Memoize(3perl) Perl Programmers Reference Guide Memoize(3perl)
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.
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