On 2016-08-11 12:24, Erik Bray wrote:
In this case the difference is just one ulp.

To be more precise: the difference is actually about 0.59 ulp on Cygwin:

sage: R = RealField(256)
sage: log3_exact = R(3).log()
sage: log3_cygwin = RDF(1.0986122886681096)
sage: (R(log3_cygwin) - log3_exact)/log3_cygwin.ulp()
-0.5914650915268009

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