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Fix ldbl-128ibm acoshl inaccuracy (bug 16384)


This patch fixes bug 16384, ldbl-128ibm acoshl inaccuracy, which
showed up while attempting to regenerate ulps for powerpc-nofpu for
2.19.  There were two separate problems, use of __log1p instead of
__log1pl and an insufficiently accurate constant value for log 2
(which this patch replaces by use of M_LN2l), each of which could
cause substantial inaccuracy in affected cases.

Tested for powerpc-nofpu.

(Note that ulps regeneration for powerpc is still a pain because of
libgcc bugs, especially the one discussed in glibc bug 15396 that
causes large inaccuracy for division involving subnormal numbers.)

2014-01-01  Joseph Myers  <joseph@codesourcery.com>

	[BZ #16384]
	* sysdeps/ieee754/ldbl-128ibm/e_acoshl.c (ln2): Initialize with
	M_LN2l.
	(__ieee754_acoshl): Use __log1pl not __log1p.

diff --git a/sysdeps/ieee754/ldbl-128ibm/e_acoshl.c b/sysdeps/ieee754/ldbl-128ibm/e_acoshl.c
index 8a4a5bb..b0b33f7 100644
--- a/sysdeps/ieee754/ldbl-128ibm/e_acoshl.c
+++ b/sysdeps/ieee754/ldbl-128ibm/e_acoshl.c
@@ -29,7 +29,7 @@
 
 static const long double
 one	= 1.0L,
-ln2	= 6.93147180559945286227e-01L;  /* 0x3FE62E42, 0xFEFA39EF */
+ln2	= M_LN2l;
 
 long double
 __ieee754_acoshl(long double x)
@@ -56,7 +56,7 @@ __ieee754_acoshl(long double x)
 	    return __ieee754_logl(2.0*x-one/(x+__ieee754_sqrtl(t-one)));
 	} else {			/* 1<x<2 */
 	    t = x-one;
-	    return __log1p(t+__ieee754_sqrtl(2.0*t+t*t));
+	    return __log1pl(t+__ieee754_sqrtl(2.0*t+t*t));
 	}
 }
 strong_alias (__ieee754_acoshl, __acoshl_finite)

-- 
Joseph S. Myers
joseph@codesourcery.com


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