Re: Re: RE:Working Precision
- To: mathgroup at smc.vnet.net
- Subject: [mg24072] Re: [mg24030] Re: [mg23928] RE:Working Precision
- From: David Withoff <withoff at wolfram.com>
- Date: Fri, 23 Jun 2000 02:26:41 -0400 (EDT)
- Sender: owner-wri-mathgroup at wolfram.com
> Here's an easily defended rule: Do all arithmetic exactly. When > you must store the result into a finite sized memory location, > round it to the nearest representable number exactly representable > in that memory location. In case of a tie, round to even. The problem is that that rule by itself makes no allowance for keeping track of the accumulated effects of all that rounding. > On a binary machine with a binary exponent, multiplication by 2 is > always exact. Think about it: it adds one to the exponent, leaving > the mantissa alone. There is no error on such a machine operation. Actually, the absolute error is multipled by 2. For example, multiplying 1 +/- 1 by 2 gives (or should give) 2 +/- 2. It shouldn't matter what sort of bit-twiddling the machine is doing internally to arrive at this result. The mathematics is the same regardless. Dave Withoff Wolfram Research