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Perf plot

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[Quy Anh] «Elliot» Nguyen
2026-06-18 11:59:50 +02:00
committed by Linus Baumberger
parent ca969564a6
commit e7af3103e8
153 changed files with 22042 additions and 24220 deletions
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variants/variant_inlining_8_SoA_AVX512_polyexp_fastinvsqrt_sr.cpp
+112 -12
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@@ -14,6 +14,8 @@
#define SEED 42
#define BOARD_WIDTH 10.0
#define BOARD_LENGTH 50.0
#define BOARD_LENGTH_MINUS_ONE BOARD_LENGTH - 1.0
#define BOARD_LENGTH_MINUS_ONE_POINT_FIVE BOARD_LENGTH - 1.5
#define WALL_EPS 1e-3
#define BOARD_WIDTH_MINUS_WALL_EPS 9.999
@@ -163,23 +165,42 @@ Pedestrian *init_pedestrians(int n_p) {
Board init_board_without_obstacles() { return Board(BOARD_LENGTH, BOARD_WIDTH, 0, nullptr); }
// # 128 MULTs, 112 ADDs
static inline __m512d _avx512_exp_pd(__m512d x) {
const __m512d log2e = _mm512_set1_pd(1.4426950408889634);
// # 8 MULTs
__m512d nf = _mm512_roundscale_pd(_mm512_mul_pd(x, log2e), _MM_FROUND_TO_NEAREST_INT | _MM_FROUND_NO_EXC);
const __m512d ln2 = _mm512_set1_pd(0.6931471805599453);
// # 8 MULTs, 8 ADDs
__m512d r = _mm512_fnmadd_pd(nf, ln2, x);
const __m512d c7 = _mm512_set1_pd(1.0 / 5040.0);
const __m512d c6 = _mm512_set1_pd(1.0 / 720.0);
const __m512d c5 = _mm512_set1_pd(1.0 / 120.0);
const __m512d c4 = _mm512_set1_pd(1.0 / 24.0);
const __m512d c3 = _mm512_set1_pd(1.0 / 6.0);
const __m512d c2 = _mm512_set1_pd(0.5);
const __m512d c1 = _mm512_set1_pd(1.0);
const __m512d c0 = _mm512_set1_pd(1.0);
const __m512d c13 = _mm512_set1_pd(c13_scalar);
const __m512d c12 = _mm512_set1_pd(c12_scalar);
const __m512d c11 = _mm512_set1_pd(c11_scalar);
const __m512d c10 = _mm512_set1_pd(c10_scalar);
const __m512d c9 = _mm512_set1_pd(c9_scalar);
const __m512d c8 = _mm512_set1_pd(c8_scalar);
const __m512d c7 = _mm512_set1_pd(c7_scalar);
const __m512d c6 = _mm512_set1_pd(c6_scalar);
const __m512d c5 = _mm512_set1_pd(c5_scalar);
const __m512d c4 = _mm512_set1_pd(c4_scalar);
const __m512d c3 = _mm512_set1_pd(c3_scalar);
const __m512d c2 = _mm512_set1_pd(c2_scalar);
const __m512d c1 = _mm512_set1_pd(c1_scalar);
const __m512d c0 = _mm512_set1_pd(c0_scalar);
__m512d p = c7;
__m512d p = c13;
// # 104 MULTs, 104 ADDs
p = _mm512_fmadd_pd(p, r, c12);
p = _mm512_fmadd_pd(p, r, c11);
p = _mm512_fmadd_pd(p, r, c10);
p = _mm512_fmadd_pd(p, r, c9);
p = _mm512_fmadd_pd(p, r, c8);
p = _mm512_fmadd_pd(p, r, c7);
p = _mm512_fmadd_pd(p, r, c6);
p = _mm512_fmadd_pd(p, r, c5);
p = _mm512_fmadd_pd(p, r, c4);
@@ -205,9 +226,11 @@ static inline __m512d _avx512_exp_pd(__m512d x) {
__m512d pow2n = _mm512_castsi512_pd(scaled);
// # 8 MULTs
return _mm512_mul_pd(p, pow2n);
}
// # 10 MULTs, 3 ADDs
static inline double fast_inv_sqrt(double number) {
double y = number;
@@ -258,9 +281,26 @@ int run_simulation(Pedestrian *pedestrians, Board &board, int n_p, int n_iter, c
const __m512d v_np = _mm512_set1_pd(n_p);
for (int t = 0; t < n_iter; t++) {
// # ADDs: n_iter * n_p * 33 +
// # n_iter * n_p * (n_p_pad / 8) * 232 +
// # n_iter * n_p * board.n_obstacles * 10
// # MULTs: n_iter * n_p * 40 +
// # n_iter * n_p * (n_p_pad / 8) * 320 +
// # n_iter * n_p * board.n_obstacles * 13
// # DIVs: n_iter * n_p * (n_p_pad / 8) * 8 +
// # n_iter * n_p * board.n_obstacles
// # SQRTs: n_iter * n_p +
// # n_iter * n_p * (n_p_pad / 8) * 24 +
// # n_iter * n_p * board.n_obstacles
// # EXPs: n_iter * n_p * board.n_obstacles
for (int t = 0; t < n_iter; t++) {
for (int i = 0; i < n_p; i++) {
double pos_x_i = pos_x[i];
double pos_y_i = pos_y[i];
double e_x_i = e_x[i];
@@ -269,6 +309,7 @@ int run_simulation(Pedestrian *pedestrians, Board &board, int n_p, int n_iter, c
double curr_vel_x_i = curr_vel_x[i];
double curr_vel_y_i = curr_vel_y[i];
// # 4 MULTs, 2 ADDs
double f_alpha_dt_x = (e_x_i * desired_v0_i - curr_vel_x_i) * dt_times_tau_alpha_inv;
double f_alpha_dt_y = (e_y_i * desired_v0_i - curr_vel_y_i) * dt_times_tau_alpha_inv;
@@ -282,6 +323,8 @@ int run_simulation(Pedestrian *pedestrians, Board &board, int n_p, int n_iter, c
__m512d acc_y = _mm512_setzero_pd();
for (int j = 0; j < n_p_pad; j += 8) {
// # 8 ADDs
__m512d j_idx = _mm512_add_pd(_mm512_set1_pd((double)j), lane_off);
__mmask8 m_neq_i = _mm512_cmp_pd_mask(j_idx, v_i, _CMP_NEQ_OQ);
@@ -294,36 +337,65 @@ int run_simulation(Pedestrian *pedestrians, Board &board, int n_p, int n_iter, c
__m512d sbe_jy = _mm512_loadu_pd(&sb_e_y[j]);
__m512d sb_jsq = _mm512_loadu_pd(&sb_sq[j]);
// # 16 ADDs
__m512d r_ab_x = _mm512_sub_pd(pix, pjx);
__m512d r_ab_y = _mm512_sub_pd(piy, pjy);
// # 16 MULTs, 8 ADDs
__m512d r_ab_n2 = _mm512_fmadd_pd(r_ab_x, r_ab_x, _mm512_mul_pd(r_ab_y, r_ab_y));
// # 8 SQRTs
__m512d r_ab_n = _mm512_sqrt_pd(r_ab_n2);
// # 16 ADDs
__m512d r_ab2_x = _mm512_sub_pd(r_ab_x, sbe_jx);
__m512d r_ab2_y = _mm512_sub_pd(r_ab_y, sbe_jy);
// # 16 MULTs, 8 ADDs
__m512d r_ab2_n2 = _mm512_fmadd_pd(r_ab2_x, r_ab2_x, _mm512_mul_pd(r_ab2_y, r_ab2_y));
// # 8 SQRTs
__m512d r_ab2_n = _mm512_sqrt_pd(r_ab2_n2);
// # 8 ADDs
__m512d r_sum = _mm512_add_pd(r_ab_n, r_ab2_n);
// # 8 MULTs, 8 ADDs
__m512d two_b_sq = _mm512_fmsub_pd(r_sum, r_sum, sb_jsq);
// # 8 SQRTs
__m512d two_b = _mm512_sqrt_pd(two_b_sq);
// # 8 MULTs
__m512d e_arg = _mm512_mul_pd(two_b, v_neg_2s_inv);
// # 128 MULTs, 112 ADDs
__m512d e_val = _avx512_exp_pd(e_arg);
// # 32 MULTs
__m512d numer = _mm512_mul_pd(_mm512_mul_pd(r_sum, v_neg_v0_div_2s), e_val);
__m512d denom = _mm512_mul_pd(_mm512_mul_pd(two_b, r_ab_n), r_ab2_n);
__m512d denom_safe = _mm512_mask_blend_pd(active, _mm512_set1_pd(1.0), denom);
// # 8 DIVs
__m512d smc = _mm512_div_pd(numer, denom_safe);
// # 16 MULTs
__m512d sm_r_ab = _mm512_mul_pd(smc, r_ab2_n);
__m512d sm_r_ab2 = _mm512_mul_pd(smc, r_ab_n);
// # 32 MULTs, 16 ADDs
__m512d f_x = _mm512_fmadd_pd(r_ab2_x, sm_r_ab2, _mm512_mul_pd(r_ab_x, sm_r_ab));
__m512d f_y = _mm512_fmadd_pd(r_ab2_y, sm_r_ab2, _mm512_mul_pd(r_ab_y, sm_r_ab));
// # 24 MULTs, 8 ADDs
__m512d a = _mm512_mul_pd(_mm512_fmadd_pd(eix, f_x, _mm512_mul_pd(eiy, f_y)), v_cos_phi_inv);
// # 8 MULTs
__m512d a_sq = _mm512_mul_pd(a, a);
// # 16 MULTs, 8 ADDs
__m512d b_sq = _mm512_fmadd_pd(f_x, f_x, _mm512_mul_pd(f_y, f_y));
__mmask8 k_ge = _mm512_cmp_pd_mask(a, v_zero, _CMP_GE_OQ);
@@ -333,10 +405,13 @@ int run_simulation(Pedestrian *pedestrians, Board &board, int n_p, int n_iter, c
__m512d f_x_safe = _mm512_maskz_mov_pd(active, f_x);
__m512d f_y_safe = _mm512_maskz_mov_pd(active, f_y);
// # 16 MULTs, 16 ADDs
acc_x = _mm512_fmadd_pd(f_x_safe, w_val, acc_x);
acc_y = _mm512_fmadd_pd(f_y_safe, w_val, acc_y);
}
// # 16 ADDs
f_alpha_dt_x += _mm512_reduce_add_pd(acc_x);
f_alpha_dt_y += _mm512_reduce_add_pd(acc_y);
@@ -348,9 +423,11 @@ int run_simulation(Pedestrian *pedestrians, Board &board, int n_p, int n_iter, c
double obs_v_y = board.obstacles[k].obstacle_v_y;
double obs_length_sq_inv = board.obstacles[k].length_sq_inv;
// # 2 ADDs
double v1_x = pos_x_i - obs_start_x;
double v1_y = pos_y_i - obs_start_y;
// # 3 MULTs, 1 ADD
double projection = (v1_x * obs_v_x + v1_y * obs_v_y) * obs_length_sq_inv;
if (projection < 0.0)
@@ -358,11 +435,17 @@ int run_simulation(Pedestrian *pedestrians, Board &board, int n_p, int n_iter, c
else if (projection > 1.0)
projection = 1.0;
// # 2 MULTs, 4 ADDs
double r_aB_x = pos_x_i - (obs_start_x + obs_v_x * projection);
double r_aB_y = pos_y_i - (obs_start_y + obs_v_y * projection);
// # 1 SQRT, 2 MULTs, 1 ADD
double r_aB_norm = sqrt(r_aB_x * r_aB_x + r_aB_y * r_aB_y);
// # 2 MULTs, 1 EXP, 1 DIV
double scalar_mult = (NEG_U0_AB_div_R * exp(r_aB_norm * NEG_R_INV)) / r_aB_norm;
// # 2 MULTs
double f_alpha_B_neg_x = r_aB_x * scalar_mult;
double f_alpha_B_neg_y = r_aB_y * scalar_mult;
@@ -371,15 +454,18 @@ int run_simulation(Pedestrian *pedestrians, Board &board, int n_p, int n_iter, c
if (e_dot_f < cos_phi)
w_val = c_neg_times_dt;
// # 2 MULTs, 2 ADDs
f_alpha_dt_x += f_alpha_B_neg_x * w_val;
f_alpha_dt_y += f_alpha_B_neg_y * w_val;
}
// # 2 ADDs
w_x[i] += f_alpha_dt_x;
w_y[i] += f_alpha_dt_y;
}
for (int i = 0; i < n_p; i++) {
double color_i = color[i];
double curr_vel_x_i = curr_vel_x[i];
double curr_vel_y_i = curr_vel_y[i];
@@ -394,17 +480,21 @@ int run_simulation(Pedestrian *pedestrians, Board &board, int n_p, int n_iter, c
double destination_x_i = destination_x[i];
double destination_y_i = destination_y[i];
// # 12 MULTs, 4 ADDs
double w_norm_inv = fast_inv_sqrt(w_x_i * w_x_i + w_y_i * w_y_i);
// # 1 MULT
double correction_factor = min(1.0, v_max_i * w_norm_inv);
// # 2 MULTs
curr_vel_x_i = w_x_i * correction_factor;
curr_vel_y_i = w_y_i * correction_factor;
// # 2 MULTs, 2 ADDs
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 && pos_x_i > (BOARD_LENGTH - 1.5)) {
if (!color_i && pos_x_i > (BOARD_LENGTH_MINUS_ONE_POINT_FIVE)) {
pos_x_i = 1.0;
destination_y_i = pos_y_i;
w_x_i = desired_v0_i;
@@ -413,7 +503,7 @@ int run_simulation(Pedestrian *pedestrians, Board &board, int n_p, int n_iter, c
curr_vel_y_i = w_y_i;
}
if (color_i && pos_x_i < 1.5) {
pos_x_i = BOARD_LENGTH - 1.0;
pos_x_i = BOARD_LENGTH_MINUS_ONE;
destination_y_i = pos_y_i;
w_x_i = -desired_v0_i;
w_y_i = 0.0;
@@ -423,16 +513,24 @@ int run_simulation(Pedestrian *pedestrians, Board &board, int n_p, int n_iter, c
pos_y_i = clamp(pos_y_i, WALL_EPS, BOARD_WIDTH_MINUS_WALL_EPS);
// # 2 ADDs
double ex = destination_x_i - pos_x_i;
double ey = destination_y_i - pos_y_i;
// # 12 MULTs, 4 ADDs
double e_norm_inv = fast_inv_sqrt(ex * ex + ey * ey);
// # 2 MULTs
e_x_i = ex * e_norm_inv;
e_y_i = ey * e_norm_inv;
// # 2 MULTs, 1 ADD
double velocity_norm_sq = curr_vel_x_i * curr_vel_x_i + curr_vel_y_i * curr_vel_y_i;
// # 1 MULT
double sb_sq_i = velocity_norm_sq * delta_t_sq;
// # 1 SQRT
double velocity_norm_mul_delta_t = sqrt(sb_sq_i);
curr_vel_x[i] = curr_vel_x_i;
@@ -450,6 +548,8 @@ int run_simulation(Pedestrian *pedestrians, Board &board, int n_p, int n_iter, c
destination_y[i] = destination_y_i;
sb_sq[i] = sb_sq_i;
// # 2 MULTs
sb_e_x[i] = e_x_i * velocity_norm_mul_delta_t;
sb_e_y[i] = e_y_i * velocity_norm_mul_delta_t;