Re: About exact results and exact endpoints
Nick et al,
On 02/13/2013 08:27 AM, N.M. Maclaren wrote:
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.
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The fact that a fixed size of decimal floating-point can represent a
wider range of decimal fractions than binary (and a stronger statement
does not hold) is no different from the fact that a binary one can
represent a wider range of binary fractions than decimal. There was
and is no mathematical reason that ten is a preferred base over two,
or even three.
Of course, if one allows an arbitrary but finite number of digits in
the mantissa and exponent, the more prime factors in the base, the more
numbers can be represented exactly.
Ancient Middle Eastern mathematicians presumably preferred base 60
for that reason.
The claims of extra accuracy for decimal floating-point are polemic,
pure and simple, and precisely the converse can be argued with rather
more reference to mathematics. Please leave it out of this discussion.
More generally, I think we should maintain our focus on clear
postings that move us towards completing
the document and obtaining consensus
within our time constraints. I apologize for
my present transgression in this regard.
(We have defined
``flavors'' and will specify common properties of all
flavors and different interval formats. However, the
core interval data type we have mostly nailed down
is an inf-sup, 754-conforming data type. Data types
involving exact representations would fall under flavors
that have not yet been defined or non-754 data types we
haven't extensively considered to date. Exact representations
might be useful in achieving standard compliance with
underlying computations in implementations, but it probably
is not our business specifying details of implementations,
beyond checking feasibility or practicality of implementation.)
Best regards,
Baker
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Ralph Baker Kearfott, rbk@xxxxxxxxxxxxx (337) 482-5346 (fax)
(337) 482-5270 (work) (337) 993-1827 (home)
URL: http://interval.louisiana.edu/kearfott.html
Department of Mathematics, University of Louisiana at Lafayette
(Room 217 Maxim D. Doucet Hall, 1403 Johnston Street)
Box 4-1010, Lafayette, LA 70504-1010, USA
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