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From: jww@bonnie.UUCP (Joel West)
Newsgroups: net.micro.mac
Subject: Re: Harmonic Series Benchmark
Message-ID: <490@bonnie.UUCP>
Date: Tue, 28-May-85 10:34:51 EDT
Article-I.D.: bonnie.490
Posted: Tue May 28 10:34:51 1985
Date-Received: Thu, 30-May-85 00:22:19 EDT
References: <1353@amd.UUCP> <385@gumby.UUCP>
Organization: CACI -- La Jolla, Calif.
Lines: 34

> > He also stated the right answer was 9.787613 determined from a Vax 11/780
> > taking 0.02 seconds.
> > 
> > Now either I'm doing it wrong or something, because I didn't get that
> > answer on an IBM 3081.  But anyway, here is my results, with the
> > actual output of the Macintosh using Mac C from Consulair.
> > ----------------------------------------------------------------------
> 
> I suspect the difference (9.787613 vs 9.787606) is due to differences
> in the number of bits of precision.  The VAX has one bit more precision
> in many cases due to the 'implied one' immediately after the binary
> point.  

Actually, it's worse than that.  The IBM S/360 architecture is "hexadecimal
normalized", which means that "1" is stored as "0x1000...." in the mantissa
field, with 3 leading (non-significant!) zeros.  This reduces precision
by 1/2 to 1 digit vs. most comparable 32- and 64-bit floating point formats
(including the VAX, which the author notes squeezes out an extra bit
of precision).  

The accuracy of the original (1964? 65?) algorithm was so abysmal that IBM
had to re-engineer the machines in the field to add a "guard digit", which
is an extra hex digit in 32-bit floating (7 hex mantissa digits) format
that exists only during intermediate computations and is rounded when
stored in 32-bits.  I'm told a UCLA professor was very mad at IBM for
changing their hardware, because he could no longer reproduce the
(erroneous) 5-digit numbers in his book... :-)
-- 
	Joel West				     (619) 457-9681
	CACI, Inc. - Federal 3344 N. Torrey Pines Ct La Jolla 92037
	jww@bonnie.UUCP (ihnp4!bonnie!jww)
	westjw@nosc.ARPA

   "The best is the enemy of the good" - A. Mullarney