Xref: utzoo comp.lang.scheme:1820 comp.lang.lisp:4015
Path: utzoo!utgpu!news-server.csri.toronto.edu!cs.utexas.edu!sun-barr!apple!julius.cs.uiuc.edu!usc!zaphod.mps.ohio-state.edu!uakari.primate.wisc.edu!dali.cs.montana.edu!ogicse!zephyr.ens.tek.com!tektronix!percy!data!kend
From: kend@data.UUCP (Ken Dickey)
Newsgroups: comp.lang.scheme,comp.lang.lisp
Subject: Numerical gotcha's
Keywords: Interval-Arithmetic Bignums Rationals
Message-ID: <431@data.UUCP>
Date: 21 Nov 90 17:10:40 GMT
Organization: Microcosm, Beaverton, OR
Lines: 54


I heard an interesting talk recently on interval arithmetic.  One of
the messages was about getting bogus answers due to numeric
instabilities but not knowing the numbers were bogus.  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

The Scheme code for the above follows...
;;=====================================================================

;; from talk on interval arithmetic by G. W. Walster, 1990 Nov 19.

(define (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))
) )

(define (tryit) (f 77617 33096))



;; with flonums is {IBM FORTRAN note wrong sign!}
;; f = 1.17260...		single precision
;; f = 1.1726039400531...	double precision
;; f = 1.172603940053178...	extended precision

;; PC Scheme: f = 1.17260394005318   [Intel 386] {bignums, but not rationals}

;; ELK 1.1: f = 1.18059162071741e+21 [Sun3]	??? {floats only}


;; THE CORRECT ANSWER IS:
;;
;;  (tryit) ->  -54767/66192	{Gambit 1.4; sun3; rationals+bignums}
;;
;; flonum approx of (- (/ 54767 66192)) is -0.827396059946821  {ELK 1.1}
;;

;			---- e o f ----
;; Thanks,
;; Ken Dickey				kend@data.uucp