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Fix x86/x86_64 expm1 inaccuracy near 0 in directed rounding modes (bug 16293)
- From: "Joseph S. Myers" <joseph at codesourcery dot com>
- To: <libc-alpha at sourceware dot org>
- Date: Thu, 19 Dec 2013 01:14:35 +0000
- Subject: Fix x86/x86_64 expm1 inaccuracy near 0 in directed rounding modes (bug 16293)
- Authentication-results: sourceware.org; auth=none
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.
(auto-libm-test-out diffs omitted below.)
2013-12-19 Joseph Myers <joseph@codesourcery.com>
[BZ #16293]
* 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.
diff --git a/math/auto-libm-test-in b/math/auto-libm-test-in
index 50e0e6b..28e9d45 100644
--- a/math/auto-libm-test-in
+++ b/math/auto-libm-test-in
@@ -281,6 +281,22 @@ expm1 -100000.0
expm1 100000.0
expm1 max
expm1 -max
+expm1 0x1p-2
+expm1 -0x1p-2
+expm1 0x1p-10
+expm1 -0x1p-10
+expm1 0x1p-20
+expm1 -0x1p-20
+expm1 0x1p-29
+expm1 -0x1p-29
+expm1 0x1p-32
+expm1 -0x1p-32
+expm1 0x1p-50
+expm1 -0x1p-50
+expm1 0x1p-64
+expm1 -0x1p-64
+expm1 0x1p-100
+expm1 -0x1p-100
hypot 0 0
hypot 0 -0
@@ -835,8 +851,7 @@ sin 10
sinh 0
sinh -0
sinh 0.75
-# Bug 16293: expm1 inaccurate in directed rounding modes.
-sinh 0x8p-32 xfail:x86_64:ldbl-96-intel xfail:x86
+sinh 0x8p-32
sinh 22
sinh 23
sinh 24
diff --git a/math/libm-test.inc b/math/libm-test.inc
index dea6c8b..aab3ed2 100644
--- a/math/libm-test.inc
+++ b/math/libm-test.inc
@@ -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 ();
diff --git a/sysdeps/i386/fpu/e_expl.S b/sysdeps/i386/fpu/e_expl.S
index af339f0..a8a5e70 100644
--- a/sysdeps/i386/fpu/e_expl.S
+++ b/sysdeps/i386/fpu/e_expl.S
@@ -130,9 +130,24 @@ ENTRY(IEEE754_EXPL)
#endif
3: FLDLOG /* 1 log2(base) */
fmul %st(1), %st /* 1 x log2(base) */
+#ifdef USE_AS_EXPM1L
+ /* Set round-to-nearest temporarily. */
+ subl $8, %esp
+ cfi_adjust_cfa_offset (8)
+ fstcw 4(%esp)
+ movl $0xf3ff, %edx
+ andl 4(%esp), %edx
+ movl %edx, (%esp)
+ fldcw (%esp)
+#endif
frndint /* 1 i */
fld %st(1) /* 2 x */
frndint /* 2 xi */
+#ifdef USE_AS_EXPM1L
+ fldcw 4(%esp)
+ addl $8, %esp
+ cfi_adjust_cfa_offset (-8)
+#endif
fld %st(1) /* 3 i */
fldt MO(c0) /* 4 c0 */
fld %st(2) /* 5 xi */
diff --git a/sysdeps/i386/fpu/libm-test-ulps b/sysdeps/i386/fpu/libm-test-ulps
index a471e5f..bb3adcb 100644
--- a/sysdeps/i386/fpu/libm-test-ulps
+++ b/sysdeps/i386/fpu/libm-test-ulps
@@ -6092,9 +6092,15 @@ idouble: 1
ifloat: 1
# expm1
+Test "expm1 (-0x1p-64)":
+ildouble: 1
+ldouble: 1
Test "expm1 (-0x2.dp+4)":
ildouble: 1
ldouble: 1
+Test "expm1 (-0x4p-12)":
+ildouble: 1
+ldouble: 1
Test "expm1 (-45.0)":
ildouble: 1
ldouble: 1
@@ -6108,6 +6114,338 @@ Test "expm1 (11356.25)":
ildouble: 1
ldouble: 1
+# expm1_downward
+Test "expm1_downward (-0x1p-100)":
+double: 1
+float: 1
+idouble: 1
+ifloat: 1
+ildouble: 1
+ldouble: 1
+Test "expm1_downward (-0x2.ep+4)":
+idouble: 1
+ifloat: 1
+ildouble: 1
+ldouble: 1
+Test "expm1_downward (-0x4.9p+4)":
+idouble: 1
+ifloat: 1
+ildouble: 1
+ldouble: 1
+Test "expm1_downward (-0x4.bp+4)":
+idouble: 1
+ifloat: 1
+ildouble: 1
+ldouble: 1
+Test "expm1_downward (-0x4p-4)":
+ildouble: 1
+ldouble: 1
+Test "expm1_downward (-0x5p+4)":
+idouble: 1
+ifloat: 1
+ildouble: 1
+ldouble: 1
+Test "expm1_downward (-0x6.4p+4)":
+idouble: 1
+ifloat: 1
+ildouble: 1
+ldouble: 1
+Test "expm1_downward (0x1p+0)":
+ildouble: 1
+ldouble: 1
+Test "expm1_downward (0x1p-100)":
+ildouble: 1
+ldouble: 1
+Test "expm1_downward (0x1p-32)":
+idouble: 1
+ildouble: 1
+ldouble: 1
+Test "expm1_downward (0x3.2p+4)":
+ildouble: 1
+ldouble: 1
+Test "expm1_downward (0x4p-12)":
+ildouble: 1
+ldouble: 1
+Test "expm1_downward (0x4p-52)":
+idouble: 1
+ildouble: 1
+ldouble: 1
+Test "expm1_downward (0x7.fp+4)":
+ildouble: 1
+ldouble: 1
+Test "expm1_downward (0x8p-32)":
+ildouble: 1
+ldouble: 1
+
+# expm1_tonearest
+Test "expm1_tonearest (-0x1p-64)":
+ildouble: 1
+ldouble: 1
+Test "expm1_tonearest (-0x2.dp+4)":
+ildouble: 1
+ldouble: 1
+Test "expm1_tonearest (-0x4p-12)":
+ildouble: 1
+ldouble: 1
+Test "expm1_tonearest (0x1p+0)":
+ildouble: 1
+ldouble: 1
+Test "expm1_tonearest (0x2.c5c4p+12)":
+ildouble: 1
+ldouble: 1
+
+# expm1_towardzero
+Test "expm1_towardzero (-0x1.2p+4)":
+float: 1
+Test "expm1_towardzero (-0x1.86ap+16)":
+double: 1
+float: 1
+idouble: 1
+ifloat: 1
+ildouble: 1
+ldouble: 1
+Test "expm1_towardzero (-0x1p-100)":
+double: 1
+float: 1
+ildouble: 1
+ldouble: 1
+Test "expm1_towardzero (-0x1p-20)":
+ildouble: 2
+ldouble: 2
+Test "expm1_towardzero (-0x1p-32)":
+idouble: 1
+ildouble: 1
+ldouble: 1
+Test "expm1_towardzero (-0x1p-64)":
+ildouble: 1
+ldouble: 1
+Test "expm1_towardzero (-0x2.4p+4)":
+float: 1
+Test "expm1_towardzero (-0x2.5p+4)":
+float: 1
+Test "expm1_towardzero (-0x2.6p+4)":
+double: 1
+float: 1
+Test "expm1_towardzero (-0x2.71p+12)":
+double: 1
+float: 1
+idouble: 1
+ifloat: 1
+ildouble: 1
+ldouble: 1
+Test "expm1_towardzero (-0x2.cp+4)":
+double: 1
+float: 1
+Test "expm1_towardzero (-0x2.dp+4)":
+double: 1
+float: 1
+ildouble: 1
+ldouble: 1
+Test "expm1_towardzero (-0x2.ep+4)":
+double: 1
+float: 1
+Test "expm1_towardzero (-0x3.e8p+8)":
+double: 1
+float: 1
+idouble: 1
+ifloat: 1
+ildouble: 1
+ldouble: 1
+Test "expm1_towardzero (-0x4.9p+4)":
+double: 1
+float: 1
+Test "expm1_towardzero (-0x4.ap+4)":
+double: 1
+float: 1
+ildouble: 1
+ldouble: 1
+Test "expm1_towardzero (-0x4.bp+4)":
+double: 1
+float: 1
+Test "expm1_towardzero (-0x4.ep+4)":
+double: 1
+float: 1
+ildouble: 1
+ldouble: 1
+Test "expm1_towardzero (-0x4.fp+4)":
+double: 1
+float: 1
+ildouble: 1
+ldouble: 1
+Test "expm1_towardzero (-0x4p-12)":
+ildouble: 1
+ldouble: 1
+Test "expm1_towardzero (-0x4p-52)":
+idouble: 1
+ildouble: 2
+ldouble: 2
+Test "expm1_towardzero (-0x5p+4)":
+double: 1
+float: 1
+Test "expm1_towardzero (-0x6.4p+4)":
+double: 1
+float: 1
+Test "expm1_towardzero (-0x8p-32)":
+ildouble: 1
+ldouble: 1
+Test "expm1_towardzero (-0xf.ffffffffffff8p+1020)":
+double: 1
+idouble: 1
+ildouble: 1
+ldouble: 1
+Test "expm1_towardzero (-0xf.fffffffffffffffp+16380)":
+ildouble: 1
+ldouble: 1
+Test "expm1_towardzero (-0xf.fffffp+124)":
+double: 1
+float: 1
+idouble: 1
+ifloat: 1
+ildouble: 1
+ldouble: 1
+Test "expm1_towardzero (0x1p+0)":
+ildouble: 1
+ldouble: 1
+Test "expm1_towardzero (0x1p-100)":
+ildouble: 1
+ldouble: 1
+Test "expm1_towardzero (0x1p-32)":
+idouble: 1
+ildouble: 1
+ldouble: 1
+Test "expm1_towardzero (0x3.2p+4)":
+ildouble: 1
+ldouble: 1
+Test "expm1_towardzero (0x4p-12)":
+ildouble: 1
+ldouble: 1
+Test "expm1_towardzero (0x4p-52)":
+idouble: 1
+ildouble: 1
+ldouble: 1
+Test "expm1_towardzero (0x7.fp+4)":
+ildouble: 1
+ldouble: 1
+Test "expm1_towardzero (0x8p-32)":
+ildouble: 1
+ldouble: 1
+
+# expm1_upward
+Test "expm1_upward (-0x1.2p+4)":
+float: 1
+Test "expm1_upward (-0x1.86ap+16)":
+double: 1
+float: 1
+idouble: 1
+ifloat: 1
+ildouble: 1
+ldouble: 1
+Test "expm1_upward (-0x1p-100)":
+double: 1
+float: 1
+ildouble: 1
+ldouble: 1
+Test "expm1_upward (-0x1p-20)":
+ildouble: 2
+ldouble: 2
+Test "expm1_upward (-0x1p-32)":
+idouble: 1
+ildouble: 1
+ldouble: 1
+Test "expm1_upward (-0x1p-64)":
+ildouble: 1
+ldouble: 1
+Test "expm1_upward (-0x2.4p+4)":
+float: 1
+Test "expm1_upward (-0x2.5p+4)":
+float: 1
+Test "expm1_upward (-0x2.6p+4)":
+double: 1
+float: 1
+Test "expm1_upward (-0x2.71p+12)":
+double: 1
+float: 1
+idouble: 1
+ifloat: 1
+ildouble: 1
+ldouble: 1
+Test "expm1_upward (-0x2.cp+4)":
+double: 1
+float: 1
+Test "expm1_upward (-0x2.dp+4)":
+double: 1
+float: 1
+ildouble: 1
+ldouble: 1
+Test "expm1_upward (-0x2.ep+4)":
+double: 1
+float: 1
+Test "expm1_upward (-0x3.e8p+8)":
+double: 1
+float: 1
+idouble: 1
+ifloat: 1
+ildouble: 1
+ldouble: 1
+Test "expm1_upward (-0x4.9p+4)":
+double: 1
+float: 1
+Test "expm1_upward (-0x4.ap+4)":
+double: 1
+float: 1
+ildouble: 1
+ldouble: 1
+Test "expm1_upward (-0x4.bp+4)":
+double: 1
+float: 1
+Test "expm1_upward (-0x4.ep+4)":
+double: 1
+float: 1
+ildouble: 1
+ldouble: 1
+Test "expm1_upward (-0x4.fp+4)":
+double: 1
+float: 1
+ildouble: 1
+ldouble: 1
+Test "expm1_upward (-0x4p-12)":
+ildouble: 1
+ldouble: 1
+Test "expm1_upward (-0x4p-52)":
+idouble: 1
+ildouble: 2
+ldouble: 2
+Test "expm1_upward (-0x5p+4)":
+double: 1
+float: 1
+Test "expm1_upward (-0x6.4p+4)":
+double: 1
+float: 1
+Test "expm1_upward (-0x8p-32)":
+ildouble: 1
+ldouble: 1
+Test "expm1_upward (-0xf.ffffffffffff8p+1020)":
+double: 1
+idouble: 1
+ildouble: 1
+ldouble: 1
+Test "expm1_upward (-0xf.fffffffffffffffp+16380)":
+ildouble: 1
+ldouble: 1
+Test "expm1_upward (-0xf.fffffp+124)":
+double: 1
+float: 1
+idouble: 1
+ifloat: 1
+ildouble: 1
+ldouble: 1
+Test "expm1_upward (0x1.f4p+8)":
+ildouble: 1
+ldouble: 1
+Test "expm1_upward (0x4p-4)":
+ildouble: 1
+ldouble: 1
+
# gamma
Test "gamma (-0.5)":
double: 1
@@ -7773,6 +8111,9 @@ ldouble: 1
Test "sinh_downward (0x1.8p+4)":
ildouble: 1
ldouble: 1
+Test "sinh_downward (0x8p-32)":
+ildouble: 1
+ldouble: 1
Test "sinh_downward (0xcp-4)":
float: 1
ildouble: 1
@@ -7810,6 +8151,9 @@ ldouble: 1
Test "sinh_towardzero (0x1.8p+4)":
ildouble: 1
ldouble: 1
+Test "sinh_towardzero (0x8p-32)":
+ildouble: 1
+ldouble: 1
Test "sinh_towardzero (0xcp-4)":
float: 1
ildouble: 1
@@ -7840,6 +8184,9 @@ ldouble: 1
Test "sinh_upward (0x1.7p+4)":
ildouble: 1
ldouble: 1
+Test "sinh_upward (0x8p-32)":
+double: 1
+float: 1
Test "sinh_upward (0xcp-4)":
float: 1
ildouble: 2
@@ -10663,6 +11010,34 @@ Function: "expm1":
ildouble: 1
ldouble: 1
+Function: "expm1_downward":
+double: 1
+float: 1
+idouble: 1
+ifloat: 1
+ildouble: 1
+ldouble: 1
+
+Function: "expm1_tonearest":
+ildouble: 1
+ldouble: 1
+
+Function: "expm1_towardzero":
+double: 1
+float: 1
+idouble: 1
+ifloat: 1
+ildouble: 2
+ldouble: 2
+
+Function: "expm1_upward":
+double: 1
+float: 1
+idouble: 1
+ifloat: 1
+ildouble: 2
+ldouble: 2
+
Function: "gamma":
double: 1
float: 2
diff --git a/sysdeps/i386/fpu/s_expm1.S b/sysdeps/i386/fpu/s_expm1.S
index 91617eb..3980552 100644
--- a/sysdeps/i386/fpu/s_expm1.S
+++ b/sysdeps/i386/fpu/s_expm1.S
@@ -78,7 +78,18 @@ ENTRY(__expm1)
5: fldt MO(l2e) // log2(e) : x
fmulp // log2(e)*x
fld %st // log2(e)*x : log2(e)*x
+ // Set round-to-nearest temporarily.
+ subl $8, %esp
+ cfi_adjust_cfa_offset (8)
+ fstcw 4(%esp)
+ movl $0xf3ff, %ecx
+ andl 4(%esp), %ecx
+ movl %ecx, (%esp)
+ fldcw (%esp)
frndint // int(log2(e)*x) : log2(e)*x
+ fldcw 4(%esp)
+ addl $8, %esp
+ cfi_adjust_cfa_offset (-8)
fsubr %st, %st(1) // int(log2(e)*x) : fract(log2(e)*x)
fxch // fract(log2(e)*x) : int(log2(e)*x)
f2xm1 // 2^fract(log2(e)*x)-1 : int(log2(e)*x)
diff --git a/sysdeps/i386/fpu/s_expm1f.S b/sysdeps/i386/fpu/s_expm1f.S
index 2f1b6f6..e5e52a0 100644
--- a/sysdeps/i386/fpu/s_expm1f.S
+++ b/sysdeps/i386/fpu/s_expm1f.S
@@ -78,7 +78,18 @@ ENTRY(__expm1f)
5: fldt MO(l2e) // log2(e) : x
fmulp // log2(e)*x
fld %st // log2(e)*x : log2(e)*x
+ // Set round-to-nearest temporarily.
+ subl $8, %esp
+ cfi_adjust_cfa_offset (8)
+ fstcw 4(%esp)
+ movl $0xf3ff, %ecx
+ andl 4(%esp), %ecx
+ movl %ecx, (%esp)
+ fldcw (%esp)
frndint // int(log2(e)*x) : log2(e)*x
+ fldcw 4(%esp)
+ addl $8, %esp
+ cfi_adjust_cfa_offset (-8)
fsubr %st, %st(1) // int(log2(e)*x) : fract(log2(e)*x)
fxch // fract(log2(e)*x) : int(log2(e)*x)
f2xm1 // 2^fract(log2(e)*x)-1 : int(log2(e)*x)
diff --git a/sysdeps/x86_64/fpu/e_expl.S b/sysdeps/x86_64/fpu/e_expl.S
index a919780..1c21f03 100644
--- a/sysdeps/x86_64/fpu/e_expl.S
+++ b/sysdeps/x86_64/fpu/e_expl.S
@@ -127,9 +127,20 @@ ENTRY(IEEE754_EXPL)
#endif
3: FLDLOG /* 1 log2(base) */
fmul %st(1), %st /* 1 x log2(base) */
+#ifdef USE_AS_EXPM1L
+ /* Set round-to-nearest temporarily. */
+ fstcw -4(%rsp)
+ movl $0xf3ff, %edx
+ andl -4(%rsp), %edx
+ movl %edx, -8(%rsp)
+ fldcw -8(%rsp)
+#endif
frndint /* 1 i */
fld %st(1) /* 2 x */
frndint /* 2 xi */
+#ifdef USE_AS_EXPM1L
+ fldcw -4(%rsp)
+#endif
fld %st(1) /* 3 i */
fldt MO(c0) /* 4 c0 */
fld %st(2) /* 5 xi */
diff --git a/sysdeps/x86_64/fpu/libm-test-ulps b/sysdeps/x86_64/fpu/libm-test-ulps
index b45ce1d..89b4bc8 100644
--- a/sysdeps/x86_64/fpu/libm-test-ulps
+++ b/sysdeps/x86_64/fpu/libm-test-ulps
@@ -7011,9 +7011,15 @@ float: 1
ifloat: 1
# expm1
+Test "expm1 (-0x1p-64)":
+ildouble: 1
+ldouble: 1
Test "expm1 (-0x2.dp+4)":
ildouble: 1
ldouble: 1
+Test "expm1 (-0x4p-12)":
+ildouble: 1
+ldouble: 1
Test "expm1 (-45.0)":
ildouble: 1
ldouble: 1
@@ -7048,6 +7054,281 @@ Test "expm1 (500.0)":
double: 1
idouble: 1
+# expm1_downward
+Test "expm1_downward (-0x1p-100)":
+ildouble: 1
+ldouble: 1
+Test "expm1_downward (-0x2.ep+4)":
+ildouble: 1
+ldouble: 1
+Test "expm1_downward (-0x4.9p+4)":
+ildouble: 1
+ldouble: 1
+Test "expm1_downward (-0x4.bp+4)":
+ildouble: 1
+ldouble: 1
+Test "expm1_downward (-0x4p-4)":
+ildouble: 1
+ldouble: 1
+Test "expm1_downward (-0x5p+4)":
+ildouble: 1
+ldouble: 1
+Test "expm1_downward (-0x6.4p+4)":
+ildouble: 1
+ldouble: 1
+Test "expm1_downward (0x1.f4p+8)":
+double: 1
+idouble: 1
+Test "expm1_downward (0x1p+0)":
+ildouble: 1
+ldouble: 1
+Test "expm1_downward (0x1p-100)":
+ildouble: 1
+ldouble: 1
+Test "expm1_downward (0x1p-32)":
+ildouble: 1
+ldouble: 1
+Test "expm1_downward (0x3.2p+4)":
+double: 1
+float: 1
+idouble: 1
+ifloat: 1
+ildouble: 1
+ldouble: 1
+Test "expm1_downward (0x4p-12)":
+ildouble: 1
+ldouble: 1
+Test "expm1_downward (0x4p-52)":
+ildouble: 1
+ldouble: 1
+Test "expm1_downward (0x7.fp+4)":
+double: 1
+idouble: 1
+ildouble: 1
+ldouble: 1
+Test "expm1_downward (0x8p-32)":
+ildouble: 1
+ldouble: 1
+
+# expm1_tonearest
+Test "expm1_tonearest (-0x1p-64)":
+ildouble: 1
+ldouble: 1
+Test "expm1_tonearest (-0x2.dp+4)":
+ildouble: 1
+ldouble: 1
+Test "expm1_tonearest (-0x4p-12)":
+ildouble: 1
+ldouble: 1
+Test "expm1_tonearest (0x1.f4p+8)":
+double: 1
+idouble: 1
+Test "expm1_tonearest (0x1p+0)":
+double: 1
+float: 1
+idouble: 1
+ifloat: 1
+ildouble: 1
+ldouble: 1
+Test "expm1_tonearest (0x2.c5c4p+12)":
+ildouble: 1
+ldouble: 1
+Test "expm1_tonearest (0xcp-4)":
+double: 1
+idouble: 1
+
+# expm1_towardzero
+Test "expm1_towardzero (-0x1.86ap+16)":
+ildouble: 1
+ldouble: 1
+Test "expm1_towardzero (-0x1p-100)":
+double: 1
+float: 1
+idouble: 1
+ifloat: 1
+ildouble: 1
+ldouble: 1
+Test "expm1_towardzero (-0x1p-20)":
+ildouble: 2
+ldouble: 2
+Test "expm1_towardzero (-0x1p-32)":
+float: 1
+ifloat: 1
+ildouble: 1
+ldouble: 1
+Test "expm1_towardzero (-0x1p-64)":
+double: 1
+float: 1
+idouble: 1
+ifloat: 1
+ildouble: 1
+ldouble: 1
+Test "expm1_towardzero (-0x2.71p+12)":
+ildouble: 1
+ldouble: 1
+Test "expm1_towardzero (-0x2.dp+4)":
+ildouble: 1
+ldouble: 1
+Test "expm1_towardzero (-0x3.e8p+8)":
+ildouble: 1
+ldouble: 1
+Test "expm1_towardzero (-0x4.ap+4)":
+ildouble: 1
+ldouble: 1
+Test "expm1_towardzero (-0x4.ep+4)":
+ildouble: 1
+ldouble: 1
+Test "expm1_towardzero (-0x4.fp+4)":
+ildouble: 1
+ldouble: 1
+Test "expm1_towardzero (-0x4p-12)":
+ildouble: 1
+ldouble: 1
+Test "expm1_towardzero (-0x4p-52)":
+float: 1
+ifloat: 1
+ildouble: 2
+ldouble: 2
+Test "expm1_towardzero (-0x8p-32)":
+float: 1
+ifloat: 1
+ildouble: 1
+ldouble: 1
+Test "expm1_towardzero (-0xf.ffffffffffff8p+1020)":
+ildouble: 1
+ldouble: 1
+Test "expm1_towardzero (-0xf.fffffffffffffffp+16380)":
+ildouble: 1
+ldouble: 1
+Test "expm1_towardzero (-0xf.fffffp+124)":
+ildouble: 1
+ldouble: 1
+Test "expm1_towardzero (0x1.f4p+8)":
+double: 1
+idouble: 1
+Test "expm1_towardzero (0x1p+0)":
+ildouble: 1
+ldouble: 1
+Test "expm1_towardzero (0x1p-100)":
+ildouble: 1
+ldouble: 1
+Test "expm1_towardzero (0x1p-32)":
+ildouble: 1
+ldouble: 1
+Test "expm1_towardzero (0x3.2p+4)":
+double: 1
+float: 1
+idouble: 1
+ifloat: 1
+ildouble: 1
+ldouble: 1
+Test "expm1_towardzero (0x4p-12)":
+ildouble: 1
+ldouble: 1
+Test "expm1_towardzero (0x4p-52)":
+ildouble: 1
+ldouble: 1
+Test "expm1_towardzero (0x7.fp+4)":
+double: 1
+idouble: 1
+ildouble: 1
+ldouble: 1
+Test "expm1_towardzero (0x8p-32)":
+ildouble: 1
+ldouble: 1
+
+# expm1_upward
+Test "expm1_upward (-0x1.86ap+16)":
+ildouble: 1
+ldouble: 1
+Test "expm1_upward (-0x1p-100)":
+double: 1
+float: 1
+idouble: 1
+ifloat: 1
+ildouble: 1
+ldouble: 1
+Test "expm1_upward (-0x1p-20)":
+ildouble: 2
+ldouble: 2
+Test "expm1_upward (-0x1p-32)":
+float: 1
+ifloat: 1
+ildouble: 1
+ldouble: 1
+Test "expm1_upward (-0x1p-64)":
+double: 1
+float: 1
+idouble: 1
+ifloat: 1
+ildouble: 1
+ldouble: 1
+Test "expm1_upward (-0x2.71p+12)":
+ildouble: 1
+ldouble: 1
+Test "expm1_upward (-0x2.dp+4)":
+ildouble: 1
+ldouble: 1
+Test "expm1_upward (-0x3.e8p+8)":
+ildouble: 1
+ldouble: 1
+Test "expm1_upward (-0x4.ap+4)":
+ildouble: 1
+ldouble: 1
+Test "expm1_upward (-0x4.ep+4)":
+ildouble: 1
+ldouble: 1
+Test "expm1_upward (-0x4.fp+4)":
+ildouble: 1
+ldouble: 1
+Test "expm1_upward (-0x4p-12)":
+ildouble: 1
+ldouble: 1
+Test "expm1_upward (-0x4p-52)":
+float: 1
+ifloat: 1
+ildouble: 2
+ldouble: 2
+Test "expm1_upward (-0x8p-32)":
+float: 1
+ifloat: 1
+ildouble: 1
+ldouble: 1
+Test "expm1_upward (-0xf.ffffffffffff8p+1020)":
+ildouble: 1
+ldouble: 1
+Test "expm1_upward (-0xf.fffffffffffffffp+16380)":
+ildouble: 1
+ldouble: 1
+Test "expm1_upward (-0xf.fffffp+124)":
+ildouble: 1
+ldouble: 1
+Test "expm1_upward (0x1.f4p+8)":
+ildouble: 1
+ldouble: 1
+Test "expm1_upward (0x1p-100)":
+double: 1
+float: 1
+idouble: 1
+ifloat: 1
+Test "expm1_upward (0x1p-32)":
+float: 1
+ifloat: 1
+Test "expm1_upward (0x1p-64)":
+double: 1
+float: 1
+idouble: 1
+ifloat: 1
+Test "expm1_upward (0x4p-4)":
+ildouble: 1
+ldouble: 1
+Test "expm1_upward (0x4p-52)":
+float: 1
+ifloat: 1
+Test "expm1_upward (0x8p-32)":
+float: 1
+ifloat: 1
+
# gamma
Test "gamma (-0.5)":
ildouble: 1
@@ -8864,6 +9145,9 @@ ldouble: 1
Test "sinh_downward (0x1.8p+4)":
ildouble: 1
ldouble: 1
+Test "sinh_downward (0x8p-32)":
+ildouble: 1
+ldouble: 1
Test "sinh_downward (22)":
float: 1
ifloat: 1
@@ -8894,6 +9178,9 @@ ldouble: 1
Test "sinh_towardzero (0x1.8p+4)":
ildouble: 1
ldouble: 1
+Test "sinh_towardzero (0x8p-32)":
+ildouble: 1
+ldouble: 1
Test "sinh_towardzero (22)":
float: 1
ifloat: 1
@@ -12014,6 +12301,38 @@ ifloat: 1
ildouble: 1
ldouble: 1
+Function: "expm1_downward":
+double: 1
+float: 1
+idouble: 1
+ifloat: 1
+ildouble: 1
+ldouble: 1
+
+Function: "expm1_tonearest":
+double: 1
+float: 1
+idouble: 1
+ifloat: 1
+ildouble: 1
+ldouble: 1
+
+Function: "expm1_towardzero":
+double: 1
+float: 1
+idouble: 1
+ifloat: 1
+ildouble: 2
+ldouble: 2
+
+Function: "expm1_upward":
+double: 1
+float: 1
+idouble: 1
+ifloat: 1
+ildouble: 2
+ldouble: 2
+
Function: "gamma":
double: 1
float: 2
--
Joseph S. Myers
joseph@codesourcery.com