#include<mpi.h>
int left, right, nxl, nx, rank, nsteps;
double * u, * u_new, k;

/*@ \mpi_collective(MPI_COMM_WORLD, P2P):
  @   requires rank == \mpi_comm_rank;
  @   requires nxl >= 0 && nxl < 5;
  @   requires \mpi_valid(u, nxl + 2, MPI_DOUBLE);
  @   assigns  \mpi_region(u, 1, MPI_DOUBLE), 
  @            \mpi_region(&u[nxl+1], 1, MPI_DOUBLE);
  @   ensures  \on(left, u[nxl]) == u[0];             
  @   ensures  \on(right, u[1]) == u[nxl + 1];        
  @   waitsfor left, right;
  @   behavior maxrank:
  @     assumes rank == \mpi_comm_size - 1;
  @     requires right == 0 && left == rank - 1;
  @   behavior minrank:
  @     assumes rank == 0;
  @     requires left == \mpi_comm_size - 1 && right == rank + 1;
  @   behavior others:
  @     assumes 0 < rank && rank < \mpi_comm_size - 1;
  @     requires left == rank - 1 && right == rank + 1;
  @*/
void exchange_ghost_cells() {
  MPI_Sendrecv(&u[1], 1, MPI_DOUBLE, left, 0,
               &u[nxl+1], 1, MPI_DOUBLE, right, 0,
               MPI_COMM_WORLD, MPI_STATUS_IGNORE);
  MPI_Sendrecv(&u[nxl], 1, MPI_DOUBLE, right, 0,
               &u[0], 1, MPI_DOUBLE, left, 0,
               MPI_COMM_WORLD, MPI_STATUS_IGNORE);
}

/*@ requires \valid(u + (0 .. (nxl + 2)));
  @ requires \valid(u_new + (0 .. (nxl + 2)));
  @ requires nxl > 0 && nxl <= 4;
  @ requires k > 0;
  @ assigns  u_new[0 .. (nxl + 2)];
  @ ensures  \forall int i; 0< i && i <= nxl
  @           ==> 
  @          u[i] == \old(u[i] + k*(u[i+1] + u[i-1] - 2*u[i]));
  @*/
void update() {
  for (int i = 1; i <= nxl; i++)
    u_new[i] = u[i] + k*(u[i+1] + u[i-1] - 2*u[i]);
  double * tmp = u_new; u_new=u; u=tmp;
}

/*@ requires nsteps > 1;
  @ \mpi_collective(MPI_COMM_WORLD, P2P):
  @   requires rank == \mpi_comm_rank;
  @   requires nxl > 0;
  @   requires \mpi_valid(u, nxl + 2, MPI_DOUBLE);
  @   requires \mpi_valid(u_new, nxl + 2, MPI_DOUBLE);
  @   requires  nx == \sum(0, \mpi_comm_size - 1, 
  @                    (\lambda int k; \on(k, nxl)));
  @   ensures  \forall int i; 0 < i <= nx
  @             ==>
  @            u[i] == \old(u[i] + k*(u[i+1] + u[i-1] - 2*u[i]));
  @   behavior maxrank:
  @     assumes rank == \mpi_comm_size - 1;
  @     requires right == 0 && left == rank - 1;
  @   behavior minrank:
  @     assumes rank == 0;
  @     requires left == \mpi_comm_size - 1 && right == rank + 1;
  @   behavior others:
  @     assumes 0 < rank && rank < \mpi_comm_size;
  @     requires left == rank - 1 && right == rank + 1;
  @*/
void diff1dIter() {
    exchange_ghost_cells();
    update();
}