I recently published Round, With Ties to Even and followed that with Round Two. Then, in an email, Andy Bartlett pointed out that my new round function fails for some large values of x between flintmax/2 and flintmax.... read more >>

I published Round, With Ties to Even a couple of days ago. Steve Eddins and Daniel Dolan immediately had substantive comments. Here is my reaction to their comments.... read more >>

We are considering a MATLAB Enhancement Request to support options for round(x) when x is exactly halfway between two integers.... read more >>

(A slight revision of the post I made a few hours ago.)... read more >>

In an unpublished 1972 technical report "Conserving confluence curbs ill-condition," Velvel Kahan coined the descriptive term pejorative manifold. In case you don't use it in everyday conversation, pejorative means "expressing contempt or disapproval."... read more >>

In an unpublished 1972 technical report "Conserving confluence curbs ill-condition," Velvel Kahan coined the descriptive term pejorative manifold. In case you don't use it in everyday conversation, pejorative means "expressing contempt or disapproval."... read more >>

My colleagues are looking for a matrix to be used in a new benchmark. They've come to the right place.... read more >>

Let me tell you about MATLAB's controversial function rat.... read more >>

For the past month I have been working with the variable format 16-bit floating point arithmetic that I described in this post. It has been frustrating work. I have found that the limited precision and limited range of half precision make it barely usable for the kind of experiments with matrix computation that I like to do. In this post I will describe a few of these experiments.... read more >>

In a comment following my post about half-precision arithmetic, "Raj C" asked how the parameters for IEEE Standard 754 floating point arithmetic were chosen. I replied that I didn't know but would try to find out. I called emeritus U. C. Berkeley Professor W. (Velvel) Kahan, who was the principle architect of 754. Here is what I learned.... read more >>