What are bad values and why should I bother with them?

Sometimes it's useful to be able to specify a certain value is 'bad' or 'missing'; for example CCDs used in astronomy produce 2D images which are not perfect since certain areas contain invalid data due to imperfections in the detector. Whilst PDL's powerful index routines and all the complicated business with dataflow, slices, etc etc mean that these regions can be ignored in processing, it's awkward to do. It would be much easier to be able to say "$c = $x + $y" and leave all the hassle to the computer.

If you're not interested in this, then you may (rightly) be concerned with how this affects the speed of PDL, since the overhead of checking for a bad value at each operation can be large. Because of this, the code has been written to be as fast as possible - particularly when operating on piddles which do not contain bad values. In fact, you should notice essentially no speed difference when working with piddles which do not contain bad values.

However, if you do not want bad values, then PDL's "WITH_BADVAL" configuration option comes to the rescue; if set to 0 or undef, the bad-value support is ignored. About the only time I think you'll need to use this - I admit, I'm biased ;) - is if you have limited disk or memory space, since the size of the code is increased (see below).

You may also ask 'well, my computer supports IEEE NaN, so I already have this'. Well, yes and no - many routines, such as "y=sin(x)", will propagate NaN's without the user having to code differently, but routines such as "qsort", or finding the median of an array, need to be re-coded to handle bad values. For floating-point datatypes, "NaN" and "Inf" are used to flag bad values IF the option "BADVAL_USENAN" is set to 1 in your config file. Otherwise special values are used (Default bad values). I do not have any benchmarks to see which option is faster.

There is an experimental feature "BADVAL_PER_PDL" which, if set, allows you to have different bad values for separate piddles of the same type. This currently does not work with the "BADVAL_USENAN" option; if both are set then PDL will ignore the "BADVAL_USENAN" value.

Code increase due to bad values

The following comparison is out of date!

On an i386 machine running Linux and Perl 5.005_03, I measured the following sizes (the Slatec code was compiled in, but none of the other options: e.g., FFTW, GSL, and TriD were):

WITH_BADVAL = 0

Size of blib directory after a successful make = 4963 kb: blib/arch = 2485 kb and blib/lib = 1587 kb.

WITH_BADVAL = 1

Size of blib directory after a successful make = 5723 kb: blib/arch = 3178 kb and blib/lib = 1613 kb.

So, the overall increase is only 15% - not much to pay for all the wonders that bad values provides ;)

The source code used for this test had the vast majority of the core routines (eg those in Basic/) converted to use bad values, whilst very few of the 'external' routines (i.e. everything else in the PDL distribution) had been changed.

A quick overview

 pdl> p $PDL::Bad::Status
 1
 pdl> $x = sequence(4,3);
 pdl> p $x
 [
  [ 0  1  2  3]
  [ 4  5  6  7]
  [ 8  9 10 11]
 ]
 pdl> $x = $x->setbadif( $x % 3 == 2 )
 pdl> p $x
 [
  [  0   1 BAD   3]
  [  4 BAD   6   7]
  [BAD   9  10 BAD]
 ]
 pdl> $x *= 3
 pdl> p $x
 [
  [  0   3 BAD   9]
  [ 12 BAD  18  21]
  [BAD  27  30 BAD]
 ]
 pdl> p $x->sum
 120

"demo bad" and "demo bad2" within perldl or pdl2 gives a demonstration of some of the things possible with bad values. These are also available on PDL's web-site, at http://pdl.perl.org/demos/. See PDL::Bad for useful routines for working with bad values and t/bad.t to see them in action.

The intention is to:

• not significantly affect PDL for users who don't need bad value support
• be as fast as possible when bad value support is installed

If you never want bad value support, then you set "WITH_BADVAL" to 0 in perldl.conf; PDL then has no bad value support compiled in, so will be as fast as it used to be.

However, in most cases, the bad value support has a negligible affect on speed, so you should set "WITH_CONFIG" to 1! One exception is if you are low on memory, since the amount of code produced is larger (but only by about 15% - see "Code increase due to bad values").

To find out if PDL has been compiled with bad value support, look at the values of either $PDL::Config{WITH_BADVAL} or $PDL::Bad::Status - if true then it has been.

To find out if a routine supports bad values, use the "badinfo" command in perldl or pdl2 or the "-b" option to pdldoc. This facility is currently a 'proof of concept' (or, more realistically, a quick hack) so expect it to be rough around the edges.

Each piddle contains a flag - accessible via "$pdl->badflag" - to say whether there's any bad data present:

• If false/0, which means there's no bad data here, the code supplied by the "Code" option to "pp_def()" is executed. This means that the speed should be very close to that obtained with "WITH_BADVAL=0", since the only overhead is several accesses to a bit in the piddles state variable.
• If true/1, then this says there MAY be bad data in the piddle, so use the code in the "BadCode" option (assuming that the "pp_def()" for this routine has been updated to have a BadCode key). You get all the advantages of threading, as with the "Code" option, but it will run slower since you are going to have to handle the presence of bad values.

If you create a piddle, it will have its bad-value flag set to 0. To change this, use "$pdl->badflag($new_bad_status)", where $new_bad_status can be 0 or 1. When a routine creates a piddle, its bad-value flag will depend on the input piddles: unless over-ridden (see the "CopyBadStatusCode" option to "pp_def"), the bad-value flag will be set true if any of the input piddles contain bad values. To check that a piddle really contains bad data, use the "check_badflag" method.

NOTE: propagation of the badflag

If you change the badflag of a piddle, this change is propagated to all the children of a piddle, so

   pdl> $x = zeroes(20,30);
   pdl> $y = $x->slice('0:10,0:10');
   pdl> $c = $y->slice(',(2)');
   pdl> print ">>c: ", $c->badflag, "\n";
   >>c: 0
   pdl> $x->badflag(1);
   pdl> print ">>c: ", $c->badflag, "\n";
   >>c: 1

No change is made to the parents of a piddle, so

   pdl> print ">>a: ", $x->badflag, "\n";
   >>a: 1
   pdl> $c->badflag(0);
   pdl> print ">>a: ", $x->badflag, "\n";
   >>a: 1

Thoughts:

• the badflag can ONLY be cleared IF a piddle has NO parents, and that this change will propagate to all the children of that piddle. I am not so keen on this anymore (too awkward to code, for one).
• "$x->badflag(1)" should propagate the badflag to BOTH parents and children.

This shouldn't be hard to implement (although an initial attempt failed!). Does it make sense though? There's also the issue of what happens if you change the badvalue of a piddle - should these propagate to children/parents (yes) or whether you should only be able to change the badvalue at the 'top' level - i.e. those piddles which do not have parents.

The "orig_badvalue()" method returns the compile-time value for a given datatype. It works on piddles, PDL::Type objects, and numbers - eg

  $pdl->orig_badvalue(), byte->orig_badvalue(), and orig_badvalue(4).

It also has a horrible name...

To get the current bad value, use the "badvalue()" method - it has the same syntax as "orig_badvalue()".

To change the current bad value, supply the new number to badvalue - eg

  $pdl->badvalue(2.3), byte->badvalue(2), badvalue(5,-3e34).

Note: the value is silently converted to the correct C type, and returned - i.e. "byte->badvalue(-26)" returns 230 on my Linux machine. It is also a "nop" for floating-point types when "BADVAL_USENAN" is true.

Note that changes to the bad value are NOT propagated to previously-created piddles - they will still have the bad value set, but suddenly the elements that were bad will become 'good', but containing the old bad value. See discussion below. It's not a problem for floating-point types which use NaN, since you can not change their badvalue.

Bad values and boolean operators

For those boolean operators in PDL::Ops, evaluation on a bad value returns the bad value. Whilst this means that

 $mask = $img > $thresh;

correctly propagates bad values, it will cause problems for checks such as

 do_something() if any( $img > $thresh );

which need to be re-written as something like

 do_something() if any( setbadtoval( ($img > $thresh), 0 ) );

When using one of the 'projection' functions in PDL::Ufunc - such as orover - bad values are skipped over (see the documentation of these functions for the current (poor) handling of the case when all elements are bad).

A bad value for each piddle, and related issues

An experimental option "BADVAL_PER_PDL" has been added to perldl.conf to allow per-piddle bad values. The documentation has not been updated to account for this change.

The following is relevant only for integer types, and for floating-point types if "BADVAL_USENAN" was not set when PDL was built.

Currently, there is one bad value for each datatype. The code is written so that we could have a separate bad value for each piddle (stored in the pdl structure) - this would then remove the current problem of:

 pdl> $x = byte( 1, 2, byte->badvalue, 4, 5 );
 pdl> p $x;
 [1 2 255 4 5]
 pdl> $x->badflag(1)
 pdl> p $x;
 [1 2 BAD 4 5]
 pdl> byte->badvalue(0);
 pdl> p $x;
 [1 2 255 4 5]

ie the bad value in $a has lost its bad status using the current implementation. It would almost certainly cause problems elsewhere though!

Why not make a PDL subclass?

The support for bad values could have been done as a PDL sub-class. The advantage of this approach would be that you only load in the code to handle bad values if you actually want to use them. The downside is that the code then gets separated: any bug fixes/improvements have to be done to the code in two different files. With the present approach the code is in the same "pp_def" function (although there is still the problem that both "Code" and "BadCode" sections need updating).

Default bad values

The default/original bad values are set to (taken from the Starlink distribution):

  #include <limits.h>
  PDL_Byte    ==  UCHAR_MAX
  PDL_Short   ==   SHRT_MIN
  PDL_Ushort  ==  USHRT_MAX
  PDL_Long    ==    INT_MIN

If "BADVAL_USENAN == 0", then we also have

  PDL_Float   ==   -FLT_MAX
  PDL_Double  ==   -DBL_MAX

otherwise all of "NaN", "+Inf", and "-Inf" are taken to be bad for floating-point types. In this case, the bad value can't be changed, unlike the integer types.

How do I change a routine to handle bad values?

Examples can be found in most of the *.pd files in Basic/ (and hopefully many more places soon!). Some of the logic might appear a bit unclear - that's probably because it is! Comments appreciated.

All routines should automatically propagate the bad status flag to output piddles, unless you declare otherwise.

If a routine explicitly deals with bad values, you must provide this option to pp_def:

   HandleBad => 1

This ensures that the correct variables are initialised for the $ISBAD etc macros. It is also used by the automatic document-creation routines to provide default information on the bad value support of a routine without the user having to type it themselves (this is in its early stages).

To flag a routine as NOT handling bad values, use

   HandleBad => 0

This should cause the routine to print a warning if it's sent any piddles with the bad flag set. Primitive's "intover" has had this set - since it would be awkward to convert - but I've not tried it out to see if it works.

If you want to handle bad values but not set the state of all the output piddles, or if it's only one input piddle that's important, then look at the PP rules "NewXSFindBadStatus" and "NewXSCopyBadStatus" and the corresponding "pp_def" options:

FindBadStatusCode

By default, "FindBadStatusCode" creates code which sets "$PRIV(bvalflag)" depending on the state of the bad flag of the input piddles: see "findbadstatus" in Basic/Gen/PP.pm. User-defined code should also store the value of "bvalflag" in the "$BADFLAGCACHE()" variable.

CopyBadStatusCode

The default code here is a bit simpler than for "FindBadStatusCode": the bad flag of the output piddles are set if "$BADFLAGCACHE()" is true after the code has been evaluated. Sometimes "CopyBadStatusCode" is set to an empty string, with the responsibility of setting the badflag of the output piddle left to the "BadCode" section (e.g. the "xxxover" routines in Basic/Primitive/primitive.pd).

Prior to PDL 2.4.3 we used "$PRIV(bvalflag)" instead of "$BADFLAGCACHE()". This is dangerous since the "$PRIV()" structure is not guaranteed to be valid at this point in the code.

If you have a routine that you want to be able to use as in-place, look at the routines in bad.pd (or ops.pd) which use the "in-place" option to see how the bad flag is propagated to children using the "xxxBadStatusCode" options. I decided not to automate this as rules would be a little complex, since not every in-place op will need to propagate the badflag (eg unary functions).

If the option

   HandleBad => 1

is given, then many things happen. For integer types, the readdata code automatically creates a variable called "<pdl name>_badval", which contains the bad value for that piddle (see "get_xsdatapdecl()" in Basic/Gen/PP/PdlParObjs.pm). However, do not hard code this name into your code! Instead use macros (thanks to Tuomas for the suggestion):

  '$ISBAD(a(n=>1))'  expands to '$a(n=>1) == a_badval'
  '$ISGOOD(a())'                '$a()     != a_badval'
  '$SETBAD(bob())'              '$bob()    = bob_badval'

well, the "$a(...)" is expanded as well. Also, you can use a "$" before the pdl name, if you so wish, but it begins to look like line noise - eg "$ISGOOD($a())".

If you cache a piddle value in a variable -- eg "index" in slices.pd -- the following routines are useful:

   '$ISBADVAR(c_var,pdl)'       'c_var == pdl_badval'
   '$ISGOODVAR(c_var,pdl)'      'c_var != pdl_badval'
   '$SETBADVAR(c_var,pdl)'      'c_var  = pdl_badval'

The following have been introduced, They may need playing around with to improve their use.

  '$PPISBAD(CHILD,[i])          'CHILD_physdatap[i] == CHILD_badval'
  '$PPISGOOD(CHILD,[i])         'CHILD_physdatap[i] != CHILD_badval'
  '$PPSETBAD(CHILD,[i])         'CHILD_physdatap[i]  = CHILD_badval'

If "BADVAL_USENAN" is set, then it's a bit different for "float" and "double", where we consider "NaN", "+Inf", and "-Inf" all to be bad. In this case:

  ISBAD   becomes   finite(piddle) == 0
  ISGOOD            finite(piddle) != 0
  SETBAD            piddle          = NaN

where the value for NaN is discussed below in Handling NaN values.

This all means that you can change

   Code => '$a() = $b() + $c();'

to

   BadCode => 'if ( $ISBAD(b()) || $ISBAD(c()) ) { 
                 $SETBAD(a()); 
               } else {
                 $a() = $b() + $c();
               }'

leaving Code as it is. PP::PDLCode will then create a loop something like

   if ( __trans->bvalflag ) {
        threadloop over BadCode
   } else { 
        threadloop over Code
   }

(it's probably easier to just look at the .xs file to see what goes on).

Going beyond the Code section

Similar to "BadCode", there's "BadBackCode", and "BadRedoDimsCode".

Handling "EquivCPOffsCode" is a bit different: under the assumption that the only access to data is via the "$EQUIVCPOFFS(i,j)" macro, then we can automatically create the 'bad' version of it; see the "[EquivCPOffsCode]" and "[Code]" rules in PDL::PP.

Macro access to the bad flag of a piddle

Macros have been provided to provide access to the bad-flag status of a pdl:

  '$PDLSTATEISBAD(a)'    -> '($PDL(a)->state & PDL_BADVAL) > 0'
  '$PDLSTATEISGOOD(a)'      '($PDL(a)->state & PDL_BADVAL) == 0'
  '$PDLSTATESETBAD(a)'      '$PDL(a)->state |= PDL_BADVAL'
  '$PDLSTATESETGOOD(a)'     '$PDL(a)->state &= ~PDL_BADVAL'

For use in "xxxxBadStatusCode" (+ other stuff that goes into the INIT: section) there are:

  '$SETPDLSTATEBAD(a)'       -> 'a->state |= PDL_BADVAL'
  '$SETPDLSTATEGOOD(a)'      -> 'a->state &= ~PDL_BADVAL'
  '$ISPDLSTATEBAD(a)'        -> '((a->state & PDL_BADVAL) > 0)'
  '$ISPDLSTATEGOOD(a)'       -> '((a->state & PDL_BADVAL) == 0)'

In PDL 2.4.3 the "$BADFLAGCACHE()" macro was introduced for use in "FindBadStatusCode" and "CopyBadStatusCode".

Handling NaN values

There are two issues:

NaN as the bad value

which is done. To select, set "BADVAL_USENAN" to 1 in perldl.conf; a value of 0 falls back to treating the floating-point types the same as the integers. I need to do some benchmarks to see which is faster, and whether it's dependent on machines (Linux seems to slow down much more than my Sparc machine in some very simple tests I did).

Ignoring BadCode sections

which is not.

For simple routines processing floating-point numbers, we should let the computer process the bad values (i.e. "NaN" and "Inf" values) instead of using the code in the "BadCode" section. Many such routines have been labeled using "NoBadifNaN => 1"; however this is currently ignored by PDL::PP.

For these routines, we want to use the "Code" section if

  the piddle does not have its bad flag set
  the datatype is a float or double

otherwise we use the "BadCode" section. This is NOT IMPLEMENTED, as it will require reasonable hacking of PP::PDLCode!

There's also the problem of how we handle 'exceptions' - since "$x = pdl(2) / pdl(0)" produces a bad value but doesn't update the badflag value of the piddle. Can we catch an exception, or do we have to trap for this (e.g. search for "exception" in Basic/Ops/ops.pd)?

Checking for "Nan", and "Inf" is done by using the "finite()" system call. If you want to set a value to the "NaN" value, the following bit of code can be used (this can be found in both Basic/Core/Core.xs.PL and Basic/Bad/bad.pd):

  /* for big-endian machines */
  static union { unsigned char __c[4]; float __d; } 
        __pdl_nan = { { 0x7f, 0xc0, 0, 0 } };
  /* for little-endian machines */
  static union { unsigned char __c[4]; float __d; } 
        __pdl_nan = { { 0, 0, 0xc0, 0x7f } };

This approach should probably be replaced by library routines such as "nan("")" or "atof("NaN")".

To find out whether a particular machine is big endian, use the routine "PDL::Core::Dev::isbigendian()".

Trapping invalid mathematical operations

Should we add exceptions to the functions in "PDL::Ops" to set the output bad for out-of-range input values?

 pdl> p log10(pdl(10,100,-1))

I would like the above to produce "[1 2 BAD]", but this would slow down operations on all piddles. We could check for "NaN"/"Inf" values after the operation, but I doubt that would be any faster.

Integration with NaN

When "BADVAL_USENAN" is true, the routines in "PDL::Ops" should just fall through to the "Code" section - i.e. don't use "BadCode" - for "float" and "double" data types.

Global versus per-piddle bad values

I think all that's needed is to change the routines in "Basic/Core/pdlconv.c.PL", although there's bound to be complications. It would also mean that the pdl structure would need to have a variable to store its bad value, which would mean binary incompatibility with previous versions of PDL with bad value support.

As of 17 March 2006, PDL contains the experimental "BADVAL_PER_PDL" configuration option which, if selected, adds per-piddle bad values.

Dataflow of the badflag

Currently changes to the bad flag are propagated to the children of a piddle, but perhaps they should also be passed on to the parents as well. With the advent of per-piddle bad values we need to consider how to handle changes to the value used to represent bad items too.