mpz_prevprime

[Niels Möller]

Seth Troisi <braintwo at gmail.com> writes:

> This was discussed previously in this thread
> https://gmplib.org/list-archives/gmp-devel/2019-September/005465.html
> TL;DR >95% of time is spent in miller rabin.

I tried out using the same dtab table used in trialdiv.c.

On my laptop, it gives a speedup of about 25% for larger sizes. Not sure
how to tune for small sizes, but clearly the old code clamping the size
of the prime table based on the bit size is better than doing nothing.

The computation of all the moduli could be speed up by using ptab, and
by using precomputed reciprocals. Not clear to me how much the speed of
that part matters. I haven't run any profiling.

Before: 

$ ./tune/speed -s 100-300 -f 1.1 mpz_nextprime
overhead 0.000000005 secs, precision 10000 units of 8.34e-10 secs, CPU freq 1198.47 MHz
        mpz_nextprime
100       0.000134064
110       0.000145867
121       0.000170687
133       0.000301883
146       0.000341107
160       0.000403326
176       0.000451402
193       0.000745043
212       0.000790877
233       0.000896869
256       0.001118979
281       0.001641613

500       0.008096105
1000      0.091219932

After:
$ ./tune/speed -s 100-300 -f 1.1 mpz_nextprime
overhead 0.000000005 secs, precision 10000 units of 8.14e-10 secs, CPU freq 1228.24 MHz
        mpz_nextprime
100       0.000212717
110       0.000223992
121       0.000241062
133       0.000355139
146       0.000388422
160       0.000435633
176       0.000477857
193       0.000716578
212       0.000757639
233       0.000847678
256       0.001018164
281       0.001435439

500       0.006692777
1000      0.072001893

Regards,
/Niels


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