variant with rsqrt
This commit is contained in:
Linus Baumberger
committed by
[Quy Anh] «Elliot» Nguyen
[Quy Anh] «Elliot» Nguyen
parent
c684c9e780
commit
9d8d63f1bf
@@ -0,0 +1,464 @@
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// # Changes: pure vrsqrtps
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// # Predecessor: variant_float_inlining_SoA_AVX2_polyexp.cpp
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//
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// We first tried rsqrt + 1 Newton step to keep full sqrt precision, but it
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// turned out slower than just using vsqrtps. The Newton step needs 2 muls
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// and an fnmadd on top of rsqrt, so the whole recovered sqrt ends up at
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// ~20 cycles of latency, while vsqrtps is only 12. Since the OoO core was
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// already running multiple sqrts in parallel, sqrt throughput wasn't really
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// the bottleneck. All the Newton step did was make the dependency chain
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// longer, which hurt more than the faster rsqrt helped.
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//
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// So we drop the Newton step. rsqrt + 1 mul gives us a sqrt in 8 cycles
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// with about 12-bit precision, which is well within the 1cm verify tolerance.
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// The main structural win is killing the vdivps. rsqrt produces 1/sqrt(x)
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// directly, so we keep the inverses around (inv_r_ab_n, inv_r_ab2_n,
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// inv_two_b) and rewrite the force scaling. The original had
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// "numer / (two_b * r_ab_n * r_ab2_n)" which needs a vdivps; now it's
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// "numer * inv_two_b * inv_r_ab_n * inv_r_ab2_n", trading one divide for
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// two muls. Divide was the long-pole op on port 0, so this is the bigger
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// of the two changes.
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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, same as the predecessor. degree-5 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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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);
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const __m256 ln2 = _mm256_set1_ps(0.6931471805599453f);
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__m256 r = _mm256_fnmadd_ps(nf, ln2, x);
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const __m256 c5 = _mm256_set1_ps(1.0f / 120.0f);
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const __m256 c4 = _mm256_set1_ps(1.0f / 24.0f);
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const __m256 c3 = _mm256_set1_ps(1.0f / 6.0f);
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const __m256 c2 = _mm256_set1_ps(0.5f);
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const __m256 c1 = _mm256_set1_ps(1.0f);
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const __m256 c0 = _mm256_set1_ps(1.0f);
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__m256 p = 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);
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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_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);
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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];
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float desired_velocity_y = e_y[i] * desired_v0[i];
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float f_alpha_dt_x = (desired_velocity_x - curr_vel_x[i]) * dt_times_tau_alpha_inv;
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float f_alpha_dt_y = (desired_velocity_y - curr_vel_y[i]) * dt_times_tau_alpha_inv;
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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);
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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);
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__m256 r_ab_y = _mm256_sub_ps(piy, pjy);
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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));
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// clamp before rsqrt: rsqrt(0) = inf, then x*inf = 0*inf = NaN downstream. EPS_SQ
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// means the inv_sqrt tops out at 1/EPS and r_ab_n = EPS_SQ/EPS = EPS, matches the predecessor.
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r_ab_n2 = _mm256_max_ps(r_ab_n2, v_eps_sq);
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__m256 inv_r_ab_n = _mm256_rsqrt_ps(r_ab_n2);
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__m256 r_ab_n = _mm256_mul_ps(r_ab_n2, inv_r_ab_n);
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__m256 r_ab2_x = _mm256_sub_ps(r_ab_x, sbe_jx);
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__m256 r_ab2_y = _mm256_sub_ps(r_ab_y, sbe_jy);
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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));
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r_ab2_n2 = _mm256_max_ps(r_ab2_n2, v_eps_sq);
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__m256 inv_r_ab2_n = _mm256_rsqrt_ps(r_ab2_n2);
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__m256 r_ab2_n = _mm256_mul_ps(r_ab2_n2, inv_r_ab2_n);
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__m256 r_sum = _mm256_add_ps(r_ab_n, r_ab2_n);
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__m256 two_b_sq = _mm256_fmsub_ps(r_sum, r_sum, sb_jsq);
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two_b_sq = _mm256_max_ps(two_b_sq, v_eps_sq);
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__m256 inv_two_b = _mm256_rsqrt_ps(two_b_sq);
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__m256 two_b = _mm256_mul_ps(two_b_sq, inv_two_b);
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__m256 e_arg = _mm256_mul_ps(two_b, v_neg_2s_inv);
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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);
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// smc = numer/denom in the predecessor. with inv-sqrts in hand the divide is free:
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// sm_r_ab = smc * r_ab2_n = numer / (two_b * r_ab_n) = numer * inv_two_b * inv_r_ab_n
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// sm_r_ab2 = smc * r_ab_n = numer / (two_b * r_ab2_n) = numer * inv_two_b * inv_r_ab2_n
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// for the i==j and padding lanes inv_two_b*inv_r_ab_n is huge, but the active-mask AND on
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// f_x/f_y below zeros the lane out before accumulation so it cant pollute anything.
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__m256 numer_inv_two_b = _mm256_mul_ps(_mm256_mul_ps(r_sum, v_neg_v0_div_2s), _mm256_mul_ps(e_val, inv_two_b));
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__m256 sm_r_ab = _mm256_mul_ps(numer_inv_two_b, inv_r_ab_n);
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__m256 sm_r_ab2 = _mm256_mul_ps(numer_inv_two_b, inv_r_ab2_n);
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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));
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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));
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__m256 f_norm_sq = _mm256_fmadd_ps(f_x, f_x, _mm256_mul_ps(f_y, f_y));
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__m256 rhs = _mm256_mul_ps(f_norm_sq, v_cos_phi_sq);
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__m256 e_dot_f = _mm256_fmadd_ps(eix, f_x, _mm256_mul_ps(eiy, f_y));
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__m256 e_dot_f_sq = _mm256_mul_ps(e_dot_f, e_dot_f);
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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);
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__m256 f_y_safe = _mm256_and_ps(f_y, active);
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acc_x = _mm256_fmadd_ps(f_x_safe, w_val, acc_x);
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acc_y = _mm256_fmadd_ps(f_y_safe, w_val, acc_y);
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}
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__m256 hsum = _mm256_hadd_ps(acc_x, acc_y);
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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);
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sum4 = _mm_hadd_ps(sum4, sum4);
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alignas(16) float sum_out[4];
|
||||
_mm_store_ps(sum_out, sum4);
|
||||
f_alpha_dt_x += sum_out[0];
|
||||
f_alpha_dt_y += sum_out[1];
|
||||
|
||||
for (int k = 0; k < board.n_obstacles; k++) {
|
||||
|
||||
float v1_x = pos_x[i] - board.obstacles[k].start_x;
|
||||
float v1_y = pos_y[i] - board.obstacles[k].start_y;
|
||||
float v2_x = board.obstacles[k].obstacle_v_x;
|
||||
float v2_y = board.obstacles[k].obstacle_v_y;
|
||||
|
||||
float projection = (v1_x * v2_x + v1_y * v2_y) * board.obstacles[k].length_sq_inv;
|
||||
|
||||
if (projection < 0.0)
|
||||
projection = 0.0;
|
||||
else if (projection > 1.0)
|
||||
projection = 1.0;
|
||||
|
||||
float r_aB_x = pos_x[i] - (board.obstacles[k].start_x + board.obstacles[k].obstacle_v_x * projection);
|
||||
float r_aB_y = pos_y[i] - (board.obstacles[k].start_y + board.obstacles[k].obstacle_v_y * projection);
|
||||
|
||||
float r_aB_norm = sqrt(r_aB_x * r_aB_x + r_aB_y * r_aB_y);
|
||||
r_aB_norm = r_aB_norm > EPS ? r_aB_norm : EPS;
|
||||
|
||||
float scalar_mult = (NEG_U0_AB_div_R * exp(r_aB_norm * NEG_R_INV)) / r_aB_norm;
|
||||
float f_alpha_B_neg_x = r_aB_x * scalar_mult;
|
||||
float f_alpha_B_neg_y = r_aB_y * scalar_mult;
|
||||
|
||||
float w_val;
|
||||
|
||||
float e_dot_f = (f_alpha_B_neg_y == 0) ? 0 : (f_alpha_B_neg_y < 0 ? -e_y[i] : e_y[i]);
|
||||
|
||||
if (e_dot_f >= cos_phi)
|
||||
w_val = dt_neg;
|
||||
else
|
||||
w_val = c_neg_times_dt;
|
||||
|
||||
float f_alpha_B_dt_x = f_alpha_B_neg_x * w_val;
|
||||
float f_alpha_B_dt_y = f_alpha_B_neg_y * w_val;
|
||||
|
||||
f_alpha_dt_x += f_alpha_B_dt_x;
|
||||
f_alpha_dt_y += f_alpha_B_dt_y;
|
||||
}
|
||||
|
||||
w_x[i] += f_alpha_dt_x;
|
||||
w_y[i] += f_alpha_dt_y;
|
||||
}
|
||||
|
||||
for (int i = 0; i < n_p; i++) {
|
||||
|
||||
float w_norm = sqrt(w_x[i] * w_x[i] + w_y[i] * w_y[i]);
|
||||
float w_norm2 = w_norm > EPS ? w_norm : EPS;
|
||||
float correction_factor = min(1.0f, v_max[i] / w_norm2);
|
||||
|
||||
curr_vel_x[i] = w_x[i] * correction_factor;
|
||||
curr_vel_y[i] = w_y[i] * correction_factor;
|
||||
|
||||
pos_x[i] = pos_x[i] + curr_vel_x[i] * dt;
|
||||
pos_y[i] = pos_y[i] + curr_vel_y[i] * dt;
|
||||
|
||||
if (color[i] == 0 && pos_x[i] > (BOARD_LENGTH - 1.5)) {
|
||||
pos_x[i] = 1.0;
|
||||
destination_y[i] = pos_y[i];
|
||||
w_x[i] = desired_v0[i];
|
||||
w_y[i] = 0.0;
|
||||
curr_vel_x[i] = w_x[i];
|
||||
curr_vel_y[i] = w_y[i];
|
||||
}
|
||||
if (color[i] == 1 && pos_x[i] < 1.5) {
|
||||
pos_x[i] = BOARD_LENGTH - 1.0;
|
||||
destination_y[i] = pos_y[i];
|
||||
w_x[i] = -desired_v0[i];
|
||||
w_y[i] = 0.0;
|
||||
curr_vel_x[i] = w_x[i];
|
||||
curr_vel_y[i] = w_y[i];
|
||||
}
|
||||
|
||||
pos_y[i] = clamp(pos_y[i], WALL_EPS, BOARD_WIDTH_MINUS_WALL_EPS);
|
||||
|
||||
float ex = destination_x[i] - pos_x[i];
|
||||
float ey = destination_y[i] - pos_y[i];
|
||||
|
||||
float e_norm = sqrt(ex * ex + ey * ey);
|
||||
float e_norm2 = e_norm > EPS ? e_norm : EPS;
|
||||
float e_norm_inv = 1.0 / e_norm2;
|
||||
|
||||
e_x[i] = ex * e_norm_inv;
|
||||
e_y[i] = ey * e_norm_inv;
|
||||
|
||||
float velocity_norm_sq = curr_vel_x[i] * curr_vel_x[i] + curr_vel_y[i] * curr_vel_y[i];
|
||||
float velocity_norm = sqrt(velocity_norm_sq);
|
||||
|
||||
sb_sq[i] = velocity_norm_sq * delta_t_sq;
|
||||
sb_e_x[i] = e_x[i] * (velocity_norm * delta_t);
|
||||
sb_e_y[i] = e_y[i] * (velocity_norm * delta_t);
|
||||
|
||||
#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";
|
||||
|
||||
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