Floating Point Arithmetic

[Richard Harter]

In article <1143 at sunc.osc.edu>, djh at xipe.osc.edu (David Heisterberg) writes:
> In article <232 at smds.UUCP> rh at smds.UUCP (Richard Harter) writes:
> >                                               Situations where 32 bit
> >precision does not suffice are usually either numerically poorly conditioned
> >or inherently require high precision.  In these cases double precision
> >is a dangerous nostrum -- one should do one's numerical analysis homework.

> There is also the case of theoretical work, such as quantum chemistry,
> for which all data is known exactly: in atomic units hbar = 1.0, qe = -1.0,
> me = 1.0, etc.  It's not uncommon to "out do" others by calculating
> energies that are less than 1 part in 10^6 lower than  previous values.
> For such comparisons to have meaning in the face of a few large matrix
> diagonalizations, double precision is a must.

Well, this is one of the categories I had in mind.  Certainly in theoretical
calculations where you want high final precision you need high intermediate
precision.  However you still need to know how much precision you need.  A 
simple minded "I need more precision so I will use double precision" is
what I was referring to as a "dangerous nostrum".  If your computational
process is not eating precision then the precision you use is the precision
you get.  If the computational process is eating precision then you do not
know what the resulting precision is unless you've done your homework.


-- 
Richard Harter, Software Maintenance and Development Systems, Inc.
Net address: jjmhome!smds!rh Phone: 508-369-7398 
US Mail: SMDS Inc., PO Box 555, Concord MA 01742
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