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From: rar (Bob Riemenschneider)
Newsgroups: comp.lang.scheme
Subject: Numerical gotcha's
Message-ID: <9011212311.AA04441@saturn.ads.com>
Date: 21 Nov 90 23:11:40 GMT
Lines: 62
In-Reply-To: kend@data.UUCP's message of 21 Nov 90 17:10:40 GMT

=>   From: kend@data.UUCP (Ken Dickey)
=>   Newsgroups: comp.lang.scheme,comp.lang.lisp
=>   Date: 21 Nov 90 17:10:40 GMT
=>
=>   ... I am interested
=>   in knowing what results are obtained for the following on various
=>   Scheme & Lisp implementations.  Please indicate machine, OS, and what
=>   numerics are available {floats, bignums, rationals}.  I will post a
=>   summary [kend@data.uucp].
=>
=>   f(x,y) = 333.75 y^6 + x^2 (11 x^2 y^2 - y^6 - 121 y^4 - 2) +
=>	   5.5 y^8 + x / (2 y).
=>
=>   for x = 77617 and y = 33096 
=>
=>   Scheme code for the above follows ...
=>
=>   ;; THE CORRECT ANSWER IS:
=>   ;;
=>   ;;  (tryit) ->  -54767/66192	{Gambit 1.4; sun3; rationals+bignums}

As you probably already know, in any Common Lisp, you should get the
"correct answer".  Just for the record, here's a transcript from running
it on a SPARCstation using Lucid CL.

   wrigley(3): lisp
   ;;; Expanding Reserved Memory
   ;;; GC: 1012 words [4048 bytes] of dynamic storage in use.
   ;;; 1309706 words [5238824 bytes] of free storage available before a GC.
   ;;; 2620424 words [10481696 bytes] of free storage available if GC is disabled.
   ;;; 
   ;;; Sun Common Lisp, Development Environment 3.0.5, 27 October 1988
   ;;; Sun-4 Version for SunOS 4.0 
   ;;;
   ;;; Copyright (c) 1985, 1986, 1987, 1988 by Sun Microsystems, Inc., All Rights Reserved
   ;;; Copyright (c) 1985, 1986, 1987, 1988 by Lucid, Inc., All Rights Reserved
   ;;;
   ;;; This software product contains confidential and trade secret
   ;;; information belonging to Sun Microsystems.  It may not be copied
   ;;; for any reason other than for archival and backup purposes.
   
   > (defun f (x y)
        (+ (* (/ 1335 4) (expt y 6))
           (* (expt x 2)
              (- (* 11 (expt x 2) (expt y 2))
                 (expt y 6)
                 (* 121 (expt y 4))
                 2))
           (* (/ 11 2) (expt y 8))
           (/ x (* 2 y))))
   F
   > (compile 'f)
   ;;; You are using the compiler in development mode (compilation-speed = 3)
   ;;; Generation of full safety checking code is enabled (safety = 3)
   ;;; Optimization of tail calls is disabled (speed = 2)
   ;;; Expanding Reserved Memory
   F
   > (f 77617 33096)
   -54767/66192


							-- rar