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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 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 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 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.
"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 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:".
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 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 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.
MAILING LIST
To join a very low-traffic mailing list for announcements about "Memoize",
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 Memoize
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 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.
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