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From: kend@data.UUCP (Ken Dickey)
Newsgroups: comp.lang.scheme,comp.lang.lisp
Subject: Numerical gotcha's
Keywords: Interval Arithmetic, Rationals, Floats, Bignums
Message-ID: <432@data.UUCP>
Date: 26 Nov 90 23:59:43 GMT
Organization: Microcosm, Beaverton, OR
Lines: 67


Thanks to all who responded to my call for numerical results.  They
came in pretty much as expected.  Implementations without rationals
(even with bignums) lost.  This includes all those based on C.  All
implementations with rationals apparently also have bignums (not much
of a suprise).  CL (Common Lisp) implementations are required to have
both rationals and bignums.  Barry Margolin's Symbolics numbers were
especially interesting!

It seems that not many numerical analysts are into interval
arithmetic.  I have not yet heard of a reals implementation based on
rationals, despite the advantage of getting error bounds.  I have
heard that Ray Moore's group at Ohio is getting super-linear
performance with some convergence algorithms using interval arithmetic
[3+ times speedup upon doubling the number of processors].  

Gosh, computers are fun!  [I do all my floats on Halloween to frighten
the adults 8^].

Thanks again,
-Ken					kend@data.uucp


Implementation	result				system
==============  ======                 		======
Scheme->C	-1.180591620717411e+21 		Sun4/110 SunOS 4.03 	
C-Scheme 7.0	 1.18059162071741e+21
XScheme		 1.18059162071741e+21
ELK 1.1		 1.18059162071741e+21		Sun3
ELK 1.2		 1.18059162071741e+21		SPARCstation 1
MacScheme 2.0   -1.805916207174113e21
T 3.0	 approx -1.1806e21 (w reals instead of rationals) Encore Multimax

Chez Scheme	  -54767/66192			SPARC
Chez Scheme 3.9g  -54767/66192			SPARCstation 1+ SunOS 4.0.3
AllegroCL 3.1.12  -54767/66192			DEC 3100/Ultrix
Mac Allegro CL	  -54767/66192			Mac IIci
T		  -54767/66192			SPARCstation 1
T 3.0		  -54767/66192			Encore Multimax
T 3.1		  -54767/66192			Sun3 SunOS 4.1
Lucid CL	  -54767/66192			SPARCstation 1
Lucid CL	  -54767/66192			HP 9000/835
Utah CL		  -54767/66192			HP 300  BSD 4.3

==================
Here are various results on a Symbolics 3600 running Genera 8.0.  The "d"
is the double-precision exponent indicator, and "e" is the single-precision
exponent indicator.

(f 77617d0 33096d0)	-1.1805916207174113d21
(f 77617e0 33096e0)	 6.338253e29
(f 77617   33096)	-54767/66192
(f 77617   33096e0)	 6.338253e29
(f 77617e0 33096)	-6.338253e29
(f 77617d0 33096)	-2.3611832414348226d21
(f 77617d0 33096e0)	 1.022335026998684d30
(f 77617e0 33096d0)	-2.0895373854550075d29


===================
Gambit 1.5: (digits from Marc Feeley)

(floor (* (tryit) (expt 10 100))) ->

-8273960599468213681411650954798162919990331157843848199178148416727096930142615421803239062122310854

;;			     --- E O F ---