2 # BioPerl module for Bio::Map::PositionI
4 # Please direct questions and support issues to <bioperl-l@bioperl.org>
6 # Cared for by Sendu Bala <bix@sendu.me.uk>
8 # Copyright Jason Stajich
10 # You may distribute this module under the same terms as perl itself
12 # POD documentation - main docs before the code
16 Bio::Map::PositionI - Abstracts the notion of a position having a value in the context of a marker and a Map
20 # do not use this module directly
21 # See Bio::Map::Position for an example of
26 This object stores one of the postions that a mappable object
27 (e.g. Marker) may have in a map.
29 Positions can have non-numeric values or other methods to store the locations,
30 so they have a method numeric() which does the conversion. numeric()
31 returns the position in a form that can be compared between other positions of
32 the same type. It is not necessarily a value suitable for sorting positions (it
33 may be the distance from the previous position); for that purpose the result of
34 sortable() should be used.
36 A 'position', in addition to being a single point, can also be an area and so
37 can be imagined as a range and compared with other positions on the basis of
38 overlap, intersection etc.
44 User feedback is an integral part of the evolution of this and other
45 Bioperl modules. Send your comments and suggestions preferably to
46 the Bioperl mailing list. Your participation is much appreciated.
48 bioperl-l@bioperl.org - General discussion
49 http://bioperl.org/wiki/Mailing_lists - About the mailing lists
53 Please direct usage questions or support issues to the mailing list:
55 I<bioperl-l@bioperl.org>
57 rather than to the module maintainer directly. Many experienced and
58 reponsive experts will be able look at the problem and quickly
59 address it. Please include a thorough description of the problem
60 with code and data examples if at all possible.
64 Report bugs to the Bioperl bug tracking system to help us keep track
65 of the bugs and their resolution. Bug reports can be submitted via the
68 https://redmine.open-bio.org/projects/bioperl/
70 =head1 AUTHOR - Jason Stajich
72 Email jason-at-bioperl.org
76 Lincoln Stein, lstein-at-cshl.org
77 Heikki Lehvaslaiho, heikki-at-bioperl-dot-org
78 Sendu Bala, bix@sendu.me.uk
82 The rest of the documentation details each of the object methods.
83 Internal methods are usually preceded with a _
87 # Let the code begin...
89 package Bio
::Map
::PositionI
;
91 use Bio
::Map
::PositionHandler
;
92 use Bio
::Map
::Mappable
;
93 use Scalar
::Util
qw(looks_like_number);
95 use base
qw(Bio::Map::EntityI Bio::RangeI);
97 =head2 EntityI methods
99 These are fundamental to coordination of Positions and other entities, so are
100 implemented at the interface level
104 =head2 get_position_handler
106 Title : get_position_handler
107 Usage : my $position_handler = $entity->get_position_handler();
108 Function: Gets a PositionHandlerI that $entity is registered with.
109 Returns : Bio::Map::PositionHandlerI object
114 sub get_position_handler
{
116 unless (defined $self->{_eh
}) {
117 my $ph = Bio
::Map
::PositionHandler
->new(-self
=> $self);
124 =head2 PositionHandlerI-related methods
126 These are fundamental to coordination of Positions and other entities, so are
127 implemented at the interface level
134 Usage : my $map = $position->map();
135 $position->map($map);
136 Function: Get/Set the map the position is in.
137 Returns : L<Bio::Map::MapI>
139 new L<Bio::Map::MapI> to set
144 my ($self, $map) = @_;
145 return $self->get_position_handler->map($map);
151 Usage : my $element = $position->element();
152 $position->element($element);
153 Function: Get/Set the element the position is for.
154 Returns : L<Bio::Map::MappableI>
156 new L<Bio::Map::MappableI> to set
161 my ($self, $element) = @_;
162 return $self->get_position_handler->element($element);
168 Function: This is a synonym of the element() method
169 Status : deprecated, will be removed in the next version
175 =head2 PositionI-specific methods
182 Usage : my $pos = $position->value();
183 Function: Get/Set the value for this position
184 Returns : scalar, value
185 Args : [optional] new value to set
191 $self->throw_not_implemented();
197 Usage : my $num = $position->numeric;
198 Function: Read-only method that is guaranteed to return a numeric
199 representation of the start of this position.
200 Returns : scalar numeric
201 Args : none to get the co-ordinate normally (see absolute() method), OR
202 Bio::Map::RelativeI to get the co-ordinate converted to be
203 relative to what this Relative describes.
209 $self->throw_not_implemented();
215 Usage : my $num = $position->sortable();
216 Function: Read-only method that is guaranteed to return a value suitable
217 for correctly sorting this kind of position amongst other positions
218 of the same kind on the same map. Note that sorting different kinds
219 of position together is unlikely to give sane results.
227 $self->throw_not_implemented();
233 Usage : my $relative = $position->relative();
234 $position->relative($relative);
235 Function: Get/set the thing this Position's coordinates (numerical(), start(),
236 end()) are relative to, as described by a Relative object.
237 Returns : Bio::Map::RelativeI (default is one describing "relative to the
238 start of the Position's map")
239 Args : none to get, OR
240 Bio::Map::RelativeI to set
246 $self->throw_not_implemented();
252 Usage : my $absolute = $position->absolute();
253 $position->absolute($absolute);
254 Function: Get/set how this Position's co-ordinates (numerical(), start(),
255 end()) are reported. When absolute is off, co-ordinates are
256 relative to the thing described by relative(). Ie. the value
257 returned by start() will be the same as the value you set start()
258 to. When absolute is on, co-ordinates are converted to be relative
259 to the start of the map.
261 So if relative() currently points to a Relative object describing
262 "relative to another position which is 100 bp from the start of
263 the map", this Position's start() had been set to 50 and absolute()
264 returns 1, $position->start() will return 150. If absolute() returns
265 0 in the same situation, $position->start() would return 50.
267 Returns : boolean (default 0)
268 Args : none to get, OR
275 $self->throw_not_implemented();
278 =head2 RangeI-based methods
285 Usage : my $start = $position->start();
286 $position->start($start);
287 Function: Get/set the start co-ordinate of this position.
288 Returns : the start of this position
289 Args : scalar numeric to set, OR
290 none to get the co-ordinate normally (see absolute() method), OR
291 Bio::Map::RelativeI to get the co-ordinate converted to be
292 relative to what this Relative describes.
299 Usage : my $end = $position->end();
300 $position->end($end);
301 Function: Get/set the end co-ordinate of this position.
302 Returns : the end of this position
303 Args : scalar numeric to set, OR
304 none to get the co-ordinate normally (see absolute() method), OR
305 Bio::Map::RelativeI to get the co-ordinate converted to be
306 relative to what this Relative describes.
313 Usage : $length = $position->length();
314 Function: Get the length of this position.
315 Returns : the length of this position
323 Usage : $strand = $position->strand();
324 Function: Get the strand of this position; it is always 1 since maps to not
338 Usage : print $position->toString(), "\n";
339 Function: stringifies this range
340 Returns : a string representation of the range of this Position
341 Args : optional Bio::Map::RelativeI to have the co-ordinates reported
342 relative to the thing described by that Relative
348 $self->throw_not_implemented();
351 =head1 RangeI-related methods
353 These methods work by considering only the values of start() and end(), as
354 modified by considering every such co-ordinate relative to the start of the map
355 (ie. absolute(1) is set temporarily during the calculation), or any supplied
356 Relative. For the boolean methods, when the comparison Position is on the same
357 map as the calling Position, there is no point supplying a Relative since the
358 answer will be the same as without. Relative is most useful when comparing
359 Positions on different maps and you have a Relative that describes some special
360 place on each map like 'the start of the gene', where the actual start of the
361 gene relative to the start of the map is different for each map.
363 The methods do not consider maps during their calculations - things on different
364 maps can overlap/contain/intersect/etc. each other.
366 The geometrical methods (intersect, union etc.) do things to the geometry of
367 ranges, and return Bio::Map::PositionI compliant objects or triplets (start,
368 stop, strand) from which new positions could be built. When a PositionI is made
369 it will have a map transferred to it if all the arguments shared the same map.
370 If a Relative was supplied the result will have that same Relative.
372 Note that the strand-testing args are there for compatability with the RangeI
373 interface. They have no meaning when only using PositionI objects since maps do
374 not have strands. Typically you will just set the argument to undef if you want
375 to supply the argument after it.
380 Usage : if ($p1->equals($p2)) {...}
381 Function: Test whether $p1 has the same start, end, length as $p2.
382 Returns : true if they are describing the same position (regardless of map)
383 Args : arg #1 = a Bio::RangeI (eg. a Bio::Map::Position) to compare this
385 arg #2 = optional strand-testing arg ('strong', 'weak', 'ignore')
386 arg #3 = optional Bio::Map::RelativeI to ask if the Positions
387 equal in terms of their relative position to the thing
388 described by that Relative
393 # overriding the RangeI implementation so we can handle Relative
394 my ($self, $other, $so, $rel) = @_;
396 my ($own_start, $own_end) = $self->_pre_rangei($self, $rel);
397 my ($other_start, $other_end) = $self->_pre_rangei($other, $rel);
399 return ($self->_testStrand($other, $so) and
400 $own_start == $other_start and $own_end == $other_end);
407 Usage : if ($position->less_than($other_position)) {...}
408 Function: Ask if this Position ends before another starts.
410 Args : arg #1 = a Bio::RangeI (eg. a Bio::Map::Position) to compare this
412 arg #2 = optional Bio::Map::RelativeI to ask if the Position is less
413 in terms of their relative position to the thing described
419 my ($self, $other, $rel) = @_;
421 my ($own_start, $own_end) = $self->_pre_rangei($self, $rel);
422 my ($other_start, $other_end) = $self->_pre_rangei($other, $rel);
424 return $own_end < $other_start;
430 Usage : if ($position->greater_than($other_position)) {...}
431 Function: Ask if this Position starts after another ends.
433 Args : arg #1 = a Bio::RangeI (eg. a Bio::Map::Position) to compare this
435 arg #2 = optional Bio::Map::RelativeI to ask if the Position is
436 greater in terms of their relative position to the thing
437 described by that Relative
442 my ($self, $other, $rel) = @_;
444 my ($own_start, $own_end) = $self->_pre_rangei($self, $rel);
445 my ($other_start, $other_end) = $self->_pre_rangei($other, $rel);
447 return $own_start > $other_end;
453 Usage : if ($p1->overlaps($p2)) {...}
454 Function: Tests if $p1 overlaps $p2.
455 Returns : True if the positions overlap (regardless of map), false otherwise
456 Args : arg #1 = a Bio::RangeI (eg. a Bio::Map::Position) to compare this
458 arg #2 = optional strand-testing arg ('strong', 'weak', 'ignore')
459 arg #3 = optional Bio::Map::RelativeI to ask if the Positions
460 overlap in terms of their relative position to the thing
461 described by that Relative
462 arg #4 = optional minimum percentage length of the overlap before
463 reporting an overlap exists (default 0)
468 # overriding the RangeI implementation so we can handle Relative
469 my ($self, $other, $so, $rel, $min_percent) = @_;
472 my ($own_min, $other_min) = (0, 0);
473 if ($min_percent > 0) {
474 $own_min = (($self->length / 100) * $min_percent) - 1;
475 $other_min = (($other->length / 100) * $min_percent) - 1;
478 my ($own_start, $own_end) = $self->_pre_rangei($self, $rel);
479 my ($other_start, $other_end) = $self->_pre_rangei($other, $rel);
481 return ($self->_testStrand($other, $so) and not
482 (($own_start + $own_min > $other_end or $own_end - $own_min < $other_start) ||
483 ($own_start > $other_end - $other_min or $own_end < $other_start + $other_min)));
489 Usage : if ($p1->contains($p2)) {...}
490 Function: Tests whether $p1 totally contains $p2.
491 Returns : true if the argument is totally contained within this position
492 (regardless of map), false otherwise
493 Args : arg #1 = a Bio::RangeI (eg. a Bio::Map::Position) to compare this
494 one to, or scalar number (mandatory)
495 arg #2 = optional strand-testing arg ('strong', 'weak', 'ignore')
496 arg #3 = optional Bio::Map::RelativeI to ask if the Position
497 is contained in terms of their relative position to the
498 thing described by that Relative
503 # overriding the RangeI implementation so we can handle Relative
504 my ($self, $other, $so, $rel) = @_;
506 my ($own_start, $own_end) = $self->_pre_rangei($self, $rel);
507 my ($other_start, $other_end) = $self->_pre_rangei($other, $rel);
509 return ($self->_testStrand($other, $so) and
510 $other_start >= $own_start and $other_end <= $own_end);
516 Usage : ($start, $stop, $strand) = $p1->intersection($p2)
517 ($start, $stop, $strand) = Bio::Map::Position->intersection(\@positions);
518 $mappable = $p1->intersection($p2, undef, $relative);
519 $mappable = Bio::Map::Position->intersection(\@positions);
520 Function: gives the range that is contained by all ranges
521 Returns : undef if they do not overlap, OR
522 Bio::Map::Mappable object who's positions are the
523 cross-map-calculated intersection of the input positions on all the
524 maps that the input positions belong to, OR, in list context, a three
525 element array (start, end, strand)
526 Args : arg #1 = [REQUIRED] a Bio::RangeI (eg. a Bio::Map::Position) to
527 compare this one to, or an array ref of Bio::RangeI
528 arg #2 = optional strand-testing arg ('strong', 'weak', 'ignore')
529 arg #3 = optional Bio::Map::RelativeI to ask how the Positions
530 intersect in terms of their relative position to the thing
531 described by that Relative
536 # overriding the RangeI implementation so we can transfer map and handle
538 my ($self, $given, $so, $rel) = @_;
539 $self->throw("missing arg: you need to pass in another argument") unless $given;
542 if ($self eq "Bio::Map::PositionI") {
543 $self = "Bio::Map::Position";
544 $self->warn("calling static methods of an interface is deprecated; use $self instead");
547 push(@positions, $self);
549 ref($given) eq 'ARRAY' ?
push(@positions, @
{$given}) : push(@positions, $given);
550 $self->throw("Need at least 2 Positions") unless @positions >= 2;
552 my ($intersect, $i_start, $i_end, $c_start, $c_end, %known_maps);
553 while (@positions > 0) {
554 unless ($intersect) {
555 $intersect = shift(@positions);
556 ($i_start, $i_end) = $self->_pre_rangei($intersect, $rel);
557 my $map = $intersect->map;
558 $known_maps{$map->unique_id} = $map;
561 my $compare = shift(@positions);
562 ($c_start, $c_end) = $self->_pre_rangei($compare, $rel);
563 return unless $compare->_testStrand($intersect, $so);
564 if ($compare->isa('Bio::Map::PositionI')) {
565 my $this_map = $compare->map;
567 $known_maps{$this_map->unique_id} = $this_map;
571 $self->throw("Only Bio::Map::PositionI objects are supported, not [$compare]");
574 my @starts = sort {$a <=> $b} ($i_start, $c_start);
575 my @ends = sort {$a <=> $b} ($i_end, $c_end);
577 my $start = pop @starts; # larger of the 2 starts
578 my $end = shift @ends; # smaller of the 2 ends
580 my $intersect_strand; # strand for the intersection
581 if (defined($intersect->strand) && defined($compare->strand) && $intersect->strand == $compare->strand) {
582 $intersect_strand = $compare->strand;
585 $intersect_strand = 0;
592 $intersect = $self->new(-start
=> $start,
594 -strand
=> $intersect_strand);
598 $intersect || return;
599 my ($start, $end, $strand) = ($intersect->start, $intersect->end, $intersect->strand);
602 foreach my $known_map (values %known_maps) {
603 my $new_intersect = $intersect->new(-start
=> $start,
607 $new_intersect->relative($rel) if $rel;
608 push(@intersects, $new_intersect);
610 unless (@intersects) {
611 $intersect->relative($rel) if $rel;
612 @intersects = ($intersect);
615 my $result = Bio
::Map
::Mappable
->new();
616 $result->add_position(@intersects); # sneaky, add_position can take a list of positions
623 Usage : ($start, $stop, $strand) = $p1->union($p2);
624 ($start, $stop, $strand) = Bio::Map::Position->union(@positions);
625 my $mappable = $p1->union($p2);
626 my $mappable = Bio::Map::Position->union(@positions);
627 Function: finds the minimal position/range that contains all of the positions
628 Returns : Bio::Map::Mappable object who's positions are the
629 cross-map-calculated union of the input positions on all the maps
630 that the input positions belong to, OR, in list context, a three
631 element array (start, end, strand)
632 Args : a Bio::Map::PositionI to compare this one to, or a list of such
634 a single Bio::Map::PositionI or array ref of such AND a
635 Bio::Map::RelativeI to ask for the Position's union in terms of their
636 relative position to the thing described by that Relative
641 # overriding the RangeI implementation so we can transfer map and handle
643 my ($self, @args) = @_;
644 $self->throw("Not enough arguments") unless @args >= 1;
648 if ($self eq "Bio::Map::PositionI") {
649 $self = "Bio::Map::Position";
650 $self->warn("calling static methods of an interface is deprecated; use $self instead");
653 push(@positions, $self);
655 if (ref $args[0] eq 'ARRAY') {
656 push(@positions, @
{shift(@args)});
659 push(@positions, shift(@args));
661 if ($args[0] && $args[0]->isa('Bio::Map::RelativeI')) {
664 foreach my $arg (@args) {
665 # avoid pushing undefined values into @positions
666 push(@positions, $arg) if $arg;
668 $self->throw("Need at least 2 Positions") unless @positions >= 2;
670 my (@starts, @ends, %known_maps, $union_strand);
671 foreach my $compare (@positions) {
672 # RangeI union allows start or end to be undefined; however _pre_rangei
674 my ($start, $end) = $self->_pre_rangei($compare, $rel);
676 if ($compare->isa('Bio::Map::PositionI')) {
677 my $this_map = $compare->map;
679 $known_maps{$this_map->unique_id} = $this_map;
683 $self->throw("Only Bio::Map::PositionI objects are supported, not [$compare]");
686 if (! defined $union_strand) {
687 $union_strand = $compare->strand;
690 if (! defined $compare->strand or $union_strand ne $compare->strand) {
695 push(@starts, $start);
699 @starts = sort { $a <=> $b } @starts;
700 @ends = sort { $a <=> $b } @ends;
701 my $start = shift @starts;
705 foreach my $known_map (values %known_maps) {
706 my $new_union = $self->new(-start
=> $start,
708 -strand
=> $union_strand,
710 $new_union->relative($rel) if $rel;
711 push(@unions, $new_union);
714 @unions = ($self->new(-start
=> $start,
716 -strand
=> $union_strand));
717 $unions[0]->relative($rel) if $rel;
720 my $result = Bio
::Map
::Mappable
->new();
721 $result->add_position(@unions); # sneaky, add_position can take a list of positions
725 =head2 overlap_extent
727 Title : overlap_extent
728 Usage : ($a_unique,$common,$b_unique) = $a->overlap_extent($b)
729 Function: Provides actual amount of overlap between two different
732 Returns : array of values containing the length unique to the calling
733 position, the length common to both, and the length unique to
734 the argument position
739 #*** should this be overridden from RangeI?
741 =head2 disconnected_ranges
743 Title : disconnected_ranges
744 Usage : my @disc_ranges = Bio::Map::Position->disconnected_ranges(@ranges);
745 Function: Creates the minimal set of positions such that each input position is
746 fully contained by at least one output position, and none of the
747 output positions overlap.
748 Returns : Bio::Map::Mappable with the calculated disconnected ranges
749 Args : a Bio::Map::PositionI to compare this one to, or a list of such,
751 a single Bio::Map::PositionI or array ref of such AND a
752 Bio::Map::RelativeI to consider all Position's co-ordinates in terms
753 of their relative position to the thing described by that Relative,
754 AND, optionally, an int for the minimum percentage of overlap that
755 must be present before considering two ranges to be overlapping
760 sub disconnected_ranges
{
761 # overriding the RangeI implementation so we can transfer map and handle
763 my ($self, @args) = @_;
764 $self->throw("Not enough arguments") unless @args >= 1;
769 if ($self eq "Bio::Map::PositionI") {
770 $self = "Bio::Map::Position";
771 $self->warn("calling static methods of an interface is deprecated; use $self instead");
774 push(@positions, $self);
776 if (ref $args[0] eq 'ARRAY') {
777 push(@positions, @
{shift(@args)});
780 push(@positions, shift(@args));
782 if ($args[0] && $args[0]->isa('Bio::Map::RelativeI')) {
784 $overlap = shift(@args);
786 foreach my $arg (@args) {
787 push(@positions, $arg) if $arg;
789 $self->throw("Need at least 2 Positions") unless @positions >= 2;
792 foreach my $pos (@positions) {
793 $pos->isa('Bio::Map::PositionI') || $self->throw("Must supply only Bio::Map::PositionI objects, not [$pos]");
794 my $map = $pos->map || next;
795 $known_maps{$map->unique_id} = $map;
798 foreach my $map (values %known_maps) {
799 foreach my $pos ($map->get_positions) {
800 $prior_positions{$pos} = 1;
805 foreach my $inrange (@positions) {
806 my @outranges_new = ();
807 my %overlapping_ranges = ();
809 for (my $i=0; $i<@outranges; $i++) {
810 my $outrange = $outranges[$i];
811 if ($inrange->overlaps($outrange, undef, $rel, $overlap)) {
812 my $union_able = $inrange->union($outrange, $rel); # using $inrange->union($outrange, $rel); gives >6x speedup,
813 # but different answer, not necessarily incorrect...
814 foreach my $pos ($union_able->get_positions) {
815 $overlapping_ranges{$pos->toString} = $pos; # we flatten down to a result on a single map
816 # to avoid creating 10s of thousands of positions during this process;
817 # we then apply the final answer to all maps at the very end
822 push(@outranges_new, $outrange);
826 @outranges = @outranges_new;
828 my @overlappers = values %overlapping_ranges;
830 if (@overlappers > 1) {
831 my $merged_range_able = shift(@overlappers)->union(\
@overlappers, $rel);
832 push(@outranges, $merged_range_able->get_positions);
835 push(@outranges, @overlappers);
839 push(@outranges, $self->new(-start
=> $inrange->start($rel), -end
=> $inrange->end($rel), -strand
=> $inrange->strand, -map => $inrange->map, -relative
=> $rel));
843 # purge positions that were created whilst calculating the answer, but
844 # aren't the final answer and weren't there previously
845 my %answers = map { $_ => 1 } @outranges;
846 foreach my $map (values %known_maps) {
847 foreach my $pos ($map->get_positions) {
848 if (! exists $prior_positions{$pos} && ! exists $answers{$pos}) {
849 $map->purge_positions($pos);
855 foreach my $map (values %known_maps) {
856 foreach my $pos ($map->get_positions) {
857 $post_positions{$pos} = 1;
861 @outranges || return;
863 # make an outrange on all known maps
865 foreach my $map (values %known_maps) {
866 foreach my $pos (@outranges) {
867 if ($pos->map eq $map) {
868 push(@final_positions, $pos);
871 push(@final_positions, $pos->new(-start
=> $pos->start,
873 -relative
=> $pos->relative,
879 # assign the positions to a result mappable
880 my $result = Bio
::Map
::Mappable
->new();
881 $result->add_position(@final_positions); # sneaky, add_position can take a list of positions
885 # get start & end suitable for rangeI methods, taking relative into account
887 my ($self, $other, $rel) = @_;
888 $self->throw("Must supply an object") unless $other;
890 $self->throw("Must supply an object for the Relative argument") unless ref($rel);
891 $self->throw("This is [$rel], not a Bio::Map::RelativeI") unless $rel->isa('Bio::Map::RelativeI');
894 my ($other_start, $other_end);
896 if (ref($other) eq 'ARRAY') {
897 $self->throw("_pre_rangei got an array");
899 $self->throw("This is [$other], not a Bio::RangeI object") unless defined $other && $other->isa('Bio::RangeI');
901 if ($other->isa('Bio::Map::PositionI')) {
902 # to get the desired start/end we need the position to be on a map;
903 # if it isn't on one temporarily place it on self's map
904 # - this lets us have 'generic' positions that aren't on any map
905 # but have a relative defined and can thus be usefully compared to
906 # positions that /are/ on maps
907 my $other_map = $other->map;
908 unless ($other_map) {
909 my $self_map = $self->map || $self->throw("Trying to compare two positions but neither had been placed on a map");
910 $other->map($self_map);
913 # want start and end positions relative to the supplied rel or map start
914 $rel ||= $other->absolute_relative;
915 $other_start = $other->start($rel);
916 $other_end = $other->end($rel);
918 unless ($other_map) {
919 $self->map->purge_positions($other);
923 $other_start = $other->start;
924 $other_end = $other->end;
928 $self->throw("not a number") unless looks_like_number
($other);
929 $other_start = $other_end = $other;
932 $other->throw("start is undefined") unless defined $other_start;
933 $other->throw("end is undefined") unless defined $other_end;
935 return ($other_start, $other_end);