cvs commit: src/lib/msun/src s_cbrt.c s_cbrtf.c

Bruce Evans bde at
Sun Dec 18 16:22:04 PST 2005

bde         2005-12-19 00:22:03 UTC

  FreeBSD src repository

  Modified files:
    lib/msun/src         s_cbrt.c s_cbrtf.c 
  Use a minimax polynomial approximation instead of a Pade rational
  function approximation for the second step.  The polynomial has degree
  2 for cbrtf() and 4 for cbrt().  These degrees are minimal for the final
  accuracy to be essentially the same as before (slightly smaller).
  Adjust the rounding between steps 2 and 3 to match.  Unfortunately,
  for cbrt(), this breaks the claimed accuracy slightly although incorrect
  rounding doesn't.  Claim less accuracy since its not worth pessimizing
  the polynomial or relying on exhaustive testing to get insignificantly
  more accuracy.
  This saves about 30 cycles on Athlons (mainly by avoiding 2 divisions)
  so it gives an overall optimization in the 10-25% range (a larger
  percentage for float precision, especially in 32-bit mode, since other
  overheads are more dominant for double precision, surprisingly more
  in 32-bit mode).
  Revision  Changes    Path
  1.13      +21 -26    src/lib/msun/src/s_cbrt.c
  1.14      +9 -11     src/lib/msun/src/s_cbrtf.c

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