(12C) Prime Factorization

[Don Shepherd]

Well, Dave Britten started this ball rolling here with a prime factor finder for the 32sii and 20s based upon an original program for the 67. Tim Wessman used this as a model for the 30b in message number 30 of that thread. I made a few modifications here for the 32s, a very nice machine. But I always wondered if this basic algorithm could be done on the 12c, and especially the fast 12c+.

At first glance, it would appear unlikely because of the heavy reliance on subroutines, which the 12c does not have. But the more I looked at the code, the more I believed that it should be possible to somehow implement this algorithm on the 12c+. Yesterday I figured out how to do it, essentially using indirect addressing via the Rcl CFj command with the cash flow registers.

The code is listed below. The 12c+ is rather slower than the 30b for this application: the 30b determines the primality of 300,000,007 in 9 seconds versus the 12c+ 38 seconds. But this algorithm represents a significant improvement over a brute-force algorithm that eliminates only multiples of 2 from the trial factor pool; that version takes 57 seconds on the 12c+.

The fact that an algorithm that is so subroutine-intensive can be done on the 12c+ at all is a testament to the greatness of the design of the 12c. No wonder it is the most successful calculator HP has ever produced.

Edited on 9/20/2010 to implement Katie Wasserman's suggestion to use Nj in addition to CFj so that no preloading of registers is necessary, a brilliant suggestion.

Prime factors program for 12c+

Eliminates multiples of 2, 3, and 5 from trial factor pool


These are the trial factor increment values that are stored
via cfj and nj in R2 to R7:
6,2,6,4,2,4,2,4,2,2,1,2


Enter number to factor, R/S
R/S after each factor displayed
0 indicates done


maximum number to factor = 999,999,999


Register usage:
R2 - R7 (and corresponding nj) = trial factor increments, begins at R7
R0 - number to factor
R1 - current trial factor
n - used to control indirect addressing
i - flag for returning to the right location from
the routine at line 56


Mem command = p-71 r-11

Code:


01 sto 0    number to factor
02 clr sigma    clears R1 for trial factor use
03 1        load trial factor increment values into cfj/nj
04 sto n    registers R2 to R7
05 6
06 cfj
07 2
08 nj
09 6
10 cfj
11 4
12 nj
13 2
14 cfj
15 4
16 nj
17 2
18 cfj
19 4
20 nj
21 2
22 cfj
23 nj
24 1
25 cfj
26 2
27 nj
28 0        loop begins here to get next series of trial factor increment values
29 sto i    flag so you return to the correct line number from routine at line 56
30 rcl nj    get the next trial factor increment value
31 goto 56    check to see if this is a factor
32 1
33 sto i    flag to return to the correct line number from line 56 routine
34 rcl cfj    get the next trial factor increment value
35 goto 56    check to see if this is a factor
36 rcl n    when n gets to 2, an iteration of loop is done
37 2
38 x<=y
39 goto 28    loop not done, so continue loop with next increment
40 rcl 0    if num to factor is 1, you are done factoring
41 ln        will be 0 if num to factor is 1
42 x=0
43 goto 00    display 0 and exit program
44 5        reset indirect pointer to 5 for second
45 sto n    and all subsequent loop iterations
46 rcl 0    number to factor
47 rcl 1    current trial factor
48 enter
49 x        no x-squared key on 12c so this does it
50 x<=y        continue loop until you get to
51 goto 28    the square root of the number to factor
52 rcl 0    the final factor is in R0 now so display
53 R/S        it, then display 0 and stop
54 0
55 goto 00
56 sto+1    beginning of routine to see if this is a factor, increment trial divisor
57 rcl 0    current number to factor
58 rcl 1    current trial divisor
59 /
60 frac        frac part will be 0 if R1 is a factor of R0
61 x=0
62 goto 67    if a factor
63 rcl i    0=return to line 32, 1=return to line 36
64 x=0
65 goto 32
66 goto 36
67 rcl 1    factor found, so update number to factor
68 sto/0    update number to factor
69 r/s        display factor wait for user to press r/s
70 goto 57    see if current trial factor is again a factor

[Paul Dale]

Couldn't the final two steps be replaced by goto 57?

Pauli

[Don Shepherd]

(11-23-2019 03:23 AM)Paul Dale Wrote:  Couldn't the final two steps be replaced by goto 57?

Pauli

Hi Pauli, thanks.

It looks like that change would work, but the 2010 post is archived and cannot be changed so I'd have to do some cutting and pasting into a new post, which I'd rather not do. There are three additional changes I wanted to make back in 2010 (to reduce the number of indirect registers by 1) but I couldn't make the changes because of the archive status. Those changes didn't really affect the speed or functionality of the program anyhow.

UPDATE: I'm going to remove the link to the archived article (that can't be updated) and post the revised code in its place--to include Pauli's suggestion and also use one fewer register for indirect addressing.

Don