Advogato blog for monniaux
http://www.advogato.org/person/monniaux/
Advogato blog for monniauxen-usmod_virguleMon, 25 May 2015 23:45:58 GMTThu, 19 Jan 2006 14:06:03 GMT19 Jan 2006
http://www.advogato.org/person/monniaux/diary.html?start=0
http://www.advogato.org/person/monniaux/diary.html?start=0Compare the following three C expressions (a and b are doubles and we are on a IEEE-754 compliant system):
<p> double x = ( (a <= b) ? a : b );
double y = ( (a < b) ? a : b );
double z = ( (a > 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.