diff --git a/variants/variant_float_inlining_SoA_symmetry_ILP_8_flopcount.cpp b/variants/variant_float_inlining_SoA_symmetry_ILP_8_flopcount.cpp new file mode 100644 index 0000000..0ef7642 --- /dev/null +++ b/variants/variant_float_inlining_SoA_symmetry_ILP_8_flopcount.cpp @@ -0,0 +1,1042 @@ +// # Changes: Added ILP for j-loop with K = 8 +// # added flopcount +// FLOPCOUNT = n_iter * ( 69 * n_p ** 2 + 55 * n_obstacles * n_p ) // the linear n_p term cancels (4*K - 32 = 0) +// # Predecessor: variant_float_inlining_SoA_symmetry_ILP_4.cpp + +#include "../headers/board_reduced_float.hpp" +#include "../headers/constants_float.hpp" +#include "../headers/pedestrian_reduced_float.hpp" + +#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; + +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); + + pos_x.resize(n_p); + pos_y.resize(n_p); + sb_sq.resize(n_p); + sb_e_x.resize(n_p); + sb_e_y.resize(n_p); + e_x.resize(n_p); + e_y.resize(n_p); + curr_vel_x.resize(n_p); + curr_vel_y.resize(n_p); + w_x.resize(n_p); + w_y.resize(n_p); + desired_v0.resize(n_p); + v_max.resize(n_p); + destination_x.resize(n_p); + destination_y.resize(n_p); + color.resize(n_p); + + 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; + 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; + } + + 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 + + vector r_ab_x_lut(n_p * n_p, 0.0); + vector r_ab_y_lut(n_p * n_p, 0.0); + vector r_ab_norm_lut(n_p * n_p, 0.0); + + // FLOPCOUNT (everything inside the t-loop). EXP kept as its own op (one real exp() per call). + // section costs: overhead 4 ADD 4 MULT (+ reductions 4*K = 32 ADD, K=8) | + // distance pair 3 ADD 2 MULT 1 SQRT | + // ped-ped j 11 ADD 22 MULT 2 SQRT 1 DIV 1 EXP | + // obstacle 10 ADD 13 MULT 1 SQRT 1 DIV 1 EXP | update 7 ADD 17 MULT 3 SQRT 2 DIV + + // # ADDs: n_iter * ( + // # n_p * 36 + + // # 0.5 * (n_p*n_p - n_p) * 3 + + // # n_p * (n_p - 1) * 11 + + // # n_p * board.n_obstacles * 10 + + // # n_p * 7 + // # ) + + // # MULTs: n_iter * ( + // # n_p * 4 + + // # 0.5 * (n_p*n_p - n_p) * 2 + + // # n_p * (n_p - 1) * 22 + + // # n_p * board.n_obstacles * 13 + + // # n_p * 17 + // # ) + + // # DIVs: n_iter * ( + // # n_p * (n_p - 1) + + // # n_p * board.n_obstacles + + // # n_p * 2 + // # ) + + // # SQRTs: n_iter * ( + // # 0.5 * (n_p*n_p - n_p) + + // # n_p * (n_p - 1) * 2 + + // # n_p * board.n_obstacles + + // # n_p * 3 + // # ) + + // # EXPs: n_iter * ( + // # n_p * (n_p - 1) + + // # n_p * board.n_obstacles + // # ) + + // total with EXP = 30: n_iter * ( 69 * n_p ** 2 + 55 * n_obstacles * n_p ) // linear term cancels + for (int t = 0; t < n_iter; t++) { + for (int i = 0; i < n_p; i++) { + + // # 1 MULT + float desired_velocity_x = e_x[i] * desired_v0[i]; + // # 1 MULT + float desired_velocity_y = e_y[i] * desired_v0[i]; + // # 1 ADD, 1 MULT + float f_alpha_dt_x = (desired_velocity_x - curr_vel_x[i]) * dt_times_tau_alpha_inv; + // # 1 ADD, 1 MULT + float f_alpha_dt_y = (desired_velocity_y - curr_vel_y[i]) * dt_times_tau_alpha_inv; + + float e_x_i = e_x[i]; + float e_y_i = e_y[i]; + float pos_x_i = pos_x[i]; + float pos_y_i = pos_y[i]; + + // distance precompute, # each pair: 6 FLOPS, total over all i = 0.5*(n_p*n_p - n_p)*6 + for (int j = i + 1; j < n_p; j++) { + // # 1 ADD + float dx = pos_x_i - pos_x[j]; + // # 1 ADD + float dy = pos_y_i - pos_y[j]; + // # 1 ADD, 2 MULTs, 1 SQRT + float norm = sqrt(dx * dx + dy * dy); + int idx = i * n_p + j; + r_ab_x_lut[idx] = dx; + r_ab_y_lut[idx] = dy; + r_ab_norm_lut[idx] = norm; + } + + int j; + + float acc_x_0 = 0.0f, acc_x_1 = 0.0f, acc_x_2 = 0.0f, acc_x_3 = 0.0f; + float acc_x_4 = 0.0f, acc_x_5 = 0.0f, acc_x_6 = 0.0f, acc_x_7 = 0.0f; + float acc_y_0 = 0.0f, acc_y_1 = 0.0f, acc_y_2 = 0.0f, acc_y_3 = 0.0f; + float acc_y_4 = 0.0f, acc_y_5 = 0.0f, acc_y_6 = 0.0f, acc_y_7 = 0.0f; + + // ILP over the j < i half. # each lane = 66 FLOPS (per-line breakdown is the + // same as the single-lane remainder loop below), K = 8 lanes per step + for (j = 0; j + 8 < i; j += 8) { + float r_ab_x_0 = -1 * r_ab_x_lut[j * n_p + i]; + float r_ab_x_1 = -1 * r_ab_x_lut[(j + 1) * n_p + i]; + float r_ab_x_2 = -1 * r_ab_x_lut[(j + 2) * n_p + i]; + float r_ab_x_3 = -1 * r_ab_x_lut[(j + 3) * n_p + i]; + float r_ab_x_4 = -1 * r_ab_x_lut[(j + 4) * n_p + i]; + float r_ab_x_5 = -1 * r_ab_x_lut[(j + 5) * n_p + i]; + float r_ab_x_6 = -1 * r_ab_x_lut[(j + 6) * n_p + i]; + float r_ab_x_7 = -1 * r_ab_x_lut[(j + 7) * n_p + i]; + + float r_ab_y_0 = -1 * r_ab_y_lut[j * n_p + i]; + float r_ab_y_1 = -1 * r_ab_y_lut[(j + 1) * n_p + i]; + float r_ab_y_2 = -1 * r_ab_y_lut[(j + 2) * n_p + i]; + float r_ab_y_3 = -1 * r_ab_y_lut[(j + 3) * n_p + i]; + float r_ab_y_4 = -1 * r_ab_y_lut[(j + 4) * n_p + i]; + float r_ab_y_5 = -1 * r_ab_y_lut[(j + 5) * n_p + i]; + float r_ab_y_6 = -1 * r_ab_y_lut[(j + 6) * n_p + i]; + float r_ab_y_7 = -1 * r_ab_y_lut[(j + 7) * n_p + i]; + + float r_ab_norm_0 = r_ab_norm_lut[j * n_p + i]; + float r_ab_norm_1 = r_ab_norm_lut[(j + 1) * n_p + i]; + float r_ab_norm_2 = r_ab_norm_lut[(j + 2) * n_p + i]; + float r_ab_norm_3 = r_ab_norm_lut[(j + 3) * n_p + i]; + float r_ab_norm_4 = r_ab_norm_lut[(j + 4) * n_p + i]; + float r_ab_norm_5 = r_ab_norm_lut[(j + 5) * n_p + i]; + float r_ab_norm_6 = r_ab_norm_lut[(j + 6) * n_p + i]; + float r_ab_norm_7 = r_ab_norm_lut[(j + 7) * n_p + i]; + + r_ab_norm_0 = r_ab_norm_0 > EPS ? r_ab_norm_0 : EPS; + r_ab_norm_1 = r_ab_norm_1 > EPS ? r_ab_norm_1 : EPS; + r_ab_norm_2 = r_ab_norm_2 > EPS ? r_ab_norm_2 : EPS; + r_ab_norm_3 = r_ab_norm_3 > EPS ? r_ab_norm_3 : EPS; + r_ab_norm_4 = r_ab_norm_4 > EPS ? r_ab_norm_4 : EPS; + r_ab_norm_5 = r_ab_norm_5 > EPS ? r_ab_norm_5 : EPS; + r_ab_norm_6 = r_ab_norm_6 > EPS ? r_ab_norm_6 : EPS; + r_ab_norm_7 = r_ab_norm_7 > EPS ? r_ab_norm_7 : EPS; + + float r_ab2_x_0 = r_ab_x_0 - sb_e_x[j]; + float r_ab2_x_1 = r_ab_x_1 - sb_e_x[j + 1]; + float r_ab2_x_2 = r_ab_x_2 - sb_e_x[j + 2]; + float r_ab2_x_3 = r_ab_x_3 - sb_e_x[j + 3]; + float r_ab2_x_4 = r_ab_x_4 - sb_e_x[j + 4]; + float r_ab2_x_5 = r_ab_x_5 - sb_e_x[j + 5]; + float r_ab2_x_6 = r_ab_x_6 - sb_e_x[j + 6]; + float r_ab2_x_7 = r_ab_x_7 - sb_e_x[j + 7]; + + float r_ab2_y_0 = r_ab_y_0 - sb_e_y[j]; + float r_ab2_y_1 = r_ab_y_1 - sb_e_y[j + 1]; + float r_ab2_y_2 = r_ab_y_2 - sb_e_y[j + 2]; + float r_ab2_y_3 = r_ab_y_3 - sb_e_y[j + 3]; + float r_ab2_y_4 = r_ab_y_4 - sb_e_y[j + 4]; + float r_ab2_y_5 = r_ab_y_5 - sb_e_y[j + 5]; + float r_ab2_y_6 = r_ab_y_6 - sb_e_y[j + 6]; + float r_ab2_y_7 = r_ab_y_7 - sb_e_y[j + 7]; + + float r_ab2_norm_0 = sqrt(r_ab2_x_0 * r_ab2_x_0 + r_ab2_y_0 * r_ab2_y_0); + float r_ab2_norm_1 = sqrt(r_ab2_x_1 * r_ab2_x_1 + r_ab2_y_1 * r_ab2_y_1); + float r_ab2_norm_2 = sqrt(r_ab2_x_2 * r_ab2_x_2 + r_ab2_y_2 * r_ab2_y_2); + float r_ab2_norm_3 = sqrt(r_ab2_x_3 * r_ab2_x_3 + r_ab2_y_3 * r_ab2_y_3); + float r_ab2_norm_4 = sqrt(r_ab2_x_4 * r_ab2_x_4 + r_ab2_y_4 * r_ab2_y_4); + float r_ab2_norm_5 = sqrt(r_ab2_x_5 * r_ab2_x_5 + r_ab2_y_5 * r_ab2_y_5); + float r_ab2_norm_6 = sqrt(r_ab2_x_6 * r_ab2_x_6 + r_ab2_y_6 * r_ab2_y_6); + float r_ab2_norm_7 = sqrt(r_ab2_x_7 * r_ab2_x_7 + r_ab2_y_7 * r_ab2_y_7); + + r_ab2_norm_0 = r_ab2_norm_0 > EPS ? r_ab2_norm_0 : EPS; + r_ab2_norm_1 = r_ab2_norm_1 > EPS ? r_ab2_norm_1 : EPS; + r_ab2_norm_2 = r_ab2_norm_2 > EPS ? r_ab2_norm_2 : EPS; + r_ab2_norm_3 = r_ab2_norm_3 > EPS ? r_ab2_norm_3 : EPS; + r_ab2_norm_4 = r_ab2_norm_4 > EPS ? r_ab2_norm_4 : EPS; + r_ab2_norm_5 = r_ab2_norm_5 > EPS ? r_ab2_norm_5 : EPS; + r_ab2_norm_6 = r_ab2_norm_6 > EPS ? r_ab2_norm_6 : EPS; + r_ab2_norm_7 = r_ab2_norm_7 > EPS ? r_ab2_norm_7 : EPS; + + float r_ab_norm_sum_0 = r_ab_norm_0 + r_ab2_norm_0; + float r_ab_norm_sum_1 = r_ab_norm_1 + r_ab2_norm_1; + float r_ab_norm_sum_2 = r_ab_norm_2 + r_ab2_norm_2; + float r_ab_norm_sum_3 = r_ab_norm_3 + r_ab2_norm_3; + float r_ab_norm_sum_4 = r_ab_norm_4 + r_ab2_norm_4; + float r_ab_norm_sum_5 = r_ab_norm_5 + r_ab2_norm_5; + float r_ab_norm_sum_6 = r_ab_norm_6 + r_ab2_norm_6; + float r_ab_norm_sum_7 = r_ab_norm_7 + r_ab2_norm_7; + + float two_b_sq_0 = r_ab_norm_sum_0 * r_ab_norm_sum_0 - sb_sq[j]; + float two_b_sq_1 = r_ab_norm_sum_1 * r_ab_norm_sum_1 - sb_sq[j + 1]; + float two_b_sq_2 = r_ab_norm_sum_2 * r_ab_norm_sum_2 - sb_sq[j + 2]; + float two_b_sq_3 = r_ab_norm_sum_3 * r_ab_norm_sum_3 - sb_sq[j + 3]; + float two_b_sq_4 = r_ab_norm_sum_4 * r_ab_norm_sum_4 - sb_sq[j + 4]; + float two_b_sq_5 = r_ab_norm_sum_5 * r_ab_norm_sum_5 - sb_sq[j + 5]; + float two_b_sq_6 = r_ab_norm_sum_6 * r_ab_norm_sum_6 - sb_sq[j + 6]; + float two_b_sq_7 = r_ab_norm_sum_7 * r_ab_norm_sum_7 - sb_sq[j + 7]; + + two_b_sq_0 = two_b_sq_0 > EPS_SQ ? two_b_sq_0 : EPS_SQ; + two_b_sq_1 = two_b_sq_1 > EPS_SQ ? two_b_sq_1 : EPS_SQ; + two_b_sq_2 = two_b_sq_2 > EPS_SQ ? two_b_sq_2 : EPS_SQ; + two_b_sq_3 = two_b_sq_3 > EPS_SQ ? two_b_sq_3 : EPS_SQ; + two_b_sq_4 = two_b_sq_4 > EPS_SQ ? two_b_sq_4 : EPS_SQ; + two_b_sq_5 = two_b_sq_5 > EPS_SQ ? two_b_sq_5 : EPS_SQ; + two_b_sq_6 = two_b_sq_6 > EPS_SQ ? two_b_sq_6 : EPS_SQ; + two_b_sq_7 = two_b_sq_7 > EPS_SQ ? two_b_sq_7 : EPS_SQ; + + float two_b_0 = sqrt(two_b_sq_0); + float two_b_1 = sqrt(two_b_sq_1); + float two_b_2 = sqrt(two_b_sq_2); + float two_b_3 = sqrt(two_b_sq_3); + float two_b_4 = sqrt(two_b_sq_4); + float two_b_5 = sqrt(two_b_sq_5); + float two_b_6 = sqrt(two_b_sq_6); + float two_b_7 = sqrt(two_b_sq_7); + + float scalar_mult_common_0 = (r_ab_norm_sum_0 / (two_b_0 * r_ab_norm_0 * r_ab2_norm_0)) * (NEG_V0_AB_div_TWO_SIGMA * exp(two_b_0 * NEG_TWO_SIGMA_INV)); + float scalar_mult_common_1 = (r_ab_norm_sum_1 / (two_b_1 * r_ab_norm_1 * r_ab2_norm_1)) * (NEG_V0_AB_div_TWO_SIGMA * exp(two_b_1 * NEG_TWO_SIGMA_INV)); + float scalar_mult_common_2 = (r_ab_norm_sum_2 / (two_b_2 * r_ab_norm_2 * r_ab2_norm_2)) * (NEG_V0_AB_div_TWO_SIGMA * exp(two_b_2 * NEG_TWO_SIGMA_INV)); + float scalar_mult_common_3 = (r_ab_norm_sum_3 / (two_b_3 * r_ab_norm_3 * r_ab2_norm_3)) * (NEG_V0_AB_div_TWO_SIGMA * exp(two_b_3 * NEG_TWO_SIGMA_INV)); + float scalar_mult_common_4 = (r_ab_norm_sum_4 / (two_b_4 * r_ab_norm_4 * r_ab2_norm_4)) * (NEG_V0_AB_div_TWO_SIGMA * exp(two_b_4 * NEG_TWO_SIGMA_INV)); + float scalar_mult_common_5 = (r_ab_norm_sum_5 / (two_b_5 * r_ab_norm_5 * r_ab2_norm_5)) * (NEG_V0_AB_div_TWO_SIGMA * exp(two_b_5 * NEG_TWO_SIGMA_INV)); + float scalar_mult_common_6 = (r_ab_norm_sum_6 / (two_b_6 * r_ab_norm_6 * r_ab2_norm_6)) * (NEG_V0_AB_div_TWO_SIGMA * exp(two_b_6 * NEG_TWO_SIGMA_INV)); + float scalar_mult_common_7 = (r_ab_norm_sum_7 / (two_b_7 * r_ab_norm_7 * r_ab2_norm_7)) * (NEG_V0_AB_div_TWO_SIGMA * exp(two_b_7 * NEG_TWO_SIGMA_INV)); + + float scalar_mult_r_ab_0 = scalar_mult_common_0 * r_ab2_norm_0; + float scalar_mult_r_ab_1 = scalar_mult_common_1 * r_ab2_norm_1; + float scalar_mult_r_ab_2 = scalar_mult_common_2 * r_ab2_norm_2; + float scalar_mult_r_ab_3 = scalar_mult_common_3 * r_ab2_norm_3; + float scalar_mult_r_ab_4 = scalar_mult_common_4 * r_ab2_norm_4; + float scalar_mult_r_ab_5 = scalar_mult_common_5 * r_ab2_norm_5; + float scalar_mult_r_ab_6 = scalar_mult_common_6 * r_ab2_norm_6; + float scalar_mult_r_ab_7 = scalar_mult_common_7 * r_ab2_norm_7; + + float scalar_mult_r_ab2_0 = scalar_mult_common_0 * r_ab_norm_0; + float scalar_mult_r_ab2_1 = scalar_mult_common_1 * r_ab_norm_1; + float scalar_mult_r_ab2_2 = scalar_mult_common_2 * r_ab_norm_2; + float scalar_mult_r_ab2_3 = scalar_mult_common_3 * r_ab_norm_3; + float scalar_mult_r_ab2_4 = scalar_mult_common_4 * r_ab_norm_4; + float scalar_mult_r_ab2_5 = scalar_mult_common_5 * r_ab_norm_5; + float scalar_mult_r_ab2_6 = scalar_mult_common_6 * r_ab_norm_6; + float scalar_mult_r_ab2_7 = scalar_mult_common_7 * r_ab_norm_7; + + float f_alpha_beta_neg_x_0 = r_ab_x_0 * scalar_mult_r_ab_0 + r_ab2_x_0 * scalar_mult_r_ab2_0; + float f_alpha_beta_neg_x_1 = r_ab_x_1 * scalar_mult_r_ab_1 + r_ab2_x_1 * scalar_mult_r_ab2_1; + float f_alpha_beta_neg_x_2 = r_ab_x_2 * scalar_mult_r_ab_2 + r_ab2_x_2 * scalar_mult_r_ab2_2; + float f_alpha_beta_neg_x_3 = r_ab_x_3 * scalar_mult_r_ab_3 + r_ab2_x_3 * scalar_mult_r_ab2_3; + float f_alpha_beta_neg_x_4 = r_ab_x_4 * scalar_mult_r_ab_4 + r_ab2_x_4 * scalar_mult_r_ab2_4; + float f_alpha_beta_neg_x_5 = r_ab_x_5 * scalar_mult_r_ab_5 + r_ab2_x_5 * scalar_mult_r_ab2_5; + float f_alpha_beta_neg_x_6 = r_ab_x_6 * scalar_mult_r_ab_6 + r_ab2_x_6 * scalar_mult_r_ab2_6; + float f_alpha_beta_neg_x_7 = r_ab_x_7 * scalar_mult_r_ab_7 + r_ab2_x_7 * scalar_mult_r_ab2_7; + + float f_alpha_beta_neg_y_0 = r_ab_y_0 * scalar_mult_r_ab_0 + r_ab2_y_0 * scalar_mult_r_ab2_0; + float f_alpha_beta_neg_y_1 = r_ab_y_1 * scalar_mult_r_ab_1 + r_ab2_y_1 * scalar_mult_r_ab2_1; + float f_alpha_beta_neg_y_2 = r_ab_y_2 * scalar_mult_r_ab_2 + r_ab2_y_2 * scalar_mult_r_ab2_2; + float f_alpha_beta_neg_y_3 = r_ab_y_3 * scalar_mult_r_ab_3 + r_ab2_y_3 * scalar_mult_r_ab2_3; + float f_alpha_beta_neg_y_4 = r_ab_y_4 * scalar_mult_r_ab_4 + r_ab2_y_4 * scalar_mult_r_ab2_4; + float f_alpha_beta_neg_y_5 = r_ab_y_5 * scalar_mult_r_ab_5 + r_ab2_y_5 * scalar_mult_r_ab2_5; + float f_alpha_beta_neg_y_6 = r_ab_y_6 * scalar_mult_r_ab_6 + r_ab2_y_6 * scalar_mult_r_ab2_6; + float f_alpha_beta_neg_y_7 = r_ab_y_7 * scalar_mult_r_ab_7 + r_ab2_y_7 * scalar_mult_r_ab2_7; + + float w_val_0, w_val_1, w_val_2, w_val_3, w_val_4, w_val_5, w_val_6, w_val_7; + + float f_norm_sq_0 = f_alpha_beta_neg_x_0 * f_alpha_beta_neg_x_0 + f_alpha_beta_neg_y_0 * f_alpha_beta_neg_y_0; + float f_norm_sq_1 = f_alpha_beta_neg_x_1 * f_alpha_beta_neg_x_1 + f_alpha_beta_neg_y_1 * f_alpha_beta_neg_y_1; + float f_norm_sq_2 = f_alpha_beta_neg_x_2 * f_alpha_beta_neg_x_2 + f_alpha_beta_neg_y_2 * f_alpha_beta_neg_y_2; + float f_norm_sq_3 = f_alpha_beta_neg_x_3 * f_alpha_beta_neg_x_3 + f_alpha_beta_neg_y_3 * f_alpha_beta_neg_y_3; + float f_norm_sq_4 = f_alpha_beta_neg_x_4 * f_alpha_beta_neg_x_4 + f_alpha_beta_neg_y_4 * f_alpha_beta_neg_y_4; + float f_norm_sq_5 = f_alpha_beta_neg_x_5 * f_alpha_beta_neg_x_5 + f_alpha_beta_neg_y_5 * f_alpha_beta_neg_y_5; + float f_norm_sq_6 = f_alpha_beta_neg_x_6 * f_alpha_beta_neg_x_6 + f_alpha_beta_neg_y_6 * f_alpha_beta_neg_y_6; + float f_norm_sq_7 = f_alpha_beta_neg_x_7 * f_alpha_beta_neg_x_7 + f_alpha_beta_neg_y_7 * f_alpha_beta_neg_y_7; + + float rhs_0 = f_norm_sq_0 * cos_phi_sq; + float rhs_1 = f_norm_sq_1 * cos_phi_sq; + float rhs_2 = f_norm_sq_2 * cos_phi_sq; + float rhs_3 = f_norm_sq_3 * cos_phi_sq; + float rhs_4 = f_norm_sq_4 * cos_phi_sq; + float rhs_5 = f_norm_sq_5 * cos_phi_sq; + float rhs_6 = f_norm_sq_6 * cos_phi_sq; + float rhs_7 = f_norm_sq_7 * cos_phi_sq; + + float e_dot_f_0 = e_x_i * f_alpha_beta_neg_x_0 + e_y_i * f_alpha_beta_neg_y_0; + float e_dot_f_1 = e_x_i * f_alpha_beta_neg_x_1 + e_y_i * f_alpha_beta_neg_y_1; + float e_dot_f_2 = e_x_i * f_alpha_beta_neg_x_2 + e_y_i * f_alpha_beta_neg_y_2; + float e_dot_f_3 = e_x_i * f_alpha_beta_neg_x_3 + e_y_i * f_alpha_beta_neg_y_3; + float e_dot_f_4 = e_x_i * f_alpha_beta_neg_x_4 + e_y_i * f_alpha_beta_neg_y_4; + float e_dot_f_5 = e_x_i * f_alpha_beta_neg_x_5 + e_y_i * f_alpha_beta_neg_y_5; + float e_dot_f_6 = e_x_i * f_alpha_beta_neg_x_6 + e_y_i * f_alpha_beta_neg_y_6; + float e_dot_f_7 = e_x_i * f_alpha_beta_neg_x_7 + e_y_i * f_alpha_beta_neg_y_7; + + float e_dot_f_sq_0 = e_dot_f_0 * e_dot_f_0; + float e_dot_f_sq_1 = e_dot_f_1 * e_dot_f_1; + float e_dot_f_sq_2 = e_dot_f_2 * e_dot_f_2; + float e_dot_f_sq_3 = e_dot_f_3 * e_dot_f_3; + float e_dot_f_sq_4 = e_dot_f_4 * e_dot_f_4; + float e_dot_f_sq_5 = e_dot_f_5 * e_dot_f_5; + float e_dot_f_sq_6 = e_dot_f_6 * e_dot_f_6; + float e_dot_f_sq_7 = e_dot_f_7 * e_dot_f_7; + + if (e_dot_f_0 >= 0.0 || e_dot_f_sq_0 <= rhs_0) + w_val_0 = dt_neg; + else + w_val_0 = c_neg_times_dt; + if (e_dot_f_1 >= 0.0 || e_dot_f_sq_1 <= rhs_1) + w_val_1 = dt_neg; + else + w_val_1 = c_neg_times_dt; + if (e_dot_f_2 >= 0.0 || e_dot_f_sq_2 <= rhs_2) + w_val_2 = dt_neg; + else + w_val_2 = c_neg_times_dt; + if (e_dot_f_3 >= 0.0 || e_dot_f_sq_3 <= rhs_3) + w_val_3 = dt_neg; + else + w_val_3 = c_neg_times_dt; + if (e_dot_f_4 >= 0.0 || e_dot_f_sq_4 <= rhs_4) + w_val_4 = dt_neg; + else + w_val_4 = c_neg_times_dt; + if (e_dot_f_5 >= 0.0 || e_dot_f_sq_5 <= rhs_5) + w_val_5 = dt_neg; + else + w_val_5 = c_neg_times_dt; + if (e_dot_f_6 >= 0.0 || e_dot_f_sq_6 <= rhs_6) + w_val_6 = dt_neg; + else + w_val_6 = c_neg_times_dt; + if (e_dot_f_7 >= 0.0 || e_dot_f_sq_7 <= rhs_7) + w_val_7 = dt_neg; + else + w_val_7 = c_neg_times_dt; + + acc_x_0 += f_alpha_beta_neg_x_0 * w_val_0; + acc_x_1 += f_alpha_beta_neg_x_1 * w_val_1; + acc_x_2 += f_alpha_beta_neg_x_2 * w_val_2; + acc_x_3 += f_alpha_beta_neg_x_3 * w_val_3; + acc_x_4 += f_alpha_beta_neg_x_4 * w_val_4; + acc_x_5 += f_alpha_beta_neg_x_5 * w_val_5; + acc_x_6 += f_alpha_beta_neg_x_6 * w_val_6; + acc_x_7 += f_alpha_beta_neg_x_7 * w_val_7; + acc_y_0 += f_alpha_beta_neg_y_0 * w_val_0; + acc_y_1 += f_alpha_beta_neg_y_1 * w_val_1; + acc_y_2 += f_alpha_beta_neg_y_2 * w_val_2; + acc_y_3 += f_alpha_beta_neg_y_3 * w_val_3; + acc_y_4 += f_alpha_beta_neg_y_4 * w_val_4; + acc_y_5 += f_alpha_beta_neg_y_5 * w_val_5; + acc_y_6 += f_alpha_beta_neg_y_6 * w_val_6; + acc_y_7 += f_alpha_beta_neg_y_7 * w_val_7; + } + + // remainder of the j < i half, single lane. # one j = 66 FLOPS + for (; j < i; j++) { + // lut lookup + -1* sign flip: not counted + float r_ab_x = -1 * r_ab_x_lut[j * n_p + i]; + float r_ab_y = -1 * r_ab_y_lut[j * n_p + i]; + float r_ab_norm = r_ab_norm_lut[j * n_p + i]; + + r_ab_norm = r_ab_norm > EPS ? r_ab_norm : EPS; + + // # 1 ADD + float r_ab2_x = r_ab_x - sb_e_x[j]; + // # 1 ADD + float r_ab2_y = r_ab_y - sb_e_y[j]; + + // # 1 ADD, 2 MULTs, 1 SQRT + float r_ab2_norm = sqrt(r_ab2_x * r_ab2_x + r_ab2_y * r_ab2_y); + r_ab2_norm = r_ab2_norm > EPS ? r_ab2_norm : EPS; + + // # 1 ADD + float r_ab_norm_sum = r_ab_norm + r_ab2_norm; + + // # 1 ADD, 1 MULT + float two_b_sq = r_ab_norm_sum * r_ab_norm_sum - sb_sq[j]; + two_b_sq = two_b_sq > EPS_SQ ? two_b_sq : EPS_SQ; + // # 1 SQRT + float two_b = sqrt(two_b_sq); + // # 5 MULTs, 1 DIV, 1 EXP (= 36 FLOPS with EXP=30) + float scalar_mult_common = (r_ab_norm_sum / (two_b * r_ab_norm * r_ab2_norm)) * (NEG_V0_AB_div_TWO_SIGMA * exp(two_b * NEG_TWO_SIGMA_INV)); + // # 1 MULT + float scalar_mult_r_ab = scalar_mult_common * r_ab2_norm; + // # 1 MULT + float scalar_mult_r_ab2 = scalar_mult_common * r_ab_norm; + + // # 1 ADD, 2 MULTs + float f_alpha_beta_neg_x = r_ab_x * scalar_mult_r_ab + r_ab2_x * scalar_mult_r_ab2; + // # 1 ADD, 2 MULTs + float f_alpha_beta_neg_y = r_ab_y * scalar_mult_r_ab + r_ab2_y * scalar_mult_r_ab2; + + float w_val; + + // # 1 ADD, 2 MULTs + float f_norm_sq = f_alpha_beta_neg_x * f_alpha_beta_neg_x + f_alpha_beta_neg_y * f_alpha_beta_neg_y; + // # 1 MULT + float rhs = f_norm_sq * cos_phi_sq; + // # 1 ADD, 2 MULTs + float e_dot_f = e_x[i] * f_alpha_beta_neg_x + e_y[i] * f_alpha_beta_neg_y; + // # 1 MULT + float e_dot_f_sq = e_dot_f * e_dot_f; + if (e_dot_f >= 0.0 || e_dot_f_sq <= rhs) + w_val = dt_neg; + else + w_val = c_neg_times_dt; + + // # 1 ADD, 1 MULT + f_alpha_dt_x += f_alpha_beta_neg_x * w_val; + // # 1 ADD, 1 MULT + f_alpha_dt_y += f_alpha_beta_neg_y * w_val; + } + + // reduction of the j < i accumulators. # K adds per line (K=8) => 16 ADDs + f_alpha_dt_x += acc_x_0 + acc_x_1 + acc_x_2 + acc_x_3 + acc_x_4 + acc_x_5 + acc_x_6 + acc_x_7; + f_alpha_dt_y += acc_y_0 + acc_y_1 + acc_y_2 + acc_y_3 + acc_y_4 + acc_y_5 + acc_y_6 + acc_y_7; + + acc_x_0 = 0.0f; + acc_x_1 = 0.0f; + acc_x_2 = 0.0f; + acc_x_3 = 0.0f; + acc_x_4 = 0.0f; + acc_x_5 = 0.0f; + acc_x_6 = 0.0f; + acc_x_7 = 0.0f; + acc_y_0 = 0.0f; + acc_y_1 = 0.0f; + acc_y_2 = 0.0f; + acc_y_3 = 0.0f; + acc_y_4 = 0.0f; + acc_y_5 = 0.0f; + acc_y_6 = 0.0f; + acc_y_7 = 0.0f; + + // ILP over the j > i half. # each lane = 66 FLOPS, K = 8 lanes per step + for (j = i + 1; j + 8 < n_p; j += 8) { + float r_ab_x_0 = r_ab_x_lut[i * n_p + j]; + float r_ab_x_1 = r_ab_x_lut[i * n_p + j + 1]; + float r_ab_x_2 = r_ab_x_lut[i * n_p + j + 2]; + float r_ab_x_3 = r_ab_x_lut[i * n_p + j + 3]; + float r_ab_x_4 = r_ab_x_lut[i * n_p + j + 4]; + float r_ab_x_5 = r_ab_x_lut[i * n_p + j + 5]; + float r_ab_x_6 = r_ab_x_lut[i * n_p + j + 6]; + float r_ab_x_7 = r_ab_x_lut[i * n_p + j + 7]; + + float r_ab_y_0 = r_ab_y_lut[i * n_p + j]; + float r_ab_y_1 = r_ab_y_lut[i * n_p + j + 1]; + float r_ab_y_2 = r_ab_y_lut[i * n_p + j + 2]; + float r_ab_y_3 = r_ab_y_lut[i * n_p + j + 3]; + float r_ab_y_4 = r_ab_y_lut[i * n_p + j + 4]; + float r_ab_y_5 = r_ab_y_lut[i * n_p + j + 5]; + float r_ab_y_6 = r_ab_y_lut[i * n_p + j + 6]; + float r_ab_y_7 = r_ab_y_lut[i * n_p + j + 7]; + + float r_ab_norm_0 = r_ab_norm_lut[i * n_p + j]; + float r_ab_norm_1 = r_ab_norm_lut[i * n_p + j + 1]; + float r_ab_norm_2 = r_ab_norm_lut[i * n_p + j + 2]; + float r_ab_norm_3 = r_ab_norm_lut[i * n_p + j + 3]; + float r_ab_norm_4 = r_ab_norm_lut[i * n_p + j + 4]; + float r_ab_norm_5 = r_ab_norm_lut[i * n_p + j + 5]; + float r_ab_norm_6 = r_ab_norm_lut[i * n_p + j + 6]; + float r_ab_norm_7 = r_ab_norm_lut[i * n_p + j + 7]; + + r_ab_norm_0 = r_ab_norm_0 > EPS ? r_ab_norm_0 : EPS; + r_ab_norm_1 = r_ab_norm_1 > EPS ? r_ab_norm_1 : EPS; + r_ab_norm_2 = r_ab_norm_2 > EPS ? r_ab_norm_2 : EPS; + r_ab_norm_3 = r_ab_norm_3 > EPS ? r_ab_norm_3 : EPS; + r_ab_norm_4 = r_ab_norm_4 > EPS ? r_ab_norm_4 : EPS; + r_ab_norm_5 = r_ab_norm_5 > EPS ? r_ab_norm_5 : EPS; + r_ab_norm_6 = r_ab_norm_6 > EPS ? r_ab_norm_6 : EPS; + r_ab_norm_7 = r_ab_norm_7 > EPS ? r_ab_norm_7 : EPS; + + float r_ab2_x_0 = r_ab_x_0 - sb_e_x[j]; + float r_ab2_x_1 = r_ab_x_1 - sb_e_x[j + 1]; + float r_ab2_x_2 = r_ab_x_2 - sb_e_x[j + 2]; + float r_ab2_x_3 = r_ab_x_3 - sb_e_x[j + 3]; + float r_ab2_x_4 = r_ab_x_4 - sb_e_x[j + 4]; + float r_ab2_x_5 = r_ab_x_5 - sb_e_x[j + 5]; + float r_ab2_x_6 = r_ab_x_6 - sb_e_x[j + 6]; + float r_ab2_x_7 = r_ab_x_7 - sb_e_x[j + 7]; + + float r_ab2_y_0 = r_ab_y_0 - sb_e_y[j]; + float r_ab2_y_1 = r_ab_y_1 - sb_e_y[j + 1]; + float r_ab2_y_2 = r_ab_y_2 - sb_e_y[j + 2]; + float r_ab2_y_3 = r_ab_y_3 - sb_e_y[j + 3]; + float r_ab2_y_4 = r_ab_y_4 - sb_e_y[j + 4]; + float r_ab2_y_5 = r_ab_y_5 - sb_e_y[j + 5]; + float r_ab2_y_6 = r_ab_y_6 - sb_e_y[j + 6]; + float r_ab2_y_7 = r_ab_y_7 - sb_e_y[j + 7]; + + float r_ab2_norm_0 = sqrt(r_ab2_x_0 * r_ab2_x_0 + r_ab2_y_0 * r_ab2_y_0); + float r_ab2_norm_1 = sqrt(r_ab2_x_1 * r_ab2_x_1 + r_ab2_y_1 * r_ab2_y_1); + float r_ab2_norm_2 = sqrt(r_ab2_x_2 * r_ab2_x_2 + r_ab2_y_2 * r_ab2_y_2); + float r_ab2_norm_3 = sqrt(r_ab2_x_3 * r_ab2_x_3 + r_ab2_y_3 * r_ab2_y_3); + float r_ab2_norm_4 = sqrt(r_ab2_x_4 * r_ab2_x_4 + r_ab2_y_4 * r_ab2_y_4); + float r_ab2_norm_5 = sqrt(r_ab2_x_5 * r_ab2_x_5 + r_ab2_y_5 * r_ab2_y_5); + float r_ab2_norm_6 = sqrt(r_ab2_x_6 * r_ab2_x_6 + r_ab2_y_6 * r_ab2_y_6); + float r_ab2_norm_7 = sqrt(r_ab2_x_7 * r_ab2_x_7 + r_ab2_y_7 * r_ab2_y_7); + + r_ab2_norm_0 = r_ab2_norm_0 > EPS ? r_ab2_norm_0 : EPS; + r_ab2_norm_1 = r_ab2_norm_1 > EPS ? r_ab2_norm_1 : EPS; + r_ab2_norm_2 = r_ab2_norm_2 > EPS ? r_ab2_norm_2 : EPS; + r_ab2_norm_3 = r_ab2_norm_3 > EPS ? r_ab2_norm_3 : EPS; + r_ab2_norm_4 = r_ab2_norm_4 > EPS ? r_ab2_norm_4 : EPS; + r_ab2_norm_5 = r_ab2_norm_5 > EPS ? r_ab2_norm_5 : EPS; + r_ab2_norm_6 = r_ab2_norm_6 > EPS ? r_ab2_norm_6 : EPS; + r_ab2_norm_7 = r_ab2_norm_7 > EPS ? r_ab2_norm_7 : EPS; + + float r_ab_norm_sum_0 = r_ab_norm_0 + r_ab2_norm_0; + float r_ab_norm_sum_1 = r_ab_norm_1 + r_ab2_norm_1; + float r_ab_norm_sum_2 = r_ab_norm_2 + r_ab2_norm_2; + float r_ab_norm_sum_3 = r_ab_norm_3 + r_ab2_norm_3; + float r_ab_norm_sum_4 = r_ab_norm_4 + r_ab2_norm_4; + float r_ab_norm_sum_5 = r_ab_norm_5 + r_ab2_norm_5; + float r_ab_norm_sum_6 = r_ab_norm_6 + r_ab2_norm_6; + float r_ab_norm_sum_7 = r_ab_norm_7 + r_ab2_norm_7; + + float two_b_sq_0 = r_ab_norm_sum_0 * r_ab_norm_sum_0 - sb_sq[j]; + float two_b_sq_1 = r_ab_norm_sum_1 * r_ab_norm_sum_1 - sb_sq[j + 1]; + float two_b_sq_2 = r_ab_norm_sum_2 * r_ab_norm_sum_2 - sb_sq[j + 2]; + float two_b_sq_3 = r_ab_norm_sum_3 * r_ab_norm_sum_3 - sb_sq[j + 3]; + float two_b_sq_4 = r_ab_norm_sum_4 * r_ab_norm_sum_4 - sb_sq[j + 4]; + float two_b_sq_5 = r_ab_norm_sum_5 * r_ab_norm_sum_5 - sb_sq[j + 5]; + float two_b_sq_6 = r_ab_norm_sum_6 * r_ab_norm_sum_6 - sb_sq[j + 6]; + float two_b_sq_7 = r_ab_norm_sum_7 * r_ab_norm_sum_7 - sb_sq[j + 7]; + + two_b_sq_0 = two_b_sq_0 > EPS_SQ ? two_b_sq_0 : EPS_SQ; + two_b_sq_1 = two_b_sq_1 > EPS_SQ ? two_b_sq_1 : EPS_SQ; + two_b_sq_2 = two_b_sq_2 > EPS_SQ ? two_b_sq_2 : EPS_SQ; + two_b_sq_3 = two_b_sq_3 > EPS_SQ ? two_b_sq_3 : EPS_SQ; + two_b_sq_4 = two_b_sq_4 > EPS_SQ ? two_b_sq_4 : EPS_SQ; + two_b_sq_5 = two_b_sq_5 > EPS_SQ ? two_b_sq_5 : EPS_SQ; + two_b_sq_6 = two_b_sq_6 > EPS_SQ ? two_b_sq_6 : EPS_SQ; + two_b_sq_7 = two_b_sq_7 > EPS_SQ ? two_b_sq_7 : EPS_SQ; + + float two_b_0 = sqrt(two_b_sq_0); + float two_b_1 = sqrt(two_b_sq_1); + float two_b_2 = sqrt(two_b_sq_2); + float two_b_3 = sqrt(two_b_sq_3); + float two_b_4 = sqrt(two_b_sq_4); + float two_b_5 = sqrt(two_b_sq_5); + float two_b_6 = sqrt(two_b_sq_6); + float two_b_7 = sqrt(two_b_sq_7); + + float scalar_mult_common_0 = (r_ab_norm_sum_0 / (two_b_0 * r_ab_norm_0 * r_ab2_norm_0)) * (NEG_V0_AB_div_TWO_SIGMA * exp(two_b_0 * NEG_TWO_SIGMA_INV)); + float scalar_mult_common_1 = (r_ab_norm_sum_1 / (two_b_1 * r_ab_norm_1 * r_ab2_norm_1)) * (NEG_V0_AB_div_TWO_SIGMA * exp(two_b_1 * NEG_TWO_SIGMA_INV)); + float scalar_mult_common_2 = (r_ab_norm_sum_2 / (two_b_2 * r_ab_norm_2 * r_ab2_norm_2)) * (NEG_V0_AB_div_TWO_SIGMA * exp(two_b_2 * NEG_TWO_SIGMA_INV)); + float scalar_mult_common_3 = (r_ab_norm_sum_3 / (two_b_3 * r_ab_norm_3 * r_ab2_norm_3)) * (NEG_V0_AB_div_TWO_SIGMA * exp(two_b_3 * NEG_TWO_SIGMA_INV)); + float scalar_mult_common_4 = (r_ab_norm_sum_4 / (two_b_4 * r_ab_norm_4 * r_ab2_norm_4)) * (NEG_V0_AB_div_TWO_SIGMA * exp(two_b_4 * NEG_TWO_SIGMA_INV)); + float scalar_mult_common_5 = (r_ab_norm_sum_5 / (two_b_5 * r_ab_norm_5 * r_ab2_norm_5)) * (NEG_V0_AB_div_TWO_SIGMA * exp(two_b_5 * NEG_TWO_SIGMA_INV)); + float scalar_mult_common_6 = (r_ab_norm_sum_6 / (two_b_6 * r_ab_norm_6 * r_ab2_norm_6)) * (NEG_V0_AB_div_TWO_SIGMA * exp(two_b_6 * NEG_TWO_SIGMA_INV)); + float scalar_mult_common_7 = (r_ab_norm_sum_7 / (two_b_7 * r_ab_norm_7 * r_ab2_norm_7)) * (NEG_V0_AB_div_TWO_SIGMA * exp(two_b_7 * NEG_TWO_SIGMA_INV)); + + float scalar_mult_r_ab_0 = scalar_mult_common_0 * r_ab2_norm_0; + float scalar_mult_r_ab_1 = scalar_mult_common_1 * r_ab2_norm_1; + float scalar_mult_r_ab_2 = scalar_mult_common_2 * r_ab2_norm_2; + float scalar_mult_r_ab_3 = scalar_mult_common_3 * r_ab2_norm_3; + float scalar_mult_r_ab_4 = scalar_mult_common_4 * r_ab2_norm_4; + float scalar_mult_r_ab_5 = scalar_mult_common_5 * r_ab2_norm_5; + float scalar_mult_r_ab_6 = scalar_mult_common_6 * r_ab2_norm_6; + float scalar_mult_r_ab_7 = scalar_mult_common_7 * r_ab2_norm_7; + + float scalar_mult_r_ab2_0 = scalar_mult_common_0 * r_ab_norm_0; + float scalar_mult_r_ab2_1 = scalar_mult_common_1 * r_ab_norm_1; + float scalar_mult_r_ab2_2 = scalar_mult_common_2 * r_ab_norm_2; + float scalar_mult_r_ab2_3 = scalar_mult_common_3 * r_ab_norm_3; + float scalar_mult_r_ab2_4 = scalar_mult_common_4 * r_ab_norm_4; + float scalar_mult_r_ab2_5 = scalar_mult_common_5 * r_ab_norm_5; + float scalar_mult_r_ab2_6 = scalar_mult_common_6 * r_ab_norm_6; + float scalar_mult_r_ab2_7 = scalar_mult_common_7 * r_ab_norm_7; + + float f_alpha_beta_neg_x_0 = r_ab_x_0 * scalar_mult_r_ab_0 + r_ab2_x_0 * scalar_mult_r_ab2_0; + float f_alpha_beta_neg_x_1 = r_ab_x_1 * scalar_mult_r_ab_1 + r_ab2_x_1 * scalar_mult_r_ab2_1; + float f_alpha_beta_neg_x_2 = r_ab_x_2 * scalar_mult_r_ab_2 + r_ab2_x_2 * scalar_mult_r_ab2_2; + float f_alpha_beta_neg_x_3 = r_ab_x_3 * scalar_mult_r_ab_3 + r_ab2_x_3 * scalar_mult_r_ab2_3; + float f_alpha_beta_neg_x_4 = r_ab_x_4 * scalar_mult_r_ab_4 + r_ab2_x_4 * scalar_mult_r_ab2_4; + float f_alpha_beta_neg_x_5 = r_ab_x_5 * scalar_mult_r_ab_5 + r_ab2_x_5 * scalar_mult_r_ab2_5; + float f_alpha_beta_neg_x_6 = r_ab_x_6 * scalar_mult_r_ab_6 + r_ab2_x_6 * scalar_mult_r_ab2_6; + float f_alpha_beta_neg_x_7 = r_ab_x_7 * scalar_mult_r_ab_7 + r_ab2_x_7 * scalar_mult_r_ab2_7; + + float f_alpha_beta_neg_y_0 = r_ab_y_0 * scalar_mult_r_ab_0 + r_ab2_y_0 * scalar_mult_r_ab2_0; + float f_alpha_beta_neg_y_1 = r_ab_y_1 * scalar_mult_r_ab_1 + r_ab2_y_1 * scalar_mult_r_ab2_1; + float f_alpha_beta_neg_y_2 = r_ab_y_2 * scalar_mult_r_ab_2 + r_ab2_y_2 * scalar_mult_r_ab2_2; + float f_alpha_beta_neg_y_3 = r_ab_y_3 * scalar_mult_r_ab_3 + r_ab2_y_3 * scalar_mult_r_ab2_3; + float f_alpha_beta_neg_y_4 = r_ab_y_4 * scalar_mult_r_ab_4 + r_ab2_y_4 * scalar_mult_r_ab2_4; + float f_alpha_beta_neg_y_5 = r_ab_y_5 * scalar_mult_r_ab_5 + r_ab2_y_5 * scalar_mult_r_ab2_5; + float f_alpha_beta_neg_y_6 = r_ab_y_6 * scalar_mult_r_ab_6 + r_ab2_y_6 * scalar_mult_r_ab2_6; + float f_alpha_beta_neg_y_7 = r_ab_y_7 * scalar_mult_r_ab_7 + r_ab2_y_7 * scalar_mult_r_ab2_7; + + float w_val_0, w_val_1, w_val_2, w_val_3, w_val_4, w_val_5, w_val_6, w_val_7; + + float f_norm_sq_0 = f_alpha_beta_neg_x_0 * f_alpha_beta_neg_x_0 + f_alpha_beta_neg_y_0 * f_alpha_beta_neg_y_0; + float f_norm_sq_1 = f_alpha_beta_neg_x_1 * f_alpha_beta_neg_x_1 + f_alpha_beta_neg_y_1 * f_alpha_beta_neg_y_1; + float f_norm_sq_2 = f_alpha_beta_neg_x_2 * f_alpha_beta_neg_x_2 + f_alpha_beta_neg_y_2 * f_alpha_beta_neg_y_2; + float f_norm_sq_3 = f_alpha_beta_neg_x_3 * f_alpha_beta_neg_x_3 + f_alpha_beta_neg_y_3 * f_alpha_beta_neg_y_3; + float f_norm_sq_4 = f_alpha_beta_neg_x_4 * f_alpha_beta_neg_x_4 + f_alpha_beta_neg_y_4 * f_alpha_beta_neg_y_4; + float f_norm_sq_5 = f_alpha_beta_neg_x_5 * f_alpha_beta_neg_x_5 + f_alpha_beta_neg_y_5 * f_alpha_beta_neg_y_5; + float f_norm_sq_6 = f_alpha_beta_neg_x_6 * f_alpha_beta_neg_x_6 + f_alpha_beta_neg_y_6 * f_alpha_beta_neg_y_6; + float f_norm_sq_7 = f_alpha_beta_neg_x_7 * f_alpha_beta_neg_x_7 + f_alpha_beta_neg_y_7 * f_alpha_beta_neg_y_7; + + float rhs_0 = f_norm_sq_0 * cos_phi_sq; + float rhs_1 = f_norm_sq_1 * cos_phi_sq; + float rhs_2 = f_norm_sq_2 * cos_phi_sq; + float rhs_3 = f_norm_sq_3 * cos_phi_sq; + float rhs_4 = f_norm_sq_4 * cos_phi_sq; + float rhs_5 = f_norm_sq_5 * cos_phi_sq; + float rhs_6 = f_norm_sq_6 * cos_phi_sq; + float rhs_7 = f_norm_sq_7 * cos_phi_sq; + + float e_dot_f_0 = e_x_i * f_alpha_beta_neg_x_0 + e_y_i * f_alpha_beta_neg_y_0; + float e_dot_f_1 = e_x_i * f_alpha_beta_neg_x_1 + e_y_i * f_alpha_beta_neg_y_1; + float e_dot_f_2 = e_x_i * f_alpha_beta_neg_x_2 + e_y_i * f_alpha_beta_neg_y_2; + float e_dot_f_3 = e_x_i * f_alpha_beta_neg_x_3 + e_y_i * f_alpha_beta_neg_y_3; + float e_dot_f_4 = e_x_i * f_alpha_beta_neg_x_4 + e_y_i * f_alpha_beta_neg_y_4; + float e_dot_f_5 = e_x_i * f_alpha_beta_neg_x_5 + e_y_i * f_alpha_beta_neg_y_5; + float e_dot_f_6 = e_x_i * f_alpha_beta_neg_x_6 + e_y_i * f_alpha_beta_neg_y_6; + float e_dot_f_7 = e_x_i * f_alpha_beta_neg_x_7 + e_y_i * f_alpha_beta_neg_y_7; + + float e_dot_f_sq_0 = e_dot_f_0 * e_dot_f_0; + float e_dot_f_sq_1 = e_dot_f_1 * e_dot_f_1; + float e_dot_f_sq_2 = e_dot_f_2 * e_dot_f_2; + float e_dot_f_sq_3 = e_dot_f_3 * e_dot_f_3; + float e_dot_f_sq_4 = e_dot_f_4 * e_dot_f_4; + float e_dot_f_sq_5 = e_dot_f_5 * e_dot_f_5; + float e_dot_f_sq_6 = e_dot_f_6 * e_dot_f_6; + float e_dot_f_sq_7 = e_dot_f_7 * e_dot_f_7; + + if (e_dot_f_0 >= 0.0 || e_dot_f_sq_0 <= rhs_0) + w_val_0 = dt_neg; + else + w_val_0 = c_neg_times_dt; + if (e_dot_f_1 >= 0.0 || e_dot_f_sq_1 <= rhs_1) + w_val_1 = dt_neg; + else + w_val_1 = c_neg_times_dt; + if (e_dot_f_2 >= 0.0 || e_dot_f_sq_2 <= rhs_2) + w_val_2 = dt_neg; + else + w_val_2 = c_neg_times_dt; + if (e_dot_f_3 >= 0.0 || e_dot_f_sq_3 <= rhs_3) + w_val_3 = dt_neg; + else + w_val_3 = c_neg_times_dt; + if (e_dot_f_4 >= 0.0 || e_dot_f_sq_4 <= rhs_4) + w_val_4 = dt_neg; + else + w_val_4 = c_neg_times_dt; + if (e_dot_f_5 >= 0.0 || e_dot_f_sq_5 <= rhs_5) + w_val_5 = dt_neg; + else + w_val_5 = c_neg_times_dt; + if (e_dot_f_6 >= 0.0 || e_dot_f_sq_6 <= rhs_6) + w_val_6 = dt_neg; + else + w_val_6 = c_neg_times_dt; + if (e_dot_f_7 >= 0.0 || e_dot_f_sq_7 <= rhs_7) + w_val_7 = dt_neg; + else + w_val_7 = c_neg_times_dt; + + acc_x_0 += f_alpha_beta_neg_x_0 * w_val_0; + acc_x_1 += f_alpha_beta_neg_x_1 * w_val_1; + acc_x_2 += f_alpha_beta_neg_x_2 * w_val_2; + acc_x_3 += f_alpha_beta_neg_x_3 * w_val_3; + acc_x_4 += f_alpha_beta_neg_x_4 * w_val_4; + acc_x_5 += f_alpha_beta_neg_x_5 * w_val_5; + acc_x_6 += f_alpha_beta_neg_x_6 * w_val_6; + acc_x_7 += f_alpha_beta_neg_x_7 * w_val_7; + acc_y_0 += f_alpha_beta_neg_y_0 * w_val_0; + acc_y_1 += f_alpha_beta_neg_y_1 * w_val_1; + acc_y_2 += f_alpha_beta_neg_y_2 * w_val_2; + acc_y_3 += f_alpha_beta_neg_y_3 * w_val_3; + acc_y_4 += f_alpha_beta_neg_y_4 * w_val_4; + acc_y_5 += f_alpha_beta_neg_y_5 * w_val_5; + acc_y_6 += f_alpha_beta_neg_y_6 * w_val_6; + acc_y_7 += f_alpha_beta_neg_y_7 * w_val_7; + } + + // remainder of the j > i half, single lane. # one j = 66 FLOPS + for (; j < n_p; j++) { + float r_ab_x = r_ab_x_lut[i * n_p + j]; + float r_ab_y = r_ab_y_lut[i * n_p + j]; + float r_ab_norm = r_ab_norm_lut[i * n_p + j]; + + r_ab_norm = r_ab_norm > EPS ? r_ab_norm : EPS; + + // # 1 ADD + float r_ab2_x = r_ab_x - sb_e_x[j]; + // # 1 ADD + float r_ab2_y = r_ab_y - sb_e_y[j]; + + // # 1 ADD, 2 MULTs, 1 SQRT + float r_ab2_norm = sqrt(r_ab2_x * r_ab2_x + r_ab2_y * r_ab2_y); + r_ab2_norm = r_ab2_norm > EPS ? r_ab2_norm : EPS; + + // # 1 ADD + float r_ab_norm_sum = r_ab_norm + r_ab2_norm; + + // # 1 ADD, 1 MULT + float two_b_sq = r_ab_norm_sum * r_ab_norm_sum - sb_sq[j]; + two_b_sq = two_b_sq > EPS_SQ ? two_b_sq : EPS_SQ; + // # 1 SQRT + float two_b = sqrt(two_b_sq); + // # 5 MULTs, 1 DIV, 1 EXP + float scalar_mult_common = (r_ab_norm_sum / (two_b * r_ab_norm * r_ab2_norm)) * (NEG_V0_AB_div_TWO_SIGMA * exp(two_b * NEG_TWO_SIGMA_INV)); + // # 1 MULT + float scalar_mult_r_ab = scalar_mult_common * r_ab2_norm; + // # 1 MULT + float scalar_mult_r_ab2 = scalar_mult_common * r_ab_norm; + + // # 1 ADD, 2 MULTs + float f_alpha_beta_neg_x = r_ab_x * scalar_mult_r_ab + r_ab2_x * scalar_mult_r_ab2; + // # 1 ADD, 2 MULTs + float f_alpha_beta_neg_y = r_ab_y * scalar_mult_r_ab + r_ab2_y * scalar_mult_r_ab2; + + float w_val; + + // # 1 ADD, 2 MULTs + float f_norm_sq = f_alpha_beta_neg_x * f_alpha_beta_neg_x + f_alpha_beta_neg_y * f_alpha_beta_neg_y; + // # 1 MULT + float rhs = f_norm_sq * cos_phi_sq; + // # 1 ADD, 2 MULTs + float e_dot_f = e_x[i] * f_alpha_beta_neg_x + e_y[i] * f_alpha_beta_neg_y; + // # 1 MULT + float e_dot_f_sq = e_dot_f * e_dot_f; + if (e_dot_f >= 0.0 || e_dot_f_sq <= rhs) + w_val = dt_neg; + else + w_val = c_neg_times_dt; + + // # 1 ADD, 1 MULT + f_alpha_dt_x += f_alpha_beta_neg_x * w_val; + // # 1 ADD, 1 MULT + f_alpha_dt_y += f_alpha_beta_neg_y * w_val; + } + + // reduction of the j > i accumulators. # K adds per line (K=8) => 16 ADDs + f_alpha_dt_x += acc_x_0 + acc_x_1 + acc_x_2 + acc_x_3 + acc_x_4 + acc_x_5 + acc_x_6 + acc_x_7; + f_alpha_dt_y += acc_y_0 + acc_y_1 + acc_y_2 + acc_y_3 + acc_y_4 + acc_y_5 + acc_y_6 + acc_y_7; + + // force between pedestrian and obstacles + // # one obstacle = 55 FLOPS (w_val sign-based, no a*a / b_sq) + for (int k = 0; k < board.n_obstacles; k++) { + // # 1 ADD + float v1_x = pos_x[i] - board.obstacles[k].start_x; + // # 1 ADD + 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; + + // # 1 ADD, 3 MULTs + 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; + + // # 2 ADDs, 1 MULT + float r_aB_x = pos_x[i] - (board.obstacles[k].start_x + board.obstacles[k].obstacle_v_x * projection); + // # 2 ADDs, 1 MULT + float r_aB_y = pos_y[i] - (board.obstacles[k].start_y + board.obstacles[k].obstacle_v_y * projection); + + // # 1 ADD, 2 MULTs, 1 SQRT + 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; + + // # 2 MULTs, 1 DIV, 1 EXP + float scalar_mult = (NEG_U0_AB_div_R * exp(r_aB_norm * NEG_R_INV)) / r_aB_norm; + // # 1 MULT + float f_alpha_B_neg_x = r_aB_x * scalar_mult; + // # 1 MULT + float f_alpha_B_neg_y = r_aB_y * scalar_mult; + + float w_val; + + // sign select only, no flops + 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; + + // # 1 MULT + 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 ADD + 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; + } + + // update each pedestrian + // # 29 FLOPS per pedestrian + for (int i = 0; i < n_p; i++) { + + // # 1 ADD, 2 MULTs, 1 SQRT + 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; + + // # 1 DIV + float correction_factor = min(1.0f, v_max[i] / w_norm2); + + // # 1 MULT + curr_vel_x[i] = w_x[i] * correction_factor; + // # 1 MULT + curr_vel_y[i] = w_y[i] * correction_factor; + + // # 1 ADD, 1 MULT + pos_x[i] = pos_x[i] + curr_vel_x[i] * dt; + // # 1 ADD, 1 MULT + 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); + + // # 1 ADD + float ex = destination_x[i] - pos_x[i]; + // # 1 ADD + float ey = destination_y[i] - pos_y[i]; + + // # 1 ADD, 2 MULTs, 1 SQRT + float e_norm = sqrt(ex * ex + ey * ey); + float e_norm2 = e_norm > EPS ? e_norm : EPS; + // # 1 DIV + float e_norm_inv = 1.0 / e_norm2; + + // # 1 MULT + e_x[i] = ex * e_norm_inv; + // # 1 MULT + e_y[i] = ey * e_norm_inv; + + // # 1 ADD, 2 MULTs + float velocity_norm_sq = curr_vel_x[i] * curr_vel_x[i] + curr_vel_y[i] * curr_vel_y[i]; + + // # 1 SQRT + float velocity_norm = sqrt(velocity_norm_sq); + + // # 1 MULT + sb_sq[i] = velocity_norm_sq * delta_t_sq; + + // # 2 MULTs (velocity_norm*delta_t written on both lines, counted as is) + sb_e_x[i] = e_x[i] * (velocity_norm * delta_t); + // # 2 MULTs + 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; +}