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=head1 NAME C<Math::Pari> - Perl interface to PARI. =head1 SYNOPSIS use Math::Pari; $a = PARI 2; print $a**10000; or use Math::Pari qw(Mod); $a = Mod(3,5); print $a**10000; =head1 DESCRIPTION This package is a Perl interface to famous library PARI for numerical/scientific/number-theoretic calculations. It allows use of most PARI functions as Perl functions, and (almost) seamless merging of PARI and Perl data. In what follows we suppose prior knowledge of what PARI is (see L<ftp://megrez.math.u-bordeaux.fr/pub/pari>, or L<Math::libPARI>). =head1 EXPORTed functions =over 4 =item DEFAULT By default the package exports functions PARI(), PARIcol(), PARIvar(), PARImat() and PARImat_tr() which convert their argument(s) to a PARI object. (In fact PARI() is just an alias for C<new Math::Pari>). The function PARI() accepts following data as its arguments =over 17 =item One integer Is converted to a PARI integer. =item One float Is converted to a PARI float. =item One string Is executed as a PARI expresion (so should not contain whitespace). =item PARI object Is passed unchanged. =item Reference to a Perl array Each element is converted using the same rules, PARI vector-row with these elements is returned. =item Several of above The same as with a reference to array. =back =item Conflicts of rules in PARI() In deciding what rule of the above to apply the preference is given to the uppermost choice of those available I<now>. If none matches, then the string rule is used. So C<PARI(1)> returns integer, C<PARI(1.)> returns float, C<PARI("1")> evaluates C<1> as a PARI expression (well, the result is the same as C<PARI(1)>, only slower). Note that for Perl these data are synonimous, since Perl freely converts between integers, float and strings. However, to PARI() only what the argument I<is now> is important. If $v is C<1> in the Perl world, C<PARI($v)> may convert it to an integer, float, or to the result of evaluating the PARI program C<1> (all depending on how $v was created and accessed in Perl). This is a fundamental limitation of creating an interface between two systems, both with polymorphic objects, but with subtly different semantic of the flavors of these objects. In reality, however, this is rarely a problem. =item PARIcol(), PARImat() and PARImat_tr() PARIcol() behaves in the same way as PARI() unless given several arguments. In the latter case it returns a vector-column instead of a vector-row. PARImat() constructs a matrix out of the given arguments. It will work if PARI() will construct a vector of vectors given the same arguments. The internal vectors become columns of the matrix. PARImat_tr() behaves similarly, but the internal vectors become rows of the matrix. Since PARI matrices are similar to vector-rows of vector-columns, PARImat() is quickier, but PARImat_tr() better corresponds to the PARI input and output forms of matrices: print PARImat [[1,2], [3,4]]; # prints [1,3;2,4] print PARImat_tr [[1,2], [3,4]]; # prints [1,2;3,4] =item C<use> with arguments If arguments are specified in the C<use Math::Pari> directive, the PARI functions appearing as arguments are exported in the caller context. In this case the function PARI() and friends is not exported, so if you need them, you should include them into export list explicitely, or include C<:DEFAULT> tag: use Math::Pari qw(factorint PARI); use Math::Pari qw(:DEFAULT factorint); or simply do it in two steps use Math::Pari; use Math::Pari 'factorint'; The other tags recognized are C<:PARI>, C<:all>, C<prec=NUMBER>, number tags (e.g., C<:4>), overloaded constants tags (C<:int>, C<:float>, C<:hex>) and section names tags. The number tags export functions from the PARI library from the given class (except for C<:PARI>, which exports all of the classes). Tag C<:all> exports all of the exportable symbols and C<:PARI>. Giving C<?> command to C<gp> (B<PARI> calculator) lists the following classes: 1: Standard monadic or dyadic OPERATORS 2: CONVERSIONS and similar elementary functions 3: TRANSCENDENTAL functions 4: NUMBER THEORETICAL functions 5: Functions related to ELLIPTIC CURVES 6: Functions related to general NUMBER FIELDS 7: POLYNOMIALS and power series 8: Vectors, matrices, LINEAR ALGEBRA and sets 9: SUMS, products, integrals and similar functions 10: GRAPHIC functions 11: PROGRAMMING under GP One can use section names instead of number tags. Recognized names are :standard :conversions :transcendental :number :elliptic :fields :polynomials :vectors :sums :graphic :programming One can get the list of all of the functions accessible by C<Math::Pari>, or the accessible functions from the given section using listPari() function. Starting from version 5.005 of Perl, three constant-overload tags are supported: C<:int>, C<:float>, C<:hex>. If used, all the integer/float/hex-or-octal-or-binary literals in Perl will be automatically converted to became PARI objects. For example, use Math::Pari ':int'; print 2**1000; is equivalent to print PARI(2)**PARI(1000); (The support for this Perl feature is buggy before the Perl version 5.005_57 - unless Perl uses mymalloc options; you can check for this with C<perl -V:usemymalloc>.) =back =head1 Available functions =head2 Directly accessible from Perl This package supports I<all> the functions from the PARI library with a I<signature> which can be recognized by Math::Pari. This means that when you update the PARI library, the newly added functions will we available without any change to this package; only a recompile is needed. In fact no recompile will be needed if you link libPARI dynamically (you need to modify the F<Makefile> manually to do this). You can "reach" unsupported functions via going directly to PARI parser using the string flavor of PARI() function, as in 3 + PARI('O(x^17)'); For some "unreachable" functions there is a special wrapper functions, such as C<O(variable,power)>). The following functions are specific to GP calculator, thus are not available to Math::Pari in any way: default error extern input print print1 printp printp1 printtex quit read system whatnow write write1 writetex whatnow() function is useless, since Math::Pari does not support the "compatibility" mode (with older PARI library). The functionality of print(), write() and variants is available via automatic string translation, and pari_print() function and its variants (see L<Printout functions>). default() is the only important function with functionality not supported by the current interface. Note however, that three most important default() actions are supported by allocatemem(), setprimelimit(), setprecision() and setseriesprecision() functions. (When called without arguments, these functions return the current values.) allocatemem($bytes) should not be called from inside Math::Pari functions (such as forprimes()). =head2 Arguments Arguments to PARI functions are automatically converted to C<long> or a PARI object depending on the signature of the actual library function. The arguments are I<forced> into the given type, so even if C<gp> rejects your code similar to func(2.5); # func() takes a long in C arguing that a particular argument should be of C<type T_INT> (i.e., a Pari integer), the corresponding code will work in C<Math::Pari>, since 2.5 is silently converted to C<long>, per the function signature. =head2 Return values PARI functions return a PARI object or a Perl's integer depending on what the actual library function returns. =head2 Additional functions Some PARI functions are available in C<gp> (i.e., in C<PARI> calculator) via infix notation only. In C<Math::Pari> these functions are available in functional notations too. Some other convenience functions are also made available. =over 5 =item Infix, prefix and postfix operations are available under names gneg, gadd, gsub, gmul, gdiv, gdivent, gmod, gpui, gle, gge, glt, ggt, geq, gne, gegal, gor, gand, gcmp, gcmp0, gcmp1, gcmp_1. C<gdivent> means euclidean quotient, C<gpui> is power, C<gegal> checks whether two objects are equal, C<gcmp> is applicable to two real numbers only, C<gcmp0>, C<gcmp1>, C<gcmp_1> compare with 0, 1 and -1 correspondingly (see PARI user manual for details, or L<Math::libPARI>). Note that all these functions are more readily available via operator overloading, so instead of gadd(gneg($x), $y) one can write -$x+$y (as far as overloading may be triggered, see L<overload>, so we assume that at least one of $x or $y is a PARI object). =item Conversion functions pari2iv, pari2nv, pari2num, pari2pv, pari2bool convert a PARI object to an integer, float, integer/float (whatever is better), string, and a boolean value correspondingly. Most the time you do not need these functions due to automatic conversions. =item Printout functions pari_print, pari_pprint, pari_texprint perform the same conversions to strings as their PARI counterparts, but do not print the result. The difference of pari_print() with pari2pv() is the number of significant digits they output, and whitespace in the output. pari2pv(), which is intended for "computer-readable strings", outputs as many digits as is supported by the current precision of the number; while pari_print(), which targets human-readable strings, takes into account the currently specified output precision too. =item Constant functions Some mathematical constants appear as function without arguments in PARI. These functions are available in Math::Pari too. If you export them as in use Math::Pari qw(:DEFAULT Pi I Euler); they can be used as barewords in your program: $x = Pi ** Euler; =item Low-level functions For convenience of low-level PARI programmers some low-level functions are made available as well (all except type_name() and changevalue() are not exportable): typ($x) lg($x) lgef($x) lgefint($x) longword($x, $n) type_name($x) changevalue($name,$newvalue) Here longword($x,$n) returns C<$n>-th word in the memory representation of $x (including non-code words). type_name() differs from the PARI function type(): type() returns a PARI object, while type_name() returns a Perl string. (PARI objects of string type behave very non-intuitive w.r.t. string comparison functions; remember that they are compared using lex() to I<the results of evaluation> of other argument of comparison!) The function listPari($number) outputs a list of names of PARI functions in the section $number. Use listPari(-1) to get the list across all of the sections. =item Uncompatible functions O Since implementing C<O(7**6)> would be very tedious, we provide a two-argument form C<O(7,6)> instead (meaning the same as C<O(7^6)> in PARI). Note that with polynomials there is no problem like this one, both C<O($x,6)> and C<O($x**6)> work. ifact(n) integer factorial functions, available from C<gp> as C<n!>. =back =head2 Looping functions PARI has a big collection of functions which loops over some set. Such a function takes two I<special> arguments: loop variable, and the code to execute in the loop. The code can be either a string (which contains PARI code to execute - thus should not contain whitespace), or a Perl code reference. The loop variable can be a string giving the name of PARI variable (as in fordiv(28, 'j', 'a=a+j+j^2'); or $j= 'j'; fordiv(28, $j, 'a=a+j+j^2'); ), a PARI monomial (as in $j = PARI 'j'; fordiv(28, $j, sub { $a += $j + $j**2 }); ), or a "delayed Math::Pari variable" (as in $j = PARIvar 'j'; fordiv(28, $j, 'a=a+j+j^2'); ). If none of these applies, as in my $j; # Have this in a separate statement fordiv(28, $j, sub { $a += $j + $j**2 }); then during the execution of the C<sub>, Math::Pari would autogenerate a PARI variable, and would put its value in $j; this value of $j is temporary only, the old contents of $j is restored when fordiv() returns. Note that since you have no control over this name, you will not be able to use this variable from your PARI code; e.g., $j = 7.8; fordiv(28, $j, 'a=a+j+j^2'); will not make C<j> mirror $j (unless you explicitely set up C<j> to be a no-argument PARI function mirroring $j, see L<"Accessing Perl functions from PARI code">). B<Caveats>. There are 2 flavors of the "code" arguments (string/C<sub>), and 4 types of the "variable" arguments (string/monomial/C<PARIvar>/other). However, not all 8 combinations make sense. As we already explained, an "other" variable cannot work with a "string" code. B<Useless musing alert! Do not read the rest of this section!> Do not use "string" variables with C<sub> code, and do not ask I<why>! Additionally, the following code will not do what you expect $x = 0; $j = PARI 'j'; fordiv(28, 'j', sub { $x += $j } ); # Use $j as a loop variable! since the PARI function C<fordiv> I<localizes> the PARI variable C<j> inside the loop, but $j will still reference the old value; the old value is a monomial, not the index of the loop (which is an integer each time C<sub> is called). The simplest workaround is not to use the above syntax (i.e., not mixing literal loop variable with Perl loop code, just using $j as the second argument to C<fordiv> is enough): $x = 0; $j = PARI 'j'; fordiv(28, $j, sub { $x += $j } ); Alternately, one can make a I<delayed> variable $j which will always reference the same thing C<j> references in PARI I<now> by using C<PARIvar> constructor $x = 0; $j = PARIvar 'j'; fordiv(28, 'j', sub { $x += $j } ); (This problem is similar to $ref = \$_; # $$ref is going to be old value even after # localizing $_ in Perl's grep/map not accessing localized values of $_ in the plain Perl.) Another possible quirk is that fordiv(28, my $j, sub { $a += $j + $j**2 }); will not work too - by a different reason. C<my> declarations change the I<meaning> of $j only I<after> the end of the current statement; thus $j inside C<sub> will access a I<different> variable $j (typically a non-lexical, global variable $j) than one you declared on this line. =head2 Accessing Perl functions from PARI code Use the same name inside PARI code: sub counter { $i += shift; } $i = 145; PARI 'k=5' ; fordiv(28, 'j', 'k=k+counter(j)'); print PARI('k'), "\n"; prints 984 Due to a difference in the semantic of variable-number-of-parameters-functions between PARI and Perl, if the Perl subroutine takes a variable number of arguments (via C<@> in the prototype or a missing prototype), up to 6 arguments are supported when this function is called from PARI. If called from PARI with fewer arguments, the rest of arguments will be set to be integers C<PARI 0>. Note also that no direct import of Perl variables is available yet (but you can write a function wrapper for this): sub getv () {$v} There is an unsupported (and undocumented ;-) function for explicitely importing Perl functions into PARI, possibly with a different name, and possibly with explicitely specifying number of arguments. =head1 PARI objects Functions from PARI library may take as arguments and/or return values the objects of C type C<GEN>. In Perl these data are encapsulated into special kind of Perl variables: PARI objects. You can check for a variable C<$obj> to be a PARI object using ref $obj and $obj->isa('Math::Pari'); Most the time you do not need this due to automatic conversions and overloading. =head1 PARI monomials and Perl barewords If very lazy, one can code in Perl the same way one does it in PARI. Variables in PARI are denoted by barewords, as in C<x>, and in the default configuration (no warnings, no strict) Perl allows the same - up to some extent. Do not do this, since there are many surprising problems. Some bareletters denote Perl operators, like C<q>, C<x>, C<y>, C<s>. This can lead to errors in Perl parsing your expression. E.g., print sin(tan(t))-tan(sin(t))-asin(atan(t))+atan(asin(t)); may parse OK after C<use Math::Pari qw(sin tan asin atan)>. Why? After importing, the word C<sin> will denote the PARI function sin(), not Perl operator sin(). The difference is subtle: the PARI function I<implicitly> forces its arguments to be converted PARI objects; it gets C<'t'> as the argument, which is a string, thus is converted to what C<t> denotes in PARI - a monomial. While the Perl operator sin() grants overloading (i.e., it will call PARI function sin() if the argument is a PARI object), it does not I<force> its argument; given C<'t'> as argument, it converts it to what sin() understands, a float (producing C<0.>), so will give C<0.> as the answer. However print sin(tan(y))-tan(sin(y))-asin(atan(y))+atan(asin(y)); would not compile. You should avoid lower-case barewords used as PARI variables, e.g., do $y = PARI 'y'; print sin(tan($y))-tan(sin($y))-asin(atan($y))+atan(asin($y)); to get -1/18*y^9+26/4725*y^11-41/1296*y^13+328721/16372125*y^15+O(y^16) (BTW, it is a very good exercise to get the leading term by hand). Well, the same advice again: do not use barewords anywhere in your program! =head1 Overloading and automatic conversion Whenever an arithmetic operation includes at least one PARI object, the other arguments are converted to a PARI object and the corresponding PARI library functions is used to implement the operation. Currently the following arithmetic operations are overloaded: unary - + - * / % ** abs cos sin exp log sqrt << >> <= == => < > != <=> le eq ge lt gt ne cmp | & ^ ~ Numeric comparison operations are converted to C<gcmp> and friends, string comparisons compare in lexicographical order using C<lex>. Additionally, whenever a PARI object appears in a situation that requires integer, numeric, boolean or string data, it is converted to the corresponding type. Boolean conversion is subject to usual PARI pitfalls related to imprecise zeros (see documentation of C<gcmp0> in PARI reference). For details on overloading, see L<overload>. Note that a check for equality is subject to same pitfalls as in PARI due to imprecise values. PARI may also refuse to compare data of different types for equality if it thinks this may lead to counterintuitive results. Note also that in PARI the numeric ordering is not defined for some types of PARI objects. For string comparison operations we use PARI-lexicographical ordering. =head1 PREREQUISITES =head2 Perl In the versions of perl earlier than 5.003 overloading used a different interface, so you may need to convert C<use overload> line to C<%OVERLOAD>, or, better, upgrade. =head2 PARI Starting from version 2.0, this module comes without a PARI library included. For the source of PARI library see L<ftp://megrez.math.u-bordeaux.fr/pub/pari>. =head1 Perl vs. PARI: different syntax Note that the PARI notations should be used in the string arguments to PARI() function, while the Perl notations should be used otherwise. =over 4 =item C<^> Power is denoted by C<**> in Perl. =item C<\> and C<\/> There are no such operators in Perl, use the word forms C<gdivent(x,y)> and C<gdivround(x,y)> instead. =item C<~> There is no postfix C<~> Perl operator. Use mattranspose() instead. =item C<'> There is no postfix C<'> Perl operator. Use deriv() instead. =item C<!> There is no postfix C<!> Perl operator. Use factorial()/ifact() instead (returning a real or an integer correspondingly). =item big integers Perl converts big I<literal> integers to doubles if they could not be put into B<C> integers (the particular flavor can be found in the output of C<perl -V> in newer version of Perl, look for C<ivtype>/C<ivsize>). If you want to input such an integer, use while ($x < PARI('12345678901234567890')) ... instead of while ($x < 12345678901234567890) ... Why? Because conversion to double leads to precision loss (typically above 1e15, see L<perlnumber>), and you will get something like 12345678901234567168 otherwise. Starting from version 5.005 of Perl, if the tag C<:int> is used on the 'use Math::Pari' line, all of the integer literals in Perl will be automatically converted to became PARI objects. E.g., use Math::Pari ':int'; print 2**1000; is equivalent to print PARI(2)**PARI(1000); Similarly, large integer literals do not lose precision. This directive is lexically scoped. There is a similar tag C<:hex> which affects hexadecimal, octal and binary constants. =item doubles Doubles in Perl are typically of precision approximately 15 digits (see L<perlnumber>). When you use them as arguments to PARI functions, they are converted to PARI real variables, and due to intermediate 15-digits-to-binary conversion of Perl variables the result may be different than with the PARI many-digits-to-binary conversion. E.g., C<PARI(0.01)> and C<PARI('0.01')> differ at 19-th place, as setprecision(38); print pari_print(0.01), "\n", pari_print('0.01'), "\n"; shows. Note that setprecision() changes the output format of pari_print() and friends, as well as the default internal precision. The generic PARI===>string conversion does not take into account the output format, thus setprecision(38); print PARI(0.01), "\n", PARI('0.01'), "\n", pari_print(0.01), "\n"; will print all the lines with different number of digits after the point: the first one with 22, since the double 0.01 was converted to a low-precision PARI object, the second one with 41, since internal form for precision 38 requires that many digits for representation, and the last one with 39 to have 38 significant digits. Starting from version 5.005 of Perl, if the tag C<:float> is used on the C<use Math::Pari> line, all the float literals in Perl will be automatically converted to became PARI objects. E.g., use Math::Pari ':float'; print atan(1.); is equivalent to print atan(PARI('1.')); Similarly, large float literals do not lose precision. This directive is lexically scoped. =item array base Arrays are 1-based in PARI, are 0-based in Perl. So while array access is possible in Perl, you need to use different indices: $nf = PARI 'nf'; # assume that PARI variable nf contains a number field $a = PARI('nf[7]'); $b = $nf->[6]; Now $a and $b contain the same value. =item matrices Note that C<PARImat([[...],...,[...])> constructor creates a matrix with specified columns, while in PARI the command C<[1,2,3;4,5,6]> creates a matrix with specified rows. Use a convenience function PARImat_tr() which will transpose a matrix created by PARImat() to use the same order of elements as in PARI. =item builtin perl functions Some PARI functions, like C<length> and C<eval>, are Perl (semi-)reserved words. To reach these functions, one should either import them: use Math::Pari qw(length eval); or call them with prefix (like C<&length>) or the full name (like C<Math::Pari::length>). =back =head1 High-resolution graphics If you have Term::Gnuplot Perl module installed, you may use high-resolution graphic primitives of B<PARI>. Before the usage you need to establish a link between Math::Pari and Term::Gnuplot by calling link_gnuplot(). You can change the output filehandle by calling set_plot_fh(), and output terminal by calling plotterm(), as in use Math::Pari qw(:graphic asin); open FH, '>out.tex' or die; link_gnuplot(); # automatically loads Term::Gnuplot set_plot_fh(\*FH); plotterm('emtex'); ploth($x, .5, .999, sub {asin $x}); close FH or die; =head1 libPARI documentation libPARI documentation is included, see L<Math::libPARI>. It is converted from Chapter 3 of B<PARI/GP> documentation by the F<gphelp> script of GP/PARI. =head1 ENVIRONMENT No environment variables are used. =head1 BUGS =over 5 =item * A few of PARI functions are available indirectly only. =item * Using overloading constants with the Perl versions below 5.005_57 could lead to segfaults (at least without C<-D usemymalloc>), as in: use Math::Pari ':int'; for ( $i = 0; $i < 10 ; $i++ ) { print "$i\n" } =item * It may be possible that conversion of a Perl value which has both the integer slot and the floating slot set may create a PARI integer, even if the actual value is not an integer. =item * problems with refcounting of array elements and Mod(). Workaround: make the modulus live longer than the result of Mod(). Until Perl version C<5.6.1>, one should exercise a special care so that the modulus goes out of scope on a different statement than the result: { my $modulus = 125; { my $res = Mod(34, $modulus); print $res; } $fake = 1; # A (fake) statement here is required } Here $res is destructed before the C<$fake = 1> statement, $modulus is destructed before the first statement after the provided block. However, if you remove the C<$fake = 1> statement, both these variables are destructed on the first statement after the provided block (and in a wrong order!). In C<5.6.1> declaring $modulus before $res is all that is needed to circumvent the same problem: { my $modulus = 125; my $res = Mod(34, $modulus); print $res; } # destruction will happen in a correct order. Access to array elements may result in similar problems. Hard to fix since in PARI the data is not refcounted. =item * Legacy implementations of dynalinking require the code of DLL to be compiled to be "position independent" code (PIC). This slows down the execution, while allowing sharing the loaded copy of the DLL between different processes. [On contemeporary architectures the same effect is allowed without the position-independent hack.] Currently, PARI assembler files are not position-independent. When compiled for the dynamic linking on legacy systems, this creates a DLL which cannot be shared between processes. Some legacy systems are reported to recognize this situation, and load the DLL as a non-shared module. However, there may be systems (are there?) on which this can cause some "problems". Summary: if the dynaloading on your system requires some kind of C<-fPIC> flag, using "assembler" compiles (anything but C<machine=none>) *may* force you to do a static build (i.e., creation of a custom Perl executable with perl Makefile.PL static make perl make test_static ). =back =head1 INITIALIZATION When Math::Pari is loaded, it examines variables $Math::Pari::initmem and $Math::Pari::initprimes. They specify up to which number the initial list of primes should be precalculated, and how large should be the arena for PARI calculations (in bytes). (These values have safe defaults.) Since setting these values before loading requires either a C<BEGIN> block, or postponing the loading (C<use> vs. C<require>), it may be more convenient to set them via Math::PariInit: use Math::PariInit qw( primes=12000000 stack=1e8 ); C<use Math::PariInit> also accepts arbitrary Math::Pari import directives, see L<Math::PariInit>. These values may be changed at runtime too, via allocatemem() and setprimelimit(), with performance penalties for recalculation/reallocation. =head1 AUTHOR Ilya Zakharevich, I<perl-module-math-pari@ilyaz.org> =cut # $Id: Pari.pm,v 1.3 1994/11/25 23:40:52 ilya Exp ilya $ package Math::Pari::Arr; #sub TIEARRAY { $_[0] } sub STORE { die "Storing into array elements unsupported" } package Math::Pari; require Exporter; require DynaLoader; #use autouse Carp => 'croak'; @ISA = qw(Exporter DynaLoader); @Math::Pari::Ep::ISA = qw(Math::Pari); # Items to export into callers namespace by default # (move infrequently used names to @EXPORT_OK below) @EXPORT = qw( PARI PARIcol PARImat PARIvar PARImat_tr ); # Other items we are prepared to export if requested (may be extended during # ->import. ) @EXPORT_OK = qw( sv2pari sv2parimat pari2iv pari2nv pari2num pari2pv pari2bool loadPari _bool listPari pari_print pari_pprint pari_texprint O ifact gdivent gdivround changevalue set_plot_fh link_gnuplot setprecision setseriesprecision setprimelimit allocatemem type_name ); use subs qw( _gneg _gadd _gsub _gmul _gdiv _gmod _gpui _gle _gge _glt _ggt _geq _gne _gcmp _lex _2bool pari2pv pari2num _abs _cos _sin _exp _log _sqrt _gbitand _gbitor _gbitxor _gbitneg _to_int _gbitshiftr _gbitshiftl ); # Otherwise overload->import would complain... my $two; sub _shiftl { my ($left,$right) = (shift,shift); ($left,$right) = ($right, $left) if shift; $left * $two**$right; } sub _shiftr { my ($left,$right) = (shift,shift); ($left,$right) = ($right, $left) if shift; floor($left / $two**$right); } $initmem = $initmem || 4000000; # How much memory for the stack $initprimes = $initprimes || 500000; # Calculate primes up to this number $VERSION = '2.010500'; bootstrap Math::Pari; use overload qw( neg _gneg + _gadd - _gsub * _gmul / _gdiv % _gmod ** _gpui <= _gle >= _gge < _glt > _ggt == _geq != _gne <=> _gcmp cmp _lex bool _2bool "" pari2pv +0 pari2num abs _abs cos _cos sin _sin exp _exp log _log sqrt _sqrt int _to_int ); if (pari_version_exp() >= 2000018) { 'overload'->import( qw( | _gbitor & _gbitand ^ _gbitxor ~ _gbitneg ) ); } if (pari_version_exp() >= 2002001) { 'overload'->import( qw( << _gbitshiftl >> _gbitshiftr ) ); } else { 'overload'->import( qw( << _shiftl >> _shiftr ) ); } sub AUTOLOAD { $AUTOLOAD =~ /^(?:Math::Pari::)?(.*)/; # warn "Autoloading $1...\n"; # exit 4 if $1 eq 'loadPari'; my $cv = loadPari($1); # goto &$cv; # goto &$AUTOLOAD; # &$cv; &$1; # &$AUTOLOAD; } # Needed this guy to circumwent autoloading while no XS definition #### sub DESTROY {} # sub AUTOLOAD { # if ((caller(0))[4]) { # $AutoLoader::AUTOLOAD = $AUTOLOAD; # goto &AutoLoader::AUTOLOAD; # } # local($constname); # ($constname = $AUTOLOAD) =~ s/.*:://; # $val = constant($constname, @_ ? $_[0] : 0); # if ($! != 0) { # if ($! =~ /Invalid/) { # $AutoLoader::AUTOLOAD = $AUTOLOAD; # goto &AutoLoader::AUTOLOAD; # } # else { # ($pack,$file,$line) = caller; # die "Your vendor has not defined Math::Pari macro $constname, used at $file line $line. # "; # } # } # eval "sub $AUTOLOAD { $val }"; # goto &$AUTOLOAD; # } # Preloaded methods go here. Autoload methods go after __END__, and are # processed by the autosplit program. sub new { shift; if (@_>1) {my(@t)=@_;return sv2pari(\@t)} return sv2pari(shift); } ###sub PARI {new Math::Pari @_} %names = qw( 1 standard 2 conversions 3 transcendental 4 number 5 elliptic 6 fields 7 polynomials 8 vectors 9 sums 10 graphic 11 programming ); @sections{values %names} = keys %names; @converted{split /,\s+/, qq(buchimag, buchreal, buchgen, buchgenforcefu, buchgenfu, buchinit, buchinitforcefu, buchinitfu, plotstring, addhelp, kill)} = (1) x 100; # Now even tested... sub _cvt { PARI(shift) } sub _hex_cvt { my $in = shift; my $mult = PARI(1); my $ret = 0; my $shift = 1<<(4*7); $in =~ s/^0([xb])?// or die; my $hex = $1; if ($hex and $1 eq 'b') { my $b = '0' x (15 * length($in) % 16) . $in; $hex = ''; while ($b) { my $s = substr $b, 0, 16; substr($b, 0, 16) = ''; $hex .= unpack 'H4', pack 'B16', $s; } $in = $hex; } $shift = 1<<(3*7) unless $hex; while ($in =~ s/([a-fA-F\d]{1,7})$//) { # In 5.6.0 hex() can return a floating number: my $part = int($hex ? hex $1 : oct $1); $ret += $part * $mult; $mult *= $shift; } die "Cannot hex '$in'" if length $in; return $ret; } %overloaded_const = ( 'int' => \&_cvt, float => \&_cvt, 'hex' => \&_hex_cvt); %overloaded_const_word = ( 'int' => 'integer', float => 'float', 'hex' => 'binary'); sub import { my $p=shift; my @consts; # Need to do it outside any block! @_ = map { if (/^:(?!DEFAULT)(.*)/) { my $tag = $1; my $sect = $tag; my @pre; $tag = -1, @pre = (@EXPORT_OK,@EXPORT) if ($tag eq 'all'); $tag = -1 if ($tag eq 'PARI'); $tag = $sections{$tag} if $tag !~ /^-?\d+$/ and exists $sections{$tag}; push @pre, 'link_gnuplot', 'set_plot_fh' if $tag eq 10; if ($tag =~ /^prec=(\d+)$/) { setprecision($1); (); } elsif ($tag =~ /^(int|hex|float)$/) { die "Overloaded constants are not supported in this version of Perl" if $] < 5.004_69; push @const, $overloaded_const_word{$tag} => $overloaded_const{$tag}; # print "Constants: $overloaded_const_word{$tag} => $overloaded_const{$tag} \n"; (); } elsif (defined $tag and $tag =~ /^-?\d+$/) { (@pre, listPari($tag)); } else { die "Unknown section '$sect' specified"; } } else { ($_); } } @_; overload::constant(splice @const, 0, 2) while @const; # print "EXPORT_OK: @EXPORT_OK\n"; push @EXPORT_OK, grep( ($_ ne ':DEFAULT' and not $export_ok{$_}++ and (eval {loadPari($_), 1} or warn $@), !$@) , @_); # Invalidate Exporter cache, so that new %EXPORT_OK is noticed: undef %EXPORT; # print "EXPORT_OK: @EXPORT_OK\n"; &Exporter::export($p,(caller(0))[0],@_); } sub _can { # Without taking into account inheritance... my ($obj, $meth) = (shift, shift); return \&$meth if defined &$meth; return \&$meth if eval {loadPari($meth), 1}; return; } sub can { my ($obj, $meth) = (@_); my $f = $obj->SUPER::can($meth); return $f if defined $f; # There is no "usual" way to get the function; try loadPari() $f = eval { loadPari($meth) }; return $f if defined $f; return; } sub O ($;$) { return PARI("O($_[0]^$_[1])") if @_ == 2; return PARI("O($_[0])") if typ($_[0]) == 10; # Poly Carp::croak("O(number**power) not implemented, use O(number,power) instead"); } sub PARImat_tr {mattranspose(PARImat(@_))} #sub string ($$) { # PARI (qq'string($_[0],"$_[1]")'); #} sub installPerlFunction {my @a=@_; $a[0] = \&{$a[0]}; installPerlFunctionCV(@a)} my $name; for $name (keys %converted) { push @EXPORT_OK, $name; next if defined &$name; # string needs to format numbers to 8.3... if ($name eq 'addhelp' or $name eq 'plotstring') { *$name = sub { PARI ( qq($name($_[0],"$_[1]")) ) } } else { *$name = sub { local $"=','; PARI("$name(@_)") } } } @export_ok{@EXPORT_OK,@EXPORT} = (1) x (@EXPORT_OK + @EXPORT); sub link_gnuplot { eval 'use Term::Gnuplot 0.56; 1' or die; int_set_term_ftable(Term::Gnuplot::get_term_ftable()); } sub set_plot_fh { eval 'use Term::Gnuplot 0.4; 1' or die; Term::Gnuplot::set_gnuplot_fh(@_); } $two = PARI(2); 1; __END__ 
