MirBSD manpage: Memoize(3p)

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


     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 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'


     `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 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.

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     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 func-
     tion does so much recomputing of old results that it takes a
     really long time to run---fib(14) makes 1,200 extra recur-
     sive 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;

             # 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:

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         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 "ColorToRGB" 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 Busi-

     You should say


     where "function" is the name of the function you want to
     memoize, or a reference to it.  "memoize" returns a refer-
     ence 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 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.


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

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             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 version.

     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

             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 invocations 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" func-
     tion for "f" 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);

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     Each of the argument lists above comes out of the
     "normalize_f" function 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 argu-
     ments 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 dif-

     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 argu-
     ment lists:

             normalizer("a\034", "b")
             normalizer("a", "\034b")

     for example.

     Since hash keys are strings, the default normalizer will not
     distinguish between "undef" and the empty string.  It also
     won't work when the function's arguments are references.
     For example, consider a function "g" which gets two argu-
     ments: 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 subsequent array of numbers might be stored at a dif-
     ferent location even though it contains the same data.  If
     this happens, "Memoize" 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

     Another use for normalizers is when the function depends on
     data other than those in its arguments.  Suppose you have a

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     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 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 "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 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 "Memoize":
     There are actually two caches, one for scalar values and one
     for list values. When your function is called in scalar con-
     text, 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:

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

         "MEMORY" 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.

         "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 typi-
         cally 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 com-
         plete 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 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 forci-
         bly 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 docu-
         mented 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...]

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         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 con-
         text 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

             $x = pi();
             ($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 cache.

         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.

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         Another use for "MERGE" 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 "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 inter-
     rupts 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 syn-
     chronizing the database.  So what you can do instead is

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

     "unmemoize" accepts a reference to, or the name of a previ-
     ously memoized function, and undoes whatever it did to pro-
     vide the memoized version in the first place, including mak-
     ing the name refer to the unmemoized version if appropriate.
     It returns a reference to the unmemoized version of the

     If you ask it to unmemoize a function that was never
     memoized, it croaks.

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     "flush_cache(function)" will flush out the caches, discard-
     ing 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:

     +   Do not memoize a function whose behavior depends on pro-
         gram state other than its own arguments, such as global
         variables, the time of day, or file input.  These func-
         tions 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 concerned, 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.

     +   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 understand 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

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         and 3, but subsequent calls will return 1 (the return
         value of "print") without actually printing anything.

     +   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 somehow, 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 references to the same array.  Had "getusers" not
         been memoized, $u1 and $u2 would have referred to dif-
         ferent arrays.

     +   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:

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

         I pointed out that "Memoize" uses a hash, and that look-
         ing 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 example,

             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 lit-
     tle 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 "Memoize::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

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     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 available
     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 memoized 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 "Memoize", send an empty note to


     Mark-Jason Dominus ("mjd-perl-memoize+@plover.com"), Plover
     Systems co.

     See the "Memoize.pm" Page at
     http://www.plover.com/~mjd/perl/Memoize/ for news and
     upgrades.  Near this page, at
     http://www.plover.com/~mjd/perl/MiniMemoize/ 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

     My upcoming book will discuss memoization (and many other
     fascinating topics) in tremendous detail.  It will be pub-
     lished by Morgan Kaufmann in 2002, possibly under the title

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     Perl Advanced Techniques Handbook.  It will also be avail-
     able on-line for free.  For more information, visit
     http://perl.plover.com/book/ .

     To join a mailing list for announcements about "Memoize",
     send an empty message to
     "mjd-perl-memoize-request@plover.com".  This mailing list is
     for announcements only and has extremely low traffic---about
     two messages 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-provoking 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 sugges-
     tions, to Jonathan Roy (again) for finding a use for
     "unmemoize()", to Philippe Verdret for enlightening discus-
     sion 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.

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