Merge branch 'elliot/flop-count-correction' into 'main'

Flop Count Correction

See merge request course-asl-fastcode26/team70!59

headers/constants_float.hpp

@@ -103,3 +103,17 @@ const float CUTOFF_SQ = CUTOFF * CUTOFF;
 const float cos_phi_sq = cos_phi * cos_phi;
 
 const size_t CACHE_BLOCK_SIZE = std::hardware_destructive_interference_size;
+
+const double c0_scalar = 1.0 / 1;
+const double c1_scalar = 1.0 / 1;
+const double c2_scalar = 1.0 / 2;
+const double c3_scalar = 1.0 / 6;
+const double c4_scalar = 1.0 / 24;
+const double c5_scalar = 1.0 / 120;
+const double c6_scalar = 1.0 / 720;
+const double c7_scalar = 1.0 / 5040;
+const double c8_scalar = 1.0 / 40320;
+const double c9_scalar = 1.0 / 362880;
+const double c10_scalar = 1.0 / 3628800;
+const double c11_scalar = 1.0 / 39916800;
+const double c12_scalar = 1.0 / 479001600;

variants/variant_float_inlining_SoA_AVX512_polyexp_moreavx_ilp_2_rsqrt_morersqrt_expfix.cpp

@@ -0,0 +1,632 @@
+// # Changes: Replaced sqrt_ps with rsqrt14_ps in the pedestrian loop, similar to @lbaumberger in variant_float_inlining_SoA_AVX2_polyexp_rsqrt.cpp
+// # Predecessor: variant_float_inlining_SoA_AVX512_polyexp_moreavx_ilp_2_rsqrt.cpp
+
+#include "../headers/board_reduced_float.hpp"
+#include "../headers/constants_float.hpp"
+#include "../headers/pedestrian_reduced_float.hpp"
+
+#include <immintrin.h>
+
+#include <fstream>
+#include <random>
+
+#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<float> pos_x, pos_y;
+alignas(64) vector<float> sb_sq;
+alignas(64) vector<float> sb_e_x, sb_e_y;
+alignas(64) vector<float> e_x, e_y;
+alignas(64) vector<float> curr_vel_x, curr_vel_y;
+alignas(64) vector<float> w_x, w_y;
+alignas(64) vector<float> desired_v0;
+alignas(64) vector<float> v_max;
+alignas(64) vector<float> destination_x, destination_y;
+alignas(64) vector<int> color;
+
+Pedestrian *init_pedestrians(int n_p) {
+#if RANDOM_SEED
+  random_device rd;
+  mt19937 gen(rd());
+#else
+  mt19937 gen(SEED);
+#endif
+
+  normal_distribution<float> velocity_gen(v0_mean, v0_std_dev);
+  uniform_real_distribution<float> y_gen(0.3, BOARD_WIDTH - 0.3);
+  uniform_real_distribution<float> x_gen_left(2.0, BOARD_LENGTH / 2.0);
+  uniform_real_distribution<float> 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); }
+
+static inline __m512 _avx512_exp_ps(__m512 x) {
+  // define own inlined intrinsic function for approximating the exponent function
+  // e^x = 2^n * e^r --> x = n * ln(2) + r
+
+  const __m512 log2e = _mm512_set1_ps(1.4426950408889634f);
+  __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);
+  // r = x - n * ln(2)
+  __m512 r = _mm512_fnmadd_ps(nf, ln2, x);
+
+  // approximation of e^r using taylor polynomial
+  // cNUM --> coefficients
+  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);
+
+  // apply coefficients
+  __m512 p = c12;
+  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);
+
+  // use bit shifting for 2^n and bias because float have 23 bit mantissa
+  __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);
+
+  // e^x
+  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<tuple<int, int, float, float, float, float, int>> samples;
+
+  if (dump_path) {
+    samples.reserve(static_cast<size_t>(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;
+
+  alignas(64) const float lane_offset_arr[16] = {0.0f, 1.0f, 2.0f, 3.0f, 4.0f, 5.0f, 6.0f, 7.0f, 8.0f, 9.0f, 10.0f, 11.0f, 12.0f, 13.0f, 14.0f, 15.0f};
+  const __m512 lane_off = _mm512_load_ps(lane_offset_arr);
+
+  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);
+
+  for (int t = 0; t < n_iter; t++) {
+    for (int i = 0; i < n_p; i++) {
+      // set the vector for the current pedestrian
+
+      // get desired velocity
+      float desired_velocity_x = e_x[i] * desired_v0[i];
+      float desired_velocity_y = e_y[i] * desired_v0[i];
+
+      // 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]);
+      // broadcast index used by mask to prevent situation pedestrian[i] == pedestrian[j], see m_neq_i_0 and m_neq_i_1
+      const __m512 v_i = _mm512_set1_ps((float)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();
+
+      // 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) {
+
+        // [j, j+1, j+2, ..., j+15] and [j+16, j+17, j+18, ..., j+31]
+        __m512 j_idx_0 = _mm512_add_ps(_mm512_set1_ps((float)j), lane_off);
+        __m512 j_idx_1 = _mm512_add_ps(_mm512_set1_ps((float)j + 16), lane_off);
+
+        // 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]);
+
+        // ---
+
+        // 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);
+
+        // |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);
+
+        // ---
+
+        // 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);
+
+        // 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);
+
+        // 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);
+
+        // |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);
+
+        // 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);
+
+        // |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);
+
+        // 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);
+
+        // 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);
+
+        // 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);
+
+        // 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);
+
+        // ---
+
+        // 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);
+
+        // 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);
+
+        // [−(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));
+
+        // 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);
+
+        // 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);
+
+        // 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));
+
+        // 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));
+
+        __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);
+
+        __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));
+
+        __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);
+
+        // take care of i == j case by zeroing it out
+        // see active_0 and active_1 at the beginning of this loop
+        // [f.x or 0, ...]
+        __m512 f_x_safe_0 = _mm512_maskz_mov_ps(active_0, f_x_0);
+        __m512 f_x_safe_1 = _mm512_maskz_mov_ps(active_1, f_x_1);
+        __m512 f_y_safe_0 = _mm512_maskz_mov_ps(active_0, f_y_0);
+        __m512 f_y_safe_1 = _mm512_maskz_mov_ps(active_1, f_y_1);
+
+        // accumulate force with weight
+        // force_P_total += weight * force_P_other
+        acc_x_0 = _mm512_fmadd_ps(f_x_safe_0, w_val_0, acc_x_0);
+        acc_x_1 = _mm512_fmadd_ps(f_x_safe_1, w_val_1, acc_x_1);
+        acc_y_0 = _mm512_fmadd_ps(f_y_safe_0, w_val_0, acc_y_0);
+        acc_y_1 = _mm512_fmadd_ps(f_y_safe_1, w_val_1, acc_y_1);
+      }
+
+      // 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++) {
+        float v1_x = pos_x[i] - board.obstacles[k].start_x;
+        float v1_y = pos_y[i] - board.obstacles[k].start_y;
+        float v2_x = board.obstacles[k].obstacle_v_x;
+        float v2_y = board.obstacles[k].obstacle_v_y;
+
+        float projection = (v1_x * v2_x + v1_y * v2_y) * board.obstacles[k].length_sq_inv;
+
+        if (projection < 0.0f)
+          projection = 0.0f;
+        else if (projection > 1.0f)
+          projection = 1.0f;
+
+        float r_aB_x = pos_x[i] - (board.obstacles[k].start_x + board.obstacles[k].obstacle_v_x * projection);
+        float r_aB_y = pos_y[i] - (board.obstacles[k].start_y + board.obstacles[k].obstacle_v_y * projection);
+
+        float r_aB_norm = sqrt(r_aB_x * r_aB_x + r_aB_y * r_aB_y);
+        r_aB_norm = r_aB_norm > EPS ? r_aB_norm : EPS;
+
+        float scalar_mult = (NEG_U0_AB_div_R * exp(r_aB_norm * NEG_R_INV)) / r_aB_norm;
+        float f_alpha_B_neg_x = r_aB_x * scalar_mult;
+        float f_alpha_B_neg_y = r_aB_y * scalar_mult;
+
+        float w_val = 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;
+
+        float f_alpha_B_dt_x = f_alpha_B_neg_x * w_val;
+        float f_alpha_B_dt_y = f_alpha_B_neg_y * w_val;
+
+        f_alpha_dt_x += f_alpha_B_dt_x;
+        f_alpha_dt_y += f_alpha_B_dt_y;
+      }
+
+      w_x[i] += f_alpha_dt_x;
+      w_y[i] += f_alpha_dt_y;
+    }
+
+    // update each pedestrian
+    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]);
+
+      __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));
+      __m512 w_norm_inv = _mm512_rsqrt14_ps(w_norm_sq);
+      __m512 correction_factor = _mm512_min_ps(_mm512_set1_ps(1.0f), _mm512_mul_ps(v_max_i_vec, w_norm_inv));
+
+      __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);
+      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));
+
+      __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);
+      __m512 e_norm_sq = _mm512_fmadd_ps(ex_vec, ex_vec, _mm512_mul_ps(ey_vec, ey_vec));
+      __m512 e_norm_inv = _mm512_rsqrt14_ps(e_norm_sq);
+      __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);
+
+      __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));
+      __m512 sb_sq_i_vec = _mm512_mul_ps(vel_norm_sq, _mm512_set1_ps(delta_t_sq));
+      __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);
+      _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;
+}

variants/variant_float_inlining_SoA_NEON_polyexp_moreavx_ilp_2_rsqrt_morrsqrt.cpp

@@ -9,7 +9,14 @@
 #include "../headers/constants_float.hpp"
 #include "../headers/pedestrian_reduced_float.hpp"
 
+#ifdef __aarch64__
 #include <arm_neon.h>
+#endif
+
+#ifdef __x86_64__
+#define SIMDE_ENABLE_NATIVE_ALIASES
+#include <simde/arm/neon.h>
+#endif
 
 #include <cmath>
 #include <fstream>
@@ -33,7 +40,6 @@
 
 using namespace std;
 
-
 alignas(64) vector<float> pos_x, pos_y;
 alignas(64) vector<float> sb_sq;
 alignas(64) vector<float> sb_e_x, sb_e_y;
@@ -58,7 +64,6 @@ Pedestrian *init_pedestrians(int n_p) {
   uniform_real_distribution<float> x_gen_left(2.0, BOARD_LENGTH / 2.0);
   uniform_real_distribution<float> x_gen_right(BOARD_LENGTH / 2.0, BOARD_LENGTH - 2.0);
 
-  
   const int n_p_pad = (n_p + 7) & ~7;
 
   pos_x.resize(n_p_pad);
@@ -170,13 +175,12 @@ Pedestrian *init_pedestrians(int n_p) {
 
 Board init_board_without_obstacles() { return Board(BOARD_LENGTH, BOARD_WIDTH, 0, nullptr); }
 
-
 static inline float32x4_t _neon_exp_ps(float32x4_t x) {
   const float32x4_t log2e = vdupq_n_f32(1.4426950408889634f);
   float32x4_t nf = vrndnq_f32(vmulq_f32(x, log2e));
 
   const float32x4_t ln2 = vdupq_n_f32(0.6931471805599453f);
-  float32x4_t r = vfmsq_f32(x, nf, ln2);   // r = x - nf*ln2
+  float32x4_t r = vfmsq_f32(x, nf, ln2); // r = x - nf*ln2
 
   const float32x4_t c5 = vdupq_n_f32(1.0f / 120.0f);
   const float32x4_t c4 = vdupq_n_f32(1.0f / 24.0f);
@@ -192,7 +196,7 @@ static inline float32x4_t _neon_exp_ps(float32x4_t x) {
   p = vfmaq_f32(c1, p, r);
   p = vfmaq_f32(c0, p, r);
 
-  int32x4_t ni     = vcvtq_s32_f32(nf);
+  int32x4_t ni = vcvtq_s32_f32(nf);
   int32x4_t biased = vaddq_s32(ni, vdupq_n_s32(127));
   int32x4_t scaled = vshlq_n_s32(biased, 23);
   float32x4_t pow2n = vreinterpretq_f32_s32(scaled);
@@ -230,19 +234,19 @@ int run_simulation(Pedestrian *pedestrians, Board &board, int n_p, int n_iter, c
   const float32x4_t lane_off = {0.0f, 1.0f, 2.0f, 3.0f};
 
   const float32x4_t v_neg_v0_div_2s = vdupq_n_f32(NEG_V0_AB_div_TWO_SIGMA);
-  const float32x4_t v_neg_2s_inv    = vdupq_n_f32(NEG_TWO_SIGMA_INV);
+  const float32x4_t v_neg_2s_inv = vdupq_n_f32(NEG_TWO_SIGMA_INV);
-  const float32x4_t v_cos_phi_sq    = vdupq_n_f32(cos_phi_sq);
+  const float32x4_t v_cos_phi_sq = vdupq_n_f32(cos_phi_sq);
-  const float32x4_t v_dt_neg        = vdupq_n_f32(dt_neg);
+  const float32x4_t v_dt_neg = vdupq_n_f32(dt_neg);
-  const float32x4_t v_c_neg_dt      = vdupq_n_f32(c_neg_times_dt);
+  const float32x4_t v_c_neg_dt = vdupq_n_f32(c_neg_times_dt);
-  const float32x4_t v_zero          = vdupq_n_f32(0.0f);
+  const float32x4_t v_zero = vdupq_n_f32(0.0f);
-  const float32x4_t v_one           = vdupq_n_f32(1.0f);
+  const float32x4_t v_one = vdupq_n_f32(1.0f);
-  const float32x4_t v_eps_sq        = vdupq_n_f32(EPS_SQ);
+  const float32x4_t v_eps_sq = vdupq_n_f32(EPS_SQ);
-  const float32x4_t v_np            = vdupq_n_f32((float)n_p);
+  const float32x4_t v_np = vdupq_n_f32((float)n_p);
-  const float32x4_t v_exp_min       = vdupq_n_f32(-87.0f);
+  const float32x4_t v_exp_min = vdupq_n_f32(-87.0f);
 
   for (int t = 0; t < n_iter; t++) {
     for (int i = 0; i < n_p; i++) {
-      
+
       float desired_velocity_x = e_x[i] * desired_v0[i];
       float desired_velocity_y = e_y[i] * desired_v0[i];
 
@@ -255,28 +259,27 @@ int run_simulation(Pedestrian *pedestrians, Board &board, int n_p, int n_iter, c
       const float32x4_t eiy = vdupq_n_f32(e_y[i]);
       const float32x4_t v_i = vdupq_n_f32((float)i);
 
-      
       float32x4_t acc_x_0 = vdupq_n_f32(0.0f);
       float32x4_t acc_y_0 = vdupq_n_f32(0.0f);
       float32x4_t acc_x_1 = vdupq_n_f32(0.0f);
       float32x4_t acc_y_1 = vdupq_n_f32(0.0f);
 
       for (int j = 0; j < n_p_pad; j += 8) {
-        
+
-        float32x4_t j_idx_0 = vaddq_f32(vdupq_n_f32((float)j),       lane_off);
+        float32x4_t j_idx_0 = vaddq_f32(vdupq_n_f32((float)j), lane_off);
         float32x4_t j_idx_1 = vaddq_f32(vdupq_n_f32((float)(j + 4)), lane_off);
 
-        uint32x4_t m_neq_i_0    = vmvnq_u32(vceqq_f32(j_idx_0, v_i));
+        uint32x4_t m_neq_i_0 = vmvnq_u32(vceqq_f32(j_idx_0, v_i));
-        uint32x4_t m_neq_i_1    = vmvnq_u32(vceqq_f32(j_idx_1, v_i));
+        uint32x4_t m_neq_i_1 = vmvnq_u32(vceqq_f32(j_idx_1, v_i));
         uint32x4_t m_in_range_0 = vcltq_f32(j_idx_0, v_np);
         uint32x4_t m_in_range_1 = vcltq_f32(j_idx_1, v_np);
-        uint32x4_t active_0     = vandq_u32(m_neq_i_0, m_in_range_0);
+        uint32x4_t active_0 = vandq_u32(m_neq_i_0, m_in_range_0);
-        uint32x4_t active_1     = vandq_u32(m_neq_i_1, m_in_range_1);
+        uint32x4_t active_1 = vandq_u32(m_neq_i_1, m_in_range_1);
 
-        float32x4_t pjx_0    = vld1q_f32(&pos_x[j]);
+        float32x4_t pjx_0 = vld1q_f32(&pos_x[j]);
-        float32x4_t pjx_1    = vld1q_f32(&pos_x[j + 4]);
+        float32x4_t pjx_1 = vld1q_f32(&pos_x[j + 4]);
-        float32x4_t pjy_0    = vld1q_f32(&pos_y[j]);
+        float32x4_t pjy_0 = vld1q_f32(&pos_y[j]);
-        float32x4_t pjy_1    = vld1q_f32(&pos_y[j + 4]);
+        float32x4_t pjy_1 = vld1q_f32(&pos_y[j + 4]);
         float32x4_t sbe_jx_0 = vld1q_f32(&sb_e_x[j]);
         float32x4_t sbe_jx_1 = vld1q_f32(&sb_e_x[j + 4]);
         float32x4_t sbe_jy_0 = vld1q_f32(&sb_e_y[j]);
@@ -284,7 +287,6 @@ int run_simulation(Pedestrian *pedestrians, Board &board, int n_p, int n_iter, c
         float32x4_t sb_jsq_0 = vld1q_f32(&sb_sq[j]);
         float32x4_t sb_jsq_1 = vld1q_f32(&sb_sq[j + 4]);
 
-        
         float32x4_t r_ab_x_0 = vsubq_f32(pix, pjx_0);
         float32x4_t r_ab_x_1 = vsubq_f32(pix, pjx_1);
         float32x4_t r_ab_y_0 = vsubq_f32(piy, pjy_0);
@@ -302,7 +304,6 @@ int run_simulation(Pedestrian *pedestrians, Board &board, int n_p, int n_iter, c
         float32x4_t r_ab_n_0 = vmulq_f32(r_ab_n2_0, inv_r_ab_n_0);
         float32x4_t r_ab_n_1 = vmulq_f32(r_ab_n2_1, inv_r_ab_n_1);
 
-        
         float32x4_t r_ab2_x_0 = vsubq_f32(r_ab_x_0, sbe_jx_0);
         float32x4_t r_ab2_x_1 = vsubq_f32(r_ab_x_1, sbe_jx_1);
         float32x4_t r_ab2_y_0 = vsubq_f32(r_ab_y_0, sbe_jy_0);
@@ -323,7 +324,6 @@ int run_simulation(Pedestrian *pedestrians, Board &board, int n_p, int n_iter, c
         float32x4_t r_sum_0 = vaddq_f32(r_ab_n_0, r_ab2_n_0);
         float32x4_t r_sum_1 = vaddq_f32(r_ab_n_1, r_ab2_n_1);
 
-        
         float32x4_t two_b_sq_0 = vsubq_f32(vmulq_f32(r_sum_0, r_sum_0), sb_jsq_0);
         float32x4_t two_b_sq_1 = vsubq_f32(vmulq_f32(r_sum_1, r_sum_1), sb_jsq_1);
 
@@ -339,33 +339,25 @@ int run_simulation(Pedestrian *pedestrians, Board &board, int n_p, int n_iter, c
         float32x4_t e_arg_0 = vmulq_f32(two_b_0, v_neg_2s_inv);
         float32x4_t e_arg_1 = vmulq_f32(two_b_1, v_neg_2s_inv);
 
-        
         e_arg_0 = vmaxq_f32(e_arg_0, v_exp_min);
         e_arg_1 = vmaxq_f32(e_arg_1, v_exp_min);
 
         float32x4_t e_val_0 = _neon_exp_ps(e_arg_0);
         float32x4_t e_val_1 = _neon_exp_ps(e_arg_1);
 
-        
+        float32x4_t numer_inv_two_b_0 = vmulq_f32(vmulq_f32(r_sum_0, v_neg_v0_div_2s), vmulq_f32(e_val_0, inv_two_b_0));
-        float32x4_t numer_inv_two_b_0 = vmulq_f32(
+        float32x4_t numer_inv_two_b_1 = vmulq_f32(vmulq_f32(r_sum_1, v_neg_v0_div_2s), vmulq_f32(e_val_1, inv_two_b_1));
-            vmulq_f32(r_sum_0, v_neg_v0_div_2s),
-            vmulq_f32(e_val_0, inv_two_b_0));
-        float32x4_t numer_inv_two_b_1 = vmulq_f32(
-            vmulq_f32(r_sum_1, v_neg_v0_div_2s),
-            vmulq_f32(e_val_1, inv_two_b_1));
 
-        float32x4_t sm_r_ab_0  = vmulq_f32(numer_inv_two_b_0, inv_r_ab_n_0);
+        float32x4_t sm_r_ab_0 = vmulq_f32(numer_inv_two_b_0, inv_r_ab_n_0);
-        float32x4_t sm_r_ab_1  = vmulq_f32(numer_inv_two_b_1, inv_r_ab_n_1);
+        float32x4_t sm_r_ab_1 = vmulq_f32(numer_inv_two_b_1, inv_r_ab_n_1);
         float32x4_t sm_r_ab2_0 = vmulq_f32(numer_inv_two_b_0, inv_r_ab2_n_0);
         float32x4_t sm_r_ab2_1 = vmulq_f32(numer_inv_two_b_1, inv_r_ab2_n_1);
 
-        
         float32x4_t f_x_0 = vfmaq_f32(vmulq_f32(r_ab_x_0, sm_r_ab_0), r_ab2_x_0, sm_r_ab2_0);
         float32x4_t f_x_1 = vfmaq_f32(vmulq_f32(r_ab_x_1, sm_r_ab_1), r_ab2_x_1, sm_r_ab2_1);
         float32x4_t f_y_0 = vfmaq_f32(vmulq_f32(r_ab_y_0, sm_r_ab_0), r_ab2_y_0, sm_r_ab2_0);
         float32x4_t f_y_1 = vfmaq_f32(vmulq_f32(r_ab_y_1, sm_r_ab_1), r_ab2_y_1, sm_r_ab2_1);
 
-        
         float32x4_t f_norm_sq_0 = vfmaq_f32(vmulq_f32(f_y_0, f_y_0), f_x_0, f_x_0);
         float32x4_t f_norm_sq_1 = vfmaq_f32(vmulq_f32(f_y_1, f_y_1), f_x_1, f_x_1);
 
@@ -389,7 +381,6 @@ int run_simulation(Pedestrian *pedestrians, Board &board, int n_p, int n_iter, c
         float32x4_t w_val_0 = vbslq_f32(cond_0, v_c_neg_dt, v_dt_neg);
         float32x4_t w_val_1 = vbslq_f32(cond_1, v_c_neg_dt, v_dt_neg);
 
-        
         float32x4_t f_x_safe_0 = vbslq_f32(active_0, f_x_0, v_zero);
         float32x4_t f_x_safe_1 = vbslq_f32(active_1, f_x_1, v_zero);
         float32x4_t f_y_safe_0 = vbslq_f32(active_0, f_y_0, v_zero);
@@ -401,11 +392,9 @@ int run_simulation(Pedestrian *pedestrians, Board &board, int n_p, int n_iter, c
         acc_y_1 = vfmaq_f32(acc_y_1, f_y_safe_1, w_val_1);
       }
 
-      
       f_alpha_dt_x += vaddvq_f32(vaddq_f32(acc_x_0, acc_x_1));
       f_alpha_dt_y += vaddvq_f32(vaddq_f32(acc_y_0, acc_y_1));
 
-      
       for (int k = 0; k < board.n_obstacles; k++) {
         float v1_x = pos_x[i] - board.obstacles[k].start_x;
         float v1_y = pos_y[i] - board.obstacles[k].start_y;
@@ -446,21 +435,19 @@ int run_simulation(Pedestrian *pedestrians, Board &board, int n_p, int n_iter, c
       w_y[i] += f_alpha_dt_y;
     }
 
-    
     for (int i = 0; i < n_p_pad; i += 4) {
 
-      float32x4_t w_x_i_vec           = vld1q_f32(&w_x[i]);
+      float32x4_t w_x_i_vec = vld1q_f32(&w_x[i]);
-      float32x4_t w_y_i_vec           = vld1q_f32(&w_y[i]);
+      float32x4_t w_y_i_vec = vld1q_f32(&w_y[i]);
-      float32x4_t v_max_i_vec         = vld1q_f32(&v_max[i]);
+      float32x4_t v_max_i_vec = vld1q_f32(&v_max[i]);
-      float32x4_t pos_x_i_vec         = vld1q_f32(&pos_x[i]);
+      float32x4_t pos_x_i_vec = vld1q_f32(&pos_x[i]);
-      float32x4_t pos_y_i_vec         = vld1q_f32(&pos_y[i]);
+      float32x4_t pos_y_i_vec = vld1q_f32(&pos_y[i]);
       float32x4_t destination_y_i_vec = vld1q_f32(&destination_y[i]);
       float32x4_t destination_x_i_vec = vld1q_f32(&destination_x[i]);
-      float32x4_t desired_v0_i_vec    = vld1q_f32(&desired_v0[i]);
+      float32x4_t desired_v0_i_vec = vld1q_f32(&desired_v0[i]);
-      int32x4_t   color_i_vec         = vld1q_s32(&color[i]);
+      int32x4_t color_i_vec = vld1q_s32(&color[i]);
 
-      
+      float32x4_t w_norm_sq = vfmaq_f32(vmulq_f32(w_y_i_vec, w_y_i_vec), w_x_i_vec, w_x_i_vec);
-      float32x4_t w_norm_sq  = vfmaq_f32(vmulq_f32(w_y_i_vec, w_y_i_vec), w_x_i_vec, w_x_i_vec);
       float32x4_t w_norm_inv = _neon_rsqrt_ps(w_norm_sq);
       float32x4_t correction_factor = vminq_f32(v_one, vmulq_f32(v_max_i_vec, w_norm_inv));
 
@@ -471,63 +458,56 @@ int run_simulation(Pedestrian *pedestrians, Board &board, int n_p, int n_iter, c
       pos_x_i_vec = vfmaq_f32(pos_x_i_vec, curr_vel_x_i_vec, dt_vec);
       pos_y_i_vec = vfmaq_f32(pos_y_i_vec, curr_vel_y_i_vec, dt_vec);
 
-      
+      uint32x4_t cond_1_left = vceqq_s32(color_i_vec, vdupq_n_s32(0));
-      uint32x4_t cond_1_left  = vceqq_s32(color_i_vec, vdupq_n_s32(0));
       uint32x4_t cond_1_right = vcgtq_f32(pos_x_i_vec, vdupq_n_f32(BOARD_LENGTH - 1.5f));
-      uint32x4_t cond_1       = vandq_u32(cond_1_left, cond_1_right);
+      uint32x4_t cond_1 = vandq_u32(cond_1_left, cond_1_right);
 
-      
+      pos_x_i_vec = vbslq_f32(cond_1, v_one, pos_x_i_vec);
-      pos_x_i_vec         = vbslq_f32(cond_1, v_one,             pos_x_i_vec);
+      destination_y_i_vec = vbslq_f32(cond_1, pos_y_i_vec, destination_y_i_vec);
-      destination_y_i_vec = vbslq_f32(cond_1, pos_y_i_vec,       destination_y_i_vec);
+      w_x_i_vec = vbslq_f32(cond_1, desired_v0_i_vec, w_x_i_vec);
-      w_x_i_vec           = vbslq_f32(cond_1, desired_v0_i_vec,  w_x_i_vec);
+      w_y_i_vec = vbslq_f32(cond_1, v_zero, w_y_i_vec);
-      w_y_i_vec           = vbslq_f32(cond_1, v_zero,            w_y_i_vec);
+      curr_vel_x_i_vec = vbslq_f32(cond_1, w_x_i_vec, curr_vel_x_i_vec);
-      curr_vel_x_i_vec    = vbslq_f32(cond_1, w_x_i_vec,         curr_vel_x_i_vec);
+      curr_vel_y_i_vec = vbslq_f32(cond_1, w_y_i_vec, curr_vel_y_i_vec);
-      curr_vel_y_i_vec    = vbslq_f32(cond_1, w_y_i_vec,         curr_vel_y_i_vec);
 
-      
+      uint32x4_t cond_2_left = vceqq_s32(color_i_vec, vdupq_n_s32(1));
-      uint32x4_t cond_2_left  = vceqq_s32(color_i_vec, vdupq_n_s32(1));
       uint32x4_t cond_2_right = vcltq_f32(pos_x_i_vec, vdupq_n_f32(1.5f));
-      uint32x4_t cond_2       = vandq_u32(cond_2_left, cond_2_right);
+      uint32x4_t cond_2 = vandq_u32(cond_2_left, cond_2_right);
 
-      pos_x_i_vec         = vbslq_f32(cond_2, vdupq_n_f32(BOARD_LENGTH - 1.0f), pos_x_i_vec);
+      pos_x_i_vec = vbslq_f32(cond_2, vdupq_n_f32(BOARD_LENGTH - 1.0f), pos_x_i_vec);
-      destination_y_i_vec = vbslq_f32(cond_2, pos_y_i_vec,                      destination_y_i_vec);
+      destination_y_i_vec = vbslq_f32(cond_2, pos_y_i_vec, destination_y_i_vec);
 
       float32x4_t neg_desired_v0 = vnegq_f32(desired_v0_i_vec);
-      w_x_i_vec        = vbslq_f32(cond_2, neg_desired_v0, w_x_i_vec);
+      w_x_i_vec = vbslq_f32(cond_2, neg_desired_v0, w_x_i_vec);
-      w_y_i_vec        = vbslq_f32(cond_2, v_zero,         w_y_i_vec);
+      w_y_i_vec = vbslq_f32(cond_2, v_zero, w_y_i_vec);
-      curr_vel_x_i_vec = vbslq_f32(cond_2, w_x_i_vec,      curr_vel_x_i_vec);
+      curr_vel_x_i_vec = vbslq_f32(cond_2, w_x_i_vec, curr_vel_x_i_vec);
-      curr_vel_y_i_vec = vbslq_f32(cond_2, w_y_i_vec,      curr_vel_y_i_vec);
+      curr_vel_y_i_vec = vbslq_f32(cond_2, w_y_i_vec, curr_vel_y_i_vec);
 
-      
       pos_y_i_vec = vmaxq_f32(pos_y_i_vec, vdupq_n_f32(WALL_EPS));
       pos_y_i_vec = vminq_f32(pos_y_i_vec, vdupq_n_f32(BOARD_WIDTH_MINUS_WALL_EPS));
 
-      
       float32x4_t ex_vec = vsubq_f32(destination_x_i_vec, pos_x_i_vec);
       float32x4_t ey_vec = vsubq_f32(destination_y_i_vec, pos_y_i_vec);
-      float32x4_t e_norm_sq  = vfmaq_f32(vmulq_f32(ey_vec, ey_vec), ex_vec, ex_vec);
+      float32x4_t e_norm_sq = vfmaq_f32(vmulq_f32(ey_vec, ey_vec), ex_vec, ex_vec);
       float32x4_t e_norm_inv = _neon_rsqrt_ps(e_norm_sq);
-      float32x4_t e_x_i_vec  = vmulq_f32(ex_vec, e_norm_inv);
+      float32x4_t e_x_i_vec = vmulq_f32(ex_vec, e_norm_inv);
-      float32x4_t e_y_i_vec  = vmulq_f32(ey_vec, e_norm_inv);
+      float32x4_t e_y_i_vec = vmulq_f32(ey_vec, e_norm_inv);
 
-      
+      float32x4_t vel_norm_sq = vfmaq_f32(vmulq_f32(curr_vel_y_i_vec, curr_vel_y_i_vec), curr_vel_x_i_vec, curr_vel_x_i_vec);
-      float32x4_t vel_norm_sq = vfmaq_f32(vmulq_f32(curr_vel_y_i_vec, curr_vel_y_i_vec),
-                                          curr_vel_x_i_vec, curr_vel_x_i_vec);
       float32x4_t sb_sq_i_vec = vmulq_f32(vel_norm_sq, vdupq_n_f32(delta_t_sq));
-      float32x4_t vel_norm_dt = vsqrtq_f32(sb_sq_i_vec);   // full-precision sqrt, matches AVX-512
+      float32x4_t vel_norm_dt = vsqrtq_f32(sb_sq_i_vec); // full-precision sqrt, matches AVX-512
 
-      vst1q_f32(&curr_vel_x[i],    curr_vel_x_i_vec);
+      vst1q_f32(&curr_vel_x[i], curr_vel_x_i_vec);
-      vst1q_f32(&curr_vel_y[i],    curr_vel_y_i_vec);
+      vst1q_f32(&curr_vel_y[i], curr_vel_y_i_vec);
-      vst1q_f32(&w_x[i],           w_x_i_vec);
+      vst1q_f32(&w_x[i], w_x_i_vec);
-      vst1q_f32(&w_y[i],           w_y_i_vec);
+      vst1q_f32(&w_y[i], w_y_i_vec);
-      vst1q_f32(&pos_x[i],         pos_x_i_vec);
+      vst1q_f32(&pos_x[i], pos_x_i_vec);
-      vst1q_f32(&pos_y[i],         pos_y_i_vec);
+      vst1q_f32(&pos_y[i], pos_y_i_vec);
-      vst1q_f32(&e_x[i],           e_x_i_vec);
+      vst1q_f32(&e_x[i], e_x_i_vec);
-      vst1q_f32(&e_y[i],           e_y_i_vec);
+      vst1q_f32(&e_y[i], e_y_i_vec);
       vst1q_f32(&destination_y[i], destination_y_i_vec);
-      vst1q_f32(&sb_sq[i],         sb_sq_i_vec);
+      vst1q_f32(&sb_sq[i], sb_sq_i_vec);
-      vst1q_f32(&sb_e_x[i],        vmulq_f32(e_x_i_vec, vel_norm_dt));
+      vst1q_f32(&sb_e_x[i], vmulq_f32(e_x_i_vec, vel_norm_dt));
-      vst1q_f32(&sb_e_y[i],        vmulq_f32(e_y_i_vec, vel_norm_dt));
+      vst1q_f32(&sb_e_y[i], vmulq_f32(e_y_i_vec, vel_norm_dt));
     }
 
 #if !BENCHMARK
@@ -550,4 +530,4 @@ int run_simulation(Pedestrian *pedestrians, Board &board, int n_p, int n_iter, c
 #endif
 
   return 0;
-}
+}