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cuberite-2a/lib/cryptopp/integer.cpp
Alexander Harkness 3438e5d3dd move cryptopp into lib
2013-11-24 14:21:13 +00:00

4236 lines
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// integer.cpp - written and placed in the public domain by Wei Dai
// contains public domain code contributed by Alister Lee and Leonard Janke
#include "pch.h"
#ifndef CRYPTOPP_IMPORTS
#include "integer.h"
#include "modarith.h"
#include "nbtheory.h"
#include "asn.h"
#include "oids.h"
#include "words.h"
#include "algparam.h"
#include "pubkey.h" // for P1363_KDF2
#include "sha.h"
#include "cpu.h"
#include <iostream>
#if _MSC_VER >= 1400
#include <intrin.h>
#endif
#ifdef __DECCXX
#include <c_asm.h>
#endif
#ifdef CRYPTOPP_MSVC6_NO_PP
#pragma message("You do not seem to have the Visual C++ Processor Pack installed, so use of SSE2 instructions will be disabled.")
#endif
#define CRYPTOPP_INTEGER_SSE2 (CRYPTOPP_BOOL_SSE2_ASM_AVAILABLE && CRYPTOPP_BOOL_X86)
NAMESPACE_BEGIN(CryptoPP)
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;
}
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)
{
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)
{
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)
{
assert(A%2==1);
word R=A%8;
for (unsigned i=3; i<WORD_BITS; i*=2)
R = R*(2-R*A);
assert(R*A==1);
return R;
}
// ********************************************************
#if !defined(CRYPTOPP_NATIVE_DWORD_AVAILABLE) || (defined(__x86_64__) && defined(CRYPTOPP_WORD128_AVAILABLE))
#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)
#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:
DWord() {}
#ifdef CRYPTOPP_NATIVE_DWORD_AVAILABLE
explicit DWord(word low)
{
m_whole = low;
}
#else
explicit DWord(word low)
{
m_halfs.low = low;
m_halfs.high = 0;
}
#endif
DWord(word low, word high)
{
m_halfs.low = low;
m_halfs.high = high;
}
static DWord Multiply(word a, word b)
{
DWord r;
#ifdef CRYPTOPP_NATIVE_DWORD_AVAILABLE
r.m_whole = (dword)a * b;
#elif defined(MultiplyWordsLoHi)
MultiplyWordsLoHi(r.m_halfs.low, r.m_halfs.high, a, b);
#endif
return r;
}
static DWord MultiplyAndAdd(word a, word b, word c)
{
DWord r = Multiply(a, b);
return r += c;
}
DWord & operator+=(word a)
{
#ifdef CRYPTOPP_NATIVE_DWORD_AVAILABLE
m_whole = m_whole + a;
#else
m_halfs.low += a;
m_halfs.high += (m_halfs.low < a);
#endif
return *this;
}
DWord operator+(word a)
{
DWord r;
#ifdef CRYPTOPP_NATIVE_DWORD_AVAILABLE
r.m_whole = m_whole + a;
#else
r.m_halfs.low = m_halfs.low + a;
r.m_halfs.high = m_halfs.high + (r.m_halfs.low < a);
#endif
return r;
}
DWord operator-(DWord a)
{
DWord r;
#ifdef CRYPTOPP_NATIVE_DWORD_AVAILABLE
r.m_whole = m_whole - a.m_whole;
#else
r.m_halfs.low = m_halfs.low - a.m_halfs.low;
r.m_halfs.high = m_halfs.high - a.m_halfs.high - (r.m_halfs.low > m_halfs.low);
#endif
return r;
}
DWord operator-(word a)
{
DWord r;
#ifdef CRYPTOPP_NATIVE_DWORD_AVAILABLE
r.m_whole = m_whole - a;
#else
r.m_halfs.low = m_halfs.low - a;
r.m_halfs.high = m_halfs.high - (r.m_halfs.low > m_halfs.low);
#endif
return r;
}
// returns quotient, which must fit in a word
word operator/(word divisor);
word operator%(word a);
bool operator!() const
{
#ifdef CRYPTOPP_NATIVE_DWORD_AVAILABLE
return !m_whole;
#else
return !m_halfs.high && !m_halfs.low;
#endif
}
word GetLowHalf() const {return m_halfs.low;}
word GetHighHalf() const {return m_halfs.high;}
word GetHighHalfAsBorrow() const {return 0-m_halfs.high;}
private:
union
{
#ifdef CRYPTOPP_NATIVE_DWORD_AVAILABLE
dword m_whole;
#endif
struct
{
#ifdef IS_LITTLE_ENDIAN
word low;
word high;
#else
word high;
word low;
#endif
} m_halfs;
};
};
class Word
{
public:
Word() {}
Word(word value)
{
m_whole = value;
}
Word(hword low, hword high)
{
m_whole = low | (word(high) << (WORD_BITS/2));
}
static Word Multiply(hword a, hword b)
{
Word r;
r.m_whole = (word)a * b;
return r;
}
Word operator-(Word a)
{
Word r;
r.m_whole = m_whole - a.m_whole;
return r;
}
Word operator-(hword a)
{
Word r;
r.m_whole = m_whole - a;
return r;
}
// returns quotient, which must fit in a word
hword operator/(hword divisor)
{
return hword(m_whole / divisor);
}
bool operator!() const
{
return !m_whole;
}
word GetWhole() const {return m_whole;}
hword GetLowHalf() const {return hword(m_whole);}
hword GetHighHalf() const {return hword(m_whole>>(WORD_BITS/2));}
hword GetHighHalfAsBorrow() const {return 0-hword(m_whole>>(WORD_BITS/2));}
private:
word m_whole;
};
// do a 3 word by 2 word divide, returns quotient and leaves remainder in A
template <class S, class D>
S DivideThreeWordsByTwo(S *A, S B0, S B1, D *dummy=NULL)
{
// assert {A[2],A[1]} < {B1,B0}, so quotient can fit in a S
assert(A[2] < B1 || (A[2]==B1 && A[1] < B0));
// estimate the quotient: do a 2 S by 1 S divide
S Q;
if (S(B1+1) == 0)
Q = A[2];
else if (B1 > 0)
Q = D(A[1], A[2]) / S(B1+1);
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++;
assert(Q); // shouldn't overflow
}
return Q;
}
// do a 4 word by 2 word divide, returns 2 word quotient in Q0 and Q1
template <class S, class D>
inline D DivideFourWordsByTwo(S *T, const D &Al, const D &Ah, const D &B)
{
if (!B) // if divisor is 0, we assume divisor==2**(2*WORD_BITS)
return D(Ah.GetLowHalf(), Ah.GetHighHalf());
else
{
S Q[2];
T[0] = Al.GetLowHalf();
T[1] = Al.GetHighHalf();
T[2] = Ah.GetLowHalf();
T[3] = Ah.GetHighHalf();
Q[1] = DivideThreeWordsByTwo<S, D>(T+1, B.GetLowHalf(), B.GetHighHalf());
Q[0] = DivideThreeWordsByTwo<S, D>(T, B.GetLowHalf(), B.GetHighHalf());
return D(Q[0], Q[1]);
}
}
// returns quotient, which must fit in a word
inline word DWord::operator/(word a)
{
#ifdef CRYPTOPP_NATIVE_DWORD_AVAILABLE
return word(m_whole / a);
#else
hword r[4];
return DivideFourWordsByTwo<hword, Word>(r, m_halfs.low, m_halfs.high, a).GetWhole();
#endif
}
inline word DWord::operator%(word a)
{
#ifdef CRYPTOPP_NATIVE_DWORD_AVAILABLE
return word(m_whole % a);
#else
if (a < (word(1) << (WORD_BITS/2)))
{
hword h = hword(a);
word r = m_halfs.high % h;
r = ((m_halfs.low >> (WORD_BITS/2)) + (r << (WORD_BITS/2))) % h;
return hword((hword(m_halfs.low) + (r << (WORD_BITS/2))) % h);
}
else
{
hword r[4];
DivideFourWordsByTwo<hword, Word>(r, m_halfs.low, m_halfs.high, a);
return Word(r[0], r[1]).GetWhole();
}
#endif
}
// ********************************************************
// use some tricks to share assembly code between MSVC and GCC
#if defined(__GNUC__)
#define AddPrologue \
int result; \
__asm__ __volatile__ \
( \
".intel_syntax noprefix;"
#define AddEpilogue \
".att_syntax prefix;" \
: "=a" (result)\
: "d" (C), "a" (A), "D" (B), "c" (N) \
: "%esi", "memory", "cc" \
);\
return result;
#define MulPrologue \
__asm__ __volatile__ \
( \
".intel_syntax noprefix;" \
AS1( push ebx) \
AS2( mov ebx, edx)
#define MulEpilogue \
AS1( pop ebx) \
".att_syntax prefix;" \
: \
: "d" (s_maskLow16), "c" (C), "a" (A), "D" (B) \
: "%esi", "memory", "cc" \
);
#define SquPrologue MulPrologue
#define SquEpilogue \
AS1( pop ebx) \
".att_syntax prefix;" \
: \
: "d" (s_maskLow16), "c" (C), "a" (A) \
: "%esi", "%edi", "memory", "cc" \
);
#define TopPrologue MulPrologue
#define TopEpilogue \
AS1( pop ebx) \
".att_syntax 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
#if _MSC_VER < 1300
#define SaveEBX __asm push ebx
#define RestoreEBX __asm pop ebx
#else
#define SaveEBX
#define RestoreEBX
#endif
#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_syntax;"
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_syntax;"
: "=&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_syntax;"
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_syntax;"
: "=&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
}
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
}
#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
}
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
}
#endif // #if CRYPTOPP_BOOL_SSE2_ASM_AVAILABLE
#else
int CRYPTOPP_FASTCALL Baseline_Add(size_t N, word *C, const word *A, const word *B)
{
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)
{
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 *A, word B, size_t N)
{
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 *A, const word *B)
{
Mul_2
}
void Baseline_Multiply4(word *R, const word *A, const word *B)
{
Mul_4
}
void Baseline_Multiply8(word *R, const word *A, const word *B)
{
Mul_8
}
void Baseline_Square2(word *R, const word *A)
{
Squ_2
}
void Baseline_Square4(word *R, const word *A)
{
Squ_4
}
void Baseline_Square8(word *R, const word *A)
{
Squ_8
}
void Baseline_MultiplyBottom2(word *R, const word *A, const word *B)
{
Bot_2
}
void Baseline_MultiplyBottom4(word *R, const word *A, const word *B)
{
Bot_4
}
void Baseline_MultiplyBottom8(word *R, const word *A, const word *B)
{
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)
{
word T[4];
Baseline_Multiply2(T, A, B);
R[0] = T[2];
R[1] = T[3];
}
void Baseline_MultiplyTop4(word *R, const word *A, const word *B, word L)
{
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 *A, const word *B, word L)
{
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 *A, const word *B)
{
Mul_16
}
void Baseline_Square16(word *R, const word *A)
{
Squ_16
}
void Baseline_MultiplyBottom16(word *R, const word *A, const word *B)
{
Bot_16
}
void Baseline_MultiplyTop16(word *R, const word *A, const word *B, word L)
{
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) static const word32 s_maskLow16[4] CRYPTOPP_SECTION_ALIGN16 = {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
static PMul s_pMul[9], s_pBot[9];
static PSqu s_pSqu[9];
static PMulTop s_pTop[9];
static 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 _MSC_VER != 1200 || defined(NDEBUG)
if (IsP4())
{
s_pAdd = &SSE2_Add;
s_pSub = &SSE2_Sub;
}
#endif
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
{
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
}
}
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
}
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
}
// ********************************************************
#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)
{
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);
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)
{
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)
{
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)
{
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);
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)
{
if (A == B)
Square(R, T, A, NA);
else
Multiply(R, T, A, B, NA);
return;
}
if (NA > NB)
{
std::swap(A, B);
std::swap(NA, NB);
}
assert(NB % NA == 0);
if (NA==2 && !A[1])
{
switch (A[0])
{
case 0:
SetWords(R, 0, NB+2);
return;
case 1:
CopyWords(R, B, NB);
R[NB] = R[NB+1] = 0;
return;
default:
R[NB] = LinearMultiply(R, B, A[0], NB);
R[NB+1] = 0;
return;
}
}
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)
{
if (N==2)
{
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);
}
else
{
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);
}
}
// 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);
assert(carry | !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)
{
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);
assert(c3>=-1 && c3<=1);
if (c3>0)
Subtract(R, R, M, N);
else if (c3<0)
Add(R, R, M, N);
#undef M0
#undef M1
#undef V0
#undef V1
#undef X0
#undef X1
#undef X2
#undef X3
}
#undef A0
#undef A1
#undef B0
#undef B1
#undef T0
#undef T1
#undef T2
#undef T3
#undef R0
#undef R1
#undef R2
#undef R3
/*
// do a 3 word by 2 word divide, returns quotient and leaves remainder in A
static word SubatomicDivide(word *A, word B0, word B1)
{
// assert {A[2],A[1]} < {B1,B0}, so quotient can fit in a word
assert(A[2] < B1 || (A[2]==B1 && A[1] < B0));
// estimate the quotient: do a 2 word by 1 word divide
word Q;
if (B1+1 == 0)
Q = A[2];
else
Q = DWord(A[1], A[2]).DividedBy(B1+1);
// now subtract Q*B from A
DWord p = DWord::Multiply(B0, Q);
DWord u = (DWord) A[0] - p.GetLowHalf();
A[0] = u.GetLowHalf();
u = (DWord) A[1] - p.GetHighHalf() - u.GetHighHalfAsBorrow() - DWord::Multiply(B1, Q);
A[1] = u.GetLowHalf();
A[2] += u.GetHighHalf();
// Q <= actual quotient, so fix it
while (A[2] || A[1] > B1 || (A[1]==B1 && A[0]>=B0))
{
u = (DWord) A[0] - B0;
A[0] = u.GetLowHalf();
u = (DWord) A[1] - B1 - u.GetHighHalfAsBorrow();
A[1] = u.GetLowHalf();
A[2] += u.GetHighHalf();
Q++;
assert(Q); // shouldn't overflow
}
return Q;
}
// do a 4 word by 2 word divide, returns 2 word quotient in Q0 and Q1
static inline void AtomicDivide(word *Q, const word *A, const word *B)
{
if (!B[0] && !B[1]) // if divisor is 0, we assume divisor==2**(2*WORD_BITS)
{
Q[0] = A[2];
Q[1] = A[3];
}
else
{
word T[4];
T[0] = A[0]; T[1] = A[1]; T[2] = A[2]; T[3] = A[3];
Q[1] = SubatomicDivide(T+1, B[0], B[1]);
Q[0] = SubatomicDivide(T, B[0], B[1]);
#ifndef NDEBUG
// multiply quotient and divisor and add remainder, make sure it equals dividend
assert(!T[2] && !T[3] && (T[1] < B[1] || (T[1]==B[1] && T[0]<B[0])));
word P[4];
LowLevel::Multiply2(P, Q, B);
Add(P, P, T, 4);
assert(memcmp(P, A, 4*WORD_SIZE)==0);
#endif
}
}
*/
static inline void AtomicDivide(word *Q, const word *A, const word *B)
{
word T[4];
DWord q = DivideFourWordsByTwo<word, DWord>(T, DWord(A[0], A[1]), DWord(A[2], A[3]), DWord(B[0], B[1]));
Q[0] = q.GetLowHalf();
Q[1] = q.GetHighHalf();
#ifndef NDEBUG
if (B[0] || B[1])
{
// multiply quotient and divisor and add remainder, make sure it equals dividend
assert(!T[2] && !T[3] && (T[1] < B[1] || (T[1]==B[1] && T[0]<B[0])));
word P[4];
s_pMul[0](P, Q, B);
Add(P, P, T, 4);
assert(memcmp(P, A, 4*WORD_SIZE)==0);
}
#endif
}
// for use by Divide(), corrects the underestimated quotient {Q1,Q0}
static void CorrectQuotientEstimate(word *R, word *T, word *Q, const word *B, size_t N)
{
assert(N && N%2==0);
AsymmetricMultiply(T, T+N+2, Q, 2, B, N);
word borrow = Subtract(R, R, T, N+2);
assert(!borrow && !R[N+1]);
while (R[N] || Compare(R, B, N) >= 0)
{
R[N] -= Subtract(R, R, B, N);
Q[1] += (++Q[0]==0);
assert(Q[0] || Q[1]); // no overflow
}
}
// R[NB] -------- remainder = A%B
// Q[NA-NB+2] --- quotient = A/B
// T[NA+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)
{
assert(NA && NB && NA%2==0 && NB%2==0);
assert(B[NB-1] || B[NB-2]);
assert(NB <= NA);
// set up temporary work space
word *const TA=T;
word *const TB=T+NA+2;
word *const TP=T+NA+2+NB;
// copy B into TB and normalize it so that TB has highest bit set to 1
unsigned shiftWords = (B[NB-1]==0);
TB[0] = TB[NB-1] = 0;
CopyWords(TB+shiftWords, B, NB-shiftWords);
unsigned shiftBits = WORD_BITS - BitPrecision(TB[NB-1]);
assert(shiftBits < WORD_BITS);
ShiftWordsLeftByBits(TB, NB, shiftBits);
// copy A into TA and normalize it
TA[0] = TA[NA] = TA[NA+1] = 0;
CopyWords(TA+shiftWords, A, NA);
ShiftWordsLeftByBits(TA, NA+2, shiftBits);
if (TA[NA+1]==0 && TA[NA] <= 1)
{
Q[NA-NB+1] = Q[NA-NB] = 0;
while (TA[NA] || Compare(TA+NA-NB, TB, NB) >= 0)
{
TA[NA] -= Subtract(TA+NA-NB, TA+NA-NB, TB, NB);
++Q[NA-NB];
}
}
else
{
NA+=2;
assert(Compare(TA+NA-NB, TB, NB) < 0);
}
word BT[2];
BT[0] = TB[NB-2] + 1;
BT[1] = TB[NB-1] + (BT[0]==0);
// start reducing TA mod TB, 2 words at a time
for (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)
{
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);
assert(bcLen <= N);
ShiftWordsLeftByWords(c, bcLen, 1);
k+=WORD_BITS;
t=f[0];
}
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);
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;
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);
}
// ******************************************************************
InitializeInteger::InitializeInteger()
{
if (!g_pAssignIntToInteger)
{
SetFunctionPointers();
g_pAssignIntToInteger = AssignIntToInteger;
}
}
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
{
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)
{
Decode(encodedInteger, byteCount, s);
}
Integer::Integer(const byte *encodedInteger, size_t byteCount, Signedness s)
{
Decode(encodedInteger, byteCount, s);
}
Integer::Integer(BufferedTransformation &bt)
{
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;
}
template <long i>
struct NewInteger
{
Integer * operator()() const
{
return new Integer(i);
}
};
const Integer &Integer::Zero()
{
return Singleton<Integer>().Ref();
}
const Integer &Integer::One()
{
return Singleton<Integer, NewInteger<1> >().Ref();
}
const Integer &Integer::Two()
{
return Singleton<Integer, NewInteger<2> >().Ref();
}
bool Integer::operator!() const
{
return IsNegative() ? false : (reg[0]==0 && WordCount()==0);
}
Integer& Integer::operator=(const Integer& t)
{
if (this != &t)
{
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
{
if (n/WORD_BITS >= reg.size())
return 0;
else
return bool((reg[n/WORD_BITS] >> (n % WORD_BITS)) & 1);
}
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
{
if (n/WORD_SIZE >= reg.size())
return 0;
else
return byte(reg[n/WORD_SIZE] >> ((n%WORD_SIZE)*8));
}
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;
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)
{
int radix;
// 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 v;
switch (str[length-1])
{
case 'h':
case 'H':
radix=16;
break;
case 'o':
case 'O':
radix=8;
break;
case 'b':
case 'B':
radix=2;
break;
default:
radix=10;
}
if (length > 2 && str[0] == '0' && str[1] == 'x')
radix = 16;
for (unsigned i=0; i<length; i++)
{
int digit;
if (str[i] >= '0' && str[i] <= '9')
digit = str[i] - '0';
else if (str[i] >= 'A' && str[i] <= 'F')
digit = str[i] - 'A' + 10;
else if (str[i] >= 'a' && str[i] <= 'f')
digit = str[i] - 'a' + 10;
else
digit = radix;
if (digit < radix)
{
v *= radix;
v += digit;
}
}
if (str[0] == '-')
v.Negate();
return v;
}
Integer::Integer(const char *str)
: reg(2), sign(POSITIVE)
{
*this = StringToInteger(str);
}
Integer::Integer(const wchar_t *str)
: reg(2), sign(POSITIVE)
{
*this = StringToInteger(str);
}
unsigned int Integer::WordCount() const
{
return (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)
{
StringStore store(input, inputLen);
Decode(store, inputLen, s);
}
void Integer::Decode(BufferedTransformation &bt, size_t inputLen, Signedness s)
{
assert(bt.MaxRetrievable() >= inputLen);
byte b;
bt.Peek(b);
sign = ((s==SIGNED) && (b & 0x80)) ? NEGATIVE : POSITIVE;
while (inputLen>0 && (sign==POSITIVE ? b==0 : b==0xff))
{
bt.Skip(1);
inputLen--;
bt.Peek(b);
}
reg.CleanNew(RoundupSize(BytesToWords(inputLen)));
for (size_t i=inputLen; i > 0; i--)
{
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
{
unsigned int outputLen = STDMAX(1U, ByteCount());
if (signedness == UNSIGNED)
return outputLen;
if (NotNegative() && (GetByte(outputLen-1) & 0x80))
outputLen++;
if (IsNegative() && *this < -Power2(outputLen*8-1))
outputLen++;
return outputLen;
}
void Integer::Encode(byte *output, size_t outputLen, Signedness signedness) const
{
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)
{
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 len) const
{
ArraySink sink(output, len);
return OpenPGPEncode(sink);
}
size_t Integer::OpenPGPEncode(BufferedTransformation &bt) const
{
word16 bitCount = BitCount();
bt.PutWord16(bitCount);
size_t byteCount = BitsToBytes(bitCount);
Encode(bt, byteCount);
return 2 + byteCount;
}
void Integer::OpenPGPDecode(const byte *input, size_t len)
{
StringStore store(input, len);
OpenPGPDecode(store);
}
void Integer::OpenPGPDecode(BufferedTransformation &bt)
{
word16 bitCount;
if (bt.GetWord16(bitCount) != 2 || bt.MaxRetrievable() < BitsToBytes(bitCount))
throw OpenPGPDecodeErr();
Decode(bt, BitsToBytes(bitCount));
}
void Integer::Randomize(RandomNumberGenerator &rng, 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)
{
PutWord(false, BIG_ENDIAN_ORDER, m_counterAndSeed, m_counter);
++m_counter;
P1363_KDF2<SHA1>::DeriveKey(output, size, m_counterAndSeed, m_counterAndSeed.size(), NULL, 0);
}
private:
word32 m_counter;
SecByteBlock m_counterAndSeed;
};
bool Integer::GenerateRandomNoThrow(RandomNumberGenerator &i_rng, const NameValuePairs &params)
{
Integer min = params.GetValueWithDefault("Min", Integer::Zero());
Integer max;
if (!params.GetValue("Max", max))
{
int bitLength;
if (params.GetIntValue("BitLength", bitLength))
max = Integer::Power2(bitLength);
else
throw InvalidArgument("Integer: missing Max argument");
}
if (min > max)
throw InvalidArgument("Integer: Min must be no greater than Max");
Integer equiv = params.GetValueWithDefault("EquivalentTo", Integer::Zero());
Integer mod = params.GetValueWithDefault("Mod", Integer::One());
if (equiv.IsNegative() || equiv >= mod)
throw InvalidArgument("Integer: invalid EquivalentTo and/or Mod argument");
Integer::RandomNumberType rnType = params.GetValueWithDefault("RandomNumberType", Integer::ANY);
member_ptr<KDF2_RNG> kdf2Rng;
ConstByteArrayParameter seed;
if (params.GetValue(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 *)NULL);
int i;
i = 0;
while (1)
{
if (++i==16)
{
// check if there are any suitable primes in [min, max]
Integer first = min;
if (FirstPrime(first, max, equiv, mod, pSelector))
{
// if there is only one suitable prime, we're done
*this = first;
if (!FirstPrime(first, max, equiv, mod, pSelector))
return true;
}
else
return false;
}
Randomize(rng, min, max);
if (FirstPrime(*this, STDMIN(*this+mod*PrimeSearchInterval(max), max), equiv, mod, pSelector))
return true;
}
}
default:
throw InvalidArgument("Integer: invalid RandomNumberType argument");
}
}
std::istream& operator>>(std::istream& in, Integer &a)
{
char c;
unsigned int length = 0;
SecBlock<char> str(length + 16);
std::ws(in);
do
{
in.read(&c, 1);
str[length++] = c;
if (length >= str.size())
str.Grow(length + 16);
}
while (in && (c=='-' || c=='x' || (c>='0' && c<='9') || (c>='a' && c<='f') || (c>='A' && c<='F') || c=='h' || c=='H' || c=='o' || c=='O' || c==',' || c=='.'));
if (in.gcount())
in.putback(c);
str[length-1] = '\0';
a = Integer(str);
return in;
}
std::ostream& operator<<(std::ostream& out, const Integer &a)
{
// Get relevant conversion specifications from ostream.
long f = out.flags() & std::ios::basefield; // Get base digits.
int base, block;
char suffix;
switch(f)
{
case std::ios::oct :
base = 8;
block = 8;
suffix = 'o';
break;
case std::ios::hex :
base = 16;
block = 4;
suffix = 'h';
break;
default :
base = 10;
block = 3;
suffix = '.';
}
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 i=0;
SecBlock<char> s(a.BitCount() / (BitPrecision(base)-1) + 1);
while (!!temp1)
{
word digit;
Integer::Divide(digit, temp2, temp1, base);
s[i++]=vec[digit];
temp1.swap(temp2);
}
while (i--)
{
out << s[i];
// if (i && !(i%block))
// out << ",";
}
return out << suffix;
}
Integer& Integer::operator++()
{
if (NotNegative())
{
if (Increment(reg, reg.size()))
{
reg.CleanGrow(2*reg.size());
reg[reg.size()/2]=1;
}
}
else
{
word borrow = Decrement(reg, reg.size());
assert(!borrow);
if (WordCount()==0)
*this = Zero();
}
return *this;
}
Integer& Integer::operator--()
{
if (IsNegative())
{
if (Increment(reg, reg.size()))
{
reg.CleanGrow(2*reg.size());
reg[reg.size()/2]=1;
}
}
else
{
if (Decrement(reg, reg.size()))
*this = -One();
}
return *this;
}
void PositiveAdd(Integer &sum, const Integer &a, const Integer& b)
{
int carry;
if (a.reg.size() == b.reg.size())
carry = Add(sum.reg, a.reg, b.reg, a.reg.size());
else if (a.reg.size() > b.reg.size())
{
carry = Add(sum.reg, a.reg, b.reg, b.reg.size());
CopyWords(sum.reg+b.reg.size(), a.reg+b.reg.size(), a.reg.size()-b.reg.size());
carry = Increment(sum.reg+b.reg.size(), a.reg.size()-b.reg.size(), carry);
}
else
{
carry = Add(sum.reg, a.reg, b.reg, a.reg.size());
CopyWords(sum.reg+a.reg.size(), b.reg+a.reg.size(), b.reg.size()-a.reg.size());
carry = Increment(sum.reg+a.reg.size(), b.reg.size()-a.reg.size(), carry);
}
if (carry)
{
sum.reg.CleanGrow(2*sum.reg.size());
sum.reg[sum.reg.size()/2] = 1;
}
sum.sign = Integer::POSITIVE;
}
void PositiveSubtract(Integer &diff, const Integer &a, const Integer& b)
{
unsigned aSize = a.WordCount();
aSize += aSize%2;
unsigned bSize = b.WordCount();
bSize += bSize%2;
if (aSize == bSize)
{
if (Compare(a.reg, b.reg, aSize) >= 0)
{
Subtract(diff.reg, a.reg, b.reg, aSize);
diff.sign = Integer::POSITIVE;
}
else
{
Subtract(diff.reg, b.reg, a.reg, aSize);
diff.sign = Integer::NEGATIVE;
}
}
else if (aSize > bSize)
{
word borrow = Subtract(diff.reg, a.reg, b.reg, bSize);
CopyWords(diff.reg+bSize, a.reg+bSize, aSize-bSize);
borrow = Decrement(diff.reg+bSize, aSize-bSize, borrow);
assert(!borrow);
diff.sign = Integer::POSITIVE;
}
else
{
word borrow = Subtract(diff.reg, b.reg, a.reg, aSize);
CopyWords(diff.reg+aSize, b.reg+aSize, bSize-aSize);
borrow = Decrement(diff.reg+aSize, bSize-aSize, borrow);
assert(!borrow);
diff.sign = Integer::NEGATIVE;
}
}
// 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;
}
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();
assert(divisor);
if ((divisor & (divisor-1)) == 0) // divisor is a power of 2
{
quotient = dividend >> (BitPrecision(divisor)-1);
remainder = dividend.reg[0] & (divisor-1);
return;
}
unsigned int i = dividend.WordCount();
quotient.reg.CleanNew(RoundupSize(i));
remainder = 0;
while (i--)
{
quotient.reg[i] = DWord(dividend.reg[i], remainder) / divisor;
remainder = DWord(dividend.reg[i], remainder) % divisor;
}
if (dividend.NotNegative())
quotient.sign = POSITIVE;
else
{
quotient.sign = NEGATIVE;
if (remainder)
{
--quotient;
remainder = divisor - remainder;
}
}
}
Integer Integer::DividedBy(word b) const
{
word remainder;
Integer quotient;
Integer::Divide(remainder, quotient, *this, b);
return quotient;
}
word Integer::Modulo(word divisor) const
{
if (!divisor)
throw Integer::DivideByZero();
assert(divisor);
word remainder;
if ((divisor & (divisor-1)) == 0) // divisor is a power of 2
remainder = reg[0] & (divisor-1);
else
{
unsigned int i = WordCount();
if (divisor <= 5)
{
DWord sum(0, 0);
while (i--)
sum += reg[i];
remainder = sum % divisor;
}
else
{
remainder = 0;
while (i--)
remainder = DWord(reg[i], remainder) % divisor;
}
}
if (IsNegative() && remainder)
remainder = divisor - remainder;
return remainder;
}
void Integer::Negate()
{
if (!!(*this)) // don't flip sign if *this==0
sign = Sign(1-sign);
}
int Integer::PositiveCompare(const Integer& t) const
{
unsigned size = WordCount(), tSize = t.WordCount();
if (size == tSize)
return CryptoPP::Compare(reg, t.reg, size);
else
return size > tSize ? 1 : -1;
}
int Integer::Compare(const Integer& t) const
{
if (NotNegative())
{
if (t.NotNegative())
return PositiveCompare(t);
else
return 1;
}
else
{
if (t.NotNegative())
return -1;
else
return -PositiveCompare(t);
}
}
Integer Integer::SquareRoot() const
{
if (!IsPositive())
return Zero();
// overestimate square root
Integer x, y = Power2((BitCount()+1)/2);
assert(y*y >= *this);
do
{
x = y;
y = (x + *this/x) >> 1;
} while (y<x);
return x;
}
bool Integer::IsSquare() const
{
Integer r = SquareRoot();
return *this == r.Squared();
}
bool Integer::IsUnit() const
{
return (WordCount() == 1) && (reg[0] == 1);
}
Integer Integer::MultiplicativeInverse() const
{
return IsUnit() ? *this : Zero();
}
Integer a_times_b_mod_c(const Integer &x, const Integer& y, const Integer& m)
{
return x*y%m;
}
Integer a_exp_b_mod_c(const Integer &x, const Integer& e, const Integer& m)
{
ModularArithmetic mr(m);
return mr.Exponentiate(x, e);
}
Integer Integer::Gcd(const Integer &a, const Integer &b)
{
return EuclideanDomainOf<Integer>().Gcd(a, b);
}
Integer Integer::InverseMod(const Integer &m) const
{
assert(m.NotNegative());
if (IsNegative())
return Modulo(m).InverseMod(m);
if (m.IsEven())
{
if (!m || IsEven())
return Zero(); // no inverse
if (*this == One())
return One();
Integer u = m.Modulo(*this).InverseMod(*this);
return !u ? Zero() : (m*(*this-u)+1)/(*this);
}
SecBlock<word> T(m.reg.size() * 4);
Integer r((word)0, m.reg.size());
unsigned k = AlmostInverse(r.reg, T, reg, reg.size(), m.reg, m.reg.size());
DivideByPower2Mod(r.reg, r.reg, k, m.reg, m.reg.size());
return r;
}
word Integer::InverseMod(word mod) const
{
word g0 = mod, g1 = *this % mod;
word v0 = 0, v1 = 1;
word y;
while (g1)
{
if (g1 == 1)
return v1;
y = g0 / g1;
g0 = g0 % g1;
v0 += y * v1;
if (!g0)
break;
if (g0 == 1)
return mod-v0;
y = g1 / g0;
g1 = g1 % g0;
v1 += y * v0;
}
return 0;
}
// ********************************************************
ModularArithmetic::ModularArithmetic(BufferedTransformation &bt)
{
BERSequenceDecoder seq(bt);
OID oid(seq);
if (oid != ASN1::prime_field())
BERDecodeError();
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();
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();
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();
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();
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;
}
NAMESPACE_END
#endif
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