Intro

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Piddles

   # check if this a piddle
   die "not a piddle" 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 a piddle 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; /* 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 *threadids;  /* Starting index of the thread index set n */
           unsigned char nthreadids;

           pdl_children children;

           PDL_Indx   def_dims[PDL_NDIMS];   /* Preallocated space for efficiency */
           PDL_Indx   def_dimincs[PDL_NDIMS];   /* Preallocated space for efficiency */
           unsigned char def_threadids[PDL_NTHREADIDS];

           struct pdl_magic *magic;

           void *hdrsv; /* "header", settable from outside */
        };

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 is the member

        void *datasv;
    

which is really a pointer to a Perl SV structure ("SV *"). The SV is expected to be representing a string, in which the data of the piddle 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 - for instance, the data might be allocated by a "mmap" operation. Note the use of an SV* was purely for convenience, it allows easy transformation of packed data from files into piddles. 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 piddle. 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, float and double types, see also PDL::Types.

Dimensions

The number of dimensions in the piddle 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 piddles 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 a piddle struct. The same applies for the threadids:

        unsigned char def_threadids[PDL_NTHREADIDS];
    

Magic

It is possible to attach magic to piddles, 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 piddles in these operations.

Transformations and virtual affine transformations

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

        $b = $a->slice("2:5");
        $b .= 1;
    

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

        pdl_trans *trans; 
        pdl_vaffine *vafftrans;
    

Both $a (the parent) and $b (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 piddles 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 he wants 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

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

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

In general, executing a PDL function on a group of piddles results in creation of a transformation of the requested type that links all input and output arguments (at least those that are piddles). In PDL functions that support data flow between input and output args (e.g. "slice", "index") this transformation links parent (input) and child (output) piddles 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 piddle 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 piddle 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:

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

Although $a should now be destroyed according to Perl's rules the underlying "pdl" structure must actually only be freed when $b also goes out of scope (since it still references internally some of $a's data). This example demonstrates that such a dataflow paradigm between PDL objects necessitates a special destruction algorithm that takes the links between piddles 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 and pdlfamily.c is concerned with making sure that piddles ("pdl *"s) are created, updated and freed at the right times depending on interactions with other piddles via PDL transformations (remember, "pdl_trans").

Accessing children and parents of a piddle

An example of processing the children of a piddle is provided by the "baddata" method of PDL::Bad (only available if you have compiled PDL with the "WITH_BADVAL" option set to 1, but still useful as an example!).

Consider the following situation:

 pdl> $a = rvals(7,7,{Centre=>[3,4]});
 pdl> $b = $a->slice('2:4,3:5');
 pdl> ? vars
 PDL variables in package main::

 Name         Type   Dimension       Flow  State          Mem
 ----------------------------------------------------------------
 $a           Double D [7,7]                P            0.38Kb 
 $b           Double D [3,3]                -C           0.00Kb

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

 pdl> $a->badflag(1)

then I want the state of $b - it's child - to be changed as well (since it will either share or inherit some of $a'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
 ----------------------------------------------------------------
 $a           Double D [7,7]                PB           0.38Kb 
 $b           Double D [3,3]                -CB          0.00Kb

This bit of magic is performed by the "propagate_badflag" function, which is listed below:

 /* newval = 1 means set flag, 0 means clear it */
 /* thanks to Christian Soeller for this */

 void propagate_badflag( pdl *it, int newval ) {
    PDL_DECL_CHILDLOOP(it)
    PDL_START_CHILDLOOP(it)
    {
        pdl_trans *trans = PDL_CHILDLOOP_THISCHILD(it);
        int i;
        for( i = trans->vtable->nparents;
             i < trans->vtable->npdls;
             i++ ) {
            pdl *child = trans->pdls[i];

            if ( newval ) child->state |=  PDL_BADVAL;
            else          child->state &= ~PDL_BADVAL;

            /* make sure we propagate to grandchildren, etc */
            propagate_badflag( child, newval );

        } /* for: i */
    }
    PDL_END_CHILDLOOP(it)
 } /* propagate_badflag */

Given a piddle ("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 piddle 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 piddle, 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 piddle, to ensure we loop through its children. This recursion ensures we get to all the offspring of a particular piddle.

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")

  struct XXX_trans {
        int magicno; /* to detect memory overwrites */
        short flags; /* state of the trans */
        pdl_transvtable *vtable;   /* the all important vtable */
        void (*freeproc)(struct pdl_trans *);  /* Call to free this trans
                (in case we had to malloc some stuff for this trans) */
        pdl *pdls[NP]; /* The pdls involved in the transformation */
        int __datatype; /* the type of the transformation */
        /* in general more members
        /* depending on the actual transformation (slice, add, etc)
         */
  };

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

  pdl *pdls[NP];

with "NP" depending on the number of piddle args of the particular trans. It records a state

  short flags;

and the datatype

  int __datatype;

of the trans (to which all piddles 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 {
        pdl_transtype transtype;
        int flags;
        int nparents;   /* number of parent pdls (input) */
        int npdls;      /* number of child pdls (output) */
        char *per_pdl_flags;  /* optimization flags */
        void (*redodims)(pdl_trans *tr);  /* figure out dims of children */
        void (*readdata)(pdl_trans *tr);  /* flow parents to children  */
        void (*writebackdata)(pdl_trans *tr); /* flow backwards */
        void (*freetrans)(pdl_trans *tr); /* Free both the contents and it of
                                        the trans member */
        pdl_trans *(*copy)(pdl_trans *tr); /* Full copy */
        int structsize;
        char *name; /* For debuggers, mostly */
  } pdl_transvtable;

We focus on the callback functions:

        void (*redodims)(pdl_trans *tr);

"redodims" will work out the dimensions of piddles that need to be created and is called from within the API function that should be called to ensure that the dimensions of a piddle are accessible (pdlapi.c):

   void pdl_make_physdims(pdl *it)

"readdata" and "writebackdata" are responsible for the actual computations of the child data from the parents or parent data from those of the children, respectively (the dataflow aspect). The PDL core makes sure that these are called as needed when piddle data is accessed (lazy-evaluation). The general API function to ensure that a piddle is up-to-date is

  void pdl_make_physvaffine(pdl *it)

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

"freetrans" frees dynamically allocated memory associated with the trans as needed and "copy" can copy the transformation. Again, functions built with PDL::PP make sure that copying and freeing via these callbacks happens at the right times. (If they fail to do that we have got a memory leak -- this has happened in the past ;).

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 a piddle sharing data with another one in this way is therefore automatically flown 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 (Perl threading "!=" PDL threading!).

Signatures: threading over elementary operations

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 threading semantics.

Defining new PDL functions -- Glue code generation

The Core struct

 /* 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 );
 #if defined(PDL_clean_namespace) || defined(PDL_OLD_API)
    pdl*   (*new)      ( );     /* make it work with gimp-perl */
 #else
    pdl*   (*pdlnew)      ( );  /* renamed because of C++ clash */
 #endif
    pdl*   (*tmp)         ( );
    pdl*   (*create)      (int type);
    void   (*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) [with the possibility of making your changes to a separate branch of the CVS tree if it's a change that will take time to complete]
• increase by 1 the value of the $pdl_core_version variable in pdlcore.h.PL. This sets the value of the "PDL_CORE_VERSION" C macro used to populate the Version field
• 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 ;)