cvs commit: src/lib/msun/src k_rem_pio2f.c

Bruce Evans bde at
Tue Oct 11 00:56:06 PDT 2005

bde         2005-10-11 07:56:05 UTC

  FreeBSD src repository

  Modified files:
    lib/msun/src         k_rem_pio2f.c 
  Fixed range reduction for large multiples of pi/2 on systems with
  broken assignment to floats (e.g., i386 with gcc -O, but not amd64 or
  ia64; i386 with gcc -O0 worked accidentally).
  Use an unnamed volatile temporary variable to trick gcc -O into clipping
  extra precision on assignment.  It's surprising that only 1 place needed
  to be changed.
  For tanf() on i386 with gcc -O, the bug caused errors > 1 ulp with a
  density of 2.3% for args larger in magnitude than 128*pi/2, with a
  maximum error of 1.624 ulps.
  After this fix, exhaustive testing shows that range reduction for
  floats works as intended assuming that it is in within a factor of
  about 2^16 of working as intended for doubles.  It provides >= 8
  extra bits of precision for all ranges.  On i386:
  range                       max error in double/single ulps    extra precision
  -----                       -------------------------------    ---------------
  0 to 3*pi/4                 0x000d3132  /  0.0016              9+ bits
  3*pi/4 to 128*pi/2          0x00160445  /  0.0027              8+
  128*pi/2 to +Inf            0x00000030  /  0.00000009          23+
  128*pi/2 up, -O0 before fix 0x00000030  /  0.00000009          23+
  128*pi/2 up, -O1 before fix 0x10000000  /  0.5                 1
  The 23+ bits of extra precision for large multiples corresponds to almost
  perfect reduction to a pair of floats (24 extra would be perfect).
  After this fix, the maximum relative error (relative to the corresponding
  fdlibm double precision function) is < 1 ulp for all basic trig functions
  on all 2^32 float args on all machines tested:
            amd64     ia64      i386-O0   i386-O1
            ------    ------    ------    ------
  cosf:     0.8681    0.8681    0.7927    0.5650
  sinf:     0.8733    0.8610    0.7849    0.5651
  tanf:     0.9708    0.9329    0.9329    0.7035
  Revision  Changes    Path
  1.8       +1 -0      src/lib/msun/src/k_rem_pio2f.c

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