Help optimize nbody bench program (c++ sse2 intrinsics)
I have succeed to optimize nbody program to be faster
than c++ what we have on shootout site currently
but is still slower than intel fortran ;)
http://shootout.alioth.debian.org/u64q/performance.php?test=nbody
I have started from java implementation and converted it to c++,
but it seems somewhat clumsy.
If someone is interested to play with this I will be glad to
see improvement ;)
On q6600 @ 2.4 GHz executes:
[bmaxa@bmaxa nbody]$ g++ -Wall -O3 -std=c++0x -msse2 nbodysse2.cpp -o nbodysse2cpp
[bmaxa@bmaxa nbody]$ time ./nbodysse2cpp 50000000
-0.169075164
-0.169059907
real 0m17.108s
user 0m17.076s
sys 0m0.022s
while program that is currently on site executes:
[bmaxa@bmaxa nbody]$ time ./nbodycpp 50000000
-0.169075164
-0.169059907
real 0m20.621s
user 0m20.554s
sys 0m0.039s
Program follows:
/* The Computer Language Benchmarks Game
http://shootout.alioth.debian.org/
contributed by Mark C. Lewis
modified slightly by Chad Whipkey
converted to c++ and added sse2 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(); ++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_sqrt_pd(dSquared);
__m128d dmag = ddt/(dSquared * distance);
_mm_store_pd(&mag[i],dmag);
}
for(unsigned i=0,k=0; i < bodies.size(); ++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());
}