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author | Joseph Myers <joseph@codesourcery.com> | 2015-06-22 21:06:19 +0000 |
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committer | Joseph Myers <joseph@codesourcery.com> | 2015-06-22 21:06:19 +0000 |
commit | 554edb23ffc7a953ca86309cc5f02dbd1a63abe0 (patch) | |
tree | 35ceb89ac22f1987f944539728fda653acd418f2 /math | |
parent | 6b142b3a1d007d7e6f50c26710de7177bc4aca74 (diff) | |
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Fix expm1 missing underflows (bug 16353).
Similar to various other bugs in this area, some expm1 implementations
do not raise the underflow exception for subnormal arguments, when the
result is tiny and inexact. This patch forces the exception in a
similar way to previous fixes.
(The issue does not apply to the ldbl-* implementations or to those
for x86 / x86_64 long double. The change to
sysdeps/ieee754/dbl-64/wordsize-64/e_cosh.c is one I missed when
previously fixing bug 16354; the bug in that implementation was
previously latent, but the expm1 fixes stopped it being latent and so
required it to be fixed to avoid spurious underflows from cosh.)
Tested for x86_64 and x86.
[BZ #16353]
* sysdeps/i386/fpu/s_expm1.S (dbl_min): New object.
(__expm1): Force underflow exception for arguments with small
absolute value.
* sysdeps/i386/fpu/s_expm1f.S (flt_min): New object.
(__expm1f): Force underflow exception for arguments with small
absolute value.
* sysdeps/ieee754/dbl-64/s_expm1.c: Include <float.h>.
(__expm1): Force underflow exception for arguments with small
absolute value.
* sysdeps/ieee754/flt-32/s_expm1f.c: Include <float.h>.
(__expm1f): Force underflow exception for arguments with small
absolute value.
* sysdeps/ieee754/dbl-64/wordsize-64/e_cosh.c (__ieee754_cosh):
Check for small arguments before calling __expm1.
* math/auto-libm-test-in: Do not mark underflow exceptions as
possibly missing for bug 16353.
* math/auto-libm-test-out: Regenerated.
Diffstat (limited to 'math')
-rw-r--r-- | math/auto-libm-test-in | 11 | ||||
-rw-r--r-- | math/auto-libm-test-out | 226 |
2 files changed, 118 insertions, 119 deletions
diff --git a/math/auto-libm-test-in b/math/auto-libm-test-in index 6b054597f1..9bae9d5570 100644 --- a/math/auto-libm-test-in +++ b/math/auto-libm-test-in @@ -1362,12 +1362,11 @@ expm1 0x6.289a78p-4 expm1 0x6.1b4d318238d4a2a8p-4 expm1 0x5.fb8dc64e91a74p-4 expm1 0x3.735f497c4e67535cp-4 -# Bug 16353: underflow exception may be missing -expm1 0x4.0000000000000028p-16384 missing-underflow -expm1 min missing-underflow -expm1 -min missing-underflow -expm1 min_subnorm missing-underflow -expm1 -min_subnorm missing-underflow +expm1 0x4.0000000000000028p-16384 +expm1 min +expm1 -min +expm1 min_subnorm +expm1 -min_subnorm fma 1.0 2.0 3.0 fma 1.25 0.75 0.0625 diff --git a/math/auto-libm-test-out b/math/auto-libm-test-out index 2aecda11f7..9f80736e86 100644 --- a/math/auto-libm-test-out +++ b/math/auto-libm-test-out @@ -109498,11 +109498,11 @@ expm1 0x3.735f497c4e67535cp-4 = expm1 tonearest ldbl-128ibm 0x3.735f497c4e67535cp-4L : 0x3.d9dcef7e7e397c649290c708e4p-4L : inexact-ok = expm1 towardzero ldbl-128ibm 0x3.735f497c4e67535cp-4L : 0x3.d9dcef7e7e397c649290c708e3p-4L : inexact-ok = expm1 upward ldbl-128ibm 0x3.735f497c4e67535cp-4L : 0x3.d9dcef7e7e397c649290c708e4p-4L : inexact-ok -expm1 0x4.0000000000000028p-16384 missing-underflow -= expm1 downward flt-32 0x8p-152f : 0x8p-152f : inexact-ok underflow underflow-ok errno-erange-ok -= expm1 tonearest flt-32 0x8p-152f : 0x8p-152f : inexact-ok underflow underflow-ok errno-erange-ok -= expm1 towardzero flt-32 0x8p-152f : 0x8p-152f : inexact-ok underflow underflow-ok errno-erange-ok -= expm1 upward flt-32 0x8p-152f : 0x1p-148f : inexact-ok underflow underflow-ok errno-erange-ok +expm1 0x4.0000000000000028p-16384 += expm1 downward flt-32 0x8p-152f : 0x8p-152f : inexact-ok underflow errno-erange-ok += expm1 tonearest flt-32 0x8p-152f : 0x8p-152f : inexact-ok underflow errno-erange-ok += expm1 towardzero flt-32 0x8p-152f : 0x8p-152f : inexact-ok underflow errno-erange-ok += expm1 upward flt-32 0x8p-152f : 0x1p-148f : inexact-ok underflow errno-erange-ok = expm1 downward dbl-64 0x8p-152 : 0x8p-152 : inexact-ok = expm1 tonearest dbl-64 0x8p-152 : 0x8p-152 : inexact-ok = expm1 towardzero dbl-64 0x8p-152 : 0x8p-152 : inexact-ok @@ -109547,10 +109547,10 @@ expm1 0x4.0000000000000028p-16384 missing-underflow = expm1 tonearest ldbl-128ibm 0x0p+0L : 0x0p+0L : inexact-ok = expm1 towardzero ldbl-128ibm 0x0p+0L : 0x0p+0L : inexact-ok = expm1 upward ldbl-128ibm 0x0p+0L : 0x0p+0L : inexact-ok -= expm1 downward dbl-64 0x4p-1076 : 0x4p-1076 : inexact-ok underflow underflow-ok errno-erange-ok -= expm1 tonearest dbl-64 0x4p-1076 : 0x4p-1076 : inexact-ok underflow underflow-ok errno-erange-ok -= expm1 towardzero dbl-64 0x4p-1076 : 0x4p-1076 : inexact-ok underflow underflow-ok errno-erange-ok -= expm1 upward dbl-64 0x4p-1076 : 0x8p-1076 : inexact-ok underflow underflow-ok errno-erange-ok += expm1 downward dbl-64 0x4p-1076 : 0x4p-1076 : inexact-ok underflow errno-erange-ok += expm1 tonearest dbl-64 0x4p-1076 : 0x4p-1076 : inexact-ok underflow errno-erange-ok += expm1 towardzero dbl-64 0x4p-1076 : 0x4p-1076 : inexact-ok underflow errno-erange-ok += expm1 upward dbl-64 0x4p-1076 : 0x8p-1076 : inexact-ok underflow errno-erange-ok = expm1 downward ldbl-96-intel 0x4p-1076L : 0x4p-1076L : inexact-ok = expm1 tonearest ldbl-96-intel 0x4p-1076L : 0x4p-1076L : inexact-ok = expm1 towardzero ldbl-96-intel 0x4p-1076L : 0x4p-1076L : inexact-ok @@ -109563,10 +109563,10 @@ expm1 0x4.0000000000000028p-16384 missing-underflow = expm1 tonearest ldbl-128 0x4p-1076L : 0x4p-1076L : inexact-ok = expm1 towardzero ldbl-128 0x4p-1076L : 0x4p-1076L : inexact-ok = expm1 upward ldbl-128 0x4p-1076L : 0x4.0000000000000000000000000004p-1076L : inexact-ok -= expm1 downward ldbl-128ibm 0x4p-1076L : 0x4p-1076L : inexact-ok underflow underflow-ok errno-erange-ok -= expm1 tonearest ldbl-128ibm 0x4p-1076L : 0x4p-1076L : inexact-ok underflow underflow-ok errno-erange-ok -= expm1 towardzero ldbl-128ibm 0x4p-1076L : 0x4p-1076L : inexact-ok underflow underflow-ok errno-erange-ok -= expm1 upward ldbl-128ibm 0x4p-1076L : 0x8p-1076L : inexact-ok underflow underflow-ok errno-erange-ok += expm1 downward ldbl-128ibm 0x4p-1076L : 0x4p-1076L : inexact-ok underflow errno-erange-ok += expm1 tonearest ldbl-128ibm 0x4p-1076L : 0x4p-1076L : inexact-ok underflow errno-erange-ok += expm1 towardzero ldbl-128ibm 0x4p-1076L : 0x4p-1076L : inexact-ok underflow errno-erange-ok += expm1 upward ldbl-128ibm 0x4p-1076L : 0x8p-1076L : inexact-ok underflow errno-erange-ok = expm1 downward ldbl-96-intel 0x4.0000000000000028p-16384L : 0x4.0000000000000028p-16384L : inexact-ok = expm1 tonearest ldbl-96-intel 0x4.0000000000000028p-16384L : 0x4.0000000000000028p-16384L : inexact-ok = expm1 towardzero ldbl-96-intel 0x4.0000000000000028p-16384L : 0x4.0000000000000028p-16384L : inexact-ok @@ -109579,7 +109579,7 @@ expm1 0x4.0000000000000028p-16384 missing-underflow = expm1 tonearest ldbl-128 0x4.0000000000000028p-16384L : 0x4.0000000000000028p-16384L : inexact-ok = expm1 towardzero ldbl-128 0x4.0000000000000028p-16384L : 0x4.0000000000000028p-16384L : inexact-ok = expm1 upward ldbl-128 0x4.0000000000000028p-16384L : 0x4.0000000000000028000000000004p-16384L : inexact-ok -expm1 min missing-underflow +expm1 min = expm1 downward flt-32 0x4p-128f : 0x4p-128f : inexact-ok underflow-ok errno-erange-ok = expm1 tonearest flt-32 0x4p-128f : 0x4p-128f : inexact-ok underflow-ok errno-erange-ok = expm1 towardzero flt-32 0x4p-128f : 0x4p-128f : inexact-ok underflow-ok errno-erange-ok @@ -109620,10 +109620,10 @@ expm1 min missing-underflow = expm1 tonearest ldbl-128 0x4p-1024L : 0x4p-1024L : inexact-ok = expm1 towardzero ldbl-128 0x4p-1024L : 0x4p-1024L : inexact-ok = expm1 upward ldbl-128 0x4p-1024L : 0x4.0000000000000000000000000004p-1024L : inexact-ok -= expm1 downward ldbl-128ibm 0x4p-1024L : 0x4p-1024L : inexact-ok underflow underflow-ok errno-erange-ok -= expm1 tonearest ldbl-128ibm 0x4p-1024L : 0x4p-1024L : inexact-ok underflow underflow-ok errno-erange-ok -= expm1 towardzero ldbl-128ibm 0x4p-1024L : 0x4p-1024L : inexact-ok underflow underflow-ok errno-erange-ok -= expm1 upward ldbl-128ibm 0x4p-1024L : 0x4.0000000000004p-1024L : inexact-ok underflow underflow-ok errno-erange-ok += expm1 downward ldbl-128ibm 0x4p-1024L : 0x4p-1024L : inexact-ok underflow errno-erange-ok += expm1 tonearest ldbl-128ibm 0x4p-1024L : 0x4p-1024L : inexact-ok underflow errno-erange-ok += expm1 towardzero ldbl-128ibm 0x4p-1024L : 0x4p-1024L : inexact-ok underflow errno-erange-ok += expm1 upward ldbl-128ibm 0x4p-1024L : 0x4.0000000000004p-1024L : inexact-ok underflow errno-erange-ok = expm1 downward ldbl-96-intel 0x4p-16384L : 0x4p-16384L : inexact-ok underflow-ok errno-erange-ok = expm1 tonearest ldbl-96-intel 0x4p-16384L : 0x4p-16384L : inexact-ok underflow-ok errno-erange-ok = expm1 towardzero ldbl-96-intel 0x4p-16384L : 0x4p-16384L : inexact-ok underflow-ok errno-erange-ok @@ -109636,18 +109636,18 @@ expm1 min missing-underflow = expm1 tonearest ldbl-128 0x4p-16384L : 0x4p-16384L : inexact-ok underflow-ok errno-erange-ok = expm1 towardzero ldbl-128 0x4p-16384L : 0x4p-16384L : inexact-ok underflow-ok errno-erange-ok = expm1 upward ldbl-128 0x4p-16384L : 0x4.0000000000000000000000000004p-16384L : inexact-ok underflow-ok errno-erange-ok -= expm1 downward ldbl-96-intel 0x2p-16384L : 0x2p-16384L : inexact-ok underflow underflow-ok errno-erange-ok -= expm1 tonearest ldbl-96-intel 0x2p-16384L : 0x2p-16384L : inexact-ok underflow underflow-ok errno-erange-ok -= expm1 towardzero ldbl-96-intel 0x2p-16384L : 0x2p-16384L : inexact-ok underflow underflow-ok errno-erange-ok -= expm1 upward ldbl-96-intel 0x2p-16384L : 0x2.0000000000000008p-16384L : inexact-ok underflow underflow-ok errno-erange-ok += expm1 downward ldbl-96-intel 0x2p-16384L : 0x2p-16384L : inexact-ok underflow errno-erange-ok += expm1 tonearest ldbl-96-intel 0x2p-16384L : 0x2p-16384L : inexact-ok underflow errno-erange-ok += expm1 towardzero ldbl-96-intel 0x2p-16384L : 0x2p-16384L : inexact-ok underflow errno-erange-ok += expm1 upward ldbl-96-intel 0x2p-16384L : 0x2.0000000000000008p-16384L : inexact-ok underflow errno-erange-ok = expm1 downward ldbl-96-m68k 0x2p-16384L : 0x2p-16384L : inexact-ok underflow-ok errno-erange-ok = expm1 tonearest ldbl-96-m68k 0x2p-16384L : 0x2p-16384L : inexact-ok underflow-ok errno-erange-ok = expm1 towardzero ldbl-96-m68k 0x2p-16384L : 0x2p-16384L : inexact-ok underflow-ok errno-erange-ok = expm1 upward ldbl-96-m68k 0x2p-16384L : 0x2.0000000000000004p-16384L : inexact-ok underflow-ok errno-erange-ok -= expm1 downward ldbl-128 0x2p-16384L : 0x2p-16384L : inexact-ok underflow underflow-ok errno-erange-ok -= expm1 tonearest ldbl-128 0x2p-16384L : 0x2p-16384L : inexact-ok underflow underflow-ok errno-erange-ok -= expm1 towardzero ldbl-128 0x2p-16384L : 0x2p-16384L : inexact-ok underflow underflow-ok errno-erange-ok -= expm1 upward ldbl-128 0x2p-16384L : 0x2.0000000000000000000000000004p-16384L : inexact-ok underflow underflow-ok errno-erange-ok += expm1 downward ldbl-128 0x2p-16384L : 0x2p-16384L : inexact-ok underflow errno-erange-ok += expm1 tonearest ldbl-128 0x2p-16384L : 0x2p-16384L : inexact-ok underflow errno-erange-ok += expm1 towardzero ldbl-128 0x2p-16384L : 0x2p-16384L : inexact-ok underflow errno-erange-ok += expm1 upward ldbl-128 0x2p-16384L : 0x2.0000000000000000000000000004p-16384L : inexact-ok underflow errno-erange-ok = expm1 downward dbl-64 0x8p-972 : 0x8p-972 : inexact-ok = expm1 tonearest dbl-64 0x8p-972 : 0x8p-972 : inexact-ok = expm1 towardzero dbl-64 0x8p-972 : 0x8p-972 : inexact-ok @@ -109668,7 +109668,7 @@ expm1 min missing-underflow = expm1 tonearest ldbl-128ibm 0x8p-972L : 0x8p-972L : inexact-ok underflow-ok errno-erange-ok = expm1 towardzero ldbl-128ibm 0x8p-972L : 0x8p-972L : inexact-ok underflow-ok errno-erange-ok = expm1 upward ldbl-128ibm 0x8p-972L : 0x8.00000000000000000000000004p-972L : inexact-ok underflow-ok errno-erange-ok -expm1 -min missing-underflow +expm1 -min = expm1 downward flt-32 -0x4p-128f : -0x4p-128f : inexact-ok underflow-ok errno-erange-ok = expm1 tonearest flt-32 -0x4p-128f : -0x4p-128f : inexact-ok underflow-ok errno-erange-ok = expm1 towardzero flt-32 -0x4p-128f : -0x3.fffff8p-128f : inexact-ok underflow-ok errno-erange-ok @@ -109709,10 +109709,10 @@ expm1 -min missing-underflow = expm1 tonearest ldbl-128 -0x4p-1024L : -0x4p-1024L : inexact-ok = expm1 towardzero ldbl-128 -0x4p-1024L : -0x3.fffffffffffffffffffffffffffep-1024L : inexact-ok = expm1 upward ldbl-128 -0x4p-1024L : -0x3.fffffffffffffffffffffffffffep-1024L : inexact-ok -= expm1 downward ldbl-128ibm -0x4p-1024L : -0x4p-1024L : inexact-ok underflow underflow-ok errno-erange-ok -= expm1 tonearest ldbl-128ibm -0x4p-1024L : -0x4p-1024L : inexact-ok underflow underflow-ok errno-erange-ok -= expm1 towardzero ldbl-128ibm -0x4p-1024L : -0x3.ffffffffffffcp-1024L : inexact-ok underflow underflow-ok errno-erange-ok -= expm1 upward ldbl-128ibm -0x4p-1024L : -0x3.ffffffffffffcp-1024L : inexact-ok underflow underflow-ok errno-erange-ok += expm1 downward ldbl-128ibm -0x4p-1024L : -0x4p-1024L : inexact-ok underflow errno-erange-ok += expm1 tonearest ldbl-128ibm -0x4p-1024L : -0x4p-1024L : inexact-ok underflow errno-erange-ok += expm1 towardzero ldbl-128ibm -0x4p-1024L : -0x3.ffffffffffffcp-1024L : inexact-ok underflow errno-erange-ok += expm1 upward ldbl-128ibm -0x4p-1024L : -0x3.ffffffffffffcp-1024L : inexact-ok underflow errno-erange-ok = expm1 downward ldbl-96-intel -0x4p-16384L : -0x4p-16384L : inexact-ok underflow-ok errno-erange-ok = expm1 tonearest ldbl-96-intel -0x4p-16384L : -0x4p-16384L : inexact-ok underflow-ok errno-erange-ok = expm1 towardzero ldbl-96-intel -0x4p-16384L : -0x3.fffffffffffffff8p-16384L : inexact-ok underflow-ok errno-erange-ok @@ -109725,18 +109725,18 @@ expm1 -min missing-underflow = expm1 tonearest ldbl-128 -0x4p-16384L : -0x4p-16384L : inexact-ok underflow-ok errno-erange-ok = expm1 towardzero ldbl-128 -0x4p-16384L : -0x3.fffffffffffffffffffffffffffcp-16384L : inexact-ok underflow-ok errno-erange-ok = expm1 upward ldbl-128 -0x4p-16384L : -0x3.fffffffffffffffffffffffffffcp-16384L : inexact-ok underflow-ok errno-erange-ok -= expm1 downward ldbl-96-intel -0x2p-16384L : -0x2p-16384L : inexact-ok underflow underflow-ok errno-erange-ok -= expm1 tonearest ldbl-96-intel -0x2p-16384L : -0x2p-16384L : inexact-ok underflow underflow-ok errno-erange-ok -= expm1 towardzero ldbl-96-intel -0x2p-16384L : -0x1.fffffffffffffff8p-16384L : inexact-ok underflow underflow-ok errno-erange-ok -= expm1 upward ldbl-96-intel -0x2p-16384L : -0x1.fffffffffffffff8p-16384L : inexact-ok underflow underflow-ok errno-erange-ok += expm1 downward ldbl-96-intel -0x2p-16384L : -0x2p-16384L : inexact-ok underflow errno-erange-ok += expm1 tonearest ldbl-96-intel -0x2p-16384L : -0x2p-16384L : inexact-ok underflow errno-erange-ok += expm1 towardzero ldbl-96-intel -0x2p-16384L : -0x1.fffffffffffffff8p-16384L : inexact-ok underflow errno-erange-ok += expm1 upward ldbl-96-intel -0x2p-16384L : -0x1.fffffffffffffff8p-16384L : inexact-ok underflow errno-erange-ok = expm1 downward ldbl-96-m68k -0x2p-16384L : -0x2p-16384L : inexact-ok underflow-ok errno-erange-ok = expm1 tonearest ldbl-96-m68k -0x2p-16384L : -0x2p-16384L : inexact-ok underflow-ok errno-erange-ok = expm1 towardzero ldbl-96-m68k -0x2p-16384L : -0x1.fffffffffffffffcp-16384L : inexact-ok underflow-ok errno-erange-ok = expm1 upward ldbl-96-m68k -0x2p-16384L : -0x1.fffffffffffffffcp-16384L : inexact-ok underflow-ok errno-erange-ok -= expm1 downward ldbl-128 -0x2p-16384L : -0x2p-16384L : inexact-ok underflow underflow-ok errno-erange-ok -= expm1 tonearest ldbl-128 -0x2p-16384L : -0x2p-16384L : inexact-ok underflow underflow-ok errno-erange-ok -= expm1 towardzero ldbl-128 -0x2p-16384L : -0x1.fffffffffffffffffffffffffffcp-16384L : inexact-ok underflow underflow-ok errno-erange-ok -= expm1 upward ldbl-128 -0x2p-16384L : -0x1.fffffffffffffffffffffffffffcp-16384L : inexact-ok underflow underflow-ok errno-erange-ok += expm1 downward ldbl-128 -0x2p-16384L : -0x2p-16384L : inexact-ok underflow errno-erange-ok += expm1 tonearest ldbl-128 -0x2p-16384L : -0x2p-16384L : inexact-ok underflow errno-erange-ok += expm1 towardzero ldbl-128 -0x2p-16384L : -0x1.fffffffffffffffffffffffffffcp-16384L : inexact-ok underflow errno-erange-ok += expm1 upward ldbl-128 -0x2p-16384L : -0x1.fffffffffffffffffffffffffffcp-16384L : inexact-ok underflow errno-erange-ok = expm1 downward dbl-64 -0x8p-972 : -0x8p-972 : inexact-ok = expm1 tonearest dbl-64 -0x8p-972 : -0x8p-972 : inexact-ok = expm1 towardzero dbl-64 -0x8p-972 : -0x7.ffffffffffffcp-972 : inexact-ok @@ -109757,11 +109757,11 @@ expm1 -min missing-underflow = expm1 tonearest ldbl-128ibm -0x8p-972L : -0x8p-972L : inexact-ok underflow-ok errno-erange-ok = expm1 towardzero ldbl-128ibm -0x8p-972L : -0x7.fffffffffffffffffffffffffcp-972L : inexact-ok underflow-ok errno-erange-ok = expm1 upward ldbl-128ibm -0x8p-972L : -0x7.fffffffffffffffffffffffffcp-972L : inexact-ok underflow-ok errno-erange-ok -expm1 min_subnorm missing-underflow -= expm1 downward flt-32 0x8p-152f : 0x8p-152f : inexact-ok underflow underflow-ok errno-erange-ok -= expm1 tonearest flt-32 0x8p-152f : 0x8p-152f : inexact-ok underflow underflow-ok errno-erange-ok -= expm1 towardzero flt-32 0x8p-152f : 0x8p-152f : inexact-ok underflow underflow-ok errno-erange-ok -= expm1 upward flt-32 0x8p-152f : 0x1p-148f : inexact-ok underflow underflow-ok errno-erange-ok +expm1 min_subnorm += expm1 downward flt-32 0x8p-152f : 0x8p-152f : inexact-ok underflow errno-erange-ok += expm1 tonearest flt-32 0x8p-152f : 0x8p-152f : inexact-ok underflow errno-erange-ok += expm1 towardzero flt-32 0x8p-152f : 0x8p-152f : inexact-ok underflow errno-erange-ok += expm1 upward flt-32 0x8p-152f : 0x1p-148f : inexact-ok underflow errno-erange-ok = expm1 downward dbl-64 0x8p-152 : 0x8p-152 : inexact-ok = expm1 tonearest dbl-64 0x8p-152 : 0x8p-152 : inexact-ok = expm1 towardzero dbl-64 0x8p-152 : 0x8p-152 : inexact-ok @@ -109782,10 +109782,10 @@ expm1 min_subnorm missing-underflow = expm1 tonearest ldbl-128ibm 0x8p-152L : 0x8p-152L : inexact-ok = expm1 towardzero ldbl-128ibm 0x8p-152L : 0x8p-152L : inexact-ok = expm1 upward ldbl-128ibm 0x8p-152L : 0x8.00000000000000000000000004p-152L : inexact-ok -= expm1 downward dbl-64 0x4p-1076 : 0x4p-1076 : inexact-ok underflow underflow-ok errno-erange-ok -= expm1 tonearest dbl-64 0x4p-1076 : 0x4p-1076 : inexact-ok underflow underflow-ok errno-erange-ok -= expm1 towardzero dbl-64 0x4p-1076 : 0x4p-1076 : inexact-ok underflow underflow-ok errno-erange-ok -= expm1 upward dbl-64 0x4p-1076 : 0x8p-1076 : inexact-ok underflow underflow-ok errno-erange-ok += expm1 downward dbl-64 0x4p-1076 : 0x4p-1076 : inexact-ok underflow errno-erange-ok += expm1 tonearest dbl-64 0x4p-1076 : 0x4p-1076 : inexact-ok underflow errno-erange-ok += expm1 towardzero dbl-64 0x4p-1076 : 0x4p-1076 : inexact-ok underflow errno-erange-ok += expm1 upward dbl-64 0x4p-1076 : 0x8p-1076 : inexact-ok underflow errno-erange-ok = expm1 downward ldbl-96-intel 0x4p-1076L : 0x4p-1076L : inexact-ok = expm1 tonearest ldbl-96-intel 0x4p-1076L : 0x4p-1076L : inexact-ok = expm1 towardzero ldbl-96-intel 0x4p-1076L : 0x4p-1076L : inexact-ok @@ -109798,39 +109798,39 @@ expm1 min_subnorm missing-underflow = expm1 tonearest ldbl-128 0x4p-1076L : 0x4p-1076L : inexact-ok = expm1 towardzero ldbl-128 0x4p-1076L : 0x4p-1076L : inexact-ok = expm1 upward ldbl-128 0x4p-1076L : 0x4.0000000000000000000000000004p-1076L : inexact-ok -= expm1 downward ldbl-128ibm 0x4p-1076L : 0x4p-1076L : inexact-ok underflow underflow-ok errno-erange-ok -= expm1 tonearest ldbl-128ibm 0x4p-1076L : 0x4p-1076L : inexact-ok underflow underflow-ok errno-erange-ok -= expm1 towardzero ldbl-128ibm 0x4p-1076L : 0x4p-1076L : inexact-ok underflow underflow-ok errno-erange-ok -= expm1 upward ldbl-128ibm 0x4p-1076L : 0x8p-1076L : inexact-ok underflow underflow-ok errno-erange-ok -= expm1 downward ldbl-96-intel 0x8p-16448L : 0x8p-16448L : inexact-ok underflow underflow-ok errno-erange-ok -= expm1 tonearest ldbl-96-intel 0x8p-16448L : 0x8p-16448L : inexact-ok underflow underflow-ok errno-erange-ok -= expm1 towardzero ldbl-96-intel 0x8p-16448L : 0x8p-16448L : inexact-ok underflow underflow-ok errno-erange-ok -= expm1 upward ldbl-96-intel 0x8p-16448L : 0x1p-16444L : inexact-ok underflow underflow-ok errno-erange-ok -= expm1 downward ldbl-96-m68k 0x8p-16448L : 0x8p-16448L : inexact-ok underflow underflow-ok errno-erange-ok -= expm1 tonearest ldbl-96-m68k 0x8p-16448L : 0x8p-16448L : inexact-ok underflow underflow-ok errno-erange-ok -= expm1 towardzero ldbl-96-m68k 0x8p-16448L : 0x8p-16448L : inexact-ok underflow underflow-ok errno-erange-ok -= expm1 upward ldbl-96-m68k 0x8p-16448L : 0xcp-16448L : inexact-ok underflow underflow-ok errno-erange-ok -= expm1 downward ldbl-128 0x8p-16448L : 0x8p-16448L : inexact-ok underflow underflow-ok errno-erange-ok -= expm1 tonearest ldbl-128 0x8p-16448L : 0x8p-16448L : inexact-ok underflow underflow-ok errno-erange-ok -= expm1 towardzero ldbl-128 0x8p-16448L : 0x8p-16448L : inexact-ok underflow underflow-ok errno-erange-ok -= expm1 upward ldbl-128 0x8p-16448L : 0x8.000000000004p-16448L : inexact-ok underflow underflow-ok errno-erange-ok -= expm1 downward ldbl-96-m68k 0x4p-16448L : 0x4p-16448L : inexact-ok underflow underflow-ok errno-erange-ok -= expm1 tonearest ldbl-96-m68k 0x4p-16448L : 0x4p-16448L : inexact-ok underflow underflow-ok errno-erange-ok -= expm1 towardzero ldbl-96-m68k 0x4p-16448L : 0x4p-16448L : inexact-ok underflow underflow-ok errno-erange-ok -= expm1 upward ldbl-96-m68k 0x4p-16448L : 0x8p-16448L : inexact-ok underflow underflow-ok errno-erange-ok -= expm1 downward ldbl-128 0x4p-16448L : 0x4p-16448L : inexact-ok underflow underflow-ok errno-erange-ok -= expm1 tonearest ldbl-128 0x4p-16448L : 0x4p-16448L : inexact-ok underflow underflow-ok errno-erange-ok -= expm1 towardzero ldbl-128 0x4p-16448L : 0x4p-16448L : inexact-ok underflow underflow-ok errno-erange-ok -= expm1 upward ldbl-128 0x4p-16448L : 0x4.000000000004p-16448L : inexact-ok underflow underflow-ok errno-erange-ok -= expm1 downward ldbl-128 0x4p-16496L : 0x4p-16496L : inexact-ok underflow underflow-ok errno-erange-ok -= expm1 tonearest ldbl-128 0x4p-16496L : 0x4p-16496L : inexact-ok underflow underflow-ok errno-erange-ok -= expm1 towardzero ldbl-128 0x4p-16496L : 0x4p-16496L : inexact-ok underflow underflow-ok errno-erange-ok -= expm1 upward ldbl-128 0x4p-16496L : 0x8p-16496L : inexact-ok underflow underflow-ok errno-erange-ok -expm1 -min_subnorm missing-underflow -= expm1 downward flt-32 -0x8p-152f : -0x8p-152f : inexact-ok underflow underflow-ok errno-erange-ok -= expm1 tonearest flt-32 -0x8p-152f : -0x8p-152f : inexact-ok underflow underflow-ok errno-erange-ok -= expm1 towardzero flt-32 -0x8p-152f : -0x0p+0f : inexact-ok underflow underflow-ok errno-erange-ok -= expm1 upward flt-32 -0x8p-152f : -0x0p+0f : inexact-ok underflow underflow-ok errno-erange-ok += expm1 downward ldbl-128ibm 0x4p-1076L : 0x4p-1076L : inexact-ok underflow errno-erange-ok += expm1 tonearest ldbl-128ibm 0x4p-1076L : 0x4p-1076L : inexact-ok underflow errno-erange-ok += expm1 towardzero ldbl-128ibm 0x4p-1076L : 0x4p-1076L : inexact-ok underflow errno-erange-ok += expm1 upward ldbl-128ibm 0x4p-1076L : 0x8p-1076L : inexact-ok underflow errno-erange-ok += expm1 downward ldbl-96-intel 0x8p-16448L : 0x8p-16448L : inexact-ok underflow errno-erange-ok += expm1 tonearest ldbl-96-intel 0x8p-16448L : 0x8p-16448L : inexact-ok underflow errno-erange-ok += expm1 towardzero ldbl-96-intel 0x8p-16448L : 0x8p-16448L : inexact-ok underflow errno-erange-ok += expm1 upward ldbl-96-intel 0x8p-16448L : 0x1p-16444L : inexact-ok underflow errno-erange-ok += expm1 downward ldbl-96-m68k 0x8p-16448L : 0x8p-16448L : inexact-ok underflow errno-erange-ok += expm1 tonearest ldbl-96-m68k 0x8p-16448L : 0x8p-16448L : inexact-ok underflow errno-erange-ok += expm1 towardzero ldbl-96-m68k 0x8p-16448L : 0x8p-16448L : inexact-ok underflow errno-erange-ok += expm1 upward ldbl-96-m68k 0x8p-16448L : 0xcp-16448L : inexact-ok underflow errno-erange-ok += expm1 downward ldbl-128 0x8p-16448L : 0x8p-16448L : inexact-ok underflow errno-erange-ok += expm1 tonearest ldbl-128 0x8p-16448L : 0x8p-16448L : inexact-ok underflow errno-erange-ok += expm1 towardzero ldbl-128 0x8p-16448L : 0x8p-16448L : inexact-ok underflow errno-erange-ok += expm1 upward ldbl-128 0x8p-16448L : 0x8.000000000004p-16448L : inexact-ok underflow errno-erange-ok += expm1 downward ldbl-96-m68k 0x4p-16448L : 0x4p-16448L : inexact-ok underflow errno-erange-ok += expm1 tonearest ldbl-96-m68k 0x4p-16448L : 0x4p-16448L : inexact-ok underflow errno-erange-ok += expm1 towardzero ldbl-96-m68k 0x4p-16448L : 0x4p-16448L : inexact-ok underflow errno-erange-ok += expm1 upward ldbl-96-m68k 0x4p-16448L : 0x8p-16448L : inexact-ok underflow errno-erange-ok += expm1 downward ldbl-128 0x4p-16448L : 0x4p-16448L : inexact-ok underflow errno-erange-ok += expm1 tonearest ldbl-128 0x4p-16448L : 0x4p-16448L : inexact-ok underflow errno-erange-ok += expm1 towardzero ldbl-128 0x4p-16448L : 0x4p-16448L : inexact-ok underflow errno-erange-ok += expm1 upward ldbl-128 0x4p-16448L : 0x4.000000000004p-16448L : inexact-ok underflow errno-erange-ok += expm1 downward ldbl-128 0x4p-16496L : 0x4p-16496L : inexact-ok underflow errno-erange-ok += expm1 tonearest ldbl-128 0x4p-16496L : 0x4p-16496L : inexact-ok underflow errno-erange-ok += expm1 towardzero ldbl-128 0x4p-16496L : 0x4p-16496L : inexact-ok underflow errno-erange-ok += expm1 upward ldbl-128 0x4p-16496L : 0x8p-16496L : inexact-ok underflow errno-erange-ok +expm1 -min_subnorm += expm1 downward flt-32 -0x8p-152f : -0x8p-152f : inexact-ok underflow errno-erange-ok += expm1 tonearest flt-32 -0x8p-152f : -0x8p-152f : inexact-ok underflow errno-erange-ok += expm1 towardzero flt-32 -0x8p-152f : -0x0p+0f : inexact-ok underflow errno-erange-ok += expm1 upward flt-32 -0x8p-152f : -0x0p+0f : inexact-ok underflow errno-erange-ok = expm1 downward dbl-64 -0x8p-152 : -0x8p-152 : inexact-ok = expm1 tonearest dbl-64 -0x8p-152 : -0x8p-152 : inexact-ok = expm1 towardzero dbl-64 -0x8p-152 : -0x7.ffffffffffffcp-152 : inexact-ok @@ -109851,10 +109851,10 @@ expm1 -min_subnorm missing-underflow = expm1 tonearest ldbl-128ibm -0x8p-152L : -0x8p-152L : inexact-ok = expm1 towardzero ldbl-128ibm -0x8p-152L : -0x7.fffffffffffffffffffffffffep-152L : inexact-ok = expm1 upward ldbl-128ibm -0x8p-152L : -0x7.fffffffffffffffffffffffffep-152L : inexact-ok -= expm1 downward dbl-64 -0x4p-1076 : -0x4p-1076 : inexact-ok underflow underflow-ok errno-erange-ok -= expm1 tonearest dbl-64 -0x4p-1076 : -0x4p-1076 : inexact-ok underflow underflow-ok errno-erange-ok -= expm1 towardzero dbl-64 -0x4p-1076 : -0x0p+0 : inexact-ok underflow underflow-ok errno-erange-ok -= expm1 upward dbl-64 -0x4p-1076 : -0x0p+0 : inexact-ok underflow underflow-ok errno-erange-ok += expm1 downward dbl-64 -0x4p-1076 : -0x4p-1076 : inexact-ok underflow errno-erange-ok += expm1 tonearest dbl-64 -0x4p-1076 : -0x4p-1076 : inexact-ok underflow errno-erange-ok += expm1 towardzero dbl-64 -0x4p-1076 : -0x0p+0 : inexact-ok underflow errno-erange-ok += expm1 upward dbl-64 -0x4p-1076 : -0x0p+0 : inexact-ok underflow errno-erange-ok = expm1 downward ldbl-96-intel -0x4p-1076L : -0x4p-1076L : inexact-ok = expm1 tonearest ldbl-96-intel -0x4p-1076L : -0x4p-1076L : inexact-ok = expm1 towardzero ldbl-96-intel -0x4p-1076L : -0x3.fffffffffffffffcp-1076L : inexact-ok @@ -109867,34 +109867,34 @@ expm1 -min_subnorm missing-underflow = expm1 tonearest ldbl-128 -0x4p-1076L : -0x4p-1076L : inexact-ok = expm1 towardzero ldbl-128 -0x4p-1076L : -0x3.fffffffffffffffffffffffffffep-1076L : inexact-ok = expm1 upward ldbl-128 -0x4p-1076L : -0x3.fffffffffffffffffffffffffffep-1076L : inexact-ok -= expm1 downward ldbl-128ibm -0x4p-1076L : -0x4p-1076L : inexact-ok underflow underflow-ok errno-erange-ok -= expm1 tonearest ldbl-128ibm -0x4p-1076L : -0x4p-1076L : inexact-ok underflow underflow-ok errno-erange-ok -= expm1 towardzero ldbl-128ibm -0x4p-1076L : -0x0p+0L : inexact-ok underflow underflow-ok errno-erange-ok -= expm1 upward ldbl-128ibm -0x4p-1076L : -0x0p+0L : inexact-ok underflow underflow-ok errno-erange-ok -= expm1 downward ldbl-96-intel -0x8p-16448L : -0x8p-16448L : inexact-ok underflow underflow-ok errno-erange-ok -= expm1 tonearest ldbl-96-intel -0x8p-16448L : -0x8p-16448L : inexact-ok underflow underflow-ok errno-erange-ok -= expm1 towardzero ldbl-96-intel -0x8p-16448L : -0x0p+0L : inexact-ok underflow underflow-ok errno-erange-ok -= expm1 upward ldbl-96-intel -0x8p-16448L : -0x0p+0L : inexact-ok underflow underflow-ok errno-erange-ok -= expm1 downward ldbl-96-m68k -0x8p-16448L : -0x8p-16448L : inexact-ok underflow underflow-ok errno-erange-ok -= expm1 tonearest ldbl-96-m68k -0x8p-16448L : -0x8p-16448L : inexact-ok underflow underflow-ok errno-erange-ok -= expm1 towardzero ldbl-96-m68k -0x8p-16448L : -0x4p-16448L : inexact-ok underflow underflow-ok errno-erange-ok -= expm1 upward ldbl-96-m68k -0x8p-16448L : -0x4p-16448L : inexact-ok underflow underflow-ok errno-erange-ok -= expm1 downward ldbl-128 -0x8p-16448L : -0x8p-16448L : inexact-ok underflow underflow-ok errno-erange-ok -= expm1 tonearest ldbl-128 -0x8p-16448L : -0x8p-16448L : inexact-ok underflow underflow-ok errno-erange-ok -= expm1 towardzero ldbl-128 -0x8p-16448L : -0x7.fffffffffffcp-16448L : inexact-ok underflow underflow-ok errno-erange-ok -= expm1 upward ldbl-128 -0x8p-16448L : -0x7.fffffffffffcp-16448L : inexact-ok underflow underflow-ok errno-erange-ok -= expm1 downward ldbl-96-m68k -0x4p-16448L : -0x4p-16448L : inexact-ok underflow underflow-ok errno-erange-ok -= expm1 tonearest ldbl-96-m68k -0x4p-16448L : -0x4p-16448L : inexact-ok underflow underflow-ok errno-erange-ok -= expm1 towardzero ldbl-96-m68k -0x4p-16448L : -0x0p+0L : inexact-ok underflow underflow-ok errno-erange-ok -= expm1 upward ldbl-96-m68k -0x4p-16448L : -0x0p+0L : inexact-ok underflow underflow-ok errno-erange-ok -= expm1 downward ldbl-128 -0x4p-16448L : -0x4p-16448L : inexact-ok underflow underflow-ok errno-erange-ok -= expm1 tonearest ldbl-128 -0x4p-16448L : -0x4p-16448L : inexact-ok underflow underflow-ok errno-erange-ok -= expm1 towardzero ldbl-128 -0x4p-16448L : -0x3.fffffffffffcp-16448L : inexact-ok underflow underflow-ok errno-erange-ok -= expm1 upward ldbl-128 -0x4p-16448L : -0x3.fffffffffffcp-16448L : inexact-ok underflow underflow-ok errno-erange-ok -= expm1 downward ldbl-128 -0x4p-16496L : -0x4p-16496L : inexact-ok underflow underflow-ok errno-erange-ok -= expm1 tonearest ldbl-128 -0x4p-16496L : -0x4p-16496L : inexact-ok underflow underflow-ok errno-erange-ok -= expm1 towardzero ldbl-128 -0x4p-16496L : -0x0p+0L : inexact-ok underflow underflow-ok errno-erange-ok -= expm1 upward ldbl-128 -0x4p-16496L : -0x0p+0L : inexact-ok underflow underflow-ok errno-erange-ok += expm1 downward ldbl-128ibm -0x4p-1076L : -0x4p-1076L : inexact-ok underflow errno-erange-ok += expm1 tonearest ldbl-128ibm -0x4p-1076L : -0x4p-1076L : inexact-ok underflow errno-erange-ok += expm1 towardzero ldbl-128ibm -0x4p-1076L : -0x0p+0L : inexact-ok underflow errno-erange-ok += expm1 upward ldbl-128ibm -0x4p-1076L : -0x0p+0L : inexact-ok underflow errno-erange-ok += expm1 downward ldbl-96-intel -0x8p-16448L : -0x8p-16448L : inexact-ok underflow errno-erange-ok += expm1 tonearest ldbl-96-intel -0x8p-16448L : -0x8p-16448L : inexact-ok underflow errno-erange-ok += expm1 towardzero ldbl-96-intel -0x8p-16448L : -0x0p+0L : inexact-ok underflow errno-erange-ok += expm1 upward ldbl-96-intel -0x8p-16448L : -0x0p+0L : inexact-ok underflow errno-erange-ok += expm1 downward ldbl-96-m68k -0x8p-16448L : -0x8p-16448L : inexact-ok underflow errno-erange-ok += expm1 tonearest ldbl-96-m68k -0x8p-16448L : -0x8p-16448L : inexact-ok underflow errno-erange-ok += expm1 towardzero ldbl-96-m68k -0x8p-16448L : -0x4p-16448L : inexact-ok underflow errno-erange-ok += expm1 upward ldbl-96-m68k -0x8p-16448L : -0x4p-16448L : inexact-ok underflow errno-erange-ok += expm1 downward ldbl-128 -0x8p-16448L : -0x8p-16448L : inexact-ok underflow errno-erange-ok += expm1 tonearest ldbl-128 -0x8p-16448L : -0x8p-16448L : inexact-ok underflow errno-erange-ok += expm1 towardzero ldbl-128 -0x8p-16448L : -0x7.fffffffffffcp-16448L : inexact-ok underflow errno-erange-ok += expm1 upward ldbl-128 -0x8p-16448L : -0x7.fffffffffffcp-16448L : inexact-ok underflow errno-erange-ok += expm1 downward ldbl-96-m68k -0x4p-16448L : -0x4p-16448L : inexact-ok underflow errno-erange-ok += expm1 tonearest ldbl-96-m68k -0x4p-16448L : -0x4p-16448L : inexact-ok underflow errno-erange-ok += expm1 towardzero ldbl-96-m68k -0x4p-16448L : -0x0p+0L : inexact-ok underflow errno-erange-ok += expm1 upward ldbl-96-m68k -0x4p-16448L : -0x0p+0L : inexact-ok underflow errno-erange-ok += expm1 downward ldbl-128 -0x4p-16448L : -0x4p-16448L : inexact-ok underflow errno-erange-ok += expm1 tonearest ldbl-128 -0x4p-16448L : -0x4p-16448L : inexact-ok underflow errno-erange-ok += expm1 towardzero ldbl-128 -0x4p-16448L : -0x3.fffffffffffcp-16448L : inexact-ok underflow errno-erange-ok += expm1 upward ldbl-128 -0x4p-16448L : -0x3.fffffffffffcp-16448L : inexact-ok underflow errno-erange-ok += expm1 downward ldbl-128 -0x4p-16496L : -0x4p-16496L : inexact-ok underflow errno-erange-ok += expm1 tonearest ldbl-128 -0x4p-16496L : -0x4p-16496L : inexact-ok underflow errno-erange-ok += expm1 towardzero ldbl-128 -0x4p-16496L : -0x0p+0L : inexact-ok underflow errno-erange-ok += expm1 upward ldbl-128 -0x4p-16496L : -0x0p+0L : inexact-ok underflow errno-erange-ok fma 1.0 2.0 3.0 = fma downward flt-32 0x1p+0f 0x2p+0f 0x3p+0f : 0x5p+0f : = fma tonearest flt-32 0x1p+0f 0x2p+0f 0x3p+0f : 0x5p+0f : |