[Bug 272742] Fixes for bugs in sinpi/cospi/tanpi

https://bugs.freebsd.org/bugzilla/show_bug.cgi?id=272742

            Bug ID: 272742
           Summary: Fixes for bugs in sinpi/cospi/tanpi
           Product: Base System
           Version: CURRENT
          Hardware: Any
                OS: Any
            Status: New
          Severity: Affects Only Me
          Priority: ---
         Component: bin
          Assignee: bugs@FreeBSD.org
          Reporter: kargl@FreeBSD.org

Created attachment 243634
  --> https://bugs.freebsd.org/bugzilla/attachment.cgi?id=243634&action=edit
patch to fix half-cycle trigonometric functions

Paul Zimmermann, a MPFR developer, contacted me about large errors in the
half-cycle trigonometric functions.  I've have investigated these issues and
developed the attached patch. The float, double, and ld80 (long double) changes
have been tested.

Caveat emptor: The ld128 changes have not been compiled.  The ld128 changes
have not been tested.  I do not have access to a system that uses ld128
floating point.

Here is an itemized list of changes:

* lib/msun/src/math_private.h:
  . Add fast floor macros to compute the integer part of |x| for
    0 <= |x| 01xp(N-1), where N is the precision of the type of x.
    These macros are used in the half-cycle trigonometric functions
    (e.g., sinpi(x)).
  . The FFLOOR80 macros is used with the Intel 80-bit extended double
    functions.  This macors corrects an off-by-one error, which led to
    enormous error for |x| > 0x1p32.

* lib/msun/src/s_cospif.c:
* lib/msun/src/s_cospi.c:
* lib/msun/ld80/s_cospil.c:
  . Update Copyright years.
  . Use FFLOOR*() macro to get integer part of |x|.
  . Correct handle the range 0x1p(N-1) <= |x| < 0x1pN.  Here, one needs
    to determine if the integral value of |x| is even or odd to choose
    +1 or -1.  If |x| >= 0x1pN, always return +1.

* lib/msun/src/s_sinpif.c:
* lib/msun/src/s_sinpi.c:
* lib/msun/ld80/s_sinpil.c:
  . Update Copyright years.
  . Use FFLOOR*() macro to get integer part of |x|.

* lib/msun/src/s_tanpif.c:
* lib/msun/src/s_tanpi.c:
* lib/msun/ld80/s_tanpil.c:
  . Update Copyright years.
  . For +-0.5, return +-inf.  Previously, tanpi[fl]() returned an NaN.
  . Use FFLOOR*() to get integer part of |x|.  Need to determine if the
    integer part is even or odd.  This is used to set +-0 for |x| integral
    and +-inf for (n+1/2). 
  . For 0x1p(N-1) <= |x| < 0x1pN need to determine if x is an even or odd
    integer to select +0 or -0.  For |x| >= 0x1pN, it is always an even
    integer, select 0.
  . Note, tanpi[fl](x) is an odd function, so one needs to consider
    tanpi[fl](-|x|) = - tanpi[fl](|x|).

* lib/msun/ld128/s_cospil.c:
* lib/msun/ld128/s_sinpil.c:
* lib/msun/ld128/s_tanpil.c:
  . Update Copyright years.
  . These routines use an FFLOOR128 macros, which likely should be
    replaced by a bit twiddling algorithm.
  . The same considerations above are applied to 0x1p112 <= |x| < 0x1p113,
    and |x| >= 0x1p113 cases.
  . Note, even and odd determination used fmodl(x,2.), which is likely
    slow.

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