diff --git a/math/libm-test.inc b/math/libm-test.inc
index 0d467a2..fa8e238 100644
--- a/math/libm-test.inc
+++ b/math/libm-test.inc
@@ -7840,9 +7840,7 @@ static const struct test_f_f_data log2_test_data[] =
 static void
 log2_test (void)
 {
-  START (log2, 0);
-  RUN_TEST_LOOP_f_f (log2, log2_test_data, );
-  END;
+  ALL_RM_TEST (log2, 0, log2_test_data, RUN_TEST_LOOP_f_f, END);
 }
 
 
diff --git a/sysdeps/i386/fpu/e_log2.S b/sysdeps/i386/fpu/e_log2.S
index a202bc7..73ff0ff 100644
--- a/sysdeps/i386/fpu/e_log2.S
+++ b/sysdeps/i386/fpu/e_log2.S
@@ -47,7 +47,13 @@ ENTRY(__ieee754_log2)
 	fnstsw			// x-1 : x : 1
 	andb	$0x45, %ah
 	jz	2f
-	fstp	%st(1)		// x-1 : 1
+	fxam
+	fnstsw
+	andb	$0x45, %ah
+	cmpb	$0x40, %ah
+	jne	5f
+	fabs			// log2(1) is +0 in all rounding modes.
+5:	fstp	%st(1)		// x-1 : 1
 	fyl2xp1			// log(x)
 	ret
 
diff --git a/sysdeps/i386/fpu/e_log2f.S b/sysdeps/i386/fpu/e_log2f.S
index f4f9a8c..344eeb4 100644
--- a/sysdeps/i386/fpu/e_log2f.S
+++ b/sysdeps/i386/fpu/e_log2f.S
@@ -47,7 +47,13 @@ ENTRY(__ieee754_log2f)
 	fnstsw			// x-1 : x : 1
 	andb	$0x45, %ah
 	jz	2f
-	fstp	%st(1)		// x-1 : 1
+	fxam
+	fnstsw
+	andb	$0x45, %ah
+	cmpb	$0x40, %ah
+	jne	5f
+	fabs			// log2(1) is +0 in all rounding modes.
+5:	fstp	%st(1)		// x-1 : 1
 	fyl2xp1			// log(x)
 	ret
 
diff --git a/sysdeps/i386/fpu/e_log2l.S b/sysdeps/i386/fpu/e_log2l.S
index bd51b56..0f5f7e5 100644
--- a/sysdeps/i386/fpu/e_log2l.S
+++ b/sysdeps/i386/fpu/e_log2l.S
@@ -47,7 +47,13 @@ ENTRY(__ieee754_log2l)
 	fnstsw			// x-1 : x : 1
 	andb	$0x45, %ah
 	jz	2f
-	fstp	%st(1)		// x-1 : 1
+	fxam
+	fnstsw
+	andb	$0x45, %ah
+	cmpb	$0x40, %ah
+	jne	5f
+	fabs			// log2(1) is +0 in all rounding modes.
+5:	fstp	%st(1)		// x-1 : 1
 	fyl2xp1			// log(x)
 	ret
 
diff --git a/sysdeps/i386/fpu/libm-test-ulps b/sysdeps/i386/fpu/libm-test-ulps
index 1e89284..d7424a6 100644
--- a/sysdeps/i386/fpu/libm-test-ulps
+++ b/sysdeps/i386/fpu/libm-test-ulps
@@ -1588,6 +1588,22 @@ ifloat: 1
 ildouble: 1
 ldouble: 1
 
+Function: "log2_towardzero":
+double: 1
+float: 1
+idouble: 1
+ifloat: 1
+ildouble: 1
+ldouble: 1
+
+Function: "log2_upward":
+double: 1
+float: 1
+idouble: 1
+ifloat: 1
+ildouble: 1
+ldouble: 1
+
 Function: "log_downward":
 ildouble: 1
 ldouble: 1
diff --git a/sysdeps/ieee754/ldbl-128/e_log2l.c b/sysdeps/ieee754/ldbl-128/e_log2l.c
index 6c7da0e..991a3b7 100644
--- a/sysdeps/ieee754/ldbl-128/e_log2l.c
+++ b/sysdeps/ieee754/ldbl-128/e_log2l.c
@@ -188,6 +188,9 @@ __ieee754_log2l (x)
   if (hx >= 0x7fff000000000000LL)
     return (x + x);
 
+  if (x == 1.0L)
+    return 0.0L;
+
 /* separate mantissa from exponent */
 
 /* Note, frexp is used so that denormal numbers
diff --git a/sysdeps/ieee754/ldbl-128ibm/e_log2l.c b/sysdeps/ieee754/ldbl-128ibm/e_log2l.c
index 323ded0..442ad97 100644
--- a/sysdeps/ieee754/ldbl-128ibm/e_log2l.c
+++ b/sysdeps/ieee754/ldbl-128ibm/e_log2l.c
@@ -190,6 +190,9 @@ __ieee754_log2l (x)
   if (hx >= 0x7ff0000000000000LL)
     return (x + x);
 
+  if (x == 1.0L)
+    return 0.0L;
+
 /* separate mantissa from exponent */
 
 /* Note, frexp is used so that denormal numbers
diff --git a/sysdeps/x86_64/fpu/e_log2l.S b/sysdeps/x86_64/fpu/e_log2l.S
index 956489f..c12906d 100644
--- a/sysdeps/x86_64/fpu/e_log2l.S
+++ b/sysdeps/x86_64/fpu/e_log2l.S
@@ -45,7 +45,13 @@ ENTRY(__ieee754_log2l)
 	fnstsw			// x-1 : x : 1
 	andb	$0x45, %ah
 	jz	2f
-	fstp	%st(1)		// x-1 : 1
+	fxam
+	fnstsw
+	andb	$0x45, %ah
+	cmpb	$0x40, %ah
+	jne	5f
+	fabs			// log2(1) is +0 in all rounding modes.
+5:	fstp	%st(1)		// x-1 : 1
 	fyl2xp1			// log(x)
 	ret
 
diff --git a/sysdeps/x86_64/fpu/libm-test-ulps b/sysdeps/x86_64/fpu/libm-test-ulps
index bb549d2..92fef5a 100644
--- a/sysdeps/x86_64/fpu/libm-test-ulps
+++ b/sysdeps/x86_64/fpu/libm-test-ulps
@@ -1665,6 +1665,28 @@ ifloat: 1
 ildouble: 1
 ldouble: 1
 
+Function: "log2_downward":
+double: 2
+float: 2
+idouble: 2
+ifloat: 2
+
+Function: "log2_towardzero":
+double: 1
+float: 1
+idouble: 1
+ifloat: 1
+ildouble: 1
+ldouble: 1
+
+Function: "log2_upward":
+double: 2
+float: 2
+idouble: 2
+ifloat: 2
+ildouble: 1
+ldouble: 1
+
 Function: "log_downward":
 float: 1
 ifloat: 1
