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Fix x86/x86_64 expm1 inaccuracy near 0 in directed rounding modes (bug 16293).

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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.
This commit is contained in:
Joseph Myers
2013-12-19 13:36:10 +00:00
parent c688b41960
commit f88acd39da
11 changed files with 1269 additions and 40 deletions
Download Patch File Download Diff File Expand all files Collapse all files

72
math/libm-test.inc
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@@ -267,18 +267,6 @@ struct ulp_data
#define TEST_COND_before_rounding (!TININESS_AFTER_ROUNDING)
#define TEST_COND_after_rounding TININESS_AFTER_ROUNDING
#ifdef __x86_64__
# define TEST_COND_x86_64 1
#else
# define TEST_COND_x86_64 0
#endif
#ifdef __i386__
# define TEST_COND_x86 1
#else
# define TEST_COND_x86 0
#endif
/* Various constants (we must supply them precalculated for accuracy). */
#define M_PI_6l .52359877559829887307710723054658383L
#define M_PI_34l 2.356194490192344928846982537459627163L /* 3*pi/4 */
@@ -7845,6 +7833,62 @@ expm1_test (void)
}
static const struct test_f_f_data expm1_tonearest_test_data[] =
{
AUTO_TESTS_f_f (expm1, tonearest),
};
static void
expm1_test_tonearest (void)
{
START (expm1_tonearest);
RUN_TEST_LOOP_f_f (expm1, expm1_tonearest_test_data, FE_TONEAREST);
END;
}
static const struct test_f_f_data expm1_towardzero_test_data[] =
{
AUTO_TESTS_f_f (expm1, towardzero),
};
static void
expm1_test_towardzero (void)
{
START (expm1_towardzero);
RUN_TEST_LOOP_f_f (expm1, expm1_towardzero_test_data, FE_TOWARDZERO);
END;
}
static const struct test_f_f_data expm1_downward_test_data[] =
{
AUTO_TESTS_f_f (expm1, downward),
};
static void
expm1_test_downward (void)
{
START (expm1_downward);
RUN_TEST_LOOP_f_f (expm1, expm1_downward_test_data, FE_DOWNWARD);
END;
}
static const struct test_f_f_data expm1_upward_test_data[] =
{
AUTO_TESTS_f_f (expm1, upward),
};
static void
expm1_test_upward (void)
{
START (expm1_upward);
RUN_TEST_LOOP_f_f (expm1, expm1_upward_test_data, FE_UPWARD);
END;
}
static const struct test_f_f_data fabs_test_data[] =
{
TEST_f_f (fabs, 0, 0, NO_INEXACT_EXCEPTION),
@@ -13337,6 +13381,10 @@ main (int argc, char **argv)
exp10_test ();
exp2_test ();
expm1_test ();
expm1_test_tonearest ();
expm1_test_towardzero ();
expm1_test_downward ();
expm1_test_upward ();
frexp_test ();
ldexp_test ();
log_test ();