(Free42 or possibly 42s with printer) Larger graphing area - now with PLOTR graphing

[arhtur]

From the first time I saw a HP 42s, I was surprised to hear that equations could be plotted on the tiny 2 line screen. On the Free42, it is possible to print the LCD to a virtual “printout”. By combining 6 calls to PRLCD, we can have a larger 131x96 area to plot pixels.

The bitmap of the pixels is stored in a 12 row by 131 column matrix where each element has an 8 bit number. Calls to STOIJ, RCLEL and STOEL make it possible to set pixels within a specific portion of the matrix.

There are 2 examples that graph the sine function (XEQ SG) and produce a checkerboard pattern (XEQ CB).

However, if you want to plot points on your own, first XEQ XYINIT to initialize the matrix.

Then, put the Y coordinate (between 0 and 95) and the X coordinate (between 0 and 130) on the stack. Then XEQ XYP. No checks are made for valid coordinates.

To “print” the graph, XEQ XYG. Because the Alpha register only holds 44 characters (on the Free42), 6 calls to AGRAPH are necessary to fill the entire LCD (3 times across and twice for the 1st and 2nd row of 8 pixels). To have a graph that is 96 pixels tall, PRLCD is called 6 times.

On the Free42, in order to see the graph, tap the LCD portion of the calculator and select “Show Print-Out”. When done, tap “Done”. You will have to press EXIT (ON) to exit the blank calculator screen. This has not been tested on the 42s with a printer, since I don't have a printer.

Code:

00 { 408-Byte Prgm }
01▸LBL "XYINIT"
02 12
03 132
04 NEWMAT
05 STO "M"
06 RTN
07▸LBL "XYP"
08 INDEX "M"
09 X<>Y
10 STO "Y"
11 8
12 ÷
13 IP
14 1
15 +
16 X<>Y
17 1
18 +
19 STOIJ
20 RCLEL
21 1
22 RCL "Y"
23 8
24 MOD
25 +/-
26 ROTXY
27 OR
28 STOEL
29 RTN
30▸LBL "XYG"
31 CLLCD
32 1.044
33 STO "X"
34 1.012
35 STO "Y"
36 CLA
37▸LBL "XYG1"
38 INDEX "M"
39 RCL "Y"
40 RCL "X"
41 STOIJ
42 RCLEL
43 XTOA
44 ISG "X"
45 GTO "XYG1"
46 1
47 1
48 AGRAPH
49 CLA
50 45.088
51 STO "X"
52▸LBL "XYG2"
53 INDEX "M"
54 RCL "Y"
55 RCL "X"
56 STOIJ
57 RCLEL
58 XTOA
59 ISG "X"
60 GTO "XYG2"
61 1
62 45
63 AGRAPH
64 CLA
65 89.132
66 STO "X"
67▸LBL "XYG3"
68 INDEX "M"
69 RCL "Y"
70 RCL "X"
71 STOIJ
72 RCLEL
73 XTOA
74 ISG "X"
75 GTO "XYG3"
76 1
77 89
78 AGRAPH
79 1
80 STO+ "Y"
81 CLA
82 1.044
83 STO "X"
84▸LBL "XYG4"
85 INDEX "M"
86 RCL "Y"
87 RCL "X"
88 STOIJ
89 RCLEL
90 XTOA
91 ISG "X"
92 GTO "XYG4"
93 9
94 1
95 AGRAPH
96 CLA
97 45.088
98 STO "X"
99▸LBL "XYG5"
100 INDEX "M"
101 RCL "Y"
102 RCL "X"
103 STOIJ
104 RCLEL
105 XTOA
106 ISG "X"
107 GTO "XYG5"
108 9
109 45
110 AGRAPH
111 CLA
112 89.132
113 STO "X"
114▸LBL "XYG6"
115 RCL "Y"
116 RCL "X"
117 STOIJ
118 RCLEL
119 XTOA
120 ISG "X"
121 GTO "XYG6"
122 9
123 89
124 AGRAPH
125 PRLCD
126 CLLCD
127 CLA
128 1.044
129 STO "X"
130 ISG "Y"
131 GTO "XYG1"
132 RTN
133 END

Plotting feature: Now I’ve added the PLOTR program that makes it easier to plot graphs. The variables XMIN, XMAX, YMIN and YMAX must be set. -10 and 10 are good starting points for the min and max values. Also, FN must hold the function to be graphed. FN must take the X value on the stack and return the Y value on the stack. For example, to plot the sine graph:

LBL FN
SIN
RTN

To graph y=2x + 3:

LBL FN
2
x (times)
3
+
RTN

The plotter will first draw the draw the X axis (DRX) and then draw the Y axis (DRY). There is no scale to the drawn dashes (they are just 8 pixels apart). If you are using X and Y min and max values that do not include the axis, you can skip drawing the axis by calling PLT01.

For a single graph, store the min and max values and the function (FN),
XEQ XYINIT
XEQ PLOTR
XEQ XYG
Tap the screen and select “Show Print-Out”.

For multiple graphs,
1. XEQ XYINIT
2. Define function in FN
3. XEQ PLOTR (PLOTR can be called the first time, but for subsequent graphs XEQ PLT01 to avoid the axis drawing erasing part of the original graph)
Repeat steps 2 and 3 for subsequent functions.
XEQ XYG
Tap the screen and select “Show Print-Out”

Of course there is the limitation that a function like ln(x) cannot be graphed for x<=0. The tangent function seemed to work for me.

PLOTR program:

Code:

00 { 390-Byte Prgm }
01▸LBL "PLOTR"
02 GTO "DRX"
03▸LBL "DRY"
04 RCL "XMIN"
05 +/-
06 RCL "XMAX"
07 RCL "XMIN"
08 -
09 ÷
10 131
11 ×
12 IP
13 STO "X"
14 1.012
15 STO "Z"
16▸LBL "PLT0"
17 INDEX "M"
18 RCL "Z"
19 RCL "X"
20 STOIJ
21 254
22 STOEL
23 ISG "Z"
24 GTO "PLT0"
25 GTO "PLT01"
26▸LBL "DRX"
27 RCL "YMAX"
28 RCL "YMAX"
29 RCL "YMIN"
30 -
31 ÷
32 95
33 ×
34 IP
35 STO "X"
36 8
37 ÷
38 1
39 +
40 STO "Y"
41 1
42 RCL "X"
43 8
44 MOD
45 +/-
46 ROTXY
47 STO "N"
48 1.131
49 STO "Z"
50▸LBL "PLT00"
51 RCL "Z"
52 IP
53 8
54 MOD
55 X=0?
56 GTO "PLT02"
57 INDEX "M"
58 RCL "Y"
59 RCL "Z"
60 STOIJ
61 RCL "N"
62 STOEL
63▸LBL "PLT02"
64 ISG "Z"
65 GTO "PLT00"
66 GTO "DRY"
67▸LBL "PLT01"
68 RCL "XMAX"
69 RCL "XMIN"
70 -
71 131
72 ÷
73 STO "STP"
74 0.130
75 STO "Z"
76 RCL "XMIN"
77 STO "X"
78▸LBL "PLT1"
79 RCL "XMIN"
80 RCL "Z"
81 RCL "STP"
82 ×
83 +
84 XEQ "FN"
85 +/-
86 RCL "YMAX"
87 +
88 96
89 ×
90 RCL "YMAX"
91 RCL "YMIN"
92 -
93 ÷
94 STO "N"
95 95
96 X<Y?
97 GTO "PLT2"
98 RCL "N"
99 0
100 X>Y?
101 GTO "PLT2"
102 RCL "N"
103 RCL "Z"
104 XEQ "XYP"
105▸LBL "PLT2"
106 ISG "Z"
107 GTO "PLT1"
108 RTN
109 END

Sine Graph:

Code:

00 { 136-Byte Prgm }
01▸LBL "SG"
02 DEG
03 0.131
04 STO "Z"
05 XEQ "XYINIT"
06▸LBL "SINEG1"
07 RCL "Z"
08 IP
09 6
10 ×
11 SIN
12 24
13 ×
14 +/-
15 48
16 +
17 RCL "Z"
18 IP
19 XEQ "XYP"
20 48
21 RCL "Z"
22 IP
23 XEQ "XYP"
24 ISG "Z"
25 GTO "SINEG1"
26 4.009
27 STO "Z"
28▸LBL "SINEG2"
29 INDEX "M"
30 RCL "Z"
31 61
32 STOIJ
33 255
34 STOEL
35 ISG "Z"
36 GTO "SINEG2"
37 XEQ "XYG"
38 RTN
39 END

Checkerboard pattern:

Code:

00 { 155-Byte Prgm }
01▸LBL "CB"
02 XEQ "XYINIT"
03 3.01
04 STO "A"
05 2.005
06 STO "B"
07▸LBL "CBOARD1"
08 RCL "B"
09 16
10 ×
11 RCL "A"
12 2
13 MOD
14 8
15 ×
16 +
17 STO "C"
18 0.007
19 STO "D"
20▸LBL "CBOARD2"
21 INDEX "M"
22 RCL "A"
23 RCL "C"
24 STOIJ
25 255
26 STOEL
27 1
28 STO+ "C"
29 ISG "D"
30 GTO "CBOARD2"
31 ISG "B"
32 GTO "CBOARD1"
33 2.005
34 STO "B"
35 ISG "A"
36 GTO "CBOARD1"
37 XEQ "XYG"
38 RTN
39 END