Path: utzoo!utgpu!news-server.csri.toronto.edu!mailrus!cs.utexas.edu!uunet!willett!ForthNet
From: ForthNet@willett.UUCP (ForthNet articles from GEnie)
Newsgroups: comp.lang.forth
Subject: Data Structures
Message-ID: <1088.UUL1.3#5129@willett.UUCP>
Date: 6 Jun 90 03:55:00 GMT
Organization: Latest link in the ForthNet chain.  (Pgh, PA)
Lines: 94

Category 3,  Topic 20
Message 97        Tue Jun 05, 1990
W.BADEN1 [Wil]               at 20:39 PDT
 
At last Thursday's Fig Bar I promised two algorithms for calculating the date
of Easter.  I gave the first the same night.  I said that the other used
UM/MOD ten times.  This is from T.H.O'Beirne's (That's O'BEIRNE) delightful
PUZZLES AND PARADOXES, Oxford Univ. Press, 1965, chapter titled "Ten Divisions
Lead to Easter."

My son programmed this for my Apple F83X some years ago, but rather than
excavating the code (I don't know where in California it is) or reproducing
O'Beirne's description, here is an executible program in ABC.

HOW TO DIVIDE dividend BY divisor GIVING quotient WITH remainder REMAINDER
   PUT floor(dividend/divisor),dividend mod divisor IN quotient, remainder

HOW TO EASTER x:
   \ Display month and day of Easter Sunday, Gregorian year x.
   DIVIDE x BY 19 GIVING junk WITH a REMAINDER
   DIVIDE x BY 100 GIVING b WITH c REMAINDER
   DIVIDE b BY 4 GIVING d WITH f REMAINDER
   DIVIDE 8*b + 13 BY 25 GIVING g WITH junk REMAINDER
   DIVIDE 19*a + b - d - g + 15 BY 30 GIVING junk WITH h REMAINDER
   DIVIDE a + 11*h BY 319 GIVING mu WITH junk REMAINDER
   DIVIDE c BY 4 GIVING i WITH k REMAINDER
   DIVIDE 2*f + 2*i - k - h + mu + 32 BY 7 GIVING junk WITH lambda REMAINDER
   DIVIDE h - mu + lambda + 90 BY 25 GIVING n WITH junk REMAINDER
   DIVIDE h - mu + lambda + n + 19 BY 32 GIVING junk WITH p REMAINDER
   WRITE {[3]: "March"; [4]: "April"}[n], p

This seems wordy, but after you define a new keyword the system prompts you
with suggestions.  E.g.,

When you start a line with "d", ABC echoes "D?ELETE ?" on top of your typing.
If you continue with "i" it suggests "DI?VIDE ? BY ? GIVING ? WITH ?
REMAINDER".  You can write over the suggestion or use tab to copy up to the
next hole, given by "?".  Notice that you do not have to shift case.

Here are some "how-to's" for stack manipulation.

HOW TO EMPTY stack
   \ Also used to make stack.
   PUT {} IN stack

HOW TO PUSH x ONTO stack
   PUT x IN stack[#stack+1]

HOW TO RETURN top stack
   RETURN stack[#stack]

HOW TO SWAP stack
   PUT stack[#stack], stack[#stack-1] IN stack[#stack-1], stack[#stack]

HOW TO DROP stack
   DELETE stack[#stack]

HOW TO DUP stack
   PUSH top stack ONTO stack

HOW TO OVER stack
   PUSH 1 th'on stack ONTO stack

HOW TO RETURN n th'on stack
   RETURN stack[#stack - n]   

Here is the clearest expression of The Sieve I've seen.

HOW TO SIEVE n
   \ Sieve of Eratosthenes.  (Not a benchmark.)
   SHARE primes
   PUT {2..n} IN primes
   PUT 2 IN prime
   PUT floor root n IN limit
   WHILE prime <= limit:
      PUT prime IN i
      WHILE i < max primes:
         PUT i + prime IN i
         IF i in primes:
            REMOVE i FROM primes
      PUT prime min primes IN prime
   WRITE "There are `#primes` primes <= `n`."

"SHARE primes" makes primes available globally.

Text files are treated as named tables with line number as the key and text as
the value of the key, so no I/O instructions are needed to manage them.  There
is a built-in editor for all named data: numbers, strings, compounds, lists,
and tables.

Procedamus in pace.  Wil.
-----
This message came from GEnie via willett through a semi-automated process.
Report problems to: uunet!willett!dwp or willett!dwp@hobbes.cert.sei.cmu.edu