http://www.advogato.org/person/monniaux/ Advogato blog for monniaux en-us mod_virgule Sun, 7 Sep 2008 05:54:34 GMT Thu, 19 Jan 2006 14:06:03 GMT http://www.advogato.org/person/monniaux/diary.html?start=0 http://www.advogato.org/person/monniaux/diary.html?start=0 Compare the following three C expressions (a and b are doubles and we are on a IEEE-754 compliant system): <p> double x = ( (a &lt;= b) ? a : b ); double y = ( (a &lt; b) ? a : b ); double z = ( (a &gt; b) ? b : a ); <p> Obviously, for the purpose of comparing real numbers (and also infinities), these functions all perform the same task: compute the minimum of a and b. <p> Are they equivalent? No, if you consider strict compliance with the standards. <p> Consider a "not-a-number" value (NaN): double a = 0./0.; double b = 1; <p> Those expressions respectively yield 1, 1, NaN. <p> Consider the different +0 and -0 values: double a = 0.; double b = -0.; <p> Those expression respectively yield 0, -0, 0. <p> A compiler that strives to comply with standards, such as gcc, will emit different code for those three functions. <p> On AMD64 (or x86 in SSE mode), gcc compiles the expression for x into a sequence involving a SSE comparison operator and some bit masks (implementing ? : without using jumps). But (with optimization turned on) it compiles y into a single minsd instruction. <p> -ffast-math turns on "unsafe" optimizations that result in x being compiled the same as y. <p> Now, this may seem innocuous enough. Unfortunately, we had the code for x inside a loop performing matrix computations, inside a "bottleneck" procedure taking up a significant part of computation times. Changing it into the y formula yielded a 2.5× speedup in a benchmark.