(42S) GCD

[Eddie W. Shore]

HP 42S: GCD (Greatest Common Divisor) by Euclid Division

Enter the two integers on the Y stack and X stack. Order doesn’t matter.

Code:

00 {42-Byte Prgm}
01 LBL “GCD”
02 X<Y?
03 X<>Y
04 STO 01  \\ store maximum in R01
05 X<>Y
06 STO 00  \\ store minimum in R00
07 LBL 00 \\ main loop
08 RCL 01
09 ENTER
10 RCL÷ 00
11 IP
12 RCL* 00
13 –
14 X=0?  \\ is max – IP(min/max)*min = 0?
15 GTO 01
16 X<>Y 
17 STO 01
18 X<>Y 
19 STO 00
20 GTO 00
21 LBL 01 \\ display GCD
22 RCL 00 
23 “GCD:”
24 ARCL ST X
25 AVIEW
26 END

Test: Find the GCD of 485 and 175.
485 [ENTER] 175 [XEQ] {GCD} Result: 5
Alternatively:
175 [ENTER] 485 [XEQ] {GCD} Result: 5

[Joe Horn]

As others have recently posted in parallel discussions, the GCD routine in the PPC ROM is probably the shortest and fastest possible:

LBL c
MOD
LASTX
X<>Y
X\=0? ("not equal to zero?")
GTO c
+
RTN

Instructions: Same.
Output: GCD is returned in X.

[Dieter]

(07-12-2016 03:48 AM)Joe Horn Wrote:  As others have recently posted in parallel discussions, the GCD routine in the PPC ROM is probably the shortest and fastest possible:

Also posted in the other GCD thread:
You can get it one step shorter (but with the same byte count):

Code:

LBL d
STO Z
MOD
X≠0?
GTO d
+
END

Note to HP42 users: STO Z is STO ST Z.

Dieter

[Paul Dale]

Of the 34S you can do even better:

Code:

01 GCD

- Pauli

[Dieter]

(07-12-2016 06:40 AM)Paul Dale Wrote:  Of the 34S you can do even better:

Code:

01 GCD

You do not even need this single line as GCD can be executed directly in run mode. ;-)

So the shortest possible code is

Code:

 

8-)

Dieter

[Csaba Tizedes]

(07-10-2016 01:39 AM)Eddie W. Shore Wrote:  GCD (Greatest Common Divisor) by Euclid

There is a 15C version as per Marcus du Sautoy explanation (in TV show 'Secrets Of Modern Living: Algorithms')

Code:


LBL E
  x=y   / there are the two numbers are equal?
  RTN   / yes, stop here and the GCD on the display
  x>y   / no, check there are the smaller number in x?
  x<>y  / no, chsnge x and y
  -     / let's substract it
  LSTx  / and get back the number of x
  GTO E / and again until numbers are equal

Deatiled discussion is here: Calculator Google Group - GCD (Euclid's Algorithm)

In that thread another version is available for SENCOR SEC103, which is a perfect clone of CASIO fx-3650P (but much cheaper, much faster and most precise )

Csaba

[Logan]

(07-12-2016 06:23 AM)Dieter Wrote:  Also posted in the other GCD thread:
You can get it one step shorter (but with the same byte count):

Code:

LBL d
STO Z
MOD
X≠0?
GTO d
+
END

I tried to come up with my own method to do this (after reading about Euclid's Algorithm), and once I had did a search to see what others had come up with. I was proud to see that the one I'd come up with was identical to this with the exception that I swapped X<>Y at the end instead of the addition.