Oskar Dudycz

Pragmatycznie o programowaniu

Memoization, a useful pattern for quick optimization

2021-05-05 oskar dudyczDesign Patterns

cover

Today I would like to show you a simple programming pattern that can be useful for quick code optimization. This pattern is called Memoization. It comes from the functional language and is used to remember the result of the function. The main idea behind it is to execute function only once. Follow up calls should not run the logic but return the cached result.

The example will be in C#, but it should be translatable into other prefered programming language.

We will create a static class that has the “extension method” Memoize. Thanks to that, we will be able to call it more conveniently for the function we choose.

The Memoize method has a single input parameter: the function that will run the business logic. The result of Memoize method is also a function. As described above, the idea is that we pass a function that does some sort of computation and returns it wrapped with a cache logic.

public static class Memoizer
{
    public static Func<TInput, TResult> Memoize<TInput, TResult>(this Func<TInput, TResult> func)
    {
        // create cache ("memo")
        var memo = new Dictionary<TInput, TResult>();

        // wrap provided function with cache handling
        return input =>
        {
            // check if result for set input was already cached
            if (memo.TryGetValue(input, out var fromMemo))
                // if yes, return value
                return fromMemo;

            // if no, call function
            var result = func(input);
            
            // cache the result
            memo.Add(input, result);

            // return it
            return result;
        };
    }
}

We’re using function scope (closure) here. We define a dictionary (variable memo) in which we will remember the results of the function.

Next, we generate a wrapping method that will check if there is already a cached result for the given input parameter. If it is, it returns the result from the cache and does not call the function itself. If not, it calls the function, adds the result to the cache, and returns it.

What is important is that the function that we are going to “memoize” should be deterministic and not cause side effects. What does it mean in practice? This means that it will always return the same result for the given input parameter and will not make any changes. For example, for the same postal code, we will always get the same city. A given insurance number corresponds to a specific person, and so on. We also call this method a “Higher Order Function”.

A more real-life example can be, e.g. slow but deterministic operations such as the reflection mechanism. For example, memoization could be useful to check whether a given type has a specific attribute (annotation).

Let’s define a method to verify whether a given type has a given attribute as:

Func<Type, Type, bool> hasAttribute =
    (type, attributeType) => type.GetCustomAttributes(attributeType, true).Any();

Unfortunately, we cannot memoize this method in its present form because our Memoize method assumes that the function will have one input parameter. The above has two.

We need to curry this function. How can this be done? The feature of higher-order functions is that they can be composed. For example, as follows:

Func<Type, bool> hasSomeCustomAttribute = 
    type => hasAttribute(type, typeof(SomeCustomAttribute));

We create an additional function that takes a specific parameter as the type of attribute - corresponding to the type of attribute we choose.

We can memoize this function by:

Func<Type, bool> hasSomeCustomAttributeMemo = hasSomeCustomAttribute.Memoize();

If we use it several times now, thanks to the memoization for the given type of the attribute, the function hasAttribute will be called only once.

Of course, our implementation is quite naive, e.g. it’s not thread-safe. We could enhance and simplify that by using ConcurrentDictionary class:

public static Func<TInput, TResult> Memoize<TInput, TResult>(this Func<TInput, TResult> func)
{
    // create cache ("memo")
    var memo = new ConcurrentDictionary<TInput, TResult>();

    // wrap provided function with cache handling
    // get a value from cache if it exists
    // if not, call factory method
    // ConcurrentDictionary will handle that internally
    return input => memo.GetOrAdd(input, func);
}

This version is still not perfect. When we are memoizing many items, our cache may grow exponentially and generate a memory usage issue. Generally, we’d like to keep in memory only the actively accessed entries. Not accessed, we can evict. We’d like to be able to set up a top limit of entries in our cache. To do that, we could use, e.g. Redis instead. If we need a simpler/lightweight solution, we can choose a MemoryCache class. A sample implementation can look like this:

public static Func<TInput, TResult> Memoize<TInput, TResult>(this Func<TInput, TResult> func)
{
    // create cache ("memo")
    var memo = new MemoryCache(new MemoryCacheOptions
    {
        // Set cache size limit.
        // Note: this is not size in bytes,
        // but sum of all entries' sizes.
        // Entry size is declared on adding to cache
        // in the factory method 
        SizeLimit = 100
    });
    
    // wrap provided function with cache handling
    // get a value from cache if it exists
    // if not, call factory method
    // MemCache will handle that internally
    return input => memo.GetOrCreate(input, entry =>
    {
        // you can set different options like e.g.
        // sliding expiration - time between now and last time
        // and the last time the entry was accessed 
        entry.SlidingExpiration = TimeSpan.FromSeconds(3);
        
        // this value is used to calculate total SizeLimit
        entry.Size = 1;
        return func(input);
    });
}

Michał motivated me, with the comment below, to even go even further. In functional programming, recursion is a widespread practice. It’s non-trivial as to understand recursion, you need to understand recursion. It can be computation expensive. How to use the Memoization with recursion? Let’s take the Fibonacci sequence as an example. The rule is: the next number is found by adding up the two numbers before it.

int Fibonacci(int n1)
{
    if (n1 <= 2)
        return 1;
                
    return Fibonacci(n1 -1) + Fibonacci(n1 - 2);
}

We’ll need to find a way to inject the memoized version of the Fibonacci function. Let’s start with breaking out function into the main and the overload:

int Fibonacci(int n1)
{
    return Fibonacci(n1, Fibonacci);
}

int Fibonacci(int n1, Func<int, int> fibonacci)
{        
    if (n1 <= 2)
        return 1;
        
    return fibonacci(n1 -1) + fibonacci(n1 - 2);
}

Now instead of the direct self-call, we can inject the function to use while doing recursion. Therfore, we have the possibility to memoize it by doing:

Func<int, int> fibonacci = null;
            
fibonacci = Memoizer.Memoize((int n1)  => Fibonacci(n1, fibonacci));
            
var result = fibonacci(3);

The trick is that the local fibonacci function is lazily evaluated. That means that effectively it will use the assigned, memoized function while doing the call (doing recursion by that).

I know that analyzing recursion can create a headache. It may be more accessible by debugging the test in my sample repo.

When is it worth using memoization?

Especially where we have to call the same code many times in one operation. If this code is deterministic, then you can cut a lot of execution time. You can also use it with, e.g. a cache in Redis. When we invalidate it, it will just get us a new value. The basis for optimization is to start with operations that are performed very often. This is simple math:

  • If we cut 0.1 seconds on an operation performed 1000 times on each call, we will gain 100 seconds.
  • If the operation is performed 10 times and we cut 1 second, we will gain 10 seconds in total.

It is a straightforward technique, but it can bring very tangible results. Additionally, it is an example that functional programming is not so abstract but also practical.

You can check the full sample in my GitHub repository: https://github.com/oskardudycz/Memoization.

I hope I helped!

Cheers!

Oskar

p.s. Per Wikipedia:

The term “memoization” was coined by Donald Michie in 1968 and is derived from the Latin word “memorandum” (“to be remembered”), usually truncated as “memo” in American English, and thus carries the meaning of “turning [the results of] a function into something to be remembered”. While “memoization” might be confused with “memorization” (because they are etymological cognates), “memoization” has a specialized meaning in computing.

Loading...
Event-Driven by Oskar Dudycz
Oskar Dudycz For over 14 years, I have been creating IT systems close to the business. I started my career when StackOverflow didn't exist yet. I am a programmer, technical leader, architect. I like to create well-thought-out systems, tools and frameworks that are used in production and make people's lives easier. I believe Event Sourcing, CQRS, and in general, Event-Driven Architectures are a good foundation by which this can be achieved.
  • © Oskar Dudycz 2020 - 2021