Re: exact dot product

[Ulrich Kulisch <ulrich.kulisch@xxxxxxx>]

Am 29.05.2013 14:54, schrieb Vincent Lefevre:

I'm not convinced that CA should be in P1788, in particular if no processor vendors have shown interest in implementing CA in hardware.

Dear Vincent:

This is an other attempt convincing you that Complete Aithmetic should be in IEEE 1788.

What you write above is not quite correct. In the 1980ies Complete Arithmetic was hardware supported on several IBM, Siemens, and Hitachi computers of the /370-architecture. On these machines the exponent range is very modest. So about 1200 bits suffice for the complete register or how Baker calls it for the "long accumulator".

The technique of using a long accumulator for accumulating numbers and products of numbers can be traced back to the early computer by G. W. Leibniz. See also the upper right corner of the poster. All these early computers provided a long accumulator. I attach copies of a few more pages of my book "Computer Arithmetic and Validity". Please read them. They give a more detailed description of this very old computing technique.

Interval arithmetic brings guarantees and safe bounds into computing. These bounds frequently are overly pessimistic. The exact dot product is the simplest and most general tool for getting close bounds. It brings accuracy and speed. A combination of both is what is needed from a modern computer. We did not get the exact dot product from IEEE 754. So it is most natural that we provide it in IEEE 1788.

The old mathematicians and computer designers knew very well how technical computing should be done. Today a number of the best numerical analysts require "inclusion of an exact dot product in the IEEE Standard P1788. ...  It is a fundamental tool for computing with guarantees and can be implemented with very high speed." , see the IFIP to IEEE 754 and IEEE 1788 letters.

Best wishes
Ulrich

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