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Fix ldbl-128 erfl spurious underflows (bug 16287)

This patch fixes bug 16287, spurious underflows from ldbl-128 erfl
arising from it calling erfcl for arguments with absolute value at
least 1.0, although for large positive arguments erfcl correctly
underflows but erfl shouldn't.  The fix is simply to avoid calling
erfcl, and just return 1, for arguments above a cut-off large enough
that erfl correctly rounds to-nearest as 1 but not so large that erfcl

Tested mips64.  Also tested x86_64 and x86 to confirm the new tests
(taken from the tests of erfc) don't cause any problems there; no ulps
updates needed.

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

2014-06-24  Joseph Myers  <>

	[BZ #16287]
	* sysdeps/ieee754/ldbl-128/s_erfl.c (__erfl): Return 1 without
	calling __erfcl for arguments at least 16.
	* math/auto-libm-test-in: Add more tests of erf.
	* math/auto-libm-test-out: Regenerated.

diff --git a/math/auto-libm-test-in b/math/auto-libm-test-in
index 4eaa013..79d276c 100644
--- a/math/auto-libm-test-in
+++ b/math/auto-libm-test-in
@@ -803,6 +803,16 @@ erf 0x1.c5bf94p-127
 erf 0x3.8b7fa8p-128
 erf -0x3.8b7f12369ded8p-1024
 erf 0x3.8b7f12369ded5518p-16384
+erf 26.0
+erf 28.0
+erf 100
+erf 106
+erf 106.5
+erf 106.625
+erf 107
+erf 108
+erf 1000
+erf max
 erfc 0.0
 erfc -0
diff --git a/sysdeps/ieee754/ldbl-128/s_erfl.c b/sysdeps/ieee754/ldbl-128/s_erfl.c
index 35ca8c1..f44d481 100644
--- a/sysdeps/ieee754/ldbl-128/s_erfl.c
+++ b/sysdeps/ieee754/ldbl-128/s_erfl.c
@@ -769,6 +769,8 @@ __erfl (long double x)
   if (ix >= 0x3fff0000) /* |x| >= 1.0 */
+      if (ix >= 0x40030000 && sign > 0)
+	return one;
       y = __erfcl (x);
       return (one - y);
       /*    return (one - __erfcl (x)); */

Joseph S. Myers

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