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| H A D | k_cosf.c | diff 151796 Fri Oct 28 13:36:58 MDT 2005 bde 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. |
| H A D | k_sinf.c | diff 151796 Fri Oct 28 13:36:58 MDT 2005 bde 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. |
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