diff --git a/CMakeLists.txt b/CMakeLists.txt index 29b152c..b4eb6e4 100644 --- a/CMakeLists.txt +++ b/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) diff --git a/main.cpp b/main.cpp index cf6369b..e4cc091 100644 --- a/main.cpp +++ b/main.cpp @@ -3,64 +3,106 @@ #include #include #include +#include + +#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 px, py, pz; + std::array vx, vy, vz; + std::array mass; }; -std::vector 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 +void sub_init(std::array &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;