performance_tests: better stats, and keep track of timing history

contrib/epee/include/stats.h

@@ -0,0 +1,58 @@
+#pragma once
+
+#include <vector>
+
+template<typename T, typename Tpod = T>
+class Stats
+{
+public:
+  Stats(const std::vector<T> &v): values(v), cached(0) {}
+  ~Stats() {}
+
+  size_t get_size() const;
+  Tpod get_min() const;
+  Tpod get_max() const;
+  Tpod get_median() const;
+  double get_mean() const;
+  double get_confidence_interval_95() const;
+  double get_confidence_interval_99() const;
+  double get_standard_deviation() const;
+  double get_standard_error() const;
+  double get_variance() const;
+  double get_kurtosis() const;
+  double get_non_parametric_skew() const;
+  double get_t_test(T t) const;
+  double get_t_test(size_t npoints, double mean, double stddev) const;
+  double get_t_test(const Stats<T> &other) const;
+  double get_z_test(const Stats<T> &other) const;
+  double get_test(const Stats<T> &other) const;
+  std::vector<Tpod> get_quantiles(unsigned int quantiles) const;
+  std::vector<size_t> get_bins(unsigned int bins) const;
+  bool is_same_distribution_95(size_t npoints, double mean, double stddev) const;
+  bool is_same_distribution_95(const Stats<T> &other) const;
+  bool is_same_distribution_99(size_t npoints, double mean, double stddev) const;
+  bool is_same_distribution_99(const Stats<T> &other) const;
+
+  double get_cdf95(size_t df) const;
+  double get_cdf95(const Stats<T> &other) const;
+  double get_cdf99(size_t df) const;
+  double get_cdf99(const Stats<T> &other) const;
+
+private:
+  inline bool is_cached(int bit) const;
+  inline void set_cached(int bit) const;
+
+  const std::vector<T> &values;
+
+  mutable uint64_t cached;
+  mutable Tpod min;
+  mutable Tpod max;
+  mutable Tpod median;
+  mutable double mean;
+  mutable double standard_deviation;
+  mutable double standard_error;
+  mutable double variance;
+  mutable double kurtosis;
+};
+
+#include "stats.inl"

contrib/epee/include/stats.inl

@@ -0,0 +1,359 @@
+#include <math.h>
+#include <limits>
+#include <algorithm>
+#include "stats.h"
+
+enum
+{
+  bit_min = 0,
+  bit_max,
+  bit_median,
+  bit_mean,
+  bit_standard_deviation,
+  bit_standard_error,
+  bit_variance,
+  bit_kurtosis,
+};
+
+static inline double square(double x)
+{
+  return x * x;
+}
+
+template<typename T>
+static inline double interpolate(T v, T v0, double i0, T v1, double i1)
+{
+  return i0 + (i1 - i0) * (v - v0) / (v1 - v0);
+}
+
+template<typename T, typename Tpod>
+inline bool Stats<T, Tpod>::is_cached(int bit) const
+{
+  return cached & (1<<bit);
+}
+
+template<typename T, typename Tpod>
+inline void Stats<T, Tpod>::set_cached(int bit) const
+{
+  cached |= 1<<bit;
+}
+
+template<typename T, typename Tpod>
+size_t Stats<T, Tpod>::get_size() const
+{
+  return values.size();
+}
+
+template<typename T, typename Tpod>
+Tpod Stats<T, Tpod>::get_min() const
+{
+  if (!is_cached(bit_min))
+  {
+    min = std::numeric_limits<Tpod>::max();
+    for (const T &v: values)
+      min = std::min<Tpod>(min, v);
+    set_cached(bit_min);
+  }
+  return min;
+}
+
+template<typename T, typename Tpod>
+Tpod Stats<T, Tpod>::get_max() const
+{
+  if (!is_cached(bit_max))
+  {
+    max = std::numeric_limits<Tpod>::min();
+    for (const T &v: values)
+      max = std::max<Tpod>(max, v);
+    set_cached(bit_max);
+  }
+  return max;
+}
+
+template<typename T, typename Tpod>
+Tpod Stats<T, Tpod>::get_median() const
+{
+  if (!is_cached(bit_median))
+  {
+    std::vector<Tpod> sorted;
+    sorted.reserve(values.size());
+    for (const T &v: values)
+      sorted.push_back(v);
+    std::sort(sorted.begin(), sorted.end());
+    if (sorted.size() & 1)
+    {
+      median = sorted[sorted.size() / 2];
+    }
+    else
+    {
+      median = (sorted[(sorted.size() - 1) / 2] + sorted[sorted.size() / 2]) / 2;
+    }
+    set_cached(bit_median);
+  }
+  return median;
+}
+
+template<typename T, typename Tpod>
+double Stats<T, Tpod>::get_mean() const
+{
+  if (values.empty())
+    return 0.0;
+  if (!is_cached(bit_mean))
+  {
+    mean = 0.0;
+    for (const T &v: values)
+      mean += v;
+    mean /= values.size();
+    set_cached(bit_mean);
+  }
+  return mean;
+}
+
+template<typename T, typename Tpod>
+double Stats<T, Tpod>::get_cdf95(size_t df) const
+{
+  static const double p[101] = {
+    -1, 12.706, 4.3027, 3.1824, 2.7765, 2.5706, 2.4469, 2.3646, 2.3060, 2.2622, 2.2281, 2.2010, 2.1788, 2.1604, 2.1448, 2.1315,
+    2.1199, 2.1098, 2.1009, 2.0930, 2.0860, 2.0796, 2.0739, 2.0687, 2.0639, 2.0595, 2.0555, 2.0518, 2.0484, 2.0452, 2.0423, 2.0395,
+    2.0369, 2.0345, 2.0322, 2.0301, 2.0281, 2.0262, 2.0244, 2.0227, 2.0211, 2.0195, 2.0181, 2.0167, 2.0154, 2.0141, 2.0129, 2.0117,
+    2.0106, 2.0096, 2.0086, 2.0076, 2.0066, 2.0057, 2.0049, 2.0040, 2.0032, 2.0025, 2.0017, 2.0010, 2.0003, 1.9996, 1.9990, 1.9983,
+    1.9977, 1.9971, 1.9966, 1.9960, 1.9955, 1.9949, 1.9944, 1.9939, 1.9935, 1.9930, 1.9925, 1.9921, 1.9917, 1.9913, 1.9908, 1.9905,
+    1.9901, 1.9897, 1.9893, 1.9890, 1.9886, 1.9883, 1.9879, 1.9876, 1.9873, 1.9870, 1.9867, 1.9864, 1.9861, 1.9858, 1.9855, 1.9852,
+    1.9850, 1.9847, 1.9845, 1.9842, 1.9840,
+  };
+  if (df <= 100)
+    return p[df];
+  if (df <= 120)
+    return interpolate<size_t>(df, 100, 1.9840, 120, 1.98);
+  return 1.96;
+}
+
+template<typename T, typename Tpod>
+double Stats<T, Tpod>::get_cdf95(const Stats<T> &other) const
+{
+  return get_cdf95(get_size() + other.get_size() - 2);
+}
+
+template<typename T, typename Tpod>
+double Stats<T, Tpod>::get_cdf99(size_t df) const
+{
+  static const double p[101] = {
+    -1, 9.9250, 5.8408, 4.6041, 4.0321, 3.7074, 3.4995, 3.3554, 3.2498, 3.1693, 3.1058, 3.0545, 3.0123, 2.9768, 2.9467, 2.9208, 2.8982,
+     2.8784, 2.8609, 2.8453, 2.8314, 2.8188, 2.8073, 2.7970, 2.7874, 2.7787, 2.7707, 2.7633, 2.7564, 2.7500, 2.7440, 2.7385, 2.7333,
+     2.7284, 2.7238, 2.7195, 2.7154, 2.7116, 2.7079, 2.7045, 2.7012, 2.6981, 2.6951, 2.6923, 2.6896, 2.6870, 2.6846, 2.6822, 2.6800,
+     2.6778, 2.6757, 2.6737, 2.6718, 2.6700, 2.6682, 2.6665, 2.6649, 2.6633, 2.6618, 2.6603, 2.6589, 2.6575, 2.6561, 2.6549, 2.6536,
+     2.6524, 2.6512, 2.6501, 2.6490, 2.6479, 2.6469, 2.6458, 2.6449, 2.6439, 2.6430, 2.6421, 2.6412, 2.6403, 2.6395, 2.6387, 2.6379,
+     2.6371, 2.6364, 2.6356, 2.6349, 2.6342, 2.6335, 2.6329, 2.6322, 2.6316, 2.6309, 2.6303, 2.6297, 2.6291, 2.6286, 2.6280, 2.6275,
+     2.6269, 2.6264, 2.6259,
+  };
+  if (df <= 100)
+    return p[df];
+  if (df <= 120)
+    return interpolate<size_t>(df, 100, 2.6529, 120, 2.617);
+  return 2.576;
+}
+
+template<typename T, typename Tpod>
+double Stats<T, Tpod>::get_cdf99(const Stats<T> &other) const
+{
+  return get_cdf99(get_size() + other.get_size() - 2);
+}
+
+template<typename T, typename Tpod>
+double Stats<T, Tpod>::get_confidence_interval_95() const
+{
+  const size_t df = get_size() - 1;
+  return get_standard_error() * get_cdf95(df);
+}
+
+template<typename T, typename Tpod>
+double Stats<T, Tpod>::get_confidence_interval_99() const
+{
+  const size_t df = get_size() - 1;
+  return get_standard_error() * get_cdf99(df);
+}
+
+template<typename T, typename Tpod>
+bool Stats<T, Tpod>::is_same_distribution_95(size_t npoints, double mean, double stddev) const
+{
+  return fabs(get_t_test(npoints, mean, stddev)) < get_cdf95(get_size() + npoints - 2);
+}
+
+template<typename T, typename Tpod>
+bool Stats<T, Tpod>::is_same_distribution_95(const Stats<T> &other) const
+{
+  return fabs(get_t_test(other)) < get_cdf95(other);
+}
+
+template<typename T, typename Tpod>
+bool Stats<T, Tpod>::is_same_distribution_99(size_t npoints, double mean, double stddev) const
+{
+  return fabs(get_t_test(npoints, mean, stddev)) < get_cdf99(get_size() + npoints - 2);
+}
+
+template<typename T, typename Tpod>
+bool Stats<T, Tpod>::is_same_distribution_99(const Stats<T> &other) const
+{
+  return fabs(get_t_test(other)) < get_cdf99(other);
+}
+
+template<typename T, typename Tpod>
+double Stats<T, Tpod>::get_standard_deviation() const
+{
+  if (values.size() <= 1)
+    return 0.0;
+  if (!is_cached(bit_standard_deviation))
+  {
+    Tpod m = get_mean(), t = 0;
+    for (const T &v: values)
+      t += ((T)v - m) * ((T)v - m);
+    standard_deviation = sqrt(t / ((double)values.size() - 1));
+    set_cached(bit_standard_deviation);
+  }
+  return standard_deviation;
+}
+
+template<typename T, typename Tpod>
+double Stats<T, Tpod>::get_standard_error() const
+{
+  if (!is_cached(bit_standard_error))
+  {
+    standard_error = get_standard_deviation() / sqrt(get_size());
+    set_cached(bit_standard_error);
+  }
+  return standard_error;
+}
+
+template<typename T, typename Tpod>
+double Stats<T, Tpod>::get_variance() const
+{
+  if (!is_cached(bit_variance))
+  {
+    double stddev = get_standard_deviation();
+    variance = stddev * stddev;
+    set_cached(bit_variance);
+  }
+  return variance;
+}
+
+template<typename T, typename Tpod>
+double Stats<T, Tpod>::get_kurtosis() const
+{
+  if (values.empty())
+    return 0.0;
+  if (!is_cached(bit_kurtosis))
+  {
+    double m = get_mean();
+    double n = 0, d = 0;
+    for (const T &v: values)
+    {
+      T p2 = (v - m) * (v - m);
+      T p4 = p2 * p2;
+      n += p4;
+      d += p2;
+    }
+    n /= values.size();
+    d /= values.size();
+    d *= d;
+    kurtosis = n / d;
+    set_cached(bit_kurtosis);
+  }
+  return kurtosis;
+}
+
+template<typename T, typename Tpod>
+double Stats<T, Tpod>::get_non_parametric_skew() const
+{
+  return (get_mean() - get_median()) / get_standard_deviation();
+}
+
+template<typename T, typename Tpod>
+double Stats<T, Tpod>::get_t_test(T t) const
+{
+  const double n = get_mean() - t;
+  const double d = get_standard_deviation() / sqrt(get_size());
+  return n / d;
+}
+
+template<typename T, typename Tpod>
+double Stats<T, Tpod>::get_t_test(size_t npoints, double mean, double stddev) const
+{
+  const double n = get_mean() - mean;
+  const double d = sqrt(get_variance() / get_size() + square(stddev) / npoints);
+  return n / d;
+}
+
+template<typename T, typename Tpod>
+double Stats<T, Tpod>::get_t_test(const Stats<T> &other) const
+{
+  const double n = get_mean() - other.get_mean();
+  const double d = sqrt(get_variance() / get_size() + other.get_variance() / other.get_size());
+  return n / d;
+}
+
+template<typename T, typename Tpod>
+double Stats<T, Tpod>::get_z_test(const Stats<T> &other) const
+{
+  const double m0 = get_mean();
+  const double m1 = other.get_mean();
+  const double sd0 = get_standard_deviation();
+  const double sd1 = other.get_standard_deviation();
+  const size_t s0 = get_size();
+  const size_t s1 = other.get_size();
+
+  const double n = m0 - m1;
+  const double d = sqrt(square(sd0 / sqrt(s0)) + square(sd1 / sqrt(s1)));
+
+  return n / d;
+}
+
+template<typename T, typename Tpod>
+double Stats<T, Tpod>::get_test(const Stats<T> &other) const
+{
+  if (get_size() >= 30 && other.get_size() >= 30)
+    return get_z_test(other);
+  else
+    return get_t_test(other);
+}
+
+template<typename T, typename Tpod>
+std::vector<Tpod> Stats<T, Tpod>::get_quantiles(unsigned int quantiles) const
+{
+  std::vector<Tpod> sorted;
+  sorted.reserve(values.size());
+  for (const T &v: values)
+    sorted.push_back(v);
+  std::sort(sorted.begin(), sorted.end());
+  std::vector<Tpod> q(quantiles + 1, 0);
+  for (unsigned int i = 1; i <= quantiles; ++i)
+  {
+    unsigned idx = (unsigned)ceil(values.size() * i / (double)quantiles);
+    q[i] = sorted[idx - 1];
+  }
+  if (!is_cached(bit_min))
+  {
+    min = sorted.front();
+    set_cached(bit_min);
+  }
+  q[0] = min;
+  if (!is_cached(bit_max))
+  {
+    max = sorted.back();
+    set_cached(bit_max);
+  }
+  return q;
+}
+
+template<typename T, typename Tpod>
+std::vector<size_t> Stats<T, Tpod>::get_bins(unsigned int bins) const
+{
+  std::vector<size_t> b(bins, 0);
+  const double scale = 1.0 / (get_max() - get_min());
+  const T base = get_min();
+  for (const T &v: values)
+  {
+    unsigned int idx = (v - base) * scale;
+    ++b[idx];
+  }
+  return b;
+}

src/common/CMakeLists.txt

@@ -45,6 +45,7 @@ set(common_sources
   threadpool.cpp
   updates.cpp
   aligned.c
+  timings.cc
   combinator.cpp)
 
 if (STACK_TRACE)
@@ -84,6 +85,7 @@ set(common_private_headers
   threadpool.h
   updates.h
   aligned.h
+  timings.h
   combinator.h)
 
 monero_private_headers(common

src/common/perf_timer.h

@@ -53,6 +53,7 @@ public:
   void resume();
   void reset();
   uint64_t value() const;
+  operator uint64_t() const { return value(); }
 
 protected:
   uint64_t ticks;

src/common/timings.cc

@@ -0,0 +1,125 @@
+#include <string.h>
+#include <error.h>
+#include <time.h>
+#include <algorithm>
+#include <boost/algorithm/string.hpp>
+#include "misc_log_ex.h"
+#include "timings.h"
+
+#define N_EXPECTED_FIELDS (8+11)
+
+TimingsDatabase::TimingsDatabase()
+{
+}
+
+TimingsDatabase::TimingsDatabase(const std::string &filename):
+  filename(filename)
+{
+  load();
+}
+
+TimingsDatabase::~TimingsDatabase()
+{
+  save();
+}
+
+bool TimingsDatabase::load()
+{
+  instances.clear();
+
+  if (filename.empty())
+    return true;
+
+  FILE *f = fopen(filename.c_str(), "r");
+  if (!f)
+  {
+    MDEBUG("Failed to load timings file " << filename << ": " << strerror(errno));
+    return false;
+  }
+  while (1)
+  {
+    char s[4096];
+    if (!fgets(s, sizeof(s), f))
+      break;
+    char *tab = strchr(s, '\t');
+    if (!tab)
+    {
+      MWARNING("Bad format: no tab found");
+      continue;
+    }
+    const std::string name = std::string(s, tab - s);
+    std::vector<std::string> fields;
+    char *ptr = tab + 1;
+    boost::split(fields, ptr, boost::is_any_of(" "));
+    if (fields.size() != N_EXPECTED_FIELDS)
+    {
+      MERROR("Bad format: wrong number of fields: got " << fields.size() << " expected " << N_EXPECTED_FIELDS);
+      continue;
+    }
+
+    instance i;
+
+    unsigned int idx = 0;
+    i.t = atoi(fields[idx++].c_str());
+    i.npoints = atoi(fields[idx++].c_str());
+    i.min = atof(fields[idx++].c_str());
+    i.max = atof(fields[idx++].c_str());
+    i.mean = atof(fields[idx++].c_str());
+    i.median = atof(fields[idx++].c_str());
+    i.stddev = atof(fields[idx++].c_str());
+    i.npskew = atof(fields[idx++].c_str());
+    i.deciles.reserve(11);
+    for (int n = 0; n < 11; ++n)
+    {
+      i.deciles.push_back(atoi(fields[idx++].c_str()));
+    }
+    instances.insert(std::make_pair(name, i));
+  }
+  fclose(f);
+  return true;
+}
+
+bool TimingsDatabase::save()
+{
+  if (filename.empty())
+    return true;
+
+  FILE *f = fopen(filename.c_str(), "w");
+  if (!f)
+  {
+    MERROR("Failed to write to file " << filename << ": " << strerror(errno));
+    return false;
+  }
+  for (const auto &i: instances)
+  {
+    fprintf(f, "%s", i.first.c_str());
+    fprintf(f, "\t%lu", (unsigned long)i.second.t);
+    fprintf(f, " %zu", i.second.npoints);
+    fprintf(f, " %f", i.second.min);
+    fprintf(f, " %f", i.second.max);
+    fprintf(f, " %f", i.second.mean);
+    fprintf(f, " %f", i.second.median);
+    fprintf(f, " %f", i.second.stddev);
+    fprintf(f, " %f", i.second.npskew);
+    for (uint64_t v: i.second.deciles)
+      fprintf(f, " %lu", (unsigned long)v);
+    fputc('\n', f);
+  }
+  fclose(f);
+  return true;
+}
+
+std::vector<TimingsDatabase::instance> TimingsDatabase::get(const char *name) const
+{
+  std::vector<instance> ret;
+  auto range = instances.equal_range(name);
+  for (auto i = range.first; i != range.second; ++i)
+    ret.push_back(i->second);
+  std::sort(ret.begin(), ret.end(), [](const instance &e0, const instance &e1){ return e0.t < e1.t; });
+  return ret;
+}
+
+void TimingsDatabase::add(const char *name, const instance &i)
+{
+  instances.insert(std::make_pair(name, i));
+}

src/common/timings.h

@@ -0,0 +1,34 @@
+#pragma once
+
+#include <stdint.h>
+#include <string>
+#include <vector>
+#include <map>
+
+class TimingsDatabase
+{
+public:
+  struct instance
+  {
+    time_t t;
+    size_t npoints;
+    double min, max, mean, median, stddev, npskew;
+    std::vector<uint64_t> deciles;
+  };
+
+public:
+  TimingsDatabase();
+  TimingsDatabase(const std::string &filename);
+  ~TimingsDatabase();
+
+  std::vector<instance> get(const char *name) const;
+  void add(const char *name, const instance &data);
+
+private:
+  bool load();
+  bool save();
+
+private:
+  std::string filename;
+  std::multimap<std::string, instance> instances;
+};

tests/performance_tests/main.cpp

@@ -77,10 +77,12 @@ int main(int argc, char** argv)
   const command_line::arg_descriptor<bool> arg_verbose = { "verbose", "Verbose output", false };
   const command_line::arg_descriptor<bool> arg_stats = { "stats", "Including statistics (min/median)", false };
   const command_line::arg_descriptor<unsigned> arg_loop_multiplier = { "loop-multiplier", "Run for that many times more loops", 1 };
+  const command_line::arg_descriptor<std::string> arg_timings_database = { "timings-database", "Keep timings history in a file" };
   command_line::add_arg(desc_options, arg_filter);
   command_line::add_arg(desc_options, arg_verbose);
   command_line::add_arg(desc_options, arg_stats);
   command_line::add_arg(desc_options, arg_loop_multiplier);
+  command_line::add_arg(desc_options, arg_timings_database);
 
   po::variables_map vm;
   bool r = command_line::handle_error_helper(desc_options, [&]()
@@ -93,7 +95,10 @@ int main(int argc, char** argv)
     return 1;
 
   const std::string filter = tools::glob_to_regex(command_line::get_arg(vm, arg_filter));
+  const std::string timings_database = command_line::get_arg(vm, arg_timings_database);
   Params p;
+  if (!timings_database.empty())
+    p.td = TimingsDatabase(timings_database);
   p.verbose = command_line::get_arg(vm, arg_verbose);
   p.stats = command_line::get_arg(vm, arg_stats);
   p.loop_multiplier = command_line::get_arg(vm, arg_loop_multiplier);

tests/performance_tests/performance_tests.h

@@ -37,7 +37,9 @@
 #include <boost/regex.hpp>
 
 #include "misc_language.h"
+#include "stats.h"
 #include "common/perf_timer.h"
+#include "common/timings.h"
 
 class performance_timer
 {
@@ -67,6 +69,7 @@ private:
 
 struct Params
 {
+  TimingsDatabase td;
   bool verbose;
   bool stats;
   unsigned loop_multiplier;
@@ -85,6 +88,8 @@ public:
 
   bool run()
   {
+    static_assert(0 < T::loop_count, "T::loop_count must be greater than 0");
+
     T test;
     if (!test.init())
       return false;
@@ -106,11 +111,13 @@ public:
         m_per_call_timers[i].pause();
     }
     m_elapsed = timer.elapsed_ms();
+    m_stats.reset(new Stats<tools::PerformanceTimer, uint64_t>(m_per_call_timers));
 
     return true;
   }
 
   int elapsed_time() const { return m_elapsed; }
+  size_t get_size() const { return m_stats->get_size(); }
 
   int time_per_call(int scale = 1) const
   {
@@ -118,59 +125,19 @@ public:
     return m_elapsed * scale / (T::loop_count * m_params.loop_multiplier);
   }
 
-  uint64_t per_call_min() const
+  uint64_t get_min() const { return m_stats->get_min(); }
-  {
+  uint64_t get_max() const { return m_stats->get_max(); }
-    uint64_t v = std::numeric_limits<uint64_t>::max();
+  double get_mean() const { return m_stats->get_mean(); }
-    for (const auto &pt: m_per_call_timers)
+  uint64_t get_median() const { return m_stats->get_median(); }
-      v = std::min(v, pt.value());
+  double get_stddev() const { return m_stats->get_standard_deviation(); }
-    return v;
+  double get_non_parametric_skew() const { return m_stats->get_non_parametric_skew(); }
-  }
+  std::vector<uint64_t> get_quantiles(size_t n) const { return m_stats->get_quantiles(n); }
 
-  uint64_t per_call_max() const
+  bool is_same_distribution(size_t npoints, double mean, double stddev) const
   {
-    uint64_t v = std::numeric_limits<uint64_t>::min();
+    return m_stats->is_same_distribution_99(npoints, mean, stddev);
-    for (const auto &pt: m_per_call_timers)
-      v = std::max(v, pt.value());
-    return v;
   }
 
-  uint64_t per_call_mean() const
-  {
-    uint64_t v = 0;
-    for (const auto &pt: m_per_call_timers)
-      v += pt.value();
-    return v / m_per_call_timers.size();
-  }
-
-  uint64_t per_call_median() const
-  {
-    std::vector<uint64_t> values;
-    values.reserve(m_per_call_timers.size());
-    for (const auto &pt: m_per_call_timers)
-      values.push_back(pt.value());
-    return epee::misc_utils::median(values);
-  }
-
-  uint64_t per_call_stddev() const
-  {
-    if (m_per_call_timers.size() <= 1)
-      return 0;
-    const uint64_t mean = per_call_mean();
-    uint64_t acc = 0;
-    for (const auto &pt: m_per_call_timers)
-    {
-      int64_t dv = pt.value() - mean;
-      acc += dv * dv;
-    }
-    acc /= m_per_call_timers.size () - 1;
-    return sqrt(acc);
-  }
-
-  uint64_t min_time_ns() const { return tools::ticks_to_ns(per_call_min()); }
-  uint64_t max_time_ns() const { return tools::ticks_to_ns(per_call_max()); }
-  uint64_t median_time_ns() const { return tools::ticks_to_ns(per_call_median()); }
-  uint64_t standard_deviation_time_ns() const { return tools::ticks_to_ns(per_call_stddev()); }
-
 private:
   /**
    * Warm up processor core, enabling turbo boost, etc.
@@ -191,10 +158,11 @@ private:
   int m_elapsed;
   Params m_params;
   std::vector<tools::PerformanceTimer> m_per_call_timers;
+  std::unique_ptr<Stats<tools::PerformanceTimer, uint64_t>> m_stats;
 };
 
 template <typename T>
-void run_test(const std::string &filter, const Params &params, const char* test_name)
+void run_test(const std::string &filter, Params &params, const char* test_name)
 {
   boost::smatch match;
   if (!filter.empty() && !boost::regex_match(std::string(test_name), match, boost::regex(filter)))
@@ -210,10 +178,10 @@ void run_test(const std::string &filter, const Params &params, const char* test_
       std::cout << "  elapsed:       " << runner.elapsed_time() << " ms\n";
       if (params.stats)
       {
-        std::cout << "  min:       " << runner.min_time_ns() << " ns\n";
+        std::cout << "  min:       " << runner.get_min() << " ns\n";
-        std::cout << "  max:       " << runner.max_time_ns() << " ns\n";
+        std::cout << "  max:       " << runner.get_max() << " ns\n";
-        std::cout << "  median:    " << runner.median_time_ns() << " ns\n";
+        std::cout << "  median:    " << runner.get_median() << " ns\n";
-        std::cout << "  std dev:   " << runner.standard_deviation_time_ns() << " ns\n";
+        std::cout << "  std dev:   " << runner.get_stddev() << " ns\n";
       }
     }
     else
@@ -221,24 +189,48 @@ void run_test(const std::string &filter, const Params &params, const char* test_
       std::cout << test_name << " (" << T::loop_count * params.loop_multiplier << " calls) - OK:";
     }
     const char *unit = "ms";
-    uint64_t scale = 1000000;
+    double scale = 1000000;
-    int time_per_call = runner.time_per_call();
+    uint64_t time_per_call = runner.time_per_call();
-    if (time_per_call < 30000) {
+    if (time_per_call < 100) {
+     scale = 1000;
      time_per_call = runner.time_per_call(1000);
 #ifdef _WIN32
      unit = "\xb5s";
 #else
      unit = "µs";
 #endif
-     scale = 1000;
     }
+    const auto quantiles = runner.get_quantiles(10);
+    double min = runner.get_min();
+    double max = runner.get_max();
+    double med = runner.get_median();
+    double mean = runner.get_mean();
+    double stddev = runner.get_stddev();
+    double npskew = runner.get_non_parametric_skew();
+
+    std::vector<TimingsDatabase::instance> prev_instances = params.td.get(test_name);
+    params.td.add(test_name, {time(NULL), runner.get_size(), min, max, mean, med, stddev, npskew, quantiles});
+
     std::cout << (params.verbose ? "  time per call: " : " ") << time_per_call << " " << unit << "/call" << (params.verbose ? "\n" : "");
     if (params.stats)
     {
-      uint64_t min_ns = runner.min_time_ns() / scale;
+      uint64_t mins = min / scale;
-      uint64_t med_ns = runner.median_time_ns() / scale;
+      uint64_t maxs = max / scale;
-      uint64_t stddev_ns = runner.standard_deviation_time_ns() / scale;
+      uint64_t meds = med / scale;
-      std::cout << " (min " << min_ns << " " << unit << ", median " << med_ns << " " << unit << ", std dev " << stddev_ns << " " << unit << ")";
+      uint64_t p95s = quantiles[9] / scale;
+      uint64_t stddevs = stddev / scale;
+      std::string cmp;
+      if (!prev_instances.empty())
+      {
+        const TimingsDatabase::instance &prev_instance = prev_instances.back();
+        if (!runner.is_same_distribution(prev_instance.npoints, prev_instance.mean, prev_instance.stddev))
+        {
+          double pc = fabs(100. * (prev_instance.mean - runner.get_mean()) / prev_instance.mean);
+          cmp = ", " + std::to_string(pc) + "% " + (mean > prev_instance.mean ? "slower" : "faster");
+        }
+cmp += "  -- " + std::to_string(prev_instance.mean);
+      }
+      std::cout << " (min " << mins << " " << unit << ", 90th " << p95s << " " << unit << ", median " << meds << " " << unit << ", std dev " << stddevs << " " << unit << ")" << cmp;
     }
     std::cout << std::endl;
   }