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From: Ralf Fritzsch on 10 May 2010 07:44
Hi,

in 1999 Joe Horn posted an algorithm to convert any fraction to "Egyptian
Fractions", I just cite it here for reference:

-----
Input any fraction (e.g. '5/7') and this HP49G program will convert it
to a sum of integer reciprocals (called "Egyptian Fractions"). Be sure
exact mode is on for infinite precision. Sometimes the output is
surprising!

<< 0 SWAP
WHILE DUP FXND NIP 1 >
REPEAT DUP INV FXND IDIV2 SIGN + INV ROT OVER + UNROT - EVAL
END DROP
>>
BYTES: #8EF6h 84.0

Examples:
Input: 5/17
Output: 1/4 + 1/23 + 1/1564
EVAL: 5/17 (simplified back to the original value)

Input: 5/91
Output:
1/19 + 1/433 + 1/249553 + 1/93414800161 + 1/17452649778145716451681 (!!)
EVAL: 5/91

-Joe-

I tried it out, but unfortunately I only get ? as an answer :-(
I double-checked it via BYTES to be sure I made no typo, all was OK. Exact
mode was On, of course.


Any idea what I may have forgot?

TIA,
-------------------------------------------------------------------------
Ralf Fritzsch
Bundesanstalt fuer Wasserbau Federal Waterways Engineering and Research
Dienststelle Kueste Institute - Department Hamburg
-------------------------------------------------------------------------
Unix _IS_ user friendly - it's just selective about who its friends are.
-------------------------------------------------------------------------

From: Bart on 10 May 2010 12:52
On May 10, 12:44 pm, Ralf.Fritz...(a)T-Online.DE (Ralf Fritzsch) wrote:
> Hi,
>
> in 1999 Joe Horn posted an algorithm to convert any fraction to "Egyptian
> Fractions", I just cite it here for reference:
>
> -----
> Input any fraction (e.g. '5/7') and this HP49G program will convert it
> to a sum of integer reciprocals (called "Egyptian Fractions").  Be sure
> exact mode is on for infinite precision.  Sometimes the output is
> surprising!
>
> << 0 SWAP
>   WHILE DUP FXND NIP 1 >
>   REPEAT DUP INV FXND IDIV2 SIGN + INV ROT OVER + UNROT - EVAL
>   END DROP
>
> BYTES: #8EF6h 84.0
>
> Examples:
> Input: 5/17
> Output: 1/4 + 1/23 + 1/1564
> EVAL: 5/17 (simplified back to the original value)
>
> Input: 5/91
> Output:
> 1/19 + 1/433 + 1/249553 + 1/93414800161 + 1/17452649778145716451681 (!!)
> EVAL: 5/91
>
> -Joe-
>
> I tried it out, but unfortunately I only get ? as an answer :-(
> I double-checked it via BYTES to be sure I made no typo, all was OK. Exact
> mode was On, of course.
>
> Any idea what I may have forgot?
>
> TIA,
> -------------------------------------------------------------------------
> Ralf Fritzsch
> Bundesanstalt fuer Wasserbau   Federal Waterways Engineering and Research
> Dienststelle Kueste            Institute  -  Department Hamburg
> -------------------------------------------------------------------------
>  Unix _IS_ user friendly - it's just selective about who its friends are.
> -------------------------------------------------------------------------


Hmmm, at some point IDIV2 results in 0 and from the AUR: "In exact
mode, the sign for argument 0 is undefined (?)"

My workaround is:
<< 0 SWAP
WHILE DUP FXND NIP 1 >
REPEAT DUP INV FXND IDIV2 DUP
IF 0 <>
THEN SIGN
END + INV ROT OVER + UNROT - EVAL
END DROP >>

Note: replace the <> after the IF with the "not equal" sign (left
shift & +/- key)

BYTES: # 6B71h 109.5

Regards,
B

Regards,
Bart
From: Joe Horn on 10 May 2010 19:11
An alternative to Bart's workaround for the EGYPT bug is to replace
IDIV2 SIGN (in the original program) with IDIV2 NOT NOT. That will
either not work, or not not work.

-Joe-
From: Jim Horn on 11 May 2010 19:45
> Examples:
> Input: 5/17
> Output: 1/4 + 1/23 + 1/1564
> EVAL: 5/17 (simplified back to the original value)

Or 1/4 + 1/34 + 1/68.

> Input: 5/91
> Output:
> 1/19 + 1/433 + 1/249553 + 1/93414800161 + 1/17452649778145716451681 (!!)
> EVAL: 5/91

Or, you could use 1/28 + 1/52.

But I cheated and used the calculator at:
<http://www.maths.surrey.ac.uk/hosted-sites/R.Knott/Fractions/
egyptian.html>
which *doesn't* just use the greedy algorithm.

Jim
From: Ralf Fritzsch on 12 May 2010 05:51
In article <a96101d2-ccf2-49f5-ae27-bc9316588166(a)i9g2000yqi.googlegroups.com>, bart(a)barend.plus.com says...
>
>On May 10, 12:44=A0pm, Ralf.Fritz...(a)T-Online.DE (Ralf Fritzsch) wrote:
>> ...
>> in 1999 Joe Horn posted an algorithm to convert any fraction to "Egyptian
>> Fractions", I just cite it here for reference:
>> ...
>Hmmm, at some point IDIV2 results in 0 and from the AUR: "In exact
>mode, the sign for argument 0 is undefined (?)"
>
>My workaround is:
><< 0 SWAP
> WHILE DUP FXND NIP 1 >
> REPEAT DUP INV FXND IDIV2 DUP
> IF 0 <>
> THEN SIGN
> END + INV ROT OVER + UNROT - EVAL
> END DROP >>
>
>Note: replace the <> after the IF with the "not equal" sign (left
>shift & +/- key)
>
>BYTES: # 6B71h 109.5
>
>Regards,
>B
> ...

Thank you very much, dear Bart, for your workaround! Unfortunately I was too
dumb to get it done myself :-(

Kind regards,
-------------------------------------------------------------------------
Ralf Fritzsch
Bundesanstalt fuer Wasserbau Federal Waterways Engineering and Research
Dienststelle Kueste Institute - Department Hamburg
-------------------------------------------------------------------------
Unix _IS_ user friendly - it's just selective about who its friends are.
-------------------------------------------------------------------------

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