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

[Bruce Evans]

bde         2005-11-28 08:32:15 UTC

  FreeBSD src repository

  Modified files:
    lib/msun/src         e_lgammaf_r.c 
  Log:
  Fixed about 50 million errors of infinity ulps and about 3 million errors
  of between 1.0 and 1.8509 ulps for lgammaf(x) with x between -2**-21 and
  -2**-70.
  
  As usual, the cutoff for tiny args was not correctly translated to
  float precision.  It was 2**-70 but 2**-21 works.  Not as usual, having
  a too-small threshold was worse than a pessimization.  It was just a
  pessimization for (positive) args between 2**-70 and 2**-21, but for
  the first ~50 million (negative) args below -2**-70, the general code
  overflowed and gave a result of infinity instead of correct (finite)
  results near 70*log(2).  For the remaining ~361 million negative args
  above -2**21, the general code gave almost-acceptable errors (lgamma[f]()
  is not very accurate in general) but the pessimization was larger than
  for misclassified tiny positive args.
  
  Now the max error for lgammaf(x) with |x| < 2**-21 is 0.7885 ulps, and
  speed and accuracy are almost the same for positive and negative args
  in this range.  The maximum error overall is still infinity ulps.
  
  A cutoff of 2**-70 is probably wastefully small for the double precision
  case.  Smaller cutoffs can be used to reduce the max error to nearly
  0.5 ulps for tiny args, but this is useless since the general algrorithm
  for nearly-tiny args is not nearly that accurate -- it has a max error of
  about 1 ulp.
  
  Revision  Changes    Path
  1.9       +1 -1      src/lib/msun/src/e_lgammaf_r.c