bug#12350: Composites identified as primes in factor.c (when HAVE_GMP)

[Jim Meyering]

Torbjorn Granlund wrote:

>   > Please do, and let me and Niels know if it takes more than 45s.  Your
>   > test case takes 28s on my 3.3 GHz Sandy bridge system with our current
>   > code.  I'm a little disappointed the code doesn't beat the old code more
>   > for small factorisations.
>
>   So on my 2.1GHz i3-2310M, running over the range 452,930,477 to 472,882,027.
>
>   old broken code = 14m
>   old fixed code  = 18m
>   new code        = 63s
>
> OK, this is about 60% slower than I would have expected.  Our code at
> http://gmplib.org:8000/factoring/ should run at about 39s on your
> system.  (I am using gcc 4.7.1.)
>
> I haven't looked at the final version that went into codeutils, so I
> have no idea why it runs slower.  A wild guess is that its actual input
> or tokenisation has been slowed down.  For smallish numbers, such things
> can dominate over actually factoring the numbers.
>
> I think the current coreutils factor performance for smallish numbers
> might be sufficient.  (Larger numbers than 2^100 need a bit too much
> time, but we are working on a fix.)

When I compare the factor built from http://gmplib.org:8000/factoring/, and
the one in coreutils.git I see these single-trial times: (on a 3.2GHz i7-970)

  $ seq 452930477 472882027|env time ./factor > k
  29.28user 0.44system 0:30.85elapsed 96%CPU (0avgtext+0avgdata 548maxresident)k
  0inputs+1011088outputs (0major+162minor)pagefaults 0swaps
  ...
  $ seq 452930477 472882027|env time /cu/src/factor > k
  26.47user 0.48system 0:28.07elapsed 96%CPU (0avgtext+0avgdata 692maxresident)k
  0inputs+1011088outputs (0major+205minor)pagefaults 0swaps

I.e., a 9% improvement.  Compiled with bleeding edge gcc 4.8.0 20121007.