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POAdvice on optimization floating point calculations: solving a quadratic equation
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copied!<p>I'm working on a granular dynamics problem. The computationally expensive part is the function below that solve a quadratic equation to detect the collision of two particles. </p> <p>I was wondering if this can be easily optimized or if I'm doing something noticeably stupid? For example, is it a good idea to use these <code>const double x1 = p1->x;</code> constructions to give the compiler a hint? Looking at the assembler code, the compiler uses SSE instructions, but I have no idea if they are optimal in any way (probably not). According to the profiler, most of the time is spend in calculating the expressions <code>a</code>, <code>b</code> and <code>c</code>. What do you (in general) do when you are trying to optimize some kernel function like the one below? </p> <pre><code>void detect_collision_of_pair(struct particle* p1, struct particle* p2){ const double x1 = p1->x; const double y1 = p1->y; const double z1 = p1->z; const double x2 = p2->x; const double y2 = p2->y; const double z2 = p2->z; const double vx1 = p1->vx; const double vy1 = p1->vy; const double vz1 = p1->vz; const double vx2 = p2->vx; const double vy2 = p2->vy; const double vz2 = p2->vz; const double a = vx1*vx1 - 2.*vx1*vx2 + vx2*vx2 + vy1*vy1 - 2.*vy1*vy2 + vy2*vy2 + vz1*vz1 - 2.*vz1*vz2 + vz2*vz2; const double b = 2.*vx1*x1 - 2.*vx2*x1 - 2.*vx1*x2 + 2.*vx2*x2 + 2.*vy1*y1 - 2.*vy2*y1 - 2.*vy1*y2 + 2.*vy2*y2 + 2.*vz1*z1 - 2.*vz2*z1 - 2.*vz1*z2 + 2.*vz2*z2; const double c = -4.*particle_radius*particle_radius + x1*x1 - 2.*x1*x2 + x2*x2 + y1*y1 - 2.*y1*y2 + y2*y2 + z1*z1 - 2.*z1*z2 + z2*z2; double root = b*b-4.*a*c; if (root>=0.){ root = sqrt(root); double time1 = (-b-root)/(2.*a); double time2 = (-b+root)/(2.*a); if ( (time1>-dt && time1<0.) || (time1<-dt && time2>0) ){ double times = -dt; if (time1>-dt || time2<0){ if (time1>-dt){ times = time1; }else{ times = time2; } } resolve_collision(p1,p2,times); } } } </code></pre>

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