lbaumberger
492 lines
17 KiB
C++
492 lines
17 KiB
C++
// This file is copied from the variant_baseline and then modified
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// The goal is that we use a look up table to precompute expensive calculations
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// especially to precompute the exp calls
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// we call exp(two_b * NEG_TWO_SIGMA_INV)
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// which is always negativ
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// if a value is smaller then -40 its so small that we can ignore it
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// for the other values we will create a lookup table
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#include "../headers/board.hpp"
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#include "../headers/constants.hpp"
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#include "../headers/pedestrian.hpp"
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#include "../headers/vector2d.hpp"
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#include <algorithm>
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#include <cmath>
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#include <fstream>
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#include <iostream>
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#include <math.h> // keep — forces code uses unqualified sqrt/exp
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#include <random>
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#include <tuple>
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#include <vector>
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#define SEED 42
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#define BOARD_WIDTH 10.0
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#define BOARD_LENGTH 50.0
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#define WALL_EPS 1e-3
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#define BOARD_WIDTH_MINUS_WALL_EPS 9.999
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#ifndef RANDOM_SEED
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#define RANDOM_SEED 0
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#endif
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#ifndef BENCHMARK
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#define BENCHMARK 0
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#endif
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using namespace std;
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// exp lookup table
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constexpr int EXP_LUT_SIZE = 69000;
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constexpr double EXP_LUT_MIN = -40.0;
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constexpr double EXP_LUT_MAX = 0.0;
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constexpr double EXP_LUT_INV_STEP = (EXP_LUT_SIZE - 1) / (EXP_LUT_MAX - EXP_LUT_MIN);
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static double exp_lut[EXP_LUT_SIZE];
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struct ExpLutInit {
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ExpLutInit() {
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const double step = (EXP_LUT_MAX - EXP_LUT_MIN) / (EXP_LUT_SIZE - 1);
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for (int i = 0; i < EXP_LUT_SIZE; i++) {
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exp_lut[i] = std::exp(EXP_LUT_MIN + i * step);
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}
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}
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};
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static ExpLutInit exp_lut_init_helper;
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// i used the following things to get a better understanding of how i can solve that problem
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// Tang, P. T. P. (1989). "Table-driven implementation of the exponential function in IEEE floating-point arithmetic." ACM TOMS 15(2), 144-157.
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// https://dl.acm.org/doi/10.1145/63522.214389
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// Cubic Hermite spline. Wikipedia.
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// https://en.wikipedia.org/wiki/Cubic_Hermite_spline
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inline double fast_exp(double x) {
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if (x <= EXP_LUT_MIN)
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return 0.0;
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if (x >= EXP_LUT_MAX)
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return 1.0;
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double pos = (x - EXP_LUT_MIN) * EXP_LUT_INV_STEP;
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int idx = static_cast<int>(pos);
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if (idx >= EXP_LUT_SIZE - 1)
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return 1.0;
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double t = pos - idx;
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double y0 = exp_lut[idx];
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double y1 = exp_lut[idx + 1];
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// For exp(x), derivative equals function value.
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// In normalized parameter space (t in [0,1] across width h),
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// dy/dt = h * y. No centered differences needed - we know the exact slope.
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constexpr double h_step = (EXP_LUT_MAX - EXP_LUT_MIN) / (EXP_LUT_SIZE - 1);
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double t2 = t * t;
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double t3 = t2 * t;
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double h00 = 2.0 * t3 - 3.0 * t2 + 1.0;
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double h10 = t3 - 2.0 * t2 + t;
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double h01 = -2.0 * t3 + 3.0 * t2;
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double h11 = t3 - t2;
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return y0 * (h00 + h_step * h10) + y1 * (h01 + h_step * h11);
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}
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// forces.cpp
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// Flop count: 2 ADDs, 5 MULTs, 1 SQRT
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double w(Vector2d e, Vector2d f) {
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if (e.dot(f) >= f.norm() * cos_phi)
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return dt_neg;
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else
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return c_neg_times_dt;
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}
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// Flop count: 2 ADDs, 4 MULTs
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Vector2d acceleration_term_dt(const Pedestrian &alpha) {
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// # 2 MULTs
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Vector2d desired_velocity = alpha.e * alpha.desired_v0;
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Vector2d actual_velocity = alpha.curr_vel;
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// # 2 ADDs, 2 MULTs
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Vector2d f_alpha_0_dt = (desired_velocity - actual_velocity) * dt_times_tau_alpha_inv;
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return f_alpha_0_dt;
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}
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// Flop count: 12 ADDs, 23 MULTs, 1 DIV, 4 SQRTs, 1 EXP
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Vector2d pedestrian_repulsion_dt(const Pedestrian &alpha, const Pedestrian &beta) {
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// # 2 ADDs
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// $\vec{r}_{\alpha\beta}$
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Vector2d r_ab = alpha.curr_pos - beta.curr_pos;
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// # 1 ADD, 2 MULTs, 1 SQRT
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// $\Arrowvert \vec{r}_{\alpha \beta} \Arrowvert$
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double r_ab_norm = r_ab.norm();
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r_ab_norm = r_ab_norm > EPS ? r_ab_norm : EPS; // Avoid division by zero
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// $v_\beta \Delta t \vec{e}_\beta$
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Vector2d s_b_e = beta.s_b_e;
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// # 2 ADDs
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// $\vec{r}_{\alpha\beta} - \vec{v}_{\beta}\varDelta_{t}\vec{e}_{\beta}$
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Vector2d r_ab2 = r_ab - s_b_e;
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// # 1 ADD, 2 MULTs, 1 SQRT
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// $\Arrowvert \vec{r}_{\alpha \beta} - v_\beta \Delta t \vec{e}_\beta \Arrowvert$
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double r_ab2_norm = r_ab2.norm();
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r_ab2_norm = r_ab2_norm > EPS ? r_ab2_norm : EPS; // Avoid division by zero
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// # 1 ADD
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// $\Arrowvert \vec{r}_{\alpha \beta} \Arrowvert + \Arrowvert \vec{r}_{\alpha \beta} - v_\beta \Delta t \vec{e}_\beta \Arrowvert$
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double r_ab_norm_sum = r_ab_norm + r_ab2_norm;
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// # 1 ADD, 1 MULTs, 1 SQRT
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//
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// $2b = \sqrt{(\Arrowvert \vec{r}_{\alpha \beta} \Arrowvert + \Arrowvert \vec{r}_{\alpha \beta} - v_\beta \Delta t \vec{e}_\beta \Arrowvert)^2 - (v_\beta \Delta t)^2}$
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//
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double two_b_sq = r_ab_norm_sum * r_ab_norm_sum - beta.s_b_sq;
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two_b_sq = two_b_sq > EPS_SQ ? two_b_sq : EPS_SQ; // Avoid sqrt of negative and avoid division by zero
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double two_b = sqrt(two_b_sq);
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// # 5 MULTs, 1 DIV, 1 EXP
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//
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// $\frac{-V^0_{\alpha\beta}}{2\sigma}\,e^{-b/\sigma}\,\frac{\Arrowvert \vec{r}_{\alpha \beta} \Arrowvert + \Arrowvert \vec{r}_{\alpha \beta} - v_\beta \Delta t \vec{e}_\beta \Arrowvert}{2b\,\Arrowvert \vec{r}_{\alpha \beta} \Arrowvert\,\Arrowvert \vec{r}_{\alpha \beta} - v_\beta \Delta t \vec{e}_\beta \Arrowvert}$
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//
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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));
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// # 1 MULT
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//
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// $\frac{-V^0_{\alpha\beta}}{2\sigma}\,e^{-b/\sigma}\,\frac{\Arrowvert \vec{r}_{\alpha \beta} \Arrowvert + \Arrowvert \vec{r}_{\alpha \beta} - v_\beta \Delta t \vec{e}_\beta \Arrowvert}{2b\,\Arrowvert \vec{r}_{\alpha \beta} \Arrowvert}$
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//
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double scalar_mult_r_ab = scalar_mult_common * r_ab2_norm;
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// # 1 MULT
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//
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// $\frac{-V^0_{\alpha\beta}}{2\sigma}\,e^{-b/\sigma}\,\frac{\Arrowvert \vec{r}_{\alpha \beta} \Arrowvert + \Arrowvert \vec{r}_{\alpha \beta} - v_\beta \Delta t \vec{e}_\beta \Arrowvert}{2b\,\Arrowvert \vec{r}_{\alpha \beta} - v_\beta \Delta t \vec{e}_\beta \Arrowvert}$
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//
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double scalar_mult_r_ab2 = scalar_mult_common * r_ab_norm;
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// # 2 ADDs, 4 MULTs
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//
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// $\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 $
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//
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//
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// $= \frac{-V^0_{\alpha\beta}}{2\sigma}\,e^{-b/\sigma}\,\frac{\Arrowvert \vec{r}_{\alpha \beta} \Arrowvert + \Arrowvert \vec{r}_{\alpha \beta} - v_\beta \Delta t \vec{e}_\beta \Arrowvert}{2b\,\Arrowvert \vec{r}_{\alpha \beta} \Arrowvert}\,\vec{r}_{\alpha \beta} + \frac{-V^0_{\alpha\beta}}{2\sigma}\,e^{-b/\sigma}\,\frac{\Arrowvert \vec{r}_{\alpha \beta} \Arrowvert + \Arrowvert \vec{r}_{\alpha \beta} - v_\beta \Delta t \vec{e}_\beta \Arrowvert}{2b\,\Arrowvert \vec{r}_{\alpha \beta} -
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// v_\beta \Delta t \vec{e}_\beta \Arrowvert}\,(\vec{r}_{\alpha \beta} - v_\beta \Delta t \vec{e}_\beta)$
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//
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//
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//
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// $2\grad_{\vec{r}_{\alpha \beta}}b = \frac{(\Arrowvert \vec{r}_{\alpha \beta} \Arrowvert + \Arrowvert \vec{r}_{\alpha \beta} - v_\beta \Delta t \vec{e}_\beta \Arrowvert)(\frac{\vec{r}_{\alpha \beta}}{\Arrowvert \vec{r}_{\alpha \beta} \Arrowvert} + \frac{\vec{r}_{\alpha \beta} - v_\beta \Delta t \vec{e}_\beta}{\Arrowvert \vec{r}_{\alpha \beta} - v_\beta \Delta t \vec{e}_\beta \Arrowvert})}{2b}$
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//
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//
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// $= \frac{\Arrowvert \vec{r}_{\alpha \beta} \Arrowvert + \Arrowvert \vec{r}_{\alpha \beta} - v_\beta Delta t \vec{e}_\beta \Arrowvert}{2b\,\Arrowvert \vec{r}_{\alpha \beta} \Arrowvert}\,\vec{r}_{\alpha \beta} + \frac{\Arrowvert \vec{r}_{\alpha \beta} \Arrowvert + \Arrowvert \vec{r}_{\alpha \beta} - v_\beta \Delta t \vec{e}_\beta \Arrowvert}{2b\,\Arrowvert \vec{r}_{\alpha \beta} - v_\beta \Delta t \vec{e}_\beta \Arrowvert}\,(\vec{r}_{\alpha \beta} - v_\beta \Delta t \vec{e}_\beta)$
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//
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//
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Vector2d f_alpha_beta_neg = r_ab * scalar_mult_r_ab + r_ab2 * scalar_mult_r_ab2;
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// # 2 ADDs, 7 MULTs, 1 SQRT
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//
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// $\vec{F}_{\alpha\beta}(\vec{e}_{\alpha}, \vec{r}_{\alpha \beta}).dt = w(\vec{e}_{\alpha}, -\vec{f}_{\alpha\beta}(\vec{r}_{\alpha \beta})).\vec{f}_{\alpha\beta}(\vec{r}_{\alpha \beta}).dt$
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//
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Vector2d f_alpha_beta_dt = f_alpha_beta_neg * w(alpha.e, f_alpha_beta_neg);
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return f_alpha_beta_dt;
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}
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// Flop count: 10 ADDs, 18 MULTs, 1 DIVs, 2 SQRTs, 1 EXP
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Vector2d obstacle_repulsion_dt(const Pedestrian &alpha, const Obstacle &B) {
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// # 7 ADDs, 5 MULTs
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// $\vec{r}_{\alpha B}$
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Vector2d r_aB = alpha.curr_pos - B.find_nearest_obstacle_point(alpha.curr_pos);
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// # 1 ADD, 2 MULTs, 1 SQRT
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// $\Arrowvert \vec{r}_{\alpha B} \Arrowvert$
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double r_aB_norm = r_aB.norm();
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r_aB_norm = r_aB_norm > EPS ? r_aB_norm : EPS; // Avoid division by zero
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// # 2 MULTs, 1 DIV, 1 EXP
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//
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// $\frac{-U^0_{\alpha B}}{R} e^{- \Arrowvert \vec{r}_{\alpha B} \Arrowvert / R}$
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//
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double scalar_mult = (NEG_U0_AB_div_R * fast_exp(r_aB_norm * NEG_R_INV)) / r_aB_norm;
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// # 2 MULTs
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//
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// $-\vec{F}_{\alpha B}(\vec{r}_{\alpha B}) = \frac{-U^0_{\alpha B}}{R} e^{- \Arrowvert \vec{r}_{\alpha B} \Arrowvert / R} \frac{\vec{r}_{\alpha B}}{\Arrowvert \vec{r}_{\alpha B} \Arrowvert}$
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//
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Vector2d f_alpha_B_neg = r_aB * scalar_mult;
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// # 2 ADDs, 7 MULTs, 1 SQRT
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//
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// $\vec{F}_{\alpha B}(\vec{e}_{\alpha}, \vec{r}_{\alpha B}).dt = w(\vec{e}_{\alpha}, -\vec{F}_{\alpha B}(\vec{r}_{\alpha B})).\vec{F}_{\alpha B}(\vec{r}_{\alpha B}).dt$
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//
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Vector2d f_alpha_B_dt = f_alpha_B_neg * w(alpha.e, f_alpha_B_neg);
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return f_alpha_B_dt;
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}
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// social_force_baseline.cpp
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Pedestrian *init_pedestrians(int n_p) {
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#if RANDOM_SEED
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random_device rd; // Platform-provided random seed source.
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mt19937 gen(rd()); // Non-reproducible initialization.
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#else
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mt19937 gen(SEED); // Reproducible initialization.
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#endif
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normal_distribution<double> velocity_gen(v0_mean, v0_std_dev);
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uniform_real_distribution<double> y_gen(0.3, BOARD_WIDTH - 0.3);
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uniform_real_distribution<double> x_gen_left(2.0, BOARD_LENGTH / 2.0);
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uniform_real_distribution<double> x_gen_right(BOARD_LENGTH / 2.0, BOARD_LENGTH - 2.0);
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Pedestrian *P = new Pedestrian[n_p];
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int n_p_half = n_p / 2;
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// Group of pedestrians walking from left to right.
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for (int i = 0; i < n_p_half; i++) {
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double x = x_gen_left(gen);
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double y = y_gen(gen);
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Vector2d start_pos = Vector2d(x, y);
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Vector2d destination = Vector2d(BOARD_LENGTH + 30.0, y);
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Vector2d init_e = destination - start_pos;
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double init_e_norm = init_e.norm();
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Vector2d init_e_unit = init_e / init_e_norm;
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// Reject near-zero desired speeds to avoid pedestrians that barely move,
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// and reject negative speeds because they would reverse the intended
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// walking direction.
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double desired_v0;
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do {
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desired_v0 = velocity_gen(gen);
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} while (desired_v0 <= 0.1);
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double v_max = 1.3 * desired_v0;
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P[i] = Pedestrian(WHITE, Vector2d(), start_pos, init_e_unit, v_max, desired_v0, destination);
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}
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// Group of pedestrians walking from right to left.
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for (int i = n_p_half; i < n_p; i++) {
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double x = x_gen_right(gen);
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double y = y_gen(gen);
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Vector2d start_pos = Vector2d(x, y);
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Vector2d destination = Vector2d(-30.0, y);
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Vector2d init_e = destination - start_pos;
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double init_e_norm = init_e.norm();
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Vector2d init_e_unit = init_e / init_e_norm;
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// Reject near-zero desired speeds to avoid pedestrians that barely move,
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// and reject negative speeds because they would reverse the intended
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// walking direction.
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double desired_v0;
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do {
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desired_v0 = velocity_gen(gen);
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} while (desired_v0 <= 0.1);
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double v_max = 1.3 * desired_v0;
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P[i] = Pedestrian(BLACK, Vector2d(), start_pos, init_e_unit, v_max, desired_v0, destination);
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}
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return P;
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}
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Board init_board_without_obstacles() { return Board(BOARD_LENGTH, BOARD_WIDTH, 0, nullptr); }
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int run_simulation(Pedestrian *pedestrians, Board &board, int n_p, int n_iter, const char *dump_path) {
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#if BENCHMARK
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// Avoid compiler unused parameter warning
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(void)dump_path;
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#endif
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#if !BENCHMARK
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const int dump_interval = 1;
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// Each sample stores: time step, pedestrian id, x, y, e.x, e.y, color.
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vector<tuple<int, int, double, double, double, double, int>> samples;
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if (dump_path) {
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samples.reserve(static_cast<size_t>(n_iter / dump_interval + 1) * n_p);
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// Store the initial state before the first simulation step.
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for (int i = 0; i < n_p; i++) {
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Pedestrian &p = pedestrians[i];
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samples.emplace_back(0, i, p.curr_pos.x, p.curr_pos.y, p.e.x, p.e.y, p.color);
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}
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}
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#endif
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// FLOPCOUNT (everything inside the t-loop). EXP = one fast_exp() call (LUT + cubic Hermite),
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// NOT a real libm exp. AoS baseline, no distance precompute, r_ab recomputed inside the j-loop.
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// section costs: overhead 4 ADD 4 MULT (accel 2 ADD 4 MULT + p.w += 2 ADD) |
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// ped-ped j 14 ADD 23 MULT 1 DIV 4 SQRT 1 EXP (12/23/1/4/1 + f_alpha += 2 ADD) |
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// obstacle 12 ADD 18 MULT 1 DIV 2 SQRT 1 EXP (10/18/1/2/1 + f_alpha += 2 ADD) |
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// update 7 ADD 16 MULT 2 DIV 3 SQRT
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// # ADDs: n_iter * (
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// # n_p * 4 +
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// # n_p * (n_p - 1) * 14 +
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// # n_p * board.n_obstacles * 12 +
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// # n_p * 7
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// # )
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// # MULTs: n_iter * (
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// # n_p * 4 +
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// # n_p * (n_p - 1) * 23 +
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// # n_p * board.n_obstacles * 18 +
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// # n_p * 16
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// # )
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// # DIVs: n_iter * (
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// # n_p * (n_p - 1) +
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// # n_p * board.n_obstacles +
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// # n_p * 2
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// # )
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// # SQRTs: n_iter * (
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// # n_p * (n_p - 1) * 4 +
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// # n_p * board.n_obstacles * 2 +
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// # n_p * 3
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// # )
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// # EXPs (fast_exp, LUT): n_iter * (
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// # n_p * (n_p - 1) +
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// # n_p * board.n_obstacles
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// # )
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for (int t = 0; t < n_iter; t++) {
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// Pass 1: Compute all forces from the current state.
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for (int i = 0; i < n_p; i++) {
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Pedestrian &p = pedestrians[i];
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// # 2 ADDs, 4 MULTs
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//
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// $\vec{F}_\alpha(\vec{v}_\alpha, v^0_\alpha \vec{e}_\alpha) = \frac{1}{\tau_\alpha}(v^0_\alpha \vec{e}_\alpha - \vec{v}_\alpha)$
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//
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Vector2d f_alpha_dt = acceleration_term_dt(p);
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// # (N-1) * (12 ADDs, 23 MULTs, 1 DIV, 4 SQRTs, 1 EXP)
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// + (N-1) * 2 ADDs
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//
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// $\sum_{\beta} \vec{F}_{\alpha\beta}(\vec{e}_{\alpha},\vec{r}_{\alpha} - \vec{r}_{\beta})$
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//
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for (int j = 0; j < n_p; j++) {
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if (i == j)
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continue;
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f_alpha_dt += pedestrian_repulsion_dt(p, pedestrians[j]);
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}
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// # board.n_obstacles * (10 ADDs, 18 MULTs, 1 DIV, 2 SQRTs, 1 EXP)
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// + board.n_obstacles * 2 ADDs
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//
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// $\sum_{B} \vec{F}_{\alpha B}(\vec{e}_{\alpha}, \vec{r}_{\alpha} - \vec{r}_{B})$
|
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//
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|
for (int k = 0; k < board.n_obstacles; k++) {
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f_alpha_dt += obstacle_repulsion_dt(p, board.obstacles[k]);
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|
}
|
|
|
|
// # 2 ADDs
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//
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|
//
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|
// $\frac{d\vec{w}_\alpha}{dt} = \vec{F}_{\alpha}(t)$
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|
//
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|
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++) {
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|
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;
|
|
} |