performance measurements
Each table row shows performance measurements for this C++ g++ program with a particular command-line input value N.
| N | CPU secs | Elapsed secs | Memory KB | Code B | ≈ CPU Load |
|---|---|---|---|---|---|
| 500,000 | 0.11 | 0.11 | ? | 2288 | 0% 0% 0% 100% |
| 5,000,000 | 1.06 | 1.07 | 616 | 2288 | 0% 1% 2% 100% |
| 50,000,000 | 10.55 | 10.56 | 868 | 2288 | 0% 0% 0% 100% |
Read the ↓ make, command line, and program output logs to see how this program was run.
Read n-body benchmark to see what this program should do.
notes
gcc (Ubuntu/Linaro 4.7.3-1ubuntu1) 4.7.3
n-body C++ g++ #2 program source code
/* The Computer Language Benchmarks Game http://benchmarksgame.alioth.debian.org/ contributed by Mark C. Lewis modified slightly by Chad Whipkey converted from java to c++,added sse support, by Branimir Maksimovic */ #include <cstdio> #include <cmath> #include <cstdlib> #include <vector> #include <immintrin.h> static const double PI = 3.141592653589793; static const double SOLAR_MASS = 4 * PI * PI; static const double DAYS_PER_YEAR = 365.24; class Body { public: double x, y, z, filler, vx, vy, vz, mass; public: Body(){} static Body& jupiter(){ static Body p; p.x = 4.84143144246472090e+00; p.y = -1.16032004402742839e+00; p.z = -1.03622044471123109e-01; p.vx = 1.66007664274403694e-03 * DAYS_PER_YEAR; p.vy = 7.69901118419740425e-03 * DAYS_PER_YEAR; p.vz = -6.90460016972063023e-05 * DAYS_PER_YEAR; p.mass = 9.54791938424326609e-04 * SOLAR_MASS; return p; } static Body& saturn(){ static Body p; p.x = 8.34336671824457987e+00; p.y = 4.12479856412430479e+00; p.z = -4.03523417114321381e-01; p.vx = -2.76742510726862411e-03 * DAYS_PER_YEAR; p.vy = 4.99852801234917238e-03 * DAYS_PER_YEAR; p.vz = 2.30417297573763929e-05 * DAYS_PER_YEAR; p.mass = 2.85885980666130812e-04 * SOLAR_MASS; return p; } static Body& uranus(){ static Body p; p.x = 1.28943695621391310e+01; p.y = -1.51111514016986312e+01; p.z = -2.23307578892655734e-01; p.vx = 2.96460137564761618e-03 * DAYS_PER_YEAR; p.vy = 2.37847173959480950e-03 * DAYS_PER_YEAR; p.vz = -2.96589568540237556e-05 * DAYS_PER_YEAR; p.mass = 4.36624404335156298e-05 * SOLAR_MASS; return p; } static Body& neptune(){ static Body p; p.x = 1.53796971148509165e+01; p.y = -2.59193146099879641e+01; p.z = 1.79258772950371181e-01; p.vx = 2.68067772490389322e-03 * DAYS_PER_YEAR; p.vy = 1.62824170038242295e-03 * DAYS_PER_YEAR; p.vz = -9.51592254519715870e-05 * DAYS_PER_YEAR; p.mass = 5.15138902046611451e-05 * SOLAR_MASS; return p; } static Body& sun(){ static Body p; p.mass = SOLAR_MASS; return p; } Body& offsetMomentum(double px, double py, double pz){ vx = -px / SOLAR_MASS; vy = -py / SOLAR_MASS; vz = -pz / SOLAR_MASS; return *this; } }; template <typename T, std::size_t N = 16> class AlignmentAllocator { public: typedef T value_type; typedef std::size_t size_type; typedef std::ptrdiff_t difference_type; typedef T * pointer; typedef const T * const_pointer; typedef T & reference; typedef const T & const_reference; public: inline AlignmentAllocator () throw () { } template <typename T2> inline AlignmentAllocator (const AlignmentAllocator<T2, N> &) throw () { } inline ~AlignmentAllocator () throw () { } inline pointer adress (reference r) { return &r; } inline const_pointer adress (const_reference r) const { return &r; } inline pointer allocate (size_type n) { return (pointer)_mm_malloc(n*sizeof(value_type), N); } inline void deallocate (pointer p, size_type) { _mm_free (p); } inline void construct (pointer p, const value_type & wert) { new (p) value_type (wert); } inline void destroy (pointer p) { p->~value_type (); } inline size_type max_size () const throw () { return size_type (-1) / sizeof (value_type); } template <typename T2> struct rebind { typedef AlignmentAllocator<T2, N> other; }; bool operator!=(const AlignmentAllocator<T,N>& other) const { return !(*this == other); } // Returns true if and only if storage allocated from *this // can be deallocated from other, and vice versa. // Always returns true for stateless allocators. bool operator==(const AlignmentAllocator<T,N>& other) const { return true; } }; class NBodySystem { private: std::vector<Body,AlignmentAllocator<Body,4096> > bodies; public: NBodySystem() : bodies { Body::sun(), Body::jupiter(), Body::saturn(), Body::uranus(), Body::neptune() } { double px = 0.0; double py = 0.0; double pz = 0.0; for(unsigned i=0; i < bodies.size(); ++i) { px += bodies[i].vx * bodies[i].mass; py += bodies[i].vy * bodies[i].mass; pz += bodies[i].vz * bodies[i].mass; } bodies[0].offsetMomentum(px,py,pz); } public: void advance(double dt) { unsigned N = (bodies.size()-1)*bodies.size()/2; struct R{ double dx,dy,dz,filler; }; __m128d ddt = _mm_set1_pd(dt); static __attribute__((aligned(16))) R r[1000]; static __attribute__((aligned(16))) double mag[1000]; for(unsigned i=0,k=0; i < bodies.size()-1; ++i) { Body& iBody = bodies[i]; __m128d idx = _mm_load_pd(&iBody.x); for(unsigned j=i+1; j < bodies.size(); ++j,++k) { __m128d jdx = _mm_load_pd(&bodies[j].x); _mm_store_pd(&r[k].dx,idx-jdx); r[k].dz = iBody.z - bodies[j].z; } } for(unsigned i=0; i < N; i+=2) { __m128d dx,dy,dz; dx = _mm_loadl_pd(dx,&r[i].dx); dy = _mm_loadl_pd(dy,&r[i].dy); dz = _mm_loadl_pd(dz,&r[i].dz); dx = _mm_loadh_pd(dx,&r[i+1].dx); dy = _mm_loadh_pd(dy,&r[i+1].dy); dz = _mm_loadh_pd(dz,&r[i+1].dz); __m128d dSquared = dx*dx + dy*dy + dz*dz; __m128d distance = _mm_cvtps_pd(_mm_rsqrt_ps(_mm_cvtpd_ps(dSquared))); for(unsigned j=0;j<2;++j) { distance = distance * _mm_set1_pd(1.5) - ((_mm_set1_pd(0.5) * dSquared) * distance) * (distance * distance); } __m128d dmag = ddt/(dSquared) * distance; _mm_store_pd(&mag[i],dmag); } for(unsigned i=0,k=0; i < bodies.size()-1; ++i) { Body& iBody = bodies[i]; for(unsigned j=i+1; j < bodies.size(); ++j,++k) { __m128d jmass = _mm_set1_pd(bodies[j].mass); __m128d kmag = _mm_set1_pd(mag[k]); __m128d jkmm = jmass * kmag; __m128d kdx = _mm_load_pd(&r[k].dx); __m128d ivx = _mm_load_pd(&iBody.vx); _mm_store_pd(&iBody.vx, ivx - kdx*jkmm); iBody.vz -= r[k].dz * bodies[j].mass * mag[k]; __m128d imass = _mm_set1_pd(iBody.mass); jkmm = imass * kmag; __m128d jvx = _mm_load_pd(&bodies[j].vx); _mm_store_pd(&bodies[j].vx, jvx + kdx * jkmm); bodies[j].vz += r[k].dz * iBody.mass * mag[k]; } } for (unsigned i = 0; i < bodies.size(); ++i) { __m128d ix = _mm_load_pd(&bodies[i].x); __m128d ivx = _mm_load_pd(&bodies[i].vx); _mm_store_pd(&bodies[i].x, ix + ddt * ivx); bodies[i].z += dt * bodies[i].vz; } } public: double energy(){ double dx, dy, dz, distance; double e = 0.0; for (unsigned i=0; i < bodies.size(); ++i) { Body& iBody = bodies[i]; e += 0.5 * iBody.mass * ( iBody.vx * iBody.vx + iBody.vy * iBody.vy + iBody.vz * iBody.vz ); for (unsigned j=i+1; j < bodies.size(); ++j) { Body& jBody = bodies[j]; dx = iBody.x - jBody.x; dy = iBody.y - jBody.y; dz = iBody.z - jBody.z; distance = sqrt(dx*dx + dy*dy + dz*dz); e -= (iBody.mass * jBody.mass) / distance; } } return e; } }; int main(int argc, char** argv) { int n = atoi(argv[1]); NBodySystem bodies; printf("%.9f\n", bodies.energy()); for (int i=0; i<n; ++i) bodies.advance(0.01); printf("%.9f\n", bodies.energy()); }
make, command-line, and program output logs
Tue, 30 Apr 2013 05:33:57 GMT
MAKE:
/usr/bin/g++ -c -pipe -O3 -fomit-frame-pointer -march=native -mfpmath=sse -msse3 --std=c++0x nbody.gpp-2.c++ -o nbody.gpp-2.c++.o && \
/usr/bin/g++ nbody.gpp-2.c++.o -o nbody.gpp-2.gpp_run
rm nbody.gpp-2.c++
0.43s to complete and log all make actions
COMMAND LINE:
./nbody.gpp-2.gpp_run 50000000
PROGRAM OUTPUT:
-0.169075164
-0.169059907