From 045dadba5f87857576e2766d4b99d1303524f8b5 Mon Sep 17 00:00:00 2001 From: smail alijagic Date: Wed, 20 May 2026 10:29:17 +0200 Subject: [PATCH] implemented pair_symmetry that uses a LUT to calculate the distances --- docs/OPTIMIZATIONS.md | 1 + docs/optimization_symmetry.md | 90 ++++++ variants/variant_inlining_7_symmetry_1.cpp | 319 +++++++++++++++++++++ 3 files changed, 410 insertions(+) create mode 100644 docs/optimization_symmetry.md create mode 100644 variants/variant_inlining_7_symmetry_1.cpp diff --git a/docs/OPTIMIZATIONS.md b/docs/OPTIMIZATIONS.md index 58c5e92..5acdb7c 100644 --- a/docs/OPTIMIZATIONS.md +++ b/docs/OPTIMIZATIONS.md @@ -35,6 +35,7 @@ System Version: IdeaPad Slim 5 14AKP10 | --- | --------------------------------------- | ---------------- | -------------- | ------------------------- | ------ | | 0 | [Baseline](optimization_baseline.md) | 1'058'400'000.00 | 850'352'900.00 | 1.24 | | | 1 | [Inlining](optimization_inlining.md) | 1'058'400'000.00 | 756'088'260.00 | 1.40 | Elliot | +| 2 | [Symmetry](optimization_symmetry.md) | | | | Smail | ### ARM (Apple) diff --git a/docs/optimization_symmetry.md b/docs/optimization_symmetry.md new file mode 100644 index 0000000..b30516a --- /dev/null +++ b/docs/optimization_symmetry.md @@ -0,0 +1,90 @@ +# Optimization: Inlining + +- **Author**: Smail +- **Predecessor**: variant_inlining_7.cpp +- **File(s)**: variants/variant_inlining_7_symmetry_1.cpp +- **Status**: TBA + +## What this changes + +Instead of calculating the distance and norm vector between two pedestrians everytime, +we created a LUT that only calculates the distances once and r_a_b_norm (with expensive sqrt flop `dx`, `dy`, `norm`). +The forces are somewhat symmetric, however it would still require a lot of calculations, +maybe this second symmetry optimization can be done at a later stage. + +When i > j we need the opposite vector which is $curr * -1$. + + +## Code (relevant snippet) + +TBD - see `variants/variant_inlining_7_symmetry_1.cpp` for the final version, and the +individual file headers for the incremental steps. + +## Benchmark + +Conditions: single run (TODO: switch to min-of-N), N_ITER=1000, +-O3 -march=native -flto. Predecessor reference for the same config is the +baseline row. + +### x86 + +**Machine**: + +``` +Processors: 16 x AMD Ryzen AI 7 350 w/ Radeon 860M +Memory: 32 GiB of RAM (30.6 GiB usable) +Graphics Processor: AMD Radeon 860M Graphics +Manufacturer: LENOVO +Product Name: 83HX +System Version: IdeaPad Slim 5 14AKP10 +``` + +**Frequency**: 2 GHz + +Existing single-point measurement (N unspecified, kept from the previous +OPTIMIZATIONS.md; W matches roughly N=120 at N_ITER=1000): + +| Variant | W(n) [Flops] | T(n) [Cycles] | Performance [Flops/Cycle] | +| -------- | ---------------- | -------------- | ------------------------- | +| Baseline | 1'058'400'000.00 | 850'352'900.00 | 1.24 | +| Inlining | 1'058'400'000.00 | 756'088'260.00 | 1.40 | +| Symmetry | | | | + +Inlining is about 12.9% faster on this point. A full N sweep with min-of-3 is TODO. + +Full sweep (TODO): + +| 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 + +Speedup likely comes mainly from halving the number of `sqrt` flops. + + +## Takeaway + +TBD diff --git a/variants/variant_inlining_7_symmetry_1.cpp b/variants/variant_inlining_7_symmetry_1.cpp new file mode 100644 index 0000000..6459072 --- /dev/null +++ b/variants/variant_inlining_7_symmetry_1.cpp @@ -0,0 +1,319 @@ +// # Use symmetrical properties to reduce flop count +// # Changes: initialized a LUT to only compute r_a_b_norm once +// # Predecessor: variant_inlining_7.cpp + +#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; + +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); + + Pedestrian *P = new Pedestrian[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 start_pos_x = x; + double start_pos_y = y; + + double destination_x = BOARD_LENGTH + 30.0; + double destination_y = y; + + double init_e_x = destination_x - start_pos_x; + double init_e_y = destination_y - start_pos_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 desired_v0; + do { + desired_v0 = velocity_gen(gen); + } while (desired_v0 <= 0.1); + + double v_max = 1.3 * desired_v0; + + P[i] = Pedestrian(0, 0, 0, start_pos_x, start_pos_y, init_e_unit_x, init_e_unit_y, v_max, desired_v0, destination_x, destination_y); + } + + for (int i = n_p_half; i < n_p; i++) { + double x = x_gen_right(gen); + double y = y_gen(gen); + + double start_pos_x = x; + double start_pos_y = y; + double destination_x = -30; + double destination_y = y; + + double init_e_x = destination_x - start_pos_x; + double init_e_y = destination_y - start_pos_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 desired_v0; + do { + desired_v0 = velocity_gen(gen); + } while (desired_v0 <= 0.1); + + double v_max = 1.3 * desired_v0; + + P[i] = Pedestrian(1, 0, 0, start_pos_x, start_pos_y, init_e_unit_x, init_e_unit_y, v_max, desired_v0, destination_x, destination_y); + } + + return P; +} + +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, p.curr_pos_x, p.curr_pos_y, p.e_x, p.e_y, p.color); + } + } +#endif + + // here we have real (simple) symmetry + std::vector r_ab_x_lut(n_p * n_p, 0.0); + std::vector r_ab_y_lut(n_p * n_p, 0.0); + std::vector r_ab_norm_lut(n_p * n_p, 0.0); + // use NAME[i * n_p + j] + + for (int t = 0; t < n_iter; t++) { + + // get all distances first + for (int i = 0; i < n_p; i++) { + for (int j = i + 1; j < n_p; j++) { + double dx = pedestrians[i].curr_pos_x - pedestrians[j].curr_pos_x; + double dy = pedestrians[i].curr_pos_y - pedestrians[j].curr_pos_y; + double norm = sqrt(dx * dx + dy * dy); + r_ab_x_lut[i * n_p + j] = dx; + r_ab_y_lut[i * n_p + j] = dy; + r_ab_norm_lut[i * n_p + j] = norm; + } + } + + for (int i = 0; i < n_p; i++) { + Pedestrian &p = pedestrians[i]; + + double desired_velocity_x = p.e_x * p.desired_v0; + double desired_velocity_y = p.e_y * p.desired_v0; + + double f_alpha_dt_x = (desired_velocity_x - p.curr_vel_x) * dt_times_tau_alpha_inv; + double f_alpha_dt_y = (desired_velocity_y - p.curr_vel_y) * dt_times_tau_alpha_inv; + + // force between pedestrians + for (int j = 0; j < n_p; j++) { + if (i == j) + continue; + + // symmetry + //double r_ab_x = p.curr_pos_x - pedestrians[j].curr_pos_x; + //double r_ab_y = p.curr_pos_y - pedestrians[j].curr_pos_y; + //double r_ab_norm = sqrt(r_ab_x * r_ab_x + r_ab_y * r_ab_y); + + double r_ab_x, r_ab_y, r_ab_norm; + if (i < j) { + r_ab_x = r_ab_x_lut[i * n_p + j]; + r_ab_y = r_ab_y_lut[i * n_p + j]; + r_ab_norm = r_ab_norm_lut[i * n_p + j]; + } else { + // other direction + r_ab_x = -1 * r_ab_x_lut[j * n_p + i]; + r_ab_y = -1 * r_ab_y_lut[j * n_p + i]; + r_ab_norm = r_ab_norm_lut[j * n_p + i]; + } + + // ---- + + double r_ab2_x = r_ab_x - pedestrians[j].s_b_e_x; + double r_ab2_y = r_ab_y - pedestrians[j].s_b_e_y; + + 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 - pedestrians[j].s_b_sq; + 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 = (p.e_x * f_alpha_beta_neg_x + p.e_y * 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; + } + + // force between pedestrian and obstacles + for (int k = 0; k < board.n_obstacles; k++) { + + double v1_x = p.curr_pos_x - board.obstacles[k].start.x; + double v1_y = p.curr_pos_y - 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 = p.curr_pos_x - (board.obstacles[k].start.x + board.obstacles[k].obstacle_v.x * projection); + double r_aB_y = p.curr_pos_y - (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 = (p.e_x * f_alpha_B_neg_x + p.e_y * 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; + } + + p.w_x += f_alpha_dt_x; + p.w_y += f_alpha_dt_y; + } + + // update the positions etc. + for (int i = 0; i < n_p; i++) { + Pedestrian &p = pedestrians[i]; + + double w_norm = sqrt(p.w_x * p.w_x + p.w_y * p.w_y); + + double correction_factor = min(1.0, p.v_max / w_norm); + + p.curr_vel_x = p.w_x * correction_factor; + p.curr_vel_y = p.w_y * correction_factor; + + p.curr_pos_x = p.curr_pos_x + p.curr_vel_x * dt; + p.curr_pos_y = p.curr_pos_y + p.curr_vel_y * dt; + + if (p.color == 0 && p.curr_pos_x > (BOARD_LENGTH - 1.5)) { + p.curr_pos_x = 1.0; + p.destination_y = p.curr_pos_y; + p.w_x = p.desired_v0; + p.w_y = 0.0; + p.curr_vel_x = p.w_x; + p.curr_vel_y = p.w_y; + } + if (p.color == 1 && p.curr_pos_x < 1.5) { + p.curr_pos_x = BOARD_LENGTH - 1.0; + p.destination_y = p.curr_pos_y; + p.w_x = -p.desired_v0; + p.w_y = 0.0; + p.curr_vel_x = p.w_x; + p.curr_vel_y = p.w_y; + } + + p.curr_pos_y = clamp(p.curr_pos_y, WALL_EPS, BOARD_WIDTH_MINUS_WALL_EPS); + + double e_x = p.destination_x - p.curr_pos_x; + double e_y = p.destination_y - p.curr_pos_y; + + double e_norm_inv = 1.0 / sqrt(e_x * e_x + e_y * e_y); + + p.e_x = e_x * e_norm_inv; + p.e_y = e_y * e_norm_inv; + + double velocity_norm_sq = p.curr_vel_x * p.curr_vel_x + p.curr_vel_y * p.curr_vel_y; + + double velocity_norm = sqrt(velocity_norm_sq); + + p.s_b_sq = velocity_norm_sq * delta_t_sq; + + p.s_b_e_x = p.e_x * (velocity_norm * delta_t); + p.s_b_e_y = p.e_y * (velocity_norm * delta_t); + +#if !BENCHMARK + if (dump_path && (t % dump_interval == 0)) { + samples.emplace_back(t + 1, i, p.curr_pos_x, p.curr_pos_y, p.e_x, p.e_y, p.color); + } +#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; +}