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
(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
(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
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
(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
(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
(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.
(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