[AP][HotFix] Fixed Bug With Solver Putting Blocks Off-Device

After moving fixed blocks to the center of tiles, there is a very small
chance that blocks go off the device due to rounding. This is such a
small effect that it does not show up locally on my machine, but it
shows up on CI. Clamping the positions of blocks after solving to be
just within the device region.

Author: AlexandreSinger

vpr/src/analytical_place/analytical_solver.cpp

@@ -819,13 +819,22 @@ void B2BSolver::store_solution_into_placement(Eigen::VectorXd& x_soln,
     for (size_t row_id_idx = 0; row_id_idx < num_moveable_blocks_; row_id_idx++) {
         // Since we are capping the number of iterations, the solver may not
         // have enough time to converge on a solution that is on the device.
-        // We just clamp the solution to zero for now.
+        // Set the solution to be within the device grid. To prevent round-off
+        // errors causing the position to move outside of the device, we add a
+        // small buffer (epsilon) to the position.
+        // TODO: Create a helper method to clamp a position to just within the
+        //       device grid.
         // TODO: Should handle this better. If the solution is very negative
         //       it may indicate a bug.
-        if (x_soln[row_id_idx] < 0.0)
-            x_soln[row_id_idx] = 0.0;
-        if (y_soln[row_id_idx] < 0.0)
-            y_soln[row_id_idx] = 0.0;
+        double epsilon = 0.0001;
+        if (x_soln[row_id_idx] < epsilon)
+            x_soln[row_id_idx] = epsilon;
+        if (x_soln[row_id_idx] >= device_grid_width_)
+            x_soln[row_id_idx] = device_grid_width_ - epsilon;
+        if (y_soln[row_id_idx] < epsilon)
+            y_soln[row_id_idx] = epsilon;
+        if (y_soln[row_id_idx] >= device_grid_height_)
+            y_soln[row_id_idx] = device_grid_height_ - epsilon;
 
         APRowId row_id = APRowId(row_id_idx);
         APBlockId blk_id = row_id_to_blk_id_[row_id];