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Eddie W. Shore · (This post was last modified: 07-15-2016 02:38 AM by Eddie W. Shore.)

HP 12C Modulus

This program takes the modulus of two numbers:
Y MOD X = X * FRAC(Y/X)
In this program, X > 0 and Y > 0.

Code:

STEP    CODE            KEY

01    10             ÷

02    43, 36    LST x

03    34             X<>Y

04    43, 24    FRAC

05    20             *

06    43, 33, 00    GTO 00

Input: Y [ENTER] X [R/S], Result: Y MOD X
Test 1: 124 MOD 77 = 47
Test 2: 3862 MOD 108 = 82

Dieter · (This post was last modified: 07-15-2016 07:00 PM by Dieter.)

(07-15-2016 02:37 AM)Eddie W. Shore Wrote: This program takes the modulus of two numbers:
Y MOD X = X * FRAC(Y/X)

That's not a good idea: roundoff errors will spoil the results.
Consider your two examples:

124 mod 77 does not return 47 but 46,99999997
3862 mod 108 does not return 82 but 82,00000008

That's why you better use the relation y mod x = y – x * INT(y/x) instead.

Code:

01-       34  x<>y

02-     44 0  STO 0

03-       34  x<>y

04-       10  ÷

05-    43 36  LSTX

06-       34  x<>y

07-    43 25  INTG

08-       20  x

09-  44 30 0  STO- 0

10-       33  R↓

11-     45 0  RCL 0

12- 44,33 00  GTO 00

That's a bit longer and requires one data register, but it works.
The R↓ in line 11 was included to preserve the initiial values in T and Z.

Dieter

bshoring · 07-18-2016, 10:12 PM

(07-15-2016 06:32 PM)Dieter Wrote:
(07-15-2016 02:37 AM)Eddie W. Shore Wrote: This program takes the modulus of two numbers:
Y MOD X = X * FRAC(Y/X)

That's not a good idea: roundoff errors will spoil the results.
Consider your two examples:

124 mod 77 does not return 47 but 46,99999997
3862 mod 108 does not return 82 but 82,00000008

That's why you better use the relation y mod x = y – x * INT(y/x) instead.

Code:

01- 34 x<>y 02- 44 0 STO 0 03- 34 x<>y 04- 10 ÷ 05- 43 36 LSTX 06- 34 x<>y 07- 43 25 INTG 08- 20 x 09- 44 30 0 STO- 0 10- 33 R↓ 11- 45 0 RCL 0 12- 44,33 00 GTO 00

That's a bit longer and requires one data register, but it works.
The R↓ in line 11 was included to preserve the initiial values in T and Z.

Dieter

Here's a routine I wrote about a month ago. One step longer, but it uses only the stack and Last-X register. I wrote it for the HP-38C, but the steps are exactly the same for the HP-12C (but the keycodes would be different). For the two examples given by Dieter, it gets the right results.

Code:

01-     x<>y

02-     Enter

03-     Enter

04-     R↓

05-     R↓

06-     R↓

07-     ÷

08-     LSTX

09-     x<>y

10-     INTG

11-     x

12-     -

13-     GTO 00

RobertM · 07-21-2016, 11:36 PM

From "ENTER: Reverse Polish Notation Made Easy", Jean-Daniel Dodin / Keith Jarett, (pg 115):

Code:

01-       36 ENTER

02-       36 ENTER

03-       30 -

04-       33 R↓

05-       34 x<>y

06-    43 36 LSTx

07-       10 ÷

08-    43 25 INTG

09-       20 x

10-       30 -

11- 43 33 00 GTO 00

Dieter · (This post was last modified: 07-25-2016 10:10 AM by Dieter.)

(07-18-2016 10:12 PM)bshoring Wrote: Here's a routine I wrote about a month ago. One step longer, but it uses only the stack and Last-X register.

Great. In the meantime I got exactly the same solution. Many/most other HPs offer a R↑ which can replace the three consecutive R↓, making the program even shorter.

(07-21-2016 11:36 PM)RobertM Wrote: From "ENTER: Reverse Polish Notation Made Easy", Jean-Daniel Dodin / Keith Jarett, (pg 115):

That's a nice one as well. Here's another 10/11 step solution:

Code:

01 ENTER

02 ENTER

03 -

04 +

05 /

06 LastX

07 x<>y

08 INT

09 x

10 -

11 GTO 00 or RTN

The first four lines copy the content of Y to Z and T while X and Y are left unchanged.

However, all these solutions destroy the stack, while the version I initially posted keeps the values of Z and T. That's why it requires one data register. I wonder if it is possible to do it only with the stack, i.e. without a data register, while Z and T are still preserved.

Here's another challenge: what about returning y mod x as well as y div x (i.e. the integer quotient of y and x). There are many applications where both values are required at the same time. That's why I once suggested a DIVMOD command for the 34s that returns these two values.

Now, what do you think ?-)

Dieter

Dieter · (This post was last modified: 07-29-2016 05:40 PM by Dieter.)

(07-25-2016 09:17 AM)I Wrote: Here's another challenge: what about returning y mod x as well as y div x (i.e. the integer quotient of y and x). There are many applications where both values are required at the same time. That's why I once suggested a DIVMOD command for the 34s that returns these two values.

I just realized that the code in the previous post can be extended easily to return both values at the same time – it's just two more steps:

Code:

01 ENTER

02 ENTER

03 -

04 +

05 /

06 LastX

07 x<>y

08 INT

09 ENTER

10 R↓

11 x

12 -

13 GTO 00 or RTN

The same can be done with the Dodin/Jarett program by inserting ENTER R↓ between step 08 and 09.

The above version returns the remainder in X and y div x in Y.

3782 [ENTER] 72 [R/S]
=> 38 [X<>Y] 52

There even is a third useful result:

[LastX] => 3744
The largest number ≤ Y that is divisible by X.

Dieter

bshoring · (This post was last modified: 07-28-2016 11:02 PM by bshoring.)

(07-25-2016 09:46 AM)Dieter Wrote:
(07-25-2016 09:17 AM)I Wrote: Here's another challenge: what about returning y mod x as well as y div x (i.e. the integer quotient of y and x). There are many applications where both values are required at the same time. That's why I once suggested a DIVMOD command for the 34s that returns these two values.

I just realized that the code in the previous post can be extended easily to return both values at the same time – it's just two more steps:

Code:

01 ENTER 02 ENTER 03 - 04 + 05 / 06 LastX 07 x<>y 08 INT 09 ENTER 10 R↓ 11 x 12 - 13 GTO 00 or RTN

The same can be done with the Dodin/Jarett program by inserting ENTER R↓ between step 08 and 09.

The above version returns the remainder in X (and Z) and y div x in Y (and T).

3782 [ENTER] 72 [R/S]
=> 38 [X<>Y] 52

There even is a third useful result:

[LastX] => 3744
The largest number ≤ Y that is divisible by X.

Dieter

Nice program.

When I run 3782 [ENTER] 72 [R/S],
it leaves 38 in X only and 52 in Y, Z, & T.

Works for me.

Dieter · (This post was last modified: 07-29-2016 05:43 PM by Dieter.)

(07-28-2016 11:01 PM)bshoring Wrote: When I run 3782 [ENTER] 72 [R/S],
it leaves 38 in X only and 52 in Y, Z, & T.

Hmmm... you're right. I am sure I had a version were the two results were in X and Z resp. Y and T.
Anyway – I now corrected my previous post. Thank you for your feedback.

Dieter