Trigonometric SIMD Benchmark - C++ Implementation

This repository accompanies the research paper "A Novel SIMD-Optimized Implementation for Fast and Memory-Efficient Trigonometric Computation" by Nikhil Dev Goyal and Parth Arora.

📄 Reference Research Paper:
📌 DOI: https://doi.org/10.48550/arXiv.2502.10831
📌 Full Paper: arXiv Link

The paper introduces a set of trigonometric functions that are significantly faster than standard C++ implementations, achieving up to a 5× speed increase. These functions are also highly memory-efficient, requiring no precomputations, making them ideal for hardware implementations on low-end FPGAs and MCUs. Benchmark comparisons demonstrate substantial hardware resource reductions, including DSPs, LUTs, and flip-flops, when compared to built-in functions.

📥 Getting Started

Follow these steps to set up, compile, and run the code to reproduce the results.

🛠️ Building the Project (Using CMake)

1️⃣ Clone the repository

sh git clone https://github.com/Nikhil0250/trigno_simd_cpp.git cd trigno_simd_cpp

2️⃣ Create a Build Directory

sh mkdir build cd build

3️⃣ Run CMake

➤ Auto-Detect MinGW (Recommended)

sh cmake -G "MinGW Makefiles" .. This will automatically detect gcc, g++, and mingw32-make.

➤ If Auto-Detection Fails

Manually specify compilers: sh cmake -G "MinGW Makefiles" -DCMAKE_C_COMPILER=gcc -DCMAKE_CXX_COMPILER=g++ If MinGW is installed in a custom location: sh cmake -G "MinGW Makefiles" -DCMAKE_MAKE_PROGRAM="C:/YourMinGW/bin/mingw32-make.exe" ..

4️⃣ Compile the Project

sh cmake --build . ✅ This compiles the project and generates the executable in bin/trigno_benchmark.exe.

🔥 Running the Benchmark

After compilation, run: sh bin\trigno_benchmark.exe ✅ This will generate the benchmark results in CSV format inside the data/ folder.

✅ A detailed performance summary is displayed in the terminal upon execution.

📊 Reproducing Research Paper Results

The results of the benchmark will be saved in the data/ directory: data/ ├── proposed_sin.csv ├── proposed_cos.csv ├── proposed_tan.csv ├── taylorcos5.csv ├── taylorsin5.csv ├── taylortan5.csv ├── ... Each CSV contains: - angle: Input angle in radians - std_result: Standard C++ function output - my_result: Optimized SIMD function output - abs_error: Absolute error between standard and optimized functions - rel_error: Relative error - std_time: Execution time of standard function (ns) - my_time: Execution time of optimized function (ns) - speedup_ratio: Speed improvement compared to the standard function

📜 Project Structure

``` trignosimdcpp/ │── include/ # Header files (.h) │ ├── anglereduction.h # Header for angle reduction optimizations │ ├── proposedtrigno.h # Header for proposed optimized trigonometric functions │ ├── taylorsimd.h # Header for SIMD-optimized Taylor series functions │ │── src/ # Source files (.cpp) │ ├── anglereduction.cpp # Implements angle reduction techniques │ ├── benchmark.cpp # Main benchmarking script │ ├── proposedtrigno.cpp # Implements proposed SIMD-optimized trigonometric functions │ ├── taylorsimd.cpp # SIMD-optimized Taylor series calculations │ │── data/ # Computed benchmark results (CSV files) │ ├── proposedsin.csv # Benchmark results for proposed sin() │ ├── proposedcos.csv # Benchmark results for proposed cos() │ ├── proposedtan.csv # Benchmark results for proposed tan() │ ├── taylorcos5.csv # Taylor series approximation (5 terms) for cos() │ ├── taylorsin5.csv # Taylor series approximation (5 terms) for sin() │ ├── taylortan5.csv # Taylor series approximation (5 terms) for tan() │ ├── ... # Other benchmark results │ │── vitishlscode/ # FPGA HLS implementations (for hardware benchmarks) │ ├── proposedcosSIMD.cpp # HLS implementation for SIMD-optimized Proposed cos() │ ├── proposedsinSIMD.cpp # HLS implementation for SIMD-optimized Proposed sin() │ ├── proposedtanSIMD.cpp # HLS implementation for SIMD-optimized Proposed tan() │ ├── taylorcosSIMD.cpp # Taylor series-based cos() for FPGA │ ├── taylorsinSIMD.cpp # Taylor series-based sin() for FPGA │ ├── taylortanSIMD.cpp # Taylor series-based tan() for FPGA │ ├── testbenchproposedcosSIMD.cpp # Testbench for cos() │ ├── testbenchproposedsinSIMD.cpp # Testbench for sin() │ ├── testbenchproposedtanSIMD.cpp # Testbench for tan() │ ├── testbenchtaylorcosSIMD.cpp # Testbench for Taylor cos() │ ├── testbenchtaylorsinSIMD.cpp # Testbench for Taylor sin() │ ├── testbenchtaylortanSIMD.cpp # Testbench for Taylor tan() │ │── vitishlsreports/ # Reports from FPGA synthesis & simulations │ ├── reportproposedcosSIMD/ # Reports for proposedcosSIMD │ ├── reportproposedsinSIMD/ # Reports for proposedsinSIMD │ ├── reportproposedtanSIMD/ # Reports for proposedtanSIMD │ ├── reporttaylorcosSIMD/ # Reports for Taylor cos() SIMD │ ├── reporttaylorsinSIMD/ # Reports for Taylor sin() SIMD │ ├── reporttaylortanSIMD/ # Reports for Taylor tan() SIMD │ ├── reportcosinbuilt/ # Baseline hardware results for standard cos() │ ├── reportsininbuilt/ # Baseline hardware results for standard sin() │ ├── reporttaninbuilt/ # Baseline hardware results for standard tan() │ │── bin/ # Compiled executables (generated after build) │ ├── trignobenchmark.exe # Final compiled executable │ │── CMakeLists.txt # CMake build configuration │── README.md # Project documentation │── LICENSE # License file │── .gitignore # Files to ignore in Git

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📬 Support & Contribution

If you have questions or want to contribute, feel free to open an issue or submit a pull request.