Re: Possible Spam: Re: re motion 50 (Just to you...)
Ulrich et al,
On 09/26/2013 05:21 AM, Ulrich Kulisch wrote:
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Bill,
.
.
.
But let us assume that the gravitational constant appears as a datum
in a computation perhaps in a matrix multiplication. If you need a
guaranteed answer you would read it into the computer as an interval
where the bounds differ perhaps in the fifth digit. So you have to
compute a dot product with this interval in one component. You would
compute the minima and the maxima of the products of the vector
components and finally you have to accumulate all the minima and all
the maxima. Let us assume that this accumulation requires computing
the sum
10²⁰⁰ + 23456 -10²⁰⁰. (1)
If your computer provides an EDP you get the correct answer 23456 and
if the EDP is supported by hardware you get it very fast.
If your computer does not provide an EDP the average user will
accumulate (1) in conventional floating-point arithmetic and he gets
the wrong answer 0.
However, you will get the nearest floating point number to the
correct result, e.g., you would get 23456 in an IEEE double
type, if you have a correctly rounded dot product. P-1788 has
already decided a correctly rounded dot product will be included.
Baker
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R. 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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