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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.
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As shown by bug 23279, strtod's round_and_return has an off-by-one
error in its overflow detection, only counting an exponent greater
than MAX_EXP as overflowing when an exponent of MAX_EXP also means
overflow (recall the ISO C definition of DBL_MAX_EXP etc. is based on
a floating-point model where 2^exp is multiplied by a value in the
interval [0.5, 1), so 2^MAX_EXP is not representable).
For decimal arguments to strtod, a separate overflow check in the main
implementation covers the case where the integer part of the argument
(truncated to the nearest integer towards zero) has more than MAX_EXP
bits, meaning that this issue in round_and_return only affects cases
(arguments with absolute value strictly between the maximum
representable value and 2^MAX_EXP) where overflow depends on the
rounding mode; in such cases, the returned value would still have been
correct on overflow but without the overflow exception being raised or
errno being set to ERANGE. For hex float arguments, however, other
cases can arise, as shown in bug 23279, where a value with exponent
already set to MAX_EXP is passed into round_and_return and a result
can wrongly end up being NaN, or infinity instead of the largest
finite value.
This patch fixes the off-by-one error, adds testing of overflow
exceptions to the tst-strtod-round framework, and adds tests of these
issues.
Tested for x86_64. Also ran the tst-strtod-round tests for powerpc to
make sure the new tests didn't introduce any new failures for IBM long
double.
[BZ #23279]
* stdlib/strtod_l.c (round_and_return): Handle an exponent of
MAX_EXP as overflowing.
* stdlib/gen-tst-strtod-round.c (string_to_fp): Clear MPFR
overflow flag.
(round_str): Output also whether result overflows in each rounding
mode.
* stdlib/tst-strtod-round-data: Add more tests.
* stdlib/tst-strtod-round-data.h: Regenerated.
* stdlib/tst-strtod-round-skeleton.c (_XNTRY): Update comment.
(TEST): Handle extra arguments for overflow flags.
(struct test_overflow): New type.
[!FE_OVERFLOW] (FE_OVERFLOW): Define to 0.
(GEN_ONE_TEST): Clear all exceptions. Test overflow flag.
(test_in_one_mode): Take argument with overflow information.
(do_test): Update calls to test_in_one_mode.
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Bug 18247 is an off-by-one error in strtof's determination of a
decimal exponent such that any value with that decimal exponent is at
most half the least subnormal and so the appropriate underflowing
value for the rounding mode can be determined with no
multiple-precision computations. (Whether the value is in fact safe
despite the off-by-one depends on the floating-point format in
question. It's wrong for float and for m68k ldbl-96 but not for other
supported formats.) This patch corrects the computation of the
exponent in question to be safe in general, adding a comment
explaining the new computation.
Tested for x86_64.
[BZ #18247]
* stdlib/strtod_l.c (____STRTOF_INTERNAL): Decrease minimum
decimal exponent by 1.
* stdlib/tst-strtod-round-data: Add more tests.
* stdlib/tst-strtod-round.c (tests): Regenerated.
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