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version 1.1.1.1, 2001/10/02 11:16:56

version 1.2, 2002/09/11 07:26:41

Line 49 reason. You should always use \tet{mpeuler} and \tet{m

the first call will actually compute the constant, unless a higher precision

is required).

In addition, some single or double-precision real numbers (like \kbd{PI}) are

predefined, and their list is in the file \kbd{paricom.h}.

Finally, one has access to a table of (differences of) primes through the

pointer \tet{diffptr}. This is used as follows: when

\fun{void}{pari_init}{long size, long maxprime}

\fun{void}{pari_init}{long size, ulong maxprime}

\noindent is called, this table is initialized with the successive

differences of primes up to (just a little beyond) \kbd{maxprime}

(see \secref{se:intro4}). \tet{maxprime} has to be less than $436272744$,

(see \secref{se:intro4}). The prime table will occupy roughly

whatever memory is available. A difference of $0$ means we have reached the

$\kbd{maxprime}/\log(\kbd{maxprime})$ bytes in memory, so be sensible when

end of the table. The largest prime computable using this table is

choosing \kbd{maxprime} (it is $500000$ by default under \kbd{gp}). In any case,

available as the output of

the implementation requires that $\tet{maxprime} < 4294965248$

(resp.~$18446744073709549568$) on 32-bit (resp.~64-bit) machines, whatever memory

is available.

The largest prime computable using this table is available as the output of

\fun{ulong}{maxprime}{}

\noindent Here's a small example:

After the following initializations (the names $p$ and \var{ptr} are arbitrary of

course)

\bprog

byteptr ptr = diffptr;

ulong p = 0;

@eprog

\noindent calling the macro \tet{NEXT_PRIME_VIADIFF_CHECK(p, ptr)} repeatedly will

assign the successive prime numbers to $p$. Overrunning the prime table boundary

will raise the error \tet{primer1}, which will just print the error message:

\kbd{*** not enough precomputed primes}

\noindent and then abort the computations. The alternative macro

\tet{NEXT_PRIME_VIADIFF} operates in the same way, but will omit that check, and

is slightly faster. It should be used in the following way:

\bprog

byteptr d = diffptr;

byteptr ptr = diffptr;

ulong p = 0;

if (maxprime() < goal) err(primer1); /*@Ccom not enough primes */

while (p <= goal) /*@Ccom run through all primes up to \kbd{goal} */

{

p += *d++;

NEXT_PRIME_VIADIFF(p, ptr);

...

}

@eprog\noindent

Here, we use the general error handling function \kbd{err} (see

\secref{se:err}), with the codeword \kbd{primer1}. This will just print

\secref{se:err}), with the codeword \kbd{primer1}, raising the ``not enough

the error message:

primes'' error.

\kbd{*** not enough precomputed primes}

\noindent and then abort the computations.

You can use the function \kbd{initprimes} from the file \kbd{arith2.c} to

compute a new table on the fly and assign it to \kbd{diffptr} or to a

similar variable of your own. Beware that before changing \kbd{diffptr},

Line 92 all pointers into the old table will become invalid.

Line 109 all pointers into the old table will become invalid.

PARI currently guarantees that the first 6547 primes, up to and including

65557, will be present in the table, even if you set \kbd{maxnum} to zero.

In addition, some single or double-precision real numbers are predefined,

and their list is in the file \kbd{paricom.h}.

\vfill\eject

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