Re: P64 Math

[Eugene Leitl <ui22204@xxxxxxxxxxxxxxxxxxxxxxx>]

On Thu, 31 Aug 1995, Steve Atkins wrote:

> >>Readers,

> [ which adder architecture ]
 
> When you hit 32 bits I think it's worthwhile to use some sort of carry
> propagate acceleration. Something like a carry skip adder doesn't cost too
> much silicon, and will be *much* faster than a ripple adder for wide words.

Can you name numbers? At least a qualitative factor. It still scales
linearly to bit length, I presume?
 
> I've been looking at 64 bit arithmetic recently, and (for the silicon we use)
> the tradeoffs do seem to change between 32 & 64 bit operations. For a fast 64
> bit processor, where addition may be a bottleneck, a good optimised adder would
> be essential - either a carry skip adder for medium speeds, a hybrid carry select
> adder (such as the one the Alpha uses) for fast speeds. If the word width grew

Can you outline their principles, at least roughly? (My numerics 
hardware book is a bit outdated :(

> beyond 64 bits, or *very* fast addition was the aim then bizarre adder
> architectures (Prefix adders, such as Brent-Kunge or Kogge-Stone (sp?)) start
> looking like a good idea. They're pretty expensive on silicon, unfortunately.

Where do _these_ break down? 128 bit? 512 bit? Do they scale linearly, too?
How many transistors does one burn per bit slice?

Another thing. Does anyone know which kind of shifter the F21 has?
A barrel one? How many shifts can we do in 12 ns?
(Sorry if I keep harping upon shifts, but a fast shifter is very instrumental
if we don't have a hardware multiplier).

-- Eugene

P.S. I apologize for the many questions.

> Cheers,
>   Steve
> --
> -- Steve Atkins -- <atkinss@inmos.co.uk> -- +44 454 611439 --
> --            http://pact.srf.ac.uk/~atkinss/              --
> "At least one good reason for studying multiplication and division is that
>  there is an infinite number of ways of performing these operations and hence
>  an infinite number of Ph.Ds (or expenses-paid visits to conferences in the
>  USA) to be won from inventing new forms of multiplier."
>                    -- Alan Clements, The Principles of Computer Hardware, 1986
> 
>