Talk:Densely packed decimal

Cryptic Sentence

The proper way to parse this sentence isn't obvious to me. Could someone clarify? "For example, 38=12×3+2 decimal digits can be encoded in 12×10+7=127 bits." Sumguysr (talk) 07:34, 23 December 2011 (UTC)[reply]

12 sets of three decimal digits can be encoded using 12 sets of 10 binary bits. The remaining two decimal digits can be encoded using 7 binary bits. I'll add that to the article. mfc (talk) 15:30, 31 December 2011 (UTC)[reply]

Chen-Ho encoding

Shouldn't the Chen-Ho encoding for 009 be 110 000 0001? --Wm243 (talk) 12:48, 17 April 2009 (UTC)[reply]

Indeed it should -- well spotted. (Fixed.) mfc (talk) 15:05, 17 April 2009 (UTC)[reply]

Yes, but what is it?

The article should explain how the scheme actually works. Superm401 - Talk 15:25, 11 November 2007 (UTC)[reply]

You're probably right. Suggestions? mfc 15:52, 15 November 2007 (UTC)[reply]

Copyright

I also just realized many parts are identical to the original paper (http://speleotrove.com/decimal/DPDecimal.html), which says it's copyrighted by IBM. Superm401 - Talk 15:34, 11 November 2007 (UTC)[reply]

See the history of the page; I contributed the initial text for this page (on request), and I am also the author of the referenced paper and summary page and so it is my copyright. It is quite likely I used similar or identical words in the two places. IBM has the use of the text, too, as does Wikipedia, but not exclusively. mfc 15:51, 15 November 2007 (UTC)[reply]

Uses for the 24 redundant codes

Possible uses for the 24 redundant codes.

HIGH-VALUES: Not useful for arithmetic, but useful for sorting and for the initial value of "min".
LOW-VALUES: Like HIGH-VALUES, but a better initial value for "max".
+INFINITY: Note: HIGH-VALUES > +INFINITY
-INFINITY: Note: LOW-VALUES < -INFINITY
-0: "Negative zero", useful for meteorologists, is slightly less than 0, i.e., 0 - epsilon
+0: Slightly more than 0, i.e., 0 + epsilon. For symmetry with -0. The canonical zero can then be "exactly zero" which will kill the "numberness" of 1/x and ln x, etc.
NaN: Not a Number.
NaDPD: Not a Densely Packed Decimal. Unicode has demonstrated the value of a "not one of mine" code, hasn't it? It can serve as a separator, for example. 111 111 1 111 would be quite suitable.

ROUND-UP: Not so much a value as a flag for the DPD ALU (arithmetic-logic unit).
ROUND-DOWN: ditto
ROUND-TO-ZERO: ditto
ROUND-TO-EVEN: ditto
ROUND-TO-ODD: ditto
ROUNDING: A query to the PDP ALU to report its rounding mode with one of the codes above. E.g.
dpd old_rounding = 0 + ROUNDING; dpd new_rounding = 0 + ROUND-UP;

111 111 1 111 NaDCD
111 111 1 110 NaN
...

mjk (talk) 22:50, 25 March 2008 (UTC)[reply]

OK, on further thought, it is strange to have negative values for a representation that is predestined for a sign-magnitude implementation. So forget about -INFINITY, +0, -0, and add:

EPSILON: which can be used by meteorologists, etc. with a sign, EPSILON replacing +0 and -EPSILON replacing -0.
CR: to explicitly indicate non-negatives, or "credits".
DB: to explicitly indicate negatives, or "debits".

mjk (talk) 13:03, 30 April 2008 (UTC)[reply]

Most applications won't use DPD for anything special beyond encoding decimal numbers. 24691358r (talk) 13:23, 20 May 2017 (UTC)[reply]

Let alone all of your suggested codes. 202.79.134.100 (talk) 08:42, 13 March 2018 (UTC)[reply]

Other bases

It's possible to have a similar system for other bases, for example storing 5 Ternary numeral system in a byte (3⁵=243 on 2⁸=256), as shown below:

000xxxxx — xxxxx 0010xxxx — xxxx2 0011xxxx — xxx2x 0100xxxx — xx2xx 0101xxxx — x2xxx 0110xxxx — 2xxxx 01110xxx — xxx22 01111xxx — xx2x2 10000xxx — xx22x 10001xxx — x2xx2 10010xxx — x2x2x 10011xxx — x22xx 10100xxx — 2xxx2 10101xxx — 2xx2x 10110xxx — 2x2xx 10111xxx — 22xxx 110000xx — xx222 110001xx — x2x22 110010xx — x22x2 110011xx — x222x 110100xx — 2xx22 110101xx — 2x2x2 110110xx — 2x22x 110111xx — 22xx2 111000xx — 22x2x 111001xx — 222xx 1110100x — x2222 1110101x — 2x222 1110110x — 22x22 1110111x — 222x2 1111000x — 2222x 11110010 — 22222

where x means 0 or 1. Uses are for example densely storing an uncompressed 3–color image. 202.79.134.100 (talk) 08:42, 13 March 2018 (UTC)[reply]

Improve table for clarity

I don't know how to edit the table

Densely packed decimal encoding rules^[1]
Code space (1024 states)	b9	b8	b7	b6	b5	b4	b3	b2	b1	b0	d2	d1	d0	Values encoded	Description	Occurrences (1000 states)
DPD encoded value											Decimal digits
50.0% (512 states)	a	b	c	d	e	f	0	g	h	i	0abc	0def	0ghi	(0–7) (0–7) (0–7)	3 small digits	51.2% (512 states)
37.5% (384 states)	a	b	c	d	e	f	1	0	0	i	0abc	0def	100i	(0–7) (0–7) (8–9)	2 small digits, 1 large digit	38.4% (384 states)
	a	b	c	g	h	f	1	0	1	i	0abc	100f	0ghi	(0–7) (8–9) (0–7)
	g	h	c	d	e	f	1	1	0	i	100c	0def	0ghi	(8–9) (0–7) (0–7)
9.375% (96 states)	g	h	c	0	0	f	1	1	1	i	100c	100f	0ghi	(8–9) (8–9) (0–7)	1 small digit, 2 large digits	9.6% (96 states)
	d	e	c	0	1	f	1	1	1	i	100c	0def	100i	(8–9) (0–7) (8–9)
	a	b	c	1	0	f	1	1	1	i	0abc	100f	100i	(0–7) (8–9) (8–9)
3.125% (32 states, 8 used)	x	x	c	1	1	f	1	1	1	i	100c	100f	100i	(8–9) (8–9) (8–9)	3 large digits, b9, b8: don't care	0.8% (8 states)

That table could be more easy to read if the last column had the observation that a b3=0, b3=1 and b2b1<11 for just one 9-8 digit, b3=1 and b2b1=11 and b6b5<11 for two 9-8 digits, and b3=1 and b2b1=11 and b6b5=11 for three 9-8 digits.

something like:

$b_{3}=0\Rightarrow {\text{all the }}d_{3},d_{2},d_{1}{\text{ are }}<8$ $b_{3}=1\land b_{2}b_{1}<11\Rightarrow {\text{ just one }}d_{3},d_{2},d_{1}{\text{ is }}\geq 8$ $b_{3}=1\land b_{2}b_{1}=11\land b_{6}b_{5}<11\Rightarrow {\text{ just two of }}d_{3},d_{2},d_{1}{\text{ are }}<8$ $b_{3}=1\land b_{2}b_{1}=11\land b_{6}b_{5}=11\Rightarrow {\text{ all three }}d_{3},d_{2},d_{1}{\text{ are }}\geq 8$

or

$b_{3}b_{2}b_{1}=0xx\Rightarrow {\text{all the }}d_{3},d_{2},d_{1}{\text{ are }}<8$ $b_{3}=1\land b_{2}b_{1}<11\Rightarrow {\text{ just one }}d_{3},d_{2},d_{1}{\text{ is }}\geq 8$ $b_{3}b_{2}b_{1}=111\land b_{6}b_{5}<11\Rightarrow {\text{ just two of }}d_{3},d_{2},d_{1}{\text{ are }}<8$ $b_{3}b_{2}b_{1}=111\land b_{6}b_{5}=11\Rightarrow {\text{ all three }}d_{3},d_{2},d_{1}{\text{ are }}\geq 8$

not all the lengthly text, maybe just the antecedent of the implication is needed.

Colors may also help. Is just a matter to do the changes to see what is visually more clear and aesthetic.

References

^ Cowlishaw, Michael Frederic (2007-02-13) [2000-10-03]. "A Summary of Densely Packed Decimal encoding". IBM. Archived from the original on 2015-09-24. Retrieved 2016-02-07.

-- (unsigned) 2018-09-15T10:56:20‎ 2806:107e:c:f09:218:deff:fe2b:121

[Cowlishaw_2000-1] Cowlishaw, Michael Frederic (2007-02-13) [2000-10-03]. "A Summary of Densely Packed Decimal encoding". IBM. Archived from the original on 2015-09-24. Retrieved 2016-02-07.

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