PDL::PP - Generate PDL routines from concise descriptions e.g. pp_def( 'sumover', Pars => 'a(n); [o]b();', Code => 'double tmp=0; loop(n) %{ tmp += $a(); %} $b() = tmp; ' ); pp_done(); In much of what follows we will assume familiarity of the reader with the concepts of implicit and explicit threading and index manipulations within PDL. If you have not yet heard of these concepts or are not very comfortable with them it is time to check PDL::Indexing. As you may appreciate from its name PDL::PP is a Pre-Processor, i.e. it expands code via substitutions to make real C-code (well, actually it outputs XS code (See perlxs) but that is very close to C). Why do we need PP? Several reasons: firstly, we want to be able to generate subroutine code for each of the PDL datatypes (PDL_Byte, PDL_Short,. etc). AUTOMATICALLY. Secondly, when referring to slices of PDL arrays in Perl (e.g. "$a->slice('0:10:2,:')" or other things such as transposes) it is nice to be able to do this transparently and to be able to do this 'in-place' - i.e, not to have to make a memory copy of the section. PP handles all the necessary element and offset arithmetic for you. There are also the notions of threading (repeated calling of the same routine for multiple slices, see PDL::Indexing) and dataflow (see PDL::Dataflow) which use of PP allows. So how do you use PP? Well for the most part you just write ordinary C code except for special PP constructs which take the form: $something(something else) or: PPfunction %{ <stuff> %} The most important PP construct is the form "$array()". Consider the very simple PP function to sum the elements of a 1D vector (in fact this is very similar to the actual code used by 'sumover'): pp_def('sumit', Pars => 'a(n); [o]b();', Code => ' double tmp; tmp = 0; loop(n) %{ tmp += $a(); %} $b() = tmp; '); What's going on? The "Pars =>" line is very important for PP - it specifies all the arguments and their dimensionality. We call this the signature of the PP function (compare also the explanations in PDL::Indexing). In this case the routine takes a 1-D function as input and returns a 0-D scalar as output. The "$a()" PP construct is used to access elements of the array a(n) for you - PP fills in all the required C code. [Aside: since PP used "$var()" for its parsing you must single-quote all Code=> arguments since you don't want perl to interpolate "$var()" into another string - i.e. don't use "" unless you know what you are doing! Tjl: it's usually easiest to use single quotes and 'something'.$interpolatable.'somethingelse'] In the simple case here where all elements are accessed the PP construct "loop(n) %{ ... %}" is used to loop over all elements in dimension "n". Note this feature of PP: ALL DIMENSIONS ARE SPECIFIED BY NAME. This is made clearer if we avoid the PP loop() construct and write the loop explicitly using conventional C: pp_def('sumit', Pars => 'a(n); [o]b();', Code => ' int i,n_size; double tmp; n_size = $SIZE(n); tmp = 0; for(i=0; i<n_size; i++) { tmp += $a(n=>i); } $b() = tmp; '); which does the same as before, except more long-windedly. You can see to get element "i" of a() we say "$a(n=>i)" - we are specifying the dimension by name "n". In 2D we might say: Pars=>'a(m,n);', ... tmp += $a(m=>i,n=>j); ... The syntax 'm=>i' borrows from Perl hashes (which are in fact used in the implementation of PP). One could also say "$a(n=>j,m=>i)" as order is not important. You can also see in the above example the use of another PP construct - $SIZE(n) to get the length of the dimension "n". It should, however, be noted that you shouldn't write an explicit C-loop when you could have used the PP "loop" construct since PDL::PP checks automatically the loop limits for you, usage of "loop" makes the code more concise, etc. But there are certainly situations where you need explicit control of the loop and now you know how to do it ;). To revisit 'Why PP?' - the above code for sumit() will be generated for each data-type. It will operate on slices of arrays 'in-place'. It will thread automatically - e.g. if a 2D array is given it will be called repeatedly for each 1D row (again check PDL::Indexing for the details of threading). And then b() will be a 1D array of sums of each row. We could call it with $a->xchg(0,1) to sum the colums instead. And Dataflow tracing etc. will be available. You can see PP saves the programmer from writing a lot of needlessly repetitive C-code -- in our opinion this is one of the best features of PDL making writing new C subroutines for PDL an amazingly concise exercise. A second reason is the ability to make PP expand your concise code definitions into different C code based on the needs of the computer architecture in question. Imagine for example you are lucky to have a supercomputer at your hands; in that case you want PDL::PP certainly to generate code that takes advantage of the vectorising/parallel computing features of your machine (this a project for the future). In any case, the bottom line is that your unchanged code should still expand to working XS code even if the internals of PDL changed. Also, because you are generating the code in an actual Perl script, there are many fun things that you can do. Let's say that you need to write both sumit (as above) and multit. With a little bit of inventivity, we can do for({Name => 'sumit', Init => '0', Op => '+='}, {Name => 'multit', Init => '1', Op => '*='}) { pp_def($_->{Name}, Pars => 'a(n); [o]b();', Code => ' double tmp; tmp = '.$_->{Init}.'; loop(n) %{ tmp '.$_->{Op}.' $a(); %} $b() = tmp; '); } which defines both the functions easily. Now, if you later need to change the signature or dimensionality or whatever, you only need to change one place in your code. Yeah, sure, your editor does have 'cut and paste' and 'search and replace' but it's still less bothersome and definitely more difficult to forget just one place and have strange bugs creep in. Also, adding 'orit' (bitwise or) later is a one-liner. And remember, you really have perl's full abilities with you - you can very easily read any input file and make routines from the information in that file. For simple cases like the above, the author (Tjl) currently favors the hash syntax like the above - it's not too much more characters than the corresponding array syntax but much easier to understand and change. We should mention here also the ability to get the pointer to the beginning of the data in memory - a prerequisite for interfacing PDL to some libraries. This is handled with the "$P(var)" directive, see below. So, after this quick overview of the general flavour of programming PDL routines using PDL::PP let's summarise in which circumstances you should actually use this preprocessor/precompiler. You should use PDL::PP if you want to interface PDL to some external library write some algorithm that would be slow if coded in perl (this is not as often as you think; take a look at threading and dataflow first). be a PDL developer (and even then it's not obligatory) Because of its architecture, PDL::PP can be both flexible and easy to use (yet exuberantly complicated) at the same time. Currently, part of the problem is that error messages are not very informative and if something goes wrong, you'd better know what you are doing and be able to hack your way through the internals (or be able to figure out by trial and error what is wrong with your args to "pp_def"). An alternative, of course, is to ask someone about it (e.g., through the mailing lists). Now that you have some idea how to use "pp_def" to define new PDL functions it is time to explain the general syntax of "pp_def". "pp_def" takes as arguments first the name of the function you are defining and then a hash list that can contain various keys. Based on these keys PP generates XS code and a .pm file. The function "pp_done" (see example in the SYNOPSIS) is used to tell PDL::PP that there are no more definitions in this file and it is time to generate the .xs and .pm file. As a consequence, there may be several pp_def() calls inside a file (by convention files with PP code have the extension .pd or .pp) but generally only one pp_done(). There are two main different types of usage of pp_def(), the 'data operation' and 'slice operation' prototypes. The 'data operation' is used to take some data, mangle it and output some other data; this includes for example the '+' operation, matrix inverse, sumover etc and all the examples we have talked about in this document so far. Implicit and explicit threading and the creation of the result are taken care of automatically in those opeartions. You can even do dataflow with "sumit", "sumover", etc (don't be dismayed if you don't understand the concept of dataflow in PDL very well yet; it is still very much experimental). The 'slice operation' is a different kind of operation: in a slice operation, you are not changing any data, you are defining correspondences between different elements of two piddles (examples include the index manipulation/slicing function definitions in the file slices.pd that is part of the PDL distribution; but beware, this is not introductory level stuff). If PDL was compiled with support for bad values (ie "WITH_BADVAL => 1"), then additional keys are required for "pp_def", as explained below. If you are just interested in communicating with some external library (for example some linear algebra/matrix library), you'll usually want the 'data operation' so we are going to discuss that first.

A simple example
In the data operation, you must know what dimensions of data you need. First, an example with scalars: pp_def('add', Pars => 'a(); b(); [o]c();', Code => '$c() = $a() + $b();' ); That looks a little strange but let's dissect it. The first line is easy: we're defining a routine with the name 'add'. The second line simply declares our parameters and the parentheses mean that they are scalars. We call the string that defines our parameters and their dimensionality the signature of that function. For its relevance with regard to threading and index manipulations check the PDL::Indexing manpage. The third line is the actual operation. You need to use the dollar signs and parentheses to refer to your parameters (this will probably change at some point in the future, once a good syntax is found). These lines are all that is necessary to actually define the function for PDL (well, actually it isn't; you aditionally need to write a Makefile.PL (see below) and build the module (something like 'perl Makefile.PL; make'); but let's ignore that for the moment). So now you can do use MyModule; $a = pdl 2,3,4; $b = pdl 5; $c = add($a,$b); # or add($a,$b,($c=null)); # Alternative form, useful if $c has been # preset to something big, not useful here. and have threading work correctly (the result is $c == [7 8 9]).

The Pars section: the signature of a PP function
Seeing the above example code you will most probably ask: what is this strange "$c=null" syntax in the second call to our new "add" function? If you take another look at the definition of "add" you will notice that the third argument "c" is flagged with the qualifier "[o]" which tells PDL::PP that this is an output argument. So the above call to add means 'create a new $c from scratch with correct dimensions' - "null" is a special token for 'empty piddle' (you might ask why we haven't used the value "undef" to flag this instead of the PDL specific "null"; we are currently thinking about it ;). [This should be explained in some other section of the manual as well!!] The reason for having this syntax as an alternative is that if you have really huge piddles, you can do $c = PDL->null; for(some long loop) { # munge a,b add($a,$b,$c); # munge c, put something back to a,b } and avoid allocating and deallocating $c each time. It is allocated once at the first add() and thereafter the memory stays until $c is destroyed. If you just say $c = add($a,$b); the code generated by PP will automatically fill in "$c=null" and return the result. If you want to learn more about the reasons why PDL::PP supports this style where output arguments are given as last arguments check the PDL::Indexing manpage. "[o]" is not the only qualifier a pdl argument can have in the signature. Another important qualifier is the "[t]" option which flags a pdl as temporary. What does that mean? You tell PDL::PP that this pdl is only used for temporary results in the course of the calculation and you are not interested in its value after the computation has been completed. But why should PDL::PP want to know about this in the first place? The reason is closely related to the concepts of pdl auto creation (you heard about that above) and implicit threading. If you use implicit threading the dimensionality of automatically created pdls is actually larger than that specified in the signature. With "[o]" flagged pdls will be created so that they have the additional dimensions as required by the number of implicit thread dimensions. When creating a temporary pdl, however, it will always only be made big enough so that it can hold the result for one iteration in a threadloop, i.e. as large as required by the signature. So less memory is wasted when you flag a pdl as temporary. Secondly, you can use output auto creation with temporary pdls even when you are using explicit threading which is forbidden for normal output pdls flagged with "[o]" (see PDL::Indexing). Here is an example where we use the [t] qualifier. We define the function "callf" that calls a C routine "f" which needs a temporary array of the same size and type as the array "a" (sorry about the forward reference for $P; it's a pointer access, see below) : pp_def('callf', Pars => 'a(n); [t] tmp(n); [o] b()', Code => 'int ns = $SIZE(n); f($P(a),$P(b),$P(tmp),ns); ' );

Argument dimensions and the signature
Now we have just talked about dimensions of pdls and the signature. How are they related? Let's say that we want to add a scalar + the index number to a vector: pp_def('add2', Pars => 'a(n); b(); [o]c(n);', Code => 'loop(n) %{ $c() = $a() + $b() + n; %}' ); There are several points to notice here: first, the "Pars" argument now contains the n arguments to show that we have a single dimensions in a and c. It is important to note that dimensions are actual entities that are accessed by name so this declares a and c to have the same first dimensions. In most PP definitions the size of named dimensions will be set from the respective dimensions of non-output pdls (those with no "[o]" flag) but sometimes you might want to set the size of a named dimension explicitly through an integer parameter. See below in the description of the "OtherPars" section how that works.

Type conversions and the signature
The signature also determines the type conversions that will be performed when a PP function is invoked. So what happens when we invoke one of our previously defined functions with pdls of different type, e.g. add2($a,$b,($ret=null)); where $a is of type "PDL_Float" and $b of type "PDL_Short"? With the signature as shown in the definition of "add2" above the datatype of the operation (as determined at runtime) is that of the pdl with the 'highest' type (sequence is byte < short < ushort < long < float < double). In the add2 example the datatype of the operation is float ($a has that datatype). All pdl arguments are then type converted to that datatype (they are not converted inplace but a copy with the right type is created if a pdl argument doesn't have the type of the operation). Null pdls don't contribute a type in the determination of the type of the operation. However, they will be created with the datatype of the operation; here, for example, $ret will be of type float. You should be aware of these rules when calling PP functions with pdls of different types to take the additional storage and runtime requirements into account. These type conversions are correct for most functions you normally define with "pp_def". However, there are certain cases where slightly modified type conversion behaviour is desired. For these cases additional qualifiers in the signature can be used to specify the desired properties with regard to type conversion. These qualifiers can be combined with those we have encountered already (the creation qualifiers "[o]" and "[t]"). Let's go through the list of qualifiers that change type conversion behaviour. The most important is the "int" qualifier which comes in handy when a pdl argument represents indices into another pdl. Let's take a look at an example from "PDL::Ufunc": pp_def('maximum_ind', Pars => 'a(n); int [o] b()', Code => '$GENERIC() cur; int curind; loop(n) %{ if (!n || $a() > cur) {cur = $a(); curind = n;} %} $b() = curind;', ); The function "maximum_ind" finds the index of the largest element of a vector. If you look at the signature you notice that the output argument "b" has been declared with the additional "int" qualifier. This has the following consequences for type conversions: regardless of the type of the input pdl "a" the output pdl "b" will be of type "PDL_Long" which makes sense since "b" will represent an index into "a". Furthermore, if you call the function with an existing output pdl "b" its type will not influence the datatype of the operation (see above). Hence, even if "a" is of a smaller type than "b" it will not be converted to match the type of "b" but stays untouched, which saves memory and CPU cycles and is the right thing to do when "b" represents indices. Also note that you can use the 'int' qualifier together with other qualifiers (the "[o]" and "[t]" qualifiers). Order is significant -- type qualifiers precede creation qualifiers ("[o]" and "[t]"). The above example also demonstrates typical usage of the "$GENERIC()" macro. It expands to the current type in a so called generic loop. What is a generic loop? As you already heard a PP function has a runtime datatype as determined by the type of the pdl arguments it has been invoked with. The PP generated XS code for this function therefore contains a switch like "switch (type) {case PDL_Byte: ... case PDL_Double: ...}" that selects a case based on the runtime datatype of the function (it's called a type ``loop'' because there is a loop in PP code that generates the cases). In any case your code is inserted once for each PDL type into this switch statement. The "$GENERIC()" macro just expands to the respective type in each copy of your parsed code in this "switch" statement, e.g., in the "case PDL_Byte" section "cur" will expand to "PDL_Byte" and so on for the other case statements. I guess you realise that this is a useful macro to hold values of pdls in some code. There are a couple of other qualifiers with similar effects as "int". For your convenience there are the "float" and "double" qualifiers with analogous consequences on type conversions as "int". Let's assume you have a very large array for which you want to compute row and column sums with an equivalent of the "sumover" function. However, with the normal definition of "sumover" you might run into problems when your data is, e.g. of type short. A call like sumover($large_pdl,($sums = null)); will result in $sums be of type short and is therefore prone to overflow errors if $large_pdl is a very large array. On the other hand calling @dims = $large_pdl->dims; shift @dims; sumover($large_pdl,($sums = zeroes(double,@dims))); is not a good alternative either. Now we don't have overflow problems with $sums but at the expense of a type conversion of $large_pdl to double, something bad if this is really a large pdl. That's where "double" comes in handy: pp_def('sumoverd', Pars => 'a(n); double [o] b()', Code => 'double tmp=0; loop(n) %{ tmp += a(); %} $b() = tmp;', ); This gets us around the type conversion and overflow problems. Again, analogous to the "int" qualifier "double" results in "b" always being of type double regardless of the type of "a" without leading to a typeconversion of "a" as a side effect. Finally, there are the "type+" qualifiers where type is one of "int" or "float". What shall that mean. Let's illustrate the "int+" qualifier with the actual definition of sumover: pp_def('sumover', Pars => 'a(n); int+ [o] b()', Code => '$GENERIC(b) tmp=0; loop(n) %{ tmp += a(); %} $b() = tmp;', ); As we had already seen for the "int", "float" and "double" qualifiers, a pdl marked with a "type+" qualifier does not influence the datatype of the pdl operation. Its meaning is "make this pdl at least of type "type" or higher, as required by the type of the operation". In the sumover example this means that when you call the function with an "a" of type PDL_Short the output pdl will be of type PDL_Long (just as would have been the case with the "int" qualifier). This again tries to avoid overflow problems when using small datatypes (e.g. byte images). However, when the datatype of the operation is higher than the type specified in the "type+" qualifier "b" will be created with the datatype of the operation, e.g. when "a" is of type double then "b" will be double as well. We hope you agree that this is sensible behaviour for "sumover". It should be obvious how the "float+" qualifier works by analogy. It may become necessary to be able to specify a set of alternative types for the parameters. However, this will probably not be implemented until someone comes up with a reasonable use for it. Note that we now had to specify the $GENERIC macro with the name of the pdl to derive the type from that argument. Why is that? If you carefully followed our explanations you will have realised that in some cases "b" will have a different type than the type of the operation. Calling the '$GENERIC' macro with "b" as argument makes sure that the type will always the same as that of "b" in that part of the generic loop. This is about all there is to say about the "Pars" section in a "pp_def" call. You should remember that this section defines the signature of a PP defined function, you can use several options to qualify certain arguments as output and temporary args and all dimensions that you can later refer to in the "Code" section are defined by name. It is important that you understand the meaning of the signature since in the latest PDL versions you can use it to define threaded functions from within perl, i.e. what we call perl level threading. Please check PDL::Indexing for details.

The Code section
The "Code" section contains the actual XS code that will be in the innermost part of a threadloop (if you don't know what a thread loop is then you still haven't read PDL::Indexing; do it now ;) after any PP macros (like $GENERIC) and PP functions have been expanded (like the "loop" function we are going to explain next). Let's quickly reiterate the "sumover" example: pp_def('sumover', Pars => 'a(n); int+ [o] b()', Code => '$GENERIC(b) tmp=0; loop(n) %{ tmp += a(); %} $b() = tmp;', ); The "loop" construct in the "Code" section also refers to the dimension name so you don't need to specify any limits: the loop is correctly sized and everything is done for you, again. Next, there is the surprising fact that "$a()" and "$b()" do not contain the index. This is not necessary because we're looping over n and both variables know which dimensions they have so they automatically know they're being looped over. This feature comes in very handy in many places and makes for much shorter code. Of course, there are times when you want to circumvent this; here is a function which symmetrizes a matrix and serves as an example of how to code explicit looping: pp_def('symm', Pars => 'a(n,n); [o]c(n,n);', Code => 'loop(n) %{ int n2; for(n2=n; n2<$SIZE(n); n2++) { $c(n0 => n, n1 => n2) = $c(n0 => n2, n1 => n) = $a(n0 => n, n1 => n2); } %} ' ); Let's dissect what is happening. Firstly, what is this function supposed to do? From its signature you see that it takes a 2D matrix with equal numbers of columns and rows and outputs a matrix of the same size. From a given input matrix $a it computes a symmetric output matrix $c (symmetric in the matrix sense that A^T = A where ^T means matrix transpose, or in PDL parlance $c == $c->xchg(0,1)). It does this by using only the values on and below the diagonal of $a. In the output matrix $c all values on and below the diagonal are the same as those in $a while those above the diagonal are a mirror image of those below the diagonal (above and below are here interpreted in the way that PDL prints 2D pdls). If this explanation still sounds a bit strange just go ahead, make a little file into which you write this definition, build the new PDL extension (see section on Makefiles for PP code) and try it out with a couple of examples. Having explained what the function is supposed to do there are a couple of points worth noting from the syntactical point of view. First, we get the size of the dimension named "n" again by using the $SIZE macro. Second, there are suddenly these funny "n0" and "n1" index names in the code though the signature defines only the dimension "n". Why this? The reason becomes clear when you note that both the first and second dimension of $a and $b are named "n" in the signature of "symm". This tells PDL::PP that the first and second dimension of these arguments should have the same size. Otherwise the generated function will raise a runtime error. However, now in an access to $a and $c PDL::PP cannot figure out which index "n" refers to any more just from the name of the index. Therefore, the indices with equal dimension names get numbered from left to right starting at 0, e.g. in the above example "n0" refers to the first dimension of $a and $c, "n1" to the second and so on. In all examples so far, we have only used the "Pars" and "Code" members of the hash that was passed to "pp_def". There are certainly other keys that are recognised by PDL::PP and we will hear about some of them in the course of this document. Find a (non-exhaustive) list of keys in Appendix A. A list of macros and PPfunctions (we have only encountered some of those in the examples above yet) that are expanded in values of the hash argument to "pp_def" is summarised in Appendix B. At this point, it might be appropriate to mention that PDL::PP is not a completely static, well designed set of routines (as Tuomas puts it: "stop thinking of PP as a set of routines carved in stone") but rather a collection of things that the PDL::PP author (Tuomas J. Lukka) considered he would have to write often into his PDL extension routines. PP tries to be expandable so that in the future, as new needs arise, new common code can be abstracted back into it. If you want to learn more on why you might want to change PDL::PP and how to do it check the section on PDL::PP internals.

Handling bad values
If you do not have bad-value support compiled into PDL you can ignore this section and the related keys: "BadCode", "HandleBad", ... (try printing out the value of $PDL::Bad::Status - if it equals 0 then move straight on). There are several keys and macros used when writing code to handle bad values. The first one is the "HandleBad" key: This flags a pp-routine as NOT handling bad values. If this routine is sent piddles with their "badflag" set, then a warning message is printed to STDOUT and the piddles are processed as if the value used to represent bad values is a valid number. The "badflag" value is not propogated to the output piddles. An example of when this is used is for FFT routines, which generally do not have a way of ignoring part of the data. This causes PDL::PP to write extra code that ensures the BadCode section is used, and that the "$ISBAD()" macro (and its brethren) work. If any of the input piddles have their "badflag" set, then the output piddles will have their "badflag" set, but any supplied BadCode is ignored. The value of "HandleBad" is used to define the contents of the "BadDoc" key, if it is not given. To handle bad values, code must be written somewhat differently; for instance, $c() = $a() + $b(); becomes something like if ( $a() != BADVAL && $b() != BADVAL ) { $c() = $a() + $b(); } else { $c() = BADVAL; } However, we only want the second version if bad values are present in the input piddles (and that bad-value support is wanted!) - otherwise we actually want the original code. This is where the "BadCode" key comes in; you use it to specify the code to execute if bad values may be present, and PP uses both it and the "Code" section to create something like: if ( bad_values_are_present ) { fancy_threadloop_stuff { BadCode } } else { fancy_threadloop_stuff { Code } } This approach means that there is virtually no overhead when bad values are not present (ie the badflag routine returns 0). The BadCode section can use the same macros and looping constructs as the Code section. However, it wouldn't be much use without the following additional macros: To check whether a piddle's value is bad, use the $ISBAD macro: if ( $ISBAD(a()) ) { printf("a() is bad\n"); } You can also access given elements of a piddle: if ( $ISBAD(a(n=>l)) ) { printf("element %d of a() is bad\n", l); } This is the opposite of the $ISBAD macro. For when you want to set an element of a piddle bad. If you have cached the value of a piddle "$a()" into a c-variable ("foo" say), then to check whether it is bad, use "$ISBADVAR(foo,a)". As above, but this time checking that the cached value isn't bad. To copy the bad value for a piddle into a c variable, use "$SETBADVAR(foo,a)". TODO: mention "$PPISBAD()" etc macros. Using these macros, the above code could be specified as: Code => '$c() = $a() + $b();', BadCode => ' if ( $ISBAD(a()) || $ISBAD(b()) ) { $SETBAD(c()); } else { $c() = $a() + $b(); }', Since this is perl, TMTOWTDI, so you could also write: BadCode => ' if ( $ISGOOD(a()) && $ISGOOD(b()) ) { $c() = $a() + $b(); } else { $SETBAD(c()); }', If you want access to the value of the badflag for a given piddle, you can use the "$PDLSTATExxxx()" macros: TODO: mention the "FindBadStatusCode" and "CopyBadStatusCode" options to "pp_def", as well as the "BadDoc" key.

Interfacing your own/library functions using PP
Now, consider the following: you have your own C function (that may in fact be part of some library you want to interface to PDL) which takes as arguments two pointers to vectors of double: void myfunc(int n,double *v1,double *v2); The correct way of defining the PDL function is pp_def('myfunc', Pars => 'a(n); [o]b(n);', GenericTypes => [D], Code => 'myfunc($SIZE(n),$P(a),$P(b));' ); The "$P("par")" syntax returns a pointer to the first element and the other elements are guaranteed to lie after that. Notice that here it is possible to make many mistakes. First, $SIZE(n) must be used instead of "n". Second, you shouldn't put any loops in this code. Third, here we encounter a new hash key recognised by PDL::PP : the "GenericTypes" declaration tells PDL::PP to ONLY GENERATE THE TYPELOOP FOP THE LIST OF TYPES SPECIFIED. In this case "double". This has two advantages. Firstly the size of the compiled code is reduced vastly, secondly if non-double arguments are passed to "myfunc()" PDL will automatically convert them to double before passing to the external C routine and convert them back afterwards. One can also use "Pars" to qualify the types of individual arguments. Thus one could also write this as: pp_def('myfunc', Pars => 'double a(n); double [o]b(n);', Code => 'myfunc($SIZE(n),$P(a),$P(b));' ); The type specification in "Pars" exempts the argument from variation in the typeloop - rather it is automatically converted too and from the type specified. This is obviously useful in a more general example, e.g.: void myfunc(int n,float *v1,long *v2); pp_def('myfunc', Pars => 'float a(n); long [o]b(n);', GenericTypes => [F], Code => 'myfunc($SIZE(n),$P(a),$P(b));' ); Note we still use "GenericTypes" to reduce the size of the type loop, obviously PP could in principle spot this and do it automatically though the code has yet to attain that level of sophistication! Finally note when types are converted automatically one MUST use the "[o]" qualifier for output variables or you hard one changes will get optimised away by PP! If you interface a large library you can automate the interfacing even further. Perl can help you again(!) in doing this. In many libraries you have certain calling conventions. This can be exploited. In short, you can write a little parser (which is really not difficult in perl) that then generates the calls to "pp_def" from parsed descriptions of the functions in that library. For an example, please check the Slatec interface in the "Lib" tree of the PDL distribution. If you want to check (during debugging) which calls to PP functions your perl code generated a little helper package comes in handy which replaces the PP functions by identically named ones that dump their arguments to stdout. Just say perl -MPDL::PP::Dump myfile.pd to see the calls to "pp_def" and friends. Try it with ops.pd and slatec.pd. If you're interested (or want to enhance it), the source is in Basic/Gen/PP/Dump.pm

Other macros and functions in the Code section
Macros: So far we have encountered the $SIZE, $GENERIC and $P macros. Now we are going to quickly explain the other macros that are expanded in the "Code" section of PDL::PP along with examples of their usage. The $T macro is used for type switches. This is very useful when you have to use different external (e.g. library) functions depending on the input type of arguments. The general syntax is $Ttypeletters(type_alternatives) where "typeletters" is a permutation of a subset of the letters "BSULFD" which stand for Byte, Short, Ushort, etc. and "type_alternatives" are the expansions when the type of the PP operation is equal to that indicated by the respective letter. Let's illustrate this incomprehensible description by an example. Assuming you have two C functions with prototypes void float_func(float *in, float *out); void double_func(double *in, double *out); which do basically the same thing but one accepts float and the other double pointers. You could interface them to PDL by defining a generic function "foofunc" (which will call the correct function depending on the type of the transformation): pp_def('foofunc', Pars => ' a(n); [o] b();', Code => ' $TFD(float_func,double_func) ($P(a),$P(b));' GenericTypes => [F,D], ); Please note that you can't say Code => ' $TFD(float,double)_func ($P(a),$P(b));' since the $T macro expands with trailing spaces, analogously to C preprocessor macros. The slightly longer form illustrated above is correct. If you really want brevity, you can of course do '$TBSULFD('.(join ',',map {"long_identifier_name_$_"} qw/byt short unseigned lounge flotte dubble/).');' The $PP macro is used for a so called physical pointer access. The physical refers to some internal optimisations of PDL (for those who are familiar with the PDL core we are talking about the vaffine optimisations). This macro is mainly for internal use and you shouldn't need to use it in any of your normal code. The $COMP macro is used to access non-pdl values in the code section. Its name is derived from the implementation of transformations in PDL. The variables you can refer to using $COMP are members of the ``compiled'' structure that represents the PDL transformation in question but does not yet contain any information about dimensions (for further details check PDL::Internals). However, you can treat $COMP just as a black box without knowing anything about the implementation of transformations in PDL. So when would you use this macro? Its main usage is to access values of arguments that are declared in the "OtherPars" section of a "pp_def" definition. But then you haven't heard about the "OtherPars" key yet?! Let's have another example that illustrates typical usage of both new features: pp_def('pnmout', Pars => 'a(m)', OtherPars => "char* fd", GenericTypes => [B,U,S,L], Code => 'PerlIO *fp; IO *io; io = GvIO(gv_fetchpv($COMP(fd),FALSE,SVt_PVIO)); if (!io || !(fp = IoIFP(io))) croak("Can\'t figure out FP"); if (PerlIO_write(fp,$P(a),len) != len) croak("Error writing pnm file"); '); This function is used to write data from a pdl to a file. The file descriptor is passed as a string into this function. This parameter does not go into the "Pars" section since it cannot be usefully treated like a pdl but rather into the aptly named "OtherPars" section. Parameters in the "OtherPars" section follow those in the "Pars" section when invoking the function, i.e. open FILE,">out.dat" or die "couldn't open out.dat"; pnmout($pdl,'FILE'); When you want to access this parameter inside the code section you have to tell PP by using the $COMP macro, i.e. you write "$COMP(fd)" as in the example. Otherwise PP wouldn't know that the "fd" you are referring to is the same as that specified in the "OtherPars" section. Another use for the "OtherPars" section is to set a named dimension in the signature. Let's have an example how that is done: pp_def('setdim', Pars => '[o] a(n)', OtherPars => 'int ns => n', Code => 'loop(n) %{ $a() = n; %}', ); This says that the named dimension "n" will be initialised from the value of the other parameter "ns" which is of integer type (I guess you have realised that we use the "CType From => named_dim" syntax). Now you can call this function in the usual way: setdim(($a=null),5); print $a; [ 0 1 2 3 4 ] Admittedly this function is not very useful but it demonstrates how it works. If you call the function with an existing pdl and you don't need to explicitly specify the size of "n" since PDL::PP can figure it out from the dimensions of the non-null pdl. In that case you just give the dimension parameter as "-1": $a = hist($b); setdim($a,-1); That should do it. The only PP function that we have used in the examples so far is "loop". Additionally, there are currently two other functions which are recognised in the "Code" section: As we heard above the signature of a PP defined function defines the dimensions of all the pdl arguments involved in a primitive operation. However, you often call the functions that you defined with PP with pdls that have more dimensions than those specified in the signature. In this case the primitive operation is performed on all subslices of appropriate dimensionality in what is called a threadloop (see also overview above and PDL::Indexing). Assuming you have some notion of this concept you will probably appreciate that the operation specified in the code section should be optimised since this is the tightest loop inside a threadloop. However, if you revisit the example where we define the "pnmout" function, you will quickly realise that looking up the "IO" file descriptor in the inner threadloop is not very efficient when writing a pdl with many rows. A better approach would be to look up the "IO" descriptor once outside the threadloop and use its value then inside the tightest threadloop. This is exactly where the "threadloop" function comes in handy. Here is an improved definition of "pnmout" which uses this function: pp_def('pnmout', Pars => 'a(m)', OtherPars => "char* fd", GenericTypes => [B,U,S,L], Code => 'PerlIO *fp; IO *io; int len; io = GvIO(gv_fetchpv($COMP(fd),FALSE,SVt_PVIO)); if (!io || !(fp = IoIFP(io))) croak("Can\'t figure out FP"); len = $SIZE(m) * sizeof($GENERIC()); threadloop %{ if (PerlIO_write(fp,$P(a),len) != len) croak("Error writing pnm file"); %} '); This works as follows. Normally the C code you write inside the "Code" section is placed inside a threadloop (i.e., PP generates the appropriate wrapping XS code around it). However, when you explicitly use the "threadloop" function, PDL::PP recognises this and doesn't wrap your code with an additional threadloop. This has the effect that code you write outside the threadloop is only executed once per transformation and just the code with in the surrounding "%{ ... %}" pair is placed within the tightest threadloop. This also comes in handy when you want to perform a decision (or any other code, especially CPU intensive code) only once per thread, i.e. pp_addhdr(' #define RAW 0 #define ASCII 1 '); pp_def('do_raworascii', Pars => 'a(); b(); [o]c()', OtherPars => 'int mode', Code => ' switch ($COMP(mode)) { case RAW: threadloop %{ /* do raw stuff */ %} break; case ASCII: threadloop %{ /* do ASCII stuff */ %} break; default: croak("unknown mode"); }' ); The types function works similar to the $T macro. However, with the "types" function the code in the following block (delimited by "%{" and "%}" as usual) is executed for all those cases in which the datatype of the operation is any of the types represented by the letters in the argument to "type", e.g. Code => '... types(BSUL) %{ /* do integer type operation */ %} types(FD) %{ /* do floating point operation */ %} ...'

Other useful PP keys in data operation definitions
You have already heard about the "OtherPars" key. Currently, there are not many other keys for a data operation that will be useful in normal (whatever that is) PP programming. In fact, it would be interesting to hear about a case where you think you need more than what is provided at the moment. Please speak up on one of the PDL mailing lists. Most other keys recognised by "pp_def" are only really useful for what we call slice operations (see also above). One thing that is strongly being planned is variable number of arguments, which will be a little tricky. An incomplete list of the available keys: Setting this key marks the routine as working inplace - ie the input and output piddles are the same. An example is "$a->inplace->sqrt()" (or "sqrt(inplace($a))"). Use when the routine is a unary function, such as "sqrt". If there are more than one input piddles, specify the name of the one that can be changed inplace using an array reference. If there are more than one output piddle, specify the name of the input piddle and output piddle in a 2-element array reference. This probably isn't needed, but left in for completeness. If bad values are being used, care must be taken to ensure the propogation of the badflag when inplace is being used; consider this excerpt from Basic/Bad/bad.pd: pp_def('replacebad',HandleBad => 1, Pars => 'a(); [o]b();', OtherPars => 'double newval', Inplace => 1, CopyBadStatusCode => '/* propogate badflag if inplace AND it has changed */ if ( a == b && $ISPDLSTATEBAD(a) ) PDL->propogate_badflag( b, 0 ); /* always make sure the output is "good" */ $SETPDLSTATEGOOD(b); ', ... Since this routine removes all bad values, then the output piddle had its bad flag cleared. If run inplace (so "a == b"), then we have to tell all the children of "a" that the bad flag has been cleared (to save time we make sure that we call "PDL->propogate_badgflag" only if the input piddle had its bad flag set). NOTE: one idea is that the documentation for the routine could be automatically flagged to indicate that it can be executed inplace, ie something similar to how "HandleBad" sets "BadDoc" if it's not supplied (it's not an ideal solution).

Other PDL::PP functions to support concise package definition
So far, we have described the "pp_def" and "pp_done" functions. PDL::PP exports a few other functions to aid you in writing concise PDL extension package definitions. Often when you interface library functions as in the above example you have to include additional C include files. Since the XS file is generated by PP we need some means to make PP insert the appropriate include directives in the right place into the generated XS file. To this end there is the "pp_addhdr" function. This is also the function to use when you want to define some C functions for internal use by some of the XS functions (which are mostly functions defined by "pp_def"). By including these functions here you make sure that PDL::PP inserts your code before the point where the actual XS module section begins and will therefore be left untouched by xsubpp (cf. perlxs and perlxstut manpages). A typical call would be pp_addhdr(' #include <unistd.h> /* we need defs of XXXX */ #include "libprotos.h" /* prototypes of library functions */ #include "mylocaldecs.h" /* Local decs */ static void do_the real_work(PDL_Byte * in, PDL_Byte * out, int n) { /* do some calculations with the data */ } '); This ensures that all the constants and prototypes you need will be properly included and that you can use the internal functions defined here in the "pp_def"s, e.g.: pp_def('barfoo', Pars => ' a(n); [o] b(n)', GenericTypes => '[B]', Code => ' int ns = $SIZE(n); do_the_real_work($P(a),$P(b),ns); ', ); In many cases the actual PP code (meaning the arguments to "pp_def" calls) is only part of the package you are currently implementing. Often there is additional perl code and XS code you would normally have written into the pm and XS files which are now automatically generated by PP. So how to get this stuff into those dynamically generated files? Fortunately, there are a couple of functions, generally called "pp_addXXX" that assist you in doing this. Let's assume you have additional perl code that should go into the generated pm-file. This is easily achieved with the "pp_addpm" command: pp_addpm(<<'EOD'); =head1 NAME PDL::Lib::Mylib -- a PDL interface to the Mylib library =head1 DESCRIPTION This package implements an interface to the Mylib package with full threading and indexing support (see L<PDL::Indexing>). =cut use PGPLOT; =head2 use_myfunc this function applies the myfunc operation to all the elements of the input pdl regardless of dimensions and returns the sum of the result =cut sub use_myfunc { my $pdl = shift; myfunc($pdl->clump(-1),($res=null)); return $res->sum; } EOD You have probably got the idea. In some cases you also want to export your additional functions. To avoid getting into trouble with PP which also messes around with the @EXPORT array you just tell PP to add your functions to the list of exported functions: pp_add_exported('', 'use_myfunc gethynx'); Note the initial empty string argument (reason for it?). The "pp_add_isa" command works like the the "pp_add_exported" function. The arguments to "pp_add_isa" are added the @ISA list, e.g. pp_add_isa(' Some::Other::Class '); Sometimes you want to add extra XS code of your own (that is generally not involved with any threading/indexing issues but supplies some other functionality you want to access from the perl side) to the generated XS file, for example pp_addxs('',' # Determine endianness of machine int isbigendian() CODE: unsigned short i; PDL_Byte *b; i = 42; b = (PDL_Byte*) (void*) &i; if (*b == 42) RETVAL = 0; else if (*(b+1) == 42) RETVAL = 1; else croak("Impossible - machine is neither big nor little endian!!\n"); OUTPUT: RETVAL '); Especially "pp_add_exported" and "pp_addxs" should be used with care. PP uses PDL::Exporter, hence letting PP export your function means that they get added to the standard list of function exported by default (the list defined by the export tag ``:Func''). If you use "pp_addxs" you shouldn't try to do anything that involves threading or indexing directly. PP is much better at generating the appropriate code from your definitions. Finally, you may want to add some code to the BOOT section of the XS file (if you don't know what that is check perlxs). This is easily done with the "pp_add_boot" command: pp_add_boot(<<EOB); descrip = mylib_initialize(KEEP_OPEN); if (descrip == NULL) croak("Can't initialize library"); GlobalStruc->descrip = descrip; GlobalStruc->maxfiles = 200; EOB By default, PP.pm puts all subs defined using the pp_def function into the output .pm file's EXPORT list. This can create problems if you are creating a subclassed object where you don't want any methods exported. (i.e. the methods will only be called using the $object->method syntax). For these cases you can call pp_export_nothing() to clear out the export list. Example (At the end of the .pd file): pp_export_nothing(); pp_done(); By default, PP.pm puts the 'use Core;' line into the output .pm file. This imports Core's exported names into the current namespace, which can create problems if you are over-riding one of Core's methods in the current file. You end up getting messages like "Warning: sub sumover redefined in file subclass.pm" when running the program. For these cases the pp_core_importList can be used to change what is imported from Core.pm. For example: pp_core_importList('()') This would result in use Core(); being generated in the output .pm file. This would result in no names being imported from Core.pm. Similarly, calling pp_core_importList(' qw/ barf /') would result in use Core qw/ barf/; being generated in the output .pm file. This would result in just 'barf' being imported from Core.pm. The slice operation section of this manual is provided using dataflow and lazy evaluation: when you need it, ask Tjl to write it. a delivery in a week from when I receive the email is 95% probable and two week delivery is 99% probable. And anyway, the slice operations require a much more intimate knowledge of PDL internals than the data operations. Furthermore, the complexity of the issues involved is considerably higher than that in the average data operation. If you would like to convince yourself of this fact take a look at the Basic/Slices/slices.pd file in the PDL distribution :-). Nevertheless, functions generated using the slice operations are at the heart of the index manipulation and dataflow capabilities of PDL. Also, there are a lot of dirty issues with virtual piddles and vaffines which we shall entirely skip here.

Slices and bad values
Slice operations need to be able to handle bad values (if support is compiled into PDL). The easiest thing to do is look at Basic/Slices/slices.pd to see how this works. Along with "BadCode", there are also the "BadBackCode" and "BadRedoDimsCode" keys for "pp_def". However, any "EquivCPOffsCode" should not need changing, since any changes are absorbed into the definition of the "$EQUIVCPOFFS()" macro (ie it is handled automatically by PDL::PP>.

A few notes on writing a slicing routine...
The following few paragraphs describe writing of a new slicing routine ('range'); any errors are CED's. (--CED 26-Aug-2002) The PDL "Core" structure, defined in Basic/Core/pdlcore.h.PL, contains pointers to a number of routines that may be useful to you. The majority of these routines deal with manipulating piddles, but some are more general: Sort the array "xx" between the indices "a" and "b". There are also versions for the other PDL datatypes, with postfix "_S", "_U", "_L", "_F", and "_D". Any module using this must ensure that "PDL::Ufunc" is loaded. As for "PDL->qsort_B", but this time sorting the indices rather than the data. The routine "med2d" in Lib/Image2D/image2d.pd shows how such routines are used. If you are going to generate a package from your PP file (typical file extensions are ".pd" or ".pp" for the files containing PP code) it is easiest and safest to leave generation of the appropriate commands to the Makefile. In the following we will outline the typical format of a perl Makefile to automatically build and install your package from a description in a PP file. Most of the rules to build the xs, pm and other required files from the PP file are already predefined in the PDL::Core::Dev package. We just have to tell MakeMaker to use it. In most cases you can define your Makefile like # Makefile.PL for a package defined by PP code. use PDL::Core::Dev; # Pick up development utilities use ExtUtils::MakeMaker; $package = ["mylib.pd",Mylib,PDL::Lib::Mylib]; %hash = pdlpp_stdargs($package); $hash{OBJECT} .= ' additional_Ccode$(OBJ_EXT) '; $hash{clean}->{FILES} .= ' todelete_Ccode$(OBJ_EXT) '; $hash{'VERSION_FROM'} = 'mylib.pd'; WriteMakefile(%hash); sub MY::postamble { pdlpp_postamble($package); } Here, the list in $package is: first: PP source file name, then the prefix for the produced files and finally the whole package name. You can modify the hash in whatever way you like but it would be reasonable to stay within some limits so that your package will continue to work with later versions of PDL. If you don't want to use prepackaged arguments, here is a generic Makefile.PL that you can adapt for your own needs: # Makefile.PL for a package defined by PP code. use PDL::Core::Dev; # Pick up development utilities use ExtUtils::MakeMaker; WriteMakefile( 'NAME' => 'PDL::Lib::Mylib', 'VERSION_FROM' => 'mylib.pd', 'TYPEMAPS' => [&PDL_TYPEMAP()], 'OBJECT' => 'mylib$(OBJ_EXT) additional_Ccode$(OBJ_EXT)', 'PM' => { 'Mylib.pm' => '$(INST_LIBDIR)/Mylib.pm'}, 'INC' => &PDL_INCLUDE(), # add include dirs as required by your lib 'LIBS' => [''], # add link directives as necessary 'clean' => {'FILES' => 'Mylib.pm Mylib.xs Mylib$(OBJ_EXT) additional_Ccode$(OBJ_EXT)'}, ); # Add genpp rule; this will invoke PDL::PP on our PP file # the argument is an array reference where the array has three string elements: # arg1: name of the source file that contains the PP code # arg2: basename of the xs and pm files to be generated # arg3: name of the package that is to be generated sub MY::postamble { pdlpp_postamble(["mylib.pd",Mylib,PDL::Lib::Mylib]); } To make life even easier PDL::Core::Dev defines the function "pdlpp_stdargs" that returns a hash with default values that can be passed (either directly or after appropriate modification) to a call to WriteMakefile. Currently, "pdlpp_stdargs" returns a hash where the keys are filled in as follows: ( 'NAME' => $mod, 'TYPEMAPS' => [&PDL_TYPEMAP()], 'OBJECT' => "$pref\$(OBJ_EXT)", PM => {"$pref.pm" => "\$(INST_LIBDIR)/$pref.pm"}, MAN3PODS => {"$src" => "\$(INST_MAN3DIR)/$mod.\$(MAN3EXT)"}, 'INC' => &PDL_INCLUDE(), 'LIBS' => [''], 'clean' => {'FILES' => "$pref.xs $pref.pm $pref\$(OBJ_EXT)"}, ) Here, $src is the name of the source file with PP code, $pref the prefix for the generated .pm and .xs files and $mod the name of the exntension module to generate. The internals of the current version consist of a large table which gives the rules according to which things are translated and the subs which implement these rules. Later on, it would be good to make the table modifiable by the user so that different things may be tried. [Meta comment: here will hopefully be more in the future; currently, your best bet will be to read the source code :-( or ask on the list (try the latter first) ] Unless otherwise specified, the arguments are strings. Keys marked with (bad) are only used if bad-value support is compiled into PDL. define the signature of your function arguments which are not pdls. Default: nothing. the actual code that implements the functionality; several PP macros and PP functions are recognised in the string value If set to 1, the routine is assumed to support bad values and the code in the BadCode key is used if bad values are present; it also sets things up so that the "$ISBAD()" etc macros can be used. If set to 0, cause the routine to print a warning if any of the input piddles have their bad flag set. Give the code to be used if bad values may be present in the input piddles. Only used if "HandleBad => 1". An array reference. The array may contain any subset of the strings `B', `S', `U', `L', `F' and `D', which specify which types your operation will accept. This is very useful (and important!) when interfacing an external library. Default: [qw/B S U L F D/] Mark a function as being able to work inplace. Inplace => 1 if Pars => 'a(); [o]b();' Inplace => ['a'] if Pars => 'a(); b(); [o]c();' Inplace => ['a','b'] if Pars => 'a(); b(); [o]c(); [o]d();' If bad values are being used, care must be taken to ensure the propogation of the badflag when inplace is being used; for instance see the code for "replacebad" in Basic/Bad/bad.pd. Used to specify a documentation string in Pod format. See PDL::Doc for information on PDL documentation conventions. Note: in the special case where the PP 'Doc' string is one line this is implicitly used for the quick reference AND the documentation! If the Doc field is omitted PP will generate default documentation (after all it knows about the Signature). If you really want the function NOT to be documented in any way at this point (e.g. for an internal routine, or because youu are doing it elsewhere in the code) explictly specify "Doc=>undef". Contains the text returned by the "badinfo" command (in "perldl") or the "-b" switch to the "pdldoc" shell script. In many cases, you will not need to specify this, since the information can be automatically created by PDL::PP. However, as befits computer-generated text, it's rather stilted; it may be much better to do it yourself!

Macros
Macros labelled by (bad) are only used if bad-value support is compiled into PDL. access a pdl (by its name) that was specified in the signature access a value in the private data structure of this transformation (mainly used to use an argument that is specified in the "OtherPar" section) replaced at runtime by the actual size of a named dimension (as specified in the signature) replaced by the C type that is equal to the runtime type of the operation a pointer access to the PDL named "a" in the signature. Useful for interfacing to C functions a physical pointer access to pdl "a"; mainly for internal use expansion alternatives according to runtime type of operation, where XXX is some string that is matched by "/[BSULFD+]/". return a pointer to the pdl data structure (pdl *) of piddle "a" returns true if the value stored in "a()" equals the bad value for this piddle. Requires "HandleBad" being set to 1. returns true if the value stored in "a()" does not equal the bad value for this piddle. Requires "HandleBad" being set to 1. Sets "a()" to equal the bad value for this piddle. Requires "HandleBad" being set to 1.

functions
loop over named dimensions; limits are generated automatically by PP enclose following code in a threadloop execute following code if type of operation is any of "TYPES" PDL For the concepts of threading and slicing check PDL::Indexing. PDL::Internals PDL::BadValues for information on bad values perlxs, perlxstut RedoDimsCode, $RESIZE() PDL::PP is still, even in its rewritten form, too complicated. It needs to be rethought a little as well as deconvoluted and modularized some more (e.g. all the NS things). After the rewrite, this can happen a little by little, though.

Undocumented functions
The following functions have been added since this manual was written and are as yet undocumented Copyright(C) 1997 Tuomas J. Lukka (lukka@fas.harvard.edu), Karl Glaazebrook (kgb@aaocbn1.aao.GOV.AU) and Christian Soeller (c.soeller@auckland.ac.nz). All rights reserved. Although destined for release as a man page with the standard PDL distribution, it is not public domain. Permission is granted to freely distribute verbatim copies of this document provided that no modifications outside of formatting be made, and that this notice remain intact. You are permitted and encouraged to use its code and derivatives thereof in your own source code for fun or for profit as you see fit.