Re: Fixed Point Arithmetic

"G Iveco" <G.Iveco@xxxxxxxxxx> writes:

"Greg Berchin" <gberchin@xxxxxxxxxxxx> wrote in message
news:vt71d3l7jqkv9uokevpmbjaeem6e98s1ir@xxxxxxxxxx
I am implementing (A+B-C-D-E) in fixed-point logic. I am implementing
it as ((A+B)-((C+D)+E)). A, B, C, D, and E are all unsigned, more or
less uniformly distributed over the range [0, MAX), where MAX>>1, and
each also carries several fractional bits. The final result is signed.
I need for the accuracy of the final result to be reasonably close to
±½, but I also need to carry as few bits as possible in the arithmetic
operations to minimize real estate and maximize speed. Is there a
deterministic way to find the minimum number of fractional bits to keep
in A, B, C, D, E, (A+B), (C+D), and ((C+D)+E) at the inputs to the
adders, and whether to round or truncate?

Thanks,
Greg

If the inputs ABCDE are undeterministic, then either A+B or A+C or whatever
doesn't
matter.

The goal of your "I need for the accuracy of the final result to be
reasonably close to
±½, " is pretty ambiguous.

I'd look at max/mins. A+B has a max of 2*MAX and a min of 0. C+D+E has
a max of 3*MAX and a min of 0. Thus A+B-(C+D+E) has a max of 2*MAX and
a min of -1*3*MAX. You must carry enough bits to cover this range or
you'll lose something (either via saturation or roundoff, depending
on how you scale things).
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