mpz_prevprime

[Marco Bodrato]

Ciao,

Il 2020-03-16 02:23 Seth Troisi ha scritto:
> On Sun, Mar 15, 2020 at 4:38 PM Marco Bodrato
> <bodrato at mail.dm.unipi.it> wrote:
>> May I write a few more comments?

> Always, my opinion about being ready is just that it's passed
> the bar of being good enough not that it's perfect.

I'm tempted to simply commit your proposal and then change it :-)
But if we keep on discussing here, we can improving the code with the 
opinions of two persons...

>> I see now:
>> + if (nbits <= 32)
>> + incr_limit = 336;

>> Probably, we should change the name of the variable to
>> odd_candidates_in_sieve, then you would probably have written:
>> if (nbits <= 32)
>> odd_numbers_in_sieve = 168;

> Renamed to odds_in_composite_sieve

Of course the name is not essential, the values are :-)
And they seem correct to me, now.

>> Then I wonder if the cost of the /* Sieve next segment */ step
[...]
>> need to allocate the possibly huge next_mult array?
> 
> You're correct, this reduces the memory use 80%

Moreover the code has now the following structure:

   SIEVE;
   for (;;) {
     CHECK_AND_POSSIBLY_BREAK;
     SIEVE;
   }

There is an unneeded code duplication, it should be:

   for (;;) {
     SIEVE;
     CHECK_AND_POSSIBLY_BREAK;
   }

>> If you need to store larger gaps, you can also save in
>> the array gap>>1, because they all are even. The prime
>> limit will be able to go beyond 2^37...
> 
>  Updated comment for how this could be done in the future.

The first gap larger than 500, if I'm not wrong, is
304599508537+514=304599509051

>> I'd expect a condition like
>> 
>> + if (nbits <= numberof (primegap_small) * 2 + 1)
>> + {
>> + primegap = primegap_small;
>> + prime_limit = nbits / 2;
>> + }

> Done

I read:
+  if (2 * nbits <= NUMBER_OF_PRIMES)
+    {
+      primegap = primegap_small;
+      prime_limit = nbits / 2;
+    }

But ... this means that at most one fourth of the constants in 
primegap_small are used, am I wrong?

Ĝis,
m