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In the x86 / x86_64 implementations of expm1l, when expm1l's result
should underflow to 0 (argument minus the least subnormal, in some
rounding modes), it can be a zero of the wrong sign. This patch fixes
this by returning the argument with underflow forced in that case
(this is a 1ulp error relative to the correctly rounded result of -0,
which is OK in terms of the documented accuracy goals, whereas a
result with the wrong sign never is).
Tested for x86_64 and x86.
[BZ #18569]
* sysdeps/i386/fpu/e_expl.S (IEEE754_EXPL) [USE_AS_EXPM1L]: Force
underflow and return argument in case of subnormal argument.
* sysdeps/x86_64/fpu/e_expl.S (IEEE754_EXPL) [USE_AS_EXPM1L]:
Likewise.
* math/auto-libm-test-in: Add more tests of expm1.
* math/auto-libm-test-out: Regenerated.
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Similar to various other bugs in this area, the x86 and x86_64
implementations of expl / exp10l can fail to produce underflow
exceptions when the unscaled result has trailing 0 bits so the scaling
down to subnormal precision is exact. This patch fixes this by
forcing the exception in the case of tiny results.
Tested for x86_64 and x86.
[BZ #16361]
* sysdeps/i386/fpu/e_expl.S [!USE_AS_EXPM1L] (cmin): New object.
[!USE_AS_EXPM1L] (IEEE754_EXPL): Force underflow exception for
tiny results.
* sysdeps/x86_64/fpu/e_expl.S [!USE_AS_EXPM1L] (cmin): New object.
[!USE_AS_EXPM1L] (IEEE754_EXPL): Force underflow exception for
tiny results.
* math/auto-libm-test-in: Add more tests of exp and exp10. Do not
mark underflow exceptions as possibly missing for bug 16361.
* math/auto-libm-test-out: Regenerated.
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This patch fixes bug 16539, spurious underflow exceptions from x86 /
x86-64 expm1l. The problem is that the computation of a base-2
exponent with extra precision involves spurious underflows for
arguments that are small but not subnormal, so a check is added to
just return the argument in those cases. (If the argument *is*
subnormal, underflowing is correct and the existing code will always
underflow, so it suffices to keep using the existing code in that
case; some expm1 implementations have a bug (bug 16353) with missing
underflow exceptions, but I don't think there's such a bug in this
particular version.)
Tested x86_64 and x86; no ulps updates needed.
(auto-libm-test-out diffs omitted below.)
[BZ #16539]
* sysdeps/i386/fpu/e_expl.S (IEEE754_EXPL) [USE_AS_EXPM1L]: Just
return the argument for normal arguments with exponent below -64.
* sysdeps/x86_64/fpu/e_expl.S (IEEE754_EXPL) [USE_AS_EXPM1L]:
Likewise.
* math/auto-libm-test-in: Add another test of expm1.
* math/auto-libm-test-out: Regenerated.
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This patch fixes bug 16348, spurious underflows from x86/x86_64 expl
on arguments close to 0. These implementations effectively use expm1
(on the fractional part of the argument) internally, so resulting in
spurious underflows when the result is very close to 1. For arguments
small enough that the round-to-nearest correct result is 1, this patch
uses 1+x instead.
These implementations are also used for exp10l and so the patch fixes
similar issues there (the 0x1p-67 threshold being small enough to be
correct for exp10l as well as expl). But because of spurious
underflows in other exp10 implementations (bug 16560), the tests
aren't added for exp10 at this point - they can be added when the
other exp10 parts of that bug are fixed.
Tested x86_64 and x86; no ulps updates needed.
[BZ #16348]
* sysdeps/i386/fpu/e_expl.S (IEEE754_EXPL) [!USE_AS_EXPM1L]: Use
1+x for argument with exponent below -67.
* sysdeps/x86_64/fpu/e_expl.S (IEEE754_EXPL) [!USE_AS_EXPM1L]:
Likewise.
* math/auto-libm-test-in: Add more tests of exp.
* math/auto-libm-test-out: Regenerated.
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16356).
This patch fixes bug 16356, bad results from x86 / x86_64 expl /
exp10l in directed rounding modes, the most serious of the bugs shown
up by my patch expanding libm test coverage. When I fixed bug 16293,
I thought it was only necessary to set round-to-nearest when using
frndint in expm1 functions, because in other cases the cancellation
error from having the resulting fractional part close to 1 or -1 would
not be significant. However, in expl and exp10l, the way the final
fractional part gets computed (something more complicated than a
simple subtraction, because more precision is needed than you'd get
that way) can result in a value outside the range [-1, 1] when the
argument to frndint was very close to an integer and was rounded the
"wrong" way because of the rounding mode - and the f2xm1 instruction
has undefined results if its argument is outside [-1, 1], so resulting
in the large errors seen. So this patch removes the USE_AS_EXPM1L
conditionals on the round-to-nearest settings, so all of expl, expm1l
and exp10l now get round-to-nearest used for frndint (meaning the
final fractional part can at most be slightly above 0.5 in
magnitude). Associated tests of exp and exp10 are added and testing
of exp10 in directed rounding modes enabled.
Tested x86_64 and x86 and ulps updated accordingly.
* sysdeps/i386/fpu/e_expl.S (IEEE754_EXPL): Also set
round-to-nearest for [!USE_AS_EXPM1L].
* sysdeps/x86_64/fpu/e_expl.S (IEEE754_EXPL): Likewise.
* math/auto-libm-test-in: Do not expect cosh tests to fail. Add
more tests of exp and exp10. Expect some exp10 tests to miss
exceptions or fail in directed rounding modes.
* math/auto-libm-test-out: Regenerated.
* math/libm-test.inc (exp10_tonearest_test_data): New array.
(exp10_test_tonearest): New function.
(exp10_towardzero_test_data): New array.
(exp10_test_towardzero): New function.
(exp10_downward_test_data): New array.
(exp10_test_downward): New function.
(exp10_upward_test_data): New array.
(exp10_test_upward): New function.
(main): Call the new functions.
* sysdeps/i386/fpu/libm-test-ulps: Update.
* sysdeps/x86_64/fpu/libm-test-ulps: Likewise.
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Bug 16293 is inaccuracy of x86/x86_64 versions of expm1, near 0 in
directed rounding modes, that arises from frndint rounding the
exponent to 1 or -1 instead of 0, resulting in large cancellation
error. This inaccuracy in turn affects other functions such as sinh
that use expm1. This patch fixes the problem by setting
round-to-nearest mode temporarily around the affected calls to
frndint. I don't think this is needed for other uses of frndint, such
as in exp itself, as only for expm1 is the cancellation error
significant.
Tested x86_64 and x86 and ulps updated accordingly.
* sysdeps/i386/fpu/e_expl.S (IEEE754_EXPL) [USE_AS_EXPM1L]: Set
round-to-nearest mode when using frndint.
* sysdeps/i386/fpu/s_expm1.S (__expm1): Likewise.
* sysdeps/i386/fpu/s_expm1f.S (__expm1f): Likewise.
* sysdeps/x86_64/fpu/e_expl.S (IEEE754_EXPL) [USE_AS_EXPM1L]:
Likewise.
* math/auto-libm-test-in: Add more tests of expm1. Do not expect
sinh test to fail.
* math/auto-libm-test-out: Regenerated.
* math/libm-test.inc (TEST_COND_x86_64): Remove macro.
(TEST_COND_x86): Likewise.
(expm1_tonearest_test_data): New array.
(expm1_test_tonearest): New function.
(expm1_towardzero_test_data): New array.
(expm1_test_towardzero): New function.
(expm1_downward_test_data): New array.
(expm1_test_downward): New function.
(expm1_upward_test_data): New array.
(expm1_test_upward): New function.
(main): Run the new test functions.
* sysdeps/i386/fpu/libm-test-ulps: Update.
* sysdeps/x86_64/fpu/libm-test-ulps: Likewise.
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