package Set::Infinite;
# Copyright (c) 2001, 2002, 2003, 2004 Flavio Soibelmann Glock.
# All rights reserved.
# This program is free software; you can redistribute it and/or
# modify it under the same terms as Perl itself.
use 5.005_03;
# These methods are inherited from Set::Infinite::Basic "as-is":
# type list fixtype numeric min max integer real new span copy
# start_set end_set universal_set empty_set minus difference
# symmetric_difference is_empty
use strict;
use base qw(Set::Infinite::Basic Exporter);
use Carp;
use Set::Infinite::Arithmetic;
use overload
'<=>' => \&spaceship,
'""' => \&as_string;
use vars qw(@EXPORT_OK $VERSION
$TRACE $DEBUG_BT $PRETTY_PRINT $inf $minus_inf $neg_inf
%_first %_last %_backtrack
$too_complex $backtrack_depth
$max_backtrack_depth $max_intersection_depth
$trace_level %level_title );
@EXPORT_OK = qw(inf $inf trace_open trace_close);
$inf = 100**100**100;
$neg_inf = $minus_inf = -$inf;
# obsolete methods - included for backward compatibility
sub inf () { $inf }
sub minus_inf () { $minus_inf }
sub no_cleanup { $_[0] }
*type = \&Set::Infinite::Basic::type;
sub compact { @_ }
BEGIN {
$VERSION = "0.65";
$TRACE = 0; # enable basic trace method execution
$DEBUG_BT = 0; # enable backtrack tracer
$PRETTY_PRINT = 0; # 0 = print 'Too Complex'; 1 = describe functions
$trace_level = 0; # indentation level when debugging
$too_complex = "Too complex";
$backtrack_depth = 0;
$max_backtrack_depth = 10; # _backtrack()
$max_intersection_depth = 5; # first()
}
sub trace { # title=>'aaa'
return $_[0] unless $TRACE;
my ($self, %parm) = @_;
my @caller = caller(1);
# print "self $self ". ref($self). "\n";
print "" . ( ' | ' x $trace_level ) .
"$parm{title} ". $self->copy .
( exists $parm{arg} ? " -- " . $parm{arg}->copy : "" ).
" $caller[1]:$caller[2] ]\n" if $TRACE == 1;
return $self;
}
sub trace_open {
return $_[0] unless $TRACE;
my ($self, %parm) = @_;
my @caller = caller(1);
print "" . ( ' | ' x $trace_level ) .
"\\ $parm{title} ". $self->copy .
( exists $parm{arg} ? " -- ". $parm{arg}->copy : "" ).
" $caller[1]:$caller[2] ]\n";
$trace_level++;
$level_title{$trace_level} = $parm{title};
return $self;
}
sub trace_close {
return $_[0] unless $TRACE;
my ($self, %parm) = @_;
my @caller = caller(0);
print "" . ( ' | ' x ($trace_level-1) ) .
"\/ $level_title{$trace_level} ".
( exists $parm{arg} ?
(
defined $parm{arg} ?
"ret ". ( UNIVERSAL::isa($parm{arg}, __PACKAGE__ ) ?
$parm{arg}->copy :
"<$parm{arg}>" ) :
"undef"
) :
"" # no arg
).
" $caller[1]:$caller[2] ]\n";
$trace_level--;
return $self;
}
# creates a 'function' object that can be solved by _backtrack()
sub _function {
my ($self, $method) = (shift, shift);
my $b = $self->empty_set();
$b->{too_complex} = 1;
$b->{parent} = $self;
$b->{method} = $method;
$b->{param} = [ @_ ];
return $b;
}
# same as _function, but with 2 arguments
sub _function2 {
my ($self, $method, $arg) = (shift, shift, shift);
unless ( $self->{too_complex} || $arg->{too_complex} ) {
return $self->$method($arg, @_);
}
my $b = $self->empty_set();
$b->{too_complex} = 1;
$b->{parent} = [ $self, $arg ];
$b->{method} = $method;
$b->{param} = [ @_ ];
return $b;
}
sub quantize {
my $self = shift;
$self->trace_open(title=>"quantize") if $TRACE;
my @min = $self->min_a;
my @max = $self->max_a;
if (($self->{too_complex}) or
(defined $min[0] && $min[0] == $neg_inf) or
(defined $max[0] && $max[0] == $inf)) {
return $self->_function( 'quantize', @_ );
}
my @a;
my %rule = @_;
my $b = $self->empty_set();
my $parent = $self;
$rule{unit} = 'one' unless $rule{unit};
$rule{quant} = 1 unless $rule{quant};
$rule{parent} = $parent;
$rule{strict} = $parent unless exists $rule{strict};
$rule{type} = $parent->{type};
my ($min, $open_begin) = $parent->min_a;
unless (defined $min) {
$self->trace_close( arg => $b ) if $TRACE;
return $b;
}
$rule{fixtype} = 1 unless exists $rule{fixtype};
$Set::Infinite::Arithmetic::Init_quantizer{$rule{unit}}->(\%rule);
$rule{sub_unit} = $Set::Infinite::Arithmetic::Offset_to_value{$rule{unit}};
carp "Quantize unit '".$rule{unit}."' not implemented" unless ref( $rule{sub_unit} ) eq 'CODE';
my ($max, $open_end) = $parent->max_a;
$rule{offset} = $Set::Infinite::Arithmetic::Value_to_offset{$rule{unit}}->(\%rule, $min);
my $last_offset = $Set::Infinite::Arithmetic::Value_to_offset{$rule{unit}}->(\%rule, $max);
$rule{size} = $last_offset - $rule{offset} + 1;
my ($index, $tmp, $this, $next);
for $index (0 .. $rule{size} ) {
# ($this, $next) = $rule{sub_unit} (\%rule, $index);
($this, $next) = $rule{sub_unit}->(\%rule, $index);
unless ( $rule{fixtype} ) {
$tmp = { a => $this , b => $next ,
open_begin => 0, open_end => 1 };
}
else {
$tmp = Set::Infinite::Basic::_simple_new($this,$next, $rule{type} );
$tmp->{open_end} = 1;
}
next if ( $rule{strict} and not $rule{strict}->intersects($tmp));
push @a, $tmp;
}
$b->{list} = \@a; # change data
$self->trace_close( arg => $b ) if $TRACE;
return $b;
}
sub _first_n {
my $self = shift;
my $n = shift;
my $tail = $self->copy;
my @result;
my $first;
for ( 1 .. $n )
{
( $first, $tail ) = $tail->first if $tail;
push @result, $first;
}
return $tail, @result;
}
sub _last_n {
my $self = shift;
my $n = shift;
my $tail = $self->copy;
my @result;
my $last;
for ( 1 .. $n )
{
( $last, $tail ) = $tail->last if $tail;
unshift @result, $last;
}
return $tail, @result;
}
sub select {
my $self = shift;
$self->trace_open(title=>"select") if $TRACE;
my %param = @_;
die "select() - parameter 'freq' is deprecated" if exists $param{freq};
my $res;
my $count;
my @by;
@by = @{ $param{by} } if exists $param{by};
$count = delete $param{count} || $inf;
# warn "select: count=$count by=[@by]";
if ($count <= 0) {
$self->trace_close( arg => $res ) if $TRACE;
return $self->empty_set();
}
my @set;
my $tail;
my $first;
my $last;
if ( @by )
{
my @res;
if ( ! $self->is_too_complex )
{
$res = $self->new;
@res = @{ $self->{list} }[ @by ] ;
}
else
{
my ( @pos_by, @neg_by );
for ( @by ) {
( $_ < 0 ) ? push @neg_by, $_ :
push @pos_by, $_;
}
my @first;
if ( @pos_by ) {
@pos_by = sort { $a <=> $b } @pos_by;
( $tail, @set ) = $self->_first_n( 1 + $pos_by[-1] );
@first = @set[ @pos_by ];
}
my @last;
if ( @neg_by ) {
@neg_by = sort { $a <=> $b } @neg_by;
( $tail, @set ) = $self->_last_n( - $neg_by[0] );
@last = @set[ @neg_by ];
}
@res = map { $_->{list}[0] } ( @first , @last );
}
$res = $self->new;
@res = sort { $a->{a} <=> $b->{a} } grep { defined } @res;
my $last;
my @a;
for ( @res ) {
push @a, $_ if ! $last || $last->{a} != $_->{a};
$last = $_;
}
$res->{list} = \@a;
}
else
{
$res = $self;
}
return $res if $count == $inf;
my $count_set = $self->empty_set();
if ( ! $self->is_too_complex )
{
my @a;
@a = grep { defined } @{ $res->{list} }[ 0 .. $count - 1 ] ;
$count_set->{list} = \@a;
}
else
{
my $last;
while ( $res ) {
( $first, $res ) = $res->first;
last unless $first;
last if $last && $last->{a} == $first->{list}[0]{a};
$last = $first->{list}[0];
push @{$count_set->{list}}, $first->{list}[0];
$count--;
last if $count <= 0;
}
}
return $count_set;
}
BEGIN {
# %_first and %_last hashes are used to backtrack the value
# of first() and last() of an infinite set
%_first = (
'complement' =>
sub {
my $self = $_[0];
my @parent_min = $self->{parent}->first;
unless ( defined $parent_min[0] ) {
return (undef, 0);
}
my $parent_complement;
my $first;
my @next;
my $parent;
if ( $parent_min[0]->min == $neg_inf ) {
my @parent_second = $parent_min[1]->first;
# (-inf..min) (second..?)
# (min..second) = complement
$first = $self->new( $parent_min[0]->complement );
$first->{list}[0]{b} = $parent_second[0]->{list}[0]{a};
$first->{list}[0]{open_end} = ! $parent_second[0]->{list}[0]{open_begin};
@{ $first->{list} } = () if
( $first->{list}[0]{a} == $first->{list}[0]{b}) &&
( $first->{list}[0]{open_begin} ||
$first->{list}[0]{open_end} );
@next = $parent_second[0]->max_a;
$parent = $parent_second[1];
}
else {
# (min..?)
# (-inf..min) = complement
$parent_complement = $parent_min[0]->complement;
$first = $self->new( $parent_complement->{list}[0] );
@next = $parent_min[0]->max_a;
$parent = $parent_min[1];
}
my @no_tail = $self->new($neg_inf,$next[0]);
$no_tail[0]->{list}[0]{open_end} = $next[1];
my $tail = $parent->union($no_tail[0])->complement;
return ($first, $tail);
}, # end: first-complement
'intersection' =>
sub {
my $self = $_[0];
my @parent = @{ $self->{parent} };
# warn "$method parents @parent";
my $retry_count = 0;
my (@first, @min, $which, $first1, $intersection);
SEARCH: while ($retry_count++ < $max_intersection_depth) {
return undef unless defined $parent[0];
return undef unless defined $parent[1];
@{$first[0]} = $parent[0]->first;
@{$first[1]} = $parent[1]->first;
unless ( defined $first[0][0] ) {
# warn "don't know first of $method";
$self->trace_close( arg => 'undef' ) if $TRACE;
return undef;
}
unless ( defined $first[1][0] ) {
# warn "don't know first of $method";
$self->trace_close( arg => 'undef' ) if $TRACE;
return undef;
}
@{$min[0]} = $first[0][0]->min_a;
@{$min[1]} = $first[1][0]->min_a;
unless ( defined $min[0][0] && defined $min[1][0] ) {
return undef;
}
# $which is the index to the bigger "first".
$which = ($min[0][0] < $min[1][0]) ? 1 : 0;
for my $which1 ( $which, 1 - $which ) {
my $tmp_parent = $parent[$which1];
($first1, $parent[$which1]) = @{ $first[$which1] };
if ( $first1->is_empty ) {
# warn "first1 empty! count $retry_count";
# trace_close;
# return $first1, undef;
$intersection = $first1;
$which = $which1;
last SEARCH;
}
$intersection = $first1->intersection( $parent[1-$which1] );
# warn "intersection with $first1 is $intersection";
unless ( $intersection->is_null ) {
# $self->trace( title=>"got an intersection" );
if ( $intersection->is_too_complex ) {
$parent[$which1] = $tmp_parent;
}
else {
$which = $which1;
last SEARCH;
}
};
}
}
if ( $#{ $intersection->{list} } > 0 ) {
my $tail;
($intersection, $tail) = $intersection->first;
$parent[$which] = $parent[$which]->union( $tail );
}
my $tmp;
if ( defined $parent[$which] and defined $parent[1-$which] ) {
$tmp = $parent[$which]->intersection ( $parent[1-$which] );
}
return ($intersection, $tmp);
}, # end: first-intersection
'union' =>
sub {
my $self = $_[0];
my (@first, @min);
my @parent = @{ $self->{parent} };
@{$first[0]} = $parent[0]->first;
@{$first[1]} = $parent[1]->first;
unless ( defined $first[0][0] ) {
# looks like one set was empty
return @{$first[1]};
}
@{$min[0]} = $first[0][0]->min_a;
@{$min[1]} = $first[1][0]->min_a;
# check min1/min2 for undef
unless ( defined $min[0][0] ) {
$self->trace_close( arg => "@{$first[1]}" ) if $TRACE;
return @{$first[1]}
}
unless ( defined $min[1][0] ) {
$self->trace_close( arg => "@{$first[0]}" ) if $TRACE;
return @{$first[0]}
}
my $which = ($min[0][0] < $min[1][0]) ? 0 : 1;
my $first = $first[$which][0];
# find out the tail
my $parent1 = $first[$which][1];
# warn $self->{parent}[$which]." - $first = $parent1";
my $parent2 = ($min[0][0] == $min[1][0]) ?
$self->{parent}[1-$which]->complement($first) :
$self->{parent}[1-$which];
my $tail;
if (( ! defined $parent1 ) || $parent1->is_null) {
# warn "union parent1 tail is null";
$tail = $parent2;
}
else {
my $method = $self->{method};
$tail = $parent1->$method( $parent2 );
}
if ( $first->intersects( $tail ) ) {
my $first2;
( $first2, $tail ) = $tail->first;
$first = $first->union( $first2 );
}
$self->trace_close( arg => "$first $tail" ) if $TRACE;
return ($first, $tail);
}, # end: first-union
'iterate' =>
sub {
my $self = $_[0];
my $parent = $self->{parent};
my ($first, $tail) = $parent->first;
$first = $first->iterate( @{$self->{param}} ) if ref($first);
$tail = $tail->_function( 'iterate', @{$self->{param}} ) if ref($tail);
my $more;
($first, $more) = $first->first if ref($first);
$tail = $tail->_function2( 'union', $more ) if defined $more;
return ($first, $tail);
},
'until' =>
sub {
my $self = $_[0];
my ($a1, $b1) = @{ $self->{parent} };
$a1->trace( title=>"computing first()" );
my @first1 = $a1->first;
my @first2 = $b1->first;
my ($first, $tail);
if ( $first2[0] <= $first1[0] ) {
# added ->first because it returns 2 spans if $a1 == $a2
$first = $a1->empty_set()->until( $first2[0] )->first;
$tail = $a1->_function2( "until", $first2[1] );
}
else {
$first = $a1->new( $first1[0] )->until( $first2[0] );
if ( defined $first1[1] ) {
$tail = $first1[1]->_function2( "until", $first2[1] );
}
else {
$tail = undef;
}
}
return ($first, $tail);
},
'offset' =>
sub {
my $self = $_[0];
my ($first, $tail) = $self->{parent}->first;
$first = $first->offset( @{$self->{param}} );
$tail = $tail->_function( 'offset', @{$self->{param}} );
my $more;
($first, $more) = $first->first;
$tail = $tail->_function2( 'union', $more ) if defined $more;
return ($first, $tail);
},
'quantize' =>
sub {
my $self = $_[0];
my @min = $self->{parent}->min_a;
if ( $min[0] == $neg_inf || $min[0] == $inf ) {
return ( $self->new( $min[0] ) , $self->copy );
}
my $first = $self->new( $min[0] )->quantize( @{$self->{param}} );
return ( $first,
$self->{parent}->
_function2( 'intersection', $first->complement )->
_function( 'quantize', @{$self->{param}} ) );
},
'tolerance' =>
sub {
my $self = $_[0];
my ($first, $tail) = $self->{parent}->first;
$first = $first->tolerance( @{$self->{param}} );
$tail = $tail->tolerance( @{$self->{param}} );
return ($first, $tail);
},
); # %_first
%_last = (
'complement' =>
sub {
my $self = $_[0];
my @parent_max = $self->{parent}->last;
unless ( defined $parent_max[0] ) {
return (undef, 0);
}
my $parent_complement;
my $last;
my @next;
my $parent;
if ( $parent_max[0]->max == $inf ) {
# (inf..min) (second..?) = parent
# (min..second) = complement
my @parent_second = $parent_max[1]->last;
$last = $self->new( $parent_max[0]->complement );
$last->{list}[0]{a} = $parent_second[0]->{list}[0]{b};
$last->{list}[0]{open_begin} = ! $parent_second[0]->{list}[0]{open_end};
@{ $last->{list} } = () if
( $last->{list}[0]{a} == $last->{list}[0]{b}) &&
( $last->{list}[0]{open_end} ||
$last->{list}[0]{open_begin} );
@next = $parent_second[0]->min_a;
$parent = $parent_second[1];
}
else {
# (min..?)
# (-inf..min) = complement
$parent_complement = $parent_max[0]->complement;
$last = $self->new( $parent_complement->{list}[-1] );
@next = $parent_max[0]->min_a;
$parent = $parent_max[1];
}
my @no_tail = $self->new($next[0], $inf);
$no_tail[0]->{list}[-1]{open_begin} = $next[1];
my $tail = $parent->union($no_tail[-1])->complement;
return ($last, $tail);
},
'intersection' =>
sub {
my $self = $_[0];
my @parent = @{ $self->{parent} };
# TODO: check max1/max2 for undef
my $retry_count = 0;
my (@last, @max, $which, $last1, $intersection);
SEARCH: while ($retry_count++ < $max_intersection_depth) {
return undef unless defined $parent[0];
return undef unless defined $parent[1];
@{$last[0]} = $parent[0]->last;
@{$last[1]} = $parent[1]->last;
unless ( defined $last[0][0] ) {
$self->trace_close( arg => 'undef' ) if $TRACE;
return undef;
}
unless ( defined $last[1][0] ) {
$self->trace_close( arg => 'undef' ) if $TRACE;
return undef;
}
@{$max[0]} = $last[0][0]->max_a;
@{$max[1]} = $last[1][0]->max_a;
unless ( defined $max[0][0] && defined $max[1][0] ) {
$self->trace( title=>"can't find max()" ) if $TRACE;
$self->trace_close( arg => 'undef' ) if $TRACE;
return undef;
}
# $which is the index to the smaller "last".
$which = ($max[0][0] > $max[1][0]) ? 1 : 0;
for my $which1 ( $which, 1 - $which ) {
my $tmp_parent = $parent[$which1];
($last1, $parent[$which1]) = @{ $last[$which1] };
if ( $last1->is_null ) {
$which = $which1;
$intersection = $last1;
last SEARCH;
}
$intersection = $last1->intersection( $parent[1-$which1] );
unless ( $intersection->is_null ) {
# $self->trace( title=>"got an intersection" );
if ( $intersection->is_too_complex ) {
$self->trace( title=>"got a too_complex intersection" ) if $TRACE;
# warn "too complex intersection";
$parent[$which1] = $tmp_parent;
}
else {
$self->trace( title=>"got an intersection" ) if $TRACE;
$which = $which1;
last SEARCH;
}
};
}
}
$self->trace( title=>"exit loop" ) if $TRACE;
if ( $#{ $intersection->{list} } > 0 ) {
my $tail;
($intersection, $tail) = $intersection->last;
$parent[$which] = $parent[$which]->union( $tail );
}
my $tmp;
if ( defined $parent[$which] and defined $parent[1-$which] ) {
$tmp = $parent[$which]->intersection ( $parent[1-$which] );
}
return ($intersection, $tmp);
},
'union' =>
sub {
my $self = $_[0];
my (@last, @max);
my @parent = @{ $self->{parent} };
@{$last[0]} = $parent[0]->last;
@{$last[1]} = $parent[1]->last;
@{$max[0]} = $last[0][0]->max_a;
@{$max[1]} = $last[1][0]->max_a;
unless ( defined $max[0][0] ) {
return @{$last[1]}
}
unless ( defined $max[1][0] ) {
return @{$last[0]}
}
my $which = ($max[0][0] > $max[1][0]) ? 0 : 1;
my $last = $last[$which][0];
# find out the tail
my $parent1 = $last[$which][1];
# warn $self->{parent}[$which]." - $last = $parent1";
my $parent2 = ($max[0][0] == $max[1][0]) ?
$self->{parent}[1-$which]->complement($last) :
$self->{parent}[1-$which];
my $tail;
if (( ! defined $parent1 ) || $parent1->is_null) {
$tail = $parent2;
}
else {
my $method = $self->{method};
$tail = $parent1->$method( $parent2 );
}
if ( $last->intersects( $tail ) ) {
my $last2;
( $last2, $tail ) = $tail->last;
$last = $last->union( $last2 );
}
return ($last, $tail);
},
'until' =>
sub {
my $self = $_[0];
my ($a1, $b1) = @{ $self->{parent} };
$a1->trace( title=>"computing last()" );
my @last1 = $a1->last;
my @last2 = $b1->last;
my ($last, $tail);
if ( $last2[0] <= $last1[0] ) {
# added ->last because it returns 2 spans if $a1 == $a2
$last = $last2[0]->until( $a1 )->last;
$tail = $a1->_function2( "until", $last2[1] );
}
else {
$last = $a1->new( $last1[0] )->until( $last2[0] );
if ( defined $last1[1] ) {
$tail = $last1[1]->_function2( "until", $last2[1] );
}
else {
$tail = undef;
}
}
return ($last, $tail);
},
'iterate' =>
sub {
my $self = $_[0];
my $parent = $self->{parent};
my ($last, $tail) = $parent->last;
$last = $last->iterate( @{$self->{param}} ) if ref($last);
$tail = $tail->_function( 'iterate', @{$self->{param}} ) if ref($tail);
my $more;
($last, $more) = $last->last if ref($last);
$tail = $tail->_function2( 'union', $more ) if defined $more;
return ($last, $tail);
},
'offset' =>
sub {
my $self = $_[0];
my ($last, $tail) = $self->{parent}->last;
$last = $last->offset( @{$self->{param}} );
$tail = $tail->_function( 'offset', @{$self->{param}} );
my $more;
($last, $more) = $last->last;
$tail = $tail->_function2( 'union', $more ) if defined $more;
return ($last, $tail);
},
'quantize' =>
sub {
my $self = $_[0];
my @max = $self->{parent}->max_a;
if (( $max[0] == $neg_inf ) || ( $max[0] == $inf )) {
return ( $self->new( $max[0] ) , $self->copy );
}
my $last = $self->new( $max[0] )->quantize( @{$self->{param}} );
if ($max[1]) { # open_end
if ( $last->min <= $max[0] ) {
$last = $self->new( $last->min - 1e-9 )->quantize( @{$self->{param}} );
}
}
return ( $last, $self->{parent}->
_function2( 'intersection', $last->complement )->
_function( 'quantize', @{$self->{param}} ) );
},
'tolerance' =>
sub {
my $self = $_[0];
my ($last, $tail) = $self->{parent}->last;
$last = $last->tolerance( @{$self->{param}} );
$tail = $tail->tolerance( @{$self->{param}} );
return ($last, $tail);
},
); # %_last
} # BEGIN
sub first {
my $self = $_[0];
unless ( exists $self->{first} ) {
$self->trace_open(title=>"first") if $TRACE;
if ( $self->{too_complex} ) {
my $method = $self->{method};
# warn "method $method ". ( exists $_first{$method} ? "exists" : "does not exist" );
if ( exists $_first{$method} ) {
@{$self->{first}} = $_first{$method}->($self);
}
else {
my $redo = $self->{parent}->$method ( @{ $self->{param} } );
@{$self->{first}} = $redo->first;
}
}
else {
return $self->SUPER::first;
}
}
return wantarray ? @{$self->{first}} : $self->{first}[0];
}
sub last {
my $self = $_[0];
unless ( exists $self->{last} ) {
$self->trace(title=>"last") if $TRACE;
if ( $self->{too_complex} ) {
my $method = $self->{method};
if ( exists $_last{$method} ) {
@{$self->{last}} = $_last{$method}->($self);
}
else {
my $redo = $self->{parent}->$method ( @{ $self->{param} } );
@{$self->{last}} = $redo->last;
}
}
else {
return $self->SUPER::last;
}
}
return wantarray ? @{$self->{last}} : $self->{last}[0];
}
# offset: offsets subsets
sub offset {
my $self = shift;
if ($self->{too_complex}) {
return $self->_function( 'offset', @_ );
}
$self->trace_open(title=>"offset") if $TRACE;
my @a;
my %param = @_;
my $b1 = $self->empty_set();
my ($interval, $ia, $i);
$param{mode} = 'offset' unless $param{mode};
unless (ref($param{value}) eq 'ARRAY') {
$param{value} = [0 + $param{value}, 0 + $param{value}];
}
$param{unit} = 'one' unless $param{unit};
my $parts = ($#{$param{value}}) / 2;
my $sub_unit = $Set::Infinite::Arithmetic::subs_offset2{$param{unit}};
my $sub_mode = $Set::Infinite::Arithmetic::_MODE{$param{mode}};
carp "unknown unit $param{unit} for offset()" unless defined $sub_unit;
carp "unknown mode $param{mode} for offset()" unless defined $sub_mode;
my ($j);
my ($cmp, $this, $next, $ib, $part, $open_begin, $open_end, $tmp);
my @value;
foreach $j (0 .. $parts) {
push @value, [ $param{value}[$j+$j], $param{value}[$j+$j + 1] ];
}
foreach $interval ( @{ $self->{list} } ) {
$ia = $interval->{a};
$ib = $interval->{b};
$open_begin = $interval->{open_begin};
$open_end = $interval->{open_end};
foreach $j (0 .. $parts) {
# print " [ofs($ia,$ib)] ";
($this, $next) = $sub_mode->( $sub_unit, $ia, $ib, @{$value[$j]} );
next if ($this > $next); # skip if a > b
if ($this == $next) {
# TODO: fix this
$open_end = $open_begin;
}
push @a, { a => $this , b => $next ,
open_begin => $open_begin , open_end => $open_end };
} # parts
} # self
@a = sort { $a->{a} <=> $b->{a} } @a;
$b1->{list} = \@a; # change data
$self->trace_close( arg => $b1 ) if $TRACE;
$b1 = $b1->fixtype if $self->{fixtype};
return $b1;
}
sub is_null {
$_[0]->{too_complex} ? 0 : $_[0]->SUPER::is_null;
}
sub is_too_complex {
$_[0]->{too_complex} ? 1 : 0;
}
# shows how a 'compacted' set looks like after quantize
sub _quantize_span {
my $self = shift;
my %param = @_;
$self->trace_open(title=>"_quantize_span") if $TRACE;
my $res;
if ($self->{too_complex}) {
$res = $self->{parent};
if ($self->{method} ne 'quantize') {
$self->trace( title => "parent is a ". $self->{method} );
if ( $self->{method} eq 'union' ) {
my $arg0 = $self->{parent}[0]->_quantize_span(%param);
my $arg1 = $self->{parent}[1]->_quantize_span(%param);
$res = $arg0->union( $arg1 );
}
elsif ( $self->{method} eq 'intersection' ) {
my $arg0 = $self->{parent}[0]->_quantize_span(%param);
my $arg1 = $self->{parent}[1]->_quantize_span(%param);
$res = $arg0->intersection( $arg1 );
}
# TODO: other methods
else {
$res = $self; # ->_function( "_quantize_span", %param );
}
$self->trace_close( arg => $res ) if $TRACE;
return $res;
}
# $res = $self->{parent};
if ($res->{too_complex}) {
$res->trace( title => "parent is complex" );
$res = $res->_quantize_span( %param );
$res = $res->quantize( @{$self->{param}} )->_quantize_span( %param );
}
else {
$res = $res->iterate (
sub {
$_[0]->quantize( @{$self->{param}} )->span;
}
);
}
}
else {
$res = $self->iterate ( sub { $_[0] } );
}
$self->trace_close( arg => $res ) if $TRACE;
return $res;
}
BEGIN {
%_backtrack = (
until => sub {
my ($self, $arg) = @_;
my $before = $self->{parent}[0]->intersection( $neg_inf, $arg->min )->max;
$before = $arg->min unless $before;
my $after = $self->{parent}[1]->intersection( $arg->max, $inf )->min;
$after = $arg->max unless $after;
return $arg->new( $before, $after );
},
iterate => sub {
my ($self, $arg) = @_;
if ( defined $self->{backtrack_callback} )
{
return $arg = $self->new( $self->{backtrack_callback}->( $arg ) );
}
my $before = $self->{parent}->intersection( $neg_inf, $arg->min )->max;
$before = $arg->min unless $before;
my $after = $self->{parent}->intersection( $arg->max, $inf )->min;
$after = $arg->max unless $after;
return $arg->new( $before, $after );
},
quantize => sub {
my ($self, $arg) = @_;
if ($arg->{too_complex}) {
return $arg;
}
else {
return $arg->quantize( @{$self->{param}} )->_quantize_span;
}
},
offset => sub {
my ($self, $arg) = @_;
# offset - apply offset with negative values
my %tmp = @{$self->{param}};
my @values = sort @{$tmp{value}};
my $backtrack_arg2 = $arg->offset(
unit => $tmp{unit},
mode => $tmp{mode},
value => [ - $values[-1], - $values[0] ] );
return $arg->union( $backtrack_arg2 ); # fixes some problems with 'begin' mode
},
);
}
sub _backtrack {
my ($self, $method, $arg) = @_;
return $self->$method ($arg) unless $self->{too_complex};
$self->trace_open( title => 'backtrack '.$self->{method} ) if $TRACE;
$backtrack_depth++;
if ( $backtrack_depth > $max_backtrack_depth ) {
carp ( __PACKAGE__ . ": Backtrack too deep " .
"(more than $max_backtrack_depth levels)" );
}
if (exists $_backtrack{ $self->{method} } ) {
$arg = $_backtrack{ $self->{method} }->( $self, $arg );
}
my $result;
if ( ref($self->{parent}) eq 'ARRAY' ) {
# has 2 parents (intersection, union, until)
my ( $result1, $result2 ) = @{$self->{parent}};
$result1 = $result1->_backtrack( $method, $arg )
if $result1->{too_complex};
$result2 = $result2->_backtrack( $method, $arg )
if $result2->{too_complex};
$method = $self->{method};
if ( $result1->{too_complex} || $result2->{too_complex} ) {
$result = $result1->_function2( $method, $result2 );
}
else {
$result = $result1->$method ($result2);
}
}
else {
# has 1 parent and parameters (offset, select, quantize, iterate)
$result = $self->{parent}->_backtrack( $method, $arg );
$method = $self->{method};
$result = $result->$method ( @{$self->{param}} );
}
$backtrack_depth--;
$self->trace_close( arg => $result ) if $TRACE;
return $result;
}
sub intersects {
my $a1 = shift;
my $b1 = (ref ($_[0]) eq ref($a1) ) ? shift : $a1->new(@_);
$a1->trace(title=>"intersects");
if ($a1->{too_complex}) {
$a1 = $a1->_backtrack('intersection', $b1 );
} # don't put 'else' here
if ($b1->{too_complex}) {
$b1 = $b1->_backtrack('intersection', $a1);
}
if (($a1->{too_complex}) or ($b1->{too_complex})) {
return undef; # we don't know the answer!
}
return $a1->SUPER::intersects( $b1 );
}
sub iterate {
my $self = shift;
my $callback = shift;
die "First argument to iterate() must be a subroutine reference"
unless ref( $callback ) eq 'CODE';
my $backtrack_callback;
if ( @_ && $_[0] eq 'backtrack_callback' )
{
( undef, $backtrack_callback ) = ( shift, shift );
}
my $set;
if ($self->{too_complex}) {
$self->trace(title=>"iterate:backtrack") if $TRACE;
$set = $self->_function( 'iterate', $callback, @_ );
}
else
{
$self->trace(title=>"iterate") if $TRACE;
$set = $self->SUPER::iterate( $callback, @_ );
}
$set->{backtrack_callback} = $backtrack_callback;
# warn "set backtrack_callback" if defined $backtrack_callback;
return $set;
}
sub intersection {
my $a1 = shift;
my $b1 = (ref ($_[0]) eq ref($a1) ) ? shift : $a1->new(@_);
$a1->trace_open(title=>"intersection", arg => $b1) if $TRACE;
if (($a1->{too_complex}) or ($b1->{too_complex})) {
my $arg0 = $a1->_quantize_span;
my $arg1 = $b1->_quantize_span;
unless (($arg0->{too_complex}) or ($arg1->{too_complex})) {
my $res = $arg0->intersection( $arg1 );
$a1->trace_close( arg => $res ) if $TRACE;
return $res;
}
}
if ($a1->{too_complex}) {
$a1 = $a1->_backtrack('intersection', $b1) unless $b1->{too_complex};
} # don't put 'else' here
if ($b1->{too_complex}) {
$b1 = $b1->_backtrack('intersection', $a1) unless $a1->{too_complex};
}
if ( $a1->{too_complex} || $b1->{too_complex} ) {
$a1->trace_close( ) if $TRACE;
return $a1->_function2( 'intersection', $b1 );
}
return $a1->SUPER::intersection( $b1 );
}
sub intersected_spans {
my $a1 = shift;
my $b1 = ref ($_[0]) eq ref($a1) ? $_[0] : $a1->new(@_);
if ($a1->{too_complex}) {
$a1 = $a1->_backtrack('intersection', $b1 ) unless $b1->{too_complex};
} # don't put 'else' here
if ($b1->{too_complex}) {
$b1 = $b1->_backtrack('intersection', $a1) unless $a1->{too_complex};
}
if ( ! $b1->{too_complex} && ! $a1->{too_complex} )
{
return $a1->SUPER::intersected_spans ( $b1 );
}
return $b1->iterate(
sub {
my $tmp = $a1->intersection( $_[0] );
return $tmp unless defined $tmp->max;
my $before = $a1->intersection( $neg_inf, $tmp->min )->last;
my $after = $a1->intersection( $tmp->max, $inf )->first;
$before = $tmp->union( $before )->first;
$after = $tmp->union( $after )->last;
$tmp = $tmp->union( $before )
if defined $before && $tmp->intersects( $before );
$tmp = $tmp->union( $after )
if defined $after && $tmp->intersects( $after );
return $tmp;
}
);
}
sub complement {
my $a1 = shift;
# do we have a parameter?
if (@_) {
my $b1 = (ref ($_[0]) eq ref($a1) ) ? shift : $a1->new(@_);
$a1->trace_open(title=>"complement", arg => $b1) if $TRACE;
$b1 = $b1->complement;
my $tmp =$a1->intersection($b1);
$a1->trace_close( arg => $tmp ) if $TRACE;
return $tmp;
}
$a1->trace_open(title=>"complement") if $TRACE;
if ($a1->{too_complex}) {
$a1->trace_close( ) if $TRACE;
return $a1->_function( 'complement', @_ );
}
return $a1->SUPER::complement;
}
sub until {
my $a1 = shift;
my $b1 = (ref ($_[0]) eq ref($a1) ) ? shift : $a1->new(@_);
if (($a1->{too_complex}) or ($b1->{too_complex})) {
return $a1->_function2( 'until', $b1 );
}
return $a1->SUPER::until( $b1 );
}
sub union {
my $a1 = shift;
my $b1 = (ref ($_[0]) eq ref($a1) ) ? shift : $a1->new(@_);
$a1->trace_open(title=>"union", arg => $b1) if $TRACE;
if (($a1->{too_complex}) or ($b1->{too_complex})) {
$a1->trace_close( ) if $TRACE;
return $a1 if $b1->is_null;
return $b1 if $a1->is_null;
return $a1->_function2( 'union', $b1);
}
return $a1->SUPER::union( $b1 );
}
# there are some ways to process 'contains':
# A CONTAINS B IF A == ( A UNION B )
# - faster
# A CONTAINS B IF B == ( A INTERSECTION B )
# - can backtrack = works for unbounded sets
sub contains {
my $a1 = shift;
$a1->trace_open(title=>"contains") if $TRACE;
if ( $a1->{too_complex} ) {
# we use intersection because it is better for backtracking
my $b0 = (ref $_[0] eq ref $a1) ? shift : $a1->new(@_);
my $b1 = $a1->intersection($b0);
if ( $b1->{too_complex} ) {
$b1->trace_close( arg => 'undef' ) if $TRACE;
return undef;
}
$a1->trace_close( arg => ($b1 == $b0 ? 1 : 0) ) if $TRACE;
return ($b1 == $b0) ? 1 : 0;
}
my $b1 = $a1->union(@_);
if ( $b1->{too_complex} ) {
$b1->trace_close( arg => 'undef' ) if $TRACE;
return undef;
}
$a1->trace_close( arg => ($b1 == $a1 ? 1 : 0) ) if $TRACE;
return ($b1 == $a1) ? 1 : 0;
}
sub min_a {
my $self = $_[0];
return @{$self->{min}} if exists $self->{min};
if ($self->{too_complex}) {
my @first = $self->first;
return @{$self->{min}} = $first[0]->min_a if defined $first[0];
return @{$self->{min}} = (undef, 0);
}
return $self->SUPER::min_a;
};
sub max_a {
my $self = $_[0];
return @{$self->{max}} if exists $self->{max};
if ($self->{too_complex}) {
my @last = $self->last;
return @{$self->{max}} = $last[0]->max_a if defined $last[0];
return @{$self->{max}} = (undef, 0);
}
return $self->SUPER::max_a;
};
sub count {
my $self = $_[0];
# NOTE: subclasses may return "undef" if necessary
return $inf if $self->{too_complex};
return $self->SUPER::count;
}
sub size {
my $self = $_[0];
if ($self->{too_complex}) {
my @min = $self->min_a;
my @max = $self->max_a;
return undef unless defined $max[0] && defined $min[0];
return $max[0] - $min[0];
}
return $self->SUPER::size;
};
sub spaceship {
my ($tmp1, $tmp2, $inverted) = @_;
carp "Can't compare unbounded sets"
if $tmp1->{too_complex} or $tmp2->{too_complex};
return $tmp1->SUPER::spaceship( $tmp2, $inverted );
}
sub _cleanup { @_ } # this subroutine is obsolete
sub tolerance {
my $self = shift;
my $tmp = pop;
if (ref($self)) {
# local
return $self->{tolerance} unless defined $tmp;
if ($self->{too_complex}) {
my $b1 = $self->_function( 'tolerance', $tmp );
$b1->{tolerance} = $tmp; # for max/min processing
return $b1;
}
return $self->SUPER::tolerance( $tmp );
}
# class method
__PACKAGE__->SUPER::tolerance( $tmp ) if defined($tmp);
return __PACKAGE__->SUPER::tolerance;
}
sub _pretty_print {
my $self = shift;
return "$self" unless $self->{too_complex};
return $self->{method} . "( " .
( ref($self->{parent}) eq 'ARRAY' ?
$self->{parent}[0] . ' ; ' . $self->{parent}[1] :
$self->{parent} ) .
" )";
}
sub as_string {
my $self = shift;
return ( $PRETTY_PRINT ? $self->_pretty_print : $too_complex )
if $self->{too_complex};
return $self->SUPER::as_string;
}
sub DESTROY {}
1;
__END__
=head1 NAME
Set::Infinite - Sets of intervals
=head1 SYNOPSIS
use Set::Infinite;
$set = Set::Infinite->new(1,2); # [1..2]
print $set->union(5,6); # [1..2],[5..6]
=head1 DESCRIPTION
Set::Infinite is a Set Theory module for infinite sets.
A set is a collection of objects.
The objects that belong to a set are called its members, or "elements".
As objects we allow (almost) anything: reals, integers, and objects (such as dates).
We allow sets to be infinite.
There is no account for the order of elements. For example, {1,2} = {2,1}.
There is no account for repetition of elements. For example, {1,2,2} = {1,1,1,2} = {1,2}.
=head1 CONSTRUCTOR
=head2 new
Creates a new set object:
$set = Set::Infinite->new; # empty set
$set = Set::Infinite->new( 10 ); # single element
$set = Set::Infinite->new( 10, 20 ); # single range
$set = Set::Infinite->new(
[ 10, 20 ], [ 50, 70 ] ); # two ranges
=over 4
=item empty set
$set = Set::Infinite->new;
=item set with a single element
$set = Set::Infinite->new( 10 );
$set = Set::Infinite->new( [ 10 ] );
=item set with a single span
$set = Set::Infinite->new( 10, 20 );
$set = Set::Infinite->new( [ 10, 20 ] );
# 10 <= x <= 20
=item set with a single, open span
$set = Set::Infinite->new(
{
a => 10, open_begin => 0,
b => 20, open_end => 1,
}
);
# 10 <= x < 20
=item set with multiple spans
$set = Set::Infinite->new( 10, 20, 100, 200 );
$set = Set::Infinite->new( [ 10, 20 ], [ 100, 200 ] );
$set = Set::Infinite->new(
{
a => 10, open_begin => 0,
b => 20, open_end => 0,
},
{
a => 100, open_begin => 0,
b => 200, open_end => 0,
}
);
=back
The C<new()> method expects I<ordered> parameters.
If you have unordered ranges, you can build the set using C<union>:
@ranges = ( [ 10, 20 ], [ -10, 1 ] );
$set = Set::Infinite->new;
$set = $set->union( @$_ ) for @ranges;
The data structures passed to C<new> must be I<immutable>.
So this is not good practice:
$set = Set::Infinite->new( $object_a, $object_b );
$object_a->set_value( 10 );
This is the recommended way to do it:
$set = Set::Infinite->new( $object_a->clone, $object_b->clone );
$object_a->set_value( 10 );
=head2 clone / copy
Creates a new object, and copy the object data.
=head2 empty_set
Creates an empty set.
If called from an existing set, the empty set inherits
the "type" and "density" characteristics.
=head2 universal_set
Creates a set containing "all" possible elements.
If called from an existing set, the universal set inherits
the "type" and "density" characteristics.
=head1 SET FUNCTIONS
=head2 union
$set = $set->union($b);
Returns the set of all elements from both sets.
This function behaves like an "OR" operation.
$set1 = new Set::Infinite( [ 1, 4 ], [ 8, 12 ] );
$set2 = new Set::Infinite( [ 7, 20 ] );
print $set1->union( $set2 );
# output: [1..4],[7..20]
=head2 intersection
$set = $set->intersection($b);
Returns the set of elements common to both sets.
This function behaves like an "AND" operation.
$set1 = new Set::Infinite( [ 1, 4 ], [ 8, 12 ] );
$set2 = new Set::Infinite( [ 7, 20 ] );
print $set1->intersection( $set2 );
# output: [8..12]
=head2 complement
=head2 minus
=head2 difference
$set = $set->complement;
Returns the set of all elements that don't belong to the set.
$set1 = new Set::Infinite( [ 1, 4 ], [ 8, 12 ] );
print $set1->complement;
# output: (-inf..1),(4..8),(12..inf)
The complement function might take a parameter:
$set = $set->minus($b);
Returns the set-difference, that is, the elements that don't
belong to the given set.
$set1 = new Set::Infinite( [ 1, 4 ], [ 8, 12 ] );
$set2 = new Set::Infinite( [ 7, 20 ] );
print $set1->minus( $set2 );
# output: [1..4]
=head2 symmetric_difference
Returns a set containing elements that are in either set,
but not in both. This is the "set" version of "XOR".
=head1 DENSITY METHODS
=head2 real
$set1 = $set->real;
Returns a set with density "0".
=head2 integer
$set1 = $set->integer;
Returns a set with density "1".
=head1 LOGIC FUNCTIONS
=head2 intersects
$logic = $set->intersects($b);
=head2 contains
$logic = $set->contains($b);
=head2 is_empty
=head2 is_null
$logic = $set->is_null;
=head2 is_nonempty
This set that has at least 1 element.
=head2 is_span
This set that has a single span or interval.
=head2 is_singleton
This set that has a single element.
=head2 is_subset( $set )
Every element of this set is a member of the given set.
=head2 is_proper_subset( $set )
Every element of this set is a member of the given set.
Some members of the given set are not elements of this set.
=head2 is_disjoint( $set )
The given set has no elements in common with this set.
=head2 is_too_complex
Sometimes a set might be too complex to enumerate or print.
This happens with sets that represent infinite recurrences, such as
when you ask for a quantization on a
set bounded by -inf or inf.
See also: C<count> method.
=head1 SCALAR FUNCTIONS
=head2 min
$i = $set->min;
=head2 max
$i = $set->max;
=head2 size
$i = $set->size;
=head2 count
$i = $set->count;
=head1 OVERLOADED OPERATORS
=head2 stringification
print $set;
$str = "$set";
See also: C<as_string>.
=head2 comparison
sort
> < == >= <= <=>
See also: C<spaceship> method.
=head1 CLASS METHODS
Set::Infinite->separators(@i)
chooses the interval separators for stringification.
default are [ ] ( ) '..' ','.
inf
returns an 'Infinity' number.
minus_inf
returns '-Infinity' number.
=head2 type
type( "My::Class::Name" )
Chooses a default object data type.
Default is none (a normal Perl SCALAR).
=head1 SPECIAL SET FUNCTIONS
=head2 span
$set1 = $set->span;
Returns the set span.
=head2 until
Extends a set until another:
0,5,7 -> until 2,6,10
gives
[0..2), [5..6), [7..10)
=head2 start_set
=head2 end_set
These methods do the inverse of the "until" method.
Given:
[0..2), [5..6), [7..10)
start_set is:
0,5,7
end_set is:
2,6,10
=head2 intersected_spans
$set = $set1->intersected_spans( $set2 );
The method returns a new set,
containing all spans that are intersected by the given set.
Unlike the C<intersection> method, the spans are not modified.
See diagram below:
set1 [....] [....] [....] [....]
set2 [................]
intersection [.] [....] [.]
intersected_spans [....] [....] [....]
=head2 quantize
quantize( parameters )
Makes equal-sized subsets.
Returns an ordered set of equal-sized subsets.
Example:
$set = Set::Infinite->new([1,3]);
print join (" ", $set->quantize( quant => 1 ) );
Gives:
[1..2) [2..3) [3..4)
=head2 select
select( parameters )
Selects set spans based on their ordered positions
C<select> has a behaviour similar to an array C<slice>.
by - default=All
count - default=Infinity
0 1 2 3 4 5 6 7 8 # original set
0 1 2 # count => 3
1 6 # by => [ -2, 1 ]
=head2 offset
offset ( parameters )
Offsets the subsets. Parameters:
value - default=[0,0]
mode - default='offset'. Possible values are: 'offset', 'begin', 'end'.
unit - type of value. Can be 'days', 'weeks', 'hours', 'minutes', 'seconds'.
=head2 iterate
iterate ( sub { } , @args )
Iterates on the set spans, over a callback subroutine.
Returns the union of all partial results.
The callback argument C<$_[0]> is a span. If there are additional arguments they are passed to the callback.
The callback can return a span, a hashref (see C<Set::Infinite::Basic>), a scalar, an object, or C<undef>.
[EXPERIMENTAL]
C<iterate> accepts an optional C<backtrack_callback> argument.
The purpose of the C<backtrack_callback> is to I<reverse> the
iterate() function, overcoming the limitations of the internal
backtracking algorithm.
The syntax is:
iterate ( sub { } , backtrack_callback => sub { }, @args )
The C<backtrack_callback> can return a span, a hashref, a scalar,
an object, or C<undef>.
For example, the following snippet adds a constant to each
element of an unbounded set:
$set1 = $set->iterate(
sub { $_[0]->min + 54, $_[0]->max + 54 },
backtrack_callback =>
sub { $_[0]->min - 54, $_[0]->max - 54 },
);
=head2 first / last
first / last
In scalar context returns the first or last interval of a set.
In list context returns the first or last interval of a set,
and the remaining set (the 'tail').
See also: C<min>, C<max>, C<min_a>, C<max_a> methods.
=head2 type
type( "My::Class::Name" )
Chooses a default object data type.
default is none (a normal perl SCALAR).
=head1 INTERNAL FUNCTIONS
=head2 _backtrack
$set->_backtrack( 'intersection', $b );
Internal function to evaluate recurrences.
=head2 numeric
$set->numeric;
Internal function to ignore the set "type".
It is used in some internal optimizations, when it is
possible to use scalar values instead of objects.
=head2 fixtype
$set->fixtype;
Internal function to fix the result of operations
that use the numeric() function.
=head2 tolerance
$set = $set->tolerance(0) # defaults to real sets (default)
$set = $set->tolerance(1) # defaults to integer sets
Internal function for changing the set "density".
=head2 min_a
($min, $min_is_open) = $set->min_a;
=head2 max_a
($max, $max_is_open) = $set->max_a;
=head2 as_string
Implements the "stringification" operator.
Stringification of unbounded recurrences is not implemented.
Unbounded recurrences are stringified as "function descriptions",
if the class variable $PRETTY_PRINT is set.
=head2 spaceship
Implements the "comparison" operator.
Comparison of unbounded recurrences is not implemented.
=head1 CAVEATS
=over 4
=item * constructor "span" notation
$set = Set::Infinite->new(10,1);
Will be interpreted as [1..10]
=item * constructor "multiple-span" notation
$set = Set::Infinite->new(1,2,3,4);
Will be interpreted as [1..2],[3..4] instead of [1,2,3,4].
You probably want ->new([1],[2],[3],[4]) instead,
or maybe ->new(1,4)
=item * "range operator"
$set = Set::Infinite->new(1..3);
Will be interpreted as [1..2],3 instead of [1,2,3].
You probably want ->new(1,3) instead.
=back
=head1 INTERNALS
The base I<set> object, without recurrences, is a C<Set::Infinite::Basic>.
A I<recurrence-set> is represented by a I<method name>,
one or two I<parent objects>, and extra arguments.
The C<list> key is set to an empty array, and the
C<too_complex> key is set to C<1>.
This is a structure that holds the union of two "complex sets":
{
too_complex => 1, # "this is a recurrence"
list => [ ], # not used
method => 'union', # function name
parent => [ $set1, $set2 ], # "leaves" in the syntax-tree
param => [ ] # optional arguments for the function
}
This is a structure that holds the complement of a "complex set":
{
too_complex => 1, # "this is a recurrence"
list => [ ], # not used
method => 'complement', # function name
parent => $set, # "leaf" in the syntax-tree
param => [ ] # optional arguments for the function
}
=head1 SEE ALSO
See modules DateTime::Set, DateTime::Event::Recurrence,
DateTime::Event::ICal, DateTime::Event::Cron
for up-to-date information on date-sets.
The perl-date-time project <http://datetime.perl.org>
=head1 AUTHOR
Flavio S. Glock <fglock@gmail.com>
=head1 COPYRIGHT
Copyright (c) 2003 Flavio Soibelmann Glock. All rights reserved.
This program is free software; you can redistribute it and/or modify
it under the same terms as Perl itself.
The full text of the license can be found in the LICENSE file included
with this module.
=cut