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re-implement stableNorm using a homemade blocky and

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vectorization friendly algorithm (slow if no vectorization)
This commit is contained in:
Gael Guennebaud
2009-07-17 16:22:39 +02:00
parent 15ed32dd6e
commit 32b08ac971
8 changed files with 256 additions and 182 deletions
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106
bench/bench_norm.cpp
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@@ -13,7 +13,7 @@ EIGEN_DONT_INLINE typename T::Scalar sqsumNorm(const T& v)
template<typename T>
EIGEN_DONT_INLINE typename T::Scalar hypotNorm(const T& v)
{
return v.stableNorm();
return v.hypotNorm();
}
template<typename T>
@@ -56,23 +56,7 @@ EIGEN_DONT_INLINE typename T::Scalar twopassNorm(T& v)
template<typename T>
EIGEN_DONT_INLINE typename T::Scalar bl2passNorm(T& v)
{
const int blockSize = 4096;
typedef typename T::Scalar Scalar;
Scalar s = 0;
Scalar ssq = 0;
for (int bi=0; bi<v.size(); bi+=blockSize)
{
int r = std::min(blockSize, v.size() - bi);
Eigen::Block<typename ei_cleantype<T>::type,Eigen::Dynamic,1,Eigen::ForceAligned> sv(v,bi,0,r,1);
Scalar m = sv.cwise().abs().maxCoeff();
if (m>s)
{
ssq = ssq * ei_abs2(s/m);
s = m;
}
ssq += (sv/s).squaredNorm();
}
return s*ei_sqrt(ssq);
return v.stableNorm();
}
template<typename T>
@@ -163,6 +147,19 @@ EIGEN_DONT_INLINE typename T::Scalar pblueNorm(const T& v)
Packet ax_s1m = ei_pmul(ax,ps1m);
Packet maskBig = ei_plt(pb2,ax);
Packet maskSml = ei_plt(ax,pb1);
// Packet maskMed = ei_pand(maskSml,maskBig);
// Packet scale = ei_pset1(Scalar(0));
// scale = ei_por(scale, ei_pand(maskBig,ps2m));
// scale = ei_por(scale, ei_pand(maskSml,ps1m));
// scale = ei_por(scale, ei_pandnot(ei_pset1(Scalar(1)),maskMed));
// ax = ei_pmul(ax,scale);
// ax = ei_pmul(ax,ax);
// pabig = ei_padd(pabig, ei_pand(maskBig, ax));
// pasml = ei_padd(pasml, ei_pand(maskSml, ax));
// pamed = ei_padd(pamed, ei_pandnot(ax,maskMed));
pabig = ei_padd(pabig, ei_pand(maskBig, ei_pmul(ax_s2m,ax_s2m)));
pasml = ei_padd(pasml, ei_pand(maskSml, ei_pmul(ax_s1m,ax_s1m)));
pamed = ei_padd(pamed, ei_pandnot(ei_pmul(ax,ax),ei_pand(maskSml,maskBig)));
@@ -215,7 +212,7 @@ EIGEN_DONT_INLINE typename T::Scalar pblueNorm(const T& v)
}
#define BENCH_PERF(NRM) { \
Eigen::BenchTimer tf, td; tf.reset(); td.reset();\
Eigen::BenchTimer tf, td, tcf; tf.reset(); td.reset(); tcf.reset();\
for (int k=0; k<tries; ++k) { \
tf.start(); \
for (int i=0; i<iters; ++i) NRM(vf); \
@@ -226,7 +223,12 @@ EIGEN_DONT_INLINE typename T::Scalar pblueNorm(const T& v)
for (int i=0; i<iters; ++i) NRM(vd); \
td.stop(); \
} \
std::cout << #NRM << "\t" << tf.value() << " " << td.value() << "\n"; \
for (int k=0; k<std::max(1,tries/3); ++k) { \
tcf.start(); \
for (int i=0; i<iters; ++i) NRM(vcf); \
tcf.stop(); \
} \
std::cout << #NRM << "\t" << tf.value() << " " << td.value() << " " << tcf.value() << "\n"; \
}
void check_accuracy(double basef, double based, int s)
@@ -263,7 +265,7 @@ void check_accuracy_var(int ef0, int ef1, int ed0, int ed1, int s)
std::cout << "pblueNorm\t" << pblueNorm(vf) << "\t" << pblueNorm(vd) << "\t" << blueNorm(vf.cast<long double>()) << "\t" << blueNorm(vd.cast<long double>()) << "\n";
std::cout << "lapackNorm\t" << lapackNorm(vf) << "\t" << lapackNorm(vd) << "\t" << lapackNorm(vf.cast<long double>()) << "\t" << lapackNorm(vd.cast<long double>()) << "\n";
std::cout << "twopassNorm\t" << twopassNorm(vf) << "\t" << twopassNorm(vd) << "\t" << twopassNorm(vf.cast<long double>()) << "\t" << twopassNorm(vd.cast<long double>()) << "\n";
std::cout << "bl2passNorm\t" << bl2passNorm(vf) << "\t" << bl2passNorm(vd) << "\t" << bl2passNorm(vf.cast<long double>()) << "\t" << bl2passNorm(vd.cast<long double>()) << "\n";
// std::cout << "bl2passNorm\t" << bl2passNorm(vf) << "\t" << bl2passNorm(vd) << "\t" << bl2passNorm(vf.cast<long double>()) << "\t" << bl2passNorm(vd.cast<long double>()) << "\n";
}
int main(int argc, char** argv)
@@ -273,34 +275,7 @@ int main(int argc, char** argv)
double y = 1.1345743233455785456788e12 * ei_random<double>();
VectorXf v = VectorXf::Ones(1024) * y;
std::cerr << "Performance (out of cache):\n";
{
int iters = 1;
VectorXf vf = VectorXf::Random(1024*1024*32) * y;
VectorXd vd = VectorXd::Random(1024*1024*32) * y;
BENCH_PERF(sqsumNorm);
BENCH_PERF(blueNorm);
BENCH_PERF(pblueNorm);
BENCH_PERF(lapackNorm);
BENCH_PERF(hypotNorm);
BENCH_PERF(twopassNorm);
BENCH_PERF(bl2passNorm);
}
std::cerr << "\nPerformance (in cache):\n";
{
int iters = 100000;
VectorXf vf = VectorXf::Random(512) * y;
VectorXd vd = VectorXd::Random(512) * y;
BENCH_PERF(sqsumNorm);
BENCH_PERF(blueNorm);
BENCH_PERF(pblueNorm);
BENCH_PERF(lapackNorm);
BENCH_PERF(hypotNorm);
BENCH_PERF(twopassNorm);
BENCH_PERF(bl2passNorm);
}
return 0;
// return 0;
int s = 10000;
double basef_ok = 1.1345743233455785456788e15;
double based_ok = 1.1345743233455785456788e95;
@@ -317,7 +292,7 @@ return 0;
check_accuracy(basef_ok, based_ok, s);
std::cerr << "\nUnderflow:\n";
check_accuracy(basef_under, based_under, 1);
check_accuracy(basef_under, based_under, s);
std::cerr << "\nOverflow:\n";
check_accuracy(basef_over, based_over, s);
@@ -335,4 +310,35 @@ return 0;
check_accuracy_var(-27,20,-302,-190,s);
std::cout << "\n";
}
std::cout.precision(4);
std::cerr << "Performance (out of cache):\n";
{
int iters = 1;
VectorXf vf = VectorXf::Random(1024*1024*32) * y;
VectorXd vd = VectorXd::Random(1024*1024*32) * y;
VectorXcf vcf = VectorXcf::Random(1024*1024*32) * y;
BENCH_PERF(sqsumNorm);
BENCH_PERF(blueNorm);
// BENCH_PERF(pblueNorm);
// BENCH_PERF(lapackNorm);
// BENCH_PERF(hypotNorm);
// BENCH_PERF(twopassNorm);
BENCH_PERF(bl2passNorm);
}
std::cerr << "\nPerformance (in cache):\n";
{
int iters = 100000;
VectorXf vf = VectorXf::Random(512) * y;
VectorXd vd = VectorXd::Random(512) * y;
VectorXcf vcf = VectorXcf::Random(512) * y;
BENCH_PERF(sqsumNorm);
BENCH_PERF(blueNorm);
// BENCH_PERF(pblueNorm);
// BENCH_PERF(lapackNorm);
// BENCH_PERF(hypotNorm);
// BENCH_PERF(twopassNorm);
BENCH_PERF(bl2passNorm);
}
}