Path: utzoo!utgpu!jarvis.csri.toronto.edu!mailrus!uunet!mstan!amull
From: amull@Morgan.COM (Andrew P. Mullhaupt)
Newsgroups: comp.lang.pascal
Subject: Re: Problem in Turbo Pascal 4.0
Summary: Reduction of Strength is probably available
Message-ID: <632@s5.Morgan.COM>
Date: 31 Dec 89 18:37:11 GMT
References: <4658@ur-cc.UUCP> <4660@ur-cc.UUCP> <1989Dec31.145504.2373@cs.dal.ca>
Organization: Morgan Stanley & Co. NY, NY
Lines: 32

In article <1989Dec31.145504.2373@cs.dal.ca>, silvert@cs.dal.ca (Bill Silvert) writes:
> In article <4660@ur-cc.UUCP> lowj_ltd@uhura.cc.rochester.edu (John Alan Low, aka "Travis" Low) writes:
> >     The best solution in terms of speed was:
> >          Make x an integer (start at 10) and increment by 1 each time. Where
> >          x is used in the loop, subsitute x/100. Terminate when x = 30.
> 
> Just for the record, if you substitute 0.01*x it will run faster.

This is a case where the program transformation called 'Reduction of
Strength' will improve the speed of your program. The idea is that
when an arithmetic progression of numbers is required in a loop, that
it is faster to generate the progression by the recurrence

x(k)  =  x(k-1) + d

where d is the common difference, than by the multiplicative formula

x(k)  =  x(1)  +  d  *  (k-1)

which requires multiplication.


There are many machines, (Especially the Cray computers or the newer
RISC machines on which integer multiplies are considerably slower
than other instructions. It is one of the advantages of the loop
invariant - monotone function style of loop construction that these
optimizations often suggest themselves when the code is written in 
this way.


Later,
Andrew Mullhaupt