In a comment followingmy 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....続きを読む >>

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 aboutfp16, 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....続きを読む >>

If you follow this blog regularly, you know that I love fractals. I recently spent a pleasant afternoon in Nashua, New Hampshire, where my daughter Teresa introduced me to Gregory Searle, a fractal artist and computer geek. Here is his logo....続きを読む >>

今天是星期五,13。在我们的许多地方rld, today is regarded asunlucky. But I want to revisit an old question: is todayunlikely? What are the chances that the 13th of any month falls on a Friday? Computing the answer makes use of a new MATLAB® feature, thedatetimemethod....続きを読む >>

My post on May 8was about "half-precision" and "quarter-precision" arithmetic. I also added code for objectsfp16andfp8toCleve's Laboratory. A few days ago I heard from Pierre Blanchard and my good friend Nick Higham at the University of Manchester about a serious bug in the constructors for those objects....続きを読む >>

I first encountered the Hilbert matrix when I was doing individual studies underProfessor John Todd在Caltech in 1960. It has been part of my professional life ever since....続きを読む >>

The floating point arithmetic format that occupies 128 bits of storage is known asbinary128orquadruple precision. This blog post describes an implementation of quadruple precision programmed entirely in the MATLAB language....続きを読む >>

The floating point arithmetic format that requires only 16 bits of storage is becoming increasingly popular. Also known ashalf precisionorbinary16, the format is useful when memory is a scarce resource....続きを読む >>

A report about a possible bug informat bankand a visit to a local hardware store made me realize that doing decimal arithmetic with binary floating point numbers is like tightening a European bolt with an American socket wrench....続きを読む >>

"ULP" stands for "unit in the last place." Anulps plotsamples a fundamental math function such as $\sin{x}$, or a more esoteric function like a Bessel function. The samples are compared with more accurate values obtained from a higher precision computation. A plot of the accuracy, measured in ulps, reveals valuable information about the underlying algorithms....続きを読む >>