Intro

This document explains various aspects of the current implementation of PDL. If you just want to use PDL for something, you definitely do not need to read this. Even if you want to interface your C routines to PDL or create new PDL::PP functions, you do not need to read this man page (though it may be informative). This document is primarily intended for people interested in debugging or changing the internals of PDL. To read this, a good understanding of the C language and programming and data structures in general is required, as well as some Perl understanding. If you read through this document and understand all of it and are able to point what any part of this document refers to in the PDL core sources and additionally struggle to understand PDL::PP, you will be awarded the title "PDL Guru".

Warning: If it seems that this document has gotten out of date, please inform the PDL porters email list (pdl-devel@lists.sourceforge.net). This may well happen.

ndarrays

The pdl data object is generally an opaque scalar reference into a pdl structure in memory. Alternatively, it may be a hash reference with the "PDL" field containing the scalar reference (this makes overloading ndarrays easy, see PDL::Objects). You can easily find out at the Perl level which type of ndarray you are dealing with. The example code below demonstrates how to do it:

   # check if this an ndarray
   die "not an ndarray" unless UNIVERSAL::isa($pdl, 'PDL');
   # is it a scalar ref or a hash ref?
   if (UNIVERSAL::isa($pdl, "HASH")) {
     die "not a valid PDL" unless exists $pdl->{PDL} &&
        UNIVERSAL::isa($pdl->{PDL},'PDL');
     print "This is a hash reference,",
        " the PDL field contains the scalar ref\n";
   } else {
     print "This is a scalar ref that points to address $$pdl in memory\n";
   }

The scalar reference points to the numeric address of a C structure of type "pdl" which is defined in pdl.h. The mapping between the object at the Perl level and the C structure containing the actual data and structural that makes up an ndarray is done by the PDL typemap. The functions used in the PDL typemap are defined pretty much at the top of the file pdlcore.h. So what does the structure look like:

        struct pdl {
           unsigned long magicno; /* Always stores PDL_MAGICNO as a sanity check */
             /* This is first so most pointer accesses to wrong type are caught */
           int state;        /* What's in this pdl */
           pdl_trans *trans_parent; /* Opaque pointer to internals of transformation from
                                parent */
           pdl_vaffine *vafftrans;
           void*    sv;      /* (optional) pointer back to original sv.
                                  ALWAYS check for non-null before use.
                                  We cannot inc refcnt on this one or we'd
                                  never get destroyed */
           void *datasv;        /* Pointer to SV containing data. Refcnt inced */
           void *data;            /* Null: no data alloced for this one */
           PDL_Indx nvals;           /* How many values allocated */
           int datatype;
           PDL_Indx   *dims;      /* Array of data dimensions */
           PDL_Indx   *dimincs;   /* Array of data default increments */
           short    ndims;     /* Number of data dimensions */
           unsigned char *broadcastids;  /* Starting index of the broadcast index set n */
           unsigned char nbroadcastids;
           pdl_trans_children trans_children;
           PDL_Indx   def_dims[PDL_NDIMS];   /* Preallocated space for efficiency */
           PDL_Indx   def_dimincs[PDL_NDIMS];   /* Preallocated space for efficiency */
           unsigned char def_broadcastids[PDL_NBROADCASTIDS];
           struct pdl_magic *magic;
           void *hdrsv; /* "header", settable from outside */
           PDL_Value value; /* to store at least one value */
        };

This is quite a structure for just storing some data in - what is going on?

Data storage

We are going to start with some of the simpler members: first of all, there are the members (as of 2.078)

        void *datasv;
        PDL_Value value; /* to store at least one value */

which are a pointer to a Perl SV structure ("SV *"), and a union value of all possible single PDL values. If the ndarray's whole data will fit in the "value", the "datasv" will not be used except by "get_dataref" in PDL::Core for temporary use by Perl code. It will then be destroyed by the call to "upd_data" in PDL::Core method unless that is passed a true value to keep the "datasv" around (largely used by the memory-mapping implementation).

Otherwise, the SV is expected to be representing a string, in which the data of the ndarray is stored in a tightly packed form. This pointer counts as a reference to the SV so the reference count has been incremented when the "SV *" was placed here (this reference count business has to do with Perl's garbage collection mechanism -- don't worry if this doesn't mean much to you). This pointer is allowed to have the value "NULL" which means that there is no actual Perl SV for this data, as alluded above. Note the use of an SV* was purely for convenience, it allows easy transformation of packed data from files into ndarrays. Other implementations are not excluded.

The actual pointer to data is stored in the member

        void *data;

which contains a pointer to a memory area with space for

        PDL_Indx nvals;

data items of the data type of this ndarray. PDL_Indx is either 'long' or 'long long' depending on whether your perl is 64bit or not.

The data type of the data is stored in the variable

        int datatype;

the values for this member are given in the enum "pdl_datatypes" (see pdl.h). Currently we have byte, short, unsigned short, long, index (either long or long long), long long, float and double (plus complex equivalents) types, see also PDL::Types.

Dimensions

The number of dimensions in the ndarray is given by the member

        int ndims;

which shows how many entries there are in the arrays

        PDL_Indx   *dims;      
        PDL_Indx   *dimincs;

These arrays are intimately related: "dims" gives the sizes of the dimensions and "dimincs" is always calculated by the code

        PDL_Indx inc = 1;
        for(i=0; i<it->ndims; i++) {
                it->dimincs[i] = inc; inc *= it->dims[i];
        }

in the routine "pdl_resize_defaultincs" in "pdlapi.c". What this means is that the dimincs can be used to calculate the offset by code like

        PDL_Indx offs = 0;
        for(i=0; i<it->ndims; i++) {
                offs += it->dimincs[i] * index[i];
        }

but this is not always the right thing to do, at least without checking for certain things first.

Default storage

Since the vast majority of ndarrays don't have more than 6 dimensions, it is more efficient to have default storage for the dimensions and dimincs inside the PDL struct.

        PDL_Indx   def_dims[PDL_NDIMS];   
        PDL_Indx   def_dimincs[PDL_NDIMS];

The "dims" and "dimincs" may be set to point to the beginning of these arrays if "ndims" is smaller than or equal to the compile-time constant "PDL_NDIMS". This is important to note when freeing an ndarray struct. The same applies for the broadcastids:

        unsigned char def_broadcastids[PDL_NBROADCASTIDS];

Magic

It is possible to attach magic to ndarrays, much like Perl's own magic mechanism. If the member pointer

           struct pdl_magic *magic;

is nonzero, the PDL has some magic attached to it. The implementation of magic can be gleaned from the file pdlmagic.c in the distribution.

State

One of the first members of the structure is

        int state;

The possible flags and their meanings are given in "pdl.h". These are mainly used to implement the lazy evaluation mechanism and keep track of ndarrays in these operations.

Transformations and virtual affine transformations

As you should already know, ndarrays often carry information about where they come from. For example, the code

        $y = $x->slice("2:5");
        $y .= 1;

will alter $x. So $y and $x know that they are connected via a "slice"-transformation. This information is stored in the members

        pdl_trans *trans_parent;
        pdl_vaffine *vafftrans;

Both $x (the parent) and $y (the child) store this information about the transformation in appropriate slots of the "pdl" structure.

"pdl_trans" and "pdl_vaffine" are structures that we will look at in more detail below.

The Perl SVs

When ndarrays are referred to through Perl SVs, we store an additional reference to it in the member

        void*    sv;

in order to be able to return a reference to the user when they want to inspect the transformation structure on the Perl side.

Also, we store an opaque

        void *hdrsv;

which is just for use by the user to hook up arbitrary data with this sv. This one is generally manipulated through sethdr and gethdr calls.

Smart references and transformations: slicing and dicing

Smart references and most other fundamental functions operating on ndarrays are implemented via transformations (as mentioned above) which are represented by the type "pdl_trans" in PDL.

A transformation links input and output ndarrays and contains all the infrastructure that defines how:

• output ndarrays are obtained from input ndarrays;
• changes in smart-linked output ndarrays (e.g. the child of a sliced parent ndarray) are flowed back to the input ndarray in transformations where this is supported (the most often used example being "slice" here);
• datatype and size of output ndarrays that need to be created are obtained.

In general, executing a PDL function on a group of ndarrays results in creation of a transformation of the requested type that links all input and output arguments (at least those that are ndarrays). In PDL functions that support data flow between input and output args (e.g. "slice", "index") this transformation links parent (input) and child (output) ndarrays permanently until either the link is explicitly broken by user request ("sever" at the Perl level) or all parents and children have been destroyed. In those cases the transformation is lazy-evaluated, e.g. only executed when ndarray values are actually accessed.

In non-flowing functions, for example addition ("+") and inner products ("inner"), the transformation is installed just as in flowing functions but then the transformation is immediately executed and destroyed (breaking the link between input and output args) before the function returns.

It should be noted that the close link between input and output args of a flowing function (like slice) requires that ndarray objects that are linked in such a way be kept alive beyond the point where they have gone out of scope from the point of view of Perl:

  $x = zeroes(20);
  $y = $x->slice('2:4');
  undef $x;    # last reference to $x is now destroyed

Although $x should now be destroyed according to Perl's rules the underlying "pdl" structure must actually only be freed when $y also goes out of scope (since it still references internally some of $x's data). This example demonstrates that such a dataflow paradigm between PDL objects necessitates a special destruction algorithm that takes the links between ndarrays into account and couples the lifespan of those objects. The non-trivial algorithm is implemented in the function "pdl_destroy" in pdlapi.c. In fact, most of the code in pdlapi.c is concerned with making sure that ndarrays ("pdl *"s) are created, updated and freed at the right times depending on interactions with other ndarrays via PDL transformations (remember, "pdl_trans").

Accessing children and parents of an ndarray

When ndarrays are dynamically linked via transformations as suggested above input and output ndarrays are referred to as parents and children, respectively.

An example of processing the children of an ndarray is provided by the method "badflag" in PDL::Bad (before 2.079, it only operated on the children, though now it propagates to parents too).

Consider the following situation:

 pdl> $x = rvals(7,7,{Centre=>[3,4]});
 pdl> $y = $x->slice('2:4,3:5');
 pdl> ? vars
 PDL variables in package main::
 Name         Type   Dimension       Flow  State          Mem
 ----------------------------------------------------------------
 $x           Double D [7,7]                P            0.38Kb 
 $y           Double D [3,3]                -C           0.00Kb

Now, if I suddenly decide that $x should be flagged as possibly containing bad values, using

 pdl> $x->badflag(1)

then I want the state of $y - its child - to be changed as well (since it will either share or inherit some of $x's data and so be also bad), so that I get a 'B' in the State field:

 pdl> ? vars                    
 PDL variables in package main::
 Name         Type   Dimension       Flow  State          Mem
 ----------------------------------------------------------------
 $x           Double D [7,7]                PB           0.38Kb 
 $y           Double D [3,3]                -CB          0.00Kb

This bit of magic is performed by the "propagate_badflag" function, which is in pdlapi.c. Given an ndarray ("pdl *it"), the routine loops through each "pdl_trans" structure, where access to this structure is provided by the "PDL_CHILDLOOP_THISCHILD" macro. The children of the ndarray are stored in the "pdls" array, after the parents, hence the loop from "i = ...nparents" to "i = ...npdls - 1". Once we have the pointer to the child ndarray, we can do what we want to it; here we change the value of the "state" variable, but the details are unimportant). What is important is that we call "propagate_badflag" on this ndarray, to ensure we loop through its children. This recursion ensures we get to all the offspring of a particular ndarray.

Access to parents is similar, with the "for" loop replaced by:

        for( i = 0;
             i < trans->vtable->nparents;
             i++ ) {
           /* do stuff with parent #i: trans->pdls[i] */
        }

What's in a transformation ("pdl_trans")

All transformations are implemented as structures

  struct pdl_trans {
        int magicno; /* to detect memory overwrites */
        short flags; /* state of the trans */
        pdl_transvtable *vtable;   /* the all important vtable */
        int __datatype; /* the type of the transformation */
        void *params; /* Opaque pointer to "compiled representation" of transformation */
        pdl *pdls[]; /* The pdls involved in the transformation */
  };

The "params" member is an opaque pointer, typically to a C struct that holds the "compiled representation" (generated by PDL::PP), and is the way that information like "OtherPars" etc get communicated from invoking code to the "redodims" function - effectively a closure, in Perl/LISP terms. This is necessary because "redodims" is called by a PDL-internal function, and therefore must have a fixed parameter list.

The transformation identifies all "pdl"s involved in the trans

  pdl *pdls[];

This is a C99 "incomplete array type", and works because it is at the end of the struct - PDL allocates the correct amount of memory based on the "npdls" member of the "vtable". The trans records the state

  short flags;

and the datatype

  int __datatype;

of the trans (to which all ndarrays must be converted unless they are explicitly typed, PDL functions created with PDL::PP make sure that these conversions are done as necessary). Most important is the pointer to the vtable (virtual table) that contains the actual functionality

 pdl_transvtable *vtable;

The vtable structure in turn looks something like (slightly simplified from pdl.h for clarity)

  typedef struct pdl_transvtable {
        int flags;
        int nparents;   /* number of parent pdls (input) */
        int npdls;      /* number of child pdls (output) */
        char *per_pdl_flags;  /* optimization flags */
        pdl_error (*redodims)(pdl_trans *tr);  /* figure out dims of children */
        pdl_error (*readdata)(pdl_trans *tr);  /* flow parents to children  */
        pdl_error (*writebackdata)(pdl_trans *tr); /* flow backwards */
        pdl_error (*freetrans)(pdl_trans *tr, char);
        int structsize;
        char *name; /* the function's name */
  } pdl_transvtable;

The transformation and vtable code is hardly ever written by hand but rather generated by PDL::PP from concise descriptions.

Certain types of transformations can be optimized very efficiently obviating the need for explicit "readdata" and "writebackdata" methods. Those transformations are called pdl_vaffine. Most dimension manipulating functions (e.g., "slice", "xchg") belong to this class.

The basic trick is that parent and child of such a transformation work on the same (shared) block of data which they just choose to interpret differently (by using different "dims", "dimincs" and "offs" on the same data, compare the "pdl" structure above). Each operation on an ndarray sharing data with another one in this way is therefore automatically flowed from child to parent and back -- after all they are reading and writing the same block of memory. This is currently not Perl thread safe -- no big loss since the whole PDL core is not reentrant.

Callback functions

redodims

Works out the dimensions of ndarrays that need to be created and is called from within the API function that should be called to ensure that the dimensions of an ndarray are accessible (pdlapi.c):

   pdl_error pdl_make_physdims(pdl *it)

readdata and writebackdata

Responsible for the actual computations of the child data from the parents or parent data from those of the children, respectively (the dataflow aspect). "readdata" populates the children from the parents, and "writebackdata" implements updating the parent(s) from the child(ren) if dataflow is part of that transformation. The PDL core makes sure that these are called as needed when ndarray data is accessed (lazy-evaluation). The general API function to ensure that an ndarray is up-to-date is

  pdl_error pdl_make_physvaffine(pdl *it)

which should be called before accessing ndarray data from XS/C (see Core.xs for some examples).

freetrans

Frees dynamically allocated memory associated with the trans as needed. If "redodims" has previously been called, it will free any vaffine-associated memory. If the "destroy" parameter is true, it will also free any bespoke "params"-connected memory - this will not be the case if called before doing another "redodims". Again, functions built with PDL::PP make sure that freeing via these callbacks happens at the right times.

Signatures: broadcasting over elementary operations

Most of that functionality of PDL broadcasting (automatic iteration of elementary operations over multi-dim ndarrays) is implemented in the file pdlbroadcast.c.

The PDL::PP generated functions (in particular the "readdata" and "writebackdata" callbacks) use this infrastructure to make sure that the fundamental operation implemented by the trans is performed in agreement with PDL's broadcasting semantics.

Defining new PDL functions -- Glue code generation

Please, see PDL::PP and examples in the PDL distribution. Implementation and syntax are currently far from perfect but it does a good job!

The Core struct

As discussed in PDL::API, PDL uses a pointer to a structure to allow PDL modules access to its core routines. The definition of this structure (the "Core" struct) is in pdlcore.h (created by pdlcore.h in Basic/Core) and looks something like

 /* Structure to hold pointers core PDL routines so as to be used by 
  * many modules
  */
 struct Core {
    I32    Version;
    pdl*   (*SvPDLV)      ( SV*  );
    void   (*SetSV_PDL)   ( SV *sv, pdl *it );
    pdl*   (*pdlnew)      ( );
    pdl*   (*tmp)         ( );
    pdl*   (*create)      (int type);
    pdl_error (*destroy)     (pdl *it);
    ...
 }
 typedef struct Core Core;

The first field of the structure ("Version") is used to ensure consistency between modules at run time; the following code is placed in the BOOT section of the generated xs code:

 if (PDL->Version != PDL_CORE_VERSION)
   Perl_croak(aTHX_ "Foo needs to be recompiled against the newly installed PDL");

If you add a new field to the Core struct you should:

• discuss it on the pdl porters email list (pdl-devel@lists.sourceforge.net) and use the techniques in PDL::FAQ 4.11.
• increase by 1 the value of the "PDL_CORE_VERSION" C macro used to populate the Version field, in pdlcore.h.
• add documentation (e.g. to PDL::API) if it's a "useful" function for external module writers (as well as ensuring the code is as well documented as the rest of PDL ;)