🚀 go-pugleaf

In article <1549@convex.UUCP>, swarren@eugene.uucp (Steve Warren) writes:
> In article <1758@crdgw1.crd.ge.com> davidsen@crdos1.UUCP(bill davidsen) writes:
< <  Could you 'splain this to me? It sounds as if you are saying that if
< <one component is large in magnitude we can afford to have less precision
< <on the other. Hope I misunderstand what you're telling me.
< <	bill davidsen		(davidsen@crdos1.crd.GE.COM)
< <  {uunet | philabs}!crdgw1!crdos1!davidsen
< <"Stupidity, like virtue, is its own reward" -me
> 
> Think of it as a vector.  Changing the mantissa of the component that is
> orders of magnitude smaller is not going to move the vector significantly.
> 
> For example, if the magnitude of the smaller (call it V1) of the two
> components is less than the least significant bit of the larger component
> (call it V2), then the truncation error introduced by V2 is greater than
> the error introduced by eliminating V1 entirely.  V1 therefore should be
> truncated at the least significant position in V2.

There are situations, like computing FTs (fast or slow) where this is the case.
There are other situations where this is not the case.  I needed the complex
error function with good relative error in both the real and imaginary parts
for the case in which the real part of the argument was small.  It was 
necessary for me to develop new algorithms to accomplish this; the existing
algorithms with good relative error were quite poor at this.
-- 
Herman Rubin, Dept. of Statistics, Purdue Univ., West Lafayette IN47907
Phone: (317)494-6054
hrubin@l.cc.purdue.edu (Internet, bitnet, UUCP)