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In an unpublished 1972 technical report "Conserving confluence curbs ill-condition," Velvel Kahan coined the descriptive term pejorative manifold.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In an unpublished 1972 technical report "Conserving confluence curbs ill-condition," Velvel Kahan coined the descriptive term pejorative manifold.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 >>

A year and a half ago I wrote a post about "half precision" 16-bit floating point arithmetic, Moler on fp16. I followed this with a bug fix, bug in fp16. Both posts were about fp16, defined in IEEE standard 754. This is only one of 15 possible 16-bit formats. In this post I am going to consider all 15.... read more >>