Hi, > With default settings the worst case error in nearest rounding mode is 0.547 > ULP > with inlined fma and fma contraction. > It uses a 1 KB lookup table, > ... > Note that the math.h header defines log2(x) to be log(x)/Ln2, this is > not changed, so the new code is only used if that macro is suppressed." > > Paul Zimmerman regularly posts library math function comparisons on the > newlib > and comparable library mailing lists, available at: > > https://members.loria.fr/PZimmermann/papers/accuracy.pdf > > that should give you an idea of the current state of the functions, if he is > even aware of the issue.
indeed, the known worst case error for Newlib log2 is 2.06 ulp: log2 0 -1 0x1.68d778f076021p+0 [2] [2.06] 2.05526 2.055255219183752 libm gives 0x1.fb1b88680e7adp-2 mpfr gives 0x1.fb1b88680e7abp-2 The 0.547 value above could match the GNU libc worst error: log2 0 -1 0x1.1406d79e1b574p+0 [1] [0.548] 0.547538 0.5475371438132311 libm gives 0x1.bd16a11d3404ep-4 mpfr gives 0x1.bd16a11d3404fp-4 If your goal is accuracy, you can try the CORE-MATH implementation: https://gitlab.inria.fr/core-math/core-math/-/blob/master/src/binary64/log2/log2.c It takes 19 cycles on average on an Intel(R) Core(TM) i7-8700, and is correctly rounded (for any rounding mode). Paul -- Problem reports: https://cygwin.com/problems.html FAQ: https://cygwin.com/faq/ Documentation: https://cygwin.com/docs.html Unsubscribe info: https://cygwin.com/ml/#unsubscribe-simple
