// bench_funcs.cpp
#include "bench_funcs.h"
#include <omp.h>
#include <cmath>
#include <cstddef>
#include <vector>
#include <algorithm>

//EXERCISE 4
// A: parallel sum 
double sum_basic(const std::vector<double>& x)
{
    double sum = 0.0;
    #pragma omp parallel for reduction(+:sum)
    for (std::size_t i = 0; i < x.size(); ++i) sum += x[i];
    return sum;
}

// A: parallel dot product 
double dot_basic(const std::vector<double>& x, const std::vector<double>& y)
{
    std::size_t N = x.size();
    double sum = 0.0;
    #pragma omp parallel for reduction(+:sum)
    for (std::size_t i = 0; i < N; ++i) sum += x[i] * y[i];
    return sum;
}

// Kahan remains same
double dot_kahan(const std::vector<double>& x, const std::vector<double>& y)
{
    double sum = 0.0;
    double c = 0.0;
    for (std::size_t i = 0; i < x.size(); ++i)
    {
        double prod = x[i] * y[i];
        double yk = prod - c;
        double t = sum + yk;
        c = (t - sum) - yk;
        sum = t;
    }
    return sum;
}

// Norm (sum of squares) 
double norm_basic(const std::vector<double>& x)
{
    double sumsq = 0.0;
    #pragma omp parallel for reduction(+:sumsq)
    for (std::size_t i = 0; i < x.size(); ++i) sumsq += x[i]*x[i];
    return sumsq;
}

// B: matvec (row-major)
void matvec_rowmajor(const std::vector<double>& A, std::size_t M, std::size_t N,
                     const std::vector<double>& x, std::vector<double>& b)
{
    b.assign(M, 0.0);
    #pragma omp parallel for
    for (std::size_t i = 0; i < M; ++i) {
        double tmp = 0.0;
        const double* Ai = &A[i*N];
        for (std::size_t j = 0; j < N; ++j) tmp += Ai[j] * x[j];
        b[i] = tmp;
    }
}

// C: matmul (row-major)
void matmul_rowmajor(const std::vector<double>& A, std::size_t M, std::size_t L,
                     const std::vector<double>& B, std::size_t N,
                     std::vector<double>& C)
{
    C.assign(M * N, 0.0);
    // Parallelize over output rows (i)
    #pragma omp parallel for
    for (std::size_t i = 0; i < M; ++i) {
        for (std::size_t k = 0; k < L; ++k) {
            double Aik = A[i*L + k];
            const double* Bk = &B[k*N];
            double* Ci = &C[i*N];
            for (std::size_t j = 0; j < N; ++j) {
                Ci[j] += Aik * Bk[j];
            }
        }
    }
}

// D: polynomial evaluation (Horner), parallel over x points
void polyp_horner(const std::vector<double>& a, const std::vector<double>& x, std::vector<double>& y)
{
    std::size_t p = a.size() - 1;
    std::size_t N = x.size();
    y.assign(N, 0.0);

    #pragma omp parallel for
    for (std::size_t i = 0; i < N; ++i) {
        double xi = x[i];
        double val = a[p];
        for (std::size_t k = p; k-- > 0; ) { 
            val = val * xi + a[k];
        }
        y[i] = val;
    }
}

//EXERCISE 5
// Parallel assembly of tridiagonal FEM matrix (CSR)
void build_fem_system(std::size_t n, CSR& K, std::vector<double>& f)
{
    K.n = n;
    K.row_ptr.resize(n+1);
    f.assign(n, 1.0);
    K.val.resize(3*n); // Each row has at most 3 non-zero entries: [-1,2,-1]
    K.col.resize(3*n);

    for (std::size_t i = 0; i < n; ++i)
        K.row_ptr[i] = 3*i;
    K.row_ptr[n] = 3*n;

    #pragma omp parallel for     // Fill matrix in parallel
    for (std::size_t i = 0; i < n; ++i) {
        std::size_t base = 3*i;

        if (i > 0) {
            K.val[base] = -1.0;
            K.col[base] = i - 1;
        } else {
            K.val[base] = 0.0;
            K.col[base] = 0;
        }

        K.val[base + 1] = 2.0;
        K.col[base + 1] = i;

        if (i + 1 < n) {
            K.val[base + 2] = -1.0;
            K.col[base + 2] = i + 1;
        } else {
            K.val[base + 2] = 0.0;
            K.col[base + 2] = i;
        }
    }
}

// Parallel Jacobi iteration
void jacobi_csr_parallel(const CSR& K, const std::vector<double>& f,
                         std::vector<double>& u,
                         std::size_t max_iter, double omega, double tol)
{
    std::size_t n = K.n;
    u.assign(n, 0.0);
    std::vector<double> u_new(n, 0.0);

    for (std::size_t iter = 0; iter < max_iter; ++iter) {
        double max_err = 0.0;

        #pragma omp parallel for reduction(max:max_err)
        for (std::size_t i = 0; i < n; ++i) {
            double diag = 0.0;
            double sum  = 0.0;

            for (std::size_t idx = K.row_ptr[i]; idx < K.row_ptr[i+1]; ++idx) {
                std::size_t j = K.col[idx];
                double v = K.val[idx];
                if (j == i) diag = v;
                else sum += v * u[j];
            }

            double ui_new = u[i] + omega * (f[i] - sum - diag*u[i]) / diag;
            u_new[i] = ui_new;

            double err = std::fabs(ui_new - u[i]);
            if (err > max_err) max_err = err;
        }

        u.swap(u_new);
        if (max_err < tol) break;
    }
}

//EXERCISE 6
// Helper: build empty CSR structure (3 entries per row)
static void prepare_tridiag_csr(std::size_t n, CSR &K)
{
    K.n = n;
    K.row_ptr.resize(n + 1);
    // Each row has 3 slots (left, diag, right)
    for (std::size_t i = 0; i < n; ++i) K.row_ptr[i] = 3 * i;
    K.row_ptr[n] = 3 * n;

    K.val.assign(3 * n, 0.0);
    K.col.resize(3 * n);

    // fill col indices
    for (std::size_t i = 0; i < n; ++i) {
        std::size_t base = 3 * i;
        // left column index
        if (i > 0) K.col[base + 0] = i - 1;
        else       K.col[base + 0] = i; // dummy (no entry)
        // diagonal
        K.col[base + 1] = i;
        // right
        if (i + 1 < n) K.col[base + 2] = i + 1;
        else           K.col[base + 2] = i; // dummy
    }
}

// Element-level element matrix (1D linear element on uniform mesh)
// local ordering: node 0 = left, node 1 = right
// element matrix (unscaled) = [ 1  -1; -1  1 ]
// For a uniform mesh with h=1/(n-1) stiffness would be 1/h. For simplicity we use 1.0 scaling.
inline void element_matrix_vals(double out[4])
{
    // ordering out = [K00, K01, K10, K11]
    out[0] = 1.0; out[1] = -1.0; out[2] = -1.0; out[3] = 1.0;
}

// Atomic assembly: parallel over elements, atomic adds to K.val
void build_fem_system_atomic(std::size_t n, CSR &K, std::vector<double> &f)
{
    prepare_tridiag_csr(n, K);
    f.assign(n, 1.0); // RHS = 1

    std::size_t nel = (n >= 2) ? (n - 1) : 0;
    // Parallel over elements
    #pragma omp parallel for
    for (std::size_t e = 0; e < nel; ++e) {
        // global node indices for element e: i = e, j = e+1
        std::size_t i = e;
        std::size_t j = e + 1;
        double Em[4];
        element_matrix_vals(Em);

        // contributions:
        // K(i,i) += Em[0]
        // K(i,j) += Em[1]
        // K(j,i) += Em[2]
        // K(j,j) += Em[3]
        std::size_t idx_ii = 3 * i + 1;            // diag of row i
        std::size_t idx_ij = 3 * i + 2;            // right of row i
        std::size_t idx_ji = 3 * j + 0;            // left of row j
        std::size_t idx_jj = 3 * j + 1;            // diag of row j

        #pragma omp atomic
        K.val[idx_ii] += Em[0];
        #pragma omp atomic
        K.val[idx_ij] += Em[1];
        #pragma omp atomic
        K.val[idx_ji] += Em[2];
        #pragma omp atomic
        K.val[idx_jj] += Em[3];
    }
}

// No-atomic grouped assembly (method (a))
// We compute each row i's three entries by summing the (<=2) contributing elements.
// Parallel over rows; no atomics.
void build_fem_system_no_atomic(std::size_t n, CSR &K, std::vector<double> &f)
{
    prepare_tridiag_csr(n, K);
    f.assign(n, 1.0);

    // element matrix values (same for all elements here)
    double Em00 = 1.0, Em01 = -1.0, Em10 = -1.0, Em11 = 1.0;

    #pragma omp parallel for // parallel over rows (global entries)
    for (std::size_t i = 0; i < n; ++i) {
        std::size_t base = 3 * i;

        // left entry (K[i, i-1]) gets contribution only from element e = i-1
        if (i > 0) K.val[base + 0] = Em10; // from element e=i-1 local(1,0)
        else       K.val[base + 0] = 0.0;

        // diagonal K[i,i] gets contributions from element e=i-1 (local(1,1)) and e=i (local(0,0))
        double diag = 0.0;
        if (i > 0)      diag += Em11; // e = i-1 local(1,1)
        if (i + 1 < n)  diag += Em00; // e = i local(0,0)
        K.val[base + 1] = diag;

        // right entry (K[i,i+1]) gets contribution only from element e = i
        if (i + 1 < n) K.val[base + 2] = Em01; // e=i local(0,1)
        else           K.val[base + 2] = 0.0;
    }
}