From: Bruce Evans <bde_at_FreeBSD.org>

Date: Thu, 15 Dec 2005 16:23:22 +0000 (UTC)

Date: Thu, 15 Dec 2005 16:23:22 +0000 (UTC)

bde 2005-12-15 16:23:22 UTC FreeBSD src repository Modified files: lib/msun/src s_cbrt.c Log: Added comments about the apparently-magic rational function used in the second step of approximating cbrt(x). It turns out to be neither very magic not nor very good. It is just the (2,2) Pade approximation to 1/cbrt(r) at r = 1, arranged in a strange way to use fewer operations at a cost of replacing 4 multiplications by 1 division, which is an especially bad tradeoff on machines where some of the multiplications can be done in parallel. A Remez rational approximation would give at least 2 more bits of accuracy, but the (2,2) Pade approximation already gives 6 more bits than needed. (Changed the comment which essentially says that it gives 3 more bits.) Lower order Pade approximations are not quite accurate enough for double precision but are plenty for float precision. A lower order Remez rational approximation might be enough for double precision too. However, rational approximations inherently require an extra division, and polynomial approximations work well for 1/cbrt(r) at r = 1, so I plan to switch to using the latter. There are some technical complications that tend to cost a division in another way. Revision Changes Path 1.11 +15 -1 src/lib/msun/src/s_cbrt.cReceived on Thu Dec 15 2005 - 16:23:23 UTC