void bigSieve (const BigInteger& base, const int numBits, BigInteger& result,
const BigInteger& smallSieve, const int smallSieveSize)
{
jassert (! base[0]); // must be even!
result.setBit (numBits);
result.clearBit (numBits); // to enlarge the array
int index = smallSieve.findNextClearBit (0);
do
{
const int prime = (index << 1) + 1;
BigInteger r (base), remainder;
r.divideBy (prime, remainder);
int i = prime - remainder.getBitRangeAsInt (0, 32);
if (r.isZero())
i += prime;
if ((i & 1) == 0)
i += prime;
i = (i - 1) >> 1;
while (i < numBits)
{
result.setBit (i);
i += prime;
}
index = smallSieve.findNextClearBit (index + 1);
}
while (index < smallSieveSize);
}
bool passesMillerRabin (const BigInteger& n, int iterations)
{
const BigInteger one (1), two (2);
const BigInteger nMinusOne (n - one);
BigInteger d (nMinusOne);
const int s = d.findNextSetBit (0);
d >>= s;
BigInteger smallPrimes;
int numBitsInSmallPrimes = 0;
for (;;)
{
numBitsInSmallPrimes += 256;
createSmallSieve (numBitsInSmallPrimes, smallPrimes);
const int numPrimesFound = numBitsInSmallPrimes - smallPrimes.countNumberOfSetBits();
if (numPrimesFound > iterations + 1)
break;
}
int smallPrime = 2;
while (--iterations >= 0)
{
smallPrime = smallPrimes.findNextClearBit (smallPrime + 1);
BigInteger r (smallPrime);
r.exponentModulo (d, n);
if (r != one && r != nMinusOne)
{
for (int j = 0; j < s; ++j)
{
r.exponentModulo (two, n);
if (r == nMinusOne)
break;
}
if (r != nMinusOne)
return false;
}
}
return true;
}
