diff --git a/ChangeLog b/ChangeLog
index ea038f764f..958b4a3a9d 100644
--- a/ChangeLog
+++ b/ChangeLog
@@ -1,5 +1,11 @@
 2015-09-30  Joseph Myers  <joseph@codesourcery.com>
 
+	[BZ #19032]
+	* sysdeps/i386/fpu/e_acosh.S (__ieee754_acosh): For arguments < 1,
+	compute result as (x - x) / (x - x) not as 0 / 0.
+	* sysdeps/i386/fpu/e_acoshf.S (__ieee754_acoshf): Likewise.
+	* math/libm-test.inc (acosh_test_data): Add another test of acosh.
+
 	* math/auto-libm-test-in: Add more tests of acos, acosh, asin,
 	atan, atan2, atanh, cbrt, cos, cosh, erf, erfc, exp, exp10, exp2
 	and expm1.
diff --git a/NEWS b/NEWS
index ea64dc7c40..e7e11bf987 100644
--- a/NEWS
+++ b/NEWS
@@ -17,7 +17,7 @@ Version 2.23
   18789, 18790, 18795, 18796, 18803, 18820, 18823, 18824, 18825, 18857,
   18863, 18870, 18872, 18873, 18875, 18887, 18921, 18951, 18952, 18956,
   18961, 18966, 18967, 18969, 18970, 18977, 18980, 18981, 18985, 19003,
-  19016.
+  19016, 19032.
 
 * The obsolete header <regexp.h> has been removed.  Programs that require
   this header must be updated to use <regex.h> instead.
diff --git a/math/libm-test.inc b/math/libm-test.inc
index 744c66dbb1..8615957600 100644
--- a/math/libm-test.inc
+++ b/math/libm-test.inc
@@ -1790,6 +1790,7 @@ static const struct test_f_f_data acosh_test_data[] =
     TEST_f_f (acosh, plus_infty, plus_infty, ERRNO_UNCHANGED),
     TEST_f_f (acosh, minus_infty, qnan_value, INVALID_EXCEPTION|ERRNO_EDOM),
     TEST_f_f (acosh, qnan_value, qnan_value, NO_INEXACT_EXCEPTION|ERRNO_UNCHANGED),
+    TEST_f_f (acosh, -qnan_value, qnan_value, NO_INEXACT_EXCEPTION|ERRNO_UNCHANGED),
 
     /* x < 1:  */
     TEST_f_f (acosh, 0.75L, qnan_value, INVALID_EXCEPTION|ERRNO_EDOM),
diff --git a/sysdeps/i386/fpu/e_acosh.S b/sysdeps/i386/fpu/e_acosh.S
index c5cd4474ec..263c01a4ed 100644
--- a/sysdeps/i386/fpu/e_acosh.S
+++ b/sysdeps/i386/fpu/e_acosh.S
@@ -91,9 +91,10 @@ ENTRY(__ieee754_acosh)
 	fyl2x				// log(2*x+1/(x+sqrt(x^2-1)))
 	ret
 
-	// x < 1 => NaN
+	// x < 1 (or -NaN) => NaN
 	.align ALIGNARG(4)
-5:	fldz
+5:	fldl	4(%esp)
+	fsub	%st
 	fdiv	%st, %st(0)
 	ret
 END(__ieee754_acosh)
diff --git a/sysdeps/i386/fpu/e_acoshf.S b/sysdeps/i386/fpu/e_acoshf.S
index 710267b11e..779a02cfab 100644
--- a/sysdeps/i386/fpu/e_acoshf.S
+++ b/sysdeps/i386/fpu/e_acoshf.S
@@ -91,9 +91,10 @@ ENTRY(__ieee754_acoshf)
 	fyl2x				// log(2*x+1/(x+sqrt(x^2-1)))
 	ret
 
-	// x < 1 => NaN
+	// x < 1 (or -NaN) => NaN
 	.align ALIGNARG(4)
-5:	fldz
+5:	flds	4(%esp)
+	fsub	%st
 	fdiv	%st, %st(0)
 	ret
 END(__ieee754_acoshf)