[Quy Anh] «Elliot» Nguyen
473 lines
17 KiB
C++
473 lines
17 KiB
C++
// # Changes: simd polynomial expf, replaces the 8 scalar expf calls in the j loop
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// # Predecessor: variant_float_inlining_SoA_AVX2.cpp
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// the for-loop of 8 scalar expf calls was serialised by gcc (it didnt unroll), big perf hit.
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// replace with one inlined simd polynomial approx, no libm call at all.
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#include "../headers/board_reduced_float.hpp"
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#include "../headers/constants_float.hpp"
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#include "../headers/pedestrian_reduced_float.hpp"
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#include <immintrin.h> // avx2
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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>
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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 10.0f
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#define BOARD_LENGTH 50.0f
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#define WALL_EPS 1e-3f
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#define BOARD_WIDTH_MINUS_WALL_EPS 9.999f
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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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vector<float> pos_x, pos_y;
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vector<float> sb_sq;
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vector<float> sb_e_x, sb_e_y;
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vector<float> e_x, e_y;
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vector<float> curr_vel_x, curr_vel_y;
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vector<float> w_x, w_y;
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vector<float> desired_v0;
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vector<float> v_max;
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vector<float> destination_x, destination_y;
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vector<int> color;
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Pedestrian *init_pedestrians(int n_p) {
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#if RANDOM_SEED
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random_device rd;
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mt19937 gen(rd());
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#else
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mt19937 gen(SEED);
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#endif
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normal_distribution<float> velocity_gen(v0_mean, v0_std_dev);
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uniform_real_distribution<float> y_gen(0.3, BOARD_WIDTH - 0.3);
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uniform_real_distribution<float> x_gen_left(2.0, BOARD_LENGTH / 2.0);
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uniform_real_distribution<float> x_gen_right(BOARD_LENGTH / 2.0, BOARD_LENGTH - 2.0);
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const int n_p_pad = (n_p + 7) & ~7;
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pos_x.resize(n_p_pad);
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pos_y.resize(n_p_pad);
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sb_sq.resize(n_p_pad);
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sb_e_x.resize(n_p_pad);
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sb_e_y.resize(n_p_pad);
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e_x.resize(n_p_pad);
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e_y.resize(n_p_pad);
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curr_vel_x.resize(n_p_pad);
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curr_vel_y.resize(n_p_pad);
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w_x.resize(n_p_pad);
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w_y.resize(n_p_pad);
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desired_v0.resize(n_p_pad);
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v_max.resize(n_p_pad);
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destination_x.resize(n_p_pad);
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destination_y.resize(n_p_pad);
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color.resize(n_p_pad);
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int n_p_half = n_p / 2;
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for (int i = 0; i < n_p_half; i++) {
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float x = x_gen_left(gen);
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float y = y_gen(gen);
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float dest_x = BOARD_LENGTH + 30.0;
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float dest_y = y;
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float init_e_x = dest_x - x;
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float init_e_y = dest_y - y;
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float init_e_norm = sqrt(init_e_x * init_e_x + init_e_y * init_e_y);
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float init_e_unit_x = init_e_x / init_e_norm;
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float init_e_unit_y = init_e_y / init_e_norm;
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float d_v0;
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do {
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d_v0 = velocity_gen(gen);
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} while (d_v0 <= 0.1);
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float v_m = 1.3 * d_v0;
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color[i] = 0;
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pos_x[i] = x;
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pos_y[i] = y;
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e_x[i] = init_e_unit_x;
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e_y[i] = init_e_unit_y;
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v_max[i] = v_m;
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desired_v0[i] = d_v0;
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destination_x[i] = dest_x;
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destination_y[i] = dest_y;
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w_x[i] = 0.0f;
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w_y[i] = 0.0f;
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curr_vel_x[i] = 0.0f;
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curr_vel_y[i] = 0.0f;
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sb_sq[i] = 0.0f;
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sb_e_x[i] = 0.0f;
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sb_e_y[i] = 0.0f;
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}
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for (int i = n_p_half; i < n_p; i++) {
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float x = x_gen_right(gen);
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float y = y_gen(gen);
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float dest_x = -30;
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float dest_y = y;
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float init_e_x = dest_x - x;
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float init_e_y = dest_y - y;
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float init_e_norm = sqrt(init_e_x * init_e_x + init_e_y * init_e_y);
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float init_e_unit_x = init_e_x / init_e_norm;
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float init_e_unit_y = init_e_y / init_e_norm;
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float d_v0;
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do {
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d_v0 = velocity_gen(gen);
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} while (d_v0 <= 0.1);
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float v_m = 1.3 * d_v0;
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color[i] = 1;
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pos_x[i] = x;
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pos_y[i] = y;
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e_x[i] = init_e_unit_x;
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e_y[i] = init_e_unit_y;
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v_max[i] = v_m;
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desired_v0[i] = d_v0;
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destination_x[i] = dest_x;
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destination_y[i] = dest_y;
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w_x[i] = 0.0f;
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w_y[i] = 0.0f;
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curr_vel_x[i] = 0.0f;
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curr_vel_y[i] = 0.0f;
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sb_sq[i] = 0.0f;
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sb_e_x[i] = 0.0f;
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sb_e_y[i] = 0.0f;
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}
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for (int j = n_p; j < n_p_pad; j++) {
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pos_x[j] = 1e9f;
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pos_y[j] = 1e9f;
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sb_sq[j] = 0.0f;
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sb_e_x[j] = 0.0f;
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sb_e_y[j] = 0.0f;
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}
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return nullptr;
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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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// simd expf, degree-12 taylor on the [-ln2/2, ln2/2] reduced range,
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// schraudolph 2^n bit trick on the exponent slot.
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// # 128 MULTs, 112 ADDs
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static inline __m256 exp256_ps(__m256 x) {
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const __m256 log2e = _mm256_set1_ps(1.4426950408889634f);
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__m256 nf = _mm256_round_ps(_mm256_mul_ps(x, log2e), _MM_FROUND_TO_NEAREST_INT | _MM_FROUND_NO_EXC); // # 8 MULTs
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const __m256 ln2 = _mm256_set1_ps(0.6931471805599453f);
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__m256 r = _mm256_fnmadd_ps(nf, ln2, x); // # 8 MULTs, 8 ADDs
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const __m256 c13 = _mm256_set1_ps(c13_scalar);
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const __m256 c12 = _mm256_set1_ps(c12_scalar);
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const __m256 c11 = _mm256_set1_ps(c11_scalar);
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const __m256 c10 = _mm256_set1_ps(c10_scalar);
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const __m256 c9 = _mm256_set1_ps(c9_scalar);
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const __m256 c8 = _mm256_set1_ps(c8_scalar);
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const __m256 c7 = _mm256_set1_ps(c7_scalar);
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const __m256 c6 = _mm256_set1_ps(c6_scalar);
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const __m256 c5 = _mm256_set1_ps(c5_scalar);
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const __m256 c4 = _mm256_set1_ps(c4_scalar);
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const __m256 c3 = _mm256_set1_ps(c3_scalar);
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const __m256 c2 = _mm256_set1_ps(c2_scalar);
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const __m256 c1 = _mm256_set1_ps(c1_scalar);
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const __m256 c0 = _mm256_set1_ps(c0_scalar);
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__m256 p = c13;
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// # 13 * (8 MULTs, 8 ADDs)
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// # = 104 MULTs, 104 ADDs
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p = _mm256_fmadd_ps(p, r, c12);
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p = _mm256_fmadd_ps(p, r, c11);
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p = _mm256_fmadd_ps(p, r, c10);
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p = _mm256_fmadd_ps(p, r, c9);
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p = _mm256_fmadd_ps(p, r, c8);
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p = _mm256_fmadd_ps(p, r, c7);
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p = _mm256_fmadd_ps(p, r, c6);
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p = _mm256_fmadd_ps(p, r, c5);
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p = _mm256_fmadd_ps(p, r, c4);
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p = _mm256_fmadd_ps(p, r, c3);
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p = _mm256_fmadd_ps(p, r, c2);
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p = _mm256_fmadd_ps(p, r, c1);
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p = _mm256_fmadd_ps(p, r, c0);
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__m256i ni = _mm256_cvtps_epi32(nf);
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__m256i biased = _mm256_add_epi32(ni, _mm256_set1_epi32(127));
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__m256i scaled = _mm256_slli_epi32(biased, 23);
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__m256 pow2n = _mm256_castsi256_ps(scaled);
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return _mm256_mul_ps(p, pow2n); // # 8 MULTs
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}
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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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(void)pedestrians;
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#if BENCHMARK
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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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vector<tuple<int, int, float, float, float, float, 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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for (int i = 0; i < n_p; i++) {
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samples.emplace_back(0, i, pos_x[i], pos_y[i], e_x[i], e_y[i], color[i]);
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}
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}
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#endif
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const int n_p_pad = (n_p + 7) & ~7;
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alignas(32) const float lane_offset_arr[8] = {0.0f, 1.0f, 2.0f, 3.0f, 4.0f, 5.0f, 6.0f, 7.0f};
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const __m256 lane_off = _mm256_load_ps(lane_offset_arr);
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const __m256 v_neg_v0_div_2s = _mm256_set1_ps(NEG_V0_AB_div_TWO_SIGMA);
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const __m256 v_neg_2s_inv = _mm256_set1_ps(NEG_TWO_SIGMA_INV);
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const __m256 v_cos_phi_sq = _mm256_set1_ps(cos_phi_sq);
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const __m256 v_dt_neg = _mm256_set1_ps(dt_neg);
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const __m256 v_c_neg_dt = _mm256_set1_ps(c_neg_times_dt);
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const __m256 v_zero = _mm256_setzero_ps();
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const __m256 v_one = _mm256_set1_ps(1.0f);
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const __m256 v_eps = _mm256_set1_ps(EPS);
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const __m256 v_eps_sq = _mm256_set1_ps(EPS_SQ);
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const __m256 v_np = _mm256_set1_ps((float)n_p);
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const __m256 v_exp_min = _mm256_set1_ps(-87.0f); // clamp for polyexp, below this exp(x) ~ 0 anyway
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// # flops per iteration (one pass of the outer time loop):
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// # ADDs: n_p * 22 + n_p * n_p_pad * 29 + n_p * board.n_obstacles * 10 + n_p * 7
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// # MULTs: n_p * 4 + n_p * n_p_pad * 40 + n_p * board.n_obstacles * 13 + n_p * 16
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// # DIVs: n_p * n_p_pad * 1 + n_p * board.n_obstacles + n_p * 2
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// # SQRTs: n_p * n_p_pad * 3 + n_p * board.n_obstacles + n_p * 3
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// # EXPs: n_p * board.n_obstacles
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for (int t = 0; t < n_iter; t++) {
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for (int i = 0; i < n_p; i++) {
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float desired_velocity_x = e_x[i] * desired_v0[i]; // # 1 MULT
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float desired_velocity_y = e_y[i] * desired_v0[i]; // # 1 MULT
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float f_alpha_dt_x = (desired_velocity_x - curr_vel_x[i]) * dt_times_tau_alpha_inv; // # 1 MULT, 1 ADD
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float f_alpha_dt_y = (desired_velocity_y - curr_vel_y[i]) * dt_times_tau_alpha_inv; // # 1 MULT, 1 ADD
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const __m256 pix = _mm256_set1_ps(pos_x[i]);
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const __m256 piy = _mm256_set1_ps(pos_y[i]);
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const __m256 eix = _mm256_set1_ps(e_x[i]);
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const __m256 eiy = _mm256_set1_ps(e_y[i]);
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const __m256 v_i = _mm256_set1_ps((float)i);
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__m256 acc_x = _mm256_setzero_ps();
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__m256 acc_y = _mm256_setzero_ps();
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for (int j = 0; j < n_p_pad; j += 8) {
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__m256 j_idx = _mm256_add_ps(_mm256_set1_ps((float)j), lane_off); // # 8 ADDs
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__m256 m_neq_i = _mm256_cmp_ps(j_idx, v_i, _CMP_NEQ_OQ);
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__m256 m_in_range = _mm256_cmp_ps(j_idx, v_np, _CMP_LT_OQ);
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__m256 active = _mm256_and_ps(m_neq_i, m_in_range);
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__m256 pjx = _mm256_loadu_ps(&pos_x[j]);
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__m256 pjy = _mm256_loadu_ps(&pos_y[j]);
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__m256 sbe_jx = _mm256_loadu_ps(&sb_e_x[j]);
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__m256 sbe_jy = _mm256_loadu_ps(&sb_e_y[j]);
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__m256 sb_jsq = _mm256_loadu_ps(&sb_sq[j]);
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__m256 r_ab_x = _mm256_sub_ps(pix, pjx); // # 8 ADDs
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__m256 r_ab_y = _mm256_sub_ps(piy, pjy); // # 8 ADDs
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__m256 r_ab_n2 = _mm256_fmadd_ps(r_ab_x, r_ab_x, _mm256_mul_ps(r_ab_y, r_ab_y)); // # 16 MULTs, 8 ADDs
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__m256 r_ab_n = _mm256_sqrt_ps(r_ab_n2); // # 8 SQRTs
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r_ab_n = _mm256_max_ps(r_ab_n, v_eps);
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__m256 r_ab2_x = _mm256_sub_ps(r_ab_x, sbe_jx); // # 8 ADDs
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__m256 r_ab2_y = _mm256_sub_ps(r_ab_y, sbe_jy); // # 8 ADDs
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__m256 r_ab2_n2 = _mm256_fmadd_ps(r_ab2_x, r_ab2_x, _mm256_mul_ps(r_ab2_y, r_ab2_y)); // # 16 MULTs, 8 ADDs
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__m256 r_ab2_n = _mm256_sqrt_ps(r_ab2_n2); // # 8 SQRTs
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r_ab2_n = _mm256_max_ps(r_ab2_n, v_eps);
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__m256 r_sum = _mm256_add_ps(r_ab_n, r_ab2_n); // # 8 ADDs
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__m256 two_b_sq = _mm256_fmsub_ps(r_sum, r_sum, sb_jsq); // # 8 MULTs, 8 ADDs
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two_b_sq = _mm256_max_ps(two_b_sq, v_eps_sq);
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__m256 two_b = _mm256_sqrt_ps(two_b_sq); // # 8 SQRTs
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// simd polynomial expf, no libm call. replaces the 8-iter scalar loop that gcc refused to unroll.
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// clamp e_arg >= -87 first: exp(-87) ~ 1.6e-38 is already basically 0, and the schraudolph 2^n
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// bit trick blows up if (nf + 127) goes negative (which happens for padding lanes where e_arg ~ -4.7e9).
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__m256 e_arg = _mm256_mul_ps(two_b, v_neg_2s_inv); // # 8 MULTs
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e_arg = _mm256_max_ps(e_arg, v_exp_min);
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__m256 e_val = exp256_ps(e_arg); // # 128 MULTs, 112 ADDs
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__m256 numer = _mm256_mul_ps(_mm256_mul_ps(r_sum, v_neg_v0_div_2s), e_val); // # 16 MULTs
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__m256 denom = _mm256_mul_ps(_mm256_mul_ps(two_b, r_ab_n), r_ab2_n); // # 16 MULTs
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__m256 denom_safe = _mm256_blendv_ps(v_one, denom, active); // bitwise, no flop
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__m256 smc = _mm256_div_ps(numer, denom_safe); // # 8 DIVs
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__m256 sm_r_ab = _mm256_mul_ps(smc, r_ab2_n); // # 8 MULTs
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__m256 sm_r_ab2 = _mm256_mul_ps(smc, r_ab_n); // # 8 MULTs
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__m256 f_x = _mm256_fmadd_ps(r_ab2_x, sm_r_ab2, _mm256_mul_ps(r_ab_x, sm_r_ab)); // # 16 MULTs, 8 ADDs
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__m256 f_y = _mm256_fmadd_ps(r_ab2_y, sm_r_ab2, _mm256_mul_ps(r_ab_y, sm_r_ab)); // # 16 MULTs, 8 ADDs
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__m256 f_norm_sq = _mm256_fmadd_ps(f_x, f_x, _mm256_mul_ps(f_y, f_y)); // # 16 MULTs, 8 ADDs
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__m256 rhs = _mm256_mul_ps(f_norm_sq, v_cos_phi_sq); // # 8 MULTs
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__m256 e_dot_f = _mm256_fmadd_ps(eix, f_x, _mm256_mul_ps(eiy, f_y)); // # 16 MULTs, 8 ADDs
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__m256 e_dot_f_sq = _mm256_mul_ps(e_dot_f, e_dot_f); // # 8 MULTs
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__m256 c1 = _mm256_cmp_ps(e_dot_f, v_zero, _CMP_LT_OQ);
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__m256 c2 = _mm256_cmp_ps(e_dot_f_sq, rhs, _CMP_GT_OQ);
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__m256 cond = _mm256_and_ps(c1, c2);
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__m256 w_val = _mm256_blendv_ps(v_dt_neg, v_c_neg_dt, cond);
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__m256 f_x_safe = _mm256_and_ps(f_x, active); // bitwise, no flop
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__m256 f_y_safe = _mm256_and_ps(f_y, active); // bitwise, no flop
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acc_x = _mm256_fmadd_ps(f_x_safe, w_val, acc_x); // # 8 MULTs, 8 ADDs
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acc_y = _mm256_fmadd_ps(f_y_safe, w_val, acc_y); // # 8 MULTs, 8 ADDs
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}
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__m256 hsum = _mm256_hadd_ps(acc_x, acc_y); // # 8 ADDs
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__m128 hsum_lo = _mm256_castps256_ps128(hsum);
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__m128 hsum_hi = _mm256_extractf128_ps(hsum, 1);
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__m128 sum4 = _mm_add_ps(hsum_lo, hsum_hi); // # 4 ADDs
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sum4 = _mm_hadd_ps(sum4, sum4); // # 4 ADDs
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alignas(16) float sum_out[4];
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_mm_store_ps(sum_out, sum4);
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f_alpha_dt_x += sum_out[0]; // # 1 ADD
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f_alpha_dt_y += sum_out[1]; // # 1 ADD
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for (int k = 0; k < board.n_obstacles; k++) {
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float v1_x = pos_x[i] - board.obstacles[k].start_x; // # 1 ADD
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float v1_y = pos_y[i] - board.obstacles[k].start_y; // # 1 ADD
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float v2_x = board.obstacles[k].obstacle_v_x;
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float v2_y = board.obstacles[k].obstacle_v_y;
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float projection = (v1_x * v2_x + v1_y * v2_y) * board.obstacles[k].length_sq_inv; // # 3 MULTs, 1 ADD
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if (projection < 0.0)
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projection = 0.0;
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else if (projection > 1.0)
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projection = 1.0;
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float r_aB_x = pos_x[i] - (board.obstacles[k].start_x + board.obstacles[k].obstacle_v_x * projection); // # 1 MULT, 2 ADDs
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float r_aB_y = pos_y[i] - (board.obstacles[k].start_y + board.obstacles[k].obstacle_v_y * projection); // # 1 MULT, 2 ADDs
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float r_aB_norm = sqrt(r_aB_x * r_aB_x + r_aB_y * r_aB_y); // # 2 MULTs, 1 ADD, 1 SQRT
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r_aB_norm = r_aB_norm > EPS ? r_aB_norm : EPS;
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float scalar_mult = (NEG_U0_AB_div_R * exp(r_aB_norm * NEG_R_INV)) / r_aB_norm; // # 2 MULTs, 1 EXP, 1 DIV
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float f_alpha_B_neg_x = r_aB_x * scalar_mult; // # 1 MULT
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float f_alpha_B_neg_y = r_aB_y * scalar_mult; // # 1 MULT
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float w_val;
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float e_dot_f = (f_alpha_B_neg_y == 0) ? 0 : (f_alpha_B_neg_y < 0 ? -e_y[i] : e_y[i]);
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if (e_dot_f >= cos_phi)
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w_val = dt_neg;
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else
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w_val = c_neg_times_dt;
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float f_alpha_B_dt_x = f_alpha_B_neg_x * w_val; // # 1 MULT
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float f_alpha_B_dt_y = f_alpha_B_neg_y * w_val; // # 1 MULT
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f_alpha_dt_x += f_alpha_B_dt_x; // # 1 ADD
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f_alpha_dt_y += f_alpha_B_dt_y; // # 1 ADD
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}
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w_x[i] += f_alpha_dt_x; // # 1 ADD
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w_y[i] += f_alpha_dt_y; // # 1 ADD
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}
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for (int i = 0; i < n_p; i++) {
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float w_norm = sqrt(w_x[i] * w_x[i] + w_y[i] * w_y[i]); // # 2 MULTs, 1 ADD, 1 SQRT
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float w_norm2 = w_norm > EPS ? w_norm : EPS;
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float correction_factor = min(1.0f, v_max[i] / w_norm2); // # 1 DIV
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curr_vel_x[i] = w_x[i] * correction_factor; // # 1 MULT
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curr_vel_y[i] = w_y[i] * correction_factor; // # 1 MULT
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pos_x[i] = pos_x[i] + curr_vel_x[i] * dt; // # 1 MULT, 1 ADD
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pos_y[i] = pos_y[i] + curr_vel_y[i] * dt; // # 1 MULT, 1 ADD
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if (color[i] == 0 && pos_x[i] > (BOARD_LENGTH - 1.5)) {
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pos_x[i] = 1.0;
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destination_y[i] = pos_y[i];
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w_x[i] = desired_v0[i];
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w_y[i] = 0.0;
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curr_vel_x[i] = w_x[i];
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curr_vel_y[i] = w_y[i];
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}
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if (color[i] == 1 && pos_x[i] < 1.5) {
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pos_x[i] = BOARD_LENGTH - 1.0;
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destination_y[i] = pos_y[i];
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w_x[i] = -desired_v0[i];
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w_y[i] = 0.0;
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curr_vel_x[i] = w_x[i];
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curr_vel_y[i] = w_y[i];
|
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}
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|
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pos_y[i] = clamp(pos_y[i], WALL_EPS, BOARD_WIDTH_MINUS_WALL_EPS);
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|
|
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float ex = destination_x[i] - pos_x[i]; // # 1 ADD
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float ey = destination_y[i] - pos_y[i]; // # 1 ADD
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|
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float e_norm = sqrt(ex * ex + ey * ey); // # 2 MULTs, 1 ADD, 1 SQRT
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float e_norm2 = e_norm > EPS ? e_norm : EPS;
|
|
float e_norm_inv = 1.0 / e_norm2; // # 1 DIV
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|
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e_x[i] = ex * e_norm_inv; // # 1 MULT
|
|
e_y[i] = ey * e_norm_inv; // # 1 MULT
|
|
|
|
float velocity_norm_sq = curr_vel_x[i] * curr_vel_x[i] + curr_vel_y[i] * curr_vel_y[i]; // # 2 MULTs, 1 ADD
|
|
float velocity_norm = sqrt(velocity_norm_sq); // # 1 SQRT
|
|
|
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sb_sq[i] = velocity_norm_sq * delta_t_sq; // # 1 MULT
|
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sb_e_x[i] = e_x[i] * (velocity_norm * delta_t); // # 2 MULTs (vel_norm*delta_t shared with next line)
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sb_e_y[i] = e_y[i] * (velocity_norm * delta_t); // # 1 MULT
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|
|
|
#if !BENCHMARK
|
|
if (dump_path && (t % dump_interval == 0)) {
|
|
samples.emplace_back(t + 1, i, pos_x[i], pos_y[i], e_x[i], e_y[i], color[i]);
|
|
}
|
|
#endif
|
|
}
|
|
}
|
|
|
|
#if !BENCHMARK
|
|
if (dump_path) {
|
|
ofstream out(dump_path);
|
|
out << "time,id,x,y,p.e.x,p.e.y,color\n";
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|
|
|
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;
|
|
}
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