Fix f64xdivf128, f64xmulf128 spurious underflows (bug 28358)

As described in bug 28358, the round-to-odd computations used in the
libm functions that round their results to a narrower format can yield
spurious underflow exceptions in the following circumstances: the
narrowing only narrows the precision of the type and not the exponent
range (i.e., it's narrowing _Float128 to _Float64x on x86_64, x86 or
ia64), the architecture does after-rounding tininess detection (which
applies to all those architectures), the result is inexact, tiny
before rounding but not tiny after rounding (with the chosen rounding
mode) for _Float64x (which is possible for narrowing mul, div and fma,
not for narrowing add, sub or sqrt), so the underflow exception
resulting from the toward-zero computation in _Float128 is spurious
for _Float64x.

Fixed by making ROUND_TO_ODD call feclearexcept (FE_UNDERFLOW) in the
problem cases (as indicated by an extra argument to the macro); there
is never any need to preserve underflow exceptions from this part of
the computation, because the conversion of the round-to-odd value to
the narrower type will underflow in exactly the cases in which the
function should raise that exception, but it may be more efficient to
avoid the extra manipulation of the floating-point environment when
not needed.

Tested for x86_64 and x86, and with build-many-glibcs.py.

4 files changed, 9586 insertions, 17 deletions

diff --git a/math/auto-libm-test-in b/math/auto-libm-test-in
index 2045a0f8d1..119e2ecb2a 100644
--- a/math/auto-libm-test-in
+++ b/math/auto-libm-test-in
@@ -4870,6 +4870,21 @@ div 0x1.0000000000008001000000000001p0 0x1.0000000000008p0
 # Similar, for double rounding to 64-bit of a division of 53-bit values.
 div 0x1ffe1p0 0xfffp0
 
+# Cases where there is underflow before rounding (for some format) but
+# might not be after rounding, depending on the rounding mode.
+div 0x1p-126 0x1.0000001p0
+div 0x1p-126 -0x1.0000001p0
+div -0x1p-126 0x1.0000001p0
+div -0x1p-126 -0x1.0000001p0
+div 0x1p-1022 0x1.00000000000001p0
+div 0x1p-1022 -0x1.00000000000001p0
+div -0x1p-1022 0x1.00000000000001p0
+div -0x1p-1022 -0x1.00000000000001p0
+div 0x1p-16382 0x1.00000000000000001p0
+div 0x1p-16382 -0x1.00000000000000001p0
+div -0x1p-16382 0x1.00000000000000001p0
+div -0x1p-16382 -0x1.00000000000000001p0
+
 erf 0
 erf -0
 erf 0.125
@@ -6645,6 +6660,21 @@ mul 0x50000000000000005p-64 0xcccccccccccccccccccccccccccdp-114
 # This product equals 2^64 + 2^11 + 1.
 mul 97689974585 188829449
 
+# Cases where there is underflow before rounding (for some format) but
+# might not be after rounding, depending on the rounding mode.
+mul 0x0.ffffff8p-126 0x1.0000001p0
+mul 0x0.ffffff8p-126 -0x1.0000001p0
+mul -0x0.ffffff8p-126 0x1.0000001p0
+mul -0x0.ffffff8p-126 -0x1.0000001p0
+mul 0x0.fffffffffffffcp-1022 0x1.00000000000001p0
+mul 0x0.fffffffffffffcp-1022 -0x1.00000000000001p0
+mul -0x0.fffffffffffffcp-1022 0x1.00000000000001p0
+mul -0x0.fffffffffffffcp-1022 -0x1.00000000000001p0
+mul 0x0.ffffffffffffffff8p-16382 0x1.00000000000000001p0
+mul 0x0.ffffffffffffffff8p-16382 -0x1.00000000000000001p0
+mul -0x0.ffffffffffffffff8p-16382 0x1.00000000000000001p0
+mul -0x0.ffffffffffffffff8p-16382 -0x1.00000000000000001p0
+
 pow 0 0
 pow 0 -0
 pow -0 0
diff --git a/math/auto-libm-test-out-narrow-div b/math/auto-libm-test-out-narrow-div
index a0ad670a22..9d29f707c6 100644
--- a/math/auto-libm-test-out-narrow-div
+++ b/math/auto-libm-test-out-narrow-div
@@ -21389,3 +21389,3375 @@ div 0x1ffe1p0 0xfffp0
 = div tonearest ibm128:arg_fmt(16,12,0,17) 0x1.ffe1p+16 0xf.ffp+8 : 0x2.0001001001001001001001001p+4 : inexact
 = div towardzero ibm128:arg_fmt(16,12,0,17) 0x1.ffe1p+16 0xf.ffp+8 : 0x2.0001001001001001001001001p+4 : inexact
 = div upward ibm128:arg_fmt(16,12,0,17) 0x1.ffe1p+16 0xf.ffp+8 : 0x2.00010010010010010010010011p+4 : inexact
+div 0x1p-126 0x1.0000001p0
+= div downward binary32:arg_fmt(0,1,-126,24) 0x4p-128 0x1.000002p+0 : 0x3.fffff8p-128 : inexact underflow errno-erange-ok
+= div tonearest binary32:arg_fmt(0,1,-126,24) 0x4p-128 0x1.000002p+0 : 0x3.fffff8p-128 : inexact underflow errno-erange-ok
+= div towardzero binary32:arg_fmt(0,1,-126,24) 0x4p-128 0x1.000002p+0 : 0x3.fffff8p-128 : inexact underflow errno-erange-ok
+= div upward binary32:arg_fmt(0,1,-126,24) 0x4p-128 0x1.000002p+0 : 0x4p-128 : inexact underflow errno-erange-ok
+= div downward binary64:arg_fmt(0,1,-126,24) 0x4p-128 0x1.000002p+0 : 0x3.fffff800000fep-128 : inexact
+= div tonearest binary64:arg_fmt(0,1,-126,24) 0x4p-128 0x1.000002p+0 : 0x3.fffff800001p-128 : inexact
+= div towardzero binary64:arg_fmt(0,1,-126,24) 0x4p-128 0x1.000002p+0 : 0x3.fffff800000fep-128 : inexact
+= div upward binary64:arg_fmt(0,1,-126,24) 0x4p-128 0x1.000002p+0 : 0x3.fffff800001p-128 : inexact
+= div downward intel96:arg_fmt(0,1,-126,24) 0x4p-128 0x1.000002p+0 : 0x3.fffff800000ffffcp-128 : inexact
+= div tonearest intel96:arg_fmt(0,1,-126,24) 0x4p-128 0x1.000002p+0 : 0x3.fffff800001p-128 : inexact
+= div towardzero intel96:arg_fmt(0,1,-126,24) 0x4p-128 0x1.000002p+0 : 0x3.fffff800000ffffcp-128 : inexact
+= div upward intel96:arg_fmt(0,1,-126,24) 0x4p-128 0x1.000002p+0 : 0x3.fffff800001p-128 : inexact
+= div downward m68k96:arg_fmt(0,1,-126,24) 0x4p-128 0x1.000002p+0 : 0x3.fffff800000ffffcp-128 : inexact
+= div tonearest m68k96:arg_fmt(0,1,-126,24) 0x4p-128 0x1.000002p+0 : 0x3.fffff800001p-128 : inexact
+= div towardzero m68k96:arg_fmt(0,1,-126,24) 0x4p-128 0x1.000002p+0 : 0x3.fffff800000ffffcp-128 : inexact
+= div upward m68k96:arg_fmt(0,1,-126,24) 0x4p-128 0x1.000002p+0 : 0x3.fffff800001p-128 : inexact
+= div downward binary128:arg_fmt(0,1,-126,24) 0x4p-128 0x1.000002p+0 : 0x3.fffff800000fffffe000003ffffep-128 : inexact
+= div tonearest binary128:arg_fmt(0,1,-126,24) 0x4p-128 0x1.000002p+0 : 0x3.fffff800000fffffe000004p-128 : inexact
+= div towardzero binary128:arg_fmt(0,1,-126,24) 0x4p-128 0x1.000002p+0 : 0x3.fffff800000fffffe000003ffffep-128 : inexact
+= div upward binary128:arg_fmt(0,1,-126,24) 0x4p-128 0x1.000002p+0 : 0x3.fffff800000fffffe000004p-128 : inexact
+= div downward ibm128:arg_fmt(0,1,-126,24) 0x4p-128 0x1.000002p+0 : 0x3.fffff800000fffffe000003fffp-128 : inexact
+= div tonearest ibm128:arg_fmt(0,1,-126,24) 0x4p-128 0x1.000002p+0 : 0x3.fffff800000fffffe000004p-128 : inexact
+= div towardzero ibm128:arg_fmt(0,1,-126,24) 0x4p-128 0x1.000002p+0 : 0x3.fffff800000fffffe000003fffp-128 : inexact
+= div upward ibm128:arg_fmt(0,1,-126,24) 0x4p-128 0x1.000002p+0 : 0x3.fffff800000fffffe000004p-128 : inexact
+= div downward binary32:arg_fmt(0,1,-126,1) 0x4p-128 0x1p+0 : 0x4p-128 :
+= div tonearest binary32:arg_fmt(0,1,-126,1) 0x4p-128 0x1p+0 : 0x4p-128 :
+= div towardzero binary32:arg_fmt(0,1,-126,1) 0x4p-128 0x1p+0 : 0x4p-128 :
+= div upward binary32:arg_fmt(0,1,-126,1) 0x4p-128 0x1p+0 : 0x4p-128 :
+= div downward binary64:arg_fmt(0,1,-126,1) 0x4p-128 0x1p+0 : 0x4p-128 :
+= div tonearest binary64:arg_fmt(0,1,-126,1) 0x4p-128 0x1p+0 : 0x4p-128 :
+= div towardzero binary64:arg_fmt(0,1,-126,1) 0x4p-128 0x1p+0 : 0x4p-128 :
+= div upward binary64:arg_fmt(0,1,-126,1) 0x4p-128 0x1p+0 : 0x4p-128 :
+= div downward intel96:arg_fmt(0,1,-126,1) 0x4p-128 0x1p+0 : 0x4p-128 :
+= div tonearest intel96:arg_fmt(0,1,-126,1) 0x4p-128 0x1p+0 : 0x4p-128 :
+= div towardzero intel96:arg_fmt(0,1,-126,1) 0x4p-128 0x1p+0 : 0x4p-128 :
+= div upward intel96:arg_fmt(0,1,-126,1) 0x4p-128 0x1p+0 : 0x4p-128 :
+= div downward m68k96:arg_fmt(0,1,-126,1) 0x4p-128 0x1p+0 : 0x4p-128 :
+= div tonearest m68k96:arg_fmt(0,1,-126,1) 0x4p-128 0x1p+0 : 0x4p-128 :
+= div towardzero m68k96:arg_fmt(0,1,-126,1) 0x4p-128 0x1p+0 : 0x4p-128 :
+= div upward m68k96:arg_fmt(0,1,-126,1) 0x4p-128 0x1p+0 : 0x4p-128 :
+= div downward binary128:arg_fmt(0,1,-126,1) 0x4p-128 0x1p+0 : 0x4p-128 :
+= div tonearest binary128:arg_fmt(0,1,-126,1) 0x4p-128 0x1p+0 : 0x4p-128 :
+= div towardzero binary128:arg_fmt(0,1,-126,1) 0x4p-128 0x1p+0 : 0x4p-128 :
+= div upward binary128:arg_fmt(0,1,-126,1) 0x4p-128 0x1p+0 : 0x4p-128 :
+= div downward ibm128:arg_fmt(0,1,-126,1) 0x4p-128 0x1p+0 : 0x4p-128 :
+= div tonearest ibm128:arg_fmt(0,1,-126,1) 0x4p-128 0x1p+0 : 0x4p-128 :
+= div towardzero ibm128:arg_fmt(0,1,-126,1) 0x4p-128 0x1p+0 : 0x4p-128 :
+= div upward ibm128:arg_fmt(0,1,-126,1) 0x4p-128 0x1p+0 : 0x4p-128 :
+= div downward binary32:arg_fmt(0,1,-126,29) 0x4p-128 0x1.0000001p+0 : 0x3.fffff8p-128 : inexact underflow errno-erange-ok
+= div tonearest binary32:arg_fmt(0,1,-126,29) 0x4p-128 0x1.0000001p+0 : 0x4p-128 : inexact underflow:before-rounding errno-erange-ok:before-rounding
+= div towardzero binary32:arg_fmt(0,1,-126,29) 0x4p-128 0x1.0000001p+0 : 0x3.fffff8p-128 : inexact underflow errno-erange-ok
+= div upward binary32:arg_fmt(0,1,-126,29) 0x4p-128 0x1.0000001p+0 : 0x4p-128 : inexact underflow:before-rounding errno-erange-ok:before-rounding
+= div downward binary64:arg_fmt(0,1,-126,29) 0x4p-128 0x1.0000001p+0 : 0x3.ffffffcp-128 : inexact
+= div tonearest binary64:arg_fmt(0,1,-126,29) 0x4p-128 0x1.0000001p+0 : 0x3.ffffffcp-128 : inexact
+= div towardzero binary64:arg_fmt(0,1,-126,29) 0x4p-128 0x1.0000001p+0 : 0x3.ffffffcp-128 : inexact
+= div upward binary64:arg_fmt(0,1,-126,29) 0x4p-128 0x1.0000001p+0 : 0x3.ffffffc000002p-128 : inexact
+= div downward intel96:arg_fmt(0,1,-126,29) 0x4p-128 0x1.0000001p+0 : 0x3.ffffffc0000003fcp-128 : inexact
+= div tonearest intel96:arg_fmt(0,1,-126,29) 0x4p-128 0x1.0000001p+0 : 0x3.ffffffc0000004p-128 : inexact
+= div towardzero intel96:arg_fmt(0,1,-126,29) 0x4p-128 0x1.0000001p+0 : 0x3.ffffffc0000003fcp-128 : inexact
+= div upward intel96:arg_fmt(0,1,-126,29) 0x4p-128 0x1.0000001p+0 : 0x3.ffffffc0000004p-128 : inexact
+= div downward m68k96:arg_fmt(0,1,-126,29) 0x4p-128 0x1.0000001p+0 : 0x3.ffffffc0000003fcp-128 : inexact
+= div tonearest m68k96:arg_fmt(0,1,-126,29) 0x4p-128 0x1.0000001p+0 : 0x3.ffffffc0000004p-128 : inexact
+= div towardzero m68k96:arg_fmt(0,1,-126,29) 0x4p-128 0x1.0000001p+0 : 0x3.ffffffc0000003fcp-128 : inexact
+= div upward m68k96:arg_fmt(0,1,-126,29) 0x4p-128 0x1.0000001p+0 : 0x3.ffffffc0000004p-128 : inexact
+= div downward binary128:arg_fmt(0,1,-126,29) 0x4p-128 0x1.0000001p+0 : 0x3.ffffffc0000003ffffffc0000002p-128 : inexact
+= div tonearest binary128:arg_fmt(0,1,-126,29) 0x4p-128 0x1.0000001p+0 : 0x3.ffffffc0000003ffffffc0000004p-128 : inexact
+= div towardzero binary128:arg_fmt(0,1,-126,29) 0x4p-128 0x1.0000001p+0 : 0x3.ffffffc0000003ffffffc0000002p-128 : inexact
+= div upward binary128:arg_fmt(0,1,-126,29) 0x4p-128 0x1.0000001p+0 : 0x3.ffffffc0000003ffffffc0000004p-128 : inexact
+= div downward ibm128:arg_fmt(0,1,-126,29) 0x4p-128 0x1.0000001p+0 : 0x3.ffffffc0000003ffffffcp-128 : inexact
+= div tonearest ibm128:arg_fmt(0,1,-126,29) 0x4p-128 0x1.0000001p+0 : 0x3.ffffffc0000003ffffffcp-128 : inexact
+= div towardzero ibm128:arg_fmt(0,1,-126,29) 0x4p-128 0x1.0000001p+0 : 0x3.ffffffc0000003ffffffcp-128 : inexact
+= div upward ibm128:arg_fmt(0,1,-126,29) 0x4p-128 0x1.0000001p+0 : 0x3.ffffffc0000003ffffffc00001p-128 : inexact
+div 0x1p-126 -0x1.0000001p0
+= div downward binary32:arg_fmt(0,1,-126,1) 0x4p-128 -0x1p+0 : -0x4p-128 :
+= div tonearest binary32:arg_fmt(0,1,-126,1) 0x4p-128 -0x1p+0 : -0x4p-128 :
+= div towardzero binary32:arg_fmt(0,1,-126,1) 0x4p-128 -0x1p+0 : -0x4p-128 :
+= div upward binary32:arg_fmt(0,1,-126,1) 0x4p-128 -0x1p+0 : -0x4p-128 :
+= div downward binary64:arg_fmt(0,1,-126,1) 0x4p-128 -0x1p+0 : -0x4p-128 :
+= div tonearest binary64:arg_fmt(0,1,-126,1) 0x4p-128 -0x1p+0 : -0x4p-128 :
+= div towardzero binary64:arg_fmt(0,1,-126,1) 0x4p-128 -0x1p+0 : -0x4p-128 :
+= div upward binary64:arg_fmt(0,1,-126,1) 0x4p-128 -0x1p+0 : -0x4p-128 :
+= div downward intel96:arg_fmt(0,1,-126,1) 0x4p-128 -0x1p+0 : -0x4p-128 :
+= div tonearest intel96:arg_fmt(0,1,-126,1) 0x4p-128 -0x1p+0 : -0x4p-128 :
+= div towardzero intel96:arg_fmt(0,1,-126,1) 0x4p-128 -0x1p+0 : -0x4p-128 :
+= div upward intel96:arg_fmt(0,1,-126,1) 0x4p-128 -0x1p+0 : -0x4p-128 :
+= div downward m68k96:arg_fmt(0,1,-126,1) 0x4p-128 -0x1p+0 : -0x4p-128 :
+= div tonearest m68k96:arg_fmt(0,1,-126,1) 0x4p-128 -0x1p+0 : -0x4p-128 :
+= div towardzero m68k96:arg_fmt(0,1,-126,1) 0x4p-128 -0x1p+0 : -0x4p-128 :
+= div upward m68k96:arg_fmt(0,1,-126,1) 0x4p-128 -0x1p+0 : -0x4p-128 :
+= div downward binary128:arg_fmt(0,1,-126,1) 0x4p-128 -0x1p+0 : -0x4p-128 :
+= div tonearest binary128:arg_fmt(0,1,-126,1) 0x4p-128 -0x1p+0 : -0x4p-128 :
+= div towardzero binary128:arg_fmt(0,1,-126,1) 0x4p-128 -0x1p+0 : -0x4p-128 :
+= div upward binary128:arg_fmt(0,1,-126,1) 0x4p-128 -0x1p+0 : -0x4p-128 :
+= div downward ibm128:arg_fmt(0,1,-126,1) 0x4p-128 -0x1p+0 : -0x4p-128 :
+= div tonearest ibm128:arg_fmt(0,1,-126,1) 0x4p-128 -0x1p+0 : -0x4p-128 :
+= div towardzero ibm128:arg_fmt(0,1,-126,1) 0x4p-128 -0x1p+0 : -0x4p-128 :
+= div upward ibm128:arg_fmt(0,1,-126,1) 0x4p-128 -0x1p+0 : -0x4p-128 :
+= div downward binary32:arg_fmt(0,1,-126,24) 0x4p-128 -0x1.000002p+0 : -0x4p-128 : inexact underflow errno-erange-ok
+= div tonearest binary32:arg_fmt(0,1,-126,24) 0x4p-128 -0x1.000002p+0 : -0x3.fffff8p-128 : inexact underflow errno-erange-ok
+= div towardzero binary32:arg_fmt(0,1,-126,24) 0x4p-128 -0x1.000002p+0 : -0x3.fffff8p-128 : inexact underflow errno-erange-ok
+= div upward binary32:arg_fmt(0,1,-126,24) 0x4p-128 -0x1.000002p+0 : -0x3.fffff8p-128 : inexact underflow errno-erange-ok
+= div downward binary64:arg_fmt(0,1,-126,24) 0x4p-128 -0x1.000002p+0 : -0x3.fffff800001p-128 : inexact
+= div tonearest binary64:arg_fmt(0,1,-126,24) 0x4p-128 -0x1.000002p+0 : -0x3.fffff800001p-128 : inexact
+= div towardzero binary64:arg_fmt(0,1,-126,24) 0x4p-128 -0x1.000002p+0 : -0x3.fffff800000fep-128 : inexact
+= div upward binary64:arg_fmt(0,1,-126,24) 0x4p-128 -0x1.000002p+0 : -0x3.fffff800000fep-128 : inexact
+= div downward intel96:arg_fmt(0,1,-126,24) 0x4p-128 -0x1.000002p+0 : -0x3.fffff800001p-128 : inexact
+= div tonearest intel96:arg_fmt(0,1,-126,24) 0x4p-128 -0x1.000002p+0 : -0x3.fffff800001p-128 : inexact
+= div towardzero intel96:arg_fmt(0,1,-126,24) 0x4p-128 -0x1.000002p+0 : -0x3.fffff800000ffffcp-128 : inexact
+= div upward intel96:arg_fmt(0,1,-126,24) 0x4p-128 -0x1.000002p+0 : -0x3.fffff800000ffffcp-128 : inexact
+= div downward m68k96:arg_fmt(0,1,-126,24) 0x4p-128 -0x1.000002p+0 : -0x3.fffff800001p-128 : inexact
+= div tonearest m68k96:arg_fmt(0,1,-126,24) 0x4p-128 -0x1.000002p+0 : -0x3.fffff800001p-128 : inexact
+= div towardzero m68k96:arg_fmt(0,1,-126,24) 0x4p-128 -0x1.000002p+0 : -0x3.fffff800000ffffcp-128 : inexact
+= div upward m68k96:arg_fmt(0,1,-126,24) 0x4p-128 -0x1.000002p+0 : -0x3.fffff800000ffffcp-128 : inexact
+= div downward binary128:arg_fmt(0,1,-126,24) 0x4p-128 -0x1.000002p+0 : -0x3.fffff800000fffffe000004p-128 : inexact
+= div tonearest binary128:arg_fmt(0,1,-126,24) 0x4p-128 -0x1.000002p+0 : -0x3.fffff800000fffffe000004p-128 : inexact
+= div towardzero binary128:arg_fmt(0,1,-126,24) 0x4p-128 -0x1.000002p+0 : -0x3.fffff800000fffffe000003ffffep-128 : inexact
+= div upward binary128:arg_fmt(0,1,-126,24) 0x4p-128 -0x1.000002p+0 : -0x3.fffff800000fffffe000003ffffep-128 : inexact
+= div downward ibm128:arg_fmt(0,1,-126,24) 0x4p-128 -0x1.000002p+0 : -0x3.fffff800000fffffe000004p-128 : inexact
+= div tonearest ibm128:arg_fmt(0,1,-126,24) 0x4p-128 -0x1.000002p+0 : -0x3.fffff800000fffffe000004p-128 : inexact
+= div towardzero ibm128:arg_fmt(0,1,-126,24) 0x4p-128 -0x1.000002p+0 : -0x3.fffff800000fffffe000003fffp-128 : inexact
+= div upward ibm128:arg_fmt(0,1,-126,24) 0x4p-128 -0x1.000002p+0 : -0x3.fffff800000fffffe000003fffp-128 : inexact
+= div downward binary32:arg_fmt(0,1,-126,29) 0x4p-128 -0x1.0000001p+0 : -0x4p-128 : inexact underflow:before-rounding errno-erange-ok:before-rounding
+= div tonearest binary32:arg_fmt(0,1,-126,29) 0x4p-128 -0x1.0000001p+0 : -0x4p-128 : inexact underflow:before-rounding errno-erange-ok:before-rounding
+= div towardzero binary32:arg_fmt(0,1,-126,29) 0x4p-128 -0x1.0000001p+0 : -0x3.fffff8p-128 : inexact underflow errno-erange-ok
+= div upward binary32:arg_fmt(0,1,-126,29) 0x4p-128 -0x1.0000001p+0 : -0x3.fffff8p-128 : inexact underflow errno-erange-ok
+= div downward binary64:arg_fmt(0,1,-126,29) 0x4p-128 -0x1.0000001p+0 : -0x3.ffffffc000002p-128 : inexact
+= div tonearest binary64:arg_fmt(0,1,-126,29) 0x4p-128 -0x1.0000001p+0 : -0x3.ffffffcp-128 : inexact
+= div towardzero binary64:arg_fmt(0,1,-126,29) 0x4p-128 -0x1.0000001p+0 : -0x3.ffffffcp-128 : inexact
+= div upward binary64:arg_fmt(0,1,-126,29) 0x4p-128 -0x1.0000001p+0 : -0x3.ffffffcp-128 : inexact
+= div downward intel96:arg_fmt(0,1,-126,29) 0x4p-128 -0x1.0000001p+0 : -0x3.ffffffc0000004p-128 : inexact
+= div tonearest intel96:arg_fmt(0,1,-126,29) 0x4p-128 -0x1.0000001p+0 : -0x3.ffffffc0000004p-128 : inexact
+= div towardzero intel96:arg_fmt(0,1,-126,29) 0x4p-128 -0x1.0000001p+0 : -0x3.ffffffc0000003fcp-128 : inexact
+= div upward intel96:arg_fmt(0,1,-126,29) 0x4p-128 -0x1.0000001p+0 : -0x3.ffffffc0000003fcp-128 : inexact
+= div downward m68k96:arg_fmt(0,1,-126,29) 0x4p-128 -0x1.0000001p+0 : -0x3.ffffffc0000004p-128 : inexact
+= div tonearest m68k96:arg_fmt(0,1,-126,29) 0x4p-128 -0x1.0000001p+0 : -0x3.ffffffc0000004p-128 : inexact
+= div towardzero m68k96:arg_fmt(0,1,-126,29) 0x4p-128 -0x1.0000001p+0 : -0x3.ffffffc0000003fcp-128 : inexact
+= div upward m68k96:arg_fmt(0,1,-126,29) 0x4p-128 -0x1.0000001p+0 : -0x3.ffffffc0000003fcp-128 : inexact
+= div downward binary128:arg_fmt(0,1,-126,29) 0x4p-128 -0x1.0000001p+0 : -0x3.ffffffc0000003ffffffc0000004p-128 : inexact
+= div tonearest binary128:arg_fmt(0,1,-126,29) 0x4p-128 -0x1.0000001p+0 : -0x3.ffffffc0000003ffffffc0000004p-128 : inexact
+= div towardzero binary128:arg_fmt(0,1,-126,29) 0x4p-128 -0x1.0000001p+0 : -0x3.ffffffc0000003ffffffc0000002p-128 : inexact
+= div upward binary128:arg_fmt(0,1,-126,29) 0x4p-128 -0x1.0000001p+0 : -0x3.ffffffc0000003ffffffc0000002p-128 : inexact
+= div downward ibm128:arg_fmt(0,1,-126,29) 0x4p-128 -0x1.0000001p+0 : -0x3.ffffffc0000003ffffffc00001p-128 : inexact
+= div tonearest ibm128:arg_fmt(0,1,-126,29) 0x4p-128 -0x1.0000001p+0 : -0x3.ffffffc0000003ffffffcp-128 : inexact
+= div towardzero ibm128:arg_fmt(0,1,-126,29) 0x4p-128 -0x1.0000001p+0 : -0x3.ffffffc0000003ffffffcp-128 : inexact
+= div upward ibm128:arg_fmt(0,1,-126,29) 0x4p-128 -0x1.0000001p+0 : -0x3.ffffffc0000003ffffffcp-128 : inexact
+div -0x1p-126 0x1.0000001p0
+= div downward binary32:arg_fmt(0,1,-126,24) -0x4p-128 0x1.000002p+0 : -0x4p-128 : inexact underflow errno-erange-ok
+= div tonearest binary32:arg_fmt(0,1,-126,24) -0x4p-128 0x1.000002p+0 : -0x3.fffff8p-128 : inexact underflow errno-erange-ok
+= div towardzero binary32:arg_fmt(0,1,-126,24) -0x4p-128 0x1.000002p+0 : -0x3.fffff8p-128 : inexact underflow errno-erange-ok
+= div upward binary32:arg_fmt(0,1,-126,24) -0x4p-128 0x1.000002p+0 : -0x3.fffff8p-128 : inexact underflow errno-erange-ok
+= div downward binary64:arg_fmt(0,1,-126,24) -0x4p-128 0x1.000002p+0 : -0x3.fffff800001p-128 : inexact
+= div tonearest binary64:arg_fmt(0,1,-126,24) -0x4p-128 0x1.000002p+0 : -0x3.fffff800001p-128 : inexact
+= div towardzero binary64:arg_fmt(0,1,-126,24) -0x4p-128 0x1.000002p+0 : -0x3.fffff800000fep-128 : inexact
+= div upward binary64:arg_fmt(0,1,-126,24) -0x4p-128 0x1.000002p+0 : -0x3.fffff800000fep-128 : inexact
+= div downward intel96:arg_fmt(0,1,-126,24) -0x4p-128 0x1.000002p+0 : -0x3.fffff800001p-128 : inexact
+= div tonearest intel96:arg_fmt(0,1,-126,24) -0x4p-128 0x1.000002p+0 : -0x3.fffff800001p-128 : inexact
+= div towardzero intel96:arg_fmt(0,1,-126,24) -0x4p-128 0x1.000002p+0 : -0x3.fffff800000ffffcp-128 : inexact
+= div upward intel96:arg_fmt(0,1,-126,24) -0x4p-128 0x1.000002p+0 : -0x3.fffff800000ffffcp-128 : inexact
+= div downward m68k96:arg_fmt(0,1,-126,24) -0x4p-128 0x1.000002p+0 : -0x3.fffff800001p-128 : inexact
+= div tonearest m68k96:arg_fmt(0,1,-126,24) -0x4p-128 0x1.000002p+0 : -0x3.fffff800001p-128 : inexact
+= div towardzero m68k96:arg_fmt(0,1,-126,24) -0x4p-128 0x1.000002p+0 : -0x3.fffff800000ffffcp-128 : inexact
+= div upward m68k96:arg_fmt(0,1,-126,24) -0x4p-128 0x1.000002p+0 : -0x3.fffff800000ffffcp-128 : inexact
+= div downward binary128:arg_fmt(0,1,-126,24) -0x4p-128 0x1.000002p+0 : -0x3.fffff800000fffffe000004p-128 : inexact
+= div tonearest binary128:arg_fmt(0,1,-126,24) -0x4p-128 0x1.000002p+0 : -0x3.fffff800000fffffe000004p-128 : inexact
+= div towardzero binary128:arg_fmt(0,1,-126,24) -0x4p-128 0x1.000002p+0 : -0x3.fffff800000fffffe000003ffffep-128 : inexact
+= div upward binary128:arg_fmt(0,1,-126,24) -0x4p-128 0x1.000002p+0 : -0x3.fffff800000fffffe000003ffffep-128 : inexact
+= div downward ibm128:arg_fmt(0,1,-126,24) -0x4p-128 0x1.000002p+0 : -0x3.fffff800000fffffe000004p-128 : inexact
+= div tonearest ibm128:arg_fmt(0,1,-126,24) -0x4p-128 0x1.000002p+0 : -0x3.fffff800000fffffe000004p-128 : inexact
+= div towardzero ibm128:arg_fmt(0,1,-126,24) -0x4p-128 0x1.000002p+0 : -0x3.fffff800000fffffe000003fffp-128 : inexact
+= div upward ibm128:arg_fmt(0,1,-126,24) -0x4p-128 0x1.000002p+0 : -0x3.fffff800000fffffe000003fffp-128 : inexact
+= div downward binary32:arg_fmt(0,1,-126,1) -0x4p-128 0x1p+0 : -0x4p-128 :
+= div tonearest binary32:arg_fmt(0,1,-126,1) -0x4p-128 0x1p+0 : -0x4p-128 :
+= div towardzero binary32:arg_fmt(0,1,-126,1) -0x4p-128 0x1p+0 : -0x4p-128 :
+= div upward binary32:arg_fmt(0,1,-126,1) -0x4p-128 0x1p+0 : -0x4p-128 :
+= div downward binary64:arg_fmt(0,1,-126,1) -0x4p-128 0x1p+0 : -0x4p-128 :
+= div tonearest binary64:arg_fmt(0,1,-126,1) -0x4p-128 0x1p+0 : -0x4p-128 :
+= div towardzero binary64:arg_fmt(0,1,-126,1) -0x4p-128 0x1p+0 : -0x4p-128 :
+= div upward binary64:arg_fmt(0,1,-126,1) -0x4p-128 0x1p+0 : -0x4p-128 :
+= div downward intel96:arg_fmt(0,1,-126,1) -0x4p-128 0x1p+0 : -0x4p-128 :
+= div tonearest intel96:arg_fmt(0,1,-126,1) -0x4p-128 0x1p+0 : -0x4p-128 :
+= div towardzero intel96:arg_fmt(0,1,-126,1) -0x4p-128 0x1p+0 : -0x4p-128 :
+= div upward intel96:arg_fmt(0,1,-126,1) -0x4p-128 0x1p+0 : -0x4p-128 :
+= div downward m68k96:arg_fmt(0,1,-126,1) -0x4p-128 0x1p+0 : -0x4p-128 :
+= div tonearest m68k96:arg_fmt(0,1,-126,1) -0x4p-128 0x1p+0 : -0x4p-128 :
+= div towardzero m68k96:arg_fmt(0,1,-126,1) -0x4p-128 0x1p+0 : -0x4p-128 :
+= div upward m68k96:arg_fmt(0,1,-126,1) -0x4p-128 0x1p+0 : -0x4p-128 :
+= div downward binary128:arg_fmt(0,1,-126,1) -0x4p-128 0x1p+0 : -0x4p-128 :
+= div tonearest binary128:arg_fmt(0,1,-126,1) -0x4p-128 0x1p+0 : -0x4p-128 :
+= div towardzero binary128:arg_fmt(0,1,-126,1) -0x4p-128 0x1p+0 : -0x4p-128 :
+= div upward binary128:arg_fmt(0,1,-126,1) -0x4p-128 0x1p+0 : -0x4p-128 :
+= div downward ibm128:arg_fmt(0,1,-126,1) -0x4p-128 0x1p+0 : -0x4p-128 :
+= div tonearest ibm128:arg_fmt(0,1,-126,1) -0x4p-128 0x1p+0 : -0x4p-128 :
+= div towardzero ibm128:arg_fmt(0,1,-126,1) -0x4p-128 0x1p+0 : -0x4p-128 :
+= div upward ibm128:arg_fmt(0,1,-126,1) -0x4p-128 0x1p+0 : -0x4p-128 :
+= div downward binary32:arg_fmt(0,1,-126,29) -0x4p-128 0x1.0000001p+0 : -0x4p-128 : inexact underflow:before-rounding errno-erange-ok:before-rounding
+= div tonearest binary32:arg_fmt(0,1,-126,29) -0x4p-128 0x1.0000001p+0 : -0x4p-128 : inexact underflow:before-rounding errno-erange-ok:before-rounding
+= div towardzero binary32:arg_fmt(0,1,-126,29) -0x4p-128 0x1.0000001p+0 : -0x3.fffff8p-128 : inexact underflow errno-erange-ok
+= div upward binary32:arg_fmt(0,1,-126,29) -0x4p-128 0x1.0000001p+0 : -0x3.fffff8p-128 : inexact underflow errno-erange-ok
+= div downward binary64:arg_fmt(0,1,-126,29) -0x4p-128 0x1.0000001p+0 : -0x3.ffffffc000002p-128 : inexact
+= div tonearest binary64:arg_fmt(0,1,-126,29) -0x4p-128 0x1.0000001p+0 : -0x3.ffffffcp-128 : inexact
+= div towardzero binary64:arg_fmt(0,1,-126,29) -0x4p-128 0x1.0000001p+0 : -0x3.ffffffcp-128 : inexact
+= div upward binary64:arg_fmt(0,1,-126,29) -0x4p-128 0x1.0000001p+0 : -0x3.ffffffcp-128 : inexact
+= div downward intel96:arg_fmt(0,1,-126,29) -0x4p-128 0x1.0000001p+0 : -0x3.ffffffc0000004p-128 : inexact
+= div tonearest intel96:arg_fmt(0,1,-126,29) -0x4p-128 0x1.0000001p+0 : -0x3.ffffffc0000004p-128 : inexact
+= div towardzero intel96:arg_fmt(0,1,-126,29) -0x4p-128 0x1.0000001p+0 : -0x3.ffffffc0000003fcp-128 : inexact
+= div upward intel96:arg_fmt(0,1,-126,29) -0x4p-128 0x1.0000001p+0 : -0x3.ffffffc0000003fcp-128 : inexact
+= div downward m68k96:arg_fmt(0,1,-126,29) -0x4p-128 0x1.0000001p+0 : -0x3.ffffffc0000004p-128 : inexact
+= div tonearest m68k96:arg_fmt(0,1,-126,29) -0x4p-128 0x1.0000001p+0 : -0x3.ffffffc0000004p-128 : inexact
+= div towardzero m68k96:arg_fmt(0,1,-126,29) -0x4p-128 0x1.0000001p+0 : -0x3.ffffffc0000003fcp-128 : inexact
+= div upward m68k96:arg_fmt(0,1,-126,29) -0x4p-128 0x1.0000001p+0 : -0x3.ffffffc0000003fcp-128 : inexact
+= div downward binary128:arg_fmt(0,1,-126,29) -0x4p-128 0x1.0000001p+0 : -0x3.ffffffc0000003ffffffc0000004p-128 : inexact
+= div tonearest binary128:arg_fmt(0,1,-126,29) -0x4p-128 0x1.0000001p+0 : -0x3.ffffffc0000003ffffffc0000004p-128 : inexact
+= div towardzero binary128:arg_fmt(0,1,-126,29) -0x4p-128 0x1.0000001p+0 : -0x3.ffffffc0000003ffffffc0000002p-128 : inexact
+= div upward binary128:arg_fmt(0,1,-126,29) -0x4p-128 0x1.0000001p+0 : -0x3.ffffffc0000003ffffffc0000002p-128 : inexact
+= div downward ibm128:arg_fmt(0,1,-126,29) -0x4p-128 0x1.0000001p+0 : -0x3.ffffffc0000003ffffffc00001p-128 : inexact
+= div tonearest ibm128:arg_fmt(0,1,-126,29) -0x4p-128 0x1.0000001p+0 : -0x3.ffffffc0000003ffffffcp-128 : inexact
+= div towardzero ibm128:arg_fmt(0,1,-126,29) -0x4p-128 0x1.0000001p+0 : -0x3.ffffffc0000003ffffffcp-128 : inexact
+= div upward ibm128:arg_fmt(0,1,-126,29) -0x4p-128 0x1.0000001p+0 : -0x3.ffffffc0000003ffffffcp-128 : inexact
+div -0x1p-126 -0x1.0000001p0
+= div downward binary32:arg_fmt(0,1,-126,1) -0x4p-128 -0x1p+0 : 0x4p-128 :
+= div tonearest binary32:arg_fmt(0,1,-126,1) -0x4p-128 -0x1p+0 : 0x4p-128 :
+= div towardzero binary32:arg_fmt(0,1,-126,1) -0x4p-128 -0x1p+0 : 0x4p-128 :
+= div upward binary32:arg_fmt(0,1,-126,1) -0x4p-128 -0x1p+0 : 0x4p-128 :
+= div downward binary64:arg_fmt(0,1,-126,1) -0x4p-128 -0x1p+0 : 0x4p-128 :
+= div tonearest binary64:arg_fmt(0,1,-126,1) -0x4p-128 -0x1p+0 : 0x4p-128 :
+= div towardzero binary64:arg_fmt(0,1,-126,1) -0x4p-128 -0x1p+0 : 0x4p-128 :
+= div upward binary64:arg_fmt(0,1,-126,1) -0x4p-128 -0x1p+0 : 0x4p-128 :
+= div downward intel96:arg_fmt(0,1,-126,1) -0x4p-128 -0x1p+0 : 0x4p-128 :
+= div tonearest intel96:arg_fmt(0,1,-126,1) -0x4p-128 -0x1p+0 : 0x4p-128 :
+= div towardzero intel96:arg_fmt(0,1,-126,1) -0x4p-128 -0x1p+0 : 0x4p-128 :
+= div upward intel96:arg_fmt(0,1,-126,1) -0x4p-128 -0x1p+0 : 0x4p-128 :
+= div downward m68k96:arg_fmt(0,1,-126,1) -0x4p-128 -0x1p+0 : 0x4p-128 :
+= div tonearest m68k96:arg_fmt(0,1,-126,1) -0x4p-128 -0x1p+0 : 0x4p-128 :
+= div towardzero m68k96:arg_fmt(0,1,-126,1) -0x4p-128 -0x1p+0 : 0x4p-128 :
+= div upward m68k96:arg_fmt(0,1,-126,1) -0x4p-128 -0x1p+0 : 0x4p-128 :
+= div downward binary128:arg_fmt(0,1,-126,1) -0x4p-128 -0x1p+0 : 0x4p-128 :
+= div tonearest binary128:arg_fmt(0,1,-126,1) -0x4p-128 -0x1p+0 : 0x4p-128 :
+= div towardzero binary128:arg_fmt(0,1,-126,1) -0x4p-128 -0x1p+0 : 0x4p-128 :
+= div upward binary128:arg_fmt(0,1,-126,1) -0x4p-128 -0x1p+0 : 0x4p-128 :
+= div downward ibm128:arg_fmt(0,1,-126,1) -0x4p-128 -0x1p+0 : 0x4p-128 :
+= div tonearest ibm128:arg_fmt(0,1,-126,1) -0x4p-128 -0x1p+0 : 0x4p-128 :
+= div towardzero ibm128:arg_fmt(0,1,-126,1) -0x4p-128 -0x1p+0 : 0x4p-128 :
+= div upward ibm128:arg_fmt(0,1,-126,1) -0x4p-128 -0x1p+0 : 0x4p-128 :
+= div downward binary32:arg_fmt(0,1,-126,24) -0x4p-128 -0x1.000002p+0 : 0x3.fffff8p-128 : inexact underflow errno-erange-ok
+= div tonearest binary32:arg_fmt(0,1,-126,24) -0x4p-128 -0x1.000002p+0 : 0x3.fffff8p-128 : inexact underflow errno-erange-ok
+= div towardzero binary32:arg_fmt(0,1,-126,24) -0x4p-128 -0x1.000002p+0 : 0x3.fffff8p-128 : inexact underflow errno-erange-ok
+= div upward binary32:arg_fmt(0,1,-126,24) -0x4p-128 -0x1.000002p+0 : 0x4p-128 : inexact underflow errno-erange-ok
+= div downward binary64:arg_fmt(0,1,-126,24) -0x4p-128 -0x1.000002p+0 : 0x3.fffff800000fep-128 : inexact
+= div tonearest binary64:arg_fmt(0,1,-126,24) -0x4p-128 -0x1.000002p+0 : 0x3.fffff800001p-128 : inexact
+= div towardzero binary64:arg_fmt(0,1,-126,24) -0x4p-128 -0x1.000002p+0 : 0x3.fffff800000fep-128 : inexact
+= div upward binary64:arg_fmt(0,1,-126,24) -0x4p-128 -0x1.000002p+0 : 0x3.fffff800001p-128 : inexact
+= div downward intel96:arg_fmt(0,1,-126,24) -0x4p-128 -0x1.000002p+0 : 0x3.fffff800000ffffcp-128 : inexact
+= div tonearest intel96:arg_fmt(0,1,-126,24) -0x4p-128 -0x1.000002p+0 : 0x3.fffff800001p-128 : inexact
+= div towardzero intel96:arg_fmt(0,1,-126,24) -0x4p-128 -0x1.000002p+0 : 0x3.fffff800000ffffcp-128 : inexact
+= div upward intel96:arg_fmt(0,1,-126,24) -0x4p-128 -0x1.000002p+0 : 0x3.fffff800001p-128 : inexact
+= div downward m68k96:arg_fmt(0,1,-126,24) -0x4p-128 -0x1.000002p+0 : 0x3.fffff800000ffffcp-128 : inexact
+= div tonearest m68k96:arg_fmt(0,1,-126,24) -0x4p-128 -0x1.000002p+0 : 0x3.fffff800001p-128 : inexact
+= div towardzero m68k96:arg_fmt(0,1,-126,24) -0x4p-128 -0x1.000002p+0 : 0x3.fffff800000ffffcp-128 : inexact
+= div upward m68k96:arg_fmt(0,1,-126,24) -0x4p-128 -0x1.000002p+0 : 0x3.fffff800001p-128 : inexact
+= div downward binary128:arg_fmt(0,1,-126,24) -0x4p-128 -0x1.000002p+0 : 0x3.fffff800000fffffe000003ffffep-128 : inexact
+= div tonearest binary128:arg_fmt(0,1,-126,24) -0x4p-128 -0x1.000002p+0 : 0x3.fffff800000fffffe000004p-128 : inexact
+= div towardzero binary128:arg_fmt(0,1,-126,24) -0x4p-128 -0x1.000002p+0 : 0x3.fffff800000fffffe000003ffffep-128 : inexact
+= div upward binary128:arg_fmt(0,1,-126,24) -0x4p-128 -0x1.000002p+0 : 0x3.fffff800000fffffe000004p-128 : inexact
+= div downward ibm128:arg_fmt(0,1,-126,24) -0x4p-128 -0x1.000002p+0 : 0x3.fffff800000fffffe000003fffp-128 : inexact
+= div tonearest ibm128:arg_fmt(0,1,-126,24) -0x4p-128 -0x1.000002p+0 : 0x3.fffff800000fffffe000004p-128 : inexact
+= div towardzero ibm128:arg_fmt(0,1,-126,24) -0x4p-128 -0x1.000002p+0 : 0x3.fffff800000fffffe000003fffp-128 : inexact
+= div upward ibm128:arg_fmt(0,1,-126,24) -0x4p-128 -0x1.000002p+0 : 0x3.fffff800000fffffe000004p-128 : inexact
+= div downward binary32:arg_fmt(0,1,-126,29) -0x4p-128 -0x1.0000001p+0 : 0x3.fffff8p-128 : inexact underflow errno-erange-ok
+= div tonearest binary32:arg_fmt(0,1,-126,29) -0x4p-128 -0x1.0000001p+0 : 0x4p-128 : inexact underflow:before-rounding errno-erange-ok:before-rounding
+= div towardzero binary32:arg_fmt(0,1,-126,29) -0x4p-128 -0x1.000000