Wallace Tree Multiplication Rules

Amr Sabry's CNF generator page at Indiana U cites just a link to Chris Wallace' homepage before describing the Wallace-tree circuit:In the Wallace-tree circuit, the rows (with appropriate shifts) are added in groups of three to produce sums and carries. The sums and carries (with appropriate shifts) are again added in groups of three, and this is repeated until there is just one sum and one carry. Then a special adder is used to add the final sum and the final carry. The products from any row need go through only a logarithmic number of adders before they get to the special adder. (emphasis added)There is no mention of half-adders. This is consistent with Wallace' original paper, as Ruben noted.Half-adders seem to be a discretion of the circuit designer and (contrary to the Wikipedia text) must not be applied greedily.Jonathan D. explained the motivation for not using a greedy approach.Indiscriminately adding every group of 2 or 3 wires will unnecessarily increase the width of the final addition, and actually expend more gates prior to that (in the extra are ductions') just to do so.But this does not explain any rule or heuristic for choosing when to add a group, or when not.The Wiki illustration shows per-layer discrimination. For example, in the 3rd layer, the two groups of 3 wires on the left are given only a half-adder each, while in the next layer all groups of 3 wires are given full-adders:It would be useful to have a heuristic to generate a Wallace-tree with half-adders programmatically. I am not an engineer, so I do not know if the answer is obvious to engineers (?). But the closest I could devise produces a final result similar to the Wikipedia illustration.Apply the rules greedily whenever doing so does not increase the number of the wires of any weight whose number of wires is 1 or 2, unless:This yields different steps compared to the illustration, but the end result is similar:Example:Will update this if I can find a better rule.

1. GitHub repo tree generator

I see nothing wrong with the code itself, but you are in dire need of docstrings. Arcane functional one-liners like the one in intersperse are impenetrable unless they are well-documented. You would also benefit from splitting that one into multiple lines. For strings like this:consider rewriting your format call as an f-string; i.e

2. Need help with an Eucalyptus tree???!!!!?

Eucalyptus trees are notorious for dropping branches at the drop of a hat, for no apparent reason. It sounds like this has already happened to your tree in the past. You can try cutting off some of the uneven branches, but that is not necessary. For looks and health, you might only cut more of the branches shorter, instead of totally removing the 2-3 really uneven ones. I have a big eucalypt in one corner of my yard that was fairly symmetrical all around when we bought the house four years ago, but since then it's lost three major branches on one-and-a-half sides, and countless smaller branches. It now leans ever-so-slightly toward the lawn and house (too far away to crash through the roof, fortunately). We simply had the branches trimmed shorter on the house sides of the tree, and the new branches came in and looked terrific. But we had a professional team do the trimming: they have much better equipment. I can not really help you with the issue of bracing. I do know that you want to get those roots back underground ASAP. But the only tree-bracing I've ever witnessed was orchardists using wooden T-braces on fruit trees, which were much shorter than 20 feet tall. These folks used one or two T-braces per branch, and I think they made a point of setting the T up against a fork (of branches, or of branch-to-trunk). The other end went gouging into the ground around the tree. If you are in the US, you might consider calling your county extension service for advice. Or, if you live in a city, call whoever manages the public street-trees, and see if they can give you any advice. I hope this helps. Good luck! ************************************************ [edit] I am so sorry, MasterGardner, but I have to disagree with you about this one. I've followed your answers for a while now, and you generally give people very good advice. Any tree can be safely pruned whenever it's dormant (meaning, the sap is not actively running through the tree, though the tree is perfectly healthy). You do not want to wait until all the sap is enabling new growth at the branch tips (such as in spring, or a month after a heavy feeding) to trim the branches back heavily. Eucalyptus trees do not necessarily lose their leaves in winter (it depends on what type you have -- there are over 200 varieties), so Faerie S, judge for yourself whether your specimen is "dormant" enough to prune right now. The priorities are getting those roots back underground, and keeping the tree upright after that. Btw, Faerie S, are you and this tree in Australia (eucalyptus native homeland), or the US (where your country-tag, down below, says you are)? The seasons are so different for the two, and that has a lot to do with seasonal advice. Maybe telling us *generally* where you are would help us, yes? :-D

3. how old is oak tree 8 foot and 2 inches around of tree?

Not young. lol Sorry, some times I just can not help it. (Bad, bad sense of humor. lol) Okay, reality here - first, it really is not young. How old? Only way to know for sure is to cut it down and count the rings. But, I am assuming you like it and want it to hang around as long as possible. Two ways to learn something of your tree's history - 1. Ask previous owners if they planted it, remember how small it was back then, or know any of its history. I know "previous owners." Why would they care? Same reason you do. It's part of their history and memories, so they would not mind passing on that history to the next generation. 2. Find out how old that house is. Unknown? Nonsense. This is America, land of the paperwork. You got a house, you got a deed, that deed has been the deed to that house, since the house was built, and that deed is on file in a courthouse. Your local one. It might require going to it and even looking through dusty old boxes...unless, you are house is not all that old, and then computers are your friend. (Bad humor. Down boy! lol) Also, that still might not tell you how old. My Dad bought a piece of land and had a house built on it in IL. Funny place, IL. Prairie land - or, at least it used to be. So, trees are a big deal there. Ends up he had to buy each tree on that land at $600 a pop. (This was in 1970, so I would imagine even more now.) They actually would remove any tree (as in hack it down, not find a new location) he was unwilling to buy, and the land was a tiny piece of woods in a huge amount of corn fields in a development, so we were one of the few people in a large development who had trees older than 5 years old on our property. BUT, there is a hint in the trees Dad kept. The address was "Oak Drive," so guess what kind of trees we had? (Good guess, and watch that. My sense of humor is contagious. lol) I was shorter and younger back then. I was only 14 and 5' 5" tall (I grew taller and older. lol) But, as my memory tells me now (and my memory is married to my humor, so both have been warped for decades. lol) they were roughly the circumference of your tree. Your worry may well be the same worry my Dad had - how much longer before that tree dies of old age and lands in my house? He kept only the trees he was sure were "middle-aged" (for a tree.) He kept only the ones that would stay alive for another 30 years (about as long as he thought we might live in that house.) So, all this to tell you, your tree is neither ancient or young. I think you have a very good chance of being able to tell a little history about your house and that tree to the next owners, even if you decided to live there for another 30 years. BUT, if I am wrong, you can always get a tree surgeon to make sure that tree is healthy. (Good thing to do with all the trees on your property. Dad now lives on another wooded lot, and had all his old trees inspected. He found out 6 were dead, and 4 were ready to fall down. He had the four removed - and now has enough firewood to give his whole town firewood for a decaded - and had the other two removed a couple of years alter. If you do not watch out, they really can land on your house.) Do that, and he probably knows about how old it is. (Yes, I am long winded and with a sense of humor. Hope you did not mind the long winded for info and humor given. lol)