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1.1     ! noro        1: % $Id: appc.tex,v 1.8 2000/11/06 18:59:00 karim Exp $
        !             2: % Copyright (c) 2000  The PARI Group
        !             3: %
        !             4: % This file is part of the PARI/GP documentation
        !             5: %
        !             6: % Permission is granted to copy, distribute and/or modify this document
        !             7: % under the terms of the GNU Free Documentation License
        !             8: \appendix{Summary of Available Constants}
        !             9:
        !            10: In this appendix we give the list of predefined constants available in the
        !            11: PARI library. All of them are in the \idx{heap} and {\it not\/} on the PARI
        !            12: \idx{stack}. We start by recalling the \idx{universal object}s introduced in
        !            13: \secref{se:intro4}:
        !            14: %
        !            15: \bprog
        !            16: t_INT: gzero (zero), gun (un), gdeux (deux)
        !            17: t_FRAC: ghalf (lhalf)
        !            18: t_COMPLEX: gi
        !            19: t_POL: polun[..] (lpolun[..]), polx[..] (lpolx[..])
        !            20: @eprog
        !            21: \noindent Only polynomials in the variables \kbd{0} and \kbd{MAXVARN} are
        !            22: defined initially. Use \kbd{fetch\_var()} (see \secref{se:fetch_var}) to
        !            23: create new ones.
        !            24:
        !            25: \noindent The other objects are not initialized by default:
        !            26:
        !            27: \tet{bern}(i). This is the $2i$-th Bernoulli number ($B_0=1$, $B_2=1/6$,
        !            28: $B_4=-1/30$, etc\dots). To initialize them, use the function:
        !            29:
        !            30: \fun{void}{mpbern}{long n, long prec}
        !            31:
        !            32: This creates the even numbered Bernoulli numbers up to $B_{2n-2}$ {\it as
        !            33: real numbers\/} of precision \kbd{prec}. They can then be used with the macro
        !            34: \kbd{bern(i)}. Note that this is not a function but simply an abbreviation,
        !            35: hence care must be taken that \kbd{i} is inside the right bounds (i.e. $0\le
        !            36: \kbd{i}\le n-1$) before using it, since no checking is done by PARI itself.
        !            37:
        !            38: \tet{geuler}. This is Euler's constant. It is initialized by the first call
        !            39: to \tet{mpeuler} (see \secref{se:euler}).
        !            40:
        !            41: \tet{gpi}. This is the number $\pi$.  It is initialized by the first call to
        !            42: \tet{mppi} (see \secref{se:pi}).
        !            43:
        !            44: The use of both \tet{geuler} and \tet{gpi} is deprecated since it's always
        !            45: possible that some library function increases the precision of the constant
        !            46: {\it after} you've computed it, hence modifying the computation accuracy
        !            47: without your asking for it and increasing your running times for no good
        !            48: reason. You should always use \tet{mpeuler} and \tet{mppi} (note that only
        !            49: the first call will actually compute the constant, unless a higher precision
        !            50: is required).
        !            51:
        !            52: Finally, one has access to a table of (differences of) primes through the
        !            53: pointer \tet{diffptr}. This is used as follows: when
        !            54:
        !            55: \fun{void}{pari_init}{long size, long maxprime}
        !            56:
        !            57: \noindent is called, this table is initialized with the successive
        !            58: differences of primes up to (just a little beyond) \kbd{maxprime}
        !            59: (see \secref{se:intro4}). \tet{maxprime} has to be less than $436272744$,
        !            60: whatever memory is available. A difference of $0$ means we have reached the
        !            61: end of the table. The largest prime computable using this table is
        !            62: available as the output of
        !            63:
        !            64: \fun{ulong}{maxprime}{}
        !            65:
        !            66: \noindent Here's a small example:
        !            67: %
        !            68: \bprog
        !            69: byteptr d = diffptr;
        !            70: ulong p = 0;
        !            71:
        !            72: if (maxprime() < goal) err(primer1); /*@Ccom not enough primes */
        !            73: while (p <= goal) /*@Ccom run through all primes up to \kbd{goal} */
        !            74: {
        !            75:   p += *d++;
        !            76:   ...
        !            77: }
        !            78: @eprog\noindent
        !            79: Here, we use the general error handling function \kbd{err} (see
        !            80: \secref{se:err}), with the codeword \kbd{primer1}. This will just print
        !            81: the error message:
        !            82:
        !            83: \kbd{*** not enough precomputed primes}
        !            84:
        !            85: \noindent and then abort the computations.
        !            86:
        !            87: You can use the function \kbd{initprimes} from the file \kbd{arith2.c} to
        !            88: compute a new table on the fly and assign it to \kbd{diffptr} or to a
        !            89: similar variable of your own. Beware that before changing \kbd{diffptr},
        !            90: you should really free the (\kbd{malloc}ed) precomputed table first, and then
        !            91: all pointers into the old table will become invalid.
        !            92:
        !            93: PARI currently guarantees that the first 6547 primes, up to and including
        !            94: 65557, will be present in the table, even if you set \kbd{maxnum} to zero.
        !            95:
        !            96: In addition, some single or double-precision real numbers are predefined,
        !            97: and their list is in the file \kbd{paricom.h}.
        !            98: \vfill\eject