Merge branch 'pair_symmetry' into 'main'

implemented pair_symmetry that uses a LUT to calculate the distances

See merge request course-asl-fastcode26/team70!21

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)
 

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

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 <algorithm>
+#include <cmath>
+#include <fstream>
+#include <iostream>
+#include <math.h>
+#include <random>
+#include <tuple>
+#include <vector>
+
+#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<double> velocity_gen(v0_mean, v0_std_dev);
+  uniform_real_distribution<double> y_gen(0.3, BOARD_WIDTH - 0.3);
+  uniform_real_distribution<double> x_gen_left(2.0, BOARD_LENGTH / 2.0);
+  uniform_real_distribution<double> 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<tuple<int, int, double, double, double, double, int>> samples;
+
+  if (dump_path) {
+    samples.reserve(static_cast<size_t>(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<double> r_ab_x_lut(n_p * n_p, 0.0);
+  std::vector<double> r_ab_y_lut(n_p * n_p, 0.0);
+  std::vector<double> 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;
+}