Am 07.02.2012 13:08, schrieb John Pryce:
Ulrich, Vincent
On 26 Jan 2012, at 13:02, Vincent Lefevre wrote:
On 2012-01-25 12:00:38 +0000, John Pryce wrote:
I send herewith a revised draft of the proposed Level 1 text, less
decorations, that I originally circulated on 5 Dec 2011.
About the basic arithmetic operations:
...
But why is the dot product included in the basic arithmetic operations?
I don't see it as important as +, -, *, /. And not more important than
recip, sqr, case, pown, abs, and perhaps some other operations.
Ulrich: on reflection I agree with Vincent. However useful the dot product is, it is essentially more complicated than +, -, *, /. I think calling it "basic" will cause more disagreement than agreement, so I have removed it from those lists.
John P
John,
I totally disagree with this decision. I am very busy with other things right now. But let me simply remind you that the IFIP Working Group on Numerical Software required the exact dot product by a letter to the standards committee IEEE
754R (dated Sept. 4, 2007) and by another letter to IEEE P1788 (dated Sept. 9, 2009). I attach copies of these letters to this mail.
I also disagree with the statement that the exact dot product is essentially more complicated than +, -, *, /.
Actually the *simplest* and *fastest* way for computing a dot product is to compute it exactly! By pipelining, it can be computed in the time the processor needs to read the data, i.e., it comes with utmost speed. No software simulation can
compete with a simple and direct hardware solution. I attach a copy of the poster that I prepared for the SCAN-Meeting at Lyon in 2010.
let me finally mention that the following is shown in my book 'Computer Arithmetic and Validity', de Gruyter 2008. With the two requirements of the IFIP Working Group letter to IEEE 754R: Fast hardware support for interval arithmetic and
the exact dot product, all operations in the usual product spaces of computation, the complex numbers, the real and complex intervals, the real and complex vectors and matrices, and the real and complex interval vectors and interval
matrices can be computed with least bit accuracy and at very high speed. These operations are distinctly different from those traditionally available on computers. This would boost both the speed of a computation and the accuracy of its result.
Best regards
Ulrich
--
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