At 10:11 AM Friday 9/22/2006, Klaus Stock wrote:
OTOH, consider the following Smalltalk code:
x := 1 / 3.
x := 3 * x.
x inspect.
Common sense tells us that the result is 0.9999999 - but Smalltalk insists
on 1.
Funny, that's exactly the example many books used
30-odd years ago to illustrate why round-off
error is a problem programmers have to keep in
mind, as mathematically division by three and
multiplication by three should be inverse operations, so
X = 1
Y= X/3
Z = 3*Y
IF (Z=X) THEN GOTO 10
PRINT (Z " IS NOT EQUAL TO " X)
GOTO 20
10 PRINT (Z " IS EQUAL TO " X)
20 END
would always return something like "0.999999 IS
NOT EQUAL TO 1" so if you expected X and Z to be
equal (as it would be in mathematics or
infinite-precision arithmetic) and were testing
for that, it would never be equal.
(In FORTRAN¹, it would be even worse if you
forgot the difference between integer arithmetic
and real arithmetic, as I = 1/3 would set I = 0
and then J = 3*I would make J = 0.)
_____
¹Yes, this dates me to the same era as
Himself. (Even though I recently re-installed
the Fortran 90 package on this machine.) I
probably still have some boxes of cards from
those days somewhere in the storage shed . . .
another benefit (?) of inheriting the house you
lived in back then from your parents . . . )
-- Ronn! :)
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