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H A D | e_powf.c | diff 176268 Thu Feb 14 08:23:51 MST 2008 bde Fix the hi+lo decomposition for 2/(3ln2). The decomposition needs to be into 12+24 bits of precision for extra-precision multiplication, but was into 13+24 bits. On i386 with -O1 the bug was hidden by accidental extra precision, but on amd64, in 2^32 trials the bug caused about 200000 errors of more than 1 ulp, with a maximum error of about 80 ulps. Now the maximum error in 2^32 trials on amd64 is 0.8573 ulps. It is still 0.8316 ulps on i386 with -O1. The nearby decomposition of 1/ln2 and the decomposition of 2/(3ln2) in the double precision version seem to be sub-optimal but not broken. |
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