From 7f235ebb203c53d5dbd9343f142f794587047978 Mon Sep 17 00:00:00 2001 From: Linus Baumberger Date: Thu, 28 May 2026 18:55:25 +0200 Subject: [PATCH] last minor loop optimization --- ...inlining_SoA_AVX2_polyexp_rsqrt_loopopt.md | 118 +++++ ...nlining_SoA_AVX2_polyexp_rsqrt_loopopt.cpp | 477 ++++++++++++++++++ 2 files changed, 595 insertions(+) create mode 100644 docs/optimization_float_inlining_SoA_AVX2_polyexp_rsqrt_loopopt.md create mode 100644 variants/variant_float_inlining_SoA_AVX2_polyexp_rsqrt_loopopt.cpp diff --git a/docs/optimization_float_inlining_SoA_AVX2_polyexp_rsqrt_loopopt.md b/docs/optimization_float_inlining_SoA_AVX2_polyexp_rsqrt_loopopt.md new file mode 100644 index 0000000..fd1a361 --- /dev/null +++ b/docs/optimization_float_inlining_SoA_AVX2_polyexp_rsqrt_loopopt.md @@ -0,0 +1,118 @@ +# Optimization: ghost-self trick + r_sum fma fuse + +- **Author**: Linus +- **Predecessor**: variant_float_inlining_SoA_AVX2_polyexp_rsqrt.cpp +- **File(s)**: variants/variant_float_inlining_SoA_AVX2_polyexp_rsqrt_loopopt.cpp +- **Status**: positive + +## What this changes + +Kill the per-block branchless mask in the j-loop. Before the loop we save +`pos[i]`, park it at `1e9`, then broadcast i's real position from the saved +copy. The j==i lane now reads like a padding lane (huge distance -> +~1e-37 force), so it self-cancels with no mask. That removes the +`m_neq_i`/`m_in_range` cmps, the active-AND, and the two safety-ANDs on +`f_x` / `f_y` before the accumulator fmadd. Restore `pos[i]` right +after the j-loop so the rest of the simulation sees the real positions. + +Second change in the same variant: fold the two sqrt-recovery muls and the +add for `r_sum = |r_ab| + |r_ab2|` into one mul + one fmadd. The two norms +are only used in this one place, so we don't need them as named values. + +## Code (relevant snippet) + +```cpp +// ghost-self trick: park pedestrian i at 1e9 for its own j-loop, broadcasting i's +// real position from a saved copy. then the j==i lane reads 1e9 like a padding lane +// -> ~1e-37 force, self-cancels with no mask. restored right after the loop. +const float saved_pix = pos_x[i]; +const float saved_piy = pos_y[i]; +const __m256 pix = _mm256_set1_ps(saved_pix); +const __m256 piy = _mm256_set1_ps(saved_piy); +const __m256 eix = _mm256_set1_ps(e_x[i]); +const __m256 eiy = _mm256_set1_ps(e_y[i]); +pos_x[i] = 1e9f; +pos_y[i] = 1e9f; + +__m256 acc_x = _mm256_setzero_ps(); +__m256 acc_y = _mm256_setzero_ps(); + +for (int j = 0; j < n_p_pad; j += 8) { + // no more j_idx / m_neq_i / m_in_range / active + + __m256 pjx = _mm256_loadu_ps(&pos_x[j]); + __m256 pjy = _mm256_loadu_ps(&pos_y[j]); + __m256 sbe_jx = _mm256_loadu_ps(&sb_e_x[j]); + __m256 sbe_jy = _mm256_loadu_ps(&sb_e_y[j]); + __m256 sb_jsq = _mm256_loadu_ps(&sb_sq[j]); + + __m256 r_ab_x = _mm256_sub_ps(pix, pjx); + __m256 r_ab_y = _mm256_sub_ps(piy, pjy); + __m256 r_ab_n2 = _mm256_fmadd_ps(r_ab_x, r_ab_x, _mm256_mul_ps(r_ab_y, r_ab_y)); + r_ab_n2 = _mm256_max_ps(r_ab_n2, v_eps_sq); + __m256 inv_r_ab_n = _mm256_rsqrt_ps(r_ab_n2); + + __m256 r_ab2_x = _mm256_sub_ps(r_ab_x, sbe_jx); + __m256 r_ab2_y = _mm256_sub_ps(r_ab_y, sbe_jy); + __m256 r_ab2_n2 = _mm256_fmadd_ps(r_ab2_x, r_ab2_x, _mm256_mul_ps(r_ab2_y, r_ab2_y)); + r_ab2_n2 = _mm256_max_ps(r_ab2_n2, v_eps_sq); + __m256 inv_r_ab2_n = _mm256_rsqrt_ps(r_ab2_n2); + + // r_sum fuse: two recovery muls + add -> one mul + one fmadd + __m256 r_sum = _mm256_fmadd_ps(r_ab2_n2, inv_r_ab2_n, + _mm256_mul_ps(r_ab_n2, inv_r_ab_n)); + + // ... force-scaling unchanged ... + + // no f_x_safe / f_y_safe AND before the accumulator + acc_x = _mm256_fmadd_ps(f_x, w_val, acc_x); + acc_y = _mm256_fmadd_ps(f_y, w_val, acc_y); +} + +// restore the real positions +pos_x[i] = saved_pix; +pos_y[i] = saved_piy; +``` + +## Benchmark + +Conditions: N_ITER=1000, -O3 -march=native -flto. + +### x86 + +**Machine**: TBD + +**Frequency**: TBD + +| N | W(n) [Flops] | T(n) [Cycles] | Performance [Flops/Cycle] | Diff vs Predecessor | +| ---- | ------------ | ------------- | ------------------------- | ------------------- | +| 50 | | | | | +| 100 | | | | | +| 200 | | | | | +| 500 | | | | | +| 1000 | | | | | + +### ARM (Apple) + +no avx2 here + +## Analysis + +ILP tricks (j-unroll, i-tiling) didn't help earlier, so the win had to come +from fewer FP ops, not from running more in parallel. Ghost-self + r_sum +fuse just drop ops. Asm diff (gcc 13.3, -O3 -march=native): + +``` + vcmpps vandps vfmadd vrsqrtps +predecessor: 4 4 33 3 +variant: 2 1 33 3 +``` + +The mask is gone, FMA/rsqrt counts unchanged. The AND that mattered was +the one between `f_x` and the accumulator fmadd, since that's on the +loop-carried chain. + +## Takeaway + +Less work, same precision. The mask was there to handle j==i but the +ghost-self lane handles it for free. diff --git a/variants/variant_float_inlining_SoA_AVX2_polyexp_rsqrt_loopopt.cpp b/variants/variant_float_inlining_SoA_AVX2_polyexp_rsqrt_loopopt.cpp new file mode 100644 index 0000000..2efc3c5 --- /dev/null +++ b/variants/variant_float_inlining_SoA_AVX2_polyexp_rsqrt_loopopt.cpp @@ -0,0 +1,477 @@ +// # Changes: pure vrsqrtps +// # Predecessor: variant_float_inlining_SoA_AVX2_polyexp.cpp + +// +// We first tried rsqrt + 1 Newton step to keep full sqrt precision, but it +// turned out slower than just using vsqrtps. The Newton step needs 2 muls +// and an fnmadd on top of rsqrt, so the whole recovered sqrt ends up at +// ~20 cycles of latency, while vsqrtps is only 12. Since the OoO core was +// already running multiple sqrts in parallel, sqrt throughput wasn't really +// the bottleneck. All the Newton step did was make the dependency chain +// longer, which hurt more than the faster rsqrt helped. +// +// So we drop the Newton step. rsqrt + 1 mul gives us a sqrt in 8 cycles +// with about 12-bit precision, which is well within the 1cm verify tolerance. + +// The main structural win is killing the vdivps. rsqrt produces 1/sqrt(x) +// directly, so we keep the inverses around (inv_r_ab_n, inv_r_ab2_n, +// inv_two_b) and rewrite the force scaling. The original had +// "numer / (two_b * r_ab_n * r_ab2_n)" which needs a vdivps; now it's +// "numer * inv_two_b * inv_r_ab_n * inv_r_ab2_n", trading one divide for +// two muls. Divide was the long-pole op on port 0, so this is the bigger +// of the two changes. + +#include "../headers/board_reduced_float.hpp" +#include "../headers/constants_float.hpp" +#include "../headers/pedestrian_reduced_float.hpp" + +#include // avx2 + +#include +#include +#include +#include +#include +#include +#include +#include + +#define SEED 42 +#define BOARD_WIDTH 10.0f +#define BOARD_LENGTH 50.0f +#define WALL_EPS 1e-3f +#define BOARD_WIDTH_MINUS_WALL_EPS 9.999f + +#ifndef RANDOM_SEED +#define RANDOM_SEED 0 +#endif + +#ifndef BENCHMARK +#define BENCHMARK 0 +#endif + +using namespace std; + +vector pos_x, pos_y; +vector sb_sq; +vector sb_e_x, sb_e_y; +vector e_x, e_y; +vector curr_vel_x, curr_vel_y; +vector w_x, w_y; +vector desired_v0; +vector v_max; +vector destination_x, destination_y; +vector color; + +Pedestrian *init_pedestrians(int n_p) { +#if RANDOM_SEED + random_device rd; + mt19937 gen(rd()); +#else + mt19937 gen(SEED); +#endif + + normal_distribution velocity_gen(v0_mean, v0_std_dev); + uniform_real_distribution y_gen(0.3, BOARD_WIDTH - 0.3); + uniform_real_distribution x_gen_left(2.0, BOARD_LENGTH / 2.0); + uniform_real_distribution x_gen_right(BOARD_LENGTH / 2.0, BOARD_LENGTH - 2.0); + + const int n_p_pad = (n_p + 7) & ~7; + + pos_x.resize(n_p_pad); + pos_y.resize(n_p_pad); + sb_sq.resize(n_p_pad); + sb_e_x.resize(n_p_pad); + sb_e_y.resize(n_p_pad); + e_x.resize(n_p_pad); + e_y.resize(n_p_pad); + curr_vel_x.resize(n_p_pad); + curr_vel_y.resize(n_p_pad); + w_x.resize(n_p_pad); + w_y.resize(n_p_pad); + desired_v0.resize(n_p_pad); + v_max.resize(n_p_pad); + destination_x.resize(n_p_pad); + destination_y.resize(n_p_pad); + color.resize(n_p_pad); + + int n_p_half = n_p / 2; + + for (int i = 0; i < n_p_half; i++) { + float x = x_gen_left(gen); + float y = y_gen(gen); + + float dest_x = BOARD_LENGTH + 30.0; + 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; + } + + 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); } + +// simd expf, same as the predecessor. degree-5 taylor on the [-ln2/2, ln2/2] reduced range, +// schraudolph 2^n bit trick on the exponent slot. +static inline __m256 exp256_ps(__m256 x) { + const __m256 log2e = _mm256_set1_ps(1.4426950408889634f); + __m256 nf = _mm256_round_ps(_mm256_mul_ps(x, log2e), _MM_FROUND_TO_NEAREST_INT | _MM_FROUND_NO_EXC); + + const __m256 ln2 = _mm256_set1_ps(0.6931471805599453f); + __m256 r = _mm256_fnmadd_ps(nf, ln2, x); + + const __m256 c5 = _mm256_set1_ps(1.0f / 120.0f); + const __m256 c4 = _mm256_set1_ps(1.0f / 24.0f); + const __m256 c3 = _mm256_set1_ps(1.0f / 6.0f); + const __m256 c2 = _mm256_set1_ps(0.5f); + const __m256 c1 = _mm256_set1_ps(1.0f); + const __m256 c0 = _mm256_set1_ps(1.0f); + + __m256 p = c5; + p = _mm256_fmadd_ps(p, r, c4); + p = _mm256_fmadd_ps(p, r, c3); + p = _mm256_fmadd_ps(p, r, c2); + p = _mm256_fmadd_ps(p, r, c1); + p = _mm256_fmadd_ps(p, r, c0); + + __m256i ni = _mm256_cvtps_epi32(nf); + __m256i biased = _mm256_add_epi32(ni, _mm256_set1_epi32(127)); + __m256i scaled = _mm256_slli_epi32(biased, 23); + __m256 pow2n = _mm256_castsi256_ps(scaled); + + return _mm256_mul_ps(p, pow2n); +} + +int run_simulation(Pedestrian *pedestrians, Board &board, int n_p, int n_iter, const char *dump_path) { + (void)pedestrians; +#if BENCHMARK + (void)dump_path; +#endif + +#if !BENCHMARK + const int dump_interval = 1; + + vector> samples; + + if (dump_path) { + samples.reserve(static_cast(n_iter / dump_interval + 1) * n_p); + + for (int i = 0; i < n_p; i++) { + samples.emplace_back(0, i, pos_x[i], pos_y[i], e_x[i], e_y[i], color[i]); + } + } +#endif + + const int n_p_pad = (n_p + 7) & ~7; + + alignas(32) const float lane_offset_arr[8] = {0.0f, 1.0f, 2.0f, 3.0f, 4.0f, 5.0f, 6.0f, 7.0f}; + const __m256 lane_off = _mm256_load_ps(lane_offset_arr); + + const __m256 v_neg_v0_div_2s = _mm256_set1_ps(NEG_V0_AB_div_TWO_SIGMA); + const __m256 v_neg_2s_inv = _mm256_set1_ps(NEG_TWO_SIGMA_INV); + const __m256 v_cos_phi_sq = _mm256_set1_ps(cos_phi_sq); + const __m256 v_dt_neg = _mm256_set1_ps(dt_neg); + const __m256 v_c_neg_dt = _mm256_set1_ps(c_neg_times_dt); + const __m256 v_zero = _mm256_setzero_ps(); + const __m256 v_eps_sq = _mm256_set1_ps(EPS_SQ); + // const __m256 v_np = _mm256_set1_ps((float)n_p); + const __m256 v_exp_min = _mm256_set1_ps(-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]; + + 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; + + // ghost-self trick: park pedestrian i at 1e9 for its own j-loop, broadcasting i's + // real position from a saved copy. then the j==i lane reads 1e9 like a padding lane + // -> ~1e-37 force, self-cancels with no mask. restored right after the loop. + const float saved_pix = pos_x[i]; + const float saved_piy = pos_y[i]; + const __m256 pix = _mm256_set1_ps(saved_pix); + const __m256 piy = _mm256_set1_ps(saved_piy); + const __m256 eix = _mm256_set1_ps(e_x[i]); + const __m256 eiy = _mm256_set1_ps(e_y[i]); + pos_x[i] = 1e9f; + pos_y[i] = 1e9f; + + __m256 acc_x = _mm256_setzero_ps(); + __m256 acc_y = _mm256_setzero_ps(); + + for (int j = 0; j < n_p_pad; j += 8) { + // __m256 j_idx = _mm256_add_ps(_mm256_set1_ps((float)j), lane_off); + // + // __m256 m_neq_i = _mm256_cmp_ps(j_idx, v_i, _CMP_NEQ_OQ); + // __m256 m_in_range = _mm256_cmp_ps(j_idx, v_np, _CMP_LT_OQ); + // __m256 active = _mm256_and_ps(m_neq_i, m_in_range); + + __m256 pjx = _mm256_loadu_ps(&pos_x[j]); + __m256 pjy = _mm256_loadu_ps(&pos_y[j]); + __m256 sbe_jx = _mm256_loadu_ps(&sb_e_x[j]); + __m256 sbe_jy = _mm256_loadu_ps(&sb_e_y[j]); + __m256 sb_jsq = _mm256_loadu_ps(&sb_sq[j]); + + __m256 r_ab_x = _mm256_sub_ps(pix, pjx); + __m256 r_ab_y = _mm256_sub_ps(piy, pjy); + __m256 r_ab_n2 = _mm256_fmadd_ps(r_ab_x, r_ab_x, _mm256_mul_ps(r_ab_y, r_ab_y)); + // clamp before rsqrt: rsqrt(0) = inf, then x*inf = 0*inf = NaN downstream. EPS_SQ + // means the inv_sqrt tops out at 1/EPS and r_ab_n = EPS_SQ/EPS = EPS, matches the predecessor. + r_ab_n2 = _mm256_max_ps(r_ab_n2, v_eps_sq); + __m256 inv_r_ab_n = _mm256_rsqrt_ps(r_ab_n2); + //__m256 r_ab_n = _mm256_mul_ps(r_ab_n2, inv_r_ab_n); + + __m256 r_ab2_x = _mm256_sub_ps(r_ab_x, sbe_jx); + __m256 r_ab2_y = _mm256_sub_ps(r_ab_y, sbe_jy); + __m256 r_ab2_n2 = _mm256_fmadd_ps(r_ab2_x, r_ab2_x, _mm256_mul_ps(r_ab2_y, r_ab2_y)); + r_ab2_n2 = _mm256_max_ps(r_ab2_n2, v_eps_sq); + __m256 inv_r_ab2_n = _mm256_rsqrt_ps(r_ab2_n2); + //__m256 r_ab2_n = _mm256_mul_ps(r_ab2_n2, inv_r_ab2_n); + + // r_sum = |r_ab| + |r_ab2|, fused. sqrt(x) = x * rsqrt(x) + // the two norms are used only here (later code uses inv_r_ab_n / inv_r_ab2_n), so fold the two + // recovery muls + add into one mul + one fmadd. -1 FP op, -2 live regs. + __m256 r_sum = _mm256_fmadd_ps(r_ab2_n2, inv_r_ab2_n, _mm256_mul_ps(r_ab_n2, inv_r_ab_n)); + __m256 two_b_sq = _mm256_fmsub_ps(r_sum, r_sum, sb_jsq); + two_b_sq = _mm256_max_ps(two_b_sq, v_eps_sq); + __m256 inv_two_b = _mm256_rsqrt_ps(two_b_sq); + __m256 two_b = _mm256_mul_ps(two_b_sq, inv_two_b); + + __m256 e_arg = _mm256_mul_ps(two_b, v_neg_2s_inv); + e_arg = _mm256_max_ps(e_arg, v_exp_min); + __m256 e_val = exp256_ps(e_arg); + + // smc = numer/denom in the predecessor. with inv-sqrts in hand the divide is free: + // sm_r_ab = smc * r_ab2_n = numer / (two_b * r_ab_n) = numer * inv_two_b * inv_r_ab_n + // sm_r_ab2 = smc * r_ab_n = numer / (two_b * r_ab2_n) = numer * inv_two_b * inv_r_ab2_n + // for the i==j and padding lanes inv_two_b*inv_r_ab_n is huge, but the active-mask AND on + // f_x/f_y below zeros the lane out before accumulation so it cant pollute anything. + __m256 numer_inv_two_b = _mm256_mul_ps(_mm256_mul_ps(r_sum, v_neg_v0_div_2s), _mm256_mul_ps(e_val, inv_two_b)); + __m256 sm_r_ab = _mm256_mul_ps(numer_inv_two_b, inv_r_ab_n); + __m256 sm_r_ab2 = _mm256_mul_ps(numer_inv_two_b, inv_r_ab2_n); + + __m256 f_x = _mm256_fmadd_ps(r_ab2_x, sm_r_ab2, _mm256_mul_ps(r_ab_x, sm_r_ab)); + __m256 f_y = _mm256_fmadd_ps(r_ab2_y, sm_r_ab2, _mm256_mul_ps(r_ab_y, sm_r_ab)); + + __m256 f_norm_sq = _mm256_fmadd_ps(f_x, f_x, _mm256_mul_ps(f_y, f_y)); + __m256 rhs = _mm256_mul_ps(f_norm_sq, v_cos_phi_sq); + __m256 e_dot_f = _mm256_fmadd_ps(eix, f_x, _mm256_mul_ps(eiy, f_y)); + __m256 e_dot_f_sq = _mm256_mul_ps(e_dot_f, e_dot_f); + + __m256 c1 = _mm256_cmp_ps(e_dot_f, v_zero, _CMP_LT_OQ); + __m256 c2 = _mm256_cmp_ps(e_dot_f_sq, rhs, _CMP_GT_OQ); + __m256 cond = _mm256_and_ps(c1, c2); + __m256 w_val = _mm256_blendv_ps(v_dt_neg, v_c_neg_dt, cond); + + //__m256 f_x_safe = _mm256_and_ps(f_x, active); + //__m256 f_y_safe = _mm256_and_ps(f_y, active); + acc_x = _mm256_fmadd_ps(f_x, w_val, acc_x); + acc_y = _mm256_fmadd_ps(f_y, w_val, acc_y); + } + + // restore the values + pos_x[i] = saved_pix; + pos_y[i] = saved_piy; + + __m256 hsum = _mm256_hadd_ps(acc_x, acc_y); + __m128 hsum_lo = _mm256_castps256_ps128(hsum); + __m128 hsum_hi = _mm256_extractf128_ps(hsum, 1); + __m128 sum4 = _mm_add_ps(hsum_lo, hsum_hi); + sum4 = _mm_hadd_ps(sum4, sum4); + alignas(16) float sum_out[4]; + _mm_store_ps(sum_out, sum4); + f_alpha_dt_x += sum_out[0]; + f_alpha_dt_y += sum_out[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; + 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 < 0.0) + projection = 0.0; + else if (projection > 1.0) + projection = 1.0; + + float r_aB_x = pos_x[i] - (board.obstacles[k].start_x + board.obstacles[k].obstacle_v_x * projection); + 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; + + float e_dot_f = (f_alpha_B_neg_y == 0) ? 0 : (f_alpha_B_neg_y < 0 ? -e_y[i] : e_y[i]); + + if (e_dot_f >= cos_phi) + w_val = dt_neg; + else + w_val = c_neg_times_dt; + + float f_alpha_B_dt_x = f_alpha_B_neg_x * w_val; + 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; + } + + for (int i = 0; i < n_p; i++) { + + 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; + float correction_factor = min(1.0f, v_max[i] / w_norm2); + + curr_vel_x[i] = w_x[i] * correction_factor; + curr_vel_y[i] = w_y[i] * correction_factor; + + pos_x[i] = pos_x[i] + curr_vel_x[i] * dt; + 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); + + float ex = destination_x[i] - pos_x[i]; + float ey = destination_y[i] - pos_y[i]; + + float e_norm = sqrt(ex * ex + ey * ey); + float e_norm2 = e_norm > EPS ? e_norm : EPS; + float e_norm_inv = 1.0 / e_norm2; + + e_x[i] = ex * e_norm_inv; + e_y[i] = ey * e_norm_inv; + + float velocity_norm_sq = curr_vel_x[i] * curr_vel_x[i] + curr_vel_y[i] * curr_vel_y[i]; + float velocity_norm = sqrt(velocity_norm_sq); + + sb_sq[i] = velocity_norm_sq * delta_t_sq; + sb_e_x[i] = e_x[i] * (velocity_norm * delta_t); + 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; +}