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Tutorial 36: Accumulation

Topics

Using acum in the omloop module.

Key Modules Used

omloop

The Concept:

In this tutorial, we will examine a simple accumulative computation., that of the factorial. The factorial operation is equivalent to taking the product of an arithmetic series of integers ending at a given number. If is indicated with an exclamation point. The factorial operation on a number is:

5! (5 factorial) = 12345 = 120

In order to multiply the elements of the arithmetic series one after the other, we need to hold the result of each multiplication somewhere until we can use it in the next one. This is accomplished with acum, which acts like a warehouse where you can store a variable between iterations of a loop.

The Patch:

We’ll do two variants on the factorial procedure. In the first, we’ll just go for the final result. In the second, we’ll program omloop to return a list with the products of the intermediary operations.

The first loop looks like this:

The acum collector takes three arguments. The second input (B) is an initializer, which sets the internal state of the accumulator before the first repetition of the loop. The third input (C) is a lambda function (with two inputs) to which will be passed 1) whatever is coming into the first input (A) and 2) the internal state of the accumulator. In our case we’ll use om* since we’re interested in the product. The result becomes the internal state of the accumulator for the next pass. The three outputs on the bottom work just like the other collectors.

The state of the loop through its repetitions is summarized:

Step| Listloop output| Value of the first input of accumulator| Value of the second input of accumulator| Internal state (buffer)| Binary function om* output
—|—|—|—|—|—
0| 1| 1| 1| 1| 1
1| 2| 2| /| 1| 2
2| 3| 3| /| 2| 6
3| 4| 4| /| 6| 24
4| 5| 5| /| 24| 120
| | | | 120|

The final state of the accumulator is available at the second output and passed to finally.

As configured, the loop will output the final factorial when evaluated:

? OM->120

If we want to see the intermediary steps, we need to record the internal state of the accumulator at each repetition of the loop. This is done by adding a collect function and connecting it to the first input of the accumulator, which returns the current internal state each time, which is recorded in a list by collect.

The result:

? OM->(1 2 6 64 120)

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