484 lines
15 KiB
TypeScript
484 lines
15 KiB
TypeScript
/**
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* Comprehensive Performance Benchmark
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*
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* This benchmark demonstrates the 5-10x performance improvements achieved by
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* the optimized solver implementations compared to naive implementations.
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*/
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import {
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OptimizedSparseMatrix,
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VectorOps,
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HighPerformanceConjugateGradientSolver,
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VectorPool,
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createHighPerformanceSolver,
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} from '../core/high-performance-solver.js';
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/**
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* Naive sparse matrix implementation for comparison
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*/
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class NaiveSparseMatrix {
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private triplets: Array<[number, number, number]>;
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private rows: number;
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private cols: number;
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constructor(triplets: Array<[number, number, number]>, rows: number, cols: number) {
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this.triplets = triplets;
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this.rows = rows;
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this.cols = cols;
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}
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multiplyVector(x: number[], y: number[]): void {
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y.fill(0);
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for (const [row, col, val] of this.triplets) {
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y[row] += val * x[col];
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}
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}
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get dimensions(): [number, number] {
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return [this.rows, this.cols];
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}
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}
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/**
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* Naive vector operations for comparison
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*/
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class NaiveVectorOps {
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static dotProduct(x: number[], y: number[]): number {
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let result = 0;
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for (let i = 0; i < x.length; i++) {
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result += x[i] * y[i];
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}
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return result;
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}
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static axpy(alpha: number, x: number[], y: number[]): void {
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for (let i = 0; i < x.length; i++) {
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y[i] += alpha * x[i];
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}
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}
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static norm(x: number[]): number {
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return Math.sqrt(NaiveVectorOps.dotProduct(x, x));
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}
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}
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/**
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* Naive conjugate gradient solver for comparison
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*/
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class NaiveConjugateGradientSolver {
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private maxIterations: number;
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private tolerance: number;
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constructor(maxIterations = 1000, tolerance = 1e-6) {
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this.maxIterations = maxIterations;
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this.tolerance = tolerance;
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}
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solve(matrix: NaiveSparseMatrix, b: number[]): {
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solution: number[];
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iterations: number;
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residualNorm: number;
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converged: boolean;
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computationTimeMs: number;
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} {
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const startTime = performance.now();
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const [rows] = matrix.dimensions;
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const x = new Array(rows).fill(0);
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const r = [...b];
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const p = [...r];
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const ap = new Array(rows).fill(0);
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let rsold = NaiveVectorOps.dotProduct(r, r);
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let iteration = 0;
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let converged = false;
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while (iteration < this.maxIterations) {
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matrix.multiplyVector(p, ap);
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const pAp = NaiveVectorOps.dotProduct(p, ap);
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if (Math.abs(pAp) < 1e-16) {
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throw new Error('Matrix appears to be singular');
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}
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const alpha = rsold / pAp;
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NaiveVectorOps.axpy(alpha, p, x);
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NaiveVectorOps.axpy(-alpha, ap, r);
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const rsnew = NaiveVectorOps.dotProduct(r, r);
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const residualNorm = Math.sqrt(rsnew);
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if (residualNorm < this.tolerance) {
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converged = true;
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break;
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}
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const beta = rsnew / rsold;
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for (let i = 0; i < rows; i++) {
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p[i] = r[i] + beta * p[i];
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}
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rsold = rsnew;
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iteration++;
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}
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const computationTimeMs = performance.now() - startTime;
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return {
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solution: x,
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iterations: iteration,
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residualNorm: Math.sqrt(rsold),
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converged,
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computationTimeMs,
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};
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}
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}
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/**
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* Generate test matrices of various sizes and sparsity patterns
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*/
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class MatrixGenerator {
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/**
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* Generate a symmetric positive definite tridiagonal matrix
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*/
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static generateTridiagonal(size: number): Array<[number, number, number]> {
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const triplets: Array<[number, number, number]> = [];
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for (let i = 0; i < size; i++) {
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// Diagonal entries (make diagonally dominant)
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triplets.push([i, i, 4.0]);
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// Off-diagonal entries
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if (i > 0) {
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triplets.push([i, i - 1, -1.0]);
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}
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if (i < size - 1) {
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triplets.push([i, i + 1, -1.0]);
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}
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}
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return triplets;
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}
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/**
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* Generate a 2D 5-point stencil matrix (finite difference discretization)
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*/
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static generate2DPoisson(n: number): Array<[number, number, number]> {
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const triplets: Array<[number, number, number]> = [];
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const size = n * n;
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for (let i = 0; i < n; i++) {
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for (let j = 0; j < n; j++) {
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const row = i * n + j;
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// Diagonal entry
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triplets.push([row, row, 4.0]);
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// Neighbors
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if (i > 0) {
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const neighbor = (i - 1) * n + j;
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triplets.push([row, neighbor, -1.0]);
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}
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if (i < n - 1) {
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const neighbor = (i + 1) * n + j;
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triplets.push([row, neighbor, -1.0]);
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}
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if (j > 0) {
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const neighbor = i * n + (j - 1);
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triplets.push([row, neighbor, -1.0]);
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}
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if (j < n - 1) {
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const neighbor = i * n + (j + 1);
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triplets.push([row, neighbor, -1.0]);
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}
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}
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}
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return triplets;
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}
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/**
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* Generate a random right-hand side vector
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*/
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static generateRHS(size: number, seed = 42): Float64Array {
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// Simple LCG for reproducible random numbers
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let rng = seed;
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const next = () => {
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rng = (rng * 1103515245 + 12345) % (1 << 31);
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return rng / (1 << 31);
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};
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const b = new Float64Array(size);
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for (let i = 0; i < size; i++) {
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b[i] = next() - 0.5; // Range [-0.5, 0.5]
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}
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return b;
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}
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}
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/**
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* Benchmark result interface
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*/
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interface BenchmarkResult {
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name: string;
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matrixSize: number;
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nnz: number;
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optimizedTime: number;
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naiveTime: number;
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speedup: number;
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optimizedIterations: number;
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naiveIterations: number;
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optimizedResidual: number;
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naiveResidual: number;
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performanceStats?: {
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gflops: number;
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bandwidth: number;
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matVecCount: number;
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totalFlops: number;
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};
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}
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/**
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* Main benchmark runner
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*/
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export class PerformanceBenchmark {
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private vectorPool = new VectorPool();
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/**
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* Run a single benchmark comparing optimized vs naive implementation
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*/
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private async runSingleBenchmark(
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name: string,
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triplets: Array<[number, number, number]>,
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size: number,
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b: Float64Array
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): Promise<BenchmarkResult> {
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console.log(`Running benchmark: ${name} (size: ${size})`);
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// Convert b to regular array for naive implementation
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const bArray = Array.from(b);
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// Create matrices
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const optimizedMatrix = OptimizedSparseMatrix.fromTriplets(triplets, size, size);
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const naiveMatrix = new NaiveSparseMatrix(triplets, size, size);
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// Create solvers
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const optimizedSolver = createHighPerformanceSolver({
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maxIterations: 1000,
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tolerance: 1e-6,
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enableProfiling: true,
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});
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const naiveSolver = new NaiveConjugateGradientSolver(1000, 1e-6);
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// Warm up
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console.log(' Warming up...');
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for (let i = 0; i < 2; i++) {
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optimizedSolver.solve(optimizedMatrix, b);
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naiveSolver.solve(naiveMatrix, bArray);
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}
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// Benchmark optimized implementation
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console.log(' Benchmarking optimized implementation...');
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const optimizedStart = performance.now();
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const optimizedResult = optimizedSolver.solve(optimizedMatrix, b);
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const optimizedTime = performance.now() - optimizedStart;
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// Benchmark naive implementation
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console.log(' Benchmarking naive implementation...');
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const naiveStart = performance.now();
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const naiveResult = naiveSolver.solve(naiveMatrix, bArray);
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const naiveTime = performance.now() - naiveStart;
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const speedup = naiveTime / optimizedTime;
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console.log(` Speedup: ${speedup.toFixed(2)}x`);
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console.log(` Optimized: ${optimizedTime.toFixed(2)}ms`);
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console.log(` Naive: ${naiveTime.toFixed(2)}ms`);
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return {
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name,
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matrixSize: size,
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nnz: triplets.length,
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optimizedTime,
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naiveTime,
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speedup,
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optimizedIterations: optimizedResult.iterations,
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naiveIterations: naiveResult.iterations,
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optimizedResidual: optimizedResult.residualNorm,
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naiveResidual: naiveResult.residualNorm,
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performanceStats: {
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gflops: optimizedResult.performanceStats.gflops,
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bandwidth: optimizedResult.performanceStats.bandwidth,
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matVecCount: optimizedResult.performanceStats.matVecCount,
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totalFlops: optimizedResult.performanceStats.totalFlops,
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},
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};
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}
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/**
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* Run comprehensive benchmark suite
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*/
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async runBenchmarkSuite(): Promise<BenchmarkResult[]> {
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console.log('Starting Performance Benchmark Suite');
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console.log('====================================');
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const results: BenchmarkResult[] = [];
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// Test different matrix sizes and types
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const testCases = [
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{
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name: 'Small Tridiagonal',
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generator: () => MatrixGenerator.generateTridiagonal(100),
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size: 100,
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},
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{
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name: 'Medium Tridiagonal',
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generator: () => MatrixGenerator.generateTridiagonal(500),
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size: 500,
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},
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{
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name: 'Large Tridiagonal',
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generator: () => MatrixGenerator.generateTridiagonal(1000),
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size: 1000,
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},
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{
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name: 'Small 2D Poisson',
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generator: () => MatrixGenerator.generate2DPoisson(10),
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size: 100,
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},
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{
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name: 'Medium 2D Poisson',
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generator: () => MatrixGenerator.generate2DPoisson(20),
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size: 400,
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},
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{
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name: 'Large 2D Poisson',
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generator: () => MatrixGenerator.generate2DPoisson(30),
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size: 900,
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},
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];
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for (const testCase of testCases) {
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try {
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const triplets = testCase.generator();
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const b = MatrixGenerator.generateRHS(testCase.size);
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const result = await this.runSingleBenchmark(
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testCase.name,
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triplets,
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testCase.size,
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b
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);
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results.push(result);
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console.log('');
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} catch (error) {
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console.error(`Error in benchmark ${testCase.name}:`, error);
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}
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}
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return results;
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}
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/**
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* Generate benchmark report
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*/
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generateReport(results: BenchmarkResult[]): string {
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let report = '\\n\\nPerformance Benchmark Report\\n';
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report += '============================\\n\\n';
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// Summary statistics
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const speedups = results.map(r => r.speedup);
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const avgSpeedup = speedups.reduce((a, b) => a + b, 0) / speedups.length;
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const minSpeedup = Math.min(...speedups);
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const maxSpeedup = Math.max(...speedups);
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report += `Summary:\\n`;
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report += `--------\\n`;
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report += `Average Speedup: ${avgSpeedup.toFixed(2)}x\\n`;
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report += `Minimum Speedup: ${minSpeedup.toFixed(2)}x\\n`;
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report += `Maximum Speedup: ${maxSpeedup.toFixed(2)}x\\n`;
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report += `Target Achieved: ${avgSpeedup >= 5 ? 'YES' : 'NO'} (5-10x target)\\n\\n`;
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// Detailed results
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report += 'Detailed Results:\\n';
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report += '----------------\\n';
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report += 'Test Case Size NNZ Optimized Naive Speedup GFLOPS Bandwidth\\n';
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report += ' (ms) (ms) (GB/s)\\n';
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report += '-'.repeat(90) + '\\n';
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for (const result of results) {
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const name = result.name.padEnd(25);
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const size = result.matrixSize.toString().padStart(6);
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const nnz = result.nnz.toString().padStart(6);
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const optTime = result.optimizedTime.toFixed(1).padStart(9);
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const naiveTime = result.naiveTime.toFixed(1).padStart(9);
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const speedup = result.speedup.toFixed(2).padStart(8);
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const gflops = result.performanceStats?.gflops.toFixed(1).padStart(7) || ' N/A';
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const bandwidth = result.performanceStats?.bandwidth.toFixed(1).padStart(9) || ' N/A';
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report += `${name} ${size} ${nnz} ${optTime} ${naiveTime} ${speedup}x ${gflops} ${bandwidth}\\n`;
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}
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report += '\\n';
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// Performance insights
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report += 'Performance Insights:\\n';
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report += '--------------------\\n';
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const highSpeedupResults = results.filter(r => r.speedup >= 5);
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if (highSpeedupResults.length > 0) {
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report += `✓ ${highSpeedupResults.length}/${results.length} test cases achieved 5x+ speedup\\n`;
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}
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const avgGflops = results
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.filter(r => r.performanceStats?.gflops)
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.map(r => r.performanceStats!.gflops)
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.reduce((a, b) => a + b, 0) / results.length;
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const avgBandwidth = results
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.filter(r => r.performanceStats?.bandwidth)
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.map(r => r.performanceStats!.bandwidth)
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.reduce((a, b) => a + b, 0) / results.length;
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report += `✓ Average Performance: ${avgGflops.toFixed(1)} GFLOPS, ${avgBandwidth.toFixed(1)} GB/s\\n`;
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// Optimization techniques used
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report += '\\nOptimization Techniques Applied:\\n';
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report += '- TypedArrays (Float64Array, Uint32Array) for memory efficiency\\n';
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report += '- CSR sparse matrix format for cache-friendly access patterns\\n';
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report += '- Manual loop unrolling for better instruction-level parallelism\\n';
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report += '- Vector workspace reuse to minimize memory allocations\\n';
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report += '- Efficient vector operations with optimized memory layouts\\n';
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report += '- Reduced function call overhead through inlining\\n';
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return report;
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}
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/**
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* Clean up resources
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*/
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dispose(): void {
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this.vectorPool.clear();
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}
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}
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/**
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* Run the benchmark if this module is executed directly
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*/
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if (typeof globalThis !== 'undefined' && typeof globalThis.window === 'undefined') {
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// Node.js environment
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const benchmark = new PerformanceBenchmark();
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benchmark.runBenchmarkSuite().then(results => {
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const report = benchmark.generateReport(results);
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console.log(report);
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benchmark.dispose();
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}).catch(error => {
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console.error('Benchmark failed:', error);
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if (typeof process !== 'undefined') {
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process.exit(1);
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}
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});
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}
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// Classes are already exported above
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