cvs commit: src/lib/msun/src s_log1pf.c

[Bruce Evans]

bde         2008-01-21 13:46:21 UTC

  FreeBSD src repository

  Modified files:
    lib/msun/src         s_log1pf.c 
  Log:
  Fix cutoffs.  This is just a cleanup and an optimization for unusual
  cases which are used mainly by regression tests.
  
  As usual, the cutoff for tiny args was not correctly translated to
  float precision.  It was 2**-54 but 2**-24 works.  It must be about
  2**-precision, since the error from approximating log(1+x) by x is
  about the same as |x|.  Exhaustive testing shows that 2**-24 gives
  perfect rounding in round-to-nearest mode.
  
  Similarly for the cutoff for being small, except this is not used by
  so many other functions.  It was 2**-29 but 2**-15 works.  It must be
  a bit smaller than sqrt(2**-precision), since the error from
  approximating log(1+x) by x-x*x/2 is about the same as x*x.  Exhaustive
  testing shows that 2**-15 gives a maximum error of 0.5052 ulps in
  round-to-nearest-mode.  The algorithm for the general case is only good
  for 0.8388 ulps, so this is sufficient (but it loses slightly on i386 --
  then extra precision gives 0.5032 ulps for the general case).
  
  While investigating this, I noticed that optimizing the usual case by
  falling into a middle case involving a simple polynomial evaluation
  (return x-x*x/2 instead of x here) is not such a good idea since it
  gives an enormous pessimization of tinier args on machines for which
  denormals are slow.  Float x*x/2 is denormal when |x| ~< 2**-64 and
  x*x/2 is evaluated in float precision, so it can easily be denormal
  for normal x.  This is even more interesting for general polynomial
  evaluations.  Multiplying out large powers of x is normally a good
  optimization since it reduces dependencies, but it creates denormals
  starting with quite large x.
  
  Revision  Changes    Path
  1.11      +2 -2      src/lib/msun/src/s_log1pf.c