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    <p>Here's a quick &amp; cheesy implementation to get you going until a good one comes along:</p> <pre><code>def mortanize(x, y) xs, ys = [x, y].map do |n| n.to_s(2) end nbits = [xs, ys].map(&amp;:size).max xs, ys = [xs, ys].map do |n| ('0' * (nbits - n.size) + n).chars end ys.zip(xs).join.to_i(2) end </code></pre> <p>As you might expect, it's no speed deamon. On my box, with MRI 1.8.7, it computes about 35,000 16-bit results per second. Yours computes 68,000 16-bit results per second. Or, see the next algorithm for 256,000 16-bit results per second.</p> <hr> <p>If you're willing to trade a little memory and startup time for speed, then:</p> <pre><code>def base_mortanize(x, y) xs, ys = [x, y].map do |n| n.to_s(2) end nbits = [xs, ys].map(&amp;:size).max xs, ys = [xs, ys].map do |n| ('0' * (nbits - n.size) + n).chars end ys.zip(xs).join.to_i(2) end MORTON_TABLE_X = 256.times.map do |x| base_mortanize(x, 0) end MORTON_TABLE_Y = 256.times.map do |y| base_mortanize(0, y) end def mortanize(x, y) z = [] while (x &gt; 0 || y &gt; 0) z &lt;&lt; (MORTON_TABLE_X[x &amp; 0xff] | MORTON_TABLE_Y[y &amp; 0xff]) x &gt;&gt;= 8 y &gt;&gt;= 8 end z.reverse.inject(0) do |result, word| result &lt;&lt; 16 | word end end </code></pre> <p>This one computes 256,000 16-bit results per second.</p> <hr> <p>There's a bug in your answer if either argument is zero. Here's one possible fix for it. First define this function:</p> <pre><code>def bit_size(x) return 1 if x == 0 Math.log2(x).floor + 1 end </code></pre> <p>And then, inside <code>interleave</code>, replace:</p> <pre><code>z, bl, ybl = 0, (Math.log2(self)).floor + 1, (Math.log2(y)).floor + 1 </code></pre> <p>with:</p> <pre><code>z = 0 bl = bit_size(x) ybl = bit_size(y) </code></pre> <hr> <p>Here is the rspec test case I used:</p> <pre><code>describe "mortanize" do it "should interleave integers" do mortanize(0, 0).should eql 0 mortanize(0, 1).should eql 2 mortanize(1, 0).should eql 1 mortanize(0xf, 0x3).should eql 0x5f mortanize(0x3, 0xf).should eql 0xaf mortanize(0xf, 0x0).should eql 0x55 mortanize(0x0, 0xf).should eql 0xaa mortanize(0x3, 0xc).should eql 0xa5 mortanize(0xf, 0xf).should eql 0xff mortanize(0x1234, 0x4321).should eql 0x210e0d12 end end </code></pre>
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    1. COThanks Wayne, a very readable impl using a bunch of Ruby stuff; I like it. If you're curious about comparison with the sample I just added to the question, the BM for this: `user 185.240000 system 0.160000 total 185.400000 real (185.204548)`
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    2. COGood point on the fix for my approach—you ought to make your version of mine a separate answer that can be accepted (tip, inline the bit_size method and call floor + 1 only once after the larger size is found for another speed boost.)
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    3. CO@Yuri, I think you ought to add it--it's your answer, after all! I don't mind losing the checkmark; besides, that degree of optimization, where the intent of the code begins to get buried, makes me queezy. It's probably time to write C (per Chuba's answer) if you need it optimized that much.
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