HHC 2013 programming contest winners

[Brian Walsh]

RPL - Bill Butler

RPN - Eric Smith

Eric's solution was 19 steps and used no data storage registers.

Edited: 22 Sept 2013, 4:57 p.m.

[Eric Smith]

My RPN entry as submitted was:

HHC 2013 RPN Programming Contest entry

Eric Smith <spacewar@gmail.com>

September 21, 2013

WP-34S version:

01: CONST #000

02: CONST #001

03: LBL 01

04: RCL Z

05: x = 0?

06: GTO 02

07: IP

08: STO- T

09: RCL* Y

10: STO+ Z

11: RDN

12: CONST #010

13: STO* T

14: CLx

15: CONST #008

16: /

18: GTO 01

18: LBL 02

19: RCL Z



HP-42S and HP-41:  replace CONST lines with ordinary numeric entry lines

HP-41C:  replace "RCL* Y" with "x<>y  STO* Y  x<>y"

[Miguel Toro]

Hi Eric,

There may be an error on the transcription of your solution. When I try it as written in your post, the value in T is lost after 12: and the program returns always 1.

If, for example, I make the following change, then the program runs correctly :

01: c# 001      (saves one step)

02: LBL 01

03: RCL Z

04: x = 0?

05: GTO 02

06: IP

07: STO- T

08: RCL* Y

09: STO+ Z

10: RDN

11: x <> T

12: SDL 001

13: STO T

14: CLx

15: CONST #008

16: /

17: GTO 01

18: LBL 02

19: RCL Z

Or perhaps there is something I am not seeing? Forgive me if am mistaken.

Miguel

[Gerson W. Barbosa]

CLx after STO* T is not disabling the stack lift as it should. Same here (v3.2r3382), but it does work on the emulator and on the HP-42S. Probably an old wp34s bug that's already been fixed. What is the version of your wp34s?

Best regards,

Gerson

PS.: This is Eric's program optimized for the wp34s:

01: CPX CONST #001              ;   CPX 1

02: RCL Z

03: x = 0?

04: SKIP 11

05: IP

06: STO- T

07: RCL* Y

08: STO+ Z

09: RDN

10: CONST #010

11: STO* T

12: CLx

13: CONST #008

14: /

15: BACK 013

16: RCL Z

Edited: 24 Sept 2013, 1:57 p.m.

[Dieter]

Quote:

---

CLx after STO* T is not disabling the stack lift as it should. Same here (v3.2r3382), but it does work on the emulator and on the HP-42S. Probably an old wp34s bug that's already been fixed.

---

Indeed. Everything works fine on my hardware 34s with v. 3.2 3405.

Dieter

[Miguel Toro]

Hello Gerson,

I am using V 3.2 3450. Physical device (not the emulator).

Regards,

Miguel

[Gerson W. Barbosa]

Strange, that's more recent than the emulator version (3448).

Regards,

Gerson.

P.S.: Eric Smith's solution works for arguments up to 7.77777777777

3.11037552421  -->  3.14159265358

7.77777777777  -->  7.99999999988

Edited: 24 Sept 2013, 3:07 p.m.

[Miguel Toro]

Well, I really do not get it. Could someone try it with version 3.2 3450 ? I think it is behaving correctly:

Suppose x = 0.5 						

    t:	 -    -   0.5   0.5   0.5   0.5   0.5   0.5   0.5   0.5    0  <-- value lost after 10: const #10

    z:	 -   0.5   0     0     0     0     0     0     0     0     1

    y:	 -    0    1     1     1     1     1     1     1     1     0

    x:	0.5   1   0.5   0.5   0.5    0     0     0     0     0    10

steps: 	 -   01   02    03    04    05    06    07    08    09    10

I do not think it is because of the CLx not disabling the stack lift. The version on post #2, works because Clx disable the stack lift

Edited: 24 Sept 2013, 3:45 p.m.

[Gerson W. Barbosa]

Hello Miguel

Quote:

---

I do not think it is because of the CLx not disabling the stack lift.

---

You are right. It turns out I was getting wrong results on the wp34c because my last line was RCL 2 instead of RCL Z. Sorry about the confusion. I will check it again step by step.

Gerson.

P.S.:

Quote:

---

The version on post #2, works because Clx disable the stack lift

---

I meant CLx disabled the stack lift (so that 8 replaces the 10 that was previously there).

Edited: 24 Sept 2013, 4:32 p.m.

[Gerson W. Barbosa]

Aren't you confusing RDN with RND? In Eric Smith's notation RDN means Rv (Roll stack down). That's the first thing I had checked previously, but I didn't detect it because I had introduced an error myself.

Regards,

Gerson.

Edited: 24 Sept 2013, 4:29 p.m.

[Paul Dale]

Or you could use DROP instead of Rv in this instance. It will also be imperceptibly faster.

At one point we had a display of program checksums in the 34S firmware which would help avoid this kind of thing. I don't remember exactly why they were removed -- I suspect due to opcodes changing but aren't certain anymore.

- Pauli

[Miguel Toro]

Yes. I was confusing those two and confused myself :-)

Thank you Gerson.

Regards,

Miguel

[Dieter]

For the record: this one is even one step shorter.

01: CPX CONST #001

02: RCL Z

03: x = 0?

04: SKIP 10

05: IP

06: STO- T

07: RCL* Y

08: STO+ Z

09: X<> T

10: SDL 001

11: CONST #008

12: STO/ Z

13: <> ZTYY

14: BACK 012

15: RCL Z

Yes, I like these 34s stack shuffle commands. :-)

Dieter

[Gerson W. Barbosa]

Quote:

---

Yes, I like these 34s stack shuffle commands. :-)

---

Me too, but they won't help here, it appears.

Gerson.

001  SDR 001

002  C #001

003  RCL Z

004  SDL 001

005  IP 

006  t<> L

007  RCL* Y

008  STO+ Z

009  DROP

010  8

011  /

012  R^

013  FP 

014  x#0?

015  BACK 011

016  RCL Z

_{Edited to correct misspelling.}

Edited: 25 Sept 2013, 2:41 p.m. after one or more responses were posted

[Paul Dale]

This piece of code almost makes me wish I'd implemented the integer mode shifts in real mode too :)

- Pauli

[Gerson W. Barbosa]

SDL and SDR are great but binary shifts would be handy in a lot of situations as well. No more room or just a matter of design philosophy?

Gerson.

[Paul Dale]

A bit of both really. Flash is basically full so finding space would take lots of effort or lose something else.

We'd also have had to convince Walter that they were useful (well, Marcus and I would also need convincing too I suspect). Two of the shifts would map to *2^x and /2^x in real mode and the rest still do nothing introducing a small inconsistency.

The alternative is 2^x * or 2^x / so these would only save one step. There would only be a performance boost if the algorithm were coded to deal with integers only -- either another inconsistency or more core. Both options are bad.

- Pauli

[Dieter]

While bit shifts for reals would be nice, I personally do not see a big advantage for real life applications. With one exception: doubling or halving a number is a common operation. A dedicated command (if possible, without affecting the stack) would add very nicely to the existing INC and DEC commands. Yes, we already had that discussion some time ago, but I still consider such commands very useful for every-day-programming. So please forgive me if I dig out this idea once again.

Dieter

[Egan Ford]

Congrats Bill and Eric.

Now that the contest is over I guess we can share our results.

I selected to use the 12C because it was designed to solve this problem (indirectly of course :-).

Embedded in the 12C is the following function:

To use: set CF₀ to 0, then set CF_{j (j=1 to n number of digits)} to each octal-decimal digit, then set your base (-1 then 100x), and then press NPV.

Code:

01 -    43 25  INTG        ; LSTx = x, x = int(x) (0 or 1)

02 -    43 35  x=0         ; if x=0

03 - 43,33 05  GTO 05      ;   then LSTx < 1, continue with x = 0

04 - 43,33 00  GTO 00      ;   else end program and leave x = 1

05 -    43 13  CFo         ; x = 0, CFo = x, n = 1

06 -    43 36  LSTx        ; x = LSTx

07 -    43 35  x=0         ; if x=0

08 - 43,33 17  GTO 17      ;   then no digits left, continue with NPV setup and NPV

09 -        1  1           ; x = x * 10

10 -        0  0           ;

11 -       20  x           ;

12 -       36  ENTER       ; y = x

13 -    43 24  FRAC        ; x = value right of decimal

14 -       30  -           ; x = y - x, i.e. value left of decimal, LSTx = right of decimal

15 -    43 14  CFj         ; CFn = int(x), n = n + 1

16 - 43,33 06  GTO 06      ; loop up for next digit

17 -        7  7           ; sto 700 in i

18 -        0  0           ;   NOTE: i = i / 100

19 -        0  0           ;

20 -       12  i           ;

21 -    42 13  NPV         ; do it, x = answer

Thanks again Gene for the challenge. It was fun to finally use NPV.

[Paul Dale]

WP34S program. Seventeen steps. Executition time three ticks for any input.

	# 099		// Scaling factor

	STO K		// Into loop counting register

	# 000		// Result

	RCL Z		// Stack rearrangement to get the input in X

	SDL[->]K	// Scale the input

			// Add IP here to avoid problems for 10^-100 arguments

	RCL X		// Begin loop

	# 010		// Extract lowest digit

	MOD

	RCL+ T		// Accumulate digit into result

	# 008		// Push result one octal digit

	/

	x[<->] Y	// Get original number back

	SDR 001		// Shift it and trim final digit off

	IP

	DSZ K		// Loop until done

	BACK 010

	+		// Could use x[<->] Y here but that doesn't handle 1 as input

Some results:

Input		Result			True			Delta

0.5		0.625			0.625			0

0.75		0.953125		0.953125		0

0.1		0.125			0.125			0

0.777777777	0.9999999925494194	0.9999999925494194	0

0		0			0			0

1		1			1			0

1e-95		1.60861174670876E-86	1.608611746708759E-86	1e-101

This routine handles inputs from 1e-99 through 1 plus 0. The range can be altered by changing the constant on the first line, decreasing this reduces execution time. E.g. if the lower limit is restricted to 1e-16, change this constant to 16 and the execution time will be essentially zero.

Take the LBLs out of Eric's solution using BACK and SKIP and his program is one step shorter than this and a bit faster.

- Pauli

Edited: 22 Sept 2013, 5:30 p.m.

[Eric Smith]

One of the things I like about the programming challenges is that I always learn new techniques from the other participants. Even though I had the winning RPN entry this year, and used a WP-34S, I wasn't familiar with the SDL, SDR, SKIP, and BACK instructions.

My program produces correct results over the domain [0 to 7.777...]

[Marcel Samek]

Although my stab at this uses 3 registers, it did come in at 15 steps on the WP-34S. It handles values down to 1e-99

CLREGS

INC 00

STO 01

x=0?

SKIP 009

IP

RCL/ 00

STO+ 02

8

STOx 00

RCL 01

FP

SDL 001

BACK 011

RCL 02

[Gerson W. Barbosa]

No numbered register was killed during the execution of this program, but down to 17 steps only:

001   C# 001

002   RCL Z

003   SDL 001

004   IP

005   8

006   STO* Z

007   Rv

008   t<> L

009   RCL/ Y

010   STO+ Z

011   <-> TYZT

012   FP

013   x#0?

014   BACK 011

015   RCL Z

016   x>1?

017   IP


0.11037552421  -->  0.14159265358

[Gerson W. Barbosa]

Quote:

---

Take the LBLs out of Eric's solution using BACK and SKIP and his program is one step shorter than this and a bit faster.

---

One more step can be save by replacing steps 001 and 002 with

01: C# 001

[Paul Dale]

The baton has passed. Others are exploiting the 34S function set better than I :-)

Congratulations to all,

Pauli

[Gerson W. Barbosa]

Here are mine:

WP-34S:

001   # 000

002   # 008

003   RCL Z

004   SDL 001

005   IP

006   STO+ Z

007   8

008   STO* T

009   STO* Z

010   Rv

011   x<> L

012   FP

013   x#0?

014   BACK 010

015   Rv

016   /

017   x>1?

018   IP



HP-15C:

001- f MATRIX 1

002- f LBL 0

003-   8

004-   STO* 1

005-   x<>y

006-   1

007-   0

008-   *

009- g INT

010-   RCL/ 1

011-   STO- 0

012-   LSTx

013-   f FRAC

014-   g TEST 0

015-   GTO 0

016-   1

017-   RCL 0

018- g TEST 2

019- g INT

020-   - 

[Gerson W. Barbosa]

Quote:

---

001   # 000

002   # 008

---

These can of course be replaced with

Quote:

---

001   C# 008

---

QBASIC equivalent of the first program:

DEFDBL A-Z

DEFINT D

DEF FNFRAC (NN) = NN - INT(NN)

CLS

INPUT N

P = 8

S = 0

DO

  N = 10 * N

  D = INT(N)

  P = P * 8

  S = 8 * (S + D)

  N = FNFRAC(N)

LOOP UNTIL N = 0

R = S / P

IF R > 1 THEN R = 1

PRINT R

? 0.11037552421

 .141592653584667

[Eric Smith]

My (non-winning) RPL entry was:

148 bytes (not including a global name)

« UNROT

   « { } SWAP 1 12 START

    10 DUP2 MOD UNROT / IP UNROT + SWAP

    NEXT DROP »

  ROT OVER EVAL UNROT EVAL

  ADD SWAP MOD REVLIST

  « SWAP 10 * + » STREAM

»

An earlier version used a logarithm to determine how many digits to use, but I made the tradeoff of assuming 12 digits for a slightly shorter program. Bill Butler's winning program is shorter than mine ever though it does compute the digit count with a logarithm.

Edited: 22 Sept 2013, 6:33 p.m.

[Eddie W. Shore]

My RPL entry was (didn't win, I got it down to 168.5 bytes) - HP 50g

<< 'N' STO 0 UNROT

DUP2 XPON SWAP XPON

MAX 1 + 1 SWAP FOR

K DUP2 K ALOG / FP

1 ALOG * IP SWAP K

ALOG / FP 1 ALOG *

IP + N MOD K 1 - ALOG

4 ROLL + UNROT NEXT

DROP2 { N K } PURGE >>

[Gerson W. Barbosa]

An RPL solution (HP 50g) to the RPN problem. The handling of 0 and 1 cases is left as an exercise to the reader.

%%HP: T(3)A(R)F(.);

\<< \->STR TAIL DUP SIZE SWAP "o" "# " ROT + SWAP + OBJ\-> B\->R 8. ROT ^ /

\>>


(63.5 bytes)


Input		Result			

0.5		0.625			

0.75		0.953125		

0.1		0.125			

0.777777777	0.9999999925494

Gerson.

[Paul Dale]

Does this handle 1e-50 ?

- Pauli

[Gerson W. Barbosa]

Only decimal numbers from 0.000000000001 through 0.777777777777, in this format only (the first zeroes may be omitted).

Gerson.

Edited: 22 Sept 2013, 11:04 p.m.

[Jim Horn]

I played with a few line non-iterated RPN approach which would use a built in octal to decimal conversion:
Multiply by 10^n (with n=number of digits for that calculator's precision)
convert that integer from octal to decimal
divide by 8^n
But, to my surprise, I don't see any RPN machines with base conversion except for display values only. So step 2 isn't available, even though the actual math is in many of them.

My congradulations to the winners - and all who submitted entries!

[Gerson W. Barbosa]

That's what I have in my HP-41C with the Advantage Module right now:

01  OCTIN

02  ENTER^

03  LN

04  8

05  LN

06  / 

07  1

08  +

09  INT

10  8

11  X<>Y

12  Y^X

13  /

        R/S 5 R/S  -->  0.625000000

       R/S 75 R/S  -->  0.953125000

R/S 777777777 R/S  -->  0.999999993

Obviously 0 and 1 are not possible here.

Gerson.

Edited: 23 Sept 2013, 12:33 p.m.

[Dieter]

I am always very careful with INT commands following transcendetal functions like the logarithm here. Unexpected behaviour may occur due to roundoff errors. Your program evaluates the base-8 log - which may cause such a problem:

  8 ENTER 7 yx

    => 2097152

  [LN]

    => 14,56609079     ; rounded down from ...79 17588 ...

  8 [LN]

    => 2,079441542     ; rounded up from ...41 67983 ...

  [/]

    => 6,999999998     ; so the quotient is below the true value

                         and INT(x) becomes 6 instead of 7

I do not know if this will also happen with the program you posted (my HP41 does not have an Advantage ROM, and I do not even know what exactly the OCTIN command does), but maybe you can try some integer powers of 8. If roundoff errors occur, using [LOG] instead of [LN] may give better results since lg 8 rounds much better to ten digits than ln 8.

Dieter

[Gerson W. Barbosa]

OCTIN allows for the input of integer octal constants. For instance:

keystrokes                               display    
            

XEQ ALPHA OCTIN ALPHA                      _ O

75301 ENTER^                             31425        ; 753018 = 3142510 

However a better program (better if DEC were not natively available) would be:

01  OCTIN

02  1073741824              ; 8^10

03  /

R/S 5000000000 R/S  -->  0.625000000

R/S 7500000000 R/S  -->  0.953125000

R/S 7777777770 R/S  -->  0.999999993   

R/3 7777777777 R/S  -->  0.999999999

Gerson.

Edited: 24 Sept 2013, 10:25 a.m.

[Paul Dale]

Isn't this the basis for the five step 41 program? Using the OCT and DEC functions?

If not, I'd like to know how they were done.

- Pauli

[Olivier De Smet]

You can have on HP41 (naked) and also on HP65 (but in 20 steps)

01 1E10

02 *

03 DEC

04 1073741824

05 /

But that's cheating as told previously

(to have 1 working, use 1E9 and 134217728)

Edited: 24 Sept 2013, 3:28 a.m. after one or more responses were posted

[Paul Dale]

Thanks, it is as I thought.

- Pauli

[Gerson W. Barbosa]

Quote:

---

But that's cheating as told previously

---

Why? Rule #4 says:

"No custom built ROM or machine code can be built and used for this problem. Any already existing functionality in the machine is ok."

I wasn't aware of that function, but DEC (octal to decimal conversion) is part of the HP-41 instruction set. So, that should be ok, except for the 1 case. Likewise, the equivalent HP-42S program should be ok too:

01 1E12

02 *

03 ->DEC

04 68719476736

05 /

[Gene Wright]

True, but that is why at the conference I had to put up some rule clarifications...such as

No base conversion functions allowed.

Wlodek came up with the large constant similar to what you indicated, but to keep things "fair" between machines, no base conversion functions were allowed.

We had entries for these machines:

HP 65 !

HP 29C

HP 41CX

HP 42S

WP 34S

HP 15c LE (by Bill Carter!) oops.

I especially like Egan's 12c approach. Fascinating! Wish you had been at the conference this year!

Thanks again all. I hope these problems were interesting.

Edited: 25 Sept 2013, 8:23 a.m. after one or more responses were posted

[Gerson W. Barbosa]

Quote:

---

at the conference I had to put up some rule clarifications...such as

No base conversion functions allowed.

---

Eric Smith said in another thread: "There was another rules clarification at the conference that no base conversion functions can be used." I'd forgotten about that, sorry!

Quote:

---

Wlodek came up with the large constant similar to what you indicated,

---

That's 8^12, as Jim Horn has suggested. I kind of found the trick but I dumbly used different constants, according to the number of significant digits rather than the machine's number of digits.

Quote:

---

I especially like Egan's 12c approach. Fascinating!

---

Really fascinating, as non-conventional approaches usually are!

Quote:

---

Wish you had been at the conference this year!

---

I visited a forum member last month and I asked him about going to the next year's conference. He told me his English was not good enough to fully enjoy it. I told him not to worry much about that, but on second thought I realize I would need to go at least one month in advance to get used to spoken language. I still watch American movies with English subtitles on :-)

Thanks again for the interesting problems. They have the right difficulty level, the real challenge being size (or speed) optimization.

Gerson.

[Paul Dale]

Programs using DEC or ->DEC aren't going to correctly deal with really small numbers in the [0, 1] interval. Try 1e-50 and see what happens.

Actually, they might be able to with some extra steps -- get the exponent via LOG and IP. Then use these to calculate the required constants instead of hard coding them. I suspect this will still be shorter than the digit by digit approaches.

- Pauli

Edited: 24 Sept 2013, 4:19 p.m.

[David Hayden]

Quote:

---

get the exponent via LOG and IP.

---

Or use EXPT and MANT to get the exponent and mantissa directly.

By the way, I noticed an inconsistency between the 34S manual and the software. On the last page of my manual (3.18 3242) it says that in version 3.0, "returned ->BIN, ->HEX, and ->OCT." These commands were removed in v2.1. But I can't find these commands in any of the menus or in the manual. Were they removed again?

Dave

[Paul Dale]

I don't remember what happened to these commands. I think we removed them because they didn't achieve anything useful -- it is easier to switch integer mode and switch back when done rather than introducing extra complexity in the display code. Walter might remember better.

I'm not sure I'd call this an inconsistency. These aren't documented in the command listing and the change log is known to not be totally complete and accurate. There have been a lot of changes and refinements and not everything made the last page.

- Pauli

[Bill Carter]

Gene-

No love at all for the 15c entrant? I'm not sure my wife really believes my account of where I was all weekend as it is!

-Bill

Edited: 25 Sept 2013, 12:05 a.m.

[Egan Ford]

Quote:

---

I especially like Egan's 12c approach.

---

Glad you liked it. When I read the challenge and given your financial background I had assumed you had NPV in mind.

Updated version that should support 0 through 7777777777 including fractional. I didn't have a lot of time to test or optimize it. Perhaps another day.

01 -    43 25  INTG        

02 - 44 48  1  STO .1      

03 -    43 35  x=0         

04 - 43,33 21  GTO 21      

05 -    43 36  LSTx        

06 -        1  1           

07 -        0  0           

08 -    43 36  LSTx        

09 -    43 23  LN          

10 -        1  1           

11 -        0  0           

12 -    43 23  LN          

13 -       10  /           

14 -    43 25  INTG        

15 -        1  1           

16 -       40  +           

17 - 44 48  1  STO .1      

18 -       21  y^x         

19 -       10  /           

20 -    43 25  INTG        

21 -    43 13  CFo         

22 -    43 36  LSTx        

23 -    43 35  x=0         

24 - 43,33 33  GTO 33      

25 -        1  1           

26 -        0  0           

27 -       20  x           

28 -       36  ENTER       

29 -    43 24  FRAC        

30 -       30  -           

31 -    43 14  CFj         

32 - 43,33 22  GTO 22      

33 -        7  7           

34 -        0  0           

35 -        0  0           

36 -       12  i           

37 -    42 13  NPV         

38 -        8  8           

39 - 45 48  1  RCL .1      

40 -       21  y^x         

41 -       20  x           

[Gerson W. Barbosa]

HP-15C version as of last Sunday:

001- g x=0

002- g RTN

003-   EEX

004-   9

005-   *

006-   STO RAN#

007- g LOG

009- g INT

009-   8

010-   -

011-   8

012-   x<>y

013-   y^x

014-   STO 1

015- g CLx

016-   STO 0

017-   RCL RAN#

018- f LBL 0

019-   1

020-   0

021-   *

022- g INT

023-   8

024-   STO/ 1

025-   x<>y

026-   RCL* 1

027-   STO+ 0

028- g LSTx

029- f FRAC

030- g TEST 0

031-   GTO 0

032-   RCL 0



 7777777777  -->  1073741823

    1234567  -->  342391.0000

3.110375524  -->  3.141592651

[Gerson W. Barbosa]

From my integer base conversion routine circa 1984, so some optimization is possible.

001- f LBL B		; define base

002-   STO .0

003- g LOG

004- g INT

005-   1

006-   +

007-   STO .1

008-   RCL .0

009- g RTN

010- f LBL E		; convert from decimal to defined base

011-   STO 1

012-   0

013-   STO I 

014-   STO 2

015- f LBL 4

016-   RCL 1

017- g INT

018-   RCL/ .0

019-   STO 1

020- f FRAC

021-   RCL* .0

022-   RCL I

023-   10^x

024-   *

025-   STO+ 2

026-   RCL .1

027-   STO+ I

028-   RCL 1

029-   GTO 4

030-   RCL 2

031- g RTN

8 GSB B  -->  8.000000000 	; octal base

    342391 GSB E  -->  1234567.000

1073741823 GSB E  -->  7777777778	; the last digit should be a 7

     25894 GSB E  -->  62446.00000

16 GSB B --> 16.00000000	; hexadecimal base

     99774 GSB E  -->  108051114	; 1.08.05.11.14, that is, 185BE

257 GSB B --> 257.0000000	; base 257

  12345678  GSB E  -->  186235169.0     ; 186.235.169257     

 123456789  GSB E  -->  7070043158      ; 7.070.043.158257          ; the last digit should be a 7

This is subject to rounding error for large inputs, as we can see from the examples. I used it mainly for decimal to hexadecimal conversions -- no problem in the short range I used. Someone ought to have told me there was something called HP-16C :-)

Edited: 25 Sept 2013, 6:12 p.m.

[cyrille de Brébisson]

Hello,

Here is some HP Prime code for both contests.
Both are solved in 1 line of code (plus declarations) and no loops (at least that meets the eye).

note: replace SigmaList byt he appropriate symbol

export RplProgContest(Base, X, Y)
begin
SigmaList(((makelist(ip(fp(X:=X/10)*10),C,1,12)+
makelist(ip(fp(Y:=Y/10)*10),C,1,12)) mod Base)*
{1,10,100,1000,10000,100000,..,100000000000});
end;

note, you can replace the {1,10..} by makelist(10^A,A,0,11), smaller, but slower

export RpnProgContest(X)
begin
SigmaList(makelist((ip(X) mod 10)*1/8^C + (0*(X:=X*10)),C,0,12));
end;

Cyrille

[Geoff Quickfall]

That's a heck of a single line of code Cyrille!

:-)

How are the renovations going?

Geoff

[Gerson W. Barbosa]

Quote:

---

export RpnProgContest(X) begin SigmaList(makelist((ip(X) mod 10)*1/8^C + (0*(X:=X*10)),C,0,12)); end;

---

Reminds me this can be done on the HP-17BII as well, in one line of code so to say:

0*L(X:X/10)+SIGMA(C:0:11:1:0*L(T:X)+L(X:(IP(10*X)))/8^C+0*L(X:FP(10*G(T))))=D

Gerson.

[David Hayden]

Over the past couple of days I've put together a solution to the RPL problem that takes a different approach. This converts the digits to binary and then does carry-free addition with bit twiddling.

At 281 bytes, it's huge, but because there are NO LOOPS it's very fast.

For base 2 you just XOR the numbers.

For base 8, you covert the octal digits as a hex number (e.g., 77. to #77h), thus there is one extra bit to the left of each octet. Now you can add the numbers and any carry goes into the extra bit, which is then masked out.

Base 10... oh you silly base 10.... As with base 8, I convert the digits in hex mode (e.g., 94. to #94h). So each digit occupies 4 bits. The trick is to add them while subtracting 10 from the sum in such a way that the sum is never greater than 15, which would cause it to spill over to the next digit's bits. If two digits are A and B, the code says "if A is greater than 5 then subtract 5 from it and add 5 to B. If B is now greater than 10 then subtract 10 from it. Now A is in the range [0..5] and B is [0..9], so you can add them and the result is [0..14] which still fits in 4 bits. If the sum is greater than 10 then subtract 10." All of this is done with bit manipulation on all digits simultaneously.

I may write this up in a Datafile article.

Replace the ">" characters with the right arrow. Sorry, I keep forgetting now to convert a listing to ascii. :(

«

    { { R>I >STR "#" SWAP + OBJ> }

      SWAP OVER EVAL UNROT EVAL  } @ You now have binaries with the same digits

    SWAP CASE

    DUP 2. == THEN

        @ This is easy. Convert to binary and XOR together

        BIN DROP EVAL

        XOR

    END

    DUP 8. == THEN

        HEX DROP EVAL

        ADD #7777777777777777h AND 

    END

    @ It better be 10

        HEX  DROP EVAL

        DUPDUP SL AND          @ a & (a<<1)

        OVER SR OR #4444444444444444h AND @ x.4 = a.8 | (a.4 & a.2)

        @ level 1 now contains 4 if a>5. subtract from a and add

        @ to b

        SWAP OVER -

        UNROT +

        @ b a

        { DUPDUP SL OR   @ b | (b<<1)

          SL OVER AND    @ b.8 & (b.4 | b.2)

          #8888888888888888h AND

          DUP SR SR OR

          -

        }

        SWAP OVER EVAL      @ sub10(b)

        @ b Sub10 a

        ROT +               @ a+b Sub10

        SWAP EVAL           @ here is the answer, but in hex

    END

    @ Level 1 contains a binary number reprenting the answer.

    @ convert the digits to a real.

    >STR

    DUP SIZE 1. - 2. SWAP SUB    @ take off the h

    OBJ>

»