add a benchmark for the different norms

1 files changed, 259 insertions, 0 deletions

diff --git a/bench/bench_norm.cpp b/bench/bench_norm.cpp
new file mode 100644
index 000000000..76c8c574d
--- /dev/null
+++ b/bench/bench_norm.cpp
@@ -0,0 +1,259 @@
+#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.stableNorm();
+}
+
+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 = 1;
+  Scalar ssq = 0;
+  for (int i=0;i<n;++i)
+  {
+    Scalar ax = ei_abs(v.coeff(i));
+    if (scale < ax)
+    {
+      ssq = Scalar(1) + ssq * ei_abs2(scale/ax);
+      scale = ax;
+    }
+    else
+      ssq += ei_abs2(ax/scale);
+  }
+  return scale * ei_sqrt(ssq);
+}
+
+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));
+}
+
+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); }
+
+template<typename T>
+EIGEN_DONT_INLINE typename T::Scalar pblueNorm(const T& v)
+{
+  typedef typename T::Scalar Scalar;
+
+  static int nmax;
+  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 = NumTraits<Scalar>::Base;                    // base for floating-point numbers
+    it    = 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    = bexp<Scalar>(ibeta, iexp);  // lower boundary of midrange
+    iexp  = (iemax + 1 - it)/2;
+    b2    = bexp<Scalar>(ibeta,iexp);   // upper boundary of midrange
+
+    iexp  = (2-iemin)/2;
+    s1m   = bexp<Scalar>(ibeta,iexp);   // scaling factor for lower range
+    iexp  = - ((iemax+it)/2);
+    s2m   = bexp<Scalar>(ibeta,iexp);   // scaling factor for upper range
+
+    overfl  = rbig*s2m;          // overfow boundary for abig
+    eps     = bexp<Scalar>(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);
+    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));
+}
+
+#define BENCH_PERF(NRM) { \
+  Eigen::BenchTimer tf, td; tf.reset(); td.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(); \
+  } \
+  std::cout << #NRM << "\t" << tf.value() << "   " << td.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";
+}
+
+int main(int argc, char** argv) 
+{
+  int tries = 5;
+  int iters = 100000;
+  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::Ones(1024*1024*32) * y;
+//     VectorXd vd = VectorXd::Ones(1024*1024*32) * y;
+//     BENCH_PERF(sqsumNorm);
+//     BENCH_PERF(blueNorm);
+//     BENCH_PERF(pblueNorm);
+//     BENCH_PERF(lapackNorm);
+//     BENCH_PERF(hypotNorm);
+//   }
+//   
+//   std::cerr << "\nPerformance (in cache):\n";
+//   {
+//     int iters = 100000;
+//     VectorXf vf = VectorXf::Ones(512) * y;
+//     VectorXd vd = VectorXd::Ones(512) * y;
+//     BENCH_PERF(sqsumNorm);
+//     BENCH_PERF(blueNorm);
+//     BENCH_PERF(pblueNorm);
+//     BENCH_PERF(lapackNorm);
+//     BENCH_PERF(hypotNorm);
+//   }
+  
+  int s = 10000;
+  double basef_ok = 1.1345743233455785456788e12;
+  double based_ok = 1.1345743233455785456788e32;
+  
+  double basef_under = 1.1345743233455785456788e-23;
+  double based_under = 1.1345743233455785456788e-180;
+  
+  double basef_over = 1.1345743233455785456788e+27;
+  double based_over = 1.1345743233455785456788e+185;
+  
+  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, 1);
+  
+  std::cerr << "\nOverflow:\n";
+  check_accuracy(basef_over, based_over, s);
+}