Trigonometric SIMD Benchmark - C++ Implementation

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

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

Note : Pre-print version might be outdated

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.

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📥 Getting Started

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

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🛠️ Building the Project (Using CMake)

1️⃣ Clone the repository

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

2️⃣ Create a Build Directory

mkdir build
cd build

3️⃣ Run CMake

➤ Auto-Detect MinGW (Recommended)

cmake -G "MinGW Makefiles" ..

This will automatically detect gcc, g++, and mingw32-make.

➤ If Auto-Detection Fails

Manually specify compilers:

cmake -G "MinGW Makefiles" -DCMAKE_C_COMPILER=gcc -DCMAKE_CXX_COMPILER=g++

If MinGW is installed in a custom location:

cmake -G "MinGW Makefiles" -DCMAKE_MAKE_PROGRAM="C:/YourMinGW/bin/mingw32-make.exe" ..

4️⃣ Compile the Project

cmake --build .

✅ This compiles the project and generates the executable in bin/trigno_benchmark.exe.

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🔥 Running the Benchmark

After compilation, run:

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

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📜 Project Structure

trigno_simd_cpp/
│── include/                      # Header files (.h)
│   ├── angle_reduction.h          # Header for angle reduction optimizations
│   ├── proposed_trigno.h          # Header for **proposed optimized trigonometric functions**
│   ├── taylorsimd.h               # Header for SIMD-optimized Taylor series functions
│
│── src/                          # Source files (.cpp)
│   ├── angle_reduction.cpp        # Implements angle reduction techniques
│   ├── benchmark.cpp              # Main benchmarking script 
│   ├── proposed_trigno.cpp        # Implements **proposed SIMD-optimized trigonometric functions**
│   ├── taylorsimd.cpp             # SIMD-optimized Taylor series calculations
│
│── data/                         # Computed benchmark results (CSV files)
│   ├── proposed_sin.csv           # Benchmark results for proposed sin()
│   ├── proposed_cos.csv           # Benchmark results for proposed cos()
│   ├── proposed_tan.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
│
│── vitis_hls_code/               # FPGA HLS implementations (for hardware benchmarks)
│   ├── proposed_cos_SIMD.cpp        # HLS implementation for SIMD-optimized Proposed cos()
│   ├── proposed_sin_SIMD.cpp        # HLS implementation for SIMD-optimized Proposed sin()
│   ├── proposed_tan_SIMD.cpp        # HLS implementation for SIMD-optimized Proposed tan()
│   ├── taylor_cos_SIMD.cpp        # Taylor series-based cos() for FPGA
│   ├── taylor_sin_SIMD.cpp        # Taylor series-based sin() for FPGA
│   ├── taylor_tan_SIMD.cpp        # Taylor series-based tan() for FPGA
│   ├── testbench_proposed_cos_SIMD.cpp  # Testbench for cos()
│   ├── testbench_proposed_sin_SIMD.cpp  # Testbench for sin()
│   ├── testbench_proposed_tan_SIMD.cpp  # Testbench for tan()
│   ├── testbench_taylor_cos_SIMD.cpp  # Testbench for Taylor cos()
│   ├── testbench_taylor_sin_SIMD.cpp  # Testbench for Taylor sin()
│   ├── testbench_taylor_tan_SIMD.cpp  # Testbench for Taylor tan()
│
│── vitis_hls_reports/            # Reports from FPGA synthesis & simulations
│   ├── report_proposed_cos_SIMD/    # Reports for proposed_cos_SIMD
│   ├── report_proposed_sin_SIMD/    # Reports for proposed_sin_SIMD
│   ├── report_proposed_tan_SIMD/    # Reports for proposed_tan_SIMD
│   ├── report_taylor_cos_SIMD/    # Reports for Taylor cos() SIMD
│   ├── report_taylor_sin_SIMD/    # Reports for Taylor sin() SIMD
│   ├── report_taylor_tan_SIMD/    # Reports for Taylor tan() SIMD
│   ├── report_cos_inbuilt/        # Baseline hardware results for standard cos()
│   ├── report_sin_inbuilt/        # Baseline hardware results for standard sin()
│   ├── report_tan_inbuilt/        # Baseline hardware results for standard tan()
│
│── bin/                          # Compiled executables (generated after build)
│   ├── trigno_benchmark.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.