AlexVaq
commented
8 years ago Is this a projection back to su(3) after some smearing? In the APE smearing code I was using an iterative method that maybe you find easier to optimize (although I think it will turn out the other way, that you can optimize APE smearing with that code).
El 12/8/2015, a las 20:29, mikeaclark notifications@github.com escribió:
The link unitarization has one of the largest performance regressions when running on Maxwell, which doesn't have fast double-precision capability. Benchmarking reveals that the bulk of the time is spent in the reciprocalRoot function.
// Also modify q if the eigenvalues are dangerously small.
templatedevice host bool reciprocalRoot(const Matrix<Cmplx,3>& q, Matrix<Cmplx,3>* res){ Matrix<Cmplx,3> qsq, tempq; typename RealTypeId<Cmplx>::Type c[3]; typename RealTypeId<Cmplx>::Type g[3]; const typename RealTypeId<Cmplx>::Type one_third = 0.333333333333333333333; const typename RealTypeId<Cmplx>::Type one_ninth = 0.111111111111111111111; const typename RealTypeId<Cmplx>::Type one_eighteenth = 0.055555555555555555555; qsq = q*q; tempq = qsq*q; c[0] = getTrace(q).x; c[1] = getTrace(qsq).x * 0.5; c[2] = getTrace(tempq).x * one_third;; g[0] = g[1] = g[2] = c[0] * one_third; typename RealTypeId<Cmplx>::Type r,s,theta; s = c[1]*one_third - c[0]*c[0]*one_eighteenth; typename RealTypeId<Cmplx>::Type cosTheta; if(fabs(s) >= FL_UNITARIZE_EPS){ // faster when this conditional is removed? const typename RealTypeId<Cmplx>::Type rsqrt_s = rsqrt(s); r = c[2]*0.5 - (c[0]*one_third)*(c[1] - c[0]*c[0]*one_ninth); cosTheta = r*rsqrt_s*rsqrt_s*rsqrt_s; if(fabs(cosTheta) >= 1.0){ theta = (r > 0) ? 0.0 : FL_UNITARIZE_PI; }else{ theta = acos(cosTheta); // this is the primary performance limiter } const typename RealTypeId<Cmplx>::Type sqrt_s = s*rsqrt_s; typename RealTypeId<Cmplx>::Type as, ac; sincos( theta*one_third, &as, &ac ); g[0] = c[0]*one_third + 2*sqrt_s*ac; g[1] = c[0]*one_third - 2*sqrt_s*(0.5*ac + as*0.8660254037844386467637); g[2] = c[0]*one_third + 2*sqrt_s*(-0.5*ac + as*0.8660254037844386467637); } // Check the eigenvalues, if the determinant does not match the product of the eigenvalues // return false. Then call SVD instead. typename RealTypeId<Cmplx>::Type det = getDeterminant(q).x; if( fabs(det) < FL_REUNIT_SVD_ABS_ERROR ) return false; if( checkRelativeError(g[0]*g[1]*g[2],det,FL_REUNIT_SVD_REL_ERROR) == false ) return false; // At this point we have finished with the c's // use these to store sqrt(g) for(int i=0; i<3; ++i) c[i] = sqrt(g[i]); // done with the g's, use these to store u, v, w g[0] = c[0]+c[1]+c[2]; g[1] = c[0]*c[1] + c[0]*c[2] + c[1]*c[2]; g[2] = c[0]*c[1]*c[2]; const typename RealTypeId<Cmplx>::Type & denominator = 1.0 / ( g[2]*(g[0]*g[1]-g[2]) ); c[0] = (g[0]*g[1]*g[1] - g[2]*(g[0]*g[0]+g[1])) * denominator; c[1] = (-g[0]*g[0]*g[0] - g[2] + 2.*g[0]*g[1]) * denominator; c[2] = g[0] * denominator; tempq = c[1]*q + c[2]*qsq; // Add a real scalar tempq(0,0).x += c[0]; tempq(1,1).x += c[0]; tempq(2,2).x += c[0]; *res = tempq; return true;} The above is an experimental version I have that replaces the 3 cos calls with a single call to sincos. The performance is dominated by the acos call, where is it seen on GM200 that performance doubles if the acos call is removed (130->260 GFLOPS).
It would be nice if we had an alternative algorithm or reformulation that simplified this computation. Link unitarization can otherwise be a bottleneck on Maxwell GPUs when running HISQ link generation.
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mathiaswagner
maddyscientist
The link unitarization has one of the largest performance regressions when running on Maxwell, which doesn't have fast double-precision capability. Benchmarking reveals that the bulk of the time is spent in the
reciprocalRootfunction.The above is an experimental version I have that replaces the 3
coscalls with a single call tosincos. The performance is dominated by theacoscall, where is it seen on GM200 that performance doubles if theacoscall is removed (130->260 GFLOPS).It would be nice if we had an alternative algorithm or reformulation that simplified this computation. Link unitarization can otherwise be a bottleneck on Maxwell GPUs when running HISQ link generation.