kmry / memo

Memoization for Nim

Memoize Nim functions

This small package offers a function and a macro to memoize Nim functions.

Usage

If f(a: A): B is a function, one can obtain a memoized version of f by doing

import memo
let g = memoize(f)

g will then be equivalent to f (modulo side effects), but results of calling g will be cached. The function memoize can be used on any function, but will not handle correctly recursive functions, as self calls of f, both direct and indirect, will still keep refering to the non-memoize version of f.

If you have access to the definition of f, one can do better with the memoized macro. Usage is as follows:

import memo
proc f(a: A): B {.memoized.} =
  ...

Then f will be memoized and recursive calls will be handled correctly (both direct self-recursion and mutual recursion).

Example

import memo

proc fib(n : int) : int {.memoized.} =
  if n < 2: n
  else: fib(n-1) + fib(n-2)

when isMainModule:
  echo fib(40)

This small program returns very fast, while without the memoized pragma, it takes a few seconds before producing a result. For an example of mutual recursive functions

import memo

proc fib(n : int) : int

proc fib1(n : int) : int {.memoized.} =
  if n < 2: n
  else: fib(n-1) + fib(n-2)

proc fib(n : int) : int {.memoized.} =
  if n < 2: n
  else: fib1(n-1) + fib1(n-2)

when isMainModule:
  echo fib(80)

Restrictions

• memoize function, as opposed to memoized macro, can only memoize functions of a single argument, altough one can convert any function in this form by using a tuple argument
• types of all arguments have to implement hash, since they will be used as parts of a key in a hashtable

An example of the first issue would be memoizing the Levenshtein distance for strings, as it is a function of two arguments. It can be done like this:

import memo

template tail(s: string): string = s[1 .. s.high]

template head(s: string): char = s[0]

# `memoized` macro handles multiple arguments:
proc lev(a: string, b: string): int {.memoized.} =
  if a.len == 0: return b.len
  if b.len == 0: return a.len
  let
    d1 = lev(a.tail, b) + 1
    d2 = lev(a, b.tail) + 1
    d3 = lev(a.tail, b.tail) + (if a.head == b.head: 0 else: 1)
  result = min(min(d1, d2), d3)

# `memoize` function does not:
template memTwoArg =
  let levMem: proc(int): int = memoize(lev)
assert: not compiles memTwoArg

when isMainModule:
  echo levenshtein("submarine", "subreddit")