diff --git a/ChangeLog b/ChangeLog
index 9cd1d707d4..23487d7e42 100644
--- a/ChangeLog
+++ b/ChangeLog
@@ -1,3 +1,10 @@
+2016-03-10  Joseph Myers  <joseph@codesourcery.com>
+
+	* manual/math.texi (Errors in Math Functions): Document relaxed
+	accuracy goals for IBM long double.
+	* math/libm-test.inc (test_exceptions): Always allow spurious
+	"underflow" and "inexact" exceptions for IBM long double.
+
 2016-03-10  H.J. Lu  <hongjiu.lu@intel.com>
 
 	[BZ #19762]
diff --git a/manual/math.texi b/manual/math.texi
index 72f3fda0a3..5c9f7b9f1c 100644
--- a/manual/math.texi
+++ b/manual/math.texi
@@ -1326,6 +1326,16 @@ interpreted in terms of a fixed-precision 106-bit mantissa, but not
 necessarily the exact value actually passed with discontiguous
 mantissa bits.
 
+@item
+For the IBM @code{long double} format, functions whose results are
+fully specified by reference to corresponding IEEE 754 floating-point
+operations have the same accuracy goals as other functions, but with
+the error bound being the same as that for division (3ulp).
+Furthermore, ``inexact'' and ``underflow'' exceptions may be raised
+for all functions for any inputs, even where such exceptions are
+inconsistent with the returned value, since the underlying
+floating-point arithmetic has that property.
+
 @item
 Functions behave as if the infinite-precision result computed is zero,
 infinity or NaN if and only if that is the mathematically correct
diff --git a/math/libm-test.inc b/math/libm-test.inc
index c9925fddb7..f1ba7dda99 100644
--- a/math/libm-test.inc
+++ b/math/libm-test.inc
@@ -672,13 +672,20 @@ test_exceptions (const char *test_name, int exception)
 	test_single_exception (test_name, exception, OVERFLOW_EXCEPTION,
 			       FE_OVERFLOW, "Overflow");
 #endif
+      /* Spurious "underflow" and "inexact" exceptions are always
+	 allowed for IBM long double, in line with the underlying
+	 arithmetic.  */
 #ifdef FE_UNDERFLOW
-      if ((exception & UNDERFLOW_EXCEPTION_OK) == 0)
+      if ((exception & UNDERFLOW_EXCEPTION_OK) == 0
+	  && !(TEST_COND_ldbl_128ibm
+	       && (exception & UNDERFLOW_EXCEPTION) == 0))
 	test_single_exception (test_name, exception, UNDERFLOW_EXCEPTION,
 			       FE_UNDERFLOW, "Underflow");
 #endif
 #ifdef FE_INEXACT
-      if ((exception & (INEXACT_EXCEPTION | NO_INEXACT_EXCEPTION)) != 0)
+      if ((exception & (INEXACT_EXCEPTION | NO_INEXACT_EXCEPTION)) != 0
+	  && !(TEST_COND_ldbl_128ibm
+	       && (exception & NO_INEXACT_EXCEPTION) != 0))
 	test_single_exception (test_name, exception, INEXACT_EXCEPTION,
 			       FE_INEXACT, "Inexact");
 #endif