Improve float range reduction accuracy near pi/2 (bug 21094).

Bug 21094 reports 3ulp errors of cosf and tanf for certain arguments
near pi/2 arising from the use of an insufficiently accurate range
reduction.  (To be clear, this is a quality-of-implementation issue
relating to the apparent intent of those particular cosf and tanf
implementations; 3ulp is within the general glibc accuracy goals, so
not inherently a bug.)

This patch fixes that error by making a wider range of cases use the
existing more accurate range reduction for arguments close to pi/2.
The wider range of values is still narrow enough for the "z -=
pio2_2;" in the more accurate case to be exact, as the code expects.

Tested for x86_64, x86 and mips64; no ulps updates needed (but at
least on mips64, the larger ulps were seen if the tests were added
without the substantive fix).

	[BZ #21094]
	* sysdeps/ieee754/flt-32/e_rem_pio2f.c (__ieee754_rem_pio2f): Use
	24+24+24-bit pi for wider range of values around pi/2.
	* math/auto-libm-test-in: Add more tests of cos and tan.
	* math/auto-libm-test-out-cos: Regenerated.
	* math/auto-libm-test-out-tan: Likewise.

1 files changed, 9 insertions, 0 deletions

diff --git a/ChangeLog b/ChangeLog
index f8b2e60bd6..f1f9ceb7ec 100644
--- a/ChangeLog
+++ b/ChangeLog
@@ -1,3 +1,12 @@
+2017-03-15  Joseph Myers  <joseph@codesourcery.com>
+
+	[BZ #21094]
+	* sysdeps/ieee754/flt-32/e_rem_pio2f.c (__ieee754_rem_pio2f): Use
+	24+24+24-bit pi for wider range of values around pi/2.
+	* math/auto-libm-test-in: Add more tests of cos and tan.
+	* math/auto-libm-test-out-cos: Regenerated.
+	* math/auto-libm-test-out-tan: Likewise.
+
 2017-03-15  John David Anglin  <danglin@gcc.gnu.org>
 
 	* sysdeps/hppa/dl-machine.h (DL_STACK_END): Define.