Improve tgamma accuracy (bug 18613).

In non-default rounding modes, tgamma can be slightly less accurate
than permitted by glibc's accuracy goals.

Part of the problem is error accumulation, addressed in this patch by
setting round-to-nearest for internal computations.  However, there
was also a bug in the code dealing with computing pow (x + n, x + n)
where x + n is not exactly representable, providing another source of
error even in round-to-nearest mode; it was necessary to address both
bugs to get errors for all testcases within glibc's accuracy goals.
Given this second fix, accuracy in round-to-nearest mode is also
improved (hence regeneration of ulps for tgamma should be from scratch
- truncate libm-test-ulps or at least remove existing tgamma entries -
so that the expected ulps can be reduced).

Some additional complications also arose.  Certain tgamma tests should
strictly, according to IEEE semantics, overflow or not depending on
the rounding mode; this is beyond the scope of glibc's accuracy goals
for any function without exactly-determined results, but
gen-auto-libm-tests doesn't handle being lax there as it does for
underflow.  (libm-test.inc also doesn't handle being lax about whether
the result in cases very close to the overflow threshold is infinity
or a finite value close to overflow, but that doesn't cause problems
in this case though I've seen it cause problems with random test
generation for some functions.)  Thus, spurious-overflow markings,
with a comment, are added to auto-libm-test-in (no bug in Bugzilla
because the issue is with the testsuite, not a user-visible bug in
glibc).  And on x86, after the patch I saw ERANGE issues as previously
reported by Carlos (see my commentary in
<https://sourceware.org/ml/libc-alpha/2015-01/msg00485.html>), which
needed addressing by ensuring excess range and precision were
eliminated at various points if FLT_EVAL_METHOD != 0.

I also noticed and fixed a cosmetic issue where 1.0f was used in long
double functions and should have been 1.0L.

This completes the move of all functions to testing in all rounding
modes with ALL_RM_TEST, so gen-libm-have-vector-test.sh is updated to
remove the workaround for some functions not using ALL_RM_TEST.

Tested for x86_64, x86, mips64 and powerpc.

	[BZ #18613]
	* sysdeps/ieee754/dbl-64/e_gamma_r.c (gamma_positive): Take log of
	X_ADJ not X when adjusting exponent.
	(__ieee754_gamma_r): Do intermediate computations in
	round-to-nearest then adjust overflowing and underflowing results
	as needed.
	* sysdeps/ieee754/flt-32/e_gammaf_r.c (gammaf_positive): Take log
	of X_ADJ not X when adjusting exponent.
	(__ieee754_gammaf_r): Do intermediate computations in
	round-to-nearest then adjust overflowing and underflowing results
	as needed.
	* sysdeps/ieee754/ldbl-128/e_gammal_r.c (gammal_positive): Take
	log of X_ADJ not X when adjusting exponent.
	(__ieee754_gammal_r): Do intermediate computations in
	round-to-nearest then adjust overflowing and underflowing results
	as needed.  Use 1.0L not 1.0f as numerator of division.
	* sysdeps/ieee754/ldbl-128ibm/e_gammal_r.c (gammal_positive): Take
	log of X_ADJ not X when adjusting exponent.
	(__ieee754_gammal_r): Do intermediate computations in
	round-to-nearest then adjust overflowing and underflowing results
	as needed.  Use 1.0L not 1.0f as numerator of division.
	* sysdeps/ieee754/ldbl-96/e_gammal_r.c (gammal_positive): Take log
	of X_ADJ not X when adjusting exponent.
	(__ieee754_gammal_r): Do intermediate computations in
	round-to-nearest then adjust overflowing and underflowing results
	as needed.  Use 1.0L not 1.0f as numerator of division.
	* math/libm-test.inc (tgamma_test_data): Remove one test.  Moved
	to auto-libm-test-in.
	(tgamma_test): Use ALL_RM_TEST.
	* math/auto-libm-test-in: Add one test of tgamma.  Mark some other
	tests of tgamma with spurious-overflow.
	* math/auto-libm-test-out: Regenerated.
	* math/gen-libm-have-vector-test.sh: Do not check for START.
	* sysdeps/i386/fpu/libm-test-ulps: Update.
	* sysdeps/x86_64/fpu/libm-test-ulps: Likewise.

1 files changed, 1 insertions, 1 deletions

diff --git a/NEWS b/NEWS
index 08899a8162..69d9f73932 100644
--- a/NEWS
+++ b/NEWS
@@ -25,7 +25,7 @@ Version 2.22
   18497, 18498, 18502, 18507, 18512, 18513, 18519, 18520, 18522, 18527,
   18528, 18529, 18530, 18532, 18533, 18534, 18536, 18539, 18540, 18542,
   18544, 18545, 18546, 18547, 18549, 18553, 18558, 18569, 18583, 18585,
-  18586, 18593, 18594, 18602, 18612.
+  18586, 18593, 18594, 18602, 18612, 18613.
 
 * Cache information can be queried via sysconf() function on s390 e.g. with
   _SC_LEVEL1_ICACHE_SIZE as argument.