Re: Re: Accuracy and Precision

*To*: mathgroup at smc.vnet.net*Subject*: [mg37009] Re: [mg36983] Re: Accuracy and Precision*From*: David Withoff <withoff at wolfram.com>*Date*: Sun, 6 Oct 2002 05:32:55 -0400 (EDT)*Sender*: owner-wri-mathgroup at wolfram.com

> The more I play with the example the more depressing it gets. Start > with floating point numbers but explicitely arbitrary-precision ones. > > In[1]:= > a=77617.00000000000000000000000000000; > b=33095.00000000000000000000000000000; > > In[3]:= > \!\(333.7500000000000000000000000000000\ b\^6 + a\^2\ \((11\ a\^2\ > b\^2 - \ > b\^6 - 121\ b\^4 - 2)\) + 5.500000000000000000000000000000\ b\^8 + > a\/\(2\ > b\)\) > > Out[3]= > \!\(\(-4.78339168666055402578083604864320577443814`26.6715*^32\)\) > > In[4]:= > Accuracy[%] > > Out[4]= > -6 > > Due to the manual section 3.1.6: > > "When you do calculations with arbitrary-precision numbers, as > discussed in the previous section, Mathematica always keeps track of > the precision of your results, and gives only those digits which are > known to be correct, given the precision of your input. When you do > calculations with machine-precision numbers, however, Mathematica > always gives you a machine?precision result, whether or not all the > digits in the result can, in fact, be determined to be correct on the > basis of your input. " > > Because I started with arbitrary-precision numbers Mathematica should display > only those digits that are correct, that is none. An accuracy of -6 means that the least significant correct digit is 6 digits to the left of the decimal point. The result Out[3] in the example above has 26 significant digits to the left of that (the most sigificant digit is 26+6=32 digits to the left of the decimal point), so there are 26 correct digits to display. Was there some other result you were referring to as a result in which the number of correct digits is "none"? Dave Withoff Wolfram Research