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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 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

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

       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 com-
       putes 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 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:

           for ($direction = 0; $direction < 300; $direction++) {
             # Figure out which object is in direction $direction
             $color = $object->{color};
             ($r, $g, $b) = @{&ColorToRGB($color)};

perl v5.8.5                 2002-11-06                          2

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

       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 sev-
       eral percent.

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

       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 ver-
       sion 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,

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

       installs the memoized version of "fib" as "fastfib"; with-
       out 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".

perl v5.8.5                 2002-11-06                          3

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


       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 com-
       pletely equivalent:

               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 equiva-
       lent arguments turn into the same string.  A "NORMALIZER"
       function 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);

       Each of the argument lists above comes out of the "normal-
       ize_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
       arguments is the same for two argument lists, then it can

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

       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 func-
       tions 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 distinguish between "undef" and the empty string.  It
       also won't work when the function's arguments are refer-
       ences.  For example, consider a function "g" which gets
       two arguments: A number, and a reference to an array of

               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
       different 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 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:

perl v5.8.5                 2002-11-06                          5

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

               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 argu-
       ment.  To fix this, include the current hour in the nor-

               sub normalize { join ' ', (localtime)[2], @_ }

       The calling context of the function (scalar or list con-
       text) 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 con-
       text, 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 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

       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

perl v5.8.5                 2002-11-06                          6

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

       element is one of these four strings, such as "[HASH,

           "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

           A tied hash can have any semantics at all.  It is typ-
           ically 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 per-
           sists 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 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 popu-
           lates 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...]

           is merely a shortcut for

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

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

           "FAULT" means that you never expect to call the func-
           tion in scalar (or list) context, and that if "Memo-
           ize" 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 distin-
           guish 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 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

           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, ...;

perl v5.8.5                 2002-11-06                          8

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

                   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: Sup-
       pose 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 nor-
       mally, this will happen anyway, but if someone types con-
       trol-C or something then the program will terminate imme-
       diately without synchronizing the database.  So what you
       can do instead is

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

       "unmemoize" accepts a reference to, or the name of a pre-
       viously 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 appro-
       priate.  It returns a reference to the unmemoized version
       of the function.

       If you ask it to unmemoize a function that was never memo-
       ized, it croaks.


       "flush_cache(function)" will flush out the caches, dis-
       carding all the cached data.  The argument may be a func-
       tion name or a reference to a function.  For finer control
       over when data is discarded or expired, see the documenta-
       tion 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

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

       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 exam-
       ine 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 "Memo-
           ize" is concerned, it always returns the same result.
           "Memoize" is wrong, of course, and the memoized ver-
           sion 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 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 and 3, but subsequent calls will return 1 (the
           return value of "print") without actually printing

       o   Do not memoize a function that returns a data struc-
           ture 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:

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

                   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.

       o   Do not memoize a very simple function.

           Recently someone mentioned to me that the Memoize mod-
           ule made his program run slower instead of faster.  It
           turned out that he was memoizing the following func-

               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" func-

           Memoization is not magical.

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

       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
       little glue.

       "SDBM_File" doesn't supply an "EXISTS" method, so included
       in this package is a glue module called "Memo-
       ize::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 mem-
       ory, 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 available on CPAN as Memoize::ExpireLRU.

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       The test suite is much better, but always needs improve-

       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, mem-
       oized 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 prob-
       lem, 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 "mjd-perl-memo-

       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 Memo-
       ize 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 Perl Advanced Techniques Handbook.  It will also be
       available 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-memo-
       ize-requestATplover.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

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       and/or modify it under the same terms as Perl itself.

       Many thanks to Jonathan Roy for bug reports and sugges-
       tions, 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 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.

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