# -*- mode: perl; perl-indent-level: 2; -*- # Memoize.pm # # Transparent memoization of idempotent functions # # Copyright 1998, 1999, 2000, 2001, 2012 M. J. Dominus. # You may copy and distribute this program under the # same terms as Perl itself. If in doubt, # write to mjd-perl-memoize+@plover.com for a license. package Memoize; $VERSION = '1.03_01'; # Compile-time constants sub SCALAR () { 0 } sub LIST () { 1 } # # Usage memoize(functionname/ref, # { NORMALIZER => coderef, INSTALL => name, # LIST_CACHE => descriptor, SCALAR_CACHE => descriptor } # use Carp; use Exporter; use vars qw($DEBUG); use Config; # Dammit. @ISA = qw(Exporter); @EXPORT = qw(memoize); @EXPORT_OK = qw(unmemoize flush_cache); use strict; my %memotable; my %revmemotable; my @CONTEXT_TAGS = qw(MERGE TIE MEMORY FAULT HASH); my %IS_CACHE_TAG = map {($_ => 1)} @CONTEXT_TAGS; # Raise an error if the user tries to specify one of thesepackage as a # tie for LIST_CACHE my %scalar_only = map {($_ => 1)} qw(DB_File GDBM_File SDBM_File ODBM_File NDBM_File); sub memoize { my $fn = shift; my %options = @_; my $options = \%options; unless (defined($fn) && (ref $fn eq 'CODE' || ref $fn eq '')) { croak "Usage: memoize 'functionname'|coderef {OPTIONS}"; } my $uppack = caller; # TCL me Elmo! my $cref; # Code reference to original function my $name = (ref $fn ? undef : $fn); # Convert function names to code references $cref = &_make_cref($fn, $uppack); # Locate function prototype, if any my $proto = prototype $cref; if (defined $proto) { $proto = "($proto)" } else { $proto = "" } # I would like to get rid of the eval, but there seems not to be any # other way to set the prototype properly. The switch here for # 'usethreads' works around a bug in threadperl having to do with # magic goto. It would be better to fix the bug and use the magic # goto version everywhere. my $wrapper = $Config{usethreads} ? eval "sub $proto { &_memoizer(\$cref, \@_); }" : eval "sub $proto { unshift \@_, \$cref; goto &_memoizer; }"; my $normalizer = $options{NORMALIZER}; if (defined $normalizer && ! ref $normalizer) { $normalizer = _make_cref($normalizer, $uppack); } my $install_name; if (defined $options->{INSTALL}) { # INSTALL => name $install_name = $options->{INSTALL}; } elsif (! exists $options->{INSTALL}) { # No INSTALL option provided; use original name if possible $install_name = $name; } else { # INSTALL => undef means don't install } if (defined $install_name) { $install_name = $uppack . '::' . $install_name unless $install_name =~ /::/; no strict; local($^W) = 0; # ``Subroutine $install_name redefined at ...'' *{$install_name} = $wrapper; # Install memoized version } $revmemotable{$wrapper} = "" . $cref; # Turn code ref into hash key # These will be the caches my %caches; for my $context (qw(SCALAR LIST)) { # suppress subsequent 'uninitialized value' warnings $options{"${context}_CACHE"} ||= ''; my $cache_opt = $options{"${context}_CACHE"}; my @cache_opt_args; if (ref $cache_opt) { @cache_opt_args = @$cache_opt; $cache_opt = shift @cache_opt_args; } if ($cache_opt eq 'FAULT') { # no cache $caches{$context} = undef; } elsif ($cache_opt eq 'HASH') { # user-supplied hash my $cache = $cache_opt_args[0]; my $package = ref(tied %$cache); if ($context eq 'LIST' && $scalar_only{$package}) { croak("You can't use $package for LIST_CACHE because it can only store scalars"); } $caches{$context} = $cache; } elsif ($cache_opt eq '' || $IS_CACHE_TAG{$cache_opt}) { # default is that we make up an in-memory hash $caches{$context} = {}; # (this might get tied later, or MERGEd away) } else { croak "Unrecognized option to `${context}_CACHE': `$cache_opt' should be one of (@CONTEXT_TAGS); aborting"; } } # Perhaps I should check here that you didn't supply *both* merge # options. But if you did, it does do something reasonable: They # both get merged to the same in-memory hash. if ($options{SCALAR_CACHE} eq 'MERGE' || $options{LIST_CACHE} eq 'MERGE') { $options{MERGED} = 1; $caches{SCALAR} = $caches{LIST}; } # Now deal with the TIE options { my $context; foreach $context (qw(SCALAR LIST)) { # If the relevant option wasn't `TIE', this call does nothing. _my_tie($context, $caches{$context}, $options); # Croaks on failure } } # We should put some more stuff in here eventually. # We've been saying that for serveral versions now. # And you know what? More stuff keeps going in! $memotable{$cref} = { O => $options, # Short keys here for things we need to access frequently N => $normalizer, U => $cref, MEMOIZED => $wrapper, PACKAGE => $uppack, NAME => $install_name, S => $caches{SCALAR}, L => $caches{LIST}, }; $wrapper # Return just memoized version } # This function tries to load a tied hash class and tie the hash to it. sub _my_tie { my ($context, $hash, $options) = @_; my $fullopt = $options->{"${context}_CACHE"}; # We already checked to make sure that this works. my $shortopt = (ref $fullopt) ? $fullopt->[0] : $fullopt; return unless defined $shortopt && $shortopt eq 'TIE'; carp("TIE option to memoize() is deprecated; use HASH instead") if $^W; my @args = ref $fullopt ? @$fullopt : (); shift @args; my $module = shift @args; if ($context eq 'LIST' && $scalar_only{$module}) { croak("You can't use $module for LIST_CACHE because it can only store scalars"); } my $modulefile = $module . '.pm'; $modulefile =~ s{::}{/}g; eval { local @INC = @INC; pop @INC if $INC[-1] eq '.'; require $modulefile }; if ($@) { croak "Memoize: Couldn't load hash tie module `$module': $@; aborting"; } my $rc = (tie %$hash => $module, @args); unless ($rc) { croak "Memoize: Couldn't tie hash to `$module': $!; aborting"; } 1; } sub flush_cache { my $func = _make_cref($_[0], scalar caller); my $info = $memotable{$revmemotable{$func}}; die "$func not memoized" unless defined $info; for my $context (qw(S L)) { my $cache = $info->{$context}; if (tied %$cache && ! (tied %$cache)->can('CLEAR')) { my $funcname = defined($info->{NAME}) ? "function $info->{NAME}" : "anonymous function $func"; my $context = {S => 'scalar', L => 'list'}->{$context}; croak "Tied cache hash for $context-context $funcname does not support flushing"; } else { %$cache = (); } } } # This is the function that manages the memo tables. sub _memoizer { my $orig = shift; # stringized version of ref to original func. my $info = $memotable{$orig}; my $normalizer = $info->{N}; my $argstr; my $context = (wantarray() ? LIST : SCALAR); if (defined $normalizer) { no strict; if ($context == SCALAR) { $argstr = &{$normalizer}(@_); } elsif ($context == LIST) { ($argstr) = &{$normalizer}(@_); } else { croak "Internal error \#41; context was neither LIST nor SCALAR\n"; } } else { # Default normalizer local $^W = 0; $argstr = join chr(28),@_; } if ($context == SCALAR) { my $cache = $info->{S}; _crap_out($info->{NAME}, 'scalar') unless $cache; if (exists $cache->{$argstr}) { return $info->{O}{MERGED} ? $cache->{$argstr}[0] : $cache->{$argstr}; } else { my $val = &{$info->{U}}(@_); # Scalars are considered to be lists; store appropriately if ($info->{O}{MERGED}) { $cache->{$argstr} = [$val]; } else { $cache->{$argstr} = $val; } $val; } } elsif ($context == LIST) { my $cache = $info->{L}; _crap_out($info->{NAME}, 'list') unless $cache; if (exists $cache->{$argstr}) { return @{$cache->{$argstr}}; } else { my @q = &{$info->{U}}(@_); $cache->{$argstr} = \@q; @q; } } else { croak "Internal error \#42; context was neither LIST nor SCALAR\n"; } } sub unmemoize { my $f = shift; my $uppack = caller; my $cref = _make_cref($f, $uppack); unless (exists $revmemotable{$cref}) { croak "Could not unmemoize function `$f', because it was not memoized to begin with"; } my $tabent = $memotable{$revmemotable{$cref}}; unless (defined $tabent) { croak "Could not figure out how to unmemoize function `$f'"; } my $name = $tabent->{NAME}; if (defined $name) { no strict; local($^W) = 0; # ``Subroutine $install_name redefined at ...'' *{$name} = $tabent->{U}; # Replace with original function } undef $memotable{$revmemotable{$cref}}; undef $revmemotable{$cref}; # This removes the last reference to the (possibly tied) memo tables # my ($old_function, $memotabs) = @{$tabent}{'U','S','L'}; # undef $tabent; # # Untie the memo tables if they were tied. # my $i; # for $i (0,1) { # if (tied %{$memotabs->[$i]}) { # warn "Untying hash #$i\n"; # untie %{$memotabs->[$i]}; # } # } $tabent->{U}; } sub _make_cref { my $fn = shift; my $uppack = shift; my $cref; my $name; if (ref $fn eq 'CODE') { $cref = $fn; } elsif (! ref $fn) { if ($fn =~ /::/) { $name = $fn; } else { $name = $uppack . '::' . $fn; } no strict; if (defined $name and !defined(&$name)) { croak "Cannot operate on nonexistent function `$fn'"; } # $cref = \&$name; $cref = *{$name}{CODE}; } else { my $parent = (caller(1))[3]; # Function that called _make_cref croak "Usage: argument 1 to `$parent' must be a function name or reference.\n"; } $DEBUG and warn "${name}($fn) => $cref in _make_cref\n"; $cref; } sub _crap_out { my ($funcname, $context) = @_; if (defined $funcname) { croak "Function `$funcname' called in forbidden $context context; faulting"; } else { croak "Anonymous function called in forbidden $context context; faulting"; } } 1; =head1 NAME Memoize - Make functions faster by trading space for time =head1 SYNOPSIS # This is the documentation for Memoize 1.03 use Memoize; memoize('slow_function'); slow_function(arguments); # Is faster than it was before This is normally all you need to know. However, many options are available: memoize(function, options...); Options include: NORMALIZER => function INSTALL => new_name SCALAR_CACHE => 'MEMORY' SCALAR_CACHE => ['HASH', \%cache_hash ] SCALAR_CACHE => 'FAULT' SCALAR_CACHE => 'MERGE' LIST_CACHE => 'MEMORY' LIST_CACHE => ['HASH', \%cache_hash ] LIST_CACHE => 'FAULT' LIST_CACHE => 'MERGE' =head1 DESCRIPTION `Memoizing' a function makes it faster by trading space for time. It does this by caching the return values of the function in a table. If you call the function again with the same arguments, C jumps in and gives you the value out of the table, instead of letting the function compute the value all over again. Here is an extreme example. Consider the Fibonacci sequence, defined by the following function: # Compute Fibonacci numbers sub fib { my $n = shift; return $n if $n < 2; fib($n-1) + fib($n-2); } This function is very slow. Why? To compute fib(14), it first wants to compute fib(13) and fib(12), and add the results. But to compute fib(13), it first has to compute fib(12) and fib(11), and then it comes back and computes fib(12) all over again even though the answer is the same. And both of the times that it wants to compute fib(12), it has to compute fib(11) from scratch, and then it has to do it again each time it wants to compute fib(13). This function does so much recomputing of old results that it takes a really long time to run---fib(14) makes 1,200 extra recursive calls to itself, to compute and recompute things that it already computed. This function is a good candidate for memoization. If you memoize the `fib' function above, it will compute fib(14) exactly once, the first time it needs to, and then save the result in a table. Then if you ask for fib(14) again, it gives you the result out of the table. While computing fib(14), instead of computing fib(12) twice, it does it once; the second time it needs the value it gets it from the table. It doesn't compute fib(11) four times; it computes it once, getting it from the table the next three times. Instead of making 1,200 recursive calls to `fib', it makes 15. This makes the function about 150 times faster. You could do the memoization yourself, by rewriting the function, like this: # Compute Fibonacci numbers, memoized version { my @fib; sub fib { my $n = shift; return $fib[$n] if defined $fib[$n]; return $fib[$n] = $n if $n < 2; $fib[$n] = fib($n-1) + fib($n-2); } } Or you could use this module, like this: use Memoize; memoize('fib'); # Rest of the fib function just like the original version. This makes it easy to turn memoizing on and off. Here's an even simpler example: I wrote a simple ray tracer; the program would look in a certain direction, figure out what it was looking at, and then convert the `color' value (typically a string like `red') of that object to a red, green, and blue pixel value, like this: for ($direction = 0; $direction < 300; $direction++) { # Figure out which object is in direction $direction $color = $object->{color}; ($r, $g, $b) = @{&ColorToRGB($color)}; ... } Since there are relatively few objects in a picture, there are only a few colors, which get looked up over and over again. Memoizing C sped up the program by several percent. =head1 DETAILS This module exports exactly one function, C. The rest of the functions in this package are None of Your Business. You should say memoize(function) where C is the name of the function you want to memoize, or a reference to it. C returns a reference to the new, memoized version of the function, or C on a non-fatal error. At present, there are no non-fatal errors, but there might be some in the future. If C was the name of a function, then C hides the old version and installs the new memoized version under the old name, so that C<&function(...)> actually invokes the memoized version. =head1 OPTIONS There are some optional options you can pass to C to change the way it behaves a little. To supply options, invoke C like this: memoize(function, NORMALIZER => function, INSTALL => newname, SCALAR_CACHE => option, LIST_CACHE => option ); Each of these options is optional; you can include some, all, or none of them. =head2 INSTALL If you supply a function name with C, memoize will install the new, memoized version of the function under the name you give. For example, memoize('fib', INSTALL => 'fastfib') installs the memoized version of C as C; without the C option it would have replaced the old C with the memoized version. To prevent C from installing the memoized version anywhere, use C undef>. =head2 NORMALIZER Suppose your function looks like this: # Typical call: f('aha!', A => 11, B => 12); sub f { my $a = shift; my %hash = @_; $hash{B} ||= 2; # B defaults to 2 $hash{C} ||= 7; # C defaults to 7 # Do something with $a, %hash } Now, the following calls to your function are all completely equivalent: f(OUCH); f(OUCH, B => 2); f(OUCH, C => 7); f(OUCH, B => 2, C => 7); f(OUCH, C => 7, B => 2); (etc.) However, unless you tell C that these calls are equivalent, it will not know that, and it will compute the values for these invocations of your function separately, and store them separately. To prevent this, supply a C function that turns the program arguments into a string in a way that equivalent arguments turn into the same string. A C function for C above might look like this: sub normalize_f { my $a = shift; my %hash = @_; $hash{B} ||= 2; $hash{C} ||= 7; join(',', $a, map ($_ => $hash{$_}) sort keys %hash); } Each of the argument lists above comes out of the C function looking exactly the same, like this: OUCH,B,2,C,7 You would tell C to use this normalizer this way: memoize('f', NORMALIZER => 'normalize_f'); C knows that if the normalized version of the arguments is the same for two argument lists, then it can safely look up the value that it computed for one argument list and return it as the result of calling the function with the other argument list, even if the argument lists look different. The default normalizer just concatenates the arguments with character 28 in between. (In ASCII, this is called FS or control-\.) This always works correctly for functions with only one string argument, and also when the arguments never contain character 28. However, it can confuse certain argument lists: normalizer("a\034", "b") normalizer("a", "\034b") normalizer("a\034\034b") for example. Since hash keys are strings, the default normalizer will not distinguish between C and the empty string. It also won't work when the function's arguments are references. For example, consider a function C which gets two arguments: A number, and a reference to an array of numbers: g(13, [1,2,3,4,5,6,7]); The default normalizer will turn this into something like C<"13\034ARRAY(0x436c1f)">. That would be all right, except that a subsequent array of numbers might be stored at a different location even though it contains the same data. If this happens, C will think that the arguments are different, even though they are equivalent. In this case, a normalizer like this is appropriate: sub normalize { join ' ', $_[0], @{$_[1]} } For the example above, this produces the key "13 1 2 3 4 5 6 7". Another use for normalizers is when the function depends on data other than those in its arguments. Suppose you have a function which returns a value which depends on the current hour of the day: sub on_duty { my ($problem_type) = @_; my $hour = (localtime)[2]; open my $fh, "$DIR/$problem_type" or die...; my $line; while ($hour-- > 0) $line = <$fh>; } return $line; } At 10:23, this function generates the 10th line of a data file; at 3:45 PM it generates the 15th line instead. By default, C will only see the $problem_type argument. To fix this, include the current hour in the normalizer: sub normalize { join ' ', (localtime)[2], @_ } The calling context of the function (scalar or list context) is propagated to the normalizer. This means that if the memoized function will treat its arguments differently in list context than it would in scalar context, you can have the normalizer function select its behavior based on the results of C. Even if called in a list context, a normalizer should still return a single string. =head2 C, C Normally, C caches your function's return values into an ordinary Perl hash variable. However, you might like to have the values cached on the disk, so that they persist from one run of your program to the next, or you might like to associate some other interesting semantics with the cached values. There's a slight complication under the hood of C: There are actually I caches, one for scalar values and one for list values. When your function is called in scalar context, its return value is cached in one hash, and when your function is called in list context, its value is cached in the other hash. You can control the caching behavior of both contexts independently with these options. The argument to C or C must either be one of the following four strings: MEMORY FAULT MERGE HASH or else it must be a reference to an array whose first element is one of these four strings, such as C<[HASH, arguments...]>. =over 4 =item C C means that return values from the function will be cached in an ordinary Perl hash variable. The hash variable will not persist after the program exits. This is the default. =item C C allows you to specify that a particular hash that you supply will be used as the cache. You can tie this hash beforehand to give it any behavior you want. A tied hash can have any semantics at all. It is typically tied to an on-disk database, so that cached values are stored in the database and retrieved from it again when needed, and the disk file typically persists after your program has exited. See C for more complete details about C. A typical example is: use DB_File; tie my %cache => 'DB_File', $filename, O_RDWR|O_CREAT, 0666; memoize 'function', SCALAR_CACHE => [HASH => \%cache]; This has the effect of storing the cache in a C database whose name is in C<$filename>. The cache will persist after the program has exited. Next time the program runs, it will find the cache already populated from the previous run of the program. Or you can forcibly populate the cache by constructing a batch program that runs in the background and populates the cache file. Then when you come to run your real program the memoized function will be fast because all its results have been precomputed. Another reason to use C is to provide your own hash variable. You can then inspect or modify the contents of the hash to gain finer control over the cache management. =item C This option is no longer supported. It is still documented only to aid in the debugging of old programs that use it. Old programs should be converted to use the C option instead. memoize ... ['TIE', PACKAGE, ARGS...] is merely a shortcut for require PACKAGE; { tie my %cache, PACKAGE, ARGS...; memoize ... [HASH => \%cache]; } =item C C means that you never expect to call the function in scalar (or list) context, and that if C detects such a call, it should abort the program. The error message is one of `foo' function called in forbidden list context at line ... `foo' function called in forbidden scalar context at line ... =item C C normally means that the memoized function does not distinguish between list and sclar context, and that return values in both contexts should be stored together. Both C MERGE> and C MERGE> mean the same thing. Consider this function: sub complicated { # ... time-consuming calculation of $result return $result; } The C function will return the same numeric C<$result> regardless of whether it is called in list or in scalar context. Normally, the following code will result in two calls to C, even if C is memoized: $x = complicated(142); ($y) = complicated(142); $z = complicated(142); The first call will cache the result, say 37, in the scalar cache; the second will cach the list C<(37)> in the list cache. The third call doesn't call the real C function; it gets the value 37 from the scalar cache. Obviously, the second call to C is a waste of time, and storing its return value is a waste of space. Specifying C MERGE> will make C use the same cache for scalar and list context return values, so that the second call uses the scalar cache that was populated by the first call. C ends up being called only once, and both subsequent calls return C<3> from the cache, regardless of the calling context. =head3 List values in scalar context Consider this function: sub iota { return reverse (1..$_[0]) } This function normally returns a list. Suppose you memoize it and merge the caches: memoize 'iota', SCALAR_CACHE => 'MERGE'; @i7 = iota(7); $i7 = iota(7); Here the first call caches the list (1,2,3,4,5,6,7). The second call does not really make sense. C cannot guess what behavior C should have in scalar context without actually calling it in scalar context. Normally C I call C in scalar context and cache the result, but the C 'MERGE'> option says not to do that, but to use the cache list-context value instead. But it cannot return a list of seven elements in a scalar context. In this case C<$i7> will receive the B of the cached list value, namely 7. =head3 Merged disk caches Another use for C is when you want both kinds of return values stored in the same disk file; this saves you from having to deal with two disk files instead of one. You can use a normalizer function to keep the two sets of return values separate. For example: tie my %cache => 'MLDBM', 'DB_File', $filename, ...; memoize 'myfunc', NORMALIZER => 'n', SCALAR_CACHE => [HASH => \%cache], LIST_CACHE => 'MERGE', ; sub n { my $context = wantarray() ? 'L' : 'S'; # ... now compute the hash key from the arguments ... $hashkey = "$context:$hashkey"; } This normalizer function will store scalar context return values in the disk file under keys that begin with C, and list context return values under keys that begin with C. =back =head1 OTHER FACILITIES =head2 C There's an C function that you can import if you want to. Why would you want to? Here's an example: Suppose you have your cache tied to a DBM file, and you want to make sure that the cache is written out to disk if someone interrupts the program. If the program exits normally, this will happen anyway, but if someone types control-C or something then the program will terminate immediately without synchronizing the database. So what you can do instead is $SIG{INT} = sub { unmemoize 'function' }; C accepts a reference to, or the name of a previously memoized function, and undoes whatever it did to provide the memoized version in the first place, including making the name refer to the unmemoized version if appropriate. It returns a reference to the unmemoized version of the function. If you ask it to unmemoize a function that was never memoized, it croaks. =head2 C C will flush out the caches, discarding I the cached data. The argument may be a function name or a reference to a function. For finer control over when data is discarded or expired, see the documentation for C, included in this package. Note that if the cache is a tied hash, C will attempt to invoke the C method on the hash. If there is no C method, this will cause a run-time error. An alternative approach to cache flushing is to use the C option (see above) to request that C use a particular hash variable as its cache. Then you can examine or modify the hash at any time in any way you desire. You may flush the cache by using C<%hash = ()>. =head1 CAVEATS Memoization is not a cure-all: =over 4 =item * Do not memoize a function whose behavior depends on program state other than its own arguments, such as global variables, the time of day, or file input. These functions will not produce correct results when memoized. For a particularly easy example: sub f { time; } This function takes no arguments, and as far as C is concerned, it always returns the same result. C is wrong, of course, and the memoized version of this function will call C