Re: remarks on significance arithmetic implementation [Was: Re: Numerical accuracy/precision - this is a bug or a feature?]

*To*: mathgroup at smc.vnet.net*Subject*: [mg120372] Re: remarks on significance arithmetic implementation [Was: Re: Numerical accuracy/precision - this is a bug or a feature?]*From*: Richard Fateman <fateman at eecs.berkeley.edu>*Date*: Wed, 20 Jul 2011 06:33:39 -0400 (EDT)

On 7/19/2011 6:49 PM, DrMajorBob wrote: > As before, I think much of this discussion is useless. But this > example DOES give me pause: > >> Consider the two expressions >> f[x_]:= (x-1)*(x+1) and g[x_]:=(x^2-1) >> >> which are analytically the same function. >> >> given the value v=Interval[{-1/2,1/2}] f[v] returns an interval with >> width 2. g[v] returns an interval with width 1/4. > > I don't see why we'd want significance tracking to act this way. > > Bobby > I think that it is considered too expensive to do it this way. If you use significance arithmetic most of the time, it can't be so expensive. Also, it is difficult to write a program to do it, in general. See http://www.cs.berkeley.edu/~fateman/papers/interval.pdf and look for SUE or Single Use Expressions. RJF