NAME

Memoize - Make your functions faster by trading space for time

SYNOPSIS

use Memoize;
memoize('slow_function');
slow_function(arguments);    # Is faster than it was before

DESCRIPTION

`Memoizing' a function makes it faster by trading space for time. It does this by cacheing the return values of the function in a table. If you call the function again with the same arguments, memoize jmups 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 speeded 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 $; in between. This always works correctly for functions with only one argument, and also when the arguments never contain $; (which is normally character #28, control-\. ) However, it can confuse certain argument lists:

normalizer("a\034", "b")
normalizer("a", "\034b")
normalizer("a\034\034b")

for example.

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
TIE
FAULT
MERGE

or else it must be a reference to a list whose first element is one of these four strings, such as [TIE, 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.

TIE

TIE means that the function's return values will be cached in a tied hash. 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 pogram has exited.

If TIE is specified as the first element of a list, the remaining list elements are taken as arguments to the tie call that sets up the tied hash. For example,

SCALAR_CACHE => [TIE, DB_File, $filename, O_RDWR | O_CREAT, 0666]

says to tie the hash into the DB_File package, and to pass the $filename, O_RDWR | O_CREAT, and 0666 arguments to the tie call. This has the effect of storing the cache in a DB_File database whose name is in $filename.

Other typical uses of TIE:

LIST_CACHE => [TIE, GDBM_File, $filename, O_RDWR | O_CREAT, 0666]
SCALAR_CACHE => [TIE, MLDBM, DB_File, $filename, O_RDWR|O_CREAT, 0666]
LIST_CACHE => [TIE, My_Package, $tablename, $key_field, $val_field]

This last might tie the cache hash to a package that you wrote yourself that stores the cache in a SQL-accessible database. A useful use of this feature: You can construct a batch program that runs in the background and populates the memo table, and then when you come to run your real program the memoized function will be screamingly fast because all its results have been precomputed.

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 cvalled 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:

memoize 'myfunc',
  NORMALIZER => 'n',
  SCALAR_CACHE => [TIE, MLDBM, DB_File, $filename, ...],
  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 FUNCTION

There's an unmemoize function that you can import if you want to. If you use it, please let me know what it was good for, since I can only think of very limited uses for it and was considering leaving it out altogether.

It 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.

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 the number 11 (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.

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,

	memoize 'function', SCALAR_CACHE => 
                            [TIE, GDBM_File, $filename, O_RDWR|O_CREAT, 0666];

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:

	memoize 'function', 
                SCALAR_CACHE => 
                [TIE, Memoize::SDBM_File, $filename, O_RDWR|O_CREAT, 0666];

NDBM_File has the same problem and the same solution.

Storable isn't a tied hash class at all. You can use it to store a hash to disk and retrieve it again, but yu 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):

	memoize 'function', 
                SCALAR_CACHE => [TIE, Memoize::Storable, $filename];

	memoize 'function', 
                SCALAR_CACHE => [TIE, Memoize::Storable, $filename, 'nstore'];

Include the `nstore' option to have the Storable database written in `network order'. (See Storable for moer details about this.)

MY BUGS

Needs a better test suite, especially for the tied stuff. That is why the version number is 0.46 instead of 0.50.

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

To install Memoize, copy and paste the appropriate command in to your terminal.

cpanm

cpanm Memoize

CPAN shell

perl -MCPAN -e shell
install Memoize

For more information on module installation, please visit the detailed CPAN module installation guide.

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