Graphical Calculator

A graphical calculator is essential for all A-level maths students and the course includes some programming. I found the language of my CASIO fx-7300G easy to pick up with my experience and enjoy writing programs for it. Sometimes when we do programs in lessons I end up teaching the teacher! I often see a better way of doing things than what is in the textbooks too.

My most impressive program was a 3D maze. There were two problems: calculators are not designed for this sort of thing and I only had 500 bytes of program memory and 26 variables. This made a relatively simple program difficult because it forced me to think carefully and make the code as short as possible. At first I did not know whether it was possible to fit it in 500 bytes; it had to be perfectly optimised for program size. The programs are shown below. Note that -> represents the assignement operator and not - then >. Also => is the conditional operator.

Program 0:
Lbl 2
Prog 7
60->M
Lbl 1
Plot 0,0
Dsz M:Goto 1
Q=1=>Prog 1
Q=1=>Goto 2
?->N
1->0
N=8=>Prog 1
N=6=>Prog 2
N=4=>Prog 3
Goto 2
Program 1:
K+I->X
L+J->Y
Prog 9
V=0=>X->K
V=0=>X->K
Program 2:
-1->O
Prog 3
Program 3:
JO->P
-IO->J
P->I
Program 6:
.2(.6^M-1)/-.4-->N
.2(.6^(M+1)-1)/-.4->O
P=1=>1-N->N
P=1=>1-O->O
V=1=>Plot N,N
V=0=>Plot N,O
Plot O,O
Line
Plot O,1-O
Line
V=1=>Plot N,1-N
V=0=>Plot N, 1-O
Line
M=0=>V=0=>0->Q
Program 7:
1->Q
Range 0,1,0,0,1,0
Plot 1,0
Plot 1,1
Line
Plot 0,1
Line
0->M
Lbl 1
K+MI-J->X
L+MJ+I->Y
1->P
Prog 9
Prog 6
0->P
K+MI+J->X
L+MJ-I->Y
Prog 9
Prog 6
Isz M
K+MI->X
L+MJ->Y
Prog 9
M>5=>Goto 2
V=0=>Goto 1
Plot O,O
Plot 1-O,O
Line
Plot O,1-O
Plot 1-O,1-O
Line
Lbl 2
M=1=>0->Q
Program 9:
X+16Y->W
Int (W/32)->U
Int (A[U]/2^(W-32U))->W
1->V
W/2=Int (W/2)=>0->V

Total Memory Used: 479

Notes:

The programs may be put in different slots but do not forget to change the subroutine calls (`Prog' command). If your calculator gives programs names instead of numbers then change the 'Prog' commands appropriately .

Controls:

To start run program 0. When the question mark is displayed enter 8 to move forward, 4 to turn left and 6 to turn right (this corresponds to the arrows on the numeric pad on a computer keyboard).

Maze Design:

The maximum size of a maze is 16x16. All of the information is stored in the value memories A to H. Each contains information for 32 squares or two rows in the maze. The programs do not include a maze, you must set it up yourself. Here is an example:

3222405119->A
2688937813->B
2197924733->C
2685516765->D
2886840279->E
2890247509->F
2902560125->G
4294943231->H
1->K:6->L:1->I:0->J

You can type these in comp mode or enter them in a program so that if you use these variables in other programs you will not have to type in all of the numbers again. K and L are the X and Y co-ordinates of you in the maze and can range from 1 to 14 (0 and 15 are at the edges of the maze and should always contain walls). I and J are the direction which you face and may only be one of four combinations:

I	1	-1	0	0
J	0	0	1	-1
Direction	East	West	North	South

If you want to design your own maze then first draw a 16 by 16 grid and mark which squares contain walls. Next split it into groups of two rows, the top pair are stored in variable A, then next in variable B and so on. Set each variable to 0. For each variable take the two rows it represents and write the numbers 0 to 15 in the top row and 16 to 31 in the bottom row. Now look at which squares have walls, for each one add 2 to the power of the number in it to the variable. There are two limitations to your design: it must have a wall all around the edge and you can not have open spaces (no corridors wider than 1 square).