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Linus/one baseline file

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This commit is contained in:
Linus Baumberger
2026-05-17 16:17:00 +02:00
committed by salijagic
parent f294167b08
commit 1c5839e1d6
9 changed files with 240320 additions and 160 deletions
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.gitignore
+7 -1
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@@ -7,11 +7,17 @@
*.csv
*.gif
*.mp4
!reference/*.csv
# Benchmark outputs (keep .gitkeep, ignore results)
benchmarks/*
!benchmarks/.gitkeep
# Compiled binaries
main
main_*
sizes
# Editor files
.vscode
.DS_Store
Makefile
+26 -6
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@@ -45,16 +45,21 @@ endif
# cross-file optimizations such as function inlining
CXXFLAGS := -O3 -march=native -std=c++23 -Wall -Wextra -flto
SRC := main.cpp forces.cpp social_force_baseline.cpp
VARIANT ?= baseline
VARIANT_SRC := variant_$(VARIANT).cpp
SRC := main.cpp $(VARIANT_SRC)
HEADERS := board.hpp forces.hpp pedestrian.hpp vector2d.hpp constants.hpp social_force.hpp
TEST_SRC := test_vector2d.cpp test_board.cpp test_forces.cpp forces.cpp
TEST_SRC := test_vector2d.cpp test_board.cpp test_forces.cpp $(VARIANT_SRC)
TEST_TARGET := run_tests
TEST_LIBS := -lgtest -lgtest_main -pthread
TARGET := main
TARGET := main_$(VARIANT)
SIZES_TARGET := sizes
# Default simulation parameters and output files.
# These can be overridden from the make command line; see examples above.
N_P ?= 60 # Default number of pedestrians.
@@ -70,7 +75,11 @@ RANDOM_SEED ?= 0
# Pass random-seeding mode to the C++ code.
CXXFLAGS += -DRANDOM_SEED=$(RANDOM_SEED)
.PHONY: all main run bench run-bench video sizes asm test clean clean-all
# Benchmark suite parameters.
BENCH_SIZES ?= 50 100 200 500 1000 2000 5000 10000
BENCH_ITER ?= 1000
.PHONY: all main run bench run-bench bench-suite video sizes asm test clean clean-all
all: main
@@ -91,6 +100,17 @@ bench: clean
run-bench: bench
$(SUDO_BENCH) ./$(TARGET) $(N_P) $(N_ITER)
# make bench-suite : compile once and run benchmarks across multiple pedestrian counts.
# Results are printed to stdout; redirect to a file to save them.
# make bench-suite > benchmarks/baseline.txt
# make bench-suite VARIANT=v1_cutoff BENCH_SIZES="100 500 1000" > benchmarks/v1_cutoff.txt
bench-suite: bench
@for n in $(BENCH_SIZES); do \
echo "=== N_P=$$n N_ITER=$(BENCH_ITER) ==="; \
$(SUDO_BENCH) ./$(TARGET) $$n $(BENCH_ITER); \
echo ""; \
done
# make video : compile the code, run the simulation, and generate the video.
video: run
python visualization.py $(CSV) $(MP4)
@@ -105,14 +125,14 @@ test: clean
./$(TEST_TARGET)
# make asm : compile and generate assembly files.
asm: clean main.s forces.s social_force_baseline.s
asm: clean main.s variant_$(VARIANT).s
%.s: %.cpp $(HEADERS)
$(CXX) -O3 -march=native -std=c++23 -Wall -Wextra -DRANDOM_SEED=$(RANDOM_SEED) -S $< -o $@
# make clean : delete generated files from previous builds.
clean:
rm -f $(TARGET) $(SIZES_TARGET) $(TEST_TARGET) *.o *.s
rm -f main_* $(SIZES_TARGET) $(TEST_TARGET) *.o *.s
# make clean-all : delete all generated files from previous builds and runs.
# WARNING: this deletes all *.csv and *.mp4 files in this directory.
README.md
+77 -7
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@@ -77,6 +77,31 @@ make run-bench
Compiles and runs benchmark measurements.
All build commands accept a `VARIANT` parameter to select an optimization variant:
```bash
make run-bench VARIANT=v1_cutoff N_P=100 N_ITER=10000
```
The default is `VARIANT=baseline`. Each variant compiles its own binary (`main_baseline`, `main_v1_cutoff`, etc.).
```bash
make bench-suite
```
Compiles once and runs benchmarks across multiple pedestrian counts (default: 50, 100, 200, 500, 1000, 2000, 5000, 10000 with 1000 iterations each). Redirect output to save results:
```bash
make bench-suite > benchmarks/baseline.txt
make bench-suite VARIANT=v1_cutoff > benchmarks/v1_cutoff.txt
```
Both `BENCH_SIZES` and `BENCH_ITER` can be overridden:
```bash
make bench-suite BENCH_SIZES="100 500 1000" BENCH_ITER=500
```
```bash
make test
```
@@ -121,6 +146,7 @@ N_ITER=4000
CSV=positions.csv
MP4=simulation.mp4
RANDOM_SEED=0
VARIANT=baseline
```
They can be overridden from the shell. Parameters can be provided selectively and in any order.
@@ -170,7 +196,7 @@ make main
This produces the executable:
```text
main
main_baseline (or main_<variant>)
```
The Makefile uses the following compiler flags:
@@ -202,13 +228,16 @@ This compiles the code and runs the simulation with the default parameters. It p
You can also run the executable manually after compiling:
```bash
./main <number_of_pedestrians> <number_of_iterations> [csv_output_path]
./main_baseline <number_of_pedestrians> <number_of_iterations> [csv_output_path]
./main_<variant> <number_of_pedestrians> <number_of_iterations> [csv_output_path]
```
Example:
```bash
./main 60 4000 positions.csv
./main_baseline 60 4000 positions.csv
./main_<variant> 60 4000 positions.csv
```
The third argument is optional. If it is provided, simulation states are written to the given CSV file.
@@ -292,9 +321,50 @@ make run-bench N_P=100 N_ITER=5000
```
The benchmark output includes estimated work, operational intensity, measured cycles, and estimated performance in flops per cycle.
---
## Optimization Variants
The project supports multiple optimization variants through the `VARIANT` Makefile parameter. Each variant provides its own implementation of the force computations and simulation loop while sharing the same interface, benchmark harness, and test suite.
The default variant is `baseline`:
```bash
make run-bench # uses baseline
make run-bench VARIANT=baseline # equivalent
make run-bench VARIANT=v1_cutoff # uses a different variant
```
### File naming convention
Each variant consists of a single file in the project root:
```bash
variant_<name>.cpp # force computations and simulation loop
```
The file must implement the interfaces defined in `forces.hpp` and `social_force.hpp`. The baseline implementation is `variant_baseline.cpp`.
### Creating a new variant
1. Copy the baseline file:
```text
cp variant_baseline.cpp variant_v1_cutoff.cpp
```
2. Edit the new file with your optimization.
3. Build and test:
```bash
make test VARIANT=v1_cutoff
make run-bench VARIANT=v1_cutoff N_P=100 N_ITER=10000
```
### Verifying correctness
A reference CSV is stored in reference/baseline_n60_i4000.csv. To verify that a variant produces the same simulation output:
```bash
make run VARIANT=v1_cutoff N_P=60 N_ITER=4000 CSV=test_output.csv
diff reference/baseline_n60_i4000.csv test_output.csv
```
If the variant changes numerical results (e.g., distance cutoff skipping negligible forces), use a tolerance-based comparison instead of exact diff and justify the deviation.
---
## Tests
Run all unit tests with:
@@ -311,7 +381,7 @@ The test target compiles and runs the unit tests for the simulation components.
## Assembly generation
To generate assembly files:
To generate assembly files for the currently selected VARIANT:
```bash
make asm
@@ -362,7 +432,7 @@ make clean
This deletes files such as:
```text
main
main_*
sizes
run_tests
*.o
@@ -378,7 +448,7 @@ make clean-all
This deletes:
```text
main
main_*
sizes
run_tests
*.o
benchmarks/.gitkeep
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forces.cpp
-140
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@@ -1,140 +0,0 @@
#include "forces.hpp"
#include "constants.hpp"
#include <math.h>
// Flop count: 2 ADDs, 5 MULTs, 1 SQRT
double w(Vector2d e, Vector2d f) {
if (e.dot(f) >= f.norm() * cos_phi)
return dt_neg;
else
return c_neg_times_dt;
}
// Flop count: 2 ADDs, 4 MULTs
Vector2d acceleration_term_dt(const Pedestrian &alpha) {
// # 2 MULTs
Vector2d desired_velocity = alpha.e * alpha.desired_v0;
Vector2d actual_velocity = alpha.curr_vel;
// # 2 ADDs, 2 MULTs
Vector2d f_alpha_0_dt = (desired_velocity - actual_velocity) * dt_times_tau_alpha_inv;
return f_alpha_0_dt;
}
// Flop count: 12 ADDs, 23 MULTs, 1 DIV, 4 SQRTs, 1 EXP
Vector2d pedestrian_repulsion_dt(const Pedestrian &alpha, const Pedestrian &beta) {
// # 2 ADDs
// $\vec{r}_{\alpha\beta}$
Vector2d r_ab = alpha.curr_pos - beta.curr_pos;
// # 1 ADD, 2 MULTs, 1 SQRT
// $\Arrowvert \vec{r}_{\alpha \beta} \Arrowvert$
double r_ab_norm = r_ab.norm();
r_ab_norm = r_ab_norm > EPS ? r_ab_norm : EPS; // Avoid division by zero
// $v_\beta \Delta t \vec{e}_\beta$
Vector2d s_b_e = beta.s_b_e;
// # 2 ADDs
// $\vec{r}_{\alpha\beta} - \vec{v}_{\beta}\varDelta_{t}\vec{e}_{\beta}$
Vector2d r_ab2 = r_ab - s_b_e;
// # 1 ADD, 2 MULTs, 1 SQRT
// $\Arrowvert \vec{r}_{\alpha \beta} - v_\beta \Delta t \vec{e}_\beta \Arrowvert$
double r_ab2_norm = r_ab2.norm();
r_ab2_norm = r_ab2_norm > EPS ? r_ab2_norm : EPS; // Avoid division by zero
// # 1 ADD
// $\Arrowvert \vec{r}_{\alpha \beta} \Arrowvert + \Arrowvert \vec{r}_{\alpha \beta} - v_\beta \Delta t \vec{e}_\beta \Arrowvert$
double r_ab_norm_sum = r_ab_norm + r_ab2_norm;
// # 1 ADD, 1 MULTs, 1 SQRT
//
// $2b = \sqrt{(\Arrowvert \vec{r}_{\alpha \beta} \Arrowvert + \Arrowvert \vec{r}_{\alpha \beta} - v_\beta \Delta t \vec{e}_\beta \Arrowvert)^2 - (v_\beta \Delta t)^2}$
//
double two_b_sq = r_ab_norm_sum * r_ab_norm_sum - beta.s_b_sq;
two_b_sq = two_b_sq > EPS_SQ ? two_b_sq : EPS_SQ; // Avoid sqrt of negative and avoid division by zero
double two_b = sqrt(two_b_sq);
// # 5 MULTs, 1 DIV, 1 EXP
//
// $\frac{-V^0_{\alpha\beta}}{2\sigma}\,e^{-b/\sigma}\,\frac{\Arrowvert \vec{r}_{\alpha \beta} \Arrowvert + \Arrowvert \vec{r}_{\alpha \beta} - v_\beta \Delta t \vec{e}_\beta \Arrowvert}{2b\,\Arrowvert \vec{r}_{\alpha \beta} \Arrowvert\,\Arrowvert \vec{r}_{\alpha \beta} - v_\beta \Delta t \vec{e}_\beta \Arrowvert}$
//
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));
// # 1 MULT
//
// $\frac{-V^0_{\alpha\beta}}{2\sigma}\,e^{-b/\sigma}\,\frac{\Arrowvert \vec{r}_{\alpha \beta} \Arrowvert + \Arrowvert \vec{r}_{\alpha \beta} - v_\beta \Delta t \vec{e}_\beta \Arrowvert}{2b\,\Arrowvert \vec{r}_{\alpha \beta} \Arrowvert}$
//
double scalar_mult_r_ab = scalar_mult_common * r_ab2_norm;
// # 1 MULT
//
// $\frac{-V^0_{\alpha\beta}}{2\sigma}\,e^{-b/\sigma}\,\frac{\Arrowvert \vec{r}_{\alpha \beta} \Arrowvert + \Arrowvert \vec{r}_{\alpha \beta} - v_\beta \Delta t \vec{e}_\beta \Arrowvert}{2b\,\Arrowvert \vec{r}_{\alpha \beta} - v_\beta \Delta t \vec{e}_\beta \Arrowvert}$
//
double scalar_mult_r_ab2 = scalar_mult_common * r_ab_norm;
// # 2 ADDs, 4 MULTs
//
// $\vec{-f}_{\alpha \beta}(\vec{r}_{\alpha \beta}) = \frac{-V^0_{\alpha \beta}}{2\sigma}e^{-b / \sigma} 2\grad_{\vec{r}_{\alpha \beta}}b $
//
//
// $= \frac{-V^0_{\alpha\beta}}{2\sigma}\,e^{-b/\sigma}\,\frac{\Arrowvert \vec{r}_{\alpha \beta} \Arrowvert + \Arrowvert \vec{r}_{\alpha \beta} - v_\beta \Delta t \vec{e}_\beta \Arrowvert}{2b\,\Arrowvert \vec{r}_{\alpha \beta} \Arrowvert}\,\vec{r}_{\alpha \beta} + \frac{-V^0_{\alpha\beta}}{2\sigma}\,e^{-b/\sigma}\,\frac{\Arrowvert \vec{r}_{\alpha \beta} \Arrowvert + \Arrowvert \vec{r}_{\alpha \beta} - v_\beta \Delta t \vec{e}_\beta \Arrowvert}{2b\,\Arrowvert \vec{r}_{\alpha \beta} - v_\beta \Delta t \vec{e}_\beta \Arrowvert}\,(\vec{r}_{\alpha \beta} - v_\beta \Delta t \vec{e}_\beta)$
//
//
//
// $2\grad_{\vec{r}_{\alpha \beta}}b = \frac{(\Arrowvert \vec{r}_{\alpha \beta} \Arrowvert + \Arrowvert \vec{r}_{\alpha \beta} - v_\beta \Delta t \vec{e}_\beta \Arrowvert)(\frac{\vec{r}_{\alpha \beta}}{\Arrowvert \vec{r}_{\alpha \beta} \Arrowvert} + \frac{\vec{r}_{\alpha \beta} - v_\beta \Delta t \vec{e}_\beta}{\Arrowvert \vec{r}_{\alpha \beta} - v_\beta \Delta t \vec{e}_\beta \Arrowvert})}{2b}$
//
//
// $= \frac{\Arrowvert \vec{r}_{\alpha \beta} \Arrowvert + \Arrowvert \vec{r}_{\alpha \beta} - v_\beta Delta t \vec{e}_\beta \Arrowvert}{2b\,\Arrowvert \vec{r}_{\alpha \beta} \Arrowvert}\,\vec{r}_{\alpha \beta} + \frac{\Arrowvert \vec{r}_{\alpha \beta} \Arrowvert + \Arrowvert \vec{r}_{\alpha \beta} - v_\beta \Delta t \vec{e}_\beta \Arrowvert}{2b\,\Arrowvert \vec{r}_{\alpha \beta} - v_\beta \Delta t \vec{e}_\beta \Arrowvert}\,(\vec{r}_{\alpha \beta} - v_\beta \Delta t \vec{e}_\beta)$
//
//
Vector2d f_alpha_beta_neg = r_ab * scalar_mult_r_ab + r_ab2 * scalar_mult_r_ab2;
// # 2 ADDs, 7 MULTs, 1 SQRT
//
// $\vec{F}_{\alpha\beta}(\vec{e}_{\alpha}, \vec{r}_{\alpha \beta}).dt = w(\vec{e}_{\alpha}, -\vec{f}_{\alpha\beta}(\vec{r}_{\alpha \beta})).\vec{f}_{\alpha\beta}(\vec{r}_{\alpha \beta}).dt$
//
Vector2d f_alpha_beta_dt = f_alpha_beta_neg * w(alpha.e, f_alpha_beta_neg);
return f_alpha_beta_dt;
}
// Flop count: 10 ADDs, 18 MULTs, 1 DIVs, 2 SQRTs, 1 EXP
Vector2d obstacle_repulsion_dt(const Pedestrian &alpha, const Obstacle &B) {
// # 7 ADDs, 5 MULTs
// $\vec{r}_{\alpha B}$
Vector2d r_aB = alpha.curr_pos - B.find_nearest_obstacle_point(alpha.curr_pos);
// # 1 ADD, 2 MULTs, 1 SQRT
// $\Arrowvert \vec{r}_{\alpha B} \Arrowvert$
double r_aB_norm = r_aB.norm();
r_aB_norm = r_aB_norm > EPS ? r_aB_norm : EPS; // Avoid division by zero
// # 2 MULTs, 1 DIV, 1 EXP
//
// $\frac{-U^0_{\alpha B}}{R} e^{- \Arrowvert \vec{r}_{\alpha B} \Arrowvert / R}$
//
double scalar_mult = (NEG_U0_AB_div_R * exp(r_aB_norm * NEG_R_INV)) / r_aB_norm;
// # 2 MULTs
//
// $-\vec{F}_{\alpha B}(\vec{r}_{\alpha B}) = \frac{-U^0_{\alpha B}}{R} e^{- \Arrowvert \vec{r}_{\alpha B} \Arrowvert / R} \frac{\vec{r}_{\alpha B}}{\Arrowvert \vec{r}_{\alpha B} \Arrowvert}$
//
Vector2d f_alpha_B_neg = r_aB * scalar_mult;
// # 2 ADDs, 7 MULTs, 1 SQRT
//
// $\vec{F}_{\alpha B}(\vec{e}_{\alpha}, \vec{r}_{\alpha B}).dt = w(\vec{e}_{\alpha}, -\vec{F}_{\alpha B}(\vec{r}_{\alpha B})).\vec{F}_{\alpha B}(\vec{r}_{\alpha B}).dt$
//
Vector2d f_alpha_B_dt = f_alpha_B_neg * w(alpha.e, f_alpha_B_neg);
return f_alpha_B_dt;
}
forces.hpp
+2 -2
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@@ -70,7 +70,7 @@ Vector2d acceleration_term_dt(const Pedestrian &alpha);
// - $\vec{r}_{\alpha \beta} = \vec{r}_\alpha - \vec{r}_\beta$ is the vector from beta's position to alpha's position,
// - $\vec{e}_\alpha$ is the desired direction of pedestrian alpha,
//
// - $\vec{f}_{\alpha\beta}(\vec{r}_{\alpha \beta}) = -\nabla_{\vec{r}_{\alpha\beta}} V_{\alpha\beta}\left[b(\vec{r}_{\alpha\beta})\right]$ is the repulsive effect from beta on alpha (The expanded formula details are given in the code comments given inside the function's implementation in forces.cpp),
// - $\vec{f}_{\alpha\beta}(\vec{r}_{\alpha \beta}) = -\nabla_{\vec{r}_{\alpha\beta}} V_{\alpha\beta}\left[b(\vec{r}_{\alpha\beta})\right]$ is the repulsive effect from beta on alpha (The expanded formula details are given in the code comments given inside the function's implementation in variants_baseline.cpp),
//
// - $w(\vec{e}_{\alpha}, -\vec{f}_{\alpha\beta}(\vec{r}_{\alpha \beta}))$ the direction-dependent perception weighting function, for which the formula is detailed in the w() function above.
//
@@ -94,7 +94,7 @@ Vector2d pedestrian_repulsion_dt(const Pedestrian &alpha, const Pedestrian &beta
// - $\vec{r}_{\alpha B} = \vec{r}_\alpha - \vec{r}^{\,\alpha}_B$ is the vector from the closest point on obstacle B (i.e., $\vec{r}^{\,\alpha}_B$) to pedestrian alpha's position,
// - $\vec{e}_\alpha$ is the desired direction of pedestrian alpha,
//
// - $\vec{F}_{\alpha B}(\vec{r}_{\alpha B}) = -\nabla_{\vec{r}_{\alpha B}} U_{\alpha B}(||\vec{r}_{\alpha B}||)$ is the repulsive effect from obstacle B on alpha (The expanded formula details are given in the code comments given inside the function's implementation in forces.cpp),
// - $\vec{F}_{\alpha B}(\vec{r}_{\alpha B}) = -\nabla_{\vec{r}_{\alpha B}} U_{\alpha B}(||\vec{r}_{\alpha B}||)$ is the repulsive effect from obstacle B on alpha (The expanded formula details are given in the code comments given inside the function's implementation in variant_baseline.cpp),
//
// - $w(\vec{e}_{\alpha}, -\vec{F}_{\alpha B}(\vec{r}_{\alpha B}))$ the direction-dependent perception weighting function, for which the formula is detailed in the w() function above.
//
reference/baseline_n60_i4000.csv
+240061
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File diff suppressed because it is too large Load Diff
test_forces.cpp
+1 -1
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@@ -1,5 +1,5 @@
// =============================================================================
// Tests for forces.cpp
// Tests for forces.hpp
// =============================================================================
#include "board.hpp"
social_force_baseline.cpp → variant_baseline.cpp
+146 -3
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@@ -1,3 +1,8 @@
// This file is merged from the forces.cpp and social_forces_baseline.cpp
// The goal is that we from now on only have one file as our baseline
// This should make it more easy in the future to implement optimizations
// Our naming convention from now on is: variant_<variant_name>.cpp (Please make sure to keep that consistent, otherwise our Makefile wont work anymore)
#include "board.hpp"
#include "constants.hpp"
#include "forces.hpp"
@@ -9,29 +14,167 @@
#include <cmath>
#include <fstream>
#include <iostream>
#include <math.h> // keep — forces code uses unqualified sqrt/exp
#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
// Fixed seeding is used by default to make simulations reproducible.
#define RANDOM_SEED 0
#endif
#ifndef BENCHMARK
// Benchmarking is disabled by default.
#define BENCHMARK 0
#endif
using namespace std;
// forces.cpp
// Flop count: 2 ADDs, 5 MULTs, 1 SQRT
double w(Vector2d e, Vector2d f) {
if (e.dot(f) >= f.norm() * cos_phi)
return dt_neg;
else
return c_neg_times_dt;
}
// Flop count: 2 ADDs, 4 MULTs
Vector2d acceleration_term_dt(const Pedestrian &alpha) {
// # 2 MULTs
Vector2d desired_velocity = alpha.e * alpha.desired_v0;
Vector2d actual_velocity = alpha.curr_vel;
// # 2 ADDs, 2 MULTs
Vector2d f_alpha_0_dt = (desired_velocity - actual_velocity) * dt_times_tau_alpha_inv;
return f_alpha_0_dt;
}
// Flop count: 12 ADDs, 23 MULTs, 1 DIV, 4 SQRTs, 1 EXP
Vector2d pedestrian_repulsion_dt(const Pedestrian &alpha, const Pedestrian &beta) {
// # 2 ADDs
// $\vec{r}_{\alpha\beta}$
Vector2d r_ab = alpha.curr_pos - beta.curr_pos;
// # 1 ADD, 2 MULTs, 1 SQRT
// $\Arrowvert \vec{r}_{\alpha \beta} \Arrowvert$
double r_ab_norm = r_ab.norm();
r_ab_norm = r_ab_norm > EPS ? r_ab_norm : EPS; // Avoid division by zero
// $v_\beta \Delta t \vec{e}_\beta$
Vector2d s_b_e = beta.s_b_e;
// # 2 ADDs
// $\vec{r}_{\alpha\beta} - \vec{v}_{\beta}\varDelta_{t}\vec{e}_{\beta}$
Vector2d r_ab2 = r_ab - s_b_e;
// # 1 ADD, 2 MULTs, 1 SQRT
// $\Arrowvert \vec{r}_{\alpha \beta} - v_\beta \Delta t \vec{e}_\beta \Arrowvert$
double r_ab2_norm = r_ab2.norm();
r_ab2_norm = r_ab2_norm > EPS ? r_ab2_norm : EPS; // Avoid division by zero
// # 1 ADD
// $\Arrowvert \vec{r}_{\alpha \beta} \Arrowvert + \Arrowvert \vec{r}_{\alpha \beta} - v_\beta \Delta t \vec{e}_\beta \Arrowvert$
double r_ab_norm_sum = r_ab_norm + r_ab2_norm;
// # 1 ADD, 1 MULTs, 1 SQRT
//
// $2b = \sqrt{(\Arrowvert \vec{r}_{\alpha \beta} \Arrowvert + \Arrowvert \vec{r}_{\alpha \beta} - v_\beta \Delta t \vec{e}_\beta \Arrowvert)^2 - (v_\beta \Delta t)^2}$
//
double two_b_sq = r_ab_norm_sum * r_ab_norm_sum - beta.s_b_sq;
two_b_sq = two_b_sq > EPS_SQ ? two_b_sq : EPS_SQ; // Avoid sqrt of negative and avoid division by zero
double two_b = sqrt(two_b_sq);
// # 5 MULTs, 1 DIV, 1 EXP
//
// $\frac{-V^0_{\alpha\beta}}{2\sigma}\,e^{-b/\sigma}\,\frac{\Arrowvert \vec{r}_{\alpha \beta} \Arrowvert + \Arrowvert \vec{r}_{\alpha \beta} - v_\beta \Delta t \vec{e}_\beta \Arrowvert}{2b\,\Arrowvert \vec{r}_{\alpha \beta} \Arrowvert\,\Arrowvert \vec{r}_{\alpha \beta} - v_\beta \Delta t \vec{e}_\beta \Arrowvert}$
//
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));
// # 1 MULT
//
// $\frac{-V^0_{\alpha\beta}}{2\sigma}\,e^{-b/\sigma}\,\frac{\Arrowvert \vec{r}_{\alpha \beta} \Arrowvert + \Arrowvert \vec{r}_{\alpha \beta} - v_\beta \Delta t \vec{e}_\beta \Arrowvert}{2b\,\Arrowvert \vec{r}_{\alpha \beta} \Arrowvert}$
//
double scalar_mult_r_ab = scalar_mult_common * r_ab2_norm;
// # 1 MULT
//
// $\frac{-V^0_{\alpha\beta}}{2\sigma}\,e^{-b/\sigma}\,\frac{\Arrowvert \vec{r}_{\alpha \beta} \Arrowvert + \Arrowvert \vec{r}_{\alpha \beta} - v_\beta \Delta t \vec{e}_\beta \Arrowvert}{2b\,\Arrowvert \vec{r}_{\alpha \beta} - v_\beta \Delta t \vec{e}_\beta \Arrowvert}$
//
double scalar_mult_r_ab2 = scalar_mult_common * r_ab_norm;
// # 2 ADDs, 4 MULTs
//
// $\vec{-f}_{\alpha \beta}(\vec{r}_{\alpha \beta}) = \frac{-V^0_{\alpha \beta}}{2\sigma}e^{-b / \sigma} 2\grad_{\vec{r}_{\alpha \beta}}b $
//
//
// $= \frac{-V^0_{\alpha\beta}}{2\sigma}\,e^{-b/\sigma}\,\frac{\Arrowvert \vec{r}_{\alpha \beta} \Arrowvert + \Arrowvert \vec{r}_{\alpha \beta} - v_\beta \Delta t \vec{e}_\beta \Arrowvert}{2b\,\Arrowvert \vec{r}_{\alpha \beta} \Arrowvert}\,\vec{r}_{\alpha \beta} + \frac{-V^0_{\alpha\beta}}{2\sigma}\,e^{-b/\sigma}\,\frac{\Arrowvert \vec{r}_{\alpha \beta} \Arrowvert + \Arrowvert \vec{r}_{\alpha \beta} - v_\beta \Delta t \vec{e}_\beta \Arrowvert}{2b\,\Arrowvert \vec{r}_{\alpha \beta} -
// v_\beta \Delta t \vec{e}_\beta \Arrowvert}\,(\vec{r}_{\alpha \beta} - v_\beta \Delta t \vec{e}_\beta)$
//
//
//
// $2\grad_{\vec{r}_{\alpha \beta}}b = \frac{(\Arrowvert \vec{r}_{\alpha \beta} \Arrowvert + \Arrowvert \vec{r}_{\alpha \beta} - v_\beta \Delta t \vec{e}_\beta \Arrowvert)(\frac{\vec{r}_{\alpha \beta}}{\Arrowvert \vec{r}_{\alpha \beta} \Arrowvert} + \frac{\vec{r}_{\alpha \beta} - v_\beta \Delta t \vec{e}_\beta}{\Arrowvert \vec{r}_{\alpha \beta} - v_\beta \Delta t \vec{e}_\beta \Arrowvert})}{2b}$
//
//
// $= \frac{\Arrowvert \vec{r}_{\alpha \beta} \Arrowvert + \Arrowvert \vec{r}_{\alpha \beta} - v_\beta Delta t \vec{e}_\beta \Arrowvert}{2b\,\Arrowvert \vec{r}_{\alpha \beta} \Arrowvert}\,\vec{r}_{\alpha \beta} + \frac{\Arrowvert \vec{r}_{\alpha \beta} \Arrowvert + \Arrowvert \vec{r}_{\alpha \beta} - v_\beta \Delta t \vec{e}_\beta \Arrowvert}{2b\,\Arrowvert \vec{r}_{\alpha \beta} - v_\beta \Delta t \vec{e}_\beta \Arrowvert}\,(\vec{r}_{\alpha \beta} - v_\beta \Delta t \vec{e}_\beta)$
//
//
Vector2d f_alpha_beta_neg = r_ab * scalar_mult_r_ab + r_ab2 * scalar_mult_r_ab2;
// # 2 ADDs, 7 MULTs, 1 SQRT
//
// $\vec{F}_{\alpha\beta}(\vec{e}_{\alpha}, \vec{r}_{\alpha \beta}).dt = w(\vec{e}_{\alpha}, -\vec{f}_{\alpha\beta}(\vec{r}_{\alpha \beta})).\vec{f}_{\alpha\beta}(\vec{r}_{\alpha \beta}).dt$
//
Vector2d f_alpha_beta_dt = f_alpha_beta_neg * w(alpha.e, f_alpha_beta_neg);
return f_alpha_beta_dt;
}
// Flop count: 10 ADDs, 18 MULTs, 1 DIVs, 2 SQRTs, 1 EXP
Vector2d obstacle_repulsion_dt(const Pedestrian &alpha, const Obstacle &B) {
// # 7 ADDs, 5 MULTs
// $\vec{r}_{\alpha B}$
Vector2d r_aB = alpha.curr_pos - B.find_nearest_obstacle_point(alpha.curr_pos);
// # 1 ADD, 2 MULTs, 1 SQRT
// $\Arrowvert \vec{r}_{\alpha B} \Arrowvert$
double r_aB_norm = r_aB.norm();
r_aB_norm = r_aB_norm > EPS ? r_aB_norm : EPS; // Avoid division by zero
// # 2 MULTs, 1 DIV, 1 EXP
//
// $\frac{-U^0_{\alpha B}}{R} e^{- \Arrowvert \vec{r}_{\alpha B} \Arrowvert / R}$
//
double scalar_mult = (NEG_U0_AB_div_R * exp(r_aB_norm * NEG_R_INV)) / r_aB_norm;
// # 2 MULTs
//
// $-\vec{F}_{\alpha B}(\vec{r}_{\alpha B}) = \frac{-U^0_{\alpha B}}{R} e^{- \Arrowvert \vec{r}_{\alpha B} \Arrowvert / R} \frac{\vec{r}_{\alpha B}}{\Arrowvert \vec{r}_{\alpha B} \Arrowvert}$
//
Vector2d f_alpha_B_neg = r_aB * scalar_mult;
// # 2 ADDs, 7 MULTs, 1 SQRT
//
// $\vec{F}_{\alpha B}(\vec{e}_{\alpha}, \vec{r}_{\alpha B}).dt = w(\vec{e}_{\alpha}, -\vec{F}_{\alpha B}(\vec{r}_{\alpha B})).\vec{F}_{\alpha B}(\vec{r}_{\alpha B}).dt$
//
Vector2d f_alpha_B_dt = f_alpha_B_neg * w(alpha.e, f_alpha_B_neg);
return f_alpha_B_dt;
}
// social_force_baseline.cpp
Pedestrian *init_pedestrians(int n_p) {
#if RANDOM_SEED
random_device rd; // Platform-provided random seed source.