cvs commit: src/lib/msun/src s_exp2f.c
Bruce Evans
bde at FreeBSD.org
Sun Feb 10 21:20:02 PST 2008
bde 2008-02-11 05:20:02 UTC
FreeBSD src repository
Modified files:
lib/msun/src s_exp2f.c
Log:
Use double precision for z and thus for the entire calculation of
exp2(i/TBLSIZE) * p(z) instead of only for the final multiplication
and addition. This fixes the code to match the comment that the maximum
error is 0.5010 ulps (except on machines that evaluate float expressions
in extra precision, e.g., i386's, where the evaluation was already
in extra precision).
Fix and expand the comment about use of double precision.
The relative roundoff error from evaluating p(z) in non-extra precision
was about 16 times larger than in exp2() because the interval length
is 16 times smaller. Its maximum was at least P1 * (1.0 ulps) *
max(|z|) ~= log(2) * 1.0 * 1/32 ~= 0.0217 ulps (1.0 ulps from the
addition in (1 + P1*z) with a cancelation error when z ~= -1/32). The
actual final maximum was 0.5313 ulps, of which 0.0303 ulps must have
come from the additional roundoff error in p(z). I can't explain why
the additional roundoff error was almost 3/2 times larger than the rough
estimate.
Revision Changes Path
1.6 +4 -3 src/lib/msun/src/s_exp2f.c
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