#include <math.h>
#include <stdlib.h>
#include <stdio.h>
#include <stdint.h>
#include <string.h>

#include <mpi.h>
#include <ndarray.h>

#include "components.h"
#include "ell_grid_solve.h"
#include "log.h"
#include "mg2d_boundary.h"
#include "mg2d_constants.h"

#define DOMAIN_SIZE 1.0
#define FD_STENCIL 2

#if 1
static double sol(double x, double y)
{
    return sin(M_PI * x) * sin(M_PI * y);
}
static double sol_dx(double x, double y)
{
    return M_PI * cos(M_PI * x) * sin(M_PI * y);
}
static double sol_dy(double x, double y)
{
    return M_PI * sin(M_PI * x) * cos(M_PI * y);
}
static double sol_dxx(double x, double y)
{
    return -M_PI * M_PI * sol(x, y);
}
static double sol_dyy(double x, double y)
{
    return -M_PI * M_PI * sol(x, y);
}
static double sol_dxy(double x, double y)
{
    return M_PI * M_PI * cos(M_PI * x) * cos(M_PI * y);
}
#endif

int main(int argc, char **argv)
{
    EGSContext *ctx;
    DomainGeometry *dg = NULL;
    DomainComponent *dc = NULL;
    long int log2N, log2maxiter;
    long int N, maxiter;
    double res_old, res_new;
    int ret = 0;

    char processor_name[MPI_MAX_PROCESSOR_NAME];
    int nb_processes, rank, processor_name_len;

    if (argc < 3) {
        fprintf(stderr, "Usage: %s <log2 N> <log2 maxiter>\n", argv[0]);
        return 1;
    }
    log2N       = strtol(argv[1], NULL, 0);
    log2maxiter = strtol(argv[2], NULL, 0);
    if (log2N <= 0 || log2maxiter < 0 ||
        log2N >= sizeof(N) * 8 || log2maxiter >= sizeof(maxiter) * 8) {
        fprintf(stderr, "Invalid log2N/log2maxiter values: %ld/%ld\n",
                log2N, log2maxiter);
        return 1;
    }

    N       = (1L << log2N) + 1;
    maxiter = 1L << log2maxiter;

    MPI_Init(NULL, NULL);

    MPI_Comm_size(MPI_COMM_WORLD, &nb_processes);
    MPI_Comm_rank(MPI_COMM_WORLD, &rank);
    MPI_Get_processor_name(processor_name, &processor_name_len);

    fprintf(stderr, "This is process %d out of %d, running on %s\n",
            rank, nb_processes, processor_name);

    dg = mg2di_dg_alloc(nb_processes);
    if (!dg) {
        fprintf(stderr, "Error allocating domain geometry\n");
        ret = 1;
        goto fail;
    }

    dg->domain_size[0] = N;
    dg->domain_size[1] = N;

    for (unsigned int i = 0; i < dg->nb_components; i++) {
        size_t patch_start, patch_end, patch_size_y;

        patch_size_y = (N + nb_processes - 1) / nb_processes;
        patch_start  = i * patch_size_y;
        patch_end    = MIN((i + 1) * patch_size_y, N);
        patch_size_y = patch_end - patch_start;
        if (patch_size_y <= 0) {
            fprintf(stderr, "Too many processes for grid size %ld: %d\n", N, nb_processes);
            ret = 1;
            goto fail;
        }

        dg->components[i].interior.start[0] = 0;
        dg->components[i].interior.start[1] = patch_start;
        dg->components[i].interior.size[0] = N;
        dg->components[i].interior.size[1] = patch_size_y;

        dg->components[i].exterior.start[0] = -FD_STENCIL_MAX;
        dg->components[i].exterior.start[1] = i ? patch_start : -FD_STENCIL_MAX;
        dg->components[i].exterior.size[0] = N + 2 * FD_STENCIL_MAX;
        dg->components[i].exterior.size[1] = patch_size_y + ((i == 0) * FD_STENCIL_MAX) + ((i == nb_processes - 1) * FD_STENCIL_MAX);

        dg->components[i].bnd_is_outer[MG2D_BOUNDARY_0L] = 1;
        dg->components[i].bnd_is_outer[MG2D_BOUNDARY_0U] = 1;
        dg->components[i].bnd_is_outer[MG2D_BOUNDARY_1L] = i == 0;
        dg->components[i].bnd_is_outer[MG2D_BOUNDARY_1U] = i == nb_processes - 1;
    }
    dc = &dg->components[rank];

    ctx = mg2di_egs_alloc_mpi(MPI_COMM_WORLD, dg);
    if (!ctx) {
        fprintf(stderr, "Error allocating the solver context\n");
        return 1;
    }

    ctx->logger.log = mg2di_log_default_callback;

    ctx->step[0] = DOMAIN_SIZE / (N - 1.0);
    ctx->step[1] = DOMAIN_SIZE / (N - 1.0);

    ctx->fd_stencil = FD_STENCIL;

    for (int bnd_loc = 0; bnd_loc < ARRAY_ELEMS(ctx->boundaries); bnd_loc++) {
        MG2DBoundary *bnd = ctx->boundaries[bnd_loc];
        const int ci      = mg2d_bnd_coord_idx(bnd_loc);
        const int bnd_dir = mg2d_bnd_out_dir(bnd_loc);

        double coord[2];

        if (!dc->bnd_is_outer[bnd_loc])
            continue;

        bnd->type = MG2D_BC_TYPE_FIXVAL;

        memset(bnd->val, 0, ctx->domain_size[!ci] * sizeof(*bnd->val));

        for (int j = 1; j < ctx->fd_stencil; j++) {
            double *dst = bnd->val + j * bnd->val_stride;

            coord[ci] = mg2d_bnd_is_upper(bnd_loc) * DOMAIN_SIZE + bnd_dir * j * ctx->step[ci];

            for (ptrdiff_t k = -j; k < (ptrdiff_t)ctx->domain_size[!ci] + j; k++) {
                coord[!ci] = (k + dc->interior.start[!ci]) * ctx->step[!ci];
                dst[k] = sol(coord[0], coord[1]);
            }
        }
    }

    for (size_t y = 0; y < ctx->domain_size[1]; y++) {
        const double y_coord = (y + dc->interior.start[1]) * ctx->step[1];

        memset(NDA_PTR2D(ctx->u, 0, y), 0, sizeof(*ctx->u->data) * ctx->domain_size[0]);

        for (size_t x = 1; x < ctx->domain_size[0]; x++) {
            const double x_coord = x * ctx->step[0];

            *NDA_PTR2D(ctx->diff_coeffs[MG2D_DIFF_COEFF_02], x, y) =  1.0;
            *NDA_PTR2D(ctx->diff_coeffs[MG2D_DIFF_COEFF_20], x, y) =  1.0;
            *NDA_PTR2D(ctx->diff_coeffs[MG2D_DIFF_COEFF_11], x, y) =  1.0;

            *NDA_PTR2D(ctx->rhs, x, y) = sol_dxx(x_coord, y_coord) + sol_dyy(x_coord, y_coord) + sol_dxy(x_coord, y_coord);
        }

        memset(NDA_PTR2D(ctx->diff_coeffs[MG2D_DIFF_COEFF_00], 0, y), 0,
               sizeof(*ctx->diff_coeffs[0]->data) * ctx->domain_size[0]);
        memset(NDA_PTR2D(ctx->diff_coeffs[MG2D_DIFF_COEFF_01], 0, y), 0,
               sizeof(*ctx->diff_coeffs[0]->data) * ctx->domain_size[0]);
        memset(NDA_PTR2D(ctx->diff_coeffs[MG2D_DIFF_COEFF_10], 0, y), 0,
               sizeof(*ctx->diff_coeffs[0]->data) * ctx->domain_size[0]);
    }

    ret = mg2di_egs_init(ctx, 0);
    if (ret < 0) {
        fprintf(stderr, "Error initializing the solver context: %d\n", ret);
        ret = 1;
        goto fail;
    }

    res_old = ctx->residual_max;

    for (int i = 0; i < maxiter; i++) {
        ret = mg2di_egs_solve(ctx, EGS_SOLVE_RELAXATION, 0);
        if (ret < 0) {
            fprintf(stderr, "Error during relaxation\n");
            ret = 1;
            goto fail;
        }
        res_new = ctx->residual_max;
        if (rank == 0) {
            if (res_new > 1e3) {
                fprintf(stderr, "Diverged at step %d: %g -> %g\n", i, res_old, res_new);
                goto fail;
            }
            fprintf(stderr, "Step %d: %g -> %g (%g)\n", i, res_old, res_new, res_old / res_new);
            res_old = res_new;
        }
    }

    {
        double max_err = 0.0;

        for (size_t y = 0; y < ctx->domain_size[1]; y++) {
            const double y_coord = (y + dc->interior.start[1]) * ctx->step[1];

            for (size_t x = 0; x < ctx->domain_size[0]; x++) {
                const double x_coord = x * ctx->step[0];
                double err = fabs(ctx->u->data[y * ctx->u->stride[0] + x] - sol(x_coord, y_coord));
                if (err > max_err)
                    max_err = err;
            }
        }
        MPI_Reduce(rank ? &max_err : MPI_IN_PLACE, &max_err, 1, MPI_DOUBLE, MPI_MAX, 0, MPI_COMM_WORLD);
        if (rank == 0)
            fprintf(stderr, "max(|solution - exact|): %g\n", max_err);
    }

fail:
    mg2di_egs_free(&ctx);
    mg2di_dg_free(&dg);
    MPI_Finalize();
    return ret;
}