Memoize(3)             Perl Programmers Reference Guide             Memoize(3)

       Memoize - Make functions faster by trading space for time

               # This is the documentation for Memoize 1.01
               use Memoize;
               slow_function(arguments);    # Is faster than it was before

       This is normally all you need to know.  However, many options are

               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'

       `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, "memoize" jumps in
       and gives you the value out of the table, instead of letting the func-
       tion 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 recomput-
       ing 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

       You could do the memoization yourself, by rewriting the function, like

               # 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;

               # 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 pro-
       gram 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 "Color-
       ToRGB" sped up the program by several percent.

       This module exports exactly one function, "memoize".  The rest of the
       functions in this package are None of Your Business.

       You should say


       where "function" is the name of the function you want to memoize, or a
       reference to it.  "memoize" returns a reference to the new, memoized
       version of the function, or "undef" on a non-fatal error.  At present,
       there are no non-fatal errors, but there might be some in the future.

       If "function" was the name of a function, then "memoize" hides the old
       version and installs the new memoized version under the old name, so
       that "&function(...)" actually invokes the memoized version.

       There are some optional options you can pass to "memoize" to change the
       way it behaves a little.  To supply options, invoke "memoize" like

               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.


       If you supply a function name with "INSTALL", memoize will install the
       new, memoized version of the function under the name you give.  For

               memoize('fib', INSTALL => 'fastfib')

       installs the memoized version of "fib" as "fastfib"; without the
       "INSTALL" option it would have replaced the old "fib" with the memoized

       To prevent "memoize" from installing the memoized version anywhere, use
       "INSTALL => undef".


       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 equiva-

               f(OUCH, B => 2);
               f(OUCH, C => 7);
               f(OUCH, B => 2, C => 7);
               f(OUCH, C => 7, B => 2);

       However, unless you tell "Memoize" that these calls are equivalent, it
       will not know that, and it will compute the values for these invoca-
       tions of your function separately, and store them separately.

       To prevent this, supply a "NORMALIZER" function that turns the program
       arguments into a string in a way that equivalent arguments turn into
       the same string.  A "NORMALIZER" function for "f" above might look like

               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 "normalize_f" func-
       tion looking exactly the same, like this:


       You would tell "Memoize" to use this normalizer this way:

               memoize('f', NORMALIZER => 'normalize_f');

       "memoize" 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 call-
       ing 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")

       for example.

       Since hash keys are strings, the default normalizer will not distin-
       guish between "undef" and the empty string.  It also won't work when
       the function's arguments are references.  For example, consider a func-
       tion "g" 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
       "13\034ARRAY(0x436c1f)".  That would be all right, except that a subse-
       quent array of numbers might be stored at a different location even
       though it contains the same data.  If this happens, "Memoize" will
       think that the arguments are different, even though they are equiva-
       lent.  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, "Memoize" 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 propa-
       gated 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 "wantarray".  Even if called in a list context, a
       normalizer should still return a single string.


       Normally, "Memoize" caches your function's return values into an ordi-
       nary 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 "Memoize": There are
       actually two 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 "LIST_CACHE" or "SCALAR_CACHE" must either be one of
       the following four strings:


       or else it must be a reference to a list whose first element is one of
       these four strings, such as "[HASH, arguments...]".

           "MEMORY" means that return values from the function will be cached
           in an ordinary Perl hash variable.  The hash variable will not per-
           sist after the program exits.  This is the default.

           "HASH" 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 "perltie"
           for more complete details about "tie".

           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 "DB_File" database
           whose name is in $filename.  The cache will persist after the pro-
           gram 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.

           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 "HASH" option instead.

                   memoize ... [TIE, PACKAGE, ARGS...]

           is merely a shortcut for

                   require PACKAGE;
                   { my %cache;
                     tie %cache, PACKAGE, ARGS...;
                   memoize ... [HASH => \%cache];

           "FAULT" means that you never expect to call the function in scalar
           (or list) context, and that if "Memoize" 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 ...

           "MERGE" normally means the function does not distinguish between
           list and sclar context, and that return values in both contexts
           should be stored together.  "LIST_CACHE => MERGE" means that list
           context return values should be stored in the same hash that is
           used for scalar context returns, and "SCALAR_CACHE => MERGE" means
           the same, mutatis mutandis.  It is an error to specify "MERGE" for
           both, but it probably does something useful.

           Consider this function:

                   sub pi { 3; }

           Normally, the following code will result in two calls to "pi":

               $x = pi();
               ($y) = pi();
               $z = pi();

           The first call caches the value 3 in the scalar cache; the second
           caches the list "(3)" in the list cache.  The third call doesn't
           call the real "pi" function; it gets the value from the scalar

           Obviously, the second call to "pi" is a waste of time, and storing
           its return value is a waste of space.  Specifying "LIST_CACHE =>
           MERGE" will make "memoize" 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.  "pi" ends up being
           called only once, and both subsequent calls return 3 from the
           cache, regardless of the calling context.

           Another use for "MERGE" is when you want both kinds of return val-
           ues 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 exam-

                   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 "S:", and list context
           return values under keys that begin with "L:".


       There's an "unmemoize" 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 synchro-
       nizing the database.  So what you can do instead is

           $SIG{INT} = sub { unmemoize 'function' };

       "unmemoize" accepts a reference to, or the name of a previously memo-
       ized function, and undoes whatever it did to provide the memoized ver-
       sion in the first place, including making the name refer to the unmemo-
       ized 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


       "flush_cache(function)" will flush out the caches, discarding all 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 "Memoize::Expire", included in this package.

       Note that if the cache is a tied hash, "flush_cache" will attempt to
       invoke the "CLEAR" method on the hash.  If there is no "CLEAR" method,
       this will cause a run-time error.

       An alternative approach to cache flushing is to use the "HASH" option
       (see above) to request that "Memoize" 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 "%hash = ()".

       Memoization is not a cure-all:

       o   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 {

           This function takes no arguments, and as far as "Memoize" is con-
           cerned, it always returns the same result.  "Memoize" is wrong, of
           course, and the memoized version of this function will call "time"
           once to get the current time, and it will return that same time
           every time you call it after that.

       o   Do not memoize a function with side effects.

                   sub f {
                     my ($a, $b) = @_;
                     my $s = $a + $b;
                     print "$a + $b = $s.\n";

           This function accepts two arguments, adds them, and prints their
           sum.  Its return value is the numuber of characters it printed, but
           you probably didn't care about that.  But "Memoize" doesn't under-
           stand that.  If you memoize this function, you will get the result
           you expect the first time you ask it to print the sum of 2 and 3,
           but subsequent calls will return 1 (the return value of "print")
           without actually printing anything.

       o   Do not memoize a function that returns a data structure that is
           modified by its caller.

           Consider these functions:  "getusers" returns a list of users some-
           how, and then "main" throws away the first user on the list and
           prints the rest:

                   sub main {
                     my $userlist = getusers();
                     shift @$userlist;
                     foreach $u (@$userlist) {
                       print "User $u\n";

                   sub getusers {
                     my @users;
                     # Do something to get a list of users;
                     \@users;  # Return reference to list.

           If you memoize "getusers" here, it will work right exactly once.
           The reference to the users list will be stored in the memo table.
           "main" will discard the first element from the referenced list.
           The next time you invoke "main", "Memoize" will not call
           "getusers"; it will just return the same reference to the same list
           it got last time.  But this time the list has already had its head
           removed; "main" will erroneously remove another element from it.
           The list will get shorter and shorter every time you call "main".

           Similarly, this:

                   $u1 = getusers();
                   $u2 = getusers();
                   pop @$u1;

           will modify $u2 as well as $u1, because both variables are refer-
           ences to the same array.  Had "getusers" not been memoized, $u1 and
           $u2 would have referred to different arrays.

       o   Do not memoize a very simple function.

           Recently someone mentioned to me that the Memoize module made his
           program run slower instead of faster.  It turned out that he was
           memoizing the following function:

               sub square {
                 $_[0] * $_[0];

           I pointed out that "Memoize" uses a hash, and that looking up a
           number in the hash is necessarily going to take a lot longer than a
           single multiplication.  There really is no way to speed up the
           "square" function.

           Memoization is not magical.

       You can tie the cache tables to any sort of tied hash that you want to,
       as long as it supports "TIEHASH", "FETCH", "STORE", and "EXISTS".  For

               tie my %cache => 'GDBM_File', $filename, O_RDWR|O_CREAT, 0666;
               memoize 'function', SCALAR_CACHE => [HASH => \%cache];

       works just fine.  For some storage methods, you need a little glue.

       "SDBM_File" doesn't supply an "EXISTS" method, so included in this
       package is a glue module called "Memoize::SDBM_File" which does provide
       one.  Use this instead of plain "SDBM_File" to store your cache table
       on disk in an "SDBM_File" database:

               tie my %cache => 'Memoize::SDBM_File', $filename, O_RDWR|O_CREAT, 0666;
               memoize 'function', SCALAR_CACHE => [HASH => \%cache];

       "NDBM_File" has the same problem and the same solution.  (Use "Memo-
       ize::NDBM_File instead of plain NDBM_File.")

       "Storable" isn't a tied hash class at all.  You can use it to store a
       hash to disk and retrieve it again, but you can't modify the hash while
       it's on the disk.  So if you want to store your cache table in a
       "Storable" database, use "Memoize::Storable", which puts a hashlike
       front-end onto "Storable".  The hash table is actually kept in memory,
       and is loaded from your "Storable" file at the time you memoize the
       function, and stored back at the time you unmemoize the function (or
       when your program exits):

               tie my %cache => 'Memoize::Storable', $filename;
               memoize 'function', SCALAR_CACHE => [HASH => \%cache];

               tie my %cache => 'Memoize::Storable', $filename, 'nstore';
               memoize 'function', SCALAR_CACHE => [HASH => \%cache];

       Include the `nstore' option to have the "Storable" database written in
       `network order'.  (See Storable for more details about this.)

       The "flush_cache()" function will raise a run-time error unless the
       tied package provides a "CLEAR" method.

       See Memoize::Expire, which is a plug-in module that adds expiration
       functionality to Memoize.  If you don't like the kinds of policies that
       Memoize::Expire implements, it is easy to write your own plug-in module
       to implement whatever policy you desire.  Memoize comes with several
       examples.  An expiration manager that implements a LRU policy is avail-
       able on CPAN as Memoize::ExpireLRU.

       The test suite is much better, but always needs improvement.

       There is some problem with the way "goto &f" works under threaded Perl,
       perhaps because of the lexical scoping of @_.  This is a bug in Perl,
       and until it is resolved, memoized functions will see a slightly
       different "caller()" and will perform a little more slowly on threaded
       perls than unthreaded perls.

       Some versions of "DB_File" won't let you store data under a key of
       length 0.  That means that if you have a function "f" which you memo-
       ized and the cache is in a "DB_File" database, then the value of "f()"
       ("f" called with no arguments) will not be memoized.  If this is a big
       problem, you can supply a normalizer function that prepends "x" to
       every key.

       To join a very low-traffic mailing list for announcements about "Memo-
       ize", send an empty note to "".

       Mark-Jason Dominus (""), Plover Systems co.

       See the "" Page at
       for news and upgrades.  Near this page, at there is an article about
       memoization and about the internals of Memoize that appeared in The
       Perl Journal, issue #13.  (This article is also included in the Memoize
       distribution as `article.html'.)

       My upcoming book will discuss memoization (and many other fascinating
       topics) in tremendous detail.  It will be published by Morgan Kaufmann
       in 2002, possibly under the title Perl Advanced Techniques Handbook.
       It will also be available on-line for free.  For more information,
       visit .

       To join a mailing list for announcements about "Memoize", send an empty
       message to "".  This mailing list is
       for announcements only and has extremely low traffic---about two mes-
       sages per year.

       Copyright 1998, 1999, 2000, 2001  by Mark Jason Dominus

       This library is free software; you may redistribute it and/or modify it
       under the same terms as Perl itself.

       Many thanks to Jonathan Roy for bug reports and suggestions, to Michael
       Schwern for other bug reports and patches, to Mike Cariaso for helping
       me to figure out the Right Thing to Do About Expiration, to Joshua
       Gerth, Joshua Chamas, Jonathan Roy (again), Mark D. Anderson, and
       Andrew Johnson for more suggestions about expiration, to Brent Powers
       for the Memoize::ExpireLRU module, to Ariel Scolnicov for delightful
       messages about the Fibonacci function, to Dion Almaer for thought-pro-
       voking suggestions about the default normalizer, to Walt Mankowski and
       Kurt Starsinic for much help investigating problems under threaded
       Perl, to Alex Dudkevich for reporting the bug in prototyped functions
       and for checking my patch, to Tony Bass for many helpful suggestions,
       to Jonathan Roy (again) for finding a use for "unmemoize()", to
       Philippe Verdret for enlightening discussion of "Hook::PrePostCall", to
       Nat Torkington for advice I ignored, to Chris Nandor for portability
       advice, to Randal Schwartz for suggesting the '"flush_cache" function,
       and to Jenda Krynicky for being a light in the world.

       Special thanks to Jarkko Hietaniemi, the 5.8.0 pumpking, for including
       this module in the core and for his patient and helpful guidance during
       the integration process.

perl v5.8.6                       2001-09-21                        Memoize(3)