From 6c339dcc3b9d43d4c2c90f34a140fbd6d25d5141 Mon Sep 17 00:00:00 2001 From: lbaumberger Date: Fri, 12 Jun 2026 16:45:05 +0200 Subject: [PATCH] flopcount for the initial float soa avx2 variant --- ...iant_float_inlining_SoA_AVX2_flopcount.cpp | 449 ++++++++++++++++++ 1 file changed, 449 insertions(+) create mode 100644 variants/variant_float_inlining_SoA_AVX2_flopcount.cpp diff --git a/variants/variant_float_inlining_SoA_AVX2_flopcount.cpp b/variants/variant_float_inlining_SoA_AVX2_flopcount.cpp new file mode 100644 index 0000000..bbc98d7 --- /dev/null +++ b/variants/variant_float_inlining_SoA_AVX2_flopcount.cpp @@ -0,0 +1,449 @@ +// # Changes: AVX2 vectorization of the ped-ped inner loop (8 floats per __m256, exp still scalar) +// # Predecessor: variant_float_inlining_SoA.cpp + +#include "../headers/board_reduced_float.hpp" +#include "../headers/constants_float.hpp" +#include "../headers/pedestrian_reduced_float.hpp" + +#include // avx2 + +#include +#include +#include +#include +#include +#include +#include +#include + +#define SEED 42 +#define BOARD_WIDTH 10.0f +#define BOARD_LENGTH 50.0f +#define WALL_EPS 1e-3f +#define BOARD_WIDTH_MINUS_WALL_EPS 9.999f + +#ifndef RANDOM_SEED +#define RANDOM_SEED 0 +#endif + +#ifndef BENCHMARK +#define BENCHMARK 0 +#endif + +using namespace std; + +// same SoA arrays as the predecessor, but we pad to multiple of 8 so the avx loop is clean +vector pos_x, pos_y; +vector sb_sq; +vector sb_e_x, sb_e_y; +vector e_x, e_y; +vector curr_vel_x, curr_vel_y; +vector w_x, w_y; +vector desired_v0; +vector v_max; +vector destination_x, destination_y; +vector color; + +Pedestrian *init_pedestrians(int n_p) { +#if RANDOM_SEED + random_device rd; + mt19937 gen(rd()); +#else + mt19937 gen(SEED); +#endif + + normal_distribution velocity_gen(v0_mean, v0_std_dev); + uniform_real_distribution y_gen(0.3, BOARD_WIDTH - 0.3); + uniform_real_distribution x_gen_left(2.0, BOARD_LENGTH / 2.0); + uniform_real_distribution x_gen_right(BOARD_LENGTH / 2.0, BOARD_LENGTH - 2.0); + + const int n_p_pad = (n_p + 7) & ~7; // round up to a multiple of 8 for avx float lanes + + pos_x.resize(n_p_pad); + pos_y.resize(n_p_pad); + sb_sq.resize(n_p_pad); + sb_e_x.resize(n_p_pad); + sb_e_y.resize(n_p_pad); + e_x.resize(n_p_pad); + e_y.resize(n_p_pad); + curr_vel_x.resize(n_p_pad); + curr_vel_y.resize(n_p_pad); + w_x.resize(n_p_pad); + w_y.resize(n_p_pad); + desired_v0.resize(n_p_pad); + v_max.resize(n_p_pad); + destination_x.resize(n_p_pad); + destination_y.resize(n_p_pad); + color.resize(n_p_pad); + + int n_p_half = n_p / 2; + + for (int i = 0; i < n_p_half; i++) { + float x = x_gen_left(gen); + float y = y_gen(gen); + + float dest_x = BOARD_LENGTH + 30.0; // renamed to avoid shadowing destination_x[] + float dest_y = y; + + float init_e_x = dest_x - x; + float init_e_y = dest_y - y; + float init_e_norm = sqrt(init_e_x * init_e_x + init_e_y * init_e_y); + float init_e_unit_x = init_e_x / init_e_norm; + float init_e_unit_y = init_e_y / init_e_norm; + + float d_v0; + do { + d_v0 = velocity_gen(gen); + } while (d_v0 <= 0.1); + + float v_m = 1.3 * d_v0; + + color[i] = 0; + pos_x[i] = x; + pos_y[i] = y; + e_x[i] = init_e_unit_x; + e_y[i] = init_e_unit_y; + v_max[i] = v_m; + desired_v0[i] = d_v0; + destination_x[i] = dest_x; + destination_y[i] = dest_y; + + w_x[i] = 0.0f; + w_y[i] = 0.0f; + curr_vel_x[i] = 0.0f; + curr_vel_y[i] = 0.0f; + sb_sq[i] = 0.0f; + sb_e_x[i] = 0.0f; + sb_e_y[i] = 0.0f; + } + + for (int i = n_p_half; i < n_p; i++) { + float x = x_gen_right(gen); + float y = y_gen(gen); + + float dest_x = -30; + float dest_y = y; + + float init_e_x = dest_x - x; + float init_e_y = dest_y - y; + float init_e_norm = sqrt(init_e_x * init_e_x + init_e_y * init_e_y); + float init_e_unit_x = init_e_x / init_e_norm; + float init_e_unit_y = init_e_y / init_e_norm; + + float d_v0; + do { + d_v0 = velocity_gen(gen); + } while (d_v0 <= 0.1); + + float v_m = 1.3 * d_v0; + + color[i] = 1; + pos_x[i] = x; + pos_y[i] = y; + e_x[i] = init_e_unit_x; + e_y[i] = init_e_unit_y; + v_max[i] = v_m; + desired_v0[i] = d_v0; + destination_x[i] = dest_x; + destination_y[i] = dest_y; + + w_x[i] = 0.0f; + w_y[i] = 0.0f; + curr_vel_x[i] = 0.0f; + curr_vel_y[i] = 0.0f; + sb_sq[i] = 0.0f; + sb_e_x[i] = 0.0f; + sb_e_y[i] = 0.0f; + } + + // padding lanes: park them far away, zero everything else. + // exp(very negative) is roughly 0 and the active mask zeroes their contribution anyway. + for (int j = n_p; j < n_p_pad; j++) { + pos_x[j] = 1e9f; + pos_y[j] = 1e9f; + sb_sq[j] = 0.0f; + sb_e_x[j] = 0.0f; + sb_e_y[j] = 0.0f; + } + return nullptr; +} + +Board init_board_without_obstacles() { return Board(BOARD_LENGTH, BOARD_WIDTH, 0, nullptr); } + +int run_simulation(Pedestrian *pedestrians, Board &board, int n_p, int n_iter, const char *dump_path) { + (void)pedestrians; +#if BENCHMARK + (void)dump_path; +#endif + +#if !BENCHMARK + const int dump_interval = 1; + + vector> samples; + + if (dump_path) { + samples.reserve(static_cast(n_iter / dump_interval + 1) * n_p); + + for (int i = 0; i < n_p; i++) { + samples.emplace_back(0, i, pos_x[i], pos_y[i], e_x[i], e_y[i], color[i]); + } + } +#endif + + const int n_p_pad = (n_p + 7) & ~7; + + // {0,1,2,3,4,5,6,7} so we can build per-iter j indices as (j + lane_off) + alignas(32) const float lane_offset_arr[8] = {0.0f, 1.0f, 2.0f, 3.0f, 4.0f, 5.0f, 6.0f, 7.0f}; + const __m256 lane_off = _mm256_load_ps(lane_offset_arr); + + // constants broadcast to all 8 lanes once + const __m256 v_neg_v0_div_2s = _mm256_set1_ps(NEG_V0_AB_div_TWO_SIGMA); + const __m256 v_neg_2s_inv = _mm256_set1_ps(NEG_TWO_SIGMA_INV); + const __m256 v_cos_phi_sq = _mm256_set1_ps(cos_phi_sq); + const __m256 v_dt_neg = _mm256_set1_ps(dt_neg); + const __m256 v_c_neg_dt = _mm256_set1_ps(c_neg_times_dt); + const __m256 v_zero = _mm256_setzero_ps(); + const __m256 v_one = _mm256_set1_ps(1.0f); + const __m256 v_eps = _mm256_set1_ps(EPS); + const __m256 v_eps_sq = _mm256_set1_ps(EPS_SQ); + const __m256 v_np = _mm256_set1_ps((float)n_p); + + // # flops per iteration (one pass of the outer time loop): + // # ADDs: n_p * 22 + n_p * n_p_pad * 15 + n_p * board.n_obstacles * 10 + n_p * 7 + // # MULTs: n_p * 4 + n_p * n_p_pad * 24 + n_p * board.n_obstacles * 13 + n_p * 16 + // # DIVs: n_p * n_p_pad * 1 + n_p * board.n_obstacles + n_p * 2 + // # SQRTs: n_p * n_p_pad * 3 + n_p * board.n_obstacles + n_p * 3 + // # EXPs: n_p * n_p_pad * 1 + n_p * board.n_obstacles + for (int t = 0; t < n_iter; t++) { + + for (int i = 0; i < n_p; i++) { + + float desired_velocity_x = e_x[i] * desired_v0[i]; // # 1 MULT + float desired_velocity_y = e_y[i] * desired_v0[i]; // # 1 MULT + + float f_alpha_dt_x = (desired_velocity_x - curr_vel_x[i]) * dt_times_tau_alpha_inv; // # 1 MULT, 1 ADD + float f_alpha_dt_y = (desired_velocity_y - curr_vel_y[i]) * dt_times_tau_alpha_inv; // # 1 MULT, 1 ADD + + // i is fixed for the inner loops, broadcast its fields once + const __m256 pix = _mm256_set1_ps(pos_x[i]); + const __m256 piy = _mm256_set1_ps(pos_y[i]); + const __m256 eix = _mm256_set1_ps(e_x[i]); + const __m256 eiy = _mm256_set1_ps(e_y[i]); + const __m256 v_i = _mm256_set1_ps((float)i); + + __m256 acc_x = _mm256_setzero_ps(); + __m256 acc_y = _mm256_setzero_ps(); + + for (int j = 0; j < n_p_pad; j += 8) { + // 8 lanes at once, lane k maps to pedestrian j+k + __m256 j_idx = _mm256_add_ps(_mm256_set1_ps((float)j), lane_off); // # 8 ADDs + + // active = (j+k != i) AND (j+k < n_p), zero in lanes we wanna skip + __m256 m_neq_i = _mm256_cmp_ps(j_idx, v_i, _CMP_NEQ_OQ); + __m256 m_in_range = _mm256_cmp_ps(j_idx, v_np, _CMP_LT_OQ); + __m256 active = _mm256_and_ps(m_neq_i, m_in_range); + + // j-side loads, SoA is contiguous. loadu because std::vector only guarantees 16B align + __m256 pjx = _mm256_loadu_ps(&pos_x[j]); + __m256 pjy = _mm256_loadu_ps(&pos_y[j]); + __m256 sbe_jx = _mm256_loadu_ps(&sb_e_x[j]); + __m256 sbe_jy = _mm256_loadu_ps(&sb_e_y[j]); + __m256 sb_jsq = _mm256_loadu_ps(&sb_sq[j]); + + // r_ab = pos_i - pos_j ; |r_ab| with the EPS clamp the scalar version does + __m256 r_ab_x = _mm256_sub_ps(pix, pjx); // # 8 ADDs + __m256 r_ab_y = _mm256_sub_ps(piy, pjy); // # 8 ADDs + __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 + __m256 r_ab_n = _mm256_sqrt_ps(r_ab_n2); // # 8 SQRTs + r_ab_n = _mm256_max_ps(r_ab_n, v_eps); + + // r_ab2 = r_ab - sb_e_j ; |r_ab2| also clamped + __m256 r_ab2_x = _mm256_sub_ps(r_ab_x, sbe_jx); // # 8 ADDs + __m256 r_ab2_y = _mm256_sub_ps(r_ab_y, sbe_jy); // # 8 ADDs + __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 + __m256 r_ab2_n = _mm256_sqrt_ps(r_ab2_n2); // # 8 SQRTs + r_ab2_n = _mm256_max_ps(r_ab2_n, v_eps); + + // 2b = sqrt((|r_ab| + |r_ab2|)^2 - sb_sq_j) ; clamp the inside with EPS_SQ + __m256 r_sum = _mm256_add_ps(r_ab_n, r_ab2_n); // # 8 ADDs + __m256 two_b_sq = _mm256_fmsub_ps(r_sum, r_sum, sb_jsq); // # 8 MULTs, 8 ADDs + two_b_sq = _mm256_max_ps(two_b_sq, v_eps_sq); + __m256 two_b = _mm256_sqrt_ps(two_b_sq); // # 8 SQRTs + + // exp scalar fallback. manually unrolled, otherwise gcc keeps it as a loop with + // one expf call and serialises all 8 (the double avx2 with 4 iters does get unrolled, the 8 here doesn't). + __m256 e_arg = _mm256_mul_ps(two_b, v_neg_2s_inv); // # 8 MULTs + alignas(32) float tmp_arg[8], tmp_val[8]; + _mm256_store_ps(tmp_arg, e_arg); + tmp_val[0] = expf(tmp_arg[0]); + tmp_val[1] = expf(tmp_arg[1]); + tmp_val[2] = expf(tmp_arg[2]); + tmp_val[3] = expf(tmp_arg[3]); + tmp_val[4] = expf(tmp_arg[4]); + tmp_val[5] = expf(tmp_arg[5]); + tmp_val[6] = expf(tmp_arg[6]); + tmp_val[7] = expf(tmp_arg[7]); // # 8 EXPs (1 per lane, scalar) + __m256 e_val = _mm256_load_ps(tmp_val); + + // smc = (r_sum * NEG_V0_AB_div_TWO_SIGMA * e_val) / (two_b * r_ab_n * r_ab2_n) + // i==j and padding lanes collapse the denom, so we swap in 1.0 there to keep smc finite. + // the AND with active below zeroes those lanes anyway. + __m256 numer = _mm256_mul_ps(_mm256_mul_ps(r_sum, v_neg_v0_div_2s), e_val); // # 16 MULTs + __m256 denom = _mm256_mul_ps(_mm256_mul_ps(two_b, r_ab_n), r_ab2_n); // # 16 MULTs + __m256 denom_safe = _mm256_blendv_ps(v_one, denom, active); // bitwise, no flop + __m256 smc = _mm256_div_ps(numer, denom_safe); // # 8 DIVs + + __m256 sm_r_ab = _mm256_mul_ps(smc, r_ab2_n); // # 8 MULTs + __m256 sm_r_ab2 = _mm256_mul_ps(smc, r_ab_n); // # 8 MULTs + + // scalar: f_x = r_ab_x * sm_r_ab + r_ab2_x * sm_r_ab2 + __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 + __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 + + // float w_val: default dt_neg, switch to c_neg_times_dt when + //(e_dot_f < 0 AND e_dot_f_sq > f_norm_sq * cos_phi_sq). + // this is the DeMorgan of the scalar's if (e_dot_f >= 0 || e_dot_f_sq <= rhs) + __m256 f_norm_sq = _mm256_fmadd_ps(f_x, f_x, _mm256_mul_ps(f_y, f_y)); // # 16 MULTs, 8 ADDs + __m256 rhs = _mm256_mul_ps(f_norm_sq, v_cos_phi_sq); // # 8 MULTs + __m256 e_dot_f = _mm256_fmadd_ps(eix, f_x, _mm256_mul_ps(eiy, f_y)); // # 16 MULTs, 8 ADDs + __m256 e_dot_f_sq = _mm256_mul_ps(e_dot_f, e_dot_f); // # 8 MULTs + + __m256 c1 = _mm256_cmp_ps(e_dot_f, v_zero, _CMP_LT_OQ); + __m256 c2 = _mm256_cmp_ps(e_dot_f_sq, rhs, _CMP_GT_OQ); + __m256 cond = _mm256_and_ps(c1, c2); + __m256 w_val = _mm256_blendv_ps(v_dt_neg, v_c_neg_dt, cond); + + // mask out i==j lane and padding before accumulating. + // AND with all-zeros = 0, AND with all-ones passes through, cheaper than blendv here. + __m256 f_x_safe = _mm256_and_ps(f_x, active); // bitwise, no flop + __m256 f_y_safe = _mm256_and_ps(f_y, active); // bitwise, no flop + acc_x = _mm256_fmadd_ps(f_x_safe, w_val, acc_x); // # 8 MULTs, 8 ADDs + acc_y = _mm256_fmadd_ps(f_y_safe, w_val, acc_y); // # 8 MULTs, 8 ADDs + } + + // horizontal sum of acc_x and acc_y at the same time + __m256 hsum = _mm256_hadd_ps(acc_x, acc_y); // # 8 ADDs (x and y interleaved) + __m128 hsum_lo = _mm256_castps256_ps128(hsum); + __m128 hsum_hi = _mm256_extractf128_ps(hsum, 1); + __m128 sum4 = _mm_add_ps(hsum_lo, hsum_hi); // # 4 ADDs + sum4 = _mm_hadd_ps(sum4, sum4); // # 4 ADDs (total hadd: 16 ADDs for x+y) + alignas(16) float sum_out[4]; + _mm_store_ps(sum_out, sum4); + f_alpha_dt_x += sum_out[0]; // # 1 ADD + f_alpha_dt_y += sum_out[1]; // # 1 ADD + + // obstacle loop kept scalar, board.n_obstacles is 0 in this setup anyway + for (int k = 0; k < board.n_obstacles; k++) { + + float v1_x = pos_x[i] - board.obstacles[k].start_x; // # 1 ADD + float v1_y = pos_y[i] - board.obstacles[k].start_y; // # 1 ADD + 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; // # 3 MULTs, 1 ADD + + 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); // # 1 MULT, 2 ADDs + float r_aB_y = pos_y[i] - (board.obstacles[k].start_y + board.obstacles[k].obstacle_v_y * projection); // # 1 MULT, 2 ADDs + + float r_aB_norm = sqrt(r_aB_x * r_aB_x + r_aB_y * r_aB_y); // # 2 MULTs, 1 ADD, 1 SQRT + 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; // # 2 MULTs, 1 EXP, 1 DIV + float f_alpha_B_neg_x = r_aB_x * scalar_mult; // # 1 MULT + float f_alpha_B_neg_y = r_aB_y * scalar_mult; // # 1 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; // # 1 MULT + float f_alpha_B_dt_y = f_alpha_B_neg_y * w_val; // # 1 MULT + + f_alpha_dt_x += f_alpha_B_dt_x; // # 1 ADD + f_alpha_dt_y += f_alpha_B_dt_y; // # 1 ADD + } + + w_x[i] += f_alpha_dt_x; // # 1 ADD + w_y[i] += f_alpha_dt_y; // # 1 ADD + } + + // position update loop stays scalar, same as the double AVX2 variant does + for (int i = 0; i < n_p; i++) { + + float w_norm = sqrt(w_x[i] * w_x[i] + w_y[i] * w_y[i]); // # 2 MULTs, 1 ADD, 1 SQRT + float w_norm2 = w_norm > EPS ? w_norm : EPS; + float correction_factor = min(1.0f, v_max[i] / w_norm2); // # 1 DIV + + curr_vel_x[i] = w_x[i] * correction_factor; // # 1 MULT + curr_vel_y[i] = w_y[i] * correction_factor; // # 1 MULT + + pos_x[i] = pos_x[i] + curr_vel_x[i] * dt; // # 1 MULT, 1 ADD + pos_y[i] = pos_y[i] + curr_vel_y[i] * dt; // # 1 MULT, 1 ADD + + 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]; // # 1 ADD + float ey = destination_y[i] - pos_y[i]; // # 1 ADD + + float e_norm = sqrt(ex * ex + ey * ey); // # 2 MULTs, 1 ADD, 1 SQRT + float e_norm2 = e_norm > EPS ? e_norm : EPS; + float e_norm_inv = 1.0 / e_norm2; // # 1 DIV + + 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 + + sb_sq[i] = velocity_norm_sq * delta_t_sq; // # 1 MULT + sb_e_x[i] = e_x[i] * (velocity_norm * delta_t); // # 2 MULTs (vel_norm*delta_t shared with next line) + sb_e_y[i] = e_y[i] * (velocity_norm * delta_t); // # 1 MULT + +#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; +}