eve-java | Java implementation of Eve , a multipurpose , web | SDK library

In the quadratic sieve algorithm, after finding bSmooth values using logarithmic approximation you need to factor the number, let's call it B, to construct the bSmooth vector.

A common solution is to use a trial division using the primes in the factor base. Unlike random numbers, in this case, the trial division is super efficient since most of the factors will be in the prime base. I am saying "most" because a common optimization will allow a small threshold to include 1-3 prims with a product of up to 2^30 or so, it's called a partial relation.

In my current implementation, this vector extraction phase takes most of the time. Another solution that I have been trying to do is receiving, walking again over the prime base, and record the vectors in the indexes knowen to be b-smooth., but that turned to be even slower.

Below is my current code, I added 4 optimizations for the trial division, please tell me if there are better solutions for it.

1. For the prime 2, I check the last set bit of B and shift right to extract it.
2. I am using BigInteger divideAndRemainder it's optimizing both the memory and the performance by combining the division and the mod actions into 1
3. if B is smaller then the max prime in the factor base, then it must be in the factor base, so I use a hash map to locate it's index
4. if no prime up to B.bitLenght() / 2 is dividing B then it must be a partial relation, I will include it only if it's a prime.