diff --git a/math/libm-test.inc b/math/libm-test.inc
index 7abc7c1..5e50f0e 100644
--- a/math/libm-test.inc
+++ b/math/libm-test.inc
@@ -7786,9 +7786,7 @@ static const struct test_f_f_data log_test_data[] =
 static void
 log_test (void)
 {
-  START (log, 0);
-  RUN_TEST_LOOP_f_f (log, log_test_data, );
-  END;
+  ALL_RM_TEST (log, 0, log_test_data, RUN_TEST_LOOP_f_f, END);
 }
 
 
diff --git a/sysdeps/i386/fpu/e_log.S b/sysdeps/i386/fpu/e_log.S
index 0877924..3fa32aa 100644
--- a/sysdeps/i386/fpu/e_log.S
+++ b/sysdeps/i386/fpu/e_log.S
@@ -46,7 +46,13 @@ ENTRY(__ieee754_log)
 	fnstsw			// x-1 : x : log(2)
 	andb	$0x45, %ah
 	jz	2f
-	fstp	%st(1)		// x-1 : log(2)
+	fxam
+	fnstsw
+	andb	$0x45, %ah
+	cmpb	$0x40, %ah
+	jne	5f
+	fabs			// log(1) is +0 in all rounding modes.
+5:	fstp	%st(1)		// x-1 : log(2)
 	fyl2xp1			// log(x)
 	ret
 
diff --git a/sysdeps/i386/fpu/e_logf.S b/sysdeps/i386/fpu/e_logf.S
index 485180e..ca83d39 100644
--- a/sysdeps/i386/fpu/e_logf.S
+++ b/sysdeps/i386/fpu/e_logf.S
@@ -47,7 +47,13 @@ ENTRY(__ieee754_logf)
 	fnstsw			// x-1 : x : log(2)
 	andb	$0x45, %ah
 	jz	2f
-	fstp	%st(1)		// x-1 : log(2)
+	fxam
+	fnstsw
+	andb	$0x45, %ah
+	cmpb	$0x40, %ah
+	jne	5f
+	fabs			// log(1) is +0 in all rounding modes.
+5:	fstp	%st(1)		// x-1 : log(2)
 	fyl2xp1			// log(x)
 	ret
 
diff --git a/sysdeps/i386/fpu/e_logl.S b/sysdeps/i386/fpu/e_logl.S
index d7a459a..edae1d7 100644
--- a/sysdeps/i386/fpu/e_logl.S
+++ b/sysdeps/i386/fpu/e_logl.S
@@ -47,7 +47,13 @@ ENTRY(__ieee754_logl)
 	fnstsw			// x-1 : x : log(2)
 	andb	$0x45, %ah
 	jz	2f
-	fstp	%st(1)		// x-1 : log(2)
+	fxam
+	fnstsw
+	andb	$0x45, %ah
+	cmpb	$0x40, %ah
+	jne	5f
+	fabs			// log(1) is +0 in all rounding modes.
+5:	fstp	%st(1)		// x-1 : log(2)
 	fyl2xp1			// log(x)
 	ret
 
diff --git a/sysdeps/i386/fpu/libm-test-ulps b/sysdeps/i386/fpu/libm-test-ulps
index 3be1806..b7b2e12 100644
--- a/sysdeps/i386/fpu/libm-test-ulps
+++ b/sysdeps/i386/fpu/libm-test-ulps
@@ -1096,6 +1096,18 @@ Function: "log1p":
 ildouble: 1
 ldouble: 1
 
+Function: "log_downward":
+ildouble: 1
+ldouble: 1
+
+Function: "log_towardzero":
+ildouble: 1
+ldouble: 1
+
+Function: "log_upward":
+ildouble: 1
+ldouble: 1
+
 Function: "pow":
 ildouble: 1
 ldouble: 1
diff --git a/sysdeps/i386/i686/fpu/e_logl.S b/sysdeps/i386/i686/fpu/e_logl.S
index 8a86222..53a3d10 100644
--- a/sysdeps/i386/i686/fpu/e_logl.S
+++ b/sysdeps/i386/i686/fpu/e_logl.S
@@ -46,7 +46,13 @@ ENTRY(__ieee754_logl)
 	fcomip	%st(1)		// |x-1| : x-1 : x : log(2)
 	fstp	%st(0)		// x-1 : x : log(2)
 	jc	2f
-	fstp	%st(1)		// x-1 : log(2)
+	fxam
+	fnstsw
+	andb	$0x45, %ah
+	cmpb	$0x40, %ah
+	jne	4f
+	fabs			// // log(1) is +0 in all rounding modes.
+4:	fstp	%st(1)		// x-1 : log(2)
 	fyl2xp1			// log(x)
 	ret
 
diff --git a/sysdeps/ieee754/dbl-64/e_log.c b/sysdeps/ieee754/dbl-64/e_log.c
index 05d318b..4ecd372 100644
--- a/sysdeps/ieee754/dbl-64/e_log.c
+++ b/sysdeps/ieee754/dbl-64/e_log.c
@@ -96,6 +96,10 @@ __ieee754_log (double x)
   if (__glibc_likely (ABS (w) > U03))
     goto case_03;
 
+  /* log (1) is +0 in all rounding modes.  */
+  if (w == 0.0)
+    return 0.0;
+
   /*--- Stage I, the case abs(x-1) < 0.03 */
 
   t8 = MHALF * w;
diff --git a/sysdeps/ieee754/ldbl-128/e_logl.c b/sysdeps/ieee754/ldbl-128/e_logl.c
index 3d1034d..cb43816 100644
--- a/sysdeps/ieee754/ldbl-128/e_logl.c
+++ b/sysdeps/ieee754/ldbl-128/e_logl.c
@@ -240,6 +240,8 @@ __ieee754_logl(long double x)
   /* On this interval the table is not used due to cancellation error.  */
   if ((x <= 1.0078125L) && (x >= 0.9921875L))
     {
+      if (x == 1.0L)
+	return 0.0L;
       z = x - 1.0L;
       k = 64;
       t.value  = 1.0L;
diff --git a/sysdeps/x86_64/fpu/e_logl.S b/sysdeps/x86_64/fpu/e_logl.S
index a8e3108..315afc0 100644
--- a/sysdeps/x86_64/fpu/e_logl.S
+++ b/sysdeps/x86_64/fpu/e_logl.S
@@ -45,7 +45,13 @@ ENTRY(__ieee754_logl)
 	fnstsw			// x-1 : x : log(2)
 	andb	$0x45, %ah
 	jz	2f
-	fstp	%st(1)		// x-1 : log(2)
+	fxam
+	fnstsw
+	andb	$0x45, %ah
+	cmpb	$0x40, %ah
+	jne	5f
+	fabs			// log(1) is +0 in all rounding modes.
+5:	fstp	%st(1)		// x-1 : log(2)
 	fyl2xp1			// log(x)
 	ret
 
diff --git a/sysdeps/x86_64/fpu/libm-test-ulps b/sysdeps/x86_64/fpu/libm-test-ulps
index 5f4ab06..301eaa6 100644
--- a/sysdeps/x86_64/fpu/libm-test-ulps
+++ b/sysdeps/x86_64/fpu/libm-test-ulps
@@ -1170,6 +1170,22 @@ ifloat: 1
 ildouble: 1
 ldouble: 1
 
+Function: "log_downward":
+float: 1
+ifloat: 1
+ildouble: 1
+ldouble: 1
+
+Function: "log_towardzero":
+ildouble: 1
+ldouble: 1
+
+Function: "log_upward":
+float: 1
+ifloat: 1
+ildouble: 1
+ldouble: 1
+
 Function: "pow":
 float: 1
 ifloat: 1
