On Wed, 28 Apr 2021 09:25:01 GMT, Andrew Haley <[email protected]> wrote:
> Re monotonicity: all is not necessarily lost. There's a theorem due to > Ferguson and Brightman which says that > > ``` > if > abs(f(m+) - f(m)) > eps < ----------------------- > abs(f(m+)) + abs(f(m))' > > for all m, the approximation is monotone. > > m is the machine number, m+ its successor > eps the maximum relative error of the approximation f(m) > ``` > > See > http://www-leland.stanford.edu/class/ee486/doc/ferguson1991.pdf, particularly > the Appendix, which contains a table of expressions for the five basic > transcendental functions. We can definitely be checked for single precision! I am uncertain how much water that would hold. ------------- PR: https://git.openjdk.java.net/jdk/pull/3510
