Memoize - a simple function memoizing annotation

This is a proof of concept for annotations, which allows you to memoize referentially transparent functions using a simple annotation.

Example

Taken from the examples folder, we define two simple, recursive implementations for calculating the Nth number in the Fibonacci sequence. The non-memoized module will take a very long time once N >= 35. Whilst there are better ways of implementing fibonacci than this, it serves as a simple example of how to use memoize.

We annotation our fib_mem implementation like so:

-module(fib_mem).
-export([fib/1]).
-include_lib("annotations/include/annotations.hrl").

-memoize([{table, ?MODULE}]).
fib(0) -> 0;
fib(1) -> 1;
fib(N) -> fib(N - 1) + fib(N - 2).

Then we see it at work in the shell:

t4@malachi:fib $ rebar get-deps clean compile
==> fib (pre_compile)
Writing config to /Users/t4/work/nebularis/memoize/examples/fib/annotations.config
==> fib (compile)
Compiled src/fib.erl
Compiled src/fib_mem.erl
==> fib (post_compile)
t4@malachi:fib $ erl -pa ebin/ -pa deps/memoize/ebin/ -pa deps/annotations/ebin/
Erlang R14B01 (erts-5.8.2) [source] [64-bit] [smp:2:2] [rq:2] [async-threads:0] [hipe] [kernel-poll:false]

Eshell V5.8.2  (abort with ^G)
1> fib_mem:fib(1).
1
2> fib_mem:fib(2).
1
3> fib_mem:fib(30).
832040
4> fib_mem:fib(35).
9227465
5> fib_mem:fib(0).         
0
6> fib_mem:fib(35).
9227465
7> fib_mem:fib(355).
69362907070206748494476200566565775354902428015845969798000696945226974645
8> fib_mem:fib(355).
69362907070206748494476200566565775354902428015845969798000696945226974645
9> fib_mem:fib(500).
139423224561697880139724382870407283950070256587697307264108962948325571622863290691557658876222521294125
10> 
BREAK: (a)bort (c)ontinue (p)roc info (i)nfo (l)oaded
       (v)ersion (k)ill (D)b-tables (d)istribution
a
t4@malachi:fib $ 

Memoizing based on a subset of all inputs

Whilst I'm not entirely convinced whether this behaviour should be described as memoization, you can instruct the annotation to use a subset of the inputs when checking the results cache.

The usual ets key used during cache lookups is {FunctionName, FunctionInputs}, but this can be tweaked by passing one of the following options:

%% this one selects a set of arguments
-memoize(IndexesOfInputsToCacheOn::list(integer())).

%% this one caches on one specific argument
-memoize(Idx::integer()).