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Programming in User RPL - First concepts
Now that you've payed 270 bucks for you HP48GX, it should at least be able to
do everything you need. Several funcitions are already avaliable, but probably
you'll need to do something the HP cannot do automatically. Say for example, you
have to calculate the determinant of a symbolic matrix. Since the HP only
supports numerical matrices, you'll have to calculate it manually. If you need
to do that only once, OK, but what to do if you need several calculations,
always doing the same thing, pressing the same keys, but with different inputs?
That's why the HP48 is different from other calculators. It is programmable.
It means it can learn how to do something. In the example above, you could write
a program that calculates the determinat of a symbolic matrix when you give the
elements. So, to calculate the determinat, you would just need to enter the
elements and run the program. Want to calculate with different elements? Just
key in them and run the program again. You'll get the new results automatically.
Basically, programmable calculator can save you time.
On the HP48, programs are delimited by << >>
(to put << >>, press left-shift-Minus.) Inside,
there is a sequence of objects, separeted by spaces. Depending on the object
type, some action is taken, according to the table:
| Command |
Run |
| Number |
Put into stack |
| Algebraic |
Put into stack |
| String |
Put into stack |
| List |
Put into stack |
| Program |
Put into stack |
Global name (between '') |
Put into stack |
Global name (without '') |
Put into stack and automatically evaluated |
Local Name (between '') |
Put into stack |
Local name (without '') |
Contents put into stack |
Let's see a simple example of a program. Suppose you have a 52 gallon
cylindrical water heater and you wish to determine how much energy is being lost
because of poor insulation. For that, you can use the formula
q = hAT
where q is the heat loss from the heater (btu
per hour); h is the heat-transfer coeficient, in our case 0.47; A
is the total surface area of the cylinder, in our example 30; and T is
the temperature difference.
The values of h and A will remain constant in or case, but we
want to calculate the heat loss for various temperature differences. You could
key in the values every time and multiply them, but this task can be simplified
with programming. Let's create a simple program to calcule the heat loss for the
heater when the temperature difference is on the stack. Key in the following
program, and press ENTER:
<< 30 * .47 * >>
Lets examine this program carefully. The first thing is the number 30. Since
it's a number, it will be put into the stack. Now the stack contains the
temperature difference (which you entered) and 30, the surface area, that the
program entered. The next object is a command, *. It will multiply
the two numbers on the stack, calculating A X T. Following,
there is another number, which will be put into the stack. And finnaly, another
command, again *. Now the program has multiplied
A X T by h, getting the result q.
Let's see if this works. If you have not already entered the program, enter
it now. You should see the program on level 1 of the stack. To save it as a
variable, type 'HT', press ENTER then
STO. Now press VAR. See HT on the first
menu key? Now, enter 15 and press the first softkey. Did you get 211.5? Now, if
you wanted to calculate again for a temperature difference of 18 degrees, just
enter 18 and press the menu key. You should get 253.8.
To see how easy it would be if you had to calculate several times, calculate
the heat loss for the differences of temperature of 10, 12, 14, 16, 18 and 20.
The answers are 141, 169.2, 197.4, 225.6, 253.8 and 282.
Stack Manipulation
Of the several commands that can be included in programs, some of the most
important ones are the ones that manipulate the stack, ie, change the order of
the elements, removes some elements or make copies of some of them. The HP
provides 13 commands for manipulating the stack. It is not recommend that you
know what them do. It is essential to know what them do. Was I
clear? You must know how to use them and their effect. Anyway, it
isn't so difficult. Here they are:
DUP |
Makes a copy of the object on level 1 of the stack |
2:
1: a |
2: a
1: a |
DUP2 |
Makes copies of the objects on levels 1 and 2 of the stack |
4:
3:
2: a
1: b |
4: a
3: b
2: a
1: b |
DUPN |
Makes copies of n objects on the stack, starting at level 2
(n is on level 1)
| 6:
5:
4: a
3: b
2: c
1:
3 |
6: a
5: b
4: c
3: a
2: b
1:
c |
DROP |
Drops the object on level 1 of the stack |
2: a
1: b |
2:
1: a |
DROP2 |
Drops the objects of levels 1 and 2 of the stack |
3: a
2: b
1: c |
3:
2:
1: a |
DROPN |
Drops the n first objects of the stack, starting on level 2
(n is on the stack) |
5: a
4: b
3: c
2: d
1: 3 |
5:
4:
3:
2:
1: a |
OVER |
Returns a copy of the object on level 2 |
3:
2: a
1: b |
3: a
2: b
1: a |
PICK |
Returns a copy of the object on level n+1 of the stack
(n is on the stack) |
4: a
3: b
2: c
1: 3 |
4: b
3: c
2: c
1: a |
SWAP |
Exchanges levels 1 and 2 |
2: a
1: b |
2: b
1: a |
ROLL
| Moves object on level n+1 to level 1 |
5: a
4: b
3: c
2: d
1: 4 |
5:
4: b
3: c
2: d
1: a |
ROLLD |
Moves object on level 2 to level n+1 |
5: a
4: b
3: c
2: d
1:
4 |
5:
4: d
3: a
2: b
1:
c |
ROT |
Moves object on level 3 to level 1 (equivalent to 3
ROLL) |
3: a
2: b
1: c |
3: b
2: c
1: a |
DEPTH |
Returns the number of elements on the stack |
4:
3: a
2: b
1: c |
4: a
3: b
2: c
1:
3 |
Now let's see another very simple program. It calculates the hypotenuse of a
right triangle, given the tow cates on the stack.
<< SQ SWAP SQ +  >>
Let's again examine closely this program. First, it squares the number on
level 1. Then, it swaps levels 1 and 2, and squares the new level 1, which was
previously level 2. Now we have both catets squared, so the program adds them,
and finally takes the square root. Simple, isn't it?
Exercises
- What happens when the following programs are run?
<< << << 1 2 + >> >> EVAL
>>
<< << << 1 2 + >> EVAL >>
>>
<< << << 1 2 + >> EVAL >> EVAL
>>
<< << << 1 2 + >> >> EVAL EVAL
>>
<< << 1 << 2 + >> >> EVAL
>>
<< << 1 << 2 + >> EVAL >> EVAL
>>
- Design a program that, when given the radius of a sphere in level 1,
calculates the volume of it. (
 )
- Write a program to convert from ºF to ºC. (
 )
- Write a program to convert from ºC to ºF
- Write a program to calculate the parallel resistance RP
of two resistors R1 and R2, whose values
are on the stack, using the formula
- Design a program that calculates the parallel resistance of two resistors
on the stack, using the formula
 . OBS: Yes, both formulas are valid,
and it isn't difficult to prove that.
- Write a program to calculate the determinant
 , assuming a, b, c and
d are on the stack, in this order.
- Write a program to calculate the distance of two points
(x1,y1) and (x2,y2),
assuming x1, x2, y1 and
y2 are on the stack in this order.
- Write a program to find one root of a quadratic equation, assuming
a, b and c are on the stack.
- Modifiy the above program so that it finds both roots of the equation.
- Write a program to find the surface area of a rectangular box, using the
equation S = 2(hw + hd + wd)
Answers to exercises
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