Newsgroups: comp.lang.apl
Path: watmath!watserv2.uwaterloo.ca!torn!spool.mu.edu!uunet!s5!hui
From: hui@fid.morgan.com (Roger Hui)
Subject: Re: John Heckman and scans in APL
Message-ID: <1993Feb13.104524.3318@fid.morgan.com>
Keywords: scan, Heckman, archaeology 
Organization: Morgan Stanley & Co., New York, NY
References: <1993Feb8.234454.2638@yrloc.ipsa.reuter.COM>
Date: Sat, 13 Feb 1993 10:45:24 GMT
Lines: 18

Bob Bernecky writes:

> I am trying to track down John Heckman, who wrote the first scan 
> functions in APL at least 20-some years ago. 

> The Heckman scans, for those of you who only are familiar with the
> adverb "\" form, were user-defined functions for performing prefix
> and suffix scans of the more common arithmetic and Boolean functions.

> They were quite clever in that they only made 2 log N iterations on
> the argument.

In non-APL circles, this is known as the "parallel prefix algorithm". 
It is applicable to any associative dyadic function, and was first 
published by Richard Ladner in the SIAM Journal of Computing circa 1979.  
(I'm not certain about the journal.)  The article also described various
applications of the algorithm, including the construction of a circuit
for binary addition which is simultanenously small and fast.  
