another comp.arch posting on IEEE 754 history

[Bob Alverson]

> 
> Getting correctly-rounded products, quotients, and square roots is
> harder than doing them like a Cray, but the hardware that does these
> things can be integrated reasonably well as on the TI 8847.  Pipelining
> is still a problem, but one which perhaps will ultimately be handled
> supercomputer-style with large multiplier arrays and multiple
> divide/sqrt functional units.  And it's always cheaper to do it right
> in hardware than to try to work around cheap hardware in software.  For
> those who enjoy the latter challenge, the sons (in spirit) of Cray will
> continue to produce partial IEEE implementations like the Intel 860
> which are as effective in certain limited applications as they are
> difficult to exploit more generally.
>

Just a little note that correctly rounded divide and square root can
be done without any divide/sqrt functional units.  All you need is a
multiplier that does more than 53x53 -> 53 products and a small lookup
table.  Our multiplier does 64x64 -> 128 products, so it has no
problem.  Divides take 6 passes through the multiplier and square
roots take 8 passes.  But everything is pipelined (and data dependent,
sigh).

I'm not sure we need any extra support for float remainder, since we
can do a single round multiply add.  When the dividend is much larger
than the divisor, it may even be better to use multiplication by the
reciprocal than division since intermediate partial remainders need
not be rigorously defined (they just need to be congruent to the final
answer).  You still have to be careful at the end, though.

Bob