Bruce Evans 11dc241777 Use fairly optimal minimax polynomials for __kernel_cosf() and
__kernel_sinf().  The old ones were the double-precision polynomials
with coefficients truncated to float.  Truncation is not a good way
to convert minimax polynomials to lower precision.  Optimize for
efficiency and use the lowest-degree polynomials that give a relative
error of less than 1 ulp -- degree 8 instead of 14 for cosf and degree
9 instead of 13 for sinf.  For sinf, the degree 8 polynomial happens
to be 6 times more accurate than the old degree 14 one, but this only
gives a tiny amount of extra accuracy in results -- we just need to
use a a degree high enough to give a polynomial whose relative accuracy
in infinite precision (but with float coefficients) is a small fraction
of a float ulp (fdlibm generally uses 1/32 for the small fraction, and
the fraction for our degree 8 polynomial is about 1/600).

The maximum relative errors for cosf() and sinf() are now 0.7719 ulps
and 0.7969 ulps, respectively.
2005-10-28 13:36:58 +00:00
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2005-06-16 21:56:03 +00:00