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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 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The following comparison is out of date!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> $a = sequence(4,3);
pdl> p $a
[
[ 0 1 2 3]
[ 4 5 6 7]
[ 8 9 10 11]
]
pdl> $a = $a->setbadif( $a % 3 == 2 )
pdl> p $a
[
[ 0 1 BAD 3]
[ 4 BAD 6 7]
[BAD 9 10 BAD]
]
pdl> $a *= 3
pdl> p $a
[
[ 0 3 BAD 9]
[ 12 BAD 18 21]
[BAD 27 30 BAD]
]
pdl> p $a->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: propogation of the badflag

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

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

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

pdl> print ">>a: ", $a->badflag, "\n";
>>a: 1
pdl> $c->badflag(0);
pdl> 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
propagate 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 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> $a = byte( 1, 2, byte->badvalue, 4, 5 );
pdl> p $a;
[1 2 255 4 5]
pdl> $a->badflag(1)
pdl> p $a;
[1 2 BAD 4 5]
pdl> byte->badvalue(0);
pdl> 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", "BADVAL_USENAN" and "BADVAL_PER_PDL" 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 "propagate_badflag" in Basic/Core/Core.xs.PL). It's not
clear what to do with parents: I can see the reason for propagating 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 (i.e. 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.

The addition of the "BADVAL_PER_PDL" option has resulted in additional changes to the
internals of piddles. These changes are not documented yet.

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 "$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 } };

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()".

WHAT ABOUT DOCUMENTATION?

One of the strengths of PDL is its on-line documentation. The aim is to use this system to
provide information 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 - i.e. in a .pm file - use the "=for bad" pod directive.

This information will be available via man/pod2man/html documentation. It's also
accessible from the "perldl" or "pdl2" shells - using the "badinfo" command - and the
"pdldoc" shell command - using the "-b" option.

This support is at a very early stage - i.e. 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?

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.

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 (i.e. this file)

t/bad.t

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

etc

TODO/SUGGESTIONS

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

See the experimental "BADVAL_PER_PDL" option.

· 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 its 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 propagated 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.

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