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Fix ldbl-128 lgammal for small negative arguments (bug 16337)

This patch fixes bug 16337, ldbl-128 lgammal spurious overflows for
small negative arguments (the arguments in question are already in the
testsuite).  The implementation uses the reflection formula to compute
lgamma of negative x from lgamma of -x, effectively resulting in a
calculation -log(x^2) + log(-x); cancellation isn't problematic in
this case (bugs for problematic cancellation in lgamma are 2542, 2543,
2558), but the x^2 calculation can underflow (in which case there is
spurious logic to return an overflowing value - lgamma can only ever
correctly overflow for large positive arguments, though tgamma can
overflow for small arguments of either sign as well as large positive
arguments).  The fix is simply to calculate the result directly with
logl when the argument is a small enough negative number.

Tested mips64.

2013-12-22  Joseph Myers  <>

	[BZ #16337]
	* sysdeps/ieee754/ldbl-128/e_lgammal_r.c (__ieee754_lgammal_r):
	Calculate results for small negative arguments directly rather
	than using reflection formula with special underflow handling.

diff --git a/sysdeps/ieee754/ldbl-128/e_lgammal_r.c b/sysdeps/ieee754/ldbl-128/e_lgammal_r.c
index 2b44afb..23ab9b9 100644
--- a/sysdeps/ieee754/ldbl-128/e_lgammal_r.c
+++ b/sysdeps/ieee754/ldbl-128/e_lgammal_r.c
@@ -782,6 +782,8 @@ __ieee754_lgammal_r (long double x, int *signgamp)
 	*signgamp = -1;
 	*signgamp = 1;
+      if (q < 0x1p-120L)
+	return -__logl (q);
       z = q - p;
       if (z > 0.5L)
@@ -789,8 +791,6 @@ __ieee754_lgammal_r (long double x, int *signgamp)
 	  z = p - q;
       z = q * __sinl (PIL * z);
-      if (z == 0.0L)
-	return (*signgamp * huge * huge);
       w = __ieee754_lgammal_r (q, &i);
       z = __logl (PIL / z) - w;
       return (z);

Joseph S. Myers

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