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+// __ _ _______ __ _ _____ ______ _______ __ _ _______ _ _
+// | \ | |_____| | \ | | | |_____] |______ | \ | | |_____|
+// | \_| | | | \_| |_____| |_____] |______ | \_| |_____ | |
+//
+// Microbenchmark framework for C++11/14/17/20
+// https://github.com/martinus/nanobench
+//
+// Licensed under the MIT License <http://opensource.org/licenses/MIT>.
+// SPDX-License-Identifier: MIT
+// Copyright (c) 2019-2020 Martin Ankerl <martin.ankerl@gmail.com>
+//
+// Permission is hereby granted, free of charge, to any person obtaining a copy
+// of this software and associated documentation files (the "Software"), to deal
+// in the Software without restriction, including without limitation the rights
+// to use, copy, modify, merge, publish, distribute, sublicense, and/or sell
+// copies of the Software, and to permit persons to whom the Software is
+// furnished to do so, subject to the following conditions:
+//
+// The above copyright notice and this permission notice shall be included in all
+// copies or substantial portions of the Software.
+//
+// THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, EXPRESS OR
+// IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY,
+// FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. IN NO EVENT SHALL THE
+// AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER
+// LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING FROM,
+// OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER DEALINGS IN THE
+// SOFTWARE.
+
+#ifndef ANKERL_NANOBENCH_H_INCLUDED
+#define ANKERL_NANOBENCH_H_INCLUDED
+
+// see https://semver.org/
+#define ANKERL_NANOBENCH_VERSION_MAJOR 4 // incompatible API changes
+#define ANKERL_NANOBENCH_VERSION_MINOR 0 // backwards-compatible changes
+#define ANKERL_NANOBENCH_VERSION_PATCH 0 // backwards-compatible bug fixes
+
+///////////////////////////////////////////////////////////////////////////////////////////////////
+// public facing api - as minimal as possible
+///////////////////////////////////////////////////////////////////////////////////////////////////
+
+#include <chrono> // high_resolution_clock
+#include <cstring> // memcpy
+#include <iosfwd> // for std::ostream* custom output target in Config
+#include <string> // all names
+#include <vector> // holds all results
+
+#define ANKERL_NANOBENCH(x) ANKERL_NANOBENCH_PRIVATE_##x()
+
+#define ANKERL_NANOBENCH_PRIVATE_CXX() __cplusplus
+#define ANKERL_NANOBENCH_PRIVATE_CXX98() 199711L
+#define ANKERL_NANOBENCH_PRIVATE_CXX11() 201103L
+#define ANKERL_NANOBENCH_PRIVATE_CXX14() 201402L
+#define ANKERL_NANOBENCH_PRIVATE_CXX17() 201703L
+
+#if ANKERL_NANOBENCH(CXX) >= ANKERL_NANOBENCH(CXX17)
+# define ANKERL_NANOBENCH_PRIVATE_NODISCARD() [[nodiscard]]
+#else
+# define ANKERL_NANOBENCH_PRIVATE_NODISCARD()
+#endif
+
+#if defined(__clang__)
+# define ANKERL_NANOBENCH_PRIVATE_IGNORE_PADDED_PUSH() \
+ _Pragma("clang diagnostic push") _Pragma("clang diagnostic ignored \"-Wpadded\"")
+# define ANKERL_NANOBENCH_PRIVATE_IGNORE_PADDED_POP() _Pragma("clang diagnostic pop")
+#else
+# define ANKERL_NANOBENCH_PRIVATE_IGNORE_PADDED_PUSH()
+# define ANKERL_NANOBENCH_PRIVATE_IGNORE_PADDED_POP()
+#endif
+
+#if defined(__GNUC__)
+# define ANKERL_NANOBENCH_PRIVATE_IGNORE_EFFCPP_PUSH() _Pragma("GCC diagnostic push") _Pragma("GCC diagnostic ignored \"-Weffc++\"")
+# define ANKERL_NANOBENCH_PRIVATE_IGNORE_EFFCPP_POP() _Pragma("GCC diagnostic pop")
+#else
+# define ANKERL_NANOBENCH_PRIVATE_IGNORE_EFFCPP_PUSH()
+# define ANKERL_NANOBENCH_PRIVATE_IGNORE_EFFCPP_POP()
+#endif
+
+#if defined(ANKERL_NANOBENCH_LOG_ENABLED)
+# include <iostream>
+# define ANKERL_NANOBENCH_LOG(x) std::cout << __FUNCTION__ << "@" << __LINE__ << ": " << x << std::endl
+#else
+# define ANKERL_NANOBENCH_LOG(x)
+#endif
+
+#if defined(__linux__) && !defined(ANKERL_NANOBENCH_DISABLE_PERF_COUNTERS)
+# define ANKERL_NANOBENCH_PRIVATE_PERF_COUNTERS() 1
+#else
+# define ANKERL_NANOBENCH_PRIVATE_PERF_COUNTERS() 0
+#endif
+
+#if defined(__clang__)
+# define ANKERL_NANOBENCH_NO_SANITIZE(...) __attribute__((no_sanitize(__VA_ARGS__)))
+#else
+# define ANKERL_NANOBENCH_NO_SANITIZE(...)
+#endif
+
+#if defined(_MSC_VER)
+# define ANKERL_NANOBENCH_PRIVATE_NOINLINE() __declspec(noinline)
+#else
+# define ANKERL_NANOBENCH_PRIVATE_NOINLINE() __attribute__((noinline))
+#endif
+
+// workaround missing "is_trivially_copyable" in g++ < 5.0
+// See https://stackoverflow.com/a/31798726/48181
+#if defined(__GNUC__) && __GNUC__ < 5
+# define ANKERL_NANOBENCH_IS_TRIVIALLY_COPYABLE(...) __has_trivial_copy(__VA_ARGS__)
+#else
+# define ANKERL_NANOBENCH_IS_TRIVIALLY_COPYABLE(...) std::is_trivially_copyable<__VA_ARGS__>::value
+#endif
+
+// declarations ///////////////////////////////////////////////////////////////////////////////////
+
+namespace ankerl {
+namespace nanobench {
+
+using Clock = std::conditional<std::chrono::high_resolution_clock::is_steady, std::chrono::high_resolution_clock,
+ std::chrono::steady_clock>::type;
+class Bench;
+struct Config;
+class Result;
+class Rng;
+class BigO;
+
+/**
+ * @brief Renders output from a mustache-like template and benchmark results.
+ *
+ * The templating facility here is heavily inspired by [mustache - logic-less templates](https://mustache.github.io/).
+ * It adds a few more features that are necessary to get all of the captured data out of nanobench. Please read the
+ * excellent [mustache manual](https://mustache.github.io/mustache.5.html) to see what this is all about.
+ *
+ * nanobench output has two nested layers, *result* and *measurement*. Here is a hierarchy of the allowed tags:
+ *
+ * * `{{#result}}` Marks the begin of the result layer. Whatever comes after this will be instantiated as often as
+ * a benchmark result is available. Within it, you can use these tags:
+ *
+ * * `{{title}}` See Bench::title().
+ *
+ * * `{{name}}` Benchmark name, usually directly provided with Bench::run(), but can also be set with Bench::name().
+ *
+ * * `{{unit}}` Unit, e.g. `byte`. Defaults to `op`, see Bench::title().
+ *
+ * * `{{batch}}` Batch size, see Bench::batch().
+ *
+ * * `{{complexityN}}` Value used for asymptotic complexity calculation. See Bench::complexityN().
+ *
+ * * `{{epochs}}` Number of epochs, see Bench::epochs().
+ *
+ * * `{{clockResolution}}` Accuracy of the clock, i.e. what's the smallest time possible to measure with the clock.
+ * For modern systems, this can be around 20 ns. This value is automatically determined by nanobench at the first
+ * benchmark that is run, and used as a static variable throughout the application's runtime.
+ *
+ * * `{{clockResolutionMultiple}}` Configuration multiplier for `clockResolution`. See Bench::clockResolutionMultiple().
+ * This is the target runtime for each measurement (epoch). That means the more accurate your clock is, the faster
+ * will be the benchmark. Basing the measurement's runtime on the clock resolution is the main reason why nanobench is so fast.
+ *
+ * * `{{maxEpochTime}}` Configuration for a maximum time each measurement (epoch) is allowed to take. Note that at least
+ * a single iteration will be performed, even when that takes longer than maxEpochTime. See Bench::maxEpochTime().
+ *
+ * * `{{minEpochTime}}` Minimum epoch time, usually not set. See Bench::minEpochTime().
+ *
+ * * `{{minEpochIterations}}` See Bench::minEpochIterations().
+ *
+ * * `{{epochIterations}}` See Bench::epochIterations().
+ *
+ * * `{{warmup}}` Number of iterations used before measuring starts. See Bench::warmup().
+ *
+ * * `{{relative}}` True or false, depending on the setting you have used. See Bench::relative().
+ *
+ * Apart from these tags, it is also possible to use some mathematical operations on the measurement data. The operations
+ * are of the form `{{command(name)}}`. Currently `name` can be one of `elapsed`, `iterations`. If performance counters
+ * are available (currently only on current Linux systems), you also have `pagefaults`, `cpucycles`,
+ * `contextswitches`, `instructions`, `branchinstructions`, and `branchmisses`. All the measuers (except `iterations`) are
+ * provided for a single iteration (so `elapsed` is the time a single iteration took). The following tags are available:
+ *
+ * * `{{median(<name>>)}}` Calculate median of a measurement data set, e.g. `{{median(elapsed)}}`.
+ *
+ * * `{{average(<name>)}}` Average (mean) calculation.
+ *
+ * * `{{medianAbsolutePercentError(<name>)}}` Calculates MdAPE, the Median Absolute Percentage Error. The MdAPE is an excellent
+ * metric for the variation of measurements. It is more robust to outliers than the
+ * [Mean absolute percentage error (M-APE)](https://en.wikipedia.org/wiki/Mean_absolute_percentage_error).
+ * @f[
+ * \mathrm{medianAbsolutePercentError}(e) = \mathrm{median}\{| \frac{e_i - \mathrm{median}\{e\}}{e_i}| \}
+ * @f]
+ * E.g. for *elapsed*: First, @f$ \mathrm{median}\{elapsed\} @f$ is calculated. This is used to calculate the absolute percentage
+ * error to this median for each measurement, as in @f$ | \frac{e_i - \mathrm{median}\{e\}}{e_i}| @f$. All these results
+ * are sorted, and the middle value is chosen as the median absolute percent error.
+ *
+ * This measurement is a bit hard to interpret, but it is very robust against outliers. E.g. a value of 5% means that half of the
+ * measurements deviate less than 5% from the median, and the other deviate more than 5% from the median.
+ *
+ * * `{{sum(<name>)}}` Sums of all the measurements. E.g. `{{sum(iterations)}}` will give you the total number of iterations
+* measured in this benchmark.
+ *
+ * * `{{minimum(<name>)}}` Minimum of all measurements.
+ *
+ * * `{{maximum(<name>)}}` Maximum of all measurements.
+ *
+ * * `{{sumProduct(<first>, <second>)}}` Calculates the sum of the products of corresponding measures:
+ * @f[
+ * \mathrm{sumProduct}(a,b) = \sum_{i=1}^{n}a_i\cdot b_i
+ * @f]
+ * E.g. to calculate total runtime of the benchmark, you multiply iterations with elapsed time for each measurement, and
+ * sum these results up:
+ * `{{sumProduct(iterations, elapsed)}}`.
+ *
+ * * `{{#measurement}}` To access individual measurement results, open the begin tag for measurements.
+ *
+ * * `{{elapsed}}` Average elapsed time per iteration, in seconds.
+ *
+ * * `{{iterations}}` Number of iterations in the measurement. The number of iterations will fluctuate due
+ * to some applied randomness, to enhance accuracy.
+ *
+ * * `{{pagefaults}}` Average number of pagefaults per iteration.
+ *
+ * * `{{cpucycles}}` Average number of CPU cycles processed per iteration.
+ *
+ * * `{{contextswitches}}` Average number of context switches per iteration.
+ *
+ * * `{{instructions}}` Average number of retired instructions per iteration.
+ *
+ * * `{{branchinstructions}}` Average number of branches executed per iteration.
+ *
+ * * `{{branchmisses}}` Average number of branches that were missed per iteration.
+ *
+ * * `{{/measurement}}` Ends the measurement tag.
+ *
+ * * `{{/result}}` Marks the end of the result layer. This is the end marker for the template part that will be instantiated
+ * for each benchmark result.
+ *
+ *
+ * For the layer tags *result* and *measurement* you additionally can use these special markers:
+ *
+ * * ``{{#-first}}`` - Begin marker of a template that will be instantiated *only for the first* entry in the layer. Use is only
+ * allowed between the begin and end marker of the layer allowed. So between ``{{#result}}`` and ``{{/result}}``, or between
+ * ``{{#measurement}}`` and ``{{/measurement}}``. Finish the template with ``{{/-first}}``.
+ *
+ * * ``{{^-first}}`` - Begin marker of a template that will be instantiated *for each except the first* entry in the layer. This,
+ * this is basically the inversion of ``{{#-first}}``. Use is only allowed between the begin and end marker of the layer allowed.
+ * So between ``{{#result}}`` and ``{{/result}}``, or between ``{{#measurement}}`` and ``{{/measurement}}``.
+ *
+ * * ``{{/-first}}`` - End marker for either ``{{#-first}}`` or ``{{^-first}}``.
+ *
+ * * ``{{#-last}}`` - Begin marker of a template that will be instantiated *only for the last* entry in the layer. Use is only
+ * allowed between the begin and end marker of the layer allowed. So between ``{{#result}}`` and ``{{/result}}``, or between
+ * ``{{#measurement}}`` and ``{{/measurement}}``. Finish the template with ``{{/-last}}``.
+ *
+ * * ``{{^-last}}`` - Begin marker of a template that will be instantiated *for each except the last* entry in the layer. This,
+ * this is basically the inversion of ``{{#-last}}``. Use is only allowed between the begin and end marker of the layer allowed.
+ * So between ``{{#result}}`` and ``{{/result}}``, or between ``{{#measurement}}`` and ``{{/measurement}}``.
+ *
+ * * ``{{/-last}}`` - End marker for either ``{{#-last}}`` or ``{{^-last}}``.
+ *
+ @verbatim embed:rst
+
+ For an overview of all the possible data you can get out of nanobench, please see the tutorial at :ref:`tutorial-template-json`.
+
+ The templates that ship with nanobench are:
+
+ * :cpp:func:`templates::csv() <ankerl::nanobench::templates::csv()>`
+ * :cpp:func:`templates::json() <ankerl::nanobench::templates::json()>`
+ * :cpp:func:`templates::htmlBoxplot() <ankerl::nanobench::templates::htmlBoxplot()>`
+
+ @endverbatim
+ *
+ * @param mustacheTemplate The template.
+ * @param bench Benchmark, containing all the results.
+ * @param out Output for the generated output.
+ */
+void render(char const* mustacheTemplate, Bench const& bench, std::ostream& out);
+
+/**
+ * Same as render(char const* mustacheTemplate, Bench const& bench, std::ostream& out), but for when
+ * you only have results available.
+ *
+ * @param mustacheTemplate The template.
+ * @param results All the results to be used for rendering.
+ * @param out Output for the generated output.
+ */
+void render(char const* mustacheTemplate, std::vector<Result> const& results, std::ostream& out);
+
+// Contains mustache-like templates
+namespace templates {
+
+/*!
+ @brief CSV data for the benchmark results.
+
+ Generates a comma-separated values dataset. First line is the header, each following line is a summary of each benchmark run.
+
+ @verbatim embed:rst
+ See the tutorial at :ref:`tutorial-template-csv` for an example.
+ @endverbatim
+ */
+char const* csv() noexcept;
+
+/*!
+ @brief HTML output that uses plotly to generate an interactive boxplot chart. See the tutorial for an example output.
+
+ The output uses only the elapsed time, and displays each epoch as a single dot.
+ @verbatim embed:rst
+ See the tutorial at :ref:`tutorial-template-html` for an example.
+ @endverbatim
+
+ @see ankerl::nanobench::render()
+ */
+char const* htmlBoxplot() noexcept;
+
+/*!
+ @brief Template to generate JSON data.
+
+ The generated JSON data contains *all* data that has been generated. All times are as double values, in seconds. The output can get
+ quite large.
+ @verbatim embed:rst
+ See the tutorial at :ref:`tutorial-template-json` for an example.
+ @endverbatim
+ */
+char const* json() noexcept;
+
+} // namespace templates
+
+namespace detail {
+
+template <typename T>
+struct PerfCountSet;
+
+class IterationLogic;
+class PerformanceCounters;
+
+#if ANKERL_NANOBENCH(PERF_COUNTERS)
+class LinuxPerformanceCounters;
+#endif
+
+} // namespace detail
+} // namespace nanobench
+} // namespace ankerl
+
+// definitions ////////////////////////////////////////////////////////////////////////////////////
+
+namespace ankerl {
+namespace nanobench {
+namespace detail {
+
+template <typename T>
+struct PerfCountSet {
+ T pageFaults{};
+ T cpuCycles{};
+ T contextSwitches{};
+ T instructions{};
+ T branchInstructions{};
+ T branchMisses{};
+};
+
+} // namespace detail
+
+ANKERL_NANOBENCH(IGNORE_PADDED_PUSH)
+struct Config {
+ // actual benchmark config
+ std::string mBenchmarkTitle = "benchmark";
+ std::string mBenchmarkName = "noname";
+ std::string mUnit = "op";
+ double mBatch = 1.0;
+ double mComplexityN = -1.0;
+ size_t mNumEpochs = 11;
+ size_t mClockResolutionMultiple = static_cast<size_t>(1000);
+ std::chrono::nanoseconds mMaxEpochTime = std::chrono::milliseconds(100);
+ std::chrono::nanoseconds mMinEpochTime{};
+ uint64_t mMinEpochIterations{1};
+ uint64_t mEpochIterations{0}; // If not 0, run *exactly* these number of iterations per epoch.
+ uint64_t mWarmup = 0;
+ std::ostream* mOut = nullptr;
+ bool mShowPerformanceCounters = true;
+ bool mIsRelative = false;
+
+ Config();
+ ~Config();
+ Config& operator=(Config const&);
+ Config& operator=(Config&&);
+ Config(Config const&);
+ Config(Config&&) noexcept;
+};
+ANKERL_NANOBENCH(IGNORE_PADDED_POP)
+
+// Result returned after a benchmark has finished. Can be used as a baseline for relative().
+ANKERL_NANOBENCH(IGNORE_PADDED_PUSH)
+class Result {
+public:
+ enum class Measure : size_t {
+ elapsed,
+ iterations,
+ pagefaults,
+ cpucycles,
+ contextswitches,
+ instructions,
+ branchinstructions,
+ branchmisses,
+ _size
+ };
+
+ explicit Result(Config const& benchmarkConfig);
+
+ ~Result();
+ Result& operator=(Result const&);
+ Result& operator=(Result&&);
+ Result(Result const&);
+ Result(Result&&) noexcept;
+
+ // adds new measurement results
+ // all values are scaled by iters (except iters...)
+ void add(Clock::duration totalElapsed, uint64_t iters, detail::PerformanceCounters const& pc);
+
+ ANKERL_NANOBENCH(NODISCARD) Config const& config() const noexcept;
+
+ ANKERL_NANOBENCH(NODISCARD) double median(Measure m) const;
+ ANKERL_NANOBENCH(NODISCARD) double medianAbsolutePercentError(Measure m) const;
+ ANKERL_NANOBENCH(NODISCARD) double average(Measure m) const;
+ ANKERL_NANOBENCH(NODISCARD) double sum(Measure m) const noexcept;
+ ANKERL_NANOBENCH(NODISCARD) double sumProduct(Measure m1, Measure m2) const noexcept;
+ ANKERL_NANOBENCH(NODISCARD) double minimum(Measure m) const noexcept;
+ ANKERL_NANOBENCH(NODISCARD) double maximum(Measure m) const noexcept;
+
+ ANKERL_NANOBENCH(NODISCARD) bool has(Measure m) const noexcept;
+ ANKERL_NANOBENCH(NODISCARD) double get(size_t idx, Measure m) const;
+ ANKERL_NANOBENCH(NODISCARD) bool empty() const noexcept;
+ ANKERL_NANOBENCH(NODISCARD) size_t size() const noexcept;
+
+ // Finds string, if not found, returns _size.
+ static Measure fromString(std::string const& str);
+
+private:
+ Config mConfig{};
+ std::vector<std::vector<double>> mNameToMeasurements{};
+};
+ANKERL_NANOBENCH(IGNORE_PADDED_POP)
+
+/**
+ * An extremely fast random generator. Currently, this implements *RomuDuoJr*, developed by Mark Overton. Source:
+ * http://www.romu-random.org/
+ *
+ * RomuDuoJr is extremely fast and provides reasonable good randomness. Not enough for large jobs, but definitely
+ * good enough for a benchmarking framework.
+ *
+ * * Estimated capacity: @f$ 2^{51} @f$ bytes
+ * * Register pressure: 4
+ * * State size: 128 bits
+ *
+ * This random generator is a drop-in replacement for the generators supplied by ``<random>``. It is not
+ * cryptographically secure. It's intended purpose is to be very fast so that benchmarks that make use
+ * of randomness are not distorted too much by the random generator.
+ *
+ * Rng also provides a few non-standard helpers, optimized for speed.
+ */
+class Rng final {
+public:
+ /**
+ * @brief This RNG provides 64bit randomness.
+ */
+ using result_type = uint64_t;
+
+ static constexpr uint64_t(min)();
+ static constexpr uint64_t(max)();
+
+ /**
+ * As a safety precausion, we don't allow copying. Copying a PRNG would mean you would have two random generators that produce the
+ * same sequence, which is generally not what one wants. Instead create a new rng with the default constructor Rng(), which is
+ * automatically seeded from `std::random_device`. If you really need a copy, use copy().
+ */
+ Rng(Rng const&) = delete;
+
+ /**
+ * Same as Rng(Rng const&), we don't allow assignment. If you need a new Rng create one with the default constructor Rng().
+ */
+ Rng& operator=(Rng const&) = delete;
+
+ // moving is ok
+ Rng(Rng&&) noexcept = default;
+ Rng& operator=(Rng&&) noexcept = default;
+ ~Rng() noexcept = default;
+
+ /**
+ * @brief Creates a new Random generator with random seed.
+ *
+ * Instead of a default seed (as the random generators from the STD), this properly seeds the random generator from
+ * `std::random_device`. It guarantees correct seeding. Note that seeding can be relatively slow, depending on the source of
+ * randomness used. So it is best to create a Rng once and use it for all your randomness purposes.
+ */
+ Rng();
+
+ /*!
+ Creates a new Rng that is seeded with a specific seed. Each Rng created from the same seed will produce the same randomness
+ sequence. This can be useful for deterministic behavior.
+
+ @verbatim embed:rst
+ .. note::
+
+ The random algorithm might change between nanobench releases. Whenever a faster and/or better random
+ generator becomes available, I will switch the implementation.
+ @endverbatim
+
+ As per the Romu paper, this seeds the Rng with splitMix64 algorithm and performs 10 initial rounds for further mixing up of the
+ internal state.
+
+ @param seed The 64bit seed. All values are allowed, even 0.
+ */
+ explicit Rng(uint64_t seed) noexcept;
+ Rng(uint64_t x, uint64_t y) noexcept;
+
+ /**
+ * Creates a copy of the Rng, thus the copy provides exactly the same random sequence as the original.
+ */
+ ANKERL_NANOBENCH(NODISCARD) Rng copy() const noexcept;
+
+ /**
+ * @brief Produces a 64bit random value. This should be very fast, thus it is marked as inline. In my benchmark, this is ~46 times
+ * faster than `std::default_random_engine` for producing 64bit random values. It seems that the fastest std contender is
+ * `std::mt19937_64`. Still, this RNG is 2-3 times as fast.
+ *
+ * @return uint64_t The next 64 bit random value.
+ */
+ inline uint64_t operator()() noexcept;
+
+ // This is slightly biased. See
+
+ /**
+ * Generates a random number between 0 and range (excluding range).
+ *
+ * The algorithm only produces 32bit numbers, and is slightly biased. The effect is quite small unless your range is close to the
+ * maximum value of an integer. It is possible to correct the bias with rejection sampling (see
+ * [here](https://lemire.me/blog/2016/06/30/fast-random-shuffling/), but this is most likely irrelevant in practices for the
+ * purposes of this Rng.
+ *
+ * See Daniel Lemire's blog post [A fast alternative to the modulo
+ * reduction](https://lemire.me/blog/2016/06/27/a-fast-alternative-to-the-modulo-reduction/)
+ *
+ * @param range Upper exclusive range. E.g a value of 3 will generate random numbers 0, 1, 2.
+ * @return uint32_t Generated random values in range [0, range(.
+ */
+ inline uint32_t bounded(uint32_t range) noexcept;
+
+ // random double in range [0, 1(
+ // see http://prng.di.unimi.it/
+
+ /**
+ * Provides a random uniform double value between 0 and 1. This uses the method described in [Generating uniform doubles in the
+ * unit interval](http://prng.di.unimi.it/), and is extremely fast.
+ *
+ * @return double Uniformly distributed double value in range [0,1(, excluding 1.
+ */
+ inline double uniform01() noexcept;
+
+ /**
+ * Shuffles all entries in the given container. Although this has a slight bias due to the implementation of bounded(), this is
+ * preferable to `std::shuffle` because it is over 5 times faster. See Daniel Lemire's blog post [Fast random
+ * shuffling](https://lemire.me/blog/2016/06/30/fast-random-shuffling/).
+ *
+ * @param container The whole container will be shuffled.
+ */
+ template <typename Container>
+ void shuffle(Container& container) noexcept;
+
+private:
+ static constexpr uint64_t rotl(uint64_t x, unsigned k) noexcept;
+
+ uint64_t mX;
+ uint64_t mY;
+};
+
+/**
+ * @brief Main entry point to nanobench's benchmarking facility.
+ *
+ * It holds configuration and results from one or more benchmark runs. Usually it is used in a single line, where the object is
+ * constructed, configured, and then a benchmark is run. E.g. like this:
+ *
+ * ankerl::nanobench::Bench().unit("byte").batch(1000).run("random fluctuations", [&] {
+ * // here be the benchmark code
+ * });
+ *
+ * In that example Bench() constructs the benchmark, it is then configured with unit() and batch(), and after configuration a
+ * benchmark is executed with run(). Once run() has finished, it prints the result to `std::cout`. It would also store the results
+ * in the Bench instance, but in this case the object is immediately destroyed so it's not available any more.
+ */
+ANKERL_NANOBENCH(IGNORE_PADDED_PUSH)
+class Bench {
+public:
+ /**
+ * @brief Creates a new benchmark for configuration and running of benchmarks.
+ */
+ Bench();
+
+ Bench(Bench&& other);
+ Bench& operator=(Bench&& other);
+ Bench(Bench const& other);
+ Bench& operator=(Bench const& other);
+ ~Bench() noexcept;
+
+ /*!
+ @brief Repeatedly calls `op()` based on the configuration, and performs measurements.
+
+ This call is marked with `noinline` to prevent the compiler to optimize beyond different benchmarks. This can have quite a big
+ effect on benchmark accuracy.
+
+ @verbatim embed:rst
+ .. note::
+
+ Each call to your lambda must have a side effect that the compiler can't possibly optimize it away. E.g. add a result to an
+ externally defined number (like `x` in the above example), and finally call `doNotOptimizeAway` on the variables the compiler
+ must not remove. You can also use :cpp:func:`ankerl::nanobench::doNotOptimizeAway` directly in the lambda, but be aware that
+ this has a small overhead.
+
+ @endverbatim
+
+ @tparam Op The code to benchmark.
+ */
+ template <typename Op>
+ ANKERL_NANOBENCH(NOINLINE)
+ Bench& run(char const* benchmarkName, Op&& op);
+
+ template <typename Op>
+ ANKERL_NANOBENCH(NOINLINE)
+ Bench& run(std::string const& benchmarkName, Op&& op);
+
+ /**
+ * @brief Same as run(char const* benchmarkName, Op op), but instead uses the previously set name.
+ * @tparam Op The code to benchmark.
+ */
+ template <typename Op>
+ ANKERL_NANOBENCH(NOINLINE)
+ Bench& run(Op&& op);
+
+ /**
+ * @brief Title of the benchmark, will be shown in the table header. Changing the title will start a new markdown table.
+ *
+ * @param benchmarkTitle The title of the benchmark.
+ */
+ Bench& title(char const* benchmarkTitle);
+ Bench& title(std::string const& benchmarkTitle);
+ ANKERL_NANOBENCH(NODISCARD) std::string const& title() const noexcept;
+
+ /// Name of the benchmark, will be shown in the table row.
+ Bench& name(char const* benchmarkName);
+ Bench& name(std::string const& benchmarkName);
+ ANKERL_NANOBENCH(NODISCARD) std::string const& name() const noexcept;
+
+ /**
+ * @brief Sets the batch size.
+ *
+ * E.g. number of processed byte, or some other metric for the size of the processed data in each iteration. If you benchmark
+ * hashing of a 1000 byte long string and want byte/sec as a result, you can specify 1000 as the batch size.
+ *
+ * @tparam T Any input type is internally cast to `double`.
+ * @param b batch size
+ */
+ template <typename T>
+ Bench& batch(T b) noexcept;
+ ANKERL_NANOBENCH(NODISCARD) double batch() const noexcept;
+
+ /**
+ * @brief Sets the operation unit.
+ *
+ * Defaults to "op". Could be e.g. "byte" for string processing. This is used for the table header, e.g. to show `ns/byte`. Use
+ * singular (*byte*, not *bytes*). A change clears the currently collected results.
+ *
+ * @param unit The unit name.
+ */
+ Bench& unit(char const* unit);
+ Bench& unit(std::string const& unit);
+ ANKERL_NANOBENCH(NODISCARD) std::string const& unit() const noexcept;
+
+ /**
+ * @brief Set the output stream where the resulting markdown table will be printed to.
+ *
+ * The default is `&std::cout`. You can disable all output by setting `nullptr`.
+ *
+ * @param outstream Pointer to output stream, can be `nullptr`.
+ */
+ Bench& output(std::ostream* outstream) noexcept;
+ ANKERL_NANOBENCH(NODISCARD) std::ostream* output() const noexcept;
+
+ /**
+ * Modern processors have a very accurate clock, being able to measure as low as 20 nanoseconds. This is the main trick nanobech to
+ * be so fast: we find out how accurate the clock is, then run the benchmark only so often that the clock's accuracy is good enough
+ * for accurate measurements.
+ *
+ * The default is to run one epoch for 1000 times the clock resolution. So for 20ns resolution and 11 epochs, this gives a total
+ * runtime of
+ *
+ * @f[
+ * 20ns * 1000 * 11 \approx 0.2ms
+ * @f]
+ *
+ * To be precise, nanobench adds a 0-20% random noise to each evaluation. This is to prevent any aliasing effects, and further
+ * improves accuracy.
+ *
+ * Total runtime will be higher though: Some initial time is needed to find out the target number of iterations for each epoch, and
+ * there is some overhead involved to start & stop timers and calculate resulting statistics and writing the output.
+ *
+ * @param multiple Target number of times of clock resolution. Usually 1000 is a good compromise between runtime and accuracy.
+ */
+ Bench& clockResolutionMultiple(size_t multiple) noexcept;
+ ANKERL_NANOBENCH(NODISCARD) size_t clockResolutionMultiple() const noexcept;
+
+ /**
+ * @brief Controls number of epochs, the number of measurements to perform.
+ *
+ * The reported result will be the median of evaluation of each epoch. The higher you choose this, the more
+ * deterministic the result be and outliers will be more easily removed. Also the `err%` will be more accurate the higher this
+ * number is. Note that the `err%` will not necessarily decrease when number of epochs is increased. But it will be a more accurate
+ * representation of the benchmarked code's runtime stability.
+ *
+ * Choose the value wisely. In practice, 11 has been shown to be a reasonable choice between runtime performance and accuracy.
+ * This setting goes hand in hand with minEpocIterations() (or minEpochTime()). If you are more interested in *median* runtime, you
+ * might want to increase epochs(). If you are more interested in *mean* runtime, you might want to increase minEpochIterations()
+ * instead.
+ *
+ * @param numEpochs Number of epochs.
+ */
+ Bench& epochs(size_t numEpochs) noexcept;
+ ANKERL_NANOBENCH(NODISCARD) size_t epochs() const noexcept;
+
+ /**
+ * @brief Upper limit for the runtime of each epoch.
+ *
+ * As a safety precausion if the clock is not very accurate, we can set an upper limit for the maximum evaluation time per
+ * epoch. Default is 100ms. At least a single evaluation of the benchmark is performed.
+ *
+ * @see minEpochTime(), minEpochIterations()
+ *
+ * @param t Maximum target runtime for a single epoch.
+ */
+ Bench& maxEpochTime(std::chrono::nanoseconds t) noexcept;
+ ANKERL_NANOBENCH(NODISCARD) std::chrono::nanoseconds maxEpochTime() const noexcept;
+
+ /**
+ * @brief Minimum time each epoch should take.
+ *
+ * Default is zero, so we are fully relying on clockResolutionMultiple(). In most cases this is exactly what you want. If you see
+ * that the evaluation is unreliable with a high `err%`, you can increase either minEpochTime() or minEpochIterations().
+ *
+ * @see maxEpochTime(), minEpochIterations()
+ *
+ * @param t Minimum time each epoch should take.
+ */
+ Bench& minEpochTime(std::chrono::nanoseconds t) noexcept;
+ ANKERL_NANOBENCH(NODISCARD) std::chrono::nanoseconds minEpochTime() const noexcept;
+
+ /**
+ * @brief Sets the minimum number of iterations each epoch should take.
+ *
+ * Default is 1, and we rely on clockResolutionMultiple(). If the `err%` is high and you want a more smooth result, you might want
+ * to increase the minimum number or iterations, or increase the minEpochTime().
+ *
+ * @see minEpochTime(), maxEpochTime(), minEpochIterations()
+ *
+ * @param numIters Minimum number of iterations per epoch.
+ */
+ Bench& minEpochIterations(uint64_t numIters) noexcept;
+ ANKERL_NANOBENCH(NODISCARD) uint64_t minEpochIterations() const noexcept;
+
+ /**
+ * Sets exactly the number of iterations for each epoch. Ignores all other epoch limits. This forces nanobench to use exactly
+ * the given number of iterations for each epoch, not more and not less. Default is 0 (disabled).
+ *
+ * @param numIters Exact number of iterations to use. Set to 0 to disable.
+ */
+ Bench& epochIterations(uint64_t numIters) noexcept;
+ ANKERL_NANOBENCH(NODISCARD) uint64_t epochIterations() const noexcept;
+
+ /**
+ * @brief Sets a number of iterations that are initially performed without any measurements.
+ *
+ * Some benchmarks need a few evaluations to warm up caches / database / whatever access. Normally this should not be needed, since
+ * we show the median result so initial outliers will be filtered away automatically. If the warmup effect is large though, you
+ * might want to set it. Default is 0.
+ *
+ * @param numWarmupIters Number of warmup iterations.
+ */
+ Bench& warmup(uint64_t numWarmupIters) noexcept;
+ ANKERL_NANOBENCH(NODISCARD) uint64_t warmup() const noexcept;
+
+ /**
+ * @brief Marks the next run as the baseline.
+ *
+ * Call `relative(true)` to mark the run as the baseline. Successive runs will be compared to this run. It is calculated by
+ *
+ * @f[
+ * 100\% * \frac{baseline}{runtime}
+ * @f]
+ *
+ * * 100% means it is exactly as fast as the baseline
+ * * >100% means it is faster than the baseline. E.g. 200% means the current run is twice as fast as the baseline.
+ * * <100% means it is slower than the baseline. E.g. 50% means it is twice as slow as the baseline.
+ *
+ * See the tutorial section "Comparing Results" for example usage.
+ *
+ * @param isRelativeEnabled True to enable processing
+ */
+ Bench& relative(bool isRelativeEnabled) noexcept;
+ ANKERL_NANOBENCH(NODISCARD) bool relative() const noexcept;
+
+ /**
+ * @brief Enables/disables performance counters.
+ *
+ * On Linux nanobench has a powerful feature to use performance counters. This enables counting of retired instructions, count
+ * number of branches, missed branches, etc. On default this is enabled, but you can disable it if you don't need that feature.
+ *
+ * @param showPerformanceCounters True to enable, false to disable.
+ */
+ Bench& performanceCounters(bool showPerformanceCounters) noexcept;
+ ANKERL_NANOBENCH(NODISCARD) bool performanceCounters() const noexcept;
+
+ /**
+ * @brief Retrieves all benchmark results collected by the bench object so far.
+ *
+ * Each call to run() generates a Result that is stored within the Bench instance. This is mostly for advanced users who want to
+ * see all the nitty gritty detials.
+ *
+ * @return All results collected so far.
+ */
+ ANKERL_NANOBENCH(NODISCARD) std::vector<Result> const& results() const noexcept;
+
+ /*!
+ @verbatim embed:rst
+
+ Convenience shortcut to :cpp:func:`ankerl::nanobench::doNotOptimizeAway`.
+
+ @endverbatim
+ */
+ template <typename Arg>
+ Bench& doNotOptimizeAway(Arg&& arg);
+
+ /*!
+ @verbatim embed:rst
+
+ Sets N for asymptotic complexity calculation, so it becomes possible to calculate `Big O
+ <https://en.wikipedia.org/wiki/Big_O_notation>`_ from multiple benchmark evaluations.
+
+ Use :cpp:func:`ankerl::nanobench::Bench::complexityBigO` when the evaluation has finished. See the tutorial
+ :ref:`asymptotic-complexity` for details.
+
+ @endverbatim
+
+ @tparam T Any type is cast to `double`.
+ @param b Length of N for the next benchmark run, so it is possible to calculate `bigO`.
+ */
+ template <typename T>
+ Bench& complexityN(T b) noexcept;
+ ANKERL_NANOBENCH(NODISCARD) double complexityN() const noexcept;
+
+ /*!
+ Calculates [Big O](https://en.wikipedia.org/wiki/Big_O_notation>) of the results with all preconfigured complexity functions.
+ Currently these complexity functions are fitted into the benchmark results:
+
+ @f$ \mathcal{O}(1) @f$,
+ @f$ \mathcal{O}(n) @f$,
+ @f$ \mathcal{O}(\log{}n) @f$,
+ @f$ \mathcal{O}(n\log{}n) @f$,
+ @f$ \mathcal{O}(n^2) @f$,
+ @f$ \mathcal{O}(n^3) @f$.
+
+ If we e.g. evaluate the complexity of `std::sort`, this is the result of `std::cout << bench.complexityBigO()`:
+
+ ```
+ | coefficient | err% | complexity
+ |--------------:|-------:|------------
+ | 5.08935e-09 | 2.6% | O(n log n)
+ | 6.10608e-08 | 8.0% | O(n)
+ | 1.29307e-11 | 47.2% | O(n^2)
+ | 2.48677e-15 | 69.6% | O(n^3)
+ | 9.88133e-06 | 132.3% | O(log n)
+ | 5.98793e-05 | 162.5% | O(1)
+ ```
+
+ So in this case @f$ \mathcal{O}(n\log{}n) @f$ provides the best approximation.
+
+ @verbatim embed:rst
+ See the tutorial :ref:`asymptotic-complexity` for details.
+ @endverbatim
+ @return Evaluation results, which can be printed or otherwise inspected.
+ */
+ std::vector<BigO> complexityBigO() const;
+
+ /**
+ * @brief Calculates bigO for a custom function.
+ *
+ * E.g. to calculate the mean squared error for @f$ \mathcal{O}(\log{}\log{}n) @f$, which is not part of the default set of
+ * complexityBigO(), you can do this:
+ *
+ * ```
+ * auto logLogN = bench.complexityBigO("O(log log n)", [](double n) {
+ * return std::log2(std::log2(n));
+ * });
+ * ```
+ *
+ * The resulting mean squared error can be printed with `std::cout << logLogN`. E.g. it prints something like this:
+ *
+ * ```text
+ * 2.46985e-05 * O(log log n), rms=1.48121
+ * ```
+ *
+ * @tparam Op Type of mapping operation.
+ * @param name Name for the function, e.g. "O(log log n)"
+ * @param op Op's operator() maps a `double` with the desired complexity function, e.g. `log2(log2(n))`.
+ * @return BigO Error calculation, which is streamable to std::cout.
+ */
+ template <typename Op>
+ BigO complexityBigO(char const* name, Op op) const;
+
+ template <typename Op>
+ BigO complexityBigO(std::string const& name, Op op) const;
+
+ /*!
+ @verbatim embed:rst
+
+ Convenience shortcut to :cpp:func:`ankerl::nanobench::render`.
+
+ @endverbatim
+ */
+ Bench& render(char const* templateContent, std::ostream& os);
+
+ Bench& config(Config const& benchmarkConfig);
+ ANKERL_NANOBENCH(NODISCARD) Config const& config() const noexcept;
+
+private:
+ Config mConfig{};
+ std::vector<Result> mResults{};
+};
+ANKERL_NANOBENCH(IGNORE_PADDED_POP)
+
+/**
+ * @brief Makes sure none of the given arguments are optimized away by the compiler.
+ *
+ * @tparam Arg Type of the argument that shouldn't be optimized away.
+ * @param arg The input that we mark as being used, even though we don't do anything with it.
+ */
+template <typename Arg>
+void doNotOptimizeAway(Arg&& arg);
+
+namespace detail {
+
+#if defined(_MSC_VER)
+void doNotOptimizeAwaySink(void const*);
+
+template <typename T>
+void doNotOptimizeAway(T const& val);
+
+#else
+
+// see folly's Benchmark.h
+template <typename T>
+constexpr bool doNotOptimizeNeedsIndirect() {
+ using Decayed = typename std::decay<T>::type;
+ return !ANKERL_NANOBENCH_IS_TRIVIALLY_COPYABLE(Decayed) || sizeof(Decayed) > sizeof(long) || std::is_pointer<Decayed>::value;
+}
+
+template <typename T>
+typename std::enable_if<!doNotOptimizeNeedsIndirect<T>()>::type doNotOptimizeAway(T const& val) {
+ // NOLINTNEXTLINE(hicpp-no-assembler)
+ asm volatile("" ::"r"(val));
+}
+
+template <typename T>
+typename std::enable_if<doNotOptimizeNeedsIndirect<T>()>::type doNotOptimizeAway(T const& val) {
+ // NOLINTNEXTLINE(hicpp-no-assembler)
+ asm volatile("" ::"m"(val) : "memory");
+}
+#endif
+
+// internally used, but visible because run() is templated.
+// Not movable/copy-able, so we simply use a pointer instead of unique_ptr. This saves us from
+// having to include <memory>, and the template instantiation overhead of unique_ptr which is unfortunately quite significant.
+ANKERL_NANOBENCH(IGNORE_EFFCPP_PUSH)
+class IterationLogic {
+public:
+ explicit IterationLogic(Bench const& config) noexcept;
+ ~IterationLogic();
+
+ ANKERL_NANOBENCH(NODISCARD) uint64_t numIters() const noexcept;
+ void add(std::chrono::nanoseconds elapsed, PerformanceCounters const& pc) noexcept;
+ void moveResultTo(std::vector<Result>& results) noexcept;
+
+private:
+ struct Impl;
+ Impl* mPimpl;
+};
+ANKERL_NANOBENCH(IGNORE_EFFCPP_POP)
+
+ANKERL_NANOBENCH(IGNORE_PADDED_PUSH)
+class PerformanceCounters {
+public:
+ PerformanceCounters(PerformanceCounters const&) = delete;
+ PerformanceCounters& operator=(PerformanceCounters const&) = delete;
+
+ PerformanceCounters();
+ ~PerformanceCounters();
+
+ void beginMeasure();
+ void endMeasure();
+ void updateResults(uint64_t numIters);
+
+ ANKERL_NANOBENCH(NODISCARD) PerfCountSet<uint64_t> const& val() const noexcept;
+ ANKERL_NANOBENCH(NODISCARD) PerfCountSet<bool> const& has() const noexcept;
+
+private:
+#if ANKERL_NANOBENCH(PERF_COUNTERS)
+ LinuxPerformanceCounters* mPc = nullptr;
+#endif
+ PerfCountSet<uint64_t> mVal{};
+ PerfCountSet<bool> mHas{};
+};
+ANKERL_NANOBENCH(IGNORE_PADDED_POP)
+
+// Gets the singleton
+PerformanceCounters& performanceCounters();
+
+} // namespace detail
+
+class BigO {
+public:
+ using RangeMeasure = std::vector<std::pair<double, double>>;
+
+ template <typename Op>
+ static RangeMeasure mapRangeMeasure(RangeMeasure data, Op op) {
+ for (auto& rangeMeasure : data) {
+ rangeMeasure.first = op(rangeMeasure.first);
+ }
+ return data;
+ }
+
+ static RangeMeasure collectRangeMeasure(std::vector<Result> const& results);
+
+ template <typename Op>
+ BigO(char const* bigOName, RangeMeasure const& rangeMeasure, Op rangeToN)
+ : BigO(bigOName, mapRangeMeasure(rangeMeasure, rangeToN)) {}
+
+ template <typename Op>
+ BigO(std::string const& bigOName, RangeMeasure const& rangeMeasure, Op rangeToN)
+ : BigO(bigOName, mapRangeMeasure(rangeMeasure, rangeToN)) {}
+
+ BigO(char const* bigOName, RangeMeasure const& scaledRangeMeasure);
+ BigO(std::string const& bigOName, RangeMeasure const& scaledRangeMeasure);
+ ANKERL_NANOBENCH(NODISCARD) std::string const& name() const noexcept;
+ ANKERL_NANOBENCH(NODISCARD) double constant() const noexcept;
+ ANKERL_NANOBENCH(NODISCARD) double normalizedRootMeanSquare() const noexcept;
+ ANKERL_NANOBENCH(NODISCARD) bool operator<(BigO const& other) const noexcept;
+
+private:
+ std::string mName{};
+ double mConstant{};
+ double mNormalizedRootMeanSquare{};
+};
+std::ostream& operator<<(std::ostream& os, BigO const& bigO);
+std::ostream& operator<<(std::ostream& os, std::vector<ankerl::nanobench::BigO> const& bigOs);
+
+} // namespace nanobench
+} // namespace ankerl
+
+// implementation /////////////////////////////////////////////////////////////////////////////////
+
+namespace ankerl {
+namespace nanobench {
+
+constexpr uint64_t(Rng::min)() {
+ return 0;
+}
+
+constexpr uint64_t(Rng::max)() {
+ return (std::numeric_limits<uint64_t>::max)();
+}
+
+ANKERL_NANOBENCH_NO_SANITIZE("integer")
+uint64_t Rng::operator()() noexcept {
+ auto x = mX;
+
+ mX = UINT64_C(15241094284759029579) * mY;
+ mY = rotl(mY - x, 27);
+
+ return x;
+}
+
+ANKERL_NANOBENCH_NO_SANITIZE("integer")
+uint32_t Rng::bounded(uint32_t range) noexcept {
+ uint64_t r32 = static_cast<uint32_t>(operator()());
+ auto multiresult = r32 * range;
+ return static_cast<uint32_t>(multiresult >> 32U);
+}
+
+double Rng::uniform01() noexcept {
+ auto i = (UINT64_C(0x3ff) << 52U) | (operator()() >> 12U);
+ // can't use union in c++ here for type puning, it's undefined behavior.
+ // std::memcpy is optimized anyways.
+ double d;
+ std::memcpy(&d, &i, sizeof(double));
+ return d - 1.0;
+}
+
+template <typename Container>
+void Rng::shuffle(Container& container) noexcept {
+ auto size = static_cast<uint32_t>(container.size());
+ for (auto i = size; i > 1U; --i) {
+ using std::swap;
+ auto p = bounded(i); // number in [0, i)
+ swap(container[i - 1], container[p]);
+ }
+}
+
+constexpr uint64_t Rng::rotl(uint64_t x, unsigned k) noexcept {
+ return (x << k) | (x >> (64U - k));
+}
+
+template <typename Op>
+ANKERL_NANOBENCH_NO_SANITIZE("integer")
+Bench& Bench::run(Op&& op) {
+ // It is important that this method is kept short so the compiler can do better optimizations/ inlining of op()
+ detail::IterationLogic iterationLogic(*this);
+ auto& pc = detail::performanceCounters();
+
+ while (auto n = iterationLogic.numIters()) {
+ pc.beginMeasure();
+ Clock::time_point before = Clock::now();
+ while (n-- > 0) {
+ op();
+ }
+ Clock::time_point after = Clock::now();
+ pc.endMeasure();
+ pc.updateResults(iterationLogic.numIters());
+ iterationLogic.add(after - before, pc);
+ }
+ iterationLogic.moveResultTo(mResults);
+ return *this;
+}
+
+// Performs all evaluations.
+template <typename Op>
+Bench& Bench::run(char const* benchmarkName, Op&& op) {
+ name(benchmarkName);
+ return run(std::forward<Op>(op));
+}
+
+template <typename Op>
+Bench& Bench::run(std::string const& benchmarkName, Op&& op) {
+ name(benchmarkName);
+ return run(std::forward<Op>(op));
+}
+
+template <typename Op>
+BigO Bench::complexityBigO(char const* benchmarkName, Op op) const {
+ return BigO(benchmarkName, BigO::collectRangeMeasure(mResults), op);
+}
+
+template <typename Op>
+BigO Bench::complexityBigO(std::string const& benchmarkName, Op op) const {
+ return BigO(benchmarkName, BigO::collectRangeMeasure(mResults), op);
+}
+
+// Set the batch size, e.g. number of processed bytes, or some other metric for the size of the processed data in each iteration.
+// Any argument is cast to double.
+template <typename T>
+Bench& Bench::batch(T b) noexcept {
+ mConfig.mBatch = static_cast<double>(b);
+ return *this;
+}
+
+// Sets the computation complexity of the next run. Any argument is cast to double.
+template <typename T>
+Bench& Bench::complexityN(T n) noexcept {
+ mConfig.mComplexityN = static_cast<double>(n);
+ return *this;
+}
+
+// Convenience: makes sure none of the given arguments are optimized away by the compiler.
+template <typename Arg>
+Bench& Bench::doNotOptimizeAway(Arg&& arg) {
+ detail::doNotOptimizeAway(std::forward<Arg>(arg));
+ return *this;
+}
+
+// Makes sure none of the given arguments are optimized away by the compiler.
+template <typename Arg>
+void doNotOptimizeAway(Arg&& arg) {
+ detail::doNotOptimizeAway(std::forward<Arg>(arg));
+}
+
+namespace detail {
+
+#if defined(_MSC_VER)
+template <typename T>
+void doNotOptimizeAway(T const& val) {
+ doNotOptimizeAwaySink(&val);
+}
+
+#endif
+
+} // namespace detail
+} // namespace nanobench
+} // namespace ankerl
+
+#if defined(ANKERL_NANOBENCH_IMPLEMENT)
+
+///////////////////////////////////////////////////////////////////////////////////////////////////
+// implementation part - only visible in .cpp
+///////////////////////////////////////////////////////////////////////////////////////////////////
+
+# include <algorithm> // sort, reverse
+# include <atomic> // compare_exchange_strong in loop overhead
+# include <cstdlib> // getenv
+# include <cstring> // strstr, strncmp
+# include <fstream> // ifstream to parse proc files
+# include <iomanip> // setw, setprecision
+# include <iostream> // cout
+# include <numeric> // accumulate
+# include <random> // random_device
+# include <sstream> // to_s in Number
+# include <stdexcept> // throw for rendering templates
+# include <tuple> // std::tie
+# if defined(__linux__)
+# include <unistd.h> //sysconf
+# endif
+# if ANKERL_NANOBENCH(PERF_COUNTERS)
+# include <map> // map
+
+# include <linux/perf_event.h>
+# include <sys/ioctl.h>
+# include <sys/syscall.h>
+# include <unistd.h>
+# endif
+
+// declarations ///////////////////////////////////////////////////////////////////////////////////
+
+namespace ankerl {
+namespace nanobench {
+
+// helper stuff that is only intended to be used internally
+namespace detail {
+
+struct TableInfo;
+
+// formatting utilities
+namespace fmt {
+
+class NumSep;
+class StreamStateRestorer;
+class Number;
+class MarkDownColumn;
+class MarkDownCode;
+
+} // namespace fmt
+} // namespace detail
+} // namespace nanobench
+} // namespace ankerl
+
+// definitions ////////////////////////////////////////////////////////////////////////////////////
+
+namespace ankerl {
+namespace nanobench {
+
+uint64_t splitMix64(uint64_t& state) noexcept;
+
+namespace detail {
+
+// helpers to get double values
+template <typename T>
+inline double d(T t) noexcept {
+ return static_cast<double>(t);
+}
+inline double d(Clock::duration duration) noexcept {
+ return std::chrono::duration_cast<std::chrono::duration<double>>(duration).count();
+}
+
+// Calculates clock resolution once, and remembers the result
+inline Clock::duration clockResolution() noexcept;
+
+} // namespace detail
+
+namespace templates {
+
+char const* csv() noexcept {
+ return R"DELIM("title";"name";"unit";"batch";"elapsed";"error %";"instructions";"branches";"branch misses";"total"
+{{#result}}"{{title}}";"{{name}}";"{{unit}}";{{batch}};{{median(elapsed)}};{{medianAbsolutePercentError(elapsed)}};{{median(instructions)}};{{median(branchinstructions)}};{{median(branchmisses)}};{{sumProduct(iterations, elapsed)}}
+{{/result}})DELIM";
+}
+
+char const* htmlBoxplot() noexcept {
+ return R"DELIM(<html>
+
+<head>
+ <script src="https://cdn.plot.ly/plotly-latest.min.js"></script>
+</head>
+
+<body>
+ <div id="myDiv"></div>
+ <script>
+ var data = [
+ {{#result}}{
+ name: '{{name}}',
+ y: [{{#measurement}}{{elapsed}}{{^-last}}, {{/last}}{{/measurement}}],
+ },
+ {{/result}}
+ ];
+ var title = '{{title}}';
+
+ data = data.map(a => Object.assign(a, { boxpoints: 'all', pointpos: 0, type: 'box' }));
+ var layout = { title: { text: title }, showlegend: false, yaxis: { title: 'time per unit', rangemode: 'tozero', autorange: true } }; Plotly.newPlot('myDiv', data, layout, {responsive: true});
+ </script>
+</body>
+
+</html>)DELIM";
+}
+
+char const* json() noexcept {
+ return R"DELIM({
+ "results": [
+{{#result}} {
+ "title": "{{title}}",
+ "name": "{{name}}",
+ "unit": "{{unit}}",
+ "batch": {{batch}},
+ "complexityN": {{complexityN}},
+ "epochs": {{epochs}},
+ "clockResolution": {{clockResolution}},
+ "clockResolutionMultiple": {{clockResolutionMultiple}},
+ "maxEpochTime": {{maxEpochTime}},
+ "minEpochTime": {{minEpochTime}},
+ "minEpochIterations": {{minEpochIterations}},
+ "epochIterations": {{epochIterations}},
+ "warmup": {{warmup}},
+ "relative": {{relative}},
+ "median(elapsed)": {{median(elapsed)}},
+ "medianAbsolutePercentError(elapsed)": {{medianAbsolutePercentError(elapsed)}},
+ "median(instructions)": {{median(instructions)}},
+ "medianAbsolutePercentError(instructions)": {{medianAbsolutePercentError(instructions)}},
+ "median(cpucycles)": {{median(cpucycles)}},
+ "median(contextswitches)": {{median(contextswitches)}},
+ "median(pagefaults)": {{median(pagefaults)}},
+ "median(branchinstructions)": {{median(branchinstructions)}},
+ "median(branchmisses)": {{median(branchmisses)}},
+ "totalTime": {{sumProduct(iterations, elapsed)}},
+ "measurements": [
+{{#measurement}} {
+ "iterations": {{iterations}},
+ "elapsed": {{elapsed}},
+ "pagefaults": {{pagefaults}},
+ "cpucycles": {{cpucycles}},
+ "contextswitches": {{contextswitches}},
+ "instructions": {{instructions}},
+ "branchinstructions": {{branchinstructions}},
+ "branchmisses": {{branchmisses}}
+ }{{^-last}},{{/-last}}
+{{/measurement}} ]
+ }{{^-last}},{{/-last}}
+{{/result}} ]
+})DELIM";
+}
+
+ANKERL_NANOBENCH(IGNORE_PADDED_PUSH)
+struct Node {
+ enum class Type { tag, content, section, inverted_section };
+
+ char const* begin;
+ char const* end;
+ std::vector<Node> children;
+ Type type;
+
+ template <size_t N>
+ // NOLINTNEXTLINE(hicpp-avoid-c-arrays,modernize-avoid-c-arrays,cppcoreguidelines-avoid-c-arrays)
+ bool operator==(char const (&str)[N]) const noexcept {
+ return static_cast<size_t>(std::distance(begin, end) + 1) == N && 0 == strncmp(str, begin, N - 1);
+ }
+};
+ANKERL_NANOBENCH(IGNORE_PADDED_POP)
+
+static std::vector<Node> parseMustacheTemplate(char const** tpl) {
+ std::vector<Node> nodes;
+
+ while (true) {
+ auto begin = std::strstr(*tpl, "{{");
+ auto end = begin;
+ if (begin != nullptr) {
+ begin += 2;
+ end = std::strstr(begin, "}}");
+ }
+
+ if (begin == nullptr || end == nullptr) {
+ // nothing found, finish node
+ nodes.emplace_back(Node{*tpl, *tpl + std::strlen(*tpl), std::vector<Node>{}, Node::Type::content});
+ return nodes;
+ }
+
+ nodes.emplace_back(Node{*tpl, begin - 2, std::vector<Node>{}, Node::Type::content});
+
+ // we found a tag
+ *tpl = end + 2;
+ switch (*begin) {
+ case '/':
+ // finished! bail out
+ return nodes;
+
+ case '#':
+ nodes.emplace_back(Node{begin + 1, end, parseMustacheTemplate(tpl), Node::Type::section});
+ break;
+
+ case '^':
+ nodes.emplace_back(Node{begin + 1, end, parseMustacheTemplate(tpl), Node::Type::inverted_section});
+ break;
+
+ default:
+ nodes.emplace_back(Node{begin, end, std::vector<Node>{}, Node::Type::tag});
+ break;
+ }
+ }
+}
+
+static bool generateFirstLast(Node const& n, size_t idx, size_t size, std::ostream& out) {
+ bool matchFirst = n == "-first";
+ bool matchLast = n == "-last";
+ if (!matchFirst && !matchLast) {
+ return false;
+ }
+
+ bool doWrite = false;
+ if (n.type == Node::Type::section) {
+ doWrite = (matchFirst && idx == 0) || (matchLast && idx == size - 1);
+ } else if (n.type == Node::Type::inverted_section) {
+ doWrite = (matchFirst && idx != 0) || (matchLast && idx != size - 1);
+ }
+
+ if (doWrite) {
+ for (auto const& child : n.children) {
+ if (child.type == Node::Type::content) {
+ out.write(child.begin, std::distance(child.begin, child.end));
+ }
+ }
+ }
+ return true;
+}
+
+static bool matchCmdArgs(std::string const& str, std::vector<std::string>& matchResult) {
+ matchResult.clear();
+ auto idxOpen = str.find('(');
+ auto idxClose = str.find(')', idxOpen);
+ if (idxClose == std::string::npos) {
+ return false;
+ }
+
+ matchResult.emplace_back(str.substr(0, idxOpen));
+
+ // split by comma
+ matchResult.emplace_back(std::string{});
+ for (size_t i = idxOpen + 1; i != idxClose; ++i) {
+ if (str[i] == ' ' || str[i] == '\t') {
+ // skip whitespace
+ continue;
+ }
+ if (str[i] == ',') {
+ // got a comma => new string
+ matchResult.emplace_back(std::string{});
+ continue;
+ }
+ // no whitespace no comma, append
+ matchResult.back() += str[i];
+ }
+ return true;
+}
+
+static bool generateConfigTag(Node const& n, Config const& config, std::ostream& out) {
+ using detail::d;
+
+ if (n == "title") {
+ out << config.mBenchmarkTitle;
+ return true;
+ } else if (n == "name") {
+ out << config.mBenchmarkName;
+ return true;
+ } else if (n == "unit") {
+ out << config.mUnit;
+ return true;
+ } else if (n == "batch") {
+ out << config.mBatch;
+ return true;
+ } else if (n == "complexityN") {
+ out << config.mComplexityN;
+ return true;
+ } else if (n == "epochs") {
+ out << config.mNumEpochs;
+ return true;
+ } else if (n == "clockResolution") {
+ out << d(detail::clockResolution());
+ return true;
+ } else if (n == "clockResolutionMultiple") {
+ out << config.mClockResolutionMultiple;
+ return true;
+ } else if (n == "maxEpochTime") {
+ out << d(config.mMaxEpochTime);
+ return true;
+ } else if (n == "minEpochTime") {
+ out << d(config.mMinEpochTime);
+ return true;
+ } else if (n == "minEpochIterations") {
+ out << config.mMinEpochIterations;
+ return true;
+ } else if (n == "epochIterations") {
+ out << config.mEpochIterations;
+ return true;
+ } else if (n == "warmup") {
+ out << config.mWarmup;
+ return true;
+ } else if (n == "relative") {
+ out << config.mIsRelative;
+ return true;
+ }
+ return false;
+}
+
+static std::ostream& generateResultTag(Node const& n, Result const& r, std::ostream& out) {
+ if (generateConfigTag(n, r.config(), out)) {
+ return out;
+ }
+ // match e.g. "median(elapsed)"
+ // g++ 4.8 doesn't implement std::regex :(
+ // static std::regex const regOpArg1("^([a-zA-Z]+)\\(([a-zA-Z]*)\\)$");
+ // std::cmatch matchResult;
+ // if (std::regex_match(n.begin, n.end, matchResult, regOpArg1)) {
+ std::vector<std::string> matchResult;
+ if (matchCmdArgs(std::string(n.begin, n.end), matchResult)) {
+ if (matchResult.size() == 2) {
+ auto m = Result::fromString(matchResult[1]);
+ if (m == Result::Measure::_size) {
+ return out << 0.0;
+ }
+
+ if (matchResult[0] == "median") {
+ return out << r.median(m);
+ }
+ if (matchResult[0] == "average") {
+ return out << r.average(m);
+ }
+ if (matchResult[0] == "medianAbsolutePercentError") {
+ return out << r.medianAbsolutePercentError(m);
+ }
+ if (matchResult[0] == "sum") {
+ return out << r.sum(m);
+ }
+ if (matchResult[0] == "minimum") {
+ return out << r.minimum(m);
+ }
+ if (matchResult[0] == "maximum") {
+ return out << r.maximum(m);
+ }
+ } else if (matchResult.size() == 3) {
+ auto m1 = Result::fromString(matchResult[1]);
+ auto m2 = Result::fromString(matchResult[2]);
+ if (m1 == Result::Measure::_size || m2 == Result::Measure::_size) {
+ return out << 0.0;
+ }
+
+ if (matchResult[0] == "sumProduct") {
+ return out << r.sumProduct(m1, m2);
+ }
+ }
+ }
+
+ // match e.g. "sumProduct(elapsed, iterations)"
+ // static std::regex const regOpArg2("^([a-zA-Z]+)\\(([a-zA-Z]*)\\s*,\\s+([a-zA-Z]*)\\)$");
+
+ // nothing matches :(
+ throw std::runtime_error("command '" + std::string(n.begin, n.end) + "' not understood");
+}
+
+static void generateResultMeasurement(std::vector<Node> const& nodes, size_t idx, Result const& r, std::ostream& out) {
+ for (auto const& n : nodes) {
+ if (!generateFirstLast(n, idx, r.size(), out)) {
+ ANKERL_NANOBENCH_LOG("n.type=" << static_cast<int>(n.type));
+ switch (n.type) {
+ case Node::Type::content:
+ out.write(n.begin, std::distance(n.begin, n.end));
+ break;
+
+ case Node::Type::inverted_section:
+ throw std::runtime_error("got a inverted section inside measurement");
+
+ case Node::Type::section:
+ throw std::runtime_error("got a section inside measurement");
+
+ case Node::Type::tag: {
+ auto m = Result::fromString(std::string(n.begin, n.end));
+ if (m == Result::Measure::_size || !r.has(m)) {
+ out << 0.0;
+ } else {
+ out << r.get(idx, m);
+ }
+ break;
+ }
+ }
+ }
+ }
+}
+
+static void generateResult(std::vector<Node> const& nodes, size_t idx, std::vector<Result> const& results, std::ostream& out) {
+ auto const& r = results[idx];
+ for (auto const& n : nodes) {
+ if (!generateFirstLast(n, idx, results.size(), out)) {
+ ANKERL_NANOBENCH_LOG("n.type=" << static_cast<int>(n.type));
+ switch (n.type) {
+ case Node::Type::content:
+ out.write(n.begin, std::distance(n.begin, n.end));
+ break;
+
+ case Node::Type::inverted_section:
+ throw std::runtime_error("got a inverted section inside result");
+
+ case Node::Type::section:
+ if (n == "measurement") {
+ for (size_t i = 0; i < r.size(); ++i) {
+ generateResultMeasurement(n.children, i, r, out);
+ }
+ } else {
+ throw std::runtime_error("got a section inside result");
+ }
+ break;
+
+ case Node::Type::tag:
+ generateResultTag(n, r, out);
+ break;
+ }
+ }
+ }
+}
+
+} // namespace templates
+
+// helper stuff that only intended to be used internally
+namespace detail {
+
+char const* getEnv(char const* name);
+bool isEndlessRunning(std::string const& name);
+
+template <typename T>
+T parseFile(std::string const& filename);
+
+void gatherStabilityInformation(std::vector<std::string>& warnings, std::vector<std::string>& recommendations);
+void printStabilityInformationOnce(std::ostream* os);
+
+// remembers the last table settings used. When it changes, a new table header is automatically written for the new entry.
+uint64_t& singletonHeaderHash() noexcept;
+
+// determines resolution of the given clock. This is done by measuring multiple times and returning the minimum time difference.
+Clock::duration calcClockResolution(size_t numEvaluations) noexcept;
+
+// formatting utilities
+namespace fmt {
+
+// adds thousands separator to numbers
+ANKERL_NANOBENCH(IGNORE_PADDED_PUSH)
+class NumSep : public std::numpunct<char> {
+public:
+ explicit NumSep(char sep);
+ char do_thousands_sep() const override;
+ std::string do_grouping() const override;
+
+private:
+ char mSep;
+};
+ANKERL_NANOBENCH(IGNORE_PADDED_POP)
+
+// RAII to save & restore a stream's state
+ANKERL_NANOBENCH(IGNORE_PADDED_PUSH)
+class StreamStateRestorer {
+public:
+ explicit StreamStateRestorer(std::ostream& s);
+ ~StreamStateRestorer();
+
+ // sets back all stream info that we remembered at construction
+ void restore();
+
+ // don't allow copying / moving
+ StreamStateRestorer(StreamStateRestorer const&) = delete;
+ StreamStateRestorer& operator=(StreamStateRestorer const&) = delete;
+ StreamStateRestorer(StreamStateRestorer&&) = delete;
+ StreamStateRestorer& operator=(StreamStateRestorer&&) = delete;
+
+private:
+ std::ostream& mStream;
+ std::locale mLocale;
+ std::streamsize const mPrecision;
+ std::streamsize const mWidth;
+ std::ostream::char_type const mFill;
+ std::ostream::fmtflags const mFmtFlags;
+};
+ANKERL_NANOBENCH(IGNORE_PADDED_POP)
+
+// Number formatter
+class Number {
+public:
+ Number(int width, int precision, double value);
+ Number(int width, int precision, int64_t value);
+ std::string to_s() const;
+
+private:
+ friend std::ostream& operator<<(std::ostream& os, Number const& n);
+ std::ostream& write(std::ostream& os) const;
+
+ int mWidth;
+ int mPrecision;
+ double mValue;
+};
+
+// helper replacement for std::to_string of signed/unsigned numbers so we are locale independent
+std::string to_s(uint64_t s);
+
+std::ostream& operator<<(std::ostream& os, Number const& n);
+
+class MarkDownColumn {
+public:
+ MarkDownColumn(int w, int prec, std::string const& tit, std::string const& suff, double val);
+ std::string title() const;
+ std::string separator() const;
+ std::string invalid() const;
+ std::string value() const;
+
+private:
+ int mWidth;
+ int mPrecision;
+ std::string mTitle;
+ std::string mSuffix;
+ double mValue;
+};
+
+// Formats any text as markdown code, escaping backticks.
+class MarkDownCode {
+public:
+ explicit MarkDownCode(std::string const& what);
+
+private:
+ friend std::ostream& operator<<(std::ostream& os, MarkDownCode const& mdCode);
+ std::ostream& write(std::ostream& os) const;
+
+ std::string mWhat{};
+};
+
+std::ostream& operator<<(std::ostream& os, MarkDownCode const& mdCode);
+
+} // namespace fmt
+} // namespace detail
+} // namespace nanobench
+} // namespace ankerl
+
+// implementation /////////////////////////////////////////////////////////////////////////////////
+
+namespace ankerl {
+namespace nanobench {
+
+void render(char const* mustacheTemplate, std::vector<Result> const& results, std::ostream& out) {
+ detail::fmt::StreamStateRestorer restorer(out);
+
+ out.precision(std::numeric_limits<double>::digits10);
+ auto nodes = templates::parseMustacheTemplate(&mustacheTemplate);
+
+ for (auto const& n : nodes) {
+ ANKERL_NANOBENCH_LOG("n.type=" << static_cast<int>(n.type));
+ switch (n.type) {
+ case templates::Node::Type::content:
+ out.write(n.begin, std::distance(n.begin, n.end));
+ break;
+
+ case templates::Node::Type::inverted_section:
+ throw std::runtime_error("unknown list '" + std::string(n.begin, n.end) + "'");
+
+ case templates::Node::Type::section:
+ if (n == "result") {
+ const size_t nbResults = results.size();
+ for (size_t i = 0; i < nbResults; ++i) {
+ generateResult(n.children, i, results, out);
+ }
+ } else {
+ throw std::runtime_error("unknown section '" + std::string(n.begin, n.end) + "'");
+ }
+ break;
+
+ case templates::Node::Type::tag:
+ // This just uses the last result's config.
+ if (!generateConfigTag(n, results.back().config(), out)) {
+ throw std::runtime_error("unknown tag '" + std::string(n.begin, n.end) + "'");
+ }
+ break;
+ }
+ }
+}
+
+void render(char const* mustacheTemplate, const Bench& bench, std::ostream& out) {
+ render(mustacheTemplate, bench.results(), out);
+}
+
+namespace detail {
+
+PerformanceCounters& performanceCounters() {
+# if defined(__clang__)
+# pragma clang diagnostic push
+# pragma clang diagnostic ignored "-Wexit-time-destructors"
+# endif
+ static PerformanceCounters pc;
+# if defined(__clang__)
+# pragma clang diagnostic pop
+# endif
+ return pc;
+}
+
+// Windows version of doNotOptimizeAway
+// see https://github.com/google/benchmark/blob/master/include/benchmark/benchmark.h#L307
+// see https://github.com/facebook/folly/blob/master/folly/Benchmark.h#L280
+// see https://docs.microsoft.com/en-us/cpp/preprocessor/optimize
+# if defined(_MSC_VER)
+# pragma optimize("", off)
+void doNotOptimizeAwaySink(void const*) {}
+# pragma optimize("", on)
+# endif
+
+template <typename T>
+T parseFile(std::string const& filename) {
+ std::ifstream fin(filename);
+ T num{};
+ fin >> num;
+ return num;
+}
+
+char const* getEnv(char const* name) {
+# if defined(_MSC_VER)
+# pragma warning(push)
+# pragma warning(disable : 4996) // getenv': This function or variable may be unsafe.
+# endif
+ return std::getenv(name);
+# if defined(_MSC_VER)
+# pragma warning(pop)
+# endif
+}
+
+bool isEndlessRunning(std::string const& name) {
+ auto endless = getEnv("NANOBENCH_ENDLESS");
+ return nullptr != endless && endless == name;
+}
+
+void gatherStabilityInformation(std::vector<std::string>& warnings, std::vector<std::string>& recommendations) {
+ warnings.clear();
+ recommendations.clear();
+
+ bool recommendCheckFlags = false;
+
+# if defined(DEBUG)
+ warnings.emplace_back("DEBUG defined");
+ recommendCheckFlags = true;
+# endif
+
+ bool recommendPyPerf = false;
+# if defined(__linux__)
+ auto nprocs = sysconf(_SC_NPROCESSORS_CONF);
+ if (nprocs <= 0) {
+ warnings.emplace_back("couldn't figure out number of processors - no governor, turbo check possible");
+ } else {
+
+ // check frequency scaling
+ for (long id = 0; id < nprocs; ++id) {
+ auto idStr = detail::fmt::to_s(static_cast<uint64_t>(id));
+ auto sysCpu = "/sys/devices/system/cpu/cpu" + idStr;
+ auto minFreq = parseFile<int64_t>(sysCpu + "/cpufreq/scaling_min_freq");
+ auto maxFreq = parseFile<int64_t>(sysCpu + "/cpufreq/scaling_max_freq");
+ if (minFreq != maxFreq) {
+ auto minMHz = static_cast<double>(minFreq) / 1000.0;
+ auto maxMHz = static_cast<double>(maxFreq) / 1000.0;
+ warnings.emplace_back("CPU frequency scaling enabled: CPU " + idStr + " between " +
+ detail::fmt::Number(1, 1, minMHz).to_s() + " and " + detail::fmt::Number(1, 1, maxMHz).to_s() +
+ " MHz");
+ recommendPyPerf = true;
+ break;
+ }
+ }
+
+ auto currentGovernor = parseFile<std::string>("/sys/devices/system/cpu/cpu0/cpufreq/scaling_governor");
+ if ("performance" != currentGovernor) {
+ warnings.emplace_back("CPU governor is '" + currentGovernor + "' but should be 'performance'");
+ recommendPyPerf = true;
+ }
+
+ if (0 == parseFile<int>("/sys/devices/system/cpu/intel_pstate/no_turbo")) {
+ warnings.emplace_back("Turbo is enabled, CPU frequency will fluctuate");
+ recommendPyPerf = true;
+ }
+ }
+# endif
+
+ if (recommendCheckFlags) {
+ recommendations.emplace_back("Make sure you compile for Release");
+ }
+ if (recommendPyPerf) {
+ recommendations.emplace_back("Use 'pyperf system tune' before benchmarking. See https://github.com/vstinner/pyperf");
+ }
+}
+
+void printStabilityInformationOnce(std::ostream* outStream) {
+ static bool shouldPrint = true;
+ if (shouldPrint && outStream) {
+ auto& os = *outStream;
+ shouldPrint = false;
+ std::vector<std::string> warnings;
+ std::vector<std::string> recommendations;
+ gatherStabilityInformation(warnings, recommendations);
+ if (warnings.empty()) {
+ return;
+ }
+
+ os << "Warning, results might be unstable:" << std::endl;
+ for (auto const& w : warnings) {
+ os << "* " << w << std::endl;
+ }
+
+ os << std::endl << "Recommendations" << std::endl;
+ for (auto const& r : recommendations) {
+ os << "* " << r << std::endl;
+ }
+ }
+}
+
+// remembers the last table settings used. When it changes, a new table header is automatically written for the new entry.
+uint64_t& singletonHeaderHash() noexcept {
+ static uint64_t sHeaderHash{};
+ return sHeaderHash;
+}
+
+ANKERL_NANOBENCH_NO_SANITIZE("integer")
+inline uint64_t fnv1a(std::string const& str) noexcept {
+ auto val = UINT64_C(14695981039346656037);
+ for (auto c : str) {
+ val = (val ^ static_cast<uint8_t>(c)) * UINT64_C(1099511628211);
+ }
+ return val;
+}
+
+ANKERL_NANOBENCH_NO_SANITIZE("integer")
+inline uint64_t hash_combine(uint64_t seed, uint64_t val) {
+ return seed ^ (val + UINT64_C(0x9e3779b9) + (seed << 6U) + (seed >> 2U));
+}
+
+// determines resolution of the given clock. This is done by measuring multiple times and returning the minimum time difference.
+Clock::duration calcClockResolution(size_t numEvaluations) noexcept {
+ auto bestDuration = Clock::duration::max();
+ Clock::time_point tBegin;
+ Clock::time_point tEnd;
+ for (size_t i = 0; i < numEvaluations; ++i) {
+ tBegin = Clock::now();
+ do {
+ tEnd = Clock::now();
+ } while (tBegin == tEnd);
+ bestDuration = (std::min)(bestDuration, tEnd - tBegin);
+ }
+ return bestDuration;
+}
+
+// Calculates clock resolution once, and remembers the result
+Clock::duration clockResolution() noexcept {
+ static Clock::duration sResolution = calcClockResolution(20);
+ return sResolution;
+}
+
+ANKERL_NANOBENCH(IGNORE_PADDED_PUSH)
+struct IterationLogic::Impl {
+ enum class State { warmup, upscaling_runtime, measuring, endless };
+
+ explicit Impl(Bench const& bench)
+ : mBench(bench)
+ , mResult(bench.config()) {
+ printStabilityInformationOnce(mBench.output());
+
+ // determine target runtime per epoch
+ mTargetRuntimePerEpoch = detail::clockResolution() * mBench.clockResolutionMultiple();
+ if (mTargetRuntimePerEpoch > mBench.maxEpochTime()) {
+ mTargetRuntimePerEpoch = mBench.maxEpochTime();
+ }
+ if (mTargetRuntimePerEpoch < mBench.minEpochTime()) {
+ mTargetRuntimePerEpoch = mBench.minEpochTime();
+ }
+
+ if (isEndlessRunning(mBench.name())) {
+ std::cerr << "NANOBENCH_ENDLESS set: running '" << mBench.name() << "' endlessly" << std::endl;
+ mNumIters = (std::numeric_limits<uint64_t>::max)();
+ mState = State::endless;
+ } else if (0 != mBench.warmup()) {
+ mNumIters = mBench.warmup();
+ mState = State::warmup;
+ } else if (0 != mBench.epochIterations()) {
+ // exact number of iterations
+ mNumIters = mBench.epochIterations();
+ mState = State::measuring;
+ } else {
+ mNumIters = mBench.minEpochIterations();
+ mState = State::upscaling_runtime;
+ }
+ }
+
+ // directly calculates new iters based on elapsed&iters, and adds a 10% noise. Makes sure we don't underflow.
+ ANKERL_NANOBENCH(NODISCARD) uint64_t calcBestNumIters(std::chrono::nanoseconds elapsed, uint64_t iters) noexcept {
+ auto doubleElapsed = d(elapsed);
+ auto doubleTargetRuntimePerEpoch = d(mTargetRuntimePerEpoch);
+ auto doubleNewIters = doubleTargetRuntimePerEpoch / doubleElapsed * d(iters);
+
+ auto doubleMinEpochIters = d(mBench.minEpochIterations());
+ if (doubleNewIters < doubleMinEpochIters) {
+ doubleNewIters = doubleMinEpochIters;
+ }
+ doubleNewIters *= 1.0 + 0.2 * mRng.uniform01();
+
+ // +0.5 for correct rounding when casting
+ // NOLINTNEXTLINE(bugprone-incorrect-roundings)
+ return static_cast<uint64_t>(doubleNewIters + 0.5);
+ }
+
+ ANKERL_NANOBENCH_NO_SANITIZE("integer") void upscale(std::chrono::nanoseconds elapsed) {
+ if (elapsed * 10 < mTargetRuntimePerEpoch) {
+ // we are far below the target runtime. Multiply iterations by 10 (with overflow check)
+ if (mNumIters * 10 < mNumIters) {
+ // overflow :-(
+ showResult("iterations overflow. Maybe your code got optimized away?");
+ mNumIters = 0;
+ return;
+ }
+ mNumIters *= 10;
+ } else {
+ mNumIters = calcBestNumIters(elapsed, mNumIters);
+ }
+ }
+
+ void add(std::chrono::nanoseconds elapsed, PerformanceCounters const& pc) noexcept {
+# if defined(ANKERL_NANOBENCH_LOG_ENABLED)
+ auto oldIters = mNumIters;
+# endif
+
+ switch (mState) {
+ case State::warmup:
+ if (isCloseEnoughForMeasurements(elapsed)) {
+ // if elapsed is close enough, we can skip upscaling and go right to measurements
+ // still, we don't add the result to the measurements.
+ mState = State::measuring;
+ mNumIters = calcBestNumIters(elapsed, mNumIters);
+ } else {
+ // not close enough: switch to upscaling
+ mState = State::upscaling_runtime;
+ upscale(elapsed);
+ }
+ break;
+
+ case State::upscaling_runtime:
+ if (isCloseEnoughForMeasurements(elapsed)) {
+ // if we are close enough, add measurement and switch to always measuring
+ mState = State::measuring;
+ mTotalElapsed += elapsed;
+ mTotalNumIters += mNumIters;
+ mResult.add(elapsed, mNumIters, pc);
+ mNumIters = calcBestNumIters(mTotalElapsed, mTotalNumIters);
+ } else {
+ upscale(elapsed);
+ }
+ break;
+
+ case State::measuring:
+ // just add measurements - no questions asked. Even when runtime is low. But we can't ignore
+ // that fluctuation, or else we would bias the result
+ mTotalElapsed += elapsed;
+ mTotalNumIters += mNumIters;
+ mResult.add(elapsed, mNumIters, pc);
+ if (0 != mBench.epochIterations()) {
+ mNumIters = mBench.epochIterations();
+ } else {
+ mNumIters = calcBestNumIters(mTotalElapsed, mTotalNumIters);
+ }
+ break;
+
+ case State::endless:
+ mNumIters = (std::numeric_limits<uint64_t>::max)();
+ break;
+ }
+
+ if (static_cast<uint64_t>(mResult.size()) == mBench.epochs()) {
+ // we got all the results that we need, finish it
+ showResult("");
+ mNumIters = 0;
+ }
+
+ ANKERL_NANOBENCH_LOG(mBench.name() << ": " << detail::fmt::Number(20, 3, static_cast<double>(elapsed.count())) << " elapsed, "
+ << detail::fmt::Number(20, 3, static_cast<double>(mTargetRuntimePerEpoch.count()))
+ << " target. oldIters=" << oldIters << ", mNumIters=" << mNumIters
+ << ", mState=" << static_cast<int>(mState));
+ }
+
+ void showResult(std::string const& errorMessage) const {
+ ANKERL_NANOBENCH_LOG(errorMessage);
+
+ if (mBench.output() != nullptr) {
+ // prepare column data ///////
+ std::vector<fmt::MarkDownColumn> columns;
+
+ auto rMedian = mResult.median(Result::Measure::elapsed);
+
+ if (mBench.relative()) {
+ double d = 100.0;
+ if (!mBench.results().empty()) {
+ d = rMedian <= 0.0 ? 0.0 : mBench.results().front().median(Result::Measure::elapsed) / rMedian * 100.0;
+ }
+ columns.emplace_back(11, 1, "relative", "%", d);
+ }
+
+ if (mBench.complexityN() > 0) {
+ columns.emplace_back(14, 0, "complexityN", "", mBench.complexityN());
+ }
+
+ columns.emplace_back(22, 2, "ns/" + mBench.unit(), "", 1e9 * rMedian / mBench.batch());
+ columns.emplace_back(22, 2, mBench.unit() + "/s", "", rMedian <= 0.0 ? 0.0 : mBench.batch() / rMedian);
+
+ double rErrorMedian = mResult.medianAbsolutePercentError(Result::Measure::elapsed);
+ columns.emplace_back(10, 1, "err%", "%", rErrorMedian * 100.0);
+
+ double rInsMedian = -1.0;
+ if (mResult.has(Result::Measure::instructions)) {
+ rInsMedian = mResult.median(Result::Measure::instructions);
+ columns.emplace_back(18, 2, "ins/" + mBench.unit(), "", rInsMedian / mBench.batch());
+ }
+
+ double rCycMedian = -1.0;
+ if (mResult.has(Result::Measure::cpucycles)) {
+ rCycMedian = mResult.median(Result::Measure::cpucycles);
+ columns.emplace_back(18, 2, "cyc/" + mBench.unit(), "", rCycMedian / mBench.batch());
+ }
+ if (rInsMedian > 0.0 && rCycMedian > 0.0) {
+ columns.emplace_back(9, 3, "IPC", "", rCycMedian <= 0.0 ? 0.0 : rInsMedian / rCycMedian);
+ }
+ if (mResult.has(Result::Measure::branchinstructions)) {
+ double rBraMedian = mResult.median(Result::Measure::branchinstructions);
+ columns.emplace_back(17, 2, "bra/" + mBench.unit(), "", rBraMedian / mBench.batch());
+ if (mResult.has(Result::Measure::branchmisses)) {
+ double p = 0.0;
+ if (rBraMedian >= 1e-9) {
+ p = 100.0 * mResult.median(Result::Measure::branchmisses) / rBraMedian;
+ }
+ columns.emplace_back(10, 1, "miss%", "%", p);
+ }
+ }
+
+ columns.emplace_back(12, 2, "total", "", mResult.sum(Result::Measure::elapsed));
+
+ // write everything
+ auto& os = *mBench.output();
+
+ uint64_t hash = 0;
+ hash = hash_combine(fnv1a(mBench.unit()), hash);
+ hash = hash_combine(fnv1a(mBench.title()), hash);
+ hash = hash_combine(mBench.relative(), hash);
+ hash = hash_combine(mBench.performanceCounters(), hash);
+
+ if (hash != singletonHeaderHash()) {
+ singletonHeaderHash() = hash;
+
+ // no result yet, print header
+ os << std::endl;
+ for (auto const& col : columns) {
+ os << col.title();
+ }
+ os << "| " << mBench.title() << std::endl;
+
+ for (auto const& col : columns) {
+ os << col.separator();
+ }
+ os << "|:" << std::string(mBench.title().size() + 1U, '-') << std::endl;
+ }
+
+ if (!errorMessage.empty()) {
+ for (auto const& col : columns) {
+ os << col.invalid();
+ }
+ os << "| :boom: " << fmt::MarkDownCode(mBench.name()) << " (" << errorMessage << ')' << std::endl;
+ } else {
+ for (auto const& col : columns) {
+ os << col.value();
+ }
+ os << "| ";
+ auto showUnstable = rErrorMedian >= 0.05;
+ if (showUnstable) {
+ os << ":wavy_dash: ";
+ }
+ os << fmt::MarkDownCode(mBench.name());
+ if (showUnstable) {
+ auto avgIters = static_cast<double>(mTotalNumIters) / static_cast<double>(mBench.epochs());
+ // NOLINTNEXTLINE(bugprone-incorrect-roundings)
+ auto suggestedIters = static_cast<uint64_t>(avgIters * 10 + 0.5);
+
+ os << " (Unstable with ~" << detail::fmt::Number(1, 1, avgIters)
+ << " iters. Increase `minEpochIterations` to e.g. " << suggestedIters << ")";
+ }
+ os << std::endl;
+ }
+ }
+ }
+
+ ANKERL_NANOBENCH(NODISCARD) bool isCloseEnoughForMeasurements(std::chrono::nanoseconds elapsed) const noexcept {
+ return elapsed * 3 >= mTargetRuntimePerEpoch * 2;
+ }
+
+ uint64_t mNumIters = 1;
+ Bench const& mBench;
+ std::chrono::nanoseconds mTargetRuntimePerEpoch{};
+ Result mResult;
+ Rng mRng{123};
+ std::chrono::nanoseconds mTotalElapsed{};
+ uint64_t mTotalNumIters = 0;
+
+ State mState = State::upscaling_runtime;
+};
+ANKERL_NANOBENCH(IGNORE_PADDED_POP)
+
+IterationLogic::IterationLogic(Bench const& bench) noexcept
+ : mPimpl(new Impl(bench)) {}
+
+IterationLogic::~IterationLogic() {
+ if (mPimpl) {
+ delete mPimpl;
+ }
+}
+
+uint64_t IterationLogic::numIters() const noexcept {
+ ANKERL_NANOBENCH_LOG(mPimpl->mBench.name() << ": mNumIters=" << mPimpl->mNumIters);
+ return mPimpl->mNumIters;
+}
+
+void IterationLogic::add(std::chrono::nanoseconds elapsed, PerformanceCounters const& pc) noexcept {
+ mPimpl->add(elapsed, pc);
+}
+
+void IterationLogic::moveResultTo(std::vector<Result>& results) noexcept {
+ results.emplace_back(std::move(mPimpl->mResult));
+}
+
+# if ANKERL_NANOBENCH(PERF_COUNTERS)
+
+ANKERL_NANOBENCH(IGNORE_PADDED_PUSH)
+class LinuxPerformanceCounters {
+public:
+ struct Target {
+ Target(uint64_t* targetValue_, bool correctMeasuringOverhead_, bool correctLoopOverhead_)
+ : targetValue(targetValue_)
+ , correctMeasuringOverhead(correctMeasuringOverhead_)
+ , correctLoopOverhead(correctLoopOverhead_) {}
+
+ uint64_t* targetValue{};
+ bool correctMeasuringOverhead{};
+ bool correctLoopOverhead{};
+ };
+
+ ~LinuxPerformanceCounters();
+
+ // quick operation
+ inline void start() {}
+
+ inline void stop() {}
+
+ bool monitor(perf_sw_ids swId, Target target);
+ bool monitor(perf_hw_id hwId, Target target);
+
+ bool hasError() const noexcept {
+ return mHasError;
+ }
+
+ // Just reading data is faster than enable & disabling.
+ // we subtract data ourselves.
+ inline void beginMeasure() {
+ if (mHasError) {
+ return;
+ }
+
+ // NOLINTNEXTLINE(hicpp-signed-bitwise)
+ mHasError = -1 == ioctl(mFd, PERF_EVENT_IOC_RESET, PERF_IOC_FLAG_GROUP);
+ if (mHasError) {
+ return;
+ }
+
+ // NOLINTNEXTLINE(hicpp-signed-bitwise)
+ mHasError = -1 == ioctl(mFd, PERF_EVENT_IOC_ENABLE, PERF_IOC_FLAG_GROUP);
+ }
+
+ inline void endMeasure() {
+ if (mHasError) {
+ return;
+ }
+
+ // NOLINTNEXTLINE(hicpp-signed-bitwise)
+ mHasError = (-1 == ioctl(mFd, PERF_EVENT_IOC_DISABLE, PERF_IOC_FLAG_GROUP));
+ if (mHasError) {
+ return;
+ }
+
+ auto const numBytes = sizeof(uint64_t) * mCounters.size();
+ auto ret = read(mFd, mCounters.data(), numBytes);
+ mHasError = ret != static_cast<ssize_t>(numBytes);
+ }
+
+ void updateResults(uint64_t numIters);
+
+ // rounded integer division
+ template <typename T>
+ static inline T divRounded(T a, T divisor) {
+ return (a + divisor / 2) / divisor;
+ }
+
+ template <typename Op>
+ ANKERL_NANOBENCH_NO_SANITIZE("integer")
+ void calibrate(Op&& op) {
+ // clear current calibration data,
+ for (auto& v : mCalibratedOverhead) {
+ v = UINT64_C(0);
+ }
+
+ // create new calibration data
+ auto newCalibration = mCalibratedOverhead;
+ for (auto& v : newCalibration) {
+ v = (std::numeric_limits<uint64_t>::max)();
+ }
+ for (size_t iter = 0; iter < 100; ++iter) {
+ beginMeasure();
+ op();
+ endMeasure();
+ if (mHasError) {
+ return;
+ }
+
+ for (size_t i = 0; i < newCalibration.size(); ++i) {
+ auto diff = mCounters[i];
+ if (newCalibration[i] > diff) {
+ newCalibration[i] = diff;
+ }
+ }
+ }
+
+ mCalibratedOverhead = std::move(newCalibration);
+
+ {
+ // calibrate loop overhead. For branches & instructions this makes sense, not so much for everything else like cycles.
+ // marsaglia's xorshift: mov, sal/shr, xor. Times 3.
+ // This has the nice property that the compiler doesn't seem to be able to optimize multiple calls any further.
+ // see https://godbolt.org/z/49RVQ5
+ uint64_t const numIters = 100000U + (std::random_device{}() & 3);
+ uint64_t n = numIters;
+ uint32_t x = 1234567;
+ auto fn = [&]() {
+ x ^= x << 13;
+ x ^= x >> 17;
+ x ^= x << 5;
+ };
+
+ beginMeasure();
+ while (n-- > 0) {
+ fn();
+ }
+ endMeasure();
+ detail::doNotOptimizeAway(x);
+ auto measure1 = mCounters;
+
+ n = numIters;
+ beginMeasure();
+ while (n-- > 0) {
+ // we now run *twice* so we can easily calculate the overhead
+ fn();
+ fn();
+ }
+ endMeasure();
+ detail::doNotOptimizeAway(x);
+ auto measure2 = mCounters;
+
+ for (size_t i = 0; i < mCounters.size(); ++i) {
+ // factor 2 because we have two instructions per loop
+ auto m1 = measure1[i] > mCalibratedOverhead[i] ? measure1[i] - mCalibratedOverhead[i] : 0;
+ auto m2 = measure2[i] > mCalibratedOverhead[i] ? measure2[i] - mCalibratedOverhead[i] : 0;
+ auto overhead = m1 * 2 > m2 ? m1 * 2 - m2 : 0;
+
+ mLoopOverhead[i] = divRounded(overhead, numIters);
+ }
+ }
+ }
+
+private:
+ bool monitor(uint32_t type, uint64_t eventid, Target target);
+
+ std::map<uint64_t, Target> mIdToTarget{};
+
+ // start with minimum size of 3 for read_format
+ std::vector<uint64_t> mCounters{3};
+ std::vector<uint64_t> mCalibratedOverhead{3};
+ std::vector<uint64_t> mLoopOverhead{3};
+
+ uint64_t mTimeEnabledNanos = 0;
+ uint64_t mTimeRunningNanos = 0;
+ int mFd = -1;
+ bool mHasError = false;
+};
+ANKERL_NANOBENCH(IGNORE_PADDED_POP)
+
+LinuxPerformanceCounters::~LinuxPerformanceCounters() {
+ if (-1 != mFd) {
+ close(mFd);
+ }
+}
+
+bool LinuxPerformanceCounters::monitor(perf_sw_ids swId, LinuxPerformanceCounters::Target target) {
+ return monitor(PERF_TYPE_SOFTWARE, swId, target);
+}
+
+bool LinuxPerformanceCounters::monitor(perf_hw_id hwId, LinuxPerformanceCounters::Target target) {
+ return monitor(PERF_TYPE_HARDWARE, hwId, target);
+}
+
+// overflow is ok, it's checked
+ANKERL_NANOBENCH_NO_SANITIZE("integer")
+void LinuxPerformanceCounters::updateResults(uint64_t numIters) {
+ // clear old data
+ for (auto& id_value : mIdToTarget) {
+ *id_value.second.targetValue = UINT64_C(0);
+ }
+
+ if (mHasError) {
+ return;
+ }
+
+ mTimeEnabledNanos = mCounters[1] - mCalibratedOverhead[1];
+ mTimeRunningNanos = mCounters[2] - mCalibratedOverhead[2];
+
+ for (uint64_t i = 0; i < mCounters[0]; ++i) {
+ auto idx = static_cast<size_t>(3 + i * 2 + 0);
+ auto id = mCounters[idx + 1U];
+
+ auto it = mIdToTarget.find(id);
+ if (it != mIdToTarget.end()) {
+
+ auto& tgt = it->second;
+ *tgt.targetValue = mCounters[idx];
+ if (tgt.correctMeasuringOverhead) {
+ if (*tgt.targetValue >= mCalibratedOverhead[idx]) {
+ *tgt.targetValue -= mCalibratedOverhead[idx];
+ } else {
+ *tgt.targetValue = 0U;
+ }
+ }
+ if (tgt.correctLoopOverhead) {
+ auto correctionVal = mLoopOverhead[idx] * numIters;
+ if (*tgt.targetValue >= correctionVal) {
+ *tgt.targetValue -= correctionVal;
+ } else {
+ *tgt.targetValue = 0U;
+ }
+ }
+ }
+ }
+}
+
+bool LinuxPerformanceCounters::monitor(uint32_t type, uint64_t eventid, Target target) {
+ *target.targetValue = (std::numeric_limits<uint64_t>::max)();
+ if (mHasError) {
+ return false;
+ }
+
+ auto pea = perf_event_attr();
+ std::memset(&pea, 0, sizeof(perf_event_attr));
+ pea.type = type;
+ pea.size = sizeof(perf_event_attr);
+ pea.config = eventid;
+ pea.disabled = 1; // start counter as disabled
+ pea.exclude_kernel = 1;
+ pea.exclude_hv = 1;
+
+ // NOLINTNEXTLINE(hicpp-signed-bitwise)
+ pea.read_format = PERF_FORMAT_GROUP | PERF_FORMAT_ID | PERF_FORMAT_TOTAL_TIME_ENABLED | PERF_FORMAT_TOTAL_TIME_RUNNING;
+
+ const int pid = 0; // the current process
+ const int cpu = -1; // all CPUs
+# if defined(PERF_FLAG_FD_CLOEXEC) // since Linux 3.14
+ const unsigned long flags = PERF_FLAG_FD_CLOEXEC;
+# else
+ const unsigned long flags = 0;
+# endif
+
+ auto fd = static_cast<int>(syscall(__NR_perf_event_open, &pea, pid, cpu, mFd, flags));
+ if (-1 == fd) {
+ return false;
+ }
+ if (-1 == mFd) {
+ // first call: set to fd, and use this from now on
+ mFd = fd;
+ }
+ uint64_t id = 0;
+ // NOLINTNEXTLINE(hicpp-signed-bitwise)
+ if (-1 == ioctl(fd, PERF_EVENT_IOC_ID, &id)) {
+ // couldn't get id
+ return false;
+ }
+
+ // insert into map, rely on the fact that map's references are constant.
+ mIdToTarget.emplace(id, target);
+
+ // prepare readformat with the correct size (after the insert)
+ auto size = 3 + 2 * mIdToTarget.size();
+ mCounters.resize(size);
+ mCalibratedOverhead.resize(size);
+ mLoopOverhead.resize(size);
+
+ return true;
+}
+
+PerformanceCounters::PerformanceCounters()
+ : mPc(new LinuxPerformanceCounters())
+ , mVal()
+ , mHas() {
+
+ mHas.pageFaults = mPc->monitor(PERF_COUNT_SW_PAGE_FAULTS, LinuxPerformanceCounters::Target(&mVal.pageFaults, true, false));
+ mHas.cpuCycles = mPc->monitor(PERF_COUNT_HW_REF_CPU_CYCLES, LinuxPerformanceCounters::Target(&mVal.cpuCycles, true, false));
+ mHas.contextSwitches =
+ mPc->monitor(PERF_COUNT_SW_CONTEXT_SWITCHES, LinuxPerformanceCounters::Target(&mVal.contextSwitches, true, false));
+ mHas.instructions = mPc->monitor(PERF_COUNT_HW_INSTRUCTIONS, LinuxPerformanceCounters::Target(&mVal.instructions, true, true));
+ mHas.branchInstructions =
+ mPc->monitor(PERF_COUNT_HW_BRANCH_INSTRUCTIONS, LinuxPerformanceCounters::Target(&mVal.branchInstructions, true, false));
+ mHas.branchMisses = mPc->monitor(PERF_COUNT_HW_BRANCH_MISSES, LinuxPerformanceCounters::Target(&mVal.branchMisses, true, false));
+ // mHas.branchMisses = false;
+
+ mPc->start();
+ mPc->calibrate([] {
+ auto before = ankerl::nanobench::Clock::now();
+ auto after = ankerl::nanobench::Clock::now();
+ (void)before;
+ (void)after;
+ });
+
+ if (mPc->hasError()) {
+ // something failed, don't monitor anything.
+ mHas = PerfCountSet<bool>{};
+ }
+}
+
+PerformanceCounters::~PerformanceCounters() {
+ if (nullptr != mPc) {
+ delete mPc;
+ }
+}
+
+void PerformanceCounters::beginMeasure() {
+ mPc->beginMeasure();
+}
+
+void PerformanceCounters::endMeasure() {
+ mPc->endMeasure();
+}
+
+void PerformanceCounters::updateResults(uint64_t numIters) {
+ mPc->updateResults(numIters);
+}
+
+# else
+
+PerformanceCounters::PerformanceCounters() = default;
+PerformanceCounters::~PerformanceCounters() = default;
+void PerformanceCounters::beginMeasure() {}
+void PerformanceCounters::endMeasure() {}
+void PerformanceCounters::updateResults(uint64_t) {}
+
+# endif
+
+ANKERL_NANOBENCH(NODISCARD) PerfCountSet<uint64_t> const& PerformanceCounters::val() const noexcept {
+ return mVal;
+}
+ANKERL_NANOBENCH(NODISCARD) PerfCountSet<bool> const& PerformanceCounters::has() const noexcept {
+ return mHas;
+}
+
+// formatting utilities
+namespace fmt {
+
+// adds thousands separator to numbers
+NumSep::NumSep(char sep)
+ : mSep(sep) {}
+
+char NumSep::do_thousands_sep() const {
+ return mSep;
+}
+
+std::string NumSep::do_grouping() const {
+ return "\003";
+}
+
+// RAII to save & restore a stream's state
+StreamStateRestorer::StreamStateRestorer(std::ostream& s)
+ : mStream(s)
+ , mLocale(s.getloc())
+ , mPrecision(s.precision())
+ , mWidth(s.width())
+ , mFill(s.fill())
+ , mFmtFlags(s.flags()) {}
+
+StreamStateRestorer::~StreamStateRestorer() {
+ restore();
+}
+
+// sets back all stream info that we remembered at construction
+void StreamStateRestorer::restore() {
+ mStream.imbue(mLocale);
+ mStream.precision(mPrecision);
+ mStream.width(mWidth);
+ mStream.fill(mFill);
+ mStream.flags(mFmtFlags);
+}
+
+Number::Number(int width, int precision, int64_t value)
+ : mWidth(width)
+ , mPrecision(precision)
+ , mValue(static_cast<double>(value)) {}
+
+Number::Number(int width, int precision, double value)
+ : mWidth(width)
+ , mPrecision(precision)
+ , mValue(value) {}
+
+std::ostream& Number::write(std::ostream& os) const {
+ StreamStateRestorer restorer(os);
+ os.imbue(std::locale(os.getloc(), new NumSep(',')));
+ os << std::setw(mWidth) << std::setprecision(mPrecision) << std::fixed << mValue;
+ return os;
+}
+
+std::string Number::to_s() const {
+ std::stringstream ss;
+ write(ss);
+ return ss.str();
+}
+
+std::string to_s(uint64_t n) {
+ std::string str;
+ do {
+ str += static_cast<char>('0' + static_cast<char>(n % 10));
+ n /= 10;
+ } while (n != 0);
+ std::reverse(str.begin(), str.end());
+ return str;
+}
+
+std::ostream& operator<<(std::ostream& os, Number const& n) {
+ return n.write(os);
+}
+
+MarkDownColumn::MarkDownColumn(int w, int prec, std::string const& tit, std::string const& suff, double val)
+ : mWidth(w)
+ , mPrecision(prec)
+ , mTitle(tit)
+ , mSuffix(suff)
+ , mValue(val) {}
+
+std::string MarkDownColumn::title() const {
+ std::stringstream ss;
+ ss << '|' << std::setw(mWidth - 2) << std::right << mTitle << ' ';
+ return ss.str();
+}
+
+std::string MarkDownColumn::separator() const {
+ std::string sep(static_cast<size_t>(mWidth), '-');
+ sep.front() = '|';
+ sep.back() = ':';
+ return sep;
+}
+
+std::string MarkDownColumn::invalid() const {
+ std::string sep(static_cast<size_t>(mWidth), ' ');
+ sep.front() = '|';
+ sep[sep.size() - 2] = '-';
+ return sep;
+}
+
+std::string MarkDownColumn::value() const {
+ std::stringstream ss;
+ auto width = mWidth - 2 - static_cast<int>(mSuffix.size());
+ ss << '|' << Number(width, mPrecision, mValue) << mSuffix << ' ';
+ return ss.str();
+}
+
+// Formats any text as markdown code, escaping backticks.
+MarkDownCode::MarkDownCode(std::string const& what) {
+ mWhat.reserve(what.size() + 2);
+ mWhat.push_back('`');
+ for (char c : what) {
+ mWhat.push_back(c);
+ if ('`' == c) {
+ mWhat.push_back('`');
+ }
+ }
+ mWhat.push_back('`');
+}
+
+std::ostream& MarkDownCode::write(std::ostream& os) const {
+ return os << mWhat;
+}
+
+std::ostream& operator<<(std::ostream& os, MarkDownCode const& mdCode) {
+ return mdCode.write(os);
+}
+} // namespace fmt
+} // namespace detail
+
+// provide implementation here so it's only generated once
+Config::Config() = default;
+Config::~Config() = default;
+Config& Config::operator=(Config const&) = default;
+Config& Config::operator=(Config&&) = default;
+Config::Config(Config const&) = default;
+Config::Config(Config&&) noexcept = default;
+
+// provide implementation here so it's only generated once
+Result::~Result() = default;
+Result& Result::operator=(Result const&) = default;
+Result& Result::operator=(Result&&) = default;
+Result::Result(Result const&) = default;
+Result::Result(Result&&) noexcept = default;
+
+namespace detail {
+template <typename T>
+inline constexpr typename std::underlying_type<T>::type u(T val) noexcept {
+ return static_cast<typename std::underlying_type<T>::type>(val);
+}
+} // namespace detail
+
+// Result returned after a benchmark has finished. Can be used as a baseline for relative().
+Result::Result(Config const& benchmarkConfig)
+ : mConfig(benchmarkConfig)
+ , mNameToMeasurements{detail::u(Result::Measure::_size)} {}
+
+void Result::add(Clock::duration totalElapsed, uint64_t iters, detail::PerformanceCounters const& pc) {
+ using detail::d;
+ using detail::u;
+
+ double dIters = d(iters);
+ mNameToMeasurements[u(Result::Measure::iterations)].push_back(dIters);
+
+ mNameToMeasurements[u(Result::Measure::elapsed)].push_back(d(totalElapsed) / dIters);
+ if (pc.has().pageFaults) {
+ mNameToMeasurements[u(Result::Measure::pagefaults)].push_back(d(pc.val().pageFaults) / dIters);
+ }
+ if (pc.has().cpuCycles) {
+ mNameToMeasurements[u(Result::Measure::cpucycles)].push_back(d(pc.val().cpuCycles) / dIters);
+ }
+ if (pc.has().contextSwitches) {
+ mNameToMeasurements[u(Result::Measure::contextswitches)].push_back(d(pc.val().contextSwitches) / dIters);
+ }
+ if (pc.has().instructions) {
+ mNameToMeasurements[u(Result::Measure::instructions)].push_back(d(pc.val().instructions) / dIters);
+ }
+ if (pc.has().branchInstructions) {
+ double branchInstructions = 0.0;
+ // correcting branches: remove branch introduced by the while (...) loop for each iteration.
+ if (pc.val().branchInstructions > iters + 1U) {
+ branchInstructions = d(pc.val().branchInstructions - (iters + 1U));
+ }
+ mNameToMeasurements[u(Result::Measure::branchinstructions)].push_back(branchInstructions / dIters);
+
+ if (pc.has().branchMisses) {
+ // correcting branch misses
+ double branchMisses = d(pc.val().branchMisses);
+ if (branchMisses > branchInstructions) {
+ // can't have branch misses when there were branches...
+ branchMisses = branchInstructions;
+ }
+
+ // assuming at least one missed branch for the loop
+ branchMisses -= 1.0;
+ if (branchMisses < 1.0) {
+ branchMisses = 1.0;
+ }
+ mNameToMeasurements[u(Result::Measure::branchmisses)].push_back(branchMisses / dIters);
+ }
+ }
+}
+
+Config const& Result::config() const noexcept {
+ return mConfig;
+}
+
+inline double calcMedian(std::vector<double>& data) {
+ if (data.empty()) {
+ return 0.0;
+ }
+ std::sort(data.begin(), data.end());
+
+ auto midIdx = data.size() / 2U;
+ if (1U == (data.size() & 1U)) {
+ return data[midIdx];
+ }
+ return (data[midIdx - 1U] + data[midIdx]) / 2U;
+}
+
+double Result::median(Measure m) const {
+ // create a copy so we can sort
+ auto data = mNameToMeasurements[detail::u(m)];
+ return calcMedian(data);
+}
+
+double Result::average(Measure m) const {
+ using detail::d;
+ auto const& data = mNameToMeasurements[detail::u(m)];
+ if (data.empty()) {
+ return 0.0;
+ }
+
+ // create a copy so we can sort
+ return sum(m) / d(data.size());
+}
+
+double Result::medianAbsolutePercentError(Measure m) const {
+ // create copy
+ auto data = mNameToMeasurements[detail::u(m)];
+
+ // calculates MdAPE which is the median of percentage error
+ // see https://www.spiderfinancial.com/support/documentation/numxl/reference-manual/forecasting-performance/mdape
+ auto med = calcMedian(data);
+
+ // transform the data to absolute error
+ for (auto& x : data) {
+ x = (x - med) / x;
+ if (x < 0) {
+ x = -x;
+ }
+ }
+ return calcMedian(data);
+}
+
+double Result::sum(Measure m) const noexcept {
+ auto const& data = mNameToMeasurements[detail::u(m)];
+ return std::accumulate(data.begin(), data.end(), 0.0);
+}
+
+double Result::sumProduct(Measure m1, Measure m2) const noexcept {
+ auto const& data1 = mNameToMeasurements[detail::u(m1)];
+ auto const& data2 = mNameToMeasurements[detail::u(m2)];
+
+ if (data1.size() != data2.size()) {
+ return 0.0;
+ }
+
+ double result = 0.0;
+ for (size_t i = 0, s = data1.size(); i != s; ++i) {
+ result += data1[i] * data2[i];
+ }
+ return result;
+}
+
+bool Result::has(Measure m) const noexcept {
+ return !mNameToMeasurements[detail::u(m)].empty();
+}
+
+double Result::get(size_t idx, Measure m) const {
+ auto const& data = mNameToMeasurements[detail::u(m)];
+ return data.at(idx);
+}
+
+bool Result::empty() const noexcept {
+ return 0U == size();
+}
+
+size_t Result::size() const noexcept {
+ auto const& data = mNameToMeasurements[detail::u(Measure::elapsed)];
+ return data.size();
+}
+
+double Result::minimum(Measure m) const noexcept {
+ auto const& data = mNameToMeasurements[detail::u(m)];
+ if (data.empty()) {
+ return 0.0;
+ }
+
+ // here its save to assume that at least one element is there
+ return *std::min_element(data.begin(), data.end());
+}
+
+double Result::maximum(Measure m) const noexcept {
+ auto const& data = mNameToMeasurements[detail::u(m)];
+ if (data.empty()) {
+ return 0.0;
+ }
+
+ // here its save to assume that at least one element is there
+ return *std::max_element(data.begin(), data.end());
+}
+
+Result::Measure Result::fromString(std::string const& str) {
+ if (str == "elapsed") {
+ return Measure::elapsed;
+ } else if (str == "iterations") {
+ return Measure::iterations;
+ } else if (str == "pagefaults") {
+ return Measure::pagefaults;
+ } else if (str == "cpucycles") {
+ return Measure::cpucycles;
+ } else if (str == "contextswitches") {
+ return Measure::contextswitches;
+ } else if (str == "instructions") {
+ return Measure::instructions;
+ } else if (str == "branchinstructions") {
+ return Measure::branchinstructions;
+ } else if (str == "branchmisses") {
+ return Measure::branchmisses;
+ } else {
+ // not found, return _size
+ return Measure::_size;
+ }
+}
+
+// Configuration of a microbenchmark.
+Bench::Bench() {
+ mConfig.mOut = &std::cout;
+}
+
+Bench::Bench(Bench&&) = default;
+Bench& Bench::operator=(Bench&&) = default;
+Bench::Bench(Bench const&) = default;
+Bench& Bench::operator=(Bench const&) = default;
+Bench::~Bench() noexcept = default;
+
+double Bench::batch() const noexcept {
+ return mConfig.mBatch;
+}
+
+double Bench::complexityN() const noexcept {
+ return mConfig.mComplexityN;
+}
+
+// Set a baseline to compare it to. 100% it is exactly as fast as the baseline, >100% means it is faster than the baseline, <100%
+// means it is slower than the baseline.
+Bench& Bench::relative(bool isRelativeEnabled) noexcept {
+ mConfig.mIsRelative = isRelativeEnabled;
+ return *this;
+}
+bool Bench::relative() const noexcept {
+ return mConfig.mIsRelative;
+}
+
+Bench& Bench::performanceCounters(bool showPerformanceCounters) noexcept {
+ mConfig.mShowPerformanceCounters = showPerformanceCounters;
+ return *this;
+}
+bool Bench::performanceCounters() const noexcept {
+ return mConfig.mShowPerformanceCounters;
+}
+
+// Operation unit. Defaults to "op", could be e.g. "byte" for string processing.
+// If u differs from currently set unit, the stored results will be cleared.
+// Use singular (byte, not bytes).
+Bench& Bench::unit(char const* u) {
+ if (u != mConfig.mUnit) {
+ mResults.clear();
+ }
+ mConfig.mUnit = u;
+ return *this;
+}
+
+Bench& Bench::unit(std::string const& u) {
+ return unit(u.c_str());
+}
+
+std::string const& Bench::unit() const noexcept {
+ return mConfig.mUnit;
+}
+
+// If benchmarkTitle differs from currently set title, the stored results will be cleared.
+Bench& Bench::title(const char* benchmarkTitle) {
+ if (benchmarkTitle != mConfig.mBenchmarkTitle) {
+ mResults.clear();
+ }
+ mConfig.mBenchmarkTitle = benchmarkTitle;
+ return *this;
+}
+Bench& Bench::title(std::string const& benchmarkTitle) {
+ if (benchmarkTitle != mConfig.mBenchmarkTitle) {
+ mResults.clear();
+ }
+ mConfig.mBenchmarkTitle = benchmarkTitle;
+ return *this;
+}
+
+std::string const& Bench::title() const noexcept {
+ return mConfig.mBenchmarkTitle;
+}
+
+Bench& Bench::name(const char* benchmarkName) {
+ mConfig.mBenchmarkName = benchmarkName;
+ return *this;
+}
+
+Bench& Bench::name(std::string const& benchmarkName) {
+ mConfig.mBenchmarkName = benchmarkName;
+ return *this;
+}
+
+std::string const& Bench::name() const noexcept {
+ return mConfig.mBenchmarkName;
+}
+
+// Number of epochs to evaluate. The reported result will be the median of evaluation of each epoch.
+Bench& Bench::epochs(size_t numEpochs) noexcept {
+ mConfig.mNumEpochs = numEpochs;
+ return *this;
+}
+size_t Bench::epochs() const noexcept {
+ return mConfig.mNumEpochs;
+}
+
+// Desired evaluation time is a multiple of clock resolution. Default is to be 1000 times above this measurement precision.
+Bench& Bench::clockResolutionMultiple(size_t multiple) noexcept {
+ mConfig.mClockResolutionMultiple = multiple;
+ return *this;
+}
+size_t Bench::clockResolutionMultiple() const noexcept {
+ return mConfig.mClockResolutionMultiple;
+}
+
+// Sets the maximum time each epoch should take. Default is 100ms.
+Bench& Bench::maxEpochTime(std::chrono::nanoseconds t) noexcept {
+ mConfig.mMaxEpochTime = t;
+ return *this;
+}
+std::chrono::nanoseconds Bench::maxEpochTime() const noexcept {
+ return mConfig.mMaxEpochTime;
+}
+
+// Sets the maximum time each epoch should take. Default is 100ms.
+Bench& Bench::minEpochTime(std::chrono::nanoseconds t) noexcept {
+ mConfig.mMinEpochTime = t;
+ return *this;
+}
+std::chrono::nanoseconds Bench::minEpochTime() const noexcept {
+ return mConfig.mMinEpochTime;
+}
+
+Bench& Bench::minEpochIterations(uint64_t numIters) noexcept {
+ mConfig.mMinEpochIterations = (numIters == 0) ? 1 : numIters;
+ return *this;
+}
+uint64_t Bench::minEpochIterations() const noexcept {
+ return mConfig.mMinEpochIterations;
+}
+
+Bench& Bench::epochIterations(uint64_t numIters) noexcept {
+ mConfig.mEpochIterations = numIters;
+ return *this;
+}
+uint64_t Bench::epochIterations() const noexcept {
+ return mConfig.mEpochIterations;
+}
+
+Bench& Bench::warmup(uint64_t numWarmupIters) noexcept {
+ mConfig.mWarmup = numWarmupIters;
+ return *this;
+}
+uint64_t Bench::warmup() const noexcept {
+ return mConfig.mWarmup;
+}
+
+Bench& Bench::config(Config const& benchmarkConfig) {
+ mConfig = benchmarkConfig;
+ return *this;
+}
+Config const& Bench::config() const noexcept {
+ return mConfig;
+}
+
+Bench& Bench::output(std::ostream* outstream) noexcept {
+ mConfig.mOut = outstream;
+ return *this;
+}
+
+ANKERL_NANOBENCH(NODISCARD) std::ostream* Bench::output() const noexcept {
+ return mConfig.mOut;
+}
+
+std::vector<Result> const& Bench::results() const noexcept {
+ return mResults;
+}
+
+Bench& Bench::render(char const* templateContent, std::ostream& os) {
+ ::ankerl::nanobench::render(templateContent, *this, os);
+ return *this;
+}
+
+std::vector<BigO> Bench::complexityBigO() const {
+ std::vector<BigO> bigOs;
+ auto rangeMeasure = BigO::collectRangeMeasure(mResults);
+ bigOs.emplace_back("O(1)", rangeMeasure, [](double) {
+ return 1.0;
+ });
+ bigOs.emplace_back("O(n)", rangeMeasure, [](double n) {
+ return n;
+ });
+ bigOs.emplace_back("O(log n)", rangeMeasure, [](double n) {
+ return std::log2(n);
+ });
+ bigOs.emplace_back("O(n log n)", rangeMeasure, [](double n) {
+ return n * std::log2(n);
+ });
+ bigOs.emplace_back("O(n^2)", rangeMeasure, [](double n) {
+ return n * n;
+ });
+ bigOs.emplace_back("O(n^3)", rangeMeasure, [](double n) {
+ return n * n * n;
+ });
+ std::sort(bigOs.begin(), bigOs.end());
+ return bigOs;
+}
+
+Rng::Rng()
+ : mX(0)
+ , mY(0) {
+ std::random_device rd;
+ std::uniform_int_distribution<uint64_t> dist;
+ do {
+ mX = dist(rd);
+ mY = dist(rd);
+ } while (mX == 0 && mY == 0);
+}
+
+ANKERL_NANOBENCH_NO_SANITIZE("integer")
+uint64_t splitMix64(uint64_t& state) noexcept {
+ uint64_t z = (state += UINT64_C(0x9e3779b97f4a7c15));
+ z = (z ^ (z >> 30U)) * UINT64_C(0xbf58476d1ce4e5b9);
+ z = (z ^ (z >> 27U)) * UINT64_C(0x94d049bb133111eb);
+ return z ^ (z >> 31U);
+}
+
+// Seeded as described in romu paper (update april 2020)
+Rng::Rng(uint64_t seed) noexcept
+ : mX(splitMix64(seed))
+ , mY(splitMix64(seed)) {
+ for (size_t i = 0; i < 10; ++i) {
+ operator()();
+ }
+}
+
+// only internally used to copy the RNG.
+Rng::Rng(uint64_t x, uint64_t y) noexcept
+ : mX(x)
+ , mY(y) {}
+
+Rng Rng::copy() const noexcept {
+ return Rng{mX, mY};
+}
+
+BigO::RangeMeasure BigO::collectRangeMeasure(std::vector<Result> const& results) {
+ BigO::RangeMeasure rangeMeasure;
+ for (auto const& result : results) {
+ if (result.config().mComplexityN > 0.0) {
+ rangeMeasure.emplace_back(result.config().mComplexityN, result.median(Result::Measure::elapsed));
+ }
+ }
+ return rangeMeasure;
+}
+
+BigO::BigO(std::string const& bigOName, RangeMeasure const& rangeMeasure)
+ : mName(bigOName) {
+
+ // estimate the constant factor
+ double sumRangeMeasure = 0.0;
+ double sumRangeRange = 0.0;
+
+ for (size_t i = 0; i < rangeMeasure.size(); ++i) {
+ sumRangeMeasure += rangeMeasure[i].first * rangeMeasure[i].second;
+ sumRangeRange += rangeMeasure[i].first * rangeMeasure[i].first;
+ }
+ mConstant = sumRangeMeasure / sumRangeRange;
+
+ // calculate root mean square
+ double err = 0.0;
+ double sumMeasure = 0.0;
+ for (size_t i = 0; i < rangeMeasure.size(); ++i) {
+ auto diff = mConstant * rangeMeasure[i].first - rangeMeasure[i].second;
+ err += diff * diff;
+
+ sumMeasure += rangeMeasure[i].second;
+ }
+
+ auto n = static_cast<double>(rangeMeasure.size());
+ auto mean = sumMeasure / n;
+ mNormalizedRootMeanSquare = std::sqrt(err / n) / mean;
+}
+
+BigO::BigO(const char* bigOName, RangeMeasure const& rangeMeasure)
+ : BigO(std::string(bigOName), rangeMeasure) {}
+
+std::string const& BigO::name() const noexcept {
+ return mName;
+}
+
+double BigO::constant() const noexcept {
+ return mConstant;
+}
+
+double BigO::normalizedRootMeanSquare() const noexcept {
+ return mNormalizedRootMeanSquare;
+}
+
+bool BigO::operator<(BigO const& other) const noexcept {
+ return std::tie(mNormalizedRootMeanSquare, mName) < std::tie(other.mNormalizedRootMeanSquare, other.mName);
+}
+
+std::ostream& operator<<(std::ostream& os, BigO const& bigO) {
+ return os << bigO.constant() << " * " << bigO.name() << ", rms=" << bigO.normalizedRootMeanSquare();
+}
+
+std::ostream& operator<<(std::ostream& os, std::vector<ankerl::nanobench::BigO> const& bigOs) {
+ detail::fmt::StreamStateRestorer restorer(os);
+ os << std::endl << "| coefficient | err% | complexity" << std::endl << "|--------------:|-------:|------------" << std::endl;
+ for (auto const& bigO : bigOs) {
+ os << "|" << std::setw(14) << std::setprecision(7) << std::scientific << bigO.constant() << " ";
+ os << "|" << detail::fmt::Number(6, 1, bigO.normalizedRootMeanSquare() * 100.0) << "% ";
+ os << "| " << bigO.name();
+ os << std::endl;
+ }
+ return os;
+}
+
+} // namespace nanobench
+} // namespace ankerl
+
+#endif // ANKERL_NANOBENCH_IMPLEMENT
+#endif // ANKERL_NANOBENCH_H_INCLUDED