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Test_MulImpl.cpp 28.97 KiB
/********************************************************************************
 * Copyright (c) 2023 CEA-List
 *
 * This program and the accompanying materials are made available under the
 * terms of the Eclipse Public License 2.0 which is available at
 * http://www.eclipse.org/legal/epl-2.0.
 *
 * SPDX-License-Identifier: EPL-2.0
 *
 ********************************************************************************/

#include <chrono>
#include <cstddef> // std::size_t
#include <cstdint> // std::uint16_t
#include <memory>
#include <numeric> // std::accumulate
#include <random>  // std::random_device, std::mt19937, std::uniform_real_distribution,
                   // std::uniform_int_distribution

#include <catch2/catch_test_macros.hpp>

#include "aidge/backend/cpu/data/TensorImpl.hpp"
#include "aidge/backend/cpu/operator/MulImpl.hpp"
#include "aidge/data/DataType.hpp"
#include "aidge/data/Tensor.hpp"
#include "aidge/operator/Mul.hpp"
#include "aidge/utils/ArrayHelpers.hpp"
#include "aidge/utils/Log.hpp"
#include "aidge/utils/TensorUtils.hpp"

namespace Aidge {

TEST_CASE("[CPU/Operator] Mul(Backward)", "[Mul][CPU][Backward]") {
    std::shared_ptr<Mul_Op> op = std::make_shared<Mul_Op>();
    op->setDataType(DataType::Float32);
    op->setBackend("cpu");

    // NOTE: The first four tests use fixed values, the last one uses random values but static dimensions.

    SECTION("Case 1: 1D and 2D Tensors") {
        const auto T0 = std::make_shared<Tensor>(
            Array2D<cpptype_t<DataType::Float32>, 2, 3>({{{1, 2, 3}, {4, 5, 6}}}));

        const auto T1 =
            std::make_shared<Tensor>(Array1D<cpptype_t<DataType::Float32>, 3>({0.1, 0.2, 0.3}));

        op->associateInput(0, T0);
        op->associateInput(1, T1);
        op->getOutput(0)->setGrad(std::make_shared<Tensor>(
            Array2D<float, 2, 3>({{{1.0, 1.0, 1.0}, {1.0, 1.0, 1.0}}})));
        op->forwardDims();

        op->backward();

        const Tensor expectedGrad0 =
            Array2D<cpptype_t<DataType::Float32>, 2, 3>({{{0.1, 0.2, 0.3}, {0.1, 0.2, 0.3}}});

        const Tensor expectedGrad1 = Array1D<cpptype_t<DataType::Float32>, 3>({5, 7, 9});

        REQUIRE(approxEq<cpptype_t<DataType::Float32>>(*(op->getInput(0)->grad()), expectedGrad0));
        REQUIRE(approxEq<cpptype_t<DataType::Float32>>(*(op->getInput(1)->grad()), expectedGrad1));
    }

    SECTION("Case 2: 3D and 1D tensors") {
        const auto T0 = std::make_shared<Tensor>(Array3D<float, 2, 2, 3>(
            {{{{1.0, 2.0, 3.0}, {4.0, 5.0, 6.0}},
              {{7.0, 8.0, 9.0}, {10.0, 11.0, 12.0}}}}));

        const auto T1 =
            std::make_shared<Tensor>(Array1D<float, 3>({0.3, 0.2, 0.1}));

        const auto newGrad = std::make_shared<Tensor>(Array3D<float, 2, 2, 3>(
            {{{{1, 1, 1}, {1, 1, 1}}, {{1, 1, 1}, {1, 1, 1}}}}));

        const Tensor expectedGrad0 =
            Array3D<float, 2, 2, 3>({{{{0.3, 0.2, 0.1}, {0.3, 0.2, 0.1}},
                                      {{0.3, 0.2, 0.1}, {0.3, 0.2, 0.1}}}});

        const Tensor expectedGrad1 = Array1D<cpptype_t<DataType::Float32>, 3>({22.0, 26.0, 30.0});

        op->associateInput(0, T0);
        op->associateInput(1, T1);
        op->getOutput(0)->setGrad(newGrad);
        op->forwardDims();

        op->backward();

        REQUIRE(approxEq<cpptype_t<DataType::Float32>>(*(op->getInput(0)->grad()), expectedGrad0));
        REQUIRE(approxEq<cpptype_t<DataType::Float32>>(*(op->getInput(1)->grad()), expectedGrad1));
    }

    SECTION("Case 3: 4D and 2D tensors") {
        const auto T0 = std::make_shared<Tensor>(Array4D<cpptype_t<DataType::Float32>, 2, 2, 3, 3>(
            {{{{{1.0, 2.0, 3.0}, {4.0, 5.0, 6.0}, {7.0, 8.0, 9.0}},
               {{10.0, 11.0, 12.0}, {13.0, 14.0, 15.0}, {16.0, 17.0, 18.0}}},
              {{{19.0, 20.0, 21.0}, {22.0, 23.0, 24.0}, {25.0, 26.0, 27.0}},
               {{28.0, 29.0, 30.0},
                {31.0, 32.0, 33.0},
                {34.0, 35.0, 36.0}}}}}));

        const auto T1 = std::make_shared<Tensor>(Array2D<cpptype_t<DataType::Float32>, 3, 3>(
            {{{0.5, 0.3, 0.1}, {0.4, 0.2, 0.6}, {0.7, 0.8, 0.9}}}));

        const auto newGrad =
            std::make_shared<Tensor>(Array4D<cpptype_t<DataType::Float32>, 2, 2, 3, 3>(
                {{{{{1.0, 1.0, 1.0}, {1.0, 1.0, 1.0}, {1.0, 1.0, 1.0}},
                   {{1.0, 1.0, 1.0}, {1.0, 1.0, 1.0}, {1.0, 1.0, 1.0}}},
                  {{{1.0, 1.0, 1.0}, {1.0, 1.0, 1.0}, {1.0, 1.0, 1.0}},
                   {{1.0, 1.0, 1.0}, {1.0, 1.0, 1.0}, {1.0, 1.0, 1.0}}}}}));

        const Tensor expectedGrad0 =
            Array4D<cpptype_t<DataType::Float32>, 2, 2, 3, 3>(
                {{{{{0.5, 0.3, 0.1}, {0.4, 0.2, 0.6}, {0.7, 0.8, 0.9}},
                   {{0.5, 0.3, 0.1}, {0.4, 0.2, 0.6}, {0.7, 0.8, 0.9}}},
                  {{{0.5, 0.3, 0.1}, {0.4, 0.2, 0.6}, {0.7, 0.8, 0.9}},
                   {{0.5, 0.3, 0.1}, {0.4, 0.2, 0.6}, {0.7, 0.8, 0.9}}}}});

        const Tensor expectedGrad1 =
            Array2D<cpptype_t<DataType::Float32>, 3, 3>({{{58.0, 62.0, 66.0},
                                   {70.0, 74.0, 78.0},
                                   {82.0, 86.0, 90.0}}});

        op->associateInput(0, T0);
        op->associateInput(1, T1);
        op->getOutput(0)->setGrad(newGrad);
        op->forwardDims();

        op->backward();

        REQUIRE(approxEq<cpptype_t<DataType::Float32>>(*(op->getInput(0)->grad()), expectedGrad0));
        REQUIRE(approxEq<cpptype_t<DataType::Float32>>(*(op->getInput(1)->grad()), expectedGrad1));
    }

    SECTION("Case 4: 3D and 2D tensors") {
        const auto T0 = std::make_shared<Tensor>(
            Array3D<float, 2, 3, 4>({{{
                                          {1.0, 2.0, 3.0, 4.0},
                                          {5.0, 6.0, 7.0, 8.0},
                                          {9.0, 10.0, 11.0, 12.0},
                                      },
                                      {
                                          {13.0, 14.0, 15.0, 16.0},
                                          {17.0, 18.0, 19.0, 20.0},
                                          {21.0, 22.0, 23.0, 24.0},
                                      }}}));

        const auto T1 = std::make_shared<Tensor>(
            Array2D<cpptype_t<DataType::Float32>, 3, 4>({{{0.1, 0.2, 0.3, 0.4},
                                   {0.5, 0.6, 0.7, 0.8},
                                   {0.9, 1.0, 1.1, 1.2}}}));

        const auto newGrad = std::make_shared<Tensor>(
            Array3D<cpptype_t<DataType::Float32>, 2, 3, 4>({{{
                                          {1.0, 1.0, 1.0, 1.0},
                                          {1.0, 1.0, 1.0, 1.0},
                                          {1.0, 1.0, 1.0, 1.0},
                                      },
                                      {
                                          {1.0, 1.0, 1.0, 1.0},
                                          {1.0, 1.0, 1.0, 1.0},
                                          {1.0, 1.0, 1.0, 1.0},
                                      }}}));

        const Tensor expectedGrad0 =
            Array3D<cpptype_t<DataType::Float32>, 2, 3, 4>({{{{0.1, 0.2, 0.3, 0.4},
                                       {0.5, 0.6, 0.7, 0.8},
                                       {0.9, 1.0, 1.1, 1.2}},
                                      {{0.1, 0.2, 0.3, 0.4},
                                       {0.5, 0.6, 0.7, 0.8},
                                       {0.9, 1.0, 1.1, 1.2}}}});

        const Tensor expectedGrad1 =
            Array2D<cpptype_t<DataType::Float32>, 3, 4>({{{14.0, 16.0, 18.0, 20.0},
                                   {22.0, 24.0, 26.0, 28.0},
                                   {30.0, 32.0, 34.0, 36.0}}});

        op->associateInput(0, T0);
        op->associateInput(1, T1);
        op->getOutput(0)->setGrad(newGrad);
        op->forwardDims();

        op->backward();

        REQUIRE(approxEq<cpptype_t<DataType::Float32>>(*(op->getInput(0)->grad()), expectedGrad0));
        REQUIRE(approxEq<cpptype_t<DataType::Float32>>(*(op->getInput(1)->grad()), expectedGrad1));
    }

    SECTION("Case 5: Tensors with random values") {

        // Use random values
        const std::vector<std::size_t> dims0 = {5, 2, 1, 7}; // First tensor
        const std::vector<std::size_t> dims1 = {2, 6, 7};    // Second tensor
        const std::vector<std::size_t> outputDims = {5, 2, 6, 7};

        std::random_device rd;
        std::mt19937 gen(rd());
        std::uniform_real_distribution<float> dist(0.1f, 1.0f);

        auto T0 = std::make_shared<Tensor>(dims0);
        T0->setDataType(DataType::Float32);
        T0->setBackend("cpu");
        float* input0Data = static_cast<float*>(T0->getImpl()->rawPtr());
        // Fill with random values
        for (std::size_t i = 0; i < T0->size(); ++i) {
            input0Data[i] = dist(gen);
        }

        auto T1 = std::make_shared<Tensor>(dims1);
        T1->setDataType(DataType::Float32);
        T1->setBackend("cpu");
        float* input1Data = static_cast<float*>(T1->getImpl()->rawPtr());
        // Fill with random values
        for (std::size_t i = 0; i < T1->size(); ++i) {
            input1Data[i] = dist(gen);
        }

        op->associateInput(0, T0);
        op->associateInput(1, T1);

        op->forwardDims();
        op->forward();

        Tensor expectedOutput{outputDims};
        expectedOutput.setBackend("cpu");
        float* expectedOutputData = static_cast<float*>(expectedOutput.getImpl()->rawPtr());

        for (std::size_t n = 0; n < 5; ++n) {
            for (std::size_t c = 0; c < 2; ++c) {
                for (std::size_t h = 0; h < 6; ++h) {
                    for (std::size_t w = 0; w < 7; ++w) {
                        std::size_t outIdx = w + 7 * (h + 6 * (c + 2 * n));
                        std::size_t in0Idx =
                            w + 7 * (0 + 1 * (c + 2 * n)); // middle dim is 1
                        std::size_t in1Idx =
                            w + 7 * (h + 6 * c);           // no n dimension

                        expectedOutputData[outIdx] = input0Data[in0Idx] * input1Data[in1Idx];
                    }
                }
            }
        }

        auto outputTensor = op->getOutput(0);

        REQUIRE(approxEq<float>(*outputTensor, expectedOutput));

        // Backward pass
        std::vector<float> gradOutputData(expectedOutput.size());
        for (auto &val : gradOutputData) {
            val = dist(gen);
        }

        op->getOutput(0)->setGrad(std::make_shared<Tensor>());
        op->getOutput(0)->grad()->resize(outputDims);
        op->getOutput(0)->grad()->getImpl()->setRawPtr(gradOutputData.data(),
                                                       expectedOutput.size());

        // Compute reference gradients
        std::vector<float> expectedGrad0(T0->size(), 0.0f);
        std::vector<float> expectedGrad1(T1->size(), 0.0f);

        for (std::size_t n = 0; n < 5; ++n) {
            for (std::size_t c = 0; c < 2; ++c) {
                for (std::size_t h = 0; h < 6; ++h) {
                    for (std::size_t w = 0; w < 7; ++w) {
                        std::size_t outIdx = w + 7 * (h + 6 * (c + 2 * n));
                        std::size_t in0Idx = w + 7 * (0 + 1 * (c + 2 * n));
                        std::size_t in1Idx = w + 7 * (h + 6 * c);

                        // Gradient for input0: grad_output * input1
                        expectedGrad0[in0Idx] +=
                            gradOutputData[outIdx] * input1Data[in1Idx];

                        // Gradient for input1: grad_output * input0
                        expectedGrad1[in1Idx] +=
                            gradOutputData[outIdx] * input0Data[in0Idx];
                    }
                }
            }
        }

        // Perform backward pass
        op->backward();

        auto expectedGrad0Tensor = std::make_shared<Tensor>();
        expectedGrad0Tensor->resize(T0->dims());
        expectedGrad0Tensor->setBackend("cpu");
        expectedGrad0Tensor->setDataType(DataType::Float32);
        expectedGrad0Tensor->getImpl()->setRawPtr(expectedGrad0.data(),
                                                    expectedGrad0.size());

        auto expectedGrad1Tensor = std::make_shared<Tensor>(T1->dims());
        expectedGrad1Tensor->setBackend("cpu");
        expectedGrad1Tensor->setDataType(DataType::Float32);
        expectedGrad1Tensor->getImpl()->setRawPtr(expectedGrad1.data(),
                                                    expectedGrad1.size());

        // Verify backward pass
        REQUIRE(approxEq<float>(*T0->grad(), *expectedGrad0Tensor));
        REQUIRE(approxEq<float>(*T1->grad(), *expectedGrad1Tensor));

        // Optional: Print some values for verification
        // std::cout << "Input shapes: (" << dims0[0] << "," << dims0[1] <<
        // "," << dims0[2] << "," << dims0[3]
        //           << ") * (" << dims1[0] << "," << dims1[1] << "," <<
        //           dims1[2]
        //           << ") -> (" << outputDims[0] << "," << outputDims[1]
        //           << "," << outputDims[2] << "," << outputDims[3] <<
        //           ")\n";
        // std::cout << "Input sizes: " << input0_size << " * " <<
        // input1_size << " -> " << output_size << "\n";
    }
}

TEST_CASE("[cpu/operator] Mul(forward)", "[Mul][CPU]") {
    constexpr std::uint16_t NBTRIALS = 10;
    // Create a random number generator
    std::random_device rd;
    std::mt19937 gen(rd());
    std::uniform_real_distribution<float> valueDist(
        0.1f,
        1.1f); // Random float distribution between 0 and 1
    std::uniform_int_distribution<std::size_t> dimSizeDist(std::size_t(2),
                                                           std::size_t(10));
    std::uniform_int_distribution<std::size_t> nbDimsDist(std::size_t(1),
                                                          std::size_t(3));
    std::uniform_int_distribution<int> boolDist(0, 1);

    std::shared_ptr<Mul_Op> op = std::make_shared<Mul_Op>();
    op->setDataType(DataType::Float32);
    op->setBackend("cpu");

    std::shared_ptr<Tensor> T0 = std::make_shared<Tensor>();
    op->associateInput(0, T0);
    T0->setDataType(DataType::Float32);
    T0->setBackend("cpu");
    std::shared_ptr<Tensor> T1 = std::make_shared<Tensor>();
    op->associateInput(1, T1);
    T1->setDataType(DataType::Float32);
    T1->setBackend("cpu");

    std::shared_ptr<Tensor> Tres = std::make_shared<Tensor>();
    Tres->setDataType(DataType::Float32);
    Tres->setBackend("cpu");

    // To measure execution time of 'MatMul_Op::forward()' member function call
    std::chrono::time_point<std::chrono::system_clock> start;
    std::chrono::time_point<std::chrono::system_clock> end;
    std::chrono::duration<double, std::micro> duration{};
    SECTION("MulImpl_cpu::forward()") {
        SECTION("Scalar / Scalar") {}
        SECTION("Scalar / +1-D Tensor") {}
        SECTION("+1-D Tensor / +1-D Tensor - same dimensions") {

            std::size_t number_of_operation = 0;

            for (std::uint16_t trial = 0; trial < NBTRIALS; ++trial) {

                // generate 2 random Tensors
                const auto nbDims = nbDimsDist(gen);
                auto dims = std::vector<std::size_t>{};

                for (std::size_t i = 0; i < nbDims; ++i) {
                    dims.push_back(dimSizeDist(gen));
                }

                const auto nb_elements =
                    std::accumulate(dims.cbegin(),
                                    dims.cend(),
                                    std::size_t(1),
                                    std::multiplies<std::size_t>());
                number_of_operation += nb_elements;

                // without broadcasting
                float *array0 = new float[nb_elements];
                float *array1 = new float[nb_elements];
                float *result = new float[nb_elements];

                for (std::size_t i = 0; i < nb_elements; ++i) {
                    array0[i] = valueDist(gen);
                    array1[i] = valueDist(gen);
                    result[i] = array0[i] * array1[i];
                }

                // input0
                T0->resize(dims);
                T0->getImpl()->setRawPtr(array0, nb_elements);

                // input1
                T1->resize(dims);
                T1->getImpl()->setRawPtr(array1, nb_elements);

                // results
                Tres->resize(dims);
                Tres->getImpl()->setRawPtr(result, nb_elements);

                op->forwardDims();
                start = std::chrono::system_clock::now();
                op->forward();
                end = std::chrono::system_clock::now();
                duration +=
                    std::chrono::duration_cast<std::chrono::microseconds>(
                        end - start);

                REQUIRE(approxEq<float>(*(op->getOutput(0)), *Tres));

                delete[] array0;
                delete[] array1;
                delete[] result;
            }
            Log::info("number of elements over time spent: {}\n", (number_of_operation / duration.count()));
            Log::info("total time: {}μs\n", duration.count());
        }

        SECTION("+1-D Tensor / +1-D Tensor - broadcasting") {
            std::size_t number_of_operation = 0;

            for (std::uint16_t trial = 0; trial < NBTRIALS; ++trial) {
                // generate 2 random Tensors
                // handle dimensions, replace some dimensions with '1' to get
                // broadcasting

                constexpr std::size_t nbDims = 4;
                std::vector<std::size_t> dimensions;

                for (std::size_t i = 0; i < nbDims; ++i) {
                    dimensions.push_back(dimSizeDist(gen));
                }

                auto dims0 = dimensions;
                auto dims1 = dimensions;
                auto dimsOut = dimensions;

                for (std::size_t i = 0; i < nbDims; ++i) {
                    if (boolDist(gen)) {
                        dims0[i] = 1;
                    }

                    if (boolDist(gen)) {
                        dims1[i] = 1;
                    }

                    dimsOut[i] = (dims0[i] == 1) ? dims1[i] : dims0[i];
                }

                for (auto dim : dims0) {
                    Log::info("Dimension of input 0 : {}", dim);
                }

                for (auto dim : dims1) {
                    Log::info("Dimension of input 1 : {}", dim);
                }

                // create arrays and fill them with random values
                float *array0 =
                    new float[dims0[0] * dims0[1] * dims0[2] * dims0[3]];
                float *array1 =
                    new float[dims1[0] * dims1[1] * dims1[2] * dims1[3]];
                float *result = new float[dimsOut[0] * dimsOut[1] *
                                          dimsOut[2] * dimsOut[3]];

                for (std::size_t i = 0;
                     i < dims0[0] * dims0[1] * dims0[2] * dims0[3];
                     ++i) {
                    array0[i] = valueDist(gen);
                }

                for (std::size_t i = 0;
                     i < dims1[0] * dims1[1] * dims1[2] * dims1[3];
                     ++i) {
                    array1[i] = valueDist(gen);
                }

                // compute true result
                const std::size_t strides0[nbDims] = {
                    dims0[1] * dims0[2] * dims0[3],
                    dims0[2] * dims0[3],
                    dims0[3],
                    1};
                const std::size_t strides1[nbDims] = {
                    dims1[1] * dims1[2] * dims1[3],
                    dims1[2] * dims1[3],
                    dims1[3],
                    1};

                for (std::size_t a = 0; a < dimsOut[0]; ++a) {
                    for (std::size_t b = 0; b < dimsOut[1]; ++b) {
                        const std::size_t idx0_0 =
                            strides0[0] * ((dims0[0] > 1) ? a : 0) +
                            strides0[1] * ((dims0[1] > 1) ? b : 0);

                        const std::size_t idx1_0 =
                            strides1[0] * ((dims1[0] > 1) ? a : 0) +
                            strides1[1] * ((dims1[1] > 1) ? b : 0);

                        for (std::size_t c = 0; c < dimsOut[2]; ++c) {
                            const std::size_t idx_out =
                                dimsOut[3] *
                                (c + dimsOut[2] * (b + dimsOut[1] * a));

                            for (std::size_t d = 0; d < dimsOut[3]; ++d) {
                                std::size_t idx0 =
                                    idx0_0 +
                                    strides0[2] * ((dims0[2] > 1) ? c : 0) +
                                    ((dims0[3] > 1) ? d : 0);

                                std::size_t idx1 =
                                    idx1_0 +
                                    strides1[2] * ((dims1[2] > 1) ? c : 0) +
                                    ((dims1[3] > 1) ? d : 0);

                                result[idx_out + d] =
                                    array0[idx0] * array1[idx1];
                                // std::cout << "(" << idx0 << ", " << idx1 <<
                                // ") -> " << array0[idx0] << " * " <<
                                // array1[idx1] << " -> " << idx_out + d <<
                                // std::endl;
                            }
                        }
                    }
                }

                // conversion to Aidge::Tensors
                // input0
                T0->resize(dims0);
                T0->getImpl()->setRawPtr(
                    array0,
                    dims0[0] * dims0[1] * dims0[2] * dims0[3]);

                // input1
                T1->resize(dims1);
                T1->getImpl()->setRawPtr(
                    array1,
                    dims1[0] * dims1[1] * dims1[2] * dims1[3]);

                // results
                Tres->resize(dimsOut);
                Tres->getImpl()->setRawPtr(
                    result,
                    dimsOut[0] * dimsOut[1] * dimsOut[2] * dimsOut[3]);

                // compute result
                op->forwardDims();
                start = std::chrono::system_clock::now();
                op->forward();
                end = std::chrono::system_clock::now();
                duration +=
                    std::chrono::duration_cast<std::chrono::microseconds>(
                        end - start);

                // comparison between truth and computed result
                REQUIRE(approxEq<float>(*(op->getOutput(0)), *Tres));

                delete[] array0;
                delete[] array1;
                delete[] result;

                const std::size_t nb_elements =
                    std::accumulate(dimsOut.cbegin(),
                                    dimsOut.cend(),
                                    std::size_t(1),
                                    std::multiplies<std::size_t>());
                number_of_operation += nb_elements;
            }
            Log::info("number of elements over time spent: {}\n", (number_of_operation / duration.count()));
            Log::info("total time: {}μs\n", duration.count());
        }
        SECTION("+1-D Tensor / 1-D Tensor") {
            std::size_t number_of_operation = 0;
            std::uniform_int_distribution<std::size_t> nbRemovedDimsDist(
                std::size_t(1),
                std::size_t(3));

            for (std::uint16_t trial = 0; trial < NBTRIALS; ++trial) {
                // generate 2 random Tensors
                // handle dimensions
                constexpr std::size_t nbDims = 4;
                std::vector<std::size_t> dims0(4);
                for (std::size_t i = 0; i < nbDims; ++i) {
                    dims0[i] = dimSizeDist(gen);
                }
                std::vector<std::size_t> dimsOut = dims0;
                std::vector<std::size_t> dims1 = dims0;
                for (std::size_t i = 0; i < nbDims; ++i) {
                    if (boolDist(gen)) {
                        dims1[i] = 1;
                    }
                }
                dims1.erase(dims1.cbegin(),
                            dims1.cbegin() + nbRemovedDimsDist(gen));

                // create arrays and fill them with random values
                float *array0 =
                    new float[dims0[0] * dims0[1] * dims0[2] * dims0[3]];
                std::size_t array1_size =
                    std::accumulate(dims1.cbegin(),
                                    dims1.cend(),
                                    std::size_t(1),
                                    std::multiplies<std::size_t>());
                float *array1 = new float[array1_size];
                float *result = new float[dimsOut[0] * dimsOut[1] *
                                          dimsOut[2] * dimsOut[3]];

                for (std::size_t i = 0;
                     i < (dims0[0] * dims0[1] * dims0[2] * dims0[3]);
                     ++i) {
                    array0[i] = valueDist(gen);
                }
                for (std::size_t i = 0; i < array1_size; ++i) {
                    array1[i] = valueDist(gen);
                }

                // compute true result
                auto dims1_tmp = dims1;
                dims1_tmp.insert(dims1_tmp.cbegin(),
                                 4 - dims1_tmp.size(),
                                 std::size_t(1));

                const std::size_t strides0[nbDims] = {
                    dims0[1] * dims0[2] * dims0[3],
                    dims0[2] * dims0[3],
                    dims0[3],
                    1};
                const std::size_t strides1[nbDims] = {
                    dims1_tmp[1] * dims1_tmp[2] * dims1_tmp[3],
                    dims1_tmp[2] * dims1_tmp[3],
                    dims1_tmp[3],
                    1};
                for (std::size_t a = 0; a < dimsOut[0]; ++a) {
                    for (std::size_t b = 0; b < dimsOut[1]; ++b) {
                        const std::size_t idx0_0 =
                            strides0[0] * ((dims0[0] > 1) ? a : 0) +
                            strides0[1] * ((dims0[1] > 1) ? b : 0);
                        const std::size_t idx1_0 =
                            strides1[0] * ((dims1_tmp[0] > 1) ? a : 0) +
                            strides1[1] * ((dims1_tmp[1] > 1) ? b : 0);
                        for (std::size_t c = 0; c < dimsOut[2]; ++c) {
                            const std::size_t idx_out =
                                dimsOut[3] *
                                (c + dimsOut[2] * (b + dimsOut[1] * a));
                            for (std::size_t d = 0; d < dimsOut[3]; ++d) {
                                std::size_t idx0 =
                                    idx0_0 +
                                    strides0[2] * ((dims0[2] > 1) ? c : 0) +
                                    ((dims0[3] > 1) ? d : 0);
                                std::size_t idx1 =
                                    idx1_0 +
                                    strides1[2] *
                                        ((dims1_tmp[2] > 1) ? c : 0) +
                                    ((dims1_tmp[3] > 1) ? d : 0);
                                result[idx_out + d] =
                                    array0[idx0] * array1[idx1];
                                // std::cout << "(" << idx0 << ", " << idx1 <<
                                // ") -> " << array0[idx0] << " * " <<
                                // array1[idx1] << " -> " << idx_out + d <<
                                // std::endl;
                            }
                        }
                    }
                }

                // conversion to Aidge::Tensors
                // input0
                T0->resize(dims0);
                T0->getImpl()->setRawPtr(
                    array0,
                    dims0[0] * dims0[1] * dims0[2] * dims0[3]);

                // input1
                T1->resize(dims1);
                T1->getImpl()->setRawPtr(array1, array1_size);

                // results
                Tres->resize(dimsOut);
                Tres->getImpl()->setRawPtr(
                    result,
                    dimsOut[0] * dimsOut[1] * dimsOut[2] * dimsOut[3]);

                // compute result
                op->forwardDims();
                start = std::chrono::system_clock::now();
                op->forward();
                end = std::chrono::system_clock::now();
                duration +=
                    std::chrono::duration_cast<std::chrono::microseconds>(
                        end - start);

                // comparison between truth and computed result
                REQUIRE(approxEq<float>(*(op->getOutput(0)), *Tres));

                delete[] array0;
                delete[] array1;
                delete[] result;

                const std::size_t nb_elements =
                    std::accumulate(dimsOut.cbegin(),
                                    dimsOut.cend(),
                                    std::size_t(1),
                                    std::multiplies<std::size_t>());
                number_of_operation += nb_elements;
            }

            Log::info("number of elements over time spent: {}\n", (number_of_operation / duration.count()));
            Log::info("total time: {}μs\n", duration.count());
        }
    }
}
} // namespace Aidge