Saturday, September 30, 2017

HP 12C: Prime Factoring (by Don Shepard)

HP 12C:  Prime Factoring (by Don Shepard)

Introduction – Cash Flow Registers to Simulate Indirect Addressing

This program uses what is called indirect addressing on the HP 12C, which can be simulated by the use of the cash flow registers. 

Cash flow registers can be registered by using the cash flow [ g ] [PMT] (CFj)  and frequency [ g ] [ FV ] (Nj) registers.  Every time a cash flow is stored, the counter is increased by 1.  The counter can be recalled by press [RCL] [ n ].

Similarly, you can recall the cash flows by the use of [RCL] [ g ] [PMT] (CFj) and the attached frequencies by the use of [RCL] [ g ] [ FV ] (Nj).  Each time a cash flow is recalled, the counter is decreased by 1. 

Each cash flow can have a frequency up to 99 copies. 

Fun fact:  the first 20 cash flows can be stored into registers R0 through R19, with the 20th flow stored in FV (future value).  The cash flow 0 is the initial cash flow, CF0 (accessed by [ g ] [ PV ] (CF0)). 

This is kind of storing values in a list and recalling them whenever necessary.

Program:

Enter the integer and press [ R/S ].  Keep pressing [ R/S ] to reveal more factors.  The factorization ends when a zero appears.

(Remember if you program using a HP 12C Platinum, step numbers are three digits instead of two.)

Step
Code
Key
01
44, 0
STO 0
02
42, 32
Clear Σ
03
2
2
04
44, 11
STO n
05
6
6
06
43, 14
[ g ] CFj
07
2
2
08
43, 15
[ g ] Nj
09
6
6
10
43, 14
[ g ] CFj
11
4
4
12
43, 15
[ g ] Nj
13
2
2
14
43, 14
[ g ] CFj
15
4
4
16
43, 15
[ g ] Nj
17
2
2
18
43, 14
[ g ] CFj
19
4
4
20
43, 15
[ g ] Nj
21
2
2
22
43, 14
[ g ] CFj
23
43, 15
[ g ] Nj
24
1
1
25
43, 14
[ g ] CFj
26
2
2
27
43, 15
[ g ] Nj
28
0
0
29
44, 12
STO i
30
45, 43, 15
RCL [ g ] Nj
31
43, 33, 56
GTO 56
32
1
1
33
44, 12
STO i
34
45, 43, 14
RCL [ g ] CFj
35
43, 33, 56
GTO 56
36
45, 11
RCL n
37
3
3
38
43, 34
x≤y
39
43, 33, 28
GTO 28
40
45, 0
RCL 0
41
43, 23
LN
42
43, 35
x=0
43
43, 33, 00
GTO 00
44
6
6
45
44, 11
STO n
46
45, 0
RCL 0
47
45, 1
RCL 1
48
36
ENTER
49
20
*
50
43, 34
x≤y
51
43, 33, 28
GTO 28
52
45, 0
RCL 0
53
31
R/S
54
0
0
55
43, 33, 00
GTO 00
56
44, 40, 1
STO+ 1
57
45, 0
RCL 0
58
45, 1
RCL 1
59
10
÷
60
43, 24
FRAC
61
43, 35
x=0
62
43, 33, 67
GTO 67
63
45, 12
RCL i
64
43, 35
x=0
65
43, 33, 32
GTO 32
66
43, 33, 36
GTO 36
67
45, 1
RCL 1
68
44, 10, 0
STO÷ 0
69
31
R/S
70
0
0
71
43, 33, 56
GTO 56


** Line 34 has been corrected.  10/3/2017


Example 1:

Factoring 148:

148 [R/S]
Display:  2, Press [R/S]
Display:  2, Press [R/S]
Display:  37, Press [R/S]
Display: 0

Result:  148 = 2 * 2 * 37 = 2^2 * 37

Example 2:

Factoring 976:

976
Display:  2, Press [R/S]
Display:  2, Press [R/S]
Display:  2, Press [R/S]
Display:  2, Press [R/S]
Display:  61, Press [R/S]
Display:  0, Press [R/S]

Result:  976 = 2 * 2 * 2 * 2 * 61 = 2^4 * 61


Special thanks to Don Shephard for letting me post his program on this blog.  Shepard attended HHC 2017, where he spoke about punch cards and their history.


Eddie


This blog is property of Edward Shore, 2017.

1 comment:

  1. This Prime Factor program that used the Cash Flow register is very powerful one.
    I try this method compare to other method and this one by far is very fast. By using the build-in functions integrated into the program make this HP 12C the fastest computation speed compare to other similar models like HP 15C.
    The other excellent program that use the cash flow functions with NPV and IRR is Polynomial Equation.

    ReplyDelete

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