Merge branch 'linus/variant_lut' into 'main'
Linus/variant lut See merge request course-asl-fastcode26/team70!22
This commit is contained in:
[Quy Anh] «Elliot» Nguyen
@@ -0,0 +1,138 @@
|
||||
# Optimization: LUT for exp()
|
||||
|
||||
- **Author**: Linus
|
||||
- **Predecessor**: variant_baseline.cpp
|
||||
- **File(s)**: variants/variant_lut_exp.cpp
|
||||
- **Status**: positive at small N (10-15%), tied at large N
|
||||
|
||||
## What this changes
|
||||
|
||||
Replaced the exp() calls in pedestrian_repulsion_dt and
|
||||
obstacle_repulsion_dt with a precomputed lookup table over the argument
|
||||
range [-40, 0]. The table stores exp at evenly spaced sample points and we
|
||||
interpolate with a cubic Hermite spline between them. Below -40 the value
|
||||
is below FP noise relative to the force accumulator, so we just return 0.
|
||||
|
||||
The thing that makes this work cleanly: for exp(x), the derivative IS the
|
||||
function value (d/dx exp(x) = exp(x)). So at every sample point we know
|
||||
the exact slope without having to estimate it with a centered difference.
|
||||
That gives O(h^4) accuracy with just 2 LUT loads per call.
|
||||
|
||||
## Code (relevant snippet)
|
||||
|
||||
```cpp
|
||||
constexpr int EXP_LUT_SIZE = 69000;
|
||||
constexpr double EXP_LUT_MIN = -40.0;
|
||||
constexpr double EXP_LUT_MAX = 0.0;
|
||||
constexpr double EXP_LUT_INV_STEP = (EXP_LUT_SIZE - 1) / (EXP_LUT_MAX - EXP_LUT_MIN);
|
||||
|
||||
static double exp_lut[EXP_LUT_SIZE];
|
||||
|
||||
// Populated before main() via a static initializer.
|
||||
struct ExpLutInit {
|
||||
ExpLutInit() {
|
||||
const double step = (EXP_LUT_MAX - EXP_LUT_MIN) / (EXP_LUT_SIZE - 1);
|
||||
for (int i = 0; i < EXP_LUT_SIZE; i++) {
|
||||
exp_lut[i] = std::exp(EXP_LUT_MIN + i * step);
|
||||
}
|
||||
}
|
||||
};
|
||||
static ExpLutInit exp_lut_init_helper;
|
||||
|
||||
inline double fast_exp(double x) {
|
||||
if (x <= EXP_LUT_MIN) return 0.0;
|
||||
if (x >= EXP_LUT_MAX) return 1.0;
|
||||
double pos = (x - EXP_LUT_MIN) * EXP_LUT_INV_STEP;
|
||||
int idx = static_cast<int>(pos);
|
||||
if (idx >= EXP_LUT_SIZE - 1) return 1.0;
|
||||
double t = pos - idx;
|
||||
double y0 = exp_lut[idx];
|
||||
double y1 = exp_lut[idx + 1];
|
||||
// For exp, slope = value. In normalized parameter space, slope = h * y.
|
||||
constexpr double h_step = (EXP_LUT_MAX - EXP_LUT_MIN) / (EXP_LUT_SIZE - 1);
|
||||
double t2 = t * t;
|
||||
double t3 = t2 * t;
|
||||
double h00 = 2.0*t3 - 3.0*t2 + 1.0;
|
||||
double h10 = t3 - 2.0*t2 + t;
|
||||
double h01 = -2.0*t3 + 3.0*t2;
|
||||
double h11 = t3 - t2;
|
||||
return y0 * (h00 + h_step * h10) + y1 * (h01 + h_step * h11);
|
||||
}
|
||||
```
|
||||
|
||||
Then in pedestrian_repulsion_dt and obstacle_repulsion_dt, the libm
|
||||
`exp(...)` is replaced with `fast_exp(...)`.
|
||||
|
||||
## Benchmark
|
||||
|
||||
Conditions: min of 3 runs, N_ITER=1000, -O3 -march=native -flto.
|
||||
|
||||
On my laptop (Intel ULTRA 9 185H @ 2.2 GHz, WSL Ubuntu): about
|
||||
15% faster at N=50, 12% at N=100, 8% at N=200, then roughly tied at N=500
|
||||
and N=1000. The shrinking speedup matches a cache story (see Analysis).
|
||||
|
||||
|
||||
### x86
|
||||
|
||||
**Machine**:
|
||||
|
||||
```
|
||||
<paste machine info here>
|
||||
```
|
||||
|
||||
**Frequency**: <e.g., 2 GHz>
|
||||
|
||||
| N | W(n) [Flops] | T(n) [Cycles] | Performance [Flops/Cycle] | Diff vs Baseline |
|
||||
| ---- | ------------ | ------------- | ------------------------- | ---------------- |
|
||||
| 50 | | | | |
|
||||
| 100 | | | | |
|
||||
| 200 | | | | |
|
||||
| 500 | | | | |
|
||||
| 1000 | | | | |
|
||||
|
||||
### ARM (Apple)
|
||||
|
||||
**Machine**:
|
||||
|
||||
```
|
||||
<paste machine info here>
|
||||
```
|
||||
|
||||
**Frequency**: <e.g., 3.2 GHz>
|
||||
|
||||
| N | W(n) [Flops] | T(n) [Cycles] | Performance [Flops/Cycle] | Diff vs Baseline |
|
||||
| ---- | ------------ | ------------- | ------------------------- | ---------------- |
|
||||
| 50 | | | | |
|
||||
| 100 | | | | |
|
||||
| 200 | | | | |
|
||||
| 500 | | | | |
|
||||
| 1000 | | | | |
|
||||
|
||||
## Analysis
|
||||
|
||||
The LUT replaces a libm exp (about 30 cycles) with a table lookup plus a
|
||||
small cubic polynomial (about 18 cycles). At small N the table fits in L2
|
||||
and the speedup is real, around 10-15%. As N grows the pedestrian array
|
||||
starts competing with the LUT for L2 cache, and the LUT lookups end
|
||||
up in L3 instead, which is about as expensive as the libm exp we were
|
||||
trying to replace.
|
||||
|
||||
About verify: the LUT introduces a small per-call error, and chaos in the
|
||||
simulation amplifies it over 4000 timesteps, but still passes our strict verification
|
||||
|
||||
If we are more tolerant with the "error" its possible to use a much smaller LUT. Maybe we could try that out
|
||||
|
||||
## Takeaway
|
||||
|
||||
LUT for exp works at small N where the table fits in cache. At large N the
|
||||
cache pressure kills the gain. A smaller LUT (or range reduction into a
|
||||
tiny table) would probably do better across the whole N range without the
|
||||
cache penalty.
|
||||
|
||||
## References
|
||||
|
||||
- Tang, P. T. P. (1989). "Table-driven implementation of the exponential
|
||||
function in IEEE floating-point arithmetic." ACM TOMS 15(2), 144-157.
|
||||
https://dl.acm.org/doi/10.1145/63522.214389
|
||||
- Cubic Hermite spline. Wikipedia.
|
||||
https://en.wikipedia.org/wiki/Cubic_Hermite_spline
|
||||
@@ -0,0 +1,454 @@
|
||||
// This file is copied from the variant_baseline and then modified
|
||||
// The goal is that we use a look up table to precompute expensive calculations
|
||||
// especially to precompute the exp calls
|
||||
// we call exp(two_b * NEG_TWO_SIGMA_INV)
|
||||
// which is always negativ
|
||||
// if a value is smaller then -40 its so small that we can ignore it
|
||||
// for the other values we will create a lookup table
|
||||
|
||||
#include "../headers/board.hpp"
|
||||
#include "../headers/constants.hpp"
|
||||
#include "../headers/pedestrian.hpp"
|
||||
#include "../headers/vector2d.hpp"
|
||||
|
||||
#include <algorithm>
|
||||
#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
|
||||
#define RANDOM_SEED 0
|
||||
#endif
|
||||
|
||||
#ifndef BENCHMARK
|
||||
#define BENCHMARK 0
|
||||
#endif
|
||||
|
||||
using namespace std;
|
||||
|
||||
// exp lookup table
|
||||
constexpr int EXP_LUT_SIZE = 69000;
|
||||
constexpr double EXP_LUT_MIN = -40.0;
|
||||
constexpr double EXP_LUT_MAX = 0.0;
|
||||
constexpr double EXP_LUT_INV_STEP = (EXP_LUT_SIZE - 1) / (EXP_LUT_MAX - EXP_LUT_MIN);
|
||||
|
||||
static double exp_lut[EXP_LUT_SIZE];
|
||||
|
||||
struct ExpLutInit {
|
||||
ExpLutInit() {
|
||||
const double step = (EXP_LUT_MAX - EXP_LUT_MIN) / (EXP_LUT_SIZE - 1);
|
||||
for (int i = 0; i < EXP_LUT_SIZE; i++) {
|
||||
exp_lut[i] = std::exp(EXP_LUT_MIN + i * step);
|
||||
}
|
||||
}
|
||||
};
|
||||
static ExpLutInit exp_lut_init_helper;
|
||||
// i used the following things to get a better understanding of how i can solve that problem
|
||||
// Tang, P. T. P. (1989). "Table-driven implementation of the exponential function in IEEE floating-point arithmetic." ACM TOMS 15(2), 144-157.
|
||||
// https://dl.acm.org/doi/10.1145/63522.214389
|
||||
// Cubic Hermite spline. Wikipedia.
|
||||
// https://en.wikipedia.org/wiki/Cubic_Hermite_spline
|
||||
inline double fast_exp(double x) {
|
||||
if (x <= EXP_LUT_MIN)
|
||||
return 0.0;
|
||||
if (x >= EXP_LUT_MAX)
|
||||
return 1.0;
|
||||
|
||||
double pos = (x - EXP_LUT_MIN) * EXP_LUT_INV_STEP;
|
||||
int idx = static_cast<int>(pos);
|
||||
if (idx >= EXP_LUT_SIZE - 1)
|
||||
return 1.0;
|
||||
|
||||
double t = pos - idx;
|
||||
double y0 = exp_lut[idx];
|
||||
double y1 = exp_lut[idx + 1];
|
||||
|
||||
// For exp(x), derivative equals function value.
|
||||
// In normalized parameter space (t in [0,1] across width h),
|
||||
// dy/dt = h * y. No centered differences needed - we know the exact slope.
|
||||
constexpr double h_step = (EXP_LUT_MAX - EXP_LUT_MIN) / (EXP_LUT_SIZE - 1);
|
||||
|
||||
double t2 = t * t;
|
||||
double t3 = t2 * t;
|
||||
|
||||
double h00 = 2.0 * t3 - 3.0 * t2 + 1.0;
|
||||
double h10 = t3 - 2.0 * t2 + t;
|
||||
double h01 = -2.0 * t3 + 3.0 * t2;
|
||||
double h11 = t3 - t2;
|
||||
|
||||
return y0 * (h00 + h_step * h10) + y1 * (h01 + h_step * h11);
|
||||
}
|
||||
// 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 * fast_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 * fast_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.
|
||||
mt19937 gen(rd()); // Non-reproducible initialization.
|
||||
#else
|
||||
mt19937 gen(SEED); // Reproducible initialization.
|
||||
#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;
|
||||
|
||||
// Group of pedestrians walking from left to right.
|
||||
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 + 30.0, y);
|
||||
|
||||
Vector2d init_e = destination - start_pos;
|
||||
double init_e_norm = init_e.norm();
|
||||
Vector2d init_e_unit = init_e / init_e_norm;
|
||||
|
||||
// Reject near-zero desired speeds to avoid pedestrians that barely move,
|
||||
// and reject negative speeds because they would reverse the intended
|
||||
// walking direction.
|
||||
double desired_v0;
|
||||
do {
|
||||
desired_v0 = velocity_gen(gen);
|
||||
} while (desired_v0 <= 0.1);
|
||||
|
||||
double v_max = 1.3 * desired_v0;
|
||||
|
||||
P[i] = Pedestrian(WHITE, Vector2d(), start_pos, init_e_unit, v_max, desired_v0, destination);
|
||||
}
|
||||
|
||||
// Group of pedestrians walking from right to left.
|
||||
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(-30.0, y);
|
||||
|
||||
Vector2d init_e = destination - start_pos;
|
||||
double init_e_norm = init_e.norm();
|
||||
Vector2d init_e_unit = init_e / init_e_norm;
|
||||
|
||||
// Reject near-zero desired speeds to avoid pedestrians that barely move,
|
||||
// and reject negative speeds because they would reverse the intended
|
||||
// walking direction.
|
||||
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, Vector2d(), start_pos, init_e_unit, v_max, desired_v0, destination);
|
||||
}
|
||||
|
||||
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
|
||||
// Avoid compiler unused parameter warning
|
||||
(void)dump_path;
|
||||
#endif
|
||||
|
||||
#if !BENCHMARK
|
||||
const int dump_interval = 1;
|
||||
|
||||
// Each sample stores: time step, pedestrian id, x, y, e.x, e.y, color.
|
||||
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);
|
||||
|
||||
// Store the initial state before the first simulation step.
|
||||
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
|
||||
|
||||
for (int t = 0; t < n_iter; t++) {
|
||||
// Pass 1: Compute all forces from the current state.
|
||||
for (int i = 0; i < n_p; i++) {
|
||||
Pedestrian &p = pedestrians[i];
|
||||
|
||||
// # 2 ADDs, 4 MULTs
|
||||
//
|
||||
// $\vec{F}_\alpha(\vec{v}_\alpha, v^0_\alpha \vec{e}_\alpha) = \frac{1}{\tau_\alpha}(v^0_\alpha \vec{e}_\alpha - \vec{v}_\alpha)$
|
||||
//
|
||||
Vector2d f_alpha_dt = acceleration_term_dt(p);
|
||||
|
||||
// # (N-1) * (12 ADDs, 23 MULTs, 1 DIV, 4 SQRTs, 1 EXP)
|
||||
// + (N-1) * 2 ADDs
|
||||
//
|
||||
// $\sum_{\beta} \vec{F}_{\alpha\beta}(\vec{e}_{\alpha},\vec{r}_{\alpha} - \vec{r}_{\beta})$
|
||||
//
|
||||
for (int j = 0; j < n_p; j++) {
|
||||
if (i == j)
|
||||
continue;
|
||||
|
||||
f_alpha_dt += pedestrian_repulsion_dt(p, pedestrians[j]);
|
||||
}
|
||||
|
||||
// # board.n_obstacles * (10 ADDs, 18 MULTs, 1 DIV, 2 SQRTs, 1 EXP)
|
||||
// + board.n_obstacles * 2 ADDs
|
||||
//
|
||||
// $\sum_{B} \vec{F}_{\alpha B}(\vec{e}_{\alpha}, \vec{r}_{\alpha} - \vec{r}_{B})$
|
||||
//
|
||||
for (int k = 0; k < board.n_obstacles; k++) {
|
||||
f_alpha_dt += obstacle_repulsion_dt(p, board.obstacles[k]);
|
||||
}
|
||||
|
||||
// # 2 ADDs
|
||||
//
|
||||
//
|
||||
// $\frac{d\vec{w}_\alpha}{dt} = \vec{F}_{\alpha}(t)$
|
||||
//
|
||||
p.w += f_alpha_dt;
|
||||
}
|
||||
|
||||
// Pass 2: Update pedestrian states after all forces have been computed.
|
||||
// # (7 ADDs, 16 MULTs, 2 DIVs, 3 SQRTs) * n_p
|
||||
for (int i = 0; i < n_p; i++) {
|
||||
Pedestrian &p = pedestrians[i];
|
||||
|
||||
// # 1 ADD, 2 MULTs, 1 SQRT
|
||||
double w_norm = p.w.norm();
|
||||
|
||||
double w_norm2 = w_norm > EPS ? w_norm : EPS; // Avoid division by zero.
|
||||
|
||||
// # 1 DIV
|
||||
double correction_factor = std::min(1.0, p.v_max / w_norm2);
|
||||
|
||||
// # 2 MULTs
|
||||
p.curr_vel = p.w * correction_factor;
|
||||
|
||||
// # 2 ADDs, 2 MULTs
|
||||
//
|
||||
// $\vec{r}_i^{t+1} = \vec{r}_i^t + \vec{v}_i^t dt$
|
||||
//
|
||||
p.curr_pos = p.curr_pos + p.curr_vel * dt;
|
||||
|
||||
// When a pedestrian reaches the end of the corridor, teleport them back
|
||||
// to the opposite entrance while keeping the same y-coordinate. This
|
||||
// maintains a constant pedestrian flow and makes lane formation easier to
|
||||
// observe.
|
||||
if (p.color == WHITE && p.curr_pos.x > (BOARD_LENGTH - 1.5)) {
|
||||
p.curr_pos.x = 1.0;
|
||||
p.destination.y = p.curr_pos.y;
|
||||
p.w = Vector2d(p.desired_v0, 0.0);
|
||||
p.curr_vel = p.w;
|
||||
}
|
||||
if (p.color == BLACK && p.curr_pos.x < 1.5) {
|
||||
p.curr_pos.x = BOARD_LENGTH - 1.0;
|
||||
p.destination.y = p.curr_pos.y;
|
||||
p.w = Vector2d(-p.desired_v0, 0.0);
|
||||
p.curr_vel = p.w;
|
||||
}
|
||||
|
||||
// Keep pedestrians inside the board boundaries.
|
||||
p.curr_pos.y = clamp(p.curr_pos.y, WALL_EPS, BOARD_WIDTH_MINUS_WALL_EPS);
|
||||
|
||||
// # 2 ADDs
|
||||
Vector2d e = p.destination - p.curr_pos;
|
||||
|
||||
// # 1 ADD, 2 MULTs, 1 DIV, 1 SQRT
|
||||
double e_norm = e.norm();
|
||||
double e_norm2 = e_norm > EPS ? e_norm : EPS; // Avoid division by zero.
|
||||
double e_norm_inv = 1.0 / e_norm2;
|
||||
|
||||
// # 2 MULTs
|
||||
p.e = e * e_norm_inv;
|
||||
|
||||
// # 1 ADD, 2 MULTs
|
||||
double velocity_norm_sq = p.curr_vel.dot(p.curr_vel);
|
||||
|
||||
// # 1 SQRT
|
||||
double velocity_norm = std::sqrt(velocity_norm_sq);
|
||||
|
||||
// # 1 MULT
|
||||
p.s_b_sq = velocity_norm_sq * delta_t_sq;
|
||||
|
||||
// # 3 MULTs
|
||||
p.s_b_e = p.e * (velocity_norm * delta_t);
|
||||
|
||||
#if !BENCHMARK
|
||||
// Store the current pedestrian state for visualization.
|
||||
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
|
||||
// Export recorded simulation states to CSV.
|
||||
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;
|
||||
}
|
||||
Reference in New Issue
Block a user