FFT context initialization speedup

[user202729]

Requires #2681 (now merged).

Note that now initialization hard-fail for primes with insufficient 2-valuation instead of just fill the root table with garbage values. This can be reverted.

Also primes with 2-valuation less than 12 is supported.

The change to no longer compute primitive root speed things up but is backwards incompatible in case someone access the primitive_root field.

It's not clear if we really want the interface of n_primitive_root_prime_prefactor and n_quadratic_nonresidue to be that general.

[fredrik-johansson]

Did you profile this? How big is the speedup?

[user202729]

Most significant case: About 20% for small n (n = 1500) and large p (p ~ 50 bits) with the benchmark added in #2681.

before:

threads,bits,p,n,depth,usec
1,14,12289,1500,12,23.875
1,16,61441,1500,12,23.625
1,17,86017,1500,12,23.875
...
1,48,140737488498689,1500,12,26.875
1,49,281474976829441,1500,12,29.125
1,50,562949953548289,1500,12,31.625

after:

threads,bits,p,n,depth,usec
1,14,12289,1500,12,23.750
1,16,61441,1500,12,23.750
1,17,86017,1500,12,23.750
...
1,48,140737488498689,1500,12,24.625
1,49,281474976829441,1500,12,24.625
1,50,562949953548289,1500,12,24.750

Mostly the culprit is the factorization of p-1.

[fredrik-johansson]

OK, that looks quite good.