[Python-Dev] One more dict trick
Eric S. Raymond
Fri, 1 Jun 2001 03:23:16 -0400
Tim Peters <email@example.com>:
> Not all scientific work consists of predicting the weather with inputs known
> to half a digit on a calm day <wink>. Knuth gives examples of
> ill-conditioned problems where resorting to unbounded rationals is faster
> than any known stable f.p. approach (stuck with limited precision) -- think,
> e.g., chaotic systems here, which includes parts of many hydrodynamics
> problems in real life.
Hmmm...good answer. I still believe it's the case that real-world
measurements max out below 48 bits or so of precision because the real
world is a noisy, fuzzy place. But I can see that most of the
algorithms for partial differential equationss would multiply those by
very small or very large quantities repeatedly. The range-doubling
trick for catching divergences is neat, too.
So maybe there's a market for 128-bit floats after all. I'm still
skeptical about how likely those applications are to influence the
architecture of general-purpose processors. I saw a study once that
said heavy-duty scientific floating point only accounts for about 2%
of the computing market -- and I think it's significant that MMX
instructions and so forth entered the Intel line to support *games*,
not Navier-Stokes calculations.
That 2% will have to get a lot bigger before I can see Intel doubling
its word size again. It's not just the processor design; the word size
has huge implications for buses, memory controllers, and the whole
<a href="http://www.tuxedo.org/~esr/">Eric S. Raymond</a>
The United States is in no way founded upon the Christian religion
-- George Washington & John Adams, in a diplomatic message to Malta.