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, 7 insertions, 3 deletions

diff --git a/math/auto-libm-test-in b/math/auto-libm-test-in
index f4313a2..f783c5b 100644
--- a/math/auto-libm-test-in
+++ b/math/auto-libm-test-in
@@ -2682,19 +2682,22 @@ tgamma 0x1p-113
 tgamma -0x1p-113
 tgamma 0x1p-127
 tgamma -0x1p-127
-tgamma 0x1p-128
+# IEEE semantics mean overflow very close to the threshold depends on
+# the rounding mode; gen-auto-libm-tests does not reflect that glibc
+# does not try to achieve this.
+tgamma 0x1p-128 spurious-overflow:flt-32
 tgamma -0x1p-128
 tgamma 0x1p-149
 tgamma -0x1p-149
 tgamma 0x1p-1023
 tgamma -0x1p-1023
-tgamma 0x1p-1024
+tgamma 0x1p-1024 spurious-overflow:dbl-64 spurious-overflow:ldbl-128ibm
 tgamma -0x1p-1024
 tgamma 0x1p-1074
 tgamma -0x1p-1074
 tgamma 0x1p-16383
 tgamma -0x1p-16383
-tgamma 0x1p-16384
+tgamma 0x1p-16384 spurious-overflow:ldbl-96-intel spurious-overflow:ldbl-96-m68k spurious-overflow:ldbl-128
 tgamma -0x1p-16384
 tgamma 0x1p-16445
 tgamma -0x1p-16445
@@ -3075,6 +3078,7 @@ tgamma 0x6.db8c603359a971081bc4a2e9dfdp+8
 tgamma 0x6.db8c603359a971081bc4a2e9dfd4p+8
 tgamma 1e3
 tgamma -100000.5
+tgamma max
 
 tgamma -0x3.06644cp+0
 tgamma -0x6.fe4636e0c5064p+0