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Fix ldbl-128ibm expm1l on large arguments (bug 16408)

This patch fixes bug 16408, ldbl-128ibm expm1l returning NaN for some
large arguments.

The basic problem is that the approach of converting the exponent to
the form n * log(2) + y, where -0.5 <= y <= 0.5, then computing 2^n *
expm1(y) + (2^n - 1) falls over when 2^n overflows (starting slightly
before the point where expm1 overflows, when y is negative and n is
the least integer for which 2^n overflows).  The ldbl-128 code, and
the x86/x86_64 code, make expm1l fall back to expl for large positive
arguments to avoid this issue.  This patch makes the ldbl-128ibm code
do the same.  (The problem appears for the particular argument in the
testsuite because the ldbl-128ibm code also uses an overflow threshold
that's for ldbl-128 and is too big for ldbl-128ibm, but the problem
described applies for large non-overflowing cases as well, although
during the freeze is not a suitable time for making the expm1 tests
cover cases close to overflow more thoroughly.)

This leaves some code for large positive arguments in expm1l that is
now dead.  To keep the code for ldbl-128 and ldbl-128ibm similar, and
to avoid unnecessary changes during the freeze, the patch doesn't
remove it; instead I propose to file a bug in Bugzilla as a reminder
that this code (for overflow, including errno setting, and for
arguments of +Inf) is no longer needed and should be removed from both
those expm1l implementations.

Tested powerpc32.

2014-01-07  Joseph Myers  <>

	[BZ #16408]
	* sysdeps/ieee754/ldbl-128ibm/s_expm1l.c (__expm1l): Use __expl
	for large positive arguments.

diff --git a/sysdeps/ieee754/ldbl-128ibm/s_expm1l.c b/sysdeps/ieee754/ldbl-128ibm/s_expm1l.c
index 007e785..0464f79 100644
--- a/sysdeps/ieee754/ldbl-128ibm/s_expm1l.c
+++ b/sysdeps/ieee754/ldbl-128ibm/s_expm1l.c
@@ -101,6 +101,8 @@ __expm1l (long double x)
   EXTRACT_WORDS (ix, lx, xhi);
   sign = ix & 0x80000000;
   ix &= 0x7fffffff;
+  if (!sign && ix >= 0x40600000)
+    return __expl (x);
   if (ix >= 0x7ff00000)
       /* Infinity. */

Joseph S. Myers

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