Fix strtod multiple-precision division bug (bug 26137).

Bug 26137 reports spurious "inexact" exceptions from strtod, on 32-bit
systems only, for a decimal argument that is exactly 1 + 2^-32.  In
fact the same issue also appears for 1 + 2^-64 and 1 + 2^-96 as
arguments to strtof128 on 32-bit systems, and 1 + 2^-64 as an argument
to strtof128 on 64-bit systems.  In FE_DOWNWARD or FE_TOWARDZERO mode,
the return value is also incorrect.

The problem is in the multiple-precision division logic used in the
case of dividing by a denominator that occupies at least three GMP
limbs.  There was a comment "The division does not work if the upper
limb of the two-limb mumerator is greater than the denominator.", but
in fact there were problems for the case of equality (that is, where
the high limbs are equal, offset by some multiple of the GMP limb
size) as well.  In such cases, the code used "quot = ~(mp_limb_t) 0;"
(with subsequent correction if that is an overestimate), because
udiv_qrnnd does not support the case of equality, but it's possible
for the shifted numerator to be greater than or equal to the
denominator, in which case that is an underestimate.  To avoid that,
this patch changes the ">" condition to ">=", meaning the first
division is done with a zero high word.

The tests added are all 1 + 2^-n for n from 1 to 113 except for those
that were already present in tst-strtod-round-data.

Tested for x86_64 and x86.

1 files changed, 3465 insertions, 0 deletions

diff --git a/stdlib/tst-strtod-round-data.h b/stdlib/tst-strtod-round-data.h
index 5ac25f7b29..8899d15f9b 100644
--- a/stdlib/tst-strtod-round-data.h
+++ b/stdlib/tst-strtod-round-data.h
@@ -11972,4 +11972,3469 @@ static const struct test tests[] = {
 	0x1p+1024, false,
 	0x1p+1024, false,
 	0x1.0000000000000000000000000001p+1024, false),
+  TEST ("1.5",
+	true,
+	0x1.8p+0, false,
+	0x1.8p+0, false,
+	0x1.8p+0, false,
+	0x1.8p+0, false,
+	true,
+	0x1.8p+0, false,
+	0x1.8p+0, false,
+	0x1.8p+0, false,
+	0x1.8p+0, false,
+	true,
+	0x1.8p+0, false,
+	0x1.8p+0, false,
+	0x1.8p+0, false,
+	0x1.8p+0, false,
+	true,
+	0x1.8p+0, false,
+	0x1.8p+0, false,
+	0x1.8p+0, false,
+	0x1.8p+0, false,
+	true,
+	0x1.8p+0, false,
+	0x1.8p+0, false,
+	0x1.8p+0, false,
+	0x1.8p+0, false,
+	true,
+	0x1.8p+0, false,
+	0x1.8p+0, false,
+	0x1.8p+0, false,
+	0x1.8p+0, false),
+  TEST ("1.25",
+	true,
+	0x1.4p+0, false,
+	0x1.4p+0, false,
+	0x1.4p+0, false,
+	0x1.4p+0, false,
+	true,
+	0x1.4p+0, false,
+	0x1.4p+0, false,
+	0x1.4p+0, false,
+	0x1.4p+0, false,
+	true,
+	0x1.4p+0, false,
+	0x1.4p+0, false,
+	0x1.4p+0, false,
+	0x1.4p+0, false,
+	true,
+	0x1.4p+0, false,
+	0x1.4p+0, false,
+	0x1.4p+0, false,
+	0x1.4p+0, false,
+	true,
+	0x1.4p+0, false,
+	0x1.4p+0, false,
+	0x1.4p+0, false,
+	0x1.4p+0, false,
+	true,
+	0x1.4p+0, false,
+	0x1.4p+0, false,
+	0x1.4p+0, false,
+	0x1.4p+0, false),
+  TEST ("1.125",
+	true,
+	0x1.2p+0, false,
+	0x1.2p+0, false,
+	0x1.2p+0, false,
+	0x1.2p+0, false,
+	true,
+	0x1.2p+0, false,
+	0x1.2p+0, false,
+	0x1.2p+0, false,
+	0x1.2p+0, false,
+	true,
+	0x1.2p+0, false,
+	0x1.2p+0, false,
+	0x1.2p+0, false,
+	0x1.2p+0, false,
+	true,
+	0x1.2p+0, false,
+	0x1.2p+0, false,
+	0x1.2p+0, false,
+	0x1.2p+0, false,
+	true,
+	0x1.2p+0, false,
+	0x1.2p+0, false,
+	0x1.2p+0, false,
+	0x1.2p+0, false,
+	true,
+	0x1.2p+0, false,
+	0x1.2p+0, false,
+	0x1.2p+0, false,
+	0x1.2p+0, false),
+  TEST ("1.0625",
+	true,
+	0x1.1p+0, false,
+	0x1.1p+0, false,
+	0x1.1p+0, false,
+	0x1.1p+0, false,
+	true,
+	0x1.1p+0, false,
+	0x1.1p+0, false,
+	0x1.1p+0, false,
+	0x1.1p+0, false,
+	true,
+	0x1.1p+0, false,
+	0x1.1p+0, false,
+	0x1.1p+0, false,
+	0x1.1p+0, false,
+	true,
+	0x1.1p+0, false,
+	0x1.1p+0, false,
+	0x1.1p+0, false,
+	0x1.1p+0, false,
+	true,
+	0x1.1p+0, false,
+	0x1.1p+0, false,
+	0x1.1p+0, false,
+	0x1.1p+0, false,
+	true,
+	0x1.1p+0, false,
+	0x1.1p+0, false,
+	0x1.1p+0, false,
+	0x1.1p+0, false),
+  TEST ("1.03125",
+	true,
+	0x1.08p+0, false,
+	0x1.08p+0, false,
+	0x1.08p+0, false,
+	0x1.08p+0, false,
+	true,
+	0x1.08p+0, false,
+	0x1.08p+0, false,
+	0x1.08p+0, false,
+	0x1.08p+0, false,
+	true,
+	0x1.08p+0, false,
+	0x1.08p+0, false,
+	0x1.08p+0, false,
+	0x1.08p+0, false,
+	true,
+	0x1.08p+0, false,
+	0x1.08p+0, false,
+	0x1.08p+0, false,
+	0x1.08p+0, false,
+	true,
+	0x1.08p+0, false,
+	0x1.08p+0, false,
+	0x1.08p+0, false,
+	0x1.08p+0, false,
+	true,
+	0x1.08p+0, false,
+	0x1.08p+0, false,
+	0x1.08p+0, false,
+	0x1.08p+0, false),
+  TEST ("1.015625",
+	true,
+	0x1.04p+0, false,
+	0x1.04p+0, false,
+	0x1.04p+0, false,
+	0x1.04p+0, false,
+	true,
+	0x1.04p+0, false,
+	0x1.04p+0, false,
+	0x1.04p+0, false,
+	0x1.04p+0, false,
+	true,
+	0x1.04p+0, false,
+	0x1.04p+0, false,
+	0x1.04p+0, false,
+	0x1.04p+0, false,
+	true,
+	0x1.04p+0, false,
+	0x1.04p+0, false,
+	0x1.04p+0, false,
+	0x1.04p+0, false,
+	true,
+	0x1.04p+0, false,
+	0x1.04p+0, false,
+	0x1.04p+0, false,
+	0x1.04p+0, false,
+	true,
+	0x1.04p+0, false,
+	0x1.04p+0, false,
+	0x1.04p+0, false,
+	0x1.04p+0, false),
+  TEST ("1.0078125",
+	true,
+	0x1.02p+0, false,
+	0x1.02p+0, false,
+	0x1.02p+0, false,
+	0x1.02p+0, false,
+	true,
+	0x1.02p+0, false,
+	0x1.02p+0, false,
+	0x1.02p+0, false,
+	0x1.02p+0, false,
+	true,
+	0x1.02p+0, false,
+	0x1.02p+0, false,
+	0x1.02p+0, false,
+	0x1.02p+0, false,
+	true,
+	0x1.02p+0, false,
+	0x1.02p+0, false,
+	0x1.02p+0, false,
+	0x1.02p+0, false,
+	true,
+	0x1.02p+0, false,
+	0x1.02p+0, false,
+	0x1.02p+0, false,
+	0x1.02p+0, false,
+	true,
+	0x1.02p+0, false,
+	0x1.02p+0, false,
+	0x1.02p+0, false,
+	0x1.02p+0, false),
+  TEST ("1.00390625",
+	true,
+	0x1.01p+0, false,
+	0x1.01p+0, false,
+	0x1.01p+0, false,
+	0x1.01p+0, false,
+	true,
+	0x1.01p+0, false,
+	0x1.01p+0, false,
+	0x1.01p+0, false,
+	0x1.01p+0, false,
+	true,
+	0x1.01p+0, false,
+	0x1.01p+0, false,
+	0x1.01p+0, false,
+	0x1.01p+0, false,
+	true,
+	0x1.01p+0, false,
+	0x1.01p+0, false,
+	0x1.01p+0, false,
+	0x1.01p+0, false,
+	true,
+	0x1.01p+0, false,
+	0x1.01p+0, false,
+	0x1.01p+0, false,
+	0x1.01p+0, false,
+	true,
+	0x1.01p+0, false,
+	0x1.01p+0, false,
+	0x1.01p+0, false,
+	0x1.01p+0, false),
+  TEST ("1.001953125",
+	true,
+	0x1.008p+0, false,
+	0x1.008p+0, false,
+	0x1.008p+0, false,
+	0x1.008p+0, false,
+	true,
+	0x1.008p+0, false,
+	0x1.008p+0, false,
+	0x1.008p+0, false,
+	0x1.008p+0, false,
+	true,
+	0x1.008p+0, false,
+	0x1.008p+0, false,
+	0x1.008p+0, false,
+	0x1.008p+0, false,
+	true,
+	0x1.008p+0, false,
+	0x1.008p+0, false,
+	0x1.008p+0, false,
+	0x1.008p+0, false,
+	true,
+	0x1.008p+0, false,
+	0x1.008p+0, false,
+	0x1.008p+0, false,
+	0x1.008p+0, false,
+	true,
+	0x1.008p+0, false,
+	0x1.008p+0, false,
+	0x1.008p+0, false,
+	0x1.008p+0, false),
+  TEST ("1.0009765625",
+	true,
+	0x1.004p+0, false,
+	0x1.004p+0, false,
+	0x1.004p+0, false,
+	0x1.004p+0, false,
+	true,
+	0x1.004p+0, false,
+	0x1.004p+0, false,
+	0x1.004p+0, false,
+	0x1.004p+0, false,
+	true,
+	0x1.004p+0, false,
+	0x1.004p+0, false,
+	0x1.004p+0, false,
+	0x1.004p+0, false,
+	true,
+	0x1.004p+0, false,
+	0x1.004p+0, false,
+	0x1.004p+0, false,
+	0x1.004p+0, false,
+	true,
+	0x1.004p+0, false,
+	0x1.004p+0, false,
+	0x1.004p+0, false,
+	0x1.004p+0, false,
+	true,
+	0x1.004p+0, false,
+	0x1.004p+0, false,
+	0x1.004p+0, false,
+	0x1.004p+0, false),
+  TEST ("1.00048828125",
+	true,
+	0x1.002p+0, false,
+	0x1.002p+0, false,
+	0x1.002p+0, false,
+	0x1.002p+0, false,
+	true,
+	0x1.002p+0, false,
+	0x1.002p+0, false,
+	0x1.002p+0, false,
+	0x1.002p+0, false,
+	true,
+	0x1.002p+0, false,
+	0x1.002p+0, false,
+	0x1.002p+0, false,
+	0x1.002p+0, false,
+	true,
+	0x1.002p+0, false,
+	0x1.002p+0, false,
+	0x1.002p+0, false,
+	0x1.002p+0, false,
+	true,
+	0x1.002p+0, false,
+	0x1.002p+0, false,
+	0x1.002p+0, false,
+	0x1.002p+0, false,
+	true,
+	0x1.002p+0, false,
+	0x1.002p+0, false,
+	0x1.002p+0, false,
+	0x1.002p+0, false),
+  TEST ("1.000244140625",
+	true,
+	0x1.001p+0, false,
+	0x1.001p+0, false,
+	0x1.001p+0, false,
+	0x1.001p+0, false,
+	true,
+	0x1.001p+0, false,
+	0x1.001p+0, false,
+	0x1.001p+0, false,
+	0x1.001p+0, false,
+	true,
+	0x1.001p+0, false,
+	0x1.001p+0, false,
+	0x1.001p+0, false,
+	0x1.001p+0, false,
+	true,
+	0x1.001p+0, false,
+	0x1.001p+0, false,
+	0x1.001p+0, false,
+	0x1.001p+0, false,
+	true,
+	0x1.001p+0, false,
+	0x1.001p+0, false,
+	0x1.001p+0, false,
+	0x1.001p+0, false,
+	true,
+	0x1.001p+0, false,
+	0x1.001p+0, false,
+	0x1.001p+0, false,
+	0x1.001p+0, false),
+  TEST ("1.0001220703125",
+	true,
+	0x1.0008p+0, false,
+	0x1.0008p+0, false,
+	0x1.0008p+0, false,
+	0x1.0008p+0, false,
+	true,
+	0x1.0008p+0, false,
+	0x1.0008p+0, false,
+	0x1.0008p+0, false,
+	0x1.0008p+0, false,
+	true,
+	0x1.0008p+0, false,
+	0x1.0008p+0, false,
+	0x1.0008p+0, false,
+	0x1.0008p+0, false,
+	true,
+	0x1.0008p+0, false,
+	0x1.0008p+0, false,
+	0x1.0008p+0, false,
+	0x1.0008p+0, false,
+	true,
+	0x1.0008p+0, false,
+	0x1.0008p+0, false,
+	0x1.0008p+0, false,
+	0x1.0008p+0, false,
+	true,
+	0x1.0008p+0, false,
+	0x1.0008p+0, false,
+	0x1.0008p+0, false,
+	0x1.0008p+0, false),
+  TEST ("1.00006103515625",
+	true,
+	0x1.0004p+0, false,
+	0x1.0004p+0, false,
+	0x1.0004p+0, false,
+	0x1.0004p+0, false,
+	true,
+	0x1.0004p+0, false,
+	0x1.0004p+0, false,
+	0x1.0004p+0, false,
+	0x1.0004p+0, false,
+	true,
+	0x1.0004p+0, false,
+	0x1.0004p+0, false,
+	0x1.0004p+0, false,
+	0x1.0004p+0, false,
+	true,
+	0x1.0004p+0, false,
+	0x1.0004p+0, false,
+	0x1.0004p+0, false,
+	0x1.0004p+0, false,
+	true,
+	0x1.0004p+0, false,
+	0x1.0004p+0, false,
+	0x1.0004p+0, false,
+	0x1.0004p+0, false,
+	true,
+	0x1.0004p+0, false,
+	0x1.0004p+0, false,
+	0x1.0004p+0, false,
+	0x1.0004p+0, false),
+  TEST ("1.000030517578125",
+	true,
+	0x1.0002p+0, false,
+	0x1.0002p+0, false,
+	0x1.0002p+0, false,
+	0x1.0002p+0, false,
+	true,
+	0x1.0002p+0, false,
+	0x1.0002p+0, false,
+	0x1.0002p+0, false,
+	0x1.0002p+0, false,
+	true,
+	0x1.0002p+0, false,
+	0x1.0002p+0, false,
+	0x1.0002p+0, false,
+	0x1.0002p+0, false,
+	true,
+	0x1.0002p+0, false,
+	0x1.0002p+0, false,
+	0x1.0002p+0, false,
+	0x1.0002p+0, false,
+	true,
+	0x1.0002p+0, false,
+	0x1.0002p+0, false,
+	0x1.0002p+0, false,
+	0x1.0002p+0, false,
+	true,
+	0x1.0002p+0, false,
+	0x1.0002p+0, false,
+	0x1.0002p+0, false,
+	0x1.0002p+0, false),
+  TEST ("1.0000152587890625",
+	true,
+	0x1.0001p+0, false,
+	0x1.0001p+0, false,
+	0x1.0001p+0, false,
+	0x1.0001p+0, false,
+	true,
+	0x1.0001p+0, false,
+	0x1.0001p+0, false,
+	0x1.0001p+0, false,
+	0x1.0001p+0, false,
+	true,
+	0x1.0001p+0, false,
+	0x1.0001p+0, false,
+	0x1.0001p+0, false,
+	0x1.0001p+0, false,
+	true,
+	0x1.0001p+0, false,
+	0x1.0001p+0, false,
+	0x1.0001p+0, false,
+	0x1.0001p+0, false,
+	true,
+	0x1.0001p+0, false,
+	0x1.0001p+0, false,
+	0x1.0001p+0, false,
+	0x1.0001p+0, false,
+	true,
+	0x1.0001p+0, false,
+	0x1.0001p+0, false,
+	0x1.0001p+0, false,
+	0x1.0001p+0, false),
+  TEST ("1.00000762939453125",
+	true,
+	0x1.00008p+0, false,
+	0x1.00008p+0, false,
+	0x1.00008p+0, false,
+	0x1.00008p+0, false,
+	true,
+	0x1.00008p+0, false,
+	0x1.00008p+0, false,
+	0x1.00008p+0, false,
+	0x1.00008p+0, false,
+	true,
+	0x1.00008p+0, false,
+	0x1.00008p+0, false,
+	0x1.00008p+0, false,
+	0x1.00008p+0, false,
+	true,
+	0x1.00008p+0, false,
+	0x1.00008p+0, false,
+	0x1.00008p+0, false,
+	0x1.00008p+0, false,
+	true,
+	0x1.00008p+0, false,
+	0x1.00008p+0, false,
+	0x1.00008p+0, false,
+	0x1.00008p+0, false,
+	true,
+	0x1.00008p+0, false,
+	0x1.00008p+0, false,
+	0x1.00008p+0, false,
+	0x1.00008p+0, false),
+  TEST ("1.000003814697265625",
+	true,
+	0x1.00004p+0, false,
+	0x1.00004p+0, false,
+	0x1.00004p+0, false,
+	0x1.00004p+0, false,
+	true,
+	0x1.00004p+0, false,
+	0x1.00004p+0, false,
+	0x1.00004p+0, false,
+	0x1.00004p+0, false,
+	true,
+	0x1.00004p+0, false,
+	0x1.00004p+0, false,
+	0x1.00004p+0, false,
+	0x1.00004p+0, false,
+	true,
+	0x1.00004p+0, false,
+	0x1.00004p+0, false,
+	0x1.00004p+0, false,
+	0x1.00004p+0, false,
+	true,
+	0x1.00004p+0, false,
+	0x1.00004p+0, false,
+	0x1.00004p+0, false,
+	0x1.00004p+0, false,
+	true,
+	0x1.00004p+0, false,
+	0x1.00004p+0, false,
+	0x1.00004p+0, false,
+	0x1.00004p+0, false),
+  TEST ("1.0000019073486328125",
+	true,
+	0x1.00002p+0, false,
+	0x1.00002p+0, false,
+	0x1.00002p+0, false,
+	0x1.00002p+0, false,
+	true,
+	0x1.00002p+0, false,
+	0x1.00002p+0, false,
+	0x1.00002p+0, false,
+	0x1.00002p+0, false,
+	true,
+	0x1.00002p+0, false,
+	0x1.00002p+0, false,
+	0x1.00002p+0, false,
+	0x1.00002p+0, false,
+	true,
+	0x1.00002p+0, false,
+	0x1.00002p+0, false,
+	0x1.00002p+0, false,
+	0x1.00002p+0, false,
+	true,
+	0x1.00002p+0, false,
+	0x1.00002p+0, false,
+	0x1.00002p+0, false,
+	0x1.00002p+0, false,
+	true,
+	0x1.00002p+0, false,
+	0x1.00002p+0, false,
+	0x1.00002p+0, false,
+	0x1.00002p+0, false),
+  TEST ("1.00000095367431640625",
+	true,
+	0x1.00001p+0, false,
+	0x1.00001p+0, false,
+	0x1.00001p+0, false,
+	0x1.00001p+0, false,
+	true,
+	0x1.00001p+0, false,
+	0x1.00001p+0, false,
+	0x1.00001p+0, false,
+	0x1.00001p+0, false,
+	true,
+	0x1.00001p+0, false,
+	0x1.00001p+0, false,
+	0x1.00001p+0, false,
+	0x1.00001p+0, false,
+	true,
+	0x1.00001p+0, false,
+	0x1.00001p+0, false,
+	0x1.00001p+0, false,
+	0x1.00001p+0, false,
+	true,
+	0x1.00001p+0, false,
+	0x1.00001p+0, false,
+	0x1.00001p+0, false,
+	0x1.00001p+0, false,
+	true,
+	0x1.00001p+0, false,
+	0x1.00001p+0, false,
+	0x1.00001p+0, false,
+	0x1.00001p+0, false),
+  TEST ("1.000000476837158203125",
+	true,
+	0x1.000008p+0, false,
+	0x1.000008p+0, false,
+	0x1.000008p+0, false,
+	0x1.000008p+0, false,
+	true,
+	0x1.000008p+0, false,
+	0x1.000008p+0, false,
+	0x1.000008p+0, false,
+	0x1.000008p+0, false,
+	true,
+	0x1.000008p+0, false,
+	0x1.000008p+0, false,
+	0x1.000008p+0, false,
+	0x1.000008p+0, false,
+	true,
+	0x1.000008p+0, false,
+	0x1.000008p+0, false,
+	0x1.000008p+0, false,
+	0x1.000008p+0, false,
+	true,
+	0x1.000008p+0, false,
+	0x1.000008p+0, false,
+	0x1.000008p+0, false,
+	0x1.000008p+0, false,
+	true,
+	0x1.000008p+0, false,
+	0x1.000008p+0, false,
+	0x1.000008p+0, false,
+	0x1.000008p+0, false),
+  TEST ("1.0000000298023223876953125",
+	false,
+	0x1p+0, false,
+	0x1p+0, false,
+	0x1p+0, false,
+	0x1.000002p+0, false,
+	true,
+	0x1.0000008p+0, false,
+	0x1.0000008p+0, false,
+	0x1.0000008p+0, false,
+	0x1.0000008p+0, false,
+	true,
+	0x1.0000008p+0, false,
+	0x1.0000008p+0, false,
+	0x1.0000008p+0, false,
+	0x1.0000008p+0, false,
+	true,
+	0x1.0000008p+0, false,
+	0x1.0000008p+0, false,
+	0x1.0000008p+0, false,
+	0x1.0000008p+0, false,
+	true,
+	0x1.0000008p+0, false,
+	0x1.0000008p+0, false,
+	0x1.0000008p+0, false,
+	0x1.0000008p+0, false,
+	true,
+	0x1.0000008p+0, false,
+	0x1.0000008p+0, false,
+	0x1.0000008p+0, false,
+	0x1.0000008p+0, false),
+  TEST ("1.00000001490116119384765625",
+	false,
+	0x1p+0, false,
+	0x1p+0, false,
+	0x1p+0, false,
+	0x1.000002p+0, false,
+	true,
+	0x1.0000004p+0, false,
+	0x1.0000004p+0, false,
+	0x1.0000004p+0, false,
+	0x1.0000004p+0, false,
+	true,
+	0x1.0000004p+0, false,
+	0x1.0000004p+0, false,
+	0x1.0000004p+0, false,
+	0x1.0000004p+0, false,
+	true,
+	0x1.0000004p+0, false,
+	0x1.0000004p+0, false,
+	0x1.0000004p+0, false,
+	0x1.0000004p+0, false,
+	true,
+	0x1.0000004p+0, false,
+	0x1.0000004p+0, false,
+	0x1.0000004p+0, false,
+	0x1.0000004p+0, false,
+	true,
+	0x1.0000004p+0, false,
+	0x1.0000004p+0, false,
+	0x1.0000004p+0, false,
+	0x1.0000004p+0, false),
+  TEST ("1.000000007450580596923828125",
+	false,
+	0x1p+0, false,
+	0x1p+0, false,
+	0x1p+0, false,
+	0x1.000002p+0, false,
+	true,
+	0x1.0000002p+0, false,
+	0x1.0000002p+0, false,
+	0x1.0000002p+0, false,
+	0x1.0000002p+0, false,
+	true,
+	0x1.0000002p+0, false,
+	0x1.0000002p+0, false,
+	0x1.0000002p+0, false,
+	0x1.0000002p+0, false,
+	true,
+	0x1.0000002p+0, false,
+	0x1.0000002p+0, false,
+	0x1.0000002p+0, false,
+	0x1.0000002p+0, false,
+	true,
+	0x1.0000002p+0, false,
+	0x1.0000002p+0, false,
+	0x1.0000002p+0, false,
+	0x1.0000002p+0, false,
+	true,
+	0x1.0000002p+0, false,
+	0x1.0000002p+0, false,
+	0x1.0000002p+0, false,
+	0x1.0000002p+0, false),
+  TEST ("1.0000000037252902984619140625",
+	false,
+	0x1p+0, false,
+	0x1p+0, false,
+	0x1p+0, false,
+	0x1.000002p+0, false,
+	true,
+	0x1.0000001p+0, false,
+	0x1.0000001p+0, false,
+	0x1.0000001p+0, false,
+	0x1.0000001p+0, false,
+	true,
+	0x1.0000001p+0, false,
+	0x1.0000001p+0, false,
+	0x1.0000001p+0, false,
+	0x1.0000001p+0, false,
+	true,
+	0x1.0000001p+0, false,
+	0x1.0000001p+0, false,
+	0x1.0000001p+0, false,
+	0x1.0000001p+0, false,
+	true,
+	0x1.0000001p+0, false,
+	0x1.0000001p+0, false,
+	0x1.0000001p+0, false,
+	0x1.0000001p+0, false,
+	true,
+	0x1.0000001p+0, false,
+	0x1.0000001p+0, false,
+	0x1.0000001p+0, false,
+	0x1.0000001p+0, false),
+  TEST ("1.00000000186264514923095703125",
+	false,
+	0x1p+0, false,
+	0x1p+0, false,
+	0x1p+0, false,
+	0x1.000002p+0, false,
+	true,
+	0x1.00000008p+0, false,
+	0x1.00000008p+0, false,
+	0x1.00000008p+0, false,
+	0x1.00000008p+0, false,
+	true,
+	0x1.00000008p+0, false,
+	0x1.00000008p+0, false,
+	0x1.00000008p+0, false,
+	0x1.00000008p+0, false,
+	true,
+	0x1.00000008p+0, false,
+	0x1.00000008p+0, false,
+	0x1.00000008p+0, false,
+	0x1.00000008p+0, false,
+	true,
+	0x1.00000008p+0, false,
+	0x1.00000008p+0, false,
+	0x1.00000008p+0, false,
+	0x1.00000008p+0, false,
+	true,
+	0x1.00000008p+0, false,
+	0x1.00000008p+0, false,
+	0x1.00000008p+0, false,
+	0x1.00000008p+0, false),
+  TEST ("1.000000000931322574615478515625",
+	false,
+	0x1p+0, false,
+	0x1p+0, false,
+	0x1p+0, false,
+	0x1.000002p+0, false,
+	true,
+	0x1.00000004p+0, false,
+	0x1.00000004p+0, false,
+	0x1.00000004p+0, false,
+	0x1.00000004p+0, false,
+	true,
+	0x1.00000004p+0, false,
+	0x1.00000004p+0, false,
+	0x1.00000004p+0, false,
+	0x1.00000004p+0, false,
+	true,
+	0x1.00000004p+0, false,
+	0x1.00000004p+0, false,
+	0x1.00000004p+0, false,
+	0x1.00000004p+0, false,
+	true,
+	0x1.00000004p+0, false,
+	0x1.00000004p+0, false,
+	0x1.00000004p+0, false,
+	0x1.00000004p+0, false,
+	true,
+	0x1.00000004p+0, false,
+	0x1.00000004p+0, false,
+	0x1.00000004p+0, false,
+	0x1.00000004p+0, false),
+  TEST ("1.0000000004656612873077392578125",
+	false,
+	0x1p+0, false,
+	0x1p+0, false,
+	0x1p+0, false,
+	0x1.000002p+0, false,
+	true,
+	0x1.00000002p+0, false,
+	0x1.00000002p+0, false,
+	0x1.00000002p+0, false,
+	0x1.00000002p+0, false,
+	true,
+	0x1.00000002p+0, false,
+	0x1.00000002p+0, false,
+	0x1.00000002p+0, false,
+	0x1.00000002p+0, false,
+	true,
+	0x1.00000002p+0, false,
+	0x1.00000002p+0, false,
+	0x1.00000002p+0, false,
+	0x1.00000002p+0, false,
+	true,
+	0x1.00000002p+0, false,
+	0x1.00000002p+0, false,
+	0x1.00000002p+0, false,
+	0x1.00000002p+0, false,
+	true,
+	0x1.00000002p+0, false,
+	0x1.00000002p+0, false,
+	0x1.00000002p+0, false,
+	0x1.00000002p+0, false),
+  TEST ("1.00000000023283064365386962890625",
+	false,
+	0x1p+0, false,
+	0x1p+0, false,
+	0x1p+0, false,
+	0x1.000002p+0, false,
+	true,
+	0x1.00000001p+0, false,
+	0x1.00000001p+0, false,
+	0x1.00000001p+0, false,
+	0x1.00000001p+0, false,
+	true,
+	0x1.00000001p+0, false,
+	0x1.00000001p+0, false,
+	0x1.00000001p+0, false,
+	0x1.00000001p+0, false,
+	true,
+	0x1.00000001p+0, false,
+	0x1.00000001p+0, false,
+	0x1.00000001p+0, false,
+	0x1.00000001p+0, false,
+	true,
+	0x1.00000001p+0, false,
+	0x1.00000001p+0, false,
+	0x1.00000001p+0, false,
+	0x1.00000001p+0, false,
+	true,
+	0x1.00000001p+0, false,
+	0x1.00000001p+0, false,
+	0x1.00000001p+0, false,
+	0x1.00000001p+0, false),
+  TEST ("1.000000000116415321826934814453125",
+	false,
+	0x1p+0, false,
+	0x1p+0, false,
+	0x1p+0, false,
+	0x1.000002p+0, false,
+	true,
+	0x1.000000008p+0, false,
+	0x1.000000008p+0, false,
+	0x1.000000008p+0, false,
+	0x1.000000008p+0, false,
+	true,
+	0x1.000000008p+0, false,
+	0x1.000000008p+0, false,
+	0x1.000000008p+0, false,
+	0x1.000000008p+0, false,
+	true,
+	0x1.000000008p+0, false,
+	0x1.000000008p+0, false,
+	0x1.000000008p+0, false,
+	0x1.000000008p+0, false,
+	true,
+	0x1.000000008p+0, false,
+	0x1.000000008p+0, false,
+	0x1.000000008p+0, false,
+	0x1.000000008p+0, false,
+	true,
+	0x1.000000008p+0, false,
+	0x1.000000008p+0, false,
+	0x1.000000008p+0, false,
+	0x1.000000008p+0, false),
+  TEST ("1.0000000000582076609134674072265625",
+	false,
+	0x1p+0, false,
+	0x1p+0, false,
+	0x1p+0, false,
+	0x1.000002p+0, false,
+	true,
+	0x1.000000004p+0, false,
+	0x1.000000004p+0, false,
+	0x1.000000004p+0, false,
+	0x1.000000004p+0, false,
+	true,
+	0x1.000000004p+0, false,
+	0x1.000000004p+0, false,
+	0x1.000000004p+0, false,
+	0x1.000000004p+0, false,
+	true,
+	0x1.000000004p+0, false,
+	0x1.000000004p+0, false,
+	0x1.000000004p+0, false,
+	0x1.000000004p+0, false,
+	true,
+	0x1.000000004p+0, false,
+	0x1.000000004p+0, false,
+	0x1.000000004p+0, false,
+	0x1.000000004p+0, false,
+	true,
+	0x1.000000004p+0, false,
+	0x1.000000004p+0, false,
+	0x1.000000004p+0, false,
+	0x1.000000004p+0, false),
+  TEST ("1.00000000002910383045673370361328125",
+	false,
+	0x1p+0, false,
+	0x1p+0, false,
+	0x1p+0, false,
+	0x1.000002p+0, false,
+	true,
+	0x1.000000002p+0, false,
+	0x1.000000002p+0, false,
+	0x1.000000002p+0, false,
+	0x1.000000002p+0, false,
+	true,
+	0x1.000000002p+0, false,
+	0x1.000000002p+0, false,
+	0x1.000000002p+0, false,
+	0x1.000000002p+0, false,
+	true,
+	0x1.000000002p+0, false,
+	0x1.000000002p+0, false,
+	0x1.000000002p+0, false,
+	0x1.000000002p+0, false,
+	true,
+	0x1.000000002p+0, false,
+	0x1.000000002p+0, false,
+	0x1.000000002p+0, false,
+	0x1.000000002p+0, false,
+	true,
+	0x1.000000002p+0, false,
+	0x1.000000002p+0, false,
+	0x1.000000002p+0, false,
+	0x1.000000002p+0, false),
+  TEST ("1.000000000014551915228366851806640625",
+	false,
+	0x1p+0, false,
+	0x1p+0, false,
+	0x1p+0, false,
+	0x1.000002p+0, false,
+	true,
+	0x1.000000001p+0, false,
+	0x1.000000001p+0, false,
+	0x1.000000001p+0, false,
+	0x1.000000001p+0, false,
+	true,
+	0x1.000000001p+0, false,
+	0x1.000000001p+0, false,
+	0x1.000000001p+0, false,
+	0x1.000000001p+0, false,
+	true,
+	0x1.000000001p+0, false,
+	0x1.000000001p+0, false,
+	0x1.000000001p+0, false,
+	0x1.000000001p+0, false,
+	true,
+	0x1.000000001p+0, false,
+	0x1.000000001p+0, false,
+	0x1.000000001p+0, false,
+	0x1.000000001p+0, false,
+	true,
+	0x1.000000001p+0, false,
+	0x1.000000001p+0, false,
+	0x1.000000001p+0, false,
+	0x1.000000001p+0, false),
+  TEST ("1.0000000000072759576141834259033203125",
+	false,
+	0x1p+0, false,
+	0x1p+0, false,
+	0x1p+0, false,
+	0x1.000002p+0, false,
+	true,
+	0x1.0000000008p+0, false,
+	0x1.0000000008p+0, false,
+	0x1.0000000008p+0, false,
+	0x1.0000000008p+0, false,
+	true,
+	0x1.0000000008p+0, false,
+	0x1.0000000008p+0, false,
+	0x1.0000000008p+0, false,
+	0x1.0000000008p+0, false,
+	true,
+	0x1.0000000008p+0, false,
+	0x1.0000000008p+0, false,
+	0x1.0000000008p+0, false,
+	0x1.0000000008p+0, false,
+	true,
+	0x1.0000000008p+0, false,
+	0x1.0000000008p+0, false,
+	0x1.0000000008p+0, false,
+	0x1.0000000008p+0, false,
+	true,
+	0x1.0000000008p+0, false,
+	0x1.0000000008p+0, false,
+	0x1.0000000008p+0, false,
+	0x1.0000000008p+0, false),
+  TEST ("1.00000000000363797880709171295166015625",
+	false,
+	0x1p+0, false,
+	0x1p+0, false,
+	0x1p+0, false,
+	0x1.000002p+0, false,
+	true,
+	0x1.0000000004p+0, false,
+	0x1.0000000004p+0, false,
+	0x1.0000000004p+0, false,
+	0x1.0000000004p+0, false,
+	true,
+	0x1.0000000004p+0, false,
+	0x1.0000000004p+0, false,
+	0x1.0000000004p+0, false,
+	0x1.0000000004p+0, false,
+	true,
+	0x1.0000000004p+0, false,
+	0x1.0000000004p+0, false,
+	0x1.0000000004p+0, false,
+	0x1.0000000004p+0, false,
+	true,
+	0x1.0000000004p+0, false,
+	0x1.0000000004p+0, false,
+	0x1.0000000004p+0, false,
+	0x1.0000000004p+0, false,
+	true,
+	0x1.0000000004p+0, false,
+	0x1.0000000004p+0, false,
+	0x1.0000000004p+0, false,
+	0x1.0000000004p+0, false),
+  TEST ("1.000000000001818989403545856475830078125",
+	false,
+	0x1p+0, false,
+	0x1p+0, false,
+	0x1p+0, false,
+	0x1.000002p+0, false,
+	true,
+	0x1.0000000002p+0, false,
+	0x1.0000000002p+0, false,
+	0x1.0000000002p+0, false,
+	0x1.0000000002p+0, false,
+	true,
+	0x1.0000000002p+0, false,
+	0x1.0000000002p+0, false,
+	0x1.0000000002p+0, false,
+	0x1.0000000002p+0, false,
+	true,
+	0x1.0000000002p+0, false,
+	0x1.0000000002p+0, false,
+	0x1.0000000002p+0, false,
+	0x1.0000000002p+0, false,
+	true,
+	0x1.0000000002p+0, false,
+	0x1.0000000002p+0, false,
+	0x1.0000000002p+0, false,
+	0x1.0000000002p+0, false,
+	true,
+	0x1.0000000002p+0, false,
+	0x1.0000000002p+0, false,
+	0x1.0000000002p+0, false,
+	0x1.0000000002p+0, false),
+  TEST ("1.0000000000009094947017729282379150390625",
+	false,
+	0x1p+0, false,
+	0x1p+0, false,
+	0x1p+0, false,
+	0x1.000002p+0, false,
+	true,
+	0x1.0000000001p+0, false,
+	0x1.0000000001p+0, false,
+	0x1.0000000001p+0, false,
+	0x1.0000000001p+0, false,
+	true,
+	0x1.0000000001p+0, false,
+	0x1.0000000001p+0, false,
+	0x1.0000000001p+0, false,
+	0x1.0000000001p+0, false,
+	true,
+	0x1.0000000001p+0, false,
+	0x1.0000000001p+0, false,
+	0x1.0000000001p+0, false,
+	0x1.0000000001p+0, false,
+	true,
+	0x1.0000000001p+0, false,
+	0x1.0000000001p+0, false,
+	0x1.0000000001p+0, false,
+	0x1.0000000001p+0, false,
+	true,
+	0x1.0000000001p+0, false,
+	0x1.0000000001p+0, false,
+	0x1.0000000001p+0, false,
+	0x1.0000000001p+0, false),
+  TEST ("1.00000000000045474735088646411895751953125",
+	false,
+	0x1p+0, false,
+	0x1p+0, false,
+	0x1p+0, false,
+	0x1.000002p+0, false,
+	true,
+	0x1.00000000008p+0, false,
+	0x1.00000000008p+0, false,
+	0x1.00000000008p+0, false,
+	0x1.00000000008p+0, false,
+	true,
+	0x1.00000000008p+0, false,
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+	0x1.00000000008p+0, false,
+	0x1.00000000008p+0, false,
+	0x1.00000000008p+0, false),
+  TEST ("1.000000000000227373675443232059478759765625",
+	false,
+	0x1p+0, false,
+	0x1p+0, false,
+	0x1p+0, false,
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+	0x1.00000000004p+0, false,
+	0x1.00000000004p+0, false,
+	0x1.00000000004p+0, false),
+  TEST ("1.0000000000001136868377216160297393798828125",
+	false,
+	0x1p+0, false,
+	0x1p+0, false,
+	0x1p+0, false,
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+	0x1.00000000002p+0, false,
+	0x1.00000000002p+0, false,
+	0x1.00000000002p+0, false),
+  TEST ("1.00000000000005684341886080801486968994140625",
+	false,
+	0x1p+0, false,
+	0x1p+0, false,
+	0x1p+0, false,
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+	0x1.00000000001p+0, false,
+	0x1.00000000001p+0, false,
+	0x1.00000000001p+0, false),
+  TEST ("1.000000000000028421709430404007434844970703125",
+	false,
+	0x1p+0, false,
+	0x1p+0, false,
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+	0x1.000000000008p+0, false,
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+	0x1.000000000008p+0, false),
+  TEST ("1.0000000000000142108547152020037174224853515625",
+	false,
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+	0x1p+0, false,
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+	0x1.000000000004p+0, false,
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+	0x1.000000000004p+0, false),
+  TEST ("1.00000000000000710542735760100185871124267578125",
+	false,
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+	false,
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+	0x1.000000000001p+0, false),
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+	false,
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+	false,
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