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Unless I'm missing something, I believe the notation (at least for
addition, I have not looked at the subtraction) can be made even lighter
(easier on the eyes), and possibly more portable, by using . instead of
\d notation, since the semicolons are literally specified and removed in
step #2.
s/(..)/\1;9876543210;9876543210/
s/(.)(.);.*\1(.*);(.*(\2.*))/\3\5\4/
s/.{10}(.).{0,9}(.{0,1}).*/0\1\2/
s/0.(.)/1\1/
I figured out a few examples, and here is the best I can make of it:
for adding 0 and 0, using 9876543210 lookup table:
step 1 - transform into ab;9876543210;9876543210 -> 00;9876543210;9876543210
step 2 - transform into segment a long, followed by segment b + 1 long,
followed by ye old lookup table -> 09876543210
step 3 - a miracle occurs -> 00
step 4 - carry one over, and discard garbage, if needed -> 00
for adding 3 and 6, using 9876543210 lookup table:
step 1 - transform into ab;9876543210;9876543210 -> 36;9876543210;9876543210
step 2 - transform into segment a long, followed by segment b + 1 long,
followed by ye old lookup table -> 21065432109876543210
step 3 - a miracle occurs -> 09
step 4 - carry one over, and discard garbage, if needed -> 09
for adding 6 and 7, using 9876543210 lookup table:
step 1 - transform into ab;9876543210;9876543210 -> 67;9876543210;9876543210
step 2 - transform into segment a long, followed by segment b + 1 long,
followed by ye old lookup table -> 543210765432109876543210
step 3 - a miracle occurs -> 033
step 4 - carry one over, and discard garbage, if needed -> 13
for adding 9 and 9, using 9876543210 lookup table:
step 1 - transform into ab;9876543210;9876543210 -> 99;9876543210;9876543210
step 2 - transform into segment a long, followed by segment b + 1 long,
followed by ye old lookup table -> 87654321098765432109876543210
step 3 - a miracle occurs -> 088
step 4 - carry one over, and discard garbage, if needed -> 18
I may be mistaken in my use of the word "garbage", but since it gets
discarded, that's what it seemed like.
I found some of the explanation, for example under "Shifting indexes"
and "Notations" very hard (for me) to understand, probably just me.
Thanks for sharing all this, I think it's very impressive.
Daniel
On 11/27/2018 11:46 AM, Gilles Arcas [email protected]
[sed-users] wrote:
>
> Hi, I have always been intrigued and fascinated by the addition and subtraction in Greg Ubben's dc. The most amazing is that both operations differ only in the order of the sequences of digits they used (0123456789 or 9876543210).
>
> I have written a details analysis of the construction and working of these snippets here https://github.com/GillesArcas/numsed/blob/master/analysis/Adding_and_subtracting_digits_with_sed.md .
>
> The working can be illustrated with the following picture. Two first columns illustrate two variants for addition, two last are for subtraction.
>
> [addsub.jpg]
>
> Regards.
> Gilles Arcas
>
>
> [Non-text portions of this message have been removed]
>
>
>
> ------------------------------------
> Posted by: Gilles Arcas <[email protected]>
> ------------------------------------
>
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<p>Unless I'm missing something, I believe the notation (at least for <br>
addition, I have not looked at the subtraction) can be made even lighter <br>
(easier on the eyes), and possibly more portable, by using . instead of <br>
\d notation, since the semicolons are literally specified and removed in <br>
step #2.<br>
<br>
s/(..)/\1;9876543210;9876543210/<br>
s/(.)(.);.*\1(.*);(.*(\2.*))/\3\5\4/<br>
s/.{10}(.).{0,9}(.{0,1}).*/0\1\2/<br>
s/0.(.)/1\1/<br>
<br>
I figured out a few examples, and here is the best I can make of it:<br>
<br>
for adding 0 and 0, using 9876543210 lookup table:<br>
<br>
step 1 - transform into ab;9876543210;9876543210 -> 00;9876543210;9876543210<br>
step 2 - transform into segment a long, followed by segment b + 1 long, <br>
followed by ye old lookup table -> 09876543210<br>
step 3 - a miracle occurs -> 00<br>
step 4 - carry one over, and discard garbage, if needed -> 00<br>
<br>
for adding 3 and 6, using 9876543210 lookup table:<br>
<br>
step 1 - transform into ab;9876543210;9876543210 -> 36;9876543210;9876543210<br>
step 2 - transform into segment a long, followed by segment b + 1 long, <br>
followed by ye old lookup table -> 21065432109876543210<br>
step 3 - a miracle occurs -> 09<br>
step 4 - carry one over, and discard garbage, if needed -> 09<br>
<br>
for adding 6 and 7, using 9876543210 lookup table:<br>
<br>
step 1 - transform into ab;9876543210;9876543210 -> 67;9876543210;9876543210<br>
step 2 - transform into segment a long, followed by segment b + 1 long, <br>
followed by ye old lookup table -> 543210765432109876543210<br>
step 3 - a miracle occurs -> 033<br>
step 4 - carry one over, and discard garbage, if needed -> 13<br>
<br>
for adding 9 and 9, using 9876543210 lookup table:<br>
<br>
step 1 - transform into ab;9876543210;9876543210 -> 99;9876543210;9876543210<br>
step 2 - transform into segment a long, followed by segment b + 1 long, <br>
followed by ye old lookup table -> 87654321098765432109876543210<br>
step 3 - a miracle occurs -> 088<br>
step 4 - carry one over, and discard garbage, if needed -> 18<br>
<br>
I may be mistaken in my use of the word "garbage", but since it gets <br>
discarded, that's what it seemed like.<br>
<br>
I found some of the explanation, for example under "Shifting indexes" <br>
and "Notations" very hard (for me) to understand, probably just me. <br>
Thanks for sharing all this, I think it's very impressive.<br>
<br>
Daniel<br>
<br>
On 11/27/2018 11:46 AM, Gilles Arcas [email protected] <br>
[sed-users] wrote:<br>
><br>
> Hi, I have always been intrigued and fascinated by the addition and subtraction in Greg Ubben's dc. The most amazing is that both operations differ only in the order of the sequences of digits they used (0123456789 or 9876543210).<br>
><br>
> I have written a details analysis of the construction and working of these snippets here https://github.com/GillesArcas/numsed/blob/master/analysis/Adding_and_subtracting_digits_with_sed.md .<br>
><br>
> The working can be illustrated with the following picture. Two first columns illustrate two variants for addition, two last are for subtraction.<br>
><br>
> [addsub.jpg]<br>
><br>
> Regards.<br>
> Gilles Arcas<br>
><br>
><br>
> [Non-text portions of this message have been removed]<br>
><br>
><br>
><br>
> ------------------------------------<br>
> Posted by: Gilles Arcas <[email protected]><br>
> ------------------------------------<br>
><br>
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#ygrp-actbar div a:first-child {
/* border-right: 0px solid #000;*/
margin-right: 2px;
padding-right: 5px;
}
#ygrp-mlmsg {
font-size: 13px;
font-family: Arial, helvetica,clean, sans-serif;
*font-size: small;
*font: x-small;
}
#ygrp-mlmsg table {
font-size: inherit;
font: 100%;
}
#ygrp-mlmsg select, input, textarea {
font: 99% Arial, Helvetica, clean, sans-serif;
}
#ygrp-mlmsg pre, code {
font:115% monospace;
*font-size:100%;
}
#ygrp-mlmsg * {
line-height: 1.22em;
}
#ygrp-mlmsg #logo {
padding-bottom: 10px;
}
#ygrp-msg p a {
font-family: Verdana;
}
#ygrp-msg p#attach-count span {
color: #1E66AE;
font-weight: 700;
}
#ygrp-reco #reco-head {
color: #ff7900;
font-weight: 700;
}
#ygrp-reco {
margin-bottom: 20px;
padding: 0px;
}
#ygrp-sponsor #ov li a {
font-size: 130%;
text-decoration: none;
}
#ygrp-sponsor #ov li {
font-size: 77%;
list-style-type: square;
padding: 6px 0;
}
#ygrp-sponsor #ov ul {
margin: 0;
padding: 0 0 0 8px;
}
#ygrp-text {
font-family: Georgia;
}
#ygrp-text p {
margin: 0 0 1em 0;
}
#ygrp-text tt {
font-size: 120%;
}
#ygrp-vital ul li:last-child {
border-right: none !important;
}
-->
</style>
</head>
<!--~-|**|PrettyHtmlEnd|**|-~-->
</html>
<!-- end group email -->
--n-pd78LABkelNGZIcmucrwO75tPAloTYmGAtPW3--