Memoize
Memoize(3) Perl Programmers Reference Guide Memoize(3)
NAME
Memoize - Make functions faster by trading space for time
SYNOPSIS
# This is the documentation for Memoize 1.01
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.
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 recur-
sive 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 pro-
gram would look in a certain direction, figure out what it was looking
at, and then convert the ‘color’ value (typically a string like ‘red’)
of that object to a red, green, and blue pixel value, like this:
for ($direction = 0; $direction < 300; $direction++) {
# Figure out which object is in direction $direction
$color = $object->{color};
($r, $g, $b) = @{&ColorToRGB($color)};
...
}
Since there are relatively few objects in a picture, there are only a
few colors, which get looked up over and over again. Memoizing "Col-
orToRGB" 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.
INSTALL
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 memo-
ized version.
To prevent "memoize" from installing the memoized version anywhere,
use "INSTALL => undef".
NORMALIZER
Suppose your function looks like this:
# Typical call: f(’aha!’, A => 11, B => 12);
sub f {
my $a = shift;
my %hash = @_;
$hash{B} ││= 2; # B defaults to 2
$hash{C} ││= 7; # C defaults to 7
# Do something with $a, %hash
}
Now, the following calls to your function are all completely equiva-
lent:
f(OUCH);
f(OUCH, B => 2);
f(OUCH, C => 7);
f(OUCH, B => 2, C => 7);
f(OUCH, C => 7, B => 2);
(etc.)
However, unless you tell "Memoize" that these calls are equivalent, it
will not know that, and it will compute the values for these invoca-
tions of your function separately, and store them separately.
To prevent this, supply a "NORMALIZER" function that turns the program
arguments into a string in a way that equivalent arguments turn into
the same string. A "NORMALIZER" function for "f" above might look
like 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" func-
tion looking exactly the same, like this:
OUCH,B,2,C,7
You would tell "Memoize" to use this normalizer this way:
memoize(’f’, NORMALIZER => ’normalize_f’);
"memoize" knows that if the normalized version of the arguments is the
same for two argument lists, then it can safely look up the value that
it computed for one argument list and return it as the result of call-
ing the function with the other argument list, even if the argument
lists look different.
The default normalizer just concatenates the arguments with character
28 in between. (In ASCII, this is called FS or control-\.) This
always works correctly for functions with only one string argument,
and also when the arguments never contain character 28. However, it
can confuse certain argument lists:
normalizer("a\034", "b")
normalizer("a", "\034b")
normalizer("a\034\034b")
for example.
Since hash keys are strings, the default normalizer will not distin-
guish between "undef" and the empty string. It also won’t work when
the function’s arguments are references. For example, consider a
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 sub-
sequent array of numbers might be stored at a different location even
though it contains the same data. If this happens, "Memoize" will
think that the arguments are different, even though they are equiva-
lent. In this case, a normalizer like this is appropriate:
sub normalize { join ’ ’, $_[0], @{$_[1]} }
For the example above, this produces the key "13 1 2 3 4 5 6 7".
Another use for normalizers is when the function depends on data other
than those in its arguments. Suppose you have a function which
returns a value which depends on the current hour of the day:
sub on_duty {
my ($problem_type) = @_;
my $hour = (localtime)[2];
open my $fh, "$DIR/$problem_type" or die...;
my $line;
while ($hour-- > 0)
$line = <$fh>;
}
return $line;
}
At 10:23, this function generates the 10th line of a data file; at
3:45 PM it generates the 15th line instead. By default, "Memoize"
will only see the $problem_type argument. To fix this, include the
current hour in the normalizer:
sub normalize { join ’ ’, (localtime)[2], @_ }
The calling context of the function (scalar or list context) is propa-
gated to the normalizer. This means that if the memoized function
will treat its arguments differently in list context than it would in
scalar context, you can have the normalizer function select its behav-
ior based on the results of "wantarray". Even if called in a list
context, a normalizer should still return a single string.
"SCALAR_CACHE", "LIST_CACHE"
Normally, "Memoize" caches your function’s return values into an ordi-
nary Perl hash variable. However, you might like to have the values
cached on the disk, so that they persist from one run of your program
to the next, or you might like to associate some other interesting
semantics with the cached values.
There’s a slight complication under the hood of "Memoize": There are
actually two caches, one for scalar values and one for list values.
When your function is called in scalar context, its return value is
cached in one hash, and when your function is called in list context,
its value is cached in the other hash. You can control the caching
behavior of both contexts independently with these options.
The argument to "LIST_CACHE" or "SCALAR_CACHE" must either be one of
the following four strings:
MEMORY
FAULT
MERGE
HASH
or else it must be a reference to a list whose first element is one of
these four strings, such as "[HASH, arguments...]".
"MEMORY"
"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"
"HASH" allows you to specify that a particular hash that you sup-
ply will be used as the cache. You can tie this hash beforehand
to give it any behavior you want.
A tied hash can have any semantics at all. It is typically tied
to an on-disk database, so that cached values are stored in the
database and retrieved from it again when needed, and the disk
file typically persists after your program has exited. See
"perltie" for more complete details about "tie".
A typical example is:
use DB_File;
tie my %cache => ’DB_File’, $filename, O_RDWR│O_CREAT, 0666;
memoize ’function’, SCALAR_CACHE => [HASH => \%cache];
This has the effect of storing the cache in a "DB_File" database
whose name is in $filename. The cache will persist after the pro-
gram has exited. Next time the program runs, it will find the
cache already populated from the previous run of the program. Or
you can forcibly populate the cache by constructing a batch pro-
gram 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.
"TIE"
This option is no longer supported. It is still documented only
to aid in the debugging of old programs that use it. Old programs
should be converted to use the "HASH" option instead.
memoize ... [TIE, PACKAGE, ARGS...]
is merely a shortcut for
require PACKAGE;
{ my %cache;
tie %cache, PACKAGE, ARGS...;
}
memoize ... [HASH => \%cache];
"FAULT"
"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"
"MERGE" normally means the function does not distinguish between
list and sclar context, and that return values in both contexts
should be stored together. "LIST_CACHE => MERGE" means that list
context return values should be stored in the same hash that is
used for scalar context returns, and "SCALAR_CACHE => MERGE" means
the same, mutatis mutandis. It is an error to specify "MERGE" for
both, but it probably does something useful.
Consider this function:
sub pi { 3; }
Normally, the following code will result in two calls to "pi":
$x = pi();
($y) = pi();
$z = pi();
The first call caches the value 3 in the scalar cache; the second
caches the list "(3)" in the list cache. The third call doesn’t
call the real "pi" function; it gets the value from the scalar
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.
Another use for "MERGE" is when you want both kinds of return val-
ues stored in the same disk file; this saves you from having to
deal with two disk files instead of one. You can use a normalizer
function to keep the two sets of return values separate. For
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:".
OTHER FACILITIES
"unmemoize"
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 writ-
ten 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
$SIG{INT} = sub { unmemoize ’function’ };
"unmemoize" accepts a reference to, or the name of a previously memo-
ized function, and undoes whatever it did to provide the memoized ver-
sion in the first place, including making the name refer to the unmem-
oized version if appropriate. It returns a reference to the unmemo-
ized version of the function.
If you ask it to unmemoize a function that was never memoized, it
croaks.
"flush_cache"
"flush_cache(function)" will flush out the caches, discarding all the
cached data. The argument may be a function name or a reference to a
function. For finer control over when data is discarded or expired,
see the documentation for "Memoize::Expire", included in this package.
Note that if the cache is a tied hash, "flush_cache" will attempt to
invoke the "CLEAR" method on the hash. If there is no "CLEAR" method,
this will cause a run-time error.
An alternative approach to cache flushing is to use the "HASH" option
(see above) to request that "Memoize" use a particular hash variable
as its cache. Then you can examine or modify the hash at any time in
any way you desire. You may flush the cache by using "%hash = ()".
CAVEATS
Memoization is not a cure-all:
· Do not memoize a function whose behavior depends on program state
other than its own arguments, such as global variables, the time
of day, or file input. These functions will not produce correct
results when memoized. For a particularly easy example:
sub f {
time;
}
This function takes no arguments, and as far as "Memoize" is con-
cerned, it always returns the same result. "Memoize" is wrong, of
course, and the memoized version of this function will call "time"
once to get the current time, and it will return that same time
every time you call it after that.
· Do not memoize a function with side effects.
sub f {
my ($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 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 refer-
ences 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 pro-
vide one. Use this instead of plain "SDBM_File" to store your cache
table on disk in an "SDBM_File" database:
tie my %cache => ’Memoize::SDBM_File’, $filename, O_RDWR│O_CREAT, 0666;
memoize ’function’, SCALAR_CACHE => [HASH => \%cache];
"NDBM_File" has the same problem and the same solution. (Use "Memo-
ize::NDBM_File instead of plain NDBM_File.")
"Storable" isn’t a tied hash class at all. You can use it to store a
hash to disk and retrieve it again, but you can’t modify the hash
while it’s on the disk. So if you want to store your cache table in a
"Storable" database, use "Memoize::Storable", which puts a hashlike
front-end onto "Storable". The hash table is actually kept in memory,
and is loaded from your "Storable" file at the time you memoize the
function, and stored back at the time you unmemoize the function (or
when your program exits):
tie my %cache => ’Memoize::Storable’, $filename;
memoize ’function’, SCALAR_CACHE => [HASH => \%cache];
tie my %cache => ’Memoize::Storable’, $filename, ’nstore’;
memoize ’function’, SCALAR_CACHE => [HASH => \%cache];
Include the ‘nstore’ option to have the "Storable" database written in
‘network order’. (See Storable for more details about this.)
The "flush_cache()" function will raise a run-time error unless the
tied package provides a "CLEAR" method.
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 memo-
ized and the cache is in a "DB_File" database, then the value of "f()"
("f" called with no arguments) will not be memoized. If this is a big
problem, you can supply a normalizer function that prepends "x" to
every key.
MAILING LIST
To join a very low-traffic mailing list for announcements about "Memo-
ize", send an empty note to "mjd-perl-memoize-request@plover.com".
AUTHOR
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 Memo-
ize distribution as ‘article.html’.)
My upcoming book will discuss memoization (and many other fascinating
topics) in tremendous detail. It will be published by Morgan Kaufmann
in 2002, possibly under the title Perl Advanced Techniques Handbook.
It will also be available on-line for free. For more information,
visit 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 AND LICENSE
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.
THANK YOU
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 proto-
typed functions and for checking my patch, to Tony Bass for many help-
ful suggestions, to Jonathan Roy (again) for finding a use for "unmem-
oize()", 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 dur-
ing the integration process.
perl v5.8.8 2001-09-21 Memoize(3)
