(42S/DM42/Free42/Plus42) Multiply Large Numbers

[Eddie W. Shore]

The program LRG× multiplies to two large integers, allowing answers to extend beyond 12 digit capacity. The product is shown in the alpha register. How is this possible? One way is to split the multiplier and multiplicand (also known as factors) into groups of digits.

Download the program here:
largemultiply.raw


Program Code:

Code:

00 { 156-Byte Prgm }
01▸LBL "LRG×"
02 ALL
03 XEQ 17
04 STO 02
05 XEQ 18
06 STO 01
07 R↓
08 XEQ 17
09 STO 04
10 XEQ 18
11 STO 03
12 RCL 02
13 RCL× 04
14 STO 06
15 RCL 01
16 RCL× 03
17 STO 05
18 RCL 01
19 RCL× 04
20 RCL 02
21 RCL× 03
22 +
23 ENTER
24 ENTER
25 XEQ 17
26 STO+ 06
27 LASTX
28 FP
29 8
30 10↑X
31 ×
32 STO+ 05
33 RCL 05
34 8
35 10↑X
36 X>Y?
37 GTO 16
38 ÷
39 ENTER
40 ENTER
41 IP
42 STO+ 06
43 R↓
44 FP
45 8
46 10↑X
47 ×
48 STO 05
49 GTO 16
50▸LBL 17
51 4
52 10↑X
53 ÷
54 IP
55 RTN
56▸LBL 18
57 LASTX
58 X<>Y
59 -
60 4
61 10↑X
62 ×
63 RTN
64▸LBL 16
65 CF 29
66 CLA
67 ARCL 06
68 8
69 RCL 05
70 X≠0?
71 GTO 21
72 8
73 GTO 22
74▸LBL 21
75 LOG
76 1
77 +
78 IP
79 -
80▸LBL 22
81 STO 07
82 X=0?
83 GTO 19
84▸LBL 20
85 48
86 XTOA
87 DSE 07
88 GTO 20
89▸LBL 19
90 ARCL 05
91 AVIEW
92 SF 29
93 .END.

Notes:

The program LRG× takes two integers from the stack. This is meant to work on positive, non-zero integers.

Flag 29 is the thousands separator flag. Setting flag 29 turns them on while clearing it turns them off. In order to allow the alpha register have the long integer, flag 29 is cleared.

Memory register R5 represents units while R6 represents the part in hundred-millions.

The program switches the display to ALL mode.

Source

Hoffman, Dean and Mohler, Lee. Mathematical Recreations for the Programmable Calculator Hayden Book Company, Inc. Rochelle Park: New Jersey. 1982. pp 146-166.