C++ vs Python vs numpy vs Numba JIT speed comparison

vec_dot.cpp

/* compile with:
 g++ -O3 -std=c++11 vec_dot.cpp -I/usr/include/openblas -fopenmp -lcblas
 
 (or clang++)
 
NOTE: 
  - in main, comment either the OpenMP or the BLAS block! using both leads to degraded performance.
  - on my TP X13 G3 with Intel i7-1260P, adding -march=native will lead to lower performance!!
  - other flags like -funroll-loops -flto -finline-functions did not seem to lead to significant performance increases
*/
#include <iostream>
#include <vector>
#include <random>
#include <chrono>
#include <cblas.h>
#include <omp.h>


double dot(std::vector<double> const &a, std::vector<double> const &b)
{
    double sum = 0.0;
    for(int i = 0; i < a.size(); ++i) {
        sum += a[i] * b[i];
    }
    return sum;
}

double dot_omp(std::vector<double> const &a, std::vector<double> const &b)
{
    double sum = 0.0;
    int target_thread_num = 16;
    omp_set_num_threads(target_thread_num);

    #pragma omp parallel for reduction(+:sum)
    for(int i = 0; i < a.size(); ++i) {
        sum += a[i] * b[i];
    }
    return sum;
}


double dot_blas(std::vector<double> const &a, std::vector<double> const &b)
{
    return cblas_ddot(a.size(), &a[0], 1, &b[0], 1);
}


std::vector<double> create_random_vector(int n) {
    std::random_device rd;  // Will be used to obtain a seed for the random number engine
    std::mt19937 gen(rd()); // Standard mersenne_twister_engine seeded with rd()
    std::uniform_real_distribution<> dis(0.0, 1.0);
    std::vector<double> vec(n, 0.0);

    for (int i = 0; i < n; ++i) {
        vec[i] = dis(gen);
    }

    return vec;
    }

int main() {
    int n = 100000000;

    std::vector<double> a = create_random_vector(n);
    std::vector<double> b = create_random_vector(n);

    std::cout << "Vector size: " << a.size() << std::endl;

    std::cout << "C++" << std::endl;
    auto t_start = std::chrono::steady_clock::now();
    std::cout << "\tdot: " << dot(a, b) << std::endl;
    auto t_stop = std::chrono::steady_clock::now();
    auto t_elapsed = t_stop - t_start;
    std::cout << "\ttime elapsed: " << std::chrono::duration<double, std::milli>(t_elapsed).count() << " ms" << std::endl;

    // OMP
    /*
    std::cout << "C++ w/ OpenMP" << std::endl;
    t_start = std::chrono::steady_clock::now();
    std::cout << "\tdot: " << dot_omp(a, b) << std::endl;
    t_stop = std::chrono::steady_clock::now();
    t_elapsed = t_stop - t_start;
    std::cout << "\ttime elapsed: " << std::chrono::duration<double, std::milli>(t_elapsed).count() << " ms" << std::endl;
    //*/

    // OpenBLAS
    //*
    std::cout << "C++ w/ OpenBLAS" << std::endl;
    std::cout << "\tOpenBLAS threads: " << openblas_get_num_threads() << std::endl;
    t_start = std::chrono::steady_clock::now();
    std::cout << "\tdot: " << dot_blas(a, b) << std::endl;
    t_stop = std::chrono::steady_clock::now();
    t_elapsed = t_stop - t_start;
    std::cout << "\ttime elapsed: " << std::chrono::duration<double, std::milli>(t_elapsed).count() << " ms" << std::endl;
    //*/


    return 0;
}

vec_dot.py

import time

import numpy
from numba import njit, prange


def dot_pure(a, b):
    sum = 0.0
    for x, y in zip(a, b):
        sum += x * y
    return sum


@njit
def dot_numba(a, b):
    sum = 0.0
    for x, y in zip(a, b):
        sum += x * y
    return sum


@njit(parallel=True)
def dot_numba_parallel(a, b):
    sum = 0.0
    for i in prange(len(a)):
        sum += a[i] * b[i]
    return sum


def dot_numpy(a, b):
    return numpy.dot(a, b)


def create_random_vector(n):
    return numpy.random.rand(n).astype(numpy.float64)


if __name__ == "__main__":
    n = 100000000
    a = create_random_vector(n)
    b = create_random_vector(n)

    print("Vector size: ", a.size)

    print("Python")
    t_start = time.perf_counter_ns()
    print("\tdot: ", dot_pure(a, b))
    t_stop = time.perf_counter_ns()
    print(f"\ttime elapsed: {(t_stop - t_start) * 1e-6} ms")

    print("NumPy")
    t_start = time.perf_counter_ns()
    print("\tdot: ", dot_numpy(a, b))
    t_stop = time.perf_counter_ns()
    print(f"\ttime elapsed: {(t_stop - t_start) * 1e-6} ms")

    print("Python+numba")
    # call once to exclude compile time in timings
    dot_numba(a, b)
    t_start = time.perf_counter_ns()
    print("\tdot: ", dot_numba(a, b))
    t_stop = time.perf_counter_ns()
    print(f"\ttime elapsed: {(t_stop - t_start) * 1e-6} ms")

    print("Python+numba parallel")
    # call once to exclude compile time in timings
    dot_numba_parallel(a, b)
    t_start = time.perf_counter_ns()
    print("\tdot: ", dot_numba_parallel(a, b))
    t_stop = time.perf_counter_ns()
    print(f"\ttime elapsed: {(t_stop - t_start) * 1e-6} ms")

Timings on Thinkpad X13 Gen3, Intel 12th Gen i7-1260P

Versions:

• Python 3.11.7, numpy 1.26.4 compiled with OpenBLAS 0.3.26, numba 0.59.0
• GCC 13.2.1, OpenBLAS 0.3.26, LLVM OpenMP 16.0.6

C++ compiled with g++ -O3 vec_dot.cpp -I/usr/include/openblas -fopenmp -lcblas (or -O3 for no opt flags case). -march=native has no beneficial effect.
The "1 core" cases are run with OMP_NUM_THREADS=1.

Method	Time (ms)
Python	8273
Python (NumPy, BLAS using 16 cores)	27
Python (NumPy, using 1 core)	50
Python (Numba JIT)	66
Python (Numba JIT & parallel)	24
C++ (no opt flags)	252
C++ (-O3)	63
C++ (-O3 with BLAS, using all 16 cores)	30
C++ (-O3 with BLAS, using 1 core)	50
C++ (-O3 with OpenMPI parallel loop execution on 16 cores)	30

Some unrolled loops and removed [] operator calls:

double dot(std::vector<double> const &a, std::vector<double> const &b)
{
    double sum = 0.0;
    const double *_a = &a[0];
    const double *_b = &b[0];
    const int len = a.size();
    for(int i = 0; i < len; ++i) {
        sum += _a[i] * _b[i];
    }
    return sum;
}

double dot_omp(std::vector<double> const &a, std::vector<double> const &b)
{
    double sum = 0.0;
    const double *_a = &a[0];
    const double *_b = &b[0];
    const int len = a.size();
    int target_thread_num = 8;
    omp_set_num_threads(target_thread_num);

#pragma omp parallel for reduction(+:sum)
    for(int i = 0; i < len; ++i) {
        if (i + 8 < len)
        {
            const double *_a2 = &_a[i];
            const double *_b2 = &_b[i];
            sum += _a2[0] * _b2[0] +
                _a2[1] * _b2[1] +
                _a2[2] * _b2[2] +
                _a2[3] * _b2[3] +
                _a2[4] * _b2[4] +
                _a2[5] * _b2[5] +
                _a2[6] * _b2[6] +
                _a2[7] * _b2[7];
            i += 7;
        }
        else
            sum += _a[i] * _b[i];
    }
    return sum;
}