Re: why extending numbers by zeros instead of dropping precision
- To: mathgroup at smc.vnet.net
- Subject: [mg118017] Re: why extending numbers by zeros instead of dropping precision
- From: Daniel Lichtblau <danl at wolfram.com>
- Date: Sat, 9 Apr 2011 07:10:32 -0400 (EDT)
Richard Fateman wrote: > [...] >> although appreciation of the problem goes back farther (why did the >> ENIAC have ten digit accumulators?). > > You might refer to MANIAC, which had significance arithmetic, and also > lost out. >>> Oh, as for subtraction being a problem... Typically if you subtract two >>> nearly equal items you get a small quantity. The small quantity is not >>> troublesome if you add it to something that is not so small. What >>> sometimes happens is that you do something ELSE. Like divide by it. >>> That is more likely to cause problems. >> Exactly. That's a very common issue in numerical analysis. And that's >> why your "hardly ever" assertion is silly. > > I recommend you look at the Kahan paper, which would explain to you this > issue. For those with an interest in the computer arithmetic of our predecessors (that is to say, a predilection for precise pronouncements about our processor's predecessors), there is a paper (scanned pdf) from 1962 describing MANIAC III arithmetic, available from the URL below. http://doi.ieeecomputersociety.org/10.1109/AFIPS.1962.31 Daniel Lichtblau Wolfram Research