Re: IEEEP1788

[Ulrich Kulisch <ulrich.kulisch@xxxxxxx>]

Am 28.04.2015 um 09:13 schrieb David Lester:

I expect that a system such as MPFR could be set up to include
a component that provides exact/complete dot product. Whether MPFR (etc) could be
hooked up to special hardware to do complete arithmetic when useful would not be out of the
question. So it appears to be a superset capability, and not necessarily slower.
And it would not make a hash of the supporting programming language.

With my supercomputer chip-designer hat on, I am doubtful about specialised hardware for any arithmetical operation.

We are now moving into the era of “internet of things” where low power consumption, and minimal chip area are king. Even for supercomputers (which are really just specially-selected stock hardware, and are cross-subsidised by the volume market) — the so-called exascale machines — we are running into power consumption issues; an exaflop machine could be built today, provided you connect it to a Fukushima-sized power plant, and can afford the electricity bills.

So the current motto is “keep it small, keep it power efficient, and place the data as close to the compute nodes as possible”.

Dave Lester

Please get informed how complete arithmetic is done!

It computes the exact dot product totally on chip without any memory involvement. In other words: It follows exactly what you call the current motto.
A coprocessor chip development for x86 computers in 1994 computed the exact dot product in a fraction of the time that the x86 computed it with rounding errors, even though the coprocessor technology was less advanced than that of the x86. So complete arithmetic increases both the accuracy and the speed. Complete arithmetic is done via a new data type for which only addition and subtraction of floating-point numbers and of products of such are defined.
For more details see my book: Computer Artithmetic and Validity. (The book was published before IEEE P1788 was founded.)

Best regards
Ulrich

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