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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_float_inlining_SoA_AVX512_polyexp_fastinvsqrt.cpp
+135 -9
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@@ -13,6 +13,8 @@
#define SEED 42
#define BOARD_WIDTH 10.0f
#define BOARD_LENGTH 50.0f
#define BOARD_LENGTH_MINUS_ONE BOARD_LENGTH - 1.0f
#define BOARD_LENGTH_MINUS_ONE_POINT_FIVE BOARD_LENGTH - 1.5f
#define WALL_EPS 1e-3f
#define BOARD_WIDTH_MINUS_WALL_EPS 9.999f
@@ -161,21 +163,46 @@ Pedestrian *init_pedestrians(int n_p) {
Board init_board_without_obstacles() { return Board(BOARD_LENGTH, BOARD_WIDTH, 0, nullptr); }
// # 256 MULTs, 224 ADDs
static inline __m512 _avx512_exp_ps(__m512 x) {
const __m512 log2e = _mm512_set1_ps(1.4426950408889634f);
// # 16 MULTs
__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);
// # 16 MULTs, 16 ADDs
__m512 r = _mm512_fnmadd_ps(nf, ln2, x);
const __m512 c5 = _mm512_set1_ps(1.0f / 120.0f);
const __m512 c4 = _mm512_set1_ps(1.0f / 24.0f);
const __m512 c3 = _mm512_set1_ps(1.0f / 6.0f);
const __m512 c2 = _mm512_set1_ps(0.5f);
const __m512 c1 = _mm512_set1_ps(1.0f);
const __m512 c0 = _mm512_set1_ps(1.0f);
const __m512 c13 = _mm512_set1_ps(c13_scalar);
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);
__m512 p = c5;
__m512 p = c13;
// # 13 * (16 MULTs, 16 ADDs)
// # = 208 MULTs, 208 ADDs
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);
@@ -187,9 +214,11 @@ static inline __m512 _avx512_exp_ps(__m512 x) {
__m512i scaled = _mm512_slli_epi32(biased, 23);
__m512 pow2n = _mm512_castsi512_ps(scaled);
// # 16 MULTs
return _mm512_mul_ps(p, pow2n);
}
// # 7 MULTs, 2 ADDs
static inline float fast_inv_sqrt(float number) {
float y = number;
@@ -199,7 +228,10 @@ static inline float fast_inv_sqrt(float number) {
y = bit_cast<float>(i);
// # 1 MULT
float x2 = number * 0.5;
// # 6 MULTs, 2 ADDs
y = y * (1.5 - (x2 * y * y));
y = y * (1.5 - (x2 * y * y));
@@ -241,11 +273,41 @@ int run_simulation(Pedestrian *pedestrians, Board &board, int n_p, int n_iter, c
const __m512 v_np = _mm512_set1_ps((float)n_p);
const __m512 v_exp_min = _mm512_set1_ps(-87.0f);
// # ADDs: n_iter * (
// # n_p * 36 +
// # n_p * n_p_pad * 29 +
// # n_p * board.n_obstacles * 10 +
// # n_p * 11
// # )
// # MULTs: n_iter * (
// # n_p * 4 +
// # n_p * n_p_pad * 40 +
// # n_p * board.n_obstacles * 13 +
// # n_p * 30
// # )
// # DIVs: n_iter * (
// # n_p * n_p_pad +
// # n_p * board.n_obstacles
// # )
// # SQRTs: n_iter * (
// # n_p * n_p_pad * 3 +
// # n_p * board.n_obstacles +
// # n_p
// # )
// # 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;
@@ -259,6 +321,8 @@ int run_simulation(Pedestrian *pedestrians, Board &board, int n_p, int n_iter, c
__m512 acc_y = _mm512_setzero_ps();
for (int j = 0; j < n_p_pad; j += 16) {
// # 16 ADDs
__m512 j_idx = _mm512_add_ps(_mm512_set1_ps((float)j), lane_off);
__mmask16 m_neq_i = _mm512_cmp_ps_mask(j_idx, v_i, _CMP_NEQ_OQ);
@@ -271,42 +335,76 @@ int run_simulation(Pedestrian *pedestrians, Board &board, int n_p, int n_iter, c
__m512 sbe_jy = _mm512_loadu_ps(&sb_e_y[j]);
__m512 sb_jsq = _mm512_loadu_ps(&sb_sq[j]);
// # 32 ADDs
__m512 r_ab_x = _mm512_sub_ps(pix, pjx);
__m512 r_ab_y = _mm512_sub_ps(piy, pjy);
// # 32 MULTs, 16 ADDs
__m512 r_ab_n2 = _mm512_fmadd_ps(r_ab_x, r_ab_x, _mm512_mul_ps(r_ab_y, r_ab_y));
// # 16 SQRTs
__m512 r_ab_n = _mm512_sqrt_ps(r_ab_n2);
r_ab_n = _mm512_max_ps(r_ab_n, v_eps);
// # 32 ADDs
__m512 r_ab2_x = _mm512_sub_ps(r_ab_x, sbe_jx);
__m512 r_ab2_y = _mm512_sub_ps(r_ab_y, sbe_jy);
// # 32 MULTs, 16 ADDs
__m512 r_ab2_n2 = _mm512_fmadd_ps(r_ab2_x, r_ab2_x, _mm512_mul_ps(r_ab2_y, r_ab2_y));
// # 16 SQRTs
__m512 r_ab2_n = _mm512_sqrt_ps(r_ab2_n2);
r_ab2_n = _mm512_max_ps(r_ab2_n, v_eps);
// # 16 ADDs
__m512 r_sum = _mm512_add_ps(r_ab_n, r_ab2_n);
// # 16 MULTs, 16 ADDs
__m512 two_b_sq = _mm512_fmsub_ps(r_sum, r_sum, sb_jsq);
two_b_sq = _mm512_max_ps(two_b_sq, v_eps_sq);
// # 16 SQRTs
__m512 two_b = _mm512_sqrt_ps(two_b_sq);
// # 16 MULTs
__m512 e_arg = _mm512_mul_ps(two_b, v_neg_2s_inv);
e_arg = _mm512_max_ps(e_arg, v_exp_min);
// # 256 MULTs, 224 ADDs
__m512 e_val = _avx512_exp_ps(e_arg);
// # 64 MULTs
__m512 numer = _mm512_mul_ps(_mm512_mul_ps(r_sum, v_neg_v0_div_2s), e_val);
__m512 denom = _mm512_mul_ps(_mm512_mul_ps(two_b, r_ab_n), r_ab2_n);
__m512 denom_safe = _mm512_mask_blend_ps(active, v_one, denom);
// # 16 DIVs
__m512 smc = _mm512_div_ps(numer, denom_safe);
// # 32 MULTs
__m512 sm_r_ab = _mm512_mul_ps(smc, r_ab2_n);
__m512 sm_r_ab2 = _mm512_mul_ps(smc, r_ab_n);
// # 64 MULTs, 32 ADDs
__m512 f_x = _mm512_fmadd_ps(r_ab2_x, sm_r_ab2, _mm512_mul_ps(r_ab_x, sm_r_ab));
__m512 f_y = _mm512_fmadd_ps(r_ab2_y, sm_r_ab2, _mm512_mul_ps(r_ab_y, sm_r_ab));
// # 32 MULTs, 16 ADDs
__m512 f_norm_sq = _mm512_fmadd_ps(f_x, f_x, _mm512_mul_ps(f_y, f_y));
// # 16 MULTs
__m512 rhs = _mm512_mul_ps(f_norm_sq, v_cos_phi_sq);
// # 32 MULTs, 16 ADDs
__m512 e_dot_f = _mm512_fmadd_ps(eix, f_x, _mm512_mul_ps(eiy, f_y));
// # 16 MULTs
__m512 e_dot_f_sq = _mm512_mul_ps(e_dot_f, e_dot_f);
__mmask16 c1 = _mm512_cmp_ps_mask(e_dot_f, v_zero, _CMP_LT_OQ);
@@ -318,19 +416,24 @@ int run_simulation(Pedestrian *pedestrians, Board &board, int n_p, int n_iter, c
__m512 f_x_safe = _mm512_maskz_mov_ps(active, f_x);
__m512 f_y_safe = _mm512_maskz_mov_ps(active, f_y);
// # 32 MULTs, 32 ADDs
acc_x = _mm512_fmadd_ps(f_x_safe, w_val, acc_x);
acc_y = _mm512_fmadd_ps(f_y_safe, w_val, acc_y);
}
// # 32 ADDs
f_alpha_dt_x += _mm512_reduce_add_ps(acc_x);
f_alpha_dt_y += _mm512_reduce_add_ps(acc_y);
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)
@@ -338,12 +441,17 @@ int run_simulation(Pedestrian *pedestrians, Board &board, int n_p, int n_iter, c
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);
// # 2 MULTs, 1 EXP, 1 DIV
float scalar_mult = (NEG_U0_AB_div_R * exp(r_aB_norm * NEG_R_INV)) / r_aB_norm;
// # 2 MULTs
float f_alpha_B_neg_x = r_aB_x * scalar_mult;
float f_alpha_B_neg_y = r_aB_y * scalar_mult;
@@ -353,28 +461,36 @@ 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
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; i++) {
// # 9 MULTs, 3 ADDs
float w_norm_inv = fast_inv_sqrt(w_x[i] * w_x[i] + w_y[i] * w_y[i]);
// # 1 MULT
float correction_factor = min(1.0f, 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] == 0 && pos_x[i] > (BOARD_LENGTH - 1.5f)) {
if (color[i] == 0 && pos_x[i] > (BOARD_LENGTH_MINUS_ONE_POINT_FIVE)) {
pos_x[i] = 1.0f;
destination_y[i] = pos_y[i];
w_x[i] = desired_v0[i];
@@ -383,7 +499,7 @@ int run_simulation(Pedestrian *pedestrians, Board &board, int n_p, int n_iter, c
curr_vel_y[i] = w_y[i];
}
if (color[i] == 1 && pos_x[i] < 1.5f) {
pos_x[i] = BOARD_LENGTH - 1.0f;
pos_x[i] = BOARD_LENGTH_MINUS_ONE;
destination_y[i] = pos_y[i];
w_x[i] = -desired_v0[i];
w_y[i] = 0.0f;
@@ -393,19 +509,29 @@ 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
float ex = destination_x[i] - pos_x[i];
float ey = destination_y[i] - pos_y[i];
// # 9 MULTs, 3 ADDs
float 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);
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;