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From: pausch@saaf.se (Paul Schlyter)
Newsgroups: comp.sys.handhelds
Subject: Re: How accurate is the 48??
Message-ID: <1991May21.120147.4627@saaf.se>
Date: 21 May 91 12:01:47 GMT
References: <7174@acorn.co.uk>
Distribution: comp
Organization: SAAF, Svensk Amat|rAstronomisk F|rening
Lines: 32

In article <7174@acorn.co.uk> asmith@acorn.co.uk (Andy Smith) writes:
>There is no doubt that the 28S and the 48SX are brilliant calculators, but
>one thing still puzzles me. Certainly with the 28S, although much better
>than most calculators (3/3=1, 2/3*3=1) it is still not "accurate" due to the
>limitations of how it stores numbers. 1/3*3 still gives 0.999999999. Does
>the 48 still suffer from this limitation?

Of course.  THis is a limitation inherent in using BCD representaion for
floating-point numbers.  1/3 is 0.33333333....... infinetley, so it must
be rounded off somewhere.  Suppose we round off after 12 digits:
0.333333333333   Now we want to multiply this with 3 - the answer to this
IS 0.999999999999 to 12 decimal places.

If one decides to always round up 0.999999999999 to 1.0000000000 just to
get 1/3*3 right, one is faced with another problem:  3 * 0.333333333333
will then yield the result 1.0000000000 instead of the correct result 
0.999999999999 .  How do you handle this problem?

The simple fact that one must live with is that ALL floating-point arithmetic
may introduce round-off errors (unless one computes with infinite precision,
which for practical reasons are impossible).  By using BCD instead of pure
binary floating-point numbers one is assured that things like 1/10*10 will
always be exactly right, but that's only because 10 is the internal base
for the floating-point number. The round-off errors still sometimes shows
up, like in 1/3*3.  There's really nothing you can do about it, without
introducing other undesireable side-effects.

-- 
---
Paul Schlyter, Swedish Amateur Astronomer's Society (SAAF)
InterNet:  pausch@saaf.se
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