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	HAKMEM Computer Encyclopedia Enterprise Resource Directory Complete Guide to Internet (via CobWeb/3.1 ... (Site not responding. Last check: 2007-10-10)
		(The title of the memo really is "HAKMEM", which is a 6-letterism for "hacks memo".) Some of them are very useful techniques, powerful theorems, or interesting unsolved problems, but most fall into the category of mathematical and computer trivia.
		Here is a sampling of the entries (with authors), slightly paraphrased: Item 41 (Gene Salamin): There are exactly 23,000 prime numbers less than 2^18.
		HAKMEM also contains some rather more complicated mathematical and technical items, but these examples show some of its fun flavour.
	www.jaysir.com.cob-web.org:8888 /computer-encyclopedia/h/hakmem-computer-terms.htm (624 words)

	11011110: Counting nonzero bits
		Probably a lot of people know about the tricks in HAKMEM for counting the number of nonzero bits in a machine word.
		The HAKMEM trick is to realize that, as this doubling idea progresses, the numbers stored in each block are considerably smaller than the maximum value representable in the number of bits used by the block.
		The actual HAKMEM code uses a division rather than a multiplication but the idea is similar.
	11011110.livejournal.com /38861.html (691 words)

	HAKMEM 175
		Hakmem 175 is probably the most famous example of bit bashing.
		In just nine PDP-10 instructions in calculates the next higher number with the same number of 1 bits.
		Note that a renaming and reusing of variables in the original PDP-10 code yields a saving one of instruction (and one variable) over the Hakmem original:
	www.safalra.com /programming/bit-bashing/hakmem-175 (463 words)

	Dr Dave » Blog Archive » HAKMEM
		All these coins tossed a million times, checkmate combinations, statistics and game theory stuff reminded me of something I used to read with much more passion (back when I could still summon some sort of enthusiasm for math-related stuff): MIT AI Lab Memo 239 aka HAKMEM.
		The HAKMEM is a compilation of tips, tricks and riddles for the math and computer geek.
		Some of them are very outmoded (unless PDP-10 programming is your thing), but most are still entirely relevant (notably a handful of small theorems and empirical results, some of which still haven’t been proven to this day, afaik).
	unknowngenius.com /blog/archives/2004/09/06/hakmem (351 words)

	HAKMEM -- CONTENTS -- DRAFT, NOT YET PROOFED
		HAKMEM -- CONTENTS -- DRAFT, NOT YET PROOFED
		The goal of this 'html' document is to make HAKMEM available to the widest possible audience -- including those without bitmapped graphics browsers.
		Therefore, equations have been formatted to be readable even on ASCII browsers such as 'lynx'.
	www.inwap.com /pdp10/hbaker/hakmem/hakmem.html (486 words)

	Books Album: Free E-Books Collection. All are new books of latest edition (Site not responding. Last check: 2007-10-10)
		I also enjoyed, in that summer of 1972, reading a brand-new MIT research memo called HAKMEM, a bizarre and eclectic potpourri of technical trivia.
		We were used to glancing at a six-character abbreviated name and instantly decoding the contractions.
		So naming the memo "HAKMEM" made sense at the time—at least to the hackers.
	www.booksalbum.com /Books/Book3/index.asp?FileName=002.htm (487 words)

	Appendix:sample texts
		Most of this memo, and all of the page 35 appears to have been printed with a Courier typeface Selectric (tm) typeball, with a few math and superscript symbols from a Symbol typeball.
		One way to start is to see what the most common size of an enclosing box is: If we find that (statistical) mode of the width of a box is a reliable statistic, we can use that as an estimate of the width of a character.
		For hakmem page35, the mode of the width is 22, the height is 23.
	www.cs.berkeley.edu /~fateman/kathey/node15.html (725 words)

	Citations: Technical Report HAKMEM Item 101B - Gosper, Arithmetic (ResearchIndex) (Site not responding. Last check: 2007-10-10)
		The four most basic arithmetic operations can be represented as follows: T add (x; y) 0 1 1 0 0 0 0 1 (x; y) x y T sub (x; y) 0 1 Gamma1 0 0 0 0 1 (x; y)....
		Consider a general 2 dimensional lft t a c e g b d f h (x; y) axy cx ey g bxy dx fy h (141) Clearly, we can define all four basic arithmetic operations by t 0 1 0 0 1 0 0 1 (x; y) x y....
		In the early and mid 90 s Di Gianantonio [5, 6] and Escard o [12] studied extensions of the theoretical language PCF with a real number data type based....
	citeseer.ist.psu.edu /context/743388/0 (1894 words)

	computation with exact real numbers by continued fractions
		In HAKMEM items 97-101, available at among other places, Bill Gosper talks about doing exact numerical computations with regular continued fractions.
		I don't know if his methods are extensible to operations other than arithmetic, although I can't imagine why anyone would care about them if they weren't.
		(Arithmetic can be done nicely with rational numbers, and the only normal way to get nonrational numbers is through non-arithmetic functions on rational numbers.) He says that Gosper used 2-dimensional Moebius transformations in the HAKMEM item, and describes what that means, at .
	lists.canonical.org /pipermail/kragen-fw/1999-February/000095.html (583 words)

	[No title] (Site not responding. Last check: 2007-10-10)
		Newsgroups: sci.math From: dtd@world.std.com (don davis) Subject: Re: Continued Fractions Date: Wed, 13 Jan 1999 22:49:13 GMT Keywords: HAKMEM Algorithms for dealing with arithmetic with continued fractions In article
		one of the contributors to HAKMEM (gosper himself?) presented a set of recursive algorithms for continued- fraction arithmetic.
		HAKMEM is a mid-70's archive of a small intradepartmental mailing list at MIT's AI Lab.
	www.math.niu.edu /~rusin/known-math/99/contfrac_hak (105 words)

	Bill Gosper - Wikipedia, the free encyclopedia
		After taking a course on programming in his second year with John McCarthy, Gosper became affiliated with the MIT AI Lab.
		His contributions to computational mathematics include HAKMEM [1] and the MIT Maclisp system.
		He also made major contributions to the Macsyma computer algebra system at MIT, later working with Symbolics and Macsyma, Inc. on the greatly improved commercial versions.
	en.wikipedia.org /wiki/Bill_Gosper (315 words)

	Comp.compilers: Re: HAKMEM #169
		I think that it would be fairer to let HAKMEM speak for itself.
		If anyone is interested, the whole HAKMEM is available online at:
		Below is the actual text of HAKMEM 169.
	compilers.iecc.com /comparch/article/95-07-080 (127 words)

	Comp.compilers: HAKMEM #169
		> * This is HAKMEM 169, as used in X11 sources.
		be loaded with optimizations tuned for code like what is in hakmem (and, in
		beat hakmem by a wide margin, and the only difference between the two was the
	compilers.iecc.com /comparch/article/95-07-065 (591 words)

	Technical Interview Questions » Bit Count: Parallel Counting - MIT HAKMEM (Site not responding. Last check: 2007-10-10)
		Technical Interview Questions » Bit Count: Parallel Counting - MIT HAKMEM
		HAKMEM (Hacks Memo) is a legendary collection of neat mathematical and programming hacks contributed mostly by people at MIT and some elsewhere.
		This source is from the MIT AI LABS and this brilliant piece of code orginally in assembly was probably conceived in the late 70’s.
	www.tekpool.com /?p=6 (1008 words)

	HAKMEM
		, FOLDOC/Jargon's entry for HAKMEM as well as their entries on PDP, PDP-10, and PDP-11.
		From: gkn@ucsd.Edu (Gerard K. Newman) Newsgroups: alt.folklore.computers Subject: HAKMEM (well, the pieces I have anyway) Keywords: HAKMEM, PDP-10 Message-ID: <18495@ucsd.Edu> Date: 6 Sep 90 16:01:18 GMT Organization: San Diego Supercomputer Center
		I got 8 requests for HAKMEM in a period of about 36 hours, so I decided to go ahead and post it.
	interglacial.com /~sburke/stuff/hakmem.html (3298 words)

	1d design
		(I think I first saw this divide-by-3 idea in HAKMEM ITEM 14 -- that code is shorter and recursive.
		HAKMEM has a section on continued fraction arithmetic and (in ITEM 97 (Schroeppel)) mentioned that ``sqrt(7) is hairy''.
		HAKMEM has a section on continued fraction arithmetic http://www.jjj.de/hakmem/cf.html
	david.carybros.com /html/1d_design.html (11706 words)

	PDP System Architecture.
		Re: HAKMEM (well, the pieces I have anyway)
		Subject: Re: HAKMEM (well, the pieces I have anyway)
		The PDP-6 is the first model of PDP-10.
	interglacial.com /~sburke/stuff/dec10as.html (495 words)

	HAKMEM?
		Hello, Lately, after reading the messages from "Mr Terse" and last nights wonderful numeric anecdote, I was wondering if you all; Dan Ingals, Ted Kaehler, et al; had ever considered writing up a paper of just those kinds of tidbits for us less enlightened folks.
		Sort of like the AI Lab's (in?)famous Hakmem?
		Maybe include some of the historical bits that have been discussed recently, too?
	lists.squeakfoundation.org /pipermail/squeak-dev/1998-July/013760.html (225 words)

	misc docs and postings
		It contained an amazing, and amazingly random, collection of stuff.
		Articles in hakmem spanned an unbelievable range of topics from simple display hacks, to mathematical riddles, questions, theorems and games, to schematics for building RF receivers and transmitters.
		online version of HAKMEM is now available (and be assured, it's vastly more interesting than my collection!)
	efault.net /npat/docs_and_postings/index.html (1250 words)

	HAKMEM /hak'mem/ n. MIT AI Memo 239 (February 1972). A legendary collection of neat mathematical and programming hacks
		memo really is "HAKMEM", which is a 6-letterism for `hacks
		Note: This last item refers to a Dissociated Press
		HAKMEM also contains some rather more complicated mathematical and
	www.anvari.org /fortune/Jargon_File/13399.html (506 words)

	Ugh (Site not responding. Last check: 2007-10-10)
		Unless otherwise stated, all original content on this site is licensed under your choice of the
		I can't think of any activity more edifying than pondering an entry in HAKMEM, coding things up here and there, and proving a lemma.
		If you haven't seen this document before, you're in for a real treat!
	www.upl.cs.wisc.edu /~bethenco/hakmem.html (427 words)

	The On-Line Encyclopedia of Integer Sequences
		Institute of Technology Artificial Intelligence Laboratory, Memo AIM-239, Item 122, Feb. 1972.
		Beeler, M., Gosper, R. and Schroeppel, R., HAKMEM, ITEM 122
		E. Weisstein, Link to a section of The World of Mathematics.
	www.research.att.com /~njas/sequences/A014572 (84 words)

	The Geometry Junkyard: Dissection
		It contains the fascinating observation that there should exist a dissection that combines pieces from a dodecahedron, icosahedron, and icosidodecahedron to form a single large cube.
		Henry Baker's hypertext version of HAKMEM includes a dissection of square and hexagon, depicted below.
		How many smaller cubes can one divide a cube into?
	www.ics.uci.edu /~eppstein/junkyard/dissect.html (1012 words)

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