HW04

CMakeLists.txt

@@ -7,3 +7,11 @@ if (NOT CMAKE_BUILD_TYPE)
 endif()
 
 add_executable(main main.cpp)
+# target_compile_options(main PUBLIC -ffast-math -march=native)
+add_executable(work work.cpp)
+target_compile_options(work PUBLIC -ffast-math -march=native)
+
+add_executable(work2 work2.cpp)
+target_compile_options(work2 PUBLIC -ffast-math -march=native)
+
+set(CMAKE_EXPORT_COMPILE_COMMANDS ON)

run.sh

@@ -2,4 +2,9 @@
 set -e
 cmake -B build
 cmake --build build
+echo "------baseline------"
 build/main
+echo "------   my   ------"
+build/work
+echo "------   my2  ------"
+build/work2

work.cpp

@@ -0,0 +1,195 @@
+#include <cstdio>
+#include <cstdlib>
+#include <vector>
+#include <chrono>
+#include <cmath>
+#include <array>
+#include <immintrin.h>
+
+float frand() {
+    return (float)rand() / RAND_MAX * 2 - 1;
+}
+
+struct Star {
+    float px, py, pz;
+    float vx, vy, vz;
+    float mass;
+};
+
+constexpr int NSTAR = 48;
+struct StarSOA
+{
+    float data[7][NSTAR];
+    inline float* operator[] (size_t pos) { return data[pos];}
+    inline const float* operator[] (const size_t pos) const { return &(*data[pos]);}
+};
+StarSOA stars2;
+std::vector<Star> stars;
+
+float G = 0.001;
+float eps = 0.001;
+float dt = 0.01;
+
+
+
+void init() {
+    for (int i = 0; i < 48; i++) {
+        stars.push_back({
+            frand(), frand(), frand(),
+            frand(), frand(), frand(),
+            frand() + 1,
+        });
+    }
+}
+
+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 (auto &star: stars) {
+        star.px += star.vx * dt;
+        star.py += star.vy * dt;
+        star.pz += star.vz * 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;
+        }
+    }
+    return energy;
+}
+void init2() {
+    // for (int i=0; i<NSTAR; i++) {
+    //     for (int j=5; j>=0; j--) {
+    //         stars2[j][i] = frand();
+    //     }
+    //     stars2[6][i] = frand() + 1;
+    // }
+    for (int i=0; i<NSTAR; i++) {
+        stars2[0][i] = stars[i].px;
+        stars2[1][i] = stars[i].py;
+        stars2[2][i] = stars[i].pz;
+        stars2[3][i] = stars[i].vx;
+        stars2[4][i] = stars[i].vy;
+        stars2[5][i] = stars[i].vz;
+        stars2[6][i] = stars[i].mass;
+    }
+}
+
+// 借鉴雷神之锤3的速算法
+inline float Q_rsqrt(float number)
+{
+    constexpr float threehalfs = 1.5F;
+    float x2 = number * 0.5F;
+    float y = number;
+    int i = *reinterpret_cast<int*>(&y);           // evil floating point bit level hacking
+    i = 0x5f3759df - (i >> 1); 
+    y = *reinterpret_cast<float*>(&i);
+    y = y * (threehalfs - (x2 * y * y)); // 1st iteration
+    y = y * (threehalfs - (x2 * y * y)); // 2nd iteration, this can be removed
+
+    return y;
+}
+
+void step2() {
+    auto other = stars2;
+    for (int i=0; i<NSTAR; i++) {
+        float vx{0}, vy{0}, vz{0};
+        for (int j=0; j<NSTAR; j++) {
+            float dx = other[0][j] - stars2[0][i];
+            float dy = other[1][j] - stars2[1][i];
+            float dz = other[2][j] - stars2[2][i];
+            float d2 = dx * dx + dy * dy + dz * dz + eps * eps;
+            if (true)
+            {
+                d2 *= std::sqrt(d2);     // 292 ms
+                vx += dx * other[6][j] * (G * dt) / d2;
+                vy += dy * other[6][j] * (G * dt) / d2;
+                vz += dz * other[6][j] * (G * dt) / d2;
+            }
+            else {
+                // d2 = 1./(std::sqrt(d2)*d2);     // 292 ms
+                d2 = Q_rsqrt(d2)/d2;            // 273ms
+                vx += dx * other[6][j] * (G * dt) * d2;
+                vy += dy * other[6][j] * (G * dt) * d2;
+                vz += dz * other[6][j] * (G * dt) * d2;
+            }
+
+        }
+        stars2[3][i] += vx;
+        stars2[4][i] += vy;
+        stars2[5][i] += vz;
+        stars2[0][i] += stars2[3][i] * dt;
+        stars2[1][i] += stars2[4][i] * dt;
+        stars2[2][i] += stars2[5][i] * dt;
+    }
+}
+
+
+float calc2() {
+    float energy = 0;
+    for (int i=0; i<NSTAR; i++) {
+        float v2 = stars2[3][i] * stars2[3][i] + stars2[4][i] * stars2[4][i] + stars2[5][i] * stars2[5][i];
+        energy += stars2[6][i] * v2 /2;
+        for (int j=0; j<NSTAR; j++) {
+            float dx = stars2[0][j] - stars2[0][i];
+            float dy = stars2[1][j] - stars2[1][i];
+            float dz = stars2[2][j] - stars2[2][i];
+            float d2 = dx * dx + dy * dy + dz * dz + eps * eps;
+            energy -= stars2[6][j] * stars2[6][i] * G / sqrt(d2) / 2;            
+        }
+    }
+    return energy;
+}
+
+template <class Func>
+long benchmark(Func const &func) {
+    auto t0 = std::chrono::steady_clock::now();
+    func();
+    auto t1 = std::chrono::steady_clock::now();
+    auto dt = std::chrono::duration_cast<std::chrono::milliseconds>(t1 - t0);
+    return dt.count();
+}
+
+int main() {
+    init();
+    init2();
+    printf("original:\n");
+    printf("Initial energy: %f\n", calc());
+    auto dt = benchmark([&] {
+        for (int i = 0; i < 100000; i++)
+            step();
+    });
+    printf("Final energy: %f\n", calc());
+    printf("Time elapsed: %ld ms\n", dt);
+
+    printf("my:\n");
+    printf("Initial energy: %f\n", calc2());
+    auto dt2 = benchmark([&] {
+        for (int i = 0; i < 100000; i++)
+            step2();
+    });
+    printf("Final energy: %f\n", calc2());
+    printf("Time elapsed: %ld ms\n", dt2);
+    return 0;
+}