mirror of
https://gitlab.com/libeigen/eigen.git
synced 2024-12-21 07:19:46 +08:00
346 lines
11 KiB
C++
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);
|
|
}
|
|
}
|