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Fix ldbl-128ibm tanhl inaccuracy for small arguments (bug 19349) [committed]

The ldbl-128ibm implementation of tanhl is inaccurate for small
arguments, because it returns x*(1+x) (maybe in an attempt to raise
"inexact") when x itself would be the accurate return value but
multiplying by 1+x introduces large errors.  This patch fixes it to
return x in that case (when the mathematical result is x plus a
negligible remainder on the order of x^3) to avoid those errors.

Tested for powerpc.  Committed.

2015-12-09  Joseph Myers  <>

	[BZ #19349]
	* sysdeps/ieee754/ldbl-128ibm/s_tanhl.c (__tanhl): Return argument
	when small.

diff --git a/sysdeps/ieee754/ldbl-128ibm/s_tanhl.c b/sysdeps/ieee754/ldbl-128ibm/s_tanhl.c
index 292020c..e6457a1 100644
--- a/sysdeps/ieee754/ldbl-128ibm/s_tanhl.c
+++ b/sysdeps/ieee754/ldbl-128ibm/s_tanhl.c
@@ -69,7 +69,7 @@ long double __tanhl(long double x)
 	    if (ix<0x3c60000000000000LL) 	/* |x|<2**-57 */
 		math_check_force_underflow (x);
-		return x*(one+x);    	/* tanh(small) = small */
+		return x;		/* tanh(small) = small */
 	    if (ix>=0x3ff0000000000000LL) {	/* |x|>=1  */
 		t = __expm1l(two*fabsl(x));

Joseph S. Myers

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