diff --git a/variants/variant_float_inlining_SoA_AVX512_polyexp_moreavx_ilp_2_rsqrt_morersqrt_expfix_improved.cpp b/variants/variant_float_inlining_SoA_AVX512_polyexp_moreavx_ilp_2_rsqrt_morersqrt_expfix_improved.cpp new file mode 100644 index 0000000..5be10ec --- /dev/null +++ b/variants/variant_float_inlining_SoA_AVX512_polyexp_moreavx_ilp_2_rsqrt_morersqrt_expfix_improved.cpp @@ -0,0 +1,724 @@ +// # Changes: - used _mm512_mask3_fmadd_ps, to save one masking instruction +// - avoid doing an expensive brodcast for index vectors update, update them through additions instead +// - replace array allocation + load with a direct set for lane_off initialization +// # Predecessor: variant_float_inlining_SoA_AVX512_polyexp_moreavx_ilp_2_rsqrt_morersqrt_expfix.cpp + +#include "../headers/board_reduced_float.hpp" +#include "../headers/constants_float.hpp" +#include "../headers/pedestrian_reduced_float.hpp" + +#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; +alignas(64) vector pos_x, pos_y; +alignas(64) vector sb_sq; +alignas(64) vector sb_e_x, sb_e_y; +alignas(64) vector e_x, e_y; +alignas(64) vector curr_vel_x, curr_vel_y; +alignas(64) vector w_x, w_y; +alignas(64) vector desired_v0; +alignas(64) vector v_max; +alignas(64) vector destination_x, destination_y; +alignas(64) 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 + 31) & ~31; + + 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 + 30.0f; + 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 <= 0.1f); + + float v_m = 1.3f * 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 = -30.0f; + 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 <= 0.1f); + + float v_m = 1.3f * 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; + } + + 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); } + +// # 256 MULTs, 224 ADDs +static inline __m512 _avx512_exp_ps(__m512 x) { + + const __m512 log2e = _mm512_set1_ps(1.4426950408889634f); + + // # 16 MULTs + __m512 nf = _mm512_roundscale_ps(_mm512_mul_ps(x, log2e), _MM_FROUND_TO_NEAREST_INT | _MM_FROUND_NO_EXC); + + const __m512 ln2 = _mm512_set1_ps(0.6931471805599453f); + + // # 16 MULTs, 16 ADDs + __m512 r = _mm512_fnmadd_ps(nf, ln2, x); + + const __m512 c12 = _mm512_set1_ps(c12_scalar); + const __m512 c11 = _mm512_set1_ps(c11_scalar); + const __m512 c10 = _mm512_set1_ps(c10_scalar); + const __m512 c9 = _mm512_set1_ps(c9_scalar); + const __m512 c8 = _mm512_set1_ps(c8_scalar); + const __m512 c7 = _mm512_set1_ps(c7_scalar); + const __m512 c6 = _mm512_set1_ps(c6_scalar); + const __m512 c5 = _mm512_set1_ps(c5_scalar); + const __m512 c4 = _mm512_set1_ps(c4_scalar); + const __m512 c3 = _mm512_set1_ps(c3_scalar); + const __m512 c2 = _mm512_set1_ps(c2_scalar); + const __m512 c1 = _mm512_set1_ps(c1_scalar); + const __m512 c0 = _mm512_set1_ps(c0_scalar); + + __m512 p = c12; + + // # 13 * (16 MULTs, 16 ADDs) + // # = 208 MULTs, 208 ADDs + p = _mm512_fmadd_ps(p, r, c12); + p = _mm512_fmadd_ps(p, r, c11); + p = _mm512_fmadd_ps(p, r, c10); + p = _mm512_fmadd_ps(p, r, c9); + p = _mm512_fmadd_ps(p, r, c8); + p = _mm512_fmadd_ps(p, r, c7); + p = _mm512_fmadd_ps(p, r, c6); + p = _mm512_fmadd_ps(p, r, c5); + p = _mm512_fmadd_ps(p, r, c4); + p = _mm512_fmadd_ps(p, r, c3); + p = _mm512_fmadd_ps(p, r, c2); + p = _mm512_fmadd_ps(p, r, c1); + p = _mm512_fmadd_ps(p, r, c0); + + __m512i ni = _mm512_cvtps_epi32(nf); + __m512i biased = _mm512_add_epi32(ni, _mm512_set1_epi32(127)); + __m512i scaled = _mm512_slli_epi32(biased, 23); + __m512 pow2n = _mm512_castsi512_ps(scaled); + + // # 16 MULTs + return _mm512_mul_ps(p, pow2n); +} + +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 + 31) & ~31; + + const __m512 lane_off = _mm512_set_ps(15.0f, 14.0f, 13.0f, 12.0f, 11.0f, 10.0f, 9.0f, 8.0f, 7.0f, 6.0f, 5.0f, 4.0f, 3.0f, 2.0f, 1.0f, 0.0f); + const __m512 lane_off2 = _mm512_set_ps(31.0f, 30.0f, 29.0f, 28.0f, 27.0f, 26.0f, 25.0f, 24.0f, 23.0f, 22.0f, 21.0f, 20.0f, 19.0f, 18.0f, 17.0f, 16.0f); + + const __m512 v_neg_v0_div_2s = _mm512_set1_ps(NEG_V0_AB_div_TWO_SIGMA); + const __m512 v_neg_2s_inv = _mm512_set1_ps(NEG_TWO_SIGMA_INV); + const __m512 v_cos_phi_sq = _mm512_set1_ps(cos_phi_sq); + const __m512 v_dt_neg = _mm512_set1_ps(dt_neg); + const __m512 v_c_neg_dt = _mm512_set1_ps(c_neg_times_dt); + const __m512 v_zero = _mm512_setzero_ps(); + const __m512 v_one = _mm512_set1_ps(1.0f); + const __m512 v_eps = _mm512_set1_ps(EPS); + const __m512 v_eps_sq = _mm512_set1_ps(EPS_SQ); + const __m512 v_np = _mm512_set1_ps((float)n_p); + const __m512 v_exp_min = _mm512_set1_ps(-87.0f); + const __m512 v_32 = _mm512_set1_ps(32.0f); + + // # ADDs: n_iter * ( + // # n_p * 84 + + // # n_p * n_p_pad * 29 + + // # n_p * board.n_obstacles * 10 + + // # n_p_pad * 7 + // # ) + + // # MULTs: n_iter * ( + // # n_p * 4 + + // # n_p * n_p_pad * 42 + + // # n_p * board.n_obstacles * 13 + + // # n_p_pad * 16 + // # ) + + // # DIVs: n_iter * ( + // # n_p * n_p_pad * 3 + + // # n_p * board.n_obstacles + + // # n_p_pad * 2 + // # ) + + // # SQRTs: n_iter * ( + // # n_p * n_p_pad * 3 + + // # n_p * board.n_obstacles + + // # n_p_pad * 3 + // # ) + + // # EXPs: n_iter * n_p * board.n_obstacles + + for (int t = 0; t < n_iter; t++) { + // i index vector for mask generation + __m512 v_i = _mm512_setzero_ps(); + + for (int i = 0; i < n_p; i++) { + // set the vector for the current pedestrian + + // # 2 MULTS + // get desired velocity + float desired_velocity_x = e_x[i] * desired_v0[i]; + float desired_velocity_y = e_y[i] * desired_v0[i]; + + // 2 ADDS, 2 MULTS + // velocity change accumulator + float f_alpha_dt_x = (desired_velocity_x - curr_vel_x[i]) * dt_times_tau_alpha_inv; + float f_alpha_dt_y = (desired_velocity_y - curr_vel_y[i]) * dt_times_tau_alpha_inv; + + // pos + const __m512 pix = _mm512_set1_ps(pos_x[i]); + const __m512 piy = _mm512_set1_ps(pos_y[i]); + // desired direction + const __m512 eix = _mm512_set1_ps(e_x[i]); + const __m512 eiy = _mm512_set1_ps(e_y[i]); + + // accumulators --> 16 pedestrians per accumulator + __m512 acc_x_0 = _mm512_setzero_ps(); + __m512 acc_y_0 = _mm512_setzero_ps(); + __m512 acc_x_1 = _mm512_setzero_ps(); + __m512 acc_y_1 = _mm512_setzero_ps(); + + // j index vectors for mask generation + __m512 j_idx_0 = lane_off; + __m512 j_idx_1 = lane_off2; + + // force between pedestrians + // loop unroll factor 32 with 2 vectors + // --> each vector has 16 lanes + for (int j = 0; j < n_p_pad; j += 32) { + + // lane is active if j != i + // [1,1,1,0,1,1,1,...] 0 --> i == j, 1 --> i != j + __mmask16 m_neq_i_0 = _mm512_cmp_ps_mask(j_idx_0, v_i, _CMP_NEQ_OQ); + __mmask16 m_neq_i_1 = _mm512_cmp_ps_mask(j_idx_1, v_i, _CMP_NEQ_OQ); + + // lane is active if j < n_p --> valid range + // [1,1,1,0,1,1,1,...] 0 --> j >= n_p, 1 --> j < n_p + __mmask16 m_in_range_0 = _mm512_cmp_ps_mask(j_idx_0, v_np, _CMP_LT_OQ); + __mmask16 m_in_range_1 = _mm512_cmp_ps_mask(j_idx_1, v_np, _CMP_LT_OQ); + + // bitwise comparison if not valid --> 0 + // finally check if lane is valid or not --> prevents i == j, and + // j >= n_p because of loop unrolling --> we can therefore omit a remainings for loop + __mmask16 active_0 = m_neq_i_0 & m_in_range_0; + __mmask16 active_1 = m_neq_i_1 & m_in_range_1; + + // --- + + // load the positions of the other pedestrians x value + // [pos[j], pos[j+1], ..., pos[j+15]] and [pos[16], pos[j+17], ..., pos[j+31]] for x and y + __m512 pjx_0 = _mm512_loadu_ps(&pos_x[j]); + __m512 pjx_1 = _mm512_loadu_ps(&pos_x[j + 16]); + __m512 pjy_0 = _mm512_loadu_ps(&pos_y[j]); + __m512 pjy_1 = _mm512_loadu_ps(&pos_y[j + 16]); + + // --- + + // step vector of j + // [(v_j * delta_t * e_j).x, (v_j+1 * delta_t * e_j+1).x, ...] + __m512 sbe_jx_0 = _mm512_loadu_ps(&sb_e_x[j]); + __m512 sbe_jx_1 = _mm512_loadu_ps(&sb_e_x[j + 16]); + __m512 sbe_jy_0 = _mm512_loadu_ps(&sb_e_y[j]); + __m512 sbe_jy_1 = _mm512_loadu_ps(&sb_e_y[j + 16]); + + // --- + + // squared step length + // [j, j+1, ...] + __m512 sb_jsq_0 = _mm512_loadu_ps(&sb_sq[j]); + __m512 sb_jsq_1 = _mm512_loadu_ps(&sb_sq[j + 16]); + + // --- + + // # 64 ADDS + // distance vector + // [j, j+1, ...] + __m512 r_ab_x_0 = _mm512_sub_ps(pix, pjx_0); + __m512 r_ab_x_1 = _mm512_sub_ps(pix, pjx_1); + __m512 r_ab_y_0 = _mm512_sub_ps(piy, pjy_0); + __m512 r_ab_y_1 = _mm512_sub_ps(piy, pjy_1); + + // # 32 ADDS, 64 MULTS + // |r_ab|^2 needed for rsqrt to prevent 0 values --> x^2 + y^2 + __m512 r_ab_n2_0 = _mm512_fmadd_ps(r_ab_x_0, r_ab_x_0, _mm512_mul_ps(r_ab_y_0, r_ab_y_0)); + __m512 r_ab_n2_1 = _mm512_fmadd_ps(r_ab_x_1, r_ab_x_1, _mm512_mul_ps(r_ab_y_1, r_ab_y_1)); + + // prevent cases where distance = 0 (=pedestrian on top of each other) + // [dist_i_j, dist_i_j+1, ...] + r_ab_n2_0 = _mm512_max_ps(r_ab_n2_0, v_eps_sq); + r_ab_n2_1 = _mm512_max_ps(r_ab_n2_1, v_eps_sq); + + // --- + + // # 32 DIVS, 32 SQRTS + // 1 / |r_ab| --> 14 bit rsqrt approx. rsqrt --> 1 / x^2 --> rsqrt(x^2) = 1/x + // [1 / dist_i_j, 1 / dist_i_j+1, ...] + __m512 inv_r_ab_n_0 = _mm512_rsqrt14_ps(r_ab_n2_0); + __m512 inv_r_ab_n_1 = _mm512_rsqrt14_ps(r_ab_n2_1); + + // # 32 MULTS + // r_ab^2 * 1 / r_ab = |r_ab| --> normed + // [r_i_j, r_i_j+1, ...] + __m512 r_ab_n_0 = _mm512_mul_ps(r_ab_n2_0, inv_r_ab_n_0); + __m512 r_ab_n_1 = _mm512_mul_ps(r_ab_n2_1, inv_r_ab_n_1); + + // # 64 ADDS + // r_ab - step[j] + // j next pos + __m512 r_ab2_x_0 = _mm512_sub_ps(r_ab_x_0, sbe_jx_0); + __m512 r_ab2_x_1 = _mm512_sub_ps(r_ab_x_1, sbe_jx_1); + __m512 r_ab2_y_0 = _mm512_sub_ps(r_ab_y_0, sbe_jy_0); + __m512 r_ab2_y_1 = _mm512_sub_ps(r_ab_y_1, sbe_jy_1); + + // # 32 ADDS, 64 MULTS + // |r_ab_2| --> needed for rsqrt trick (r_ab - step) + __m512 r_ab2_n2_0 = _mm512_fmadd_ps(r_ab2_x_0, r_ab2_x_0, _mm512_mul_ps(r_ab2_y_0, r_ab2_y_0)); + __m512 r_ab2_n2_1 = _mm512_fmadd_ps(r_ab2_x_1, r_ab2_x_1, _mm512_mul_ps(r_ab2_y_1, r_ab2_y_1)); + + // prevent 0 case --> infinity + r_ab2_n2_0 = _mm512_max_ps(r_ab2_n2_0, v_eps_sq); + r_ab2_n2_1 = _mm512_max_ps(r_ab2_n2_1, v_eps_sq); + + // # 32 DIVS, 32 SQRTS + // same as before use rsqrt with 14bit approx + // [1 / |r_ab_2|, 1 / |r_ab_2|, ...] + __m512 inv_r_ab2_n_0 = _mm512_rsqrt14_ps(r_ab2_n2_0); + __m512 inv_r_ab2_n_1 = _mm512_rsqrt14_ps(r_ab2_n2_1); + + // # 32 MULTS + // |r_ab_2_second_distance_vector| * 1 / |r_ab_2_first_distance_vector| + __m512 r_ab2_n_0 = _mm512_mul_ps(r_ab2_n2_0, inv_r_ab2_n_0); + __m512 r_ab2_n_1 = _mm512_mul_ps(r_ab2_n2_1, inv_r_ab2_n_1); + + // # 32 ADDS + // r_sum = |r_ab| + |r_ab - step[j]| --> [w_0, w_1, w_2, ..., w_15] and [w_16, ..., w_31] + __m512 r_sum_0 = _mm512_add_ps(r_ab_n_0, r_ab2_n_0); + __m512 r_sum_1 = _mm512_add_ps(r_ab_n_1, r_ab2_n_1); + + // # 32 ADDS, 32 MULTS + // 2_b^2 = r_sum^2 - step[j]^2 + __m512 two_b_sq_0 = _mm512_fmsub_ps(r_sum_0, r_sum_0, sb_jsq_0); + __m512 two_b_sq_1 = _mm512_fmsub_ps(r_sum_1, r_sum_1, sb_jsq_1); + + // prevent 0 case + two_b_sq_0 = _mm512_max_ps(two_b_sq_0, v_eps_sq); + two_b_sq_1 = _mm512_max_ps(two_b_sq_1, v_eps_sq); + + // # 32 DIVS, 32 SQRTS + // 2_b + // 1 / 2_b^(2*0.5) --> 1 / 2_b + __m512 inv_two_b_0 = _mm512_rsqrt14_ps(two_b_sq_0); + __m512 inv_two_b_1 = _mm512_rsqrt14_ps(two_b_sq_1); + + // # 32 MULTS + // 2_b = 2_b^2 * 1 / 2_b + __m512 two_b_0 = _mm512_mul_ps(two_b_sq_0, inv_two_b_0); + __m512 two_b_1 = _mm512_mul_ps(two_b_sq_1, inv_two_b_1); + + // --- + + // # 32 MULTS + // two_b * -1 / (2*sigma) --> exp + __m512 e_arg_0 = _mm512_mul_ps(two_b_0, v_neg_2s_inv); + __m512 e_arg_1 = _mm512_mul_ps(two_b_1, v_neg_2s_inv); + + // exp(x) + // when x is small just assume constant value --> faster exp + e_arg_0 = _mm512_max_ps(e_arg_0, v_exp_min); + e_arg_1 = _mm512_max_ps(e_arg_1, v_exp_min); + + // # 448 ADDS, 512 MULTS + // custom fast exponent intrinsic using polynomial approximations and some precomputed constants + __m512 e_val_0 = _avx512_exp_ps(e_arg_0); + __m512 e_val_1 = _avx512_exp_ps(e_arg_1); + + // # 96 MULTS + // [−(V0/σ) * e^(−b/σ) * w/(4b), ...] --> scalar + __m512 numer_inv_two_b_0 = _mm512_mul_ps(_mm512_mul_ps(r_sum_0, v_neg_v0_div_2s), _mm512_mul_ps(e_val_0, inv_two_b_0)); + __m512 numer_inv_two_b_1 = _mm512_mul_ps(_mm512_mul_ps(r_sum_1, v_neg_v0_div_2s), _mm512_mul_ps(e_val_1, inv_two_b_1)); + + // # 32 MULTS + // scalar * 1 / |r_ab| + __m512 sm_r_ab_0 = _mm512_mul_ps(numer_inv_two_b_0, inv_r_ab_n_0); + __m512 sm_r_ab_1 = _mm512_mul_ps(numer_inv_two_b_1, inv_r_ab_n_1); + + // # 32 MULTS + // scalar * 1 / |r_ab_2| + __m512 sm_r_ab2_0 = _mm512_mul_ps(numer_inv_two_b_0, inv_r_ab2_n_0); + __m512 sm_r_ab2_1 = _mm512_mul_ps(numer_inv_two_b_1, inv_r_ab2_n_1); + + // # 64 ADDS, 128 MULTS + // summed force + __m512 f_x_0 = _mm512_fmadd_ps(r_ab2_x_0, sm_r_ab2_0, _mm512_mul_ps(r_ab_x_0, sm_r_ab_0)); + __m512 f_x_1 = _mm512_fmadd_ps(r_ab2_x_1, sm_r_ab2_1, _mm512_mul_ps(r_ab_x_1, sm_r_ab_1)); + __m512 f_y_0 = _mm512_fmadd_ps(r_ab2_y_0, sm_r_ab2_0, _mm512_mul_ps(r_ab_y_0, sm_r_ab_0)); + __m512 f_y_1 = _mm512_fmadd_ps(r_ab2_y_1, sm_r_ab2_1, _mm512_mul_ps(r_ab_y_1, sm_r_ab_1)); + + // # 32 ADDS, 64 MULTS + // using masking to perform --> field of view formula + // if (e_dot_f >= 0.0 || e_dot_f_sq <= rhs) + // return dt_neg; + // else + // return c_neg_times_dt; + // + __m512 f_norm_sq_0 = _mm512_fmadd_ps(f_x_0, f_x_0, _mm512_mul_ps(f_y_0, f_y_0)); + __m512 f_norm_sq_1 = _mm512_fmadd_ps(f_x_1, f_x_1, _mm512_mul_ps(f_y_1, f_y_1)); + + // # 32 MULTS + __m512 rhs_0 = _mm512_mul_ps(f_norm_sq_0, v_cos_phi_sq); + __m512 rhs_1 = _mm512_mul_ps(f_norm_sq_1, v_cos_phi_sq); + + // # 32 ADDS, 64 MULTS + __m512 e_dot_f_0 = _mm512_fmadd_ps(eix, f_x_0, _mm512_mul_ps(eiy, f_y_0)); + __m512 e_dot_f_1 = _mm512_fmadd_ps(eix, f_x_1, _mm512_mul_ps(eiy, f_y_1)); + + // # 32 MULTS + __m512 e_dot_f_sq_0 = _mm512_mul_ps(e_dot_f_0, e_dot_f_0); + __m512 e_dot_f_sq_1 = _mm512_mul_ps(e_dot_f_1, e_dot_f_1); + + // e_i * f < 0 --> behind + __mmask16 c1_0 = _mm512_cmp_ps_mask(e_dot_f_0, v_zero, _CMP_LT_OQ); + __mmask16 c1_1 = _mm512_cmp_ps_mask(e_dot_f_1, v_zero, _CMP_LT_OQ); + + // (e_i * f)^2 > cos(phi) --> out of view + __mmask16 c2_0 = _mm512_cmp_ps_mask(e_dot_f_sq_0, rhs_0, _CMP_GT_OQ); + __mmask16 c2_1 = _mm512_cmp_ps_mask(e_dot_f_sq_1, rhs_1, _CMP_GT_OQ); + + // get the case (in field of view or not) + // 1 = reduced weight, 0 = regular + __mmask16 cond_0 = c1_0 & c2_0; + __mmask16 cond_1 = c1_1 & c2_1; + + // apply the correct weight + __m512 w_val_0 = _mm512_mask_blend_ps(cond_0, v_dt_neg, v_c_neg_dt); + __m512 w_val_1 = _mm512_mask_blend_ps(cond_1, v_dt_neg, v_c_neg_dt); + + // # 64 ADDS, 64 MULTS + // accumulate force with weight + // force_P_total += weight * force_P_other + // only active lanes are added to the accumulator because of masking --> prevents i == j and j >= n_p + acc_x_0 = _mm512_mask3_fmadd_ps(f_x_0, w_val_0, acc_x_0, active_0); + acc_x_1 = _mm512_mask3_fmadd_ps(f_x_1, w_val_1, acc_x_1, active_1); + acc_y_0 = _mm512_mask3_fmadd_ps(f_y_0, w_val_0, acc_y_0, active_0); + acc_y_1 = _mm512_mask3_fmadd_ps(f_y_1, w_val_1, acc_y_1, active_1); + + // # 32 ADDS + // increment j index vectors for next iteration + j_idx_0 = _mm512_add_ps(j_idx_0, v_32); + j_idx_1 = _mm512_add_ps(j_idx_1, v_32); + } + // # 16 ADDS + // increment i vector for next iteration + v_i = _mm512_add_ps(v_i, v_one); + + // # 64 ADDs + // scalar force accumulator + f_alpha_dt_x += _mm512_reduce_add_ps(_mm512_add_ps(acc_x_0, acc_x_1)); + f_alpha_dt_y += _mm512_reduce_add_ps(_mm512_add_ps(acc_y_0, acc_y_1)); + + // force between pedestrian and obstacles + // no optimizations, because force between pedestrian is the bottleneck of the computation + for (int k = 0; k < board.n_obstacles; k++) { + // # 2 ADDs + 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; + + // # 3 MULTs, 1 ADD + float projection = (v1_x * v2_x + v1_y * v2_y) * board.obstacles[k].length_sq_inv; + + if (projection < 0.0f) + projection = 0.0f; + else if (projection > 1.0f) + projection = 1.0f; + + // # 4 ADDs, 2 MULTs + 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); + + // # 1 SQRT, 2 MULTs, 1 ADD + 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; + + // # 4 MULTs, 1 EXP, 1 DIV + 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 = dt_neg; + 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 = c_neg_times_dt; + + // # 2 MULTS + 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; + + // # 2 ADDs + f_alpha_dt_x += f_alpha_B_dt_x; + f_alpha_dt_y += f_alpha_B_dt_y; + } + + // # 2 ADDs + w_x[i] += f_alpha_dt_x; + w_y[i] += f_alpha_dt_y; + } + + // update each pedestrian state + for (int i = 0; i < n_p_pad; i += 16) { + // load 16 pedestrians per iteration with their data + // SoA in vectors + __m512 w_x_i_vec = _mm512_loadu_ps(&w_x[i]); + __m512 w_y_i_vec = _mm512_loadu_ps(&w_y[i]); + __m512 v_max_i_vec = _mm512_loadu_ps(&v_max[i]); + __m512 pos_x_i_vec = _mm512_loadu_ps(&pos_x[i]); + __m512 pos_y_i_vec = _mm512_loadu_ps(&pos_y[i]); + __m512 destination_y_i_vec = _mm512_loadu_ps(&destination_y[i]); + __m512 destination_x_i_vec = _mm512_loadu_ps(&destination_x[i]); + __m512 desired_v0_i_vec = _mm512_loadu_ps(&desired_v0[i]); + + __m512i color_i_vec = _mm512_loadu_si512((__m512i *)&color[i]); + + // # 32 MULTs, 16 ADDs + __m512 w_norm_sq = _mm512_fmadd_ps(w_x_i_vec, w_x_i_vec, _mm512_mul_ps(w_y_i_vec, w_y_i_vec)); + + // # 16 SQRTs, 16 DIVs + __m512 w_norm_inv = _mm512_rsqrt14_ps(w_norm_sq); + + // # 16 MULTs + __m512 correction_factor = _mm512_min_ps(_mm512_set1_ps(1.0f), _mm512_mul_ps(v_max_i_vec, w_norm_inv)); + + // # 32 MULTs + __m512 curr_vel_x_i_vec = _mm512_mul_ps(w_x_i_vec, correction_factor); + __m512 curr_vel_y_i_vec = _mm512_mul_ps(w_y_i_vec, correction_factor); + + __m512 dt_vec = _mm512_set1_ps(dt); + + // # 32 MULTs, 32 ADDs + pos_x_i_vec = _mm512_fmadd_ps(curr_vel_x_i_vec, dt_vec, pos_x_i_vec); + pos_y_i_vec = _mm512_fmadd_ps(curr_vel_y_i_vec, dt_vec, pos_y_i_vec); + + // differentiate whether pedestrian came from left or right using masking + __mmask16 cond_1_left = _mm512_cmpeq_epi32_mask(color_i_vec, _mm512_setzero_si512()); + __mmask16 cond_1_right = _mm512_cmp_ps_mask(pos_x_i_vec, _mm512_set1_ps(BOARD_LENGTH - 1.5f), _CMP_GT_OQ); + __mmask16 cond_1 = cond_1_left & cond_1_right; + + pos_x_i_vec = _mm512_mask_blend_ps(cond_1, pos_x_i_vec, _mm512_set1_ps(1.0f)); + destination_y_i_vec = _mm512_mask_blend_ps(cond_1, destination_y_i_vec, pos_y_i_vec); + w_x_i_vec = _mm512_mask_blend_ps(cond_1, w_x_i_vec, desired_v0_i_vec); + w_y_i_vec = _mm512_mask_blend_ps(cond_1, w_y_i_vec, _mm512_setzero_ps()); + curr_vel_x_i_vec = _mm512_mask_blend_ps(cond_1, curr_vel_x_i_vec, w_x_i_vec); + curr_vel_y_i_vec = _mm512_mask_blend_ps(cond_1, curr_vel_y_i_vec, w_y_i_vec); + + __mmask16 cond_2_left = _mm512_cmpeq_epi32_mask(color_i_vec, _mm512_set1_epi32(1)); + __mmask16 cond_2_right = _mm512_cmp_ps_mask(pos_x_i_vec, _mm512_set1_ps(1.5f), _CMP_LT_OQ); + __mmask16 cond_2 = cond_2_left & cond_2_right; + + pos_x_i_vec = _mm512_mask_blend_ps(cond_2, pos_x_i_vec, _mm512_set1_ps(BOARD_LENGTH - 1.0f)); + destination_y_i_vec = _mm512_mask_blend_ps(cond_2, destination_y_i_vec, pos_y_i_vec); + __m512 neg_desired_v0 = _mm512_xor_ps(desired_v0_i_vec, _mm512_set1_ps(-0.0f)); + w_x_i_vec = _mm512_mask_blend_ps(cond_2, w_x_i_vec, neg_desired_v0); + w_y_i_vec = _mm512_mask_blend_ps(cond_2, w_y_i_vec, _mm512_setzero_ps()); + curr_vel_x_i_vec = _mm512_mask_blend_ps(cond_2, curr_vel_x_i_vec, w_x_i_vec); + curr_vel_y_i_vec = _mm512_mask_blend_ps(cond_2, curr_vel_y_i_vec, w_y_i_vec); + + pos_y_i_vec = _mm512_max_ps(pos_y_i_vec, _mm512_set1_ps(WALL_EPS)); + pos_y_i_vec = _mm512_min_ps(pos_y_i_vec, _mm512_set1_ps(BOARD_WIDTH_MINUS_WALL_EPS)); + + // # 32 ADDs + __m512 ex_vec = _mm512_sub_ps(destination_x_i_vec, pos_x_i_vec); + __m512 ey_vec = _mm512_sub_ps(destination_y_i_vec, pos_y_i_vec); + + // # 32 MULTs, 16 ADDs + __m512 e_norm_sq = _mm512_fmadd_ps(ex_vec, ex_vec, _mm512_mul_ps(ey_vec, ey_vec)); + + // # 16 SQRTs, 16 DIVs + __m512 e_norm_inv = _mm512_rsqrt14_ps(e_norm_sq); + + // # 32 MULTs + __m512 e_x_i_vec = _mm512_mul_ps(ex_vec, e_norm_inv); + __m512 e_y_i_vec = _mm512_mul_ps(ey_vec, e_norm_inv); + + // # 32 MULTs, 16 ADDs + __m512 vel_norm_sq = _mm512_fmadd_ps(curr_vel_x_i_vec, curr_vel_x_i_vec, _mm512_mul_ps(curr_vel_y_i_vec, curr_vel_y_i_vec)); + + // # 16 MULTs + __m512 sb_sq_i_vec = _mm512_mul_ps(vel_norm_sq, _mm512_set1_ps(delta_t_sq)); + + // # 16 SQRTs + __m512 vel_norm_dt = _mm512_sqrt_ps(sb_sq_i_vec); + + // write the data + _mm512_storeu_ps(&curr_vel_x[i], curr_vel_x_i_vec); + _mm512_storeu_ps(&curr_vel_y[i], curr_vel_y_i_vec); + _mm512_storeu_ps(&w_x[i], w_x_i_vec); + _mm512_storeu_ps(&w_y[i], w_y_i_vec); + _mm512_storeu_ps(&pos_x[i], pos_x_i_vec); + _mm512_storeu_ps(&pos_y[i], pos_y_i_vec); + _mm512_storeu_ps(&e_x[i], e_x_i_vec); + _mm512_storeu_ps(&e_y[i], e_y_i_vec); + _mm512_storeu_ps(&destination_y[i], destination_y_i_vec); + _mm512_storeu_ps(&sb_sq[i], sb_sq_i_vec); + + // # 32 MULTs + _mm512_storeu_ps(&sb_e_x[i], _mm512_mul_ps(e_x_i_vec, vel_norm_dt)); + _mm512_storeu_ps(&sb_e_y[i], _mm512_mul_ps(e_y_i_vec, vel_norm_dt)); + } + +#if !BENCHMARK + for (int i = 0; i < n_p; i++) { + 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; +} diff --git a/variants/variant_float_inlining_SoA_AVX512_polyexp_moreavx_ilp_2_rsqrt_morersqrt_expfix_improved_moreilp.cpp b/variants/variant_float_inlining_SoA_AVX512_polyexp_moreavx_ilp_2_rsqrt_morersqrt_expfix_improved_moreilp.cpp new file mode 100644 index 0000000..eb21dc4 --- /dev/null +++ b/variants/variant_float_inlining_SoA_AVX512_polyexp_moreavx_ilp_2_rsqrt_morersqrt_expfix_improved_moreilp.cpp @@ -0,0 +1,765 @@ +// # Changes: - vectorized full force computation for pedestrians +// # Predecessor: variant_float_inlining_SoA_AVX512_polyexp_moreavx_ilp_2_rsqrt_moresqrt_expfix_improved.cpp + +#include "../headers/board_reduced_float.hpp" +#include "../headers/constants_float.hpp" +#include "../headers/pedestrian_reduced_float.hpp" + +#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; +alignas(64) vector pos_x, pos_y; +alignas(64) vector sb_sq; +alignas(64) vector sb_e_x, sb_e_y; +alignas(64) vector e_x, e_y; +alignas(64) vector curr_vel_x, curr_vel_y; +alignas(64) vector w_x, w_y; +alignas(64) vector desired_v0; +alignas(64) vector v_max; +alignas(64) vector destination_x, destination_y; +alignas(64) 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 + 15) & ~15; + + 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 + 30.0f; + 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 <= 0.1f); + + float v_m = 1.3f * 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 = -30.0f; + 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 <= 0.1f); + + float v_m = 1.3f * 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; + } + + 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); } + +// # 256 MULTs, 224 ADDs +static inline __m512 _avx512_exp_ps(__m512 x) { + + const __m512 log2e = _mm512_set1_ps(1.4426950408889634f); + + // # 16 MULTs + __m512 nf = _mm512_roundscale_ps(_mm512_mul_ps(x, log2e), _MM_FROUND_TO_NEAREST_INT | _MM_FROUND_NO_EXC); + + const __m512 ln2 = _mm512_set1_ps(0.6931471805599453f); + + // # 16 MULTs, 16 ADDs + __m512 r = _mm512_fnmadd_ps(nf, ln2, x); + + const __m512 c12 = _mm512_set1_ps(c12_scalar); + const __m512 c11 = _mm512_set1_ps(c11_scalar); + const __m512 c10 = _mm512_set1_ps(c10_scalar); + const __m512 c9 = _mm512_set1_ps(c9_scalar); + const __m512 c8 = _mm512_set1_ps(c8_scalar); + const __m512 c7 = _mm512_set1_ps(c7_scalar); + const __m512 c6 = _mm512_set1_ps(c6_scalar); + const __m512 c5 = _mm512_set1_ps(c5_scalar); + const __m512 c4 = _mm512_set1_ps(c4_scalar); + const __m512 c3 = _mm512_set1_ps(c3_scalar); + const __m512 c2 = _mm512_set1_ps(c2_scalar); + const __m512 c1 = _mm512_set1_ps(c1_scalar); + const __m512 c0 = _mm512_set1_ps(c0_scalar); + + __m512 p = c12; + + // # 13 * (16 MULTs, 16 ADDs) + // # = 208 MULTs, 208 ADDs + p = _mm512_fmadd_ps(p, r, c12); + p = _mm512_fmadd_ps(p, r, c11); + p = _mm512_fmadd_ps(p, r, c10); + p = _mm512_fmadd_ps(p, r, c9); + p = _mm512_fmadd_ps(p, r, c8); + p = _mm512_fmadd_ps(p, r, c7); + p = _mm512_fmadd_ps(p, r, c6); + p = _mm512_fmadd_ps(p, r, c5); + p = _mm512_fmadd_ps(p, r, c4); + p = _mm512_fmadd_ps(p, r, c3); + p = _mm512_fmadd_ps(p, r, c2); + p = _mm512_fmadd_ps(p, r, c1); + p = _mm512_fmadd_ps(p, r, c0); + + __m512i ni = _mm512_cvtps_epi32(nf); + __m512i biased = _mm512_add_epi32(ni, _mm512_set1_epi32(127)); + __m512i scaled = _mm512_slli_epi32(biased, 23); + __m512 pow2n = _mm512_castsi512_ps(scaled); + + // # 16 MULTs + return _mm512_mul_ps(p, pow2n); +} + +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 + 15) & ~15; + + const __m512 lane_off = _mm512_set_ps(15.0f, 14.0f, 13.0f, 12.0f, 11.0f, 10.0f, 9.0f, 8.0f, 7.0f, 6.0f, 5.0f, 4.0f, 3.0f, 2.0f, 1.0f, 0.0f); + + const __m512 v_neg_v0_div_2s = _mm512_set1_ps(NEG_V0_AB_div_TWO_SIGMA); + const __m512 v_neg_2s_inv = _mm512_set1_ps(NEG_TWO_SIGMA_INV); + const __m512 v_cos_phi_sq = _mm512_set1_ps(cos_phi_sq); + const __m512 v_cos_phi = _mm512_set1_ps(cos_phi); + const __m512 v_dt_neg = _mm512_set1_ps(dt_neg); + const __m512 v_c_neg_dt = _mm512_set1_ps(c_neg_times_dt); + const __m512 v_zero = _mm512_setzero_ps(); + const __m512 v_eps_sq = _mm512_set1_ps(EPS_SQ); + const __m512 v_exp_min = _mm512_set1_ps(-87.0f); + const __m512 v_dt_tau = _mm512_set1_ps(dt_times_tau_alpha_inv); + const __m512 v_neg_u0_div_r = _mm512_set1_ps(NEG_U0_AB_div_R); + const __m512 v_neg_r_inv = _mm512_set1_ps(NEG_R_INV); + const __m512 v_sign_mask = _mm512_set1_ps(-0.0f); + const __m512 v_16 = _mm512_set1_ps(16.0f); + const __m512 v_one = _mm512_set1_ps(1.0f); + const __m512 v_two = _mm512_set1_ps(2.0f); + const __m512 osx = _mm512_set1_ps(board.obstacles[0].start_x); + const __m512 osy = _mm512_set1_ps(board.obstacles[0].start_y); + const __m512 ovx = _mm512_set1_ps(board.obstacles[0].obstacle_v_x); + const __m512 ovy = _mm512_set1_ps(board.obstacles[0].obstacle_v_y); + const __m512 olen_inv = _mm512_set1_ps(board.obstacles[0].length_sq_inv); + const __m512 osx1 = _mm512_set1_ps(board.obstacles[1].start_x); + const __m512 osy1 = _mm512_set1_ps(board.obstacles[1].start_y); + const __m512 ovx1 = _mm512_set1_ps(board.obstacles[1].obstacle_v_x); + const __m512 ovy1 = _mm512_set1_ps(board.obstacles[1].obstacle_v_y); + const __m512 olen_inv1 = _mm512_set1_ps(board.obstacles[1].length_sq_inv); + + // # ADDs: n_iter * ( + // # n_p_pad * 7 + + // # n_p_pad * n_p * 29 + + // # n_p_pad * 2(=board.n_obstacles) * 24 + + // # n_p_pad * 7 + // # ) + + // # MULTs: n_iter * ( + // # n_p_pad * 4 + + // # n_p_pad * n_p * 42 + + // # n_p_pad * 2(=board.n_obstacles) * 31 + + // # n_p_pad * 16 + // # ) + + // # DIVs: n_iter * ( + // # n_p_pad * n_p * 3 + + // # n_p_pad * 2(=board.n_obstacles) * 1 + + // # n_p_pad * 2 + // # ) + + // # SQRTs: n_iter * ( + // # n_p_pad * n_p * 3 + + // # n_p_pad * 2(=board.n_obstacles) * 1 + + // # n_p_pad * 3 + // # ) + + for (int t = 0; t < n_iter; t++) { + + // Pass 1 : compute force terms + __m512 i_idx = lane_off; + for (int i = 0; i < n_p_pad; i += 16) { + + // i-side data (loaded once per block, reused for all j) + const __m512 pix = _mm512_loadu_ps(&pos_x[i]); + const __m512 piy = _mm512_loadu_ps(&pos_y[i]); + const __m512 eix = _mm512_loadu_ps(&e_x[i]); + const __m512 eiy = _mm512_loadu_ps(&e_y[i]); + __m512 wix = _mm512_loadu_ps(&w_x[i]); + __m512 wiy = _mm512_loadu_ps(&w_y[i]); + + // acceleration term, vectorized over the 16 alphas: + // acc = (e * v0 - v) * (dt / tau) + const __m512 v0i = _mm512_loadu_ps(&desired_v0[i]); + const __m512 vix = _mm512_loadu_ps(&curr_vel_x[i]); + const __m512 viy = _mm512_loadu_ps(&curr_vel_y[i]); + + // # 64 ADDS, 64 MULTS + __m512 acc_x = _mm512_fmadd_ps(_mm512_fmsub_ps(eix, v0i, vix), v_dt_tau, wix); + __m512 acc_y = _mm512_fmadd_ps(_mm512_fmsub_ps(eiy, v0i, viy), v_dt_tau, wiy); + + // second accumulator pair for the second dependency chain + __m512 acc_x2 = _mm512_setzero_ps(); + __m512 acc_y2 = _mm512_setzero_ps(); + + const int n_p_even = n_p & ~1; + + // Initialize j index vectors + __m512 j_idx_0 = v_zero; + __m512 j_idx_1 = v_one; + + // Pedestrians repulsion terms unrolled by 2 to have two independent accumulators and trigger more ilp + for (int j = 0; j < n_p_even; j += 2) { + + const __m512 pjx_0 = _mm512_set1_ps(pos_x[j]); + const __m512 pjy_0 = _mm512_set1_ps(pos_y[j]); + const __m512 sbe_jx_0 = _mm512_set1_ps(sb_e_x[j]); + const __m512 sbe_jy_0 = _mm512_set1_ps(sb_e_y[j]); + const __m512 sb_jsq_0 = _mm512_set1_ps(sb_sq[j]); + const __mmask16 active_0 = _mm512_cmp_ps_mask(i_idx, j_idx_0, _CMP_NEQ_OQ); + + const __m512 pjx_1 = _mm512_set1_ps(pos_x[j + 1]); + const __m512 pjy_1 = _mm512_set1_ps(pos_y[j + 1]); + const __m512 sbe_jx_1 = _mm512_set1_ps(sb_e_x[j + 1]); + const __m512 sbe_jy_1 = _mm512_set1_ps(sb_e_y[j + 1]); + const __m512 sb_jsq_1 = _mm512_set1_ps(sb_sq[j + 1]); + const __mmask16 active_1 = _mm512_cmp_ps_mask(i_idx, j_idx_1, _CMP_NEQ_OQ); + + // # 64 ADDS + // r_ab = r_i - r_j + __m512 r_ab_x_0 = _mm512_sub_ps(pix, pjx_0); + __m512 r_ab_x_1 = _mm512_sub_ps(pix, pjx_1); + __m512 r_ab_y_0 = _mm512_sub_ps(piy, pjy_0); + __m512 r_ab_y_1 = _mm512_sub_ps(piy, pjy_1); + + // # 32 ADDS, 64 MULTS + // |r_ab|^2 + __m512 r_ab_n2_0 = _mm512_fmadd_ps(r_ab_x_0, r_ab_x_0, _mm512_mul_ps(r_ab_y_0, r_ab_y_0)); + __m512 r_ab_n2_1 = _mm512_fmadd_ps(r_ab_x_1, r_ab_x_1, _mm512_mul_ps(r_ab_y_1, r_ab_y_1)); + r_ab_n2_0 = _mm512_max_ps(r_ab_n2_0, v_eps_sq); + r_ab_n2_1 = _mm512_max_ps(r_ab_n2_1, v_eps_sq); + + // # 32 DIVS, 32 SQRTS + // 1 / |r_ab| and |r_ab| + __m512 inv_r_ab_n_0 = _mm512_rsqrt14_ps(r_ab_n2_0); + __m512 inv_r_ab_n_1 = _mm512_rsqrt14_ps(r_ab_n2_1); + + // # 32 MULTS + __m512 r_ab_n_0 = _mm512_mul_ps(r_ab_n2_0, inv_r_ab_n_0); + __m512 r_ab_n_1 = _mm512_mul_ps(r_ab_n2_1, inv_r_ab_n_1); + + // # 64 ADDS + // r_ab - sbe_j + __m512 r_ab2_x_0 = _mm512_sub_ps(r_ab_x_0, sbe_jx_0); + __m512 r_ab2_x_1 = _mm512_sub_ps(r_ab_x_1, sbe_jx_1); + __m512 r_ab2_y_0 = _mm512_sub_ps(r_ab_y_0, sbe_jy_0); + __m512 r_ab2_y_1 = _mm512_sub_ps(r_ab_y_1, sbe_jy_1); + + // # 32 ADDS, 64 MULTS + // |r_ab - sbe_j|^2 + __m512 r_ab2_n2_0 = _mm512_fmadd_ps(r_ab2_x_0, r_ab2_x_0, _mm512_mul_ps(r_ab2_y_0, r_ab2_y_0)); + __m512 r_ab2_n2_1 = _mm512_fmadd_ps(r_ab2_x_1, r_ab2_x_1, _mm512_mul_ps(r_ab2_y_1, r_ab2_y_1)); + r_ab2_n2_0 = _mm512_max_ps(r_ab2_n2_0, v_eps_sq); + r_ab2_n2_1 = _mm512_max_ps(r_ab2_n2_1, v_eps_sq); + + // # 32 DIVS, 32 SQRTS + // 1 / |r_ab - sbe_j| and |r_ab - sbe_j| + __m512 inv_r_ab2_n_0 = _mm512_rsqrt14_ps(r_ab2_n2_0); + __m512 inv_r_ab2_n_1 = _mm512_rsqrt14_ps(r_ab2_n2_1); + + // # 32 MULTS + __m512 r_ab2_n_0 = _mm512_mul_ps(r_ab2_n2_0, inv_r_ab2_n_0); + __m512 r_ab2_n_1 = _mm512_mul_ps(r_ab2_n2_1, inv_r_ab2_n_1); + + // # 32 ADDS + // w = |r_ab| + |r_ab - step_j|, (2b)^2 = w^2 - step^2 + __m512 r_sum_0 = _mm512_add_ps(r_ab_n_0, r_ab2_n_0); + __m512 r_sum_1 = _mm512_add_ps(r_ab_n_1, r_ab2_n_1); + + // # 32 ADDS, 32 MULTS + // 2_b^2 = r_sum^2 - step[j]^2 + __m512 two_b_sq_0 = _mm512_fmsub_ps(r_sum_0, r_sum_0, sb_jsq_0); + __m512 two_b_sq_1 = _mm512_fmsub_ps(r_sum_1, r_sum_1, sb_jsq_1); + two_b_sq_0 = _mm512_max_ps(two_b_sq_0, v_eps_sq); + two_b_sq_1 = _mm512_max_ps(two_b_sq_1, v_eps_sq); + + // # 32 DIVS, 32 SQRTS + // 1/2_b and 2_b + __m512 inv_two_b_0 = _mm512_rsqrt14_ps(two_b_sq_0); + __m512 inv_two_b_1 = _mm512_rsqrt14_ps(two_b_sq_1); + + // # 32 MULTS + __m512 two_b_0 = _mm512_mul_ps(two_b_sq_0, inv_two_b_0); + __m512 two_b_1 = _mm512_mul_ps(two_b_sq_1, inv_two_b_1); + + // # 32 MULTS + // exp(-b / sigma) + __m512 e_arg_0 = _mm512_max_ps(_mm512_mul_ps(two_b_0, v_neg_2s_inv), v_exp_min); + __m512 e_arg_1 = _mm512_max_ps(_mm512_mul_ps(two_b_1, v_neg_2s_inv), v_exp_min); + + // # 512 MULTs, 448 ADDs + __m512 e_val_0 = _avx512_exp_ps(e_arg_0); + __m512 e_val_1 = _avx512_exp_ps(e_arg_1); + + // # 96 MULTS + // -(V0/sigma) * e^(-b/sigma) * w / (4b) + __m512 numer_inv_two_b_0 = _mm512_mul_ps(_mm512_mul_ps(r_sum_0, v_neg_v0_div_2s), _mm512_mul_ps(e_val_0, inv_two_b_0)); + __m512 numer_inv_two_b_1 = _mm512_mul_ps(_mm512_mul_ps(r_sum_1, v_neg_v0_div_2s), _mm512_mul_ps(e_val_1, inv_two_b_1)); + + // # 32 MULTS + // -(V0/sigma) * e^(-b/sigma) * w / (4b) * (1/|r_ab|) + __m512 sm_r_ab_0 = _mm512_mul_ps(numer_inv_two_b_0, inv_r_ab_n_0); + __m512 sm_r_ab_1 = _mm512_mul_ps(numer_inv_two_b_1, inv_r_ab_n_1); + + // # 32 MULTS + // -(V0/sigma) * e^(-b/sigma) * w / (4b) * (1/|r_ab - sbe_j|) + __m512 sm_r_ab2_0 = _mm512_mul_ps(numer_inv_two_b_0, inv_r_ab2_n_0); + __m512 sm_r_ab2_1 = _mm512_mul_ps(numer_inv_two_b_1, inv_r_ab2_n_1); + + // # 64 ADDS, 128 MULTS + // -(V0/sigma) * e^(-b/sigma) * w / (4b) * (1/|r_ab|) * r_ab + -(V0/sigma) * e^(-b/sigma) * w / (4b) * (1/|r_ab - sbe_j|) * (r_ab - sbe_j) + __m512 f_x_0 = _mm512_fmadd_ps(r_ab2_x_0, sm_r_ab2_0, _mm512_mul_ps(r_ab_x_0, sm_r_ab_0)); + __m512 f_x_1 = _mm512_fmadd_ps(r_ab2_x_1, sm_r_ab2_1, _mm512_mul_ps(r_ab_x_1, sm_r_ab_1)); + __m512 f_y_0 = _mm512_fmadd_ps(r_ab2_y_0, sm_r_ab2_0, _mm512_mul_ps(r_ab_y_0, sm_r_ab_0)); + __m512 f_y_1 = _mm512_fmadd_ps(r_ab2_y_1, sm_r_ab2_1, _mm512_mul_ps(r_ab_y_1, sm_r_ab_1)); + + // field-of-view weight + // if (e_dot_f >= 0.0 || e_dot_f_sq <= rhs) + // return dt_neg; + // else + // return c_neg_times_dt; + // + // # 32 ADDS, 64 MULTS + __m512 f_norm_sq_0 = _mm512_fmadd_ps(f_x_0, f_x_0, _mm512_mul_ps(f_y_0, f_y_0)); + __m512 f_norm_sq_1 = _mm512_fmadd_ps(f_x_1, f_x_1, _mm512_mul_ps(f_y_1, f_y_1)); + + // # 32 MULTS + __m512 rhs_0 = _mm512_mul_ps(f_norm_sq_0, v_cos_phi_sq); + __m512 rhs_1 = _mm512_mul_ps(f_norm_sq_1, v_cos_phi_sq); + + // # 32 ADDS, 64 MULTS + __m512 e_dot_f_0 = _mm512_fmadd_ps(eix, f_x_0, _mm512_mul_ps(eiy, f_y_0)); + __m512 e_dot_f_1 = _mm512_fmadd_ps(eix, f_x_1, _mm512_mul_ps(eiy, f_y_1)); + + // # 32 MULTS + __m512 e_dot_f_sq_0 = _mm512_mul_ps(e_dot_f_0, e_dot_f_0); + __m512 e_dot_f_sq_1 = _mm512_mul_ps(e_dot_f_1, e_dot_f_1); + + __mmask16 cond_0 = _mm512_cmp_ps_mask(e_dot_f_0, v_zero, _CMP_LT_OQ) & _mm512_cmp_ps_mask(e_dot_f_sq_0, rhs_0, _CMP_GT_OQ); + __mmask16 cond_1 = _mm512_cmp_ps_mask(e_dot_f_1, v_zero, _CMP_LT_OQ) & _mm512_cmp_ps_mask(e_dot_f_sq_1, rhs_1, _CMP_GT_OQ); + + __m512 w_val_0 = _mm512_mask_blend_ps(cond_0, v_dt_neg, v_c_neg_dt); + __m512 w_val_1 = _mm512_mask_blend_ps(cond_1, v_dt_neg, v_c_neg_dt); + + // # 64 ADDS, 64 MULTS + // masked accumulate (lane i == j contributes nothing) + acc_x = _mm512_mask3_fmadd_ps(f_x_0, w_val_0, acc_x, active_0); + acc_y = _mm512_mask3_fmadd_ps(f_y_0, w_val_0, acc_y, active_0); + acc_x2 = _mm512_mask3_fmadd_ps(f_x_1, w_val_1, acc_x2, active_1); + acc_y2 = _mm512_mask3_fmadd_ps(f_y_1, w_val_1, acc_y2, active_1); + + // 32 ADDS + // Increment j index vectors + j_idx_0 = _mm512_add_ps(j_idx_0, v_two); + j_idx_1 = _mm512_add_ps(j_idx_1, v_two); + } + + // Same flop count as above + // if n_p is odd one remaining iteration needs to be performed + if (n_p & 1) { + const int j = n_p - 1; + const __m512 pjx = _mm512_set1_ps(pos_x[j]); + const __m512 pjy = _mm512_set1_ps(pos_y[j]); + const __m512 sbe_jx = _mm512_set1_ps(sb_e_x[j]); + const __m512 sbe_jy = _mm512_set1_ps(sb_e_y[j]); + const __m512 sb_jsq = _mm512_set1_ps(sb_sq[j]); + const __mmask16 active = _mm512_cmp_ps_mask(i_idx, j_idx_0, _CMP_NEQ_OQ); + + __m512 r_ab_x = _mm512_sub_ps(pix, pjx); + __m512 r_ab_y = _mm512_sub_ps(piy, pjy); + __m512 r_ab_n2 = _mm512_fmadd_ps(r_ab_x, r_ab_x, _mm512_mul_ps(r_ab_y, r_ab_y)); + r_ab_n2 = _mm512_max_ps(r_ab_n2, v_eps_sq); + __m512 inv_r_ab_n = _mm512_rsqrt14_ps(r_ab_n2); + __m512 r_ab_n = _mm512_mul_ps(r_ab_n2, inv_r_ab_n); + + __m512 r_ab2_x = _mm512_sub_ps(r_ab_x, sbe_jx); + __m512 r_ab2_y = _mm512_sub_ps(r_ab_y, sbe_jy); + __m512 r_ab2_n2 = _mm512_fmadd_ps(r_ab2_x, r_ab2_x, _mm512_mul_ps(r_ab2_y, r_ab2_y)); + r_ab2_n2 = _mm512_max_ps(r_ab2_n2, v_eps_sq); + __m512 inv_r_ab2_n = _mm512_rsqrt14_ps(r_ab2_n2); + __m512 r_ab2_n = _mm512_mul_ps(r_ab2_n2, inv_r_ab2_n); + + __m512 r_sum = _mm512_add_ps(r_ab_n, r_ab2_n); + __m512 two_b_sq = _mm512_fmsub_ps(r_sum, r_sum, sb_jsq); + two_b_sq = _mm512_max_ps(two_b_sq, v_eps_sq); + __m512 inv_two_b = _mm512_rsqrt14_ps(two_b_sq); + __m512 two_b = _mm512_mul_ps(two_b_sq, inv_two_b); + + __m512 e_arg = _mm512_max_ps(_mm512_mul_ps(two_b, v_neg_2s_inv), v_exp_min); + __m512 e_val = _avx512_exp_ps(e_arg); + + __m512 numer_inv_two_b = _mm512_mul_ps(_mm512_mul_ps(r_sum, v_neg_v0_div_2s), _mm512_mul_ps(e_val, inv_two_b)); + __m512 sm_r_ab = _mm512_mul_ps(numer_inv_two_b, inv_r_ab_n); + __m512 sm_r_ab2 = _mm512_mul_ps(numer_inv_two_b, inv_r_ab2_n); + + __m512 f_x = _mm512_fmadd_ps(r_ab2_x, sm_r_ab2, _mm512_mul_ps(r_ab_x, sm_r_ab)); + __m512 f_y = _mm512_fmadd_ps(r_ab2_y, sm_r_ab2, _mm512_mul_ps(r_ab_y, sm_r_ab)); + + __m512 f_norm_sq = _mm512_fmadd_ps(f_x, f_x, _mm512_mul_ps(f_y, f_y)); + __m512 rhs = _mm512_mul_ps(f_norm_sq, v_cos_phi_sq); + __m512 e_dot_f = _mm512_fmadd_ps(eix, f_x, _mm512_mul_ps(eiy, f_y)); + __m512 e_dot_f_sq = _mm512_mul_ps(e_dot_f, e_dot_f); + __mmask16 cond = _mm512_cmp_ps_mask(e_dot_f, v_zero, _CMP_LT_OQ) & _mm512_cmp_ps_mask(e_dot_f_sq, rhs, _CMP_GT_OQ); + __m512 w_val = _mm512_mask_blend_ps(cond, v_dt_neg, v_c_neg_dt); + + acc_x = _mm512_mask3_fmadd_ps(f_x, w_val, acc_x, active); + acc_y = _mm512_mask3_fmadd_ps(f_y, w_val, acc_y, active); + } + + // # 64 ADDS + // Compute and add the obstacle repulsion for the two obstacles (unrolled) + __m512 v1_x = _mm512_sub_ps(pix, osx); + __m512 v1_y = _mm512_sub_ps(piy, osy); + __m512 v1_x1 = _mm512_sub_ps(pix, osx1); + __m512 v1_y1 = _mm512_sub_ps(piy, osy1); + + // # 16 ADDS, 48 MULTS + // projection of pedestrian onto the obstacle segment + __m512 proj = _mm512_mul_ps(_mm512_fmadd_ps(v1_x, ovx, _mm512_mul_ps(v1_y, ovy)), olen_inv); + proj = _mm512_max_ps(proj, v_zero); + proj = _mm512_min_ps(proj, v_one); + + // # 16 ADDS, 48 MULTS + __m512 proj1 = _mm512_mul_ps(_mm512_fmadd_ps(v1_x1, ovx1, _mm512_mul_ps(v1_y1, ovy1)), olen_inv1); + proj1 = _mm512_max_ps(proj1, v_zero); + proj1 = _mm512_min_ps(proj1, v_one); + + // # 128 ADDS, 64 MULTS + // r_aB = r_i - closest point on segment + __m512 r_aB_x = _mm512_sub_ps(pix, _mm512_fmadd_ps(ovx, proj, osx)); + __m512 r_aB_y = _mm512_sub_ps(piy, _mm512_fmadd_ps(ovy, proj, osy)); + __m512 r_aB_x1 = _mm512_sub_ps(pix, _mm512_fmadd_ps(ovx1, proj1, osx1)); + __m512 r_aB_y1 = _mm512_sub_ps(piy, _mm512_fmadd_ps(ovy1, proj1, osy1)); + + // # 16 ADDS, 32 MULTS + __m512 r_aB_n2 = _mm512_fmadd_ps(r_aB_x, r_aB_x, _mm512_mul_ps(r_aB_y, r_aB_y)); + r_aB_n2 = _mm512_max_ps(r_aB_n2, v_eps_sq); + + // # 16 SQRT, 16 DIVS + __m512 inv_r_aB_n = _mm512_rsqrt14_ps(r_aB_n2); + + // # 16 MULTS + __m512 r_aB_n = _mm512_mul_ps(r_aB_n2, inv_r_aB_n); + + // # 16 ADDS, 32 MULTS + __m512 r_aB_n2_1 = _mm512_fmadd_ps(r_aB_x1, r_aB_x1, _mm512_mul_ps(r_aB_y1, r_aB_y1)); + r_aB_n2_1 = _mm512_max_ps(r_aB_n2_1, v_eps_sq); + + // # 16 SQRT, 16 DIVS + __m512 inv_r_aB_n_1 = _mm512_rsqrt14_ps(r_aB_n2_1); + + // # 16 MULTS + __m512 r_aB_n_1 = _mm512_mul_ps(r_aB_n2_1, inv_r_aB_n_1); + + // # 16 MULTS + __m512 e_arg = _mm512_max_ps(_mm512_mul_ps(r_aB_n, v_neg_r_inv), v_exp_min); + + // # 256 MULTs, 224 ADDs + __m512 e_val = _avx512_exp_ps(e_arg); + + // # 32 MULTS + // scalar_mult = NEG_U0_AB_div_R * exp(-|r_aB| / R) / |r_aB| + __m512 scalar_mult = _mm512_mul_ps(_mm512_mul_ps(v_neg_u0_div_r, e_val), inv_r_aB_n); + + // # 16 MULTS + __m512 e_arg1 = _mm512_max_ps(_mm512_mul_ps(r_aB_n_1, v_neg_r_inv), v_exp_min); + + // # 256 MULTs, 224 ADDs + __m512 e_val1 = _avx512_exp_ps(e_arg1); + + // # 32 MULTS + __m512 scalar_mult1 = _mm512_mul_ps(_mm512_mul_ps(v_neg_u0_div_r, e_val1), inv_r_aB_n_1); + + // # 64 MULTS + // NEG_U0_AB_div_R * exp(-|r_aB| / R) / |r_aB| * r_aB + __m512 f_B_x = _mm512_mul_ps(r_aB_x, scalar_mult); + __m512 f_B_y = _mm512_mul_ps(r_aB_y, scalar_mult); + __m512 f_B_x1 = _mm512_mul_ps(r_aB_x1, scalar_mult1); + __m512 f_B_y1 = _mm512_mul_ps(r_aB_y1, scalar_mult1); + + // field-of-view weight: (f_x is always 0.0 so we only consider f_y) + // e_dot_f = (f_y == 0) ? 0 : (f_y < 0 ? -e_y : e_y) + // w = (e_dot_f < cos_phi) ? c_neg_dt : dt_neg + __mmask16 m_fy_neg = _mm512_cmp_ps_mask(f_B_y, v_zero, _CMP_LT_OQ); + __mmask16 m_fy_zero = _mm512_cmp_ps_mask(f_B_y, v_zero, _CMP_EQ_OQ); + __m512 neg_eiy = _mm512_xor_ps(eiy, v_sign_mask); + __m512 e_dot_f = _mm512_mask_blend_ps(m_fy_neg, eiy, neg_eiy); + e_dot_f = _mm512_mask_blend_ps(m_fy_zero, e_dot_f, v_zero); + + __mmask16 m_fy_neg1 = _mm512_cmp_ps_mask(f_B_y1, v_zero, _CMP_LT_OQ); + __mmask16 m_fy_zero1 = _mm512_cmp_ps_mask(f_B_y1, v_zero, _CMP_EQ_OQ); + __m512 neg_eiy1 = _mm512_xor_ps(eiy, v_sign_mask); + __m512 e_dot_f1 = _mm512_mask_blend_ps(m_fy_neg1, eiy, neg_eiy1); + e_dot_f1 = _mm512_mask_blend_ps(m_fy_zero1, e_dot_f1, v_zero); + + __mmask16 m_w = _mm512_cmp_ps_mask(e_dot_f, v_cos_phi, _CMP_LT_OQ); + __m512 w_val = _mm512_mask_blend_ps(m_w, v_dt_neg, v_c_neg_dt); + + __mmask16 m_w1 = _mm512_cmp_ps_mask(e_dot_f1, v_cos_phi, _CMP_LT_OQ); + __m512 w_val1 = _mm512_mask_blend_ps(m_w1, v_dt_neg, v_c_neg_dt); + + // # 64 MULTS, 64 ADDS + // Add obstacle force terms to the accs + acc_x = _mm512_fmadd_ps(f_B_x, w_val, acc_x); + acc_y = _mm512_fmadd_ps(f_B_y, w_val, acc_y); + acc_x2 = _mm512_fmadd_ps(f_B_x1, w_val1, acc_x2); + acc_y2 = _mm512_fmadd_ps(f_B_y1, w_val1, acc_y2); + + // # 32 ADDS + // Update the w arrays + _mm512_storeu_ps(&w_x[i], _mm512_add_ps(acc_x, acc_x2)); + _mm512_storeu_ps(&w_y[i], _mm512_add_ps(acc_y, acc_y2)); + + // # 16 ADDS + // Increment the i index vector + i_idx = _mm512_add_ps(i_idx, v_16); + } + + // Pass 2 : Update pedestrians state + for (int i = 0; i < n_p_pad; i += 16) { + // load 16 pedestrians per iteration with their data + // SoA in vectors + __m512 w_x_i_vec = _mm512_loadu_ps(&w_x[i]); + __m512 w_y_i_vec = _mm512_loadu_ps(&w_y[i]); + __m512 v_max_i_vec = _mm512_loadu_ps(&v_max[i]); + __m512 pos_x_i_vec = _mm512_loadu_ps(&pos_x[i]); + __m512 pos_y_i_vec = _mm512_loadu_ps(&pos_y[i]); + __m512 destination_y_i_vec = _mm512_loadu_ps(&destination_y[i]); + __m512 destination_x_i_vec = _mm512_loadu_ps(&destination_x[i]); + __m512 desired_v0_i_vec = _mm512_loadu_ps(&desired_v0[i]); + + __m512i color_i_vec = _mm512_loadu_si512((__m512i *)&color[i]); + + // # 32 MULTs, 16 ADDs + __m512 w_norm_sq = _mm512_fmadd_ps(w_x_i_vec, w_x_i_vec, _mm512_mul_ps(w_y_i_vec, w_y_i_vec)); + + // # 16 SQRTs, 16 DIVs + __m512 w_norm_inv = _mm512_rsqrt14_ps(w_norm_sq); + + // # 16 MULTs + __m512 correction_factor = _mm512_min_ps(_mm512_set1_ps(1.0f), _mm512_mul_ps(v_max_i_vec, w_norm_inv)); + + // # 32 MULTs + __m512 curr_vel_x_i_vec = _mm512_mul_ps(w_x_i_vec, correction_factor); + __m512 curr_vel_y_i_vec = _mm512_mul_ps(w_y_i_vec, correction_factor); + + __m512 dt_vec = _mm512_set1_ps(dt); + + // # 32 MULTs, 32 ADDs + pos_x_i_vec = _mm512_fmadd_ps(curr_vel_x_i_vec, dt_vec, pos_x_i_vec); + pos_y_i_vec = _mm512_fmadd_ps(curr_vel_y_i_vec, dt_vec, pos_y_i_vec); + + // differentiate whether pedestrian came from left or right using masking + __mmask16 cond_1_left = _mm512_cmpeq_epi32_mask(color_i_vec, _mm512_setzero_si512()); + __mmask16 cond_1_right = _mm512_cmp_ps_mask(pos_x_i_vec, _mm512_set1_ps(BOARD_LENGTH - 1.5f), _CMP_GT_OQ); + __mmask16 cond_1 = cond_1_left & cond_1_right; + + pos_x_i_vec = _mm512_mask_blend_ps(cond_1, pos_x_i_vec, _mm512_set1_ps(1.0f)); + destination_y_i_vec = _mm512_mask_blend_ps(cond_1, destination_y_i_vec, pos_y_i_vec); + w_x_i_vec = _mm512_mask_blend_ps(cond_1, w_x_i_vec, desired_v0_i_vec); + w_y_i_vec = _mm512_mask_blend_ps(cond_1, w_y_i_vec, _mm512_setzero_ps()); + curr_vel_x_i_vec = _mm512_mask_blend_ps(cond_1, curr_vel_x_i_vec, w_x_i_vec); + curr_vel_y_i_vec = _mm512_mask_blend_ps(cond_1, curr_vel_y_i_vec, w_y_i_vec); + + __mmask16 cond_2_left = _mm512_cmpeq_epi32_mask(color_i_vec, _mm512_set1_epi32(1)); + __mmask16 cond_2_right = _mm512_cmp_ps_mask(pos_x_i_vec, _mm512_set1_ps(1.5f), _CMP_LT_OQ); + __mmask16 cond_2 = cond_2_left & cond_2_right; + + pos_x_i_vec = _mm512_mask_blend_ps(cond_2, pos_x_i_vec, _mm512_set1_ps(BOARD_LENGTH - 1.0f)); + destination_y_i_vec = _mm512_mask_blend_ps(cond_2, destination_y_i_vec, pos_y_i_vec); + __m512 neg_desired_v0 = _mm512_xor_ps(desired_v0_i_vec, _mm512_set1_ps(-0.0f)); + w_x_i_vec = _mm512_mask_blend_ps(cond_2, w_x_i_vec, neg_desired_v0); + w_y_i_vec = _mm512_mask_blend_ps(cond_2, w_y_i_vec, _mm512_setzero_ps()); + curr_vel_x_i_vec = _mm512_mask_blend_ps(cond_2, curr_vel_x_i_vec, w_x_i_vec); + curr_vel_y_i_vec = _mm512_mask_blend_ps(cond_2, curr_vel_y_i_vec, w_y_i_vec); + + pos_y_i_vec = _mm512_max_ps(pos_y_i_vec, _mm512_set1_ps(WALL_EPS)); + pos_y_i_vec = _mm512_min_ps(pos_y_i_vec, _mm512_set1_ps(BOARD_WIDTH_MINUS_WALL_EPS)); + + // # 32 ADDs + __m512 ex_vec = _mm512_sub_ps(destination_x_i_vec, pos_x_i_vec); + __m512 ey_vec = _mm512_sub_ps(destination_y_i_vec, pos_y_i_vec); + + // # 32 MULTs, 16 ADDs + __m512 e_norm_sq = _mm512_fmadd_ps(ex_vec, ex_vec, _mm512_mul_ps(ey_vec, ey_vec)); + + // # 16 SQRTs, 16 DIVs + __m512 e_norm_inv = _mm512_rsqrt14_ps(e_norm_sq); + + // # 32 MULTs + __m512 e_x_i_vec = _mm512_mul_ps(ex_vec, e_norm_inv); + __m512 e_y_i_vec = _mm512_mul_ps(ey_vec, e_norm_inv); + + // # 32 MULTs, 16 ADDs + __m512 vel_norm_sq = _mm512_fmadd_ps(curr_vel_x_i_vec, curr_vel_x_i_vec, _mm512_mul_ps(curr_vel_y_i_vec, curr_vel_y_i_vec)); + + // # 16 MULTs + __m512 sb_sq_i_vec = _mm512_mul_ps(vel_norm_sq, _mm512_set1_ps(delta_t_sq)); + + // # 16 SQRTs + __m512 vel_norm_dt = _mm512_sqrt_ps(sb_sq_i_vec); + + // write the data + _mm512_storeu_ps(&curr_vel_x[i], curr_vel_x_i_vec); + _mm512_storeu_ps(&curr_vel_y[i], curr_vel_y_i_vec); + _mm512_storeu_ps(&w_x[i], w_x_i_vec); + _mm512_storeu_ps(&w_y[i], w_y_i_vec); + _mm512_storeu_ps(&pos_x[i], pos_x_i_vec); + _mm512_storeu_ps(&pos_y[i], pos_y_i_vec); + _mm512_storeu_ps(&e_x[i], e_x_i_vec); + _mm512_storeu_ps(&e_y[i], e_y_i_vec); + _mm512_storeu_ps(&destination_y[i], destination_y_i_vec); + _mm512_storeu_ps(&sb_sq[i], sb_sq_i_vec); + + // # 32 MULTs + _mm512_storeu_ps(&sb_e_x[i], _mm512_mul_ps(e_x_i_vec, vel_norm_dt)); + _mm512_storeu_ps(&sb_e_y[i], _mm512_mul_ps(e_y_i_vec, vel_norm_dt)); + } + +#if !BENCHMARK + for (int i = 0; i < n_p; i++) { + 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; +}