21 Apr
2001
21 Apr
'01
9:13 a.m.
From: Jim Battle <frustum(a)pacbell.net>
clarifies the matter at hand. I claim that a floating
point
representation
specifies precision and has nothing to say about
accuracy (other than
accuracy is limited by precision).
Floating point binary is infamous for it's errors in that regard.
To clarify, say a number is 175.136985. This
represents my weight very
precisely, but whether it is accurate or not is a different matter.
Ah but if you convert it to a 24bit floating point (more bits would help
but limiting it makes the error glaring) you may not be able to express
it
accurately enough. The BCD case induces more truncation limiting
precision.
Again, I must be missing something, or perhaps it is a
definitional
thing. I've given my definition for precision (or what you call
resolution) and accuracy. I claim accuracy is largely outside the scope
of
a number representation. Perhaps you and others have a
different
definition than I do and are also internally consistent. I'd like to
hear
it, since I keep running into it and don't
understand it.
Accuracy express 1/3 binary and decimals for the same total bits.
Limit the case to something shorter than the usual 32 or 64 bits
say like 10 or 12 bits and you see the error. This is the gray zone
where
resolution, accuracy and range can collide. Of course with 128 bits of
either
case it's really meaningless then.
Back in the olden days (8080/z80/6502) when math was often limited in
the number of bits to something less than 32 bits this was more accutely
noticed by the users. The infamous MSbasic 3.99999=4 and other examples
come to mind. This led to things like NS* basic and HP using BCD to
avoid
the SQRT(16)=3.99999!
If, on the other hand, you want to know what is
sin(0.1), I claim the
binary representation is more precise (and thus allows more accuracy;
accuracy here depends on the implementation of the trig algorithms and
not
inherently in the number system).
But the number of bits do make a difference.
maybe I should give up and take this to the
alt.ieee.vs.bcd.floating-point
newsgroup. :-)
Logically your correct but in the realm of older machines this was a real
issue.
Allison