[AP][Solver][3D] 3D AP Solver Support

Upgraded the solver in the AP flow to support a "Z" dimension
representing the layer. This code only kicks on when the architecture
has more than one layer, since in the single layer case there is no
point to compute the Z dimension.

Author: AlexandreSinger

vpr/src/analytical_place/analytical_solver.cpp

@@ -531,6 +531,16 @@ class B2BSolver : public AnalyticalSolver {
     ///        number, the solver will focus more on timing and less on wirelength.
     static constexpr double timing_slope_fac_ = 0.75;
 
+    /// @brief For most FPGA architectures, the cost of moving horizontally is
+    ///        equivalent to the cost moving vertically (i.e. moving in increasing
+    ///        x-dimension has the same cost as moving the same amount in the
+    ///        y-dimension). However, for 3D FPGAs, moving between layers is
+    ///        much more expensive than moving in the x or y dimension. We account
+    ///        for this by adding a cost penalty factor to the "z"-dimension.
+    /// TODO: This cost factor was randomly selected because it felt ok. Should
+    ///       choose a better factor that is chosen empirically.
+    static constexpr double layer_distance_cost_fac_ = 10.0;
+
   public:
     B2BSolver(const APNetlist& ap_netlist,
               const DeviceGrid& device_grid,
@@ -699,15 +709,41 @@ class B2BSolver : public AnalyticalSolver {
     void update_linear_system_with_anchors(unsigned iteration);
 
     /**
-     * @brief Store the x and y solutions in Eigen's vectors into the partial
-     *        placement object.
-     *
-     * Note: The x_soln and y_soln may be modified if it is found that the
-     *       solution is imposible (i.e. has negative positions).
+     * @brief Solves the linear system of equations using the connectivity
+     *        matrix (A), the constant vector (b), and a guess for the solution.
      */
-    void store_solution_into_placement(Eigen::VectorXd& x_soln,
-                                       Eigen::VectorXd& y_soln,
-                                       PartialPlacement& p_placement);
+    Eigen::VectorXd solve_linear_system(Eigen::SparseMatrix<double> &A,
+                                        Eigen::VectorXd &b,
+                                        Eigen::VectorXd &guess);
+
+    /**
+     * @brief Store the solutions from the linear system into the partial
+     *        placement object for the given dimension.
+     *
+     * Note: The dim_soln may be modified if it is found that the solution is
+     *       imposible (e.g. has negative positions).
+     *
+     *  @param dim_soln
+     *      The solution of the linear system for a given dimension.
+     *  @param block_dim_locs
+     *      The block locations in the partial placement for the dimension.
+     *  @param dim_max_pos
+     *      The maximum position allowed for the dimension. For example, for the
+     *      x-dimension, this would be the width of the device. This is used to
+     *      ensure that the positions do not go off device.
+     */
+    void store_solution_into_placement(Eigen::VectorXd &dim_soln,
+                                       vtr::vector<APBlockId, double> &block_dim_locs,
+                                       double dim_max_pos);
+
+    /**
+     * @brief Does the FPGA that the AP flow is currently targeting have more
+     *        than one die. Having multiple dies would imply that the solver
+     *        needs to add another dimension to solve for.
+     */
+    inline bool is_multi_die() const {
+        return device_grid_num_layers_ > 1;
+    }
 
     // The following are variables used to store the system of equations to be
     // solved in the x and y dimensions. The equations are of the form:
@@ -720,22 +756,28 @@ class B2BSolver : public AnalyticalSolver {
     Eigen::SparseMatrix<double> A_sparse_x;
     /// @brief The coefficient / connectivity matrix for the y dimension.
     Eigen::SparseMatrix<double> A_sparse_y;
+    /// @brief The coefficient / connectivity matrix for the z dimension (layer dimension).
+    Eigen::SparseMatrix<double> A_sparse_z;
     /// @brief The constant vector in the x dimension.
     Eigen::VectorXd b_x;
     /// @brief The constant vector in the y dimension.
     Eigen::VectorXd b_y;
+    /// @brief The constant vector in the z dimension (layer dimension).
+    Eigen::VectorXd b_z;
 
     // The following is the solution of the previous iteration of this solver.
     // They are updated at the end of solve() and are used as the starting point
     // for the next call to solve.
     vtr::vector<APBlockId, double> block_x_locs_solved;
     vtr::vector<APBlockId, double> block_y_locs_solved;
+    vtr::vector<APBlockId, double> block_z_locs_solved;
 
     // The following are the legalized solution coming into the analytical solver
     // (other than the first iteration). These are stored to be used as anchor
     // blocks during the solver.
     vtr::vector<APBlockId, double> block_x_locs_legalized;
     vtr::vector<APBlockId, double> block_y_locs_legalized;
+    vtr::vector<APBlockId, double> block_z_locs_legalized;
 
     /// @brief The total number of CG iterations that this solver has performed
     ///        so far. This can be a useful metric for the amount of work the

vpr/src/analytical_place/analytical_solver.h

@@ -653,21 +653,23 @@ static t_flat_pl_loc find_centroid_loc_from_flat_placement(const t_pl_macro& pl_
         // and save the closest of all regions.
         t_flat_pl_loc best_projected_pos = centroid;
         float best_distance = std::numeric_limits<float>::max();
-        VTR_ASSERT_MSG(centroid.layer == 0,
-                       "3D FPGAs not supported for this part of the code yet");
         for (const Region& region : head_pr.get_regions()) {
             const vtr::Rect<int>& rect = region.get_rect();
             // Note: We add 0.999 here since the partition region is in grid
             //       space, so it treats tile positions as having size 0x0 when
             //       they really are 1x1.
             float proj_x = std::clamp<float>(centroid.x, rect.xmin(), rect.xmax() + 0.999);
             float proj_y = std::clamp<float>(centroid.y, rect.ymin(), rect.ymax() + 0.999);
+            float proj_layer = std::clamp<float>(centroid.layer, region.get_layer_range().first,
+                                                                 region.get_layer_range().second + 0.999);
             float dx = std::abs(proj_x - centroid.x);
             float dy = std::abs(proj_y - centroid.y);
-            float dist = dx + dy;
+            float dlayer = std::abs(proj_layer - centroid.layer);
+            float dist = dx + dy + dlayer;
             if (dist < best_distance) {
                 best_projected_pos.x = proj_x;
                 best_projected_pos.y = proj_y;
+                best_projected_pos.layer = proj_layer;
                 best_distance = dist;
             }
         }

vpr/src/place/initial_placement.cpp

@@ -27,6 +27,11 @@ circuit_list_add=mm9b.blif
 circuit_list_add=styr.blif
 circuit_list_add=s953.blif
 
+# Constrain the IOs
+# TODO: Should create a unique config file that tests fixed blocks for 3D AP.
+#       - For now, just add one so we can test the solver effectively.
+circuit_constraint_list_add=(mm9a.blif, constraints=../../../../constraints/mm9a_io_constraint.xml)
+
 # Parse info and how to parse
 parse_file=vpr_fixed_chan_width.txt
 
@@ -42,4 +47,6 @@ script_params_common=-starting_stage vpr -track_memory_usage --analytical_place
 script_params_list_add=--ap_analytical_solver identity --ap_partial_legalizer none
 # Force unrelated clustering on.
 script_params_list_add=--ap_analytical_solver identity --ap_partial_legalizer none --allow_unrelated_clustering on
+# Test that the solver will work with 3D
+script_params_list_add=--ap_partial_legalizer none --allow_unrelated_clustering on