#include "board.hpp" #include "forces.hpp" #include "math.h" #include "pedestrian.hpp" #include "tsc_x86.h" #include "vector2d.hpp" #include #include #include #include #include #define SEED 42 #define BOARD_WIDTH 10.0 #define BOARD_LENGTH 50.0 #define BOARD_LENGTH_MINUS_ONE BOARD_LENGTH - 1 #define BOARD_LENGTH_MINUS_ONE_POINT_FIVE BOARD_LENGTH - 1.5 #define WALL_EPS 1e-3 #define BOARD_WIDTH_MINUS_WALL_EPS BOARD_WIDTH - WALL_EPS #define BOARD_LENGTH_HALF BOARD_LENGTH / 2 #define BOARD_LENGTH_MINUS_TWO BOARD_LENGTH - 2 #define BOARD_WIDTH_MINUS_ZERO_POINT_THREE BOARD_WIDTH - 0.3 #define BOARD_LENGTH_PLUS_THIRTY BOARD_LENGTH + 30 using namespace std; Pedestrian *init_pedestrians(int n_p) { Pedestrian *P = new Pedestrian[n_p]; // Platform-specific non-deterministic random number generator (if available) // random_device rd; // mt19937 gen(rd()); // Use rd for true randomness mt19937 gen(SEED); // Use fixed seed for reproducibility normal_distribution velocity_gen(v0_mean, v0_std_dev); uniform_real_distribution x_gen_left(2, BOARD_LENGTH_HALF); uniform_real_distribution x_gen_right(BOARD_LENGTH_HALF, BOARD_LENGTH_MINUS_TWO); uniform_real_distribution y_gen(0.3, BOARD_WIDTH_MINUS_ZERO_POINT_THREE); int n_p_half = n_p / 2; for (int i = 0; i < n_p_half; i++) { double x = x_gen_left(gen); double y = y_gen(gen); Vector2d start_pos = Vector2d(x, y); Vector2d destination = Vector2d(BOARD_LENGTH_PLUS_THIRTY, y); Vector2d init_e = destination - start_pos; double init_e_norm = init_e.norm(); Vector2d init_e_unit = init_e / init_e_norm; double desired_v0; // Avoid values are too small since they would make the pedestrians walk backwards do { desired_v0 = velocity_gen(gen); } while (desired_v0 <= 0.1); double v_max = 1.3 * desired_v0; P[i] = Pedestrian(WHITE, init_e_unit * desired_v0, start_pos, init_e_unit, v_max, desired_v0, destination, Vector2d()); } for (int i = n_p_half; i < n_p; i++) { double x = x_gen_right(gen); double y = y_gen(gen); Vector2d start_pos = Vector2d(x, y); Vector2d destination = Vector2d(-30, y); Vector2d init_e = destination - start_pos; double init_e_norm = init_e.norm(); Vector2d init_e_unit = init_e / init_e_norm; double desired_v0; do { desired_v0 = velocity_gen(gen); } while (desired_v0 <= 0.1); double v_max = 1.3 * desired_v0; P[i] = Pedestrian(BLACK, init_e_unit * desired_v0, start_pos, init_e_unit, v_max, desired_v0, destination, Vector2d(0, 0)); } return P; } int main(int argc, const char *argv[]) { // Ensure that arguments are passed if (argc < 3) { printf("Usage: ./sim \n"); printf("Each iteration takes %.2f seconds in the simulation.\n", dt); return 1; } // Parse command-line arguments int n_p = atoi(argv[1]); int n_iter = atoi(argv[2]); if (n_p <= 0) { printf("Error: must be a positive integer, got '%s' instead\n", argv[1]); return 1; } if (n_iter <= 0) { printf("Error: must be a positive integer, got '%s' instead\n", argv[2]); return 1; } Obstacle obs[] = {}; Board board = Board(BOARD_LENGTH, BOARD_WIDTH, 0, obs); // Logic for importing/exporting the simulation data const int dump_interval = 1; const char *dump_path = (argc >= 4) ? argv[3] : nullptr; vector> samples; // t, id, x, y, e.x, e.y, color if (dump_path) { samples.reserve((size_t)n_iter / dump_interval * n_p); } Pedestrian *pedestrians = init_pedestrians(n_p); uint64_t start = start_tsc(); for (int t = 0; t < n_iter; t++) { // Pass 1: Conmpute all the forces given the current state for (int i = 0; i < n_p; i++) { Pedestrian &p = pedestrians[i]; p.f_i.reset(); // # 6 ADDs, 2 DIVs // // $\vec{F}_\alpha(\vec{v}_\alpha, v^0_\alpha \vec{e}_\alpha) = \frac{1}{\tau_\alpha}(v^0_\alpha \vec{e}_\alpha - \vec{v}_\alpha)$ // add_acceleration_term(&p); // # 15 ADDs, 24 MULTs, 8 DIVs, 5 SQRTs, 1 EXP // // $\sum_{\beta} \vec{F}_{\alpha\beta}(\vec{e}_{\alpha}, \vec{r}_{\alpha} - \vec{r}_{\beta})$ // add_repulsive_effects_from_pedestrians(pedestrians, &p, n_p); // # board.n_obstacles * (13 ADDs, 19 MULTs, 4 DIVs, 2 SQRTs, 1 EXP) // // $\sum_{B} \vec{F}_{\alpha B}(\vec{e}_{\alpha}, \vec{r}_{\alpha} - \vec{r}_{B})$ // add_repulsive_effects_from_borders(board, &p); } // Pass 2: Integrate the forces and update the current state for (int i = 0; i < n_p; i++) { Pedestrian &p = pedestrians[i]; // # 2 ADDs, 2 MULTs // // $\frac{d\vec{w_\alpha}}{dt} = \vec{F}_{\alpha}(t)$ // // p.w = p.w + p.f_i * dt; // # 1 ADD, 2 MULTs, 1 SQRT double w_norm = p.w.norm(); // # Assumption for calculating W(n): The "if" statement always evaluates to true. if (w_norm > p.v_max) { // # 2 MULTs, 1 DIV p.w = p.w * (p.v_max / w_norm); } // # 1 ADD, 4 MULTs, 1 DIV, 1 SQRT p.curr_vel = p.w * g(p.v_max, p.w.norm()); // # 2 ADDs, 2 MULTs // // $\vec{r}_i^{t+1} = \vec{r}^t_i + v^t_idt$ // p.curr_pos = p.curr_pos + p.curr_vel * dt; // When a pedestrian reaches the end of the hallway we simply "teleport" the person back to the beginning. // This way, we have a constant flow of pedestrians, and it is easier to see lanes forming. if (p.color == WHITE && p.curr_pos.x > BOARD_LENGTH_MINUS_ONE_POINT_FIVE) { // keep y, reset x p.curr_pos.x = 1.0; p.destination.y = p.curr_pos.y; p.w = Vector2d(p.desired_v0, 0); p.curr_vel = p.w; } if (p.color == BLACK && p.curr_pos.x < 1.5) { p.curr_pos.x = BOARD_LENGTH_MINUS_ONE; p.destination.y = p.curr_pos.y; p.w = Vector2d(-p.desired_v0, 0); p.curr_vel = p.w; } // # 2 ADDs Vector2d e = p.destination - p.curr_pos; // # 1 ADD, 2 MULTs, 1 SQRT double e_norm = e.norm(); // # 2 DIVs p.e = e / e_norm; if (p.curr_pos.y < 0.0) { p.curr_pos.y = WALL_EPS; if (p.curr_vel.y < 0) p.curr_vel.y = 0; if (p.w.y < 0) p.w.y = 0; } if (p.curr_pos.y > BOARD_WIDTH) { p.curr_pos.y = BOARD_WIDTH_MINUS_WALL_EPS; if (p.curr_vel.y > 0) p.curr_vel.y = 0; if (p.w.y > 0) p.w.y = 0; } // Save the data for visualization if (dump_path && (t % dump_interval == 0)) { samples.emplace_back(t, i, p.curr_pos.x, p.curr_pos.y, p.e.x, p.e.y, p.color); } } } long double T = stop_tsc(start); long long add_count_per_iter = n_p * (21 + board.n_obstacles * 13) + n_p * 9; long long mult_count_per_iter = n_p * (24 + board.n_obstacles * 19) + n_p * 14; long long div_count_per_iter = n_p * (10 + board.n_obstacles * 4) + n_p * 4; long long sqrt_count_per_iter = n_p * (5 + board.n_obstacles * 2) + n_p * 3; long long exp_count_per_iter = n_p * (1 + board.n_obstacles * 1); long double W_per_iter = add_count_per_iter * cost_add + mult_count_per_iter * cost_mult + div_count_per_iter * cost_div + sqrt_count_per_iter * cost_sqrt + exp_count_per_iter * cost_exp; long long Q_per_iter = sizeof(Pedestrian) * n_p + sizeof(Obstacle) * board.n_obstacles; // TODO: Refine this long double I = W_per_iter / Q_per_iter; long double W = W_per_iter * n_iter; long double P = W / T; printf("W(n) per iteration: %.2Lf flops\n", W_per_iter); printf("Q(n) per iteration: %Ld bytes\n", Q_per_iter); printf("I(n): %.2Lf flops/byte\n", I); printf("W(n): %.2Lf flops\n", W); printf("T(n): %.2Lf cycles\n", T); printf("P(n): %.2Lf flops/cycle\n", P); // Export the data to a .csv file if (dump_path) { ofstream out(dump_path); out << "time,id,x,y,p.e.x,p.e.y,color\n"; for (auto &[t, id, x, y, e_x, e_y, c] : samples) { out << t << ',' << id << ',' << x << ',' << y << ',' << e_x << ',' << e_y << ',' << c << '\n'; } } delete[] pedestrians; return 0; }