Fixes for bugs in sinpi/cospi/tanpi

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.

PR: 272742
MFC after: 1 week