eigen/bench/bench_norm.cpp

346 lines
11 KiB
C++

#include <typeinfo>
#include <iostream>
#include <Eigen/Core>
#include "BenchTimer.h"
using namespace Eigen;
using namespace std;
template<typename T>
EIGEN_DONT_INLINE typename T::Scalar sqsumNorm(const T& v)
{
return v.norm();
}
template<typename T>
EIGEN_DONT_INLINE typename T::Scalar hypotNorm(const T& v)
{
return v.hypotNorm();
}
template<typename T>
EIGEN_DONT_INLINE typename T::Scalar blueNorm(const T& v)
{
return v.blueNorm();
}
template<typename T>
EIGEN_DONT_INLINE typename T::Scalar lapackNorm(T& v)
{
typedef typename T::Scalar Scalar;
int n = v.size();
Scalar scale = 0;
Scalar ssq = 1;
for (int i=0;i<n;++i)
{
Scalar ax = ei_abs(v.coeff(i));
if (scale >= ax)
{
ssq += ei_abs2(ax/scale);
}
else
{
ssq = Scalar(1) + ssq * ei_abs2(scale/ax);
scale = ax;
}
}
return scale * ei_sqrt(ssq);
}
template<typename T>
EIGEN_DONT_INLINE typename T::Scalar twopassNorm(T& v)
{
typedef typename T::Scalar Scalar;
Scalar s = v.cwise().abs().maxCoeff();
return s*(v/s).norm();
}
template<typename T>
EIGEN_DONT_INLINE typename T::Scalar bl2passNorm(T& v)
{
return v.stableNorm();
}
template<typename T>
EIGEN_DONT_INLINE typename T::Scalar divacNorm(T& v)
{
int n =v.size() / 2;
for (int i=0;i<n;++i)
v(i) = v(2*i)*v(2*i) + v(2*i+1)*v(2*i+1);
n = n/2;
while (n>0)
{
for (int i=0;i<n;++i)
v(i) = v(2*i) + v(2*i+1);
n = n/2;
}
return ei_sqrt(v(0));
}
#ifdef EIGEN_VECTORIZE
Packet4f ei_plt(const Packet4f& a, Packet4f& b) { return _mm_cmplt_ps(a,b); }
Packet2d ei_plt(const Packet2d& a, Packet2d& b) { return _mm_cmplt_pd(a,b); }
Packet4f ei_pandnot(const Packet4f& a, Packet4f& b) { return _mm_andnot_ps(a,b); }
Packet2d ei_pandnot(const Packet2d& a, Packet2d& b) { return _mm_andnot_pd(a,b); }
#endif
template<typename T>
EIGEN_DONT_INLINE typename T::Scalar pblueNorm(const T& v)
{
#ifndef EIGEN_VECTORIZE
return v.blueNorm();
#else
typedef typename T::Scalar Scalar;
static int nmax = 0;
static Scalar b1, b2, s1m, s2m, overfl, rbig, relerr;
int n;
if(nmax <= 0)
{
int nbig, ibeta, it, iemin, iemax, iexp;
Scalar abig, eps;
nbig = std::numeric_limits<int>::max(); // largest integer
ibeta = std::numeric_limits<Scalar>::radix; //NumTraits<Scalar>::Base; // base for floating-point numbers
it = std::numeric_limits<Scalar>::digits; //NumTraits<Scalar>::Mantissa; // number of base-beta digits in mantissa
iemin = std::numeric_limits<Scalar>::min_exponent; // minimum exponent
iemax = std::numeric_limits<Scalar>::max_exponent; // maximum exponent
rbig = std::numeric_limits<Scalar>::max(); // largest floating-point number
// Check the basic machine-dependent constants.
if(iemin > 1 - 2*it || 1+it>iemax || (it==2 && ibeta<5)
|| (it<=4 && ibeta <= 3 ) || it<2)
{
ei_assert(false && "the algorithm cannot be guaranteed on this computer");
}
iexp = -((1-iemin)/2);
b1 = std::pow(ibeta, iexp); // lower boundary of midrange
iexp = (iemax + 1 - it)/2;
b2 = std::pow(ibeta,iexp); // upper boundary of midrange
iexp = (2-iemin)/2;
s1m = std::pow(ibeta,iexp); // scaling factor for lower range
iexp = - ((iemax+it)/2);
s2m = std::pow(ibeta,iexp); // scaling factor for upper range
overfl = rbig*s2m; // overfow boundary for abig
eps = std::pow(ibeta, 1-it);
relerr = ei_sqrt(eps); // tolerance for neglecting asml
abig = 1.0/eps - 1.0;
if (Scalar(nbig)>abig) nmax = abig; // largest safe n
else nmax = nbig;
}
typedef typename ei_packet_traits<Scalar>::type Packet;
const int ps = ei_packet_traits<Scalar>::size;
Packet pasml = ei_pset1(Scalar(0));
Packet pamed = ei_pset1(Scalar(0));
Packet pabig = ei_pset1(Scalar(0));
Packet ps2m = ei_pset1(s2m);
Packet ps1m = ei_pset1(s1m);
Packet pb2 = ei_pset1(b2);
Packet pb1 = ei_pset1(b1);
for(int j=0; j<v.size(); j+=ps)
{
Packet ax = ei_pabs(v.template packet<Aligned>(j));
Packet ax_s2m = ei_pmul(ax,ps2m);
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)));
}
Scalar abig = ei_predux(pabig);
Scalar asml = ei_predux(pasml);
Scalar amed = ei_predux(pamed);
if(abig > Scalar(0))
{
abig = ei_sqrt(abig);
if(abig > overfl)
{
ei_assert(false && "overflow");
return rbig;
}
if(amed > Scalar(0))
{
abig = abig/s2m;
amed = ei_sqrt(amed);
}
else
{
return abig/s2m;
}
}
else if(asml > Scalar(0))
{
if (amed > Scalar(0))
{
abig = ei_sqrt(amed);
amed = ei_sqrt(asml) / s1m;
}
else
{
return ei_sqrt(asml)/s1m;
}
}
else
{
return ei_sqrt(amed);
}
asml = std::min(abig, amed);
abig = std::max(abig, amed);
if(asml <= abig*relerr)
return abig;
else
return abig * ei_sqrt(Scalar(1) + ei_abs2(asml/abig));
#endif
}
#define BENCH_PERF(NRM) { \
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); \
tf.stop(); \
} \
for (int k=0; k<tries; ++k) { \
td.start(); \
for (int i=0; i<iters; ++i) NRM(vd); \
td.stop(); \
} \
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)
{
double yf = basef * ei_abs(ei_random<double>());
double yd = based * ei_abs(ei_random<double>());
VectorXf vf = VectorXf::Ones(s) * yf;
VectorXd vd = VectorXd::Ones(s) * yd;
std::cout << "reference\t" << ei_sqrt(double(s))*yf << "\t" << ei_sqrt(double(s))*yd << "\n";
std::cout << "sqsumNorm\t" << sqsumNorm(vf) << "\t" << sqsumNorm(vd) << "\n";
std::cout << "hypotNorm\t" << hypotNorm(vf) << "\t" << hypotNorm(vd) << "\n";
std::cout << "blueNorm\t" << blueNorm(vf) << "\t" << blueNorm(vd) << "\n";
std::cout << "pblueNorm\t" << pblueNorm(vf) << "\t" << pblueNorm(vd) << "\n";
std::cout << "lapackNorm\t" << lapackNorm(vf) << "\t" << lapackNorm(vd) << "\n";
std::cout << "twopassNorm\t" << twopassNorm(vf) << "\t" << twopassNorm(vd) << "\n";
std::cout << "bl2passNorm\t" << bl2passNorm(vf) << "\t" << bl2passNorm(vd) << "\n";
}
void check_accuracy_var(int ef0, int ef1, int ed0, int ed1, int s)
{
VectorXf vf(s);
VectorXd vd(s);
for (int i=0; i<s; ++i)
{
vf[i] = ei_abs(ei_random<double>()) * std::pow(double(10), ei_random<int>(ef0,ef1));
vd[i] = ei_abs(ei_random<double>()) * std::pow(double(10), ei_random<int>(ed0,ed1));
}
//std::cout << "reference\t" << ei_sqrt(double(s))*yf << "\t" << ei_sqrt(double(s))*yd << "\n";
std::cout << "sqsumNorm\t" << sqsumNorm(vf) << "\t" << sqsumNorm(vd) << "\t" << sqsumNorm(vf.cast<long double>()) << "\t" << sqsumNorm(vd.cast<long double>()) << "\n";
std::cout << "hypotNorm\t" << hypotNorm(vf) << "\t" << hypotNorm(vd) << "\t" << hypotNorm(vf.cast<long double>()) << "\t" << hypotNorm(vd.cast<long double>()) << "\n";
std::cout << "blueNorm\t" << blueNorm(vf) << "\t" << blueNorm(vd) << "\t" << blueNorm(vf.cast<long double>()) << "\t" << blueNorm(vd.cast<long double>()) << "\n";
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";
}
int main(int argc, char** argv)
{
int tries = 10;
int iters = 100000;
double y = 1.1345743233455785456788e12 * ei_random<double>();
VectorXf v = VectorXf::Ones(1024) * y;
// return 0;
int s = 10000;
double basef_ok = 1.1345743233455785456788e15;
double based_ok = 1.1345743233455785456788e95;
double basef_under = 1.1345743233455785456788e-27;
double based_under = 1.1345743233455785456788e-303;
double basef_over = 1.1345743233455785456788e+27;
double based_over = 1.1345743233455785456788e+302;
std::cout.precision(20);
std::cerr << "\nNo under/overflow:\n";
check_accuracy(basef_ok, based_ok, s);
std::cerr << "\nUnderflow:\n";
check_accuracy(basef_under, based_under, s);
std::cerr << "\nOverflow:\n";
check_accuracy(basef_over, based_over, s);
std::cerr << "\nVarying (over):\n";
for (int k=0; k<1; ++k)
{
check_accuracy_var(20,27,190,302,s);
std::cout << "\n";
}
std::cerr << "\nVarying (under):\n";
for (int k=0; k<1; ++k)
{
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);
}
}