hpc-patterns

# HPC Patterns for C++20

Domain knowledge for building high-performance computing applications with optimal hardware utilization.

## Cache-Friendly Data Structures

### Structure of Arrays (SoA) vs Array of Structures (AoS)

```cpp
// BAD: Array of Structures (poor cache utilization for position-only access)
struct ParticleAoS {
  double x, y, z;         // position
  double vx, vy, vz;      // velocity
  double fx, fy, fz;      // force
  double mass;
  int type;
  bool active;
};
std::vector<ParticleAoS> particles(N);  // Stride = sizeof(ParticleAoS)

// GOOD: Structure of Arrays (contiguous access per field)
struct ParticlesSoA {
  std::vector<double> x, y, z;
  std::vector<double> vx, vy, vz;
  std::vector<double> fx, fy, fz;
  std::vector<double> mass;
  std::vector<int> type;
  std::vector<bool> active;

  explicit ParticlesSoA(size_t n)
      : x(n), y(n), z(n), vx(n), vy(n), vz(n),
        fx(n), fy(n), fz(n), mass(n), type(n), active(n) {}
};
```

### Cache Line Alignment

```cpp
// Align to cache line boundaries
struct alignas(64) CacheAlignedBlock {
  std::array<double, 8> data;  // 64 bytes = 1 cache line
};

// Padding to avoid false sharing in multithreaded code
struct alignas(64) ThreadLocalCounter {
  std::atomic<int64_t> count{0};
  char padding[64 - sizeof(std::atomic<int64_t>)];  // Fill cache line
};
```

### Tiling for Cache Reuse

```cpp
// Cache-oblivious matrix multiply (blocked)
void MatMulBlocked(std::span<const double> A, std::span<const double> B,
                   std::span<double> C, int N, int block_size = 64) {
  for (int ii = 0; ii < N; ii += block_size) {
    for (int jj = 0; jj < N; jj += block_size) {
      for (int kk = 0; kk < N; kk += block_size) {
        int i_end = std::min(ii + block_size, N);
        int j_end = std::min(jj + block_size, N);
        int k_end = std::min(kk + block_size, N);

        for (int i = ii; i < i_end; ++i) {
          for (int k = kk; k < k_end; ++k) {
            double a_ik = A[i * N + k];