What is the source code of Quaternion.LookRotation?

This is what I was able to come out with. Seems to work. Just note that forward and up vector must be orthogonal, the function doesn't have orthogonization of up vector.

 private static Quaternion QuaternionLookRotation(Vector3 forward, Vector3 up)
 {
     forward.Normalize();
 
     Vector3 vector = Vector3.Normalize(forward);
     Vector3 vector2 = Vector3.Normalize(Vector3.Cross(up, vector));
     Vector3 vector3 = Vector3.Cross(vector, vector2);
     var m00 = vector2.x;
     var m01 = vector2.y;
     var m02 = vector2.z;
     var m10 = vector3.x;
     var m11 = vector3.y;
     var m12 = vector3.z;
     var m20 = vector.x;
     var m21 = vector.y;
     var m22 = vector.z;
 
 
     float num8 = (m00 + m11) + m22;
     var quaternion = new Quaternion();
     if (num8 > 0f)
     {
         var num = (float)Math.Sqrt(num8 + 1f);
         quaternion.w = num * 0.5f;
         num = 0.5f / num;
         quaternion.x = (m12 - m21) * num;
         quaternion.y = (m20 - m02) * num;
         quaternion.z = (m01 - m10) * num;
         return quaternion;
     }
     if ((m00 >= m11) && (m00 >= m22))
     {
         var num7 = (float)Math.Sqrt(((1f + m00) - m11) - m22);
         var num4 = 0.5f / num7;
         quaternion.x = 0.5f * num7;
         quaternion.y = (m01 + m10) * num4;
         quaternion.z = (m02 + m20) * num4;
         quaternion.w = (m12 - m21) * num4;
         return quaternion;
     }
     if (m11 > m22)
     {
         var num6 = (float)Math.Sqrt(((1f + m11) - m00) - m22);
         var num3 = 0.5f / num6;
         quaternion.x = (m10+ m01) * num3;
         quaternion.y = 0.5f * num6;
         quaternion.z = (m21 + m12) * num3;
         quaternion.w = (m20 - m02) * num3;
         return quaternion; 
     }
     var num5 = (float)Math.Sqrt(((1f + m22) - m00) - m11);
     var num2 = 0.5f / num5;
     quaternion.x = (m20 + m02) * num2;
     quaternion.y = (m21 + m12) * num2;
     quaternion.z = 0.5f * num5;
     quaternion.w = (m01 - m10) * num2;
     return quaternion;
 }