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    <p>There is an efficient way to perform bit reversal, using O(log n) shift operations. If you interpret a 64-bit UINT as an 8x8 array of bits, then bit reversal corresponds to a rotation by 180 degrees.</p> <p>Half of these shifts effectively perform a horizontal reflection; the other half perform a vertical reflection. To obtain rotations by 90 and 270 degrees, an orthogonal (i.e. vertical or horizontal) reflection could be combined with a diagonal reflection, but the latter remains an awkward bit.</p> <pre><code>typedef unsigned long long uint64; uint64 reflect_vert (uint64 value) { value = ((value &amp; 0xFFFFFFFF00000000ull) &gt;&gt; 32) | ((value &amp; 0x00000000FFFFFFFFull) &lt;&lt; 32); value = ((value &amp; 0xFFFF0000FFFF0000ull) &gt;&gt; 16) | ((value &amp; 0x0000FFFF0000FFFFull) &lt;&lt; 16); value = ((value &amp; 0xFF00FF00FF00FF00ull) &gt;&gt; 8) | ((value &amp; 0x00FF00FF00FF00FFull) &lt;&lt; 8); return value; } uint64 reflect_horiz (uint64 value) { value = ((value &amp; 0xF0F0F0F0F0F0F0F0ull) &gt;&gt; 4) | ((value &amp; 0x0F0F0F0F0F0F0F0Full) &lt;&lt; 4); value = ((value &amp; 0xCCCCCCCCCCCCCCCCull) &gt;&gt; 2) | ((value &amp; 0x3333333333333333ull) &lt;&lt; 2); value = ((value &amp; 0xAAAAAAAAAAAAAAAAull) &gt;&gt; 1) | ((value &amp; 0x5555555555555555ull) &lt;&lt; 1); return value; } uint64 reflect_diag (uint64 value) { uint64 new_value = value &amp; 0x8040201008040201ull; // stationary bits new_value |= (value &amp; 0x0100000000000000ull) &gt;&gt; 49; new_value |= (value &amp; 0x0201000000000000ull) &gt;&gt; 42; new_value |= (value &amp; 0x0402010000000000ull) &gt;&gt; 35; new_value |= (value &amp; 0x0804020100000000ull) &gt;&gt; 28; new_value |= (value &amp; 0x1008040201000000ull) &gt;&gt; 21; new_value |= (value &amp; 0x2010080402010000ull) &gt;&gt; 14; new_value |= (value &amp; 0x4020100804020100ull) &gt;&gt; 7; new_value |= (value &amp; 0x0080402010080402ull) &lt;&lt; 7; new_value |= (value &amp; 0x0000804020100804ull) &lt;&lt; 14; new_value |= (value &amp; 0x0000008040201008ull) &lt;&lt; 21; new_value |= (value &amp; 0x0000000080402010ull) &lt;&lt; 28; new_value |= (value &amp; 0x0000000000804020ull) &lt;&lt; 35; new_value |= (value &amp; 0x0000000000008040ull) &lt;&lt; 42; new_value |= (value &amp; 0x0000000000000080ull) &lt;&lt; 49; return new_value; } uint64 rotate_90 (uint64 value) { return reflect_diag (reflect_vert (value)); } uint64 rotate_180 (uint64 value) { return reflect_horiz (reflect_vert (value)); } uint64 rotate_270 (uint64 value) { return reflect_diag (reflect_horiz (value)); } </code></pre> <p>In the above code, the reflect_diag() function still requires many shifts. I suspect that it is possible to implement this function with fewer shifts, but I have not yet found a way to do that.</p>
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    1. CO+1 probably more efficient than the accepted answer, and fully satisfies the requirements of 'no lookup table'.
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