Hw04 frsama

CMakeLists.txt

@@ -7,3 +7,5 @@ if (NOT CMAKE_BUILD_TYPE)
 endif()
 
 add_executable(main main.cpp)
+
+target_compile_options(main PUBLIC -ffast-math -march=native)

main.cpp

@@ -3,64 +3,106 @@
 #include <vector>
 #include <chrono>
 #include <cmath>
+#include <array>
+
+#define N 48
 
 float frand() {
     return (float)rand() / RAND_MAX * 2 - 1;
 }
 
-struct Star {
-    float px, py, pz;
-    float vx, vy, vz;
-    float mass;
+struct alignas(16) Star {
+    std::array<float,N> px, py, pz;
+    std::array<float,N> vx, vy, vz;
+    std::array<float,N> mass;
 };
 
-std::vector<Star> stars;
+Star stars;
 
-void init() {
-    for (int i = 0; i < 48; i++) {
-        stars.push_back({
-            frand(), frand(), frand(),
-            frand(), frand(), frand(),
-            frand() + 1,
-        });
+// 原计划的初始化，但是完全没有矢量化
+// void init() {
+//     for (size_t i = 0; i < N; ++i) {
+//         stars.px[i] = frand();
+//         stars.py[i] = frand();
+//         stars.pz[i] = frand();
+//         stars.vx[i] = frand();
+//         stars.vy[i] = frand();
+//         stars.vz[i] = frand();
+//         stars.mass[i] = frand() + 1;
+//     }
+// }
+
+template <int M = 0>
+void sub_init(std::array<float,N> &arr) {
+    #pragma GCC unroll 4
+    for (size_t i = 0; i < N; ++i) {
+        arr[i] = frand() + M;
     }
 }
 
+void init() {
+    sub_init<0>(stars.px);
+    sub_init<0>(stars.py);
+    sub_init<0>(stars.pz);
+    sub_init<0>(stars.vx);
+    sub_init<0>(stars.vy);
+    sub_init<0>(stars.vz);
+    sub_init<1>(stars.mass);
+}
+
+
 float G = 0.001;
 float eps = 0.001;
 float dt = 0.01;
 
+float eps2 = eps * eps;
+float Gdt = G * dt;
+
 void step() {
-    for (auto &star: stars) {
-        for (auto &other: stars) {
-            float dx = other.px - star.px;
-            float dy = other.py - star.py;
-            float dz = other.pz - star.pz;
-            float d2 = dx * dx + dy * dy + dz * dz + eps * eps;
-            d2 *= sqrt(d2);
-            star.vx += dx * other.mass * G * dt / d2;
-            star.vy += dy * other.mass * G * dt / d2;
-            star.vz += dz * other.mass * G * dt / d2;
+    for (size_t i = 0; i < N; ++i) {
+        float dvx = 0, dvy = 0, dvz = 0;
+        #pragma GCC unroll 4
+        for (size_t j = 0; j < N; ++j) {
+            float dx = stars.px[j] - stars.px[i];
+            float dy = stars.py[j] - stars.py[i];
+            float dz = stars.pz[j] - stars.pz[i];
+            float d2 = dx * dx + dy * dy + dz * dz + eps2;
+            d2 *= std::sqrt(d2);
+
+            float tmp = stars.mass[j] * Gdt / d2;
+            dvx += dx * tmp;
+            dvy += dy * tmp;
+            dvz += dz * tmp;
         }
+        stars.vx[i] += dvx;
+        stars.vy[i] += dvy;
+        stars.vz[i] += dvz;
     }
-    for (auto &star: stars) {
-        star.px += star.vx * dt;
-        star.py += star.vy * dt;
-        star.pz += star.vz * dt;
+    #pragma GCC unroll 4
+    for (size_t i = 0; i < N; ++i) {
+        stars.px[i] += stars.vx[i] * dt;
+        stars.py[i] += stars.vy[i] * dt;
+        stars.pz[i] += stars.vz[i] * dt;
     }
 }
 
 float calc() {
     float energy = 0;
-    for (auto &star: stars) {
-        float v2 = star.vx * star.vx + star.vy * star.vy + star.vz * star.vz;
-        energy += star.mass * v2 / 2;
-        for (auto &other: stars) {
-            float dx = other.px - star.px;
-            float dy = other.py - star.py;
-            float dz = other.pz - star.pz;
-            float d2 = dx * dx + dy * dy + dz * dz + eps * eps;
-            energy -= other.mass * star.mass * G / sqrt(d2) / 2;
+    #pragma GCC unroll 4
+    for (size_t i = 0; i < N; ++i) {
+        float v2 = stars.vx[i] * stars.vx[i] + stars.vy[i] * stars.vy[i] + stars.vz[i] * stars.vz[i];
+        energy += stars.mass[i] * v2 / 2;
+    }
+    for (size_t i = 0; i < N; ++i) {
+        float tmp = stars.mass[i] * G / 2;
+        #pragma GCC unroll 4
+        for (size_t j = 0; j < N; ++j) {
+            float dx = stars.px[j] - stars.px[i];
+            float dy = stars.py[j] - stars.py[i];
+            float dz = stars.pz[j] - stars.pz[i];
+            float d2 = dx * dx + dy * dy + dz * dz + eps2;
+            float reverse_sqrt_d2 = 1 / std::sqrt(d2);
+            energy -= stars.mass[j] * tmp *reverse_sqrt_d2;
         }
     }
     return energy;