internal void Add(ChineseRemainder ToAdd)
{
for (int Count = 0; Count < DigitsArraySize; Count++)
{
// Operations like this could be very fast if
// they were done on a GPU processor.
// They could be done in parallel, which would
// make it a lot faster than the way this is
// done, one digit at a time. Notice that
// there is no carry operation here.
DigitsArray[Count] += ToAdd.DigitsArray[Count];
int Prime = (int)IntMath.GetPrimeAt(Count);
if (DigitsArray[Count] >= Prime)
{
DigitsArray[Count] -= Prime;
}
// DigitsArray[Count] = DigitsArray[Count] % Prime;
}
}
internal bool IsFermatPrime(Integer ToTest, int HowMany)
{
// Use bigger primes for Fermat test because the
// modulus can't be too small. And also it's
// more likely to be congruent to 1 with a very
// small modulus. In other words it's a lot more
// likely to appear to be a prime when it isn't.
// This Fermat primality test is usually
// described as using random primes to test with,
// and you could do it that way too.
// A common way of doing this is to use a multiple
// of several primes as the base, like
// 2 * 3 * 5 * 7 = 210.
int PArrayLength = IntMath.GetPrimeArrayLength();
if (PArrayLength < 2 * (1024 * 16))
{
throw(new Exception("The PrimeArray length is too short for doing IsFermatPrime()."));
}
int StartAt = PArrayLength - (1024 * 16); // Or much bigger.
if (StartAt < 100)
{
StartAt = 100;
}
for (int Count = StartAt; Count < (HowMany + StartAt); Count++)
{
if (!IsFermatPrimeForOneValue(ToTest, IntMath.GetPrimeAt(Count)))
{
return(false);
}
}
// It _might_ be a prime if it passed this test.
// Increasing HowMany increases the probability that it's a prime.
return(true);
}