diff --git a/board.hpp b/board.hpp index e76b5ea..33da163 100644 --- a/board.hpp +++ b/board.hpp @@ -7,16 +7,27 @@ struct Obstacle { Obstacle() : start(0, 0), end(0, 0) {} Obstacle(Vector2d s, Vector2d e) : start(s), end(e) {} - // find the point of the obstacle that is nearest to p + + // Find the point of the obstacle that is nearest to p + // # 15 flops Vector2d find_nearest_obstacle_point(Vector2d p) { + + // # 2 ADDs Vector2d obstacle_v = end - start; + + // # 9 flops = 2 ADDs, 2 MULTs, 1 ADD, 1 DIV, 2 MULTs, 1 ADD double projection = (p - start).dot(obstacle_v) / obstacle_v.dot(obstacle_v); + if (projection < 0.0) projection = 0.0; - if (projection > 1.0) + else if (projection > 1.0) projection = 1.0; + + // # 4 flops = 2 ADDs, 2 MULTs return start + obstacle_v * projection; + } + }; struct Board { diff --git a/forces.cpp b/forces.cpp index 24dfa5f..5911909 100644 --- a/forces.cpp +++ b/forces.cpp @@ -1,6 +1,7 @@ #include "forces.hpp" #include +// # 8 flops = 5 MULTs, 2 ADD, 1 SQRT double w(Vector2d e, Vector2d f) { if (e.dot(f) >= f.norm() * cos_phi) return 1.0; @@ -8,6 +9,7 @@ double w(Vector2d e, Vector2d f) { return c; } +// # 2 DIVs double g(double v_max_alpha, double w_alpha_norm) { if (w_alpha_norm <= v_max_alpha) { return 1; @@ -15,12 +17,16 @@ double g(double v_max_alpha, double w_alpha_norm) { return v_max_alpha / w_alpha_norm; } +// # 8 flops void compute_acceleration_term(Pedestrian *p) { + // # 2 flops Vector2d desired_velocity = p->e * p->desired_v0; Vector2d actual_velocity = p->curr_vel; + // # 6 flops = 4 ADDs, 2 DIVs p->f_i += (desired_velocity - actual_velocity) / tau_alpha; } +// # 55(N - 1) = 55N - 55 flops void compute_repulsive_effects_from_pedestrians(Pedestrian *pedestrians, Pedestrian *p, int N) { for (int i = 0; i < N; i++) { @@ -34,28 +40,39 @@ void compute_repulsive_effects_from_pedestrians(Pedestrian *pedestrians, Pedestr // continue; // } + // # 2 ADDs Vector2d r_ab = p->curr_pos - pedestrians[i].curr_pos; + // # 4 flops = 1 SQRT, 2 MULTs, 1 ADD double r_ab_norm = r_ab.norm(); Vector2d e_b = pedestrians[i].e; + // # 2 MULTs double s_b = pedestrians[i].desired_v0 * delta_t; + // # 4 flops = 2 ADDs, 2 MULTs Vector2d r_ab2 = r_ab - (e_b * s_b); + // # 4 flops = 1 SQRT, 2 MULTs, 1 ADD double r_ab2_norm = r_ab2.norm(); - double b = sqrt(pow(r_ab_norm + r_ab2_norm, 2) - pow(s_b, 2)) / 2; + // # 7 flops = 1 SQRT, 3 ADDs, 2 MULTs, 1 DIV + double b = sqrt((r_ab_norm + r_ab2_norm) * (r_ab_norm + r_ab2_norm) - s_b * s_b) / 2; + // # 12 flops = 6 DIVs, 3 ADDs, 3 MULTs Vector2d b_grad = (r_ab / r_ab_norm + r_ab2 / r_ab2_norm) * (r_ab_norm + r_ab2_norm) / (4 * b); + // # 6 flops = 3 MULTs, 2 DIVs, 1 EXP Vector2d f_ped = b_grad * ((V0_AB / SIGMA) * (exp(-b / SIGMA))); + // # 14 flops: 9 MULTs, 4 ADDs, 1 SQRT p->f_i += f_ped * w(p->e, f_ped * -1); } } +// # Assume that the four borders are also 4 obstacles +// # 36 n_obstacles flops = 144 flops void compute_repulsive_effects_from_borders(Board &board, Pedestrian *p) { Obstacle *obstacles = board.obstacles; @@ -65,10 +82,13 @@ void compute_repulsive_effects_from_borders(Board &board, Pedestrian *p) { Obstacle obstacle = obstacles[i]; + // # 17 flops Vector2d r_aB = p->curr_pos - obstacle.find_nearest_obstacle_point(p->curr_pos); + // # 17 flops = 2 DIVs, 1 SQRT, 2 MULTs, 1 ADD, 2 MULTs, 1 DIV, 2 MULTs, 1 EXP, 1 SQRT, 2 MULTs, 1 ADD, 1 DIV Vector2d f_obst = (r_aB / r_aB.norm()) * (U0_AB / R) * std::exp(-r_aB.norm() / R); + // # 2 ADDs p->f_i += f_obst; } } diff --git a/main b/main new file mode 100755 index 0000000..6df5076 Binary files /dev/null and b/main differ diff --git a/main.cpp b/main.cpp index 10ee86e..ffbc725 100644 --- a/main.cpp +++ b/main.cpp @@ -2,7 +2,9 @@ #include "forces.hpp" #include "math.h" #include "pedestrian.hpp" +#include "tsc_x86.h" #include "vector2d.hpp" +#include #define BOARD_WIDTH 10.0 #define BOARD_LENGTH 50.0 @@ -50,6 +52,11 @@ int main(int argc, const char *argv[]) { int n_p = atoi(argv[1]); int n_iter = atoi(argv[2]); Pedestrian *pedestrians = init_pedestrians(n_p); + + // # Start here or right after function signature + uint64_t start = start_tsc(); + + // # (8 + 55N - 55 + 144 + 4 + 8 + 4 + 10)*n_p*n_iter for (int t = 0; t < n_iter; t++) { for (int i = 0; i < n_p; i++) { @@ -58,21 +65,44 @@ int main(int argc, const char *argv[]) { p.f_i.reset(); + // # 8 flops compute_acceleration_term(&p); + // # 55N - 55 flops compute_repulsive_effects_from_pedestrians(pedestrians, &p, n_p); + // # 144 flops compute_repulsive_effects_from_borders(board, &p); + // # 4 flops = 2 ADDs, 2 MULTs Vector2d w_alpha = p.curr_vel + p.f_i * dt; + // # 8 flops = 2 MULTs, 2 DIVs, 1 SQRT, 2 MULTs, 1 ADD p.curr_vel = w_alpha * g(p.v_max, w_alpha.norm()); + // # 4 flops = 2 ADDs, 2 MULTs p.curr_pos = p.curr_pos + p.curr_vel * dt; + // # 10 flops = 5 ADDs, 2 DIVs, 1 SQRT, 2 MULTs p.e = (p.destination - p.curr_pos) / (p.destination - p.curr_pos).norm(); } } + int W = (8 + 55 * n_p - 55 + 144 + 4 + 8 + 4 + 10) * n_p * n_iter; + std::cout << "W(n): "; + std::cout << W; + std::cout << " flops\n"; + + double T = stop_tsc(start); + std::cout << "T(n): "; + std::cout << T; + std::cout << " cycles\n"; + double P = W/T; + + std::cout << "P(n): "; + std::cout << P; + std::cout << " flops/cycle\n"; + + delete []pedestrians; return 0; } diff --git a/questions.md b/questions.md new file mode 100644 index 0000000..6de7008 --- /dev/null +++ b/questions.md @@ -0,0 +1,6 @@ +- [ ] SQRT == 1 flop? EXP == 1 flop? +- [ ] Where to start measurements, do we include measurements? +- [ ] Can Vector2d be reused? +- [ ] How precise do we have to be? How do we define "correctness"? +- [ ] Do borders count as obstacles? +- [ ] Do we use a fixed machine, frequency scaling, etc. diff --git a/tsc_x86.h b/tsc_x86.h index 4e4baf4..be144a3 100644 --- a/tsc_x86.h +++ b/tsc_x86.h @@ -1,24 +1,24 @@ /* ==================== GNU C and possibly other UNIX compilers ===================== */ - #ifndef _WIN32 +#ifndef _WIN32 - #if defined(__GNUC__) || defined(__linux__) - #define VOLATILE __volatile__ - #define ASM __asm__ - #else - /* if we're neither compiling with gcc or under linux, we can hope - * the following lines work, they probably won't */ - #define ASM asm - #define VOLATILE - #endif +#if defined(__GNUC__) || defined(__linux__) +#define VOLATILE __volatile__ +#define ASM __asm__ +#else +/* if we're neither compiling with gcc or under linux, we can hope + * the following lines work, they probably won't */ +#define ASM asm +#define VOLATILE +#endif - #define myInt64 unsigned long long - #define INT32 unsigned int +#define myInt64 unsigned long long +#define INT32 unsigned int /* ======================== WIN32 ======================= */ #else - #define myInt64 signed __int64 - #define INT32 unsigned __int32 +#define myInt64 signed __int64 +#define INT32 unsigned __int32 #endif @@ -27,68 +27,57 @@ * Time Stamp Counter. The Intel manuals contain more information. */ - #define COUNTER_LO(a) ((a).int32.lo) #define COUNTER_HI(a) ((a).int32.hi) #define COUNTER_VAL(a) ((a).int64) -#define COUNTER(a) \ - ((unsigned long long)COUNTER_VAL(a)) +#define COUNTER(a) ((unsigned long long)COUNTER_VAL(a)) -#define COUNTER_DIFF(a,b) \ - (COUNTER(a)-COUNTER(b)) +#define COUNTER_DIFF(a, b) (COUNTER(a) - COUNTER(b)) /* ==================== GNU C and possibly other UNIX compilers ===================== */ #ifndef _WIN32 - typedef union - { myInt64 int64; - struct {INT32 lo, hi;} int32; - } tsc_counter; +typedef union { + myInt64 int64; + struct { + INT32 lo, hi; + } int32; +} tsc_counter; - #define RDTSC(cpu_c) \ - ASM VOLATILE ("rdtsc" : "=a" ((cpu_c).int32.lo), "=d"((cpu_c).int32.hi)) - #define CPUID() \ - ASM VOLATILE ("cpuid" : : "a" (0) : "bx", "cx", "dx" ) +#define RDTSC(cpu_c) ASM VOLATILE("rdtsc" : "=a"((cpu_c).int32.lo), "=d"((cpu_c).int32.hi)) +#define CPUID() ASM VOLATILE("cpuid" : : "a"(0) : "bx", "cx", "dx") /* ======================== WIN32 ======================= */ #else - typedef union - { myInt64 int64; - struct {INT32 lo, hi;} int32; - } tsc_counter; +typedef union { + myInt64 int64; + struct { + INT32 lo, hi; + } int32; +} tsc_counter; - #define RDTSC(cpu_c) \ - { __asm rdtsc \ - __asm mov (cpu_c).int32.lo,eax \ - __asm mov (cpu_c).int32.hi,edx \ - } +#define RDTSC(cpu_c) {__asm rdtsc __asm mov(cpu_c).int32.lo, eax __asm mov(cpu_c).int32.hi, edx} - #define CPUID() \ - { \ - __asm mov eax, 0 \ - __asm cpuid \ - } +#define CPUID() {__asm mov eax, 0 __asm cpuid} #endif - static void init_tsc() { - ; // no need to initialize anything for x86 + ; // no need to initialize anything for x86 } static myInt64 start_tsc(void) { - tsc_counter start; - CPUID(); - RDTSC(start); - return COUNTER_VAL(start); + tsc_counter start; + CPUID(); + RDTSC(start); + return COUNTER_VAL(start); } static myInt64 stop_tsc(myInt64 start) { - tsc_counter end; - RDTSC(end); - CPUID(); - return COUNTER_VAL(end) - start; + tsc_counter end; + RDTSC(end); + CPUID(); + return COUNTER_VAL(end) - start; } - diff --git a/vector2d.hpp b/vector2d.hpp index b4eef41..b9bf1f0 100644 --- a/vector2d.hpp +++ b/vector2d.hpp @@ -15,7 +15,9 @@ struct Vector2d { *this = *this + v; return *this; } + // # 4 flops = 1 SQRT, 2 MULTs, 1 ADD double norm() { return sqrt(x * x + y * y); } + // # 3 flops = 2 MULTs, 1 ADD double dot(Vector2d v) { return x * v.x + y * v.y; } void reset() { x = 0;