In article <4dRdg.27449$zn1.10846@[EMAIL PROTECTED]
>,
James J. Weinkam <jjw@[EMAIL PROTECTED]
> wrote:
> Well, if it really is a logarithmic system, I suppose the terms
characteristic
> and mantissa are appropriate, but can you give a reference?
"FOCUS Microcomputer Number System"
Albert D. Edgar and Samuel C. Lee
_Communications of the ACM_ Vol 22 #3, pp 166-177, March 1979.
----------------------------------------------------------------------
Abstract: FOCUS is a number system and sup****ting computational
algorithms especially useful for microcomputer control and other signal
processing applications. FOCUS has the wide-ranging character of
floating-point numbers with a uniformity of state distributions that
give FOCUS better than a twofold accuracy advantage over an equal word
length floating-point system. FOCUS computations are typically five
times faster than single precision fixed-point or integer arithmetic
for a mixture of operations, comparable in speed with hardware
arithmetic for many applications. Algorithms for 8-bit and 16-bit
implementations of FOCUS are included.
FOCUS actually stored the log of (1+x) to represent x.
> The question I have is why anyone would want to do this.
It effectively saves a bit of precision; more, if you are comparing to a
hex FPS such as the IBM/360, or one that wastes a bit to carry the
(always-on for nonzero numbers) leading bit of the fractional part.
> In Napier's time, logarithms were used to reduce multiplication to
> addition when there were no mechanical or electronic calculators.
> Now that we have them, what's the point for that purpose?
Harware multiply is not ubiquitous, and used to be absent from inexpensive
CPUs. Even now, hardware multiply is often slower than hardware add, and
hardware divide nearly alweays is. If the numbers being stored will be
used
for division or multiplication far more often than for addition,
subtraction, or display, then logarithmic representation allows faster
programs.
--
Randy Hudson
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