Beta Shell v2.0

File Manager

~ /usr/share/perl5/vendor_perl/Set/Infinite
Name	Size	Perms	Modified	Actions
[ .. / .. ]
Arithmetic.pm	10.86 KB	-rw-r--r--	2008-06-21 07:37:52	Edit Del
Basic.pm	27.44 KB	-rw-r--r--	2010-04-26 18:30:54	Edit Del
_recurrence.pm	12.65 KB	-rw-r--r--	2020-06-25 16:07:39	Edit Del
Editing: Basic.pm (27.44 KB)

package Set::Infinite::Basic;

# Copyright (c) 2001, 2002, 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.

require 5.005_03;
use strict;

require Exporter;
use Carp;
use Data::Dumper; 
use vars qw( @ISA @EXPORT_OK @EXPORT );
use vars qw( $Type $tolerance $fixtype $inf $minus_inf @Separators $neg_inf );

@ISA = qw(Exporter);
@EXPORT_OK = qw( INFINITY NEG_INFINITY );
@EXPORT = qw();

use constant INFINITY => 100**100**100;
use constant NEG_INFINITY => - INFINITY;

$inf       = INFINITY;
$minus_inf = $neg_inf = NEG_INFINITY;

use overload
    '<=>' => \&spaceship,
    qw("" as_string),
;


# TODO: make this an object _and_ class method
# TODO: POD
sub separators {
    shift;
    return $Separators[ $_[0] ] if $#_ == 0;
    @Separators = @_ if @_;
    return @Separators;
}

BEGIN {
    __PACKAGE__->separators (
        '[', ']',    # a closed interval
        '(', ')',    # an open interval
        '..',        # number separator
        ',',         # list separator
        '', '',      # set delimiter  '{' '}'
    );
    # global defaults for object private vars
    $Type = undef;
    $tolerance = 0;
    $fixtype = 1;
}

# _simple_* set of internal methods: basic processing of "spans"

sub _simple_intersects {
    my $tmp1 = $_[0];
    my $tmp2 = $_[1];
    my ($i_beg, $i_end, $open_beg, $open_end);
    my $cmp = $tmp1->{a} <=> $tmp2->{a};
    if ($cmp < 0) {
        $i_beg       = $tmp2->{a};
        $open_beg    = $tmp2->{open_begin};
    }
    elsif ($cmp > 0) {
        $i_beg       = $tmp1->{a};
        $open_beg    = $tmp1->{open_begin};
    }
    else {
        $i_beg       = $tmp1->{a};
        $open_beg    = $tmp1->{open_begin} || $tmp2->{open_begin};
    }
    $cmp = $tmp1->{b} <=> $tmp2->{b};
    if ($cmp > 0) {
        $i_end       = $tmp2->{b};
        $open_end    = $tmp2->{open_end};
    }
    elsif ($cmp < 0) {
        $i_end       = $tmp1->{b};
        $open_end    = $tmp1->{open_end};
    }
    else { 
        $i_end       = $tmp1->{b};
        $open_end    = ($tmp1->{open_end} || $tmp2->{open_end});
    }
    $cmp = $i_beg <=> $i_end;
    return 0 if 
        ( $cmp > 0 ) || 
        ( ($cmp == 0) && ($open_beg || $open_end) ) ;
    return 1;
}


sub _simple_complement {
    my $self = $_[0];
    if ($self->{b} == $inf) {
        return if $self->{a} == $neg_inf;
        return { a => $neg_inf, 
                 b => $self->{a}, 
                 open_begin => 1, 
                 open_end => ! $self->{open_begin} };
    }
    if ($self->{a} == $neg_inf) {
        return { a => $self->{b}, 
                 b => $inf,  
                 open_begin => ! $self->{open_end}, 
                 open_end => 1 };
    }
    ( { a => $neg_inf, 
        b => $self->{a}, 
        open_begin => 1, 
        open_end => ! $self->{open_begin} 
      },
      { a => $self->{b}, 
        b => $inf,  
        open_begin => ! $self->{open_end}, 
        open_end => 1 
      }
    );
}

sub _simple_union {
    my ($tmp2, $tmp1, $tolerance) = @_; 
    my $cmp; 
    if ($tolerance) {
        # "integer"
        my $a1_open =  $tmp1->{open_begin} ? -$tolerance : $tolerance ;
        my $b1_open =  $tmp1->{open_end}   ? -$tolerance : $tolerance ;
        my $a2_open =  $tmp2->{open_begin} ? -$tolerance : $tolerance ;
        my $b2_open =  $tmp2->{open_end}   ? -$tolerance : $tolerance ;
        # open_end touching?
        if ((($tmp1->{b}+$tmp1->{b}) + $b1_open ) < 
            (($tmp2->{a}+$tmp2->{a}) - $a2_open)) {
            # self disjuncts b
            return ( $tmp1, $tmp2 );
        }
        if ((($tmp1->{a}+$tmp1->{a}) - $a1_open ) > 
            (($tmp2->{b}+$tmp2->{b}) + $b2_open)) {
            # self disjuncts b
            return ( $tmp2, $tmp1 );
        }
    }
    else {
        # "real"
        $cmp = $tmp1->{b} <=> $tmp2->{a};
        if ( $cmp < 0 ||
             ( $cmp == 0 && $tmp1->{open_end} && $tmp2->{open_begin} ) ) {
            return ( $tmp1, $tmp2 );
        }
        $cmp = $tmp1->{a} <=> $tmp2->{b};
        if ( $cmp > 0 || 
             ( $cmp == 0 && $tmp2->{open_end} && $tmp1->{open_begin} ) ) {
            return ( $tmp2, $tmp1 );
        }
    }

    my $tmp;
    $cmp = $tmp1->{a} <=> $tmp2->{a};
    if ($cmp > 0) {
        $tmp->{a} = $tmp2->{a};
        $tmp->{open_begin} = $tmp2->{open_begin};
    }
    elsif ($cmp == 0) {
        $tmp->{a} = $tmp1->{a};
        $tmp->{open_begin} = $tmp1->{open_begin} ? $tmp2->{open_begin} : 0;
    }
    else {
        $tmp->{a} = $tmp1->{a};
        $tmp->{open_begin} = $tmp1->{open_begin};
    }

    $cmp = $tmp1->{b} <=> $tmp2->{b};
    if ($cmp < 0) {
        $tmp->{b} = $tmp2->{b};
        $tmp->{open_end} = $tmp2->{open_end};
    }
    elsif ($cmp == 0) {
        $tmp->{b} = $tmp1->{b};
        $tmp->{open_end} = $tmp1->{open_end} ? $tmp2->{open_end} : 0;
    }
    else {
        $tmp->{b} = $tmp1->{b};
        $tmp->{open_end} = $tmp1->{open_end};
    }
    return $tmp;
}


sub _simple_spaceship {
    my ($tmp1, $tmp2, $inverted) = @_;
    my $cmp;
    if ($inverted) {
        $cmp = $tmp2->{a} <=> $tmp1->{a};
        return $cmp if $cmp;
        $cmp = $tmp1->{open_begin} <=> $tmp2->{open_begin};
        return $cmp if $cmp;
        $cmp = $tmp2->{b} <=> $tmp1->{b};
        return $cmp if $cmp;
        return $tmp1->{open_end} <=> $tmp2->{open_end};
    }
    $cmp = $tmp1->{a} <=> $tmp2->{a};
    return $cmp if $cmp;
    $cmp = $tmp2->{open_begin} <=> $tmp1->{open_begin};
    return $cmp if $cmp;
    $cmp = $tmp1->{b} <=> $tmp2->{b};
    return $cmp if $cmp;
    return $tmp2->{open_end} <=> $tmp1->{open_end};
}


sub _simple_new {
    my ($tmp, $tmp2, $type) = @_;
    if ($type) {
        if ( ref($tmp) ne $type ) { 
            $tmp = new $type $tmp;
        }
        if ( ref($tmp2) ne $type ) {
            $tmp2 = new $type $tmp2;
        }
    }
    if ($tmp > $tmp2) {
        carp "Invalid interval specification: start value is after end";
        # ($tmp, $tmp2) = ($tmp2, $tmp);
    }
    return { a => $tmp , b => $tmp2 , open_begin => 0 , open_end => 0 };
}


sub _simple_as_string {
    my $set = shift;
    my $self = $_[0];
    my $s;
    return "" unless defined $self;
    $self->{open_begin} = 1 if ($self->{a} == -$inf );
    $self->{open_end}   = 1 if ($self->{b} == $inf );
    my $tmp1 = $self->{a};
    $tmp1 = $tmp1->datetime if UNIVERSAL::can( $tmp1, 'datetime' );
    $tmp1 = "$tmp1";
    my $tmp2 = $self->{b};
    $tmp2 = $tmp2->datetime if UNIVERSAL::can( $tmp2, 'datetime' );
    $tmp2 = "$tmp2";
    return $tmp1 if $tmp1 eq $tmp2;
    $s = $self->{open_begin} ? $set->separators(2) : $set->separators(0);
    $s .= $tmp1 . $set->separators(4) . $tmp2;
    $s .= $self->{open_end} ? $set->separators(3) : $set->separators(1);
    return $s;
}

# end of "_simple_" methods


sub type {
    my $self = shift;
    unless (@_) {
        return ref($self) ? $self->{type} : $Type;
    }
    my $tmp_type = shift;
    eval "use " . $tmp_type;
    carp "Warning: can't start $tmp_type : $@" if $@;
    if (ref($self))  {
        $self->{type} = $tmp_type;
        return $self;
    }
    else {
        $Type = $tmp_type;
        return $Type;
    }
}

sub list {
    my $self = shift;
    my @b = ();
    foreach (@{$self->{list}}) {
        push @b, $self->new($_);
    }
    return @b;
}

sub fixtype {
    my $self = shift;
    $self = $self->copy;
    $self->{fixtype} = 1;
    my $type = $self->type;
    return $self unless $type;
    foreach (@{$self->{list}}) {
        $_->{a} = $type->new($_->{a}) unless ref($_->{a}) eq $type;
        $_->{b} = $type->new($_->{b}) unless ref($_->{b}) eq $type;
    }
    return $self;
}

sub numeric {
    my $self = shift;
    return $self unless $self->{fixtype};
    $self = $self->copy;
    $self->{fixtype} = 0;
    foreach (@{$self->{list}}) {
        $_->{a} = 0 + $_->{a};
        $_->{b} = 0 + $_->{b};
    }
    return $self;
}

sub _no_cleanup { $_[0] }   # obsolete

sub first {
    my $self = $_[0];
    if (exists $self->{first} ) {
        return wantarray ? @{$self->{first}} : $self->{first}[0];
    }
    unless ( @{$self->{list}} ) {
        return wantarray ? (undef, 0) : undef; 
    }
    my $first = $self->new( $self->{list}[0] );
    return $first unless wantarray;
    my $res = $self->new;   
    push @{$res->{list}}, @{$self->{list}}[1 .. $#{$self->{list}}];
    return @{$self->{first}} = ($first) if $res->is_null;
    return @{$self->{first}} = ($first, $res);
}

sub last {
    my $self = $_[0];
    if (exists $self->{last} ) {
        return wantarray ? @{$self->{last}} : $self->{last}[0];
    }
    unless ( @{$self->{list}} ) {
        return wantarray ? (undef, 0) : undef;
    }
    my $last = $self->new( $self->{list}[-1] );
    return $last unless wantarray;  
    my $res = $self->new; 
    push @{$res->{list}}, @{$self->{list}}[0 .. $#{$self->{list}}-1];
    return @{$self->{last}} = ($last) if $res->is_null;
    return @{$self->{last}} = ($last, $res);
}

sub is_null {
    @{$_[0]->{list}} ? 0 : 1;
}

sub is_empty {
    $_[0]->is_null;
}

sub is_nonempty {
    ! $_[0]->is_null;
}

sub is_span {
    ( $#{$_[0]->{list}} == 0 ) ? 1 : 0;
}

sub is_singleton {
    ( $#{$_[0]->{list}} == 0 &&
      $_[0]->{list}[0]{a} == $_[0]->{list}[0]{b} ) ? 1 : 0;
}

sub is_subset {
    my $a1 = shift;
    my $b1;
    if (ref ($_[0]) eq ref($a1) ) { 
        $b1 = shift;
    } 
    else {
        $b1 = $a1->new(@_);  
    }
    return $b1->contains( $a1 );
}

sub is_proper_subset {
    my $a1 = shift;
    my $b1;
    if (ref ($_[0]) eq ref($a1) ) { 
        $b1 = shift;
    } 
    else {
        $b1 = $a1->new(@_);  
    }

    my $contains = $b1->contains( $a1 );
    return $contains unless $contains;
     
    my $equal = ( $a1 == $b1 );
    return $equal if !defined $equal || $equal;

    return 1;
}

sub is_disjoint {
    my $intersects = shift->intersects( @_ );
    return ! $intersects if defined $intersects;
    return $intersects;
}

sub iterate {
    # TODO: options 'no-sort', 'no-merge', 'keep-null' ...
    my $a1 = shift;
    my $iterate = $a1->empty_set();
    my (@tmp, $ia);
    my $subroutine = shift;
    foreach $ia (0 .. $#{$a1->{list}}) {
        @tmp = $subroutine->( $a1->new($a1->{list}[$ia]), @_ );
        $iterate = $iterate->union(@tmp) if @tmp; 
    }
    return $iterate;    
}


sub intersection {
    my $a1 = shift;
    my $b1 = ref ($_[0]) eq ref($a1) ? $_[0] : $a1->new(@_);
    return _intersection ( 'intersection', $a1, $b1 );
}

sub intersects {
    my $a1 = shift;
    my $b1 = ref ($_[0]) eq ref($a1) ? $_[0] : $a1->new(@_);
    return _intersection ( 'intersects', $a1, $b1 );
}

sub intersected_spans {
    my $a1 = shift;
    my $b1 = ref ($_[0]) eq ref($a1) ? $_[0] : $a1->new(@_);
    return _intersection ( 'intersected_spans', $a1, $b1 );
}


sub _intersection {
    my ( $op, $a1, $b1 ) = @_;

    my $ia;   
    my ( $a0, $na ) = ( 0, $#{$a1->{list}} );
    my ( $tmp1, $tmp1a, $tmp2a, $tmp1b, $tmp2b, $i_beg, $i_end, $open_beg, $open_end );
    my ( $cmp1, $cmp2 );
    my @a;

    # for-loop optimization (makes little difference)
    # This was kept for backward compatibility with Date::Set tests
    my $self = $a1;
    if ($na < $#{ $b1->{list} })
    {
        $na = $#{ $b1->{list} };
        ($a1, $b1) = ($b1, $a1);
    }
    # ---

    B: foreach my $tmp2 ( @{ $b1->{list} } ) {
        $tmp2a = $tmp2->{a};
        $tmp2b = $tmp2->{b};
        A: foreach $ia ($a0 .. $na) {
            $tmp1 = $a1->{list}[$ia];
            $tmp1b = $tmp1->{b};

            if ($tmp1b < $tmp2a) {
                $a0++;
                next A;
            }
            $tmp1a = $tmp1->{a};
            if ($tmp1a > $tmp2b) {
                next B;
            }

            $cmp1 = $tmp1a <=> $tmp2a;
            if ( $cmp1 < 0 ) {
                $tmp1a        = $tmp2a;
                $open_beg     = $tmp2->{open_begin};
            }
            elsif ( $cmp1 ) {
                $open_beg     = $tmp1->{open_begin};
            }
            else {
                $open_beg     = $tmp1->{open_begin} || $tmp2->{open_begin};
            }

            $cmp2 = $tmp1b <=> $tmp2b;
            if ( $cmp2 > 0 ) {
                $tmp1b        = $tmp2b;
                $open_end     = $tmp2->{open_end};
            }
            elsif ( $cmp2 ) {
                $open_end     = $tmp1->{open_end};
            }
            else {
                $open_end     = $tmp1->{open_end} || $tmp2->{open_end};
            }

            if ( ( $tmp1a <= $tmp1b ) &&
                 ( ($tmp1a != $tmp1b) || 
                   (!$open_beg and !$open_end) ||
                   ($tmp1a == $inf)   ||               # XXX
                   ($tmp1a == $neg_inf)
                 )
               ) 
            {
                if ( $op eq 'intersection' )
                {
                    push @a, {
                        a => $tmp1a, b => $tmp1b, 
                        open_begin => $open_beg, open_end => $open_end } ;
                }
                if ( $op eq 'intersects' )
                {
                    return 1;
                }
                if ( $op eq 'intersected_spans' )
                {
                    push @a, $tmp1;
                    $a0++;
                    next A;
                }
            }
        }
    }

    return 0 if $op eq 'intersects';
   
    my $intersection = $self->new();
    $intersection->{list} = \@a;
    return $intersection;    
}


sub complement {
    my $self = shift;
    if (@_) {
        my $a1;
        if (ref ($_[0]) eq ref($self) ) {
            $a1 = shift;
        } 
        else {
            $a1 = $self->new(@_);  
        }
        return $self->intersection( $a1->complement );
    }

    unless ( @{$self->{list}} ) {
        return $self->universal_set;
    }
    my $complement = $self->empty_set();
    @{$complement->{list}} = _simple_complement($self->{list}[0]); 

    my $tmp = $self->empty_set();    
    foreach my $ia (1 .. $#{$self->{list}}) {
        @{$tmp->{list}} = _simple_complement($self->{list}[$ia]);
        $complement = $complement->intersection($tmp); 
    }
    return $complement;    
}


sub until {
    my $a1 = shift;
    my $b1;
    if (ref ($_[0]) eq ref($a1) ) {
        $b1 = shift;
    } 
    else {
        $b1 = $a1->new(@_);  
    }
    my @b1_min = $b1->min_a;
    my @a1_max = $a1->max_a;

    unless (defined $b1_min[0]) {
        return $a1->until($inf);
    } 
    unless (defined $a1_max[0]) {
        return $a1->new(-$inf)->until($b1);
    }

    my ($ia, $ib, $begin, $end);
    $ia = 0;
    $ib = 0;

    my $u = $a1->new;   
    my $last = -$inf;
    while ( ($ia <= $#{$a1->{list}}) && ($ib <= $#{$b1->{list}})) {
        $begin = $a1->{list}[$ia]{a};
        $end   = $b1->{list}[$ib]{b};
        if ( $end <= $begin ) {
            push @{$u->{list}}, {
                a => $last ,
                b => $end ,
                open_begin => 0 ,
                open_end => 1 };
            $ib++;
            $last = $end;
            next;
        }
        push @{$u->{list}}, { 
            a => $begin , 
            b => $end ,
            open_begin => 0 , 
            open_end => 1 };
        $ib++;
        $ia++;
        $last = $end;
    }
    if ($ia <= $#{$a1->{list}}  &&
        $a1->{list}[$ia]{a} >= $last ) 
    {
        push @{$u->{list}}, {
            a => $a1->{list}[$ia]{a} ,
            b => $inf ,
            open_begin => 0 ,
            open_end => 1 };
    }
    return $u;    
}

sub start_set {
    return $_[0]->iterate(
        sub { $_[0]->min }
    );
}


sub end_set {
    return $_[0]->iterate(
        sub { $_[0]->max }
    );
}

sub union {
    my $a1 = shift;
    my $b1;
    if (ref ($_[0]) eq ref($a1) ) {
        $b1 = shift;
    } 
    else {
        $b1 = $a1->new(@_);  
    }
    # test for union with empty set
    if ( $#{ $a1->{list} } < 0 ) {
        return $b1;
    }
    if ( $#{ $b1->{list} } < 0 ) {
        return $a1;
    }
    my @b1_min = $b1->min_a;
    my @a1_max = $a1->max_a;
    unless (defined $b1_min[0]) {
        return $a1;
    }
    unless (defined $a1_max[0]) {
        return $b1;
    }
    my ($ia, $ib);
    $ia = 0;
    $ib = 0;

    #  size+order matters on speed 
    $a1 = $a1->new($a1);    # don't modify ourselves 
    my $b_list = $b1->{list};
    # -- frequent case - $b1 is after $a1
    if ($b1_min[0] > $a1_max[0]) {
        push @{$a1->{list}}, @$b_list;
        return $a1;
    }

    my @tmp;
    my $is_real = !$a1->tolerance && !$b1->tolerance;
    B: foreach $ib ($ib .. $#{$b_list}) {
        foreach $ia ($ia .. $#{$a1->{list}}) {
            @tmp = _simple_union($a1->{list}[$ia], $b_list->[$ib], $a1->{tolerance});
            if ($#tmp == 0) {
                    $a1->{list}[$ia] = $tmp[0];

                    while (1) {
                        last if $ia >= $#{$a1->{list}};    
                        last unless _simple_intersects ( $a1->{list}[$ia], $a1->{list}[$ia + 1] )
                            ||    $is_real 
                               && $a1->{list}[$ia]{b} == $a1->{list}[$ia + 1]{a};
                        @tmp = _simple_union($a1->{list}[$ia], $a1->{list}[$ia + 1], $a1->{tolerance});
                        last unless @tmp == 1;
                        $a1->{list}[$ia] = $tmp[0];
                        splice( @{$a1->{list}}, $ia + 1, 1 );
                    }
                    
                    next B;
            }
            if ($a1->{list}[$ia]{a} >= $b_list->[$ib]{a}) {
                splice (@{$a1->{list}}, $ia, 0, $b_list->[$ib]);
                next B;
            }
        }
        push @{$a1->{list}}, $b_list->[$ib];
    }
    return $a1;    
}


# 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;
    my $b1 = $a1->union(@_);
    return ($b1 == $a1) ? 1 : 0;
}


sub copy {
    my $self = shift;
    my $copy = $self->empty_set();
    ## return $copy unless ref($self);   # constructor!
    foreach my $key (keys %{$self}) {
        if ( ref( $self->{$key} ) eq 'ARRAY' ) {
            @{ $copy->{$key} } = @{ $self->{$key} };
        }
        else {
            $copy->{$key} = $self->{$key};
        }
    }
    return $copy;
}

*clone = \&copy;


sub new {
    my $class = shift;
    my $self;
    if ( ref $class ) {
        $self = bless {
                    list      => [],
                    tolerance => $class->{tolerance},
                    type      => $class->{type},
                    fixtype   => $class->{fixtype},
                }, ref($class);
    }
    else {
        $self = bless { 
                    list      => [],
                    tolerance => $tolerance ? $tolerance : 0,
                    type      => $class->type,
                    fixtype   => $fixtype   ? $fixtype : 0,
                }, $class;
    }
    my ($tmp, $tmp2, $ref);
    while (@_) {
        $tmp = shift;
        $ref = ref($tmp);
        if ($ref) {
            if ($ref eq 'ARRAY') {
                # allows arrays of arrays
                $tmp = $class->new(@$tmp);  # call new() recursively
                push @{ $self->{list} }, @{$tmp->{list}};
                next;
            }
            if ($ref eq 'HASH') {
                push @{ $self->{list} }, $tmp; 
                next;
            }
            if ($tmp->isa(__PACKAGE__)) {
                push @{ $self->{list} }, @{$tmp->{list}};
                next;
            }
        }
        if ( @_ ) { 
            $tmp2 = shift
        }
        else {
            $tmp2 = $tmp
        }
        push @{ $self->{list} }, _simple_new($tmp,$tmp2, $self->{type} )
    }
    $self;
}

sub empty_set {
    $_[0]->new;
}

sub universal_set {
    $_[0]->new( NEG_INFINITY, INFINITY );
}

*minus = \&complement;

*difference = \&complement;

sub symmetric_difference {
    my $a1 = shift;
    my $b1;
    if (ref ($_[0]) eq ref($a1) ) {
        $b1 = shift;
    }
    else {
        $b1 = $a1->new(@_);
    }

    return $a1->complement( $b1 )->union(
           $b1->complement( $a1 ) );
}

*simmetric_difference = \&symmetric_difference; # bugfix

sub min { 
    ($_[0]->min_a)[0];
}

sub min_a { 
    my $self = $_[0];
    return @{$self->{min}} if exists $self->{min};
    return @{$self->{min}} = (undef, 0) unless @{$self->{list}};
    my $tmp = $self->{list}[0]{a};
    my $tmp2 = $self->{list}[0]{open_begin} || 0;
    if ($tmp2 && $self->{tolerance}) {
        $tmp2 = 0;
        $tmp += $self->{tolerance};
    }
    return @{$self->{min}} = ($tmp, $tmp2);  
};

sub max { 
    ($_[0]->max_a)[0];
}

sub max_a { 
    my $self = $_[0];
    return @{$self->{max}} if exists $self->{max};
    return @{$self->{max}} = (undef, 0) unless @{$self->{list}};
    my $tmp = $self->{list}[-1]{b};
    my $tmp2 = $self->{list}[-1]{open_end} || 0;
    if ($tmp2 && $self->{tolerance}) {
        $tmp2 = 0;
        $tmp -= $self->{tolerance};
    }
    return @{$self->{max}} = ($tmp, $tmp2);  
};

sub count {
    1 + $#{$_[0]->{list}};
}

sub size { 
    my $self = $_[0];
    my $size;  
    foreach( @{$self->{list}} ) {
        if ( $size ) {
            $size += $_->{b} - $_->{a};
        }
        else {
            $size = $_->{b} - $_->{a};
        }
        if ( $self->{tolerance} ) {
            $size += $self->{tolerance} unless $_->{open_end};
            $size -= $self->{tolerance} if $_->{open_begin};
            $size -= $self->{tolerance} if $_->{open_end};
        }
    }
    return $size; 
};

sub span { 
    my $self = $_[0];
    my @max = $self->max_a;
    my @min = $self->min_a;
    return undef unless defined $min[0] && defined $max[0];
    my $a1 = $self->new($min[0], $max[0]);
    $a1->{list}[0]{open_end} = $max[1];
    $a1->{list}[0]{open_begin} = $min[1];
    return $a1;
};

sub spaceship {
    my ($tmp1, $tmp2, $inverted) = @_;
    if ($inverted) {
        ($tmp2, $tmp1) = ($tmp1, $tmp2);
    }
    foreach(0 .. $#{$tmp1->{list}}) {
        my $this  = $tmp1->{list}[$_];
        if ($_ > $#{ $tmp2->{list} } ) { 
            return 1; 
        }
        my $other = $tmp2->{list}[$_];
        my $cmp = _simple_spaceship($this, $other);
        return $cmp if $cmp;   # this != $other;
    }
    return $#{ $tmp1->{list} } == $#{ $tmp2->{list} } ? 0 : -1;
}

sub tolerance {
    my $self = shift;
    my $tmp = pop;
    if (ref($self)) {  
        # local
        return $self->{tolerance} unless defined $tmp;
        $self = $self->copy;
        $self->{tolerance} = $tmp;
        delete $self->{max};  # tolerance may change "max"

        $_ = 1;
        my @tmp;
        while ( $_ <= $#{$self->{list}} ) {
            @tmp = Set::Infinite::Basic::_simple_union($self->{list}->[$_],
                $self->{list}->[$_ - 1],
                $self->{tolerance});
            if ($#tmp == 0) {
                $self->{list}->[$_ - 1] = $tmp[0];
                splice (@{$self->{list}}, $_, 1);
            }
            else {
                $_ ++;
            }
        }

        return $self;
    }
    # global
    $tolerance = $tmp if defined($tmp);
    return $tolerance;
}

sub integer { 
    $_[0]->tolerance (1);
}

sub real {
    $_[0]->tolerance (0);
}

sub as_string {
    my $self = shift;
    return $self->separators(6) . 
           join( $self->separators(5), 
                 map { $self->_simple_as_string($_) } @{$self->{list}} ) .
           $self->separators(7),;
}


sub DESTROY {}

1;

__END__

=head1 NAME

Set::Infinite::Basic - Sets of intervals
6
=head1 SYNOPSIS

  use Set::Infinite::Basic;

  $set = Set::Infinite::Basic->new(1,2);    # [1..2]
  print $set->union(5,6);            # [1..2],[5..6]

=head1 DESCRIPTION

Set::Infinite::Basic is a Set Theory module for infinite sets.

It works on reals, integers, and objects.

This module does not support recurrences. Recurrences are implemented in Set::Infinite.

=head1 METHODS

=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.

=head2 until

Extends a set until another:

    0,5,7 -> until 2,6,10

gives

    [0..2), [5..6), [7..10)

Note: this function is still experimental.

=head2 copy

=head2 clone

Makes a new object from the object's data.

=head2 Mode functions:    

    $set = $set->real;

    $set = $set->integer;

=head2 Logic functions:

    $logic = $set->intersects($b);

    $logic = $set->contains($b);

    $logic = $set->is_null;  # also called "is_empty"

=head2 Set functions:

    $set = $set->union($b);    

    $set = $set->intersection($b);

    $set = $set->complement;
    $set = $set->complement($b);   # can also be called "minus" or "difference"

    $set = $set->symmetric_difference( $b );

    $set = $set->span;   

        result is (min .. max)

=head2 Scalar functions:

    $i = $set->min;

    $i = $set->max;

    $i = $set->size;  

    $i = $set->count;  # number of spans

=head2 Overloaded Perl functions:

    print    

    sort, <=> 

=head2 Global functions:

    separators(@i)

        chooses the interval separators. 

        default are [ ] ( ) '..' ','.

    INFINITY

        returns an 'Infinity' number.

    NEG_INFINITY

        returns a '-Infinity' number.

    iterate ( sub { } )

        Iterates over a subroutine. 
        Returns the union of partial results.

    first

        In scalar context returns the first interval of a set.

        In list context returns the first interval of a set, and the
        'tail'.

        Works in unbounded sets

    type($i)

        chooses an object data type. 

        default is none (a normal perl SCALAR).

        examples: 

        type('Math::BigFloat');
        type('Math::BigInt');
        type('Set::Infinite::Date');
            See notes on Set::Infinite::Date below.

    tolerance(0)    defaults to real sets (default)
    tolerance(1)    defaults to integer sets

    real            defaults to real sets (default)

    integer         defaults to integer sets

=head2 Internal functions:

    $set->fixtype; 

    $set->numeric;

=head1 CAVEATS

    $set = Set::Infinite->new(10,1);
        Will be interpreted as [1..10]

    $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) 

    $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.

=head1 INTERNALS

The internal representation of a I<span> is a hash:

    { a =>   start of span,
      b =>   end of span,
      open_begin =>   '0' the span starts in 'a'
                      '1' the span starts after 'a'
      open_end =>     '0' the span ends in 'b'
                      '1' the span ends before 'b'
    }

For example, this set:

    [100..200),300,(400..infinity)

is represented by the array of hashes:

    list => [
        { a => 100, b => 200, open_begin => 0, open_end => 1 },
        { a => 300, b => 300, open_begin => 0, open_end => 0 },
        { a => 400, b => infinity, open_begin => 0, open_end => 1 },
    ]

The I<density> of a set is stored in the C<tolerance> variable:

    tolerance => 0;  # the set is made of real numbers.

    tolerance => 1;  # the set is made of integers.

The C<type> variable stores the I<class> of objects that will be stored in the set.

    type => 'DateTime';   # this is a set of DateTime objects

The I<infinity> value is generated by Perl, when it finds a numerical overflow:

    $inf = 100**100**100;

=head1 SEE ALSO

    Set::Infinite

=head1 AUTHOR

    Flavio S. Glock <fglock@gmail.com>

=cut