On Wed, 28 Apr 2021 09:25:01 GMT, Andrew Haley <aph@openjdk.org> 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