- NAME
- DESCRIPTION

- What are bad values and why should I bother with them?
- Code increase due to bad values
- A quick overview
- Bad values and boolean operators
- A bad value for each piddle, and related issues

- IMPLEMENTATION DETAILS

- Why not make a PDL subclass?
- Default bad values
- How do I change a routine to handle bad values?
- Going beyond the Code section
- Macro access to the bad flag of a piddle
- Handling NaN values

- WHAT ABOUT DOCUMENTATION?
- CURRENT ISSUES

- Trapping invalid mathematical operations
- Integration with NaN
- Global versus per-piddle bad values
- Dataflow of the badflag

- EVERYTHING ELSE
- TODO/SUGGESTIONS
- AUTHOR

# NAME

PDL::BadValues - Discussion of bad value support in PDL

# DESCRIPTION

## 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 = $a + $b` 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 propogate 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.

## Code increase due to bad values

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: eg Karma, FFTW, GSL, and 3d 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 (ie everything else in the PDL distribution) had been changed.

## A quick overview

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

`demo bad` and `demo bad2` within perldl 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 the PDL::Bad manpage 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 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, it's 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: propogation of the badflag

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

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

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

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

Thoughts:

- the badflag can ONLY be cleared IF a piddle has NO parents, and that this change will propogate to all the children of that piddle. I am not so keen on this anymore (too awkward to code, for one).

- `$a->badflag(1)` should propogate 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 propogate to children/parents (yes) or whether you should only be able to change the badvalue at the 'top' level - ie 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 - ie `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 propogated 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, since you can't 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 propogates 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

The following is relevant only for integer types, where there is a choice of value to use as the bad flag.

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:

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

# IMPLEMENTATION DETAILS

During a `perl Makefile.PL`, the file Basic/Core/badsupport.p is created; this file contains the values of the `WITH_BADVAL` and `BADVAL_USENAN` variables, and should be used by code that is executed before the PDL::Config file is created (e.g. Basic/Core/pdlcore.c.PL. However, most PDL code will just need to access the `%PDL::Config` array (e.g. Basic/Bad/bad.pd) to find out whether bad-value support is required.

A new flag has been added to the state of a piddle - `PDL_BADVAL`. If unset, then the piddle does not contain bad values, and so all the support code can be ignored. If set, it does not guarantee that bad values are present, just that they should be checked for. Thanks to Christian, `badflag()` - which sets/clears this flag (see Basic/Bad/bad.pd) - will update ALL the children/grandchildren/etc of a piddle if its state changes (see `badflag` in Basic/Bad/bad.pd and `propogate_badflag` in Basic/Core/Core.xs.PL). It's not clear what to do with parents: I can see the reason for propogating a 'set badflag' request to parents, but I think a child should NOT be able to clear the badflag of a parent. There's also the issue of what happens when you change the bad value for a piddle.

The `pdl_trans` structure has been extended to include an integer value, `bvalflag`, which acts as a switch to tell the code whether to handle bad values or not. This value is set if any of the input piddles have their `PDL_BADVAL` flag set (although this code can be replaced by setting `FindBadStateCode` in pp_def). The logic of the check is going to get a tad more complicated if I allow routines to fall back to using the `Code` section for floating-point types (ie those routines with `NoBadifNaN => 1` when `BADVAL_USENAN` is true).

The bad values for the integer types are now stored in a structure within the Core PDL structure - `PDL.bvals` (eg Basic/Core/pdlcore.h.PL); see also `typedef badvals` in Basic/Core/pdl.h.PL and the BOOT code of Basic/Core/Core.xs.PL where the values are initialised to (hopefully) sensible values. See PDL/Bad/bad.pd for read/write routines to the values.

All this means that the internals of PDL are not binary compatible with PDL 2.1.1 and earlier; external modules will need to be recompiled.

## 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 propogate 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 `__privtrans->bvalflag` depending on the state of the bad flag of the input piddles: see `findbadstatus` in Basic/Gen/PP.pm.

CopyBadStatusCode
  The default code here is a bit simpler than for `FindBadStatusCode`: the bad flag of the output piddles are set if `__privtrans->bvalflag` 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).

If you have a routine that you want to be able to use as inplace, look at the routines in bad.pd (or ops.pd) which use the `Inplace` option to see how the bad flag is propogated to children using the `xxxBadStatusCode` options. I decided not to automate this as rules would be a little complex, since not every inplace op will need to propogate 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 the PDL::PP manpage.

## 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)'

## 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 (ie `NaN` and `Inf` values) instead of using the code in the `BadCode` section. Many such routines have been labelled 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 `$a = 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 } };

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

# WHAT ABOUT DOCUMENTATION?

One of the strengths of PDL is it's on-line documentation. The aim is to use this system to provide informtion on how/if a routine supports bad values: in many cases `pp_def()` contains all the information anyway, so the function-writer doesn't need to do anything at all! For the cases when this is not sufficient, there's the `BadDoc` option. For code written at the perl level - ie in a .pm file - use the `=for bad` pod directive.

This information will be available via man/pod2man/html documenation. It's also accessible from the `perldl` shell - using the `badinfo` command - and the `pdldoc` shell command - using the `-b` option.

This support is at a very early stage - ie not much thought has gone into it: comments are welcome; improvements to the code preferred ;) One awkward problem is for *.pm code: you have to write a *.pm.PL file which only inserts the `=for bad` directive (+ text) if bad value support is compiled in. In fact, this is a pain when handling bad values at the perl, rather than PDL::PP, level: perhaps I should just scrap the `WITH_BADVAL` option...

# CURRENT ISSUES

There are a number of areas that need work, user input, or both! They are mentioned elsewhere in this document, but this is just to make sure they don't get lost.

## 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?

     perldl> 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 - ie 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 incompatability with previous versions of PDL with bad value support.

## Dataflow of the badflag

Currently changes to the bad flag are propogated to the children of a piddle, but perhaps they should also be passed on to the parents as well.

# EVERYTHING ELSE

The build process has been affected. The following files are now created during the build:

      Basic/Core/pdlcore.h      pdlcore.h.PL
                 pdlcore.c      pdlcore.c.PL
                 pdlapi.c       pdlapi.c.PL
                 Core.xs        Core.xs.PL
                 Core.pm        Core.pm.PL

Several new files have been added:

      Basic/Pod/Badvalues.pod (ie this file)

      t/bad.t

      Basic/Bad/
      Basic/Bad/Makefile.PL
                bad.pd

      IO/NDF/NDF.xs.PL

etc

# TODO/SUGGESTIONS

- Look at using per-piddle bad values. Would mean a change to the pdl structure (ie binary incompatability) and the routines in `Basic/Core/pdlconv.c.PL` would need changing to handle this. Most other routines should not need to be changed ...

- what to do about `$b = pdl(-2); $a = log10($b)` - `$a` should be set bad, but it currently isn't.

- Allow the operations in PDL::Ops to skip the check for bad values when using NaN as a bad value and processing a floating-point piddle. Needs a fair bit of work to PDL::PP::PDLCode.

- `$pdl->baddata()` now updates all the children of this piddle as well. However, not sure what to do with parents, since:

        $b = $a->slice();
        $b->baddata(0)

  doesn't mean that `$a` shouldn't have it's badvalue cleared. however, after

        $b->baddata(1)

  it's sensible to assume that the parents now get flagged as containing bad values.

  PERHAPS you can only clear the bad value flag if you are NOT a child of another piddle, whereas if you set the flag then all children AND parents should be set as well?

  Similarly, if you change the bad value in a piddle, should this be propogated to parent & children? Or should you only be able to do this on the 'top-level' piddle? Nasty...

- get some code set up to do benchmarks to see how much things are slowed down (and to check that I haven't messed things up if `WITH_BADVAL` is 0/undef).

- some of the names aren't appealing - I'm thinking of `orig_badvalue()` in Basic/Bad/bad.pd in particular. Any suggestions appreciated.

# AUTHOR

Copyright (C) Doug Burke (burke@ifa.hawaii.edu), 2000. Commercial reproduction of this documentation in a different format is forbidden.