Playing with the Basic Calculator

So as we created a calculator back to chapter 11, we know how to to display information using the title. However we also know about Stored Spaces and Functions. We can now use them to add more awesome features to our tiny calculator. First, we can save our result in a file using Stored Spaces:


( space ,

// something here

) ( $result , @space )

'ANS: | @space |'

Let’s create some functions for our calculator. Do you remember the `!pow(number,power)` function we wrote together? If you put the `pow.arendelle` file into the folder where your `calc.arendelle` file is you can then use it in our calc:
( space ,

!pow ( 2 , 7 )

) ( $result , @space )

'ANS: | @space |'


And you will see the ANS: 128 in the title! Something I want to show you are recursive functions:



Recursive Functions

Do you know the factorial operator? It’s like this: When you write 5! ( ! is the factorial sign ) you get this:

5! = 5 × 4 × 3 × 2 × 1

And so the factorial of 12 will be:

12! = 12 × 11 × 10 … 3 × 2 × 1

So as you saw 5! was 5 × 4 × 3 × 2 × 1 just like the end of the 12! and that’s why we can write this:

12! = 12 × 11 × 10 × 9 × 8 × 7 × 6 × 5!

Or even this

12! = 12 × 11!

You see each factorial is connected to it’s preview factorials for example if you want to calculate factorial of 4, you have to do 4 × 3! and then you have to calculate 3! using 3! × 2! till you get to 1! which you know it’s 1.

In the programming there is a very fun thing called Recursive Function which is a function that uses itself! Each math operator like factorial is a function. So as you saw we used factorial to calculate factorial which means we used a function in itself!

Let’s write factorial using recursive technique to see how can you use a function in itself. First create the function !fact(number) and then write this code for it:


< number >
{ @number = 1 ,
   ( return , 1 )
,
   ( return , @number * !fact( @number - 1 ) )
}


You see? We’re calling for function !fact() from the function !fact()! It’s really an amazing possibility we have in programming to call a function from itself!




Exercise

Do you know the Fibonacci sequence? It’s a sequence of numbers which each number is the sum of it’s two previous number like:

1  1  2  3  5  8  13  21 …

You see 2 is the sum of 1 and 1, 13 is the sum of 5 and 8, 5 is the sum of 2 and 3 and so on… Write a recursive function named !sumOfFibonacci(number) that calculate the sum of the @number first members of the sequence like:

!sumOfFibonacci( 4 ) = sum ( 1 , 1 , 2 , 3 ) = 7
!sumOfFibonacci( 7 ) = sum ( 1 , 1 , 2 , 3 , 5 , 8 , 13 ) = 33