NAME

Memoize - Make functions faster by trading space for time

SYNOPSIS

use Memoize;
memoize('slow_function');
slow_function(arguments);    # Is faster than it was before

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

memoize(function, options...);

Options include:

NORMALIZER => function
INSTALL => new_name
SCALAR_CACHE => 'MEMORY'
SCALAR_CACHE => ['HASH', \%cache_hash ]
SCALAR_CACHE => 'FAULT'
SCALAR_CACHE => 'MERGE'
LIST_CACHE => 'MEMORY'
LIST_CACHE => ['HASH', \%cache_hash ]
LIST_CACHE => 'FAULT'
LIST_CACHE => 'MERGE'

DESCRIPTION

Memoizing a function makes it faster by trading space for time. It does this by caching the return values of the function in a table. If you call the function again with the same arguments, "memoize" jumps in and gives you the value out of the table, instead of letting the function compute the value all over again.

EXAMPLE

Here is an extreme example. Consider the Fibonacci sequence, defined by the following function:

# Compute Fibonacci numbers
sub fib {
  my $n = shift;
  return $n if $n < 2;
  fib($n-1) + fib($n-2);
}

This function is very slow. Why? To compute fib(14), it first wants to compute fib(13) and fib(12), and add the results. But to compute fib(13), it first has to compute fib(12) and fib(11), and then it comes back and computes fib(12) all over again even though the answer is the same. And both of the times that it wants to compute fib(12), it has to compute fib(11) from scratch, and then it has to do it again each time it wants to compute fib(13). This function does so much recomputing of old results that it takes a really long time to run---fib(14) makes 1,200 extra recursive calls to itself, to compute and recompute things that it already computed.

This function is a good candidate for memoization. If you memoize the "fib" function above, it will compute fib(14) exactly once, the first time it needs to, and then save the result in a table. Then if you ask for fib(14) again, it gives you the result out of the table. While computing fib(14), instead of computing fib(12) twice, it does it once; the second time it needs the value it gets it from the table. It doesn't compute fib(11) four times; it computes it once, getting it from the table the next three times. Instead of making 1,200 recursive calls to "fib", it makes 15. This makes the function about 150 times faster.

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

# Compute Fibonacci numbers, memoized version
{ my @fib;
  sub fib {
    my $n = shift;
    return $fib[$n] if defined $fib[$n];
    return $fib[$n] = $n if $n < 2;
    $fib[$n] = fib($n-1) + fib($n-2);
  }
}

Or you could use this module, like this:

use Memoize;
memoize('fib');
# Rest of the fib function just like the original version.

This makes it easy to turn memoizing on and off.

Here's an even simpler example: I wrote a simple ray tracer; the program would look in a certain direction, figure out what it was looking at, and then convert the "color" value (typically a string like "red") of that object to a red, green, and blue pixel value, like this:

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

Since there are relatively few objects in a picture, there are only a few colors, which get looked up over and over again. Memoizing "ColorToRGB" sped up the program by several percent.

DETAILS

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

You should say

memoize(function)

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.

OPTIONS

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.

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

# 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
}

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

sub normalize_f {
  my $a = shift;
  my %hash = @_;
  $hash{B} ||= 2;
  $hash{C} ||= 7;
  join(',', $a, map ($_ => $hash{$_}) sort keys %hash);
}

OUCH,B,2,C,7

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

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

g(13, [1,2,3,4,5,6,7]);

sub normalize { join ' ', $_[0], @{$_[1]} }

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;
}

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

MEMORY
FAULT
MERGE
HASH

sub iota { return reverse (1..$_[0]) }

memoize 'iota', SCALAR_CACHE => 'MERGE';
@i7 = iota(7);
$i7 = iota(7);

local $MLDBM::UseDB = 'DB_File';
tie my %cache => 'MLDBM', $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";
}

OTHER FACILITIES

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

CAVEATS

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 {
    time;
  }
  

  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 number 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 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 different 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:

  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.

PERSISTENT CACHE SUPPORT

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.

EXPIRATION SUPPORT

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.

BUGS

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.

SEE ALSO

At https://perl.plover.com/MiniMemoize/ there is an article about memoization and about the internals of Memoize that appeared in The Perl Journal, issue #13.

Mark-Jason Dominus'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 https://hop.perl.plover.com/.

THANK YOU

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.

AUTHOR

Mark Jason Dominus

COPYRIGHT AND LICENSE

This software is copyright (c) 2012 by Mark Jason Dominus.

This is free software; you can redistribute it and/or modify it under the same terms as the Perl 5 programming language system itself.