source code
/* The Computer Language Benchmarks Game
https://salsa.debian.org/benchmarksgame-team/benchmarksgame/
contributed by Martin Jambrek
based off the Java #2 program contributed by Mark C. Lewis and modified slightly by Chad Whipkey
*/
#include <cmath>
#include <cstdio>
#include <cstdlib>
#include <utility>
static constexpr double PI = 3.141592653589793;
static constexpr double SOLAR_MASS = 4 * PI * PI;
static constexpr double DAYS_PER_YEAR = 365.24;
template <auto start, auto stop, auto step = 1, class F>
constexpr void static_for(F&& f)
{
if constexpr (start < stop) {
f(std::integral_constant<decltype(start), start>());
static_for<start + step, stop, step>(std::move(f));
}
}
struct alignas(32) Body {
double x, y, z, pad0;
double vx, vy, vz, pad1;
double mass;
constexpr Body(double x, double y, double z,
double vx, double vy, double vz,
double mass)
: x(x)
, y(y)
, z(z)
, pad0()
, vx(vx)
, vy(vy)
, vz(vz)
, pad1()
, mass(mass)
{
}
};
static constexpr size_t N_BODIES = 5;
using System = Body[N_BODIES];
static constexpr Body sun = {
0, 0, 0, 0, 0, 0, SOLAR_MASS
};
static constexpr Body jupiter = {
4.84143144246472090e+00,
-1.16032004402742839e+00,
-1.03622044471123109e-01,
1.66007664274403694e-03 * DAYS_PER_YEAR,
7.69901118419740425e-03 * DAYS_PER_YEAR,
-6.90460016972063023e-05 * DAYS_PER_YEAR,
9.54791938424326609e-04 * SOLAR_MASS
};
static constexpr Body saturn = {
8.34336671824457987e+00,
4.12479856412430479e+00,
-4.03523417114321381e-01,
-2.76742510726862411e-03 * DAYS_PER_YEAR,
4.99852801234917238e-03 * DAYS_PER_YEAR,
2.30417297573763929e-05 * DAYS_PER_YEAR,
2.85885980666130812e-04 * SOLAR_MASS
};
static constexpr Body uranus = {
1.28943695621391310e+01,
-1.51111514016986312e+01,
-2.23307578892655734e-01,
2.96460137564761618e-03 * DAYS_PER_YEAR,
2.37847173959480950e-03 * DAYS_PER_YEAR,
-2.96589568540237556e-05 * DAYS_PER_YEAR,
4.36624404335156298e-05 * SOLAR_MASS
};
static constexpr Body neptune = {
1.53796971148509165e+01,
-2.59193146099879641e+01,
1.79258772950371181e-01,
2.68067772490389322e-03 * DAYS_PER_YEAR,
1.62824170038242295e-03 * DAYS_PER_YEAR,
-9.51592254519715870e-05 * DAYS_PER_YEAR,
5.15138902046611451e-05 * SOLAR_MASS
};
constexpr void offset_momentum(System& bodies)
{
double px = 0.0;
double py = 0.0;
double pz = 0.0;
static_for<0, N_BODIES>([&](auto i) {
px += bodies[i].vx * bodies[i].mass;
py += bodies[i].vy * bodies[i].mass;
pz += bodies[i].vz * bodies[i].mass;
});
bodies[0].vx = -px / SOLAR_MASS;
bodies[0].vy = -py / SOLAR_MASS;
bodies[0].vz = -pz / SOLAR_MASS;
}
constexpr void advance(System& bodies, double dt)
{
static_for<0, N_BODIES>([&](auto i) {
static_for<i + 1, N_BODIES>([&](auto j) {
double dx = bodies[i].x - bodies[j].x;
double dy = bodies[i].y - bodies[j].y;
double dz = bodies[i].z - bodies[j].z;
double dSquared = dx * dx + dy * dy + dz * dz;
double mag = dt / (dSquared * std::sqrt(dSquared));
bodies[i].vx -= dx * bodies[j].mass * mag;
bodies[i].vy -= dy * bodies[j].mass * mag;
bodies[i].vz -= dz * bodies[j].mass * mag;
bodies[j].vx += dx * bodies[i].mass * mag;
bodies[j].vy += dy * bodies[i].mass * mag;
bodies[j].vz += dz * bodies[i].mass * mag;
});
});
static_for<0, N_BODIES>([&](auto i) {
bodies[i].x += dt * bodies[i].vx;
bodies[i].y += dt * bodies[i].vy;
bodies[i].z += dt * bodies[i].vz;
});
}
constexpr double energy(const System& bodies)
{
double e = 0.0;
static_for<0, N_BODIES>([&](auto i) {
const Body& iBody = bodies[i];
e += 0.5 * iBody.mass * (iBody.vx * iBody.vx + iBody.vy * iBody.vy + iBody.vz * iBody.vz);
static_for<i + 1, N_BODIES>([&](auto j) {
double dx = iBody.x - bodies[j].x;
double dy = iBody.y - bodies[j].y;
double dz = iBody.z - bodies[j].z;
double distance = std::sqrt(dx * dx + dy * dy + dz * dz);
e -= (iBody.mass * bodies[j].mass) / distance;
});
});
return e;
}
int main(int argc, char* argv[])
{
const auto n = std::atoi(argv[1]);
System system = {
sun,
jupiter,
saturn,
uranus,
neptune
};
offset_momentum(system);
std::printf("%.9f\n", energy(system));
for (size_t i = 0; i < n; ++i)
advance(system, 0.01);
std::printf("%.9f\n", energy(system));
}