cvs commit: src/lib/msun/src e_rem_pio2.c e_rem_pio2f.c k_rem_pio2.c

[Bruce Evans]

bde         2008-02-25 11:43:20 UTC

  FreeBSD src repository

  Modified files:
    lib/msun/src         e_rem_pio2.c e_rem_pio2f.c k_rem_pio2.c 
  Log:
  Fix some off-by-1 errors.
  
  e_rem_pio2.c:
  Float and double precision didn't work because init_jk[] was 1 too small.
  It needs to be 2 larger than you might expect, and 1 larger than it was
  for these precisions, since its test for recomputing needs a margin of
  47 bits (almost 2 24-bit units).
  
  init_jk[] seems to be barely enough for extended and quad precisions.
  This hasn't been completely verified.  Callers now get about 24 bits
  of extra precision for float, and about 19 for double, but only about
  8 for extended and quad.  8 is not enough for callers that want to
  produce extra-precision results, but current callers have rounding
  errors of at least 0.8 ulps, so another 1/2**8 ulps of error from the
  reduction won't affect them much.
  
  Add a comment about some of the magic for init_jk[].
  
  e_rem_pio2.c:
  Double precision worked in practice because of a compensating off-by-1
  error here.  Extended precision was asked for, and it executed exactly
  the same code as the unbroken double precision.
  
  e_rem_pio2f.c:
  Float precision worked in practice because of a compensating off-by-1
  error here.  Double precision was asked for, and was almost needed,
  since the cosf() and sinf() callers want to produce extra-precision
  results, at least internally so that their error is only 0.5009 ulps.
  However, the extra precision provided by unbroken float precision is
  enough, and the double-precision code has extra overheads, so the
  off-by-1 error cost about 5% in efficiency on amd64 and i386.
  
  Revision  Changes    Path
  1.16      +1 -1      src/lib/msun/src/e_rem_pio2.c
  1.25      +2 -2      src/lib/msun/src/e_rem_pio2f.c
  1.11      +8 -3      src/lib/msun/src/k_rem_pio2.c