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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.
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 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"
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:
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 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")
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 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.
"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
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 an array 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 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
precomputed.
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
management.
"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;
{ tie my %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 that the memoized function does not distinguish between list
and scalar 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);
$z = complicated(142);
The first call will cache the result, say 37, in the scalar cache; the second will
cache the list "(37)" in the list cache. The third call doesn't call the real
"complicated" function; it gets the value 37 from the scalar cache.
Obviously, the second call to "complicated" is a waste of time, and storing its return
value is a waste of space. Specifying "LIST_CACHE => MERGE" will make "memoize" use
the same cache for scalar and list context return values, so that the second call uses
the scalar cache that was populated by the first call. "complicated" ends up being
called only once, and both subsequent calls return 37 from the cache, regardless of
the calling context.
List values in scalar context
Consider this function:
sub iota { return reverse (1..$_[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:
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";
}
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 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
$SIG{INT} = sub { unmemoize 'function' };
"unmemoize" accepts a reference to, or the name of a previously memoized function, and
undoes whatever it did to provide the memoized version in the first place, including
making the name refer to the unmemoized version if appropriate. It returns a reference to
the unmemoized version of the function.
If you ask it to unmemoize a function that was never memoized, it croaks.
"flush_cache"
flush_cache(function) will flush out the caches, discarding all the cached data. The
argument may be a function name or a reference to a function. For finer control over when
data is discarded or expired, see the documentation for "Memoize::Expire", included in
this package.
Note that if the cache is a tied hash, "flush_cache" will attempt to invoke the "CLEAR"
method on the hash. If there is no "CLEAR" method, this will cause a run-time error.
An alternative approach to cache flushing is to use the "HASH" option (see above) to
request that "Memoize" use a particular hash variable as its cache. Then you can examine
or modify the hash at any time in any way you desire. You may flush the cache by using
"%hash = ()".
CAVEATS
Memoization is not a cure-all:
• Do not memoize a function whose behavior depends on program state other than its own
arguments, such as global variables, the time of day, or file input. These functions
will not produce correct results when memoized. For a particularly easy example:
sub f {
time;
}
This function takes no arguments, and as far as "Memoize" is concerned, it always
returns the same result. "Memoize" is wrong, of course, and the memoized version of
this function will call "time" once to get the current time, and it will return that
same time every time you call it after that.
• Do not memoize a function with side effects.
sub f {
my ($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.