diff --git a/ChangeLog b/ChangeLog
index 70771d634a..577304273e 100644
--- a/ChangeLog
+++ b/ChangeLog
@@ -1,5 +1,13 @@
 2013-08-20  Joseph Myers  <joseph@codesourcery.com>
 
+	[BZ #15531]
+	* math/s_cproj.c (__cproj): Only return an infinity if one part of
+	argument is infinite.
+	* math/s_cprojf.c (__cprojf): Likewise.
+	* math/s_cprojl.c (__cprojl): Likewise.
+	* sysdeps/ieee754/ldbl-128ibm/s_cprojl.c (__cprojl): Likewise.
+	* math/libm-test.inc (cproj_test_data): Add more tests.
+
 	* sysdeps/unix/sysv/linux/mmap64.c: Include <string.h>.
 
 	* sysdeps/unix/sysv/linux/mmap64.c (__mmap64)
diff --git a/NEWS b/NEWS
index 9f44db061e..4b79c3dc7b 100644
--- a/NEWS
+++ b/NEWS
@@ -9,7 +9,7 @@ Version 2.19
 
 * The following bugs are resolved with this release:
 
-  14699, 15749
+  14699, 15531, 15749
 
 * CVE-2013-4237 The readdir_r function could write more than NAME_MAX bytes
   to the d_name member of struct dirent, or omit the terminating NUL
diff --git a/math/libm-test.inc b/math/libm-test.inc
index 851f1beafc..25ea33603c 100644
--- a/math/libm-test.inc
+++ b/math/libm-test.inc
@@ -7066,11 +7066,51 @@ static const struct test_c_c_data cproj_test_data[] =
 
     TEST_c_c (cproj, qnan_value, qnan_value, qnan_value, qnan_value, NO_INEXACT_EXCEPTION),
 
+    TEST_c_c (cproj, plus_zero, qnan_value, plus_zero, qnan_value, NO_INEXACT_EXCEPTION),
+    TEST_c_c (cproj, minus_zero, qnan_value, minus_zero, qnan_value, NO_INEXACT_EXCEPTION),
+    TEST_c_c (cproj, qnan_value, plus_zero, qnan_value, plus_zero, NO_INEXACT_EXCEPTION),
+    TEST_c_c (cproj, qnan_value, minus_zero, qnan_value, minus_zero, NO_INEXACT_EXCEPTION),
+
+    TEST_c_c (cproj, 1.0, qnan_value, 1.0, qnan_value, NO_INEXACT_EXCEPTION),
+    TEST_c_c (cproj, -1.0, qnan_value, -1.0, qnan_value, NO_INEXACT_EXCEPTION),
+    TEST_c_c (cproj, qnan_value, 1.0, qnan_value, 1.0, NO_INEXACT_EXCEPTION),
+    TEST_c_c (cproj, qnan_value, -1.0, qnan_value, -1.0, NO_INEXACT_EXCEPTION),
+
     TEST_c_c (cproj, plus_infty, plus_infty, plus_infty, 0.0, NO_INEXACT_EXCEPTION),
     TEST_c_c (cproj, plus_infty, minus_infty, plus_infty, minus_zero, NO_INEXACT_EXCEPTION),
     TEST_c_c (cproj, minus_infty, plus_infty, plus_infty, 0.0, NO_INEXACT_EXCEPTION),
     TEST_c_c (cproj, minus_infty, minus_infty, plus_infty, minus_zero, NO_INEXACT_EXCEPTION),
 
+    TEST_c_c (cproj, plus_infty, plus_zero, plus_infty, 0.0, NO_INEXACT_EXCEPTION),
+    TEST_c_c (cproj, plus_infty, minus_zero, plus_infty, minus_zero, NO_INEXACT_EXCEPTION),
+    TEST_c_c (cproj, minus_infty, plus_zero, plus_infty, 0.0, NO_INEXACT_EXCEPTION),
+    TEST_c_c (cproj, minus_infty, minus_zero, plus_infty, minus_zero, NO_INEXACT_EXCEPTION),
+
+    TEST_c_c (cproj, plus_zero, plus_infty, plus_infty, 0.0, NO_INEXACT_EXCEPTION),
+    TEST_c_c (cproj, plus_zero, minus_infty, plus_infty, minus_zero, NO_INEXACT_EXCEPTION),
+    TEST_c_c (cproj, minus_zero, plus_infty, plus_infty, 0.0, NO_INEXACT_EXCEPTION),
+    TEST_c_c (cproj, minus_zero, minus_infty, plus_infty, minus_zero, NO_INEXACT_EXCEPTION),
+
+    TEST_c_c (cproj, plus_infty, 1.0, plus_infty, 0.0, NO_INEXACT_EXCEPTION),
+    TEST_c_c (cproj, plus_infty, -1.0, plus_infty, minus_zero, NO_INEXACT_EXCEPTION),
+    TEST_c_c (cproj, minus_infty, 1.0, plus_infty, 0.0, NO_INEXACT_EXCEPTION),
+    TEST_c_c (cproj, minus_infty, -1.0, plus_infty, minus_zero, NO_INEXACT_EXCEPTION),
+
+    TEST_c_c (cproj, 1.0, plus_infty, plus_infty, 0.0, NO_INEXACT_EXCEPTION),
+    TEST_c_c (cproj, 1.0, minus_infty, plus_infty, minus_zero, NO_INEXACT_EXCEPTION),
+    TEST_c_c (cproj, -1.0, plus_infty, plus_infty, 0.0, NO_INEXACT_EXCEPTION),
+    TEST_c_c (cproj, -1.0, minus_infty, plus_infty, minus_zero, NO_INEXACT_EXCEPTION),
+
+    TEST_c_c (cproj, plus_infty, qnan_value, plus_infty, 0.0, NO_INEXACT_EXCEPTION),
+    TEST_c_c (cproj, plus_infty, -qnan_value, plus_infty, minus_zero, NO_INEXACT_EXCEPTION),
+    TEST_c_c (cproj, minus_infty, qnan_value, plus_infty, 0.0, NO_INEXACT_EXCEPTION),
+    TEST_c_c (cproj, minus_infty, -qnan_value, plus_infty, minus_zero, NO_INEXACT_EXCEPTION),
+
+    TEST_c_c (cproj, qnan_value, plus_infty, plus_infty, 0.0, NO_INEXACT_EXCEPTION),
+    TEST_c_c (cproj, qnan_value, minus_infty, plus_infty, minus_zero, NO_INEXACT_EXCEPTION),
+    TEST_c_c (cproj, -qnan_value, plus_infty, plus_infty, 0.0, NO_INEXACT_EXCEPTION),
+    TEST_c_c (cproj, -qnan_value, minus_infty, plus_infty, minus_zero, NO_INEXACT_EXCEPTION),
+
     TEST_c_c (cproj, 1.0, 0.0, 1.0, 0.0, NO_INEXACT_EXCEPTION),
     TEST_c_c (cproj, 2.0, 3.0, 2.0, 3.0, NO_INEXACT_EXCEPTION),
   };
diff --git a/math/s_cproj.c b/math/s_cproj.c
index c0be4618db..98f1a4c4b2 100644
--- a/math/s_cproj.c
+++ b/math/s_cproj.c
@@ -24,9 +24,7 @@
 __complex__ double
 __cproj (__complex__ double x)
 {
-  if (isnan (__real__ x) && isnan (__imag__ x))
-    return x;
-  else if (!isfinite (__real__ x) || !isfinite (__imag__ x))
+  if (__isinf_ns (__real__ x) || __isinf_ns (__imag__ x))
     {
       __complex__ double res;
 
diff --git a/math/s_cprojf.c b/math/s_cprojf.c
index 188bbe3beb..e4dbc181bd 100644
--- a/math/s_cprojf.c
+++ b/math/s_cprojf.c
@@ -24,9 +24,7 @@
 __complex__ float
 __cprojf (__complex__ float x)
 {
-  if (isnan (__real__ x) && isnan (__imag__ x))
-    return x;
-  else if (!isfinite (__real__ x) || !isfinite (__imag__ x))
+  if (__isinf_nsf (__real__ x) || __isinf_nsf (__imag__ x))
     {
       __complex__ float res;
 
diff --git a/math/s_cprojl.c b/math/s_cprojl.c
index fbdf2797e4..b564a83e63 100644
--- a/math/s_cprojl.c
+++ b/math/s_cprojl.c
@@ -24,9 +24,7 @@
 __complex__ long double
 __cprojl (__complex__ long double x)
 {
-  if (isnan (__real__ x) && isnan (__imag__ x))
-    return x;
-  else if (!isfinite (__real__ x) || !isfinite (__imag__ x))
+  if (__isinf_nsl (__real__ x) || __isinf_nsl (__imag__ x))
     {
       __complex__ long double res;
 
diff --git a/sysdeps/ieee754/ldbl-128ibm/s_cprojl.c b/sysdeps/ieee754/ldbl-128ibm/s_cprojl.c
index 3b4af5423a..a344e9288f 100644
--- a/sysdeps/ieee754/ldbl-128ibm/s_cprojl.c
+++ b/sysdeps/ieee754/ldbl-128ibm/s_cprojl.c
@@ -24,9 +24,7 @@
 __complex__ long double
 __cprojl (__complex__ long double x)
 {
-  if (isnan (__real__ x) && isnan (__imag__ x))
-    return x;
-  else if (!isfinite (__real__ x) || !isfinite (__imag__ x))
+  if (__isinf_nsl (__real__ x) || __isinf_nsl (__imag__ x))
     {
       __complex__ long double res;