[/
            Copyright Hans Dembinski 2018 - 2019.
   Distributed under the Boost Software License, Version 1.0.
      (See accompanying file LICENSE_1_0.txt or copy at
            https://www.boost.org/LICENSE_1_0.txt)
]

[section:benchmarks Benchmarks]

The library is designed to be fast. When configured correctly, it is one of the fastest libraries on the market. If you find a library that is faster than Boost.Histogram, please submit an issue on Github. We care about performance.

That being said, the time spend in filling the histogram is usually not the bottleneck of an application. Only in processing of really large data sets the performance of the histogram can be important.

All benchmarks are compiled on a laptop with a 2,9 GHz Intel Core i5 processor with Apple LLVM (clang-1001.0.46.4) and the flags `-DNDEBUG -O3 -funsafe-math-optimizations`. Adding `-fno-exceptions -fno-rtti` would increase the Boost.Histogram performance by another (10-20) %, but this is not done here out of fairness, since the ROOT histograms do not compile with these options.

[section:fill_performance Fill performance]

The fill performance of different configurations of Boost.Histogram are compared with histogram classes and functions from other libraries. Random numbers from a uniform and a normal distribution are filled into histograms with 1, 2, 3, and 6 axes. 100 bins per axis are used for 1, 2, 3 axes. 10 bins per axis for the case with 6 axes. The histogram are filled with the call operator `operator()` and the more efficient `fill`-method, which accepts large chunks of values at once. The GSL offers only 1D and 2D histograms, so there are no entries for the higher dimensional benchmarks. Raw timing results are converted to average number of CPU cycles used per input value.

There is one bar for each benchmark and the upper end has a hatched part. The full bar is the result when the histograms are filled with random normally distributed data that falls outside of the axis domain in about 10 % of the cases. This makes the branch predictors in the CPU fail every now and then, which degrades performance. The bar without the hatched part is the result when the histograms are filled with uniform random numbers which are always inside the axis range.

[$../fill_performance.svg]

[variablelist
	[[ROOT 6] [[@https://root.cern.ch ROOT classes] (`TH1I` for 1D, `TH2I` for 2D, `TH3I` for 3D and `THnI` for 6D)]]

	[[GSL] [[@https://www.gnu.org/software/gsl/doc/html/histogram.html GSL histograms] for 1D and 2D]]

	[[boost-sta] [Histogram with `std::tuple<axis::regular<>>` and `std::vector<int>` storage]]

	[[boost-dyn] [Histogram with `std::vector<axis::variant<axis::regular<>>>` and `std::vector<int>` storage]]
]

Boost.Histogram is faster than other libraries. Simultaneously, it is much more flexible, since the axis and storage types can be customized. When `operator()` is used, a histogram with compile-time configured axes (boost-sta-...) is always faster than the equivalent alternatives from other libraries. The histogram with run-time configured axes (boost-dyn-...) is comparable or slower than other libraries, but offers a run-time flexibility that the alternatives do not. If the `fill` method is used, filling either type of histogram is much faster (up to a factor 6) than filling histograms in other libraries, and the performance difference between compile-time and run-time configured axes is mostly vanishes.

[endsect]

[section:iteration_performance Iteration performance]

Boost.Histogram provides the [funcref boost::histogram::indexed] range generator for convenient iteration over the histogram cells. Using the range generator is very convenient and it is faster than by writing nested for-loops.
```
// nested for loops over 2d histogram
for (int i = 0; i < h.axis(0).size(); ++i) {
  for (int j = 0; j < h.axis(1).size(); ++j) {
    std::cout << i << " " << j << " " << h.at(i, j) << std::endl;
  }
}

// same, with indexed range generator
for (auto&& x : boost::histogram::indexed(h)) {
  std::cout << x.index(0) << " " << x.index(1) << " " << *x << std::endl;
}
```

The access time per bin is compared for these two iteration strategies for histograms that hold the axes in a `std::tuple` (tuple), in a `std::vector` (vector), and in a `std::vector<boost::histogram::axis::variant>` (vector of variants). The access time per bin is measured for axis with 4 to 128 bins per axis.

[$../iteration_performance.svg]

[endsect]

[endsect]