Fix atan / atan2 missing underflows (bug 15319).

This patch fixes bug 15319, missing underflows from atan / atan2 when
the result of atan is very close to its small argument (or that of
atan2 is very close to the ratio of its arguments, which may be an
exact division).

The usual approach of doing an underflowing computation if the
computed result is subnormal is followed.  For 32-bit x86, there are
extra complications: the inline __ieee754_atan2 in bits/mathinline.h
needs to be disabled for float and double because other libm functions
using it generally rely on getting proper underflow exceptions from
it, while the out-of-line functions have to remove excess range and
precision from the underflowing result so as to return an exact 0 in
the case where errno should be set for underflow to 0.  (The failures
I saw without that are similar to those Carlos reported for other
functions, where I haven't seen a response to
<https://sourceware.org/ml/libc-alpha/2015-01/msg00485.html>
confirming if my diagnosis is correct.  Arguably all libm functions
with float and double returns should remove excess range and
precision, but that's a separate matter.)

The x86_64 long double case reported in a comment in bug 15319 is not
a bug (it's an argument of LDBL_MIN, and x86_64 is an after-rounding
architecture so the correct IEEE result is not to raise underflow in
the given rounding mode, in addition to treating the result as an
exact LDBL_MIN being within the newly clarified documentation of
accuracy goals).  I'm presuming that the fpatan instruction can be
trusted to raise appropriate exceptions when the (long double) result
underflows (after rounding) and so no changes are needed for x86 /
x86_64 long double functions here; empirically this is the case for
the cases covered in the testsuite, on my system.

Tested for x86_64, x86, powerpc and mips64.  Only 32-bit x86 needs
ulps updates (for the changes to inlines meaning some functions no
longer get excess precision from their __ieee754_atan2* calls).

	[BZ #15319]
	* sysdeps/i386/fpu/e_atan2.S (dbl_min): New object.
	(MO): New macro.
	(__ieee754_atan2): For results with small absolute value, force
	underflow exception and remove excess range and precision from
	return value.
	* sysdeps/i386/fpu/e_atan2f.S (flt_min): New object.
	(MO): New macro.
	(__ieee754_atan2f): For results with small absolute value, force
	underflow exception and remove excess range and precision from
	return value.
	* sysdeps/i386/fpu/s_atan.S (dbl_min): New object.
	(MO): New macro.
	(__atan): For results with small absolute value, force underflow
	exception and remove excess range and precision from return value.
	* sysdeps/i386/fpu/s_atanf.S (flt_min): New object.
	(MO): New macro.
	(__atanf): For results with small absolute value, force underflow
	exception and remove excess range and precision from return value.
	* sysdeps/ieee754/dbl-64/e_atan2.c: Include <float.h> and
	<math.h>.
	(__ieee754_atan2): Force underflow exception for results with
	small absolute value.
	* sysdeps/ieee754/dbl-64/s_atan.c: Include <float.h> and
	<math_private.h>.
	(atan): Force underflow exception for results with small absolute
	value.
	* sysdeps/ieee754/flt-32/s_atanf.c: Include <float.h>.
	(__atanf): Force underflow exception for results with small
	absolute value.
	* sysdeps/ieee754/ldbl-128/s_atanl.c: Include <float.h> and
	<math.h>.
	(__atanl): Force underflow exception for results with small
	absolute value.
	* sysdeps/ieee754/ldbl-128ibm/s_atanl.c: Include <float.h>.
	(__atanl): Force underflow exception for results with small
	absolute value.
	* sysdeps/x86/fpu/bits/mathinline.h
	[!__SSE2_MATH__ && !__x86_64__ && __LIBC_INTERNAL_MATH_INLINES]
	(__ieee754_atan2): Only define inline for long double.
	* sysdeps/x86_64/fpu/multiarch/e_atan2.c
	[HAVE_FMA4_SUPPORT || HAVE_AVX_SUPPORT]: Include <math.h>.
	* math/auto-libm-test-in: Do not mark underflow exceptions as
	possibly missing for bug 15319.  Add more tests of atan2.
	* math/auto-libm-test-out: Regenerated.
	* math/libm-test.inc (casin_test_data): Do not mark underflow
	exceptions as possibly missing for bug 15319.
	(casinh_test_data): Likewise.
	* sysdeps/i386/fpu/libm-test-ulps: Update.

3 files changed, 1594 insertions, 966 deletions

diff --git a/math/auto-libm-test-in b/math/auto-libm-test-in
index 6bcfd54e55..62e1439c02 100644
--- a/math/auto-libm-test-in
+++ b/math/auto-libm-test-in
@@ -93,14 +93,13 @@ atan 0x1p-5
 atan 2.5
 atan 10
 atan 1e6
-# Bug 15319: underflow exception may be missing.
-atan 0x1p-100 missing-underflow
-atan 0x1p-600 missing-underflow
-atan 0x1p-10000 missing-underflow
-atan min missing-underflow
-atan -min missing-underflow
-atan min_subnorm missing-underflow
-atan -min_subnorm missing-underflow
+atan 0x1p-100
+atan 0x1p-600
+atan 0x1p-10000
+atan min
+atan -min
+atan min_subnorm
+atan -min_subnorm
 
 # atan2 (0,x) == 0 for x > 0.
 atan2 0 1
@@ -156,13 +155,20 @@ atan2 min -max
 atan2 -min -max
 atan2 min_subnorm -max
 atan2 -min_subnorm -max
-# Bug 15319: underflow exception may be missing.
-atan2 1 max missing-underflow
-atan2 -1 max missing-underflow
-atan2 min max missing-underflow
-atan2 -min max missing-underflow
-atan2 min_subnorm max missing-underflow
-atan2 -min_subnorm max missing-underflow
+atan2 1 max
+atan2 -1 max
+atan2 min max
+atan2 -min max
+atan2 min_subnorm max
+atan2 -min_subnorm max
+atan2 min 1
+atan2 -min 1
+atan2 min_subnorm 1
+atan2 -min_subnorm 1
+atan2 min -1
+atan2 -min -1
+atan2 min_subnorm -1
+atan2 -min_subnorm -1
 
 atanh 0
 atanh -0
diff --git a/math/auto-libm-test-out b/math/auto-libm-test-out
index 7b569cf12a..9d00c3be12 100644
--- a/math/auto-libm-test-out
+++ b/math/auto-libm-test-out
@@ -3353,7 +3353,7 @@ atan 1e6
 = atan tonearest ldbl-128ibm 0xf.424p+16L : 0x1.921fa47d4b30ce822275563fcb8p+0L : inexact-ok
 = atan towardzero ldbl-128ibm 0xf.424p+16L : 0x1.921fa47d4b30ce822275563fcb8p+0L : inexact-ok
 = atan upward ldbl-128ibm 0xf.424p+16L : 0x1.921fa47d4b30ce822275563fccp+0L : inexact-ok
-atan 0x1p-100 missing-underflow
+atan 0x1p-100
 = atan downward flt-32 0x1p-100f : 0xf.fffffp-104f : inexact-ok
 = atan tonearest flt-32 0x1p-100f : 0x1p-100f : inexact-ok
 = atan towardzero flt-32 0x1p-100f : 0xf.fffffp-104f : inexact-ok
@@ -3378,11 +3378,11 @@ atan 0x1p-100 missing-underflow
 = atan tonearest ldbl-128ibm 0x1p-100L : 0x1p-100L : inexact-ok
 = atan towardzero ldbl-128ibm 0x1p-100L : 0xf.fffffffffffffffffffffffffcp-104L : inexact-ok
 = atan upward ldbl-128ibm 0x1p-100L : 0x1p-100L : inexact-ok
-atan 0x1p-600 missing-underflow
-= atan downward flt-32 0x8p-152f : 0x0p+0f : inexact-ok underflow underflow-ok errno-erange-ok
-= atan tonearest flt-32 0x8p-152f : 0x8p-152f : inexact-ok underflow underflow-ok errno-erange-ok
-= atan towardzero flt-32 0x8p-152f : 0x0p+0f : inexact-ok underflow underflow-ok errno-erange-ok
-= atan upward flt-32 0x8p-152f : 0x8p-152f : inexact-ok underflow underflow-ok errno-erange-ok
+atan 0x1p-600
+= atan downward flt-32 0x8p-152f : 0x0p+0f : inexact-ok underflow errno-erange-ok
+= atan tonearest flt-32 0x8p-152f : 0x8p-152f : inexact-ok underflow errno-erange-ok
+= atan towardzero flt-32 0x8p-152f : 0x0p+0f : inexact-ok underflow errno-erange-ok
+= atan upward flt-32 0x8p-152f : 0x8p-152f : inexact-ok underflow errno-erange-ok
 = atan downward dbl-64 0x8p-152 : 0x7.ffffffffffffcp-152 : inexact-ok
 = atan tonearest dbl-64 0x8p-152 : 0x8p-152 : inexact-ok
 = atan towardzero dbl-64 0x8p-152 : 0x7.ffffffffffffcp-152 : inexact-ok
@@ -3447,11 +3447,11 @@ atan 0x1p-600 missing-underflow
 = atan tonearest ldbl-128ibm 0x1p-600L : 0x1p-600L : inexact-ok
 = atan towardzero ldbl-128ibm 0x1p-600L : 0xf.fffffffffffffffffffffffffcp-604L : inexact-ok
 = atan upward ldbl-128ibm 0x1p-600L : 0x1p-600L : inexact-ok
-atan 0x1p-10000 missing-underflow
-= atan downward flt-32 0x8p-152f : 0x0p+0f : inexact-ok underflow underflow-ok errno-erange-ok
-= atan tonearest flt-32 0x8p-152f : 0x8p-152f : inexact-ok underflow underflow-ok errno-erange-ok
-= atan towardzero flt-32 0x8p-152f : 0x0p+0f : inexact-ok underflow underflow-ok errno-erange-ok
-= atan upward flt-32 0x8p-152f : 0x8p-152f : inexact-ok underflow underflow-ok errno-erange-ok
+atan 0x1p-10000
+= atan downward flt-32 0x8p-152f : 0x0p+0f : inexact-ok underflow errno-erange-ok
+= atan tonearest flt-32 0x8p-152f : 0x8p-152f : inexact-ok underflow errno-erange-ok
+= atan towardzero flt-32 0x8p-152f : 0x0p+0f : inexact-ok underflow errno-erange-ok
+= atan upward flt-32 0x8p-152f : 0x8p-152f : inexact-ok underflow errno-erange-ok
 = atan downward dbl-64 0x8p-152 : 0x7.ffffffffffffcp-152 : inexact-ok
 = atan tonearest dbl-64 0x8p-152 : 0x8p-152 : inexact-ok
 = atan towardzero dbl-64 0x8p-152 : 0x7.ffffffffffffcp-152 : inexact-ok
@@ -3496,10 +3496,10 @@ atan 0x1p-10000 missing-underflow
 = atan tonearest ldbl-128ibm 0x0p+0L : 0x0p+0L : inexact-ok
 = atan towardzero ldbl-128ibm 0x0p+0L : 0x0p+0L : inexact-ok
 = atan upward ldbl-128ibm 0x0p+0L : 0x0p+0L : inexact-ok
-= atan downward dbl-64 0x4p-1076 : 0x0p+0 : inexact-ok underflow underflow-ok errno-erange-ok
-= atan tonearest dbl-64 0x4p-1076 : 0x4p-1076 : inexact-ok underflow underflow-ok errno-erange-ok
-= atan towardzero dbl-64 0x4p-1076 : 0x0p+0 : inexact-ok underflow underflow-ok errno-erange-ok
-= atan upward dbl-64 0x4p-1076 : 0x4p-1076 : inexact-ok underflow underflow-ok errno-erange-ok
+= atan downward dbl-64 0x4p-1076 : 0x0p+0 : inexact-ok underflow errno-erange-ok
+= atan tonearest dbl-64 0x4p-1076 : 0x4p-1076 : inexact-ok underflow errno-erange-ok
+= atan towardzero dbl-64 0x4p-1076 : 0x0p+0 : inexact-ok underflow errno-erange-ok
+= atan upward dbl-64 0x4p-1076 : 0x4p-1076 : inexact-ok underflow errno-erange-ok
 = atan downward ldbl-96-intel 0x4p-1076L : 0x3.fffffffffffffffcp-1076L : inexact-ok
 = atan tonearest ldbl-96-intel 0x4p-1076L : 0x4p-1076L : inexact-ok
 = atan towardzero ldbl-96-intel 0x4p-1076L : 0x3.fffffffffffffffcp-1076L : inexact-ok
@@ -3512,10 +3512,10 @@ atan 0x1p-10000 missing-underflow
 = atan tonearest ldbl-128 0x4p-1076L : 0x4p-1076L : inexact-ok
 = atan towardzero ldbl-128 0x4p-1076L : 0x3.fffffffffffffffffffffffffffep-1076L : inexact-ok
 = atan upward ldbl-128 0x4p-1076L : 0x4p-1076L : inexact-ok
-= atan downward ldbl-128ibm 0x4p-1076L : 0x0p+0L : inexact-ok underflow underflow-ok errno-erange-ok
-= atan tonearest ldbl-128ibm 0x4p-1076L : 0x4p-1076L : inexact-ok underflow underflow-ok errno-erange-ok
-= atan towardzero ldbl-128ibm 0x4p-1076L : 0x0p+0L : inexact-ok underflow underflow-ok errno-erange-ok
-= atan upward ldbl-128ibm 0x4p-1076L : 0x4p-1076L : inexact-ok underflow underflow-ok errno-erange-ok
+= atan downward ldbl-128ibm 0x4p-1076L : 0x0p+0L : inexact-ok underflow errno-erange-ok
+= atan tonearest ldbl-128ibm 0x4p-1076L : 0x4p-1076L : inexact-ok underflow errno-erange-ok
+= atan towardzero ldbl-128ibm 0x4p-1076L : 0x0p+0L : inexact-ok underflow errno-erange-ok
+= atan upward ldbl-128ibm 0x4p-1076L : 0x4p-1076L : inexact-ok underflow errno-erange-ok
 = atan downward ldbl-96-intel 0x1p-10000L : 0xf.fffffffffffffffp-10004L : inexact-ok
 = atan tonearest ldbl-96-intel 0x1p-10000L : 0x1p-10000L : inexact-ok
 = atan towardzero ldbl-96-intel 0x1p-10000L : 0xf.fffffffffffffffp-10004L : inexact-ok
@@ -3528,7 +3528,7 @@ atan 0x1p-10000 missing-underflow
 = atan tonearest ldbl-128 0x1p-10000L : 0x1p-10000L : inexact-ok
 = atan towardzero ldbl-128 0x1p-10000L : 0xf.fffffffffffffffffffffffffff8p-10004L : inexact-ok
 = atan upward ldbl-128 0x1p-10000L : 0x1p-10000L : inexact-ok
-atan min missing-underflow
+atan min
 = atan downward flt-32 0x4p-128f : 0x3.fffff8p-128f : inexact-ok underflow-ok errno-erange-ok
 = atan tonearest flt-32 0x4p-128f : 0x4p-128f : inexact-ok underflow-ok errno-erange-ok
 = atan towardzero flt-32 0x4p-128f : 0x3.fffff8p-128f : inexact-ok underflow-ok errno-erange-ok
@@ -3569,10 +3569,10 @@ atan min missing-underflow
 = atan tonearest ldbl-128 0x4p-1024L : 0x4p-1024L : inexact-ok
 = atan towardzero ldbl-128 0x4p-1024L : 0x3.fffffffffffffffffffffffffffep-1024L : inexact-ok
 = atan upward ldbl-128 0x4p-1024L : 0x4p-1024L : inexact-ok
-= atan downward ldbl-128ibm 0x4p-1024L : 0x3.ffffffffffffcp-1024L : inexact-ok underflow underflow-ok errno-erange-ok
-= atan tonearest ldbl-128ibm 0x4p-1024L : 0x4p-1024L : inexact-ok underflow underflow-ok errno-erange-ok
-= atan towardzero ldbl-128ibm 0x4p-1024L : 0x3.ffffffffffffcp-1024L : inexact-ok underflow underflow-ok errno-erange-ok
-= atan upward ldbl-128ibm 0x4p-1024L : 0x4p-1024L : inexact-ok underflow underflow-ok errno-erange-ok
+= atan downward ldbl-128ibm 0x4p-1024L : 0x3.ffffffffffffcp-1024L : inexact-ok underflow errno-erange-ok
+= atan tonearest ldbl-128ibm 0x4p-1024L : 0x4p-1024L : inexact-ok underflow errno-erange-ok
+= atan towardzero ldbl-128ibm 0x4p-1024L : 0x3.ffffffffffffcp-1024L : inexact-ok underflow errno-erange-ok
+= atan upward ldbl-128ibm 0x4p-1024L : 0x4p-1024L : inexact-ok underflow errno-erange-ok
 = atan downward ldbl-96-intel 0x4p-16384L : 0x3.fffffffffffffff8p-16384L : inexact-ok underflow-ok errno-erange-ok
 = atan tonearest ldbl-96-intel 0x4p-16384L : 0x4p-16384L : inexact-ok underflow-ok errno-erange-ok
 = atan towardzero ldbl-96-intel 0x4p-16384L : 0x3.fffffffffffffff8p-16384L : inexact-ok underflow-ok errno-erange-ok
@@ -3585,18 +3585,18 @@ atan min missing-underflow
 = atan tonearest ldbl-128 0x4p-16384L : 0x4p-16384L : inexact-ok underflow-ok errno-erange-ok
 = atan towardzero ldbl-128 0x4p-16384L : 0x3.fffffffffffffffffffffffffffcp-16384L : inexact-ok underflow-ok errno-erange-ok
 = atan upward ldbl-128 0x4p-16384L : 0x4p-16384L : inexact-ok underflow-ok errno-erange-ok
-= atan downward ldbl-96-intel 0x2p-16384L : 0x1.fffffffffffffff8p-16384L : inexact-ok underflow underflow-ok errno-erange-ok
-= atan tonearest ldbl-96-intel 0x2p-16384L : 0x2p-16384L : inexact-ok underflow underflow-ok errno-erange-ok
-= atan towardzero ldbl-96-intel 0x2p-16384L : 0x1.fffffffffffffff8p-16384L : inexact-ok underflow underflow-ok errno-erange-ok
-= atan upward ldbl-96-intel 0x2p-16384L : 0x2p-16384L : inexact-ok underflow underflow-ok errno-erange-ok
+= atan downward ldbl-96-intel 0x2p-16384L : 0x1.fffffffffffffff8p-16384L : inexact-ok underflow errno-erange-ok
+= atan tonearest ldbl-96-intel 0x2p-16384L : 0x2p-16384L : inexact-ok underflow errno-erange-ok
+= atan towardzero ldbl-96-intel 0x2p-16384L : 0x1.fffffffffffffff8p-16384L : inexact-ok underflow errno-erange-ok
+= atan upward ldbl-96-intel 0x2p-16384L : 0x2p-16384L : inexact-ok underflow errno-erange-ok
 = atan downward ldbl-96-m68k 0x2p-16384L : 0x1.fffffffffffffffcp-16384L : inexact-ok underflow-ok errno-erange-ok
 = atan tonearest ldbl-96-m68k 0x2p-16384L : 0x2p-16384L : inexact-ok underflow-ok errno-erange-ok
 = atan towardzero ldbl-96-m68k 0x2p-16384L : 0x1.fffffffffffffffcp-16384L : inexact-ok underflow-ok errno-erange-ok
 = atan upward ldbl-96-m68k 0x2p-16384L : 0x2p-16384L : inexact-ok underflow-ok errno-erange-ok
-= atan downward ldbl-128 0x2p-16384L : 0x1.fffffffffffffffffffffffffffcp-16384L : inexact-ok underflow underflow-ok errno-erange-ok
-= atan tonearest ldbl-128 0x2p-16384L : 0x2p-16384L : inexact-ok underflow underflow-ok errno-erange-ok
-= atan towardzero ldbl-128 0x2p-16384L : 0x1.fffffffffffffffffffffffffffcp-16384L : inexact-ok underflow underflow-ok errno-erange-ok
-= atan upward ldbl-128 0x2p-16384L : 0x2p-16384L : inexact-ok underflow underflow-ok errno-erange-ok
+= atan downward ldbl-128 0x2p-16384L : 0x1.fffffffffffffffffffffffffffcp-16384L : inexact-ok underflow errno-erange-ok
+= atan tonearest ldbl-128 0x2p-16384L : 0x2p-16384L : inexact-ok underflow errno-erange-ok
+= atan towardzero ldbl-128 0x2p-16384L : 0x1.fffffffffffffffffffffffffffcp-16384L : inexact-ok underflow errno-erange-ok
+= atan upward ldbl-128 0x2p-16384L : 0x2p-16384L : inexact-ok underflow errno-erange-ok
 = atan downward dbl-64 0x8p-972 : 0x7.ffffffffffffcp-972 : inexact-ok
 = atan tonearest dbl-64 0x8p-972 : 0x8p-972 : inexact-ok
 = atan towardzero dbl-64 0x8p-972 : 0x7.ffffffffffffcp-972 : inexact-ok
@@ -3617,7 +3617,7 @@ atan min missing-underflow
 = atan tonearest ldbl-128ibm 0x8p-972L : 0x8p-972L : inexact-ok underflow-ok errno-erange-ok
 = atan towardzero ldbl-128ibm 0x8p-972L : 0x7.fffffffffffffffffffffffffcp-972L : inexact-ok underflow-ok errno-erange-ok
 = atan upward ldbl-128ibm 0x8p-972L : 0x8p-972L : inexact-ok underflow-ok errno-erange-ok
-atan -min missing-underflow
+atan -min
 = atan downward flt-32 -0x4p-128f : -0x4p-128f : inexact-ok underflow-ok errno-erange-ok
 = atan tonearest flt-32 -0x4p-128f : -0x4p-128f : inexact-ok underflow-ok errno-erange-ok
 = atan towardzero flt-32 -0x4p-128f : -0x3.fffff8p-128f : inexact-ok underflow-ok errno-erange-ok
@@ -3658,10 +3658,10 @@ atan -min missing-underflow
 = atan tonearest ldbl-128 -0x4p-1024L : -0x4p-1024L : inexact-ok
 = atan towardzero ldbl-128 -0x4p-1024L : -0x3.fffffffffffffffffffffffffffep-1024L : inexact-ok
 = atan upward ldbl-128 -0x4p-1024L : -0x3.fffffffffffffffffffffffffffep-1024L : inexact-ok
-= atan downward ldbl-128ibm -0x4p-1024L : -0x4p-1024L : inexact-ok underflow underflow-ok errno-erange-ok
-= atan tonearest ldbl-128ibm -0x4p-1024L : -0x4p-1024L : inexact-ok underflow underflow-ok errno-erange-ok
-= atan towardzero ldbl-128ibm -0x4p-1024L : -0x3.ffffffffffffcp-1024L : inexact-ok underflow underflow-ok errno-erange-ok
-= atan upward ldbl-128ibm -0x4p-1024L : -0x3.ffffffffffffcp-1024L : inexact-ok underflow underflow-ok errno-erange-ok
+= atan downward ldbl-128ibm -0x4p-1024L : -0x4p-1024L : inexact-ok underflow errno-erange-ok
+= atan tonearest ldbl-128ibm -0x4p-1024L : -0x4p-1024L : inexact-ok underflow errno-erange-ok
+= atan towardzero ldbl-128ibm -0x4p-1024L : -0x3.ffffffffffffcp-1024L : inexact-ok underflow errno-erange-ok
+= atan upward ldbl-128ibm -0x4p-1024L : -0x3.ffffffffffffcp-1024L : inexact-ok underflow errno-erange-ok
 = atan downward ldbl-96-intel -0x4p-16384L : -0x4p-16384L : inexact-ok underflow-ok errno-erange-ok
 = atan tonearest ldbl-96-intel -0x4p-16384L : -0x4p-16384L : inexact-ok underflow-ok errno-erange-ok
 = atan towardzero ldbl-96-intel -0x4p-16384L : -0x3.fffffffffffffff8p-16384L : inexact-ok underflow-ok errno-erange-ok
@@ -3674,18 +3674,18 @@ atan -min missing-underflow
 = atan tonearest ldbl-128 -0x4p-16384L : -0x4p-16384L : inexact-ok underflow-ok errno-erange-ok
 = atan towardzero ldbl-128 -0x4p-16384L : -0x3.fffffffffffffffffffffffffffcp-16384L : inexact-ok underflow-ok errno-erange-ok
 = atan upward ldbl-128 -0x4p-16384L : -0x3.fffffffffffffffffffffffffffcp-16384L : inexact-ok underflow-ok errno-erange-ok
-= atan downward ldbl-96-intel -0x2p-16384L : -0x2p-16384L : inexact-ok underflow underflow-ok errno-erange-ok
-= atan tonearest ldbl-96-intel -0x2p-16384L : -0x2p-16384L : inexact-ok underflow underflow-ok errno-erange-ok
-= atan towardzero ldbl-96-intel -0x2p-16384L : -0x1.fffffffffffffff8p-16384L : inexact-ok underflow underflow-ok errno-erange-ok
-= atan upward ldbl-96-intel -0x2p-16384L : -0x1.fffffffffffffff8p-16384L : inexact-ok underflow underflow-ok errno-erange-ok
+= atan downward ldbl-96-intel -0x2p-16384L : -0x2p-16384L : inexact-ok underflow errno-erange-ok
+= atan tonearest ldbl-96-intel -0x2p-16384L : -0x2p-16384L : inexact-ok underflow errno-erange-ok
+= atan towardzero ldbl-96-intel -0x2p-16384L : -0x1.fffffffffffffff8p-16384L : inexact-ok underflow errno-erange-ok
+= atan upward ldbl-96-intel -0x2p-16384L : -0x1.fffffffffffffff8p-16384L : inexact-ok underflow errno-erange-ok
 = atan downward ldbl-96-m68k -0x2p-16384L : -0x2p-16384L : inexact-ok underflow-ok errno-erange-ok
 = atan tonearest ldbl-96-m68k -0x2p-16384L : -0x2p-16384L : inexact-ok underflow-ok errno-erange-ok
 = atan towardzero ldbl-96-m68k -0x2p-16384L : -0x1.fffffffffffffffcp-16384L : inexact-ok underflow-ok errno-erange-ok
 = atan upward ldbl-96-m68k -0x2p-16384L : -0x1.fffffffffffffffcp-16384L : inexact-ok underflow-ok errno-erange-ok
-= atan downward ldbl-128 -0x2p-16384L : -0x2p-16384L : inexact-ok underflow underflow-ok errno-erange-ok
-= atan tonearest ldbl-128 -0x2p-16384L : -0x2p-16384L : inexact-ok underflow underflow-ok errno-erange-ok
-= atan towardzero ldbl-128 -0x2p-16384L : -0x1.fffffffffffffffffffffffffffcp-16384L : inexact-ok underflow underflow-ok errno-erange-ok
-= atan upward ldbl-128 -0x2p-16384L : -0x1.fffffffffffffffffffffffffffcp-16384L : inexact-ok underflow underflow-ok errno-erange-ok
+= atan downward ldbl-128 -0x2p-16384L : -0x2p-16384L : inexact-ok underflow errno-erange-ok
+= atan tonearest ldbl-128 -0x2p-16384L : -0x2p-16384L : inexact-ok underflow errno-erange-ok
+= atan towardzero ldbl-128 -0x2p-16384L : -0x1.fffffffffffffffffffffffffffcp-16384L : inexact-ok underflow errno-erange-ok
+= atan upward ldbl-128 -0x2p-16384L : -0x1.fffffffffffffffffffffffffffcp-16384L : inexact-ok underflow errno-erange-ok
 = atan downward dbl-64 -0x8p-972 : -0x8p-972 : inexact-ok
 = atan tonearest dbl-64 -0x8p-972 : -0x8p-972 : inexact-ok
 = atan towardzero dbl-64 -0x8p-972 : -0x7.ffffffffffffcp-972 : inexact-ok
@@ -3706,11 +3706,11 @@ atan -min missing-underflow
 = atan tonearest ldbl-128ibm -0x8p-972L : -0x8p-972L : inexact-ok underflow-ok errno-erange-ok
 = atan towardzero ldbl-128ibm -0x8p-972L : -0x7.fffffffffffffffffffffffffcp-972L : inexact-ok underflow-ok errno-erange-ok
 = atan upward ldbl-128ibm -0x8p-972L : -0x7.fffffffffffffffffffffffffcp-972L : inexact-ok underflow-ok errno-erange-ok
-atan min_subnorm missing-underflow
-= atan downward flt-32 0x8p-152f : 0x0p+0f : inexact-ok underflow underflow-ok errno-erange-ok
-= atan tonearest flt-32 0x8p-152f : 0x8p-152f : inexact-ok underflow underflow-ok errno-erange-ok
-= atan towardzero flt-32 0x8p-152f : 0x0p+0f : inexact-ok underflow underflow-ok errno-erange-ok
-= atan upward flt-32 0x8p-152f : 0x8p-152f : inexact-ok underflow underflow-ok errno-erange-ok
+atan min_subnorm
+= atan downward flt-32 0x8p-152f : 0x0p+0f : inexact-ok underflow errno-erange-ok
+= atan tonearest flt-32 0x8p-152f : 0x8p-152f : inexact-ok underflow errno-erange-ok
+= atan towardzero flt-32 0x8p-152f : 0x0p+0f : inexact-ok underflow errno-erange-ok
+= atan upward flt-32 0x8p-152f : 0x8p-152f : inexact-ok underflow errno-erange-ok
 = atan downward dbl-64 0x8p-152 : 0x7.ffffffffffffcp-152 : inexact-ok
 = atan tonearest dbl-64 0x8p-152 : 0x8p-152 : inexact-ok
 = atan towardzero dbl-64 0x8p-152 : 0x7.ffffffffffffcp-152 : inexact-ok
@@ -3731,10 +3731,10 @@ atan min_subnorm missing-underflow
 = atan tonearest ldbl-128ibm 0x8p-152L : 0x8p-152L : inexact-ok
 = atan towardzero ldbl-128ibm 0x8p-152L : 0x7.fffffffffffffffffffffffffep-152L : inexact-ok
 = atan upward ldbl-128ibm 0x8p-152L : 0x8p-152L : inexact-ok
-= atan downward dbl-64 0x4p-1076 : 0x0p+0 : inexact-ok underflow underflow-ok errno-erange-ok
-= atan tonearest dbl-64 0x4p-1076 : 0x4p-1076 : inexact-ok underflow underflow-ok errno-erange-ok
-= atan towardzero dbl-64 0x4p-1076 : 0x0p+0 : inexact-ok underflow underflow-ok errno-erange-ok
-= atan upward dbl-64 0x4p-1076 : 0x4p-1076 : inexact-ok underflow underflow-ok errno-erange-ok
+= atan downward dbl-64 0x4p-1076 : 0x0p+0 : inexact-ok underflow errno-erange-ok
+= atan tonearest dbl-64 0x4p-1076 : 0x4p-1076 : inexact-ok underflow errno-erange-ok
+= atan towardzero dbl-64 0x4p-1076 : 0x0p+0 : inexact-ok underflow errno-erange-ok
+= atan upward dbl-64 0x4p-1076 : 0x4p-1076 : inexact-ok underflow errno-erange-ok
 = atan downward ldbl-96-intel 0x4p-1076L : 0x3.fffffffffffffffcp-1076L : inexact-ok
 = atan tonearest ldbl-96-intel 0x4p-1076L : 0x4p-1076L : inexact-ok
 = atan towardzero ldbl-96-intel 0x4p-1076L : 0x3.fffffffffffffffcp-1076L : inexact-ok
@@ -3747,39 +3747,39 @@ atan min_subnorm missing-underflow
 = atan tonearest ldbl-128 0x4p-1076L : 0x4p-1076L : inexact-ok
 = atan towardzero ldbl-128 0x4p-1076L : 0x3.fffffffffffffffffffffffffffep-1076L : inexact-ok
 = atan upward ldbl-128 0x4p-1076L : 0x4p-1076L : inexact-ok
-= atan downward ldbl-128ibm 0x4p-1076L : 0x0p+0L : inexact-ok underflow underflow-ok errno-erange-ok
-= atan tonearest ldbl-128ibm 0x4p-1076L : 0x4p-1076L : inexact-ok underflow underflow-ok errno-erange-ok
-= atan towardzero ldbl-128ibm 0x4p-1076L : 0x0p+0L : inexact-ok underflow underflow-ok errno-erange-ok
-= atan upward ldbl-128ibm 0x4p-1076L : 0x4p-1076L : inexact-ok underflow underflow-ok errno-erange-ok
-= atan downward ldbl-96-intel 0x8p-16448L : 0x0p+0L : inexact-ok underflow underflow-ok errno-erange-ok
-= atan tonearest ldbl-96-intel 0x8p-16448L : 0x8p-16448L : inexact-ok underflow underflow-ok errno-erange-ok
-= atan towardzero ldbl-96-intel 0x8p-16448L : 0x0p+0L : inexact-ok underflow underflow-ok errno-erange-ok
-= atan upward ldbl-96-intel 0x8p-16448L : 0x8p-16448L : inexact-ok underflow underflow-ok errno-erange-ok
-= atan downward ldbl-96-m68k 0x8p-16448L : 0x4p-16448L : inexact-ok underflow underflow-ok errno-erange-ok
-= atan tonearest ldbl-96-m68k 0x8p-16448L : 0x8p-16448L : inexact-ok underflow underflow-ok errno-erange-ok
-= atan towardzero ldbl-96-m68k 0x8p-16448L : 0x4p-16448L : inexact-ok underflow underflow-ok errno-erange-ok
-= atan upward ldbl-96-m68k 0x8p-16448L : 0x8p-16448L : inexact-ok underflow underflow-ok errno-erange-ok
-= atan downward ldbl-128 0x8p-16448L : 0x7.fffffffffffcp-16448L : inexact-ok underflow underflow-ok errno-erange-ok
-= atan tonearest ldbl-128 0x8p-16448L : 0x8p-16448L : inexact-ok underflow underflow-ok errno-erange-ok
-= atan towardzero ldbl-128 0x8p-16448L : 0x7.fffffffffffcp-16448L : inexact-ok underflow underflow-ok errno-erange-ok
-= atan upward ldbl-128 0x8p-16448L : 0x8p-16448L : inexact-ok underflow underflow-ok errno-erange-ok
-= atan downward ldbl-96-m68k 0x4p-16448L : 0x0p+0L : inexact-ok underflow underflow-ok errno-erange-ok
-= atan tonearest ldbl-96-m68k 0x4p-16448L : 0x4p-16448L : inexact-ok underflow underflow-ok errno-erange-ok
-= atan towardzero ldbl-96-m68k 0x4p-16448L : 0x0p+0L : inexact-ok underflow underflow-ok errno-erange-ok
-= atan upward ldbl-96-m68k 0x4p-16448L : 0x4p-16448L : inexact-ok underflow underflow-ok errno-erange-ok
-= atan downward ldbl-128 0x4p-16448L : 0x3.fffffffffffcp-16448L : inexact-ok underflow underflow-ok errno-erange-ok
-= atan tonearest ldbl-128 0x4p-16448L : 0x4p-16448L : inexact-ok underflow underflow-ok errno-erange-ok
-= atan towardzero ldbl-128 0x4p-16448L : 0x3.fffffffffffcp-16448L : inexact-ok underflow underflow-ok errno-erange-ok
-= atan upward ldbl-128 0x4p-16448L : 0x4p-16448L : inexact-ok underflow underflow-ok errno-erange-ok
-= atan downward ldbl-128 0x4p-16496L : 0x0p+0L : inexact-ok underflow underflow-ok errno-erange-ok
-= atan tonearest ldbl-128 0x4p-16496L : 0x4p-16496L : inexact-ok underflow underflow-ok errno-erange-ok
-= atan towardzero ldbl-128 0x4p-16496L : 0x0p+0L : inexact-ok underflow underflow-ok errno-erange-ok
-= atan upward ldbl-128 0x4p-16496L : 0x4p-16496L : inexact-ok underflow underflow-ok errno-erange-ok
-atan -min_subnorm missing-underflow
-= atan downward flt-32 -0x8p-152f : -0x8p-152f : inexact-ok underflow underflow-ok errno-erange-ok
-= atan tonearest flt-32 -0x8p-152f : -0x8p-152f : inexact-ok underflow underflow-ok errno-erange-ok
-= atan towardzero flt-32 -0x8p-152f : -0x0p+0f : inexact-ok underflow underflow-ok errno-erange-ok
-= atan upward flt-32 -0x8p-152f : -0x0p+0f : inexact-ok underflow underflow-ok errno-erange-ok
+= atan downward ldbl-128ibm 0x4p-1076L : 0x0p+0L : inexact-ok underflow errno-erange-ok
+= atan tonearest ldbl-128ibm 0x4p-1076L : 0x4p-1076L : inexact-ok underflow errno-erange-ok
+= atan towardzero ldbl-128ibm 0x4p-1076L : 0x0p+0L : inexact-ok underflow errno-erange-ok
+= atan upward ldbl-128ibm 0x4p-1076L : 0x4p-1076L : inexact-ok underflow errno-erange-ok
+= atan downward ldbl-96-intel 0x8p-16448L : 0x0p+0L : inexact-ok underflow errno-erange-ok
+= atan tonearest ldbl-96-intel 0x8p-16448L : 0x8p-16448L : inexact-ok underflow errno-erange-ok
+= atan towardzero ldbl-96-intel 0x8p-16448L : 0x0p+0L : inexact-ok underflow errno-erange-ok
+= atan upward ldbl-96-intel 0x8p-16448L : 0x8p-16448L : inexact-ok underflow errno-erange-ok
+= atan downward ldbl-96-m68k 0x8p-16448L : 0x4p-16448L : inexact-ok underflow errno-erange-ok
+= atan tonearest ldbl-96-m68k 0x8p-16448L : 0x8p-16448L : inexact-ok underflow errno-erange-ok
+= atan towardzero ldbl-96-m68k 0x8p-16448L : 0x4p-16448L : inexact-ok underflow errno-erange-ok
+= atan upward ldbl-96-m68k 0x8p-16448L : 0x8p-16448L : inexact-ok underflow errno-erange-ok
+= atan downward ldbl-128 0x8p-16448L : 0x7.fffffffffffcp-16448L : inexact-ok underflow errno-erange-ok
+= atan tonearest ldbl-128 0x8p-16448L : 0x8p-16448L : inexact-ok underflow errno-erange-ok
+= atan towardzero ldbl-128 0x8p-16448L : 0x7.fffffffffffcp-16448L : inexact-ok underflow errno-erange-ok
+= atan upward ldbl-128 0x8p-16448L : 0x8p-16448L : inexact-ok underflow errno-erange-ok
+= atan downward ldbl-96-m68k 0x4p-16448L : 0x0p+0L : inexact-ok underflow errno-erange-ok
+= atan tonearest ldbl-96-m68k 0x4p-16448L : 0x4p-16448L : inexact-ok underflow errno-erange-ok
+= atan towardzero ldbl-96-m68k 0x4p-16448L : 0x0p+0L : inexact-ok underflow errno-erange-ok
+= atan upward ldbl-96-m68k 0x4p-16448L : 0x4p-16448L : inexact-ok underflow errno-erange-ok
+= atan downward ldbl-128 0x4p-16448L : 0x3.fffffffffffcp-16448L : inexact-ok underflow errno-erange-ok
+= atan tonearest ldbl-128 0x4p-16448L : 0x4p-16448L : inexact-ok underflow errno-erange-ok
+= atan towardzero ldbl-128 0x4p-16448L : 0x3.fffffffffffcp-16448L : inexact-ok underflow errno-erange-ok
+= atan upward ldbl-128 0x4p-16448L : 0x4p-16448L : inexact-ok underflow errno-erange-ok
+= atan downward ldbl-128 0x4p-16496L : 0x0p+0L : inexact-ok underflow errno-erange-ok
+= atan tonearest ldbl-128 0x4p-16496L : 0x4p-16496L : inexact-ok underflow errno-erange-ok
+= atan towardzero ldbl-128 0x4p-16496L : 0x0p+0L : inexact-ok underflow errno-erange-ok
+= atan upward ldbl-128 0x4p-16496L : 0x4p-16496L : inexact-ok underflow errno-erange-ok
+atan -min_subnorm
+= atan downward flt-32 -0x8p-152f : -0x8p-152f : inexact-ok underflow errno-erange-ok
+= atan tonearest flt-32 -0x8p-152f : -0x8p-152f : inexact-ok underflow errno-erange-ok
+= atan towardzero flt-32 -0x8p-152f : -0x0p+0f : inexact-ok underflow errno-erange-ok
+= atan upward flt-32 -0x8p-152f : -0x0p+0f : inexact-ok underflow errno-erange-ok
 = atan downward dbl-64 -0x8p-152 : -0x8p-152 : inexact-ok
 = atan tonearest dbl-64 -0x8p-152 : -0x8p-152 : inexact-ok
 = atan towardzero dbl-64 -0x8p-152 : -0x7.ffffffffffffcp-152 : inexact-ok
@@ -3800,10 +3800,10 @@ atan -min_subnorm missing-underflow