Nithin Bekal

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Memoization in Ruby Using Metaprogramming

27 Oct 2014

I recently came across this blog post showing how you can write a method decorator in Ruby for memoizing the results of a method call. Playing around with the example and trying to extend it was very interesting. I’ll try to walk through the code in this post.

What is memoization?

Memoization is an optimization technique where you cache the results of expensive method calls. When the method is called with the same set of arguments, the cached result is returned.

As an example, let’s look at a function that calculates factorial recursively. Suppose we’ve already calculated fact(8), and now want to calculate fact(9). This is the same as 9 * fact(8). If we store the result of fact(8) in a lookup table, we just need to fetch the value and the function is reduced to a simple multiplication.

Writing a Memoization module

In this example, we will write a module called Memoization that has a method memoize, such that we will be able to use it like this:

class Calculator
  extend Memoization

  memoize def fact(n)
    return 1 if n <= 1
    n * fact(n-1)
  end
end

We use extend Memoization instead of include because we need memoize as a class method. Because of this, we can call call memoize outside any method.

This also makes use of a feature that was introduced in Ruby 2.1 - a method definition returns the name of the method in symbol form, ie. in the above case, def fact(n) would return :fact. This symbol is passed as argument to the memoize method.

This is what the module looks like:

module Memoization
  def memoize(name)
    @@lookup ||= Hash.new { |h, k| h[k] = {} }

    f = instance_method(name)

    define_method(name) do |args|
      return @@lookup[name][args] if @@lookup[name].include?(args)
      @@lookup[name][args] = f.bind(self).call(args)
    end
  end
end

We start off by defining a class variable @@lookup where we will cache our results. It is a hash where each method’s name is the key to another hash that has the cached results for that method.

Let’s imagine we had two memoized methods fact(n) and sum(x, y) and we’ve called fact(0) and sum(2, 3). The @@lookup class variable gets updated to:

{
  fact: { [0] => 1 },
  sum: { [2, 3] => 5 }
}

The keys for the computed values is an array because this allows us to have the same memoize method irrespective of the number of arguments for the method being memoized.

Next, we come across the line: f = instance_method(name). This creates an object that represents the current definition of the fact method. This lets us redefine the fact method, while still being able to call it when the result isn’t present in the lookup table.

Finally, we come to the define_method block. Here we overwrite the existing method with our memoized version. If @@lookup contains a calculated value for the given argument list, that is returned. Otherwise, we call the original function which is in the for of the UnboundMethod object f.

The way the original method is called might look a little confusing: f.bind(self).call(args). An UnboundMethod can only be called after binding with an instance of the same class (or its subclasses). This binds the function to the instance of Calculator that called it, and then calls it with the given arguments.

Once the method returns, the value is added to the lookup table. All subsequent method calls with the same input will be read from the lookup table.

Conclusion

Calculating factorials is not the most computationally expensive operation, but it demonstrates how writing this method recursively makes it easier to memoize.

It is useful for method calls that do very time consuming computations. As long as the result depends only on the arguments of the method, this method decorator works fine.

If the result depended on some instance variables in addition to the arguments, it becomes a bit harder to do this. In that case, we would need to include the arguments and all the instance variables used in the method as the key in the lookup table.

Further reading

Hi, I’m Nithin Bekal, a software craftsman with over 7 years of experience in shipping web applications. I mostly use Ruby, but lately have also been exploring Elixir. Co-founder of CrowdStudio.in, and helping organize Rubyconf India. Tweet to me at @nithinbekal.