Fix cosh spurious underflows from expm1 (bug 16354), inaccurate results near 0 (bug...

This patch fixes bug 16354, spurious underflows from cosh when a tiny
argument is passed to expm1 and expm1 correctly underflows although
the final result of cosh should be 1.  As noted in that bug, some
cases are latent because of expm1 implementations not raising
underflow (bug 16353), but all the implementations are fixed
similarly.  They already contained checks for tiny arguments, but the
checks were too late to avoid underflow from expm1 (although they
would avoid underflow from subsequent squaring of the result of
expm1); they are moved before the expm1 calls.

The thresholds used for considering arguments tiny are not
particularly consistent in how they relate to the precision of the
floating-point format in question.  They are, however, all sufficient
to ensure that the round-to-nearest result of cosh is indeed 1 below
the threshold (although sometimes they are smaller than necessary).
But the previous logic did not return 1, but the previously computed 1
+ expm1(abs(x)) value.  And the thresholds in the ldbl-128 and
ldbl-128ibm code (0x1p-71L - I suspect 0x3f8b was intended in the code
instead of 0x3fb8 - and (roughly) 0x1p-55L) are not sufficient for
that value to be 1.  So by moving the test for tiny arguments, and
consequently returning 1 directly now the expm1 value hasn't been
computed by that point, this patch also fixes bug 17061, the (large
number of ulps) inaccuracy for small arguments in those
implementations.  Tests for that bug are duly added.

Tested x86_64 and x86 and ulps updated accordingly.  Also tested for
mips64 and powerpc32 to validate the ldbl-128 and ldbl-128ibm changes.

	[BZ #16354]
	[BZ #17061]
	* sysdeps/ieee754/dbl-64/e_cosh.c (__ieee754_cosh): Check for
	small arguments before calling __expm1.
	* sysdeps/ieee754/flt-32/e_coshf.c (__ieee754_coshf): Check for
	small arguments before calling __expm1f.
	* sysdeps/ieee754/ldbl-128/e_coshl.c (__ieee754_coshl): Check for
	small arguments before calling __expm1l.
	* sysdeps/ieee754/ldbl-128ibm/e_coshl.c (__ieee754_coshl):
	Likewise.
	* sysdeps/ieee754/ldbl-96/e_coshl.c (__ieee754_coshl): Likewise.
	* math/auto-libm-test-in: Add more cosh tests.  Do not allow
	spurious underflow for some cosh tests.
	* math/auto-libm-test-out: Regenerated.
	* sysdeps/i386/fpu/libm-test-ulps: Update.

diff --git a/ChangeLog b/ChangeLog
index 9694fe5516eb16ab4f482288e2eea8ea8815ecb1..08e26514ed8deb35bee15046792fba269aa6f07d 100644 (file)
--- a/ChangeLog
+++ b/ChangeLog
@@ -1,5 +1,21 @@
 2014-06-23  Joseph Myers  <joseph@codesourcery.com>
 
+       [BZ #16354]
+       [BZ #17061]
+       * sysdeps/ieee754/dbl-64/e_cosh.c (__ieee754_cosh): Check for
+       small arguments before calling __expm1.
+       * sysdeps/ieee754/flt-32/e_coshf.c (__ieee754_coshf): Check for
+       small arguments before calling __expm1f.
+       * sysdeps/ieee754/ldbl-128/e_coshl.c (__ieee754_coshl): Check for
+       small arguments before calling __expm1l.
+       * sysdeps/ieee754/ldbl-128ibm/e_coshl.c (__ieee754_coshl):
+       Likewise.
+       * sysdeps/ieee754/ldbl-96/e_coshl.c (__ieee754_coshl): Likewise.
+       * math/auto-libm-test-in: Add more cosh tests.  Do not allow
+       spurious underflow for some cosh tests.
+       * math/auto-libm-test-out: Regenerated.
+       * sysdeps/i386/fpu/libm-test-ulps: Update.
+
        [BZ #17050]
        * sysdeps/ieee754/dbl-64/e_j1.c: Include <errno.h>.
        (__ieee754_y1): Set errno if return value overflows.

diff --git a/NEWS b/NEWS
index 66e4891a60b2e4b3c4293e35330fba387ae1fd27..140f84ad6acf4136ed1c3cfa242e2be5de49a5d5 100644 (file)
--- a/NEWS
+++ b/NEWS
@@ -11,16 +11,16 @@ Version 2.20
 
   6804, 9894, 12994, 13347, 13651, 14308, 14770, 15119, 15132, 15347, 15514,
   15698, 15804, 15894, 15946, 16002, 16064, 16095, 16198, 16284, 16315,
-  16348, 16349, 16357, 16362, 16447, 16516, 16532, 16545, 16564, 16574,
-  16599, 16600, 16609, 16610, 16611, 16613, 16619, 16623, 16629, 16632,
-  16634, 16639, 16642, 16648, 16649, 16670, 16674, 16677, 16680, 16681,
-  16683, 16689, 16695, 16701, 16706, 16707, 16712, 16713, 16714, 16724,
-  16731, 16739, 16740, 16743, 16754, 16758, 16759, 16760, 16770, 16786,
-  16789, 16791, 16796, 16799, 16800, 16815, 16823, 16824, 16831, 16838,
-  16849, 16854, 16876, 16877, 16878, 16882, 16885, 16888, 16890, 16912,
-  16915, 16916, 16917, 16922, 16927, 16928, 16932, 16943, 16958, 16965,
-  16966, 16967, 16977, 16978, 16984, 16990, 16996, 17009, 17022, 17031,
-  17042, 17048, 17050, 17058, 17062, 17069, 17075, 17079.
+  16348, 16349, 16354, 16357, 16362, 16447, 16516, 16532, 16545, 16564,
+  16574, 16599, 16600, 16609, 16610, 16611, 16613, 16619, 16623, 16629,
+  16632, 16634, 16639, 16642, 16648, 16649, 16670, 16674, 16677, 16680,
+  16681, 16683, 16689, 16695, 16701, 16706, 16707, 16712, 16713, 16714,
+  16724, 16731, 16739, 16740, 16743, 16754, 16758, 16759, 16760, 16770,
+  16786, 16789, 16791, 16796, 16799, 16800, 16815, 16823, 16824, 16831,
+  16838, 16849, 16854, 16876, 16877, 16878, 16882, 16885, 16888, 16890,
+  16912, 16915, 16916, 16917, 16922, 16927, 16928, 16932, 16943, 16958,
+  16965, 16966, 16967, 16977, 16978, 16984, 16990, 16996, 17009, 17022,
+  17031, 17042, 17048, 17050, 17058, 17061, 17062, 17069, 17075, 17079.
 
 * Optimized strchr implementation for AArch64.  Contributed by ARM Ltd.
 

diff --git a/math/auto-libm-test-in b/math/auto-libm-test-in
index 86333846ace964cc4b76bf80efb64a30fcc22365..4eaa0135a4bb4dbf36c9cd47cdd112296cf5b63d 100644 (file)
--- a/math/auto-libm-test-in
+++ b/math/auto-libm-test-in
@@ -624,11 +624,14 @@ cosh 50
 # GCC bug 59666: results on directed rounding may be incorrect.
 cosh max no-test-inline xfail-rounding:ldbl-128ibm
 cosh -max no-test-inline xfail-rounding:ldbl-128ibm
-# Bug 16354: spurious underflow may occur.
-cosh min spurious-underflow
-cosh -min spurious-underflow
-cosh min_subnorm spurious-underflow
-cosh -min_subnorm spurious-underflow
+cosh min
+cosh -min
+cosh min_subnorm
+cosh -min_subnorm
+cosh 0x1p-56
+cosh -0x1p-56
+cosh 0x1p-72
+cosh -0x1p-72
 # Test values either side of overflow for each floating-point format.
 cosh 0x5.96a7ep+4
 cosh 0x5.96a7e8p+4

diff --git a/math/auto-libm-test-out b/math/auto-libm-test-out
index 3d3e0187f8569bbe6d552c82ac2eb51ed717796d..e47c3ab622cf6c0febafc46b84a47d573e030dbf 100644 (file)
--- a/math/auto-libm-test-out
+++ b/math/auto-libm-test-out
@@ -75745,322 +75745,422 @@ cosh -max no-test-inline xfail-rounding:ldbl-128ibm
 = cosh tonearest ldbl-128ibm -0xf.ffffffffffffbffffffffffffcp+1020L : plus_infty : no-test-inline inexact-ok overflow errno-erange
 = cosh towardzero ldbl-128ibm -0xf.ffffffffffffbffffffffffffcp+1020L : 0xf.ffffffffffffbffffffffffffcp+1020L : no-test-inline xfail:ldbl-128ibm inexact-ok overflow errno-erange-ok
 = cosh upward ldbl-128ibm -0xf.ffffffffffffbffffffffffffcp+1020L : plus_infty : no-test-inline xfail:ldbl-128ibm inexact-ok overflow errno-erange
-cosh min spurious-underflow
-= cosh downward flt-32 0x4p-128f : 0x1p+0f : inexact-ok underflow-ok
-= cosh tonearest flt-32 0x4p-128f : 0x1p+0f : inexact-ok underflow-ok
-= cosh towardzero flt-32 0x4p-128f : 0x1p+0f : inexact-ok underflow-ok
-= cosh upward flt-32 0x4p-128f : 0x1.000002p+0f : inexact-ok underflow-ok
-= cosh downward dbl-64 0x4p-128 : 0x1p+0 : inexact-ok underflow-ok
-= cosh tonearest dbl-64 0x4p-128 : 0x1p+0 : inexact-ok underflow-ok
-= cosh towardzero dbl-64 0x4p-128 : 0x1p+0 : inexact-ok underflow-ok
-= cosh upward dbl-64 0x4p-128 : 0x1.0000000000001p+0 : inexact-ok underflow-ok
-= cosh downward ldbl-96-intel 0x4p-128L : 0x1p+0L : inexact-ok underflow-ok
-= cosh tonearest ldbl-96-intel 0x4p-128L : 0x1p+0L : inexact-ok underflow-ok
-= cosh towardzero ldbl-96-intel 0x4p-128L : 0x1p+0L : inexact-ok underflow-ok
-= cosh upward ldbl-96-intel 0x4p-128L : 0x1.0000000000000002p+0L : inexact-ok underflow-ok
-= cosh downward ldbl-96-m68k 0x4p-128L : 0x1p+0L : inexact-ok underflow-ok
-= cosh tonearest ldbl-96-m68k 0x4p-128L : 0x1p+0L : inexact-ok underflow-ok
-= cosh towardzero ldbl-96-m68k 0x4p-128L : 0x1p+0L : inexact-ok underflow-ok
-= cosh upward ldbl-96-m68k 0x4p-128L : 0x1.0000000000000002p+0L : inexact-ok underflow-ok
-= cosh downward ldbl-128 0x4p-128L : 0x1p+0L : inexact-ok underflow-ok
-= cosh tonearest ldbl-128 0x4p-128L : 0x1p+0L : inexact-ok underflow-ok
-= cosh towardzero ldbl-128 0x4p-128L : 0x1p+0L : inexact-ok underflow-ok
-= cosh upward ldbl-128 0x4p-128L : 0x1.0000000000000000000000000001p+0L : inexact-ok underflow-ok
-= cosh downward ldbl-128ibm 0x4p-128L : 0x1p+0L : inexact-ok underflow-ok
-= cosh tonearest ldbl-128ibm 0x4p-128L : 0x1p+0L : inexact-ok underflow-ok
-= cosh towardzero ldbl-128ibm 0x4p-128L : 0x1p+0L : inexact-ok underflow-ok
-= cosh upward ldbl-128ibm 0x4p-128L : 0x1.000000000000000000000000008p+0L : inexact-ok underflow-ok
-= cosh downward dbl-64 0x4p-1024 : 0x1p+0 : inexact-ok underflow-ok
-= cosh tonearest dbl-64 0x4p-1024 : 0x1p+0 : inexact-ok underflow-ok
-= cosh towardzero dbl-64 0x4p-1024 : 0x1p+0 : inexact-ok underflow-ok
-= cosh upward dbl-64 0x4p-1024 : 0x1.0000000000001p+0 : inexact-ok underflow-ok
-= cosh downward ldbl-96-intel 0x4p-1024L : 0x1p+0L : inexact-ok underflow-ok
-= cosh tonearest ldbl-96-intel 0x4p-1024L : 0x1p+0L : inexact-ok underflow-ok
-= cosh towardzero ldbl-96-intel 0x4p-1024L : 0x1p+0L : inexact-ok underflow-ok
-= cosh upward ldbl-96-intel 0x4p-1024L : 0x1.0000000000000002p+0L : inexact-ok underflow-ok
-= cosh downward ldbl-96-m68k 0x4p-1024L : 0x1p+0L : inexact-ok underflow-ok
-= cosh tonearest ldbl-96-m68k 0x4p-1024L : 0x1p+0L : inexact-ok underflow-ok
-= cosh towardzero ldbl-96-m68k 0x4p-1024L : 0x1p+0L : inexact-ok underflow-ok
-= cosh upward ldbl-96-m68k 0x4p-1024L : 0x1.0000000000000002p+0L : inexact-ok underflow-ok
-= cosh downward ldbl-128 0x4p-1024L : 0x1p+0L : inexact-ok underflow-ok
-= cosh tonearest ldbl-128 0x4p-1024L : 0x1p+0L : inexact-ok underflow-ok
-= cosh towardzero ldbl-128 0x4p-1024L : 0x1p+0L : inexact-ok underflow-ok
-= cosh upward ldbl-128 0x4p-1024L : 0x1.0000000000000000000000000001p+0L : inexact-ok underflow-ok
-= cosh downward ldbl-128ibm 0x4p-1024L : 0x1p+0L : inexact-ok underflow-ok
-= cosh tonearest ldbl-128ibm 0x4p-1024L : 0x1p+0L : inexact-ok underflow-ok
-= cosh towardzero ldbl-128ibm 0x4p-1024L : 0x1p+0L : inexact-ok underflow-ok
-= cosh upward ldbl-128ibm 0x4p-1024L : 0x1.000000000000000000000000008p+0L : inexact-ok underflow-ok
-= cosh downward ldbl-96-intel 0x4p-16384L : 0x1p+0L : inexact-ok underflow-ok
-= cosh tonearest ldbl-96-intel 0x4p-16384L : 0x1p+0L : inexact-ok underflow-ok
-= cosh towardzero ldbl-96-intel 0x4p-16384L : 0x1p+0L : inexact-ok underflow-ok
-= cosh upward ldbl-96-intel 0x4p-16384L : 0x1.0000000000000002p+0L : inexact-ok underflow-ok
-= cosh downward ldbl-96-m68k 0x4p-16384L : 0x1p+0L : inexact-ok underflow-ok
-= cosh tonearest ldbl-96-m68k 0x4p-16384L : 0x1p+0L : inexact-ok underflow-ok
-= cosh towardzero ldbl-96-m68k 0x4p-16384L : 0x1p+0L : inexact-ok underflow-ok
-= cosh upward ldbl-96-m68k 0x4p-16384L : 0x1.0000000000000002p+0L : inexact-ok underflow-ok
-= cosh downward ldbl-128 0x4p-16384L : 0x1p+0L : inexact-ok underflow-ok
-= cosh tonearest ldbl-128 0x4p-16384L : 0x1p+0L : inexact-ok underflow-ok
-= cosh towardzero ldbl-128 0x4p-16384L : 0x1p+0L : inexact-ok underflow-ok
-= cosh upward ldbl-128 0x4p-16384L : 0x1.0000000000000000000000000001p+0L : inexact-ok underflow-ok
-= cosh downward ldbl-96-intel 0x2p-16384L : 0x1p+0L : inexact-ok underflow-ok
-= cosh tonearest ldbl-96-intel 0x2p-16384L : 0x1p+0L : inexact-ok underflow-ok
-= cosh towardzero ldbl-96-intel 0x2p-16384L : 0x1p+0L : inexact-ok underflow-ok
-= cosh upward ldbl-96-intel 0x2p-16384L : 0x1.0000000000000002p+0L : inexact-ok underflow-ok
-= cosh downward ldbl-96-m68k 0x2p-16384L : 0x1p+0L : inexact-ok underflow-ok
-= cosh tonearest ldbl-96-m68k 0x2p-16384L : 0x1p+0L : inexact-ok underflow-ok
-= cosh towardzero ldbl-96-m68k 0x2p-16384L : 0x1p+0L : inexact-ok underflow-ok
-= cosh upward ldbl-96-m68k 0x2p-16384L : 0x1.0000000000000002p+0L : inexact-ok underflow-ok
-= cosh downward ldbl-128 0x2p-16384L : 0x1p+0L : inexact-ok underflow-ok
-= cosh tonearest ldbl-128 0x2p-16384L : 0x1p+0L : inexact-ok underflow-ok
-= cosh towardzero ldbl-128 0x2p-16384L : 0x1p+0L : inexact-ok underflow-ok
-= cosh upward ldbl-128 0x2p-16384L : 0x1.0000000000000000000000000001p+0L : inexact-ok underflow-ok
-= cosh downward dbl-64 0x8p-972 : 0x1p+0 : inexact-ok underflow-ok
-= cosh tonearest dbl-64 0x8p-972 : 0x1p+0 : inexact-ok underflow-ok
-= cosh towardzero dbl-64 0x8p-972 : 0x1p+0 : inexact-ok underflow-ok
-= cosh upward dbl-64 0x8p-972 : 0x1.0000000000001p+0 : inexact-ok underflow-ok
-= cosh downward ldbl-96-intel 0x8p-972L : 0x1p+0L : inexact-ok underflow-ok
-= cosh tonearest ldbl-96-intel 0x8p-972L : 0x1p+0L : inexact-ok underflow-ok
-= cosh towardzero ldbl-96-intel 0x8p-972L : 0x1p+0L : inexact-ok underflow-ok
-= cosh upward ldbl-96-intel 0x8p-972L : 0x1.0000000000000002p+0L : inexact-ok underflow-ok
-= cosh downward ldbl-96-m68k 0x8p-972L : 0x1p+0L : inexact-ok underflow-ok
-= cosh tonearest ldbl-96-m68k 0x8p-972L : 0x1p+0L : inexact-ok underflow-ok
-= cosh towardzero ldbl-96-m68k 0x8p-972L : 0x1p+0L : inexact-ok underflow-ok
-= cosh upward ldbl-96-m68k 0x8p-972L : 0x1.0000000000000002p+0L : inexact-ok underflow-ok
-= cosh downward ldbl-128 0x8p-972L : 0x1p+0L : inexact-ok underflow-ok
-= cosh tonearest ldbl-128 0x8p-972L : 0x1p+0L : inexact-ok underflow-ok
-= cosh towardzero ldbl-128 0x8p-972L : 0x1p+0L : inexact-ok underflow-ok
-= cosh upward ldbl-128 0x8p-972L : 0x1.0000000000000000000000000001p+0L : inexact-ok underflow-ok
-= cosh downward ldbl-128ibm 0x8p-972L : 0x1p+0L : inexact-ok underflow-ok
-= cosh tonearest ldbl-128ibm 0x8p-972L : 0x1p+0L : inexact-ok underflow-ok
-= cosh towardzero ldbl-128ibm 0x8p-972L : 0x1p+0L : inexact-ok underflow-ok
-= cosh upward ldbl-128ibm 0x8p-972L : 0x1.000000000000000000000000008p+0L : inexact-ok underflow-ok
-cosh -min spurious-underflow
-= cosh downward flt-32 -0x4p-128f : 0x1p+0f : inexact-ok underflow-ok
-= cosh tonearest flt-32 -0x4p-128f : 0x1p+0f : inexact-ok underflow-ok
-= cosh towardzero flt-32 -0x4p-128f : 0x1p+0f : inexact-ok underflow-ok
-= cosh upward flt-32 -0x4p-128f : 0x1.000002p+0f : inexact-ok underflow-ok
-= cosh downward dbl-64 -0x4p-128 : 0x1p+0 : inexact-ok underflow-ok
-= cosh tonearest dbl-64 -0x4p-128 : 0x1p+0 : inexact-ok underflow-ok
-= cosh towardzero dbl-64 -0x4p-128 : 0x1p+0 : inexact-ok underflow-ok
-= cosh upward dbl-64 -0x4p-128 : 0x1.0000000000001p+0 : inexact-ok underflow-ok
-= cosh downward ldbl-96-intel -0x4p-128L : 0x1p+0L : inexact-ok underflow-ok
-= cosh tonearest ldbl-96-intel -0x4p-128L : 0x1p+0L : inexact-ok underflow-ok
-= cosh towardzero ldbl-96-intel -0x4p-128L : 0x1p+0L : inexact-ok underflow-ok
-= cosh upward ldbl-96-intel -0x4p-128L : 0x1.0000000000000002p+0L : inexact-ok underflow-ok
-= cosh downward ldbl-96-m68k -0x4p-128L : 0x1p+0L : inexact-ok underflow-ok
-= cosh tonearest ldbl-96-m68k -0x4p-128L : 0x1p+0L : inexact-ok underflow-ok
-= cosh towardzero ldbl-96-m68k -0x4p-128L : 0x1p+0L : inexact-ok underflow-ok
-= cosh upward ldbl-96-m68k -0x4p-128L : 0x1.0000000000000002p+0L : inexact-ok underflow-ok
-= cosh downward ldbl-128 -0x4p-128L : 0x1p+0L : inexact-ok underflow-ok
-= cosh tonearest ldbl-128 -0x4p-128L : 0x1p+0L : inexact-ok underflow-ok
-= cosh towardzero ldbl-128 -0x4p-128L : 0x1p+0L : inexact-ok underflow-ok
-= cosh upward ldbl-128 -0x4p-128L : 0x1.0000000000000000000000000001p+0L : inexact-ok underflow-ok
-= cosh downward ldbl-128ibm -0x4p-128L : 0x1p+0L : inexact-ok underflow-ok
-= cosh tonearest ldbl-128ibm -0x4p-128L : 0x1p+0L : inexact-ok underflow-ok
-= cosh towardzero ldbl-128ibm -0x4p-128L : 0x1p+0L : inexact-ok underflow-ok
-= cosh upward ldbl-128ibm -0x4p-128L : 0x1.000000000000000000000000008p+0L : inexact-ok underflow-ok
-= cosh downward dbl-64 -0x4p-1024 : 0x1p+0 : inexact-ok underflow-ok
-= cosh tonearest dbl-64 -0x4p-1024 : 0x1p+0 : inexact-ok underflow-ok
-= cosh towardzero dbl-64 -0x4p-1024 : 0x1p+0 : inexact-ok underflow-ok
-= cosh upward dbl-64 -0x4p-1024 : 0x1.0000000000001p+0 : inexact-ok underflow-ok
-= cosh downward ldbl-96-intel -0x4p-1024L : 0x1p+0L : inexact-ok underflow-ok
-= cosh tonearest ldbl-96-intel -0x4p-1024L : 0x1p+0L : inexact-ok underflow-ok
-= cosh towardzero ldbl-96-intel -0x4p-1024L : 0x1p+0L : inexact-ok underflow-ok
-= cosh upward ldbl-96-intel -0x4p-1024L : 0x1.0000000000000002p+0L : inexact-ok underflow-ok
-= cosh downward ldbl-96-m68k -0x4p-1024L : 0x1p+0L : inexact-ok underflow-ok
-= cosh tonearest ldbl-96-m68k -0x4p-1024L : 0x1p+0L : inexact-ok underflow-ok
-= cosh towardzero ldbl-96-m68k -0x4p-1024L : 0x1p+0L : inexact-ok underflow-ok
-= cosh upward ldbl-96-m68k -0x4p-1024L : 0x1.0000000000000002p+0L : inexact-ok underflow-ok
-= cosh downward ldbl-128 -0x4p-1024L : 0x1p+0L : inexact-ok underflow-ok
-= cosh tonearest ldbl-128 -0x4p-1024L : 0x1p+0L : inexact-ok underflow-ok
-= cosh towardzero ldbl-128 -0x4p-1024L : 0x1p+0L : inexact-ok underflow-ok
-= cosh upward ldbl-128 -0x4p-1024L : 0x1.0000000000000000000000000001p+0L : inexact-ok underflow-ok
-= cosh downward ldbl-128ibm -0x4p-1024L : 0x1p+0L : inexact-ok underflow-ok
-= cosh tonearest ldbl-128ibm -0x4p-1024L : 0x1p+0L : inexact-ok underflow-ok
-= cosh towardzero ldbl-128ibm -0x4p-1024L : 0x1p+0L : inexact-ok underflow-ok
-= cosh upward ldbl-128ibm -0x4p-1024L : 0x1.000000000000000000000000008p+0L : inexact-ok underflow-ok
-= cosh downward ldbl-96-intel -0x4p-16384L : 0x1p+0L : inexact-ok underflow-ok
-= cosh tonearest ldbl-96-intel -0x4p-16384L : 0x1p+0L : inexact-ok underflow-ok
-= cosh towardzero ldbl-96-intel -0x4p-16384L : 0x1p+0L : inexact-ok underflow-ok
-= cosh upward ldbl-96-intel -0x4p-16384L : 0x1.0000000000000002p+0L : inexact-ok underflow-ok
-= cosh downward ldbl-96-m68k -0x4p-16384L : 0x1p+0L : inexact-ok underflow-ok
-= cosh tonearest ldbl-96-m68k -0x4p-16384L : 0x1p+0L : inexact-ok underflow-ok
-= cosh towardzero ldbl-96-m68k -0x4p-16384L : 0x1p+0L : inexact-ok underflow-ok
-= cosh upward ldbl-96-m68k -0x4p-16384L : 0x1.0000000000000002p+0L : inexact-ok underflow-ok
-= cosh downward ldbl-128 -0x4p-16384L : 0x1p+0L : inexact-ok underflow-ok
-= cosh tonearest ldbl-128 -0x4p-16384L : 0x1p+0L : inexact-ok underflow-ok
-= cosh towardzero ldbl-128 -0x4p-16384L : 0x1p+0L : inexact-ok underflow-ok
-= cosh upward ldbl-128 -0x4p-16384L : 0x1.0000000000000000000000000001p+0L : inexact-ok underflow-ok
-= cosh downward ldbl-96-intel -0x2p-16384L : 0x1p+0L : inexact-ok underflow-ok
-= cosh tonearest ldbl-96-intel -0x2p-16384L : 0x1p+0L : inexact-ok underflow-ok
-= cosh towardzero ldbl-96-intel -0x2p-16384L : 0x1p+0L : inexact-ok underflow-ok
-= cosh upward ldbl-96-intel -0x2p-16384L : 0x1.0000000000000002p+0L : inexact-ok underflow-ok
-= cosh downward ldbl-96-m68k -0x2p-16384L : 0x1p+0L : inexact-ok underflow-ok
-= cosh tonearest ldbl-96-m68k -0x2p-16384L : 0x1p+0L : inexact-ok underflow-ok
-= cosh towardzero ldbl-96-m68k -0x2p-16384L : 0x1p+0L : inexact-ok underflow-ok
-= cosh upward ldbl-96-m68k -0x2p-16384L : 0x1.0000000000000002p+0L : inexact-ok underflow-ok
-= cosh downward ldbl-128 -0x2p-16384L : 0x1p+0L : inexact-ok underflow-ok
-= cosh tonearest ldbl-128 -0x2p-16384L : 0x1p+0L : inexact-ok underflow-ok
-= cosh towardzero ldbl-128 -0x2p-16384L : 0x1p+0L : inexact-ok underflow-ok
-= cosh upward ldbl-128 -0x2p-16384L : 0x1.0000000000000000000000000001p+0L : inexact-ok underflow-ok
-= cosh downward dbl-64 -0x8p-972 : 0x1p+0 : inexact-ok underflow-ok
-= cosh tonearest dbl-64 -0x8p-972 : 0x1p+0 : inexact-ok underflow-ok
-= cosh towardzero dbl-64 -0x8p-972 : 0x1p+0 : inexact-ok underflow-ok
-= cosh upward dbl-64 -0x8p-972 : 0x1.0000000000001p+0 : inexact-ok underflow-ok
-= cosh downward ldbl-96-intel -0x8p-972L : 0x1p+0L : inexact-ok underflow-ok
-= cosh tonearest ldbl-96-intel -0x8p-972L : 0x1p+0L : inexact-ok underflow-ok
-= cosh towardzero ldbl-96-intel -0x8p-972L : 0x1p+0L : inexact-ok underflow-ok
-= cosh upward ldbl-96-intel -0x8p-972L : 0x1.0000000000000002p+0L : inexact-ok underflow-ok
-= cosh downward ldbl-96-m68k -0x8p-972L : 0x1p+0L : inexact-ok underflow-ok
-= cosh tonearest ldbl-96-m68k -0x8p-972L : 0x1p+0L : inexact-ok underflow-ok
-= cosh towardzero ldbl-96-m68k -0x8p-972L : 0x1p+0L : inexact-ok underflow-ok
-= cosh upward ldbl-96-m68k -0x8p-972L : 0x1.0000000000000002p+0L : inexact-ok underflow-ok
-= cosh downward ldbl-128 -0x8p-972L : 0x1p+0L : inexact-ok underflow-ok
-= cosh tonearest ldbl-128 -0x8p-972L : 0x1p+0L : inexact-ok underflow-ok
-= cosh towardzero ldbl-128 -0x8p-972L : 0x1p+0L : inexact-ok underflow-ok
-= cosh upward ldbl-128 -0x8p-972L : 0x1.0000000000000000000000000001p+0L : inexact-ok underflow-ok
-= cosh downward ldbl-128ibm -0x8p-972L : 0x1p+0L : inexact-ok underflow-ok
-= cosh tonearest ldbl-128ibm -0x8p-972L : 0x1p+0L : inexact-ok underflow-ok
-= cosh towardzero ldbl-128ibm -0x8p-972L : 0x1p+0L : inexact-ok underflow-ok
-= cosh upward ldbl-128ibm -0x8p-972L : 0x1.000000000000000000000000008p+0L : inexact-ok underflow-ok
-cosh min_subnorm spurious-underflow
-= cosh downward flt-32 0x8p-152f : 0x1p+0f : inexact-ok underflow-ok
-= cosh tonearest flt-32 0x8p-152f : 0x1p+0f : inexact-ok underflow-ok
-= cosh towardzero flt-32 0x8p-152f : 0x1p+0f : inexact-ok underflow-ok
-= cosh upward flt-32 0x8p-152f : 0x1.000002p+0f : inexact-ok underflow-ok
-= cosh downward dbl-64 0x8p-152 : 0x1p+0 : inexact-ok underflow-ok
-= cosh tonearest dbl-64 0x8p-152 : 0x1p+0 : inexact-ok underflow-ok
-= cosh towardzero dbl-64 0x8p-152 : 0x1p+0 : inexact-ok underflow-ok
-= cosh upward dbl-64 0x8p-152 : 0x1.0000000000001p+0 : inexact-ok underflow-ok
-= cosh downward ldbl-96-intel 0x8p-152L : 0x1p+0L : inexact-ok underflow-ok
-= cosh tonearest ldbl-96-intel 0x8p-152L : 0x1p+0L : inexact-ok underflow-ok
-= cosh towardzero ldbl-96-intel 0x8p-152L : 0x1p+0L : inexact-ok underflow-ok
-= cosh upward ldbl-96-intel 0x8p-152L : 0x1.0000000000000002p+0L : inexact-ok underflow-ok
-= cosh downward ldbl-96-m68k 0x8p-152L : 0x1p+0L : inexact-ok underflow-ok
-= cosh tonearest ldbl-96-m68k 0x8p-152L : 0x1p+0L : inexact-ok underflow-ok
-= cosh towardzero ldbl-96-m68k 0x8p-152L : 0x1p+0L : inexact-ok underflow-ok
-= cosh upward ldbl-96-m68k 0x8p-152L : 0x1.0000000000000002p+0L : inexact-ok underflow-ok
-= cosh downward ldbl-128 0x8p-152L : 0x1p+0L : inexact-ok underflow-ok
-= cosh tonearest ldbl-128 0x8p-152L : 0x1p+0L : inexact-ok underflow-ok
-= cosh towardzero ldbl-128 0x8p-152L : 0x1p+0L : inexact-ok underflow-ok
-= cosh upward ldbl-128 0x8p-152L : 0x1.0000000000000000000000000001p+0L : inexact-ok underflow-ok
-= cosh downward ldbl-128ibm 0x8p-152L : 0x1p+0L : inexact-ok underflow-ok
-= cosh tonearest ldbl-128ibm 0x8p-152L : 0x1p+0L : inexact-ok underflow-ok
-= cosh towardzero ldbl-128ibm 0x8p-152L : 0x1p+0L : inexact-ok underflow-ok
-= cosh upward ldbl-128ibm 0x8p-152L : 0x1.000000000000000000000000008p+0L : inexact-ok underflow-ok
-= cosh downward dbl-64 0x4p-1076 : 0x1p+0 : inexact-ok underflow-ok
-= cosh tonearest dbl-64 0x4p-1076 : 0x1p+0 : inexact-ok underflow-ok
-= cosh towardzero dbl-64 0x4p-1076 : 0x1p+0 : inexact-ok underflow-ok
-= cosh upward dbl-64 0x4p-1076 : 0x1.0000000000001p+0 : inexact-ok underflow-ok
-= cosh downward ldbl-96-intel 0x4p-1076L : 0x1p+0L : inexact-ok underflow-ok
-= cosh tonearest ldbl-96-intel 0x4p-1076L : 0x1p+0L : inexact-ok underflow-ok
-= cosh towardzero ldbl-96-intel 0x4p-1076L : 0x1p+0L : inexact-ok underflow-ok
-= cosh upward ldbl-96-intel 0x4p-1076L : 0x1.0000000000000002p+0L : inexact-ok underflow-ok
-= cosh downward ldbl-96-m68k 0x4p-1076L : 0x1p+0L : inexact-ok underflow-ok
-= cosh tonearest ldbl-96-m68k 0x4p-1076L : 0x1p+0L : inexact-ok underflow-ok
-= cosh towardzero ldbl-96-m68k 0x4p-1076L : 0x1p+0L : inexact-ok underflow-ok
-= cosh upward ldbl-96-m68k 0x4p-1076L : 0x1.0000000000000002p+0L : inexact-ok underflow-ok
-= cosh downward ldbl-128 0x4p-1076L : 0x1p+0L : inexact-ok underflow-ok
-= cosh tonearest ldbl-128 0x4p-1076L : 0x1p+0L : inexact-ok underflow-ok
-= cosh towardzero ldbl-128 0x4p-1076L : 0x1p+0L : inexact-ok underflow-ok
-= cosh upward ldbl-128 0x4p-1076L : 0x1.0000000000000000000000000001p+0L : inexact-ok underflow-ok
-= cosh downward ldbl-128ibm 0x4p-1076L : 0x1p+0L : inexact-ok underflow-ok
-= cosh tonearest ldbl-128ibm 0x4p-1076L : 0x1p+0L : inexact-ok underflow-ok
-= cosh towardzero ldbl-128ibm 0x4p-1076L : 0x1p+0L : inexact-ok underflow-ok
-= cosh upward ldbl-128ibm 0x4p-1076L : 0x1.000000000000000000000000008p+0L : inexact-ok underflow-ok
-= cosh downward ldbl-96-intel 0x8p-16448L : 0x1p+0L : inexact-ok underflow-ok
-= cosh tonearest ldbl-96-intel 0x8p-16448L : 0x1p+0L : inexact-ok underflow-ok
-= cosh towardzero ldbl-96-intel 0x8p-16448L : 0x1p+0L : inexact-ok underflow-ok
-= cosh upward ldbl-96-intel 0x8p-16448L : 0x1.0000000000000002p+0L : inexact-ok underflow-ok
-= cosh downward ldbl-96-m68k 0x8p-16448L : 0x1p+0L : inexact-ok underflow-ok
-= cosh tonearest ldbl-96-m68k 0x8p-16448L : 0x1p+0L : inexact-ok underflow-ok
-= cosh towardzero ldbl-96-m68k 0x8p-16448L : 0x1p+0L : inexact-ok underflow-ok
-= cosh upward ldbl-96-m68k 0x8p-16448L : 0x1.0000000000000002p+0L : inexact-ok underflow-ok
-= cosh downward ldbl-128 0x8p-16448L : 0x1p+0L : inexact-ok underflow-ok
-= cosh tonearest ldbl-128 0x8p-16448L : 0x1p+0L : inexact-ok underflow-ok
-= cosh towardzero ldbl-128 0x8p-16448L : 0x1p+0L : inexact-ok underflow-ok
-= cosh upward ldbl-128 0x8p-16448L : 0x1.0000000000000000000000000001p+0L : inexact-ok underflow-ok
-= cosh downward ldbl-96-m68k 0x4p-16448L : 0x1p+0L : inexact-ok underflow-ok
-= cosh tonearest ldbl-96-m68k 0x4p-16448L : 0x1p+0L : inexact-ok underflow-ok
-= cosh towardzero ldbl-96-m68k 0x4p-16448L : 0x1p+0L : inexact-ok underflow-ok
-= cosh upward ldbl-96-m68k 0x4p-16448L : 0x1.0000000000000002p+0L : inexact-ok underflow-ok
-= cosh downward ldbl-128 0x4p-16448L : 0x1p+0L : inexact-ok underflow-ok
-= cosh tonearest ldbl-128 0x4p-16448L : 0x1p+0L : inexact-ok underflow-ok
-= cosh towardzero ldbl-128 0x4p-16448L : 0x1p+0L : inexact-ok underflow-ok
-= cosh upward ldbl-128 0x4p-16448L : 0x1.0000000000000000000000000001p+0L : inexact-ok underflow-ok
-= cosh downward ldbl-128 0x4p-16496L : 0x1p+0L : inexact-ok underflow-ok
-= cosh tonearest ldbl-128 0x4p-16496L : 0x1p+0L : inexact-ok underflow-ok
-= cosh towardzero ldbl-128 0x4p-16496L : 0x1p+0L : inexact-ok underflow-ok
-= cosh upward ldbl-128 0x4p-16496L : 0x1.0000000000000000000000000001p+0L : inexact-ok underflow-ok
-cosh -min_subnorm spurious-underflow
-= cosh downward flt-32 -0x8p-152f : 0x1p+0f : inexact-ok underflow-ok
-= cosh tonearest flt-32 -0x8p-152f : 0x1p+0f : inexact-ok underflow-ok
-= cosh towardzero flt-32 -0x8p-152f : 0x1p+0f : inexact-ok underflow-ok
-= cosh upward flt-32 -0x8p-152f : 0x1.000002p+0f : inexact-ok underflow-ok
-= cosh downward dbl-64 -0x8p-152 : 0x1p+0 : inexact-ok underflow-ok
-= cosh tonearest dbl-64 -0x8p-152 : 0x1p+0 : inexact-ok underflow-ok
-= cosh towardzero dbl-64 -0x8p-152 : 0x1p+0 : inexact-ok underflow-ok
-= cosh upward dbl-64 -0x8p-152 : 0x1.0000000000001p+0 : inexact-ok underflow-ok
-= cosh downward ldbl-96-intel -0x8p-152L : 0x1p+0L : inexact-ok underflow-ok
-= cosh tonearest ldbl-96-intel -0x8p-152L : 0x1p+0L : inexact-ok underflow-ok
-= cosh towardzero ldbl-96-intel -0x8p-152L : 0x1p+0L : inexact-ok underflow-ok
-= cosh upward ldbl-96-intel -0x8p-152L : 0x1.0000000000000002p+0L : inexact-ok underflow-ok
-= cosh downward ldbl-96-m68k -0x8p-152L : 0x1p+0L : inexact-ok underflow-ok
-= cosh tonearest ldbl-96-m68k -0x8p-152L : 0x1p+0L : inexact-ok underflow-ok
-= cosh towardzero ldbl-96-m68k -0x8p-152L : 0x1p+0L : inexact-ok underflow-ok
-= cosh upward ldbl-96-m68k -0x8p-152L : 0x1.0000000000000002p+0L : inexact-ok underflow-ok
-= cosh downward ldbl-128 -0x8p-152L : 0x1p+0L : inexact-ok underflow-ok
-= cosh tonearest ldbl-128 -0x8p-152L : 0x1p+0L : inexact-ok underflow-ok
-= cosh towardzero ldbl-128 -0x8p-152L : 0x1p+0L : inexact-ok underflow-ok
-= cosh upward ldbl-128 -0x8p-152L : 0x1.0000000000000000000000000001p+0L : inexact-ok underflow-ok
-= cosh downward ldbl-128ibm -0x8p-152L : 0x1p+0L : inexact-ok underflow-ok
-= cosh tonearest ldbl-128ibm -0x8p-152L : 0x1p+0L : inexact-ok underflow-ok
-= cosh towardzero ldbl-128ibm -0x8p-152L : 0x1p+0L : inexact-ok underflow-ok
-= cosh upward ldbl-128ibm -0x8p-152L : 0x1.000000000000000000000000008p+0L : inexact-ok underflow-ok
-= cosh downward dbl-64 -0x4p-1076 : 0x1p+0 : inexact-ok underflow-ok
-= cosh tonearest dbl-64 -0x4p-1076 : 0x1p+0 : inexact-ok underflow-ok
-= cosh towardzero dbl-64 -0x4p-1076 : 0x1p+0 : inexact-ok underflow-ok
-= cosh upward dbl-64 -0x4p-1076 : 0x1.0000000000001p+0 : inexact-ok underflow-ok
-= cosh downward ldbl-96-intel -0x4p-1076L : 0x1p+0L : inexact-ok underflow-ok
-= cosh tonearest ldbl-96-intel -0x4p-1076L : 0x1p+0L : inexact-ok underflow-ok
-= cosh towardzero ldbl-96-intel -0x4p-1076L : 0x1p+0L : inexact-ok underflow-ok
-= cosh upward ldbl-96-intel -0x4p-1076L : 0x1.0000000000000002p+0L : inexact-ok underflow-ok
-= cosh downward ldbl-96-m68k -0x4p-1076L : 0x1p+0L : inexact-ok underflow-ok
-= cosh tonearest ldbl-96-m68k -0x4p-1076L : 0x1p+0L : inexact-ok underflow-ok
-= cosh towardzero ldbl-96-m68k -0x4p-1076L : 0x1p+0L : inexact-ok underflow-ok
-= cosh upward ldbl-96-m68k -0x4p-1076L : 0x1.0000000000000002p+0L : inexact-ok underflow-ok
-= cosh downward ldbl-128 -0x4p-1076L : 0x1p+0L : inexact-ok underflow-ok
-= cosh tonearest ldbl-128 -0x4p-1076L : 0x1p+0L : inexact-ok underflow-ok
-= cosh towardzero ldbl-128 -0x4p-1076L : 0x1p+0L : inexact-ok underflow-ok
-= cosh upward ldbl-128 -0x4p-1076L : 0x1.0000000000000000000000000001p+0L : inexact-ok underflow-ok
-= cosh downward ldbl-128ibm -0x4p-1076L : 0x1p+0L : inexact-ok underflow-ok
-= cosh tonearest ldbl-128ibm -0x4p-1076L : 0x1p+0L : inexact-ok underflow-ok
-= cosh towardzero ldbl-128ibm -0x4p-1076L : 0x1p+0L : inexact-ok underflow-ok
-= cosh upward ldbl-128ibm -0x4p-1076L : 0x1.000000000000000000000000008p+0L : inexact-ok underflow-ok
-= cosh downward ldbl-96-intel -0x8p-16448L : 0x1p+0L : inexact-ok underflow-ok
-= cosh tonearest ldbl-96-intel -0x8p-16448L : 0x1p+0L : inexact-ok underflow-ok
-= cosh towardzero ldbl-96-intel -0x8p-16448L : 0x1p+0L : inexact-ok underflow-ok
-= cosh upward ldbl-96-intel -0x8p-16448L : 0x1.0000000000000002p+0L : inexact-ok underflow-ok
-= cosh downward ldbl-96-m68k -0x8p-16448L : 0x1p+0L : inexact-ok underflow-ok
-= cosh tonearest ldbl-96-m68k -0x8p-16448L : 0x1p+0L : inexact-ok underflow-ok
-= cosh towardzero ldbl-96-m68k -0x8p-16448L : 0x1p+0L : inexact-ok underflow-ok
-= cosh upward ldbl-96-m68k -0x8p-16448L : 0x1.0000000000000002p+0L : inexact-ok underflow-ok
-= cosh downward ldbl-128 -0x8p-16448L : 0x1p+0L : inexact-ok underflow-ok
-= cosh tonearest ldbl-128 -0x8p-16448L : 0x1p+0L : inexact-ok underflow-ok
-= cosh towardzero ldbl-128 -0x8p-16448L : 0x1p+0L : inexact-ok underflow-ok
-= cosh upward ldbl-128 -0x8p-16448L : 0x1.0000000000000000000000000001p+0L : inexact-ok underflow-ok
-= cosh downward ldbl-96-m68k -0x4p-16448L : 0x1p+0L : inexact-ok underflow-ok
-= cosh tonearest ldbl-96-m68k -0x4p-16448L : 0x1p+0L : inexact-ok underflow-ok
-= cosh towardzero ldbl-96-m68k -0x4p-16448L : 0x1p+0L : inexact-ok underflow-ok
-= cosh upward ldbl-96-m68k -0x4p-16448L : 0x1.0000000000000002p+0L : inexact-ok underflow-ok
-= cosh downward ldbl-128 -0x4p-16448L : 0x1p+0L : inexact-ok underflow-ok
-= cosh tonearest ldbl-128 -0x4p-16448L : 0x1p+0L : inexact-ok underflow-ok
-= cosh towardzero ldbl-128 -0x4p-16448L : 0x1p+0L : inexact-ok underflow-ok
-= cosh upward ldbl-128 -0x4p-16448L : 0x1.0000000000000000000000000001p+0L : inexact-ok underflow-ok
-= cosh downward ldbl-128 -0x4p-16496L : 0x1p+0L : inexact-ok underflow-ok
-= cosh tonearest ldbl-128 -0x4p-16496L : 0x1p+0L : inexact-ok underflow-ok
-= cosh towardzero ldbl-128 -0x4p-16496L : 0x1p+0L : inexact-ok underflow-ok
-= cosh upward ldbl-128 -0x4p-16496L : 0x1.0000000000000000000000000001p+0L : inexact-ok underflow-ok
+cosh min
+= cosh downward flt-32 0x4p-128f : 0x1p+0f : inexact-ok
+= cosh tonearest flt-32 0x4p-128f : 0x1p+0f : inexact-ok
+= cosh towardzero flt-32 0x4p-128f : 0x1p+0f : inexact-ok
+= cosh upward flt-32 0x4p-128f : 0x1.000002p+0f : inexact-ok
+= cosh downward dbl-64 0x4p-128 : 0x1p+0 : inexact-ok
+= cosh tonearest dbl-64 0x4p-128 : 0x1p+0 : inexact-ok
+= cosh towardzero dbl-64 0x4p-128 : 0x1p+0 : inexact-ok
+= cosh upward dbl-64 0x4p-128 : 0x1.0000000000001p+0 : inexact-ok
+= cosh downward ldbl-96-intel 0x4p-128L : 0x1p+0L : inexact-ok
+= cosh tonearest ldbl-96-intel 0x4p-128L : 0x1p+0L : inexact-ok
+= cosh towardzero ldbl-96-intel 0x4p-128L : 0x1p+0L : inexact-ok
+= cosh upward ldbl-96-intel 0x4p-128L : 0x1.0000000000000002p+0L : inexact-ok
+= cosh downward ldbl-96-m68k 0x4p-128L : 0x1p+0L : inexact-ok
+= cosh tonearest ldbl-96-m68k 0x4p-128L : 0x1p+0L : inexact-ok
+= cosh towardzero ldbl-96-m68k 0x4p-128L : 0x1p+0L : inexact-ok
+= cosh upward ldbl-96-m68k 0x4p-128L : 0x1.0000000000000002p+0L : inexact-ok
+= cosh downward ldbl-128 0x4p-128L : 0x1p+0L : inexact-ok
+= cosh tonearest ldbl-128 0x4p-128L : 0x1p+0L : inexact-ok
+= cosh towardzero ldbl-128 0x4p-128L : 0x1p+0L : inexact-ok
+= cosh upward ldbl-128 0x4p-128L : 0x1.0000000000000000000000000001p+0L : inexact-ok
+= cosh downward ldbl-128ibm 0x4p-128L : 0x1p+0L : inexact-ok
+= cosh tonearest ldbl-128ibm 0x4p-128L : 0x1p+0L : inexact-ok
+= cosh towardzero ldbl-128ibm 0x4p-128L : 0x1p+0L : inexact-ok
+= cosh upward ldbl-128ibm 0x4p-128L : 0x1.000000000000000000000000008p+0L : inexact-ok
+= cosh downward dbl-64 0x4p-1024 : 0x1p+0 : inexact-ok
+= cosh tonearest dbl-64 0x4p-1024 : 0x1p+0 : inexact-ok
+= cosh towardzero dbl-64 0x4p-1024 : 0x1p+0 : inexact-ok
+= cosh upward dbl-64 0x4p-1024 : 0x1.0000000000001p+0 : inexact-ok
+= cosh downward ldbl-96-intel 0x4p-1024L : 0x1p+0L : inexact-ok
+= cosh tonearest ldbl-96-intel 0x4p-1024L : 0x1p+0L : inexact-ok
+= cosh towardzero ldbl-96-intel 0x4p-1024L : 0x1p+0L : inexact-ok
+= cosh upward ldbl-96-intel 0x4p-1024L : 0x1.0000000000000002p+0L : inexact-ok
+= cosh downward ldbl-96-m68k 0x4p-1024L : 0x1p+0L : inexact-ok
+= cosh tonearest ldbl-96-m68k 0x4p-1024L : 0x1p+0L : inexact-ok
+= cosh towardzero ldbl-96-m68k 0x4p-1024L : 0x1p+0L : inexact-ok
+= cosh upward ldbl-96-m68k 0x4p-1024L : 0x1.0000000000000002p+0L : inexact-ok
+= cosh downward ldbl-128 0x4p-1024L : 0x1p+0L : inexact-ok
+= cosh tonearest ldbl-128 0x4p-1024L : 0x1p+0L : inexact-ok
+= cosh towardzero ldbl-128 0x4p-1024L : 0x1p+0L : inexact-ok
+= cosh upward ldbl-128 0x4p-1024L : 0x1.0000000000000000000000000001p+0L : inexact-ok
+= cosh downward ldbl-128ibm 0x4p-1024L : 0x1p+0L : inexact-ok
+= cosh tonearest ldbl-128ibm 0x4p-1024L : 0x1p+0L : inexact-ok
+= cosh towardzero ldbl-128ibm 0x4p-1024L : 0x1p+0L : inexact-ok
+= cosh upward ldbl-128ibm 0x4p-1024L : 0x1.000000000000000000000000008p+0L : inexact-ok
+= cosh downward ldbl-96-intel 0x4p-16384L : 0x1p+0L : inexact-ok
+= cosh tonearest ldbl-96-intel 0x4p-16384L : 0x1p+0L : inexact-ok
+= cosh towardzero ldbl-96-intel 0x4p-16384L : 0x1p+0L : inexact-ok
+= cosh upward ldbl-96-intel 0x4p-16384L : 0x1.0000000000000002p+0L : inexact-ok
+= cosh downward ldbl-96-m68k 0x4p-16384L : 0x1p+0L : inexact-ok
+= cosh tonearest ldbl-96-m68k 0x4p-16384L : 0x1p+0L : inexact-ok
+= cosh towardzero ldbl-96-m68k 0x4p-16384L : 0x1p+0L : inexact-ok
+= cosh upward ldbl-96-m68k 0x4p-16384L : 0x1.0000000000000002p+0L : inexact-ok
+= cosh downward ldbl-128 0x4p-16384L : 0x1p+0L : inexact-ok
+= cosh tonearest ldbl-128 0x4p-16384L : 0x1p+0L : inexact-ok
+= cosh towardzero ldbl-128 0x4p-16384L : 0x1p+0L : inexact-ok
+= cosh upward ldbl-128 0x4p-16384L : 0x1.0000000000000000000000000001p+0L : inexact-ok
+= cosh downward ldbl-96-intel 0x2p-16384L : 0x1p+0L : inexact-ok
+= cosh tonearest ldbl-96-intel 0x2p-16384L : 0x1p+0L : inexact-ok
+= cosh towardzero ldbl-96-intel 0x2p-16384L : 0x1p+0L : inexact-ok
+= cosh upward ldbl-96-intel 0x2p-16384L : 0x1.0000000000000002p+0L : inexact-ok
+= cosh downward ldbl-96-m68k 0x2p-16384L : 0x1p+0L : inexact-ok
+= cosh tonearest ldbl-96-m68k 0x2p-16384L : 0x1p+0L : inexact-ok
+= cosh towardzero ldbl-96-m68k 0x2p-16384L : 0x1p+0L : inexact-ok
+= cosh upward ldbl-96-m68k 0x2p-16384L : 0x1.0000000000000002p+0L : inexact-ok
+= cosh downward ldbl-128 0x2p-16384L : 0x1p+0L : inexact-ok
+= cosh tonearest ldbl-128 0x2p-16384L : 0x1p+0L : inexact-ok
+= cosh towardzero ldbl-128 0x2p-16384L : 0x1p+0L : inexact-ok
+= cosh upward ldbl-128 0x2p-16384L : 0x1.0000000000000000000000000001p+0L : inexact-ok
+= cosh downward dbl-64 0x8p-972 : 0x1p+0 : inexact-ok
+= cosh tonearest dbl-64 0x8p-972 : 0x1p+0 : inexact-ok
+= cosh towardzero dbl-64 0x8p-972 : 0x1p+0 : inexact-ok
+= cosh upward dbl-64 0x8p-972 : 0x1.0000000000001p+0 : inexact-ok
+= cosh downward ldbl-96-intel 0x8p-972L : 0x1p+0L : inexact-ok
+= cosh tonearest ldbl-96-intel 0x8p-972L : 0x1p+0L : inexact-ok
+= cosh towardzero ldbl-96-intel 0x8p-972L : 0x1p+0L : inexact-ok
+= cosh upward ldbl-96-intel 0x8p-972L : 0x1.0000000000000002p+0L : inexact-ok
+= cosh downward ldbl-96-m68k 0x8p-972L : 0x1p+0L : inexact-ok
+= cosh tonearest ldbl-96-m68k 0x8p-972L : 0x1p+0L : inexact-ok
+= cosh towardzero ldbl-96-m68k 0x8p-972L : 0x1p+0L : inexact-ok
+= cosh upward ldbl-96-m68k 0x8p-972L : 0x1.0000000000000002p+0L : inexact-ok
+= cosh downward ldbl-128 0x8p-972L : 0x1p+0L : inexact-ok
+= cosh tonearest ldbl-128 0x8p-972L : 0x1p+0L : inexact-ok
+= cosh towardzero ldbl-128 0x8p-972L : 0x1p+0L : inexact-ok
+= cosh upward ldbl-128 0x8p-972L : 0x1.0000000000000000000000000001p+0L : inexact-ok
+= cosh downward ldbl-128ibm 0x8p-972L : 0x1p+0L : inexact-ok
+= cosh tonearest ldbl-128ibm 0x8p-972L : 0x1p+0L : inexact-ok
+= cosh towardzero ldbl-128ibm 0x8p-972L : 0x1p+0L : inexact-ok
+= cosh upward ldbl-128ibm 0x8p-972L : 0x1.000000000000000000000000008p+0L : inexact-ok
+cosh -min
+= cosh downward flt-32 -0x4p-128f : 0x1p+0f : inexact-ok
+= cosh tonearest flt-32 -0x4p-128f : 0x1p+0f : inexact-ok
+= cosh towardzero flt-32 -0x4p-128f : 0x1p+0f : inexact-ok
+= cosh upward flt-32 -0x4p-128f : 0x1.000002p+0f : inexact-ok
+= cosh downward dbl-64 -0x4p-128 : 0x1p+0 : inexact-ok
+= cosh tonearest dbl-64 -0x4p-128 : 0x1p+0 : inexact-ok
+= cosh towardzero dbl-64 -0x4p-128 : 0x1p+0 : inexact-ok
+= cosh upward dbl-64 -0x4p-128 : 0x1.0000000000001p+0 : inexact-ok
+= cosh downward ldbl-96-intel -0x4p-128L : 0x1p+0L : inexact-ok
+= cosh tonearest ldbl-96-intel -0x4p-128L : 0x1p+0L : inexact-ok
+= cosh towardzero ldbl-96-intel -0x4p-128L : 0x1p+0L : inexact-ok
+= cosh upward ldbl-96-intel -0x4p-128L : 0x1.0000000000000002p+0L : inexact-ok
+= cosh downward ldbl-96-m68k -0x4p-128L : 0x1p+0L : inexact-ok
+= cosh tonearest ldbl-96-m68k -0x4p-128L : 0x1p+0L : inexact-ok
+= cosh towardzero ldbl-96-m68k -0x4p-128L : 0x1p+0L : inexact-ok
+= cosh upward ldbl-96-m68k -0x4p-128L : 0x1.0000000000000002p+0L : inexact-ok
+= cosh downward ldbl-128 -0x4p-128L : 0x1p+0L : inexact-ok
+= cosh tonearest ldbl-128 -0x4p-128L : 0x1p+0L : inexact-ok
+= cosh towardzero ldbl-128 -0x4p-128L : 0x1p+0L : inexact-ok
+= cosh upward ldbl-128 -0x4p-128L : 0x1.0000000000000000000000000001p+0L : inexact-ok
+= cosh downward ldbl-128ibm -0x4p-128L : 0x1p+0L : inexact-ok
+= cosh tonearest ldbl-128ibm -0x4p-128L : 0x1p+0L : inexact-ok
+= cosh towardzero ldbl-128ibm -0x4p-128L : 0x1p+0L : inexact-ok
+= cosh upward ldbl-128ibm -0x4p-128L : 0x1.000000000000000000000000008p+0L : inexact-ok
+= cosh downward dbl-64 -0x4p-1024 : 0x1p+0 : inexact-ok
+= cosh tonearest dbl-64 -0x4p-1024 : 0x1p+0 : inexact-ok
+= cosh towardzero dbl-64 -0x4p-1024 : 0x1p+0 : inexact-ok
+= cosh upward dbl-64 -0x4p-1024 : 0x1.0000000000001p+0 : inexact-ok
+= cosh downward ldbl-96-intel -0x4p-1024L : 0x1p+0L : inexact-ok
+= cosh tonearest ldbl-96-intel -0x4p-1024L : 0x1p+0L : inexact-ok
+= cosh towardzero ldbl-96-intel -0x4p-1024L : 0x1p+0L : inexact-ok
+= cosh upward ldbl-96-intel -0x4p-1024L : 0x1.0000000000000002p+0L : inexact-ok
+= cosh downward ldbl-96-m68k -0x4p-1024L : 0x1p+0L : inexact-ok
+= cosh tonearest ldbl-96-m68k -0x4p-1024L : 0x1p+0L : inexact-ok
+= cosh towardzero ldbl-96-m68k -0x4p-1024L : 0x1p+0L : inexact-ok
+= cosh upward ldbl-96-m68k -0x4p-1024L : 0x1.0000000000000002p+0L : inexact-ok
+= cosh downward ldbl-128 -0x4p-1024L : 0x1p+0L : inexact-ok
+= cosh tonearest ldbl-128 -0x4p-1024L : 0x1p+0L : inexact-ok
+= cosh towardzero ldbl-128 -0x4p-1024L : 0x1p+0L : inexact-ok
+= cosh upward ldbl-128 -0x4p-1024L : 0x1.0000000000000000000000000001p+0L : inexact-ok
+= cosh downward ldbl-128ibm -0x4p-1024L : 0x1p+0L : inexact-ok
+= cosh tonearest ldbl-128ibm -0x4p-1024L : 0x1p+0L : inexact-ok
+= cosh towardzero ldbl-128ibm -0x4p-1024L : 0x1p+0L : inexact-ok
+= cosh upward ldbl-128ibm -0x4p-1024L : 0x1.000000000000000000000000008p+0L : inexact-ok
+= cosh downward ldbl-96-intel -0x4p-16384L : 0x1p+0L : inexact-ok
+= cosh tonearest ldbl-96-intel -0x4p-16384L : 0x1p+0L : inexact-ok
+= cosh towardzero ldbl-96-intel -0x4p-16384L : 0x1p+0L : inexact-ok
+= cosh upward ldbl-96-intel -0x4p-16384L : 0x1.0000000000000002p+0L : inexact-ok
+= cosh downward ldbl-96-m68k -0x4p-16384L : 0x1p+0L : inexact-ok
+= cosh tonearest ldbl-96-m68k -0x4p-16384L : 0x1p+0L : inexact-ok
+= cosh towardzero ldbl-96-m68k -0x4p-16384L : 0x1p+0L : inexact-ok
+= cosh upward ldbl-96-m68k -0x4p-16384L : 0x1.0000000000000002p+0L : inexact-ok
+= cosh downward ldbl-128 -0x4p-16384L : 0x1p+0L : inexact-ok
+= cosh tonearest ldbl-128 -0x4p-16384L : 0x1p+0L : inexact-ok
+= cosh towardzero ldbl-128 -0x4p-16384L : 0x1p+0L : inexact-ok
+= cosh upward ldbl-128 -0x4p-16384L : 0x1.0000000000000000000000000001p+0L : inexact-ok
+= cosh downward ldbl-96-intel -0x2p-16384L : 0x1p+0L : inexact-ok
+= cosh tonearest ldbl-96-intel -0x2p-16384L : 0x1p+0L : inexact-ok
+= cosh towardzero ldbl-96-intel -0x2p-16384L : 0x1p+0L : inexact-ok
+= cosh upward ldbl-96-intel -0x2p-16384L : 0x1.0000000000000002p+0L : inexact-ok
+= cosh downward ldbl-96-m68k -0x2p-16384L : 0x1p+0L : inexact-ok
+= cosh tonearest ldbl-96-m68k -0x2p-16384L : 0x1p+0L : inexact-ok
+= cosh towardzero ldbl-96-m68k -0x2p-16384L : 0x1p+0L : inexact-ok
+= cosh upward ldbl-96-m68k -0x2p-16384L : 0x1.0000000000000002p+0L : inexact-ok
+= cosh downward ldbl-128 -0x2p-16384L : 0x1p+0L : inexact-ok
+= cosh tonearest ldbl-128 -0x2p-16384L : 0x1p+0L : inexact-ok
+= cosh towardzero ldbl-128 -0x2p-16384L : 0x1p+0L : inexact-ok
+= cosh upward ldbl-128 -0x2p-16384L : 0x1.0000000000000000000000000001p+0L : inexact-ok
+= cosh downward dbl-64 -0x8p-972 : 0x1p+0 : inexact-ok
+= cosh tonearest dbl-64 -0x8p-972 : 0x1p+0 : inexact-ok
+= cosh towardzero dbl-64 -0x8p-972 : 0x1p+0 : inexact-ok
+= cosh upward dbl-64 -0x8p-972 : 0x1.0000000000001p+0 : inexact-ok
+= cosh downward ldbl-96-intel -0x8p-972L : 0x1p+0L : inexact-ok
+= cosh tonearest ldbl-96-intel -0x8p-972L : 0x1p+0L : inexact-ok
+= cosh towardzero ldbl-96-intel -0x8p-972L : 0x1p+0L : inexact-ok
+= cosh upward ldbl-96-intel -0x8p-972L : 0x1.0000000000000002p+0L : inexact-ok
+= cosh downward ldbl-96-m68k -0x8p-972L : 0x1p+0L : inexact-ok
+= cosh tonearest ldbl-96-m68k -0x8p-972L : 0x1p+0L : inexact-ok
+= cosh towardzero ldbl-96-m68k -0x8p-972L : 0x1p+0L : inexact-ok
+= cosh upward ldbl-96-m68k -0x8p-972L : 0x1.0000000000000002p+0L : inexact-ok
+= cosh downward ldbl-128 -0x8p-972L : 0x1p+0L : inexact-ok
+= cosh tonearest ldbl-128 -0x8p-972L : 0x1p+0L : inexact-ok
+= cosh towardzero ldbl-128 -0x8p-972L : 0x1p+0L : inexact-ok
+= cosh upward ldbl-128 -0x8p-972L : 0x1.0000000000000000000000000001p+0L : inexact-ok
+= cosh downward ldbl-128ibm -0x8p-972L : 0x1p+0L : inexact-ok
+= cosh tonearest ldbl-128ibm -0x8p-972L : 0x1p+0L : inexact-ok
+= cosh towardzero ldbl-128ibm -0x8p-972L : 0x1p+0L : inexact-ok
+= cosh upward ldbl-128ibm -0x8p-972L : 0x1.000000000000000000000000008p+0L : inexact-ok
+cosh min_subnorm
+= cosh downward flt-32 0x8p-152f : 0x1p+0f : inexact-ok
+= cosh tonearest flt-32 0x8p-152f : 0x1p+0f : inexact-ok
+= cosh towardzero flt-32 0x8p-152f : 0x1p+0f : inexact-ok
+= cosh upward flt-32 0x8p-152f : 0x1.000002p+0f : inexact-ok
+= cosh downward dbl-64 0x8p-152 : 0x1p+0 : inexact-ok
+= cosh tonearest dbl-64 0x8p-152 : 0x1p+0 : inexact-ok
+= cosh towardzero dbl-64 0x8p-152 : 0x1p+0 : inexact-ok
+= cosh upward dbl-64 0x8p-152 : 0x1.0000000000001p+0 : inexact-ok
+= cosh downward ldbl-96-intel 0x8p-152L : 0x1p+0L : inexact-ok
+= cosh tonearest ldbl-96-intel 0x8p-152L : 0x1p+0L : inexact-ok
+= cosh towardzero ldbl-96-intel 0x8p-152L : 0x1p+0L : inexact-ok
+= cosh upward ldbl-96-intel 0x8p-152L : 0x1.0000000000000002p+0L : inexact-ok
+= cosh downward ldbl-96-m68k 0x8p-152L : 0x1p+0L : inexact-ok
+= cosh tonearest ldbl-96-m68k 0x8p-152L : 0x1p+0L : inexact-ok
+= cosh towardzero ldbl-96-m68k 0x8p-152L : 0x1p+0L : inexact-ok
+= cosh upward ldbl-96-m68k 0x8p-152L : 0x1.0000000000000002p+0L : inexact-ok
+= cosh downward ldbl-128 0x8p-152L : 0x1p+0L : inexact-ok
+= cosh tonearest ldbl-128 0x8p-152L : 0x1p+0L : inexact-ok
+= cosh towardzero ldbl-128 0x8p-152L : 0x1p+0L : inexact-ok
+= cosh upward ldbl-128 0x8p-152L : 0x1.0000000000000000000000000001p+0L : inexact-ok
+= cosh downward ldbl-128ibm 0x8p-152L : 0x1p+0L : inexact-ok
+= cosh tonearest ldbl-128ibm 0x8p-152L : 0x1p+0L : inexact-ok
+= cosh towardzero ldbl-128ibm 0x8p-152L : 0x1p+0L : inexact-ok
+= cosh upward ldbl-128ibm 0x8p-152L : 0x1.000000000000000000000000008p+0L : inexact-ok
+= cosh downward dbl-64 0x4p-1076 : 0x1p+0 : inexact-ok
+= cosh tonearest dbl-64 0x4p-1076 : 0x1p+0 : inexact-ok
+= cosh towardzero dbl-64 0x4p-1076 : 0x1p+0 : inexact-ok
+= cosh upward dbl-64 0x4p-1076 : 0x1.0000000000001p+0 : inexact-ok
+= cosh downward ldbl-96-intel 0x4p-1076L : 0x1p+0L : inexact-ok
+= cosh tonearest ldbl-96-intel 0x4p-1076L : 0x1p+0L : inexact-ok
+= cosh towardzero ldbl-96-intel 0x4p-1076L : 0x1p+0L : inexact-ok
+= cosh upward ldbl-96-intel 0x4p-1076L : 0x1.0000000000000002p+0L : inexact-ok
+= cosh downward ldbl-96-m68k 0x4p-1076L : 0x1p+0L : inexact-ok
+= cosh tonearest ldbl-96-m68k 0x4p-1076L : 0x1p+0L : inexact-ok
+= cosh towardzero ldbl-96-m68k 0x4p-1076L : 0x1p+0L : inexact-ok
+= cosh upward ldbl-96-m68k 0x4p-1076L : 0x1.0000000000000002p+0L : inexact-ok
+= cosh downward ldbl-128 0x4p-1076L : 0x1p+0L : inexact-ok
+= cosh tonearest ldbl-128 0x4p-1076L : 0x1p+0L : inexact-ok
+= cosh towardzero ldbl-128 0x4p-1076L : 0x1p+0L : inexact-ok
+= cosh upward ldbl-128 0x4p-1076L : 0x1.0000000000000000000000000001p+0L : inexact-ok
+= cosh downward ldbl-128ibm 0x4p-1076L : 0x1p+0L : inexact-ok
+= cosh tonearest ldbl-128ibm 0x4p-1076L : 0x1p+0L : inexact-ok
+= cosh towardzero ldbl-128ibm 0x4p-1076L : 0x1p+0L : inexact-ok
+= cosh upward ldbl-128ibm 0x4p-1076L : 0x1.000000000000000000000000008p+0L : inexact-ok
+= cosh downward ldbl-96-intel 0x8p-16448L : 0x1p+0L : inexact-ok
+= cosh tonearest ldbl-96-intel 0x8p-16448L : 0x1p+0L : inexact-ok
+= cosh towardzero ldbl-96-intel 0x8p-16448L : 0x1p+0L : inexact-ok
+= cosh upward ldbl-96-intel 0x8p-16448L : 0x1.0000000000000002p+0L : inexact-ok
+= cosh downward ldbl-96-m68k 0x8p-16448L : 0x1p+0L : inexact-ok
+= cosh tonearest ldbl-96-m68k 0x8p-16448L : 0x1p+0L : inexact-ok
+= cosh towardzero ldbl-96-m68k 0x8p-16448L : 0x1p+0L : inexact-ok
+= cosh upward ldbl-96-m68k 0x8p-16448L : 0x1.0000000000000002p+0L : inexact-ok
+= cosh downward ldbl-128 0x8p-16448L : 0x1p+0L : inexact-ok
+= cosh tonearest ldbl-128 0x8p-16448L : 0x1p+0L : inexact-ok
+= cosh towardzero ldbl-128 0x8p-16448L : 0x1p+0L : inexact-ok
+= cosh upward ldbl-128 0x8p-16448L : 0x1.0000000000000000000000000001p+0L : inexact-ok
+= cosh downward ldbl-96-m68k 0x4p-16448L : 0x1p+0L : inexact-ok
+= cosh tonearest ldbl-96-m68k 0x4p-16448L : 0x1p+0L : inexact-ok
+= cosh towardzero ldbl-96-m68k 0x4p-16448L : 0x1p+0L : inexact-ok
+= cosh upward ldbl-96-m68k 0x4p-16448L : 0x1.0000000000000002p+0L : inexact-ok
+= cosh downward ldbl-128 0x4p-16448L : 0x1p+0L : inexact-ok
+= cosh tonearest ldbl-128 0x4p-16448L : 0x1p+0L : inexact-ok
+= cosh towardzero ldbl-128 0x4p-16448L : 0x1p+0L : inexact-ok
+= cosh upward ldbl-128 0x4p-16448L : 0x1.0000000000000000000000000001p+0L : inexact-ok
+= cosh downward ldbl-128 0x4p-16496L : 0x1p+0L : inexact-ok
+= cosh tonearest ldbl-128 0x4p-16496L : 0x1p+0L : inexact-ok
+= cosh towardzero ldbl-128 0x4p-16496L : 0x1p+0L : inexact-ok
+= cosh upward ldbl-128 0x4p-16496L : 0x1.0000000000000000000000000001p+0L : inexact-ok
+cosh -min_subnorm
+= cosh downward flt-32 -0x8p-152f : 0x1p+0f : inexact-ok
+= cosh tonearest flt-32 -0x8p-152f : 0x1p+0f : inexact-ok
+= cosh towardzero flt-32 -0x8p-152f : 0x1p+0f : inexact-ok
+= cosh upward flt-32 -0x8p-152f : 0x1.000002p+0f : inexact-ok
+= cosh downward dbl-64 -0x8p-152 : 0x1p+0 : inexact-ok
+= cosh tonearest dbl-64 -0x8p-152 : 0x1p+0 : inexact-ok
+= cosh towardzero dbl-64 -0x8p-152 : 0x1p+0 : inexact-ok
+= cosh upward dbl-64 -0x8p-152 : 0x1.0000000000001p+0 : inexact-ok
+= cosh downward ldbl-96-intel -0x8p-152L : 0x1p+0L : inexact-ok
+= cosh tonearest ldbl-96-intel -0x8p-152L : 0x1p+0L : inexact-ok
+= cosh towardzero ldbl-96-intel -0x8p-152L : 0x1p+0L : inexact-ok
+= cosh upward ldbl-96-intel -0x8p-152L : 0x1.0000000000000002p+0L : inexact-ok
+= cosh downward ldbl-96-m68k -0x8p-152L : 0x1p+0L : inexact-ok
+= cosh tonearest ldbl-96-m68k -0x8p-152L : 0x1p+0L : inexact-ok
+= cosh towardzero ldbl-96-m68k -0x8p-152L : 0x1p+0L : inexact-ok
+= cosh upward ldbl-96-m68k -0x8p-152L : 0x1.0000000000000002p+0L : inexact-ok
+= cosh downward ldbl-128 -0x8p-152L : 0x1p+0L : inexact-ok
+= cosh tonearest ldbl-128 -0x8p-152L : 0x1p+0L : inexact-ok
+= cosh towardzero ldbl-128 -0x8p-152L : 0x1p+0L : inexact-ok
+= cosh upward ldbl-128 -0x8p-152L : 0x1.0000000000000000000000000001p+0L : inexact-ok
+= cosh downward ldbl-128ibm -0x8p-152L : 0x1p+0L : inexact-ok
+= cosh tonearest ldbl-128ibm -0x8p-152L : 0x1p+0L : inexact-ok
+= cosh towardzero ldbl-128ibm -0x8p-152L : 0x1p+0L : inexact-ok
+= cosh upward ldbl-128ibm -0x8p-152L : 0x1.000000000000000000000000008p+0L : inexact-ok
+= cosh downward dbl-64 -0x4p-1076 : 0x1p+0 : inexact-ok
+= cosh tonearest dbl-64 -0x4p-1076 : 0x1p+0 : inexact-ok
+= cosh towardzero dbl-64 -0x4p-1076 : 0x1p+0 : inexact-ok
+= cosh upward dbl-64 -0x4p-1076 : 0x1.0000000000001p+0 : inexact-ok
+= cosh downward ldbl-96-intel -0x4p-1076L : 0x1p+0L : inexact-ok
+= cosh tonearest ldbl-96-intel -0x4p-1076L : 0x1p+0L : inexact-ok
+= cosh towardzero ldbl-96-intel -0x4p-1076L : 0x1p+0L : inexact-ok
+= cosh upward ldbl-96-intel -0x4p-1076L : 0x1.0000000000000002p+0L : inexact-ok
+= cosh downward ldbl-96-m68k -0x4p-1076L : 0x1p+0L : inexact-ok
+= cosh tonearest ldbl-96-m68k -0x4p-1076L : 0x1p+0L : inexact-ok
+= cosh towardzero ldbl-96-m68k -0x4p-1076L : 0x1p+0L : inexact-ok
+= cosh upward ldbl-96-m68k -0x4p-1076L : 0x1.0000000000000002p+0L : inexact-ok
+= cosh downward ldbl-128 -0x4p-1076L : 0x1p+0L : inexact-ok
+= cosh tonearest ldbl-128 -0x4p-1076L : 0x1p+0L : inexact-ok
+= cosh towardzero ldbl-128 -0x4p-1076L : 0x1p+0L : inexact-ok
+= cosh upward ldbl-128 -0x4p-1076L : 0x1.0000000000000000000000000001p+0L : inexact-ok
+= cosh downward ldbl-128ibm -0x4p-1076L : 0x1p+0L : inexact-ok
+= cosh tonearest ldbl-128ibm -0x4p-1076L : 0x1p+0L : inexact-ok
+= cosh towardzero ldbl-128ibm -0x4p-1076L : 0x1p+0L : inexact-ok
+= cosh upward ldbl-128ibm -0x4p-1076L : 0x1.000000000000000000000000008p+0L : inexact-ok
+= cosh downward ldbl-96-intel -0x8p-16448L : 0x1p+0L : inexact-ok
+= cosh tonearest ldbl-96-intel -0x8p-16448L : 0x1p+0L : inexact-ok
+= cosh towardzero ldbl-96-intel -0x8p-16448L : 0x1p+0L : inexact-ok
+= cosh upward ldbl-96-intel -0x8p-16448L : 0x1.0000000000000002p+0L : inexact-ok
+= cosh downward ldbl-96-m68k -0x8p-16448L : 0x1p+0L : inexact-ok
+= cosh tonearest ldbl-96-m68k -0x8p-16448L : 0x1p+0L : inexact-ok
+= cosh towardzero ldbl-96-m68k -0x8p-16448L : 0x1p+0L : inexact-ok
+= cosh upward ldbl-96-m68k -0x8p-16448L : 0x1.0000000000000002p+0L : inexact-ok
+= cosh downward ldbl-128 -0x8p-16448L : 0x1p+0L : inexact-ok
+= cosh tonearest ldbl-128 -0x8p-16448L : 0x1p+0L : inexact-ok
+= cosh towardzero ldbl-128 -0x8p-16448L : 0x1p+0L : inexact-ok
+= cosh upward ldbl-128 -0x8p-16448L : 0x1.0000000000000000000000000001p+0L : inexact-ok
+= cosh downward ldbl-96-m68k -0x4p-16448L : 0x1p+0L : inexact-ok
+= cosh tonearest ldbl-96-m68k -0x4p-16448L : 0x1p+0L : inexact-ok
+= cosh towardzero ldbl-96-m68k -0x4p-16448L : 0x1p+0L : inexact-ok
+= cosh upward ldbl-96-m68k -0x4p-16448L : 0x1.0000000000000002p+0L : inexact-ok
+= cosh downward ldbl-128 -0x4p-16448L : 0x1p+0L : inexact-ok
+= cosh tonearest ldbl-128 -0x4p-16448L : 0x1p+0L : inexact-ok
+= cosh towardzero ldbl-128 -0x4p-16448L : 0x1p+0L : inexact-ok
+= cosh upward ldbl-128 -0x4p-16448L : 0x1.0000000000000000000000000001p+0L : inexact-ok
+= cosh downward ldbl-128 -0x4p-16496L : 0x1p+0L : inexact-ok
+= cosh tonearest ldbl-128 -0x4p-16496L : 0x1p+0L : inexact-ok
+= cosh towardzero ldbl-128 -0x4p-16496L : 0x1p+0L : inexact-ok
+= cosh upward ldbl-128 -0x4p-16496L : 0x1.0000000000000000000000000001p+0L : inexact-ok
+cosh 0x1p-56
+= cosh downward flt-32 0x1p-56f : 0x1p+0f : inexact-ok
+= cosh tonearest flt-32 0x1p-56f : 0x1p+0f : inexact-ok
+= cosh towardzero flt-32 0x1p-56f : 0x1p+0f : inexact-ok
+= cosh upward flt-32 0x1p-56f : 0x1.000002p+0f : inexact-ok
+= cosh downward dbl-64 0x1p-56 : 0x1p+0 : inexact-ok
+= cosh tonearest dbl-64 0x1p-56 : 0x1p+0 : inexact-ok
+= cosh towardzero dbl-64 0x1p-56 : 0x1p+0 : inexact-ok
+= cosh upward dbl-64 0x1p-56 : 0x1.0000000000001p+0 : inexact-ok
+= cosh downward ldbl-96-intel 0x1p-56L : 0x1p+0L : inexact-ok
+= cosh tonearest ldbl-96-intel 0x1p-56L : 0x1p+0L : inexact-ok
+= cosh towardzero ldbl-96-intel 0x1p-56L : 0x1p+0L : inexact-ok
+= cosh upward ldbl-96-intel 0x1p-56L : 0x1.0000000000000002p+0L : inexact-ok
+= cosh downward ldbl-96-m68k 0x1p-56L : 0x1p+0L : inexact-ok
+= cosh tonearest ldbl-96-m68k 0x1p-56L : 0x1p+0L : inexact-ok
+= cosh towardzero ldbl-96-m68k 0x1p-56L : 0x1p+0L : inexact-ok
+= cosh upward ldbl-96-m68k 0x1p-56L : 0x1.0000000000000002p+0L : inexact-ok
+= cosh downward ldbl-128 0x1p-56L : 0x1p+0L : inexact-ok
+= cosh tonearest ldbl-128 0x1p-56L : 0x1.0000000000000000000000000001p+0L : inexact-ok
+= cosh towardzero ldbl-128 0x1p-56L : 0x1p+0L : inexact-ok
+= cosh upward ldbl-128 0x1p-56L : 0x1.0000000000000000000000000001p+0L : inexact-ok
+= cosh downward ldbl-128ibm 0x1p-56L : 0x1p+0L : inexact-ok
+= cosh tonearest ldbl-128ibm 0x1p-56L : 0x1p+0L : inexact-ok
+= cosh towardzero ldbl-128ibm 0x1p-56L : 0x1p+0L : inexact-ok
+= cosh upward ldbl-128ibm 0x1p-56L : 0x1.000000000000000000000000008p+0L : inexact-ok
+cosh -0x1p-56
+= cosh downward flt-32 -0x1p-56f : 0x1p+0f : inexact-ok
+= cosh tonearest flt-32 -0x1p-56f : 0x1p+0f : inexact-ok
+= cosh towardzero flt-32 -0x1p-56f : 0x1p+0f : inexact-ok
+= cosh upward flt-32 -0x1p-56f : 0x1.000002p+0f : inexact-ok
+= cosh downward dbl-64 -0x1p-56 : 0x1p+0 : inexact-ok
+= cosh tonearest dbl-64 -0x1p-56 : 0x1p+0 : inexact-ok
+= cosh towardzero dbl-64 -0x1p-56 : 0x1p+0 : inexact-ok
+= cosh upward dbl-64 -0x1p-56 : 0x1.0000000000001p+0 : inexact-ok
+= cosh downward ldbl-96-intel -0x1p-56L : 0x1p+0L : inexact-ok
+= cosh tonearest ldbl-96-intel -0x1p-56L : 0x1p+0L : inexact-ok
+= cosh towardzero ldbl-96-intel -0x1p-56L : 0x1p+0L : inexact-ok
+= cosh upward ldbl-96-intel -0x1p-56L : 0x1.0000000000000002p+0L : inexact-ok
+= cosh downward ldbl-96-m68k -0x1p-56L : 0x1p+0L : inexact-ok
+= cosh tonearest ldbl-96-m68k -0x1p-56L : 0x1p+0L : inexact-ok
+= cosh towardzero ldbl-96-m68k -0x1p-56L : 0x1p+0L : inexact-ok
+= cosh upward ldbl-96-m68k -0x1p-56L : 0x1.0000000000000002p+0L : inexact-ok
+= cosh downward ldbl-128 -0x1p-56L : 0x1p+0L : inexact-ok
+= cosh tonearest ldbl-128 -0x1p-56L : 0x1.0000000000000000000000000001p+0L : inexact-ok
+= cosh towardzero ldbl-128 -0x1p-56L : 0x1p+0L : inexact-ok
+= cosh upward ldbl-128 -0x1p-56L : 0x1.0000000000000000000000000001p+0L : inexact-ok
+= cosh downward ldbl-128ibm -0x1p-56L : 0x1p+0L : inexact-ok
+= cosh tonearest ldbl-128ibm -0x1p-56L : 0x1p+0L : inexact-ok
+= cosh towardzero ldbl-128ibm -0x1p-56L : 0x1p+0L : inexact-ok
+= cosh upward ldbl-128ibm -0x1p-56L : 0x1.000000000000000000000000008p+0L : inexact-ok
+cosh 0x1p-72
+= cosh downward flt-32 0x1p-72f : 0x1p+0f : inexact-ok
+= cosh tonearest flt-32 0x1p-72f : 0x1p+0f : inexact-ok
+= cosh towardzero flt-32 0x1p-72f : 0x1p+0f : inexact-ok
+= cosh upward flt-32 0x1p-72f : 0x1.000002p+0f : inexact-ok
+= cosh downward dbl-64 0x1p-72 : 0x1p+0 : inexact-ok
+= cosh tonearest dbl-64 0x1p-72 : 0x1p+0 : inexact-ok
+= cosh towardzero dbl-64 0x1p-72 : 0x1p+0 : inexact-ok
+= cosh upward dbl-64 0x1p-72 : 0x1.0000000000001p+0 : inexact-ok
+= cosh downward ldbl-96-intel 0x1p-72L : 0x1p+0L : inexact-ok
+= cosh tonearest ldbl-96-intel 0x1p-72L : 0x1p+0L : inexact-ok
+= cosh towardzero ldbl-96-intel 0x1p-72L : 0x1p+0L : inexact-ok
+= cosh upward ldbl-96-intel 0x1p-72L : 0x1.0000000000000002p+0L : inexact-ok
+= cosh downward ldbl-96-m68k 0x1p-72L : 0x1p+0L : inexact-ok
+= cosh tonearest ldbl-96-m68k 0x1p-72L : 0x1p+0L : inexact-ok
+= cosh towardzero ldbl-96-m68k 0x1p-72L : 0x1p+0L : inexact-ok
+= cosh upward ldbl-96-m68k 0x1p-72L : 0x1.0000000000000002p+0L : inexact-ok
+= cosh downward ldbl-128 0x1p-72L : 0x1p+0L : inexact-ok
+= cosh tonearest ldbl-128 0x1p-72L : 0x1p+0L : inexact-ok
+= cosh towardzero ldbl-128 0x1p-72L : 0x1p+0L : inexact-ok
+= cosh upward ldbl-128 0x1p-72L : 0x1.0000000000000000000000000001p+0L : inexact-ok
+= cosh downward ldbl-128ibm 0x1p-72L : 0x1p+0L : inexact-ok
+= cosh tonearest ldbl-128ibm 0x1p-72L : 0x1p+0L : inexact-ok
+= cosh towardzero ldbl-128ibm 0x1p-72L : 0x1p+0L : inexact-ok
+= cosh upward ldbl-128ibm 0x1p-72L : 0x1.000000000000000000000000008p+0L : inexact-ok
+cosh -0x1p-72
+= cosh downward flt-32 -0x1p-72f : 0x1p+0f : inexact-ok
+= cosh tonearest flt-32 -0x1p-72f : 0x1p+0f : inexact-ok
+= cosh towardzero flt-32 -0x1p-72f : 0x1p+0f : inexact-ok
+= cosh upward flt-32 -0x1p-72f : 0x1.000002p+0f : inexact-ok
+= cosh downward dbl-64 -0x1p-72 : 0x1p+0 : inexact-ok
+= cosh tonearest dbl-64 -0x1p-72 : 0x1p+0 : inexact-ok
+= cosh towardzero dbl-64 -0x1p-72 : 0x1p+0 : inexact-ok
+= cosh upward dbl-64 -0x1p-72 : 0x1.0000000000001p+0 : inexact-ok
+= cosh downward ldbl-96-intel -0x1p-72L : 0x1p+0L : inexact-ok
+= cosh tonearest ldbl-96-intel -0x1p-72L : 0x1p+0L : inexact-ok
+= cosh towardzero ldbl-96-intel -0x1p-72L : 0x1p+0L : inexact-ok
+= cosh upward ldbl-96-intel -0x1p-72L : 0x1.0000000000000002p+0L : inexact-ok
+= cosh downward ldbl-96-m68k -0x1p-72L : 0x1p+0L : inexact-ok
+= cosh tonearest ldbl-96-m68k -0x1p-72L : 0x1p+0L : inexact-ok
+= cosh towardzero ldbl-96-m68k -0x1p-72L : 0x1p+0L : inexact-ok
+= cosh upward ldbl-96-m68k -0x1p-72L : 0x1.0000000000000002p+0L : inexact-ok
+= cosh downward ldbl-128 -0x1p-72L : 0x1p+0L : inexact-ok
+= cosh tonearest ldbl-128 -0x1p-72L : 0x1p+0L : inexact-ok
+= cosh towardzero ldbl-128 -0x1p-72L : 0x1p+0L : inexact-ok
+= cosh upward ldbl-128 -0x1p-72L : 0x1.0000000000000000000000000001p+0L : inexact-ok
+= cosh downward ldbl-128ibm -0x1p-72L : 0x1p+0L : inexact-ok
+= cosh tonearest ldbl-128ibm -0x1p-72L : 0x1p+0L : inexact-ok
+= cosh towardzero ldbl-128ibm -0x1p-72L : 0x1p+0L : inexact-ok
+= cosh upward ldbl-128ibm -0x1p-72L : 0x1.000000000000000000000000008p+0L : inexact-ok
 cosh 0x5.96a7ep+4
 = cosh downward flt-32 0x5.96a7ep+4f : 0xf.fffecp+124f : inexact-ok
 = cosh tonearest flt-32 0x5.96a7ep+4f : 0xf.fffecp+124f : inexact-ok

diff --git a/sysdeps/i386/fpu/libm-test-ulps b/sysdeps/i386/fpu/libm-test-ulps
index 8d9c83d0caf7a867bbb51b4ed38335e0e3253713..7cf958608d6246101ce46685251cb2ffb40c4a6e 100644 (file)
--- a/sysdeps/i386/fpu/libm-test-ulps
+++ b/sysdeps/i386/fpu/libm-test-ulps
@@ -895,6 +895,7 @@ ldouble: 2
 
 Function: "cosh_upward":
 double: 1
+float: 1
 idouble: 1
 ifloat: 1
 ildouble: 2

diff --git a/sysdeps/ieee754/dbl-64/e_cosh.c b/sysdeps/ieee754/dbl-64/e_cosh.c
index 6caf943ed0d4840a7eaf026899ed1517b59d1fc4..af3910dd6ebdb6b64881c07c366c1121046a0c97 100644 (file)
--- a/sysdeps/ieee754/dbl-64/e_cosh.c
+++ b/sysdeps/ieee754/dbl-64/e_cosh.c
@@ -53,10 +53,10 @@ __ieee754_cosh (double x)
       /* |x| in [0,0.5*ln2], return 1+expm1(|x|)^2/(2*exp(|x|)) */
       if (ix < 0x3fd62e43)
        {
+         if (ix < 0x3c800000)
+           return one;                                   /* cosh(tiny) = 1 */
          t = __expm1 (fabs (x));
          w = one + t;
-         if (ix < 0x3c800000)
-           return w;                                   /* cosh(tiny) = 1 */
          return one + (t * t) / (w + w);
        }
 

diff --git a/sysdeps/ieee754/flt-32/e_coshf.c b/sysdeps/ieee754/flt-32/e_coshf.c
index 7eeea4d8dae7df9b5dd593f52f999b4036afaf9e..dedda47c093dfd0f107808607d1fe131da28ca71 100644 (file)
--- a/sysdeps/ieee754/flt-32/e_coshf.c
+++ b/sysdeps/ieee754/flt-32/e_coshf.c
@@ -33,9 +33,9 @@ __ieee754_coshf (float x)
        if (ix < 0x41b00000) {
            /* |x| in [0,0.5*ln2], return 1+expm1(|x|)^2/(2*exp(|x|)) */
                if(ix<0x3eb17218) {
+                   if (ix<0x24000000) return one;      /* cosh(tiny) = 1 */
                    t = __expm1f(fabsf(x));
                    w = one+t;
-                   if (ix<0x24000000) return w;        /* cosh(tiny) = 1 */
                    return one+(t*t)/(w+w);
                }
 

diff --git a/sysdeps/ieee754/ldbl-128/e_coshl.c b/sysdeps/ieee754/ldbl-128/e_coshl.c
index 59f2030d544ff5654cd36b62bb539f8410d6e98a..488c318d2781baae8c44ec9681c2c25bf175102b 100644 (file)
--- a/sysdeps/ieee754/ldbl-128/e_coshl.c
+++ b/sysdeps/ieee754/ldbl-128/e_coshl.c
@@ -77,10 +77,10 @@ __ieee754_coshl (long double x)
   /* |x| in [0,0.5*ln2], return 1+expm1l(|x|)^2/(2*expl(|x|)) */
   if (ex < 0x3ffd62e4) /* 0.3465728759765625 */
     {
+      if (ex < 0x3fb80000) /* |x| < 2^-116 */
+       return one;             /* cosh(tiny) = 1 */
       t = __expm1l (u.value);
       w = one + t;
-      if (ex < 0x3fb80000) /* |x| < 2^-116 */
-       return w;               /* cosh(tiny) = 1 */
 
       return one + (t * t) / (w + w);
     }

diff --git a/sysdeps/ieee754/ldbl-128ibm/e_coshl.c b/sysdeps/ieee754/ldbl-128ibm/e_coshl.c
index 92313e25e236b1d5a5445b9f4d9d87e8719ccfe6..327b2ab9600028f6c22b45e86440a7104d8964b0 100644 (file)
--- a/sysdeps/ieee754/ldbl-128ibm/e_coshl.c
+++ b/sysdeps/ieee754/ldbl-128ibm/e_coshl.c
@@ -53,9 +53,9 @@ __ieee754_coshl (long double x)
 
     /* |x| in [0,0.5*ln2], return 1+expm1(|x|)^2/(2*exp(|x|)) */
        if(ix<0x3fd62e42fefa39efLL) {
+           if (ix<0x3c80000000000000LL) return one;    /* cosh(tiny) = 1 */
            t = __expm1l(fabsl(x));
            w = one+t;
-           if (ix<0x3c80000000000000LL) return w;      /* cosh(tiny) = 1 */
            return one+(t*t)/(w+w);
        }
 

diff --git a/sysdeps/ieee754/ldbl-96/e_coshl.c b/sysdeps/ieee754/ldbl-96/e_coshl.c
index 995c9922cbfc87083fb98e751d0422e506881a6f..dd22cae36379aaec1b540fac36e0f951a038aad8 100644 (file)
--- a/sysdeps/ieee754/ldbl-96/e_coshl.c
+++ b/sysdeps/ieee754/ldbl-96/e_coshl.c
@@ -54,9 +54,9 @@ __ieee754_coshl (long double x)
        if (ex < 0x4003 || (ex == 0x4003 && mx < 0xb0000000u)) {
            /* |x| in [0,0.5*ln2], return 1+expm1l(|x|)^2/(2*expl(|x|)) */
                if(ex < 0x3ffd || (ex == 0x3ffd && mx < 0xb17217f7u)) {
+                   if (ex<0x3fbc) return one;  /* cosh(tiny) = 1 */
                    t = __expm1l(fabsl(x));
                    w = one+t;
-                   if (ex<0x3fbc) return w;    /* cosh(tiny) = 1 */
                    return one+(t*t)/(w+w);
                }