--- /dev/null
+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
+
projects / kivitendo-erp.git / blobdiff