cvs commit: src/lib/msun/src k_tan.c k_tanf.c s_tan.c s_tanf.c

[Bruce Evans]

bde         2005-11-02 14:01:45 UTC

  FreeBSD src repository

  Modified files:
    lib/msun/src         k_tan.c k_tanf.c s_tan.c s_tanf.c 
  Log:
  Moved the optimization for tiny x from __kernel_tan[f](x) to tan[f](x)
  so that it can be faster for tiny x and avoided for reduced x.
  
  This improves things a little differently than for cosine and sine.
  We still need to reclassify x in the "kernel" functions, but we get
  an extra optimization for tiny x, and an overall optimization since
  tiny reduced x rarely happens.  We also get optimizations for space
  and style.  A large block of poorly duplicated code to fix a special
  case is no longer needed.  This supersedes the fixes in k_sin.c revs
  1.9 and 1.11 and k_sinf.c 1.8 and 1.10.
  
  Fixed wrong constant for the cutoff for "tiny" in tanf().  It was
  2**-28, but should be almost the same as the cutoff in sinf() (2**-12).
  The incorrect cutoff protected us from the bugs fixed in k_sinf.c 1.8
  and 1.10, except 4 cases of reduced args passed the cutoff and needed
  special handling in theory although not in practice.  Now we essentially
  use a cutoff of 0 for the case of reduced args, so we now have 0 special
  args instead of 4.
  
  This change makes no difference to the results for sinf() (since it
  only changes the algorithm for the 4 special args and the results for
  those happen not to change), but it changes lots of results for sin().
  Exhaustive testing is impossible for sin(), but exhaustive testing
  for sinf() (relative to a version with the old algorithm and a fixed
  cutoff) shows that the changes in the error are either reductions or
  from 0.5-epsilon ulps to 0.5+epsilon ulps.  The new method just uses
  some extra terms in approximations so it tends to give more accurate
  results, and there are apparently no problems from having extra
  accuracy.  On amd64 with -O1, on all float args the error range in ulps
  is reduced from (0.500, 0.665] to [0.335, 0.500) in 24168 cases and
  increased from 0.500-epsilon to 0.500+epsilon in 24 cases.  Non-
  exhaustive testing by ucbtest shows no differences.
  
  Revision  Changes    Path
  1.12      +4 -23     src/lib/msun/src/k_tan.c
  1.11      +0 -21     src/lib/msun/src/k_tanf.c
  1.10      +5 -1      src/lib/msun/src/s_tan.c
  1.8       +5 -1      src/lib/msun/src/s_tanf.c