On Mon, 20 Mar 2017 14:18:16 -0700, Henry Baker <hbaker1@pipeline.com> wrote: FYI --
https://www.youtube.com/watch?v=aP0Y1uAA-2Y
Stanford Seminar: Beyond Floating Point: Next Generation Computer Arithmetic
John L. Gustafson, Natl Univ of Singapore
https://web.stanford.edu/class/ee380/Abstracts/170201.html
A new data type called a "posit" is designed for direct drop-in replacement for IEEE Standard 754 floats.
I whipped up my own C++ implementation and verified that the formula on page 40 is indeed evaluated with better precision using 32-bit posits than 32-bit floats. However, using "posits" will require more care to avoid losing precision due to the order of magnitude of the intermediate results. I've plugged my Posit class into enquire.c ( http://homepages.cwi.nl/~steven/enquire.html) and paranoia.c ( http://www.netlib.org/paranoia/paranoia.c). The former gets very confused, claiming that some bits aren't used, and the latter finds several flaws, defects, and failures. Leo