diff --git a/library/compiler-builtins/libm/src/math/rem_pio2.rs b/library/compiler-builtins/libm/src/math/rem_pio2.rs
index 285663ea2c09..536dfac3c42c 100644
--- a/library/compiler-builtins/libm/src/math/rem_pio2.rs
+++ b/library/compiler-builtins/libm/src/math/rem_pio2.rs
@@ -85,7 +85,7 @@ pub(crate) fn rem_pio2(x: f64) -> (i32, f64, f64) {
         /* |x| ~<= 5pi/4 */
         if (ix & 0xfffff) == 0x921fb {
             /* |x| ~= pi/2 or 2pi/2 */
-            medium(x, ix); /* cancellation -- use medium case */
+            return medium(x, ix); /* cancellation -- use medium case */
         }
         if ix <= 0x4002d97c {
             /* |x| ~<= 3pi/4 */
@@ -185,3 +185,23 @@ pub(crate) fn rem_pio2(x: f64) -> (i32, f64, f64) {
     }
     (n, ty[0], ty[1])
 }
+
+#[test]
+fn test_near_pi() {
+    assert_eq!(
+        rem_pio2(3.141592025756836),
+        (2, -6.278329573009626e-7, -2.1125998133974653e-23)
+    );
+    assert_eq!(
+        rem_pio2(3.141592033207416),
+        (2, -6.20382377148128e-7, -2.1125998133974653e-23)
+    );
+    assert_eq!(
+        rem_pio2(3.141592144966125),
+        (2, -5.086236681942706e-7, -2.1125998133974653e-23)
+    );
+    assert_eq!(
+        rem_pio2(3.141592979431152),
+        (2, 3.2584135866119817e-7, -2.1125998133974653e-23)
+    );
+}
diff --git a/library/compiler-builtins/libm/src/math/sin.rs b/library/compiler-builtins/libm/src/math/sin.rs
index b7307441646f..51aed88a8dbb 100644
--- a/library/compiler-builtins/libm/src/math/sin.rs
+++ b/library/compiler-builtins/libm/src/math/sin.rs
@@ -77,3 +77,10 @@ pub fn sin(x: f64) -> f64 {
         _ => -k_cos(y0, y1),
     }
 }
+
+#[test]
+fn test_near_pi() {
+    let x = f64::from_bits(0x400921fb000FD5DD); // 3.141592026217707
+    let sx = f64::from_bits(0x3ea50d15ced1a4a2); // 6.273720864039205e-7
+    assert_eq!(sin(x), sx);
+}