Q function of HP-21S unveiled

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Q function of HP-21S unveiled

Postby mike-stgt » Thu Jul 09, 2020 1:53 pm

With the trace feature of Emu42 I was able to find out the two procedures of the HP-21S to compute Q(z) -- one of them was new to me.
Here an HP-42S program using the same algorithms.
Code: Select all
00 { 131-Byte Prgm }
01▶LBL "Q(z)"
02 X<0?
03 AON
04 ABS
05 ENTER
06 X^2
07 -2
08 ÷
09 E^X
10 PI
11 STO+ ST X
12 SQRT
13 ÷
14 STO 02
15 X<>Y
16 2,32
17 X>Y?
18 GTO 02
19 Rv
20 STO 04
21 STO 06
22 ÷
23 STO 05
24 CLX
25 STO 00
26 STO 01
27 SIGN
28 STO 03
29▶LBL 01
30 ISG 00
31 CLD
32 RCL 01
33 RCL× 00
34 RCL 02
35 STO 01
36 RCL× 06
37 +
38 STO 02
39 RCL 03
40 RCL× 00
41 RCL 04
42 STO 03
43 RCL× 06
44 +
45 STO 04
46 ÷
47 ENTER
48 X<> 05
49 -
50 RCL÷ ST L
51 ABS
52 -9
53 10^X
54 X≤Y?
55 GTO 01
56 SIGN
57 RCL 05
58 FS? 48
59 -
60 GTO 09
61▶LBL 02
62 SIGN
63 STO 00
64 Rv
65 ×
66 STO 01
67 LASTX
68 X^2
69 STO 02
70 X<>Y
71▶LBL 03
72 RCL 01
73 RCL× 02
74 2
75 RCL+ 00
76 STO 00
77 ÷
78 STO 01
79 RCL+ ST Y
80 X≠Y?
81 GTO 03
82 2
83 1/X
84 FC? 48
85 +/-
86 +
87 ABS
88▶LBL 09
89 AOFF
90 END

Note: in contrast to the HP-32E the HP-21S calculates "the upper tail" of the Q function.

The formulas? If you are truly interested take a closer look to this user code routine, it is much simpler than analysing some firmware trace.

M.

Edit: replaced lines 13 1/x and 14 * by 13 / only. It was a holdover from the HP-21S, which uses the constant @03966: #0398942280401432.
mike-stgt
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