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)

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)

Chen-Ho encoding

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

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

Yes, but what is it?

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

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

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)

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)

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)

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)

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

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

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)

Improve table for clarity

I don't know how to edit the table

Densely packed decimal encoding rules

DPD encoded value												Decimal digits
Code space (1024 states)	b9	b8	b7	b6	b5	b4	b3	b2	b1	b0		d2	d1	d0	Values encoded	Description	Occurrences (1000 states)
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.