLen] = 1;
			bcLen+=2;
			assert(bcLen <= N);
		}
	}
}

// R[N] - result = A/(2^k) mod M
// A[N] - input
// M[N] - modulus

void DivideByPower2Mod(word *R, const word *A, unsigned int k, const word *M, unsigned int N)
{
	CopyWords(R, A, N);

	while (k--)
	{
		if (R[0]%2==0)
			ShiftWordsRightByBits(R, N, 1);
		else
		{
			word carry = Add(R, R, M, N);
			ShiftWordsRightByBits(R, N, 1);
			R[N-1] += carry<<(WORD_BITS-1);
		}
	}
}

// R[N] - result = A*(2^k) mod M
// A[N] - input
// M[N] - modulus

void MultiplyByPower2Mod(word *R, const word *A, unsigned int k, const word *M, unsigned int N)
{
	CopyWords(R, A, N);

	while (k--)
		if (ShiftWordsLeftByBits(R, N, 1) || Compare(R, M, N)>=0)
			Subtract(R, R, M, N);
}

// ******************************************************************

static const unsigned int RoundupSizeTable[] = {2, 2, 2, 4, 4, 8, 8, 8, 8};

static inline unsigned int RoundupSize(unsigned int n)
{
	if (n<=8)
		return RoundupSizeTable[n];
	else if (n<=16)
		return 16;
	else if (n<=32)
		return 32;
	else if (n<=64)
		return 64;
	else return 1U << BitPrecision(n-1);
}

Integer::Integer()
	: reg(2), sign(POSITIVE)
{
	reg[0] = reg[1] = 0;
}

Integer::Integer(const Integer& t)
	: reg(RoundupSize(t.WordCount())), sign(t.sign)
{
	CopyWords(reg, t.reg, reg.size());
}

Integer::Integer(Sign s, lword value)
	: reg(2), sign(s)
{
	reg[0] = word(value);
	reg[1] = word(SafeRightShift<WORD_BITS>(value));
}

Integer::Integer(signed long value)
	: reg(2)
{
	if (value >= 0)
		sign = POSITIVE;
	else
	{
		sign = NEGATIVE;
		value = -value;
	}
	reg[0] = word(value);
	reg[1] = word(SafeRightShift<WORD_BITS>((unsigned long)value));
}

Integer::Integer(Sign s, word high, word low)
	: reg(2), sign(s)
{
	reg[0] = low;
	reg[1] = high;
}

bool Integer::IsConvertableToLong() const
{
	if (ByteCount() > sizeof(long))
		return false;

	unsigned long value = reg[0];
	value += SafeLeftShift<WORD_BITS, unsigned long>(reg[1]);

	if (sign==POSITIVE)
		return (signed long)value >= 0;
	else
		return -(signed long)value < 0;
}

signed long Integer::ConvertToLong() const
{
	assert(IsConvertableToLong());

	unsigned long value = reg[0];
	value += SafeLeftShift<WORD_BITS, unsigned long>(reg[1]);
	return sign==POSITIVE ? value : -(signed long)value;
}

Integer::Integer(BufferedTransformation &encodedInteger, unsigned int byteCount, Signedness s)
{
	Decode(encodedInteger, byteCount, s);
}

Integer::Integer(const byte *encodedInteger, unsigned int byteCount, Signedness s)
{
	Decode(encodedInteger, byteCount, s);
}

Integer::Integer(BufferedTransformation &bt)
{
	BERDecode(bt);
}

Integer::Integer(RandomNumberGenerator &rng, unsigned int bitcount)
{
	Randomize(rng, bitcount);
}

Integer::Integer(RandomNumberGenerator &rng, const Integer &min, const Integer &max, RandomNumberType rnType, const Integer &equiv, const Integer &mod)
{
	if (!Randomize(rng, min, max, rnType, equiv, mod))
		throw Integer::RandomNumberNotFound();
}

Integer Integer::Power2(unsigned int e)
{
	Integer r((word)0, BitsToWords(e+1));
	r.SetBit(e);
	return r;
}

template <long i>
struct NewInteger
{
	Integer * operator()() const
	{
		return new Integer(i);
	}
};

const Integer &Integer::Zero()
{
	return Singleton<Integer>().Ref();
}

const Integer &Integer::One()
{
	return Singleton<Integer, NewInteger<1> >().Ref();
}

const Integer &Integer::Two()
{
	return Singleton<Integer, NewInteger<2> >().Ref();
}

bool Integer::operator!() const
{
	return IsNegative() ? false : (reg[0]==0 && WordCount()==0);
}

Integer& Integer::operator=(const Integer& t)
{
	if (this != &t)
	{
		reg.New(RoundupSize(t.WordCount()));
		CopyWords(reg, t.reg, reg.size());
		sign = t.sign;
	}
	return *this;
}

bool Integer::GetBit(unsigned int n) const
{
	if (n/WORD_BITS >= reg.size())
		return 0;
	else
		return bool((reg[n/WORD_BITS] >> (n % WORD_BITS)) & 1);
}

void Integer::SetBit(unsigned int n, bool value)
{
	if (value)
	{
		reg.CleanGrow(RoundupSize(BitsToWords(n+1)));
		reg[n/WORD_BITS] |= (word(1) << (n%WORD_BITS));
	}
	else
	{
		if (n/WORD_BITS < reg.size())
			reg[n/WORD_BITS] &= ~(word(1) << (n%WORD_BITS));
	}
}

byte Integer::GetByte(unsigned int n) const
{
	if (n/WORD_SIZE >= reg.size())
		return 0;
	else
		return byte(reg[n/WORD_SIZE] >> ((n%WORD_SIZE)*8));
}

void Integer::SetByte(unsigned int n, byte value)
{
	reg.CleanGrow(RoundupSize(BytesToWords(n+1)));
	reg[n/WORD_SIZE] &= ~(word(0xff) << 8*(n%WORD_SIZE));
	reg[n/WORD_SIZE] |= (word(value) << 8*(n%WORD_SIZE));
}

unsigned long Integer::GetBits(unsigned int i, unsigned int n) const
{
	assert(n <= sizeof(unsigned long)*8);
	unsigned long v = 0;
	for (unsigned int j=0; j<n; j++)
		v |= GetBit(i+j) << j;
	return v;
}

Integer Integer::operator-() const
{
	Integer result(*this);
	result.Negate();
	return result;
}

Integer Integer::AbsoluteValue() const
{
	Integer result(*this);
	result.sign = POSITIVE;
	return result;
}

void Integer::swap(Integer &a)
{
	reg.swap(a.reg);
	std::swap(sign, a.sign);
}

Integer::Integer(word value, unsigned int length)
	: reg(RoundupSize(length)), sign(POSITIVE)
{
	reg[0] = value;
	SetWords(reg+1, 0, reg.size()-1);
}

template <class T>
static Integer StringToInteger(const T *str)
{
	word radix;
	// GCC workaround
	// std::char_traits doesn't exist in GCC 2.x
	// std::char_traits<wchar_t>::length() not defined in GCC 3.2 and STLport 4.5.3
	unsigned int length;
	for (length = 0; str[length] != 0; length++) {}

	Integer v;

	if (length == 0)
		return v;

	switch (str[length-1])
	{
	case 'h':
	case 'H':
		radix=16;
		break;
	case 'o':
	case 'O':
		radix=8;
		break;
	case 'b':
	case 'B':
		radix=2;
		break;
	default:
		radix=10;
	}

	if (length > 2 && str[0] == '0' && str[1] == 'x')
		radix = 16;

	for (unsigned i=0; i<length; i++)
	{
		word digit;

		if (str[i] >= '0' && str[i] <= '9')
			digit = str[i] - '0';
		else if (str[i] >= 'A' && str[i] <= 'F')
			digit = str[i] - 'A' + 10;
		else if (str[i] >= 'a' && str[i] <= 'f')
			digit = str[i] - 'a' + 10;
		else
			digit = radix;

		if (digit < radix)
		{
			v *= radix;
			v += digit;
		}
	}

	if (str[0] == '-')
		v.Negate();

	return v;
}

Integer::Integer(const char *str)
	: reg(2), sign(POSITIVE)
{
	*this = StringToInteger(str);
}

Integer::Integer(const wchar_t *str)
	: reg(2), sign(POSITIVE)
{
	*this = StringToInteger(str);
}

unsigned int Integer::WordCount() const
{
	return CountWords(reg, reg.size());
}

unsigned int Integer::ByteCount() const
{
	unsigned wordCount = WordCount();
	if (wordCount)
		return (wordCount-1)*WORD_SIZE + BytePrecision(reg[wordCount-1]);
	else
		return 0;
}

unsigned int Integer::BitCount() const
{
	unsigned wordCount = WordCount();
	if (wordCount)
		return (wordCount-1)*WORD_BITS + BitPrecision(reg[wordCount-1]);
	else
		return 0;
}

void Integer::Decode(const byte *input, unsigned int inputLen, Signedness s)
{
	StringStore store(input, inputLen);
	Decode(store, inputLen, s);
}

void Integer::Decode(BufferedTransformation &bt, unsigned int inputLen, Signedness s)
{
	assert(bt.MaxRetrievable() >= inputLen);

	byte b;
	bt.Peek(b);
	sign = ((s==SIGNED) && (b & 0x80)) ? NEGATIVE : POSITIVE;

	while (inputLen>0 && (sign==POSITIVE ? b==0 : b==0xff))
	{
		bt.Skip(1);
		inputLen--;
		bt.Peek(b);
	}

	reg.CleanNew(RoundupSize(BytesToWords(inputLen)));

	for (unsigned int i=inputLen; i > 0; i--)
	{
		bt.Get(b);
		reg[(i-1)/WORD_SIZE] |= word(b) << ((i-1)%WORD_SIZE)*8;
	}

	if (sign == NEGATIVE)
	{
		for (unsigned i=inputLen; i<reg.size()*WORD_SIZE; i++)
			reg[i/WORD_SIZE] |= word(0xff) << (i%WORD_SIZE)*8;
		TwosComplement(reg, reg.size());
	}
}

unsigned int Integer::MinEncodedSize(Signedness signedness) const
{
	unsigned int outputLen = STDMAX(1U, ByteCount());
	if (signedness == UNSIGNED)
		return outputLen;
	if (NotNegative() && (GetByte(outputLen-1) & 0x80))
		outputLen++;
	if (IsNegative() && *this < -Power2(outputLen*8-1))
		outputLen++;
	return outputLen;
}

unsigned int Integer::Encode(byte *output, unsigned int outputLen, Signedness signedness) const
{
	ArraySink sink(output, outputLen);
	return Encode(sink, outputLen, signedness);
}

unsigned int Integer::Encode(BufferedTransformation &bt, unsigned int outputLen, Signedness signedness) const
{
	if (signedness == UNSIGNED || NotNegative())
	{
		for (unsigned int i=outputLen; i > 0; i--)
			bt.Put(GetByte(i-1));
	}
	else
	{
		// take two's complement of *this
		Integer temp = Integer::Power2(8*STDMAX(ByteCount(), outputLen)) + *this;
		for (unsigned i=0; i<outputLen; i++)
			bt.Put(temp.GetByte(outputLen-i-1));
	}
	return outputLen;
}

void Integer::DEREncode(BufferedTransformation &bt) const
{
	DERGeneralEncoder enc(bt, INTEGER);
	Encode(enc, MinEncodedSize(SIGNED), SIGNED);
	enc.MessageEnd();
}

void Integer::BERDecode(const byte *input, unsigned int len)
{
	StringStore store(input, len);
	BERDecode(store);
}

void Integer::BERDecode(BufferedTransformation &bt)
{
	BERGeneralDecoder dec(bt, INTEGER);
	if (!dec.IsDefiniteLength() || dec.MaxRetrievable() < dec.RemainingLength())
		BERDecodeError();
	Decode(dec, dec.RemainingLength(), SIGNED);
	dec.MessageEnd();
}

void Integer::DEREncodeAsOctetString(BufferedTransformation &bt, unsigned int length) const
{
	DERGeneralEncoder enc(bt, OCTET_STRING);
	Encode(enc, length);
	enc.MessageEnd();
}

void Integer::BERDecodeAsOctetString(BufferedTransformation &bt, unsigned int length)
{
	BERGeneralDecoder dec(bt, OCTET_STRING);
	if (!dec.IsDefiniteLength() || dec.RemainingLength() != length)
		BERDecodeError();
	Decode(dec, length);
	dec.MessageEnd();
}

unsigned int Integer::OpenPGPEncode(byte *output, unsigned int len) const
{
	ArraySink sink(output, len);
	return OpenPGPEncode(sink);
}

unsigned int Integer::OpenPGPEncode(BufferedTransformation &bt) const
{
	word16 bitCount = BitCount();
	bt.PutWord16(bitCount);
	return 2 + Encode(bt, BitsToBytes(bitCount));
}

void Integer::OpenPGPDecode(const byte *input, unsigned int len)
{
	StringStore store(input, len);
	OpenPGPDecode(store);
}

void Integer::OpenPGPDecode(BufferedTransformation &bt)
{
	word16 bitCount;
	if (bt.GetWord16(bitCount) != 2 || bt.MaxRetrievable() < BitsToBytes(bitCount))
		throw OpenPGPDecodeErr();
	Decode(bt, BitsToBytes(bitCount));
}

void Integer::Randomize(RandomNumberGenerator &rng, unsigned int nbits)
{
	const unsigned int nbytes = nbits/8 + 1;
	SecByteBlock buf(nbytes);
	rng.GenerateBlock(buf, nbytes);
	if (nbytes)
		buf[0] = (byte)Crop(buf[0], nbits % 8);
	Decode(buf, nbytes, UNSIGNED);
}

void Integer::Randomize(RandomNumberGenerator &rng, const Integer &min, const Integer &max)
{
	if (min > max)
		throw InvalidArgument("Integer: Min must be no greater than Max");

	Integer range = max - min;
	const unsigned int nbits = range.BitCount();

	do
	{
		Randomize(rng, nbits);
	}
	while (*this > range);

	*this += min;
}

bool Integer::Randomize(RandomNumberGenerator &rng, const Integer &min, const Integer &max, RandomNumberType rnType, const Integer &equiv, const Integer &mod)
{
	return GenerateRandomNoThrow(rng, MakeParameters("Min", min)("Max", max)("RandomNumberType", rnType)("EquivalentTo", equiv)("Mod", mod));
}

class KDF2_RNG : public RandomNumberGenerator
{
public:
	KDF2_RNG(const byte *seed, unsigned int seedSize)
		: m_counter(0), m_counterAndSeed(seedSize + 4)
	{
		memcpy(m_counterAndSeed + 4, seed, seedSize);
	}

	byte GenerateByte()
	{
		byte b;
		GenerateBlock(&b, 1);
		return b;
	}

	void GenerateBlock(byte *output, unsigned int size)
	{
		UnalignedPutWord(BIG_ENDIAN_ORDER, m_counterAndSeed, m_counter);
		++m_counter;
		P1363_KDF2<SHA1>::DeriveKey(output, size, m_counterAndSeed, m_counterAndSeed.size(), NULL, 0);
	}

private:
	word32 m_counter;
	SecByteBlock m_counterAndSeed;
};

bool Integer::GenerateRandomNoThrow(RandomNumberGenerator &i_rng, const NameValuePairs &params)
{
	Integer min = params.GetValueWithDefault("Min", Integer::Zero());
	Integer max;
	if (!params.GetValue("Max", max))
	{
		int bitLength;
		if (params.GetIntValue("BitLength", bitLength))
			max = Integer::Power2(bitLength);
		else
			throw InvalidArgument("Integer: missing Max argument");
	}
	if (min > max)
		throw InvalidArgument("Integer: Min must be no greater than Max");

	Integer equiv = params.GetValueWithDefault("EquivalentTo", Integer::Zero());
	Integer mod = params.GetValueWithDefault("Mod", Integer::One());

	if (equiv.IsNegative() || equiv >= mod)
		throw InvalidArgument("Integer: invalid EquivalentTo and/or Mod argument");

	Integer::RandomNumberType rnType = params.GetValueWithDefault("RandomNumberType", Integer::ANY);

	member_ptr<KDF2_RNG> kdf2Rng;
	ConstByteArrayParameter seed;
	if (params.GetValue("Seed", seed))
	{
		ByteQueue bq;
		DERSequenceEncoder seq(bq);
		min.DEREncode(seq);
		max.DEREncode(seq);
		equiv.DEREncode(seq);
		mod.DEREncode(seq);
		DEREncodeUnsigned(seq, rnType);
		DEREncodeOctetString(seq, seed.begin(), seed.size());
		seq.MessageEnd();

		SecByteBlock finalSeed(bq.MaxRetrievable());
		bq.Get(finalSeed, finalSeed.size());
		kdf2Rng.reset(new KDF2_RNG(finalSeed.begin(), finalSeed.size()));
	}
	RandomNumberGenerator &rng = kdf2Rng.get() ? (RandomNumberGenerator &)*kdf2Rng : i_rng;

	switch (rnType)
	{
		case ANY:
			if (mod == One())
				Randomize(rng, min, max);
			else
			{
				Integer min1 = min + (equiv-min)%mod;
				if (max < min1)
					return false;
				Randomize(rng, Zero(), (max - min1) / mod);
				*this *= mod;
				*this += min1;
			}
			return true;

		case PRIME:
		{
			const PrimeSelector *pSelector = params.GetValueWithDefault(Name::PointerToPrimeSelector(), (const PrimeSelector *)NULL);

			int i;
			i = 0;
			while (1)
			{
				if (++i==16)
				{
					// check if there are any suitable primes in [min, max]
					Integer first = min;
					if (FirstPrime(first, max, equiv, mod, pSelector))
					{
						// if there is only one suitable prime, we're done
						*this = first;
						if (!FirstPrime(first, max, equiv, mod, pSelector))
							return true;
					}
					else
						return false;
				}

				Randomize(rng, min, max);
				if (FirstPrime(*this, STDMIN(*this+mod*PrimeSearchInterval(max), max), equiv, mod, pSelector))
					return true;
			}
		}

		default:
			throw InvalidArgument("Integer: invalid RandomNumberType argument");
	}
}

std::istream& operator>>(std::istream& in, Integer &a)
{
	char c;
	unsigned int length = 0;
	SecBlock<char> str(length + 16);

	std::ws(in);

	do
	{
		in.read(&c, 1);
		str[length++] = c;
		if (length >= str.size())
			str.Grow(length + 16);
	}
	while (in && (c=='-' || c=='x' || (c>='0' && c<='9') || (c>='a' && c<='f') || (c>='A' && c<='F') || c=='h' || c=='H' || c=='o' || c=='O' || c==',' || c=='.'));

	if (in.gcount())
		in.putback(c);
	str[length-1] = '\0';
	a = Integer(str);

	return in;
}

std::ostream& operator<<(std::ostream& out, const Integer &a)
{
	// Get relevant conversion specifications from ostream.
	long f = out.flags() & std::ios::basefield; // Get base digits.
	int base, block;
	char suffix;
	switch(f)
	{
	case std::ios::oct :
		base = 8;
		block = 8;
		suffix = 'o';
		break;
	case std::ios::hex :
		base = 16;
		block = 4;
		suffix = 'h';
		break;
	default :
		base = 10;
		block = 3;
		suffix = '.';
	}

	SecBlock<char> s(a.BitCount() / (BitPrecision(base)-1) + 1);
	Integer temp1=a, temp2;
	unsigned i=0;
	const char vec[]="0123456789ABCDEF";

	if (a.IsNegative())
	{
		out << '-';
		temp1.Negate();
	}

	if (!a)
		out << '0';

	while (!!temp1)
	{
		word digit;
		Integer::Divide(digit, temp2, temp1, base);
		s[i++]=vec[digit];
		temp1=temp2;
	}

	while (i--)
	{
		out << s[i];
//		if (i && !(i%block))
//			out << ",";
	}
	return out << suffix;
}

Integer& Integer::operator++()
{
	if (NotNegative())
	{
		if (Increment(reg, reg.size()))
		{
			reg.CleanGrow(2*reg.size());
			reg[reg.size()/2]=1;
		}
	}
	else
	{
		word borrow = Decrement(reg, reg.size());
		assert(!borrow);
		if (WordCount()==0)
			*this = Zero();
	}
	return *this;
}

Integer& Integer::operator--()
{
	if (IsNegative())
	{
		if (Increment(reg, reg.size()))
		{
			reg.CleanGrow(2*reg.size());
			reg[reg.size()/2]=1;
		}
	}
	else
	{
		if (Decrement(reg, reg.size()))
			*this = -One();
	}
	return *this;
}

void PositiveAdd(Integer &sum, const Integer &a, const Integer& b)
{
	word carry;
	if (a.reg.size() == b.reg.size())
		carry = Add(sum.reg, a.reg, b.reg, a.reg.size());
	else if (a.reg.size() > b.reg.size())
	{
		carry = Add(sum.reg, a.reg, b.reg, b.reg.size());
		CopyWords(sum.reg+b.reg.size(), a.reg+b.reg.size(), a.reg.size()-b.reg.size());
		carry = Increment(sum.reg+b.reg.size(), a.reg.size()-b.reg.size(), carry);
	}
	else
	{
		carry = Add(sum.reg, a.reg, b.reg, a.reg.size());
		CopyWords(sum.reg+a.reg.size(), b.reg+a.reg.size(), b.reg.size()-a.reg.size());
		carry = Increment(sum.reg+a.reg.size(), b.reg.size()-a.reg.size(), carry);
	}

	if (carry)
	{
		sum.reg.CleanGrow(2*sum.reg.size());
		sum.reg[sum.reg.size()/2] = 1;
	}
	sum.sign = Integer::POSITIVE;
}

void PositiveSubtract(Integer &diff, const Integer &a, const Integer& b)
{
	unsigned aSize = a.WordCount();
	aSize += aSize%2;
	unsigned bSize = b.WordCount();
	bSize += bSize%2;

	if (aSize == bSize)
	{
		if (Compare(a.reg, b.reg, aSize) >= 0)
		{
			Subtract(diff.reg, a.reg, b.reg, aSize);
			diff.sign = Integer::POSITIVE;
		}
		else
		{
			Subtract(diff.reg, b.reg, a.reg, aSize);
			diff.sign = Integer::NEGATIVE;
		}
	}
	else if (aSize > bSize)
	{
		word borrow = Subtract(diff.reg, a.reg, b.reg, bSize);
		CopyWords(diff.reg+bSize, a.reg+bSize, aSize-bSize);
		borrow = Decrement(diff.reg+bSize, aSize-bSize, borrow);
		assert(!borrow);
		diff.sign = Integer::POSITIVE;
	}
	else
	{
		word borrow = Subtract(diff.reg, b.reg, a.reg, aSize);
		CopyWords(diff.reg+aSize, b.reg+aSize, bSize-aSize);
		borrow = Decrement(diff.reg+aSize, bSize-aSize, borrow);
		assert(!borrow);
		diff.sign = Integer::NEGATIVE;
	}
}

Integer Integer::Plus(const Integer& b) const
{
	Integer sum((word)0, STDMAX(reg.size(), b.reg.size()));
	if (NotNegative())
	{
		if (b.NotNegative())
			PositiveAdd(sum, *this, b);
		else
			PositiveSubtract(sum, *this, b);
	}
	else
	{
		if (b.NotNegative())
			PositiveSubtract(sum, b, *this);
		else
		{
			PositiveAdd(sum, *this, b);
			sum.sign = Integer::NEGATIVE;
		}
	}
	return sum;
}

Integer& Integer::operator+=(const Integer& t)
{
	reg.CleanGrow(t.reg.size());
	if (NotNegative())
	{
		if (t.NotNegative())
			PositiveAdd(*this, *this, t);
		else
			PositiveSubtract(*this, *this, t);
	}
	else
	{
		if (t.NotNegative())
			PositiveSubtract(*this, t, *this);
		else
		{
			PositiveAdd(*this, *this, t);
			sign = Integer::NEGATIVE;
		}
	}
	return *this;
}

Integer Integer::Minus(const Integer& b) const
{
	Integer diff((word)0, STDMAX(reg.size(), b.reg.size()));
	if (NotNegative())
	{
		if (b.NotNegative())
			PositiveSubtract(diff, *this, b);
		else
			PositiveAdd(diff, *this, b);
	}
	else
	{
		if (b.NotNegative())
		{
			PositiveAdd(diff, *this, b);
			diff.sign = Integer::NEGATIVE;
		}
		else
			PositiveSubtract(diff, b, *this);
	}
	return diff;
}

Integer& Integer::operator-=(const Integer& t)
{
	reg.CleanGrow(t.reg.size());
	if (NotNegative())
	{
		if (t.NotNegative())
			PositiveSubtract(*this, *this, t);
		else
			PositiveAdd(*this, *this, t);
	}
	else
	{
		if (t.NotNegative())
		{
			PositiveAdd(*this, *this, t);
			sign = Integer::NEGATIVE;
		}
		else
			PositiveSubtract(*this, t, *this);
	}
	return *this;
}

Integer& Integer::operator<<=(unsigned int n)
{
	const unsigned int wordCount = WordCount();
	const unsigned int shiftWords = n / WORD_BITS;
	const unsigned int shiftBits = n % WORD_BITS;

	reg.CleanGrow(RoundupSize(wordCount+BitsToWords(n)));
	ShiftWordsLeftByWords(reg, wordCount + shiftWords, shiftWords);
	ShiftWordsLeftByBits(reg+shiftWords, wordCount+BitsToWords(shiftBits), shiftBits);
	return *this;
}

Integer& Integer::operator>>=(unsigned int n)
{
	const unsigned int wordCount = WordCount();
	const unsigned int shiftWords = n / WORD_BITS;
	const unsigned int shiftBits = n % WORD_BITS;

	ShiftWordsRightByWords(reg, wordCount, shiftWords);
	if (wordCount > shiftWords)
		ShiftWordsRightByBits(reg, wordCount-shiftWords, shiftBits);
	if (IsNegative() && WordCount()==0)   // avoid -0
		*this = Zero();
	return *this;
}

void PositiveMultiply(Integer &product, const Integer &a, const Integer &b)
{
	unsigned aSize = RoundupSize(a.WordCount());
	unsigned bSize = RoundupSize(b.WordCount());

	product.reg.CleanNew(RoundupSize(aSize+bSize));
	product.sign = Integer::POSITIVE;

	SecAlignedWordBlock workspace(aSize + bSize);
	AsymmetricMultiply(product.reg, workspace, a.reg, aSize, b.reg, bSize);
}

void Multiply(Integer &product, const Integer &a, const Integer &b)
{
	PositiveMultiply(product, a, b);

	if (a.NotNegative() != b.NotNegative())
		product.Negate();
}

Integer Integer::Times(const Integer &b) const
{
	Integer product;
	Multiply(product, *this, b);
	return product;
}

/*
void PositiveDivide(Integer &remainder, Integer &quotient,
				   const Integer &dividend, const Integer &divisor)
{
	remainder.reg.CleanNew(divisor.reg.size());
	remainder.sign = Integer::POSITIVE;
	quotient.reg.New(0);
	quotient.sign = Integer::POSITIVE;
	unsigned i=dividend.BitCount();
	while (i--)
	{
		word overflow = ShiftWordsLeftByBits(remainder.reg, remainder.reg.size(), 1);
		remainder.reg[0] |= dividend[i];
		if (overflow || remainder >= divisor)
		{
			Subtract(remainder.reg, remainder.reg, divisor.reg, remainder.reg.size());
			quotient.SetBit(i);
		}
	}
}
*/

void PositiveDivide(Integer &remainder, Integer &quotient,
				   const Integer &a, const Integer &b)
{
	unsigned aSize = a.WordCount();
	unsigned bSize = b.WordCount();

	if (!bSize)
		throw Integer::DivideByZero();

	if (a.PositiveCompare(b) == -1)
	{
		remainder = a;
		remainder.sign = Integer::POSITIVE;
		quotient = Integer::Zero();
		return;
	}

	aSize += aSize%2;	// round up to next even number
	bSize += bSize%2;

	remainder.reg.CleanNew(RoundupSize(bSize));
	remainder.sign = Integer::POSITIVE;
	quotient.reg.CleanNew(RoundupSize(aSize-bSize+2));
	quotient.sign = Integer::POSITIVE;

	SecAlignedWordBlock T(aSize+2*bSize+4);
	Divide(remainder.reg, quotient.reg, T, a.reg, aSize, b.reg, bSize);
}

void Integer::Divide(Integer &remainder, Integer &quotient, const Integer &dividend, const Integer &divisor)
{
	PositiveDivide(remainder, quotient, dividend, divisor);

	if (dividend.IsNegative())
	{
		quotient.Negate();
		if (remainder.NotZero())
		{
			--quotient;
			remainder = divisor.AbsoluteValue() - remainder;
		}
	}

	if (divisor.IsNegative())
		quotient.Negate();
}

void Integer::DivideByPowerOf2(Integer &r, Integer &q, const Integer &a, unsigned int n)
{
	q = a;
	q >>= n;

	const unsigned int wordCount = BitsToWords(n);
	if (wordCount <= a.WordCount())
	{
		r.reg.resize(RoundupSize(wordCount));
		CopyWords(r.reg, a.reg, wordCount);
		SetWords(r.reg+wordCount, 0, r.reg.size()-wordCount);
		if (n % WORD_BITS != 0)
			r.reg[wordCount-1] %= (1 << (n % WORD_BITS));
	}
	else
	{
		r.reg.resize(RoundupSize(a.WordCount()));
		CopyWords(r.reg, a.reg, r.reg.size());
	}
	r.sign = POSITIVE;

	if (a.IsNegative() && r.NotZero())
	{
		--q;
		r = Power2(n) - r;
	}
}

Integer Integer::DividedBy(const Integer &b) const
{
	Integer remainder, quotient;
	Integer::Divide(remainder, quotient, *this, b);
	return quotient;
}

Integer Integer::Modulo(const Integer &b) const
{
	Integer remainder, quotient;
	Integer::Divide(remainder, quotient, *this, b);
	return remainder;
}

void Integer::Divide(word &remainder, Integer &quotient, const Integer &dividend, word divisor)
{
	if (!divisor)
		throw Integer::DivideByZero();

	assert(divisor);

	if ((divisor & (divisor-1)) == 0)	// divisor is a power of 2
	{
		quotient = dividend >> (BitPrecision(divisor)-1);
		remainder = dividend.reg[0] & (divisor-1);
		return;
	}

	unsigned int i = dividend.WordCount();
	quotient.reg.CleanNew(RoundupSize(i));
	remainder = 0;
	while (i--)
	{
		quotient.reg[i] = DWord(dividend.reg[i], remainder) / divisor;
		remainder = DWord(dividend.reg[i], remainder) % divisor;
	}

	if (dividend.NotNegative())
		quotient.sign = POSITIVE;
	else
	{
		quotient.sign = NEGATIVE;
		if (remainder)
		{
			--quotient;
			remainder = divisor - remainder;
		}
	}
}

Integer Integer::DividedBy(word b) const
{
	word remainder;
	Integer quotient;
	Integer::Divide(remainder, quotient, *this, b);
	return quotient;
}

word Integer::Modulo(word divisor) const
{
	if (!divisor)
		throw Integer::DivideByZero();

	assert(divisor);

	word remainder;

	if ((divisor & (divisor-1)) == 0)	// divisor is a power of 2
		remainder = reg[0] & (divisor-1);
	else
	{
		unsigned int i = WordCount();

		if (divisor <= 5)
		{
			DWord sum(0, 0);
			while (i--)
				sum += reg[i];
			remainder = sum % divisor;
		}
		else
		{
			remainder = 0;
			while (i--)
				remainder = DWord(reg[i], remainder) % divisor;
		}
	}

	if (IsNegative() && remainder)
		remainder = divisor - remainder;

	return remainder;
}

void Integer::Negate()
{
	if (!!(*this))	// don't flip sign if *this==0
		sign = Sign(1-sign);
}

int Integer::PositiveCompare(const Integer& t) const
{
	unsigned size = WordCount(), tSize = t.WordCount();

	if (size == tSize)
		return CryptoPP::Compare(reg, t.reg, size);
	else
		return size > tSize ? 1 : -1;
}

int Integer::Compare(const Integer& t) const
{
	if (NotNegative())
	{
		if (t.NotNegative())
			return PositiveCompare(t);
		else
			return 1;
	}
	else
	{
		if (t.NotNegative())
			return -1;
		else
			return -PositiveCompare(t);
	}
}

Integer Integer::SquareRoot() const
{
	if (!IsPositive())
		return Zero();

	// overestimate square root
	Integer x, y = Power2((BitCount()+1)/2);
	assert(y*y >= *this);

	do
	{
		x = y;
		y = (x + *this/x) >> 1;
	} while (y<x);

	return x;
}

bool Integer::IsSquare() const
{
	Integer r = SquareRoot();
	return *this == r.Squared();
}

bool Integer::IsUnit() const
{
	return (WordCount() == 1) && (reg[0] == 1);
}

Integer Integer::MultiplicativeInverse() const
{
	return IsUnit() ? *this : Zero();
}

Integer a_times_b_mod_c(const Integer &x, const Integer& y, const Integer& m)
{
	return x*y%m;
}

Integer a_exp_b_mod_c(const Integer &x, const Integer& e, const Integer& m)
{
	ModularArithmetic mr(m);
	return mr.Exponentiate(x, e);
}

Integer Integer::Gcd(const Integer &a, const Integer &b)
{
	return EuclideanDomainOf<Integer>().Gcd(a, b);
}

Integer Integer::InverseMod(const Integer &m) const
{
	assert(m.NotNegative());

	if (IsNegative() || *this>=m)
		return (*this%m).InverseMod(m);

	if (m.IsEven())
	{
		if (!m || IsEven())
			return Zero();	// no inverse
		if (*this == One())
			return One();

		Integer u = m.InverseMod(*this);
		return !u ? Zero() : (m*(*this-u)+1)/(*this);
	}

	SecBlock<word> T(m.reg.size() * 4);
	Integer r((word)0, m.reg.size());
	unsigned k = AlmostInverse(r.reg, T, reg, reg.size(), m.reg, m.reg.size());
	DivideByPower2Mod(r.reg, r.reg, k, m.reg, m.reg.size());
	return r;
}

word Integer::InverseMod(const word mod) const
{
	word g0 = mod, g1 = *this % mod;
	word v0 = 0, v1 = 1;
	word y;

	while (g1)
	{
		if (g1 == 1)
			return v1;
		y = g0 / g1;
		g0 = g0 % g1;
		v0 += y * v1;

		if (!g0)
			break;
		if (g0 == 1)
			return mod-v0;
		y = g1 / g0;
		g1 = g1 % g0;
		v1 += y * v0;
	}
	return 0;
}

// ********************************************************

ModularArithmetic::ModularArithmetic(BufferedTransformation &bt)
{
	BERSequenceDecoder seq(bt);
	OID oid(seq);
	if (oid != ASN1::prime_field())
		BERDecodeError();
	modulus.BERDecode(seq);
	seq.MessageEnd();
	result.reg.resize(modulus.reg.size());
}

void ModularArithmetic::DEREncode(BufferedTransformation &bt) const
{
	DERSequenceEncoder seq(bt);
	ASN1::prime_field().DEREncode(seq);
	modulus.DEREncode(seq);
	seq.MessageEnd();
}

void ModularArithmetic::DEREncodeElement(BufferedTransformation &out, const Element &a) const
{
	a.DEREncodeAsOctetString(out, MaxElementByteLength());
}

void ModularArithmetic::BERDecodeElement(BufferedTransformation &in, Element &a) const
{
	a.BERDecodeAsOctetString(in, MaxElementByteLength());
}

const Integer& ModularArithmetic::Half(const Integer &a) const
{
	if (a.reg.size()==modulus.reg.size())
	{
		CryptoPP::DivideByPower2Mod(result.reg.begin(), a.reg, 1, modulus.reg, a.reg.size());
		return result;
	}
	else
		return result1 = (a.IsEven() ? (a >> 1) : ((a+modulus) >> 1));
}

const Integer& ModularArithmetic::Add(const Integer &a, const Integer &b) const
{
	if (a.reg.size()==modulus.reg.size() && b.reg.size()==modulus.reg.size())
	{
		if (CryptoPP::Add(result.reg.begin(), a.reg, b.reg, a.reg.size())
			|| Compare(result.reg, modulus.reg, a.reg.size()) >= 0)
		{
			CryptoPP::Subtract(result.reg.begin(), result.reg, modulus.reg, a.reg.size());
		}
		return result;
	}
	else
	{
		result1 = a+b;
		if (result1 >= modulus)
			result1 -= modulus;
		return result1;
	}
}

Integer& ModularArithmetic::Accumulate(Integer &a, const Integer &b) const
{
	if (a.reg.size()==modulus.reg.size() && b.reg.size()==modulus.reg.size())
	{
		if (CryptoPP::Add(a.reg, a.reg, b.reg, a.reg.size())
			|| Compare(a.reg, modulus.reg, a.reg.size()) >= 0)
		{
			CryptoPP::Subtract(a.reg, a.reg, modulus.reg, a.reg.size());
		}
	}
	else
	{
		a+=b;
		if (a>=modulus)
			a-=modulus;
	}

	return a;
}

const Integer& ModularArithmetic::Subtract(const Integer &a, const Integer &b) const
{
	if (a.reg.size()==modulus.reg.size() && b.reg.size()==modulus.reg.size())
	{
		if (CryptoPP::Subtract(result.reg.begin(), a.reg, b.reg, a.reg.size()))
			CryptoPP::Add(result.reg.begin(), result.reg, modulus.reg, a.reg.size());
		return result;
	}
	else
	{
		result1 = a-b;
		if (result1.IsNegative())
			result1 += modulus;
		return result1;
	}
}

Integer& ModularArithmetic::Reduce(Integer &a, const Integer &b) const
{
	if (a.reg.size()==modulus.reg.size() && b.reg.size()==modulus.reg.size())
	{
		if (CryptoPP::Subtract(a.reg, a.reg, b.reg, a.reg.size()))
			CryptoPP::Add(a.reg, a.reg, modulus.reg, a.reg.size());
	}
	else
	{
		a-=b;
		if (a.IsNegative())
			a+=modulus;
	}

	return a;
}

const Integer& ModularArithmetic::Inverse(const Integer &a) const
{
	if (!a)
		return a;

	CopyWords(result.reg.begin(), modulus.reg, modulus.reg.size());
	if (CryptoPP::Subtract(result.reg.begin(), result.reg, a.reg, a.reg.size()))
		Decrement(result.reg.begin()+a.reg.size(), 1, modulus.reg.size()-a.reg.size());

	return result;
}

Integer ModularArithmetic::CascadeExponentiate(const Integer &x, const Integer &e1, const Integer &y, const Integer &e2) const
{
	if (modulus.IsOdd())
	{
		MontgomeryRepresentation dr(modulus);
		return dr.ConvertOut(dr.CascadeExponentiate(dr.ConvertIn(x), e1, dr.ConvertIn(y), e2));
	}
	else
		return AbstractRing<Integer>::CascadeExponentiate(x, e1, y, e2);
}

void ModularArithmetic::SimultaneousExponentiate(Integer *results, const Integer &base, const Integer *exponents, unsigned int exponentsCount) const
{
	if (modulus.IsOdd())
	{
		MontgomeryRepresentation dr(modulus);
		dr.SimultaneousExponentiate(results, dr.ConvertIn(base), exponents, exponentsCount);
		for (unsigned int i=0; i<exponentsCount; i++)
			results[i] = dr.ConvertOut(results[i]);
	}
	else
		AbstractRing<Integer>::SimultaneousExponentiate(results, base, exponents, exponentsCount);
}

MontgomeryRepresentation::MontgomeryRepresentation(const Integer &m)	// modulus must be odd
	: ModularArithmetic(m),
	  u((word)0, modulus.reg.size()),
	  workspace(5*modulus.reg.size())
{
	if (!modulus.IsOdd())
		throw InvalidArgument("MontgomeryRepresentation: Montgomery representation requires an odd modulus");

	RecursiveInverseModPower2(u.reg, workspace, modulus.reg, modulus.reg.size());
}

const Integer& MontgomeryRepresentation::Multiply(const Integer &a, const Integer &b) const
{
	word *const T = workspace.begin();
	word *const R = result.reg.begin();
	const unsigned int N = modulus.reg.size();
	assert(a.reg.size()<=N && b.reg.size()<=N);

	AsymmetricMultiply(T, T+2*N, a.reg, a.reg.size(), b.reg, b.reg.size());
	SetWords(T+a.reg.size()+b.reg.size(), 0, 2*N-a.reg.size()-b.reg.size());
	MontgomeryReduce(R, T+2*N, T, modulus.reg, u.reg, N);
	return result;
}

const Integer& MontgomeryRepresentation::Square(const Integer &a) const
{
	word *const T = workspace.begin();
	word *const R = result.reg.begin();
	const unsigned int N = modulus.reg.size();
	assert(a.reg.size()<=N);

	CryptoPP::Square(T, T+2*N, a.reg, a.reg.size());
	SetWords(T+2*a.reg.size(), 0, 2*N-2*a.reg.size());
	MontgomeryReduce(R, T+2*N, T, modulus.reg, u.reg, N);
	return result;
}

Integer MontgomeryRepresentation::ConvertOut(const Integer &a) const
{
	word *const T = workspace.begin();
	word *const R = result.reg.begin();
	const unsigned int N = modulus.reg.size();
	assert(a.reg.size()<=N);

	CopyWords(T, a.reg, a.reg.size());
	SetWords(T+a.reg.size(), 0, 2*N-a.reg.size());
	MontgomeryReduce(R, T+2*N, T, modulus.reg, u.reg, N);
	return result;
}

const Integer& MontgomeryRepresentation::MultiplicativeInverse(const Integer &a) const
{
//	  return (EuclideanMultiplicativeInverse(a, modulus)<<(2*WORD_BITS*modulus.reg.size()))%modulus;
	word *const T = workspace.begin();
	word *const R = result.reg.begin();
	const unsigned int N = modulus.reg.size();
	assert(a.reg.size()<=N);

	CopyWords(T, a.reg, a.reg.size());
	SetWords(T+a.reg.size(), 0, 2*N-a.reg.size());
	MontgomeryReduce(R, T+2*N, T, modulus.reg, u.reg, N);
	unsigned k = AlmostInverse(R, T, R, N, modulus.reg, N);

//	cout << "k=" << k << " N*32=" << 32*N << endl;

	if (k>N*WORD_BITS)
		DivideByPower2Mod(R, R, k-N*WORD_BITS, modulus.reg, N);
	else
		MultiplyByPower2Mod(R, R, N*WORD_BITS-k, modulus.reg, N);

	return result;
}

NAMESPACE_END

#endif