An introduction to gp2c
Contents
1. 3 3 Effect of types declaration on default values Under GP all GP variables start with a default value which is 0 for a local variable and v for a global variable v The gp2c compiler follows this rule for variables declared without a type However when a variable is declared with a type gp2c will not assign it a default value This means that the declaration local g is equivalent to lo cal g gen 0 but not to local g gen global g is equivalent to global g gen q but not to global g gen and f g is equivalent to f g gen 0 but not to f g gen This rule was chosen for several reasons e The default value 0 or v might not be an object suitable for the type in question For example local v vec declares v as being of type vec It would make no sense to initialize v to 0 since 0 does not belong to type vec Similarly global N int declares N as being of type int It would make no sense to initialize N to N since N does not belong to type int e This allows defining GP functions with mandatory arguments This way GP will issue an error if a mandatory argument is missing Without this rule there is no way to tell apart 0 from a missing argument e This allows telling gp2c not to generate useless default values 3 4 Type casting Sometimes we know a more precise type than the one the transtyping algorithm can derive For example if x is a real number its logarithm might be complex However if we2. to recompile the shared library 3 Advanced use of gp2c 3 1 gp2c types Internally gp2c assign types to objects The most common types are given below name description void like in C bool boolean true 1 or false 0 negbool antiboolean true 0 or false 1 small C integer long int multiprecision integer real multiprecision floating point mp multiprecision number var variable pol polynomial vecsmall vector of C long t VECSMALL vec vector and matrices excluding vecsmall list GP lists str characters string as a char genstr characters string as a GEN t_STR gen generic PARI object GEN lg length of object returned by length typ type of object returned by type gen wf pol vec mp var int real small negbool bool void Table 1 Types preorder Types are preordered as in Table 1 The complete preorder known by gp2c can be accessed by running gp2c t Variables are typed A variable can only take values having a type equal or lower than its type By default variables are of type gen 3 2 Type declaration To declare a variable as belonging to type type use function x type y type 2 local x type y type 2 global x type y type 2 for i type To declare several variables of the same type type at once use local x y 2 type global x y 2 type You can even mix the two ways local x y type2 2 typel will declare x to be of type type1 and y of type type2
3. n x modii addis sqri x 1 n y modii addis sqri y 1 n y modii addis sqri y 1 n return gcdii n subii y x Now the code now uses the more specific functions sqri addis modii and gcdii The most efficient way to use typing is to declare some variables of type small This way these variables will be implemented by C long variables which are faster than PARI integers and do not require garbage collecting However you will not be protected from integer overflow For that reason gp2c will automatically declare some loop indices of type small when the range cannot cause overflow Sometimes gp2c can be too conservative but you can force a loop index to be small with the syntax for i small a b 3 6 Types and member functions For use with members functions gp2c provides the following types nf for ordinary number fields i e a result given by the GP function nfinit bnf for big number fields i e a result given by the GP function bnfinit which includes class and unit group data bnr for ray class groups i e a result given by the GP function bnrinit ell for elliptic curves i e a result given by the GP function ellinit gal for galois extensions i e a result given by the GP function galoisinit prid for prime ideals i e a component of the result given by the GP function idealprimedec Members functions on typed objects are much more efficient 4 Common problems 4 1 Meta
4. An introduction to gp2c By Bill Allombert and Ariel Pacetti February 22 2012 Contents 1 1 What is gp2c Tl Installing gp2 ya sargai oe es Be tae a A gp2c tutorial 2 1 How can I compile and run my scripts 2 2 How can I compile directly with gp2c 002 2 3 Using gp2c to find errors in GP scripts 2 4 Using compiled functions in a new program 2 5 Hand editing the C file generated by gp2c Advanced use of gp2c Bil BPA LY PES sod a5 Ko ee eau eh ie SaaS Gs ate ey RU es 3 2 Type declaration 2 2 0 200022 eee ee 3 3 Effect of types declaration on default values 3 4 Typescasting iena bh ee bee Poe a eee ee a 3 5 Example of optimisation 000 3 6 Types and member functions 000 Common problems 4 1 Metacommands 2 000000 ee ee 4 2 Unsupported functions 02 0020 000 4 3 Memory handling and global variables 2 0 002 4 As GR lists 24s e gary ges SiGe ek SB aoe Hove ee 4 5 The install command 02 0000054 Command line options of gp2c What is gp2c The gp2c compiler is a package for translating GP routines into the C program ming language so that they can be compiled and used with the PARI system or the GP calculator The main advantage of doing this is to speed up computations and to include your own routines within the preexisting GP on
5. PARI GP already has a squfof function and the linker will pick the wrong one which is unfortunate So use the p option to gp2c run to change squfof to my_squfof gp2c run pmy _ g pari examples squfof gp This option prefixes my_ to every GP name in the program so as to avoid name clashes Change fact gp to install my_squfof D0 G p squfof pari examples squfof gp so fact_mersenne p squfof 2 p 1 and run gp2c run g fact gp parisize 4000000 primelimit 500000 fact_mersenne 67 i 2418 Qfb 10825778209 4021505768 13258245519 0 E 28 1 193707721 Nice isn t it But it gets even better instead of writing the install command directly in your script you can just load the squfof gp run using r just change fact gp to r pari examples squfof gp run fact_mersenne p squfof 2 p 1 2 5 Hand editing the C file generated by gp2c If you have some experience in PARI programming you may want to manually edit the C file generated by gp2c for example to improve memory handling Here some tips e If you preserve the install at the start of the file you can use the com mand gp2c run file c to recompile your file and start a new GP session with your functions added just as you use gp2c run with GP scripts e More generally gp2c run automatically passes any line in the C file start ing with GP to GP at start up e As explained in Section 2 2 under emacs you can type M x compile
6. able undeclared dd Warning pari examples squfof gp 11 variable undeclared d Warning pari examples squfof gp 11 variable undeclared b Warning pari examples squfof gp 45 variable undeclared b1 This option lists variables that are used but not declared It is important to declare all your variables with local or with global For gp2c undeclared variables are taken to be formal variables for polynomials For example if you write a function to build a second degree polynomial like pol a b c a x 2 b x c you must not declare x here since it stands for the formal variable z 2 4 Using compiled functions in a new program One you have successfully compiled and tested your functions you may want to reuse them in another GP program The best way is to copy the install commands of the functions you use at the start of the new program so that reading it will automatically load the compiled functions As an example we write a simple program fact gp that reads install squfof D0 G p squfof pari examples squfof gp so fact_mersenne p squfof 2 p 1 and run GP parisize 4000000 primelimit 500000 rfact fact_mersenne 67 i 2418 Qfb 10825778209 4021505768 13258245519 0 E 28 1 193707721 So all goes well But what is even better is that gp2c understands the install command and will be able to compile this new program Also this particular example will fail because as stated above
7. are sure x is positive the logarithm will be real To force an expression to belong to type type use the syntax expr type gp2c will check types consistency and output warnings if necessary For example f a int local r real r log x 2 1 gp2c will complain that the logarithm might not be real Since 7 2 1 is always positive we can write f z int local r real r log x 2 1 real 3 5 Example of optimisation Declaring the types of variables allow gp2c to perform some optimisations For example the following piece of GP code rho n local x y x 2 y 5 while gcd y x n 1 x x72 1 n y y 2 1 n y y 2 1 n gcd n y x ir generates the following output GEN rho GEN n GEN x gen_0 y gen_0 x gen_2 y stoi 5 while gcmp1 ggcd gsub y x n x gmod gaddgs gsqr x 1 n y gmod gaddgs gsqr y 1 n y gmod gaddgs gsqr y 1 n return ggcd n gsub y x The functions gsqr gaddgs gmod ggcd are generic PARI functions that handle gen objects Since we only want to factor integers with this method we can declare n x y of type int rho n int local x int y int x 2 y 5 while gcd y x n 1 x x72 1 n y y 2 1 dn y y 2 1 n gcd n y x The new C code output by gp2c is GEN rho GEN n int GEN x y int if typ n t_INT pari_err typeer rho x gen_2 stoi 5 te l 10 while gcmpi gcdii subii y x
8. bose enough and if you are not familiar with the PARI code and C in general Example of conflicting names are top bot prec un but there are thousands of others and they may be system dependent e ssuffix Add suffix to the names of the installed functions under GP This is to avoid clashes with the original GP script For example if you want to compare timings you may want to use the option s_c This does not affect the C code only the install commands 14 e S Assume strict prototypes for functions This means that you have declared all the local variables with local and not as parameters Also when a parameter is not mandatory a default value must be assigned to it in the declaration like for flag in test data flag 0 CODE This does not affect the C code only the install commands e h gives the help e v gives the gp2c version e prints a list of all the GP functions known by the compiler So if a routine contains a GP routine not on this list gp2c will show an error when trying to translate it For example the routine forvec is not yet implemented so you should not use it Reasons why a GP function may not be known by the compiler are The function is not part of the PARI library See Section 4 2 You use the old PARI 1 39 function names instead of the new ones gp2c currently does not know about the compat default Use what now under GP to get the current name For example mod is now Mo
9. but after that you can use T safely GP itself currently does not know about clone and unclone but you can use dummy functions clone x x unclone x while 0 when running uncompiled 4 4 GP lists GP lists are not fully supported by gp2c A partial support is available with the list type You must tell gp2c that a variable will contain a list by using L list inside a declaration where L is the name of the variable as explained in Section 3 Currently assigning to a list element L 2 x will not work and lists will not be freed unless you explicitly use listkill Note The PARI user s manual states that lists are useless in library mode 4 5 The install command The install command is interpreted as a gp2c directive This allows using installed function in compiled programs see Section 2 4 However this has some side effects e If present the lib argument must be a string not an expression that evaluate to a string e The install command is not compiled instead it is added to the list of functions to install 13 5 Command line options of gp2c Here is a brief description of the main options of gp2c which can be seen with gp2c h In Section 2 1 we saw how to use the g option e g tells gp2c to generate gerepile calls to clean up the PARI stack and reduce memory usage You will probably need this option although the C code will be easier to read or hand edit without it e ofile tells gp2c to write th
10. commands Meta commands commands starting with a other than r are currently ignored by gp2c though a warning will be issued because it is not clear what they should do in a compiled program Instead you probably want to run the meta command in the GP session itself The meta command rinclude is replaced with the content of the file include or include gp when gp2c reads the file If you would prefer gp2c to link include so to the program instead see Section 2 4 11 4 2 Unsupported functions The functions forell and forsubgroup are currently not implemented as an iter ator but as a procedure with callbacks which limits what you can do inside the loop Some functions are passed to GP by gp2c run at start up using the GP syntax instead of being translated in C install and addhelp In practice they can be considered as supported Some functions are built in in GP and so are not available to libpari pro grams So if you use them gp2c generate a program that needs to run under GP or with gp2c run Since the C prototype for those functions are not avail able the C compiler will output a warning This serves as a reminder of the problem They are all the plotting functions and allocatemem default extern input quit read system whatnow Some GP functions are not available for C programs so the compiler cannot handle them If you use them you will get the infamous unhandled letter in prototype error Sorry for the
11. d You use a GP function that does not exists in the GP version gp2c was compiled against Please recompile gp2c against this GP version Normally no functions are added between two stable releases of GP with the same minor version number say 2 1 1 and 2 1 2 so there is no need to recompile gp2c when you upgrade But if you use the developement versions you need to recompile Also some new developement versions may break old versions of gp2c so upgrade gp2c at the same time However if you want to compile scripts which do not use the new functions you do not need to recompile Note that you may use the GP environment variables to tell gp2c run which GP to use t Output the table of types known to the compiler see Section 3 15
12. e generated C file to the file file instead of the standard output e iN allows you to change the indentation of the generated C file So if you want 4 spaces just use the i4 option with gp2c The default is 2 e W is useful for debugging the gp file in the sense that it detects if some local variable is undeclared For example if the file algorithm gp has a routine like radical x F factor x 1 prod i 1 length F F i The variable F is undeclared in this routine so when running gp2c with the W option it prints Warning algorithm gp 1 variable undeclared F At present an undeclared variable is taken to be a formal variable for polynomials by gp2c so do not declare it if that is what you intend For example in pol a b c a x 2 b xt c you must not declare x since it stands for the formal variable z e pprefix A problem with C is that it is subject to name clashes i e if a GP variable in your routine has the same name as a C symbol in the pari library the compiler will report strange errors So this option changes ALL user variables and user routine names by adding a prefix prefix to them For example the GP routine add z y with pmy_ will become the C function my_add x y Try this option each time the compiler fails to compile gp2c output to see if there is a name conflict If this is the case change the name in your GP script It may be difficult to find conflicting names if your compiler is not ver
13. es It may also find bugs in GP scripts This package including the latest versions can be obtained at the URL http pari math u bordeaux fr download html gp2c 1 1 Installing gp2c After downloading the file gp2c z y zplt tar gz where x y z and t depend on the version you first have to unzip the file with the command gunzip gp2c 2z y zplt tar gz This will create the new file gp2c z y zplt tar Next you have to extract the files with the tar program tar xvf gp2c z y zplt tar Note You can do both steps at once with GNU tar by using the command tar zxvf gp2c 2 y zplt tar gz This creates a directory gp2c az y zplt which contains the main gp2c files Now you have to install the program You need the file pari cfg This file can be found in the PARI object directory and is installed in prefix lib pari Copy or link this file in the gp2c directory be sure to call it pari cfg In s lib pari pari cfg pari cfg Run configure which will search for the PARI version and some other configuration tools of the system To install the program type make and the program will be compiled You can then run make check to verify that everything has gone fine a bunch of OK s should show up All of this is completely standard and you are now ready to use gp2c You can use gp2c directly from this directory or you can install it by running make install as root If you do not install it you can run it from the gp2c directory by typing
14. gp2c 2 A gp2c tutorial 2 1 How can I compile and run my scripts The simplest way to use gp2c is to call gp2c run If you want to know what happens in detail see next section To make the examples easier to follow please move to the gp2c directory and link the root of your PARI source there In s pari As an example we will take the file pari examples squfof gp which is a simple implementation of the well known SQUFOF factoring method of D Shanks We just run the command gp2c run pari examples squfof gp After a little processing we get a GP session But this session is special because it contains the compiled squfof function Hence we can do the following parisize 4000000 primelimit 500000 squfof 3097180303181 419 i 596 Qfb 133225 1719841 261451 0 E 28 1 1691693 Let s try a bigger example squfof 122294051504814979 20137 the PARI stack overflows current stack size 4 0 Mbytes hint you can increase GP stack with allocatemem allocatemem Warning doubling stack size new stack 8 0 MBytes squfof 122294051504814979 20137 20137 3445 i 46474 Qf b 321233929 131349818 367273962 0 E 28 2 73823023 We need a large stack because by default gp2c does not generate code to handle the stack the so called gerepile code To instruct gp2c to add gerepile code automatically we must use the g option So quit this GP session and launch a new one wi
15. imelimit 500000 r pari examples squfof gp timer 1 on squfof 122294051504814979 20137 20137 3445 i 46474 Qfb 321233929 131349818 367273962 0 E 28 time 5 810 ms 1 73823023 squfof_c 122294051504814979 20137 20137 3445 i 46474 Qf b 321233929 131349818 367273962 0 E 28 time 560 ms 2 73823023 So the compiled version is more than ten times faster than the noncompiled one However for more complex examples compiled code usually runs only three times faster on average An extra trick once you have run gp2c run on your script it is compiled and you can use the compiled version outside gp2c run in any GP session by loading the file with extension gp run For example quit the gp2c run session and start gp and do parisize 4000000 primelimit 500000 r pari examples squfof gp run Now you have access to the compiled function squfof_c as well 2 2 How can I compile directly with gp2c Now we want to compile directly with gp2c to understand what happens We should run the command gp2c pari examples squfof gp gt squfof gp c This creates a file squfof gp c in the gp2c directory Now read this file with your favorite editor The first line is highly system dependent but should be similar to compile command usr bin gcc c o pari examples squfof gp o 03 Wall I usr local include pari examples squfof gp c amp amp usr bin gcc o pari examples squfof gp so
16. inconvenience These are plot ploth plotrecth Also the functions read eval kill may compile fine but have a surprising be haviour in some case because they may modify the state of the GP interpreter not of the compiled program Please see Section 4 3 for details For example f n eval n 2 is very different from f n n 2 The forstep function is supported when the step is a number If it is a vector you must add a tag vec to make GP know about it like in f x local v v 2 4 6 6 6 6 6 2 4 6 6 forstep y 7 x v vec print y This is not needed if the step is a vector or a variable of type vec but is needed if the step is only an expression which evaluates to a vector There is little that can be done about these problems without changing PARI GP itself 4 3 Memory handling and global variables While a lot of work has been done to ensure that gp2c handles global variables properly the use of global variables is still a lot of trouble so try to avoid them if you do not understand the implications on memory handling First there is a common practice to use undeclared variables as formal vari ables for example we assume z x and write a r b instead of a z b So gp2c will not raise an undeclared variable to the rank of global variable unless you declare it with the global command or you use it at toplevel i e outside any function See also Section 2 3 Second global variables seen by a compiled functi
17. nd gp2c s_c pari examples squfof gp gt squfof2 gp c and look at the difference between squfof gp c and squfof2 gp c diff u squfof gp c squfof2 gp c squfof gp c Tue Feb 26 13 44 42 2002 squfof2 gp c Tue Feb 26 13 44 49 2002 1 8 1 8 compile command usr bin gcc c o pari examples squfof gp o DMEMSTEP 1048576 g Wall Wno implicit I usr local include pari examples squfof gp c amp amp usr bin ld o pari examples squfof gp so shared pari examples squfof gp o include lt pari pari h gt GP install squfof D0 G p squfof pari examples squfof gp so GP install init_squfof v init_squfof pari squfof gp so GP install squfof D0 G p squfof_c pari les squfof gp so GP install init_squfof v init_squfof_c par squfof gp so GEN squfof GEN n long prec void init_squfof void If you are not familiar with the diff utility the above means that only the two lines starting with GP install have changed In fact squfof is still named squfof in the C file but the install command tells GP to rename it squfof_c in the GP session 2 3 Using gp2c to find errors in GP scripts The gp2c compiler can also be used to find errors in GP programs For that we should use the W option like in gp2c W pari examples squfof gp gt squfof gp c Warning pari examples squfof gp 7 variable undeclared P Warning pari examples squfof gp 11 vari
18. on are C variables not GP variables There is no connection between the two You may well have two variables with the same name and a different content Currently GP knows only how to install functions not variables so you need to write compiled functions in order to access global variables under GP 12 Basically global variables are allocated in the main stack which is destroyed each time GP prints a new prompt This means you must put all your com mands on the same line Also global variables must be initialized using the init_ lt filename gt function before being used and are only supported with the g flag So you end up doing gp2c run g global gp parisize 4000000 primelimit 500000 init_global myfunction args Note that nothing prevents you from calling init_global in the GP program In that case you can omit the parentheses i e write init_global not init_global so that you can still run your noncompiled program Another way to handle global variables is to use the clone function which copies a PARI object to the heap hence avoids its destruction when GP prints a new prompt You can use unclone to free a clone Please read the PARI GP manual for more information about clone A good use of clone is for initializing constant variables for example in test gp initfunc gp the vector T is initialized by T clone 4 3 2 2 1 1 1 1 0 0 0 0 0 0 0 0 You must still run the init_ lt filename gt after starting GP
19. shared pari examples squfof gp o This is the command needed to compile this C file to an object file with the C compiler and then to make a shared library with the linker If you use emacs typing M x compile will know about this command so you will just need to type Return to compile The second line is include lt pari pari h gt This includes the PARI header files It is important that the header files come from the same PARI version as GP else it will create problems The next lines are GP install squfof D0 G p squfof pari examples squfof gp so GP install init_squfof v init_squfof pari squfof gp so The characters GP denote a command that should be read by GP at start up Here the install commands above must be given to GP to let it know about functions defined by the library gp2c run copy such commands to the file pari examples squfof gp run Please read the entry about the install command in the PARI manual The init_squfof function is an initialization function that is created auto matically by gp2c to hold codes that is outside any function Since in our case there are none this is a dummy function In other cases it is essential The next lines are GEN squfof GEN n long prec void init_squfof void End of prototype This is the C prototypes of your functions The rest of the file is the C code proper For teaching purpose let s run the comma
20. th g Oh well before that type ls pari examples squfof gp pari examples squfof gp pari examples squfof gp run pari examples squfof gp c pari examples squfof gp so pari examples squfof gp o These are the files generated by gp2c run e pari examples squfof gp c is the C file generated by gp2c e pari examples squfof gp o is the object file generated by the C compiler e pari examples squfof gp so is the shared library generated by the linker e pari examples squfof gp run is a file that contains the commands needed to load the compiled functions inside GP It is the shared library which is used by GP Now let s continue gp2c run g pari examples squfof gp parisize 4000000 primelimit 500000 squfof 122294051504814979 20137 20137 3445 i 46474 Qf b 321233929 131349818 367273962 0 E 28 1 73823023 This time it works with no difficulty using the default stack We would like to know how much faster the compiled code runs so we need to load the non compiled squfof file in GP r pari examples squfof gp k unexpected character squfof n if isprime n retur Why Because squfof already exists as an installed function and GP refuses to overwrite it To solve this problem we will add a suffix to the name of the compiled function under GP Quit the session and type gp2c run g s_c pari examples squfof gp Now the function squfof is named squfof_c instead so we can do parisize 4000000 pr
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