diff --git a/Eigen/src/Core/arch/Default/Half.h b/Eigen/src/Core/arch/Default/Half.h
index 402b8d463..7f9e6c12a 100644
--- a/Eigen/src/Core/arch/Default/Half.h
+++ b/Eigen/src/Core/arch/Default/Half.h
@@ -591,7 +591,12 @@ EIGEN_STRONG_INLINE EIGEN_DEVICE_FUNC __half_raw float_to_half_rtne(float ff) {
 
 #elif defined(EIGEN_HAS_FP16_C)
   __half_raw h;
-  h.x = _cvtss_sh(ff, 0);
+  #if EIGEN_COMP_MSVC
+    // MSVC does not have scalar instructions.
+    h.x =_mm_extract_epi16(_mm_cvtps_ph(_mm_set_ss(ff), 0), 0);
+  #else
+    h.x = _cvtss_sh(ff, 0);
+  #endif
   return h;
 
 #elif defined(EIGEN_HAS_ARM64_FP16_SCALAR_ARITHMETIC)
@@ -652,7 +657,12 @@ EIGEN_STRONG_INLINE EIGEN_DEVICE_FUNC float half_to_float(__half_raw h) {
   (defined(EIGEN_HAS_HIP_FP16) && defined(EIGEN_HIP_DEVICE_COMPILE))
   return __half2float(h);
 #elif defined(EIGEN_HAS_FP16_C)
-  return _cvtsh_ss(h.x);
+  #if EIGEN_COMP_MSVC
+    // MSVC does not have scalar instructions.
+    return _mm_cvtss_f32(_mm_cvtph_ps(_mm_set1_epi16(h.x)));
+  #else
+    return _cvtsh_ss(h.x);
+  #endif
 #elif defined(EIGEN_HAS_ARM64_FP16_SCALAR_ARITHMETIC)
   return static_cast<float>(h.x);
 #else
diff --git a/test/half_float.cpp b/test/half_float.cpp
index f2c1ac8b6..00a8b487d 100644
--- a/test/half_float.cpp
+++ b/test/half_float.cpp
@@ -230,6 +230,8 @@ void test_comparison()
 
 void test_basic_functions()
 {
+  constexpr float PI = static_cast<float>(EIGEN_PI);
+
   VERIFY_IS_EQUAL(float(numext::abs(half(3.5f))), 3.5f);
   VERIFY_IS_EQUAL(float(abs(half(3.5f))), 3.5f);
   VERIFY_IS_EQUAL(float(numext::abs(half(-3.5f))), 3.5f);
@@ -257,8 +259,8 @@ void test_basic_functions()
 
   VERIFY_IS_EQUAL(float(numext::exp(half(0.0f))), 1.0f);
   VERIFY_IS_EQUAL(float(exp(half(0.0f))), 1.0f);
-  VERIFY_IS_APPROX(float(numext::exp(half(EIGEN_PI))), 20.f + float(EIGEN_PI));
-  VERIFY_IS_APPROX(float(exp(half(EIGEN_PI))), 20.f + float(EIGEN_PI));
+  VERIFY_IS_APPROX(float(numext::exp(half(PI))), 20.f + PI);
+  VERIFY_IS_APPROX(float(exp(half(PI))), 20.f + PI);
 
   VERIFY_IS_EQUAL(float(numext::expm1(half(0.0f))), 0.0f);
   VERIFY_IS_EQUAL(float(expm1(half(0.0f))), 0.0f);
@@ -283,25 +285,26 @@ void test_basic_functions()
 
 void test_trigonometric_functions()
 {
+  constexpr float PI = static_cast<float>(EIGEN_PI);
   VERIFY_IS_APPROX(numext::cos(half(0.0f)), half(cosf(0.0f)));
   VERIFY_IS_APPROX(cos(half(0.0f)), half(cosf(0.0f)));
-  VERIFY_IS_APPROX(numext::cos(half(EIGEN_PI)), half(cosf(EIGEN_PI)));
-  // VERIFY_IS_APPROX(numext::cos(half(EIGEN_PI/2)), half(cosf(EIGEN_PI/2)));
-  // VERIFY_IS_APPROX(numext::cos(half(3*EIGEN_PI/2)), half(cosf(3*EIGEN_PI/2)));
+  VERIFY_IS_APPROX(numext::cos(half(PI)), half(cosf(PI)));
+  // VERIFY_IS_APPROX(numext::cos(half(PI/2)), half(cosf(PI/2)));
+  // VERIFY_IS_APPROX(numext::cos(half(3*PI/2)), half(cosf(3*PI/2)));
   VERIFY_IS_APPROX(numext::cos(half(3.5f)), half(cosf(3.5f)));
 
   VERIFY_IS_APPROX(numext::sin(half(0.0f)), half(sinf(0.0f)));
   VERIFY_IS_APPROX(sin(half(0.0f)), half(sinf(0.0f)));
-  //  VERIFY_IS_APPROX(numext::sin(half(EIGEN_PI)), half(sinf(EIGEN_PI)));
-  VERIFY_IS_APPROX(numext::sin(half(EIGEN_PI/2)), half(sinf(EIGEN_PI/2)));
-  VERIFY_IS_APPROX(numext::sin(half(3*EIGEN_PI/2)), half(sinf(3*EIGEN_PI/2)));
+  //  VERIFY_IS_APPROX(numext::sin(half(PI)), half(sinf(PI)));
+  VERIFY_IS_APPROX(numext::sin(half(PI/2)), half(sinf(PI/2)));
+  VERIFY_IS_APPROX(numext::sin(half(3*PI/2)), half(sinf(3*PI/2)));
   VERIFY_IS_APPROX(numext::sin(half(3.5f)), half(sinf(3.5f)));
 
   VERIFY_IS_APPROX(numext::tan(half(0.0f)), half(tanf(0.0f)));
   VERIFY_IS_APPROX(tan(half(0.0f)), half(tanf(0.0f)));
-  //  VERIFY_IS_APPROX(numext::tan(half(EIGEN_PI)), half(tanf(EIGEN_PI)));
-  //  VERIFY_IS_APPROX(numext::tan(half(EIGEN_PI/2)), half(tanf(EIGEN_PI/2)));
-  //VERIFY_IS_APPROX(numext::tan(half(3*EIGEN_PI/2)), half(tanf(3*EIGEN_PI/2)));
+  //  VERIFY_IS_APPROX(numext::tan(half(PI)), half(tanf(PI)));
+  //  VERIFY_IS_APPROX(numext::tan(half(PI/2)), half(tanf(PI/2)));
+  //VERIFY_IS_APPROX(numext::tan(half(3*PI/2)), half(tanf(3*PI/2)));
   VERIFY_IS_APPROX(numext::tan(half(3.5f)), half(tanf(3.5f)));
 }