Re: Clause 10, Expression Evaluation

[David Hough 754R work <754r@xxxxxxxxxxx>]

> > 1. For programs whose PERFORMANCE is DOMINATED by FLOATING-POINT  
> > arithmetic,
> > binary floating-point arithmetic is always faster and more accurate
> > than decimal floating-point arithmetic, OTHER THINGS BEING EQUAL.


The emphasis added may make the original point clearer.

Other things being equal includes transistor count/area/technology/power.
Any hardware guys who really can make high-performance decimal 
arithmetic equal in performance to binary, other things being equal,
probably have a bright career ahead of them.

As to accuracy, there's no question once you get much beyond reading in
a number and printing it out unchanged.     In that simple filter case,
decimal is more accurate if no rounding is required.
But of course the I/O time dominates the arithmetic time.

When the situation is reversed, smaller radices have an inherent advantage
over larger ones, basically because the hump in ulp size at powers of the
radix is smaller with smaller radices, and so analytical or computed error
bounds grow more slowly.     That hump is what made hexadecimal floating
point so problematic, especially in single precision - 
it was much like losing a couple of bits of precision -
and changed the default binary floating-point datapath
size from 32 to 64 as part of the transition from 7094 to 360... although
that might have happened a few years later anyway as larger memories led
to larger feasible problem sizes and error bounds growing due to number
of operations as well as ulp size.

> BTW, I also think that if decimal FP is more than 10% slower in the  
> eventual
> hardware it will be very hard to get it accepted in a large part of the
> "high performance" community.

Any program containing high enough economic value to pay for the analysis
will probably be coded with binary floating-point arithmetic and optimized
for particular platforms.     That would include all the major simulation
type areas (weather, crash tests, nuclear physics, fluid dynamics,
quantitative financial stuff, ...)    I don't think that will ever change.
But a POSSIBLE future is that mass-market computers will put more resources
into decimal floating point than binary... then decimal could outperform
binary on those computers.    Computers intended to support high performance
technical computing might not do that (although as we all have seen, 
mass-market volume economics eventually seems to be able to overcome 
all kinds of inherent technical disadvantages).