Profile: /opt/wise/lib/perl5/5.10.0/overload.pm

File	/opt/wise/lib/perl5/5.10.0/overload.pm
Statements Executed	167
Total Time	0.001686 seconds

Subroutines — ordered by exclusive time
Calls	P	F	Exclusive Time	Inclusive Time	Subroutine
6	1	1	0.00133	0.00133	overload::	OVERLOAD
6	6	6	0.00017	0.00150	overload::	import
0	0	0	0	0	overload::	AddrRef
0	0	0	0	0	overload::	BEGIN
0	0	0	0	0	overload::	Method
0	0	0	0	0	overload::	Overloaded
0	0	0	0	0	overload::	OverloadedStringify
0	0	0	0	0	overload::	constant
0	0	0	0	0	overload::	mycan
0	0	0	0	0	overload::	nil
0	0	0	0	0	overload::	ov_method
0	0	0	0	0	overload::	remove_constant
0	0	0	0	0	overload::	unimport

Line	Stmts.	Exclusive Time	Avg.	Code
1				package overload;
2
3	1	1.0e-6	1.0e-6	our $VERSION = '1.06';
4
5				sub nil {}
6
7				# spent 1.33ms within overload::OVERLOAD which was called 6 times, avg 221µs/call: # 6 times (1.33ms+0) by overload::import at line 33, avg 221µs/call sub OVERLOAD {
8	6	7.0e-6	1.2e-6	$package = shift;
9	6	4.4e-5	7.3e-6	my %arg = @_;
10	6	6.0e-6	1.0e-6	my ($sub, $fb);
11	6	5.4e-5	9.0e-6	$ {$package . "::OVERLOAD"}{dummy}++; # Register with magic by touching.
12	6	4.4e-5	7.3e-6	*{$package . "::()"} = \&nil; # Make it findable via fetchmethod.
13	6	2.3e-5	3.8e-6	for (keys %arg) {
14	27	0.00095	3.5e-5	if ($_ eq 'fallback') {
15				$fb = $arg{$_};
16				} else {
17	24	1.2e-5	5.0e-7	$sub = $arg{$_};
18	24	3.0e-5	1.3e-6	if (not ref $sub and $sub !~ /::/) {
19				$ {$package . "::(" . $_} = $sub;
20				$sub = \&nil;
21				}
22				#print STDERR "Setting `$ {'package'}::\cO$_' to \\&`$sub'.\n";
23	24	9.0e-5	3.8e-6	*{$package . "::(" . $_} = \&{ $sub };
24				}
25				}
26	6	2.6e-5	4.3e-6	${$package . "::()"} = $fb; # Make it findable too (fallback only).
27				}
28
29				# spent 1.50ms (173µs+1.33) within overload::import which was called 6 times, avg 250µs/call: # once (61µs+1.06ms) by Math::Complex::BEGIN at line 78 of /opt/wise/lib/perl5/5.10.0/Math/Complex.pm # once (18µs+69µs) by TestRHBug::BEGIN or DBIx::Class::StartupCheck::BEGIN or TestRHBug::__ANON__[/wise/base/static/lib/perl5/site_perl/5.10.0/DBIx/Class/StartupCheck.pm:5] at line 5 of /wise/base/static/lib/perl5/site_perl/5.10.0/DBIx/Class/StartupCheck.pm # once (15µs+64µs) by DBIx::Class::Exception::BEGIN at line 11 of /wise/base/static/lib/perl5/site_perl/5.10.0/DBIx/Class/Exception.pm # once (26µs+51µs) by DBIx::Class::ResultSourceHandle::BEGIN at line 13 of /wise/base/static/lib/perl5/site_perl/5.10.0/DBIx/Class/ResultSourceHandle.pm # once (33µs+44µs) at line 8 of /wise/base/static/lib/perl5/site_perl/5.10.0/DBIx/Class/ResultSet.pm # once (20µs+41µs) by DBIx::Class::Storage::NESTED_ROLLBACK_EXCEPTION::BEGIN or DBIx::Class::Storage::NESTED_ROLLBACK_EXCEPTION::__ANON__[/wise/base/static/lib/perl5/site_perl/5.10.0/DBIx/Class/Storage.pm:24] at line 24 of /wise/base/static/lib/perl5/site_perl/5.10.0/DBIx/Class/Storage.pm sub import {
30	6	3.0e-5	5.0e-6	$package = (caller())[0];
31				# *{$package . "::OVERLOAD"} = \&OVERLOAD;
32	6	4.0e-6	6.7e-7	shift;
33	6	8.5e-5	1.4e-5	$package->overload::OVERLOAD(@_); # spent 1.33ms making 6 calls to overload::OVERLOAD, avg 221µs/call
34				}
35
36				sub unimport {
37				$package = (caller())[0];
38				${$package . "::OVERLOAD"}{dummy}++; # Upgrade the table
39				shift;
40				for (@_) {
41				if ($_ eq 'fallback') {
42				undef $ {$package . "::()"};
43				} else {
44				delete $ {$package . "::"}{"(" . $_};
45				}
46				}
47				}
48
49				sub Overloaded {
50				my $package = shift;
51				$package = ref $package if ref $package;
52				$package->can('()');
53				}
54
55				sub ov_method {
56				my $globref = shift;
57				return undef unless $globref;
58				my $sub = \&{*$globref};
59				return $sub if $sub ne \&nil;
60				return shift->can($ {*$globref});
61				}
62
63				sub OverloadedStringify {
64				my $package = shift;
65				$package = ref $package if ref $package;
66				#$package->can('(""')
67				ov_method mycan($package, '(""'), $package
68				or ov_method mycan($package, '(0+'), $package
69				or ov_method mycan($package, '(bool'), $package
70				or ov_method mycan($package, '(nomethod'), $package;
71				}
72
73				sub Method {
74				my $package = shift;
75				if(ref $package) {
76				local $@;
77				local $!;
78				require Scalar::Util;
79				$package = Scalar::Util::blessed($package);
80				return undef if !defined $package;
81				}
82				#my $meth = $package->can('(' . shift);
83				ov_method mycan($package, '(' . shift), $package;
84				#return $meth if $meth ne \&nil;
85				#return $ {*{$meth}};
86				}
87
88				sub AddrRef {
89				my $package = ref $_[0];
90				return "$_[0]" unless $package;
91
92				local $@;
93				local $!;
94				require Scalar::Util;
95				my $class = Scalar::Util::blessed($_[0]);
96				my $class_prefix = defined($class) ? "$class=" : "";
97				my $type = Scalar::Util::reftype($_[0]);
98				my $addr = Scalar::Util::refaddr($_[0]);
99				return sprintf("$class_prefix$type(0x%x)", $addr);
100				}
101
102	1	2.0e-6	2.0e-6	StrVal = AddrRef;
103
104				sub mycan { # Real can would leave stubs.
105				my ($package, $meth) = @_;
106
107				my $mro = mro::get_linear_isa($package);
108				foreach my $p (@$mro) {
109				my $fqmeth = $p . q{::} . $meth;
110				return \*{$fqmeth} if defined &{$fqmeth};
111				}
112
113				return undef;
114				}
115
116	1	4.0e-6	4.0e-6	%constants = (
117				'integer' => 0x1000, # HINT_NEW_INTEGER
118				'float' => 0x2000, # HINT_NEW_FLOAT
119				'binary' => 0x4000, # HINT_NEW_BINARY
120				'q' => 0x8000, # HINT_NEW_STRING
121				'qr' => 0x10000, # HINT_NEW_RE
122				);
123
124	1	7.0e-6	7.0e-6	%ops = ( with_assign => "+ - * / % ** << >> x .",
125				assign => "+= -= = /= %= *= <<= >>= x= .=",
126				num_comparison => "< <= > >= == !=",
127				'3way_comparison'=> "<=> cmp",
128				str_comparison => "lt le gt ge eq ne",
129				binary => '& &= \| \|= ^ ^=',
130				unary => "neg ! ~",
131				mutators => '++ --',
132				func => "atan2 cos sin exp abs log sqrt int",
133				conversion => 'bool "" 0+',
134				iterators => '<>',
135				dereferencing => '${} @{} %{} &{} *{}',
136				special => 'nomethod fallback =');
137
138	3	0.00025	8.4e-5	use warnings::register; # spent 176µs making 1 call to warnings::register::import
139				sub constant {
140				# Arguments: what, sub
141				while (@_) {
142				if (@_ == 1) {
143				warnings::warnif ("Odd number of arguments for overload::constant");
144				last;
145				}
146				elsif (!exists $constants {$_ [0]}) {
147				warnings::warnif ("`$_[0]' is not an overloadable type");
148				}
149				elsif (!ref $_ [1] \|\| "$_[1]" !~ /CODE$0x[\da-f]+$$/) {
150				# Can't use C<ref $_[1] eq "CODE"> above as code references can be
151				# blessed, and C<ref> would return the package the ref is blessed into.
152				if (warnings::enabled) {
153				$_ [1] = "undef" unless defined $_ [1];
154				warnings::warn ("`$_[1]' is not a code reference");
155				}
156				}
157				else {
158				$^H{$_[0]} = $_[1];
159				$^H \|= $constants{$_[0]};
160				}
161				shift, shift;
162				}
163				}
164
165				sub remove_constant {
166				# Arguments: what, sub
167				while (@_) {
168				delete $^H{$_[0]};
169				$^H &= ~ $constants{$_[0]};
170				shift, shift;
171				}
172				}
173
174	1	1.0e-5	1.0e-5	1;
175
176				__END__
177
178				=head1 NAME
179
180				overload - Package for overloading Perl operations
181
182				=head1 SYNOPSIS
183
184				package SomeThing;
185
186				use overload
187				'+' => \&myadd,
188				'-' => \&mysub;
189				# etc
190				...
191
192				package main;
193				$a = new SomeThing 57;
194				$b=5+$a;
195				...
196				if (overload::Overloaded $b) {...}
197				...
198				$strval = overload::StrVal $b;
199
200				=head1 DESCRIPTION
201
202				=head2 Declaration of overloaded functions
203
204				The compilation directive
205
206				package Number;
207				use overload
208				"+" => \&add,
209				"*=" => "muas";
210
211				declares function Number::add() for addition, and method muas() in
212				the "class" C<Number> (or one of its base classes)
213				for the assignment form C<*=> of multiplication.
214
215				Arguments of this directive come in (key, value) pairs. Legal values
216				are values legal inside a C<&{ ... }> call, so the name of a
217				subroutine, a reference to a subroutine, or an anonymous subroutine
218				will all work. Note that values specified as strings are
219				interpreted as methods, not subroutines. Legal keys are listed below.
220
221				The subroutine C<add> will be called to execute C<$a+$b> if $a
222				is a reference to an object blessed into the package C<Number>, or if $a is
223				not an object from a package with defined mathemagic addition, but $b is a
224				reference to a C<Number>. It can also be called in other situations, like
225				C<$a+=7>, or C<$a++>. See L<MAGIC AUTOGENERATION>. (Mathemagical
226				methods refer to methods triggered by an overloaded mathematical
227				operator.)
228
229				Since overloading respects inheritance via the @ISA hierarchy, the
230				above declaration would also trigger overloading of C<+> and C<*=> in
231				all the packages which inherit from C<Number>.
232
233				=head2 Calling Conventions for Binary Operations
234
235				The functions specified in the C<use overload ...> directive are called
236				with three (in one particular case with four, see L<Last Resort>)
237				arguments. If the corresponding operation is binary, then the first
238				two arguments are the two arguments of the operation. However, due to
239				general object calling conventions, the first argument should always be
240				an object in the package, so in the situation of C<7+$a>, the
241				order of the arguments is interchanged. It probably does not matter
242				when implementing the addition method, but whether the arguments
243				are reversed is vital to the subtraction method. The method can
244				query this information by examining the third argument, which can take
245				three different values:
246
247				=over 7
248
249				=item FALSE
250
251				the order of arguments is as in the current operation.
252
253				=item TRUE
254
255				the arguments are reversed.
256
257				=item C<undef>
258
259				the current operation is an assignment variant (as in
260				C<$a+=7>), but the usual function is called instead. This additional
261				information can be used to generate some optimizations. Compare
262				L<Calling Conventions for Mutators>.
263
264				=back
265
266				=head2 Calling Conventions for Unary Operations
267
268				Unary operation are considered binary operations with the second
269				argument being C<undef>. Thus the functions that overloads C<{"++"}>
270				is called with arguments C<($a,undef,'')> when $a++ is executed.
271
272				=head2 Calling Conventions for Mutators
273
274				Two types of mutators have different calling conventions:
275
276				=over
277
278				=item C<++> and C<-->
279
280				The routines which implement these operators are expected to actually
281				I<mutate> their arguments. So, assuming that $obj is a reference to a
282				number,
283
284				sub incr { my $n = $ {$_[0]}; ++$n; $_[0] = bless \$n}
285
286				is an appropriate implementation of overloaded C<++>. Note that
287
288				sub incr { ++$ {$_[0]} ; shift }
289
290				is OK if used with preincrement and with postincrement. (In the case
291				of postincrement a copying will be performed, see L<Copy Constructor>.)
292
293				=item C<x=> and other assignment versions
294
295				There is nothing special about these methods. They may change the
296				value of their arguments, and may leave it as is. The result is going
297				to be assigned to the value in the left-hand-side if different from
298				this value.
299
300				This allows for the same method to be used as overloaded C<+=> and
301				C<+>. Note that this is I<allowed>, but not recommended, since by the
302				semantic of L<"Fallback"> Perl will call the method for C<+> anyway,
303				if C<+=> is not overloaded.
304
305				=back
306
307				B<Warning.> Due to the presence of assignment versions of operations,
308				routines which may be called in assignment context may create
309				self-referential structures. Currently Perl will not free self-referential
310				structures until cycles are C<explicitly> broken. You may get problems
311				when traversing your structures too.
312
313				Say,
314
315				use overload '+' => sub { bless [ \$_[0], \$_[1] ] };
316
317				is asking for trouble, since for code C<$obj += $foo> the subroutine
318				is called as C<$obj = add($obj, $foo, undef)>, or C<$obj = [\$obj,
319				\$foo]>. If using such a subroutine is an important optimization, one
320				can overload C<+=> explicitly by a non-"optimized" version, or switch
321				to non-optimized version if C<not defined $_[2]> (see
322				L<Calling Conventions for Binary Operations>).
323
324				Even if no I<explicit> assignment-variants of operators are present in
325				the script, they may be generated by the optimizer. Say, C<",$obj,"> or
326				C<',' . $obj . ','> may be both optimized to
327
328				my $tmp = ',' . $obj; $tmp .= ',';
329
330				=head2 Overloadable Operations
331
332				The following symbols can be specified in C<use overload> directive:
333
334				=over 5
335
336				=item * I<Arithmetic operations>
337
338				"+", "+=", "-", "-=", "", "=", "/", "/=", "%", "%=",
339				"", "=", "<<", "<<=", ">>", ">>=", "x", "x=", ".", ".=",
340
341				For these operations a substituted non-assignment variant can be called if
342				the assignment variant is not available. Methods for operations C<+>,
343				C<->, C<+=>, and C<-=> can be called to automatically generate
344				increment and decrement methods. The operation C<-> can be used to
345				autogenerate missing methods for unary minus or C<abs>.
346
347				See L<"MAGIC AUTOGENERATION">, L<"Calling Conventions for Mutators"> and
348				L<"Calling Conventions for Binary Operations">) for details of these
349				substitutions.
350
351				=item * I<Comparison operations>
352
353				"<", "<=", ">", ">=", "==", "!=", "<=>",
354				"lt", "le", "gt", "ge", "eq", "ne", "cmp",
355
356				If the corresponding "spaceship" variant is available, it can be
357				used to substitute for the missing operation. During C<sort>ing
358				arrays, C<cmp> is used to compare values subject to C<use overload>.
359
360				=item * I<Bit operations>
361
362				"&", "&=", "^", "^=", "\|", "\|=", "neg", "!", "~",
363
364				C<neg> stands for unary minus. If the method for C<neg> is not
365				specified, it can be autogenerated using the method for
366				subtraction. If the method for C<!> is not specified, it can be
367				autogenerated using the methods for C<bool>, or C<"">, or C<0+>.
368
369				The same remarks in L<"Arithmetic operations"> about
370				assignment-variants and autogeneration apply for
371				bit operations C<"&">, C<"^">, and C<"\|"> as well.
372
373				=item * I<Increment and decrement>
374
375				"++", "--",
376
377				If undefined, addition and subtraction methods can be
378				used instead. These operations are called both in prefix and
379				postfix form.
380
381				=item * I<Transcendental functions>
382
383				"atan2", "cos", "sin", "exp", "abs", "log", "sqrt", "int"
384
385				If C<abs> is unavailable, it can be autogenerated using methods
386				for "E<lt>" or "E<lt>=E<gt>" combined with either unary minus or subtraction.
387
388				Note that traditionally the Perl function L<int> rounds to 0, thus for
389				floating-point-like types one should follow the same semantic. If
390				C<int> is unavailable, it can be autogenerated using the overloading of
391				C<0+>.
392
393				=item * I<Boolean, string and numeric conversion>
394
395				'bool', '""', '0+',
396
397				If one or two of these operations are not overloaded, the remaining ones can
398				be used instead. C<bool> is used in the flow control operators
399				(like C<while>) and for the ternary C<?:> operation. These functions can
400				return any arbitrary Perl value. If the corresponding operation for this value
401				is overloaded too, that operation will be called again with this value.
402
403				As a special case if the overload returns the object itself then it will
404				be used directly. An overloaded conversion returning the object is
405				probably a bug, because you're likely to get something that looks like
406				C<YourPackage=HASH(0x8172b34)>.
407
408				=item * I<Iteration>
409
410				"<>"
411
412				If not overloaded, the argument will be converted to a filehandle or
413				glob (which may require a stringification). The same overloading
414				happens both for the I<read-filehandle> syntax C<E<lt>$varE<gt>> and
415				I<globbing> syntax C<E<lt>${var}E<gt>>.
416
417				B<BUGS> Even in list context, the iterator is currently called only
418				once and with scalar context.
419
420				=item * I<Dereferencing>
421
422				'${}', '@{}', '%{}', '&{}', '*{}'.
423
424				If not overloaded, the argument will be dereferenced I<as is>, thus
425				should be of correct type. These functions should return a reference
426				of correct type, or another object with overloaded dereferencing.
427
428				As a special case if the overload returns the object itself then it
429				will be used directly (provided it is the correct type).
430
431				The dereference operators must be specified explicitly they will not be passed to
432				"nomethod".
433
434				=item * I<Special>
435
436				"nomethod", "fallback", "=", "~~",
437
438				see L<SPECIAL SYMBOLS FOR C<use overload>>.
439
440				=back
441
442				See L<"Fallback"> for an explanation of when a missing method can be
443				autogenerated.
444
445				A computer-readable form of the above table is available in the hash
446				%overload::ops, with values being space-separated lists of names:
447
448				with_assign => '+ - * / % ** << >> x .',
449				assign => '+= -= = /= %= *= <<= >>= x= .=',
450				num_comparison => '< <= > >= == !=',
451				'3way_comparison'=> '<=> cmp',
452				str_comparison => 'lt le gt ge eq ne',
453				binary => '& &= \| \|= ^ ^=',
454				unary => 'neg ! ~',
455				mutators => '++ --',
456				func => 'atan2 cos sin exp abs log sqrt',
457				conversion => 'bool "" 0+',
458				iterators => '<>',
459				dereferencing => '${} @{} %{} &{} *{}',
460				special => 'nomethod fallback ='
461
462				=head2 Inheritance and overloading
463
464				Inheritance interacts with overloading in two ways.
465
466				=over
467
468				=item Strings as values of C<use overload> directive
469
470				If C<value> in
471
472				use overload key => value;
473
474				is a string, it is interpreted as a method name.
475
476				=item Overloading of an operation is inherited by derived classes
477
478				Any class derived from an overloaded class is also overloaded. The
479				set of overloaded methods is the union of overloaded methods of all
480				the ancestors. If some method is overloaded in several ancestor, then
481				which description will be used is decided by the usual inheritance
482				rules:
483
484				If C<A> inherits from C<B> and C<C> (in this order), C<B> overloads
485				C<+> with C<\&D::plus_sub>, and C<C> overloads C<+> by C<"plus_meth">,
486				then the subroutine C<D::plus_sub> will be called to implement
487				operation C<+> for an object in package C<A>.
488
489				=back
490
491				Note that since the value of the C<fallback> key is not a subroutine,
492				its inheritance is not governed by the above rules. In the current
493				implementation, the value of C<fallback> in the first overloaded
494				ancestor is used, but this is accidental and subject to change.
495
496				=head1 SPECIAL SYMBOLS FOR C<use overload>
497
498				Three keys are recognized by Perl that are not covered by the above
499				description.
500
501				=head2 Last Resort
502
503				C<"nomethod"> should be followed by a reference to a function of four
504				parameters. If defined, it is called when the overloading mechanism
505				cannot find a method for some operation. The first three arguments of
506				this function coincide with the arguments for the corresponding method if
507				it were found, the fourth argument is the symbol
508				corresponding to the missing method. If several methods are tried,
509				the last one is used. Say, C<1-$a> can be equivalent to
510
511				&nomethodMethod($a,1,1,"-")
512
513				if the pair C<"nomethod" =E<gt> "nomethodMethod"> was specified in the
514				C<use overload> directive.
515
516				The C<"nomethod"> mechanism is I<not> used for the dereference operators
517				( ${} @{} %{} &{} *{} ).
518
519
520				If some operation cannot be resolved, and there is no function
521				assigned to C<"nomethod">, then an exception will be raised via die()--
522				unless C<"fallback"> was specified as a key in C<use overload> directive.
523
524
525				=head2 Fallback
526
527				The key C<"fallback"> governs what to do if a method for a particular
528				operation is not found. Three different cases are possible depending on
529				the value of C<"fallback">:
530
531				=over 16
532
533				=item * C<undef>
534
535				Perl tries to use a
536				substituted method (see L<MAGIC AUTOGENERATION>). If this fails, it
537				then tries to calls C<"nomethod"> value; if missing, an exception
538				will be raised.
539
540				=item * TRUE
541
542				The same as for the C<undef> value, but no exception is raised. Instead,
543				it silently reverts to what it would have done were there no C<use overload>
544				present.
545
546				=item * defined, but FALSE
547
548				No autogeneration is tried. Perl tries to call
549				C<"nomethod"> value, and if this is missing, raises an exception.
550
551				=back
552
553				B<Note.> C<"fallback"> inheritance via @ISA is not carved in stone
554				yet, see L<"Inheritance and overloading">.
555
556				=head2 Smart Match
557
558				The key C<"~~"> allows you to override the smart matching used by
559				the switch construct. See L<feature>.
560
561				=head2 Copy Constructor
562
563				The value for C<"="> is a reference to a function with three
564				arguments, i.e., it looks like the other values in C<use
565				overload>. However, it does not overload the Perl assignment
566				operator. This would go against Camel hair.
567
568				This operation is called in the situations when a mutator is applied
569				to a reference that shares its object with some other reference, such
570				as
571
572				$a=$b;
573				++$a;
574
575				To make this change $a and not change $b, a copy of C<$$a> is made,
576				and $a is assigned a reference to this new object. This operation is
577				done during execution of the C<++$a>, and not during the assignment,
578				(so before the increment C<$$a> coincides with C<$$b>). This is only
579				done if C<++> is expressed via a method for C<'++'> or C<'+='> (or
580				C<nomethod>). Note that if this operation is expressed via C<'+'>
581				a nonmutator, i.e., as in
582
583				$a=$b;
584				$a=$a+1;
585
586				then C<$a> does not reference a new copy of C<$$a>, since $$a does not
587				appear as lvalue when the above code is executed.
588
589				If the copy constructor is required during the execution of some mutator,
590				but a method for C<'='> was not specified, it can be autogenerated as a
591				string copy if the object is a plain scalar.
592
593				=over 5
594
595				=item B<Example>
596
597				The actually executed code for
598
599				$a=$b;
600				Something else which does not modify $a or $b....
601				++$a;
602
603				may be
604
605				$a=$b;
606				Something else which does not modify $a or $b....
607				$a = $a->clone(undef,"");
608				$a->incr(undef,"");
609
610				if $b was mathemagical, and C<'++'> was overloaded with C<\&incr>,
611				C<'='> was overloaded with C<\&clone>.
612
613				=back
614
615				Same behaviour is triggered by C<$b = $a++>, which is consider a synonym for
616				C<$b = $a; ++$a>.
617
618				=head1 MAGIC AUTOGENERATION
619
620				If a method for an operation is not found, and the value for C<"fallback"> is
621				TRUE or undefined, Perl tries to autogenerate a substitute method for
622				the missing operation based on the defined operations. Autogenerated method
623				substitutions are possible for the following operations:
624
625				=over 16
626
627				=item I<Assignment forms of arithmetic operations>
628
629				C<$a+=$b> can use the method for C<"+"> if the method for C<"+=">
630				is not defined.
631
632				=item I<Conversion operations>
633
634				String, numeric, and boolean conversion are calculated in terms of one
635				another if not all of them are defined.
636
637				=item I<Increment and decrement>
638
639				The C<++$a> operation can be expressed in terms of C<$a+=1> or C<$a+1>,
640				and C<$a--> in terms of C<$a-=1> and C<$a-1>.
641
642				=item C<abs($a)>
643
644				can be expressed in terms of C<$aE<lt>0> and C<-$a> (or C<0-$a>).
645
646				=item I<Unary minus>
647
648				can be expressed in terms of subtraction.
649
650				=item I<Negation>
651
652				C<!> and C<not> can be expressed in terms of boolean conversion, or
653				string or numerical conversion.
654
655				=item I<Concatenation>
656
657				can be expressed in terms of string conversion.
658
659				=item I<Comparison operations>
660
661				can be expressed in terms of its "spaceship" counterpart: either
662				C<E<lt>=E<gt>> or C<cmp>:
663
664				<, >, <=, >=, ==, != in terms of <=>
665				lt, gt, le, ge, eq, ne in terms of cmp
666
667				=item I<Iterator>
668
669				<> in terms of builtin operations
670
671				=item I<Dereferencing>
672
673				${} @{} %{} &{} *{} in terms of builtin operations
674
675				=item I<Copy operator>
676
677				can be expressed in terms of an assignment to the dereferenced value, if this
678				value is a scalar and not a reference.
679
680				=back
681
682				=head1 Minimal set of overloaded operations
683
684				Since some operations can be automatically generated from others, there is
685				a minimal set of operations that need to be overloaded in order to have
686				the complete set of overloaded operations at one's disposal.
687				Of course, the autogenerated operations may not do exactly what the user
688				expects. See L<MAGIC AUTOGENERATION> above. The minimal set is:
689
690				+ - * / % ** << >> x
691				<=> cmp
692				& \| ^ ~
693				atan2 cos sin exp log sqrt int
694
695				Additionally, you need to define at least one of string, boolean or
696				numeric conversions because any one can be used to emulate the others.
697				The string conversion can also be used to emulate concatenation.
698
699				=head1 Losing overloading
700
701				The restriction for the comparison operation is that even if, for example,
702				`C<cmp>' should return a blessed reference, the autogenerated `C<lt>'
703				function will produce only a standard logical value based on the
704				numerical value of the result of `C<cmp>'. In particular, a working
705				numeric conversion is needed in this case (possibly expressed in terms of
706				other conversions).
707
708				Similarly, C<.=> and C<x=> operators lose their mathemagical properties
709				if the string conversion substitution is applied.
710
711				When you chop() a mathemagical object it is promoted to a string and its
712				mathemagical properties are lost. The same can happen with other
713				operations as well.
714
715				=head1 Run-time Overloading
716
717				Since all C<use> directives are executed at compile-time, the only way to
718				change overloading during run-time is to
719
720				eval 'use overload "+" => \&addmethod';
721
722				You can also use
723
724				eval 'no overload "+", "--", "<="';
725
726				though the use of these constructs during run-time is questionable.
727
728				=head1 Public functions
729
730				Package C<overload.pm> provides the following public functions:
731
732				=over 5
733
734				=item overload::StrVal(arg)
735
736				Gives string value of C<arg> as in absence of stringify overloading. If you
737				are using this to get the address of a reference (useful for checking if two
738				references point to the same thing) then you may be better off using
739				C<Scalar::Util::refaddr()>, which is faster.
740
741				=item overload::Overloaded(arg)
742
743				Returns true if C<arg> is subject to overloading of some operations.
744
745				=item overload::Method(obj,op)
746
747				Returns C<undef> or a reference to the method that implements C<op>.
748
749				=back
750
751				=head1 Overloading constants
752
753				For some applications, the Perl parser mangles constants too much.
754				It is possible to hook into this process via C<overload::constant()>
755				and C<overload::remove_constant()> functions.
756
757				These functions take a hash as an argument. The recognized keys of this hash
758				are:
759
760				=over 8
761
762				=item integer
763
764				to overload integer constants,
765
766				=item float
767
768				to overload floating point constants,
769
770				=item binary
771
772				to overload octal and hexadecimal constants,
773
774				=item q
775
776				to overload C<q>-quoted strings, constant pieces of C<qq>- and C<qx>-quoted
777				strings and here-documents,
778
779				=item qr
780
781				to overload constant pieces of regular expressions.
782
783				=back
784
785				The corresponding values are references to functions which take three arguments:
786				the first one is the I<initial> string form of the constant, the second one
787				is how Perl interprets this constant, the third one is how the constant is used.
788				Note that the initial string form does not
789				contain string delimiters, and has backslashes in backslash-delimiter
790				combinations stripped (thus the value of delimiter is not relevant for
791				processing of this string). The return value of this function is how this
792				constant is going to be interpreted by Perl. The third argument is undefined
793				unless for overloaded C<q>- and C<qr>- constants, it is C<q> in single-quote
794				context (comes from strings, regular expressions, and single-quote HERE
795				documents), it is C<tr> for arguments of C<tr>/C<y> operators,
796				it is C<s> for right-hand side of C<s>-operator, and it is C<qq> otherwise.
797
798				Since an expression C<"ab$cd,,"> is just a shortcut for C<'ab' . $cd . ',,'>,
799				it is expected that overloaded constant strings are equipped with reasonable
800				overloaded catenation operator, otherwise absurd results will result.
801				Similarly, negative numbers are considered as negations of positive constants.
802
803				Note that it is probably meaningless to call the functions overload::constant()
804				and overload::remove_constant() from anywhere but import() and unimport() methods.
805				From these methods they may be called as
806
807				sub import {
808				shift;
809				return unless @_;
810				die "unknown import: @_" unless @_ == 1 and $_[0] eq ':constant';
811				overload::constant integer => sub {Math::BigInt->new(shift)};
812				}
813
814				=head1 IMPLEMENTATION
815
816				What follows is subject to change RSN.
817
818				The table of methods for all operations is cached in magic for the
819				symbol table hash for the package. The cache is invalidated during
820				processing of C<use overload>, C<no overload>, new function
821				definitions, and changes in @ISA. However, this invalidation remains
822				unprocessed until the next C<bless>ing into the package. Hence if you
823				want to change overloading structure dynamically, you'll need an
824				additional (fake) C<bless>ing to update the table.
825
826				(Every SVish thing has a magic queue, and magic is an entry in that
827				queue. This is how a single variable may participate in multiple
828				forms of magic simultaneously. For instance, environment variables
829				regularly have two forms at once: their %ENV magic and their taint
830				magic. However, the magic which implements overloading is applied to
831				the stashes, which are rarely used directly, thus should not slow down
832				Perl.)
833
834				If an object belongs to a package using overload, it carries a special
835				flag. Thus the only speed penalty during arithmetic operations without
836				overloading is the checking of this flag.
837
838				In fact, if C<use overload> is not present, there is almost no overhead
839				for overloadable operations, so most programs should not suffer
840				measurable performance penalties. A considerable effort was made to
841				minimize the overhead when overload is used in some package, but the
842				arguments in question do not belong to packages using overload. When
843				in doubt, test your speed with C<use overload> and without it. So far
844				there have been no reports of substantial speed degradation if Perl is
845				compiled with optimization turned on.
846
847				There is no size penalty for data if overload is not used. The only
848				size penalty if overload is used in some package is that I<all> the
849				packages acquire a magic during the next C<bless>ing into the
850				package. This magic is three-words-long for packages without
851				overloading, and carries the cache table if the package is overloaded.
852
853				Copying (C<$a=$b>) is shallow; however, a one-level-deep copying is
854				carried out before any operation that can imply an assignment to the
855				object $a (or $b) refers to, like C<$a++>. You can override this
856				behavior by defining your own copy constructor (see L<"Copy Constructor">).
857
858				It is expected that arguments to methods that are not explicitly supposed
859				to be changed are constant (but this is not enforced).
860
861				=head1 Metaphor clash
862
863				One may wonder why the semantic of overloaded C<=> is so counter intuitive.
864				If it I<looks> counter intuitive to you, you are subject to a metaphor
865				clash.
866
867				Here is a Perl object metaphor:
868
869				I< object is a reference to blessed data>
870
871				and an arithmetic metaphor:
872
873				I< object is a thing by itself>.
874
875				The I<main> problem of overloading C<=> is the fact that these metaphors
876				imply different actions on the assignment C<$a = $b> if $a and $b are
877				objects. Perl-think implies that $a becomes a reference to whatever
878				$b was referencing. Arithmetic-think implies that the value of "object"
879				$a is changed to become the value of the object $b, preserving the fact
880				that $a and $b are separate entities.
881
882				The difference is not relevant in the absence of mutators. After
883				a Perl-way assignment an operation which mutates the data referenced by $a
884				would change the data referenced by $b too. Effectively, after
885				C<$a = $b> values of $a and $b become I<indistinguishable>.
886
887				On the other hand, anyone who has used algebraic notation knows the
888				expressive power of the arithmetic metaphor. Overloading works hard
889				to enable this metaphor while preserving the Perlian way as far as
890				possible. Since it is not possible to freely mix two contradicting
891				metaphors, overloading allows the arithmetic way to write things I<as
892				far as all the mutators are called via overloaded access only>. The
893				way it is done is described in L<Copy Constructor>.
894
895				If some mutator methods are directly applied to the overloaded values,
896				one may need to I<explicitly unlink> other values which references the
897				same value:
898
899				$a = new Data 23;
900				...
901				$b = $a; # $b is "linked" to $a
902				...
903				$a = $a->clone; # Unlink $b from $a
904				$a->increment_by(4);
905
906				Note that overloaded access makes this transparent:
907
908				$a = new Data 23;
909				$b = $a; # $b is "linked" to $a
910				$a += 4; # would unlink $b automagically
911
912				However, it would not make
913
914				$a = new Data 23;
915				$a = 4; # Now $a is a plain 4, not 'Data'
916
917				preserve "objectness" of $a. But Perl I<has> a way to make assignments
918				to an object do whatever you want. It is just not the overload, but
919				tie()ing interface (see L<perlfunc/tie>). Adding a FETCH() method
920				which returns the object itself, and STORE() method which changes the
921				value of the object, one can reproduce the arithmetic metaphor in its
922				completeness, at least for variables which were tie()d from the start.
923
924				(Note that a workaround for a bug may be needed, see L<"BUGS">.)
925
926				=head1 Cookbook
927
928				Please add examples to what follows!
929
930				=head2 Two-face scalars
931
932				Put this in F<two_face.pm> in your Perl library directory:
933
934				package two_face; # Scalars with separate string and
935				# numeric values.
936				sub new { my $p = shift; bless [@_], $p }
937				use overload '""' => \&str, '0+' => \&num, fallback => 1;
938				sub num {shift->[1]}
939				sub str {shift->[0]}
940
941				Use it as follows:
942
943				require two_face;
944				my $seven = new two_face ("vii", 7);
945				printf "seven=$seven, seven=%d, eight=%d\n", $seven, $seven+1;
946				print "seven contains `i'\n" if $seven =~ /i/;
947
948				(The second line creates a scalar which has both a string value, and a
949				numeric value.) This prints:
950
951				seven=vii, seven=7, eight=8
952				seven contains `i'
953
954				=head2 Two-face references
955
956				Suppose you want to create an object which is accessible as both an
957				array reference and a hash reference.
958
959				package two_refs;
960				use overload '%{}' => \&gethash, '@{}' => sub { $ {shift()} };
961				sub new {
962				my $p = shift;
963				bless \ [@_], $p;
964				}
965				sub gethash {
966				my %h;
967				my $self = shift;
968				tie %h, ref $self, $self;
969				\%h;
970				}
971
972				sub TIEHASH { my $p = shift; bless \ shift, $p }
973				my %fields;
974				my $i = 0;
975				$fields{$_} = $i++ foreach qw{zero one two three};
976				sub STORE {
977				my $self = ${shift()};
978				my $key = $fields{shift()};
979				defined $key or die "Out of band access";
980				$$self->[$key] = shift;
981				}
982				sub FETCH {
983				my $self = ${shift()};
984				my $key = $fields{shift()};
985				defined $key or die "Out of band access";
986				$$self->[$key];
987				}
988
989				Now one can access an object using both the array and hash syntax:
990
991				my $bar = new two_refs 3,4,5,6;
992				$bar->[2] = 11;
993				$bar->{two} == 11 or die 'bad hash fetch';
994
995				Note several important features of this example. First of all, the
996				I<actual> type of $bar is a scalar reference, and we do not overload
997				the scalar dereference. Thus we can get the I<actual> non-overloaded
998				contents of $bar by just using C<$$bar> (what we do in functions which
999				overload dereference). Similarly, the object returned by the
1000				TIEHASH() method is a scalar reference.
1001
1002				Second, we create a new tied hash each time the hash syntax is used.
1003				This allows us not to worry about a possibility of a reference loop,
1004				which would lead to a memory leak.
1005
1006				Both these problems can be cured. Say, if we want to overload hash
1007				dereference on a reference to an object which is I<implemented> as a
1008				hash itself, the only problem one has to circumvent is how to access
1009				this I<actual> hash (as opposed to the I<virtual> hash exhibited by the
1010				overloaded dereference operator). Here is one possible fetching routine:
1011
1012				sub access_hash {
1013				my ($self, $key) = (shift, shift);
1014				my $class = ref $self;
1015				bless $self, 'overload::dummy'; # Disable overloading of %{}
1016				my $out = $self->{$key};
1017				bless $self, $class; # Restore overloading
1018				$out;
1019				}
1020
1021				To remove creation of the tied hash on each access, one may an extra
1022				level of indirection which allows a non-circular structure of references:
1023
1024				package two_refs1;
1025				use overload '%{}' => sub { ${shift()}->[1] },
1026				'@{}' => sub { ${shift()}->[0] };
1027				sub new {
1028				my $p = shift;
1029				my $a = [@_];
1030				my %h;
1031				tie %h, $p, $a;
1032				bless \ [$a, \%h], $p;
1033				}
1034				sub gethash {
1035				my %h;
1036				my $self = shift;
1037				tie %h, ref $self, $self;
1038				\%h;
1039				}
1040
1041				sub TIEHASH { my $p = shift; bless \ shift, $p }
1042				my %fields;
1043				my $i = 0;
1044				$fields{$_} = $i++ foreach qw{zero one two three};
1045				sub STORE {
1046				my $a = ${shift()};
1047				my $key = $fields{shift()};
1048				defined $key or die "Out of band access";
1049				$a->[$key] = shift;
1050				}
1051				sub FETCH {
1052				my $a = ${shift()};
1053				my $key = $fields{shift()};
1054				defined $key or die "Out of band access";
1055				$a->[$key];
1056				}
1057
1058				Now if $baz is overloaded like this, then C<$baz> is a reference to a
1059				reference to the intermediate array, which keeps a reference to an
1060				actual array, and the access hash. The tie()ing object for the access
1061				hash is a reference to a reference to the actual array, so
1062
1063				=over
1064
1065				=item *
1066
1067				There are no loops of references.
1068
1069				=item *
1070
1071				Both "objects" which are blessed into the class C<two_refs1> are
1072				references to a reference to an array, thus references to a I<scalar>.
1073				Thus the accessor expression C<$$foo-E<gt>[$ind]> involves no
1074				overloaded operations.
1075
1076				=back
1077
1078				=head2 Symbolic calculator
1079
1080				Put this in F<symbolic.pm> in your Perl library directory:
1081
1082				package symbolic; # Primitive symbolic calculator
1083				use overload nomethod => \&wrap;
1084
1085				sub new { shift; bless ['n', @_] }
1086				sub wrap {
1087				my ($obj, $other, $inv, $meth) = @_;
1088				($obj, $other) = ($other, $obj) if $inv;
1089				bless [$meth, $obj, $other];
1090				}
1091
1092				This module is very unusual as overloaded modules go: it does not
1093				provide any usual overloaded operators, instead it provides the L<Last
1094				Resort> operator C<nomethod>. In this example the corresponding
1095				subroutine returns an object which encapsulates operations done over
1096				the objects: C<new symbolic 3> contains C<['n', 3]>, C<2 + new
1097				symbolic 3> contains C<['+', 2, ['n', 3]]>.
1098
1099				Here is an example of the script which "calculates" the side of
1100				circumscribed octagon using the above package:
1101
1102				require symbolic;
1103				my $iter = 1; # 2**($iter+2) = 8
1104				my $side = new symbolic 1;
1105				my $cnt = $iter;
1106
1107				while ($cnt--) {
1108				$side = (sqrt(1 + $side**2) - 1)/$side;
1109				}
1110				print "OK\n";
1111
1112				The value of $side is
1113
1114				['/', ['-', ['sqrt', ['+', 1, ['**', ['n', 1], 2]],
1115				undef], 1], ['n', 1]]
1116
1117				Note that while we obtained this value using a nice little script,
1118				there is no simple way to I<use> this value. In fact this value may
1119				be inspected in debugger (see L<perldebug>), but only if
1120				C<bareStringify> B<O>ption is set, and not via C<p> command.
1121
1122				If one attempts to print this value, then the overloaded operator
1123				C<""> will be called, which will call C<nomethod> operator. The
1124				result of this operator will be stringified again, but this result is
1125				again of type C<symbolic>, which will lead to an infinite loop.
1126
1127				Add a pretty-printer method to the module F<symbolic.pm>:
1128
1129				sub pretty {
1130				my ($meth, $a, $b) = @{+shift};
1131				$a = 'u' unless defined $a;
1132				$b = 'u' unless defined $b;
1133				$a = $a->pretty if ref $a;
1134				$b = $b->pretty if ref $b;
1135				"[$meth $a $b]";
1136				}
1137
1138				Now one can finish the script by
1139
1140				print "side = ", $side->pretty, "\n";
1141
1142				The method C<pretty> is doing object-to-string conversion, so it
1143				is natural to overload the operator C<""> using this method. However,
1144				inside such a method it is not necessary to pretty-print the
1145				I<components> $a and $b of an object. In the above subroutine
1146				C<"[$meth $a $b]"> is a catenation of some strings and components $a
1147				and $b. If these components use overloading, the catenation operator
1148				will look for an overloaded operator C<.>; if not present, it will
1149				look for an overloaded operator C<"">. Thus it is enough to use
1150
1151				use overload nomethod => \&wrap, '""' => \&str;
1152				sub str {
1153				my ($meth, $a, $b) = @{+shift};
1154				$a = 'u' unless defined $a;
1155				$b = 'u' unless defined $b;
1156				"[$meth $a $b]";
1157				}
1158
1159				Now one can change the last line of the script to
1160
1161				print "side = $side\n";
1162
1163				which outputs
1164
1165				side = [/ [- [sqrt [+ 1 [** [n 1 u] 2]] u] 1] [n 1 u]]
1166
1167				and one can inspect the value in debugger using all the possible
1168				methods.
1169
1170				Something is still amiss: consider the loop variable $cnt of the
1171				script. It was a number, not an object. We cannot make this value of
1172				type C<symbolic>, since then the loop will not terminate.
1173
1174				Indeed, to terminate the cycle, the $cnt should become false.
1175				However, the operator C<bool> for checking falsity is overloaded (this
1176				time via overloaded C<"">), and returns a long string, thus any object
1177				of type C<symbolic> is true. To overcome this, we need a way to
1178				compare an object to 0. In fact, it is easier to write a numeric
1179				conversion routine.
1180
1181				Here is the text of F<symbolic.pm> with such a routine added (and
1182				slightly modified str()):
1183
1184				package symbolic; # Primitive symbolic calculator
1185				use overload
1186				nomethod => \&wrap, '""' => \&str, '0+' => \&num;
1187
1188				sub new { shift; bless ['n', @_] }
1189				sub wrap {
1190				my ($obj, $other, $inv, $meth) = @_;
1191				($obj, $other) = ($other, $obj) if $inv;
1192				bless [$meth, $obj, $other];
1193				}
1194				sub str {
1195				my ($meth, $a, $b) = @{+shift};
1196				$a = 'u' unless defined $a;
1197				if (defined $b) {
1198				"[$meth $a $b]";
1199				} else {
1200				"[$meth $a]";
1201				}
1202				}
1203				my %subr = ( n => sub {$_[0]},
1204				sqrt => sub {sqrt $_[0]},
1205				'-' => sub {shift() - shift()},
1206				'+' => sub {shift() + shift()},
1207				'/' => sub {shift() / shift()},
1208				'' => sub {shift() shift()},
1209				'' => sub {shift() shift()},
1210				);
1211				sub num {
1212				my ($meth, $a, $b) = @{+shift};
1213				my $subr = $subr{$meth}
1214				or die "Do not know how to ($meth) in symbolic";
1215				$a = $a->num if ref $a eq __PACKAGE__;
1216				$b = $b->num if ref $b eq __PACKAGE__;
1217				$subr->($a,$b);
1218				}
1219
1220				All the work of numeric conversion is done in %subr and num(). Of
1221				course, %subr is not complete, it contains only operators used in the
1222				example below. Here is the extra-credit question: why do we need an
1223				explicit recursion in num()? (Answer is at the end of this section.)
1224
1225				Use this module like this:
1226
1227				require symbolic;
1228				my $iter = new symbolic 2; # 16-gon
1229				my $side = new symbolic 1;
1230				my $cnt = $iter;
1231
1232				while ($cnt) {
1233				$cnt = $cnt - 1; # Mutator `--' not implemented
1234				$side = (sqrt(1 + $side**2) - 1)/$side;
1235				}
1236				printf "%s=%f\n", $side, $side;
1237				printf "pi=%f\n", $side(2*($iter+2));
1238
1239				It prints (without so many line breaks)
1240
1241				[/ [- [sqrt [+ 1 [ [/ [- [sqrt [+ 1 [ [n 1] 2]]] 1]
1242				[n 1]] 2]]] 1]
1243				[/ [- [sqrt [+ 1 [** [n 1] 2]]] 1] [n 1]]]=0.198912
1244				pi=3.182598
1245
1246				The above module is very primitive. It does not implement
1247				mutator methods (C<++>, C<-=> and so on), does not do deep copying
1248				(not required without mutators!), and implements only those arithmetic
1249				operations which are used in the example.
1250
1251				To implement most arithmetic operations is easy; one should just use
1252				the tables of operations, and change the code which fills %subr to
1253
1254				my %subr = ( 'n' => sub {$_[0]} );
1255				foreach my $op (split " ", $overload::ops{with_assign}) {
1256				$subr{$op} = $subr{"$op="} = eval "sub {shift() $op shift()}";
1257				}
1258				my @bins = qw(binary 3way_comparison num_comparison str_comparison);
1259				foreach my $op (split " ", "@overload::ops{ @bins }") {
1260				$subr{$op} = eval "sub {shift() $op shift()}";
1261				}
1262				foreach my $op (split " ", "@overload::ops{qw(unary func)}") {
1263				print "defining `$op'\n";
1264				$subr{$op} = eval "sub {$op shift()}";
1265				}
1266
1267				Due to L<Calling Conventions for Mutators>, we do not need anything
1268				special to make C<+=> and friends work, except filling C<+=> entry of
1269				%subr, and defining a copy constructor (needed since Perl has no
1270				way to know that the implementation of C<'+='> does not mutate
1271				the argument, compare L<Copy Constructor>).
1272
1273				To implement a copy constructor, add C<< '=' => \&cpy >> to C<use overload>
1274				line, and code (this code assumes that mutators change things one level
1275				deep only, so recursive copying is not needed):
1276
1277				sub cpy {
1278				my $self = shift;
1279				bless [@$self], ref $self;
1280				}
1281
1282				To make C<++> and C<--> work, we need to implement actual mutators,
1283				either directly, or in C<nomethod>. We continue to do things inside
1284				C<nomethod>, thus add
1285
1286				if ($meth eq '++' or $meth eq '--') {
1287				@$obj = ($meth, (bless [@$obj]), 1); # Avoid circular reference
1288				return $obj;
1289				}
1290
1291				after the first line of wrap(). This is not a most effective
1292				implementation, one may consider
1293
1294				sub inc { $_[0] = bless ['++', shift, 1]; }
1295
1296				instead.
1297
1298				As a final remark, note that one can fill %subr by
1299
1300				my %subr = ( 'n' => sub {$_[0]} );
1301				foreach my $op (split " ", $overload::ops{with_assign}) {
1302				$subr{$op} = $subr{"$op="} = eval "sub {shift() $op shift()}";
1303				}
1304				my @bins = qw(binary 3way_comparison num_comparison str_comparison);
1305				foreach my $op (split " ", "@overload::ops{ @bins }") {
1306				$subr{$op} = eval "sub {shift() $op shift()}";
1307				}
1308				foreach my $op (split " ", "@overload::ops{qw(unary func)}") {
1309				$subr{$op} = eval "sub {$op shift()}";
1310				}
1311				$subr{'++'} = $subr{'+'};
1312				$subr{'--'} = $subr{'-'};
1313
1314				This finishes implementation of a primitive symbolic calculator in
1315				50 lines of Perl code. Since the numeric values of subexpressions
1316				are not cached, the calculator is very slow.
1317
1318				Here is the answer for the exercise: In the case of str(), we need no
1319				explicit recursion since the overloaded C<.>-operator will fall back
1320				to an existing overloaded operator C<"">. Overloaded arithmetic
1321				operators I<do not> fall back to numeric conversion if C<fallback> is
1322				not explicitly requested. Thus without an explicit recursion num()
1323				would convert C<['+', $a, $b]> to C<$a + $b>, which would just rebuild
1324				the argument of num().
1325
1326				If you wonder why defaults for conversion are different for str() and
1327				num(), note how easy it was to write the symbolic calculator. This
1328				simplicity is due to an appropriate choice of defaults. One extra
1329				note: due to the explicit recursion num() is more fragile than sym():
1330				we need to explicitly check for the type of $a and $b. If components
1331				$a and $b happen to be of some related type, this may lead to problems.
1332
1333				=head2 I<Really> symbolic calculator
1334
1335				One may wonder why we call the above calculator symbolic. The reason
1336				is that the actual calculation of the value of expression is postponed
1337				until the value is I<used>.
1338
1339				To see it in action, add a method
1340
1341				sub STORE {
1342				my $obj = shift;
1343				$#$obj = 1;
1344				@$obj->[0,1] = ('=', shift);
1345				}
1346
1347				to the package C<symbolic>. After this change one can do
1348
1349				my $a = new symbolic 3;
1350				my $b = new symbolic 4;
1351				my $c = sqrt($a2 + $b2);
1352
1353				and the numeric value of $c becomes 5. However, after calling
1354
1355				$a->STORE(12); $b->STORE(5);
1356
1357				the numeric value of $c becomes 13. There is no doubt now that the module
1358				symbolic provides a I<symbolic> calculator indeed.
1359
1360				To hide the rough edges under the hood, provide a tie()d interface to the
1361				package C<symbolic> (compare with L<Metaphor clash>). Add methods
1362
1363				sub TIESCALAR { my $pack = shift; $pack->new(@_) }
1364				sub FETCH { shift }
1365				sub nop { } # Around a bug
1366
1367				(the bug is described in L<"BUGS">). One can use this new interface as
1368
1369				tie $a, 'symbolic', 3;
1370				tie $b, 'symbolic', 4;
1371				$a->nop; $b->nop; # Around a bug
1372
1373				my $c = sqrt($a2 + $b2);
1374
1375				Now numeric value of $c is 5. After C<$a = 12; $b = 5> the numeric value
1376				of $c becomes 13. To insulate the user of the module add a method
1377
1378				sub vars { my $p = shift; tie($_, $p), $_->nop foreach @_; }
1379
1380				Now
1381
1382				my ($a, $b);
1383				symbolic->vars($a, $b);
1384				my $c = sqrt($a2 + $b2);
1385
1386				$a = 3; $b = 4;
1387				printf "c5 %s=%f\n", $c, $c;
1388
1389				$a = 12; $b = 5;
1390				printf "c13 %s=%f\n", $c, $c;
1391
1392				shows that the numeric value of $c follows changes to the values of $a
1393				and $b.
1394
1395				=head1 AUTHOR
1396
1397				Ilya Zakharevich E<lt>F<ilya@math.mps.ohio-state.edu>E<gt>.
1398
1399				=head1 DIAGNOSTICS
1400
1401				When Perl is run with the B<-Do> switch or its equivalent, overloading
1402				induces diagnostic messages.
1403
1404				Using the C<m> command of Perl debugger (see L<perldebug>) one can
1405				deduce which operations are overloaded (and which ancestor triggers
1406				this overloading). Say, if C<eq> is overloaded, then the method C<(eq>
1407				is shown by debugger. The method C<()> corresponds to the C<fallback>
1408				key (in fact a presence of this method shows that this package has
1409				overloading enabled, and it is what is used by the C<Overloaded>
1410				function of module C<overload>).
1411
1412				The module might issue the following warnings:
1413
1414				=over 4
1415
1416				=item Odd number of arguments for overload::constant
1417
1418				(W) The call to overload::constant contained an odd number of arguments.
1419				The arguments should come in pairs.
1420
1421				=item `%s' is not an overloadable type
1422
1423				(W) You tried to overload a constant type the overload package is unaware of.
1424
1425				=item `%s' is not a code reference
1426
1427				(W) The second (fourth, sixth, ...) argument of overload::constant needs
1428				to be a code reference. Either an anonymous subroutine, or a reference
1429				to a subroutine.
1430
1431				=back
1432
1433				=head1 BUGS
1434
1435				Because it is used for overloading, the per-package hash %OVERLOAD now
1436				has a special meaning in Perl. The symbol table is filled with names
1437				looking like line-noise.
1438
1439				For the purpose of inheritance every overloaded package behaves as if
1440				C<fallback> is present (possibly undefined). This may create
1441				interesting effects if some package is not overloaded, but inherits
1442				from two overloaded packages.
1443
1444				Relation between overloading and tie()ing is broken. Overloading is
1445				triggered or not basing on the I<previous> class of tie()d value.
1446
1447				This happens because the presence of overloading is checked too early,
1448				before any tie()d access is attempted. If the FETCH()ed class of the
1449				tie()d value does not change, a simple workaround is to access the value
1450				immediately after tie()ing, so that after this call the I<previous> class
1451				coincides with the current one.
1452
1453				B<Needed:> a way to fix this without a speed penalty.
1454
1455				Barewords are not covered by overloaded string constants.
1456
1457				This document is confusing. There are grammos and misleading language
1458				used in places. It would seem a total rewrite is needed.
1459
1460				=cut
1461