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bench_norm.cpp
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Thu, Feb 20, 22:43

bench_norm.cpp
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#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(T& v)
{
return v.norm();
}
template<typename T>
EIGEN_DONT_INLINE typename T::Scalar stableNorm(T& v)
{
return v.stableNorm();
}
template<typename T>
EIGEN_DONT_INLINE typename T::Scalar hypotNorm(T& v)
{
return v.hypotNorm();
}
template<typename T>
EIGEN_DONT_INLINE typename T::Scalar blueNorm(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 = std::abs(v.coeff(i));
if (scale >= ax)
{
ssq += numext::abs2(ax/scale);
}
else
{
ssq = Scalar(1) + ssq * numext::abs2(scale/ax);
scale = ax;
}
}
return scale * std::sqrt(ssq);
}
template<typename T>
EIGEN_DONT_INLINE typename T::Scalar twopassNorm(T& v)
{
typedef typename T::Scalar Scalar;
Scalar s = v.array().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 std::sqrt(v(0));
}
namespace Eigen {
namespace internal {
#ifdef EIGEN_VECTORIZE
Packet4f plt(const Packet4f& a, Packet4f& b) { return _mm_cmplt_ps(a,b); }
Packet2d plt(const Packet2d& a, Packet2d& b) { return _mm_cmplt_pd(a,b); }
Packet4f pandnot(const Packet4f& a, Packet4f& b) { return _mm_andnot_ps(a,b); }
Packet2d 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 = NumTraits<int>::highest(); // largest integer
ibeta = std::numeric_limits<Scalar>::radix; // NumTraits<Scalar>::Base; // base for floating-point numbers
it = NumTraits<Scalar>::digits(); // NumTraits<Scalar>::Mantissa; // number of base-beta digits in mantissa
iemin = NumTraits<Scalar>::min_exponent(); // minimum exponent
iemax = NumTraits<Scalar>::max_exponent(); // maximum exponent
rbig = NumTraits<Scalar>::highest(); // 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)
{
eigen_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; // overflow boundary for abig
eps = std::pow(ibeta, 1-it);
relerr = std::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 internal::packet_traits<Scalar>::type Packet;
const int ps = internal::packet_traits<Scalar>::size;
Packet pasml = internal::pset1<Packet>(Scalar(0));
Packet pamed = internal::pset1<Packet>(Scalar(0));
Packet pabig = internal::pset1<Packet>(Scalar(0));
Packet ps2m = internal::pset1<Packet>(s2m);
Packet ps1m = internal::pset1<Packet>(s1m);
Packet pb2 = internal::pset1<Packet>(b2);
Packet pb1 = internal::pset1<Packet>(b1);
for(int j=0; j<v.size(); j+=ps)
{
Packet ax = internal::pabs(v.template packet<Aligned>(j));
Packet ax_s2m = internal::pmul(ax,ps2m);
Packet ax_s1m = internal::pmul(ax,ps1m);
Packet maskBig = internal::plt(pb2,ax);
Packet maskSml = internal::plt(ax,pb1);
// Packet maskMed = internal::pand(maskSml,maskBig);
// Packet scale = internal::pset1(Scalar(0));
// scale = internal::por(scale, internal::pand(maskBig,ps2m));
// scale = internal::por(scale, internal::pand(maskSml,ps1m));
// scale = internal::por(scale, internal::pandnot(internal::pset1(Scalar(1)),maskMed));
// ax = internal::pmul(ax,scale);
// ax = internal::pmul(ax,ax);
// pabig = internal::padd(pabig, internal::pand(maskBig, ax));
// pasml = internal::padd(pasml, internal::pand(maskSml, ax));
// pamed = internal::padd(pamed, internal::pandnot(ax,maskMed));
pabig = internal::padd(pabig, internal::pand(maskBig, internal::pmul(ax_s2m,ax_s2m)));
pasml = internal::padd(pasml, internal::pand(maskSml, internal::pmul(ax_s1m,ax_s1m)));
pamed = internal::padd(pamed, internal::pandnot(internal::pmul(ax,ax),internal::pand(maskSml,maskBig)));
}
Scalar abig = internal::predux(pabig);
Scalar asml = internal::predux(pasml);
Scalar amed = internal::predux(pamed);
if(abig > Scalar(0))
{
abig = std::sqrt(abig);
if(abig > overfl)
{
eigen_assert(false && "overflow");
return rbig;
}
if(amed > Scalar(0))
{
abig = abig/s2m;
amed = std::sqrt(amed);
}
else
{
return abig/s2m;
}
}
else if(asml > Scalar(0))
{
if (amed > Scalar(0))
{
abig = std::sqrt(amed);
amed = std::sqrt(asml) / s1m;
}
else
{
return std::sqrt(asml)/s1m;
}
}
else
{
return std::sqrt(amed);
}
asml = std::min(abig, amed);
abig = std::max(abig, amed);
if(asml <= abig*relerr)
return abig;
else
return abig * std::sqrt(Scalar(1) + numext::abs2(asml/abig));
#endif
}
#define BENCH_PERF(NRM) { \
float af = 0; double ad = 0; std::complex<float> ac = 0; \
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) { af += NRM(vf); } \
tf.stop(); \
} \
for (int k=0; k<tries; ++k) { \
td.start(); \
for (int i=0; i<iters; ++i) { ad += NRM(vd); } \
td.stop(); \
} \
/*for (int k=0; k<std::max(1,tries/3); ++k) { \
tcf.start(); \
for (int i=0; i<iters; ++i) { ac += 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 * std::abs(internal::random<double>());
double yd = based * std::abs(internal::random<double>());
VectorXf vf = VectorXf::Ones(s) * yf;
VectorXd vd = VectorXd::Ones(s) * yd;
std::cout << "reference\t" << std::sqrt(double(s))*yf << "\t" << std::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] = std::abs(internal::random<double>()) * std::pow(double(10), internal::random<int>(ef0,ef1));
vd[i] = std::abs(internal::random<double>()) * std::pow(double(10), internal::random<int>(ed0,ed1));
}
//std::cout << "reference\t" << internal::sqrt(double(s))*yf << "\t" << internal::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 * internal::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";
}
y = 1;
std::cout.precision(4);
int s1 = 1024*1024*32;
std::cerr << "Performance (out of cache, " << s1 << "):\n";
{
int iters = 1;
VectorXf vf = VectorXf::Random(s1) * y;
VectorXd vd = VectorXd::Random(s1) * y;
VectorXcf vcf = VectorXcf::Random(s1) * y;
BENCH_PERF(sqsumNorm);
BENCH_PERF(stableNorm);
BENCH_PERF(blueNorm);
BENCH_PERF(pblueNorm);
BENCH_PERF(lapackNorm);
BENCH_PERF(hypotNorm);
BENCH_PERF(twopassNorm);
BENCH_PERF(bl2passNorm);
}
std::cerr << "\nPerformance (in cache, " << 512 << "):\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(stableNorm);
BENCH_PERF(blueNorm);
BENCH_PERF(pblueNorm);
BENCH_PERF(lapackNorm);
BENCH_PERF(hypotNorm);
BENCH_PERF(twopassNorm);
BENCH_PERF(bl2passNorm);
}
}

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