PHP Matrix multiplication benchmark

matrix_benchmark.php

<?php
declare(strict_types=1);


/**
 * Requires the DS extension (see https://github.com/php-ds/extension).
 * This script is a benchmark for many possible combinations to perform matrix multiplications:
 *     - Ds\Vector vs PHP array
 *     - Single array vs Nested arrays
 *     - iterations order: I,J,K vs I,K,J
 */

/**
 * RESULTS (the times are not divided by the number of iterations, only numbers in the same row can be compared):
 *
 *         ijk cont. array        ijk nest. array       ijk cont. vector       ijk nest. vector       ikj cont. array        ikj nest. array        ikj cont. vector       ikj nest. vector
 *   4 ->  0.00042104721069336    0.0004429817199707    0.00049710273742676    0.00060391426086426    0.00030279159545898    0.00032591819763184    0.00038003921508789    0.00046491622924805
 *   8 ->  0.002924919128418      0.003281831741333     0.0034310817718506     0.0043010711669922     0.0017859935760498     0.0020260810852051     0.0023138523101807     0.0028958320617676
 *  16 ->  0.019437074661255      0.020691156387329     0.020630836486816      0.025195837020874      0.0088889598846436     0.010462045669556      0.011255979537964      0.014892101287842
 *  32 ->  0.094998121261597      0.1055748462677       0.11357617378235       0.15099906921387       0.052932024002075      0.064934968948364      0.0711350440979        0.10097599029541
 *  64 ->  0.72782516479492       0.83726596832275      0.9531569480896        1.1677219867706        0.39643001556396       0.49447298049927       0.53884315490723       0.7768931388855
 * 128 ->  2.8404879570007        3.2943258285522       3.5353372097015        4.66787981987          1.5506911277771        1.9599390029907        2.1567468643188        3.1205151081085
 * 256 ->  22.941949129105        26.903174877167       28.000234127045        38.06840801239         12.362766981125        15.758536100388        17.036547899246        24.780100107193
 * 512 ->  281.45276784897        298.90023684502       236.78369307518        324.35555291176        99.469950199127        126.31004500389        135.40308403969        198.58974289894
 *
 */


require __DIR__ . '/../vendor/autoload.php';


use Ds\Vector;


$matSizes = [4, 8, 16, 32, 64, 128, 256, 512];


if (\extension_loaded('ds')) {
    echo "\n\nLOADED DS\n\n";
} else {
    echo "\n\nNO EXTENSION\n\n";
}


foreach ($matSizes as $matSize) {
    list($ca1, $na1, $cv1, $nv1) = getMatrixInstances($matSize);
    list($ca2, $na2, $cv2, $nv2) = getMatrixInstances($matSize);
    list($caR, $naR, $cvR, $nvR) = getMatrixInstances($matSize, true);

    $limit = $matSize < 128 ? 40 : 20;

    $tIJK_ca_1 = \microtime(true);
    for ($x = 0; $x < $limit; $x++) {
        for ($i = 0, $im = 0; $i < $matSize; $i++, $im += $matSize) {
            for ($j = 0; $j < $matSize; $j++) {
                for ($k = 0, $km = 0; $k < $matSize; $k++, $km += $matSize) {
                    $caR[$im + $j] += $ca1[$im + $k] * $ca2[$km + $j];
                }
            }
        }
    }
    $tIJK_ca_2 = \microtime(true);

    $tIJK_na_1 = \microtime(true);
    for ($x = 0; $x < $limit; $x++) {
        for ($i = 0; $i < $matSize; $i++) {
            for ($j = 0; $j < $matSize; $j++) {
                for ($k = 0; $k < $matSize; $k++) {
                    $naR[$i][$j] += $na1[$i][$k] * $na2[$k][$j];
                }
            }
        }
    }
    $tIJK_na_2 = \microtime(true);

    $tIJK_cv_1 = \microtime(true);
    for ($x = 0; $x < $limit; $x++) {
        for ($i = 0, $im = 0; $i < $matSize; $i++, $im += $matSize) {
            for ($j = 0; $j < $matSize; $j++) {
                for ($k = 0, $km = 0; $k < $matSize; $k++, $km += $matSize) {
                    $cvR[$im + $j] += $cv1[$im + $k] * $cv2[$km + $j];
                }
            }
        }
    }
    $tIJK_cv_2 = \microtime(true);

    $tIJK_nv_1 = \microtime(true);
    for ($x = 0; $x < $limit; $x++) {
        for ($i = 0; $i < $matSize; $i++) {
            for ($j = 0; $j < $matSize; $j++) {
                for ($k = 0; $k < $matSize; $k++) {
                    $nvR[$i][$j] += $nv1[$i][$k] * $nv2[$k][$j];
                }
            }
        }
    }
    $tIJK_nv_2 = \microtime(true);

    ////////////////////////////////////////////////////////////////////////////////////////////////////////////////////

    list($caR, $naR, $cvR, $nvR) = getMatrixInstances($matSize, true);

    $tIKJ_ca_1 = \microtime(true);
    for ($x = 0; $x < $limit; $x++) {
        for ($i = 0, $im = 0; $i < $matSize; $i++, $im += $matSize) {
            for ($k = 0, $km = 0; $k < $matSize; $k++, $km += $matSize) {
                $t = $ca1[$im + $k];

                for ($j = 0; $j < $matSize; $j++) {
                    $caR[$im + $j] += $t * $ca2[$km + $j];
                }
            }
        }
    }
    $tIKJ_ca_2 = \microtime(true);

    $tIKJ_na_1 = \microtime(true);
    for ($x = 0; $x < $limit; $x++) {
        for ($i = 0; $i < $matSize; $i++) {
            for ($k = 0; $k < $matSize; $k++) {
                $t = $na1[$i][$k];

                for ($j = 0; $j < $matSize; $j++) {
                    $naR[$i][$j] += $t * $naR[$k][$j];
                }
            }
        }
    }
    $tIKJ_na_2 = \microtime(true);

    $tIKJ_cv_1 = \microtime(true);
    for ($x = 0; $x < $limit; $x++) {
        for ($i = 0, $im = 0; $i < $matSize; $i++, $im += $matSize) {
            for ($k = 0, $km = 0; $k < $matSize; $k++, $km += $matSize) {
                $t = $cv1[$im + $k];

                for ($j = 0; $j < $matSize; $j++) {
                    $cvR[$im + $j] += $t * $cv2[$km + $j];
                }
            }
        }
    }
    $tIKJ_cv_2 = \microtime(true);

    $tIKJ_nv_1 = \microtime(true);
    for ($x = 0; $x < $limit; $x++) {
        for ($i = 0; $i < $matSize; $i++) {
            for ($k = 0; $k < $matSize; $k++) {
                $t = $nv1[$i][$k];

                for ($j = 0; $j < $matSize; $j++) {
                    $nvR[$i][$j] += $t * $nvR[$k][$j];
                }
            }
        }
    }
    $tIKJ_nv_2 = \microtime(true);

    $result = [
        $matSize => [
            'ca_ijk' => $tIJK_ca_2 - $tIJK_ca_1,
            'na_ijk' => $tIJK_na_2 - $tIJK_na_1,
            'cv_ijk' => $tIJK_cv_2 - $tIJK_cv_1,
            'nv_ijk' => $tIJK_nv_2 - $tIJK_nv_1,

            'ca_ikj' => $tIKJ_ca_2 - $tIKJ_ca_1,
            'na_ikj' => $tIKJ_na_2 - $tIKJ_na_1,
            'cv_ikj' => $tIKJ_cv_2 - $tIKJ_cv_1,
            'nv_ikj' => $tIKJ_nv_2 - $tIKJ_nv_1,
        ]
    ];
    echo \json_encode($result) . "\n";
}

/**
 * @param int $matSize
 * @param bool $zeros
 * @return array [$singleArray, $nestedArray, $singleVector, $nestedVector]
 */
function getMatrixInstances(int $matSize, bool $zeros = false) : array
{
    $totalSize = $matSize * $matSize;

    $singleArray  = \array_fill(0, $totalSize, 0.0);                // ARRAY - contiguous memory

    $rowTemplate  = \array_fill(0, $matSize, 0);
    $rowTmplVect  = new Vector($rowTemplate);

    $nestedArray  = \array_fill(0, $matSize, $rowTemplate);         // ARRAY  - nested rows
    $nestedVector = new Vector();                                   // VECTOR - nested rows
    $nestedVector->allocate($matSize);

    for ($i = 0, $im = 0; $i < $matSize; $i++, $im += $matSize) {
        $nestedVector->push(clone $rowTmplVect);

        if (!$zeros) {
            for ($j = 0; $j < $matSize; $j++) {
                $v = \random_int(-5000, 5000);

                $singleArray[$im + $j] = $v;
                $nestedArray[$i][$j] = $v;
                $nestedVector[$i][$j] = $v;
            }
        }
    }

    $singleVector = new Vector($singleArray);                       // VECTOR - contiguous memory

    return [$singleArray, $nestedArray, $singleVector, $nestedVector];
}