Fix x86/x86_64 expm1l spurious underflow exceptions (bug 16539).

This patch fixes bug 16539, spurious underflow exceptions from x86 /
x86-64 expm1l.  The problem is that the computation of a base-2
exponent with extra precision involves spurious underflows for
arguments that are small but not subnormal, so a check is added to
just return the argument in those cases.  (If the argument *is*
subnormal, underflowing is correct and the existing code will always
underflow, so it suffices to keep using the existing code in that
case; some expm1 implementations have a bug (bug 16353) with missing
underflow exceptions, but I don't think there's such a bug in this
particular version.)

Tested x86_64 and x86; no ulps updates needed.

(auto-libm-test-out diffs omitted below.)

	[BZ #16539]
	* sysdeps/i386/fpu/e_expl.S (IEEE754_EXPL) [USE_AS_EXPM1L]: Just
	return the argument for normal arguments with exponent below -64.
	* sysdeps/x86_64/fpu/e_expl.S (IEEE754_EXPL) [USE_AS_EXPM1L]:
	Likewise.
	* math/auto-libm-test-in: Add another test of expm1.
	* math/auto-libm-test-out: Regenerated.

6 files changed, 122 insertions, 11 deletions

diff --git a/ChangeLog b/ChangeLog
index 8ddb74fff6..ce6c4d8f24 100644
--- a/ChangeLog
+++ b/ChangeLog
@@ -1,5 +1,13 @@
 2014-06-24  Joseph Myers  <joseph@codesourcery.com>
 
+	[BZ #16539]
+	* sysdeps/i386/fpu/e_expl.S (IEEE754_EXPL) [USE_AS_EXPM1L]: Just
+	return the argument for normal arguments with exponent below -64.
+	* sysdeps/x86_64/fpu/e_expl.S (IEEE754_EXPL) [USE_AS_EXPM1L]:
+	Likewise.
+	* math/auto-libm-test-in: Add another test of expm1.
+	* math/auto-libm-test-out: Regenerated.
+
 	[BZ #16287]
 	* sysdeps/ieee754/ldbl-128/s_erfl.c (__erfl): Return 1 without
 	calling __erfcl for arguments at least 16.
diff --git a/NEWS b/NEWS
index e365acd915..66e363e384 100644
--- a/NEWS
+++ b/NEWS
@@ -11,17 +11,17 @@ Version 2.20
 
   6804, 9894, 12994, 13347, 13651, 14308, 14770, 15119, 15132, 15347, 15514,
   15698, 15804, 15894, 15946, 16002, 16064, 16095, 16198, 16284, 16287,
-  16315, 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, 16918, 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, 17084.
+  16315, 16348, 16349, 16354, 16357, 16362, 16447, 16516, 16532, 16539,
+  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, 16918, 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, 17084.
 
 * Optimized strchr implementation for AArch64.  Contributed by ARM Ltd.
 
diff --git a/math/auto-libm-test-in b/math/auto-libm-test-in
index 79d276ce99..f36d200df5 100644
--- a/math/auto-libm-test-in
+++ b/math/auto-libm-test-in
@@ -970,6 +970,8 @@ expm1 0x1p-64
 expm1 -0x1p-64
 expm1 0x1p-100
 expm1 -0x1p-100
+# Bug 16353: underflow exception may be missing
+expm1 0x4.0000000000000028p-16384 missing-underflow
 
 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 d1ec2be279..ced5283ab2 100644
--- a/math/auto-libm-test-out
+++ b/math/auto-libm-test-out
@@ -93045,6 +93045,87 @@ expm1 -0x1p-100
 = expm1 tonearest ldbl-128ibm -0x1p-100L : -0xf.ffffffffffffffffffffffff8p-104L : inexact-ok
 = expm1 towardzero ldbl-128ibm -0x1p-100L : -0xf.ffffffffffffffffffffffff8p-104L : inexact-ok
 = expm1 upward ldbl-128ibm -0x1p-100L : -0xf.ffffffffffffffffffffffff8p-104L : 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 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
+= expm1 upward dbl-64 0x8p-152 : 0x8.0000000000008p-152 : inexact-ok
+= expm1 downward ldbl-96-intel 0x8p-152L : 0x8p-152L : inexact-ok
+= expm1 tonearest ldbl-96-intel 0x8p-152L : 0x8p-152L : inexact-ok
+= expm1 towardzero ldbl-96-intel 0x8p-152L : 0x8p-152L : inexact-ok
+= expm1 upward ldbl-96-intel 0x8p-152L : 0x8.000000000000001p-152L : inexact-ok
+= expm1 downward ldbl-96-m68k 0x8p-152L : 0x8p-152L : inexact-ok
+= expm1 tonearest ldbl-96-m68k 0x8p-152L : 0x8p-152L : inexact-ok
+= expm1 towardzero ldbl-96-m68k 0x8p-152L : 0x8p-152L : inexact-ok
+= expm1 upward ldbl-96-m68k 0x8p-152L : 0x8.000000000000001p-152L : inexact-ok
+= expm1 downward ldbl-128 0x8p-152L : 0x8p-152L : inexact-ok
+= expm1 tonearest ldbl-128 0x8p-152L : 0x8p-152L : inexact-ok
+= expm1 towardzero ldbl-128 0x8p-152L : 0x8p-152L : inexact-ok
+= expm1 upward ldbl-128 0x8p-152L : 0x8.0000000000000000000000000008p-152L : inexact-ok
+= expm1 downward ldbl-128ibm 0x8p-152L : 0x8p-152L : inexact-ok
+= 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 flt-32 0x0p+0f : 0x0p+0f : inexact-ok
+= expm1 tonearest flt-32 0x0p+0f : 0x0p+0f : inexact-ok
+= expm1 towardzero flt-32 0x0p+0f : 0x0p+0f : inexact-ok
+= expm1 upward flt-32 0x0p+0f : 0x0p+0f : inexact-ok
+= expm1 downward dbl-64 0x0p+0 : 0x0p+0 : inexact-ok
+= expm1 tonearest dbl-64 0x0p+0 : 0x0p+0 : inexact-ok
+= expm1 towardzero dbl-64 0x0p+0 : 0x0p+0 : inexact-ok
+= expm1 upward dbl-64 0x0p+0 : 0x0p+0 : inexact-ok
+= expm1 downward ldbl-96-intel 0x0p+0L : 0x0p+0L : inexact-ok
+= expm1 tonearest ldbl-96-intel 0x0p+0L : 0x0p+0L : inexact-ok
+= expm1 towardzero ldbl-96-intel 0x0p+0L : 0x0p+0L : inexact-ok
+= expm1 upward ldbl-96-intel 0x0p+0L : 0x0p+0L : inexact-ok
+= expm1 downward ldbl-96-m68k 0x0p+0L : 0x0p+0L : inexact-ok
+= expm1 tonearest ldbl-96-m68k 0x0p+0L : 0x0p+0L : inexact-ok
+= expm1 towardzero ldbl-96-m68k 0x0p+0L : 0x0p+0L : inexact-ok
+= expm1 upward ldbl-96-m68k 0x0p+0L : 0x0p+0L : inexact-ok
+= expm1 downward ldbl-128 0x0p+0L : 0x0p+0L : inexact-ok
+= expm1 tonearest ldbl-128 0x0p+0L : 0x0p+0L : inexact-ok
+= expm1 towardzero ldbl-128 0x0p+0L : 0x0p+0L : inexact-ok
+= expm1 upward ldbl-128 0x0p+0L : 0x0p+0L : inexact-ok
+= expm1 downward ldbl-128ibm 0x0p+0L : 0x0p+0L : inexact-ok
+= 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 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
+= expm1 upward ldbl-96-intel 0x4p-1076L : 0x4.0000000000000008p-1076L : inexact-ok
+= expm1 downward ldbl-96-m68k 0x4p-1076L : 0x4p-1076L : inexact-ok
+= expm1 tonearest ldbl-96-m68k 0x4p-1076L : 0x4p-1076L : inexact-ok
+= expm1 towardzero ldbl-96-m68k 0x4p-1076L : 0x4p-1076L : inexact-ok
+= expm1 upward ldbl-96-m68k 0x4p-1076L : 0x4.0000000000000008p-1076L : inexact-ok
+= expm1 downward ldbl-128 0x4p-1076L : 0x4p-1076L : inexact-ok
+= 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 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
+= expm1 upward ldbl-96-intel 0x4.0000000000000028p-16384L : 0x4.000000000000003p-16384L : inexact-ok
+= expm1 downward ldbl-96-m68k 0x4.0000000000000028p-16384L : 0x4.0000000000000028p-16384L : inexact-ok
+= expm1 tonearest ldbl-96-m68k 0x4.0000000000000028p-16384L : 0x4.0000000000000028p-16384L : inexact-ok
+= expm1 towardzero ldbl-96-m68k 0x4.0000000000000028p-16384L : 0x4.0000000000000028p-16384L : inexact-ok
+= expm1 upward ldbl-96-m68k 0x4.0000000000000028p-16384L : 0x4.000000000000003p-16384L : inexact-ok
+= expm1 downward ldbl-128 0x4.0000000000000028p-16384L : 0x4.0000000000000028p-16384L : inexact-ok
+= 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
 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 :
diff --git a/sysdeps/i386/fpu/e_expl.S b/sysdeps/i386/fpu/e_expl.S
index eb4086b3f5..c7e43732dc 100644
--- a/sysdeps/i386/fpu/e_expl.S
+++ b/sysdeps/i386/fpu/e_expl.S
@@ -108,6 +108,16 @@ ENTRY(IEEE754_EXPL)
 	andb	%ah, %dh
 	cmpb	$0x40, %dh
 	je	2f
+
+	/* Test for arguments that are small but not subnormal.  */
+	movzwl	4+8(%esp), %eax
+	andl	$0x7fff, %eax
+	cmpl	$0x3fbf, %eax
+	jge	3f
+	/* Argument's exponent below -64; avoid spurious underflow if
+	   normal.  */
+	cmpl	$0x0001, %eax
+	jge	2f
 #else
 	movzwl	4+8(%esp), %eax
 	andl	$0x7fff, %eax
diff --git a/sysdeps/x86_64/fpu/e_expl.S b/sysdeps/x86_64/fpu/e_expl.S
index 338527b3de..0ebe3882a5 100644
--- a/sysdeps/x86_64/fpu/e_expl.S
+++ b/sysdeps/x86_64/fpu/e_expl.S
@@ -105,6 +105,16 @@ ENTRY(IEEE754_EXPL)
 	andb	%ah, %dh
 	cmpb	$0x40, %dh
 	je	2f
+
+	/* Test for arguments that are small but not subnormal.  */
+	movzwl	8+8(%rsp), %eax
+	andl	$0x7fff, %eax
+	cmpl	$0x3fbf, %eax
+	jge	3f
+	/* Argument's exponent below -64; avoid spurious underflow if
+	   normal.  */
+	cmpl	$0x0001, %eax
+	jge	2f
 #else
 	movzwl	8+8(%rsp), %eax
 	andl	$0x7fff, %eax