Faster factor finder method for 42S

11262019, 04:24 PM
Post: #1




Faster factor finder method for 42S
There's nothing novel here from a mathematics standpoint  it's just the same old mod30 sieve we've been doing for decades. Rather, I found a way to use matrices on the 42S to do the trial divisions much faster.
Here's the code with some Clike comments: Code: LBL "FACTOR" "SS" and "RS" are the savestack and restorestack routines I have on my 42S. You can remove/substitute these calls as needed. Variables, registers, and flags: Code: Regs The basic idea is that rather than repeatedly doing 4, XEQ 01, 2, XEQ 01, 4 XEQ 01... making 8 calls in each loop, all the trial divisors are stored in a matrix and divided all at once. Then FP takes their fractional parts, and the undocumented matrix function [MIN] identifies any of the divisions with no remainder. Found factors get fully divided out and displayed, and if none are found, 30 is added to the divisor matrix and the loop repeats. This continues until the divisors exceed the square root of the remaining product, or the input number has been fully factored down to 1. A couple of informal timing tests of factoring 9,999,999,971: Original mod210 factor finder with incr. XEQ  1m30s New matrixbased mod30 factor finder  53s I got the idea from a TI84 factor finder that uses essentially the same technique with lists. It dawned on me that it could be done with matrices on the 42S. The code is still kind of rough and unrefined, but I'm seeing execution times cut as much as in half for certain inputs. I haven't yet tried extending this into a full mod210 algorithm, so there may be more speed gains to be had yet. It would require larger divisor and remainder matrices, though, so more memory would be required to run the program. 

11292019, 09:38 AM
Post: #2




RE: Faster factor finder method for 42S  
11292019, 10:16 AM
Post: #3




RE: Faster factor finder method for 42S  
11292019, 11:27 AM
(This post was last modified: 11292019 11:28 AM by grsbanks.)
Post: #4




RE: Faster factor finder method for 42S
Or this page, which predates Joe's post by about 5 years
There are only 10 types of people in this world. Those who understand binary and those who don't. 

11292019, 01:12 PM
(This post was last modified: 11292019 01:13 PM by Joe Horn.)
Post: #5




RE: Faster factor finder method for 42S
(11292019 11:27 AM)grsbanks Wrote: Or this page, which predates Joe's post by about 5 years The earliest reference is on pages 1516 of HPX Exchange (August/December 1988), where the verbatim content of my posting above first appeared. For the record, the 3 hidden HP42S functions were discovered in a Jack in the Box fastfood eatery (23812 El Toro Rd, Lake Forest, California 92630) while eating a cheeseburger, on 9 November 1988. Museums always seek historical context, so there it is. <0ɸ0> Joe 

11292019, 01:25 PM
Post: #6




RE: Faster factor finder method for 42S
(11292019 01:12 PM)Joe Horn Wrote: For the record, the 3 hidden HP42S functions were discovered in a Jack in the Box fastfood eatery (23812 El Toro Rd, Lake Forest, California 92630) while eating a cheeseburger, on 9 November 1988. Museums always seek historical context, so there it is. Absolutely! Does anyone still know exactly how they were discovered? They're not mentioned in the manual as far as I remember, they don't appear in the function catalog and they don't appear in the matrix menu either. Did someone have access to a ROM listing or something? There are only 10 types of people in this world. Those who understand binary and those who don't. 

11292019, 01:26 PM
Post: #7




RE: Faster factor finder method for 42S
(11292019 09:38 AM)Csaba Tizedes Wrote:(11262019 04:24 PM)Dave Britten Wrote: undocumented matrix function [MIN] There are sooo many factoring programs for the 83/84 floating around that I honestly couldn't tell you where I found it. Here's the code, though. It also does some clever tricks with End, so it's a bit tough to follow. Code: Input "X=",X For info on the "[MIN]" function (yes, the brackets are included in the function name), see Joe's post linked above. 

11292019, 02:04 PM
Post: #8




RE: Faster factor finder method for 42S
(11292019 01:25 PM)grsbanks Wrote:(11292019 01:12 PM)Joe Horn Wrote: For the record, the 3 hidden HP42S functions were discovered in a Jack in the Box fastfood eatery (23812 El Toro Rd, Lake Forest, California 92630) while eating a cheeseburger, on 9 November 1988. Museums always seek historical context, so there it is. I remember how they were discovered, because it was quite thrilling. I used the 42S's builtin memory hex browser/editor (AKA "debugger") to find where programs were stored, then poked every possible hex value into program memory and exited to normal program mode to see what the corresponding commands were. That's how I created the 42S Hex Table (which also appears in that issue of HPX Exchange) and discovered the "hidden functions" lurking in there. What those functions do, and how to use them, was then a matter of trial and error, turbopowered by a Jack in the Box cheeseburger. <0ɸ0> Joe 

11292019, 04:27 PM
Post: #9




RE: Faster factor finder method for 42S
(11292019 02:04 PM)Joe Horn Wrote: I remember how they were discovered, because it was quite thrilling. I used the 42S's builtin memory hex browser/editor (AKA "debugger") to find where programs were stored, then poked every possible hex value into program memory and exited to normal program mode to see what the corresponding commands were. That's how I created the 42S Hex Table (which also appears in that issue of HPX Exchange) and discovered the "hidden functions" lurking in there. What those functions do, and how to use them, was then a matter of trial and error, turbopowered by a Jack in the Box cheeseburger. That's a clever way to do it! I wonder why they went undocumented/hidden, though. Has anybody ever found any grievous bugs in any of them? 

11302019, 09:32 PM
Post: #10




RE: Faster factor finder method for 42S
The undocumented functions appear to be implemented in Free42 (the DM42 and iOS, anyway) and behave as (un)documented. They don't show up in the catalog (preserving full fidelity with the original, I guess).


12012019, 08:02 PM
Post: #11




RE: Faster factor finder method for 42S
(11302019 09:32 PM)DMaier Wrote: The undocumented functions appear to be implemented in Free42 (the DM42 and iOS, anyway) and behave as (un)documented. They don't show up in the catalog (preserving full fidelity with the original, I guess). There is also the hidden (and useless) XFCN function, which is of course not in Free42, I documented it years ago here: https://www.hpmuseum.org/cgisys/cgiwrap...i?read=266 JF 

12022019, 07:17 AM
Post: #12




RE: Faster factor finder method for 42S
Great idea, Dave!
Can't wait to rewrite my own routine using this idea! (using only the stack, and without flags ;) There's a simpler way of finding out whether there's a zero in your remainders: (and no need for the matrix R) Code: SF 25 And nice story, Joe! If this were Facebook, you'd get a 'like' ;) Cheers, Werner 

12022019, 12:19 PM
Post: #13




RE: Faster factor finder method for 42S
(12022019 07:17 AM)Werner Wrote: Great idea, Dave! Very clever! That won't tell you where in the matrix there was a zero, so you'll have to take additional steps to find it, but optimizing for the common case (i.e. no factors found) makes sense. It's a shame that MOD won't work with matrices the same way division and 1/X will. In its current state, the matrix approach won't work with 12digit numbers, since the fractional part will be lost with small divisors (any result where the fractional part rounds down to .0 will have the same issue). 

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