integer.cpp

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

// Notes by JW: The Integer class needs to do two things. First, it needs
//  to set function pointers on some platforms, like X86 and X64. The
//  function pointers select a fast multiply and addition based on the cpu.
//  Second, it wants to create Integer::Zero(), Integer::One() and
//  Integer::Two().
// The function pointers are initialized in the InitializeInteger class by
//  calling SetFunctionPointers(). The call to SetFunctionPointers() is
//  guarded to run once using a double-checked pattern. We don't use C++
//  std::call_once due to bad interactions between libstdc++, glibc and
//  pthreads. The bad interactions were causing crashes for us on platforms
//  like Sparc and PowerPC. Since we are only setting function pointers we
//  don't have to worry about leaking memory. The worst case seems to be the
//  pointers gets written twice until the init flag is set and visible to
//  all threads.
// For Integer::Zero(), Integer::One() and Integer::Two(), we use one of three
//  strategies. First, if initialization priorities are available then we use
//  them. Initialization priorities are init_priority() on Linux and init_seg()
//  on Windows. AIX, OS X and several other platforms lack them. Initialization
//  priorities are platform specific but they are also the most trouble free
//  with determisitic destruction.
// Second, if C++11 dynamic initialization is available, then we use it. After
//  the std::call_once fiasco we dropped the priority dynamic initialization
//  to avoid unknown troubles platforms that are tested less frequently. In
//  addition Microsoft platforms mostly do not provide dynamic initialization.
//  The MSDN docs claim they do but they don't in practice because we need
//  Visual Studio 2017 and Windows 10 or above.
// Third, we fall back to Wei's original code of a Singleton. Wei's original
//  code was much simpler. It simply used the Singleton pattern, but it always
//  produced memory findings on some platforms. The Singleton generates memory
//  findings because it uses a Create On First Use pattern (a dumb Nifty
//  Counter) and the compiler had to be smart enough to fold them to return
//  the same object. Unix and Linux compilers do a good job of folding objects,
//  but Microsoft compilers do a rather poor job for some versions of the
//  compiler.
// Another problem with the Singleton is resource destruction requires running
//  resource acquisition in reverse. For resources provided through the
//  Singletons, there is no way to express the dependency order to safely
//  destroy resources. (That's one of the problems C++11 dynamic
//  intitialization with concurrent execution is supposed to solve).
// The final problem with Singletons is resource/memory exhaustion in languages
//  like Java and .Net. Java and .Net load and unload a native DLL hundreds or
//  thousands of times during the life of a program. Each load produces a
//  memory leak and they can add up quickly. If they library is being used in
//  Java or .Net then Singleton must be avoided at all costs.

#include "pch.h"
#include "config.h"

#ifndef CRYPTOPP_IMPORTS

#include "integer.h"
#include "secblock.h"
#include "modarith.h"
#include "nbtheory.h"
#include "smartptr.h"
#include "algparam.h"
#include "filters.h"
#include "stdcpp.h"
#include "asn.h"
#include "oids.h"
#include "words.h"
#include "pubkey.h"     // for P1363_KDF2
#include "sha.h"
#include "cpu.h"
#include "misc.h"

#include <iostream>

#if (_MSC_VER >= 1400) && !defined(_M_ARM)
    #include <intrin.h>
#endif

#ifdef __DECCXX
    #include <c_asm.h>
#endif

// "Error: The operand ___LKDB cannot be assigned to", http://github.com/weidai11/cryptopp/issues/188
#if (__SUNPRO_CC >= 0x5130)
# define MAYBE_CONST
# define MAYBE_UNCONST_CAST(x) const_cast<word*>(x)
#else
# define MAYBE_CONST const
# define MAYBE_UNCONST_CAST(x) x
#endif

// "Inline assembly operands don't work with .intel_syntax",
//   http://llvm.org/bugs/show_bug.cgi?id=24232
#if CRYPTOPP_BOOL_X32 || defined(CRYPTOPP_DISABLE_MIXED_ASM)
# undef CRYPTOPP_X86_ASM_AVAILABLE
# undef CRYPTOPP_X32_ASM_AVAILABLE
# undef CRYPTOPP_X64_ASM_AVAILABLE
# undef CRYPTOPP_SSE2_ASM_AVAILABLE
# undef CRYPTOPP_SSSE3_ASM_AVAILABLE
#else
# define CRYPTOPP_INTEGER_SSE2 (CRYPTOPP_SSE2_ASM_AVAILABLE && (CRYPTOPP_BOOL_X86))
#endif

// ***************** C++ Static Initialization ********************

NAMESPACE_BEGIN(CryptoPP)

// Function body near the middle of the file
static void SetFunctionPointers();

// Use a double-checked pattern. We are not leaking anything so it
// does not matter if a pointer is written twice during a race.
// Avoid std::call_once due to too many problems on platforms like
// Solaris and Sparc. Also see
// http://gcc.gnu.org/bugzilla/show_bug.cgi?id=66146 and
// http://github.com/weidai11/cryptopp/issues/707.
InitializeInteger::InitializeInteger()
{
    static bool s_flag;
    MEMORY_BARRIER();
    if (s_flag == false)
    {
        SetFunctionPointers();
        s_flag = true;
        MEMORY_BARRIER();
    }
}

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

// ***************** Library code ********************

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

    return 0;
}

inline static int Increment(word *A, size_t N, word B=1)
{
    CRYPTOPP_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;
}

inline static int Decrement(word *A, size_t N, word B=1)
{
    CRYPTOPP_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, size_t N)
{
    Decrement(A, N);
    for (unsigned i=0; i<N; i++)
        A[i] = ~A[i];
}

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

    word R=A%8;

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

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

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

#if !defined(CRYPTOPP_NATIVE_DWORD_AVAILABLE) || (defined(__x86_64__) && defined(CRYPTOPP_WORD128_AVAILABLE))
    #define TWO_64_BIT_WORDS 1
    #define Declare2Words(x)            word x##0, x##1;
    #define AssignWord(a, b)            a##0 = b; a##1 = 0;
    #define Add2WordsBy1(a, b, c)       a##0 = b##0 + c; a##1 = b##1 + (a##0 < c);
    #define LowWord(a)                  a##0
    #define HighWord(a)                 a##1
    #ifdef _MSC_VER
        #define MultiplyWordsLoHi(p0, p1, a, b)     p0 = _umul128(a, b, &p1);
        #ifndef __INTEL_COMPILER
            #define Double3Words(c, d)      d##1 = __shiftleft128(d##0, d##1, 1); d##0 = __shiftleft128(c, d##0, 1); c *= 2;
        #endif
    #elif defined(__DECCXX)
        #define MultiplyWordsLoHi(p0, p1, a, b)     p0 = a*b; p1 = asm("umulh %a0, %a1, %v0", a, b);
    #elif defined(__x86_64__)
        #if defined(__SUNPRO_CC) && __SUNPRO_CC < 0x5100
            // Sun Studio's gcc-style inline assembly is heavily bugged as of version 5.9 Patch 124864-09 2008/12/16, but this one works
            #define MultiplyWordsLoHi(p0, p1, a, b)     asm ("mulq %3" : "=a"(p0), "=d"(p1) : "a"(a), "r"(b) : "cc");
        #else
            #define MultiplyWordsLoHi(p0, p1, a, b)     asm ("mulq %3" : "=a"(p0), "=d"(p1) : "a"(a), "g"(b) : "cc");
            #define MulAcc(c, d, a, b)      asm ("mulq %6; addq %3, %0; adcq %4, %1; adcq $0, %2;" : "+r"(c), "+r"(d##0), "+r"(d##1), "=a"(p0), "=d"(p1) : "a"(a), "g"(b) : "cc");
            #define Double3Words(c, d)      asm ("addq %0, %0; adcq %1, %1; adcq %2, %2;" : "+r"(c), "+r"(d##0), "+r"(d##1) : : "cc");
            #define Acc2WordsBy1(a, b)      asm ("addq %2, %0; adcq $0, %1;" : "+r"(a##0), "+r"(a##1) : "r"(b) : "cc");
            #define Acc2WordsBy2(a, b)      asm ("addq %2, %0; adcq %3, %1;" : "+r"(a##0), "+r"(a##1) : "r"(b##0), "r"(b##1) : "cc");
            #define Acc3WordsBy2(c, d, e)   asm ("addq %5, %0; adcq %6, %1; adcq $0, %2;" : "+r"(c), "=r"(e##0), "=r"(e##1) : "1"(d##0), "2"(d##1), "r"(e##0), "r"(e##1) : "cc");
        #endif
    #endif
    #define MultiplyWords(p, a, b)      MultiplyWordsLoHi(p##0, p##1, a, b)
    #ifndef Double3Words
        #define Double3Words(c, d)      d##1 = 2*d##1 + (d##0>>(WORD_BITS-1)); d##0 = 2*d##0 + (c>>(WORD_BITS-1)); c *= 2;
    #endif
    #ifndef Acc2WordsBy2
        #define Acc2WordsBy2(a, b)      a##0 += b##0; a##1 += a##0 < b##0; a##1 += b##1;
    #endif
    #define AddWithCarry(u, a, b)       {word t = a+b; u##0 = t + u##1; u##1 = (t<a) + (u##0<t);}
    #define SubtractWithBorrow(u, a, b) {word t = a-b; u##0 = t - u##1; u##1 = (t>a) + (u##0>t);}
    #define GetCarry(u)                 u##1
    #define GetBorrow(u)                u##1
#else
    #define Declare2Words(x)            dword x;
    #if _MSC_VER >= 1400 && !defined(__INTEL_COMPILER) && !defined(_M_ARM)
        #define MultiplyWords(p, a, b)      p = __emulu(a, b);
    #else
        #define MultiplyWords(p, a, b)      p = (dword)a*b;
    #endif
    #define AssignWord(a, b)            a = b;
    #define Add2WordsBy1(a, b, c)       a = b + c;
    #define Acc2WordsBy2(a, b)          a += b;
    #define LowWord(a)                  word(a)
    #define HighWord(a)                 word(a>>WORD_BITS)
    #define Double3Words(c, d)          d = 2*d + (c>>(WORD_BITS-1)); c *= 2;
    #define AddWithCarry(u, a, b)       u = dword(a) + b + GetCarry(u);
    #define SubtractWithBorrow(u, a, b) u = dword(a) - b - GetBorrow(u);
    #define GetCarry(u)                 HighWord(u)
    #define GetBorrow(u)                word(u>>(WORD_BITS*2-1))
#endif
#ifndef MulAcc
    #define MulAcc(c, d, a, b)          MultiplyWords(p, a, b); Acc2WordsBy1(p, c); c = LowWord(p); Acc2WordsBy1(d, HighWord(p));
#endif
#ifndef Acc2WordsBy1
    #define Acc2WordsBy1(a, b)          Add2WordsBy1(a, a, b)
#endif
#ifndef Acc3WordsBy2
    #define Acc3WordsBy2(c, d, e)       Acc2WordsBy1(e, c); c = LowWord(e); Add2WordsBy1(e, d, HighWord(e));
#endif

class DWord
{
public:
#if defined(CRYPTOPP_NATIVE_DWORD_AVAILABLE)
    DWord() {std::memset(&m_whole, 0x00, sizeof(m_whole));}
#else
    DWord() {std::memset(&m_halfs, 0x00, sizeof(m_halfs));}
#endif

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

#if defined(CRYPTOPP_NATIVE_DWORD_AVAILABLE)
    DWord(word low, word high) : m_whole()
#else
    DWord(word low, word high) : m_halfs()
#endif
    {
#if defined(CRYPTOPP_NATIVE_DWORD_AVAILABLE)
#  if (CRYPTOPP_LITTLE_ENDIAN)
        const word t[2] = {low,high};
        memcpy(&m_whole, t, sizeof(m_whole));
#  else
        const word t[2] = {high,low};
        memcpy(&m_whole, t, sizeof(m_whole));
#  endif
#else
        m_halfs.low = low;
        m_halfs.high = high;
#endif
    }

    static DWord Multiply(word a, word b)
    {
        DWord r;
        #ifdef CRYPTOPP_NATIVE_DWORD_AVAILABLE
            r.m_whole = (dword)a * b;
        #elif defined(MultiplyWordsLoHi)
            MultiplyWordsLoHi(r.m_halfs.low, r.m_halfs.high, a, b);
        #else
            CRYPTOPP_ASSERT(0);
        #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
    }

    // TODO: When NATIVE_DWORD is in effect, we access high and low, which are inactive
    //  union members, and that's UB. Also see http://stackoverflow.com/q/11373203.
    word GetLowHalf() const {return m_halfs.low;}
    word GetHighHalf() const {return m_halfs.high;}
    word GetHighHalfAsBorrow() const {return 0-m_halfs.high;}

private:
    // Issue 274, "Types cannot be declared in anonymous union",
    //   http://github.com/weidai11/cryptopp/issues/274
    //   Thanks to Martin Bonner at http://stackoverflow.com/a/39507183
    struct half_words
    {
    #if (CRYPTOPP_LITTLE_ENDIAN)
        word low;
        word high;
    #else
        word high;
        word low;
    #endif
   };
   union
   {
   #ifdef CRYPTOPP_NATIVE_DWORD_AVAILABLE
       dword m_whole;
   #endif
       half_words m_halfs;
   };
};

class Word
{
public:
    Word() : m_whole(0) {}
    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=NULLPTR)
{
    CRYPTOPP_UNUSED(dummy);

    // Assert {A[2],A[1]} < {B1,B0}, so quotient can fit in a S
    CRYPTOPP_ASSERT(A[2] < B1 || (A[2]==B1 && A[1] < B0));

    // estimate the quotient: do a 2 S by 1 S divide.
    // Profiling tells us the original second case was dominant, so it was promoted to the first If statement.
    // The code change occurred at Commit dc99266599a0e72d.

    S Q; bool pre = (S(B1+1) == 0);
    if (B1 > 0 && !pre)
        Q = D(A[1], A[2]) / S(B1+1);
    else if (pre)
        Q = A[2];
    else
        Q = D(A[0], A[1]) / B0;

    // 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++;
        CRYPTOPP_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)
{
    // Profiling tells us the original second case was dominant, so it was promoted to the first If statement.
    // The code change occurred at Commit dc99266599a0e72d.

    if (!!B)
    {
        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]);
    }
    else  // if divisor is 0, we assume divisor==2**(2*WORD_BITS)
    {
        return D(Ah.GetLowHalf(), Ah.GetHighHalf());
    }
}

// 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
}

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

// Use some tricks to share assembly code between MSVC, GCC, Clang and Sun CC.
#if defined(__GNUC__)
    #define AddPrologue \
        int result; \
        __asm__ __volatile__ \
        ( \
            INTEL_NOPREFIX
    #define AddEpilogue \
            ATT_PREFIX \
                    : "=a" (result)\
                    : "d" (C), "a" (A), "D" (B), "c" (N) \
                    : "%esi", "memory", "cc" \
        );\
        return result;
    #define MulPrologue \
        __asm__ __volatile__ \
        ( \
            INTEL_NOPREFIX \
            AS1(    push    ebx) \
            AS2(    mov     ebx, edx)
    #define MulEpilogue \
            AS1(    pop     ebx) \
            ATT_PREFIX \
            : \
            : "d" (s_maskLow16), "c" (C), "a" (A), "D" (B) \
            : "%esi", "memory", "cc" \
        );
    #define SquPrologue     MulPrologue
    #define SquEpilogue \
            AS1(    pop     ebx) \
            ATT_PREFIX \
            : \
            : "d" (s_maskLow16), "c" (C), "a" (A) \
            : "%esi", "%edi", "memory", "cc" \
        );
    #define TopPrologue     MulPrologue
    #define TopEpilogue \
            AS1(    pop     ebx) \
            ATT_PREFIX \
            : \
            : "d" (s_maskLow16), "c" (C), "a" (A), "D" (B), "S" (L) \
            : "memory", "cc" \
        );
#else
    #define AddPrologue \
        __asm   push edi \
        __asm   push esi \
        __asm   mov     eax, [esp+12] \
        __asm   mov     edi, [esp+16]
    #define AddEpilogue \
        __asm   pop esi \
        __asm   pop edi \
        __asm   ret 8
    #define SaveEBX
    #define RestoreEBX
    #define SquPrologue                 \
        AS2(    mov     eax, A)         \
        AS2(    mov     ecx, C)         \
        SaveEBX                         \
        AS2(    lea     ebx, s_maskLow16)
    #define MulPrologue                 \
        AS2(    mov     eax, A)         \
        AS2(    mov     edi, B)         \
        AS2(    mov     ecx, C)         \
        SaveEBX                         \
        AS2(    lea     ebx, s_maskLow16)
    #define TopPrologue                 \
        AS2(    mov     eax, A)         \
        AS2(    mov     edi, B)         \
        AS2(    mov     ecx, C)         \
        AS2(    mov     esi, L)         \
        SaveEBX                         \
        AS2(    lea     ebx, s_maskLow16)
    #define SquEpilogue     RestoreEBX
    #define MulEpilogue     RestoreEBX
    #define TopEpilogue     RestoreEBX
#endif

#ifdef CRYPTOPP_X64_MASM_AVAILABLE
extern "C" {
int Baseline_Add(size_t N, word *C, const word *A, const word *B);
int Baseline_Sub(size_t N, word *C, const word *A, const word *B);
}
#elif defined(CRYPTOPP_X64_ASM_AVAILABLE) && defined(__GNUC__) && defined(CRYPTOPP_WORD128_AVAILABLE)
int Baseline_Add(size_t N, word *C, const word *A, const word *B)
{
    word result;
    __asm__ __volatile__
    (
    INTEL_NOPREFIX
    AS1(    neg     %1)
    ASJ(    jz,     1, f)
    AS2(    mov     %0,[%3+8*%1])
    AS2(    add     %0,[%4+8*%1])
    AS2(    mov     [%2+8*%1],%0)
    ASL(0)
    AS2(    mov     %0,[%3+8*%1+8])
    AS2(    adc     %0,[%4+8*%1+8])
    AS2(    mov     [%2+8*%1+8],%0)
    AS2(    lea     %1,[%1+2])
    ASJ(    jrcxz,  1, f)
    AS2(    mov     %0,[%3+8*%1])
    AS2(    adc     %0,[%4+8*%1])
    AS2(    mov     [%2+8*%1],%0)
    ASJ(    jmp,    0, b)
    ASL(1)
    AS2(    mov     %0, 0)
    AS2(    adc     %0, %0)
    ATT_NOPREFIX
    : "=&r" (result), "+c" (N)
    : "r" (C+N), "r" (A+N), "r" (B+N)
    : "memory", "cc"
    );
    return (int)result;
}

int Baseline_Sub(size_t N, word *C, const word *A, const word *B)
{
    word result;
    __asm__ __volatile__
    (
    INTEL_NOPREFIX
    AS1(    neg     %1)
    ASJ(    jz,     1, f)
    AS2(    mov     %0,[%3+8*%1])
    AS2(    sub     %0,[%4+8*%1])
    AS2(    mov     [%2+8*%1],%0)
    ASL(0)
    AS2(    mov     %0,[%3+8*%1+8])
    AS2(    sbb     %0,[%4+8*%1+8])
    AS2(    mov     [%2+8*%1+8],%0)
    AS2(    lea     %1,[%1+2])
    ASJ(    jrcxz,  1, f)
    AS2(    mov     %0,[%3+8*%1])
    AS2(    sbb     %0,[%4+8*%1])
    AS2(    mov     [%2+8*%1],%0)
    ASJ(    jmp,    0, b)
    ASL(1)
    AS2(    mov     %0, 0)
    AS2(    adc     %0, %0)
    ATT_NOPREFIX
    : "=&r" (result), "+c" (N)
    : "r" (C+N), "r" (A+N), "r" (B+N)
    : "memory", "cc"
    );
    return (int)result;
}
#elif defined(CRYPTOPP_X86_ASM_AVAILABLE) && CRYPTOPP_BOOL_X86
CRYPTOPP_NAKED int CRYPTOPP_FASTCALL Baseline_Add(size_t N, word *C, const word *A, const word *B)
{
    AddPrologue

    // now: eax = A, edi = B, edx = C, ecx = N
    AS2(    lea     eax, [eax+4*ecx])
    AS2(    lea     edi, [edi+4*ecx])
    AS2(    lea     edx, [edx+4*ecx])

    AS1(    neg     ecx)                // ecx is negative index
    AS2(    test    ecx, 2)             // this clears carry flag
    ASJ(    jz,     0, f)
    AS2(    sub     ecx, 2)
    ASJ(    jmp,    1, f)

    ASL(0)
    ASJ(    jecxz,  2, f)               // loop until ecx overflows and becomes zero
    AS2(    mov     esi,[eax+4*ecx])
    AS2(    adc     esi,[edi+4*ecx])
    AS2(    mov     [edx+4*ecx],esi)
    AS2(    mov     esi,[eax+4*ecx+4])
    AS2(    adc     esi,[edi+4*ecx+4])
    AS2(    mov     [edx+4*ecx+4],esi)
    ASL(1)
    AS2(    mov     esi,[eax+4*ecx+8])
    AS2(    adc     esi,[edi+4*ecx+8])
    AS2(    mov     [edx+4*ecx+8],esi)
    AS2(    mov     esi,[eax+4*ecx+12])
    AS2(    adc     esi,[edi+4*ecx+12])
    AS2(    mov     [edx+4*ecx+12],esi)

    AS2(    lea     ecx,[ecx+4])        // advance index, avoid inc which causes slowdown on Intel Core 2
    ASJ(    jmp,    0, b)

    ASL(2)
    AS2(    mov     eax, 0)
    AS1(    setc    al)                 // store carry into eax (return result register)

    AddEpilogue

    // http://github.com/weidai11/cryptopp/issues/340
    CRYPTOPP_UNUSED(A); CRYPTOPP_UNUSED(B);
    CRYPTOPP_UNUSED(C); CRYPTOPP_UNUSED(N);
}

CRYPTOPP_NAKED int CRYPTOPP_FASTCALL Baseline_Sub(size_t N, word *C, const word *A, const word *B)
{
    AddPrologue

    // now: eax = A, edi = B, edx = C, ecx = N
    AS2(    lea     eax, [eax+4*ecx])
    AS2(    lea     edi, [edi+4*ecx])
    AS2(    lea     edx, [edx+4*ecx])

    AS1(    neg     ecx)                // ecx is negative index
    AS2(    test    ecx, 2)             // this clears carry flag
    ASJ(    jz,     0, f)
    AS2(    sub     ecx, 2)
    ASJ(    jmp,    1, f)

    ASL(0)
    ASJ(    jecxz,  2, f)               // loop until ecx overflows and becomes zero
    AS2(    mov     esi,[eax+4*ecx])
    AS2(    sbb     esi,[edi+4*ecx])
    AS2(    mov     [edx+4*ecx],esi)
    AS2(    mov     esi,[eax+4*ecx+4])
    AS2(    sbb     esi,[edi+4*ecx+4])
    AS2(    mov     [edx+4*ecx+4],esi)
    ASL(1)
    AS2(    mov     esi,[eax+4*ecx+8])
    AS2(    sbb     esi,[edi+4*ecx+8])
    AS2(    mov     [edx+4*ecx+8],esi)
    AS2(    mov     esi,[eax+4*ecx+12])
    AS2(    sbb     esi,[edi+4*ecx+12])
    AS2(    mov     [edx+4*ecx+12],esi)

    AS2(    lea     ecx,[ecx+4])        // advance index, avoid inc which causes slowdown on Intel Core 2
    ASJ(    jmp,    0, b)

    ASL(2)
    AS2(    mov     eax, 0)
    AS1(    setc    al)                 // store carry into eax (return result register)

    AddEpilogue

    // http://github.com/weidai11/cryptopp/issues/340
    CRYPTOPP_UNUSED(A); CRYPTOPP_UNUSED(B);
    CRYPTOPP_UNUSED(C); CRYPTOPP_UNUSED(N);
}

#if CRYPTOPP_INTEGER_SSE2
CRYPTOPP_NAKED int CRYPTOPP_FASTCALL SSE2_Add(size_t N, word *C, const word *A, const word *B)
{
    AddPrologue

    // now: eax = A, edi = B, edx = C, ecx = N
    AS2(    lea     eax, [eax+4*ecx])
    AS2(    lea     edi, [edi+4*ecx])
    AS2(    lea     edx, [edx+4*ecx])

    AS1(    neg     ecx)                // ecx is negative index
    AS2(    pxor    mm2, mm2)
    ASJ(    jz,     2, f)
    AS2(    test    ecx, 2)             // this clears carry flag
    ASJ(    jz,     0, f)
    AS2(    sub     ecx, 2)
    ASJ(    jmp,    1, f)

    ASL(0)
    AS2(    movd     mm0, DWORD PTR [eax+4*ecx])
    AS2(    movd     mm1, DWORD PTR [edi+4*ecx])
    AS2(    paddq    mm0, mm1)
    AS2(    paddq    mm2, mm0)
    AS2(    movd     DWORD PTR [edx+4*ecx], mm2)
    AS2(    psrlq    mm2, 32)

    AS2(    movd     mm0, DWORD PTR [eax+4*ecx+4])
    AS2(    movd     mm1, DWORD PTR [edi+4*ecx+4])
    AS2(    paddq    mm0, mm1)
    AS2(    paddq    mm2, mm0)
    AS2(    movd     DWORD PTR [edx+4*ecx+4], mm2)
    AS2(    psrlq    mm2, 32)

    ASL(1)
    AS2(    movd     mm0, DWORD PTR [eax+4*ecx+8])
    AS2(    movd     mm1, DWORD PTR [edi+4*ecx+8])
    AS2(    paddq    mm0, mm1)
    AS2(    paddq    mm2, mm0)
    AS2(    movd     DWORD PTR [edx+4*ecx+8], mm2)
    AS2(    psrlq    mm2, 32)

    AS2(    movd     mm0, DWORD PTR [eax+4*ecx+12])
    AS2(    movd     mm1, DWORD PTR [edi+4*ecx+12])
    AS2(    paddq    mm0, mm1)
    AS2(    paddq    mm2, mm0)
    AS2(    movd     DWORD PTR [edx+4*ecx+12], mm2)
    AS2(    psrlq    mm2, 32)

    AS2(    add     ecx, 4)
    ASJ(    jnz,    0, b)

    ASL(2)
    AS2(    movd    eax, mm2)
    AS1(    emms)

    AddEpilogue

    // http://github.com/weidai11/cryptopp/issues/340
    CRYPTOPP_UNUSED(A); CRYPTOPP_UNUSED(B);
    CRYPTOPP_UNUSED(C); CRYPTOPP_UNUSED(N);
}
CRYPTOPP_NAKED int CRYPTOPP_FASTCALL SSE2_Sub(size_t N, word *C, const word *A, const word *B)
{
    AddPrologue

    // now: eax = A, edi = B, edx = C, ecx = N
    AS2(    lea     eax, [eax+4*ecx])
    AS2(    lea     edi, [edi+4*ecx])
    AS2(    lea     edx, [edx+4*ecx])

    AS1(    neg     ecx)                // ecx is negative index
    AS2(    pxor    mm2, mm2)
    ASJ(    jz,     2, f)
    AS2(    test    ecx, 2)             // this clears carry flag
    ASJ(    jz,     0, f)
    AS2(    sub     ecx, 2)
    ASJ(    jmp,    1, f)

    ASL(0)
    AS2(    movd     mm0, DWORD PTR [eax+4*ecx])
    AS2(    movd     mm1, DWORD PTR [edi+4*ecx])
    AS2(    psubq    mm0, mm1)
    AS2(    psubq    mm0, mm2)
    AS2(    movd     DWORD PTR [edx+4*ecx], mm0)
    AS2(    psrlq    mm0, 63)

    AS2(    movd     mm2, DWORD PTR [eax+4*ecx+4])
    AS2(    movd     mm1, DWORD PTR [edi+4*ecx+4])
    AS2(    psubq    mm2, mm1)
    AS2(    psubq    mm2, mm0)
    AS2(    movd     DWORD PTR [edx+4*ecx+4], mm2)
    AS2(    psrlq    mm2, 63)

    ASL(1)
    AS2(    movd     mm0, DWORD PTR [eax+4*ecx+8])
    AS2(    movd     mm1, DWORD PTR [edi+4*ecx+8])
    AS2(    psubq    mm0, mm1)
    AS2(    psubq    mm0, mm2)
    AS2(    movd     DWORD PTR [edx+4*ecx+8], mm0)
    AS2(    psrlq    mm0, 63)

    AS2(    movd     mm2, DWORD PTR [eax+4*ecx+12])
    AS2(    movd     mm1, DWORD PTR [edi+4*ecx+12])
    AS2(    psubq    mm2, mm1)
    AS2(    psubq    mm2, mm0)
    AS2(    movd     DWORD PTR [edx+4*ecx+12], mm2)
    AS2(    psrlq    mm2, 63)

    AS2(    add     ecx, 4)
    ASJ(    jnz,    0, b)

    ASL(2)
    AS2(    movd    eax, mm2)
    AS1(    emms)

    AddEpilogue

    // http://github.com/weidai11/cryptopp/issues/340
    CRYPTOPP_UNUSED(A); CRYPTOPP_UNUSED(B);
    CRYPTOPP_UNUSED(C); CRYPTOPP_UNUSED(N);
}
#endif  // CRYPTOPP_INTEGER_SSE2
#else   // CRYPTOPP_SSE2_ASM_AVAILABLE
int CRYPTOPP_FASTCALL Baseline_Add(size_t N, word *C, const word *A, const word *B)
{
    CRYPTOPP_ASSERT (N%2 == 0);

    Declare2Words(u);
    AssignWord(u, 0);
    for (size_t i=0; i<N; i+=2)
    {
        AddWithCarry(u, A[i], B[i]);
        C[i] = LowWord(u);
        AddWithCarry(u, A[i+1], B[i+1]);
        C[i+1] = LowWord(u);
    }
    return int(GetCarry(u));
}

int CRYPTOPP_FASTCALL Baseline_Sub(size_t N, word *C, const word *A, const word *B)
{
    CRYPTOPP_ASSERT (N%2 == 0);

    Declare2Words(u);
    AssignWord(u, 0);
    for (size_t i=0; i<N; i+=2)
    {
        SubtractWithBorrow(u, A[i], B[i]);
        C[i] = LowWord(u);
        SubtractWithBorrow(u, A[i+1], B[i+1]);
        C[i+1] = LowWord(u);
    }
    return int(GetBorrow(u));
}
#endif

static word LinearMultiply(word *C, const word *AA, word B, size_t N)
{
    // http://github.com/weidai11/cryptopp/issues/188
    MAYBE_CONST word* A = MAYBE_UNCONST_CAST(AA);

    word carry=0;
    for(unsigned i=0; i<N; i++)
    {
        Declare2Words(p);
        MultiplyWords(p, A[i], B);
        Acc2WordsBy1(p, carry);
        C[i] = LowWord(p);
        carry = HighWord(p);
    }
    return carry;
}

#ifndef CRYPTOPP_DOXYGEN_PROCESSING

#define Mul_2 \
    Mul_Begin(2) \
    Mul_SaveAcc(0, 0, 1) Mul_Acc(1, 0) \
    Mul_End(1, 1)

#define Mul_4 \
    Mul_Begin(4) \
    Mul_SaveAcc(0, 0, 1) Mul_Acc(1, 0) \
    Mul_SaveAcc(1, 0, 2) Mul_Acc(1, 1) Mul_Acc(2, 0)  \
    Mul_SaveAcc(2, 0, 3) Mul_Acc(1, 2) Mul_Acc(2, 1) Mul_Acc(3, 0)  \
    Mul_SaveAcc(3, 1, 3) Mul_Acc(2, 2) Mul_Acc(3, 1)  \
    Mul_SaveAcc(4, 2, 3) Mul_Acc(3, 2) \
    Mul_End(5, 3)

#define Mul_8 \
    Mul_Begin(8) \
    Mul_SaveAcc(0, 0, 1) Mul_Acc(1, 0) \
    Mul_SaveAcc(1, 0, 2) Mul_Acc(1, 1) Mul_Acc(2, 0)  \
    Mul_SaveAcc(2, 0, 3) Mul_Acc(1, 2) Mul_Acc(2, 1) Mul_Acc(3, 0)  \
    Mul_SaveAcc(3, 0, 4) Mul_Acc(1, 3) Mul_Acc(2, 2) Mul_Acc(3, 1) Mul_Acc(4, 0) \
    Mul_SaveAcc(4, 0, 5) Mul_Acc(1, 4) Mul_Acc(2, 3) Mul_Acc(3, 2) Mul_Acc(4, 1) Mul_Acc(5, 0) \
    Mul_SaveAcc(5, 0, 6) Mul_Acc(1, 5) Mul_Acc(2, 4) Mul_Acc(3, 3) Mul_Acc(4, 2) Mul_Acc(5, 1) Mul_Acc(6, 0) \
    Mul_SaveAcc(6, 0, 7) Mul_Acc(1, 6) Mul_Acc(2, 5) Mul_Acc(3, 4) Mul_Acc(4, 3) Mul_Acc(5, 2) Mul_Acc(6, 1) Mul_Acc(7, 0) \
    Mul_SaveAcc(7, 1, 7) Mul_Acc(2, 6) Mul_Acc(3, 5) Mul_Acc(4, 4) Mul_Acc(5, 3) Mul_Acc(6, 2) Mul_Acc(7, 1) \
    Mul_SaveAcc(8, 2, 7) Mul_Acc(3, 6) Mul_Acc(4, 5) Mul_Acc(5, 4) Mul_Acc(6, 3) Mul_Acc(7, 2) \
    Mul_SaveAcc(9, 3, 7) Mul_Acc(4, 6) Mul_Acc(5, 5) Mul_Acc(6, 4) Mul_Acc(7, 3) \
    Mul_SaveAcc(10, 4, 7) Mul_Acc(5, 6) Mul_Acc(6, 5) Mul_Acc(7, 4) \
    Mul_SaveAcc(11, 5, 7) Mul_Acc(6, 6) Mul_Acc(7, 5) \
    Mul_SaveAcc(12, 6, 7) Mul_Acc(7, 6) \
    Mul_End(13, 7)

#define Mul_16 \
    Mul_Begin(16) \
    Mul_SaveAcc(0, 0, 1) Mul_Acc(1, 0) \
    Mul_SaveAcc(1, 0, 2) Mul_Acc(1, 1) Mul_Acc(2, 0) \
    Mul_SaveAcc(2, 0, 3) Mul_Acc(1, 2) Mul_Acc(2, 1) Mul_Acc(3, 0) \
    Mul_SaveAcc(3, 0, 4) Mul_Acc(1, 3) Mul_Acc(2, 2) Mul_Acc(3, 1) Mul_Acc(4, 0) \
    Mul_SaveAcc(4, 0, 5) Mul_Acc(1, 4) Mul_Acc(2, 3) Mul_Acc(3, 2) Mul_Acc(4, 1) Mul_Acc(5, 0) \
    Mul_SaveAcc(5, 0, 6) Mul_Acc(1, 5) Mul_Acc(2, 4) Mul_Acc(3, 3) Mul_Acc(4, 2) Mul_Acc(5, 1) Mul_Acc(6, 0) \
    Mul_SaveAcc(6, 0, 7) Mul_Acc(1, 6) Mul_Acc(2, 5) Mul_Acc(3, 4) Mul_Acc(4, 3) Mul_Acc(5, 2) Mul_Acc(6, 1) Mul_Acc(7, 0) \
    Mul_SaveAcc(7, 0, 8) Mul_Acc(1, 7) Mul_Acc(2, 6) Mul_Acc(3, 5) Mul_Acc(4, 4) Mul_Acc(5, 3) Mul_Acc(6, 2) Mul_Acc(7, 1) Mul_Acc(8, 0) \
    Mul_SaveAcc(8, 0, 9) Mul_Acc(1, 8) Mul_Acc(2, 7) Mul_Acc(3, 6) Mul_Acc(4, 5) Mul_Acc(5, 4) Mul_Acc(6, 3) Mul_Acc(7, 2) Mul_Acc(8, 1) Mul_Acc(9, 0) \
    Mul_SaveAcc(9, 0, 10) Mul_Acc(1, 9) Mul_Acc(2, 8) Mul_Acc(3, 7) Mul_Acc(4, 6) Mul_Acc(5, 5) Mul_Acc(6, 4) Mul_Acc(7, 3) Mul_Acc(8, 2) Mul_Acc(9, 1) Mul_Acc(10, 0) \
    Mul_SaveAcc(10, 0, 11) Mul_Acc(1, 10) Mul_Acc(2, 9) Mul_Acc(3, 8) Mul_Acc(4, 7) Mul_Acc(5, 6) Mul_Acc(6, 5) Mul_Acc(7, 4) Mul_Acc(8, 3) Mul_Acc(9, 2) Mul_Acc(10, 1) Mul_Acc(11, 0) \
    Mul_SaveAcc(11, 0, 12) Mul_Acc(1, 11) Mul_Acc(2, 10) Mul_Acc(3, 9) Mul_Acc(4, 8) Mul_Acc(5, 7) Mul_Acc(6, 6) Mul_Acc(7, 5) Mul_Acc(8, 4) Mul_Acc(9, 3) Mul_Acc(10, 2) Mul_Acc(11, 1) Mul_Acc(12, 0) \
    Mul_SaveAcc(12, 0, 13) Mul_Acc(1, 12) Mul_Acc(2, 11) Mul_Acc(3, 10) Mul_Acc(4, 9) Mul_Acc(5, 8) Mul_Acc(6, 7) Mul_Acc(7, 6) Mul_Acc(8, 5) Mul_Acc(9, 4) Mul_Acc(10, 3) Mul_Acc(11, 2) Mul_Acc(12, 1) Mul_Acc(13, 0) \
    Mul_SaveAcc(13, 0, 14) Mul_Acc(1, 13) Mul_Acc(2, 12) Mul_Acc(3, 11) Mul_Acc(4, 10) Mul_Acc(5, 9) Mul_Acc(6, 8) Mul_Acc(7, 7) Mul_Acc(8, 6) Mul_Acc(9, 5) Mul_Acc(10, 4) Mul_Acc(11, 3) Mul_Acc(12, 2) Mul_Acc(13, 1) Mul_Acc(14, 0) \
    Mul_SaveAcc(14, 0, 15) Mul_Acc(1, 14) Mul_Acc(2, 13) Mul_Acc(3, 12) Mul_Acc(4, 11) Mul_Acc(5, 10) Mul_Acc(6, 9) Mul_Acc(7, 8) Mul_Acc(8, 7) Mul_Acc(9, 6) Mul_Acc(10, 5) Mul_Acc(11, 4) Mul_Acc(12, 3) Mul_Acc(13, 2) Mul_Acc(14, 1) Mul_Acc(15, 0) \
    Mul_SaveAcc(15, 1, 15) Mul_Acc(2, 14) Mul_Acc(3, 13) Mul_Acc(4, 12) Mul_Acc(5, 11) Mul_Acc(6, 10) Mul_Acc(7, 9) Mul_Acc(8, 8) Mul_Acc(9, 7) Mul_Acc(10, 6) Mul_Acc(11, 5) Mul_Acc(12, 4) Mul_Acc(13, 3) Mul_Acc(14, 2) Mul_Acc(15, 1) \
    Mul_SaveAcc(16, 2, 15) Mul_Acc(3, 14) Mul_Acc(4, 13) Mul_Acc(5, 12) Mul_Acc(6, 11) Mul_Acc(7, 10) Mul_Acc(8, 9) Mul_Acc(9, 8) Mul_Acc(10, 7) Mul_Acc(11, 6) Mul_Acc(12, 5) Mul_Acc(13, 4) Mul_Acc(14, 3) Mul_Acc(15, 2) \
    Mul_SaveAcc(17, 3, 15) Mul_Acc(4, 14) Mul_Acc(5, 13) Mul_Acc(6, 12) Mul_Acc(7, 11) Mul_Acc(8, 10) Mul_Acc(9, 9) Mul_Acc(10, 8) Mul_Acc(11, 7) Mul_Acc(12, 6) Mul_Acc(13, 5) Mul_Acc(14, 4) Mul_Acc(15, 3) \
    Mul_SaveAcc(18, 4, 15) Mul_Acc(5, 14) Mul_Acc(6, 13) Mul_Acc(7, 12) Mul_Acc(8, 11) Mul_Acc(9, 10) Mul_Acc(10, 9) Mul_Acc(11, 8) Mul_Acc(12, 7) Mul_Acc(13, 6) Mul_Acc(14, 5) Mul_Acc(15, 4) \
    Mul_SaveAcc(19, 5, 15) Mul_Acc(6, 14) Mul_Acc(7, 13) Mul_Acc(8, 12) Mul_Acc(9, 11) Mul_Acc(10, 10) Mul_Acc(11, 9) Mul_Acc(12, 8) Mul_Acc(13, 7) Mul_Acc(14, 6) Mul_Acc(15, 5) \
    Mul_SaveAcc(20, 6, 15) Mul_Acc(7, 14) Mul_Acc(8, 13) Mul_Acc(9, 12) Mul_Acc(10, 11) Mul_Acc(11, 10) Mul_Acc(12, 9) Mul_Acc(13, 8) Mul_Acc(14, 7) Mul_Acc(15, 6) \
    Mul_SaveAcc(21, 7, 15) Mul_Acc(8, 14) Mul_Acc(9, 13) Mul_Acc(10, 12) Mul_Acc(11, 11) Mul_Acc(12, 10) Mul_Acc(13, 9) Mul_Acc(14, 8) Mul_Acc(15, 7) \
    Mul_SaveAcc(22, 8, 15) Mul_Acc(9, 14) Mul_Acc(10, 13) Mul_Acc(11, 12) Mul_Acc(12, 11) Mul_Acc(13, 10) Mul_Acc(14, 9) Mul_Acc(15, 8) \
    Mul_SaveAcc(23, 9, 15) Mul_Acc(10, 14) Mul_Acc(11, 13) Mul_Acc(12, 12) Mul_Acc(13, 11) Mul_Acc(14, 10) Mul_Acc(15, 9) \
    Mul_SaveAcc(24, 10, 15) Mul_Acc(11, 14) Mul_Acc(12, 13) Mul_Acc(13, 12) Mul_Acc(14, 11) Mul_Acc(15, 10) \
    Mul_SaveAcc(25, 11, 15) Mul_Acc(12, 14) Mul_Acc(13, 13) Mul_Acc(14, 12) Mul_Acc(15, 11) \
    Mul_SaveAcc(26, 12, 15) Mul_Acc(13, 14) Mul_Acc(14, 13) Mul_Acc(15, 12) \
    Mul_SaveAcc(27, 13, 15) Mul_Acc(14, 14) Mul_Acc(15, 13) \
    Mul_SaveAcc(28, 14, 15) Mul_Acc(15, 14) \
    Mul_End(29, 15)

#define Squ_2 \
    Squ_Begin(2) \
    Squ_End(2)

#define Squ_4 \
    Squ_Begin(4) \
    Squ_SaveAcc(1, 0, 2) Squ_Diag(1) \
    Squ_SaveAcc(2, 0, 3) Squ_Acc(1, 2) Squ_NonDiag \
    Squ_SaveAcc(3, 1, 3) Squ_Diag(2) \
    Squ_SaveAcc(4, 2, 3) Squ_NonDiag \
    Squ_End(4)

#define Squ_8 \
    Squ_Begin(8) \
    Squ_SaveAcc(1, 0, 2) Squ_Diag(1) \
    Squ_SaveAcc(2, 0, 3) Squ_Acc(1, 2) Squ_NonDiag \
    Squ_SaveAcc(3, 0, 4) Squ_Acc(1, 3) Squ_Diag(2) \
    Squ_SaveAcc(4, 0, 5) Squ_Acc(1, 4) Squ_Acc(2, 3) Squ_NonDiag \
    Squ_SaveAcc(5, 0, 6) Squ_Acc(1, 5) Squ_Acc(2, 4) Squ_Diag(3) \
    Squ_SaveAcc(6, 0, 7) Squ_Acc(1, 6) Squ_Acc(2, 5) Squ_Acc(3, 4) Squ_NonDiag \
    Squ_SaveAcc(7, 1, 7) Squ_Acc(2, 6) Squ_Acc(3, 5) Squ_Diag(4) \
    Squ_SaveAcc(8, 2, 7) Squ_Acc(3, 6) Squ_Acc(4, 5)  Squ_NonDiag \
    Squ_SaveAcc(9, 3, 7) Squ_Acc(4, 6) Squ_Diag(5) \
    Squ_SaveAcc(10, 4, 7) Squ_Acc(5, 6) Squ_NonDiag \
    Squ_SaveAcc(11, 5, 7) Squ_Diag(6) \
    Squ_SaveAcc(12, 6, 7) Squ_NonDiag \
    Squ_End(8)

#define Squ_16 \
    Squ_Begin(16) \
    Squ_SaveAcc(1, 0, 2) Squ_Diag(1) \
    Squ_SaveAcc(2, 0, 3) Squ_Acc(1, 2) Squ_NonDiag \
    Squ_SaveAcc(3, 0, 4) Squ_Acc(1, 3) Squ_Diag(2) \
    Squ_SaveAcc(4, 0, 5) Squ_Acc(1, 4) Squ_Acc(2, 3) Squ_NonDiag \
    Squ_SaveAcc(5, 0, 6) Squ_Acc(1, 5) Squ_Acc(2, 4) Squ_Diag(3) \
    Squ_SaveAcc(6, 0, 7) Squ_Acc(1, 6) Squ_Acc(2, 5) Squ_Acc(3, 4) Squ_NonDiag \
    Squ_SaveAcc(7, 0, 8) Squ_Acc(1, 7) Squ_Acc(2, 6) Squ_Acc(3, 5) Squ_Diag(4) \
    Squ_SaveAcc(8, 0, 9) Squ_Acc(1, 8) Squ_Acc(2, 7) Squ_Acc(3, 6) Squ_Acc(4, 5) Squ_NonDiag \
    Squ_SaveAcc(9, 0, 10) Squ_Acc(1, 9) Squ_Acc(2, 8) Squ_Acc(3, 7) Squ_Acc(4, 6) Squ_Diag(5) \
    Squ_SaveAcc(10, 0, 11) Squ_Acc(1, 10) Squ_Acc(2, 9) Squ_Acc(3, 8) Squ_Acc(4, 7) Squ_Acc(5, 6) Squ_NonDiag \
    Squ_SaveAcc(11, 0, 12) Squ_Acc(1, 11) Squ_Acc(2, 10) Squ_Acc(3, 9) Squ_Acc(4, 8) Squ_Acc(5, 7) Squ_Diag(6) \
    Squ_SaveAcc(12, 0, 13) Squ_Acc(1, 12) Squ_Acc(2, 11) Squ_Acc(3, 10) Squ_Acc(4, 9) Squ_Acc(5, 8) Squ_Acc(6, 7) Squ_NonDiag \
    Squ_SaveAcc(13, 0, 14) Squ_Acc(1, 13) Squ_Acc(2, 12) Squ_Acc(3, 11) Squ_Acc(4, 10) Squ_Acc(5, 9) Squ_Acc(6, 8) Squ_Diag(7) \
    Squ_SaveAcc(14, 0, 15) Squ_Acc(1, 14) Squ_Acc(2, 13) Squ_Acc(3, 12) Squ_Acc(4, 11) Squ_Acc(5, 10) Squ_Acc(6, 9) Squ_Acc(7, 8) Squ_NonDiag \
    Squ_SaveAcc(15, 1, 15) Squ_Acc(2, 14) Squ_Acc(3, 13) Squ_Acc(4, 12) Squ_Acc(5, 11) Squ_Acc(6, 10) Squ_Acc(7, 9) Squ_Diag(8) \
    Squ_SaveAcc(16, 2, 15) Squ_Acc(3, 14) Squ_Acc(4, 13) Squ_Acc(5, 12) Squ_Acc(6, 11) Squ_Acc(7, 10) Squ_Acc(8, 9) Squ_NonDiag \
    Squ_SaveAcc(17, 3, 15) Squ_Acc(4, 14) Squ_Acc(5, 13) Squ_Acc(6, 12) Squ_Acc(7, 11) Squ_Acc(8, 10) Squ_Diag(9) \
    Squ_SaveAcc(18, 4, 15) Squ_Acc(5, 14) Squ_Acc(6, 13) Squ_Acc(7, 12) Squ_Acc(8, 11) Squ_Acc(9, 10) Squ_NonDiag \
    Squ_SaveAcc(19, 5, 15) Squ_Acc(6, 14) Squ_Acc(7, 13) Squ_Acc(8, 12) Squ_Acc(9, 11) Squ_Diag(10) \
    Squ_SaveAcc(20, 6, 15) Squ_Acc(7, 14) Squ_Acc(8, 13) Squ_Acc(9, 12) Squ_Acc(10, 11) Squ_NonDiag \
    Squ_SaveAcc(21, 7, 15) Squ_Acc(8, 14) Squ_Acc(9, 13) Squ_Acc(10, 12) Squ_Diag(11) \
    Squ_SaveAcc(22, 8, 15) Squ_Acc(9, 14) Squ_Acc(10, 13) Squ_Acc(11, 12) Squ_NonDiag \
    Squ_SaveAcc(23, 9, 15) Squ_Acc(10, 14) Squ_Acc(11, 13) Squ_Diag(12) \
    Squ_SaveAcc(24, 10, 15) Squ_Acc(11, 14) Squ_Acc(12, 13) Squ_NonDiag \
    Squ_SaveAcc(25, 11, 15) Squ_Acc(12, 14) Squ_Diag(13) \
    Squ_SaveAcc(26, 12, 15) Squ_Acc(13, 14) Squ_NonDiag \
    Squ_SaveAcc(27, 13, 15) Squ_Diag(14) \
    Squ_SaveAcc(28, 14, 15) Squ_NonDiag \
    Squ_End(16)

#define Bot_2 \
    Mul_Begin(2) \
    Bot_SaveAcc(0, 0, 1) Bot_Acc(1, 0) \
    Bot_End(2)

#define Bot_4 \
    Mul_Begin(4) \
    Mul_SaveAcc(0, 0, 1) Mul_Acc(1, 0) \
    Mul_SaveAcc(1, 2, 0) Mul_Acc(1, 1) Mul_Acc(0, 2)  \
    Bot_SaveAcc(2, 0, 3) Bot_Acc(1, 2) Bot_Acc(2, 1) Bot_Acc(3, 0)  \
    Bot_End(4)

#define Bot_8 \
    Mul_Begin(8) \
    Mul_SaveAcc(0, 0, 1) Mul_Acc(1, 0) \
    Mul_SaveAcc(1, 0, 2) Mul_Acc(1, 1) Mul_Acc(2, 0)  \
    Mul_SaveAcc(2, 0, 3) Mul_Acc(1, 2) Mul_Acc(2, 1) Mul_Acc(3, 0)  \
    Mul_SaveAcc(3, 0, 4) Mul_Acc(1, 3) Mul_Acc(2, 2) Mul_Acc(3, 1) Mul_Acc(4, 0) \
    Mul_SaveAcc(4, 0, 5) Mul_Acc(1, 4) Mul_Acc(2, 3) Mul_Acc(3, 2) Mul_Acc(4, 1) Mul_Acc(5, 0) \
    Mul_SaveAcc(5, 0, 6) Mul_Acc(1, 5) Mul_Acc(2, 4) Mul_Acc(3, 3) Mul_Acc(4, 2) Mul_Acc(5, 1) Mul_Acc(6, 0) \
    Bot_SaveAcc(6, 0, 7) Bot_Acc(1, 6) Bot_Acc(2, 5) Bot_Acc(3, 4) Bot_Acc(4, 3) Bot_Acc(5, 2) Bot_Acc(6, 1) Bot_Acc(7, 0) \
    Bot_End(8)

#define Bot_16 \
    Mul_Begin(16) \
    Mul_SaveAcc(0, 0, 1) Mul_Acc(1, 0) \
    Mul_SaveAcc(1, 0, 2) Mul_Acc(1, 1) Mul_Acc(2, 0) \
    Mul_SaveAcc(2, 0, 3) Mul_Acc(1, 2) Mul_Acc(2, 1) Mul_Acc(3, 0) \
    Mul_SaveAcc(3, 0, 4) Mul_Acc(1, 3) Mul_Acc(2, 2) Mul_Acc(3, 1) Mul_Acc(4, 0) \
    Mul_SaveAcc(4, 0, 5) Mul_Acc(1, 4) Mul_Acc(2, 3) Mul_Acc(3, 2) Mul_Acc(4, 1) Mul_Acc(5, 0) \
    Mul_SaveAcc(5, 0, 6) Mul_Acc(1, 5) Mul_Acc(2, 4) Mul_Acc(3, 3) Mul_Acc(4, 2) Mul_Acc(5, 1) Mul_Acc(6, 0) \
    Mul_SaveAcc(6, 0, 7) Mul_Acc(1, 6) Mul_Acc(2, 5) Mul_Acc(3, 4) Mul_Acc(4, 3) Mul_Acc(5, 2) Mul_Acc(6, 1) Mul_Acc(7, 0) \
    Mul_SaveAcc(7, 0, 8) Mul_Acc(1, 7) Mul_Acc(2, 6) Mul_Acc(3, 5) Mul_Acc(4, 4) Mul_Acc(5, 3) Mul_Acc(6, 2) Mul_Acc(7, 1) Mul_Acc(8, 0) \
    Mul_SaveAcc(8, 0, 9) Mul_Acc(1, 8) Mul_Acc(2, 7) Mul_Acc(3, 6) Mul_Acc(4, 5) Mul_Acc(5, 4) Mul_Acc(6, 3) Mul_Acc(7, 2) Mul_Acc(8, 1) Mul_Acc(9, 0) \
    Mul_SaveAcc(9, 0, 10) Mul_Acc(1, 9) Mul_Acc(2, 8) Mul_Acc(3, 7) Mul_Acc(4, 6) Mul_Acc(5, 5) Mul_Acc(6, 4) Mul_Acc(7, 3) Mul_Acc(8, 2) Mul_Acc(9, 1) Mul_Acc(10, 0) \
    Mul_SaveAcc(10, 0, 11) Mul_Acc(1, 10) Mul_Acc(2, 9) Mul_Acc(3, 8) Mul_Acc(4, 7) Mul_Acc(5, 6) Mul_Acc(6, 5) Mul_Acc(7, 4) Mul_Acc(8, 3) Mul_Acc(9, 2) Mul_Acc(10, 1) Mul_Acc(11, 0) \
    Mul_SaveAcc(11, 0, 12) Mul_Acc(1, 11) Mul_Acc(2, 10) Mul_Acc(3, 9) Mul_Acc(4, 8) Mul_Acc(5, 7) Mul_Acc(6, 6) Mul_Acc(7, 5) Mul_Acc(8, 4) Mul_Acc(9, 3) Mul_Acc(10, 2) Mul_Acc(11, 1) Mul_Acc(12, 0) \
    Mul_SaveAcc(12, 0, 13) Mul_Acc(1, 12) Mul_Acc(2, 11) Mul_Acc(3, 10) Mul_Acc(4, 9) Mul_Acc(5, 8) Mul_Acc(6, 7) Mul_Acc(7, 6) Mul_Acc(8, 5) Mul_Acc(9, 4) Mul_Acc(10, 3) Mul_Acc(11, 2) Mul_Acc(12, 1) Mul_Acc(13, 0) \
    Mul_SaveAcc(13, 0, 14) Mul_Acc(1, 13) Mul_Acc(2, 12) Mul_Acc(3, 11) Mul_Acc(4, 10) Mul_Acc(5, 9) Mul_Acc(6, 8) Mul_Acc(7, 7) Mul_Acc(8, 6) Mul_Acc(9, 5) Mul_Acc(10, 4) Mul_Acc(11, 3) Mul_Acc(12, 2) Mul_Acc(13, 1) Mul_Acc(14, 0) \
    Bot_SaveAcc(14, 0, 15) Bot_Acc(1, 14) Bot_Acc(2, 13) Bot_Acc(3, 12) Bot_Acc(4, 11) Bot_Acc(5, 10) Bot_Acc(6, 9) Bot_Acc(7, 8) Bot_Acc(8, 7) Bot_Acc(9, 6) Bot_Acc(10, 5) Bot_Acc(11, 4) Bot_Acc(12, 3) Bot_Acc(13, 2) Bot_Acc(14, 1) Bot_Acc(15, 0) \
    Bot_End(16)

#endif

#if 0
#define Mul_Begin(n)                \
    Declare2Words(p)                \
    Declare2Words(c)                \
    Declare2Words(d)                \
    MultiplyWords(p, A[0], B[0])    \
    AssignWord(c, LowWord(p))       \
    AssignWord(d, HighWord(p))

#define Mul_Acc(i, j)               \
    MultiplyWords(p, A[i], B[j])    \
    Acc2WordsBy1(c, LowWord(p))     \
    Acc2WordsBy1(d, HighWord(p))

#define Mul_SaveAcc(k, i, j)        \
    R[k] = LowWord(c);              \
    Add2WordsBy1(c, d, HighWord(c)) \
    MultiplyWords(p, A[i], B[j])    \
    AssignWord(d, HighWord(p))      \
    Acc2WordsBy1(c, LowWord(p))

#define Mul_End(n)                  \
    R[2*n-3] = LowWord(c);          \
    Acc2WordsBy1(d, HighWord(c))    \
    MultiplyWords(p, A[n-1], B[n-1])\
    Acc2WordsBy2(d, p)              \
    R[2*n-2] = LowWord(d);          \
    R[2*n-1] = HighWord(d);

#define Bot_SaveAcc(k, i, j)        \
    R[k] = LowWord(c);              \
    word e = LowWord(d) + HighWord(c);  \
    e += A[i] * B[j];

#define Bot_Acc(i, j)   \
    e += A[i] * B[j];

#define Bot_End(n)      \
    R[n-1] = e;
#else
#define Mul_Begin(n)                \
    Declare2Words(p)                \
    word c; \
    Declare2Words(d)                \
    MultiplyWords(p, A[0], B[0])    \
    c = LowWord(p);     \
    AssignWord(d, HighWord(p))

#define Mul_Acc(i, j)               \
    MulAcc(c, d, A[i], B[j])

#define Mul_SaveAcc(k, i, j)        \
    R[k] = c;               \
    c = LowWord(d); \
    AssignWord(d, HighWord(d))  \
    MulAcc(c, d, A[i], B[j])

#define Mul_End(k, i)                   \
    R[k] = c;           \
    MultiplyWords(p, A[i], B[i])    \
    Acc2WordsBy2(p, d)              \
    R[k+1] = LowWord(p);            \
    R[k+2] = HighWord(p);

#define Bot_SaveAcc(k, i, j)        \
    R[k] = c;               \
    c = LowWord(d); \
    c += A[i] * B[j];

#define Bot_Acc(i, j)   \
    c += A[i] * B[j];

#define Bot_End(n)      \
    R[n-1] = c;
#endif

#define Squ_Begin(n)                \
    Declare2Words(p)                \
    word c;             \
    Declare2Words(d)                \
    Declare2Words(e)                \
    MultiplyWords(p, A[0], A[0])    \
    R[0] = LowWord(p);              \
    AssignWord(e, HighWord(p))      \
    MultiplyWords(p, A[0], A[1])    \
    c = LowWord(p);     \
    AssignWord(d, HighWord(p))      \
    Squ_NonDiag                     \

#define Squ_NonDiag             \
    Double3Words(c, d)

#define Squ_SaveAcc(k, i, j)        \
    Acc3WordsBy2(c, d, e)           \
    R[k] = c;               \
    MultiplyWords(p, A[i], A[j])    \
    c = LowWord(p);     \
    AssignWord(d, HighWord(p))      \

#define Squ_Acc(i, j)               \
    MulAcc(c, d, A[i], A[j])

#define Squ_Diag(i)                 \
    Squ_NonDiag                     \
    MulAcc(c, d, A[i], A[i])

#define Squ_End(n)                  \
    Acc3WordsBy2(c, d, e)           \
    R[2*n-3] = c;           \
    MultiplyWords(p, A[n-1], A[n-1])\
    Acc2WordsBy2(p, e)              \
    R[2*n-2] = LowWord(p);          \
    R[2*n-1] = HighWord(p);


void Baseline_Multiply2(word *R, const word *AA, const word *BB)
{
    // http://github.com/weidai11/cryptopp/issues/188
    MAYBE_CONST word* A = MAYBE_UNCONST_CAST(AA);
    MAYBE_CONST word* B = MAYBE_UNCONST_CAST(BB);

    Mul_2
}

void Baseline_Multiply4(word *R, const word *AA, const word *BB)
{
    // http://github.com/weidai11/cryptopp/issues/188
    MAYBE_CONST word* A = MAYBE_UNCONST_CAST(AA);
    MAYBE_CONST word* B = MAYBE_UNCONST_CAST(BB);

    Mul_4
}

void Baseline_Multiply8(word *R, const word *AA, const word *BB)
{
    // http://github.com/weidai11/cryptopp/issues/188
    MAYBE_CONST word* A = MAYBE_UNCONST_CAST(AA);
    MAYBE_CONST word* B = MAYBE_UNCONST_CAST(BB);

    Mul_8
}

void Baseline_Square2(word *R, const word *AA)
{
    // http://github.com/weidai11/cryptopp/issues/188
    MAYBE_CONST word* A = MAYBE_UNCONST_CAST(AA);

    Squ_2
}

void Baseline_Square4(word *R, const word *AA)
{
    // http://github.com/weidai11/cryptopp/issues/188
    MAYBE_CONST word* A = MAYBE_UNCONST_CAST(AA);

    Squ_4
}

void Baseline_Square8(word *R, const word *AA)
{
    // http://github.com/weidai11/cryptopp/issues/188
    MAYBE_CONST word* A = MAYBE_UNCONST_CAST(AA);

    Squ_8
}

void Baseline_MultiplyBottom2(word *R, const word *AA, const word *BB)
{
    // http://github.com/weidai11/cryptopp/issues/188
    MAYBE_CONST word* A = MAYBE_UNCONST_CAST(AA);
    MAYBE_CONST word* B = MAYBE_UNCONST_CAST(BB);

    Bot_2

// http://github.com/weidai11/cryptopp/issues/340
#if defined(TWO_64_BIT_WORDS)
    CRYPTOPP_UNUSED(d0); CRYPTOPP_UNUSED(d1);
#endif
}

void Baseline_MultiplyBottom4(word *R, const word *AA, const word *BB)
{
    // http://github.com/weidai11/cryptopp/issues/188
    MAYBE_CONST word* A = MAYBE_UNCONST_CAST(AA);
    MAYBE_CONST word* B = MAYBE_UNCONST_CAST(BB);

    Bot_4
}

void Baseline_MultiplyBottom8(word *R, const word *AA, const word *BB)
{
    // http://github.com/weidai11/cryptopp/issues/188
    MAYBE_CONST word* A = MAYBE_UNCONST_CAST(AA);
    MAYBE_CONST word* B = MAYBE_UNCONST_CAST(BB);

    Bot_8
}

#define Top_Begin(n)                \
    Declare2Words(p)                \
    word c; \
    Declare2Words(d)                \
    MultiplyWords(p, A[0], B[n-2]);\
    AssignWord(d, HighWord(p));

#define Top_Acc(i, j)   \
    MultiplyWords(p, A[i], B[j]);\
    Acc2WordsBy1(d, HighWord(p));

#define Top_SaveAcc0(i, j)      \
    c = LowWord(d); \
    AssignWord(d, HighWord(d))  \
    MulAcc(c, d, A[i], B[j])

#define Top_SaveAcc1(i, j)      \
    c = L<c; \
    Acc2WordsBy1(d, c); \
    c = LowWord(d); \
    AssignWord(d, HighWord(d))  \
    MulAcc(c, d, A[i], B[j])

void Baseline_MultiplyTop2(word *R, const word *A, const word *B, word L)
{
    CRYPTOPP_UNUSED(L);
    word T[4];
    Baseline_Multiply2(T, A, B);
    R[0] = T[2];
    R[1] = T[3];
}

void Baseline_MultiplyTop4(word *R, const word *AA, const word *BB, word L)
{
    // http://github.com/weidai11/cryptopp/issues/188
    MAYBE_CONST word* A = MAYBE_UNCONST_CAST(AA);
    MAYBE_CONST word* B = MAYBE_UNCONST_CAST(BB);

    Top_Begin(4)
    Top_Acc(1, 1) Top_Acc(2, 0)  \
    Top_SaveAcc0(0, 3) Mul_Acc(1, 2) Mul_Acc(2, 1) Mul_Acc(3, 0)  \
    Top_SaveAcc1(1, 3) Mul_Acc(2, 2) Mul_Acc(3, 1)  \
    Mul_SaveAcc(0, 2, 3) Mul_Acc(3, 2) \
    Mul_End(1, 3)
}

void Baseline_MultiplyTop8(word *R, const word *AA, const word *BB, word L)
{
    // http://github.com/weidai11/cryptopp/issues/188
    MAYBE_CONST word* A = MAYBE_UNCONST_CAST(AA);
    MAYBE_CONST word* B = MAYBE_UNCONST_CAST(BB);

    Top_Begin(8)
    Top_Acc(1, 5) Top_Acc(2, 4) Top_Acc(3, 3) Top_Acc(4, 2) Top_Acc(5, 1) Top_Acc(6, 0) \
    Top_SaveAcc0(0, 7) Mul_Acc(1, 6) Mul_Acc(2, 5) Mul_Acc(3, 4) Mul_Acc(4, 3) Mul_Acc(5, 2) Mul_Acc(6, 1) Mul_Acc(7, 0) \
    Top_SaveAcc1(1, 7) Mul_Acc(2, 6) Mul_Acc(3, 5) Mul_Acc(4, 4) Mul_Acc(5, 3) Mul_Acc(6, 2) Mul_Acc(7, 1) \
    Mul_SaveAcc(0, 2, 7) Mul_Acc(3, 6) Mul_Acc(4, 5) Mul_Acc(5, 4) Mul_Acc(6, 3) Mul_Acc(7, 2) \
    Mul_SaveAcc(1, 3, 7) Mul_Acc(4, 6) Mul_Acc(5, 5) Mul_Acc(6, 4) Mul_Acc(7, 3) \
    Mul_SaveAcc(2, 4, 7) Mul_Acc(5, 6) Mul_Acc(6, 5) Mul_Acc(7, 4) \
    Mul_SaveAcc(3, 5, 7) Mul_Acc(6, 6) Mul_Acc(7, 5) \
    Mul_SaveAcc(4, 6, 7) Mul_Acc(7, 6) \
    Mul_End(5, 7)
}

#if !CRYPTOPP_INTEGER_SSE2  // save memory by not compiling these functions when SSE2 is available
void Baseline_Multiply16(word *R, const word *AA, const word *BB)
{
    // http://github.com/weidai11/cryptopp/issues/188
    MAYBE_CONST word* A = MAYBE_UNCONST_CAST(AA);
    MAYBE_CONST word* B = MAYBE_UNCONST_CAST(BB);

    Mul_16
}

void Baseline_Square16(word *R, const word *AA)
{
    // http://github.com/weidai11/cryptopp/issues/188
    MAYBE_CONST word* A = MAYBE_UNCONST_CAST(AA);

    Squ_16
}

void Baseline_MultiplyBottom16(word *R, const word *AA, const word *BB)
{
    // http://github.com/weidai11/cryptopp/issues/188
    MAYBE_CONST word* A = MAYBE_UNCONST_CAST(AA);
    MAYBE_CONST word* B = MAYBE_UNCONST_CAST(BB);

    Bot_16
}

void Baseline_MultiplyTop16(word *R, const word *AA, const word *BB, word L)
{
    // http://github.com/weidai11/cryptopp/issues/188
    MAYBE_CONST word* A = MAYBE_UNCONST_CAST(AA);
    MAYBE_CONST word* B = MAYBE_UNCONST_CAST(BB);

    Top_Begin(16)
    Top_Acc(1, 13) Top_Acc(2, 12) Top_Acc(3, 11) Top_Acc(4, 10) Top_Acc(5, 9) Top_Acc(6, 8) Top_Acc(7, 7) Top_Acc(8, 6) Top_Acc(9, 5) Top_Acc(10, 4) Top_Acc(11, 3) Top_Acc(12, 2) Top_Acc(13, 1) Top_Acc(14, 0) \
    Top_SaveAcc0(0, 15) Mul_Acc(1, 14) Mul_Acc(2, 13) Mul_Acc(3, 12) Mul_Acc(4, 11) Mul_Acc(5, 10) Mul_Acc(6, 9) Mul_Acc(7, 8) Mul_Acc(8, 7) Mul_Acc(9, 6) Mul_Acc(10, 5) Mul_Acc(11, 4) Mul_Acc(12, 3) Mul_Acc(13, 2) Mul_Acc(14, 1) Mul_Acc(15, 0) \
    Top_SaveAcc1(1, 15) Mul_Acc(2, 14) Mul_Acc(3, 13) Mul_Acc(4, 12) Mul_Acc(5, 11) Mul_Acc(6, 10) Mul_Acc(7, 9) Mul_Acc(8, 8) Mul_Acc(9, 7) Mul_Acc(10, 6) Mul_Acc(11, 5) Mul_Acc(12, 4) Mul_Acc(13, 3) Mul_Acc(14, 2) Mul_Acc(15, 1) \
    Mul_SaveAcc(0, 2, 15) Mul_Acc(3, 14) Mul_Acc(4, 13) Mul_Acc(5, 12) Mul_Acc(6, 11) Mul_Acc(7, 10) Mul_Acc(8, 9) Mul_Acc(9, 8) Mul_Acc(10, 7) Mul_Acc(11, 6) Mul_Acc(12, 5) Mul_Acc(13, 4) Mul_Acc(14, 3) Mul_Acc(15, 2) \
    Mul_SaveAcc(1, 3, 15) Mul_Acc(4, 14) Mul_Acc(5, 13) Mul_Acc(6, 12) Mul_Acc(7, 11) Mul_Acc(8, 10) Mul_Acc(9, 9) Mul_Acc(10, 8) Mul_Acc(11, 7) Mul_Acc(12, 6) Mul_Acc(13, 5) Mul_Acc(14, 4) Mul_Acc(15, 3) \
    Mul_SaveAcc(2, 4, 15) Mul_Acc(5, 14) Mul_Acc(6, 13) Mul_Acc(7, 12) Mul_Acc(8, 11) Mul_Acc(9, 10) Mul_Acc(10, 9) Mul_Acc(11, 8) Mul_Acc(12, 7) Mul_Acc(13, 6) Mul_Acc(14, 5) Mul_Acc(15, 4) \
    Mul_SaveAcc(3, 5, 15) Mul_Acc(6, 14) Mul_Acc(7, 13) Mul_Acc(8, 12) Mul_Acc(9, 11) Mul_Acc(10, 10) Mul_Acc(11, 9) Mul_Acc(12, 8) Mul_Acc(13, 7) Mul_Acc(14, 6) Mul_Acc(15, 5) \
    Mul_SaveAcc(4, 6, 15) Mul_Acc(7, 14) Mul_Acc(8, 13) Mul_Acc(9, 12) Mul_Acc(10, 11) Mul_Acc(11, 10) Mul_Acc(12, 9) Mul_Acc(13, 8) Mul_Acc(14, 7) Mul_Acc(15, 6) \
    Mul_SaveAcc(5, 7, 15) Mul_Acc(8, 14) Mul_Acc(9, 13) Mul_Acc(10, 12) Mul_Acc(11, 11) Mul_Acc(12, 10) Mul_Acc(13, 9) Mul_Acc(14, 8) Mul_Acc(15, 7) \
    Mul_SaveAcc(6, 8, 15) Mul_Acc(9, 14) Mul_Acc(10, 13) Mul_Acc(11, 12) Mul_Acc(12, 11) Mul_Acc(13, 10) Mul_Acc(14, 9) Mul_Acc(15, 8) \
    Mul_SaveAcc(7, 9, 15) Mul_Acc(10, 14) Mul_Acc(11, 13) Mul_Acc(12, 12) Mul_Acc(13, 11) Mul_Acc(14, 10) Mul_Acc(15, 9) \
    Mul_SaveAcc(8, 10, 15) Mul_Acc(11, 14) Mul_Acc(12, 13) Mul_Acc(13, 12) Mul_Acc(14, 11) Mul_Acc(15, 10) \
    Mul_SaveAcc(9, 11, 15) Mul_Acc(12, 14) Mul_Acc(13, 13) Mul_Acc(14, 12) Mul_Acc(15, 11) \
    Mul_SaveAcc(10, 12, 15) Mul_Acc(13, 14) Mul_Acc(14, 13) Mul_Acc(15, 12) \
    Mul_SaveAcc(11, 13, 15) Mul_Acc(14, 14) Mul_Acc(15, 13) \
    Mul_SaveAcc(12, 14, 15) Mul_Acc(15, 14) \
    Mul_End(13, 15)
}
#endif

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

#if CRYPTOPP_INTEGER_SSE2

CRYPTOPP_ALIGN_DATA(16)
CRYPTOPP_TABLE
const word32 s_maskLow16[4] = {
    0xffff,0xffff,0xffff,0xffff
};

#undef Mul_Begin
#undef Mul_Acc
#undef Top_Begin
#undef Top_Acc
#undef Squ_Acc
#undef Squ_NonDiag
#undef Squ_Diag
#undef Squ_SaveAcc
#undef Squ_Begin
#undef Mul_SaveAcc
#undef Bot_Acc
#undef Bot_SaveAcc
#undef Bot_End
#undef Squ_End
#undef Mul_End

#define SSE2_FinalSave(k)           \
    AS2(    psllq       xmm5, 16)   \
    AS2(    paddq       xmm4, xmm5) \
    AS2(    movq        QWORD PTR [ecx+8*(k)], xmm4)

#define SSE2_SaveShift(k)           \
    AS2(    movq        xmm0, xmm6) \
    AS2(    punpckhqdq  xmm6, xmm0) \
    AS2(    movq        xmm1, xmm7) \
    AS2(    punpckhqdq  xmm7, xmm1) \
    AS2(    paddd       xmm6, xmm0) \
    AS2(    pslldq      xmm6, 4)    \
    AS2(    paddd       xmm7, xmm1) \
    AS2(    paddd       xmm4, xmm6) \
    AS2(    pslldq      xmm7, 4)    \
    AS2(    movq        xmm6, xmm4) \
    AS2(    paddd       xmm5, xmm7) \
    AS2(    movq        xmm7, xmm5) \
    AS2(    movd        DWORD PTR [ecx+8*(k)], xmm4)    \
    AS2(    psrlq       xmm6, 16)   \
    AS2(    paddq       xmm6, xmm7) \
    AS2(    punpckhqdq  xmm4, xmm0) \
    AS2(    punpckhqdq  xmm5, xmm0) \
    AS2(    movq        QWORD PTR [ecx+8*(k)+2], xmm6)  \
    AS2(    psrlq       xmm6, 3*16) \
    AS2(    paddd       xmm4, xmm6) \

#define Squ_SSE2_SaveShift(k)           \
    AS2(    movq        xmm0, xmm6) \
    AS2(    punpckhqdq  xmm6, xmm0) \
    AS2(    movq        xmm1, xmm7) \
    AS2(    punpckhqdq  xmm7, xmm1) \
    AS2(    paddd       xmm6, xmm0) \
    AS2(    pslldq      xmm6, 4)    \
    AS2(    paddd       xmm7, xmm1) \
    AS2(    paddd       xmm4, xmm6) \
    AS2(    pslldq      xmm7, 4)    \
    AS2(    movhlps     xmm6, xmm4) \
    AS2(    movd        DWORD PTR [ecx+8*(k)], xmm4)    \
    AS2(    paddd       xmm5, xmm7) \
    AS2(    movhps      QWORD PTR [esp+12], xmm5)\
    AS2(    psrlq       xmm4, 16)   \
    AS2(    paddq       xmm4, xmm5) \
    AS2(    movq        QWORD PTR [ecx+8*(k)+2], xmm4)  \
    AS2(    psrlq       xmm4, 3*16) \
    AS2(    paddd       xmm4, xmm6) \
    AS2(    movq        QWORD PTR [esp+4], xmm4)\

#define SSE2_FirstMultiply(i)               \
    AS2(    movdqa      xmm7, [esi+(i)*16])\
    AS2(    movdqa      xmm5, [edi-(i)*16])\
    AS2(    pmuludq     xmm5, xmm7)     \
    AS2(    movdqa      xmm4, [ebx])\
    AS2(    movdqa      xmm6, xmm4)     \
    AS2(    pand        xmm4, xmm5)     \
    AS2(    psrld       xmm5, 16)       \
    AS2(    pmuludq     xmm7, [edx-(i)*16])\
    AS2(    pand        xmm6, xmm7)     \
    AS2(    psrld       xmm7, 16)

#define Squ_Begin(n)                            \
    SquPrologue                                 \
    AS2(    mov     esi, esp)\
    AS2(    and     esp, 0xfffffff0)\
    AS2(    lea     edi, [esp-32*n])\
    AS2(    sub     esp, 32*n+16)\
    AS1(    push    esi)\
    AS2(    mov     esi, edi)                   \
    AS2(    xor     edx, edx)                   \
    ASL(1)                                      \
    ASS(    pshufd  xmm0, [eax+edx], 3,1,2,0)   \
    ASS(    pshufd  xmm1, [eax+edx], 2,0,3,1)   \
    AS2(    movdqa  [edi+2*edx], xmm0)      \
    AS2(    psrlq   xmm0, 32)                   \
    AS2(    movdqa  [edi+2*edx+16], xmm0)   \
    AS2(    movdqa  [edi+16*n+2*edx], xmm1)     \
    AS2(    psrlq   xmm1, 32)                   \
    AS2(    movdqa  [edi+16*n+2*edx+16], xmm1)  \
    AS2(    add     edx, 16)                    \
    AS2(    cmp     edx, 8*(n))                 \
    ASJ(    jne,    1, b)                       \
    AS2(    lea     edx, [edi+16*n])\
    SSE2_FirstMultiply(0)                           \

#define Squ_Acc(i)                              \
    ASL(LSqu##i)                                \
    AS2(    movdqa      xmm1, [esi+(i)*16]) \
    AS2(    movdqa      xmm0, [edi-(i)*16]) \
    AS2(    movdqa      xmm2, [ebx])    \
    AS2(    pmuludq     xmm0, xmm1)             \
    AS2(    pmuludq     xmm1, [edx-(i)*16]) \
    AS2(    movdqa      xmm3, xmm2)         \
    AS2(    pand        xmm2, xmm0)         \
    AS2(    psrld       xmm0, 16)           \
    AS2(    paddd       xmm4, xmm2)         \
    AS2(    paddd       xmm5, xmm0)         \
    AS2(    pand        xmm3, xmm1)         \
    AS2(    psrld       xmm1, 16)           \
    AS2(    paddd       xmm6, xmm3)         \
    AS2(    paddd       xmm7, xmm1)     \

#define Squ_Acc1(i)
#define Squ_Acc2(i)     ASC(call, LSqu##i)
#define Squ_Acc3(i)     Squ_Acc2(i)
#define Squ_Acc4(i)     Squ_Acc2(i)
#define Squ_Acc5(i)     Squ_Acc2(i)
#define Squ_Acc6(i)     Squ_Acc2(i)
#define Squ_Acc7(i)     Squ_Acc2(i)
#define Squ_Acc8(i)     Squ_Acc2(i)

#define SSE2_End(E, n)                  \
    SSE2_SaveShift(2*(n)-3)         \
    AS2(    movdqa      xmm7, [esi+16]) \
    AS2(    movdqa      xmm0, [edi])    \
    AS2(    pmuludq     xmm0, xmm7)             \
    AS2(    movdqa      xmm2, [ebx])        \
    AS2(    pmuludq     xmm7, [edx])    \
    AS2(    movdqa      xmm6, xmm2)             \
    AS2(    pand        xmm2, xmm0)             \
    AS2(    psrld       xmm0, 16)               \
    AS2(    paddd       xmm4, xmm2)             \
    AS2(    paddd       xmm5, xmm0)             \
    AS2(    pand        xmm6, xmm7)             \
    AS2(    psrld       xmm7, 16)   \
    SSE2_SaveShift(2*(n)-2)         \
    SSE2_FinalSave(2*(n)-1)         \
    AS1(    pop     esp)\
    E

#define Squ_End(n)      SSE2_End(SquEpilogue, n)
#define Mul_End(n)      SSE2_End(MulEpilogue, n)
#define Top_End(n)      SSE2_End(TopEpilogue, n)

#define Squ_Column1(k, i)   \
    Squ_SSE2_SaveShift(k)                   \
    AS2(    add         esi, 16)    \
    SSE2_FirstMultiply(1)\
    Squ_Acc##i(i)   \
    AS2(    paddd       xmm4, xmm4)     \
    AS2(    paddd       xmm5, xmm5)     \
    AS2(    movdqa      xmm3, [esi])                \
    AS2(    movq        xmm1, QWORD PTR [esi+8])    \
    AS2(    pmuludq     xmm1, xmm3)     \
    AS2(    pmuludq     xmm3, xmm3)     \
    AS2(    movdqa      xmm0, [ebx])\
    AS2(    movdqa      xmm2, xmm0)     \
    AS2(    pand        xmm0, xmm1)     \
    AS2(    psrld       xmm1, 16)       \
    AS2(    paddd       xmm6, xmm0)     \
    AS2(    paddd       xmm7, xmm1)     \
    AS2(    pand        xmm2, xmm3)     \
    AS2(    psrld       xmm3, 16)       \
    AS2(    paddd       xmm6, xmm6)     \
    AS2(    paddd       xmm7, xmm7)     \
    AS2(    paddd       xmm4, xmm2)     \
    AS2(    paddd       xmm5, xmm3)     \
    AS2(    movq        xmm0, QWORD PTR [esp+4])\
    AS2(    movq        xmm1, QWORD PTR [esp+12])\
    AS2(    paddd       xmm4, xmm0)\
    AS2(    paddd       xmm5, xmm1)\

#define Squ_Column0(k, i)   \
    Squ_SSE2_SaveShift(k)                   \
    AS2(    add         edi, 16)    \
    AS2(    add         edx, 16)    \
    SSE2_FirstMultiply(1)\
    Squ_Acc##i(i)   \
    AS2(    paddd       xmm6, xmm6)     \
    AS2(    paddd       xmm7, xmm7)     \
    AS2(    paddd       xmm4, xmm4)     \
    AS2(    paddd       xmm5, xmm5)     \
    AS2(    movq        xmm0, QWORD PTR [esp+4])\
    AS2(    movq        xmm1, QWORD PTR [esp+12])\
    AS2(    paddd       xmm4, xmm0)\
    AS2(    paddd       xmm5, xmm1)\

#define SSE2_MulAdd45                       \
    AS2(    movdqa      xmm7, [esi])    \
    AS2(    movdqa      xmm0, [edi])    \
    AS2(    pmuludq     xmm0, xmm7)             \
    AS2(    movdqa      xmm2, [ebx])        \
    AS2(    pmuludq     xmm7, [edx])    \
    AS2(    movdqa      xmm6, xmm2)             \
    AS2(    pand        xmm2, xmm0)             \
    AS2(    psrld       xmm0, 16)               \
    AS2(    paddd       xmm4, xmm2)             \
    AS2(    paddd       xmm5, xmm0)             \
    AS2(    pand        xmm6, xmm7)             \
    AS2(    psrld       xmm7, 16)

#define Mul_Begin(n)                            \
    MulPrologue                                 \
    AS2(    mov     esi, esp)\
    AS2(    and     esp, 0xfffffff0)\
    AS2(    sub     esp, 48*n+16)\
    AS1(    push    esi)\
    AS2(    xor     edx, edx)                   \
    ASL(1)                                      \
    ASS(    pshufd  xmm0, [eax+edx], 3,1,2,0)   \
    ASS(    pshufd  xmm1, [eax+edx], 2,0,3,1)   \
    ASS(    pshufd  xmm2, [edi+edx], 3,1,2,0)   \
    AS2(    movdqa  [esp+20+2*edx], xmm0)       \
    AS2(    psrlq   xmm0, 32)                   \
    AS2(    movdqa  [esp+20+2*edx+16], xmm0)    \
    AS2(    movdqa  [esp+20+16*n+2*edx], xmm1)      \
    AS2(    psrlq   xmm1, 32)                   \
    AS2(    movdqa  [esp+20+16*n+2*edx+16], xmm1)   \
    AS2(    movdqa  [esp+20+32*n+2*edx], xmm2)      \
    AS2(    psrlq   xmm2, 32)                   \
    AS2(    movdqa  [esp+20+32*n+2*edx+16], xmm2)   \
    AS2(    add     edx, 16)                    \
    AS2(    cmp     edx, 8*(n))                 \
    ASJ(    jne,    1, b)                       \
    AS2(    lea     edi, [esp+20])\
    AS2(    lea     edx, [esp+20+16*n])\
    AS2(    lea     esi, [esp+20+32*n])\
    SSE2_FirstMultiply(0)                           \

#define Mul_Acc(i)                              \
    ASL(LMul##i)                                        \
    AS2(    movdqa      xmm1, [esi+i/2*(1-(i-2*(i/2))*2)*16])   \
    AS2(    movdqa      xmm0, [edi-i/2*(1-(i-2*(i/2))*2)*16])   \
    AS2(    movdqa      xmm2, [ebx])    \
    AS2(    pmuludq     xmm0, xmm1)             \
    AS2(    pmuludq     xmm1, [edx-i/2*(1-(i-2*(i/2))*2)*16])   \
    AS2(    movdqa      xmm3, xmm2)         \
    AS2(    pand        xmm2, xmm0)         \
    AS2(    psrld       xmm0, 16)           \
    AS2(    paddd       xmm4, xmm2)         \
    AS2(    paddd       xmm5, xmm0)         \
    AS2(    pand        xmm3, xmm1)         \
    AS2(    psrld       xmm1, 16)           \
    AS2(    paddd       xmm6, xmm3)         \
    AS2(    paddd       xmm7, xmm1)     \

#define Mul_Acc1(i)
#define Mul_Acc2(i)     ASC(call, LMul##i)
#define Mul_Acc3(i)     Mul_Acc2(i)
#define Mul_Acc4(i)     Mul_Acc2(i)
#define Mul_Acc5(i)     Mul_Acc2(i)
#define Mul_Acc6(i)     Mul_Acc2(i)
#define Mul_Acc7(i)     Mul_Acc2(i)
#define Mul_Acc8(i)     Mul_Acc2(i)
#define Mul_Acc9(i)     Mul_Acc2(i)
#define Mul_Acc10(i)    Mul_Acc2(i)
#define Mul_Acc11(i)    Mul_Acc2(i)
#define Mul_Acc12(i)    Mul_Acc2(i)
#define Mul_Acc13(i)    Mul_Acc2(i)
#define Mul_Acc14(i)    Mul_Acc2(i)
#define Mul_Acc15(i)    Mul_Acc2(i)
#define Mul_Acc16(i)    Mul_Acc2(i)

#define Mul_Column1(k, i)   \
    SSE2_SaveShift(k)                   \
    AS2(    add         esi, 16)    \
    SSE2_MulAdd45\
    Mul_Acc##i(i)   \

#define Mul_Column0(k, i)   \
    SSE2_SaveShift(k)                   \
    AS2(    add         edi, 16)    \
    AS2(    add         edx, 16)    \
    SSE2_MulAdd45\
    Mul_Acc##i(i)   \

#define Bot_Acc(i)                          \
    AS2(    movdqa      xmm1, [esi+i/2*(1-(i-2*(i/2))*2)*16])   \
    AS2(    movdqa      xmm0, [edi-i/2*(1-(i-2*(i/2))*2)*16])   \
    AS2(    pmuludq     xmm0, xmm1)             \
    AS2(    pmuludq     xmm1, [edx-i/2*(1-(i-2*(i/2))*2)*16])       \
    AS2(    paddq       xmm4, xmm0)             \
    AS2(    paddd       xmm6, xmm1)

#define Bot_SaveAcc(k)                  \
    SSE2_SaveShift(k)                           \
    AS2(    add         edi, 16)    \
    AS2(    add         edx, 16)    \
    AS2(    movdqa      xmm6, [esi])    \
    AS2(    movdqa      xmm0, [edi])    \
    AS2(    pmuludq     xmm0, xmm6)             \
    AS2(    paddq       xmm4, xmm0)             \
    AS2(    psllq       xmm5, 16)               \
    AS2(    paddq       xmm4, xmm5)             \
    AS2(    pmuludq     xmm6, [edx])

#define Bot_End(n)                          \
    AS2(    movhlps     xmm7, xmm6)         \
    AS2(    paddd       xmm6, xmm7)         \
    AS2(    psllq       xmm6, 32)           \
    AS2(    paddd       xmm4, xmm6)         \
    AS2(    movq        QWORD PTR [ecx+8*((n)-1)], xmm4)    \
    AS1(    pop     esp)\
    MulEpilogue

#define Top_Begin(n)                            \
    TopPrologue                                 \
    AS2(    mov     edx, esp)\
    AS2(    and     esp, 0xfffffff0)\
    AS2(    sub     esp, 48*n+16)\
    AS1(    push    edx)\
    AS2(    xor     edx, edx)                   \
    ASL(1)                                      \
    ASS(    pshufd  xmm0, [eax+edx], 3,1,2,0)   \
    ASS(    pshufd  xmm1, [eax+edx], 2,0,3,1)   \
    ASS(    pshufd  xmm2, [edi+edx], 3,1,2,0)   \
    AS2(    movdqa  [esp+20+2*edx], xmm0)       \
    AS2(    psrlq   xmm0, 32)                   \
    AS2(    movdqa  [esp+20+2*edx+16], xmm0)    \
    AS2(    movdqa  [esp+20+16*n+2*edx], xmm1)      \
    AS2(    psrlq   xmm1, 32)                   \
    AS2(    movdqa  [esp+20+16*n+2*edx+16], xmm1)   \
    AS2(    movdqa  [esp+20+32*n+2*edx], xmm2)      \
    AS2(    psrlq   xmm2, 32)                   \
    AS2(    movdqa  [esp+20+32*n+2*edx+16], xmm2)   \
    AS2(    add     edx, 16)                    \
    AS2(    cmp     edx, 8*(n))                 \
    ASJ(    jne,    1, b)                       \
    AS2(    mov     eax, esi)                   \
    AS2(    lea     edi, [esp+20+00*n+16*(n/2-1)])\
    AS2(    lea     edx, [esp+20+16*n+16*(n/2-1)])\
    AS2(    lea     esi, [esp+20+32*n+16*(n/2-1)])\
    AS2(    pxor    xmm4, xmm4)\
    AS2(    pxor    xmm5, xmm5)

#define Top_Acc(i)                          \
    AS2(    movq        xmm0, QWORD PTR [esi+i/2*(1-(i-2*(i/2))*2)*16+8])   \
    AS2(    pmuludq     xmm0, [edx-i/2*(1-(i-2*(i/2))*2)*16])   \
    AS2(    psrlq       xmm0, 48)               \
    AS2(    paddd       xmm5, xmm0)\

#define Top_Column0(i)  \
    AS2(    psllq       xmm5, 32)               \
    AS2(    add         edi, 16)    \
    AS2(    add         edx, 16)    \
    SSE2_MulAdd45\
    Mul_Acc##i(i)   \

#define Top_Column1(i)  \
    SSE2_SaveShift(0)                   \
    AS2(    add         esi, 16)    \
    SSE2_MulAdd45\
    Mul_Acc##i(i)   \
    AS2(    shr         eax, 16)    \
    AS2(    movd        xmm0, eax)\
    AS2(    movd        xmm1, [ecx+4])\
    AS2(    psrld       xmm1, 16)\
    AS2(    pcmpgtd     xmm1, xmm0)\
    AS2(    psrld       xmm1, 31)\
    AS2(    paddd       xmm4, xmm1)\

void SSE2_Square4(word *C, const word *A)
{
    Squ_Begin(2)
    Squ_Column0(0, 1)
    Squ_End(2)
}

void SSE2_Square8(word *C, const word *A)
{
    Squ_Begin(4)
#ifndef __GNUC__
    ASJ(    jmp,    0, f)
    Squ_Acc(2)
    AS1(    ret) ASL(0)
#endif
    Squ_Column0(0, 1)
    Squ_Column1(1, 1)
    Squ_Column0(2, 2)
    Squ_Column1(3, 1)
    Squ_Column0(4, 1)
    Squ_End(4)
}

void SSE2_Square16(word *C, const word *A)
{
    Squ_Begin(8)
#ifndef __GNUC__
    ASJ(    jmp,    0, f)
    Squ_Acc(4) Squ_Acc(3) Squ_Acc(2)
    AS1(    ret) ASL(0)
#endif
    Squ_Column0(0, 1)
    Squ_Column1(1, 1)
    Squ_Column0(2, 2)
    Squ_Column1(3, 2)
    Squ_Column0(4, 3)
    Squ_Column1(5, 3)
    Squ_Column0(6, 4)
    Squ_Column1(7, 3)
    Squ_Column0(8, 3)
    Squ_Column1(9, 2)
    Squ_Column0(10, 2)
    Squ_Column1(11, 1)
    Squ_Column0(12, 1)
    Squ_End(8)
}

void SSE2_Square32(word *C, const word *A)
{
    Squ_Begin(16)
    ASJ(    jmp,    0, f)
    Squ_Acc(8) Squ_Acc(7) Squ_Acc(6) Squ_Acc(5) Squ_Acc(4) Squ_Acc(3) Squ_Acc(2)
    AS1(    ret) ASL(0)
    Squ_Column0(0, 1)
    Squ_Column1(1, 1)
    Squ_Column0(2, 2)
    Squ_Column1(3, 2)
    Squ_Column0(4, 3)
    Squ_Column1(5, 3)
    Squ_Column0(6, 4)
    Squ_Column1(7, 4)
    Squ_Column0(8, 5)
    Squ_Column1(9, 5)
    Squ_Column0(10, 6)
    Squ_Column1(11, 6)
    Squ_Column0(12, 7)
    Squ_Column1(13, 7)
    Squ_Column0(14, 8)
    Squ_Column1(15, 7)
    Squ_Column0(16, 7)
    Squ_Column1(17, 6)
    Squ_Column0(18, 6)
    Squ_Column1(19, 5)
    Squ_Column0(20, 5)
    Squ_Column1(21, 4)
    Squ_Column0(22, 4)
    Squ_Column1(23, 3)
    Squ_Column0(24, 3)
    Squ_Column1(25, 2)
    Squ_Column0(26, 2)
    Squ_Column1(27, 1)
    Squ_Column0(28, 1)
    Squ_End(16)
}

void SSE2_Multiply4(word *C, const word *A, const word *B)
{
    Mul_Begin(2)
#ifndef __GNUC__
    ASJ(    jmp,    0, f)
    Mul_Acc(2)
    AS1(    ret) ASL(0)
#endif
    Mul_Column0(0, 2)
    Mul_End(2)
}

void SSE2_Multiply8(word *C, const word *A, const word *B)
{
    Mul_Begin(4)
#ifndef __GNUC__
    ASJ(    jmp,    0, f)
    Mul_Acc(4) Mul_Acc(3) Mul_Acc(2)
    AS1(    ret) ASL(0)
#endif
    Mul_Column0(0, 2)
    Mul_Column1(1, 3)
    Mul_Column0(2, 4)
    Mul_Column1(3, 3)
    Mul_Column0(4, 2)
    Mul_End(4)
}

void SSE2_Multiply16(word *C, const word *A, const word *B)
{
    Mul_Begin(8)
#ifndef __GNUC__
    ASJ(    jmp,    0, f)
    Mul_Acc(8) Mul_Acc(7) Mul_Acc(6) Mul_Acc(5) Mul_Acc(4) Mul_Acc(3) Mul_Acc(2)
    AS1(    ret) ASL(0)
#endif
    Mul_Column0(0, 2)
    Mul_Column1(1, 3)
    Mul_Column0(2, 4)
    Mul_Column1(3, 5)
    Mul_Column0(4, 6)
    Mul_Column1(5, 7)
    Mul_Column0(6, 8)
    Mul_Column1(7, 7)
    Mul_Column0(8, 6)
    Mul_Column1(9, 5)
    Mul_Column0(10, 4)
    Mul_Column1(11, 3)
    Mul_Column0(12, 2)
    Mul_End(8)
}

void SSE2_Multiply32(word *C, const word *A, const word *B)
{
    Mul_Begin(16)
    ASJ(    jmp,    0, f)
    Mul_Acc(16) Mul_Acc(15) Mul_Acc(14) Mul_Acc(13) Mul_Acc(12) Mul_Acc(11) Mul_Acc(10) Mul_Acc(9) Mul_Acc(8) Mul_Acc(7) Mul_Acc(6) Mul_Acc(5) Mul_Acc(4) Mul_Acc(3) Mul_Acc(2)
    AS1(    ret) ASL(0)
    Mul_Column0(0, 2)
    Mul_Column1(1, 3)
    Mul_Column0(2, 4)
    Mul_Column1(3, 5)
    Mul_Column0(4, 6)
    Mul_Column1(5, 7)
    Mul_Column0(6, 8)
    Mul_Column1(7, 9)
    Mul_Column0(8, 10)
    Mul_Column1(9, 11)
    Mul_Column0(10, 12)
    Mul_Column1(11, 13)
    Mul_Column0(12, 14)
    Mul_Column1(13, 15)
    Mul_Column0(14, 16)
    Mul_Column1(15, 15)
    Mul_Column0(16, 14)
    Mul_Column1(17, 13)
    Mul_Column0(18, 12)
    Mul_Column1(19, 11)
    Mul_Column0(20, 10)
    Mul_Column1(21, 9)
    Mul_Column0(22, 8)
    Mul_Column1(23, 7)
    Mul_Column0(24, 6)
    Mul_Column1(25, 5)
    Mul_Column0(26, 4)
    Mul_Column1(27, 3)
    Mul_Column0(28, 2)
    Mul_End(16)
}

void SSE2_MultiplyBottom4(word *C, const word *A, const word *B)
{
    Mul_Begin(2)
    Bot_SaveAcc(0) Bot_Acc(2)
    Bot_End(2)
}

void SSE2_MultiplyBottom8(word *C, const word *A, const word *B)
{
    Mul_Begin(4)
#ifndef __GNUC__
    ASJ(    jmp,    0, f)
    Mul_Acc(3) Mul_Acc(2)
    AS1(    ret) ASL(0)
#endif
    Mul_Column0(0, 2)
    Mul_Column1(1, 3)
    Bot_SaveAcc(2) Bot_Acc(4) Bot_Acc(3) Bot_Acc(2)
    Bot_End(4)
}

void SSE2_MultiplyBottom16(word *C, const word *A, const word *B)
{
    Mul_Begin(8)
#ifndef __GNUC__
    ASJ(    jmp,    0, f)
    Mul_Acc(7) Mul_Acc(6) Mul_Acc(5) Mul_Acc(4) Mul_Acc(3) Mul_Acc(2)
    AS1(    ret) ASL(0)
#endif
    Mul_Column0(0, 2)
    Mul_Column1(1, 3)
    Mul_Column0(2, 4)
    Mul_Column1(3, 5)
    Mul_Column0(4, 6)
    Mul_Column1(5, 7)
    Bot_SaveAcc(6) Bot_Acc(8) Bot_Acc(7) Bot_Acc(6) Bot_Acc(5) Bot_Acc(4) Bot_Acc(3) Bot_Acc(2)
    Bot_End(8)
}

void SSE2_MultiplyBottom32(word *C, const word *A, const word *B)
{
    Mul_Begin(16)
#ifndef __GNUC__
    ASJ(    jmp,    0, f)
    Mul_Acc(15) Mul_Acc(14) Mul_Acc(13) Mul_Acc(12) Mul_Acc(11) Mul_Acc(10) Mul_Acc(9) Mul_Acc(8) Mul_Acc(7) Mul_Acc(6) Mul_Acc(5) Mul_Acc(4) Mul_Acc(3) Mul_Acc(2)
    AS1(    ret) ASL(0)
#endif
    Mul_Column0(0, 2)
    Mul_Column1(1, 3)
    Mul_Column0(2, 4)
    Mul_Column1(3, 5)
    Mul_Column0(4, 6)
    Mul_Column1(5, 7)
    Mul_Column0(6, 8)
    Mul_Column1(7, 9)
    Mul_Column0(8, 10)
    Mul_Column1(9, 11)
    Mul_Column0(10, 12)
    Mul_Column1(11, 13)
    Mul_Column0(12, 14)
    Mul_Column1(13, 15)
    Bot_SaveAcc(14) Bot_Acc(16) Bot_Acc(15) Bot_Acc(14) Bot_Acc(13) Bot_Acc(12) Bot_Acc(11) Bot_Acc(10) Bot_Acc(9) Bot_Acc(8) Bot_Acc(7) Bot_Acc(6) Bot_Acc(5) Bot_Acc(4) Bot_Acc(3) Bot_Acc(2)
    Bot_End(16)
}

void SSE2_MultiplyTop8(word *C, const word *A, const word *B, word L)
{
    Top_Begin(4)
    Top_Acc(3) Top_Acc(2) Top_Acc(1)
#ifndef __GNUC__
    ASJ(    jmp,    0, f)
    Mul_Acc(4) Mul_Acc(3) Mul_Acc(2)
    AS1(    ret) ASL(0)
#endif
    Top_Column0(4)
    Top_Column1(3)
    Mul_Column0(0, 2)
    Top_End(2)
}

void SSE2_MultiplyTop16(word *C, const word *A, const word *B, word L)
{
    Top_Begin(8)
    Top_Acc(7) Top_Acc(6) Top_Acc(5) Top_Acc(4) Top_Acc(3) Top_Acc(2) Top_Acc(1)
#ifndef __GNUC__
    ASJ(    jmp,    0, f)
    Mul_Acc(8) Mul_Acc(7) Mul_Acc(6) Mul_Acc(5) Mul_Acc(4) Mul_Acc(3) Mul_Acc(2)
    AS1(    ret) ASL(0)
#endif
    Top_Column0(8)
    Top_Column1(7)
    Mul_Column0(0, 6)
    Mul_Column1(1, 5)
    Mul_Column0(2, 4)
    Mul_Column1(3, 3)
    Mul_Column0(4, 2)
    Top_End(4)
}

void SSE2_MultiplyTop32(word *C, const word *A, const word *B, word L)
{
    Top_Begin(16)
    Top_Acc(15) Top_Acc(14) Top_Acc(13) Top_Acc(12) Top_Acc(11) Top_Acc(10) Top_Acc(9) Top_Acc(8) Top_Acc(7) Top_Acc(6) Top_Acc(5) Top_Acc(4) Top_Acc(3) Top_Acc(2) Top_Acc(1)
#ifndef __GNUC__
    ASJ(    jmp,    0, f)
    Mul_Acc(16) Mul_Acc(15) Mul_Acc(14) Mul_Acc(13) Mul_Acc(12) Mul_Acc(11) Mul_Acc(10) Mul_Acc(9) Mul_Acc(8) Mul_Acc(7) Mul_Acc(6) Mul_Acc(5) Mul_Acc(4) Mul_Acc(3) Mul_Acc(2)
    AS1(    ret) ASL(0)
#endif
    Top_Column0(16)
    Top_Column1(15)
    Mul_Column0(0, 14)
    Mul_Column1(1, 13)
    Mul_Column0(2, 12)
    Mul_Column1(3, 11)
    Mul_Column0(4, 10)
    Mul_Column1(5, 9)
    Mul_Column0(6, 8)
    Mul_Column1(7, 7)
    Mul_Column0(8, 6)
    Mul_Column1(9, 5)
    Mul_Column0(10, 4)
    Mul_Column1(11, 3)
    Mul_Column0(12, 2)
    Top_End(8)
}

#endif  // #if CRYPTOPP_INTEGER_SSE2

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

typedef int (CRYPTOPP_FASTCALL * PAdd)(size_t N, word *C, const word *A, const word *B);
typedef void (* PMul)(word *C, const word *A, const word *B);
typedef void (* PSqu)(word *C, const word *A);
typedef void (* PMulTop)(word *C, const word *A, const word *B, word L);

#if CRYPTOPP_INTEGER_SSE2
static PAdd s_pAdd = &Baseline_Add, s_pSub = &Baseline_Sub;
static size_t s_recursionLimit = 8;
#else
static const size_t s_recursionLimit = 16;
#endif  // CRYPTOPP_INTEGER_SSE2

static PMul s_pMul[9], s_pBot[9];
static PSqu s_pSqu[9];
static PMulTop s_pTop[9];

void SetFunctionPointers()
{
    s_pMul[0] = &Baseline_Multiply2;
    s_pBot[0] = &Baseline_MultiplyBottom2;
    s_pSqu[0] = &Baseline_Square2;
    s_pTop[0] = &Baseline_MultiplyTop2;
    s_pTop[1] = &Baseline_MultiplyTop4;

#if CRYPTOPP_INTEGER_SSE2
    if (HasSSE2())
    {
        if (IsP4())
        {
            s_pAdd = &SSE2_Add;
            s_pSub = &SSE2_Sub;
        }

        s_recursionLimit = 32;

        s_pMul[1] = &SSE2_Multiply4;
        s_pMul[2] = &SSE2_Multiply8;
        s_pMul[4] = &SSE2_Multiply16;
        s_pMul[8] = &SSE2_Multiply32;

        s_pBot[1] = &SSE2_MultiplyBottom4;
        s_pBot[2] = &SSE2_MultiplyBottom8;
        s_pBot[4] = &SSE2_MultiplyBottom16;
        s_pBot[8] = &SSE2_MultiplyBottom32;

        s_pSqu[1] = &SSE2_Square4;
        s_pSqu[2] = &SSE2_Square8;
        s_pSqu[4] = &SSE2_Square16;
        s_pSqu[8] = &SSE2_Square32;

        s_pTop[2] = &SSE2_MultiplyTop8;
        s_pTop[4] = &SSE2_MultiplyTop16;
        s_pTop[8] = &SSE2_MultiplyTop32;
    }
    else
#endif  // CRYPTOPP_INTEGER_SSE2
    {
        s_pMul[1] = &Baseline_Multiply4;
        s_pMul[2] = &Baseline_Multiply8;

        s_pBot[1] = &Baseline_MultiplyBottom4;
        s_pBot[2] = &Baseline_MultiplyBottom8;

        s_pSqu[1] = &Baseline_Square4;
        s_pSqu[2] = &Baseline_Square8;

        s_pTop[2] = &Baseline_MultiplyTop8;

#if !CRYPTOPP_INTEGER_SSE2
        s_pMul[4] = &Baseline_Multiply16;
        s_pBot[4] = &Baseline_MultiplyBottom16;
        s_pSqu[4] = &Baseline_Square16;
        s_pTop[4] = &Baseline_MultiplyTop16;
#endif  // !CRYPTOPP_INTEGER_SSE2
    }
}

inline int Add(word *C, const word *A, const word *B, size_t N)
{
#if CRYPTOPP_INTEGER_SSE2
    return s_pAdd(N, C, A, B);
#else
    return Baseline_Add(N, C, A, B);
#endif  // CRYPTOPP_INTEGER_SSE2
}

inline int Subtract(word *C, const word *A, const word *B, size_t N)
{
#if CRYPTOPP_INTEGER_SSE2
    return s_pSub(N, C, A, B);
#else
    return Baseline_Sub(N, C, A, B);
#endif  // CRYPTOPP_INTEGER_SSE2
}

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


#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, size_t N)
{
    CRYPTOPP_ASSERT(N>=2 && N%2==0);

    if (N <= s_recursionLimit)
        s_pMul[N/4](R, A, B);
    else
    {
        const size_t N2 = N/2;

        size_t AN2 = Compare(A0, A1, N2) > 0 ?  0 : N2;
        Subtract(R0, A + AN2, A + (N2 ^ AN2), N2);

        size_t BN2 = Compare(B0, B1, N2) > 0 ?  0 : N2;
        Subtract(R1, B + BN2, B + (N2 ^ BN2), N2);

        RecursiveMultiply(R2, T2, A1, B1, N2);
        RecursiveMultiply(T0, T2, R0, R1, N2);
        RecursiveMultiply(R0, T2, A0, B0, N2);

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

        int c2 = Add(R2, R2, R1, N2);
        int c3 = c2;
        c2 += Add(R1, R2, R0, N2);
        c3 += Add(R2, R2, R3, N2);

        if (AN2 == BN2)
            c3 -= Subtract(R1, R1, T0, N);
        else
            c3 += Add(R1, R1, T0, N);

        c3 += Increment(R2, N2, c2);
        CRYPTOPP_ASSERT (c3 >= 0 && c3 <= 2);
        Increment(R3, N2, c3);
    }
}

// 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, size_t N)
{
    CRYPTOPP_ASSERT(N && N%2==0);

    if (N <= s_recursionLimit)
        s_pSqu[N/4](R, A);
    else
    {
        const size_t N2 = N/2;

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

        int carry = Add(R1, R1, T0, N);
        carry += Add(R1, R1, T0, N);
        Increment(R3, N2, carry);
    }
}

// R[N] - bottom half of A*B
// T[3*N/2] - temporary work space
// A[N] - multiplier
// B[N] - multiplicant

void RecursiveMultiplyBottom(word *R, word *T, const word *A, const word *B, size_t N)
{
    CRYPTOPP_ASSERT(N>=2 && N%2==0);

    if (N <= s_recursionLimit)
        s_pBot[N/4](R, A, B);
    else
    {
        const size_t N2 = N/2;

        RecursiveMultiply(R, T, A0, B0, N2);
        RecursiveMultiplyBottom(T0, T1, A1, B0, N2);
        Add(R1, R1, T0, N2);
        RecursiveMultiplyBottom(T0, T1, A0, B1, N2);
        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 MultiplyTop(word *R, word *T, const word *L, const word *A, const word *B, size_t N)
{
    CRYPTOPP_ASSERT(N>=2 && N%2==0);

    if (N <= s_recursionLimit)
        s_pTop[N/4](R, A, B, L[N-1]);
    else
    {
        const size_t N2 = N/2;

        size_t AN2 = Compare(A0, A1, N2) > 0 ?  0 : N2;
        Subtract(R0, A + AN2, A + (N2 ^ AN2), N2);

        size_t BN2 = Compare(B0, B1, N2) > 0 ?  0 : N2;
        Subtract(R1, B + BN2, B + (N2 ^ BN2), N2);

        RecursiveMultiply(T0, T2, R0, R1, N2);
        RecursiveMultiply(R0, T2, A1, B1, N2);

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

        int t, c3;
        int c2 = Subtract(T2, L+N2, L, N2);

        if (AN2 == BN2)
        {
            c2 -= Add(T2, T2, T0, N2);
            t = (Compare(T2, R0, N2) == -1);
            c3 = t - Subtract(T2, T2, T1, N2);
        }
        else
        {
            c2 += Subtract(T2, T2, T0, N2);
            t = (Compare(T2, R0, N2) == -1);
            c3 = t + Add(T2, T2, T1, N2);
        }

        c2 += t;
        if (c2 >= 0)
            c3 += Increment(T2, N2, c2);
        else
            c3 -= Decrement(T2, N2, -c2);
        c3 += Add(R0, T2, R1, N2);

        CRYPTOPP_ASSERT (c3 >= 0 && c3 <= 2);
        Increment(R1, N2, c3);
    }
}

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

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

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

// 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, size_t NA, const word *B, size_t NB)
{
    if (NA == NB)
    {
        // Profiling tells us the original second case was dominant, so it was promoted to the first If statement.
        // The code change occurred at Commit dc99266599a0e72d.
        if (A != B)
            Multiply(R, T, A, B, NA);
        else
            Square(R, T, A, NA);

        return;
    }

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

    CRYPTOPP_ASSERT(NB % NA == 0);

    if (NA==2 && !A[1])
    {
        // Profiling tells us the original Default case was dominant, so it was promoted to the first Case statement.
        // The code change occurred at Commit dc99266599a0e72d.
        switch (A[0])
        {
        default:
            R[NB] = LinearMultiply(R, B, A[0], NB);
            R[NB+1] = 0;
            return;
        case 0:
            SetWords(R, 0, NB+2);
            return;
        case 1:
            CopyWords(R, B, NB);
            R[NB] = R[NB+1] = 0;
            return;
        }
    }

    size_t i;
    if ((NB/NA)%2 == 0)
    {
        Multiply(R, T, A, B, NA);
        CopyWords(T+2*NA, R+NA, NA);

        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);
    }
    else
    {
        for (i=0; i<NB; i+=2*NA)
            Multiply(R+i, T, A, B+i, NA);
        for (i=NA; i<NB; i+=2*NA)
            Multiply(T+NA+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, size_t N)
{
    // Profiling tells us the original Else was dominant, so it was promoted to the first If statement.
    // The code change occurred at Commit dc99266599a0e72d.
    if (N!=2)
    {
        const size_t 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);
    }
    else
    {
        T[0] = AtomicInverseModPower2(A[0]);
        T[1] = 0;
        s_pBot[0](T+2, T, A);
        TwosComplement(T+2, 2);
        Increment(T+2, 2, 2);
        s_pBot[0](R, T, T+2);
    }
}

// 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, word *X, const word *M, const word *U, size_t N)
{
#if 1
    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);
    CRYPTOPP_ASSERT(carry | !borrow);
    CRYPTOPP_UNUSED(carry), CRYPTOPP_UNUSED(borrow);
    CopyWords(R, T + ((0-borrow) & N), N);
#elif 0
    const word u = 0-U[0];
    Declare2Words(p)
    for (size_t i=0; i<N; i++)
    {
        const word t = u * X[i];
        word c = 0;
        for (size_t j=0; j<N; j+=2)
        {
            MultiplyWords(p, t, M[j]);
            Acc2WordsBy1(p, X[i+j]);
            Acc2WordsBy1(p, c);
            X[i+j] = LowWord(p);
            c = HighWord(p);
            MultiplyWords(p, t, M[j+1]);
            Acc2WordsBy1(p, X[i+j+1]);
            Acc2WordsBy1(p, c);
            X[i+j+1] = LowWord(p);
            c = HighWord(p);
        }

        if (Increment(X+N+i, N-i, c))
            while (!Subtract(X+N, X+N, M, N)) {}
    }

    memcpy(R, X+N, N*WORD_SIZE);
#else
    __m64 u = _mm_cvtsi32_si64(0-U[0]), p;
    for (size_t i=0; i<N; i++)
    {
        __m64 t = _mm_cvtsi32_si64(X[i]);
        t = _mm_mul_su32(t, u);
        __m64 c = _mm_setzero_si64();
        for (size_t j=0; j<N; j+=2)
        {
            p = _mm_mul_su32(t, _mm_cvtsi32_si64(M[j]));
            p = _mm_add_si64(p, _mm_cvtsi32_si64(X[i+j]));
            c = _mm_add_si64(c, p);
            X[i+j] = _mm_cvtsi64_si32(c);
            c = _mm_srli_si64(c, 32);
            p = _mm_mul_su32(t, _mm_cvtsi32_si64(M[j+1]));
            p = _mm_add_si64(p, _mm_cvtsi32_si64(X[i+j+1]));
            c = _mm_add_si64(c, p);
            X[i+j+1] = _mm_cvtsi64_si32(c);
            c = _mm_srli_si64(c, 32);
        }

        if (Increment(X+N+i, N-i, _mm_cvtsi64_si32(c)))
            while (!Subtract(X+N, X+N, M, N)) {}
    }

    memcpy(R, X+N, N*WORD_SIZE);
    _mm_empty();
#endif
}

// 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, size_t N)
{
    CRYPTOPP_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 size_t 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);

    CRYPTOPP_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
    CRYPTOPP_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++;
        CRYPTOPP_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]);

#if defined(CRYPTOPP_DEBUG)
        // multiply quotient and divisor and add remainder, make sure it equals dividend
        CRYPTOPP_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);
        CRYPTOPP_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();

#if defined(CRYPTOPP_DEBUG)
    if (B[0] || B[1])
    {
        // multiply quotient and divisor and add remainder, make sure it equals dividend
        CRYPTOPP_ASSERT(!T[2] && !T[3] && (T[1] < B[1] || (T[1]==B[1] && T[0]<B[0])));
        word P[4];
        s_pMul[0](P, Q, B);
        Add(P, P, T, 4);
        CRYPTOPP_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, size_t N)
{
    CRYPTOPP_ASSERT(N && N%2==0);

    AsymmetricMultiply(T, T+N+2, Q, 2, B, N);

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

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

// R[NB] -------- remainder = A%B
// Q[NA-NB+2] --- quotient  = A/B
// T[NA+3*(NB+2)] - temp work space
// A[NA] -------- dividend
// B[NB] -------- divisor

void Divide(word *R, word *Q, word *T, const word *A, size_t NA, const word *B, size_t NB)
{
    CRYPTOPP_ASSERT(NA && NB && NA%2==0 && NB%2==0);
    CRYPTOPP_ASSERT(B[NB-1] || B[NB-2]);
    CRYPTOPP_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]);
    CRYPTOPP_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;
        CRYPTOPP_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 (size_t 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 size_t EvenWordCount(const word *X, size_t 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, size_t NA, const word *M, size_t N)
{
    CRYPTOPP_ASSERT(NA<=N && N && N%2==0);

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

    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);
            bcLen += 2 * (c[bcLen-1] != 0);
            CRYPTOPP_ASSERT(bcLen <= N);
            ShiftWordsLeftByWords(c, bcLen, 1);
            k+=WORD_BITS;
            t=f[0];
        }

        // t must be non-0; otherwise undefined.
        unsigned int i = TrailingZeros(t);
        t >>= i;
        k += i;

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

        ShiftWordsRightByBits(f, fgLen, i);
        t = ShiftWordsLeftByBits(c, bcLen, i);
        c[bcLen] += t;
        bcLen += 2 * (t!=0);
        CRYPTOPP_ASSERT(bcLen <= N);

        bool swap = Compare(f, g, fgLen)==-1;
        ConditionalSwapPointers(swap, f, g);
        ConditionalSwapPointers(swap, b, c);
        s ^= swap;

        fgLen -= 2 * !(f[fgLen-2] | f[fgLen-1]);

        Subtract(f, f, g, fgLen);
        t = Add(b, b, c, bcLen);
        b[bcLen] += t;
        bcLen += 2*t;
        CRYPTOPP_ASSERT(bcLen <= N);
    }
}

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

void DivideByPower2Mod(word *R, const word *A, size_t k, const word *M, size_t 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, size_t k, const word *M, size_t 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 size_t RoundupSize(size_t 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 size_t(1) << 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 = (unsigned long)reg[0];
    value += SafeLeftShift<WORD_BITS, unsigned long>((unsigned long)reg[1]);

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

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

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

Integer::Integer(BufferedTransformation &encodedInteger, size_t byteCount, Signedness s, ByteOrder o)
{
    CRYPTOPP_ASSERT(o == BIG_ENDIAN_ORDER || o == LITTLE_ENDIAN_ORDER);

    if (o != LITTLE_ENDIAN_ORDER)
    {
        Decode(encodedInteger, byteCount, s);
    }
    else
    {
        SecByteBlock block(byteCount);
        encodedInteger.Get(block, block.size());
        std::reverse(block.begin(), block.begin()+block.size());

        Decode(block.begin(), block.size(), s);
    }
}

Integer::Integer(const byte *encodedInteger, size_t byteCount, Signedness s, ByteOrder o)
{
    CRYPTOPP_ASSERT(encodedInteger && byteCount); // NULL buffer
    CRYPTOPP_ASSERT(o == BIG_ENDIAN_ORDER || o == LITTLE_ENDIAN_ORDER);

    if (o != LITTLE_ENDIAN_ORDER)
    {
        Decode(encodedInteger, byteCount, s);
    }
    else
    {
        SecByteBlock block(byteCount);
#if (_MSC_VER >= 1500)
        std::reverse_copy(encodedInteger, encodedInteger+byteCount,
            stdext::make_checked_array_iterator(block.begin(), block.size()));
#else
        std::reverse_copy(encodedInteger, encodedInteger+byteCount, block.begin());
#endif
        Decode(block.begin(), block.size(), s);
        return;
    }
}

Integer::Integer(BufferedTransformation &bt)
{
    // Make explicit call to avoid virtual-dispatch findings in ctor
    Integer::BERDecode(bt);
}

Integer::Integer(RandomNumberGenerator &rng, size_t 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(size_t e)
{
    Integer r((word)0, BitsToWords(e+1));
    r.SetBit(e);
    return r;
}

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

Integer& Integer::operator=(const Integer& t)
{
    if (this != &t)
    {
        if (reg.size() != t.reg.size() || t.reg[t.reg.size()/2] == 0)
            reg.New(RoundupSize(t.WordCount()));
        CopyWords(reg, t.reg, reg.size());
        sign = t.sign;
    }
    return *this;
}

bool Integer::GetBit(size_t n) const
{
    // Profiling tells us the original Else was dominant, so it was promoted to the first If statement.
    // The code change occurred at Commit dc99266599a0e72d.
    if (n/WORD_BITS < reg.size())
        return bool((reg[n/WORD_BITS] >> (n % WORD_BITS)) & 1);
    else
        return 0;
}

void Integer::SetBit(size_t 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(size_t n) const
{
    // Profiling tells us the original Else was dominant, so it was promoted to the first If statement.
    // The code change occurred at Commit dc99266599a0e72d.
    if (n/WORD_SIZE < reg.size())
        return byte(reg[n/WORD_SIZE] >> ((n%WORD_SIZE)*8));
    else
        return 0;
}

void Integer::SetByte(size_t 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));
}

lword Integer::GetBits(size_t i, size_t n) const
{
    lword v = 0;
    CRYPTOPP_ASSERT(n <= sizeof(v)*8);
    for (unsigned int j=0; j<n; j++)
        v |= lword(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, size_t 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, ByteOrder order)
{
    CRYPTOPP_ASSERT( order == BIG_ENDIAN_ORDER || order == LITTLE_ENDIAN_ORDER );

    int radix, sign = 1;
    // GCC workaround
    // 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 Integer::Zero();

    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;
    }

    // 'str' is of length 1 or more
    if (str[0] == '-')
    {
        sign = -1;
        str += 1, length -= 1;
    }

    if (length > 2 && str[0] == '0' && (str[1] == 'x' || str[1] == 'X'))
    {
        radix = 16;
        str += 2, length -= 2;
    }

    if (order == BIG_ENDIAN_ORDER)
    {
        for (unsigned int i=0; i<length; i++)
        {
            int digit, ch = static_cast<int>(str[i]);

            //  Profiling showd the second and third Else needed to be swapped
            // The code change occurred at Commit dc99266599a0e72d.
            if (ch >= '0' && ch <= '9')
                digit = ch - '0';
            else if (ch >= 'a' && ch <= 'f')
                digit = ch - 'a' + 10;
            else if (ch >= 'A' && ch <= 'F')
                digit = ch - 'A' + 10;
            else
                digit = radix;

            if (digit < radix)
            {
                v *= radix;
                v += digit;
            }
        }
    }
    else if (radix == 16 && order == LITTLE_ENDIAN_ORDER)
    {
        // Nibble high, low and count
        unsigned int nh = 0, nl = 0, nc = 0;
        Integer position(Integer::One());

        for (unsigned int i=0; i<length; i++)
        {
            int digit, ch = static_cast<int>(str[i]);

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

            if (digit < radix)
            {
                if (nc++ == 0)
                    nh = digit;
                else
                    nl = digit;

                if (nc == 2)
                {
                    v += position * (nh << 4 | nl);
                    nc = 0, position <<= 8;
                }
            }
        }

        if (nc == 1)
            v += nh * position;
    }
    else // LITTLE_ENDIAN_ORDER && radix != 16
    {
        for (int i=static_cast<int>(length)-1; i>=0; i--)
        {
            int digit, ch = static_cast<int>(str[i]);

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

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

    if (sign == -1)
        v.Negate();

    return v;
}

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

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

unsigned int Integer::WordCount() const
{
    return (unsigned int)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, size_t inputLen, Signedness s)
{
    CRYPTOPP_ASSERT(input && inputLen); // NULL buffer
    StringStore store(input, inputLen);
    Decode(store, inputLen, s);
}

void Integer::Decode(BufferedTransformation &bt, size_t inputLen, Signedness s)
{
    CRYPTOPP_ASSERT(bt.MaxRetrievable() >= inputLen);
    if (bt.MaxRetrievable() < inputLen)
        throw InvalidArgument("Integer: input length is too small");

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

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

size_t Integer::MinEncodedSize(Signedness signedness) const
{
    // Profiling tells us the original second If was dominant, so it was promoted to the first If statement.
    // The code change occurred at Commit dc99266599a0e72d.
    unsigned int outputLen = STDMAX(1U, ByteCount());
    const bool pre = (signedness == UNSIGNED);
    if (!pre && NotNegative() && (GetByte(outputLen-1) & 0x80))
        outputLen++;
    if (pre)
        return outputLen;
    if (IsNegative() && *this < -Power2(outputLen*8-1))
        outputLen++;
    return outputLen;
}

// PKCS12_PBKDF and other classes use undersized buffers
void Integer::Encode(byte *output, size_t outputLen, Signedness signedness) const
{
    CRYPTOPP_ASSERT(output && outputLen);            // NULL buffer
    ArraySink sink(output, outputLen);
    Encode(sink, outputLen, signedness);
}

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

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

void Integer::BERDecode(const byte *input, size_t len)
{
    CRYPTOPP_ASSERT(input && len); // NULL buffer
    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, (size_t)dec.RemainingLength(), SIGNED);
    dec.MessageEnd();
}

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

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

size_t Integer::OpenPGPEncode(byte *output, size_t bufferSize) const
{
    CRYPTOPP_ASSERT(output && bufferSize);            // NULL buffer
    CRYPTOPP_ASSERT(bufferSize >= MinEncodedSize());  // Undersized buffer
    ArraySink sink(output, bufferSize);
    return OpenPGPEncode(sink);
}

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

void Integer::OpenPGPDecode(const byte *input, size_t len)
{
    CRYPTOPP_ASSERT(input && len);  // NULL buffer
    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, size_t nbits)
{
    const size_t 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, size_t seedSize)
        : m_counter(0), m_counterAndSeed(seedSize + 4)
    {
        memcpy(m_counterAndSeed + 4, seed, seedSize);
    }

    void GenerateBlock(byte *output, size_t size)
    {
        CRYPTOPP_ASSERT(output && size); // NULL buffer
        PutWord(false, BIG_ENDIAN_ORDER, m_counterAndSeed, m_counter);
        ++m_counter;
        P1363_KDF2<SHA1>::DeriveKey(output, size, m_counterAndSeed, m_counterAndSeed.size(), NULLPTR, 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(Name::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((size_t)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 *)NULLPTR);

            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;
}

// Ensure base 10 is default
inline int FlagToBase(long f) {
    return f == std::ios::hex ? 16 : (f == std::ios::oct ? 8 : 10);
}

inline char FlagToSuffix(long f) {
    return f == std::ios::hex ? 'h' : (f == std::ios::oct ? 'o' : '.');
}

// Ensure base 10 is default
std::ostream& operator<<(std::ostream& out, const Integer &a)
{
    // Get relevant conversion specifications from ostream.
    const long f = out.flags() & std::ios::basefield;
    const int base = FlagToBase(f);
    const char suffix = FlagToSuffix(f);

    Integer temp1=a, temp2;
    if (a.IsNegative())
    {
        out << '-';
        temp1.Negate();
    }

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

    static const char upper[]="0123456789ABCDEF";
    static const char lower[]="0123456789abcdef";

    const char* vec = (out.flags() & std::ios::uppercase) ? upper : lower;
    unsigned int i=0;
    SecBlock<char> s(a.BitCount() / (SaturatingSubtract1(BitPrecision(base),1U)) + 1);

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

    while (i--)
    {
        out << s[i];
    }

#ifdef CRYPTOPP_USE_STD_SHOWBASE
    if (out.flags() & std::ios_base::showbase)
        out << suffix;

    return out;
#else
    return out << suffix;
#endif
}

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());
        CRYPTOPP_ASSERT(!borrow); CRYPTOPP_UNUSED(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;
}

// This is a bit operation. We set sign to POSITIVE, so there's no need to
//  worry about negative zero. Also see http://stackoverflow.com/q/11644362.
Integer Integer::And(const Integer& t) const
{
    if (this == &t)
    {
        return AbsoluteValue();
    }
    else if (reg.size() >= t.reg.size())
    {
        Integer result(t);
        AndWords(result.reg, reg, t.reg.size());

        result.sign = POSITIVE;
        return result;
    }
    else // reg.size() < t.reg.size()
    {
        Integer result(*this);
        AndWords(result.reg, t.reg, reg.size());

        result.sign = POSITIVE;
        return result;
    }
}

// This is a bit operation. We set sign to POSITIVE, so there's no need to
//  worry about negative zero. Also see http://stackoverflow.com/q/11644362.
Integer Integer::Or(const Integer& t) const
{
    if (this == &t)
    {
        return AbsoluteValue();
    }
    else if (reg.size() >= t.reg.size())
    {
        Integer result(*this);
        OrWords(result.reg, t.reg, t.reg.size());

        result.sign = POSITIVE;
        return result;
    }
    else // reg.size() < t.reg.size()
    {
        Integer result(t);
        OrWords(result.reg, reg, reg.size());

        result.sign = POSITIVE;
        return result;
    }
}

// This is a bit operation. We set sign to POSITIVE, so there's no need to
//  worry about negative zero. Also see http://stackoverflow.com/q/11644362.
Integer Integer::Xor(const Integer& t) const
{
    if (this == &t)
    {
        return Integer::Zero();
    }
    else if (reg.size() >= t.reg.size())
    {
        Integer result(*this);
        XorWords(result.reg, t.reg, t.reg.size());

        result.sign = POSITIVE;
        return result;
    }
    else // reg.size() < t.reg.size()
    {
        Integer result(t);
        XorWords(result.reg, reg, reg.size());

        result.sign = POSITIVE;
        return result;
    }
}

void PositiveAdd(Integer &sum, const Integer &a, const Integer& b)
{
    // Profiling tells us the original second Else If was dominant, so it was promoted to the first If statement.
    // The code change occurred at Commit dc99266599a0e72d.
    int carry; const bool pre = (a.reg.size() == b.reg.size());
    if (!pre && 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 if (pre)
    {
        carry = Add(sum.reg, a.reg, b.reg, a.reg.size());
    }
    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;

    // Profiling tells us the original second Else If was dominant, so it was promoted to the first If statement.
    // The code change occurred at Commit dc99266599a0e72d.
    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);
        CRYPTOPP_ASSERT(!borrow); CRYPTOPP_UNUSED(borrow);
        diff.sign = Integer::POSITIVE;
    }
    else 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
    {
        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);
        CRYPTOPP_ASSERT(!borrow); CRYPTOPP_UNUSED(borrow);
        diff.sign = Integer::NEGATIVE;
    }
}

// MSVC .NET 2003 workaround
template <class T> inline const T& STDMAX2(const T& a, const T& b)
{
    return a < b ? b : a;
}

Integer Integer::Plus(const Integer& b) const
{
    Integer sum((word)0, STDMAX2(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, STDMAX2(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<<=(size_t n)
{
    const size_t wordCount = WordCount();
    const size_t shiftWords = n / WORD_BITS;
    const unsigned int shiftBits = (unsigned int)(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>>=(size_t n)
{
    const size_t wordCount = WordCount();
    const size_t shiftWords = n / WORD_BITS;
    const unsigned int shiftBits = (unsigned int)(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;
}

Integer& Integer::operator&=(const Integer& t)
{
    if (this != &t)
    {
        const size_t size = STDMIN(reg.size(), t.reg.size());
        reg.resize(size);
        AndWords(reg, t.reg, size);
    }
    sign = POSITIVE;
    return *this;
}

Integer& Integer::operator|=(const Integer& t)
{
    if (this != &t)
    {
        if (reg.size() >= t.reg.size())
        {
            OrWords(reg, t.reg, t.reg.size());
        }
        else  // reg.size() < t.reg.size()
        {
            const size_t head = reg.size();
            const size_t tail = t.reg.size() - reg.size();
            reg.resize(head+tail);
            OrWords(reg, t.reg, head);
            CopyWords(reg+head,t.reg+head,tail);
        }
    }
    sign = POSITIVE;
    return *this;
}

Integer& Integer::operator^=(const Integer& t)
{
    if (this == &t)
    {
        *this = Zero();
    }
    else
    {
        if (reg.size() >= t.reg.size())
        {
            XorWords(reg, t.reg, t.reg.size());
        }
        else  // reg.size() < t.reg.size()
        {
            const size_t head = reg.size();
            const size_t tail = t.reg.size() - reg.size();
            reg.resize(head+tail);
            XorWords(reg, t.reg, head);
            CopyWords(reg+head,t.reg+head,tail);
        }
    }
    sign = POSITIVE;
    return *this;
}

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

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

    IntegerSecBlock 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 (aSize < bSize)
    {
        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;

    IntegerSecBlock T(aSize+3*(bSize+2));
    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 size_t 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] %= (word(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();

    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();

    word remainder;

    // Profiling tells us the original Else was dominant, so it was promoted to the first If statement.
    // The code change occurred at Commit dc99266599a0e72d.
    if ((divisor & (divisor-1)) != 0)   // divisor is not a power of 2
    {
        // Profiling tells us the original Else was dominant, so it was promoted to the first If statement.
        // The code change occurred at Commit dc99266599a0e72d.
        unsigned int i = WordCount();
        if (divisor > 5)
        {
            remainder = 0;
            while (i--)
                remainder = DWord(reg[i], remainder) % divisor;
        }
        else
        {
            DWord sum(0, 0);
            while (i--)
                sum += reg[i];
            remainder = sum % divisor;
        }
    }
    else  // divisor is a power of 2
    {
        remainder = reg[0] & (divisor-1);
    }

    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
{
    // Profiling tells us the original Else was dominant, so it was promoted to the first If statement.
    // The code change occurred at Commit dc99266599a0e72d.
    const unsigned size = WordCount(), tSize = t.WordCount();
    if (size != tSize)
        return size > tSize ? 1 : -1;
    else
        return CryptoPP::Compare(reg, t.reg, size);
}

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);
    CRYPTOPP_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)
{
    CRYPTOPP_ASSERT(m.NotZero());
    if (m.IsZero())
        throw Integer::DivideByZero();

    return x*y%m;
}

Integer a_exp_b_mod_c(const Integer &x, const Integer& e, const Integer& m)
{
    CRYPTOPP_ASSERT(m.NotZero());
    if (m.IsZero())
        throw Integer::DivideByZero();

    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
{
    CRYPTOPP_ASSERT(m.NotNegative());
    CRYPTOPP_ASSERT(m.NotZero());

    if (IsNegative())
        return Modulo(m).InverseModNext(m);

    // http://github.com/weidai11/cryptopp/issues/602
    if (*this >= m)
        return Modulo(m).InverseModNext(m);

    return InverseModNext(m);
}

Integer Integer::InverseModNext(const Integer &m) const
{
    CRYPTOPP_ASSERT(m.NotNegative());
    CRYPTOPP_ASSERT(m.NotZero());

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

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

    // AlmostInverse requires a 4x workspace
    IntegerSecBlock 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(word mod) const
{
    CRYPTOPP_ASSERT(mod != 0);

    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();
    m_modulus.BERDecode(seq);
    seq.MessageEnd();
    m_result.reg.resize(m_modulus.reg.size());
}

void ModularArithmetic::DEREncode(BufferedTransformation &bt) const
{
    DERSequenceEncoder seq(bt);
    ASN1::prime_field().DEREncode(seq);
    m_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()==m_modulus.reg.size())
    {
        CryptoPP::DivideByPower2Mod(m_result.reg.begin(), a.reg, 1, m_modulus.reg, a.reg.size());
        return m_result;
    }
    else
        return m_result1 = (a.IsEven() ? (a >> 1) : ((a+m_modulus) >> 1));
}

const Integer& ModularArithmetic::Add(const Integer &a, const Integer &b) const
{
    if (a.reg.size()==m_modulus.reg.size() && b.reg.size()==m_modulus.reg.size())
    {
        if (CryptoPP::Add(m_result.reg.begin(), a.reg, b.reg, a.reg.size())
            || Compare(m_result.reg, m_modulus.reg, a.reg.size()) >= 0)
        {
            CryptoPP::Subtract(m_result.reg.begin(), m_result.reg, m_modulus.reg, a.reg.size());
        }
        return m_result;
    }
    else
    {
        m_result1 = a+b;
        if (m_result1 >= m_modulus)
            m_result1 -= m_modulus;
        return m_result1;
    }
}

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

    return a;
}

const Integer& ModularArithmetic::Subtract(const Integer &a, const Integer &b) const
{
    if (a.reg.size()==m_modulus.reg.size() && b.reg.size()==m_modulus.reg.size())
    {
        if (CryptoPP::Subtract(m_result.reg.begin(), a.reg, b.reg, a.reg.size()))
            CryptoPP::Add(m_result.reg.begin(), m_result.reg, m_modulus.reg, a.reg.size());
        return m_result;
    }
    else
    {
        m_result1 = a-b;
        if (m_result1.IsNegative())
            m_result1 += m_modulus;
        return m_result1;
    }
}

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

    return a;
}

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

    CopyWords(m_result.reg.begin(), m_modulus.reg, m_modulus.reg.size());
    if (CryptoPP::Subtract(m_result.reg.begin(), m_result.reg, a.reg, a.reg.size()))
        Decrement(m_result.reg.begin()+a.reg.size(), m_modulus.reg.size()-a.reg.size());

    return m_result;
}

Integer ModularArithmetic::CascadeExponentiate(const Integer &x, const Integer &e1, const Integer &y, const Integer &e2) const
{
    if (m_modulus.IsOdd())
    {
        MontgomeryRepresentation dr(m_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 (m_modulus.IsOdd())
    {
        MontgomeryRepresentation dr(m_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),
      m_u((word)0, m_modulus.reg.size()),
      m_workspace(5*m_modulus.reg.size())
{
    if (!m_modulus.IsOdd())
        throw InvalidArgument("MontgomeryRepresentation: Montgomery representation requires an odd modulus");

    RecursiveInverseModPower2(m_u.reg, m_workspace, m_modulus.reg, m_modulus.reg.size());
}

const Integer& MontgomeryRepresentation::Multiply(const Integer &a, const Integer &b) const
{
    word *const T = m_workspace.begin();
    word *const R = m_result.reg.begin();
    const size_t N = m_modulus.reg.size();
    CRYPTOPP_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, m_modulus.reg, m_u.reg, N);
    return m_result;
}

const Integer& MontgomeryRepresentation::Square(const Integer &a) const
{
    word *const T = m_workspace.begin();
    word *const R = m_result.reg.begin();
    const size_t N = m_modulus.reg.size();
    CRYPTOPP_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, m_modulus.reg, m_u.reg, N);
    return m_result;
}

Integer MontgomeryRepresentation::ConvertOut(const Integer &a) const
{
    word *const T = m_workspace.begin();
    word *const R = m_result.reg.begin();
    const size_t N = m_modulus.reg.size();
    CRYPTOPP_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, m_modulus.reg, m_u.reg, N);
    return m_result;
}

const Integer& MontgomeryRepresentation::MultiplicativeInverse(const Integer &a) const
{
//    return (EuclideanMultiplicativeInverse(a, modulus)<<(2*WORD_BITS*modulus.reg.size()))%modulus;
    word *const T = m_workspace.begin();
    word *const R = m_result.reg.begin();
    const size_t N = m_modulus.reg.size();
    CRYPTOPP_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, m_modulus.reg, m_u.reg, N);
    unsigned k = AlmostInverse(R, T, R, N, m_modulus.reg, N);

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

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

    return m_result;
}

// Specialization declared in misc.h to allow us to print integers
//  with additional control options, like arbirary bases and uppercase.
template <> CRYPTOPP_DLL
std::string IntToString<Integer>(Integer value, unsigned int base)
{
    // Hack... set the high bit for uppercase. Set the next bit fo a suffix.
    static const unsigned int BIT_32 = (1U << 31);
    const bool UPPER = !!(base & BIT_32);
    static const unsigned int BIT_31 = (1U << 30);
    const bool BASE = !!(base & BIT_31);

    const char CH = UPPER ? 'A' : 'a';
    base &= ~(BIT_32|BIT_31);
    CRYPTOPP_ASSERT(base >= 2 && base <= 32);

    if (value == 0)
        return "0";

    bool negative = false, zero = false;
    if (value.IsNegative())
    {
        negative = true;
        value.Negate();
    }

    if (!value)
        zero = true;

    SecBlock<char> s(value.BitCount() / (SaturatingSubtract1(BitPrecision(base),1U)) + 1);
    Integer temp;

    unsigned int i=0;
    while (!!value)
    {
        word digit;
        Integer::Divide(digit, temp, value, word(base));
        s[i++]=char((digit < 10 ? '0' : (CH - 10)) + digit);
        value.swap(temp);
    }

    std::string result;
    result.reserve(i+2);

    if (negative)
        result += '-';

    if (zero)
        result += '0';

    while (i--)
        result += s[i];

    if (BASE)
    {
        if (base == 10)
            result += '.';
        else if (base == 16)
            result += 'h';
        else if (base == 8)
            result += 'o';
        else if (base == 2)
            result += 'b';
    }

    return result;
}

// Specialization declared in misc.h to avoid Coverity findings.
template <> CRYPTOPP_DLL
std::string IntToString<word64>(word64 value, unsigned int base)
{
    // Hack... set the high bit for uppercase.
    static const unsigned int HIGH_BIT = (1U << 31);
    const char CH = !!(base & HIGH_BIT) ? 'A' : 'a';
    base &= ~HIGH_BIT;

    CRYPTOPP_ASSERT(base >= 2);
    if (value == 0)
        return "0";

    std::string result;
    while (value > 0)
    {
        word64 digit = value % base;
        result = char((digit < 10 ? '0' : (CH - 10)) + digit) + result;
        value /= base;
    }
    return result;
}

#ifndef CRYPTOPP_NO_ASSIGN_TO_INTEGER
// Allow the linker to discard Integer code if not needed.
// Also see http://github.com/weidai11/cryptopp/issues/389.
bool AssignIntToInteger(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;
}
#endif  // CRYPTOPP_NO_ASSIGN_TO_INTEGER

// *************************** C++ Static Initialization ***************************

class InitInteger
{
public:
    InitInteger()
    {
        SetFunctionPointers();
    }
};

// This is not really needed because each Integer can dynamically initialize
// itself, but we take a peephole optimization and initialize the class once
// if init priorities are available. Dynamic initialization will be used if
// init priorities are not available.

#if defined(HAVE_GCC_INIT_PRIORITY)
    const InitInteger s_init __attribute__ ((init_priority (CRYPTOPP_INIT_PRIORITY + 10))) = InitInteger();
    const Integer g_zero __attribute__ ((init_priority (CRYPTOPP_INIT_PRIORITY + 11))) = Integer(0L);
    const Integer g_one __attribute__ ((init_priority (CRYPTOPP_INIT_PRIORITY + 12))) = Integer(1L);
    const Integer g_two __attribute__ ((init_priority (CRYPTOPP_INIT_PRIORITY + 13))) = Integer(2L);
#elif defined(HAVE_MSC_INIT_PRIORITY)
    #pragma warning(disable: 4075)
    #pragma init_seg(".CRT$XCU")
    const InitInteger s_init;
    const Integer g_zero(0L);
    const Integer g_one(1L);
    const Integer g_two(2L);
    #pragma warning(default: 4075)
#elif HAVE_XLC_INIT_PRIORITY
    // XLC needs constant, not a define
    #pragma priority(280)
    const InitInteger s_init;
    const Integer g_zero(0L);
    const Integer g_one(1L);
    const Integer g_two(2L);
#else
    const InitInteger s_init;
#endif

// ***************** Library code ********************

const Integer &Integer::Zero()
{
#if defined(HAVE_GCC_INIT_PRIORITY) || defined(HAVE_MSC_INIT_PRIORITY) || defined(HAVE_XLC_INIT_PRIORITY)
    return g_zero;
#elif defined(CRYPTOPP_CXX11_DYNAMIC_INIT)
    static const Integer s_zero(0L);
    return s_zero;
#else  // Potential memory leak. Avoid if possible.
    return Singleton<Integer, NewInteger<0L> >().Ref();
#endif
}

const Integer &Integer::One()
{
#if defined(HAVE_GCC_INIT_PRIORITY) || defined(HAVE_MSC_INIT_PRIORITY) || defined(HAVE_XLC_INIT_PRIORITY)
    return g_one;
#elif defined(CRYPTOPP_CXX11_DYNAMIC_INIT)
    static const Integer s_one(1L);
    return s_one;
#else  // Potential memory leak. Avoid if possible.
    return Singleton<Integer, NewInteger<1L> >().Ref();
#endif
}

const Integer &Integer::Two()
{
#if defined(HAVE_GCC_INIT_PRIORITY) || defined(HAVE_MSC_INIT_PRIORITY) || defined(HAVE_XLC_INIT_PRIORITY)
    return g_two;
#elif defined(CRYPTOPP_CXX11_DYNAMIC_INIT)
    static const Integer s_two(2L);
    return s_two;
#else  // Potential memory leak. Avoid if possible.
    return Singleton<Integer, NewInteger<2L> >().Ref();
#endif
}

NAMESPACE_END

#endif  // CRYPTOPP_IMPORTS