// Test Probable BiTwin Chain for: mpzOrigin
// Test the numbers in the optimal order for any given chain length
// Gives the correct length of a BiTwin chain even for short chains
static void ProbableBiTwinChainTestFast(const mpz_class& mpzOrigin, unsigned int& nProbableChainLength, CPrimalityTestParams& testParams)
{
mpz_class& mpzOriginMinusOne = testParams.mpzOriginMinusOne;
mpz_class& mpzOriginPlusOne = testParams.mpzOriginPlusOne;
nProbableChainLength = 0;
// Fermat test for origin-1 first
mpzOriginMinusOne = mpzOrigin - 1;
if (!FermatProbablePrimalityTestFast(mpzOriginMinusOne, nProbableChainLength, testParams, true))
return;
TargetIncrementLength(nProbableChainLength);
// Fermat test for origin+1
mpzOriginPlusOne = mpzOrigin + 1;
if (!FermatProbablePrimalityTestFast(mpzOriginPlusOne, nProbableChainLength, testParams, true))
return;
TargetIncrementLength(nProbableChainLength);
// Euler-Lagrange-Lifchitz test for the following numbers in chain
for (unsigned int nChainSeq = 2; true; nChainSeq += 2)
{
mpzOriginMinusOne <<= 1;
mpzOriginMinusOne++;
bool fFastFail = nChainSeq < 4;
if (!EulerLagrangeLifchitzPrimalityTestFast(mpzOriginMinusOne, true, nProbableChainLength, testParams, fFastFail))
break;
TargetIncrementLength(nProbableChainLength);
mpzOriginPlusOne <<= 1;
mpzOriginPlusOne--;
if (!EulerLagrangeLifchitzPrimalityTestFast(mpzOriginPlusOne, false, nProbableChainLength, testParams, fFastFail))
break;
TargetIncrementLength(nProbableChainLength);
}
}
// Test Probable Cunningham Chain for: n
// fSophieGermain:
// true - Test for Cunningham Chain of first kind (n, 2n+1, 4n+3, ...)
// false - Test for Cunningham Chain of second kind (n, 2n-1, 4n-3, ...)
// Return value:
// true - Probable Cunningham Chain found (length at least 2)
// false - Not Cunningham Chain
static bool ProbableCunninghamChainTestFast(const mpz_class& n,
bool fSophieGermain,
bool fFermatTest,
unsigned int& nProbableChainLength,
CPrimalityTestParams& testParams)
{
nProbableChainLength = 0;
// Fermat test for n first
if (!FermatProbablePrimalityTestFast(n, nProbableChainLength, testParams, true))
return false;
// Euler-Lagrange-Lifchitz test for the following numbers in chain
mpz_class &N = testParams.N;
N = n;
while (true) {
incrementChainLengthInBits(&nProbableChainLength);
N <<= 1;
N += (fSophieGermain? 1 : (-1));
if (fFermatTest) {
if (!FermatProbablePrimalityTestFast(N, nProbableChainLength, testParams))
break;
} else {
if (!EulerLagrangeLifchitzPrimalityTestFast(N, fSophieGermain, nProbableChainLength, testParams))
break;
}
}
return (chainLengthFromBits(nProbableChainLength) >= 2);
}
// Test Probable Cunningham Chain for: n
// fSophieGermain:
// true - Test for Cunningham Chain of first kind (n, 2n+1, 4n+3, ...)
// false - Test for Cunningham Chain of second kind (n, 2n-1, 4n-3, ...)
// Return value:
// true - Probable Cunningham Chain found (length at least 2)
// false - Not Cunningham Chain
static bool ProbableCunninghamChainTestFast(const mpz_class& n, bool fSophieGermain, bool fFermatTest, unsigned int& nProbableChainLength, CPrimalityTestParams& testParams, bool use_gpu_fermat_test)
{
nProbableChainLength = 0;
mpz_class &N = testParams.N;
N = n;
if (!use_gpu_fermat_test && !FermatProbablePrimalityTestFast(N, nProbableChainLength, testParams, true))
{
return false;
}
// Euler-Lagrange-Lifchitz test for the following numbers in chain
while (true)
{
TargetIncrementLength(nProbableChainLength);
N = N + N + (fSophieGermain? 1 : (-1));
if (fFermatTest)
{
if (!FermatProbablePrimalityTestFast(N, nProbableChainLength, testParams, true))
break;
}
else
{
if (!EulerLagrangeLifchitzPrimalityTestFast(N, fSophieGermain, nProbableChainLength, testParams, true))
break;
}
}
return (TargetGetLength(nProbableChainLength) >= 2);
}
bool ProbablePrimalityTestWithTrialDivisionFast(const mpz_class &candidate,
unsigned trialDivisionLimit,
const PrimeSource &primeSource,
CPrimalityTestParams &testParams)
{
for (unsigned i = 0; i < trialDivisionLimit; i++) {
if (candidate % primeSource.prime(i) == 0)
return false;
}
unsigned nLength = 0;
return FermatProbablePrimalityTestFast(candidate, nLength, testParams, true);
}
// Test Probable Cunningham Chain for: n
// fSophieGermain:
// true - Test for Cunningham Chain of first kind (n, 2n+1, 4n+3, ...)
// false - Test for Cunningham Chain of second kind (n, 2n-1, 4n-3, ...)
static void ProbableCunninghamChainTestFast(const mpz_class& n, bool fSophieGermain, unsigned int& nProbableChainLength, CPrimalityTestParams& testParams)
{
nProbableChainLength = 0;
// Fermat test for n first
if (!FermatProbablePrimalityTestFast(n, nProbableChainLength, testParams, true))
return;
// Euler-Lagrange-Lifchitz test for the following numbers in chain
mpz_class &N = testParams.mpzN;
N = n;
for (unsigned int nChainSeq = 1; true; nChainSeq++)
{
TargetIncrementLength(nProbableChainLength);
N <<= 1;
N += (fSophieGermain? 1 : (-1));
bool fFastFail = nChainSeq < 4;
if (!EulerLagrangeLifchitzPrimalityTestFast(N, fSophieGermain, nProbableChainLength, testParams, fFastFail))
break;
}
}
