/**
* It uses the sieve of Eratosthenes to discard several composite numbers in
* some appropriate range (at the moment {@code [this, this + 1024]}). After
* this process it applies the Miller-Rabin test to the numbers that were
* not discarded in the sieve.
*
* @see BigInteger#nextProbablePrime()
* @see #millerRabin(BigInteger, int)
*/
internal static BigInteger nextProbablePrime(BigInteger n)
{
// PRE: n >= 0
int i, j;
int certainty;
int gapSize = 1024; // for searching of the next probable prime number
int [] modules = new int[primes.Length];
bool[] isDivisible = new bool[gapSize];
BigInteger startPoint;
BigInteger probPrime;
// If n < "last prime of table" searches next prime in the table
if ((n.numberLength == 1) && (n.digits[0] >= 0) &&
(n.digits[0] < primes[primes.Length - 1]))
{
for (i = 0; n.digits[0] >= primes[i]; i++)
{
;
}
return(BIprimes[i]);
}
/*
* Creates a "N" enough big to hold the next probable prime Note that: N <
* "next prime" < 2*N
*/
startPoint = new BigInteger(1, n.numberLength,
new int[n.numberLength + 1]);
java.lang.SystemJ.arraycopy(n.digits, 0, startPoint.digits, 0, n.numberLength);
// To fix N to the "next odd number"
if (n.testBit(0))
{
Elementary.inplaceAdd(startPoint, 2);
}
else
{
startPoint.digits[0] |= 1;
}
// To set the improved certainly of Miller-Rabin
j = startPoint.bitLength();
for (certainty = 2; j < BITS[certainty]; certainty++)
{
;
}
// To calculate modules: N mod p1, N mod p2, ... for first primes.
for (i = 0; i < primes.Length; i++)
{
modules[i] = Division.remainder(startPoint, primes[i]) - gapSize;
}
while (true)
{
// At this point, all numbers in the gap are initialized as
// probably primes
java.util.Arrays <Object> .fill(isDivisible, false);
// To discard multiples of first primes
for (i = 0; i < primes.Length; i++)
{
modules[i] = (modules[i] + gapSize) % primes[i];
j = (modules[i] == 0) ? 0 : (primes[i] - modules[i]);
for (; j < gapSize; j += primes[i])
{
isDivisible[j] = true;
}
}
// To execute Miller-Rabin for non-divisible numbers by all first
// primes
for (j = 0; j < gapSize; j++)
{
if (!isDivisible[j])
{
probPrime = startPoint.copy();
Elementary.inplaceAdd(probPrime, j);
if (millerRabin(probPrime, certainty))
{
return(probPrime);
}
}
}
Elementary.inplaceAdd(startPoint, gapSize);
}
}
