void CBitPatternTreeMethod::convertToIntegers(CMatrix< C_FLOAT64 > & values)
{
bool Problems = false;
static const C_FLOAT64 limit = 10.0 / std::numeric_limits< C_INT32 >::max();
size_t Size = values.size();
size_t Columns = values.numCols();
C_FLOAT64 * pColumn = values.array();
C_FLOAT64 * pColumnEnd = pColumn + Columns;
C_FLOAT64 * pValue = values.array();
C_FLOAT64 * pValueEnd = pColumn + Size;
for (; pColumn < pColumnEnd; ++pColumn)
{
unsigned C_INT32 Multiplier = 1;
unsigned C_INT32 m00, m01, m10, m11;
unsigned C_INT32 maxden = 10000000;
C_INT32 GCD1, GCD2;
unsigned C_INT32 ai;
C_FLOAT64 x;
for (pValue = pColumn; pValue < pValueEnd; pValue += Columns)
{
x = fabs(*pValue);
if (x < 100 * std::numeric_limits< C_FLOAT64 >::epsilon())
{
continue;
}
/*
* Find rational approximation to given real number
* David Eppstein / UC Irvine / 8 Aug 1993
*
* With corrections from:
* Arno Formella, May 2008
* Stefan Hoops, Sept 2009
*
* Based on the theory of continued fractions
* if x = a1 + 1/(a2 + 1/(a3 + 1/(a4 + ...)))
* then best approximation is found by truncating this series
* (with some adjustments in the last term).
*
* Note the fraction can be recovered as the first column of the matrix
* (a1 1 ) (a2 1 ) (a3 1 ) ...
* (1 0 ) (1 0 ) (1 0)
* Instead of keeping the sequence of continued fraction terms,
* we just keep the last partial product of these matrices.
*/
/* initialize matrix */
m00 = m11 = 1;
m01 = m10 = 0;
/* loop finding terms until denom gets too big */
while (m10 *(ai = (unsigned C_INT32) x) + m11 <= maxden)
{
C_INT32 t;
t = m00 * ai + m01;
m01 = m00;
m00 = t;
t = m10 * ai + m11;
m11 = m10;
m10 = t;
if (fabs(x - (C_FLOAT64) ai) < limit)
break; // SH: We reached the numerical precision of the machine;
x = 1 / (x - (C_FLOAT64) ai);
}
if ((C_FLOAT64) m10 *(C_FLOAT64) ai + (C_FLOAT64) m11 > (C_FLOAT64) maxden)
{
Problems = true;
}
if (fabs(fabs(*pValue) - ((C_FLOAT64) m00) / ((C_FLOAT64) m10)) > 100.0 * std::numeric_limits< C_FLOAT64 >::epsilon())
{
ai = (maxden - m11) / m10;
m00 = m00 * ai + m01;
m10 = m10 * ai + m11;
}
// Find the greatest common divisor (GCD) of the multiplier and the current denominator.
// Euclidean algorithm
GCD1 = m10;
GCD2 = Multiplier;
GCD(GCD1, GCD2);
// Calculate the least common multiplier: LCM = v1 * v2 / GCD(v1, v2)
Multiplier *= m10 / GCD1;
}
for (pValue = pColumn; pValue < pValueEnd; pValue += Columns)
{
*pValue *= Multiplier;
}
}
}
// Euclid's algorithm
int GCD(int x, int y) {
if (y == 0)
return x;
return GCD(y, x%y);
}
LL LCM(LL a, LL b)
{
return a * b / GCD(a, b);
}
static int LCMDenoCalculator( int n, int m )
{
int gcd = GCD( n, m );
return m/gcd;
}
int main()
{
long n;
GF2X a, b, c, c1, ss, ss1, tt, tt1;
double t;
long iter, i;
cout << WD(12,"n") << WD(12,"OldGCD") << WD(12,"GCD") << WD(12,"OldXGCD")
<< WD(12, "XGCD") << "\n";
cout.precision(3);
cout.setf(ios::scientific);
for (n = 32; n <= (1L << 18); n = n << 3) {
random(a, n);
random(b, n);
OldGCD(c, a, b);
GCD(c1, a, b);
OldXGCD(c, ss, tt, a, b);
XGCD(c1, ss1, tt1, a, b);
if (c1 != c || ss1 != ss || tt1 != tt) {
cerr << "**** GF2XTest FAILED!\n";
return 1;
}
cout << WD(12,n);
iter = 0;
do {
iter = iter ? (2*iter) : 1;
t = GetTime();
for (i = 0; i < iter; i++)
OldGCD(c, a, b);
t = GetTime()-t;
} while (t < 0.5);
cout << WD(12,t/iter);
iter = 0;
do {
iter = iter ? (2*iter) : 1;
t = GetTime();
for (i = 0; i < iter; i++)
GCD(c, a, b);
t = GetTime()-t;
} while (t < 0.5);
cout << WD(12,t/iter);
iter = 0;
do {
iter = iter ? (2*iter) : 1;
t = GetTime();
for (i = 0; i < iter; i++)
OldXGCD(c, ss, tt, a, b);
t = GetTime()-t;
} while (t < 0.5);
cout << WD(12,t/iter);
iter = 0;
do {
iter = iter ? (2*iter) : 1;
t = GetTime();
for (i = 0; i < iter; i++)
XGCD(c, ss, tt, a, b);
t = GetTime()-t;
} while (t < 0.5);
cout << WD(12,t/iter);
cout << "\n";
}
return 0;
}
int LCM(int x, int y){
return x * y / GCD(x, y);
}
long IterIrredTest(const ZZ_pEX& f)
{
if (deg(f) <= 0) return 0;
if (deg(f) == 1) return 1;
ZZ_pEXModulus F;
build(F, f);
ZZ_pEX h;
FrobeniusMap(h, F);
long CompTableSize = 2*SqrRoot(deg(f));
ZZ_pEXArgument H;
build(H, h, F, CompTableSize);
long i, d, limit, limit_sqr;
ZZ_pEX g, X, t, prod;
SetX(X);
i = 0;
g = h;
d = 1;
limit = 2;
limit_sqr = limit*limit;
set(prod);
while (2*d <= deg(f)) {
sub(t, g, X);
MulMod(prod, prod, t, F);
i++;
if (i == limit_sqr) {
GCD(t, f, prod);
if (!IsOne(t)) return 0;
set(prod);
limit++;
limit_sqr = limit*limit;
i = 0;
}
d = d + 1;
if (2*d <= deg(f)) {
CompMod(g, g, H, F);
}
}
if (i > 0) {
GCD(t, f, prod);
if (!IsOne(t)) return 0;
}
return 1;
}
unsigned int LCM( unsigned int a, unsigned int b ) {
unsigned int tmp=a/GCD(a,b);
return tmp*b;
}
int main(int argc, char *argv[])
{
if (argc<2) {
cout << "\nUsage: " << argv[0] << " L [c=2 w=64 k=80 d=1]" << endl;
cout << " L is the number of levels\n";
cout << " optional c is number of columns in the key-switching matrices (default=2)\n";
cout << " optional w is Hamming weight of the secret key (default=64)\n";
cout << " optional k is the security parameter (default=80)\n";
cout << " optional d specifies GF(2^d) arithmetic (default=1, must be <=16)\n";
// cout << " k is the security parameter\n";
// cout << " m determines the ring mod Phi_m(X)" << endl;
cout << endl;
exit(0);
}
cout.unsetf(ios::floatfield);
cout.precision(4);
long L = atoi(argv[1]);
long c = 2;
long w = 64;
long k = 80;
long d = 1;
if (argc>2) c = atoi(argv[2]);
if (argc>3) w = atoi(argv[3]);
if (argc>4) k = atoi(argv[4]);
if (argc>5) d = atoi(argv[5]);
if (d>16) Error("d cannot be larger than 16\n");
cout << "\nTesting FHE with parameters L="<<L
<< ", c="<<c<<", w="<<w<<", k="<<k<<", d="<<d<< endl;
// get a lower-bound on the parameter N=phi(m):
// 1. Empirically, we use ~20-bit small primes in the modulus chain (the main
// constraints is that 2m must divide p-1 for every prime p). The first
// prime is larger, a 40-bit prime. (If this is a 32-bit machine then we
// use two 20-bit primes instead.)
// 2. With L levels, the largest modulus for "fresh ciphertexts" has size
// q0 ~ p0 * p^{L} ~ 2^{40+20L}
// 3. We break each ciphertext into upto c digits, do each digit is as large
// as D=2^{(40+20L)/c}
// 4. The added noise variance term from the key-switching operation is
// c*N*sigma^2*D^2, and this must be mod-switched down to w*N (so it is
// on part with the added noise from modulus-switching). Hence the ratio
// P that we use for mod-switching must satisfy c*N*sigma^2*D^2/P^2<w*N,
// or P > sqrt(c/w) * sigma * 2^{(40+20L)/c}
// 5. With this extra P factor, the key-switching matrices are defined
// relative to a modulus of size
// Q0 = q0*P ~ sqrt{c/w} sigma 2^{(40+20L)(1+1/c)}
// 6. To get k-bit security we need N>log(Q0/sigma)(k+110)/7.2, i.e. roughly
// N > (40+20L)(1+1/c)(k+110) / 7.2
long ptxtSpace = 2;
double cc = 1.0+(1.0/(double)c);
long N = (long) ceil((pSize*L+p0Size)*cc*(k+110)/7.2);
cout << " bounding phi(m) > " << N << endl;
#if 0 // A small m for debugging purposes
long m = 15;
#else
// pre-computed values of [phi(m),m,d]
long ms[][4] = {
//phi(m) m ord(2) c_m*1000
{ 1176, 1247, 28, 3736},
{ 1936, 2047, 11, 3870},
{ 2880, 3133, 24, 3254},
{ 4096, 4369, 16, 3422},
{ 5292, 5461, 14, 4160},
{ 5760, 8435, 24, 8935},
{ 8190, 8191, 13, 1273},
{10584, 16383, 14, 8358},
{10752, 11441, 48, 3607},
{12000, 13981, 20, 2467},
{11520, 15665, 24, 14916},
{14112, 18415, 28, 11278},
{15004, 15709, 22, 3867},
{15360, 20485, 24, 12767},
// {16384, 21845, 16, 12798},
{17208 ,21931, 24, 18387},
{18000, 18631, 25, 4208},
{18816, 24295, 28, 16360},
{19200, 21607, 40, 35633},
{21168, 27305, 28, 15407},
{23040, 23377, 48, 5292},
{24576, 24929, 48, 5612},
{27000, 32767, 15, 20021},
{31104, 31609, 71, 5149},
{42336, 42799, 21, 5952},
{46080, 53261, 24, 33409},
{49140, 57337, 39, 2608},
{51840, 59527, 72, 21128},
{61680, 61681, 40, 1273},
{65536, 65537, 32, 1273},
{75264, 82603, 56, 36484},
{84672, 92837, 56, 38520}
};
#if 0
for (long i = 0; i < 25; i++) {
long m = ms[i][1];
PAlgebra alg(m);
alg.printout();
cout << "\n";
// compute phi(m) directly
long phim = 0;
for (long j = 0; j < m; j++)
if (GCD(j, m) == 1) phim++;
if (phim != alg.phiM()) cout << "ERROR\n";
}
exit(0);
#endif
// find the first m satisfying phi(m)>=N and d | ord(2) in Z_m^*
long m = 0;
for (unsigned i=0; i<sizeof(ms)/sizeof(long[3]); i++)
if (ms[i][0]>=N && (ms[i][2] % d) == 0) {
m = ms[i][1];
c_m = 0.001 * (double) ms[i][3];
break;
}
if (m==0) Error("Cannot support this L,d combination");
#endif
// m = 257;
FHEcontext context(m);
#if 0
context.stdev = to_xdouble(0.5); // very low error
#endif
activeContext = &context; // Mark this as the "current" context
context.zMstar.printout();
cout << endl;
// Set the modulus chain
#if 1
// The first 1-2 primes of total p0size bits
#if (NTL_SP_NBITS > p0Size)
AddPrimesByNumber(context, 1, 1UL<<p0Size); // add a single prime
#else
AddPrimesByNumber(context, 2, 1UL<<(p0Size/2)); // add two primes
#endif
#endif
// The next L primes, as small as possible
AddPrimesByNumber(context, L);
ZZ productOfCtxtPrimes = context.productOfPrimes(context.ctxtPrimes);
double productSize = context.logOfProduct(context.ctxtPrimes);
// might as well test that the answer is roughly correct
cout << " context.logOfProduct(...)-log(context.productOfPrimes(...)) = "
<< productSize-log(productOfCtxtPrimes) << endl;
// calculate the size of the digits
context.digits.resize(c);
IndexSet s1;
#if 0
for (long i=0; i<c-1; i++) context.digits[i] = IndexSet(i,i);
context.digits[c-1] = context.ctxtPrimes / IndexSet(0,c-2);
AddPrimesByNumber(context, 2, 1, true);
#else
double sizeSoFar = 0.0;
double maxDigitSize = 0.0;
if (c>1) { // break ciphetext into a few digits
double dsize = productSize/c; // initial estimate
double target = dsize-(pSize/3.0);
long idx = context.ctxtPrimes.first();
for (long i=0; i<c-1; i++) { // compute next digit
IndexSet s;
while (idx <= context.ctxtPrimes.last() && sizeSoFar < target) {
s.insert(idx);
sizeSoFar += log((double)context.ithPrime(idx));
idx = context.ctxtPrimes.next(idx);
}
context.digits[i] = s;
s1.insert(s);
double thisDigitSize = context.logOfProduct(s);
if (maxDigitSize < thisDigitSize) maxDigitSize = thisDigitSize;
cout << " digit #"<<i+1<< " " <<s << ": size " << thisDigitSize << endl;
target += dsize;
}
IndexSet s = context.ctxtPrimes / s1; // all the remaining primes
context.digits[c-1] = s;
double thisDigitSize = context.logOfProduct(s);
if (maxDigitSize < thisDigitSize) maxDigitSize = thisDigitSize;
cout << " digit #"<<c<< " " <<s << ": size " << thisDigitSize << endl;
}
else {
maxDigitSize = context.logOfProduct(context.ctxtPrimes);
context.digits[0] = context.ctxtPrimes;
}
// Add primes to the chain for the P factor of key-switching
double sizeOfSpecialPrimes
= maxDigitSize + log(c/(double)w)/2 + log(context.stdev *2);
AddPrimesBySize(context, sizeOfSpecialPrimes, true);
#endif
cout << "* ctxtPrimes: " << context.ctxtPrimes
<< ", log(q0)=" << context.logOfProduct(context.ctxtPrimes) << endl;
cout << "* specialPrimes: " << context.specialPrimes
<< ", log(P)=" << context.logOfProduct(context.specialPrimes) << endl;
for (long i=0; i<context.numPrimes(); i++) {
cout << " modulus #" << i << " " << context.ithPrime(i) << endl;
}
cout << endl;
setTimersOn();
const ZZX& PhimX = context.zMstar.PhimX(); // The polynomial Phi_m(X)
long phim = context.zMstar.phiM(); // The integer phi(m)
FHESecKey secretKey(context);
const FHEPubKey& publicKey = secretKey;
#if 0 // Debug mode: use sk=1,2
DoubleCRT newSk(to_ZZX(2), context);
long id1 = secretKey.ImportSecKey(newSk, 64, ptxtSpace);
newSk -= 1;
long id2 = secretKey.ImportSecKey(newSk, 64, ptxtSpace);
#else
long id1 = secretKey.GenSecKey(w,ptxtSpace); // A Hamming-weight-w secret key
long id2 = secretKey.GenSecKey(w,ptxtSpace); // A second Hamming-weight-w secret key
#endif
ZZX zero = to_ZZX(0);
// Ctxt zeroCtxt(publicKey);
/******************************************************************/
/** TESTS BEGIN HERE ***/
/******************************************************************/
cout << "ptxtSpace = " << ptxtSpace << endl;
GF2X G; // G is the AES polynomial, G(X)= X^8 +X^4 +X^3 +X +1
SetCoeff(G,8); SetCoeff(G,4); SetCoeff(G,3); SetCoeff(G,1); SetCoeff(G,0);
GF2X X;
SetX(X);
#if 1
// code for rotations...
{
GF2X::HexOutput = 1;
const PAlgebra& al = context.zMstar;
const PAlgebraModTwo& al2 = context.modTwo;
long ngens = al.numOfGens();
long nslots = al.NSlots();
DoubleCRT tmp(context);
vector< vector< DoubleCRT > > maskTable;
maskTable.resize(ngens);
for (long i = 0; i < ngens; i++) {
if (i==0 && al.SameOrd(i)) continue;
long ord = al.OrderOf(i);
maskTable[i].resize(ord+1, tmp);
for (long j = 0; j <= ord; j++) {
// initialize the mask that is 1 whenever
// the ith coordinate is at least j
vector<GF2X> maps, alphas, betas;
al2.mapToSlots(maps, G); // Change G to X to get bits in the slots
alphas.resize(nslots);
for (long k = 0; k < nslots; k++)
if (coordinate(al, i, k) >= j)
alphas[k] = 1;
else alphas[k] = 0;
GF2X ptxt;
al2.embedInSlots(ptxt, alphas, maps);
// Sanity-check, make sure that encode/decode works as expected
al2.decodePlaintext(betas, ptxt, G, maps);
for (long k = 0; k < nslots; k++) {
if (alphas[k] != betas[k]) {
cout << " Mask computation failed, i="<<i<<", j="<<j<<"\n";
return 0;
}
}
maskTable[i][j] = to_ZZX(ptxt);
}
}
vector<GF2X> maps;
al2.mapToSlots(maps, G);
vector<GF2X> alphas(nslots);
for (long i=0; i < nslots; i++)
random(alphas[i], 8); // random degree-7 polynomial mod 2
for (long amt = 0; amt < 20; amt++) {
cout << ".";
GF2X ptxt;
al2.embedInSlots(ptxt, alphas, maps);
DoubleCRT pp(context);
pp = to_ZZX(ptxt);
rotate(pp, amt, maskTable);
GF2X ptxt1 = to_GF2X(to_ZZX(pp));
vector<GF2X> betas;
al2.decodePlaintext(betas, ptxt1, G, maps);
for (long i = 0; i < nslots; i++) {
if (alphas[i] != betas[(i+amt)%nslots]) {
cout << " amt="<<amt<<" oops\n";
return 0;
}
}
}
cout << "\n";
#if 0
long ord0 = al.OrderOf(0);
for (long i = 0; i < nslots; i++) {
cout << alphas[i] << " ";
if ((i+1) % (nslots/ord0) == 0) cout << "\n";
}
cout << "\n\n";
cout << betas.size() << "\n";
for (long i = 0; i < nslots; i++) {
cout << betas[i] << " ";
if ((i+1) % (nslots/ord0) == 0) cout << "\n";
}
#endif
return 0;
}
#endif
// an initial sanity check on noise estimates,
// comparing the estimated variance to the actual average
cout << "pk:"; checkCiphertext(publicKey.pubEncrKey, zero, secretKey);
ZZX ptxt[6]; // first four are plaintext, last two are constants
std::vector<Ctxt> ctxt(4, Ctxt(publicKey));
// Initialize the plaintext and constants to random 0-1 polynomials
for (size_t j=0; j<6; j++) {
ptxt[j].rep.SetLength(phim);
for (long i = 0; i < phim; i++)
ptxt[j].rep[i] = RandomBnd(ptxtSpace);
ptxt[j].normalize();
if (j<4) {
publicKey.Encrypt(ctxt[j], ptxt[j], ptxtSpace);
cout << "c"<<j<<":"; checkCiphertext(ctxt[j], ptxt[j], secretKey);
}
}
// perform upto 2L levels of computation, each level computing:
// 1. c0 += c1
// 2. c1 *= c2 // L1' = max(L1,L2)+1
// 3. c1.reLinearlize
// 4. c2 *= p4
// 5. c2.automorph(k) // k is the first generator of Zm^* /(2)
// 6. c2.reLinearlize
// 7. c3 += p5
// 8. c3 *= c0 // L3' = max(L3,L0,L1)+1
// 9. c2 *= c3 // L2' = max(L2,L0+1,L1+1,L3+1)+1
// 10. c0 *= c0 // L0' = max(L0,L1)+1
// 11. c0.reLinearlize
// 12. c2.reLinearlize
// 13. c3.reLinearlize
//
// The levels of the four ciphertexts behave as follows:
// 0, 0, 0, 0 => 1, 1, 2, 1 => 2, 3, 3, 2
// => 4, 4, 5, 4 => 5, 6, 6, 5
// => 7, 7, 8, 7 => 8,,9, 9, 10 => [...]
//
// We perform the same operations on the plaintext, and after each operation
// we check that decryption still works, and print the curretn modulus and
// noise estimate. We stop when we get the first decryption error, or when
// we reach 2L levels (which really should not happen).
zz_pContext zzpc;
zz_p::init(ptxtSpace);
zzpc.save();
const zz_pXModulus F = to_zz_pX(PhimX);
long g = context.zMstar.ZmStarGen(0); // the first generator in Zm*
zz_pX x2g(g, 1);
zz_pX p2;
// generate a key-switching matrix from s(X^g) to s(X)
secretKey.GenKeySWmatrix(/*powerOfS= */ 1,
/*powerOfX= */ g,
0, 0,
/*ptxtSpace=*/ ptxtSpace);
// generate a key-switching matrix from s^2 to s
secretKey.GenKeySWmatrix(/*powerOfS= */ 2,
/*powerOfX= */ 1,
0, 0,
/*ptxtSpace=*/ ptxtSpace);
// generate a key-switching matrix from s^3 to s
secretKey.GenKeySWmatrix(/*powerOfS= */ 3,
/*powerOfX= */ 1,
0, 0,
/*ptxtSpace=*/ ptxtSpace);
for (long lvl=0; lvl<2*L; lvl++) {
cout << "=======================================================\n";
ctxt[0] += ctxt[1];
ptxt[0] += ptxt[1];
PolyRed(ptxt[0], ptxtSpace, true);
cout << "c0+=c1: "; checkCiphertext(ctxt[0], ptxt[0], secretKey);
ctxt[1].multiplyBy(ctxt[2]);
ptxt[1] = (ptxt[1] * ptxt[2]) % PhimX;
PolyRed(ptxt[1], ptxtSpace, true);
cout << "c1*=c2: "; checkCiphertext(ctxt[1], ptxt[1], secretKey);
ctxt[2].multByConstant(ptxt[4]);
ptxt[2] = (ptxt[2] * ptxt[4]) % PhimX;
PolyRed(ptxt[2], ptxtSpace, true);
cout << "c2*=p4: "; checkCiphertext(ctxt[2], ptxt[2], secretKey);
ctxt[2] >>= g;
zzpc.restore();
p2 = to_zz_pX(ptxt[2]);
CompMod(p2, p2, x2g, F);
ptxt[2] = to_ZZX(p2);
cout << "c2>>="<<g<<":"; checkCiphertext(ctxt[2], ptxt[2], secretKey);
ctxt[2].reLinearize();
cout << "c2.relin:"; checkCiphertext(ctxt[2], ptxt[2], secretKey);
ctxt[3].addConstant(ptxt[5]);
ptxt[3] += ptxt[5];
PolyRed(ptxt[3], ptxtSpace, true);
cout << "c3+=p5: "; checkCiphertext(ctxt[3], ptxt[3], secretKey);
ctxt[3].multiplyBy(ctxt[0]);
ptxt[3] = (ptxt[3] * ptxt[0]) % PhimX;
PolyRed(ptxt[3], ptxtSpace, true);
cout << "c3*=c0: "; checkCiphertext(ctxt[3], ptxt[3], secretKey);
ctxt[0].square();
ptxt[0] = (ptxt[0] * ptxt[0]) % PhimX;
PolyRed(ptxt[0], ptxtSpace, true);
cout << "c0*=c0: "; checkCiphertext(ctxt[0], ptxt[0], secretKey);
ctxt[2].multiplyBy(ctxt[3]);
ptxt[2] = (ptxt[2] * ptxt[3]) % PhimX;
PolyRed(ptxt[2], ptxtSpace, true);
cout << "c2*=c3: "; checkCiphertext(ctxt[2], ptxt[2], secretKey);
}
/******************************************************************/
/** TESTS END HERE ***/
/******************************************************************/
cout << endl;
return 0;
}
// Generate the representation of Z_m^* for a given odd integer m
// and plaintext base p
PAlgebra::PAlgebra(unsigned long mm, unsigned long pp)
{
m = mm;
p = pp;
assert( (m&1) == 1 );
assert( ProbPrime(p) );
// replaced by Mahdi after a conversation with Shai
// assert( m > p && (m % p) != 0 ); // original line
assert( (m % p) != 0 );
// end of replace by Mahdi
assert( m < NTL_SP_BOUND );
// Compute the generators for (Z/mZ)^*
vector<unsigned long> classes(m);
vector<long> orders(m);
unsigned long i;
for (i=0; i<m; i++) { // initially each element in its own class
if (GCD(i,m)!=1)
classes[i] = 0; // i is not in (Z/mZ)^*
else
classes[i] = i;
}
// Start building a representation of (Z/mZ)^*, first use the generator p
conjClasses(classes,p,m); // merge classes that have a factor of 2
// The order of p is the size of the equivalence class of 1
ordP = (unsigned long) count (classes.begin(), classes.end(), 1);
// Compute orders in (Z/mZ)^*/<p> while comparing to (Z/mZ)^*
long idx, largest;
while (true) {
compOrder(orders,classes,true,m);
idx = argmax(orders); // find the element with largest order
largest = orders[idx];
if (largest <= 0) break; // stop comparing to order in (Z/mZ)^*
// store generator with same order as in (Z/mZ)^*
gens.push_back(idx);
ords.push_back(largest);
conjClasses(classes,idx,m); // merge classes that have a factor of idx
}
// Compute orders in (Z/mZ)^*/<p> without comparing to (Z/mZ)^*
while (true) {
compOrder(orders,classes,false,m);
idx = argmax(orders); // find the element with largest order
largest = orders[idx];
if (largest <= 0) break; // we have the trivial group, we are done
// store generator with different order than (Z/mZ)^*
gens.push_back(idx);
ords.push_back(-largest); // store with negative sign
conjClasses(classes,idx,m); // merge classes that have a factor of idx
}
nSlots = qGrpOrd();
phiM = ordP * nSlots;
// Allocate space for the various arrays
T.resize(nSlots);
dLogT.resize(nSlots*gens.size());
Tidx.assign(m,-1); // allocate m slots, initialize them to -1
zmsIdx.assign(m,-1); // allocate m slots, initialize them to -1
for (i=idx=0; i<m; i++) if (GCD(i,m)==1) zmsIdx[i] = idx++;
// Now fill the Tidx and dLogT translation tables. We identify an element
// t\in T with its representation t = \prod_{i=0}^n gi^{ei} mod m (where
// the gi's are the generators in gens[]) , represent t by the vector of
// exponents *in reverse order* (en,...,e1,e0), and order these vectors
// in lexicographic order.
// buffer is initialized to all-zero, which represents 1=\prod_i gi^0
vector<unsigned long> buffer(gens.size()); // temporaty holds exponents
i = idx = 0;
do {
unsigned long t = exponentiate(buffer);
for (unsigned long j=0; j<buffer.size(); j++) dLogT[idx++] = buffer[j];
T[i] = t; // The i'th element in T it t
Tidx[t] = i++; // the index of t in T is i
// increment buffer by one (in lexigoraphic order)
} while (nextExpVector(buffer)); // until we cover all the group
PhimX = Cyclotomic(m); // compute and store Phi_m(X)
// initialize prods array
long ndims = gens.size();
prods.resize(ndims+1);
prods[ndims] = 1;
for (long j = ndims-1; j >= 0; j--) {
prods[j] = OrderOf(j) * prods[j+1];
}
}
/**************************
//Paillier HE system
//len: length of params p,q
**************************/
void Paillier(int len=512){
ZZ n, n2, p, q, g, lamda;
ZZ p1, q1, p1q1;
ZZ miu;
ZZ m1, m2;
ZZ BSm, HEm; //baseline and HE result
ZZ c, c1, c2, cm1, cm2, r;
//key gen
start = std::clock();
GenPrime(p, len);
GenPrime(q, len);
mul(n, p, q);
mul(n2, n, n);
sub(p1,p,1);
sub(q1,q,1);
GCD(lamda,p1,q1);
mul(p1q1,p1,q1);
div(lamda, p1q1, lamda);
RandomBnd(g, n2);
PowerMod(miu,g,lamda,n2);
sub(miu, miu, 1);
div(miu,miu,n); //should add 1?
InvMod(miu, miu, n);
duration = ( std::clock() - start ) / (double) CLOCKS_PER_SEC;
cout<<"Pailler Setup:"<< duration <<'\n';
//Enc
start = std::clock();
RandomBnd(m1,n);
RandomBnd(m2,n);
RandomBnd(r,n); //enc m1
PowerMod(c1, g,m1,n2);
PowerMod(c2, r,n,n2);
MulMod(cm1, c1,c2, n2);
RandomBnd(r,n); //enc m2
PowerMod(c1, g,m2,n2);
PowerMod(c2, r,n,n2);
MulMod(cm2, c1,c2, n2);
duration = ( std::clock() - start ) / (double) CLOCKS_PER_SEC;
cout<<"Pailler Enc:"<< duration/2 <<'\n';
//Evaluation
start = std::clock();
c=cm1;
for(int i=0; i<TIMES; i++)
MulMod(c,c,cm2,n2);
duration = ( std::clock() - start ) / (double) CLOCKS_PER_SEC;
cout<<"Pailler Eval:"<< duration <<'\n';
//c=cm2;
//Dec
start = std::clock();
PowerMod(c,c,lamda,n2);
sub(c,c,1);
div(c,c,n); //should add 1?
MulMod(HEm, c, miu, n);
duration = ( std::clock() - start ) / (double) CLOCKS_PER_SEC;
cout<<"Pailler Dec:"<< duration <<'\n';
//baseline
BSm=m1;
for(int i=0; i<TIMES; i++)
AddMod(BSm,BSm,m2,n);
assert(BSm==HEm);
}
int GCD(int a, int b) {
//printf(">> %d %d\n", a, b);
if (b==0) return a;
else return GCD(b, a%b);
};
void main(void){
printf("%d\n",GCD(6,12));
}
// static
bool CBitPatternTreeMethod::CalculateKernel(CMatrix< C_INT64 > & matrix,
CMatrix< C_INT64 > & kernel,
CVector< size_t > & rowPivot)
{
// std::cout << matrix << std::endl;
// Gaussian elimination
size_t NumRows = matrix.numRows();
size_t NumCols = matrix.numCols();
assert(NumRows > 0);
assert(NumCols > 0);
// Initialize row pivots
rowPivot.resize(NumRows);
size_t * pPivot = rowPivot.array();
for (size_t i = 0; i < NumRows; i++, pPivot++)
{
*pPivot = i;
}
CVector< size_t > RowPivot(rowPivot);
CVector< C_INT64 > Identity(NumRows);
Identity = 1;
C_INT64 * pColumn = matrix.array();
C_INT64 * pColumnEnd = pColumn + NumCols;
C_INT64 * pActiveRow;
C_INT64 * pActiveRowStart = pColumn;
C_INT64 * pActiveRowEnd = pColumnEnd;
C_INT64 * pRow;
C_INT64 * pRowEnd = pColumn + matrix.size();
C_INT64 * pCurrent;
C_INT64 * pIdentity;
CVector< C_INT64 > SwapTmp(NumCols);
size_t CurrentRowIndex = 0;
size_t CurrentColumnIndex = 0;
size_t NonZeroIndex = 0;
CVector< bool > IgnoredColumns(NumCols);
IgnoredColumns = false;
bool * pIgnoredColumn = IgnoredColumns.array();
size_t IgnoredColumnCount = 0;
// For each column
for (; pColumn < pColumnEnd; ++pColumn, ++CurrentColumnIndex, ++pIgnoredColumn)
{
assert(CurrentColumnIndex == CurrentRowIndex + IgnoredColumnCount);
// Find non zero entry in current column.
pRow = pActiveRowStart + CurrentColumnIndex;
NonZeroIndex = CurrentRowIndex;
for (; pRow < pRowEnd; pRow += NumCols, ++NonZeroIndex)
{
if (*pRow != 0)
break;
}
if (NonZeroIndex >= NumRows)
{
*pIgnoredColumn = true;
IgnoredColumnCount++;
continue;
}
if (NonZeroIndex != CurrentRowIndex)
{
// Swap rows
memcpy(SwapTmp.array(), matrix[CurrentRowIndex], NumCols * sizeof(C_INT64));
memcpy(matrix[CurrentRowIndex], matrix[NonZeroIndex], NumCols * sizeof(C_INT64));
memcpy(matrix[NonZeroIndex], SwapTmp.array(), NumCols * sizeof(C_INT64));
// Record pivot
size_t tmp = RowPivot[CurrentRowIndex];
RowPivot[CurrentRowIndex] = RowPivot[NonZeroIndex];
RowPivot[NonZeroIndex] = tmp;
C_INT64 TMP = Identity[CurrentRowIndex];
Identity[CurrentRowIndex] = Identity[NonZeroIndex];
Identity[NonZeroIndex] = TMP;
}
if (*(pActiveRowStart + CurrentColumnIndex) < 0)
{
for (pRow = pActiveRowStart; pRow < pActiveRowEnd; ++pRow)
{
*pRow *= -1;
}
Identity[CurrentRowIndex] *= -1;
}
// For each row
pRow = pActiveRowStart + NumCols;
pIdentity = Identity.array() + CurrentRowIndex + 1;
C_INT64 ActiveRowValue = *(pActiveRowStart + CurrentColumnIndex);
*(pActiveRowStart + CurrentColumnIndex) = Identity[CurrentRowIndex];
for (; pRow < pRowEnd; pRow += NumCols, ++pIdentity)
{
C_INT64 RowValue = *(pRow + CurrentColumnIndex);
if (RowValue == 0)
continue;
*(pRow + CurrentColumnIndex) = 0;
// compute GCD(*pActiveRowStart, *pRow)
C_INT64 GCD1 = abs64(ActiveRowValue);
C_INT64 GCD2 = abs64(RowValue);
GCD(GCD1, GCD2);
C_INT64 alpha = ActiveRowValue / GCD1;
C_INT64 beta = RowValue / GCD1;
// update rest of row
pActiveRow = pActiveRowStart;
pCurrent = pRow;
*pIdentity *= alpha;
GCD1 = abs64(*pIdentity);
for (; pActiveRow < pActiveRowEnd; ++pActiveRow, ++pCurrent)
{
// Assert that we do not have a numerical overflow.
assert(fabs(((C_FLOAT64) alpha) *((C_FLOAT64) * pCurrent) - ((C_FLOAT64) beta) *((C_FLOAT64) * pActiveRow)) < std::numeric_limits< C_INT64 >::max());
*pCurrent = alpha * *pCurrent - beta * *pActiveRow;
// We check that the row values do not have any common divisor.
if (GCD1 > 1 &&
(GCD2 = abs64(*pCurrent)) > 0)
{
GCD(GCD1, GCD2);
}
}
if (GCD1 > 1)
{
*pIdentity /= GCD1;
pActiveRow = pActiveRowStart;
pCurrent = pRow;
for (; pActiveRow < pActiveRowEnd; ++pActiveRow, ++pCurrent)
{
*pCurrent /= GCD1;
}
}
}
pActiveRowStart += NumCols;
pActiveRowEnd += NumCols;
CurrentRowIndex++;
}
assert(CurrentColumnIndex == CurrentRowIndex + IgnoredColumnCount);
assert(CurrentColumnIndex == NumCols);
// std::cout << matrix << std::endl;
// std::cout << IgnoredColumns << std::endl;
// std::cout << Identity << std::endl;
// std::cout << RowPivot << std::endl << std::endl;
size_t KernelRows = NumRows;
size_t KernelCols = NumRows + IgnoredColumnCount - NumCols;
assert(KernelCols > 0);
kernel.resize(KernelRows, KernelCols);
CMatrix< C_INT64 > Kernel(KernelRows, KernelCols);
Kernel = 0;
C_INT64 * pKernelInt = Kernel.array();
C_INT64 * pKernelIntEnd = pKernelInt + Kernel.size();
pActiveRowStart = matrix[CurrentRowIndex];
pActiveRowEnd = matrix[NumRows];
// Null space matrix identity part
pIdentity = Identity.array() + CurrentRowIndex;
C_INT64 * pKernelColumn = Kernel.array();
for (; pActiveRowStart < pActiveRowEnd; pActiveRowStart += NumCols, ++pKernelColumn, ++pIdentity)
{
pKernelInt = pKernelColumn;
pIgnoredColumn = IgnoredColumns.array();
pRow = pActiveRowStart;
pRowEnd = pRow + NumCols;
if (*pIdentity < 0)
{
*pIdentity *= -1;
for (; pRow < pRowEnd; ++pRow, ++pIgnoredColumn)
{
if (*pIgnoredColumn)
{
continue;
}
*pKernelInt = - *pRow;
pKernelInt += KernelCols;
}
}
else
{
for (; pRow < pRowEnd; ++pRow, ++pIgnoredColumn)
{
if (*pIgnoredColumn)
{
continue;
}
*pKernelInt = *pRow;
pKernelInt += KernelCols;
}
}
}
pIdentity = Identity.array() + CurrentRowIndex;
pKernelInt = Kernel[CurrentRowIndex];
for (; pKernelInt < pKernelIntEnd; pKernelInt += KernelCols + 1, ++pIdentity)
{
*pKernelInt = *pIdentity;
}
// std::cout << Kernel << std::endl;
// std::cout << RowPivot << std::endl << std::endl;
// Undo the reordering introduced by Gaussian elimination to the kernel matrix.
pPivot = RowPivot.array();
pRow = Kernel.array();
pRowEnd = pRow + Kernel.size();
for (; pRow < pRowEnd; ++pPivot, pRow += KernelCols)
{
memcpy(kernel[*pPivot], pRow, KernelCols * sizeof(C_INT64));
}
// std::cout << kernel << std::endl << std::endl;
// std::cout << rowPivot << std::endl << std::endl;
return true;
}
// TODO: Add the ability to set a maximum number of iterations
inline BigInt FindFactor
( const BigInt& n,
Int a,
const PollardRhoCtrl& ctrl )
{
if( a == 0 || a == -2 )
Output("WARNING: Problematic choice of Pollard rho shift");
BigInt tmp, gcd;
BigInt one(1);
auto xAdvance =
[&]( BigInt& x )
{
if( ctrl.numSteps == 1 )
{
// TODO: Determine if there is a penalty to x *= x
/*
tmp = x;
tmp *= x;
tmp += a;
x = tmp;
x %= n;
*/
x *= x;
x += a;
x %= n;
}
else
{
PowMod( x, 2*ctrl.numSteps, n, x );
x += a;
x %= n;
}
};
auto QAdvance =
[&]( const BigInt& x, const BigInt& x2, BigInt& Q )
{
tmp = x2;
tmp -= x;
Q *= tmp;
Q %= n;
};
Int gcdDelay = ctrl.gcdDelay;
BigInt xi=ctrl.x0;
BigInt x2i(xi);
BigInt xiSave=xi, x2iSave=x2i;
BigInt Qi(1);
Int k=1, i=1; // it is okay for i to overflow since it is just for printing
while( true )
{
// Advance xi once
xAdvance( xi );
// Advance x2i twice
xAdvance( x2i );
xAdvance( x2i );
// Advance Qi
QAdvance( xi, x2i, Qi );
if( k >= gcdDelay )
{
GCD( Qi, n, gcd );
if( gcd > one )
{
// NOTE: This was not suggested by Pollard's original paper
if( gcd == n )
{
if( gcdDelay == 1 )
{
RuntimeError("(x) converged before (x mod p) at i=",i);
}
else
{
if( ctrl.progress )
Output("Backtracking at i=",i);
i = Max( i-(gcdDelay+1), 0 );
gcdDelay = 1;
xi = xiSave;
x2i = x2iSave;
}
}
else
{
if( ctrl.progress )
Output("Found factor ",gcd," at i=",i);
return gcd;
}
}
// NOTE: This was not suggested by Pollard's original paper
k = 0;
xiSave = xi;
x2iSave = x2i;
Qi = 1;
}
++k;
++i;
}
}
// Reduce plaintext space to a divisor of the original plaintext space
void Ctxt::reducePtxtSpace(long newPtxtSpace)
{
long g = GCD(ptxtSpace, newPtxtSpace);
assert (g>1);
ptxtSpace = g;
}
bool FirstPrime(Integer &p, const Integer &max, const Integer &equiv, const Integer &mod)
{
assert(!equiv.IsNegative() && equiv < mod);
Integer gcd = GCD(equiv, mod);
if (gcd != Integer::One())
{
// the only possible prime p such that p%mod==equiv where GCD(mod,equiv)!=1 is GCD(mod,equiv)
if (p <= gcd && gcd <= max && IsPrime(gcd))
{
p = gcd;
return true;
}
else
return false;
}
BuildPrimeTable();
if (p <= primeTable[primeTableSize-1])
{
word *pItr;
--p;
if (p.IsPositive())
pItr = std::upper_bound(primeTable, primeTable+primeTableSize, p.ConvertToLong());
else
pItr = primeTable;
while (pItr < primeTable+primeTableSize && *pItr%mod != equiv)
++pItr;
if (pItr < primeTable+primeTableSize)
{
p = *pItr;
return p <= max;
}
p = primeTable[primeTableSize-1]+1;
}
assert(p > primeTable[primeTableSize-1]);
if (mod.IsOdd())
return FirstPrime(p, max, CRT(equiv, mod, 1, 2, 1), mod<<1);
p += (equiv-p)%mod;
if (p>max)
return false;
PrimeSieve sieve(p, max, mod);
while (sieve.NextCandidate(p))
{
if (FastProbablePrimeTest(p) && IsPrime(p))
return true;
}
return false;
}
// Encrypts plaintext, result returned in the ciphertext argument. The
// returned value is the plaintext-space for that ciphertext. When called
// with highNoise=true, returns a ciphertext with noise level~q/8.
long FHEPubKey::Encrypt(Ctxt &ctxt, const ZZX& ptxt, long ptxtSpace,
bool highNoise) const
{
FHE_TIMER_START;
assert(this == &ctxt.pubKey);
if (ptxtSpace != pubEncrKey.ptxtSpace) { // plaintext-space mistamtch
ptxtSpace = GCD(ptxtSpace, pubEncrKey.ptxtSpace);
if (ptxtSpace <= 1) Error("Plaintext-space mismatch on encryption");
}
// generate a random encryption of zero from the public encryption key
ctxt = pubEncrKey; // already an encryption of zero, just not a random one
// choose a random small scalar r and a small random error vector e,
// then set ctxt = r*pubEncrKey + ptstSpace*e + (ptxt,0)
DoubleCRT e(context, context.ctxtPrimes);
DoubleCRT r(context, context.ctxtPrimes);
r.sampleSmall();
for (size_t i=0; i<ctxt.parts.size(); i++) { // add noise to all the parts
ctxt.parts[i] *= r;
if (highNoise && i == 0) {
// we sample e so that coefficients are uniform over
// [-Q/(8*ptxtSpace)..Q/(8*ptxtSpace)]
ZZ B;
B = context.productOfPrimes(context.ctxtPrimes);
B /= ptxtSpace;
B /= 8;
e.sampleUniform(B);
}
else {
e.sampleGaussian();
}
e *= ptxtSpace;
ctxt.parts[i] += e;
}
// add in the plaintext
// FIXME: This relies on the first part, ctxt[0], to have handle to 1
if (ptxtSpace==2) ctxt.parts[0] += ptxt;
else { // The general case of ptxtSpace>2: for a ciphertext
// relative to modulus Q, we add ptxt * Q mod ptxtSpace.
long QmodP = rem(context.productOfPrimes(ctxt.primeSet), ptxtSpace);
ctxt.parts[0] += MulMod(ptxt,QmodP,ptxtSpace); // MulMod from module NumbTh
}
// fill in the other ciphertext data members
ctxt.ptxtSpace = ptxtSpace;
if (highNoise) {
// hack: we set noiseVar to Q^2/8, which is just below threshold
// that will signal an error
ctxt.noiseVar = xexp(2*context.logOfProduct(context.ctxtPrimes) - log(8.0));
}
else {
// We have <skey,ctxt>= r*<skey,pkey> +p*(e0+e1*s) +m, where VAR(<skey,pkey>)
// is recorded in pubEncrKey.noiseVar, VAR(ei)=sigma^2*phi(m), and VAR(s) is
// determined by the secret-key Hamming weight (skHwt).
// VAR(r)=phi(m)/2, hence the expected size squared is bounded by:
// E(X^2) <= pubEncrKey.noiseVar *phi(m) *stdev^2
// + p^2*sigma^2 *phi(m) *(skHwt+1) + p^2
long hwt = skHwts[0];
xdouble phim = to_xdouble(context.zMStar.getPhiM());
xdouble sigma2 = context.stdev * context.stdev;
xdouble p2 = to_xdouble(ptxtSpace) * to_xdouble(ptxtSpace);
ctxt.noiseVar = pubEncrKey.noiseVar*phim*0.5
+ p2*sigma2*phim*(hwt+1)*context.zMStar.get_cM() + p2;
}
return ptxtSpace;
}
void TranslateBetweenGrids
( const DistMatrix<T,MC,MR>& A, DistMatrix<T,MC,MR>& B )
{
DEBUG_ONLY(CSE cse("copy::TranslateBetweenGrids [MC,MR]"))
B.Resize( A.Height(), A.Width() );
// Just need to ensure that each viewing comm contains the other team's
// owning comm. Congruence is too strong.
// Compute the number of process rows and columns that each process
// needs to send to.
const Int colStride = B.ColStride();
const Int rowStride = B.RowStride();
const Int colRank = B.ColRank();
const Int rowRank = B.RowRank();
const Int colStrideA = A.ColStride();
const Int rowStrideA = A.RowStride();
const Int colGCD = GCD( colStride, colStrideA );
const Int rowGCD = GCD( rowStride, rowStrideA );
const Int colLCM = colStride*colStrideA / colGCD;
const Int rowLCM = rowStride*rowStrideA / rowGCD;
const Int numColSends = colStride / colGCD;
const Int numRowSends = rowStride / rowGCD;
const Int colAlign = B.ColAlign();
const Int rowAlign = B.RowAlign();
const Int colAlignA = A.ColAlign();
const Int rowAlignA = A.RowAlign();
const bool inBGrid = B.Participating();
const bool inAGrid = A.Participating();
if( !inBGrid && !inAGrid )
return;
const Int maxSendSize =
(A.Height()/(colStrideA*numColSends)+1) *
(A.Width()/(rowStrideA*numRowSends)+1);
// Translate the ranks from A's VC communicator to B's viewing so that
// we can match send/recv communicators. Since A's VC communicator is not
// necessarily defined on every process, we instead work with A's owning
// group and account for row-major ordering if necessary.
const int sizeA = A.Grid().Size();
vector<int> rankMap(sizeA), ranks(sizeA);
if( A.Grid().Order() == COLUMN_MAJOR )
{
for( int j=0; j<sizeA; ++j )
ranks[j] = j;
}
else
{
// The (i,j) = i + j*colStrideA rank in the column-major ordering is
// equal to the j + i*rowStrideA rank in a row-major ordering.
// Since we desire rankMap[i+j*colStrideA] to correspond to process
// (i,j) in A's grid's rank in this viewing group, ranks[i+j*colStrideA]
// should correspond to process (i,j) in A's owning group. Since the
// owning group is ordered row-major in this case, its rank is
// j+i*rowStrideA. Note that setting
// ranks[j+i*rowStrideA] = i+j*colStrideA is *NOT* valid.
for( int i=0; i<colStrideA; ++i )
for( int j=0; j<rowStrideA; ++j )
ranks[i+j*colStrideA] = j+i*rowStrideA;
}
mpi::Translate
( A.Grid().OwningGroup(), sizeA, &ranks[0],
B.Grid().ViewingComm(), &rankMap[0] );
// Have each member of A's grid individually send to all numRow x numCol
// processes in order, while the members of this grid receive from all
// necessary processes at each step.
Int requiredMemory = 0;
if( inAGrid )
requiredMemory += maxSendSize;
if( inBGrid )
requiredMemory += maxSendSize;
vector<T> auxBuf( requiredMemory );
Int offset = 0;
T* sendBuf = &auxBuf[offset];
if( inAGrid )
offset += maxSendSize;
T* recvBuf = &auxBuf[offset];
Int recvRow = 0; // avoid compiler warnings...
if( inAGrid )
recvRow = Mod(Mod(A.ColRank()-colAlignA,colStrideA)+colAlign,colStride);
for( Int colSend=0; colSend<numColSends; ++colSend )
{
Int recvCol = 0; // avoid compiler warnings...
if( inAGrid )
recvCol=Mod(Mod(A.RowRank()-rowAlignA,rowStrideA)+rowAlign,
rowStride);
for( Int rowSend=0; rowSend<numRowSends; ++rowSend )
{
mpi::Request sendRequest;
// Fire off this round of non-blocking sends
if( inAGrid )
{
// Pack the data
Int sendHeight = Length(A.LocalHeight(),colSend,numColSends);
Int sendWidth = Length(A.LocalWidth(),rowSend,numRowSends);
copy::util::InterleaveMatrix
( sendHeight, sendWidth,
A.LockedBuffer(colSend,rowSend),
numColSends, numRowSends*A.LDim(),
sendBuf, 1, sendHeight );
// Send data
const Int recvVCRank = recvRow + recvCol*colStride;
const Int recvViewingRank = B.Grid().VCToViewing( recvVCRank );
mpi::ISend
( sendBuf, sendHeight*sendWidth, recvViewingRank,
B.Grid().ViewingComm(), sendRequest );
}
// Perform this round of recv's
if( inBGrid )
{
const Int sendColOffset = colAlignA;
const Int recvColOffset =
(colSend*colStrideA+colAlign) % colStride;
const Int sendRowOffset = rowAlignA;
const Int recvRowOffset =
(rowSend*rowStrideA+rowAlign) % rowStride;
const Int firstSendRow =
Mod( Mod(colRank-recvColOffset,colStride)+sendColOffset,
colStrideA );
const Int firstSendCol =
Mod( Mod(rowRank-recvRowOffset,rowStride)+sendRowOffset,
rowStrideA );
const Int colShift = Mod( colRank-recvColOffset, colStride );
const Int rowShift = Mod( rowRank-recvRowOffset, rowStride );
const Int numColRecvs = Length( colStrideA, colShift, colStride );
const Int numRowRecvs = Length( rowStrideA, rowShift, rowStride );
// Recv data
// For now, simply receive sequentially. Until we switch to
// nonblocking recv's, we won't be using much of the
// recvBuf
Int sendRow = firstSendRow;
for( Int colRecv=0; colRecv<numColRecvs; ++colRecv )
{
const Int sendColShift = Shift( sendRow, colAlignA, colStrideA ) + colSend*colStrideA;
const Int sendHeight = Length( A.Height(), sendColShift, colLCM );
const Int localColOffset = (sendColShift-B.ColShift()) / colStride;
Int sendCol = firstSendCol;
for( Int rowRecv=0; rowRecv<numRowRecvs; ++rowRecv )
{
const Int sendRowShift = Shift( sendCol, rowAlignA, rowStrideA ) + rowSend*rowStrideA;
const Int sendWidth = Length( A.Width(), sendRowShift, rowLCM );
const Int localRowOffset = (sendRowShift-B.RowShift()) / rowStride;
const Int sendVCRank = sendRow+sendCol*colStrideA;
mpi::Recv
( recvBuf, sendHeight*sendWidth, rankMap[sendVCRank],
B.Grid().ViewingComm() );
// Unpack the data
copy::util::InterleaveMatrix
( sendHeight, sendWidth,
recvBuf, 1, sendHeight,
B.Buffer(localColOffset,localRowOffset),
colLCM/colStride, (rowLCM/rowStride)*B.LDim() );
// Set up the next send col
sendCol = (sendCol + rowStride) % rowStrideA;
}
// Set up the next send row
sendRow = (sendRow + colStride) % colStrideA;
}
}
// Ensure that this round of non-blocking sends completes
if( inAGrid )
{
mpi::Wait( sendRequest );
recvCol = (recvCol + rowStrideA) % rowStride;
}
}
if( inAGrid )
recvRow = (recvRow + colStrideA) % colStride;
}
}
int GCD(int num1, int num2) {
if ( num1 % num2 == 0)
return num2;
else
return GCD( num2, num1 % num2);
}
static int LCMNomiCalculator( int n, int m )
{
int gcd = GCD( n, m );
return n/gcd;
}
void CRational::Normalize()
{
const int gcd = GCD(abs(m_numerator), m_denominator);
m_numerator /= gcd;
m_denominator /= gcd;
}
PAlgebra::PAlgebra(unsigned long mm, unsigned long pp,
const vector<long>& _gens, const vector<long>& _ords )
{
assert( ProbPrime(pp) );
assert( (mm % pp) != 0 );
assert( mm < NTL_SP_BOUND );
assert( mm > 1 );
cM = 1.0; // default value for the ring constant
m = mm;
p = pp;
long k = NextPowerOfTwo(m);
if (mm == (1UL << k))
pow2 = k;
else
pow2 = 0;
// For dry-run, use a tiny m value for the PAlgebra tables
if (isDryRun()) mm = (p==3)? 4 : 3;
// Compute the generators for (Z/mZ)^* (defined in NumbTh.cpp)
if (_gens.size() == 0 || isDryRun())
ordP = findGenerators(this->gens, this->ords, mm, pp);
else {
assert(_gens.size() == _ords.size());
gens = _gens;
ords = _ords;
ordP = multOrd(pp, mm);
}
nSlots = qGrpOrd();
phiM = ordP * nSlots;
// Allocate space for the various arrays
T.resize(nSlots);
dLogT.resize(nSlots*gens.size());
Tidx.assign(mm,-1); // allocate m slots, initialize them to -1
zmsIdx.assign(mm,-1); // allocate m slots, initialize them to -1
long i, idx;
for (i=idx=0; i<(long)mm; i++) if (GCD(i,mm)==1) zmsIdx[i] = idx++;
// Now fill the Tidx and dLogT translation tables. We identify an element
// t\in T with its representation t = \prod_{i=0}^n gi^{ei} mod m (where
// the gi's are the generators in gens[]) , represent t by the vector of
// exponents *in reverse order* (en,...,e1,e0), and order these vectors
// in lexicographic order.
// FIXME: is the comment above about reverse order true? It doesn't
// seem like it to me. VJS.
// buffer is initialized to all-zero, which represents 1=\prod_i gi^0
vector<unsigned long> buffer(gens.size()); // temporaty holds exponents
i = idx = 0;
long ctr = 0;
do {
ctr++;
unsigned long t = exponentiate(buffer);
for (unsigned long j=0; j<buffer.size(); j++) dLogT[idx++] = buffer[j];
assert(GCD(t,mm) == 1); // sanity check for user-supplied gens
assert(Tidx[t] == -1);
T[i] = t; // The i'th element in T it t
Tidx[t] = i++; // the index of t in T is i
// increment buffer by one (in lexigoraphic order)
} while (nextExpVector(buffer)); // until we cover all the group
assert(ctr == long(nSlots)); // sanity check for user-supplied gens
PhimX = Cyclotomic(mm); // compute and store Phi_m(X)
// initialize prods array
long ndims = gens.size();
prods.resize(ndims+1);
prods[ndims] = 1;
for (long j = ndims-1; j >= 0; j--) {
prods[j] = OrderOf(j) * prods[j+1];
}
// pp_factorize(mFactors,mm); // prime-power factorization from NumbTh.cpp
}
int GCD(int a,int b)
{
if(b==0)return a;
else return GCD(b,a%b);
}
static CYTHON_INLINE struct ZZX* ZZX_gcd(struct ZZX* x, struct ZZX* y)
{
struct ZZX* g = new ZZX();
GCD(*g, *x, *y);
return g;
}
ll GCD(ll a, ll b) { return b == 0 ? a : GCD(b, a%b); }
int main() {
int a, b;
printf("Input two numbers:\n");
scanf("%d %d", &a, &b);
printf("Greatest common divisor: %d\n", GCD(a, b));
}
static int LCM( int a, int b )
{
return a * b / GCD( a, b );
}
static unsigned long LCM(unsigned long x, unsigned long y)
{
unsigned long gcd = GCD(x, y);
return (gcd == 0) ? 0 : ((x / gcd) * y);
}
int main(void) {
int num1, num2, denom1, denom2, num3, denom3, isLoop = 1;
char op, input[3], charContinue;
printf("Welcome to the fraction calculator program!\n");
while (isLoop == 1) {
printf("Please insert the first numerator:\n");
scanf("%s", input);
num1 = atoi(input);
fflush(NULL);
printf("Please insert the first denominator:\n");
scanf("%s", input);
denom1 = atoi(input);
fflush(NULL);
printf("This gives us a fraction of %i/%i.\n", num1,denom1);
printf("Please insert the second numerator:\n");
scanf("%s", input);
num2 = atoi(input);
fflush(NULL);
printf("Please insert the second denominator:\n");
scanf("%s", input);
denom2 = atoi(input);
fflush(NULL);
printf("This gives us a second fraction of %i/%i.\n", num2,denom2);
printf("Please insert the operand for the computation: [+ or - or * or /]\n");
scanf("%s", &op);
switch(op) {
case '+':
printf("You have chosen addition.\n");
if (denom1 != denom2) {
denom3 = denom1 * denom2;
num1 = num1 * denom2;
num2 = num2 * denom1;
num3 = num1 + num2;
denom1 = denom3;
denom2 = denom3;
}
else {
denom3 = denom1;
num3 = num1 + num2;
}
break;
case '-':
printf("You have chosen substraction.\n");
if (denom1 != denom2) {
denom3 = denom1 * denom2;
num1 = num1 * denom2;
num2 = num2 * denom1;
num3 = num1 - num2;
denom1 = denom3;
denom2 = denom3;
}
else {
denom3 = denom1;
num3 = num1 - num2;
}
break;
case '*':
printf("You have chosen multiplication.\n");
num3 = num1 * num2;
denom3 = denom1 * denom2;
break;
case '/':
printf("You have chosen division.\n");
num3 = num1 * denom2;
denom3 = denom1 * num2;
break;
}
printf("Thus, we have %i/%i %c %i/%i = %i/%i.\n",num1,denom1,op,num2,denom2,num3,denom3);
printf("Would you like a simplified answer? [y/n]\n");
scanf("%s", &charContinue);
if (charContinue == 'y') {
int gcd;
gcd = GCD(num3,denom3);
if (gcd != 0) {
if (num3 == (num3 / gcd)) {
printf("Your fraction could not be simplified any further.\n");
}
else {
num3 = num3 / gcd;
denom3 = denom3 / gcd;
printf("Your simplified fraction is %i/%i.\n", num3, denom3);
}
}
else {
printf("Your simplified fraction is 0.\n");
}
}
printf("Would you like to continue? [y/n]\n");
scanf("%s", &charContinue);
if (charContinue != 'y') {
printf("Goodbye!\n");
isLoop = 0;
}
}
return 0;
}
