Ahmed moreilp

measurements/variant_float_inlining_SoA_NEON_polyexp_morevect_ilp_2_rsqrt_morersqrt_expfix/arm/1.log

@@ -1,58 +1,66 @@
 rm -f main_*  run_tests *.o *.s variants/*.s variants/*.o headers/*.s headers/*.o
-sudo /usr/bin/g++ main-float.cpp ./variants/variant_float_inlining_SoA_NEON_polyexp_moreavx_ilp_2_rsqrt_morrsqrt.cpp -o main_float_inlining_SoA_NEON_polyexp_moreavx_ilp_2_rsqrt_morrsqrt -O3 -march=native -std=c++23 -Wall -Wextra -flto -DFLOPCOUNT=0 -DRANDOM_SEED=0 -DROOFLINE=0 -DBENCHMARK=1
+sudo /usr/bin/g++ main-float.cpp ./variants/variant_float_inlining_SoA_NEON_polyexp_morevect_ilp_2_rsqrt_morersqrt_expfix.cpp -o main_float_inlining_SoA_NEON_polyexp_morevect_ilp_2_rsqrt_morersqrt_expfix -O3 -march=native -std=c++23 -Wall -Wextra -flto -DFLOPCOUNT=0 -DRANDOM_SEED=0 -DROOFLINE=0 -DBENCHMARK=1
 === N_P=50 N_ITER=200 ===
 W(n) per iteration: 183700.00 flops
 Q(n) per iteration: 3256 bytes
 I(n): 56.42 flops/byte
 W(n): 36740000.00 flops
-T(n): 4492093.50 cycles
-P(n): 8.18 flops/cycle
+T(n): 5891612.50 cycles
+P(n): 6.24 flops/cycle
 
 === N_P=100 N_ITER=200 ===
 W(n) per iteration: 727400.00 flops
 Q(n) per iteration: 6456 bytes
 I(n): 112.67 flops/byte
 W(n): 145480000.00 flops
-T(n): 15717616.00 cycles
-P(n): 9.26 flops/cycle
+T(n): 20903770.00 cycles
+P(n): 6.96 flops/cycle
 
 === N_P=200 N_ITER=200 ===
 W(n) per iteration: 2894800.00 flops
 Q(n) per iteration: 12856 bytes
 I(n): 225.17 flops/byte
 W(n): 578960000.00 flops
-T(n): 58648184.00 cycles
-P(n): 9.87 flops/cycle
+T(n): 78269008.00 cycles
+P(n): 7.40 flops/cycle
 
 === N_P=500 N_ITER=200 ===
 W(n) per iteration: 18037000.00 flops
 Q(n) per iteration: 32056 bytes
 I(n): 562.67 flops/byte
 W(n): 3607399936.00 flops
-T(n): 359248768.00 cycles
-P(n): 10.04 flops/cycle
+T(n): 484667776.00 cycles
+P(n): 7.44 flops/cycle
 
 === N_P=1000 N_ITER=200 ===
 W(n) per iteration: 72074000.00 flops
 Q(n) per iteration: 64056 bytes
 I(n): 1125.17 flops/byte
 W(n): 14414799872.00 flops
-T(n): 1415209856.00 cycles
-P(n): 10.19 flops/cycle
+T(n): 1917664384.00 cycles
+P(n): 7.52 flops/cycle
 
 === N_P=2000 N_ITER=200 ===
 W(n) per iteration: 288148000.00 flops
 Q(n) per iteration: 128056 bytes
 I(n): 2250.17 flops/byte
 W(n): 57629601792.00 flops
-T(n): 5657639936.00 cycles
-P(n): 10.19 flops/cycle
+T(n): 7683078656.00 cycles
+P(n): 7.50 flops/cycle
 
 === N_P=5000 N_ITER=200 ===
 W(n) per iteration: 1800369920.00 flops
 Q(n) per iteration: 320056 bytes
 I(n): 5625.17 flops/byte
 W(n): 360073986048.00 flops
-T(n): 35147825152.00 cycles
-P(n): 10.24 flops/cycle
+T(n): 48221761536.00 cycles
+P(n): 7.47 flops/cycle
+
+=== N_P=10000 N_ITER=200 ===
+W(n) per iteration: 7200739840.00 flops
+Q(n) per iteration: 640056 bytes
+I(n): 11250.17 flops/byte
+W(n): 1440147963904.00 flops
+T(n): 222472847360.00 cycles
+P(n): 6.47 flops/cycle
 

measurements/variant_float_inlining_SoA_NEON_polyexp_morevect_ilp_2_rsqrt_morersqrt_expfix/arm/2.log

@@ -0,0 +1,66 @@
+rm -f main_*  run_tests *.o *.s variants/*.s variants/*.o headers/*.s headers/*.o
+sudo /usr/bin/g++ main-float.cpp ./variants/variant_float_inlining_SoA_NEON_polyexp_morevect_ilp_2_rsqrt_morersqrt_expfix.cpp -o main_float_inlining_SoA_NEON_polyexp_morevect_ilp_2_rsqrt_morersqrt_expfix -O3 -march=native -std=c++23 -Wall -Wextra -flto -DFLOPCOUNT=0 -DRANDOM_SEED=0 -DROOFLINE=0 -DBENCHMARK=1
+=== N_P=50 N_ITER=200 ===
+W(n) per iteration: 183700.00 flops
+Q(n) per iteration: 3256 bytes
+I(n): 56.42 flops/byte
+W(n): 36740000.00 flops
+T(n): 5881106.00 cycles
+P(n): 6.25 flops/cycle
+
+=== N_P=100 N_ITER=200 ===
+W(n) per iteration: 727400.00 flops
+Q(n) per iteration: 6456 bytes
+I(n): 112.67 flops/byte
+W(n): 145480000.00 flops
+T(n): 20868150.00 cycles
+P(n): 6.97 flops/cycle
+
+=== N_P=200 N_ITER=200 ===
+W(n) per iteration: 2894800.00 flops
+Q(n) per iteration: 12856 bytes
+I(n): 225.17 flops/byte
+W(n): 578960000.00 flops
+T(n): 78350920.00 cycles
+P(n): 7.39 flops/cycle
+
+=== N_P=500 N_ITER=200 ===
+W(n) per iteration: 18037000.00 flops
+Q(n) per iteration: 32056 bytes
+I(n): 562.67 flops/byte
+W(n): 3607399936.00 flops
+T(n): 484657088.00 cycles
+P(n): 7.44 flops/cycle
+
+=== N_P=1000 N_ITER=200 ===
+W(n) per iteration: 72074000.00 flops
+Q(n) per iteration: 64056 bytes
+I(n): 1125.17 flops/byte
+W(n): 14414799872.00 flops
+T(n): 1920107648.00 cycles
+P(n): 7.51 flops/cycle
+
+=== N_P=2000 N_ITER=200 ===
+W(n) per iteration: 288148000.00 flops
+Q(n) per iteration: 128056 bytes
+I(n): 2250.17 flops/byte
+W(n): 57629601792.00 flops
+T(n): 7641970176.00 cycles
+P(n): 7.54 flops/cycle
+
+=== N_P=5000 N_ITER=200 ===
+W(n) per iteration: 1800369920.00 flops
+Q(n) per iteration: 320056 bytes
+I(n): 5625.17 flops/byte
+W(n): 360073986048.00 flops
+T(n): 47656402944.00 cycles
+P(n): 7.56 flops/cycle
+
+=== N_P=10000 N_ITER=200 ===
+W(n) per iteration: 7200739840.00 flops
+Q(n) per iteration: 640056 bytes
+I(n): 11250.17 flops/byte
+W(n): 1440147963904.00 flops
+T(n): 221504274432.00 cycles
+P(n): 6.50 flops/cycle
+

measurements/variant_float_inlining_SoA_NEON_polyexp_morevect_ilp_2_rsqrt_morersqrt_expfix/arm/3.log

@@ -0,0 +1,66 @@
+rm -f main_*  run_tests *.o *.s variants/*.s variants/*.o headers/*.s headers/*.o
+sudo /usr/bin/g++ main-float.cpp ./variants/variant_float_inlining_SoA_NEON_polyexp_morevect_ilp_2_rsqrt_morersqrt_expfix.cpp -o main_float_inlining_SoA_NEON_polyexp_morevect_ilp_2_rsqrt_morersqrt_expfix -O3 -march=native -std=c++23 -Wall -Wextra -flto -DFLOPCOUNT=0 -DRANDOM_SEED=0 -DROOFLINE=0 -DBENCHMARK=1
+=== N_P=50 N_ITER=200 ===
+W(n) per iteration: 183700.00 flops
+Q(n) per iteration: 3256 bytes
+I(n): 56.42 flops/byte
+W(n): 36740000.00 flops
+T(n): 5887339.50 cycles
+P(n): 6.24 flops/cycle
+
+=== N_P=100 N_ITER=200 ===
+W(n) per iteration: 727400.00 flops
+Q(n) per iteration: 6456 bytes
+I(n): 112.67 flops/byte
+W(n): 145480000.00 flops
+T(n): 20857236.00 cycles
+P(n): 6.98 flops/cycle
+
+=== N_P=200 N_ITER=200 ===
+W(n) per iteration: 2894800.00 flops
+Q(n) per iteration: 12856 bytes
+I(n): 225.17 flops/byte
+W(n): 578960000.00 flops
+T(n): 78339488.00 cycles
+P(n): 7.39 flops/cycle
+
+=== N_P=500 N_ITER=200 ===
+W(n) per iteration: 18037000.00 flops
+Q(n) per iteration: 32056 bytes
+I(n): 562.67 flops/byte
+W(n): 3607399936.00 flops
+T(n): 483592896.00 cycles
+P(n): 7.46 flops/cycle
+
+=== N_P=1000 N_ITER=200 ===
+W(n) per iteration: 72074000.00 flops
+Q(n) per iteration: 64056 bytes
+I(n): 1125.17 flops/byte
+W(n): 14414799872.00 flops
+T(n): 1918282240.00 cycles
+P(n): 7.51 flops/cycle
+
+=== N_P=2000 N_ITER=200 ===
+W(n) per iteration: 288148000.00 flops
+Q(n) per iteration: 128056 bytes
+I(n): 2250.17 flops/byte
+W(n): 57629601792.00 flops
+T(n): 7707683840.00 cycles
+P(n): 7.48 flops/cycle
+
+=== N_P=5000 N_ITER=200 ===
+W(n) per iteration: 1800369920.00 flops
+Q(n) per iteration: 320056 bytes
+I(n): 5625.17 flops/byte
+W(n): 360073986048.00 flops
+T(n): 47889321984.00 cycles
+P(n): 7.52 flops/cycle
+
+=== N_P=10000 N_ITER=200 ===
+W(n) per iteration: 7200739840.00 flops
+Q(n) per iteration: 640056 bytes
+I(n): 11250.17 flops/byte
+W(n): 1440147963904.00 flops
+T(n): 221847699456.00 cycles
+P(n): 6.49 flops/cycle
+

variants/variant_float_inlining_SoA_NEON_polyexp_morevect_ilp_2_rsqrt_morersqrt_expfix.cpp

@@ -0,0 +1,648 @@
+// # Changes: NEON port of variant_float_inlining_SoA_AVX512_polyexp_moreavx_ilp_2_rsqrt.cpp
+//   - 16-wide AVX-512 → 4-wide NEON; ILP unroll by 2 preserved (inner loop processes 8 j's per iter)
+//   - rsqrt14_ps → vrsqrteq_f32 + 1 Newton iteration (single-precision accuracy)
+//   - reduce_add_ps → vaddvq_f32
+//   - Padding multiple changed from 32 to 8
+//   - Scalar obstacle loop unchanged
+
+#include "../headers/board_reduced_float.hpp"
+#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>
+#include <random>
+#include <tuple>
+#include <vector>
+
+#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 + 7) & ~7;
+
+  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); }
+
+// # 64 MULTs, 56 ADDs
+static inline float32x4_t _neon_exp_ps(float32x4_t x) {
+  const float32x4_t log2e = vdupq_n_f32(1.4426950408889634f);
+
+  // # 4 MULTS
+  float32x4_t nf = vrndnq_f32(vmulq_f32(x, log2e));
+
+  const float32x4_t ln2 = vdupq_n_f32(0.6931471805599453f);
+
+  // # 4 MULTs, 4 ADDs
+  float32x4_t r = vfmsq_f32(x, nf, ln2); // r = x - nf*ln2
+
+  const float32x4_t c12 = vdupq_n_f32(c12_scalar);
+  const float32x4_t c11 = vdupq_n_f32(c11_scalar);
+  const float32x4_t c10 = vdupq_n_f32(c10_scalar);
+  const float32x4_t c9 = vdupq_n_f32(c9_scalar);
+  const float32x4_t c8 = vdupq_n_f32(c8_scalar);
+  const float32x4_t c7 = vdupq_n_f32(c7_scalar);
+  const float32x4_t c6 = vdupq_n_f32(c6_scalar);
+  const float32x4_t c5 = vdupq_n_f32(c5_scalar);
+  const float32x4_t c4 = vdupq_n_f32(c4_scalar);
+  const float32x4_t c3 = vdupq_n_f32(c3_scalar);
+  const float32x4_t c2 = vdupq_n_f32(c2_scalar);
+  const float32x4_t c1 = vdupq_n_f32(c1_scalar);
+  const float32x4_t c0 = vdupq_n_f32(c0_scalar);
+
+  float32x4_t p = c12;
+
+  // #   13 * (4 MULTs, 4 ADDs)
+  // # = 52 MULTs, 52 ADDs
+  p = vfmaq_f32(c12, p, r);
+  p = vfmaq_f32(c11, p, r);
+  p = vfmaq_f32(c10, p, r);
+  p = vfmaq_f32(c9, p, r);
+  p = vfmaq_f32(c8, p, r);
+  p = vfmaq_f32(c7, p, r);
+  p = vfmaq_f32(c6, p, r);
+  p = vfmaq_f32(c5, p, r);
+  p = vfmaq_f32(c4, p, r);
+  p = vfmaq_f32(c3, p, r);
+  p = vfmaq_f32(c2, p, r);
+  p = vfmaq_f32(c1, p, r);
+  p = vfmaq_f32(c0, p, r);
+
+  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);
+
+  // # 4 MULTs
+  return vmulq_f32(p, pow2n);
+}
+
+// # 4 ADD, 16 MULTS, 4 SQRT, 4 DIV
+// Newton-Raphson refinement formula.
+static inline float32x4_t _neon_rsqrt_ps(float32x4_t x) {
+  // # 4 SQRT, 4 DIV
+  float32x4_t y = vrsqrteq_f32(x);
+
+  // # 16 MULTS, 4 ADD
+  y = vmulq_f32(y, vrsqrtsq_f32(vmulq_f32(x, y), y));
+  return y;
+}
+
+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 + 7) & ~7;
+
+  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_cos_phi_sq = vdupq_n_f32(cos_phi_sq);
+  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_zero = vdupq_n_f32(0.0f);
+  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_np = vdupq_n_f32((float)n_p);
+  const float32x4_t v_exp_min = vdupq_n_f32(-87.0f);
+
+  // # ADDs: n_iter * (
+  // #   n_p * 20 +
+  // #   n_p * n_p_pad * 32 +
+  // #   n_p * board.n_obstacles * 10 +
+  // #   n_p_pad * 9
+  // # )
+
+  // # MULTs: n_iter * (
+  // #   n_p * 4 +
+  // #   n_p * n_p_pad * 54 +
+  // #   n_p * board.n_obstacles * 13 +
+  // #   n_p_pad * 24
+  // # )
+
+  // # 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++) {
+    for (int i = 0; i < n_p; i++) {
+
+      // # 2 MULTS
+      float desired_velocity_x = e_x[i] * desired_v0[i];
+      float desired_velocity_y = e_y[i] * desired_v0[i];
+
+      // # 2 ADDS, 2 MULTS
+      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;
+
+      const float32x4_t pix = vdupq_n_f32(pos_x[i]);
+      const float32x4_t piy = vdupq_n_f32(pos_y[i]);
+      const float32x4_t eix = vdupq_n_f32(e_x[i]);
+      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) {
+
+        // # 8 ADDS
+        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_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_1 = vandq_u32(m_neq_i_1, m_in_range_1);
+
+        float32x4_t pjx_0 = vld1q_f32(&pos_x[j]);
+        float32x4_t pjx_1 = vld1q_f32(&pos_x[j + 4]);
+        float32x4_t pjy_0 = vld1q_f32(&pos_y[j]);
+        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]);
+        float32x4_t sbe_jy_1 = vld1q_f32(&sb_e_y[j + 4]);
+
+        // We negate the values to be able to perform an fma when computing two_b below
+        float32x4_t sb_jsq_0_neg = vnegq_f32(vld1q_f32(&sb_sq[j]));
+        float32x4_t sb_jsq_1_neg = vnegq_f32(vld1q_f32(&sb_sq[j + 4]));
+
+        // # 16 ADDS
+        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);
+        float32x4_t r_ab_y_1 = vsubq_f32(piy, pjy_1);
+
+        // # 8 ADDS, 16 MULTS
+        float32x4_t r_ab_n2_0 = vfmaq_f32(vmulq_f32(r_ab_y_0, r_ab_y_0), r_ab_x_0, r_ab_x_0);
+        float32x4_t r_ab_n2_1 = vfmaq_f32(vmulq_f32(r_ab_y_1, r_ab_y_1), r_ab_x_1, r_ab_x_1);
+
+        r_ab_n2_0 = vmaxq_f32(r_ab_n2_0, v_eps_sq);
+        r_ab_n2_1 = vmaxq_f32(r_ab_n2_1, v_eps_sq);
+
+        // # 8 ADD, 32 MULTS, 8 SQRT, 8 DIV
+        float32x4_t inv_r_ab_n_0 = _neon_rsqrt_ps(r_ab_n2_0);
+        float32x4_t inv_r_ab_n_1 = _neon_rsqrt_ps(r_ab_n2_1);
+
+        // # 8 MULTS
+        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);
+
+        // # 16 ADDS
+        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);
+        float32x4_t r_ab2_y_1 = vsubq_f32(r_ab_y_1, sbe_jy_1);
+
+        // # 8 ADDS, 16 MULTS
+        float32x4_t r_ab2_n2_0 = vfmaq_f32(vmulq_f32(r_ab2_y_0, r_ab2_y_0), r_ab2_x_0, r_ab2_x_0);
+        float32x4_t r_ab2_n2_1 = vfmaq_f32(vmulq_f32(r_ab2_y_1, r_ab2_y_1), r_ab2_x_1, r_ab2_x_1);
+
+        r_ab2_n2_0 = vmaxq_f32(r_ab2_n2_0, v_eps_sq);
+        r_ab2_n2_1 = vmaxq_f32(r_ab2_n2_1, v_eps_sq);
+
+        // # 8 ADD, 32 MULTS, 8 SQRT, 8 DIV
+        float32x4_t inv_r_ab2_n_0 = _neon_rsqrt_ps(r_ab2_n2_0);
+        float32x4_t inv_r_ab2_n_1 = _neon_rsqrt_ps(r_ab2_n2_1);
+
+        // # 8 MULTS
+        float32x4_t r_ab2_n_0 = vmulq_f32(r_ab2_n2_0, inv_r_ab2_n_0);
+        float32x4_t r_ab2_n_1 = vmulq_f32(r_ab2_n2_1, inv_r_ab2_n_1);
+
+        // # 8 ADDS
+        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);
+
+        // # 8 ADDS, 8 MULTS
+        float32x4_t two_b_sq_0 = vfmaq_f32(sb_jsq_0_neg, r_sum_0, r_sum_0);
+        float32x4_t two_b_sq_1 = vfmaq_f32(sb_jsq_1_neg, r_sum_1, r_sum_1);
+
+        two_b_sq_0 = vmaxq_f32(two_b_sq_0, v_eps_sq);
+        two_b_sq_1 = vmaxq_f32(two_b_sq_1, v_eps_sq);
+
+        // # 8 ADD, 32 MULTS, 8 SQRT, 8 DIV
+        float32x4_t inv_two_b_0 = _neon_rsqrt_ps(two_b_sq_0);
+        float32x4_t inv_two_b_1 = _neon_rsqrt_ps(two_b_sq_1);
+
+        // # 8 MULTS
+        float32x4_t two_b_0 = vmulq_f32(two_b_sq_0, inv_two_b_0);
+        float32x4_t two_b_1 = vmulq_f32(two_b_sq_1, inv_two_b_1);
+
+        // # 8 MULTS
+        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);
+
+        // # 128 MULTs, 112 ADDs
+        float32x4_t e_val_0 = _neon_exp_ps(e_arg_0);
+        float32x4_t e_val_1 = _neon_exp_ps(e_arg_1);
+
+        // # 24 MULTS
+        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_1 = vmulq_f32(vmulq_f32(r_sum_1, v_neg_v0_div_2s), vmulq_f32(e_val_1, inv_two_b_1));
+
+        // # 16 MULTS
+        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_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);
+
+        // # 16 ADDS, 32 MULTS
+        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);
+
+        // # 8 ADDS, 16 MULTS
+        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);
+
+        // # 8 MULTS
+        float32x4_t rhs_0 = vmulq_f32(f_norm_sq_0, v_cos_phi_sq);
+        float32x4_t rhs_1 = vmulq_f32(f_norm_sq_1, v_cos_phi_sq);
+
+        // # 8 ADDS, 16 MULTS
+        float32x4_t e_dot_f_0 = vfmaq_f32(vmulq_f32(eiy, f_y_0), eix, f_x_0);
+        float32x4_t e_dot_f_1 = vfmaq_f32(vmulq_f32(eiy, f_y_1), eix, f_x_1);
+
+        // # 8 MULTS
+        float32x4_t e_dot_f_sq_0 = vmulq_f32(e_dot_f_0, e_dot_f_0);
+        float32x4_t e_dot_f_sq_1 = vmulq_f32(e_dot_f_1, e_dot_f_1);
+
+        uint32x4_t c1_0 = vcltq_f32(e_dot_f_0, v_zero);
+        uint32x4_t c1_1 = vcltq_f32(e_dot_f_1, v_zero);
+        uint32x4_t c2_0 = vcgtq_f32(e_dot_f_sq_0, rhs_0);
+        uint32x4_t c2_1 = vcgtq_f32(e_dot_f_sq_1, rhs_1);
+
+        uint32x4_t cond_0 = vandq_u32(c1_0, c2_0);
+        uint32x4_t cond_1 = vandq_u32(c1_1, c2_1);
+
+        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);
+        float32x4_t f_y_safe_1 = vbslq_f32(active_1, f_y_1, v_zero);
+
+        // # 16 ADDS, 16 MULTS
+        acc_x_0 = vfmaq_f32(acc_x_0, f_x_safe_0, w_val_0);
+        acc_x_1 = vfmaq_f32(acc_x_1, f_x_safe_1, w_val_1);
+        acc_y_0 = vfmaq_f32(acc_y_0, f_y_safe_0, w_val_0);
+        acc_y_1 = vfmaq_f32(acc_y_1, f_y_safe_1, w_val_1);
+      }
+
+      // # 16 ADDS
+      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++) {
+
+        // # 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;
+    }
+
+    for (int i = 0; i < n_p_pad; i += 4) {
+
+      float32x4_t w_x_i_vec = vld1q_f32(&w_x[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 pos_x_i_vec = vld1q_f32(&pos_x[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]);
+      int32x4_t color_i_vec = vld1q_s32(&color[i]);
+
+      // # 4 ADDS, 8 MULTS
+      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);
+
+      // # 4 ADD, 16 MULTS, 4 SQRT, 4 DIV
+      float32x4_t w_norm_inv = _neon_rsqrt_ps(w_norm_sq);
+
+      // # 4 MULTS
+      float32x4_t correction_factor = vminq_f32(v_one, vmulq_f32(v_max_i_vec, w_norm_inv));
+
+      // # 8 MULTS
+      float32x4_t curr_vel_x_i_vec = vmulq_f32(w_x_i_vec, correction_factor);
+      float32x4_t curr_vel_y_i_vec = vmulq_f32(w_y_i_vec, correction_factor);
+
+      const float32x4_t dt_vec = vdupq_n_f32(dt);
+
+      // # 8 ADDS, 8 MULTS
+      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_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);
+
+      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);
+      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);
+      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);
+
+      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);
+
+      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);
+
+      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_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_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));
+
+      // # 8 ADDS
+      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);
+
+      // # 4 ADDS, 8 MULTS
+      float32x4_t e_norm_sq = vfmaq_f32(vmulq_f32(ey_vec, ey_vec), ex_vec, ex_vec);
+
+      // # 4 ADD, 16 MULTS, 4 SQRT, 4 DIV
+      float32x4_t e_norm_inv = _neon_rsqrt_ps(e_norm_sq);
+
+      // # 8 MULTS
+      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);
+
+      // # 4 ADDS, 8 MULTS
+      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);
+
+      // # 4 MULTS
+      float32x4_t sb_sq_i_vec = vmulq_f32(vel_norm_sq, vdupq_n_f32(delta_t_sq));
+
+      // # 4 SQRT
+      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_y[i], curr_vel_y_i_vec);
+      vst1q_f32(&w_x[i], w_x_i_vec);
+      vst1q_f32(&w_y[i], w_y_i_vec);
+      vst1q_f32(&pos_x[i], pos_x_i_vec);
+      vst1q_f32(&pos_y[i], pos_y_i_vec);
+      vst1q_f32(&e_x[i], e_x_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);
+
+      // # 8 MULTS
+      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));
+    }
+
+#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;
+}