pp_addpm({At => 'Top'},<< 'EOD');

=head1 NAME

PDL::Slices -- Indexing, slicing, and dicing

=head1 SYNOPSIS

  use PDL;
  $a = ones(3,3);
  $b = $a->slice('-1:0,(1)');
  $c = $a->dummy(2);


=head1 DESCRIPTION

This package provides many of the powerful PerlDL core index
manipulation routines.  These routines mostly allow two-way data flow,
so you can modify your data in the most convenient representation.
For example, you can make a 1000x1000 unit matrix with 

 $a = zeroes(1000,1000);
 $a->diagonal(0,1) ++;

which is quite efficient. See L<PDL::Indexing> and L<PDL::Tips> for
more examples.  

Slicing is so central to the PDL language that a special compile-time
syntax has been introduced to handle it compactly; see L<PDL::NiceSlice> 
for details.

PDL indexing and slicing functions usually include two-way data flow, 
so that you can separate the actions of reshaping your data structures
and modifying the data themselves.  Two special methods, L<copy|copy> and
L<sever|sever>, help you control the data flow connection between related 
variables.

 $b = $a->slice("1:3"); # Slice maintains a link between $a and $b.
 $b += 5;   		# $a is changed!

If you want to force a physical copy and no data flow, you can copy or
sever the slice expression:

 $b = $a->slice("1:3")->copy;
 $b += 5;		# $a is not changed.

 $b = $a->slice("1:3")->sever;
 $b += 5;               # $a is not changed.

The difference between C<sever> and C<copy> is that sever acts on (and
returns) its argument, while copy produces a disconnected copy.  If you
say

 $b = $a->slice("1:3");
 $c = $b->sever;

then the variables C<$b> and C<$c> point to the same object but with 
C<-E<gt>copy> they would not.

=cut

use PDL::Core ':Internal';

EOD

=head1
FUNCTIONS
=cut

# $::PP_VERBOSE=1;

pp_add_boot(
"  PDL->readdata_affine = pdl_readdata_affineinternal;\n" . 
"     PDL->writebackdata_affine = pdl_writebackdata_affineinternal;\n"
);

## Several routines use the 'Dims' and 'ParentInds'
## rules - these currently do nothing

pp_def(
       'affineinternal',
       HandleBad => 1,
       AffinePriv => 1,
       DefaultFlow => 1,
       P2Child => 1,
       NoPdlThread => 1,
       ReadDataFuncName => "pdl_readdata_affineinternal",
       WriteBackDataFuncName => "pdl_writebackdata_affineinternal",
       MakeComp => '$CROAK("AFMC MUSTNT BE CALLED");',
       RedoDims => '$CROAK("AFRD MUSTNT BE CALLED");',
       EquivCPOffsCode => '
		int i; int poffs=$PRIV(offs); int nd;
		for(i=0; i<$CHILD_P(nvals); i++) {
			$EQUIVCPOFFS(i,poffs);
			for(nd=0; nd<$CHILD_P(ndims); nd++) {
				poffs += $PRIV(incs[nd]);
				if(nd<$CHILD_P(ndims)-1 &&
				   (i+1)%$CHILD_P(dimincs[nd+1]) ||
				   nd == $CHILD_P(ndims)-1)
					break;
				poffs -= $PRIV(incs[nd]) *
					$CHILD_P(dims[nd]);
			}
                }',
       Doc => undef,    # 'internal',
);

=head2 s_identity
=cut

$doc = <<'DOC';
=for ref

Internal vaffine identity function.

=cut

DOC

pp_def(
	's_identity',
        HandleBad => 1,
	P2Child => 1,
        NoPdlThread => 1,
	DefaultFlow => 1,
	OtherPars => '',
	Reversible => 1,
	Dims => '$COPYDIMS();',
	ParentInds => '$COPYINDS();',
	Identity => 1,
	Doc => $doc,
);

=head2 index, index2d

=cut

$doc = <<'EOD';
=for ref

C<index> and C<index2d> provide rudimentary index indirection.

=for example

 $c = index($source,$ind);
 $c = index2d($source2,$ind1,$ind2);

use the C<$ind> variables as indices to look up values in C<$source>.  
C<index2d> uses separate piddles for X and Y coordinates.  For more
general N-dimensional indexing, see L<PDL::Slices> or the L<PDL::NiceSlice>
syntax.

These functions are two-way, i.e. after

 $c = $a->index(pdl[0,5,8]);
 $c .= pdl [0,2,4];

the changes in C<$c> will flow back to C<$a>.

C<index> provids simple threading:  multiple-dimensioned arrays are treated
as collections of 1-D arrays, so that

 $a = xvals(10,10)+10*yvals(10,10);
 $b = $a->index(3);
 $c = $a->index(9-xvals(10));

puts a single column from C<$a> into C<$b>, and puts a single element
from each column of C<$a> into C<$c>.  If you want to extract multiple
columns from an array in one operation, see L<dice|/dice> or
L<indexND|/indexND>.

=cut

EOD

my $index_init_good = 
       'register int foo = $ind(); 
        if( foo<0 || foo>=$SIZE(n) ) {
	   barf("PDL::index: invalid index %d (valid range 0..%d)",
                foo,$SIZE(n)-1);
        }';
my $index_init_bad = 
       'register int foo = $ind(); 
        if( $ISBADVAR(foo,ind) || foo<0 || foo>=$SIZE(n) ) {
	   barf("PDL::index: invalid index %d (valid range 0..%d)",
                foo,$SIZE(n)-1);
        }';

pp_def(
       'index',
       HandleBad => 1,
       DefaultFlow => 1,
       Reversible => 1,	
       Pars => 'a(n); int ind(); [oca] c();',
       Code => 
       $index_init_good . ' $c() = $a(n => foo);',
       BadCode => 
       $index_init_bad . ' $c() = $a(n => foo);',
       BackCode => 
       $index_init_good . ' $a(n => foo) = $c();',
       BadBackCode => 
       $index_init_bad . ' $a(n => foo) = $c();',
       Doc => $doc,
       BadDoc =>
       'index barfs if any of the index values are bad.',
       );

my $index2d_init_good =
       'register int fooa,foob;
	fooa = $inda(); 
        if( fooa<0 || fooa>=$SIZE(na) ) {
           barf("PDL::index: invalid x-index %d (valid range 0..%d)",
                fooa,$SIZE(na)-1);
        }
	foob = $indb(); 
        if( foob<0 || foob>=$SIZE(nb) ) {
	   barf("PDL::index: invalid y-index %d (valid range 0..%d)",
                foob,$SIZE(nb)-1);
        }';
my $index2d_init_bad =
       'register int fooa,foob;
	fooa = $inda(); 
        if( $ISBADVAR(fooa,inda) || fooa<0 || fooa>=$SIZE(na) ) {
           barf("PDL::index: invalid index 1");
        }
	foob = $indb(); 
        if( $ISBADVAR(foob,indb) || foob<0 || foob>=$SIZE(nb) ) {
	   barf("PDL::index: invalid index 2");
        }';

pp_def(
       'index2d',
       HandleBad => 1,
       DefaultFlow => 1,
       Reversible => 1,	
       Pars => 'a(na,nb); int inda(); int indb(); [oca] c();',
       Code => 
       $index2d_init_good . ' $c() = $a(na => fooa, nb => foob);',
       BadCode => 
       $index2d_init_bad . '$c() = $a(na => fooa, nb => foob);',
       BackCode => 
       $index2d_init_good . ' $a(na => fooa, nb => foob) = $c();',
       BadBackCode => 
       $index2d_init_bad . '$a(na => fooa, nb => foob) = $c();',
       Doc => $doc,
       BadDoc =>
       'index2d barfs if either of the index values are bad.',
);


# indexND: CED 2-Aug-2002
pp_add_exported('','indexND indexNDb');
pp_addpm(<<'EOD-indexND');

=head2 indexNDb

=for ref 

  Backwards-compatibility alias for indexND

=head2 indexND

=for ref

  Find selected elements in an N-D piddle, with optional boundary handling

=for example

  $out = $source->indexND( $index, [$method] )

  $source = 10*xvals(10,10) + yvals(10,10);
  $index  = pdl([[2,3],[4,5]],[[6,7],[8,9]]);
  print $source->indexND( $index );

  [
   [23 45]
   [67 89]
  ]

IndexND collapses C<$index> by lookup into C<$source>.  The 
0th dimension of C<$index> is treated as coordinates in C<$source>, and 
the return value has the same dimensions as the rest of C<$index>.
The returned elements are looked up from C<$source>.  Dataflow
works -- propagated assignment flows back into C<$source>.  

IndexND and IndexNDb were originally separate routines but they are both
now implemented as a call to L<range|/range>, and have identical syntax to
one another.

=cut

sub PDL::indexND {
	my($source,$index, $boundary) = @_;
	return PDL::range($source,$index,undef,$boundary);
}

*PDL::indexNDb = \&PDL::indexND;

EOD-indexND

pp_addpm(<<'EOD-range');

sub PDL::range {
  my($source,$ind,$sz,$bound) = @_;
  my $index = PDL->pdl($ind);

  my $size = defined($sz) ? PDL->pdl($sz) : undef;


  # Handle empty PDL case: return a properly constructed Empty.
  if($index->isempty) {
      my @sdims= $source->dims;
      splice(@sdims, 0, $index->dim(0) + ($index->dim(0)==0)); # added term is to treat Empty[0] like a single empty coordinate
      unshift(@sdims, $size->list) if(defined($size));
      return PDL->new_from_specification(0 x ($index->ndims-1), @sdims);
  }


  $index = $index->dummy(0,1) unless $index->ndims;

	
  # Pack boundary string if necessary
  if(defined $bound) {
    if(ref $bound eq 'ARRAY') {
      my ($s,$el);
      foreach $el(@$bound) {
	barf "Illegal boundary value '$el' in range"
  	  unless( $el =~ m/^([0123fFtTeEpPmM])/ );
	$s .= $1;
      }
      $bound = $s;
    }
    elsif($bound !~ m/^[0123ftepx]+$/  && $bound =~ m/^([0123ftepx])/i ) {
      $bound = $1;
    }
  }

  no warnings; # shut up about passing undef into rangeb
  $source->rangeb($index,$size,$bound);
}
EOD-range

=head2 rangeb

=cut

pp_def(
	'rangeb',
	Doc => <<'EOD',
=for ref

Engine for L<range|/range>

=for example

Same calling convention as L<range|/range>, but you must supply all
parameters.  C<rangeb> is marginally faster as it makes a direct PP call,
avoiding the perl argument-parsing step. 

=cut

=head2 range

=for ref 

Extract selected chunks from a source piddle, with boundary conditions

=for example

	$out = $source->range($index,[$size,[$boundary]])

Returns elements or rectangular slices of the original piddle, indexed by 
the C<$index> piddle.  C<$source> is an N-dimensional piddle, and C<$index> is 
a piddle whose first dimension has size up to N.  Each row of C<$index> is 
treated as coordinates of a single value or chunk from C<$source>, specifying 
the location(s) to extract.  

If you specify a single index location, then range is essentially an expensive
slice, with controllable boundary conditions.

B<INPUTS>

C<$index> and C<$size> can be piddles or array refs such as you would
feed to L<zeroes|PDL::Core/zeroes> and its ilk.  If C<$index>'s 0th dimension
has size higher than the number of dimensions in C<$source>, then
C<$source> is treated as though it had trivial dummy dimensions of
size 1, up to the required size to be indexed by C<$index> -- so if
your source array is 1-D and your index array is a list of 3-vectors, 
you get two dummy dimensions of size 1 on the end of your source array.

You can extract single elements or N-D rectangular ranges from C<$source>,
by setting C<$size>.  If C<$size> is undef or zero, then you get a single
sample for each row of C<$index>.  This behavior is similar to 
L<indexNDb|/indexNDb>, which is in fact implemented as a call to L<range|/range>.

If C<$size> is positive then you get a range of values from C<$source> at 
each location, and the output has extra dimensions allocated for them.
C<$size> can be a scalar, in which case it applies to all dimensions, or an 
N-vector, in which case each element is applied independently to the 
corresponding dimension in C<$source>.  See below for details.

C<$boundary> is a number, string, or list ref indicating the type of 
boundary conditions to use when ranges reach the edge of C<$source>.  If you
specify no boundary conditions the default is to forbid boundary violations
on all axes.  If you specify exactly one boundary condition, it applies to 
all axes.  If you specify more (as elements of a list ref, or as a packed
string, see below), then they apply to dimensions in the order in which they
appear, and the last one applies to all subsequent dimensions.  (This is 
less difficult than it sounds; see the examples below).

=over 3

=item 0 (synonyms: 'f','forbid') B<(default)>

Ranges are not allowed to cross the boundary of the original PDL.  Disallowed
ranges throw an error.  The errors are thrown at evaluation time, not
at the time of the range call (this is the same behavior as L<slice|/slice>).

=item 1 (synonyms: 't','truncate')

Values outside the original piddle get BAD if you've got bad value
support compiled into your PDL and set the badflag for the source PDL;
or 0 if you haven't (you must set the badflag if you want BADs for out
of bound values, otherwise you get 0).  Reverse dataflow works OK for
the portion of the child that is in-bounds.  The out-of-bounds part of
the child is reset to (BAD|0) during each dataflow operation, but
execution continues.

=item 2 (synonyms: 'e','x','extend')

Values that would be outside the original piddle point instead to the 
nearest allowed value within the piddle.  See the CAVEAT below on 
mappings that are not single valued.

=item 3 (synonyms: 'p','periodic')

Periodic boundary conditions apply: the numbers in $index are applied,
strict-modulo the corresponding dimensions of $source.  This is equivalent to
duplicating the $source piddle throughout N-D space.  See the CAVEAT below 
about mappings that are not single valued.

=item 4 (synonyms: 'm','mirror')

Mirror-reflection periodic boundary conditions apply.  See the CAVEAT
below about mappings that are not single valued.

=back

The boundary condition identifiers all begin with unique characters, so 
you can feed in multiple boundary conditions as either a list ref or a 
packed string.  (The packed string is marginally faster to run).  For 
example, the four expressions [0,1], ['forbid','truncate'], ['f','t'], 
and 'ft' all specify that violating the boundary in the 0th dimension 
throws an error, and all other dimensions get truncated.  

If you feed in a single string, it is interpreted as a packed boundary
array if all of its characters are valid boundary specifiers (e.g. 'pet'),
but as a single word-style specifier if they are not (e.g. 'forbid').

B<OUTPUT>

The output threads over both C<$index> and C<$source>.  Because implicit 
threading can happen in a couple of ways, a little thought is needed.  The
returned dimension list is stacked up like this:

   (index thread dims), (index dims (size)), (source thread dims)

The first few dims of the output correspond to the extra dims of
C<$index> (beyond the 0 dim). They allow you to pick out individual
ranges from a large, threaded collection.

The middle few dims of the output correspond to the size dims
specified in C<$size>, and contain the range of values that is extracted
at each location in C<$source>.  Every nonzero element of C<$size> is copied to
the dimension list here, so that if you feed in (for example) C<$size
= [2,0,1]> you get an index dim list of C<(2,1)>.

The last few dims of the output correspond to extra dims of C<$source> beyond
the number of dims indexed by C<$index>.  These dims act like ordinary 
thread dims, because adding more dims to C<$source> just tacks extra dims
on the end of the output.  Each source thread dim ranges over the entire
corresponding dim of C<$source>.

B<Dataflow>: Dataflow is bidirectional.

B<Examples>:
Here are basic examples of C<range> operation, showing how to get 
ranges out of a small matrix.  The first few examples show extraction
and selection of individual chunks.  The last example shows
how to mark loci in the original matrix (using dataflow).

 pdl> $src = 10*xvals(10,5)+yvals(10,5)
 pdl> print $src->range([2,3])    # Cut out a single element
 23
 pdl> print $src->range([2,3],1)  # Cut out a single 1x1 block
 [
  [23]
 ]
 pdl> print $src->range([2,3], [2,1]) # Cut a 2x1 chunk
 [
  [23 33]
 ]
 pdl> print $src->range([[2,3]],[2,1]) # Trivial list of 1 chunk
 [
  [
   [23]
   [33]
  ]
 ]
 pdl> print $src->range([[2,3],[0,1]], [2,1])   # two 2x1 chunks
 [
  [
   [23  1]
   [33 11]
  ]
 ]
 pdl> # A 2x2 collection of 2x1 chunks
 pdl> print $src->range([[[1,1],[2,2]],[[2,3],[0,1]]],[2,1])
 [
  [
   [
    [11 22]
    [23  1]
   ]
   [
    [21 32]
    [33 11]
   ]
  ]
 ]
 pdl> $src = xvals(5,3)*10+yvals(5,3)
 pdl> print $src->range(3,1)  # Thread over y dimension in $src 
 [
  [30]
  [31]
  [32]
 ]

 pdl> $src = zeroes(5,4);
 pdl> $src->range(pdl([2,3],[0,1]),pdl(2,1)) .= xvals(2,2,1) + 1
 pdl> print $src
 [
  [0 0 0 0 0]
  [2 2 0 0 0]
  [0 0 0 0 0]
  [0 0 1 1 0]
 ]

B<CAVEAT>: It's quite possible to select multiple ranges that
intersect.  In that case, modifying the ranges doesn't have a
guaranteed result in the original PDL -- the result is an arbitrary
choice among the valid values.  For some things that's OK; but for
others it's not. In particular, this doesn't work:

    pdl> $photon_list = new PDL::RandVar->sample(500)->reshape(2,250)*10
    pdl> histogram = zeroes(10,10)
    pdl> histogram->range($photon_list,1)++;  #not what you wanted

The reason is that if two photons land in the same bin, then that bin 
doesn't get incremented twice.  (That may get fixed in a later version...)

B<PERMISSIVE RANGING>: If C<$index> has too many dimensions compared
to C<$source>, then $source is treated as though it had dummy
dimensions of size 1, up to the required number of dimensions.  These
virtual dummy dimensions have the usual boundary conditions applied to
them.  

If the 0 dimension of C<$index> is ludicrously large (if its size is
more than 5 greater than the number of dims in the source PDL) then
range will insist that you specify a size in every dimension, to make
sure that you know what you're doing.  That catches a common error with
range usage: confusing the initial dim (which is usually small) with another
index dim (perhaps of size 1000).

If the index variable is Empty, then range() always returns the Empty PDL.
If the index variable is not Empty, indexing it always yields a boundary
violation.  All non-barfing conditions are treated as truncation, since
there are no actual data to return.

B<EFFICIENCY>: Because C<range> isn't an affine transformation (it
involves lookup into a list of N-D indices), it is somewhat
memory-inefficient for long lists of ranges, and keeping dataflow open
is much slower than for affine transformations (which don't have to copy
data around).  

Doing operations on small subfields of a large range is inefficient
because the engine must flow the entire range back into the original
PDL with every atomic perl operation, even if you only touch a single element.
One way to speed up such code is to sever your range, so that PDL
doesn't have to copy the data with each operation, then copy the
elements explicitly at the end of your loop.  Here's an example that
labels each region in a range sequentially, using many small
operations rather than a single xvals assignment:

  ### How to make a collection of small ops run fast with range...
  $a =  $data->range($index, $sizes, $bound)->sever; 
  $aa = $data->range($index, $sizes, $bound);        
  map { $a($_ - 1) .= $_; } (1..$a->nelem);    # Lots of little ops
  $aa .= $a;

C<range> is a perl front-end to a PP function, C<rangeb>.  Calling
C<rangeb> is marginally faster but requires that you include all arguments.

DEVEL NOTES

* index thread dimensions are effectively clumped internally.  This
makes it easier to loop over the index array but a little more brain-bending 
to tease out the algorithm.

* Currently the index threads really do run fastest in memory; this is 
probably the wrong direction to thread, for fastest behavior -- modifying 
the appropriate dimincs in RedoDims ought to take care of it.

=cut 

EOD
	HandleBad => 1,
	DefaultFlow => 1,
	Reversible => 1,
	P2Child => 1,
        NoPdlThread => 1,
	OtherPars => 'SV *index; SV *size; SV *boundary',


#
# rdim: dimensionality of each range (0 dim of index PDL)
#
# ntsize: number of nonzero size dimensions
# sizes:  array of range sizes, indexed (0..rdim-1).  A zero element means
#	  that the dimension is omitted from the child dim list.
# corners: parent coordinates of each corner, running fastest over coord index.
#	(indexed 0 .. (nitems-1)*(rdim)+rdim-1)
# nitems: total number of list elements   (product of itdims)
# itdim:  number of index thread dimensions
# itdims: Size of each index thread dimension, indexed (0..itdim-1)
# 
# bsize: Number of independently specified boundary conditions
# nsizes: Number of independently specified range dim sizes
# boundary: Array containing all the boundary condition specs
# indord: Order/size of the indexing dim (0th dim of $index)

	Comp => 'PDL_Long rdim; 
                 PDL_Long nitems;
                 PDL_Long itdim;
                 PDL_Long ntsize;
                 PDL_Long bsize;
		 PDL_Long nsizes;
		 PDL_Long sizes[$COMP(rdim)];
		 PDL_Long itdims[$COMP(itdim)];
		 PDL_Long corners[$COMP(rdim) * $COMP(nitems)];
	         char boundary[$COMP(rdim)];
		 ',
	MakeComp => <<'EOD-MakeComp',
pdl *ind_pdl;
pdl *size_pdl;

/***
 * Check and condition the index piddle.  Some of this is apparently
 * done by XS -- but XS doesn't check for existing SVs that are undef.
 */
if ((index==NULL) || (index == &PL_sv_undef))
   { $CROAK("rangeb: index variable must be defined"); }

if(!(ind_pdl = PDL->SvPDLV(index))) /* assignment */
   { $CROAK("rangeb: unable to convert index variable to a PDL"); }
  
PDL->make_physdims(ind_pdl);

if(ind_pdl->dims[0] == 0) 
    { $CROAK("rangeb: can't handle Empty indices -- call range instead"); }

/***
 * Ensure that the index is a long.  If there's no loss of information,
 * just upgrade it -- otherwise, make a temporary copy.
 */
switch(ind_pdl->datatype) {
 default:                              /* Most types: */
   ind_pdl = PDL->hard_copy(ind_pdl);  /*   copy and fall through */
 case PDL_B: case PDL_S: case PDL_US:  
   PDL->converttype(&ind_pdl,PDL_L,1); /* convert in place. */
   break;
 case PDL_L:                           
   break;
}

/***
 * Figure sizes of the COMP arrrays and allocate them.
 */
{
  PDL_Long i,nitems;

  $COMP(rdim) = ind_pdl->ndims ? ind_pdl->dims[0] : 1;
  for(i=nitems=1; i < ind_pdl->ndims; i++)  /* Accumulate item list size */
    nitems *= ind_pdl->dims[i];
  $COMP(nitems) = nitems;
  $COMP(itdim) = ind_pdl->ndims ? ind_pdl->ndims - 1 : 0;
  $DOCOMPDIMS();
}

/***
 * Fill in the boundary condition array
 */
{
  char *bstr;
  STRLEN blen;
  bstr = SvPV(boundary,blen);
  
  if(blen == 0) {
    /* If no boundary is specified then every dim gets forbidden */
    int i;
    for (i=0;i<$COMP(rdim);i++) 
      $COMP(boundary[i]) = 0;
  } else {
    int i;
    for(i=0;i<$COMP(rdim);i++) {
      switch(bstr[i < blen ? i : blen-1 ]) {
      case '0': case 'f': case 'F':               /* forbid */
	$COMP(boundary[i]) = 0;
	break;
      case '1': case 't': case 'T':               /* truncate */
	$COMP(boundary[i]) = 1;
	break;
      case '2': case 'e': case 'E':               /* extend */
	$COMP(boundary[i]) = 2;
	break;
      case '3': case 'p': case 'P':               /* periodic */
	$COMP(boundary[i]) = 3;
	break;
      case '4': case 'm': case 'M':               /* mirror */
	$COMP(boundary[i]) = 4;
	break;
      default:
	{
	  /* No need to check if i < blen -- this will barf out the
	   * first time it gets hit.  I didn't use $ CROAK 'coz that
	   * macro doesn't let you pass in a string variable -- only a 
	   * constant.
	   */
	  barf("Error in rangeb: Unknown boundary condition '%c' in range",bstr[i]);
	}
	break;
      } // end of switch
    }
  }
}  
/***
 * Store the sizes of the index-thread dims
 */
{
  PDL_Long i;
  PDL_Long nd = ind_pdl->ndims - 1;
  for(i=0; i < nd ; i++)
    $COMP(itdims[i]) = ind_pdl->dims[i+1];
}

/*** 
 * Check and condition the size piddle, and store sizes of the ranges
 */
{
  PDL_Long i,ntsize;

  if( (size == NULL) || (size == &PL_sv_undef) ) {
    // NO size was passed in (not normally executed even if you passed in no size to range(), 
    // as range() generates a size array...
    for(i=0;i<$COMP(rdim);i++)
	  $COMP(sizes[i]) = 0;

  } else {
    /* Normal case with sizes present in a PDL */
    
    if(!(size_pdl = PDL->SvPDLV(size))) /* assignment */
      $CROAK("Unable to convert size to a PDL in range");

    if(size_pdl->nvals == 0) {
      // no values in the size_pdl - Empty or Null.  Just copy 0s to all the range dims
      for(i=0;i<$COMP(rdim);i++)
	$COMP(sizes[i]) = 0;

    } else {
      
      // Convert size PDL to long
      switch(size_pdl->datatype) {
      default:                              /* Most types: */
	size_pdl = PDL->hard_copy(size_pdl);  /*   copy and fall through */
      case PDL_B: case PDL_S: case PDL_US:  
	PDL->converttype(&size_pdl,PDL_L,1); /* convert in place. */
	break;
      case PDL_L:                           
	break;
      }
      
      $COMP(nsizes) = size_pdl->nvals; /* Store for later permissiveness check */

      /* Copy the sizes, or die if they're the wrong shape */
      if(size_pdl->nvals == 1) {
	for(i=0;i<$COMP(rdim);i++) {
	  $COMP(sizes[i]) = *((PDL_Long *)(size_pdl->data));
	}
	
	/* Check for nonnegativity of sizes.  The rdim>0 mask ensures that */
	/* we don't barf on the Empty PDL (as an index). */
	if( $COMP(rdim) > 0 && $COMP(sizes[0]) < 0 ) {
	  $CROAK("  Negative range size is not allowed in range\n");
        }
      }
      else if( size_pdl->nvals <= $COMP(rdim) && size_pdl->ndims == 1) {
	for(i=0;i<$COMP(rdim);i++) {
	  $COMP(sizes[i]) = ( 	(i < size_pdl->nvals) ? 
	                    	((PDL_Long *)(size_pdl->data))[i] :
		                0
			    );
	  if($COMP(sizes[i]) < 0) 
		$CROAK("  Negative range sizes are not allowed in range\n");
        }
      }
      else {
	$CROAK(" Size must match index's 0th dim in range\n");
      }
	
    } /* end of nonempty size-piddle code */
  } /* end of defined-size-piddle code */

  /* Insert the number of nontrivial sizes (these get output dimensions) */
  for(i=ntsize=0;i<$COMP(rdim);i++)
    if($COMP(sizes[i]))
      ntsize++;
  $COMP(ntsize) = ntsize;
}

/***
 * Stash coordinates of the corners
 */

{
  PDL_Long i,j,k,ioff;
  PDL_Long *cptr;
  PDL_Long *iter = (PDL_Long *)(PDL->smalloc((STRLEN) (sizeof(PDL_Long) * ($COMP(itdim)))));
  
  /* initialize iterator to loop over index threads */
  cptr = iter;
  for(k=0;k<$COMP(itdim);k++)
    *(cptr++) = 0;
  
  cptr = $COMP(corners);  
  do {
    /* accumulate offset into the index from the iterator */
    for(k=ioff=0;k<$COMP(itdim);k++)
      ioff += iter[k] * ind_pdl->dimincs[k+1];
    
    /* Loop over the 0th dim of index, copying coords. */ 
    /* This is the natural place to check for permissive ranging; too */
    /* bad we don't have access to the parent piddle here... */
	
    for(j=0;j<$COMP(rdim);j++) 
        *(cptr++) = ((PDL_Long *)(ind_pdl->data))[ioff + ind_pdl->dimincs[0] * j];
    
    /* Increment the iterator -- the test increments, the body carries. */
    for(k=0; k<$COMP(itdim) && (++(iter[k]))>=($COMP(itdims)[k]) ;k++)
      iter[k] = 0;
  } while(k<$COMP(itdim));



}


$SETREVERSIBLE(1);

EOD-MakeComp

	RedoDims => <<'EOD-RedoDims' ,
{		      
  PDL_Long stdim = $PARENT(ndims) - $COMP(rdim);
  PDL_Long dim,inc;
  PDL_Long i;

    // Speed bump for ludicrous cases
    if( $COMP(rdim) > $PARENT(ndims)+5 && $COMP(nsizes) != $COMP(rdim)) {
      barf("Ludicrous number of extra dims in range index; leaving child null.\n    (%d implicit dims is > 5; index has %d dims; source has %d dim%s.)\n    This often means that your index PDL is incorrect.  To avoid this message,\n    allocate dummy dims in the source or use %d dims in range's size field.\n",$COMP(rdim)-$PARENT(ndims),$COMP(rdim),$PARENT(ndims),($PARENT(ndims))>1?"s":"",$COMP(rdim));
    }
    
    if(stdim < 0) 
      stdim = 0;
    
    /* Set dimensionality of child */
    $CHILD(ndims) = $COMP(itdim) + $COMP(ntsize) + stdim;
    $SETNDIMS($COMP(itdim)+$COMP(ntsize)+stdim);
    
    /* Copy index thread dimensions to child */
    inc = 1;
    for(dim=0; dim<$COMP(itdim); dim++) {
      $CHILD(dimincs[dim]) = inc;
      inc *= ($CHILD(dims[dim]) = $COMP(itdims[dim])); /* assignment */
      
    }
    
    /* Copy size dimensions to child, crunching as we go. */
    for(i=0;i<$COMP(rdim);i++) {
      if($COMP(sizes[i])) {
	$CHILD(dimincs[dim]) = inc;
	inc *= ($CHILD(dims[dim++]) = $COMP(sizes[i])); /* assignment */
      }
    }
    
    /* Copy source thread dimensions to child */
    for(i=0;i<stdim;i++) {
      $CHILD(dimincs[dim]) = inc;
      inc *= ($CHILD(dims[dim++]) = $PARENT(dims[i+$COMP(rdim)])); /* assignment */
    }

    /* Cover bizarre case where the source PDL is empty - in that case, change */
    /* all non-barfing boundary conditions to truncation, since we have no data */
    /* to reflect, extend, or mirror. */
    if($PARENT(dims[0])==0) {
      for(dim=0; dim<$COMP(rdim); dim++) {
	if($COMP(boundary[dim])) 
	  $COMP(boundary[dim]) = 1; // force truncation
      }
    }



  $CHILD(datatype) = $PARENT(datatype);

  $SETDIMS();
}

EOD-RedoDims

	EquivCPOffsCode => <<'EOD-EquivCPOffsCode',
{
  PDL_Long *iter, *ip;  /* vector iterator */
  PDL_Long *sizes, *sp; /* size vector including stdims */
  PDL_Long *coords;     /* current coordinates */

  PDL_Long k;           /* index */
  PDL_Long item;        /* index thread iterator */
  PDL_Long pdim = $PARENT_P(ndims);
  PDL_Long rdim = $COMP(rdim);
  PDL_Long prdim = (rdim < pdim) ? rdim : pdim;
  PDL_Long stdim = pdim - prdim;

  /* Allocate iterator and larger size vector -- do it all in one foop 
   * to avoid extra calls to smalloc.
   */
    if(!(iter = (PDL_Long *)(PDL->smalloc((STRLEN) (sizeof(PDL_Long) * ($PARENT_P(ndims) * 2 + rdim)))))) {
    barf("couldn't get memory for range iterator");
  }
  sizes  = iter + $PARENT_P(ndims);
  coords = sizes + $PARENT_P(ndims);

  /* Figure out size vector */
  for(ip = $COMP(sizes), sp = sizes, k=0; k<rdim; k++)
     *(sp++) = *(ip++);
  for(; k < $PARENT_P(ndims); k++) 
     *(sp++) = $PARENT_P(dims[k]);


  /* Loop over all the ranges in the index list */
  for(item=0; item<$COMP(nitems); item++) {

    /* initialize in-range iterator to loop within each range */
    for(ip = iter, k=0; k<$PARENT_P(ndims); k++) 
      *(ip++) = 0;
    
    do {
      PDL_Long poff = 0;
      PDL_Long coff;
      PDL_Long k2;
      char trunc = 0;       /* Flag used to skip truncation case */

      /* Collect and boundary-check the current N-D coords */
      for(k=0; k < prdim; k++){

	PDL_Long ck = iter[k] + $COMP(corners[ item * rdim + k  ]) ;

     	/* normal case */
    	  if(ck < 0 || ck >= $PARENT_P(dims[k])) {
 	    switch($COMP(boundary[k])) {
 	    case 0: /* no boundary breakage allowed */
 	      barf("index out-of-bounds in range");
 	      break;
 	    case 1: /* truncation */
	      trunc = 1;
 	      break;
 	    case 2: /* extension -- crop */
 	      ck = (ck >= $PARENT_P(dims[k])) ? $PARENT_P(dims[k])-1 : 0;
 	      break;
 	    case 3: /* periodic -- mod it */
 	      ck %= $PARENT_P(dims[k]);
 	      if(ck < 0)   /* Fix mod breakage in C */
 	        ck += $PARENT_P(dims[k]);
 	      break;
	    case 4: /* mirror -- reflect off the edges */
	      ck += $PARENT_P(dims[k]);
	      ck %= ($PARENT_P(dims[k]) * 2);
	      if(ck < 0) /* Fix mod breakage in C */
		ck += $PARENT_P(dims[k])*2;
	      ck -= $PARENT_P(dims[k]);
	      if(ck < 0) {
		ck *= -1;
	        ck -= 1;
	      }
	      break;
 	    default:
 	      barf("Unknown boundary condition in range -- bug alert!");
 	      break;
 	    }
 	  }

	coords[k] = ck;

      }

      /* Check extra dimensions -- pick up where k left off... */
      for( ; k < rdim ; k++) {
        /* Check for indexing off the end of the dimension list */

	PDL_Long ck = iter[k] + $COMP(corners[ item * rdim + k  ]) ;

  	switch($COMP(boundary[k])) {
	    case 0: /* No boundary breakage allowed -- nonzero corners cause barfage */
	      if(ck != 0)
		 barf("Too many dims in range index (and you've forbidden boundary violations)");
              break;
            case 1: /* truncation - just truncate if the corner is nonzero */
	      trunc |= (ck != 0);
	      break;
	    case 2: /* extension -- ignore the corner (same as 3) */
	    case 3: /* periodic  -- ignore the corner */
            case 4: /* mirror -- ignore the corner */
              ck = 0;
              break;
	    default:
	      barf("Unknown boudnary condition in range -- bug alert!");
	      /* Note clever misspelling of boundary to distinguish from other case */
	      break;
	  }
      }

      /* Find offsets into the child and parent arrays, from the N-D coords */
      /* Note we only loop over real source dims (prdim) to accumulate -- */
      /* because the offset is trivial and/or we're truncating for virtual */
      /* dims caused by permissive ranging. */
      coff = $CHILD_P(dimincs[0]) * item;
      for(k2 = $COMP(itdim), poff = k = 0; 
	  k < prdim;
	  k++) { 
	poff += coords[k]*$PARENT_P(dimincs[k]);
	if($COMP(sizes[k])) 
	  coff += iter[k] * $CHILD_P(dimincs[k2++]);
      }

      /* Loop the copy over all the source thread dims (above rdim). */
      do {
	PDL_Long poff1 = poff;
	PDL_Long coff1 = coff;
	
	/* Accumulate the offset due to source threading */
	for(k2 = $COMP(itdim) + $COMP(ntsize), k = rdim; 
	    k < pdim;
	    k++) {
	  poff1 += iter[k] * $PARENT_P(dimincs[k]);
	  coff1 += iter[k] * $CHILD_P(dimincs[k2++]);
	}

	/* Finally -- make the copy 
	 * EQUIVCPTRUNC works like EQUIVCPOFFS but with checking for 
	 * out-of-bounds conditions.  
	 */
	$EQUIVCPTRUNC(coff1,poff1,trunc);		
	
	/* Increment the source thread iterator */
	for( k=$COMP(rdim); 
	     k < $PARENT_P(ndims) && (++(iter[k]) >= $PARENT_P(dims[k])); 
	     k++)
	  iter[k] = 0;
      } while(k < $PARENT_P(ndims)); /* end of source-thread iteration */

      /* Increment the in-range iterator */
      for(k = 0;
	  k < $COMP(rdim) && (++(iter[k]) >= $COMP(sizes[k]));
	  k++)
	iter[k] = 0;
    } while(k < $COMP(rdim)); /* end of main iteration */
  } /* end of item do loop */

}

EOD-EquivCPOffsCode

);


=head2 rld
=cut

pp_def(
	'rld',
	Pars=>'int a(n); b(n); [o]c(m);',
	PMCode =><<'EOD',
sub PDL::rld {
  my ($a,$b) = @_;
  my ($c);
  if ($#_ == 2) {
    $c = $_[2];
  } else {
# XXX Need to improve emulation of threading in auto-generating c
    my ($size) = $a->sumover->max;
    my (@dims) = $a->dims;
    shift @dims;
    $c = $b->zeroes($size,@dims);
  }
  &PDL::_rld_int($a,$b,$c);
  $c;
}
EOD
	Code=>'
	  int i,j=0,an;
	  $GENERIC(b) bv;
	  loop (n) %{
	    an = $a();
	    bv = $b();
	    for (i=0;i<an;i++) {
	      $c(m=>j) = bv;
	      j++;
	    }
	  %}',
	Doc => <<'EOD'
=for ref

Run-length decode a vector

Given a vector C<$a> of the numbers of instances of values C<$b>, run-length
decode to C<$c>.

=for example

 rld($a,$b,$c=null);

=cut

EOD
);

=head2 rle
=cut

pp_def(
	'rle',
	Pars=>'c(n); int [o]a(n); [o]b(n);',
	Code=>'
	  int j=0,sn=$SIZE(n);
	  $GENERIC(c) cv, clv;
	  clv = $c(n=>0);
	  $b(n=>0) = clv;
	  $a(n=>0) = 0;
	  loop (n) %{
	    cv = $c();
	    if (cv == clv) {
	      $a(n=>j)++;
	    } else {
	      j++;
	      $b(n=>j) = clv = cv;
	      $a(n=>j) = 1;
	    }
	  %}
	  for (j++;j<sn;j++) {
	    $a(n=>j) = 0;
	    $b(n=>j) = 0;
	  }
	',
	Doc => <<'EOD'
=for ref

Run-length encode a vector

Given vector C<$c>, generate a vector C<$a> with the number of each element,
and a vector C<$b> of the unique values.  Only the elements up to the
first instance of C<0> in C<$a> should be considered.

=for example

 rle($c,$a=null,$b=null);

=cut

EOD
);

# this one can convert vaffine piddles without(!) physicalising them
# maybe it can replace 'converttypei' in the future?
#
# XXX do not know whether the HandleBad stuff will work here
#
pp_def('flowconvert',
       HandleBad => 1,
       DefaultFlow => 1,
       Reversible => 1,	
       Pars => 'PARENT(); [oca]CHILD()',
       OtherPars => 'int totype;',
       Reversible => 1,
       # Forced types
       FTypes => {CHILD => '$COMP(totype)'},
       Code => 
       '$CHILD() = $PARENT();',
       BadCode => 
       'if ( $ISBAD(PARENT()) ) { 
           $SETBAD(CHILD());
        } else {
           $CHILD() = $PARENT();
        }',
       BackCode => '$PARENT() = $CHILD();',
       BadBackCode => 
       'if ( $ISBAD(CHILD()) ) { 
           $SETBAD(PARENT());
        } else {
           $PARENT() = $CHILD();
        }',
       Doc => 'internal',
);


pp_def(
	'converttypei',
        HandleBad => 1,
	DefaultFlow => 1,
	GlobalNew => 'converttypei_new',
	OtherPars => 'int totype;',
	P2Child => 1,
        NoPdlThread => 1,
	Identity => 1,
	Reversible => 1,
# Forced types
	FTypes => {CHILD => '$COMP(totype)'},
	Doc => 'internal',
);



# XXX Make clump work with optional parameter!
if(0) {
# Special-case
pp_def(
	'clump',
	DefaultFlow => 1,
	OtherPars => 'int n',
	P2Child => 1,
	Priv => 'int nnew; int nrem;',
	RedoDims => 'int i; int d1;
		if($COMP(n) > $PARENT(ndims)) 
			/* Now with more flavor: truncate overly long clumps to 
			   just clump existing dimensions...  (CED 17-Mar-2002) */

			$COMP(n) = $PARENT(ndims);

			/* Old croaking code: */
			/*$CROAK("Too many dimensions %d to clump from %d", */
			/*		$COMP(n),$PARENT(ndims)); */

		 $COMP(nrem) = ($COMP(n)==-1 ? $PARENT(threadids[0]) : $COMP(n));
		 $PRIV(nnew) = $PARENT(ndims) - $COMP(nrem) + 1;
		 $SETNDIMS($PRIV(nnew));
		 d1=1;
		 for(i=0; i<$PRIV(nrem); i++) {
		 	d1 *= $PARENT(dims[i]);
		 }
		 $CHILD(dims[0]) = d1;
		 for(; i<$PARENT(ndims); i++) {
		 	$CHILD(dims[i-$PRIV(nrem)+1]) = $PARENT(dims[i]);
		 }
		 $SETDIMS();
		 $SETDELTATHREADIDS(1-$COMP(nrem));
		 ',
	EquivCPOffsCode => '
		int i;
		for(i=0; i<$CHILD_P(nvals); i++) {
			$EQUIVCPOFFS(i,i);
		}
		',
	Reversible => 1,
);
} else {

# Affine! Make sure vaffine chaining understands to stop in the right
# place.
# the perl wrapper clump is now defined in Core.pm
# this is just the low level interface
pp_def(
	'_clump_int',
	P2Child => 1,
        NoPdlThread => 1,
	DefaultFlow => 1,
	Reversible => 1,
	AffinePriv => 1,
	OtherPars => 'int n',
	RedoDims => 'int i; int d1;
		int nrem; int nnew;
		if($COMP(n) > $PARENT(ndims)) {
			/* Now with more flavor:  truncate clumping in this case to 
			 * the total number of dimensions that actually exist...
			 *  --CED 17-Mar-2002
			 */
 			$COMP(n) = -1;
			
#ifdef older_croaking_code
			$SETNDIMS(0);  /* fix to make sure we do not get problems later */
			$PRIV(offs) = 0;
			$SETDIMS();
			$CROAK("Too many dimensions %d to clump from %d",
				$COMP(n),$PARENT(ndims));
#endif
		}
		 nrem = ($COMP(n)< 0 ? $PARENT(threadids[0]) + 1 + ($COMP(n)) : $COMP(n));
	         if(nrem < 0) {
			$CROAK("Too many dimensions %d to leave behind when clumping from %d",-$COMP(n),$PARENT(ndims));
		 }

		 nnew = $PARENT(ndims) - nrem + 1;
		 $SETNDIMS(nnew);
		 $DOPRIVDIMS();
		 $PRIV(offs) = 0;
		 d1=1;
		 for(i=0; i<nrem; i++) {
		 	d1 *= $PARENT(dims[i]);
		 }
		 $CHILD(dims[0]) = d1;
		 $PRIV(incs[0]) = 1;
		 for(; i<$PARENT(ndims); i++) {
		 	$CHILD(dims[i-nrem+1]) = $PARENT(dims[i]);
			$PRIV(incs[i-nrem+1]) = $PARENT(dimincs[i]);
		 }
		 $SETDIMS();
		 $SETDELTATHREADIDS(1-nrem);
		 ',
	Doc => 'internal',
);
}


=head2 xchg
=cut

pp_def(
	'xchg',
	OtherPars => 'int n1; int n2;',
	DefaultFlow => 1,
	Reversible => 1,
	P2Child => 1,
        NoPdlThread => 1,
	XCHGOnly => 1,
	EquivDimCheck => 'if ($COMP(n1) <0)
				$COMP(n1) += $PARENT(threadids[0]);
			  if ($COMP(n2) <0)
				$COMP(n2) += $PARENT(threadids[0]);
			  if ($COMP(n1) <0 ||$COMP(n2) <0 ||
			     $COMP(n1) >= $PARENT(threadids[0]) ||
			     $COMP(n2) >= $PARENT(threadids[0]))
		barf("One of dims %d, %d out of range: should be 0<=dim<%d",
			$COMP(n1),$COMP(n2),$PARENT(threadids[0]));',
	EquivPDimExpr => '(($CDIM == $COMP(n1)) ? $COMP(n2) : ($CDIM == $COMP(n2)) ? $COMP(n1) : $CDIM)',
	EquivCDimExpr => '(($PDIM == $COMP(n1)) ? $COMP(n2) : ($PDIM == $COMP(n2)) ? $COMP(n1) : $PDIM)',
	Doc => <<'EOD',
=for ref

exchange two dimensions

Negative dimension indices count from the end.

The command

=for example

 $b = $a->xchg(2,3);

creates C<$b> to be like C<$a> except that the dimensions 2 and 3
are exchanged with each other i.e.

 $b->at(5,3,2,8) == $a->at(5,3,8,2)

=cut

EOD
);

pp_addpm(<< 'EOD');

=head2 reorder

=for ref

Re-orders the dimensions of a PDL based on the supplied list.

Similar to the L<xchg|/xchg> method, this method re-orders the dimensions
of a PDL. While the L<xchg|/xchg> method swaps the position of two dimensions,
the reorder method can change the positions of many dimensions at
once.

=for usage

 # Completely reverse the dimension order of a 6-Dim array.
 $reOrderedPDL = $pdl->reorder(5,4,3,2,1,0); 

The argument to reorder is an array representing where the current dimensions
should go in the new array. In the above usage, the argument to reorder 
C<(5,4,3,2,1,0)>
indicates that the old dimensions (C<$pdl>'s dims) should be re-arranged to make the
new pdl (C<$reOrderPDL>) according to the following:

   Old Position   New Position
   ------------   ------------
   5              0
   4              1
   3 		  2
   2		  3
   1		  4
   0		  5

You do not need to specify all dimensions, only a complete set
starting at position 0.  (Extra dimensions are left where they are).
This means, for example, that you can reorder() the X and Y dimensions of
an image, and not care whether it is an RGB image with a third dimension running
across color plane.

=for example 

Example:

 pdl> $a = sequence(5,3,2);	  # Create a 3-d Array
 pdl> p $a
 [
  [
   [ 0  1  2  3  4]
   [ 5  6  7  8  9]
   [10 11 12 13 14]
  ]
  [
   [15 16 17 18 19]
   [20 21 22 23 24]
   [25 26 27 28 29]
  ]
 ]
 pdl> p $a->reorder(2,1,0); # Reverse the order of the 3-D PDL
 [
  [
   [ 0 15]
   [ 5 20]
   [10 25]
  ]
  [
   [ 1 16]
   [ 6 21]
   [11 26]
  ]
  [
   [ 2 17]
   [ 7 22]
   [12 27]
  ]
  [
   [ 3 18]
   [ 8 23]
   [13 28]
  ]
  [
   [ 4 19]
   [ 9 24]
   [14 29]
  ]
 ]

The above is a simple example that could be duplicated by calling
C<$a-E<gt>xchg(0,2)>, but it demonstrates the basic functionality of reorder.

As this is an index function, any modifications to the
result PDL will change the parent.

=cut

sub PDL::reorder {
	my ($pdl,@newDimOrder) = @_;
	
	my $arrayMax = $#newDimOrder;
  
	#Error Checking:
	if( $pdl->getndims < scalar(@newDimOrder) ){
		my $errString = "PDL::reorder: Number of elements (".scalar(@newDimOrder).") in newDimOrder array exceeds\n";
		$errString .= "the number of dims in the supplied PDL (".$pdl->getndims.")";
		barf($errString);
	}
	
	# Check to make sure all the dims are within bounds
	for my $i(0..$#newDimOrder) {
	  my $dim = $newDimOrder[$i];
	  if($dim < 0 || $dim > $#newDimOrder) {
	      my $errString = "PDL::reorder: Dim index $newDimOrder[$i] out of range in position $i\n(range is 0-$#newDimOrder)";
	      barf($errString);
	  }
	}

	# Checking that they are all present and also not duplicated is done by thread() [I think]

	# a quicker way to do the reorder
	return $pdl->thread(@newDimOrder)->unthread(0);
}

EOD

=head2 mv
=cut

pp_def(
	'mv',
	OtherPars => 'int n1; int n2;',
	DefaultFlow => 1,
	Reversible => 1,
	P2Child => 1,
        NoPdlThread => 1,
	XCHGOnly => 1,
	EquivDimCheck => 'if ($COMP(n1) <0)
				$COMP(n1) += $PARENT(threadids[0]);
			  if ($COMP(n2) <0)
				$COMP(n2) += $PARENT(threadids[0]);
			  if ($COMP(n1) <0 ||$COMP(n2) <0 ||
			     $COMP(n1) >= $PARENT(threadids[0]) ||
			     $COMP(n2) >= $PARENT(threadids[0]))
		barf("One of dims %d, %d out of range: should be 0<=dim<%d",
			$COMP(n1),$COMP(n2),$PARENT(threadids[0]));',
	EquivPDimExpr => '(($COMP(n1) < $COMP(n2)) ?
	(($CDIM < $COMP(n1) || $CDIM > $COMP(n2)) ?
		$CDIM : (($CDIM == $COMP(n2)) ? $COMP(n1) : $CDIM+1))
	: (($COMP(n2) < $COMP(n1)) ?
		(($CDIM > $COMP(n1) || $CDIM < $COMP(n2)) ?
			$CDIM : (($CDIM == $COMP(n2)) ? $COMP(n1) : $CDIM-1))
		: $CDIM))',
	EquivCDimExpr => '(($COMP(n2) < $COMP(n1)) ?
	(($PDIM < $COMP(n2) || $PDIM > $COMP(n1)) ?
		$PDIM : (($PDIM == $COMP(n1)) ? $COMP(n2) : $PDIM+1))
	: (($COMP(n1) < $COMP(n2)) ?
		(($PDIM > $COMP(n2) || $PDIM < $COMP(n1)) ?
			$PDIM : (($PDIM == $COMP(n1)) ? $COMP(n2) : $PDIM-1))
		: $PDIM))',
	Doc => << 'EOD',
=for ref

move a dimension to another position

The command

=for example

 $b = $a->mv(4,1);

creates C<$b> to be like C<$a> except that the dimension 4 is moved to the
place 1, so:

 $b->at(1,2,3,4,5,6) == $a->at(1,5,2,3,4,6);

The other dimensions are moved accordingly.
Negative dimension indices count from the end.
=cut
EOD
);

=head2 onceslice
=cut

pp_def(
	'oneslice',
	Doc => <<'EOD',
=for ref

experimental function - not for public use

=for example

 $a = oneslice();

This is not for public use currently. See the source if you have to.
This function can be used to accomplish run-time changing of
transformations i.e. changing the size of some piddle at run-time.

However, the mechanism is not yet finalized and this is just a demonstration.
=cut
EOD
	P2Child => 1,
        NoPdlThread => 1,
	DefaultFlow => 1,
	Reversible => 1,
	OtherPars => 'int nth; int from; int step; int nsteps;',
	AffinePriv => 1,
	RedoDims => '
		int nth = $PRIV(nth);
		int from = $PRIV(from);
		int step = $PRIV(step);
		int nsteps = $PRIV(nsteps);
		int i;
		printf("ONESLICE_REDODIMS %d %d %d %d\n",nth,from,step,nsteps);
		if(nth >= $PARENT(ndims)) {
			die("Oneslice: too large nthdim");
		}
		if(from + step * (nsteps-1) >= $PARENT(dims[nth])) {
			die("Oneslice: too many, too large steps");
		}
		if(from < 0 || step < 0) {
			die("Oneslice: can only support positive from & step");
		}
		$PRIV(offs) = 0;
		$SETNDIMS($PARENT(ndims));
		$DOPRIVDIMS();
		for(i=0; i<$PARENT(ndims); i++) {
			$CHILD(dims)[i] = $PARENT(dims)[i];
			$PRIV(incs)[i] = $PARENT(dimincs)[i];
		}
		$CHILD(dims)[nth] = nsteps;
		$PRIV(incs)[nth] *= step;
		$PRIV(offs) += from * $PARENT(dimincs)[nth];
		$SETDELTATHREADIDS(0);
		$SETDIMS();
	',
	FooCode => # This is why we have this stupid function
	'	$COMP(from) = i1;
		$COMP(step) = i2;
		$COMP(nsteps) = i3;
		printf("ONESLICE_FOOFUNC %d %d %d %d\n",
		    $COMP(nth),$COMP(from),$COMP(step),$COMP(nsteps));
	',
);


pp_addhdr << 'EOH';
#define sign(x) ( (x) < 0 ? -1 : 1)
EOH

=head2 slice
=cut

# I think the quotes in the =item ":" lines
# confuse the perldoc stuff
#
pp_def(
	'slice',
	Doc => << 'EOD',
=for ref

Extract a rectangular slice of a piddle, from a string specifier.

C<slice> was the original Swiss-army-knife PDL indexing routine, but is
largely superseded by the L<NiceSlice|PDL::NiceSlice> source prefilter
and its associated L<nslice|PDL::Core/nslice> method.  It is still used as the
basic underlying slicing engine for L<nslice|PDL::Core/nslice>,
and is especially useful in particular niche applications.

=for example

 $a->slice('1:3');  #  return the second to fourth elements of $a
 $a->slice('3:1');  #  reverse the above
 $a->slice('-2:1'); #  return last-but-one to second elements of $a

The argument string is a comma-separated list of what to do
for each dimension. The current formats include
the following, where I<a>, I<b> and I<c> are integers and can
take legal array index values (including -1 etc):

=over 8

=item :

takes the whole dimension intact.

=item ''

(nothing) is a synonym for ":"
(This means that C<$a-E<gt>slice(':,3')> is equal to C<$a-E<gt>slice(',3')>).

=item a

slices only this value out of the corresponding dimension.

=item (a)

means the same as "a" by itself except that the resulting
dimension of length one is deleted (so if C<$a> has dims C<(3,4,5)> then
C<$a-E<gt>slice(':,(2),:')> has dimensions C<(3,5)> whereas
C<$a-E<gt>slice(':,2,:')> has dimensions C<(3,1,5))>.

=item a:b

slices the range I<a> to I<b> inclusive out of the dimension.

=item a:b:c

slices the range I<a> to I<b>, with step I<c> (i.e. C<3:7:2> gives the indices
C<(3,5,7)>). This may be confusing to Matlab users but several other
packages already use this syntax.

=item '*'

inserts an extra dimension of width 1 and

=item '*a'

inserts an extra (dummy) dimension of width I<a>.

=back

An extension is planned for a later stage allowing
C<$a-E<gt>slice('(=1),(=1|5:8),3:6(=1),4:6')>
to express a multidimensional diagonal of C<$a>.

Trivial out-of-bounds slicing is allowed: if you slice a source
dimension that doesn't exist, but only index the 0th element, then
C<slice> treats the source as if there were a dummy dimension there.
The following are all equivalent:

	xvals(5)->dummy(1,1)->slice('(2),0')  # Add dummy dim, then slice
	xvals(5)->slice('(2),0')              # Out-of-bounds slice adds dim.
	xvals(5)->slice((2),0)                # NiceSlice syntax
	xvals(5)->((2))->dummy(0,1) 	      # NiceSlice syntax

This is an error:

	xvals(5)->slice('(2),1')	# nontrivial out-of-bounds slice dies

Because slicing doesn't directly manipulate the source and destination 
pdl -- it just sets up a transformation between them -- indexing errors 
often aren't reported until later.  This is either a bug or a feature,
depending on whether you prefer error-reporting clarity or speed of execution.

=cut

EOD
	P2Child => 1,
        NoPdlThread => 1,
	DefaultFlow => 1,
	OtherPars => 'char* str',
	Comp => 'int nnew; int nthintact; int intactnew; int ndum;
	         int corresp[$COMP(intactnew)]; int start[$COMP(intactnew)];
		 int inc[$COMP(intactnew)]; int end[$COMP(intactnew)];
		 int nolddims;
		 int whichold[$COMP(nolddims)]; int oldind[$COMP(nolddims)];
		 ',
	AffinePriv => 1,
	MakeComp => q~
		int i;
		int nthnew; int nthold; int nthreal;
		int dumsize;
		char *s; char *ns;
		int nums[3]; int nthnum;
		$COMP(nnew)=0;
		$COMP(ndum)=0;
		$COMP(nolddims) = 0;
		if(str[0] == '(')
			$COMP(nolddims)++;
		else if (str[0] == '*')
			$COMP(ndum)++;
		else if (str[0] != '\0') /* handle empty string */
			$COMP(nnew)++;
		for(i=0; str[i]; i++)
			if(str[i] == ',') {
				if(str[i+1] == '(')
					$COMP(nolddims)++;
				else if(str[i+1] == '*')
					$COMP(ndum)++;
				else
					$COMP(nnew)++;
			}
		$COMP(nthintact) = $COMP(nolddims) + $COMP(nnew);
		$COMP(intactnew) = $COMP(nnew)+$COMP(ndum);
		$DOCOMPDIMS();
		nthnew=0; nthold=0; i=0; nthreal=0;
		s=str-1;
		do {
			s++;
			if(isdigit(*s) || *s == '-') {
				nthnew++; nthreal++;
				$COMP(inc[nthnew-1]) = 1;
				$COMP(corresp[nthnew-1]) = nthreal-1;
				$COMP(start[nthnew-1]) = strtol(s,&s,10);
				if(*s != ':') {
					$COMP(end[nthnew-1]) =
						$COMP(start[nthnew-1]);
					goto outlab;
				}
				s++;
				if(!isdigit(*s) && !(*s == '-')) {
					barf("Invalid slice str ind1 '%s': '%s'",str,s);
				}
				$COMP(end[nthnew-1]) = strtol(s,&s,10);
				if(*s != ':') {goto outlab;}
				s++;
				if(!isdigit(*s) && !(*s == '-')) {
					barf("Invalid slice str ind2 '%s': '%s'",str,s);
				}
				$COMP(inc[nthnew-1]) = strtol(s,&s,10);
			} else switch(*s) {
			case ':':
				s++;
				/* FALLTHRU */
			case ',': case '\0':  /* In these cases, no inc s */
				if ($COMP(intactnew) > 0) {
				  $COMP(start[nthnew]) = 0;
				  $COMP(end[nthnew]) = -1;
				  $COMP(inc[nthnew]) = 1;
				  $COMP(corresp[nthnew]) = nthreal;
				  nthnew++; nthreal++;
				}
				break;
			case '(':
				s++;
				$COMP(oldind[nthold]) = strtol(s,&s,10);
				$COMP(whichold[nthold]) = nthreal;
				nthold++; nthreal++;
				if(*s != ')') {
					barf("Sliceoblit must end with ')': '%s': '%s'",str,s);
				}
				s++;
				break;
			case '*':
				s++;
				if(isdigit(*s)) {
					dumsize = strtol(s,&s,10);
				} else {dumsize = 1;}
				$COMP(corresp[nthnew]) = -1;
				$COMP(start[nthnew]) = 0;
				$COMP(end[nthnew]) = dumsize-1;
				$COMP(inc[nthnew]) = 1;
				nthnew++;
				break;
			}
		   outlab:
			if(*s != ',' && *s != '\0') {
				barf("Invalid slice str '%s': '%s'",str,s);
			}
		} while(*s);
		$SETREVERSIBLE(1); /* XXX Only if incs>0, no dummies */
	~,
	RedoDims => '
		int i; int start; int end; int inc;
		if ($COMP(nthintact) > $PARENT(ndims)) {

	/* Slice has more dims than parent.  Check that the extra dims are 		
         * all zero, and if they are then give back What You Probably Wanted,
	 * which is a slice with dummy dimensions of order 1 in place of each excessive 
	 * dimension.  (Note that there are two ways to indicate a zero index: "0" and "-<w>",
	 * where <w> happens to be the order of that dimension in the original
	 * piddle.  The latter case still causes an error.  That is a feature.)
	 *    --CED 15-March-2002
	 */
			int ii,parentdim,ok;
			int n_xtra_dims=0, n_xtra_olddims=0;

			   /* Check index for each extra dim in the ordinary affine list */

			for(ok=1, ii = 0; ok && ii < $COMP(intactnew) ; ii++) {
				parentdim = $COMP(corresp[ii]);
/*				fprintf(stderr,"ii=%d,parent=%d, ndum=%d, nnew=%d...",ii,parentdim,$COMP(ndum),$COMP(nnew));				*/
				if(parentdim >= $PARENT(ndims)) {					

					ok = ( ( $COMP(start[ii]) == 0 ) && 
					  	( $COMP(end[ii]) == 0 || $COMP(end[ii])== -1 )
					);
					if(ok) {
						/* Change this into a dummy dimension, rank 1 */
						$COMP(corresp[ii]) = -1;
						$COMP(start[ii])   = 0;
						$COMP(end[ii])     = 0;
						$COMP(inc[ii])     = 1;
						$COMP(ndum)++;      /* One more dummy dimension... */
						$COMP(nnew)--;      /* ... one less real dimension */
						$COMP(nthintact)--; /* ... one less intact dim */
/*						fprintf(stderr,"ok, ndum=%d, nnew=%d\n",$COMP(ndum), $COMP(nnew));*/
					}
/*				fflush(stderr);*/
				}
			}	
			
			  /* Check index for each indexed parent dimension */
			for(ii=0; ok && ii < $COMP(nolddims); ii++) {
				if($COMP(whichold[ii]) >= $PARENT(ndims)) {
					ok = ( $COMP(whichold[ii]) < $PARENT(ndims) ) ||
						( $COMP(oldind[ii]) == 0 ) ||
						( $COMP(oldind[ii]) == -1) ;
					if(ok) {
					  int ij;
					  /* crunch indexed dimensions -- slow but sure */
					  $COMP(nolddims)--;
					  for(ij=ii; ij<$COMP(nolddims); ij++) {
						$COMP(oldind[ij]) = $COMP(oldind[ij+1]);
					 	$COMP(whichold[ij]) = $COMP(whichold[ij+1]);
					  }
					  $COMP(nthintact)--;
					}
				}
			}	
/*	fprintf(stderr,"ok=%d\n",ok);fflush(stderr);*/
			if(ok) {
			   /* Valid slice: all extra dims are zero. Adjust indices accordingly. */
/*			  $COMP(intactnew) -= $COMP(nthintact) - $PARENT(ndims); */
/*			  $COMP(nthintact) = $PARENT(ndims);*/
			} else { 	

			   /* Invalid slice: nonzero extra dimension.  Clean up and die.  */

  			 $SETNDIMS(0); /* dirty fix */
			 $PRIV(offs) = 0;	
			 $SETDIMS();
			 $CROAK("Too many dims in slice");
			}
 	        }
		$SETNDIMS($PARENT(ndims)-$COMP(nthintact)+$COMP(intactnew));
		$DOPRIVDIMS();
		$PRIV(offs) = 0;
		for(i=0; i<$COMP(intactnew); i++) {
			int parentdim = $COMP(corresp[i]);
			start = $COMP(start[i]); end = $COMP(end[i]);
			inc = $COMP(inc[i]);
			if(parentdim!=-1) {
				if(-start > $PARENT(dims[parentdim]) ||
				   -end > $PARENT(dims[parentdim])) {
					barf("Negative slice cannot start or end above limit");
                                }
				if(start < 0)
					start = $PARENT(dims[parentdim]) + start;
				if(end < 0)
					end = $PARENT(dims[parentdim]) + end;
				if(start >= $PARENT(dims[parentdim]) ||
				   end >= $PARENT(dims[parentdim])) {
					barf("Slice cannot start or end above limit");
				}
				if(sign(end-start)*sign(inc) < 0)
					inc = -inc;
				$PRIV(incs[i]) = $PARENT(dimincs[parentdim]) * inc;
				$PRIV(offs) += start * $PARENT(dimincs[parentdim]);
			} else {
				$PRIV(incs[i]) = 0;
			}
			$CHILD(dims[i]) = ((int)((end-start)/inc))+1;
                        if ($CHILD(dims[i]) <= 0)
                           barf("slice internal error: computed slice dimension must be positive");
		}
		for(i=$COMP(nthintact); i<$PARENT(ndims); i++) {
			int cdim = i - $COMP(nthintact) + $COMP(intactnew);
			$PRIV(incs[cdim]) = $PARENT(dimincs[i]);
			$CHILD(dims[cdim]) = $PARENT(dims[i]);
		}
		for(i=0; i<$COMP(nolddims); i++) {
			int oi = $COMP(oldind[i]);
			int wo = $COMP(whichold[i]);
			if(oi < 0)
				oi += $PARENT(dims[wo]);
			if( oi >= $PARENT(dims[wo]) )
				$CROAK("Cannot obliterate dimension after end");
			$PRIV(offs) += $PARENT(dimincs[wo])
					* oi;
		}
	/*
		for(i=0; i<$CHILD(ndims)-$PRIV(nnew); i++) {
			$CHILD(dims[i+$COMP(intactnew)]) =
				$PARENT(dims[i+$COMP(nthintact)]);
			$PRIV(incs[i+$COMP(intactnew)]) =
				$PARENT(dimincs[i+$COMP(nthintact)]);
		}
	*/
		$SETDIMS();
	',
);

pp_addpm(<<'EOD'

=head2 using

=for ref

Returns array of column numbers requested

=for usage

 line $pdl->using(1,2);

Plot, as a line, column 1 of C<$pdl> vs. column 2

=for example

 pdl> $pdl = rcols("file");
 pdl> line $pdl->using(1,2);

=cut

*using = \&PDL::using;
sub PDL::using {
  my ($x,@ind)=@_;
  @ind = list $ind[0] if (ref $ind[0] eq 'PDL');
  foreach (@ind) {
    $_ = $x->slice("($_)");
  }
  @ind;
}

EOD
);

pp_add_exported('', 'using');

pp_addhdr(<<END
static int cmp_pdll(const void *a_,const void *b_) {
	PDL_Long *a = (PDL_Long *)a_; PDL_Long *b=(PDL_Long *)b_;
	if(*a>*b) return 1;
	else if(*a==*b) return 0;
	else return -1;
}
END
);
	

pp_def( 'affine',
	P2Child => 1,
        NoPdlThread => 1,
	DefaultFlow => 1,
	Reversible => 1,
	AffinePriv => 1,
	GlobalNew => 'affine_new',
	OtherPars => 'int offspar; SV *dimlist; SV *inclist;',
	Comp => 'int nd; PDL_Long offset; PDL_Long sdims[$COMP(nd)];
		PDL_Long sincs[$COMP(nd)];',
	MakeComp => '
		int i,n2;
		PDL_Long *tmpi;
		PDL_Long *tmpd = PDL->packdims(dimlist,&($COMP(nd)));
		tmpi = PDL->packdims(inclist,&n2);		
		if ($COMP(nd) < 0) {
		      $CROAK("Affine: can not have negative no of dims");
		}
		if ($COMP(nd) != n2)
		      $CROAK("Affine: number of incs does not match dims");
		$DOCOMPDIMS();
		$COMP(offset) = offspar;
		for (i=0; i<$COMP(nd); i++) {
			$COMP(sdims)[i] = tmpd[i];
			$COMP(sincs)[i] = tmpi[i];
		}
		',
	RedoDims => '
		int i;
		$SETNDIMS($COMP(nd));
		$DOPRIVDIMS();
		$PRIV(offs) = $COMP(offset);
		for (i=0;i<$CHILD(ndims);i++) {
			$PRIV(incs)[i] = $COMP(sincs)[i];
			$CHILD(dims)[i] = $COMP(sdims)[i];
		}
		$SETDIMS();
		',
	Doc => undef,
);

=head2 diagonalI
=cut

pp_def(
	'diagonalI',
	P2Child => 1,
        NoPdlThread => 1,
	DefaultFlow => 1,
	Reversible => 1,
	AffinePriv => 1,
	OtherPars => 'SV *list',
	Comp => 'int nwhichdims; PDL_Long whichdims[$COMP(nwhichdims)];',
	MakeComp => '
		int i,j;
		PDL_Long *tmp= PDL->packdims(list,&($COMP(nwhichdims)));
		if($COMP(nwhichdims) < 1) {
			$CROAK("Diagonal: must have at least 1 dimension");
		}
		$DOCOMPDIMS();
		for(i=0; i<$COMP(nwhichdims); i++)
			$COMP(whichdims)[i] = tmp[i];
		qsort($COMP(whichdims), $COMP(nwhichdims), sizeof(PDL_Long),
			cmp_pdll);
	',
	RedoDims => '
		int nthp,nthc,nthd; int cd = $COMP(whichdims[0]);
		$SETNDIMS($PARENT(ndims)-$COMP(nwhichdims)+1);
		$DOPRIVDIMS();
		$PRIV(offs) = 0;
		if ($COMP(whichdims)[$COMP(nwhichdims)-1] >= $PARENT(ndims) ||
			$COMP(whichdims)[0] < 0)
			$CROAK("Diagonal: dim out of range");
		nthd=0; nthc=0;
		for(nthp=0; nthp<$PARENT(ndims); nthp++)
			if (nthd < $COMP(nwhichdims) &&
			    nthp == $COMP(whichdims)[nthd]) {
				if (!nthd) {
					$CHILD(dims)[cd] = $PARENT(dims)[cd];
					nthc++;
					$PRIV(incs)[cd] = 0;
				}
				if (nthd && $COMP(whichdims)[nthd] ==
				    $COMP(whichdims)[nthd-1])
				       $CROAK("Diagonal: dims must be unique");
				nthd++; /* advance pointer into whichdims */
				if($CHILD(dims)[cd] !=
				    $PARENT(dims)[nthp]) {
					$CROAK("Different dims %d and %d",
						$CHILD(dims)[cd],
						$PARENT(dims)[nthp]);
				}
				$PRIV(incs)[cd] += $PARENT(dimincs)[nthp];
			} else {
				$PRIV(incs)[nthc] = $PARENT(dimincs)[nthp];
				$CHILD(dims)[nthc] = $PARENT(dims)[nthp];
				nthc++;
			}
		$SETDIMS();
	',
	Doc => << 'EOD',
=for ref

Returns the multidimensional diagonal over the specified dimensions.

The diagonal is placed at the first (by number) dimension that is
diagonalized.
The other diagonalized dimensions are removed. So if C<$a> has dimensions
C<(5,3,5,4,6,5)> then after

=for example

 $b = $a->diagonal(0,2,5);

the piddle C<$b> has dimensions C<(5,3,4,6)> and 
C<$b-E<gt>at(2,1,0,1)> refers
to C<$a-E<gt>at(2,1,2,0,1,2)>.

NOTE: diagonal doesn't handle threadids correctly. XXX FIX
=cut
EOD
);

=head2 lags
=cut

pp_def(
	'lags',
	Doc => <<'EOD',
=for ref

Returns a piddle of lags to parent.

Usage:

=for usage

  $lags = $a->lags($nthdim,$step,$nlags);

I.e. if C<$a> contains

 [0,1,2,3,4,5,6,7]

then

=for example

 $b = $a->lags(0,2,2);

is a (5,2) matrix

 [2,3,4,5,6,7]
 [0,1,2,3,4,5]

This order of returned indices is kept because the function is
called "lags" i.e. the nth lag is n steps behind the original.

C<$step> and C<$nlags> must be positive. C<$nthdim> can be
negative and will then be counted from the last dim backwards
in the usual way (-1 = last dim).
=cut
EOD
	P2Child => 1,
        NoPdlThread => 1,
	DefaultFlow => 1,
	Reversible => 1, # XXX Not really
	AffinePriv => 1,
	OtherPars => 'int nthdim; int step; int n;',
	RedoDims => '
		int i;
		if ($PRIV(nthdim) < 0)  /* the usual conventions */
	           $PRIV(nthdim) = $PARENT(ndims) + $PRIV(nthdim);
		if ($PRIV(nthdim) < 0 || $PRIV(nthdim) >= $PARENT(ndims))
		   $CROAK("lags: dim out of range");
		if ($COMP(n) < 1)
		   $CROAK("lags: number of lags must be positive");
		if ($COMP(step) < 1)
		   $CROAK("lags: step must be positive");
		$PRIV(offs) = 0;
		$SETNDIMS($PARENT(ndims)+1);
		$DOPRIVDIMS();
		for(i=0; i<$PRIV(nthdim); i++) {
			$CHILD(dims)[i] = $PARENT(dims)[i];
			$PRIV(incs)[i] = $PARENT(dimincs)[i];
		}
		$CHILD(dims)[i] = $PARENT(dims)[i] - $COMP(step) * ($COMP(n)-1);
		if ($CHILD(dims)[i] < 1)
		  $CROAK("lags: product of step size and "
			 "number of lags too large");
		$CHILD(dims)[i+1] = $COMP(n);
		$PRIV(incs)[i] = ($PARENT(dimincs)[i]);
		$PRIV(incs)[i+1] = - $PARENT(dimincs)[i] * $COMP(step);
                $PRIV(offs) += ($CHILD(dims)[i+1] - 1) * (-$PRIV(incs)[i+1]);
		i++;
		for(; i<$PARENT(ndims); i++) {
			$CHILD(dims)[i+1] = $PARENT(dims)[i];
			$PRIV(incs)[i+1] = $PARENT(dimincs)[i];
		}
		$SETDIMS();
	'
);

=head2 splitdim
=cut

pp_def(
	'splitdim',
	Doc => <<'EOD',
=for ref

Splits a dimension in the parent piddle (opposite of L<clump|PDL::Core/clump>)

After

=for example

 $b = $a->splitdim(2,3);

the expression

 $b->at(6,4,x,y,3,6) == $a->at(6,4,x+3*y)

is always true (C<x> has to be less than 3).
=cut
EOD
	P2Child => 1,
        NoPdlThread => 1,
	DefaultFlow => 1,
	Reversible => 1, # XXX Not really
	OtherPars => 'int nthdim; int nsp;',
	AffinePriv => 1,
	RedoDims => '
		int i = $COMP(nthdim);
		int nsp = $COMP(nsp);
		if(nsp == 0) {die("Splitdim: Cannot split to 0\n");}
		if(i <0 || i >= $PARENT(ndims)) {
			die("Splitdim: nthdim (%d) must not be negative or greater or equal to number of dims (%d)\n",
				i, $PARENT(ndims));
		}
		if(nsp > $PARENT(dims[i])) {
			die("Splitdim: nsp (%d) cannot be greater than dim (%d)\n",
				nsp, $PARENT(dims[i]));
		}
		$PRIV(offs) = 0;
		$SETNDIMS($PARENT(ndims)+1);
		$DOPRIVDIMS();
		for(i=0; i<$PRIV(nthdim); i++) {
			$CHILD(dims)[i] = $PARENT(dims)[i];
			$PRIV(incs)[i] = $PARENT(dimincs)[i];
		}
		$CHILD(dims)[i] = $COMP(nsp);
		$CHILD(dims)[i+1] = $PARENT(dims)[i] / $COMP(nsp);
		$PRIV(incs)[i] = $PARENT(dimincs)[i];
		$PRIV(incs)[i+1] = $PARENT(dimincs)[i] * $COMP(nsp);
		i++;
		for(; i<$PARENT(ndims); i++) {
			$CHILD(dims)[i+1] = $PARENT(dims)[i];
			$PRIV(incs)[i+1] = $PARENT(dimincs)[i];
		}
		$SETDIMS();
	',
);

=head2 rotate
=cut

pp_def('rotate',
	Doc => <<'EOD',
=for ref

Shift vector elements along with wrap. Flows data back&forth.
=cut
EOD
 	Pars=>'x(n); int shift(); [oca]y(n)',
        DefaultFlow => 1,
        Reversible => 1,
        Code=>'
        int i,j;
        int n_size = $SIZE(n);
	if (n_size == 0)
          barf("can not shift zero size piddle (n_size is zero)");
        j = ($shift()) % n_size;
        if (j < 0)
                j += n_size;
        for(i=0; i<n_size; i++,j++) {
            if (j == n_size)
               j = 0;
            $y(n=>j) = $x(n=>i);
        }',
        BackCode=>'
        int i,j;
        int n_size = $SIZE(n);
        j = ($shift()) % n_size;
        if (j < 0)
                j += n_size;
        for(i=0; i<n_size; i++,j++) {
            if (j == n_size)
               j = 0;
            $x(n=>i) = $y(n=>j);
        }
        '
);

# This is a bit tricky. Hope I haven't missed any cases.

=head2 threadI
=cut

pp_def(
	'threadI',
	Doc => <<'EOD',
=for ref

internal

Put some dimensions to a threadid.

=for example

 $b = $a->threadI(0,1,5); # thread over dims 1,5 in id 1

=cut

EOD
	P2Child => 1,
        NoPdlThread => 1,
	DefaultFlow => 1,
	Reversible => 1,
	AffinePriv => 1,
	CallCopy => 0,  # Don't CallCopy for subclassed objects because PDL::Copy calls ThreadI
			#  (Wouldn't cause recursive loop otherwise)
	OtherPars => 'int id; SV *list',
	Comp => 'int id; int nwhichdims; PDL_Long whichdims[$COMP(nwhichdims)];
			int nrealwhichdims; ',
	MakeComp => '
		int i,j;
		PDL_Long *tmp= PDL->packdims(list,&($COMP(nwhichdims)));
		$DOCOMPDIMS();
		for(i=0; i<$COMP(nwhichdims); i++)
			$COMP(whichdims)[i] = tmp[i];
		$COMP(nrealwhichdims) = 0;
		for(i=0; i<$COMP(nwhichdims); i++) {
			for(j=i+1; j<$COMP(nwhichdims); j++)
				if($COMP(whichdims[i]) == $COMP(whichdims[j]) &&
				   $COMP(whichdims[i]) != -1) {
				$CROAK("Thread: duplicate arg %d %d %d",
					i,j,$COMP(whichdims[i]));
			}
			if($COMP(whichdims)[i] != -1) {
				$COMP(nrealwhichdims) ++;
			}
		}
		$COMP(id) = id;
		',
	RedoDims => '
		int nthc,i,j,flag;
		$SETNDIMS($PARENT(ndims));
		$DOPRIVDIMS();
		$PRIV(offs) = 0;
		nthc=0;
		for(i=0; i<$PARENT(ndims); i++) {
			flag=0;
			if($PARENT(nthreadids) > $COMP(id) && $COMP(id) >= 0 &&
			   i == $PARENT(threadids[$COMP(id)])) {
			   nthc += $COMP(nwhichdims);
			}
			for(j=0; j<$COMP(nwhichdims); j++) {
				if($COMP(whichdims[j] == i)) {flag=1; break;}
			}
			if(flag) {
				continue;
			}
			$CHILD(dims[nthc]) = $PARENT(dims[i]);
			$PRIV(incs[nthc]) = $PARENT(dimincs[i]);
			nthc++;
		}
		for(i=0; i<$COMP(nwhichdims); i++) {
			int cdim,pdim;
			cdim = i +
			 ($PARENT(nthreadids) > $COMP(id) && $COMP(id) >= 0?
			  $PARENT(threadids[$COMP(id)]) : $PARENT(ndims))
			  - $COMP(nrealwhichdims);
			pdim = $COMP(whichdims[i]);
			if(pdim == -1) {
				$CHILD(dims[cdim]) = 1;
				$PRIV(incs[cdim]) = 0;
			} else {
				$CHILD(dims[cdim]) = $PARENT(dims[pdim]);
				$PRIV(incs[cdim]) = $PARENT(dimincs[pdim]);
			}
		}
		$SETDIMS();
		PDL->reallocthreadids($CHILD_PTR(),
			($PARENT(nthreadids)<=$COMP(id) ?
				$COMP(id)+1 : $PARENT(nthreadids)));
		for(i=0; i<$CHILD(nthreadids); i++) {
			$CHILD(threadids[i]) =
			 ($PARENT(nthreadids) > i ?
			  $PARENT(threadids[i]) : $PARENT(ndims)) +
			 (i <= $COMP(id) ? - $COMP(nrealwhichdims) :
			  $COMP(nwhichdims) - $COMP(nrealwhichdims));
		}
		$CHILD(threadids[$CHILD(nthreadids)]) = $CHILD(ndims);
		',
);


=head2 identvaff
=cut

# we don't really need this one since it can be achieved with
# a ->threadI(-1,[])
pp_def('identvaff',
	P2Child => 1,
        NoPdlThread => 1,
	DefaultFlow => 1,
	Reversible => 1,
	AffinePriv => 1,
	RedoDims => '
		int i;
		$SETNDIMS($PARENT(ndims));
		$DOPRIVDIMS();
		$PRIV(offs) = 0;
		for(i=0; i<$PARENT(ndims); i++) {
			$CHILD(dims[i]) = $PARENT(dims[i]);
			$PRIV(incs[i]) = $PARENT(dimincs[i]);
		}
		$SETDIMS();
		$SETDELTATHREADIDS(0);
		$CHILD(threadids[$CHILD(nthreadids)]) = $CHILD(ndims);
		',
	Doc => <<'EOD',
=for ref

A vaffine identity transformation (includes thread_id copying).

Mainly for internal use.
=cut
EOD
);


=head2 unthread
=cut

pp_def(
	'unthread',
	Doc => <<'EOD',
=for ref

All threaded dimensions are made real again.

See [TBD Doc] for details and examples.
=cut
EOD
	P2Child => 1,
        NoPdlThread => 1,
	DefaultFlow => 1,
	Reversible => 1,
	AffinePriv => 1,
	OtherPars => 'int atind;',
	RedoDims => '
		int i;
		$SETNDIMS($PARENT(ndims));
		$DOPRIVDIMS();
		$PRIV(offs) = 0;
		for(i=0; i<$PARENT(ndims); i++) {
			int corc;
			if(i<$COMP(atind)) {
				corc = i;
			} else if(i < $PARENT(threadids[0])) {
				corc = i + $PARENT(ndims)-$PARENT(threadids[0]);
			} else {
				corc = i - $PARENT(threadids[0]) + $COMP(atind);
			}
			$CHILD(dims[corc]) = $PARENT(dims[i]);
			$PRIV(incs[corc]) = $PARENT(dimincs[i]);
		}
		$SETDIMS();
	',
);


pp_add_exported('', 'dice dice_axis');
pp_addpm(<<'EOD');

=head2 dice

=for ref

Dice rows/columns/planes out of a PDL using indexes for
each dimension.

This function can be used to extract irregular subsets
along many dimension of a PDL, e.g. only certain rows in an image,
or planes in a cube. This can of course be done with
the usual dimension tricks but this saves having to
figure it out each time!

This method is similar in functionality to the L<slice|/slice>
method, but L<slice|/slice> requires that contiguous ranges or ranges
with constant offset be extracted. ( i.e. L<slice|/slice> requires 
ranges of the form C<1,2,3,4,5> or C<2,4,6,8,10>). Because of this
restriction, L<slice|/slice> is more memory efficient and slightly faster
than dice

=for usage

 $slice = $data->dice([0,2,6],[2,1,6]); # Dicing a 2-D array

The arguments to dice are arrays (or 1D PDLs) for each dimension
in the PDL. These arrays are used as indexes to which rows/columns/cubes,etc
to dice-out (or extract) from the C<$data> PDL. 

Use C<X> to select all indices along a given dimension (compare also
L<mslice|PDL::Core/mslice>). As usual (in slicing methods) trailing
dimensions can be omitted implying C<X>'es for those.

=for example 

 pdl> $a = sequence(10,4)
 pdl> p $a
 [
  [ 0  1  2  3  4  5  6  7  8  9]
  [10 11 12 13 14 15 16 17 18 19]
  [20 21 22 23 24 25 26 27 28 29]
  [30 31 32 33 34 35 36 37 38 39]
 ]
 pdl> p $a->dice([1,2],[0,3]) # Select columns 1,2 and rows 0,3
 [
  [ 1  2]
  [31 32]
 ]
 pdl> p $a->dice(X,[0,3])
 [
  [ 0  1  2  3  4  5  6  7  8  9]
  [30 31 32 33 34 35 36 37 38 39]
 ]
 pdl> p $a->dice([0,2,5])
 [
  [ 0  2  5]
  [10 12 15]
  [20 22 25]
  [30 32 35]
 ]

As this is an index function, any modifications to the
slice change the parent (use the C<.=> operator).

=cut

sub PDL::dice { 

	my $self = shift;
	my @dim_indexes = @_;  # array of dimension indexes
	
	# Check that the number of dim indexes <=
	#    number of dimensions in the PDL
	my $no_indexes = scalar(@dim_indexes);
	my $noDims = $self->getndims;
	barf("PDL::dice: Number of index arrays ($no_indexes) not equal to the dimensions of the PDL ($noDims")
			 if $no_indexes > $noDims;
	my $index;
	my $pdlIndex;
	my $outputPDL=$self;
	my $indexNo = 0;

	# Go thru each index array and dice the input PDL:
	foreach $index(@dim_indexes){
		$outputPDL = $outputPDL->dice_axis($indexNo,$index)
			unless !ref $index && $index eq 'X';

		$indexNo++;
	}

	return $outputPDL;
}  
*dice = \&PDL::dice;


=head2 dice_axis

=for ref

Dice rows/columns/planes from a single PDL axis (dimension)
using index along a specified axis

This function can be used to extract irregular subsets
along any dimension, e.g. only certain rows in an image,
or planes in a cube. This can of course be done with
the usual dimension tricks but this saves having to
figure it out each time!

=for usage

 $slice = $data->dice_axis($axis,$index);

=for example

 pdl> $a = sequence(10,4)
 pdl> $idx = pdl(1,2)
 pdl> p $a->dice_axis(0,$idx) # Select columns
 [
  [ 1  2]
  [11 12]
  [21 22]
  [31 32]
 ]
 pdl> $t = $a->dice_axis(1,$idx) # Select rows
 pdl> $t.=0
 pdl> p $a
 [
  [ 0  1  2  3  4  5  6  7  8  9]
  [ 0  0  0  0  0  0  0  0  0  0]
  [ 0  0  0  0  0  0  0  0  0  0]
  [30 31 32 33 34 35 36 37 38 39]
 ]

The trick to using this is that the index selects
elements along the dimensions specified, so if you
have a 2D image C<axis=0> will select certain C<X> values
- i.e. extract columns

As this is an index function, any modifications to the
slice change the parent.

=cut

sub PDL::dice_axis { 
  my($self,$axis,$idx) = @_;
  
  # Convert to PDLs: array refs using new, otherwise use topdl:
  my $ix = (ref($idx) eq 'ARRAY') ? ref($self)->new($idx) : ref($self)->topdl($idx);
  my $n = $self->getndims;
  my $a = $ix->getndims;
  barf("index_axis: index must be <=1D") if $a>1;
  for ($a..$n-1) {
     $ix = $ix->dummy(0);
  }
  	
  return $self->mv($axis,0)->index($ix)->mv($n-1,$axis);
}  
*dice_axis = \&PDL::dice_axis;


EOD

pp_done();
__DATA__

# A very useful transformation for e.g. axis values: hexagonal
# arrays can be made like this.

if(0) {
deftrans(
	Name => 'repeat',
	Pars => 'int whichind, int howmany',
	MakeComp => '
		$COMP(howmany) = howmany;
		$COMP(whichind) = whichind;
		$SETREVERSIBLE($COMP(howmany)==1);
		',
	Dims => '
		$SETNDIMS($PARENT(ndims));
		LOOPDIMS %{
			$CHILD(dims[$DIM]) = $PARENT(dims[$DIM]);
		%}
		$CHILD(dims[$COMP(whichind)]) *= $PRIV(howmany);
		$SETDIMS();
		',
	ParentInds =>
		'$COPYINDS();
		 $PARENTINDS($COMP(whichind)) %= $PARENT(dims[$PRIV(whichind)]);',
	Print => 'printf("REPEAT: %d, %d\n",
			$COMP(whichind), $COMP(howmany));'
);
}

# Parent's first index is value of indices.

if(0) {
deftrans(
	Name => 'indexed',
	Pars => 'pdl* indices',
	Dims => '
		$SETNDIMS($COMP(indices)->ndims);
		LOOPDIMS %{
			$CHILD(dims[$DIM]) = $COMP(indices)->dims[$DIM];
		%}
		',
	ParentInds =>
		'$COPYINDS();
		 $PARENTINDS(0) = PDL->get($COMP(indices),&($MYINDS(0)));'
);
}

pp_addpm({At => 'Bot'},<< 'EOD');

=head1 BUGS 

For the moment, you can't slice the empty piddle.  This should probably
change:  slices of the empty piddle should probably return the empty piddle.

Many types of index errors are reported far from the indexing
operation that caused them.  This is caused by the underlying architecture:
slice() sets up a mapping between variables, but that mapping isn't 
tested for correctness until it is used (potentially much later).

=head1 AUTHOR

Copyright (C) 1997 Tuomas J. Lukka.  Contributions by
Craig DeForest, deforest@boulder.swri.edu.
Documentation contributions by David Mertens.
All rights reserved. There is no warranty. You are allowed
to redistribute this software / documentation under certain
conditions. For details, see the file COPYING in the PDL
distribution. If this file is separated from the PDL distribution,
the copyright notice should be included in the file.

=cut

EOD