Golf this Thumb-2 Constant!
JavaScript (ES6), 57 bytes
Returns false for &quot;mov&quot;, true for &quot;movs&quot;, 2 for &quot;ldr&quot;, 3 for &quot;mvn&quot; or 4 for &quot;movw&quot;.

f=(n,r)=&gt;n&gt;&gt;8?~n&gt;&gt;8?r&gt;31?n&gt;&gt;16?2:4:f(n&gt;&gt;&gt;31|n*2,-~r):3:!r

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Commented
f = (                       // f is a recursive function taking:
  n,                        //   n = input
  r                         //   r = rotation counter, initially undefined
) =&gt;                        //
  n &gt;&gt; 8 ?                  // if some of the upper 24 bits of n are not 0's:
    ~n &gt;&gt; 8 ?               //   if some of the upper 24 bits of n are not 1's:
      r &gt; 31 ?              //     if the input was rotated 32 times (which means
                            //     that we've tried all possible rotations and we
                            //     are back to the original value):
        n &gt;&gt; 16 ?           //       if some of the upper 16 bits of n are not 0's:
          2                 //         return 2 for &quot;ldr&quot;
        :                   //       else:
          4                 //         return 4 for &quot;movw&quot;
      :                     //     else:
        f(                  //       do a recursive call:
          n &gt;&gt;&gt; 31 | n * 2, //         rotate n by 1 position to the left
          -~r               //         increment r
        )                   //       end of recursive call
    :                       //   else:
      3                     //     return 3 for &quot;mvn&quot;
  :                         // else:
    !r                      //   return true for &quot;movs&quot; if r is zero'ish
                            //   or false for &quot;mov&quot; if r is greater than 0