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/*
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* Copyright (c) 2003-2009 Nokia Corporation and/or its subsidiary(-ies).
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* All rights reserved.
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* This component and the accompanying materials are made available
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* under the terms of the License "Eclipse Public License v1.0"
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* which accompanies this distribution, and is available
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* at the URL "http://www.eclipse.org/legal/epl-v10.html".
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*
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* Initial Contributors:
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* Nokia Corporation - initial contribution.
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*
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* Contributors:
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*
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* Description:
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*
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*/
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#include "words.h"
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#include "algorithms.h"
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word Add(word *C, const word *A, const word *B, unsigned int N)
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{
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assert (N%2 == 0);
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word carry = 0;
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for (unsigned int i = 0; i < N; i+=2)
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{
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dword u = (dword) carry + A[i] + B[i];
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C[i] = LOW_WORD(u);
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u = (dword) HIGH_WORD(u) + A[i+1] + B[i+1];
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C[i+1] = LOW_WORD(u);
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carry = HIGH_WORD(u);
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}
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return carry;
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}
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word Subtract(word *C, const word *A, const word *B, unsigned int N)
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{
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assert (N%2 == 0);
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word borrow=0;
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for (unsigned i = 0; i < N; i+=2)
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{
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dword u = (dword) A[i] - B[i] - borrow;
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C[i] = LOW_WORD(u);
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u = (dword) A[i+1] - B[i+1] - (word)(0-HIGH_WORD(u));
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C[i+1] = LOW_WORD(u);
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borrow = 0-HIGH_WORD(u);
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}
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return borrow;
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}
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int Compare(const word *A, const word *B, unsigned int N)
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{
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while (N--)
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if (A[N] > B[N])
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return 1;
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else if (A[N] < B[N])
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return -1;
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return 0;
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}
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// It is the job of the calling code to ensure that this won't carry.
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// If you aren't sure, use the next version that will tell you if you need to
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// grow your integer.
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// Having two of these creates ever so slightly more code but avoids having
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// ifdefs all over the rest of the code checking the following type stuff which
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// causes warnings in certain compilers about unused parameters in release
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// builds. We can't have that can we!
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/*
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Allows avoid this all over bigint.cpp and primes.cpp
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ifdef _DEBUG
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TUint carry = Increment(Ptr(), Size());
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assert(!carry);
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else
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Increment(Ptr(), Size())
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endif
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*/
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void IncrementNoCarry(word *A, unsigned int N, word B)
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{
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assert(N);
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word t = A[0];
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A[0] = t+B;
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if (A[0] >= t)
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return;
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for (unsigned i=1; i<N; i++)
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if (++A[i])
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return;
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assert(0);
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}
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word Increment(word *A, unsigned int N, word B)
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{
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assert(N);
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word t = A[0];
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A[0] = t+B;
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if (A[0] >= t)
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return 0;
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for (unsigned i=1; i<N; i++)
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if (++A[i])
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return 0;
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return 1;
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}
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//See commments above about IncrementNoCarry
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void DecrementNoCarry(word *A, unsigned int N, word B)
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{
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assert(N);
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word t = A[0];
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A[0] = t-B;
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if (A[0] <= t)
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return;
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for (unsigned i=1; i<N; i++)
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if (A[i]--)
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return;
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assert(0);
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}
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word Decrement(word *A, unsigned int N, word B)
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{
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assert(N);
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word t = A[0];
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A[0] = t-B;
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if (A[0] <= t)
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return 0;
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for (unsigned i=1; i<N; i++)
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if (A[i]--)
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return 0;
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return 1;
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}
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void TwosComplement(word *A, unsigned int N)
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{
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Decrement(A, N);
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for (unsigned i=0; i<N; i++)
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A[i] = ~A[i];
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}
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static word LinearMultiply(word *C, const word *A, word B, unsigned int N)
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{
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word carry=0;
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for(unsigned i=0; i<N; i++)
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{
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dword p = (dword)A[i] * B + carry;
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C[i] = LOW_WORD(p);
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carry = HIGH_WORD(p);
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}
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return carry;
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}
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static void AtomicMultiply(word *C, const word *A, const word *B)
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{
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/*
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word s;
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dword d;
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if (A1 >= A0)
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if (B0 >= B1)
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{
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s = 0;
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d = (dword)(A1-A0)*(B0-B1);
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}
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else
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{
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s = (A1-A0);
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d = (dword)s*(word)(B0-B1);
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}
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else
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if (B0 > B1)
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{
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s = (B0-B1);
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d = (word)(A1-A0)*(dword)s;
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}
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else
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{
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s = 0;
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d = (dword)(A0-A1)*(B1-B0);
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}
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*/
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// this segment is the branchless equivalent of above
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word D[4] = {A[1]-A[0], A[0]-A[1], B[0]-B[1], B[1]-B[0]};
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unsigned int ai = A[1] < A[0];
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unsigned int bi = B[0] < B[1];
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unsigned int di = ai & bi;
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dword d = (dword)D[di]*D[di+2];
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D[1] = D[3] = 0;
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unsigned int si = ai + !bi;
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word s = D[si];
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dword A0B0 = (dword)A[0]*B[0];
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C[0] = LOW_WORD(A0B0);
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dword A1B1 = (dword)A[1]*B[1];
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dword t = (dword) HIGH_WORD(A0B0) + LOW_WORD(A0B0) + LOW_WORD(d) + LOW_WORD(A1B1);
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C[1] = LOW_WORD(t);
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t = A1B1 + HIGH_WORD(t) + HIGH_WORD(A0B0) + HIGH_WORD(d) + HIGH_WORD(A1B1) - s;
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C[2] = LOW_WORD(t);
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C[3] = HIGH_WORD(t);
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}
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static word AtomicMultiplyAdd(word *C, const word *A, const word *B)
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{
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word D[4] = {A[1]-A[0], A[0]-A[1], B[0]-B[1], B[1]-B[0]};
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unsigned int ai = A[1] < A[0];
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unsigned int bi = B[0] < B[1];
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unsigned int di = ai & bi;
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dword d = (dword)D[di]*D[di+2];
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D[1] = D[3] = 0;
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unsigned int si = ai + !bi;
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word s = D[si];
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dword A0B0 = (dword)A[0]*B[0];
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dword t = A0B0 + C[0];
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C[0] = LOW_WORD(t);
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dword A1B1 = (dword)A[1]*B[1];
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t = (dword) HIGH_WORD(t) + LOW_WORD(A0B0) + LOW_WORD(d) + LOW_WORD(A1B1) + C[1];
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C[1] = LOW_WORD(t);
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t = (dword) HIGH_WORD(t) + LOW_WORD(A1B1) + HIGH_WORD(A0B0) + HIGH_WORD(d) + HIGH_WORD(A1B1) - s + C[2];
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C[2] = LOW_WORD(t);
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t = (dword) HIGH_WORD(t) + HIGH_WORD(A1B1) + C[3];
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C[3] = LOW_WORD(t);
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return HIGH_WORD(t);
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}
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static inline void AtomicMultiplyBottom(word *C, const word *A, const word *B)
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{
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dword t = (dword)A[0]*B[0];
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C[0] = LOW_WORD(t);
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C[1] = HIGH_WORD(t) + A[0]*B[1] + A[1]*B[0];
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}
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#define MulAcc(x, y) \
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p = (dword)A[x] * B[y] + c; \
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c = LOW_WORD(p); \
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p = (dword)d + HIGH_WORD(p); \
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d = LOW_WORD(p); \
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e += HIGH_WORD(p);
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#define SaveMulAcc(s, x, y) \
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R[s] = c; \
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p = (dword)A[x] * B[y] + d; \
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c = LOW_WORD(p); \
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p = (dword)e + HIGH_WORD(p); \
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d = LOW_WORD(p); \
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e = HIGH_WORD(p);
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#define MulAcc1(x, y) \
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p = (dword)A[x] * A[y] + c; \
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c = LOW_WORD(p); \
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p = (dword)d + HIGH_WORD(p); \
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d = LOW_WORD(p); \
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e += HIGH_WORD(p);
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#define SaveMulAcc1(s, x, y) \
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R[s] = c; \
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p = (dword)A[x] * A[y] + d; \
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c = LOW_WORD(p); \
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p = (dword)e + HIGH_WORD(p); \
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d = LOW_WORD(p); \
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e = HIGH_WORD(p);
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#define SquAcc(x, y) \
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p = (dword)A[x] * A[y]; \
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p = p + p + c; \
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c = LOW_WORD(p); \
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p = (dword)d + HIGH_WORD(p); \
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d = LOW_WORD(p); \
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e += HIGH_WORD(p);
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#define SaveSquAcc(s, x, y) \
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R[s] = c; \
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p = (dword)A[x] * A[y]; \
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p = p + p + d; \
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c = LOW_WORD(p); \
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p = (dword)e + HIGH_WORD(p); \
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d = LOW_WORD(p); \
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e = HIGH_WORD(p);
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// VC60 workaround: MSVC 6.0 has an optimization problem that makes
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// (dword)A*B where either A or B has been cast to a dword before
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// very expensive. Revisit a CombaSquare4() function when this
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// problem is fixed.
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// WARNING: KeithR. 05/08/03 This routine doesn't work with gcc on hardware
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// either. I've completely removed it. It may be worth looking into sometime
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// in the future.
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/*#ifndef __WINS__
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static void CombaSquare4(word *R, const word *A)
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{
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dword p;
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word c, d, e;
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p = (dword)A[0] * A[0];
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R[0] = LOW_WORD(p);
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c = HIGH_WORD(p);
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d = e = 0;
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SquAcc(0, 1);
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SaveSquAcc(1, 2, 0);
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MulAcc1(1, 1);
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SaveSquAcc(2, 0, 3);
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SquAcc(1, 2);
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SaveSquAcc(3, 3, 1);
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MulAcc1(2, 2);
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SaveSquAcc(4, 2, 3);
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R[5] = c;
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p = (dword)A[3] * A[3] + d;
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R[6] = LOW_WORD(p);
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R[7] = e + HIGH_WORD(p);
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}
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#endif */
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static void CombaMultiply4(word *R, const word *A, const word *B)
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{
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dword p;
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word c, d, e;
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p = (dword)A[0] * B[0];
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R[0] = LOW_WORD(p);
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c = HIGH_WORD(p);
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d = e = 0;
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MulAcc(0, 1);
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MulAcc(1, 0);
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SaveMulAcc(1, 2, 0);
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MulAcc(1, 1);
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MulAcc(0, 2);
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SaveMulAcc(2, 0, 3);
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MulAcc(1, 2);
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MulAcc(2, 1);
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MulAcc(3, 0);
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SaveMulAcc(3, 3, 1);
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MulAcc(2, 2);
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MulAcc(1, 3);
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SaveMulAcc(4, 2, 3);
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MulAcc(3, 2);
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R[5] = c;
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|
352 |
p = (dword)A[3] * B[3] + d;
|
|
|
353 |
R[6] = LOW_WORD(p);
|
|
|
354 |
R[7] = e + HIGH_WORD(p);
|
|
|
355 |
}
|
|
|
356 |
|
|
|
357 |
static void CombaMultiply8(word *R, const word *A, const word *B)
|
|
|
358 |
{
|
|
|
359 |
dword p;
|
|
|
360 |
word c, d, e;
|
|
|
361 |
|
|
|
362 |
p = (dword)A[0] * B[0];
|
|
|
363 |
R[0] = LOW_WORD(p);
|
|
|
364 |
c = HIGH_WORD(p);
|
|
|
365 |
d = e = 0;
|
|
|
366 |
|
|
|
367 |
MulAcc(0, 1);
|
|
|
368 |
MulAcc(1, 0);
|
|
|
369 |
|
|
|
370 |
SaveMulAcc(1, 2, 0);
|
|
|
371 |
MulAcc(1, 1);
|
|
|
372 |
MulAcc(0, 2);
|
|
|
373 |
|
|
|
374 |
SaveMulAcc(2, 0, 3);
|
|
|
375 |
MulAcc(1, 2);
|
|
|
376 |
MulAcc(2, 1);
|
|
|
377 |
MulAcc(3, 0);
|
|
|
378 |
|
|
|
379 |
SaveMulAcc(3, 0, 4);
|
|
|
380 |
MulAcc(1, 3);
|
|
|
381 |
MulAcc(2, 2);
|
|
|
382 |
MulAcc(3, 1);
|
|
|
383 |
MulAcc(4, 0);
|
|
|
384 |
|
|
|
385 |
SaveMulAcc(4, 0, 5);
|
|
|
386 |
MulAcc(1, 4);
|
|
|
387 |
MulAcc(2, 3);
|
|
|
388 |
MulAcc(3, 2);
|
|
|
389 |
MulAcc(4, 1);
|
|
|
390 |
MulAcc(5, 0);
|
|
|
391 |
|
|
|
392 |
SaveMulAcc(5, 0, 6);
|
|
|
393 |
MulAcc(1, 5);
|
|
|
394 |
MulAcc(2, 4);
|
|
|
395 |
MulAcc(3, 3);
|
|
|
396 |
MulAcc(4, 2);
|
|
|
397 |
MulAcc(5, 1);
|
|
|
398 |
MulAcc(6, 0);
|
|
|
399 |
|
|
|
400 |
SaveMulAcc(6, 0, 7);
|
|
|
401 |
MulAcc(1, 6);
|
|
|
402 |
MulAcc(2, 5);
|
|
|
403 |
MulAcc(3, 4);
|
|
|
404 |
MulAcc(4, 3);
|
|
|
405 |
MulAcc(5, 2);
|
|
|
406 |
MulAcc(6, 1);
|
|
|
407 |
MulAcc(7, 0);
|
|
|
408 |
|
|
|
409 |
SaveMulAcc(7, 1, 7);
|
|
|
410 |
MulAcc(2, 6);
|
|
|
411 |
MulAcc(3, 5);
|
|
|
412 |
MulAcc(4, 4);
|
|
|
413 |
MulAcc(5, 3);
|
|
|
414 |
MulAcc(6, 2);
|
|
|
415 |
MulAcc(7, 1);
|
|
|
416 |
|
|
|
417 |
SaveMulAcc(8, 2, 7);
|
|
|
418 |
MulAcc(3, 6);
|
|
|
419 |
MulAcc(4, 5);
|
|
|
420 |
MulAcc(5, 4);
|
|
|
421 |
MulAcc(6, 3);
|
|
|
422 |
MulAcc(7, 2);
|
|
|
423 |
|
|
|
424 |
SaveMulAcc(9, 3, 7);
|
|
|
425 |
MulAcc(4, 6);
|
|
|
426 |
MulAcc(5, 5);
|
|
|
427 |
MulAcc(6, 4);
|
|
|
428 |
MulAcc(7, 3);
|
|
|
429 |
|
|
|
430 |
SaveMulAcc(10, 4, 7);
|
|
|
431 |
MulAcc(5, 6);
|
|
|
432 |
MulAcc(6, 5);
|
|
|
433 |
MulAcc(7, 4);
|
|
|
434 |
|
|
|
435 |
SaveMulAcc(11, 5, 7);
|
|
|
436 |
MulAcc(6, 6);
|
|
|
437 |
MulAcc(7, 5);
|
|
|
438 |
|
|
|
439 |
SaveMulAcc(12, 6, 7);
|
|
|
440 |
MulAcc(7, 6);
|
|
|
441 |
|
|
|
442 |
R[13] = c;
|
|
|
443 |
p = (dword)A[7] * B[7] + d;
|
|
|
444 |
R[14] = LOW_WORD(p);
|
|
|
445 |
R[15] = e + HIGH_WORD(p);
|
|
|
446 |
}
|
|
|
447 |
|
|
|
448 |
static void CombaMultiplyBottom4(word *R, const word *A, const word *B)
|
|
|
449 |
{
|
|
|
450 |
dword p;
|
|
|
451 |
word c, d, e;
|
|
|
452 |
|
|
|
453 |
p = (dword)A[0] * B[0];
|
|
|
454 |
R[0] = LOW_WORD(p);
|
|
|
455 |
c = HIGH_WORD(p);
|
|
|
456 |
d = e = 0;
|
|
|
457 |
|
|
|
458 |
MulAcc(0, 1);
|
|
|
459 |
MulAcc(1, 0);
|
|
|
460 |
|
|
|
461 |
SaveMulAcc(1, 2, 0);
|
|
|
462 |
MulAcc(1, 1);
|
|
|
463 |
MulAcc(0, 2);
|
|
|
464 |
|
|
|
465 |
R[2] = c;
|
|
|
466 |
R[3] = d + A[0] * B[3] + A[1] * B[2] + A[2] * B[1] + A[3] * B[0];
|
|
|
467 |
}
|
|
|
468 |
|
|
|
469 |
static void CombaMultiplyBottom8(word *R, const word *A, const word *B)
|
|
|
470 |
{
|
|
|
471 |
dword p;
|
|
|
472 |
word c, d, e;
|
|
|
473 |
|
|
|
474 |
p = (dword)A[0] * B[0];
|
|
|
475 |
R[0] = LOW_WORD(p);
|
|
|
476 |
c = HIGH_WORD(p);
|
|
|
477 |
d = e = 0;
|
|
|
478 |
|
|
|
479 |
MulAcc(0, 1);
|
|
|
480 |
MulAcc(1, 0);
|
|
|
481 |
|
|
|
482 |
SaveMulAcc(1, 2, 0);
|
|
|
483 |
MulAcc(1, 1);
|
|
|
484 |
MulAcc(0, 2);
|
|
|
485 |
|
|
|
486 |
SaveMulAcc(2, 0, 3);
|
|
|
487 |
MulAcc(1, 2);
|
|
|
488 |
MulAcc(2, 1);
|
|
|
489 |
MulAcc(3, 0);
|
|
|
490 |
|
|
|
491 |
SaveMulAcc(3, 0, 4);
|
|
|
492 |
MulAcc(1, 3);
|
|
|
493 |
MulAcc(2, 2);
|
|
|
494 |
MulAcc(3, 1);
|
|
|
495 |
MulAcc(4, 0);
|
|
|
496 |
|
|
|
497 |
SaveMulAcc(4, 0, 5);
|
|
|
498 |
MulAcc(1, 4);
|
|
|
499 |
MulAcc(2, 3);
|
|
|
500 |
MulAcc(3, 2);
|
|
|
501 |
MulAcc(4, 1);
|
|
|
502 |
MulAcc(5, 0);
|
|
|
503 |
|
|
|
504 |
SaveMulAcc(5, 0, 6);
|
|
|
505 |
MulAcc(1, 5);
|
|
|
506 |
MulAcc(2, 4);
|
|
|
507 |
MulAcc(3, 3);
|
|
|
508 |
MulAcc(4, 2);
|
|
|
509 |
MulAcc(5, 1);
|
|
|
510 |
MulAcc(6, 0);
|
|
|
511 |
|
|
|
512 |
R[6] = c;
|
|
|
513 |
R[7] = d + A[0] * B[7] + A[1] * B[6] + A[2] * B[5] + A[3] * B[4] +
|
|
|
514 |
A[4] * B[3] + A[5] * B[2] + A[6] * B[1] + A[7] * B[0];
|
|
|
515 |
}
|
|
|
516 |
|
|
|
517 |
#undef MulAcc
|
|
|
518 |
#undef SaveMulAcc
|
|
|
519 |
static void AtomicInverseModPower2(word *C, word A0, word A1)
|
|
|
520 |
{
|
|
|
521 |
assert(A0%2==1);
|
|
|
522 |
|
|
|
523 |
dword A=MAKE_DWORD(A0, A1), R=A0%8;
|
|
|
524 |
|
|
|
525 |
for (unsigned i=3; i<2*WORD_BITS; i*=2)
|
|
|
526 |
R = R*(2-R*A);
|
|
|
527 |
|
|
|
528 |
assert(R*A==1);
|
|
|
529 |
|
|
|
530 |
C[0] = LOW_WORD(R);
|
|
|
531 |
C[1] = HIGH_WORD(R);
|
|
|
532 |
}
|
|
|
533 |
// ********************************************************
|
|
|
534 |
|
|
|
535 |
#define A0 A
|
|
|
536 |
#define A1 (A+N2)
|
|
|
537 |
#define B0 B
|
|
|
538 |
#define B1 (B+N2)
|
|
|
539 |
|
|
|
540 |
#define T0 T
|
|
|
541 |
#define T1 (T+N2)
|
|
|
542 |
#define T2 (T+N)
|
|
|
543 |
#define T3 (T+N+N2)
|
|
|
544 |
|
|
|
545 |
#define R0 R
|
|
|
546 |
#define R1 (R+N2)
|
|
|
547 |
#define R2 (R+N)
|
|
|
548 |
#define R3 (R+N+N2)
|
|
|
549 |
|
|
|
550 |
// R[2*N] - result = A*B
|
|
|
551 |
// T[2*N] - temporary work space
|
|
|
552 |
// A[N] --- multiplier
|
|
|
553 |
// B[N] --- multiplicant
|
|
|
554 |
|
|
|
555 |
void RecursiveMultiply(word *R, word *T, const word *A, const word *B, unsigned int N)
|
|
|
556 |
{
|
|
|
557 |
assert(N>=2 && N%2==0);
|
|
|
558 |
|
|
|
559 |
if (N==2)
|
|
|
560 |
AtomicMultiply(R, A, B);
|
|
|
561 |
else if (N==4)
|
|
|
562 |
CombaMultiply4(R, A, B);
|
|
|
563 |
else if (N==8)
|
|
|
564 |
CombaMultiply8(R, A, B);
|
|
|
565 |
else
|
|
|
566 |
{
|
|
|
567 |
const unsigned int N2 = N/2;
|
|
|
568 |
int carry;
|
|
|
569 |
|
|
|
570 |
int aComp = Compare(A0, A1, N2);
|
|
|
571 |
int bComp = Compare(B0, B1, N2);
|
|
|
572 |
|
|
|
573 |
switch (2*aComp + aComp + bComp)
|
|
|
574 |
{
|
|
|
575 |
case -4:
|
|
|
576 |
Subtract(R0, A1, A0, N2);
|
|
|
577 |
Subtract(R1, B0, B1, N2);
|
|
|
578 |
RecursiveMultiply(T0, T2, R0, R1, N2);
|
|
|
579 |
Subtract(T1, T1, R0, N2);
|
|
|
580 |
carry = -1;
|
|
|
581 |
break;
|
|
|
582 |
case -2:
|
|
|
583 |
Subtract(R0, A1, A0, N2);
|
|
|
584 |
Subtract(R1, B0, B1, N2);
|
|
|
585 |
RecursiveMultiply(T0, T2, R0, R1, N2);
|
|
|
586 |
carry = 0;
|
|
|
587 |
break;
|
|
|
588 |
case 2:
|
|
|
589 |
Subtract(R0, A0, A1, N2);
|
|
|
590 |
Subtract(R1, B1, B0, N2);
|
|
|
591 |
RecursiveMultiply(T0, T2, R0, R1, N2);
|
|
|
592 |
carry = 0;
|
|
|
593 |
break;
|
|
|
594 |
case 4:
|
|
|
595 |
Subtract(R0, A1, A0, N2);
|
|
|
596 |
Subtract(R1, B0, B1, N2);
|
|
|
597 |
RecursiveMultiply(T0, T2, R0, R1, N2);
|
|
|
598 |
Subtract(T1, T1, R1, N2);
|
|
|
599 |
carry = -1;
|
|
|
600 |
break;
|
|
|
601 |
default:
|
|
|
602 |
SetWords(T0, 0, N);
|
|
|
603 |
carry = 0;
|
|
|
604 |
}
|
|
|
605 |
|
|
|
606 |
RecursiveMultiply(R0, T2, A0, B0, N2);
|
|
|
607 |
RecursiveMultiply(R2, T2, A1, B1, N2);
|
|
|
608 |
|
|
|
609 |
// now T[01] holds (A1-A0)*(B0-B1), R[01] holds A0*B0, R[23] holds A1*B1
|
|
|
610 |
|
|
|
611 |
carry += Add(T0, T0, R0, N);
|
|
|
612 |
carry += Add(T0, T0, R2, N);
|
|
|
613 |
carry += Add(R1, R1, T0, N);
|
|
|
614 |
|
|
|
615 |
assert (carry >= 0 && carry <= 2);
|
|
|
616 |
Increment(R3, N2, carry);
|
|
|
617 |
}
|
|
|
618 |
}
|
|
|
619 |
|
|
|
620 |
// R[2*N] - result = A*A
|
|
|
621 |
// T[2*N] - temporary work space
|
|
|
622 |
// A[N] --- number to be squared
|
|
|
623 |
|
|
|
624 |
void RecursiveSquare(word *R, word *T, const word *A, unsigned int N)
|
|
|
625 |
{
|
|
|
626 |
assert(N && N%2==0);
|
|
|
627 |
|
|
|
628 |
if (N==2)
|
|
|
629 |
AtomicMultiply(R, A, A);
|
|
|
630 |
else if (N==4)
|
|
|
631 |
{
|
|
|
632 |
// VC60 workaround: MSVC 6.0 has an optimization problem that makes
|
|
|
633 |
// (dword)A*B where either A or B has been cast to a dword before
|
|
|
634 |
// very expensive. Revisit a CombaSquare4() function when this
|
|
|
635 |
// problem is fixed.
|
|
|
636 |
|
|
|
637 |
// WARNING: KeithR. 05/08/03 This routine doesn't work with gcc on hardware
|
|
|
638 |
// either. I've completely removed it. It may be worth looking into sometime
|
|
|
639 |
// in the future. Therefore, we use the CombaMultiply4 on all targets.
|
|
|
640 |
//#ifdef __WINS__
|
|
|
641 |
CombaMultiply4(R, A, A);
|
|
|
642 |
/*#else
|
|
|
643 |
CombaSquare4(R, A);
|
|
|
644 |
#endif*/
|
|
|
645 |
}
|
|
|
646 |
else
|
|
|
647 |
{
|
|
|
648 |
const unsigned int N2 = N/2;
|
|
|
649 |
|
|
|
650 |
RecursiveSquare(R0, T2, A0, N2);
|
|
|
651 |
RecursiveSquare(R2, T2, A1, N2);
|
|
|
652 |
RecursiveMultiply(T0, T2, A0, A1, N2);
|
|
|
653 |
|
|
|
654 |
word carry = Add(R1, R1, T0, N);
|
|
|
655 |
carry += Add(R1, R1, T0, N);
|
|
|
656 |
Increment(R3, N2, carry);
|
|
|
657 |
}
|
|
|
658 |
}
|
|
|
659 |
// R[N] - bottom half of A*B
|
|
|
660 |
// T[N] - temporary work space
|
|
|
661 |
// A[N] - multiplier
|
|
|
662 |
// B[N] - multiplicant
|
|
|
663 |
|
|
|
664 |
void RecursiveMultiplyBottom(word *R, word *T, const word *A, const word *B, unsigned int N)
|
|
|
665 |
{
|
|
|
666 |
assert(N>=2 && N%2==0);
|
|
|
667 |
|
|
|
668 |
if (N==2)
|
|
|
669 |
AtomicMultiplyBottom(R, A, B);
|
|
|
670 |
else if (N==4)
|
|
|
671 |
CombaMultiplyBottom4(R, A, B);
|
|
|
672 |
else if (N==8)
|
|
|
673 |
CombaMultiplyBottom8(R, A, B);
|
|
|
674 |
else
|
|
|
675 |
{
|
|
|
676 |
const unsigned int N2 = N/2;
|
|
|
677 |
|
|
|
678 |
RecursiveMultiply(R, T, A0, B0, N2);
|
|
|
679 |
RecursiveMultiplyBottom(T0, T1, A1, B0, N2);
|
|
|
680 |
Add(R1, R1, T0, N2);
|
|
|
681 |
RecursiveMultiplyBottom(T0, T1, A0, B1, N2);
|
|
|
682 |
Add(R1, R1, T0, N2);
|
|
|
683 |
}
|
|
|
684 |
}
|
|
|
685 |
|
|
|
686 |
// R[N] --- upper half of A*B
|
|
|
687 |
// T[2*N] - temporary work space
|
|
|
688 |
// L[N] --- lower half of A*B
|
|
|
689 |
// A[N] --- multiplier
|
|
|
690 |
// B[N] --- multiplicant
|
|
|
691 |
|
|
|
692 |
void RecursiveMultiplyTop(word *R, word *T, const word *L, const word *A, const word *B, unsigned int N)
|
|
|
693 |
{
|
|
|
694 |
assert(N>=2 && N%2==0);
|
|
|
695 |
|
|
|
696 |
if (N==2)
|
|
|
697 |
{
|
|
|
698 |
AtomicMultiply(T, A, B);
|
|
|
699 |
((dword *)R)[0] = ((dword *)T)[1];
|
|
|
700 |
}
|
|
|
701 |
else if (N==4)
|
|
|
702 |
{
|
|
|
703 |
CombaMultiply4(T, A, B);
|
|
|
704 |
((dword *)R)[0] = ((dword *)T)[2];
|
|
|
705 |
((dword *)R)[1] = ((dword *)T)[3];
|
|
|
706 |
}
|
|
|
707 |
else
|
|
|
708 |
{
|
|
|
709 |
const unsigned int N2 = N/2;
|
|
|
710 |
int carry;
|
|
|
711 |
|
|
|
712 |
int aComp = Compare(A0, A1, N2);
|
|
|
713 |
int bComp = Compare(B0, B1, N2);
|
|
|
714 |
|
|
|
715 |
switch (2*aComp + aComp + bComp)
|
|
|
716 |
{
|
|
|
717 |
case -4:
|
|
|
718 |
Subtract(R0, A1, A0, N2);
|
|
|
719 |
Subtract(R1, B0, B1, N2);
|
|
|
720 |
RecursiveMultiply(T0, T2, R0, R1, N2);
|
|
|
721 |
Subtract(T1, T1, R0, N2);
|
|
|
722 |
carry = -1;
|
|
|
723 |
break;
|
|
|
724 |
case -2:
|
|
|
725 |
Subtract(R0, A1, A0, N2);
|
|
|
726 |
Subtract(R1, B0, B1, N2);
|
|
|
727 |
RecursiveMultiply(T0, T2, R0, R1, N2);
|
|
|
728 |
carry = 0;
|
|
|
729 |
break;
|
|
|
730 |
case 2:
|
|
|
731 |
Subtract(R0, A0, A1, N2);
|
|
|
732 |
Subtract(R1, B1, B0, N2);
|
|
|
733 |
RecursiveMultiply(T0, T2, R0, R1, N2);
|
|
|
734 |
carry = 0;
|
|
|
735 |
break;
|
|
|
736 |
case 4:
|
|
|
737 |
Subtract(R0, A1, A0, N2);
|
|
|
738 |
Subtract(R1, B0, B1, N2);
|
|
|
739 |
RecursiveMultiply(T0, T2, R0, R1, N2);
|
|
|
740 |
Subtract(T1, T1, R1, N2);
|
|
|
741 |
carry = -1;
|
|
|
742 |
break;
|
|
|
743 |
default:
|
|
|
744 |
SetWords(T0, 0, N);
|
|
|
745 |
carry = 0;
|
|
|
746 |
}
|
|
|
747 |
|
|
|
748 |
RecursiveMultiply(T2, R0, A1, B1, N2);
|
|
|
749 |
|
|
|
750 |
// now T[01] holds (A1-A0)*(B0-B1), T[23] holds A1*B1
|
|
|
751 |
|
|
|
752 |
CopyWords(R0, L+N2, N2);
|
|
|
753 |
word c2 = Subtract(R0, R0, L, N2);
|
|
|
754 |
c2 += Subtract(R0, R0, T0, N2);
|
|
|
755 |
word t = (Compare(R0, T2, N2) == -1);
|
|
|
756 |
|
|
|
757 |
carry += t;
|
|
|
758 |
carry += Increment(R0, N2, c2+t);
|
|
|
759 |
carry += Add(R0, R0, T1, N2);
|
|
|
760 |
carry += Add(R0, R0, T3, N2);
|
|
|
761 |
|
|
|
762 |
CopyWords(R1, T3, N2);
|
|
|
763 |
assert (carry >= 0 && carry <= 2);
|
|
|
764 |
Increment(R1, N2, carry);
|
|
|
765 |
}
|
|
|
766 |
}
|
|
|
767 |
|
|
|
768 |
// R[NA+NB] - result = A*B
|
|
|
769 |
// T[NA+NB] - temporary work space
|
|
|
770 |
// A[NA] ---- multiplier
|
|
|
771 |
// B[NB] ---- multiplicant
|
|
|
772 |
|
|
|
773 |
void AsymmetricMultiply(word *R, word *T, const word *A, unsigned int NA, const word *B, unsigned int NB)
|
|
|
774 |
{
|
|
|
775 |
if (NA == NB)
|
|
|
776 |
{
|
|
|
777 |
if (A == B)
|
|
|
778 |
RecursiveSquare(R, T, A, NA);
|
|
|
779 |
else
|
|
|
780 |
RecursiveMultiply(R, T, A, B, NA);
|
|
|
781 |
|
|
|
782 |
return;
|
|
|
783 |
}
|
|
|
784 |
|
|
|
785 |
if (NA > NB)
|
|
|
786 |
{
|
|
|
787 |
TClassSwap(A, B);
|
|
|
788 |
TClassSwap(NA, NB);
|
|
|
789 |
//std::swap(A, B);
|
|
|
790 |
//std::swap(NA, NB);
|
|
|
791 |
}
|
|
|
792 |
|
|
|
793 |
assert(NB % NA == 0);
|
|
|
794 |
assert((NB/NA)%2 == 0); // NB is an even multiple of NA
|
|
|
795 |
|
|
|
796 |
if (NA==2 && !A[1])
|
|
|
797 |
{
|
|
|
798 |
switch (A[0])
|
|
|
799 |
{
|
|
|
800 |
case 0:
|
|
|
801 |
SetWords(R, 0, NB+2);
|
|
|
802 |
return;
|
|
|
803 |
case 1:
|
|
|
804 |
CopyWords(R, B, NB);
|
|
|
805 |
R[NB] = R[NB+1] = 0;
|
|
|
806 |
return;
|
|
|
807 |
default:
|
|
|
808 |
R[NB] = LinearMultiply(R, B, A[0], NB);
|
|
|
809 |
R[NB+1] = 0;
|
|
|
810 |
return;
|
|
|
811 |
}
|
|
|
812 |
}
|
|
|
813 |
|
|
|
814 |
RecursiveMultiply(R, T, A, B, NA);
|
|
|
815 |
CopyWords(T+2*NA, R+NA, NA);
|
|
|
816 |
|
|
|
817 |
unsigned i;
|
|
|
818 |
|
|
|
819 |
for (i=2*NA; i<NB; i+=2*NA)
|
|
|
820 |
RecursiveMultiply(T+NA+i, T, A, B+i, NA);
|
|
|
821 |
for (i=NA; i<NB; i+=2*NA)
|
|
|
822 |
RecursiveMultiply(R+i, T, A, B+i, NA);
|
|
|
823 |
|
|
|
824 |
if (Add(R+NA, R+NA, T+2*NA, NB-NA))
|
|
|
825 |
Increment(R+NB, NA);
|
|
|
826 |
}
|
|
|
827 |
// R[N] ----- result = A inverse mod 2**(WORD_BITS*N)
|
|
|
828 |
// T[3*N/2] - temporary work space
|
|
|
829 |
// A[N] ----- an odd number as input
|
|
|
830 |
|
|
|
831 |
void RecursiveInverseModPower2(word *R, word *T, const word *A, unsigned int N)
|
|
|
832 |
{
|
|
|
833 |
if (N==2)
|
|
|
834 |
AtomicInverseModPower2(R, A[0], A[1]);
|
|
|
835 |
else
|
|
|
836 |
{
|
|
|
837 |
const unsigned int N2 = N/2;
|
|
|
838 |
RecursiveInverseModPower2(R0, T0, A0, N2);
|
|
|
839 |
T0[0] = 1;
|
|
|
840 |
SetWords(T0+1, 0, N2-1);
|
|
|
841 |
RecursiveMultiplyTop(R1, T1, T0, R0, A0, N2);
|
|
|
842 |
RecursiveMultiplyBottom(T0, T1, R0, A1, N2);
|
|
|
843 |
Add(T0, R1, T0, N2);
|
|
|
844 |
TwosComplement(T0, N2);
|
|
|
845 |
RecursiveMultiplyBottom(R1, T1, R0, T0, N2);
|
|
|
846 |
}
|
|
|
847 |
}
|
|
|
848 |
#undef A0
|
|
|
849 |
#undef A1
|
|
|
850 |
#undef B0
|
|
|
851 |
#undef B1
|
|
|
852 |
|
|
|
853 |
#undef T0
|
|
|
854 |
#undef T1
|
|
|
855 |
#undef T2
|
|
|
856 |
#undef T3
|
|
|
857 |
|
|
|
858 |
#undef R0
|
|
|
859 |
#undef R1
|
|
|
860 |
#undef R2
|
|
|
861 |
#undef R3
|
|
|
862 |
|
|
|
863 |
// R[N] --- result = X/(2**(WORD_BITS*N)) mod M
|
|
|
864 |
// T[3*N] - temporary work space
|
|
|
865 |
// X[2*N] - number to be reduced
|
|
|
866 |
// M[N] --- modulus
|
|
|
867 |
// U[N] --- multiplicative inverse of M mod 2**(WORD_BITS*N)
|
|
|
868 |
|
|
|
869 |
void MontgomeryReduce(word *R, word *T, const word *X, const word *M, const word *U, unsigned int N)
|
|
|
870 |
{
|
|
|
871 |
RecursiveMultiplyBottom(R, T, X, U, N);
|
|
|
872 |
RecursiveMultiplyTop(T, T+N, X, R, M, N);
|
|
|
873 |
if (Subtract(R, X+N, T, N))
|
|
|
874 |
{
|
|
|
875 |
#ifdef _DEBUG
|
|
|
876 |
word carry = Add(R, R, M, N);
|
|
|
877 |
assert(carry);
|
|
|
878 |
#else
|
|
|
879 |
Add(R, R, M, N);
|
|
|
880 |
#endif
|
|
|
881 |
}
|
|
|
882 |
}
|
|
|
883 |
|
|
|
884 |
// do a 3 word by 2 word divide, returns quotient and leaves remainder in A
|
|
|
885 |
static word SubatomicDivide(word *A, word B0, word B1)
|
|
|
886 |
{
|
|
|
887 |
// assert {A[2],A[1]} < {B1,B0}, so quotient can fit in a word
|
|
|
888 |
assert(A[2] < B1 || (A[2]==B1 && A[1] < B0));
|
|
|
889 |
|
|
|
890 |
dword p, u;
|
|
|
891 |
word Q;
|
|
|
892 |
|
|
|
893 |
// estimate the quotient: do a 2 word by 1 word divide
|
|
|
894 |
if (B1+1 == 0)
|
|
|
895 |
Q = A[2];
|
|
|
896 |
else
|
|
|
897 |
Q = word(MAKE_DWORD(A[1], A[2]) / (B1+1));
|
|
|
898 |
|
|
|
899 |
// now subtract Q*B from A
|
|
|
900 |
p = (dword) B0*Q;
|
|
|
901 |
u = (dword) A[0] - LOW_WORD(p);
|
|
|
902 |
A[0] = LOW_WORD(u);
|
|
|
903 |
u = (dword) A[1] - HIGH_WORD(p) - (word)(0-HIGH_WORD(u)) - (dword)B1*Q;
|
|
|
904 |
A[1] = LOW_WORD(u);
|
|
|
905 |
A[2] += HIGH_WORD(u);
|
|
|
906 |
|
|
|
907 |
// Q <= actual quotient, so fix it
|
|
|
908 |
while (A[2] || A[1] > B1 || (A[1]==B1 && A[0]>=B0))
|
|
|
909 |
{
|
|
|
910 |
u = (dword) A[0] - B0;
|
|
|
911 |
A[0] = LOW_WORD(u);
|
|
|
912 |
u = (dword) A[1] - B1 - (word)(0-HIGH_WORD(u));
|
|
|
913 |
A[1] = LOW_WORD(u);
|
|
|
914 |
A[2] += HIGH_WORD(u);
|
|
|
915 |
Q++;
|
|
|
916 |
assert(Q); // shouldn't overflow
|
|
|
917 |
}
|
|
|
918 |
|
|
|
919 |
return Q;
|
|
|
920 |
}
|
|
|
921 |
|
|
|
922 |
// do a 4 word by 2 word divide, returns 2 word quotient in Q0 and Q1
|
|
|
923 |
static inline void AtomicDivide(word *Q, const word *A, const word *B)
|
|
|
924 |
{
|
|
|
925 |
if (!B[0] && !B[1]) // if divisor is 0, we assume divisor==2**(2*WORD_BITS)
|
|
|
926 |
{
|
|
|
927 |
Q[0] = A[2];
|
|
|
928 |
Q[1] = A[3];
|
|
|
929 |
}
|
|
|
930 |
else
|
|
|
931 |
{
|
|
|
932 |
word T[4];
|
|
|
933 |
T[0] = A[0]; T[1] = A[1]; T[2] = A[2]; T[3] = A[3];
|
|
|
934 |
Q[1] = SubatomicDivide(T+1, B[0], B[1]);
|
|
|
935 |
Q[0] = SubatomicDivide(T, B[0], B[1]);
|
|
|
936 |
|
|
|
937 |
#ifdef _DEBUG
|
|
|
938 |
// multiply quotient and divisor and add remainder, make sure it equals dividend
|
|
|
939 |
assert(!T[2] && !T[3] && (T[1] < B[1] || (T[1]==B[1] && T[0]<B[0])));
|
|
|
940 |
word P[4];
|
|
|
941 |
AtomicMultiply(P, Q, B);
|
|
|
942 |
Add(P, P, T, 4);
|
|
|
943 |
assert(Mem::Compare((TUint8*)P, 4*WORD_SIZE, (TUint8*)A, 4*WORD_SIZE)==0);
|
|
|
944 |
#endif
|
|
|
945 |
}
|
|
|
946 |
}
|
|
|
947 |
|
|
|
948 |
// for use by Divide(), corrects the underestimated quotient {Q1,Q0}
|
|
|
949 |
static void CorrectQuotientEstimate(word *R, word *T, word *Q, const word *B, unsigned int N)
|
|
|
950 |
{
|
|
|
951 |
assert(N && N%2==0);
|
|
|
952 |
|
|
|
953 |
if (Q[1])
|
|
|
954 |
{
|
|
|
955 |
T[N] = T[N+1] = 0;
|
|
|
956 |
unsigned i;
|
|
|
957 |
for (i=0; i<N; i+=4)
|
|
|
958 |
AtomicMultiply(T+i, Q, B+i);
|
|
|
959 |
for (i=2; i<N; i+=4)
|
|
|
960 |
if (AtomicMultiplyAdd(T+i, Q, B+i))
|
|
|
961 |
T[i+5] += (++T[i+4]==0);
|
|
|
962 |
}
|
|
|
963 |
else
|
|
|
964 |
{
|
|
|
965 |
T[N] = LinearMultiply(T, B, Q[0], N);
|
|
|
966 |
T[N+1] = 0;
|
|
|
967 |
}
|
|
|
968 |
|
|
|
969 |
#ifdef _DEBUG
|
|
|
970 |
word borrow = Subtract(R, R, T, N+2);
|
|
|
971 |
assert(!borrow && !R[N+1]);
|
|
|
972 |
#else
|
|
|
973 |
Subtract(R, R, T, N+2);
|
|
|
974 |
#endif
|
|
|
975 |
|
|
|
976 |
while (R[N] || Compare(R, B, N) >= 0)
|
|
|
977 |
{
|
|
|
978 |
R[N] -= Subtract(R, R, B, N);
|
|
|
979 |
Q[1] += (++Q[0]==0);
|
|
|
980 |
assert(Q[0] || Q[1]); // no overflow
|
|
|
981 |
}
|
|
|
982 |
}
|
|
|
983 |
|
|
|
984 |
// R[NB] -------- remainder = A%B
|
|
|
985 |
// Q[NA-NB+2] --- quotient = A/B
|
|
|
986 |
// T[NA+2*NB+4] - temp work space
|
|
|
987 |
// A[NA] -------- dividend
|
|
|
988 |
// B[NB] -------- divisor
|
|
|
989 |
|
|
|
990 |
void Divide(word *R, word *Q, word *T, const word *A, unsigned int NA, const word *B, unsigned int NB)
|
|
|
991 |
{
|
|
|
992 |
assert(NA && NB && NA%2==0 && NB%2==0);
|
|
|
993 |
assert(B[NB-1] || B[NB-2]);
|
|
|
994 |
assert(NB <= NA);
|
|
|
995 |
|
|
|
996 |
// set up temporary work space
|
|
|
997 |
word *const TA=T;
|
|
|
998 |
word *const TB=T+NA+2;
|
|
|
999 |
word *const TP=T+NA+2+NB;
|
|
|
1000 |
|
|
|
1001 |
// copy B into TB and normalize it so that TB has highest bit set to 1
|
|
|
1002 |
unsigned shiftWords = (B[NB-1]==0);
|
|
|
1003 |
TB[0] = TB[NB-1] = 0;
|
|
|
1004 |
CopyWords(TB+shiftWords, B, NB-shiftWords);
|
|
|
1005 |
unsigned shiftBits = WORD_BITS - BitPrecision(TB[NB-1]);
|
|
|
1006 |
assert(shiftBits < WORD_BITS);
|
|
|
1007 |
ShiftWordsLeftByBits(TB, NB, shiftBits);
|
|
|
1008 |
|
|
|
1009 |
// copy A into TA and normalize it
|
|
|
1010 |
TA[0] = TA[NA] = TA[NA+1] = 0;
|
|
|
1011 |
CopyWords(TA+shiftWords, A, NA);
|
|
|
1012 |
ShiftWordsLeftByBits(TA, NA+2, shiftBits);
|
|
|
1013 |
|
|
|
1014 |
if (TA[NA+1]==0 && TA[NA] <= 1)
|
|
|
1015 |
{
|
|
|
1016 |
Q[NA-NB+1] = Q[NA-NB] = 0;
|
|
|
1017 |
while (TA[NA] || Compare(TA+NA-NB, TB, NB) >= 0)
|
|
|
1018 |
{
|
|
|
1019 |
TA[NA] -= Subtract(TA+NA-NB, TA+NA-NB, TB, NB);
|
|
|
1020 |
++Q[NA-NB];
|
|
|
1021 |
}
|
|
|
1022 |
}
|
|
|
1023 |
else
|
|
|
1024 |
{
|
|
|
1025 |
NA+=2;
|
|
|
1026 |
assert(Compare(TA+NA-NB, TB, NB) < 0);
|
|
|
1027 |
}
|
|
|
1028 |
|
|
|
1029 |
word BT[2];
|
|
|
1030 |
BT[0] = TB[NB-2] + 1;
|
|
|
1031 |
BT[1] = TB[NB-1] + (BT[0]==0);
|
|
|
1032 |
|
|
|
1033 |
// start reducing TA mod TB, 2 words at a time
|
|
|
1034 |
for (unsigned i=NA-2; i>=NB; i-=2)
|
|
|
1035 |
{
|
|
|
1036 |
AtomicDivide(Q+i-NB, TA+i-2, BT);
|
|
|
1037 |
CorrectQuotientEstimate(TA+i-NB, TP, Q+i-NB, TB, NB);
|
|
|
1038 |
}
|
|
|
1039 |
|
|
|
1040 |
// copy TA into R, and denormalize it
|
|
|
1041 |
CopyWords(R, TA+shiftWords, NB);
|
|
|
1042 |
ShiftWordsRightByBits(R, NB, shiftBits);
|
|
|
1043 |
}
|
|
|
1044 |
|
|
|
1045 |
static inline unsigned int EvenWordCount(const word *X, unsigned int N)
|
|
|
1046 |
{
|
|
|
1047 |
while (N && X[N-2]==0 && X[N-1]==0)
|
|
|
1048 |
N-=2;
|
|
|
1049 |
return N;
|
|
|
1050 |
}
|
|
|
1051 |
|
|
|
1052 |
// return k
|
|
|
1053 |
// R[N] --- result = A^(-1) * 2^k mod M
|
|
|
1054 |
// T[4*N] - temporary work space
|
|
|
1055 |
// A[NA] -- number to take inverse of
|
|
|
1056 |
// M[N] --- modulus
|
|
|
1057 |
|
|
|
1058 |
unsigned int AlmostInverse(word *R, word *T, const word *A, unsigned int NA, const word *M, unsigned int N)
|
|
|
1059 |
{
|
|
|
1060 |
assert(NA<=N && N && N%2==0);
|
|
|
1061 |
|
|
|
1062 |
word *b = T;
|
|
|
1063 |
word *c = T+N;
|
|
|
1064 |
word *f = T+2*N;
|
|
|
1065 |
word *g = T+3*N;
|
|
|
1066 |
unsigned int bcLen=2, fgLen=EvenWordCount(M, N);
|
|
|
1067 |
unsigned int k=0, s=0;
|
|
|
1068 |
|
|
|
1069 |
SetWords(T, 0, 3*N);
|
|
|
1070 |
b[0]=1;
|
|
|
1071 |
CopyWords(f, A, NA);
|
|
|
1072 |
CopyWords(g, M, N);
|
|
|
1073 |
|
|
|
1074 |
FOREVER
|
|
|
1075 |
{
|
|
|
1076 |
word t=f[0];
|
|
|
1077 |
while (!t)
|
|
|
1078 |
{
|
|
|
1079 |
if (EvenWordCount(f, fgLen)==0)
|
|
|
1080 |
{
|
|
|
1081 |
SetWords(R, 0, N);
|
|
|
1082 |
return 0;
|
|
|
1083 |
}
|
|
|
1084 |
|
|
|
1085 |
ShiftWordsRightByWords(f, fgLen, 1);
|
|
|
1086 |
if (c[bcLen-1]) bcLen+=2;
|
|
|
1087 |
assert(bcLen <= N);
|
|
|
1088 |
ShiftWordsLeftByWords(c, bcLen, 1);
|
|
|
1089 |
k+=WORD_BITS;
|
|
|
1090 |
t=f[0];
|
|
|
1091 |
}
|
|
|
1092 |
|
|
|
1093 |
unsigned int i=0;
|
|
|
1094 |
while (t%2 == 0)
|
|
|
1095 |
{
|
|
|
1096 |
t>>=1;
|
|
|
1097 |
i++;
|
|
|
1098 |
}
|
|
|
1099 |
k+=i;
|
|
|
1100 |
|
|
|
1101 |
if (t==1 && f[1]==0 && EvenWordCount(f, fgLen)==2)
|
|
|
1102 |
{
|
|
|
1103 |
if (s%2==0)
|
|
|
1104 |
CopyWords(R, b, N);
|
|
|
1105 |
else
|
|
|
1106 |
Subtract(R, M, b, N);
|
|
|
1107 |
return k;
|
|
|
1108 |
}
|
|
|
1109 |
|
|
|
1110 |
ShiftWordsRightByBits(f, fgLen, i);
|
|
|
1111 |
t=ShiftWordsLeftByBits(c, bcLen, i);
|
|
|
1112 |
if (t)
|
|
|
1113 |
{
|
|
|
1114 |
c[bcLen] = t;
|
|
|
1115 |
bcLen+=2;
|
|
|
1116 |
assert(bcLen <= N);
|
|
|
1117 |
}
|
|
|
1118 |
|
|
|
1119 |
if (f[fgLen-2]==0 && g[fgLen-2]==0 && f[fgLen-1]==0 && g[fgLen-1]==0)
|
|
|
1120 |
fgLen-=2;
|
|
|
1121 |
|
|
|
1122 |
if (Compare(f, g, fgLen)==-1)
|
|
|
1123 |
{
|
|
|
1124 |
TClassSwap<word*>(f,g);
|
|
|
1125 |
TClassSwap<word*>(b,c);
|
|
|
1126 |
s++;
|
|
|
1127 |
}
|
|
|
1128 |
|
|
|
1129 |
Subtract(f, f, g, fgLen);
|
|
|
1130 |
|
|
|
1131 |
if (Add(b, b, c, bcLen))
|
|
|
1132 |
{
|
|
|
1133 |
b[bcLen] = 1;
|
|
|
1134 |
bcLen+=2;
|
|
|
1135 |
assert(bcLen <= N);
|
|
|
1136 |
}
|
|
|
1137 |
}
|
|
|
1138 |
}
|
|
|
1139 |
|
|
|
1140 |
// R[N] - result = A/(2^k) mod M
|
|
|
1141 |
// A[N] - input
|
|
|
1142 |
// M[N] - modulus
|
|
|
1143 |
|
|
|
1144 |
void DivideByPower2Mod(word *R, const word *A, unsigned int k, const word *M, unsigned int N)
|
|
|
1145 |
{
|
|
|
1146 |
CopyWords(R, A, N);
|
|
|
1147 |
|
|
|
1148 |
while (k--)
|
|
|
1149 |
{
|
|
|
1150 |
if (R[0]%2==0)
|
|
|
1151 |
ShiftWordsRightByBits(R, N, 1);
|
|
|
1152 |
else
|
|
|
1153 |
{
|
|
|
1154 |
word carry = Add(R, R, M, N);
|
|
|
1155 |
ShiftWordsRightByBits(R, N, 1);
|
|
|
1156 |
R[N-1] += carry<<(WORD_BITS-1);
|
|
|
1157 |
}
|
|
|
1158 |
}
|
|
|
1159 |
}
|
|
|
1160 |
|