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Re: back to the roots

Am 01.07.2013 14:36, schrieb Vincent Lefevre:
On 2013-06-30 12:08:15 +0200, "Neher, Markus (IANM) [IANM ist die Organisationseinheit Institut für Angewandte und Numerische Mathematik am KIT]" wrote:

Many problems end up in solving some linear system. Ulrich Kulisch has
already pointed out how solving linear systems benefits from an EDP.

I haven't seen any algorithm using EDP to solve linear systems.

You also need to show why plain multiple-precision dot product (which
could take much less resource thanks to good precision control)
wouldn't be sufficient.
Let me repeat a paragraph of my mail of June 28:
"The simplest and fastest way of 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 intermediate roundings and normalizations have to be performed. No intermediate overflow can occur. No exceptions are to be delt with. No error analysis is necessary. The result is always exact. It is independent of the order in which the summands are added. It should be applied as often as possible. Any method that just computes an approximation also has to consider the relative values of the summands. This results in a more complicated method. Rounding the EDP to a lower precision is done, if required at the very end of the accumulation."

With respect to simplicity and speed the multiple-precision dot product with precision control MPDP has no chance to win the game.
With respect to resources I also see the EDP in front, no error control is necessary, no exceptions. All that is needed is some local memory (silicon) on the arithmetic unit of about 1/2 k bytes in case of IEEE 754 double precision.
On the IBM mainframes we needed only 1/4th of this memory because of the smaller exponent range and I do not remember a serious application where this was not eough. So at the cost of allowing simple overflow exceptions (which easily could be dealt with by software) the silicon area would still shrink considerably.

Best regards
Ulrich

-- 
Karlsruher Institut für Technologie (KIT)
Institut für Angewandte und Numerische Mathematik
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Prof. Ulrich Kulisch

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www.kit.edu
www.math.kit.edu/ianm2/~kulisch/

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