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       Memoize - Make functions faster by trading space for time


               # This is the documentation for Memoize 1.03
               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

               # 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;

               # 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

           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


       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 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"; 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 =>

       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, 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"
       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 "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 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")

       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 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 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:

               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
       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


       or else it must be a reference to an array 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 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 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 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

           Another reason to use "HASH" 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

           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;
                   { tie my %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 that the memoized function does not distinguish between list
           and sclar context, and that return values in both contexts should be stored together.
           Both "LIST_CACHE => MERGE" and "SCALAR_CACHE => MERGE" mean the same thing.

           Consider this function:

                   sub complicated {
                     # ... time-consuming calculation of $result
                     return $result;

           The "complicated" function will return the same numeric $result regardless of whether
           it is called in list or in scalar context.

           Normally, the following code will result in two calls to "complicated", even if
           "complicated" 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 "(37)" in the list cache.  The third call doesn't call the real
           "complicated" function; it gets the value 37 from the scalar cache.

           Obviously, the second call to "complicated" 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.  "complicated" ends up being
           called only once, and both subsequent calls return 3 from the cache, regardless of the
           calling context.

       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. "Memoize" cannot guess what behavior "iota" should have in scalar context without
       actually calling it in scalar context.  Normally "Memoize" would call "iota" in scalar
       context and cache the result, but the "SCALAR_CACHE => '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 $i7 will receive the first element of the
       cached list value, namely 7.

       Merged disk caches

       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 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' };

       "unmemoize" 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.

       "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:

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

       ·   Do not memoize a function that returns a data structure that is modified by its

           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 different

       ·   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 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 "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 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


       To join a very low-traffic mailing list for announcements about "Memoize", 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'.)

       The author's book Higher-Order Perl (2005, ISBN 1558607013, published by Morgan Kaufmann)
       discusses memoization (and many other topics) in tremendous detail. It is 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---fewer than two messages per year.


       Copyright 1998, 1999, 2000, 2001, 2012  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 Florian Ragwitz for administration and packaging assistance, to John Tromp
       for bug reports, 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 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.