Ed Chester wrote:

> Part of the problem has been that in order to challenge floating-point on
> its own playing field, we have techniques for 32b, and have neglected the
> probably more useful area of uCs and short-word applications where some
> real math could be a big bonus.

Floating point is a general purpose large dynamic range number system with
moderate complexity of all of its operations. When the application warrants
there are a lot of other representations  that can be used including
variations
on Logarithmic Number Systems. LNS provide good dynamic range and
definable resolution and can be used in cases where good error control is
needed. uLaw and aLaw are both specialized number systems with a
logarithmic base. Byte Craft has over the years sponsored or engaged in
quite a bit of research on number systems and data representations.
There is nothing in this work that would suggest that  logarithmic based
number systems can easily compute addition and subtraction
operations.

There are application specific reasons to use specialized number systems.
The trade-offs are calculation complexity, dynamic range, precision and
error control.

LNS and LEB128 both extend dynamic range for given storage size.
(LEB is statistical improvement in storage size). LEB retains its
full precision, LNS has fixed precision not the same as its dynamic
range. The trade-offs are often subtle

Walter Banks

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