I've updated the code that is relevant for mpz_fac_ui from GMP 5.1.3.

The new files associated with this are:

mpn/generic/comb_tables.c
mpz/oddfac_1.c
mpz/prodlimbs.c
nextprime.c
primesieve.c

Brian, you might like to add these to the Windows build.

There is more to come I think. There seem to be some additional factorial
functions, double factorial, binomial central series, primorial, etc. I'll
work on them tomorrow.

Everything should vaguely work at this point though. If not, please let me
know.

On Penryn, the fac_ui benchmark now shows that we have pretty much caught
up to GMP (sometimes beating it) for this part of the benchmark.

I think our overall bench on the base functions is now just higher than
GMP's on penryn, though there are still some points where I need to make
some improvements, such as very unbalanced multiplication and
asymptotically fast division.

Bill.

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