Re: [math-fun] reversing the order of bits in a word
Given Intel's close relationship with un-named agencies, how do you know that bit reverse, and a lot of other instructions, aren't already "standard" (but whose existence is classified) ? So long as an instruction doesn't require new datapaths, it would be nearly impossible to notice its existence in a chip mask. The existence of the AES instruction is an obvious (unclassified) example of this type of extension. http://en.wikipedia.org/wiki/AES_instruction_set There are companies that can reverse engineer chips by shaving them layer by layer, and eventually reconstruct their netlists. But this may be quite difficult at the bleeding edge of the latest technologies. It may well be that there are a number of Snowden disclosures that appear so bizarre that the journalists can't figure out what they mean; references to obscure instructions might well fall into this class. At 02:03 PM 3/28/2014, Eugene Salamin wrote:
Due to it's utility in FFT, I'm surprised that bit reverse is not a standard instruction.
This video raises the question: what are all the "circle crystals," i.e., 3D "lattices" of identical circles with each contacting n equally spaced neighbors, all with the same twist angle (as seen along a line connecting two centers and the point of contact). (Roughly: the symmetry group acts transitively on the circles.) https://www.youtube.com/watch?v=_XfwgngPrhE Three 2D cases, one 1D continuous family, and two interesting 3D cases are shown. Are there any other discrete examples I missed? Is there a succinct proof of completeness? Are there others that deserve to be physically constructed? George http://georgehart.com/
Great project, nice video. If you don’t make mistakes, then pop rivets would be a much easier, faster, and most stable assembly technique than screws and nuts. On Mar 30, 2014, at 8:31 PM, George Hart <george@georgehart.com> wrote:
This video raises the question: what are all the "circle crystals," i.e., 3D "lattices" of identical circles with each contacting n equally spaced neighbors, all with the same twist angle (as seen along a line connecting two centers and the point of contact). (Roughly: the symmetry group acts transitively on the circles.)
https://www.youtube.com/watch?v=_XfwgngPrhE
Three 2D cases, one 1D continuous family, and two interesting 3D cases are shown. Are there any other discrete examples I missed? Is there a succinct proof of completeness? Are there others that deserve to be physically constructed?
George http://georgehart.com/
_______________________________________________ math-fun mailing list math-fun@mailman.xmission.com http://mailman.xmission.com/cgi-bin/mailman/listinfo/math-fun
participants (3)
-
George Hart -
Henry Baker -
Tom Knight