C++ Trapezoid Rule Benchmarks

This project was created for my personal website with the aim to explore how to implement the trapezoidal rule with C++ and benchmark a few different implementations.

So far, the implementations included here are:

• Standard library implementation: an implementation solely using the CPP standard library (stl) was provided, using vectors and functions in the header algorithm.

• Numerical library implementation (Eigen3): Eigen3 is one of the most popular linear algebra libraries for C++, and it provides means of handling matrices and vectors. It's quite optimised for numerical programming.

Tools And Dependencies

In order to build the project, you will need a recent version of CMake (anything >3.16). The code should compile in any modern C++ compiler; since C++14 features were used, make sure your compiler supports that (gcc, clang,and msvc should all support it).

There are a couple of library dependencies to this project, which are handled with conan. Conan is a package manager for C/C++, and it will pull all dependencies (libraries and headers) with a single command once it's installed, so install the latest version from the Conan's website.

The dependencies are:

• Eigen3: The numerical library used for one of the trapezium rule implementations.
• Google Benchmark: Used to create the benchmark executable.

Building The Project

Assuming you installed the tools mentioned in the previous section, and assuming you have a working compiler installed, building the project is as easy as typing the following commands.

# where the build files will be created
mkdir build && cd build
# pull the dependencies and find scripts with
# conan
conan install --build=missing -sbuild_type=Release ..

# configure the project with the dir for
# conan find_package scripts
cmake -DCMAKE_BUILD_TYPE=Release \
      -DCMAKE_MODULE_PATH:FILEPATH="PATH-TO-REPO/build" \
      ..

# build the project
cmake --build .

# run the benchmarks
./benchmarks/benchmarks

Of course, replacing PATH-TO-REPO with the path in your computer where this repository is located (where the main CMakeLists.txt is).

Project Organisation

The project is organised in three CMake targets:

• standard: A static library containing the pure C++ std implementation. The files standard_trapezium.{cpp, h} defines the estimate_area(...) function that estimates area of a function using std libraries.
• eigen_trapezium: A static library containing the Eigen3 trapezoidal rule implementation. The files eigen_trapezium.{cpp,h} also defines a function estimate_area(...) that uses Eigen3 to implement the trapezium rule.
• benchmarks: An executable created from benchmarks.cpp that uses Google's benchmark library to benchmark the standard and eigen implementation with different inputs and sizes.

Learn More About The Trapezoidal Rule

If you are struggling to understand the code here, check out my the post I made on understanding the trapezoidal rule. This particular repo was created to show people how to implement the trapezoidal rule with modern C++.

Benchmark Results

On a modest computer (fairly powerful Lenovo Legion Y740), the improvement between the standard C++ implementation and the Eigen3 one is noticeable. The table below shows benchmarks for the trapezium rule applied to the function , with varying start and end points {a, b}, and the number of trapeziums N:

Inputs {a, b, N}	std C++	Eigen3
{-10, 10, 100}	2.035μs	1.154μs
{-10, 10, 1000}	14.49μs	7.470μs
{-15, 15, 10000}	175.3μs	76.96μs
{-15, 15, 20000}	346.6μs	155.5μs
{-20, 20, 50000}	1.366ms	0.372ms