cvs commit: src/lib/msun/src k_tanf.c

[Bruce Evans]

bde         2005-11-10 17:43:50 UTC

  FreeBSD src repository

  Modified files:
    lib/msun/src         k_tanf.c 
  Log:
  As for __kernel_cosf() and __kernel_sinf(), use a fairly optimal minimax
  polynomial for __kernel_tanf().  The old one was the double-precision
  polynomial 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 polynomial that gives a
  relative error of less than 1 ulp.  It has degree 13 instead of 27,
  and happens to be 2.5 times more accurate (in infinite precision) than
  the old polynomial (the maximum error is 0.017 ulps instead of 0.041
  ulps).
  
  Unlike for cosf and sinf, the old accuracy was close to being inadequate
  -- the polynomial for double precision has a max error of 0.014 ulps
  and nearly this small an error is needed.  The new accuracy is also a
  bit small, but exhaustive checking shows that even the old accuracy
  was enough.  The increased accuracy reduces the maximum relative error
  in the final result on amd64 -O1 from 0.9588 ulps to 0.9044 ulps.
  
  Revision  Changes    Path
  1.12      +11 -17    src/lib/msun/src/k_tanf.c