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;
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'
`Memoizing' a function makes it faster by trading space for
time. It does this by caching the return values of the
function in a table. If you call the function again with the
same arguments, "memoize" jumps in and gives you the value
out of the table, instead of letting the function compute
the value all over again.
Here is an extreme example. Consider the Fibonacci
sequence, defined by the following function:
# Compute Fibonacci numbers
sub fib {
my $n = shift;
return $n if $n < 2;
fib($n-1) + fib($n-2);
}
This function is very slow. Why? To compute fib(14), it
first wants to compute fib(13) and fib(12), and add the
results. But to compute fib(13), it first has to compute
fib(12) and fib(11), and then it comes back and computes
fib(12) all over again even though the answer is the same.
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And both of the times that it wants to compute fib(12), it
has to compute fib(11) from scratch, and then it has to do
it again each time it wants to compute fib(13). This func-
tion does so much recomputing of old results that it takes a
really long time to run---fib(14) makes 1,200 extra recur-
sive calls to itself, to compute and recompute things that
it already computed.
This function is a good candidate for memoization. If you
memoize the `fib' function above, it will compute fib(14)
exactly once, the first time it needs to, and then save the
result in a table. Then if you ask for fib(14) again, it
gives you the result out of the table. While computing
fib(14), instead of computing fib(12) twice, it does it
once; the second time it needs the value it gets it from the
table. It doesn't compute fib(11) four times; it computes it
once, getting it from the table the next three times.
Instead of making 1,200 recursive calls to `fib', it makes
15. This makes the function about 150 times faster.
You could do the memoization yourself, by rewriting the
function, like this:
# Compute Fibonacci numbers, memoized version
{ my @fib;
sub fib {
my $n = shift;
return $fib[$n] if defined $fib[$n];
return $fib[$n] = $n if $n < 2;
$fib[$n] = fib($n-1) + fib($n-2);
}
}
Or you could use this module, like this:
use Memoize;
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:
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for ($direction = 0; $direction < 300; $direction++) {
# Figure out which object is in direction $direction
$color = $object->{color};
($r, $g, $b) = @{&ColorToRGB($color)};
...
}
Since there are relatively few objects in a picture, there
are only a few colors, which get looked up over and over
again. Memoizing "ColorToRGB" sped up the program by
several percent.
This module exports exactly one function, "memoize". The
rest of the functions in this package are None of Your Busi-
ness.
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 refer-
ence to the new, memoized version of the function, or
"undef" on a non-fatal error. At present, there are no non-
fatal errors, but there might be some in the future.
If "function" was the name of a function, then "memoize"
hides the old version and installs the new memoized version
under the old name, so that "&function(...)" actually
invokes the memoized version.
There are some optional options you can pass to "memoize" to
change the way it behaves a little. To supply options,
invoke "memoize" like this:
memoize(function, NORMALIZER => function,
INSTALL => newname,
SCALAR_CACHE => option,
LIST_CACHE => option
);
Each of these options is optional; you can include some,
all, or none of them.
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,
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memoize('fib', INSTALL => 'fastfib')
installs the memoized version of "fib" as "fastfib"; without
the "INSTALL" option it would have replaced the old "fib"
with the memoized version.
To prevent "memoize" from installing the memoized version
anywhere, use "INSTALL => undef".
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
equivalent:
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 invocations of your function separately,
and store them separately.
To prevent this, supply a "NORMALIZER" function that turns
the program arguments into a string in a way that equivalent
arguments turn into the same string. A "NORMALIZER" func-
tion for "f" above might look like this:
sub normalize_f {
my $a = shift;
my %hash = @_;
$hash{B} ||= 2;
$hash{C} ||= 7;
join(',', $a, map ($_ => $hash{$_}) sort keys %hash);
}
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Each of the argument lists above comes out of the
"normalize_f" function looking exactly the same, like this:
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 argu-
ments is the same for two argument lists, then it can safely
look up the value that it computed for one argument list and
return it as the result of calling the function with the
other argument list, even if the argument lists look dif-
ferent.
The default normalizer just concatenates the arguments with
character 28 in between. (In ASCII, this is called FS or
control-\.) This always works correctly for functions with
only one string argument, and also when the arguments never
contain character 28. However, it can confuse certain argu-
ment lists:
normalizer("a\034", "b")
normalizer("a", "\034b")
normalizer("a\034\034b")
for example.
Since hash keys are strings, the default normalizer will not
distinguish between "undef" and the empty string. It also
won't work when the function's arguments are references.
For example, consider a function "g" which gets two argu-
ments: A number, and a reference to an array of numbers:
g(13, [1,2,3,4,5,6,7]);
The default normalizer will turn this into something like
"13\034ARRAY(0x436c1f)". That would be all right, except
that a subsequent array of numbers might be stored at a dif-
ferent location even though it contains the same data. If
this happens, "Memoize" will think that the arguments are
different, even though they are equivalent. In this case, a
normalizer like this is appropriate:
sub normalize { join ' ', $_[0], @{$_[1]} }
For the example above, this produces the key "13 1 2 3 4 5 6
7".
Another use for normalizers is when the function depends on
data other than those in its arguments. Suppose you have a
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function which returns a value which depends on the current
hour of the day:
sub on_duty {
my ($problem_type) = @_;
my $hour = (localtime)[2];
open my $fh, "$DIR/$problem_type" or die...;
my $line;
while ($hour-- > 0)
$line = <$fh>;
}
return $line;
}
At 10:23, this function generates the 10th line of a data
file; at 3:45 PM it generates the 15th line instead. By
default, "Memoize" will only see the $problem_type argument.
To fix this, include the current hour in the normalizer:
sub normalize { join ' ', (localtime)[2], @_ }
The calling context of the function (scalar or list context)
is propagated to the normalizer. This means that if the
memoized function will treat its arguments differently in
list context than it would in scalar context, you can have
the normalizer function select its behavior based on the
results of "wantarray". Even if called in a list context, a
normalizer should still return a single string.
"SCALAR_CACHE", "LIST_CACHE"
Normally, "Memoize" caches your function's return values
into an ordinary Perl hash variable. However, you might
like to have the values cached on the disk, so that they
persist from one run of your program to the next, or you
might like to associate some other interesting semantics
with the cached values.
There's a slight complication under the hood of "Memoize":
There are actually two caches, one for scalar values and one
for list values. When your function is called in scalar con-
text, its return value is cached in one hash, and when your
function is called in list context, its value is cached in
the other hash. You can control the caching behavior of
both contexts independently with these options.
The argument to "LIST_CACHE" or "SCALAR_CACHE" must either
be one of the following four strings:
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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, argu-
ments...]".
"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 supply will be used as the cache. You can tie this
hash beforehand to give it any behavior you want.
A tied hash can have any semantics at all. It is typi-
cally tied to an on-disk database, so that cached values
are stored in the database and retrieved from it again
when needed, and the disk file typically persists after
your program has exited. See "perltie" for more com-
plete details about "tie".
A typical example is:
use DB_File;
tie my %cache => 'DB_File', $filename, O_RDWR|O_CREAT, 0666;
memoize 'function', SCALAR_CACHE => [HASH => \%cache];
This has the effect of storing the cache in a "DB_File"
database whose name is in $filename. The cache will
persist after the program has exited. Next time the
program runs, it will find the cache already populated
from the previous run of the program. Or you can forci-
bly populate the cache by constructing a batch program
that runs in the background and populates the cache
file. Then when you come to run your real program the
memoized function will be fast because all its results
have been precomputed.
"TIE"
This option is no longer supported. It is still docu-
mented only to aid in the debugging of old programs that
use it. Old programs should be converted to use the
"HASH" option instead.
memoize ... [TIE, PACKAGE, ARGS...]
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is merely a shortcut for
require PACKAGE;
{ my %cache;
tie %cache, PACKAGE, ARGS...;
}
memoize ... [HASH => \%cache];
"FAULT"
"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 con-
text returns, and "SCALAR_CACHE => MERGE" means the
same, mutatis mutandis. It is an error to specify
"MERGE" for both, but it probably does something useful.
Consider this function:
sub pi { 3; }
Normally, the following code will result in two calls to
"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.
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Another use for "MERGE" is when you want both kinds of
return values stored in the same disk file; this saves
you from having to deal with two disk files instead of
one. You can use a normalizer function to keep the two
sets of return values separate. For example:
tie my %cache => 'MLDBM', 'DB_File', $filename, ...;
memoize 'myfunc',
NORMALIZER => 'n',
SCALAR_CACHE => [HASH => \%cache],
LIST_CACHE => MERGE,
;
sub n {
my $context = wantarray() ? 'L' : 'S';
# ... now compute the hash key from the arguments ...
$hashkey = "$context:$hashkey";
}
This normalizer function will store scalar context
return values in the disk file under keys that begin
with "S:", and list context return values under keys
that begin with "L:".
"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 written out to disk if someone inter-
rupts the program. If the program exits normally, this will
happen anyway, but if someone types control-C or something
then the program will terminate immediately without syn-
chronizing the database. So what you can do instead is
$SIG{INT} = sub { unmemoize 'function' };
"unmemoize" accepts a reference to, or the name of a previ-
ously memoized function, and undoes whatever it did to pro-
vide the memoized version in the first place, including mak-
ing the name refer to the unmemoized version if appropriate.
It returns a reference to the unmemoized version of the
function.
If you ask it to unmemoize a function that was never
memoized, it croaks.
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"flush_cache"
"flush_cache(function)" will flush out the caches, discard-
ing all the cached data. The argument may be a function
name or a reference to a function. For finer control over
when data is discarded or expired, see the documentation for
"Memoize::Expire", included in this package.
Note that if the cache is a tied hash, "flush_cache" will
attempt to invoke the "CLEAR" method on the hash. If there
is no "CLEAR" method, this will cause a run-time error.
An alternative approach to cache flushing is to use the
"HASH" option (see above) to request that "Memoize" use a
particular hash variable as its cache. Then you can examine
or modify the hash at any time in any way you desire. You
may flush the cache by using "%hash = ()".
Memoization is not a cure-all:
+ Do not memoize a function whose behavior depends on pro-
gram state other than its own arguments, such as global
variables, the time of day, or file input. These func-
tions will not produce correct results when memoized.
For a particularly easy example:
sub f {
time;
}
This function takes no arguments, and as far as
"Memoize" is concerned, it always returns the same
result. "Memoize" is wrong, of course, and the memoized
version of this function will call "time" once to get
the current time, and it will return that same time
every time you call it after that.
+ Do not memoize a function with side effects.
sub f {
my ($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 numuber of
characters it printed, but you probably didn't care
about that. But "Memoize" doesn't understand that. If
you memoize this function, you will get the result you
expect the first time you ask it to print the sum of 2
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and 3, but subsequent calls will return 1 (the return
value of "print") without actually printing anything.
+ Do not memoize a function that returns a data structure
that is modified by its caller.
Consider these functions: "getusers" returns a list of
users somehow, and then "main" throws away the first
user on the list and prints the rest:
sub main {
my $userlist = getusers();
shift @$userlist;
foreach $u (@$userlist) {
print "User $u\n";
}
}
sub getusers {
my @users;
# Do something to get a list of users;
\@users; # Return reference to list.
}
If you memoize "getusers" here, it will work right
exactly once. The reference to the users list will be
stored in the memo table. "main" will discard the first
element from the referenced list. The next time you
invoke "main", "Memoize" will not call "getusers"; it
will just return the same reference to the same list it
got last time. But this time the list has already had
its head removed; "main" will erroneously remove another
element from it. The list will get shorter and shorter
every time you call "main".
Similarly, this:
$u1 = getusers();
$u2 = getusers();
pop @$u1;
will modify $u2 as well as $u1, because both variables
are references to the same array. Had "getusers" not
been memoized, $u1 and $u2 would have referred to dif-
ferent arrays.
+ Do not memoize a very simple function.
Recently someone mentioned to me that the Memoize module
made his program run slower instead of faster. It
turned out that he was memoizing the following function:
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sub square {
$_[0] * $_[0];
}
I pointed out that "Memoize" uses a hash, and that look-
ing up a number in the hash is necessarily going to take
a lot longer than a single multiplication. There really
is no way to speed up the "square" function.
Memoization is not magical.
You can tie the cache tables to any sort of tied hash that
you want to, as long as it supports "TIEHASH", "FETCH",
"STORE", and "EXISTS". For example,
tie my %cache => 'GDBM_File', $filename, O_RDWR|O_CREAT, 0666;
memoize 'function', SCALAR_CACHE => [HASH => \%cache];
works just fine. For some storage methods, you need a lit-
tle glue.
"SDBM_File" doesn't supply an "EXISTS" method, so included
in this package is a glue module called "Memoize::SDBM_File"
which does provide one. Use this instead of plain
"SDBM_File" to store your cache table on disk in an
"SDBM_File" database:
tie my %cache => 'Memoize::SDBM_File', $filename, O_RDWR|O_CREAT, 0666;
memoize 'function', SCALAR_CACHE => [HASH => \%cache];
"NDBM_File" has the same problem and the same solution.
(Use "Memoize::NDBM_File instead of plain NDBM_File.")
"Storable" isn't a tied hash class at all. You can use it
to store a hash to disk and retrieve it again, but you can't
modify the hash while it's on the disk. So if you want to
store your cache table in a "Storable" database, use
"Memoize::Storable", which puts a hashlike front-end onto
"Storable". The hash table is actually kept in memory, and
is loaded from your "Storable" file at the time you memoize
the function, and stored back at the time you unmemoize the
function (or when your program exits):
tie my %cache => 'Memoize::Storable', $filename;
memoize 'function', SCALAR_CACHE => [HASH => \%cache];
tie my %cache => 'Memoize::Storable', $filename, 'nstore';
memoize 'function', SCALAR_CACHE => [HASH => \%cache];
Include the `nstore' option to have the "Storable" database
written in `network order'. (See Storable for more details
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about this.)
The "flush_cache()" function will raise a run-time error
unless the tied package provides a "CLEAR" method.
See Memoize::Expire, which is a plug-in module that adds
expiration functionality to Memoize. If you don't like the
kinds of policies that Memoize::Expire implements, it is
easy to write your own plug-in module to implement whatever
policy you desire. Memoize comes with several examples. An
expiration manager that implements a LRU policy is available
on CPAN as Memoize::ExpireLRU.
The test suite is much better, but always needs improvement.
There is some problem with the way "goto &f" works under
threaded Perl, perhaps because of the lexical scoping of @_.
This is a bug in Perl, and until it is resolved, memoized
functions will see a slightly different "caller()" and will
perform a little more slowly on threaded perls than
unthreaded perls.
Some versions of "DB_File" won't let you store data under a
key of length 0. That means that if you have a function "f"
which you memoized and the cache is in a "DB_File" database,
then the value of "f()" ("f" called with no arguments) will
not be memoized. If this is a big problem, you can supply a
normalizer function that prepends "x" to every key.
To join a very low-traffic mailing list for announcements
about "Memoize", send an empty note to
"mjd-perl-memoize-request@plover.com".
Mark-Jason Dominus ("mjd-perl-memoize+@plover.com"), Plover
Systems co.
See the "Memoize.pm" Page at
http://www.plover.com/~mjd/perl/Memoize/ for news and
upgrades. Near this page, at
http://www.plover.com/~mjd/perl/MiniMemoize/ there is an
article about memoization and about the internals of Memoize
that appeared in The Perl Journal, issue #13. (This article
is also included in the Memoize distribution as
`article.html'.)
My upcoming book will discuss memoization (and many other
fascinating topics) in tremendous detail. It will be pub-
lished by Morgan Kaufmann in 2002, possibly under the title
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Perl Advanced Techniques Handbook. It will also be avail-
able on-line for free. For more information, visit
http://perl.plover.com/book/ .
To join a mailing list for announcements about "Memoize",
send an empty message to
"mjd-perl-memoize-request@plover.com". This mailing list is
for announcements only and has extremely low traffic---about
two messages per year.
Copyright 1998, 1999, 2000, 2001 by Mark Jason Dominus
This library is free software; you may redistribute it
and/or modify it under the same terms as Perl itself.
Many thanks to Jonathan Roy for bug reports and suggestions,
to Michael Schwern for other bug reports and patches, to
Mike Cariaso for helping me to figure out the Right Thing to
Do About Expiration, to Joshua Gerth, Joshua Chamas,
Jonathan Roy (again), Mark D. Anderson, and Andrew Johnson
for more suggestions about expiration, to Brent Powers for
the Memoize::ExpireLRU module, to Ariel Scolnicov for
delightful messages about the Fibonacci function, to Dion
Almaer for thought-provoking suggestions about the default
normalizer, to Walt Mankowski and Kurt Starsinic for much
help investigating problems under threaded Perl, to Alex
Dudkevich for reporting the bug in prototyped functions and
for checking my patch, to Tony Bass for many helpful sugges-
tions, to Jonathan Roy (again) for finding a use for
"unmemoize()", to Philippe Verdret for enlightening discus-
sion of "Hook::PrePostCall", to Nat Torkington for advice I
ignored, to Chris Nandor for portability advice, to Randal
Schwartz for suggesting the '"flush_cache" function, and to
Jenda Krynicky for being a light in the world.
Special thanks to Jarkko Hietaniemi, the 5.8.0 pumpking, for
including this module in the core and for his patient and
helpful guidance during the integration process.
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