hakmem
2 definitions found
hakmem - Free On-line Dictionary of Computing (26 May 2007) :
HAKMEM
<publication> /hak'mem/ MIT AI Memo 239 (February 1972). A
legendary collection of neat mathematical and programming
hacks contributed by many people at MIT and elsewhere. (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.
Item 46 (Rich Schroeppel): The most *probable* suit
distribution in bridge hands is 4-4-3-2, as compared to
4-3-3-3, which is the most *evenly* distributed. This is
because the world likes to have unequal numbers: a
thermodynamic effect saying things will not be in the state of
lowest energy, but in the state of lowest disordered energy.
Item 81 (Rich Schroeppel): Count the magic squares of order 5
(that is, all the 5-by-5 arrangements of the numbers from 1 to
25 such that all rows, columns, and diagonals add up to the
same number). There are about 320 million, not counting those
that differ only by rotation and reflection.
Item 154 (Bill Gosper): The myth that any given programming
language is machine independent is easily exploded by
computing the sum of powers of 2. If the result loops with
period = 1 with sign +, you are on a sign-magnitude machine.
If the result loops with period = 1 at -1, you are on a
twos-complement machine. If the result loops with period
greater than 1, including the beginning, you are on a
ones-complement machine. If the result loops with period
greater than 1, not including the beginning, your machine
isn't binary - the pattern should tell you the base. If you
run out of memory, you are on a string or bignum system. If
arithmetic overflow is a fatal error, some fascist pig with a
read-only mind is trying to enforce machine independence. But
the very ability to trap overflow is machine dependent. By
this strategy, consider the universe, or, more precisely,
algebra: Let X = the sum of many powers of 2 = ...111111 (base
2). Now add X to itself: X + X = ...111110. Thus, 2X = X -
1, so X = -1. Therefore algebra is run on a machine (the
universe) that is two's-complement.
Item 174 (Bill Gosper and Stuart Nelson): 21963283741 is the
only number such that if you represent it on the PDP-10 as
both an integer and a floating-point number, the bit
patterns of the two representations are identical.
Item 176 (Gosper): The "banana phenomenon" was encountered
when processing a character string by taking the last 3
letters typed out, searching for a random occurrence of that
sequence in the text, taking the letter following that
occurrence, typing it out, and iterating. This ensures that
every 4-letter string output occurs in the original. The
program typed BANANANANANANANA.... We note an ambiguity in
the phrase, "the Nth occurrence of." In one sense, there are
five 00's in 0000000000; in another, there are nine. The
editing program TECO finds five. Thus it finds only the first
ANA in BANANA, and is thus obligated to type N next. By
Murphy's Law, there is but one NAN, thus forcing A, and thus a
loop. An option to find overlapped instances would be useful,
although it would require backing up N - 1 characters before
seeking the next N-character string.
Note: This last item refers to a Dissociated Press
implementation. See also banana problem.
HAKMEM also contains some rather more complicated mathematical
and technical items, but these examples show some of its fun
flavour.
HAKMEM is available from MIT Publications as a TIFF file.
(ftp://ftp.netcom.com/pub/hb/hbaker).
(1996-01-19)
hakmem - Jargon File (4.4.4, 14 Aug 2003) :
HAKMEM
/hak'mem/, n.
MIT AI Memo 239 (February 1972). A legendary collection of neat
mathematical and programming hacks contributed by many people at MIT
and elsewhere. (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.
Item 46 (Rich Schroeppel): The most probable suit distribution in
bridge hands is 4-4-3-2, as compared to 4-3-3-3, which is the most
evenly distributed. This is because the world likes to have unequal
numbers: a thermodynamic effect saying things will not be in the
state
of lowest energy, but in the state of lowest disordered energy.
Item 81 (Rich Schroeppel): Count the magic squares of order 5 (that
is, all the 5-by-5 arrangements of the numbers from 1 to 25 such that
all rows, columns, and diagonals add up to the same number). There
are
about 320 million, not counting those that differ only by rotation
and
reflection.
Item 154 (Bill Gosper): The myth that any given programming language
is machine independent is easily exploded by computing the sum of
powers of 2. If the result loops with period = 1 with sign +, you are
on a sign-magnitude machine. If the result loops with period = 1 at
-1, you are on a twos-complement machine. If the result loops with
period greater than 1, including the beginning, you are on a
ones-complement machine. If the result loops with period greater than
1, not including the beginning, your machine isn't binary -- the
pattern should tell you the base. If you run out of memory, you are
on
a string or bignum system. If arithmetic overflow is a fatal error,
some fascist pig with a read-only mind is trying to enforce machine
independence. But the very ability to trap overflow is machine
dependent. By this strategy, consider the universe, or, more
precisely, algebra: Let X = the sum of many powers of 2 = ...111111
(base 2). Now add X to itself: X + X = ...111110. Thus, 2X = X - 1,
so
X = -1. Therefore algebra is run on a machine (the universe) that is
two's-complement.
Item 174 (Bill Gosper and Stuart Nelson): 21963283741 is the only
number such that if you represent it on the PDP-10 as both an
integer and a floating-point number, the bit patterns of the two
representations are identical.
Item 176 (Gosper): The "banana phenomenon" was encountered when
processing a character string by taking the last 3 letters typed out,
searching for a random occurrence of that sequence in the text,
taking
the letter following that occurrence, typing it out, and iterating.
This ensures that every 4-letter string output occurs in the
original.
The program typed BANANANANANANANA.... We note an ambiguity in the
phrase, "the Nth occurrence of." In one sense, there are five 00's in
0000000000; in another, there are nine. The editing program TECO
finds
five. Thus it finds only the first ANA in BANANA, and is thus
obligated to type N next. By Murphy's Law, there is but one NAN, thus
forcing A, and thus a loop. An option to find overlapped instances
would be useful, although it would require backing up N - 1
characters
before seeking the next N-character string.
Note: This last item refers to a Dissociated Press implementation.
See also banana problem.
HAKMEM also contains some rather more complicated mathematical and
technical items, but these examples show some of its fun flavor.
An HTML transcription of the entire document is available at
http://www.inwap.com/pdp10/hbaker/hakmem/hakmem.html.
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