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The best I can come up with is this <pre><code>char a, b, c; std::cin >> a >> b >> c; if (((b-a) | (c-a)) & 0x80) { // a > b || a > c } </code></pre> With <code>gcc -O2</code> this generates only one conditional branch <pre><code>40072e: 29 c8 sub %ecx,%eax 400730: 29 ca sub %ecx,%edx 400732: 09 d0 or %edx,%eax 400734: a8 80 test $0x80,%al 400736: 74 17 je 40074f <main+0x3f> </code></pre> This leverages the constraints of the input values, since the values cannot be greater than 26 then subtracting <code>a</code> from <code>b</code> will give you a negative value when <code>a > b</code>, in two's complement you know bit <code>7</code> will be set in that case - the same applies to <code>c</code>. I then OR both so that bit <code>7</code> indicates whether <code>a > b || a > c</code>, lastly we inspect bit <code>7</code> by AND with 0x80 and branch on that. Update: Out of curiosity I timed 4 different ways of coding this. To generate test data I used a simple linear congruential pseudo-random number generator. I timed it in a loop for 100 million iterations. I assumed for simplicity that if the condition is true we want to add 5 to a counter, do nothing otherwise. I timed it using <code>g++ (GCC) 4.6.3 20120306 (Red Hat 4.6.3-2)</code> on an <code>Intel Xeon X5570 @ 2.93GHz</code> using <code>-O2</code> optimization level. Here's the code (comment out all but one of the conditional variants): <pre><code>#include <iostream> unsigned myrand() { static unsigned x = 1; return (x = x * 1664525 + 1013904223); } int main() { size_t count = 0; for(size_t i=0; i<100000000; ++i ) { int a = 1 + myrand() % 26; int b = 1 + myrand() % 26; int c = 1 + myrand() % 26; count += 5 & (((b-a) | (c-a)) >> 31); // 0.635 sec //if (((b-a) | (c-a)) & 0x80) count += 5; // 0.660 sec //if (a > std::max(b,c)) count += 5; // 0.677 sec //if ( a > b || a > c) count += 5; // 1.164 sec } std::cout << count << std::endl; return 0; } </code></pre> The fastest is a modification on the suggestion in my answer, where we use sign extension to generate a mask that is either 32 <code>1s</code> or 32 <code>0s</code> depending on whether the condition is true of false, and use that to mask the <code>5</code> being added so that it either adds 5 or 0. This variation has no branches. The times are in a comment on each line. The slowest was the original expression <code>( a > b || a > c)</code>.
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1. POLogical / Relational Expression Optimization
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1. COYou should make sure the compiler isn't doing this for you. Keep your code simple first, and then micro-optimize only if you can identify a bottleneck.
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 USCory Nelson

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