Numerical computing is a vital part of the modern scientific infrastructure. Almost all numerical computing uses floating point arithmetic, and almost every modern computer implements the IEEE binary floating point standard, published in 1985. This standard is arguably the most important in the computer industry, the result of an unprecedented cooperation between academic computer scientists and the cutting edge of industry. A book by the speaker on this topic was published in 2001. Although the basic principles of IEEE floating point arithmetic have remained largely unchanged since the first edition of this book was published in 2001, the technology that supports it has changed enormously. Every chapter of the book has been rewritten extensively in a second edition published in 2025, and two new chapters have been added: one on computations with higher precision than that mandated by the standard, needed for a variety of scientific applications, and one on computations with lower precision than was ever contemplated by those who wrote the standard, driven by the massive computational demands of machine learning. There is an emphasis on historical development throughout the book, from the history of computing to the details of the 2008 and 2019 revisions of the floating point standard to the latest developments in microprocessor support for it.
     This talk will discuss the origins of the standard and of the book, highlights in the second edition, and the outlook for the future of numerical computing.

Refreshments will be served preceding the talk, starting at 2:45.