Cleve’s Corner: Cleve Moler on Mathematics and ComputingScientific computing, math & more

Posts 11 - 20 of 27

Floating Point Arithmetic Before IEEE 7541

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.... 続きを読む >>

Variable Format Half Precision Floating Point Arithmetic3

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.... 続きを読む >>

Greg Searle, Fractal Art and Design

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 >>

Friday the 13th and the Datetime Method3

Today is Friday, the 13th. In many parts of the world, today is regarded as unlucky. But I want to revisit an old question: is today unlikely? What are the chances that the 13th of any month falls on a Friday? Computing the answer makes use of a new MATLAB® feature, the datetime method.... 続きを読む >>

Bug in Half-Precision Floating Point Object

My post on May 8 was about "half-precision" and "quarter-precision" arithmetic. I also added code for objects fp16 and fp8 to Cleve'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 >>

Quadruple Precision, 128-bit Floating Point Arithmetic9

The floating point arithmetic format that occupies 128 bits of storage is known as binary128 or quadruple precision. This blog post describes an implementation of quadruple precision programmed entirely in the MATLAB language.... 続きを読む >>

“Half Precision” 16-bit Floating Point Arithmetic5

The floating point arithmetic format that requires only 16 bits of storage is becoming increasingly popular. Also known as half precision or binary16, the format is useful when memory is a scarce resource.... 続きを読む >>

Bank Format and Metric Socket Wrenches2

A report about a possible bug in format bank and 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 >>

Ulps Plots Reveal Math Function Accuracy2

"ULP" stands for "unit in the last place." An ulps plot samples 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 >>

Posts 11 - 20 of 27