Thursday, October 6, 2011

RPL Programming Tutorial - Part 2 - HP 49g+/50g: Local Variables

Welcome!

Welcome to Part 2 of the RPL Programming Tutorial for the HP 49g+ and 50g calculators. To recap, Part 1 talked about how to create, save, run, and (if need be) delete a program.

In Part 2, introduces the concept of the local variable. Simply put, a local variable is a variable that is used in a program and is then purged (deleted) at the end of the program. Local variables are not stored outside of the program, which saves memory.

A general structure of declaring local variables goes like this:

<< commands needed to set up the local variables, if any &rarr Local Variables
<< main program >> >>

=================================================================
Hint: There are times that you want to store information outside of a program. To do so, just store the data in a variable enclosed in single quotes followed by a STO command. These variables are called global variables.
=================================================================

Fibonacci Sequence

The well known Fibonacci Sequence is:
1, 1, 2, 3, 5, 8, 13, 21, 34,...

After the first two numbers, each succeed number is the sum of the last two numbers.

F_n = F_(n-1) + F_(n-2) where F_1 = 1 and F_2=1.

You can quickly find the mth term of the Fibonacci Sequence by using this closed formula:

f(n) = (ø^(n + 2) - (1 - ø)^(n + 2)) ÷ √5

Where:
ø = (1 + √5) ÷ 2, the Golden Ratio
n = m - 2

There are two local variables used in this program:
N = M - 2, the user supplies where M is the desired mth term
H = ø

The Program FIBN

Comments will be italicized, starting with an asterisk *. This program starts with M on Level 1 of the stack.

[RS] [ + ] (<< >>)
* Start of the program
2 [ - ]
* Subtract 2 from M to get N
1 [SPC] 5 [ √ ] [ + ]
2 [ ÷ ]

* Set up the Golden Ratio Constant, to be stored in H
[RS] [ 0 ] (&rarr)
* Prepare to name the local variables
[ALPHA] [EVAL] (N) [SPC]
[ALPHA] [MODE] (H)
[RS] [ + ] (<< >>)

* Start the main program
[ALPHA] [MODE] (H) [SPC]
* Leave spaces in between H and N
[ALPHA] [EVAL] (N) [SPC]
2 [ + ] [y^x]

* H^(N + 2); [y^x] is shown as ^
1 [SPC] [ALPHA] [MODE] (H) [ - ]
[ALPHA] [EVAL] (N) [SPC] 2
[ + ] [y^x]

* (1 - H)^(N + 2)
[ - ]
* H^(N + 2) - (1 - H)^(N + 2)
5 [ √ ] [ ÷ ]
* ( H^(N + 2) - (1 - H)^(N + 2) ) ÷ √5
[EVAL]
* To simplify the answer
[ENTER]
* To terminate program entry

[ ' ] [ALPHA] [ALPHA]
[F6] (F) [TOOL] (I) [F2] (B) [EVAL] (N)
[ENTER] [STO>]


Here is the completed program:

<< 2 - 1 5 √ + 2 / → N H
<< H N 2 + ^ 1 H - N 2 + ^ - 5 √ / EVAL >> >>


How to run FIBN:
1. Enter M on the Stack
2. Run FIBN

Results:
FIBN(1) = 1
FIBN(2) = 1
FIBN(3) = 2
FIBN(4) = 3
FIBN(5) = 5
etc...

That wraps up Part 2. In Part 3, the IF-THEN-END and IF-THEN-ELSE-END program structures are introduced. Until then, Cheers! Eddie

Source Used: Math Formulas and Tables from Mobile Reference. SoundTells, LLC 2003-2010

This tutorial is created and is the property of Edward Shore. No mass reproduction without express permission of the author.


Edit: 10/20/11: correct an error in the formula in the text. The program is correct.

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