diff --git a/docs/optimization_soa.md b/docs/optimization_soa.md new file mode 100644 index 0000000..0b61f40 --- /dev/null +++ b/docs/optimization_soa.md @@ -0,0 +1,70 @@ +# Optimization: Struct of Arrays (SoA) + +- **Author**: Linus +- **Predecessor**: variant_inlining_7.cpp +- **File(s)**: variants/variant_inlining_7_SoA.cpp +- **Status**: TBD + +## What this changes + +Replaced the `Pedestrian` struct with parallel `vector` arrays, one +per field (`pos_x`, `pos_y`, `e_x`, `e_y`, `sb_e_x`, `sb_e_y`, `sb_sq`, ...). +Board obstacles are left as AoS since there are only a handful of them. + +Mostly a setup step for AVX2: with SoA the inner ped-ped loop reads +contiguous chunks of `pos_x[j..]`, which is what we'll want for aligned +vector loads. + +## Code (relevant snippet) + +```cpp +vector pos_x, pos_y; +vector sb_sq, sb_e_x, sb_e_y; +vector e_x, e_y; +vector curr_vel_x, curr_vel_y; +// ... +``` + +See `variants/variant_inlining_7_SoA.cpp`. + +## Benchmark + +Conditions: 2 runs, N_ITER=1000, -O3 -march=native -flto. Diff is vs +`variant_inlining_7`. +On my local machine i had an improvement of about 10-15% for low N and about 5% speed up for higher N + +### x86 + +**Machine**: TBD + +**Frequency**: TBD + +| N | W(n) [Flops] | T(n) [Cycles] | Performance [Flops/Cycle] | Diff vs Predecessor | +| ---- | ------------ | ------------- | ------------------------- | ------------------- | +| 50 | | | | | +| 100 | | | | | +| 200 | | | | | +| 500 | | | | | +| 1000 | | | | | + +### ARM (Apple) + +**Machine**: TBD + +**Frequency**: TBD + +| N | W(n) [Flops] | T(n) [Cycles] | Performance [Flops/Cycle] | Diff vs Predecessor | +| ---- | ------------ | ------------- | ------------------------- | ------------------- | +| 50 | | | | | +| 100 | | | | | +| 200 | | | | | +| 500 | | | | | +| 1000 | | | | | + +## Analysis + +No in depth Analysis done, just thought i wanna share it so you can also use it for further optimizations + +## Takeaway + +Layout change, not a performance win by itself. Sets up the AVX2 variant. diff --git a/variants/variant_inlining_7_SoA.cpp b/variants/variant_inlining_7_SoA.cpp new file mode 100644 index 0000000..dc79c77 --- /dev/null +++ b/variants/variant_inlining_7_SoA.cpp @@ -0,0 +1,343 @@ +// # This file uses avx2 +// # This is the first variant and should serve as a base for further avx2 optimizations + +// Okay our first step is to use a SoA instead of an AoS +// We only do SoA for the pedestrian struct, there we wanna optimize such that we access for the ped-ped forces adjacent pedestrians (in the arrays) + +#include "../headers/board.hpp" +#include "../headers/constants.hpp" +#include "../headers/pedestrian_reduced.hpp" + +#include +#include +#include +#include +#include +#include +#include +#include + +#define SEED 42 +#define BOARD_WIDTH 10.0 +#define BOARD_LENGTH 50.0 +#define WALL_EPS 1e-3 +#define BOARD_WIDTH_MINUS_WALL_EPS 9.999 + +#ifndef RANDOM_SEED +#define RANDOM_SEED 0 +#endif + +#ifndef BENCHMARK +#define BENCHMARK 0 +#endif + +using namespace std; + +// we wanna use arrays so we can implement SOA, we create arrays for all the data we need and access +vector pos_x, pos_y; +vector sb_sq; +vector sb_e_x, sb_e_y; +vector e_x, e_y; +vector curr_vel_x, curr_vel_y; +vector w_x, w_y; +vector desired_v0; +vector v_max; +vector destination_x, destination_y; +vector color; + +Pedestrian *init_pedestrians(int n_p) { + +#if RANDOM_SEED + random_device rd; + mt19937 gen(rd()); +#else + mt19937 gen(SEED); +#endif + + normal_distribution velocity_gen(v0_mean, v0_std_dev); + uniform_real_distribution y_gen(0.3, BOARD_WIDTH - 0.3); + uniform_real_distribution x_gen_left(2.0, BOARD_LENGTH / 2.0); + uniform_real_distribution x_gen_right(BOARD_LENGTH / 2.0, BOARD_LENGTH - 2.0); + + // resize all our arrays for this run + pos_x.resize(n_p); + pos_y.resize(n_p); + sb_sq.resize(n_p); + sb_e_x.resize(n_p); + sb_e_y.resize(n_p); + e_x.resize(n_p); + e_y.resize(n_p); + curr_vel_x.resize(n_p); + curr_vel_y.resize(n_p); + w_x.resize(n_p); + w_y.resize(n_p); + desired_v0.resize(n_p); + v_max.resize(n_p); + destination_x.resize(n_p); + destination_y.resize(n_p); + color.resize(n_p); + + 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); + + double dest_x = BOARD_LENGTH + 30.0; // renamed to avoid shadowing destination_x[] + double dest_y = y; // same idea for destination_y[] + + double init_e_x = dest_x - x; + double init_e_y = dest_y - y; + double init_e_norm = sqrt(init_e_x * init_e_x + init_e_y * init_e_y); + double init_e_unit_x = init_e_x / init_e_norm; + double init_e_unit_y = init_e_y / init_e_norm; + + double d_v0; + do { + d_v0 = velocity_gen(gen); + } while (d_v0 <= 0.1); + + double v_m = 1.3 * d_v0; + + color[i] = 0; + pos_x[i] = x; + pos_y[i] = y; + e_x[i] = init_e_unit_x; + e_y[i] = init_e_unit_y; + v_max[i] = v_m; + desired_v0[i] = d_v0; + destination_x[i] = dest_x; + destination_y[i] = dest_y; + + // Fields the Pedestrian constructor would have zero-initialized: + w_x[i] = 0.0; + w_y[i] = 0.0; + curr_vel_x[i] = 0.0; + curr_vel_y[i] = 0.0; + sb_sq[i] = 0.0; + sb_e_x[i] = 0.0; + sb_e_y[i] = 0.0; + } + + for (int i = n_p_half; i < n_p; i++) { + double x = x_gen_right(gen); + double y = y_gen(gen); + + double dest_x = -30; + double dest_y = y; + + double init_e_x = dest_x - x; + double init_e_y = dest_y - y; + double init_e_norm = sqrt(init_e_x * init_e_x + init_e_y * init_e_y); + double init_e_unit_x = init_e_x / init_e_norm; + double init_e_unit_y = init_e_y / init_e_norm; + + double d_v0; + do { + d_v0 = velocity_gen(gen); + } while (d_v0 <= 0.1); + + double v_m = 1.3 * d_v0; + + color[i] = 1; + pos_x[i] = x; + pos_y[i] = y; + e_x[i] = init_e_unit_x; + e_y[i] = init_e_unit_y; + v_max[i] = v_m; + desired_v0[i] = d_v0; + destination_x[i] = dest_x; + destination_y[i] = dest_y; + + // Fields the Pedestrian constructor would have zero-initialized: + w_x[i] = 0.0; + w_y[i] = 0.0; + curr_vel_x[i] = 0.0; + curr_vel_y[i] = 0.0; + sb_sq[i] = 0.0; + sb_e_x[i] = 0.0; + sb_e_y[i] = 0.0; + } + + return nullptr; +} + +Board init_board_without_obstacles() { return Board(BOARD_LENGTH, BOARD_WIDTH, 0, nullptr); } + +int run_simulation(Pedestrian *pedestrians, Board &board, int n_p, int n_iter, const char *dump_path) { + +#if BENCHMARK + (void)dump_path; +#endif + +#if !BENCHMARK + const int dump_interval = 1; + + vector> samples; + + if (dump_path) { + samples.reserve(static_cast(n_iter / dump_interval + 1) * n_p); + + for (int i = 0; i < n_p; i++) { + // Pedestrian &p = pedestrians[i]; + samples.emplace_back(0, i, pos_x[i], pos_y[i], e_x[i], e_y[i], color[i]); + } + } +#endif + + for (int t = 0; t < n_iter; t++) { + + for (int i = 0; i < n_p; i++) { + + double desired_velocity_x = e_x[i] * desired_v0[i]; + double desired_velocity_y = e_y[i] * desired_v0[i]; + + double f_alpha_dt_x = (desired_velocity_x - curr_vel_x[i]) * dt_times_tau_alpha_inv; + double f_alpha_dt_y = (desired_velocity_y - curr_vel_y[i]) * dt_times_tau_alpha_inv; + + for (int j = 0; j < n_p; j++) { + + if (i == j) + continue; + + double r_ab_x = pos_x[i] - pos_x[j]; + double r_ab_y = pos_y[i] - pos_y[j]; + + double r_ab_norm = sqrt(r_ab_x * r_ab_x + r_ab_y * r_ab_y); + + double r_ab2_x = r_ab_x - sb_e_x[j]; + double r_ab2_y = r_ab_y - sb_e_y[j]; + + double r_ab2_norm = sqrt(r_ab2_x * r_ab2_x + r_ab2_y * r_ab2_y); + double r_ab_norm_sum = r_ab_norm + r_ab2_norm; + double two_b_sq = r_ab_norm_sum * r_ab_norm_sum - sb_sq[j]; + double two_b = sqrt(two_b_sq); + double scalar_mult_common = (r_ab_norm_sum / (two_b * r_ab_norm * r_ab2_norm)) * (NEG_V0_AB_div_TWO_SIGMA * exp(two_b * NEG_TWO_SIGMA_INV)); + double scalar_mult_r_ab = scalar_mult_common * r_ab2_norm; + double scalar_mult_r_ab2 = scalar_mult_common * r_ab_norm; + + double f_alpha_beta_neg_x = r_ab_x * scalar_mult_r_ab + r_ab2_x * scalar_mult_r_ab2; + double f_alpha_beta_neg_y = r_ab_y * scalar_mult_r_ab + r_ab2_y * scalar_mult_r_ab2; + + double w_val; + double a = (e_x[i] * f_alpha_beta_neg_x + e_y[i] * f_alpha_beta_neg_y) * cos_phi_inv; + double b_sq = f_alpha_beta_neg_x * f_alpha_beta_neg_x + f_alpha_beta_neg_y * f_alpha_beta_neg_y; + + w_val = dt_neg; + if (a >= 0 && (a * a > b_sq)) { + w_val = c_neg_times_dt; + } + + f_alpha_dt_x = f_alpha_dt_x + f_alpha_beta_neg_x * w_val; + f_alpha_dt_y = f_alpha_dt_y + f_alpha_beta_neg_y * w_val; + } + + for (int k = 0; k < board.n_obstacles; k++) { + + double v1_x = pos_x[i] - board.obstacles[k].start.x; + double v1_y = pos_y[i] - board.obstacles[k].start.y; + + double projection = (v1_x * board.obstacles[k].obstacle_v.x + v1_y * board.obstacles[k].obstacle_v.y) * board.obstacles[k].length_sq_inv; + + if (projection < 0.0) + projection = 0.0; + else if (projection > 1.0) + projection = 1.0; + + double r_aB_x = pos_x[i] - (board.obstacles[k].start.x + board.obstacles[k].obstacle_v.x * projection); + double r_aB_y = pos_y[i] - (board.obstacles[k].start.y + board.obstacles[k].obstacle_v.y * projection); + + double r_aB_norm = sqrt(r_aB_x * r_aB_x + r_aB_y * r_aB_y); + double scalar_mult = (NEG_U0_AB_div_R * exp(r_aB_norm * NEG_R_INV)) / r_aB_norm; + double f_alpha_B_neg_x = r_aB_x * scalar_mult; + double f_alpha_B_neg_y = r_aB_y * scalar_mult; + + double w_val; + double a = (e_x[i] * f_alpha_B_neg_x + e_y[i] * f_alpha_B_neg_y) * cos_phi_inv; + double b_sq = f_alpha_B_neg_x * f_alpha_B_neg_x + f_alpha_B_neg_y * f_alpha_B_neg_y; + + w_val = dt_neg; + if (a >= 0 && (a * a > b_sq)) { + w_val = c_neg_times_dt; + } + + double f_alpha_B_dt_x = f_alpha_B_neg_x * w_val; + double f_alpha_B_dt_y = f_alpha_B_neg_y * w_val; + + f_alpha_dt_x += f_alpha_B_dt_x; + f_alpha_dt_y += f_alpha_B_dt_y; + } + + w_x[i] += f_alpha_dt_x; + w_y[i] += f_alpha_dt_y; + } + + for (int i = 0; i < n_p; i++) { + + double w_norm = sqrt(w_x[i] * w_x[i] + w_y[i] * w_y[i]); + + double correction_factor = min(1.0, v_max[i] / w_norm); + + curr_vel_x[i] = w_x[i] * correction_factor; + curr_vel_y[i] = w_y[i] * correction_factor; + + pos_x[i] = pos_x[i] + curr_vel_x[i] * dt; + pos_y[i] = pos_y[i] + curr_vel_y[i] * dt; + + if (color[i] == 0 && pos_x[i] > (BOARD_LENGTH - 1.5)) { + pos_x[i] = 1.0; + destination_y[i] = pos_y[i]; + w_x[i] = desired_v0[i]; + w_y[i] = 0.0; + curr_vel_x[i] = w_x[i]; + curr_vel_y[i] = w_y[i]; + } + if (color[i] == 1 && pos_x[i] < 1.5) { + pos_x[i] = BOARD_LENGTH - 1.0; + destination_y[i] = pos_y[i]; + w_x[i] = -desired_v0[i]; + w_y[i] = 0.0; + curr_vel_x[i] = w_x[i]; + curr_vel_y[i] = w_y[i]; + } + + pos_y[i] = clamp(pos_y[i], WALL_EPS, BOARD_WIDTH_MINUS_WALL_EPS); + + double ex = destination_x[i] - pos_x[i]; + double ey = destination_y[i] - pos_y[i]; + + double e_norm_inv = 1.0 / sqrt(ex * ex + ey * ey); + + e_x[i] = ex * e_norm_inv; + e_y[i] = ey * e_norm_inv; + + double velocity_norm_sq = curr_vel_x[i] * curr_vel_x[i] + curr_vel_y[i] * curr_vel_y[i]; + + double velocity_norm = sqrt(velocity_norm_sq); + + sb_sq[i] = velocity_norm_sq * delta_t_sq; + + sb_e_x[i] = e_x[i] * (velocity_norm * delta_t); + sb_e_y[i] = e_y[i] * (velocity_norm * delta_t); + +#if !BENCHMARK + if (dump_path && (t % dump_interval == 0)) { + samples.emplace_back(t + 1, i, pos_x[i], pos_y[i], e_x[i], e_y[i], color[i]); + } +#endif + } + } + +#if !BENCHMARK + 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'; + } + } +#endif + + return 0; +}