+++ /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