// OF THE POSSIBILITY OF SUCH DAMAGE.
use std::mem;
+use std::ops::{Add, Sub, Mul};
const PI: f64 = 3.141592653589793;
const SOLAR_MASS: f64 = 4.0 * PI * PI;
const YEAR: f64 = 365.24;
const N_BODIES: usize = 5;
+const N_PAIRS: usize = N_BODIES * (N_BODIES - 1) / 2;
-static BODIES: [Planet;N_BODIES] = [
+const BODIES: [Planet; N_BODIES] = [
// Sun
Planet {
- x: 0.0, y: 0.0, z: 0.0,
- vx: 0.0, vy: 0.0, vz: 0.0,
+ pos: Vec3(0.0, 0.0, 0.0),
+ vel: Vec3(0.0, 0.0, 0.0),
mass: SOLAR_MASS,
},
// Jupiter
Planet {
- x: 4.84143144246472090e+00,
- y: -1.16032004402742839e+00,
- z: -1.03622044471123109e-01,
- vx: 1.66007664274403694e-03 * YEAR,
- vy: 7.69901118419740425e-03 * YEAR,
- vz: -6.90460016972063023e-05 * YEAR,
+ pos: Vec3(4.84143144246472090e+00,
+ -1.16032004402742839e+00,
+ -1.03622044471123109e-01),
+ vel: Vec3(1.66007664274403694e-03 * YEAR,
+ 7.69901118419740425e-03 * YEAR,
+ -6.90460016972063023e-05 * YEAR),
mass: 9.54791938424326609e-04 * SOLAR_MASS,
},
// Saturn
Planet {
- x: 8.34336671824457987e+00,
- y: 4.12479856412430479e+00,
- z: -4.03523417114321381e-01,
- vx: -2.76742510726862411e-03 * YEAR,
- vy: 4.99852801234917238e-03 * YEAR,
- vz: 2.30417297573763929e-05 * YEAR,
+ pos: Vec3(8.34336671824457987e+00,
+ 4.12479856412430479e+00,
+ -4.03523417114321381e-01),
+ vel: Vec3(-2.76742510726862411e-03 * YEAR,
+ 4.99852801234917238e-03 * YEAR,
+ 2.30417297573763929e-05 * YEAR),
mass: 2.85885980666130812e-04 * SOLAR_MASS,
},
// Uranus
Planet {
- x: 1.28943695621391310e+01,
- y: -1.51111514016986312e+01,
- z: -2.23307578892655734e-01,
- vx: 2.96460137564761618e-03 * YEAR,
- vy: 2.37847173959480950e-03 * YEAR,
- vz: -2.96589568540237556e-05 * YEAR,
+ pos: Vec3(1.28943695621391310e+01,
+ -1.51111514016986312e+01,
+ -2.23307578892655734e-01),
+ vel: Vec3(2.96460137564761618e-03 * YEAR,
+ 2.37847173959480950e-03 * YEAR,
+ -2.96589568540237556e-05 * YEAR),
mass: 4.36624404335156298e-05 * SOLAR_MASS,
},
// Neptune
Planet {
- x: 1.53796971148509165e+01,
- y: -2.59193146099879641e+01,
- z: 1.79258772950371181e-01,
- vx: 2.68067772490389322e-03 * YEAR,
- vy: 1.62824170038242295e-03 * YEAR,
- vz: -9.51592254519715870e-05 * YEAR,
+ pos: Vec3(1.53796971148509165e+01,
+ -2.59193146099879641e+01,
+ 1.79258772950371181e-01),
+ vel: Vec3(2.68067772490389322e-03 * YEAR,
+ 1.62824170038242295e-03 * YEAR,
+ -9.51592254519715870e-05 * YEAR),
mass: 5.15138902046611451e-05 * SOLAR_MASS,
},
];
-#[derive(Copy, Clone)]
+/// A 3d Vector type with oveloaded operators to improve readability.
+#[derive(Clone, Copy)]
+struct Vec3(pub f64, pub f64, pub f64);
+
+impl Vec3 {
+ fn zero() -> Self { Vec3(0.0, 0.0, 0.0) }
+
+ fn norm(&self) -> f64 { self.squared_norm().sqrt() }
+
+ fn squared_norm(&self) -> f64 {
+ self.0 * self.0 + self.1 * self.1 + self.2 * self.2
+ }
+}
+
+impl Add for Vec3 {
+ type Output = Self;
+ fn add(self, rhs: Self) -> Self {
+ Vec3(self.0 + rhs.0, self.1 + rhs.1, self.2 + rhs.2)
+ }
+}
+
+impl Sub for Vec3 {
+ type Output = Self;
+ fn sub(self, rhs: Self) -> Self {
+ Vec3(self.0 - rhs.0, self.1 - rhs.1, self.2 - rhs.2)
+ }
+}
+
+impl Mul<f64> for Vec3 {
+ type Output = Self;
+ fn mul(self, rhs: f64) -> Self {
+ Vec3(self.0 * rhs, self.1 * rhs, self.2 * rhs)
+ }
+}
+
+#[derive(Clone, Copy)]
struct Planet {
- x: f64, y: f64, z: f64,
- vx: f64, vy: f64, vz: f64,
+ pos: Vec3,
+ vel: Vec3,
mass: f64,
}
-fn advance(bodies: &mut [Planet;N_BODIES], dt: f64, steps: isize) {
- for _ in 0..steps {
- let mut b_slice: &mut [_] = bodies;
- loop {
- let bi = match shift_mut_ref(&mut b_slice) {
- Some(bi) => bi,
- None => break
- };
- for bj in &mut *b_slice {
- let dx = bi.x - bj.x;
- let dy = bi.y - bj.y;
- let dz = bi.z - bj.z;
-
- let d2 = dx * dx + dy * dy + dz * dz;
- let mag = dt / (d2 * d2.sqrt());
-
- let massj_mag = bj.mass * mag;
- bi.vx -= dx * massj_mag;
- bi.vy -= dy * massj_mag;
- bi.vz -= dz * massj_mag;
-
- let massi_mag = bi.mass * mag;
- bj.vx += dx * massi_mag;
- bj.vy += dy * massi_mag;
- bj.vz += dz * massi_mag;
- }
- bi.x += dt * bi.vx;
- bi.y += dt * bi.vy;
- bi.z += dt * bi.vz;
+/// Computes all pairwise position differences between the planets.
+fn pairwise_diffs(bodies: &[Planet; N_BODIES], diff: &mut [Vec3; N_PAIRS]) {
+ let mut bodies = bodies.iter();
+ let mut diff = diff.iter_mut();
+ while let Some(bi) = bodies.next() {
+ for bj in bodies.clone() {
+ *diff.next().unwrap() = bi.pos - bj.pos;
+ }
+ }
+}
+
+/// Computes the magnitude of the force between each pair of planets.
+fn magnitudes(diff: &[Vec3; N_PAIRS], dt: f64, mag: &mut [f64; N_PAIRS]) {
+ for (mag, diff) in mag.iter_mut().zip(diff.iter()) {
+ let d2 = diff.squared_norm();
+ *mag = dt / (d2 * d2.sqrt());
+ }
+}
+
+/// Updates the velocities of the planets by computing their gravitational
+/// accelerations and performing one step of Euler integration.
+fn update_velocities(bodies: &mut [Planet; N_BODIES], dt: f64,
+ diff: &mut [Vec3; N_PAIRS], mag: &mut [f64; N_PAIRS]) {
+ pairwise_diffs(bodies, diff);
+ magnitudes(&diff, dt, mag);
+
+ let mut bodies = &mut bodies[..];
+ let mut mag = mag.iter();
+ let mut diff = diff.iter();
+ while let Some(bi) = shift_mut_ref(&mut bodies) {
+ for bj in bodies.iter_mut() {
+ let diff = *diff.next().unwrap();
+ let mag = *mag.next().unwrap();
+ bi.vel = bi.vel - diff * (bj.mass * mag);
+ bj.vel = bj.vel + diff * (bi.mass * mag);
}
}
}
-fn energy(bodies: &[Planet;N_BODIES]) -> f64 {
+/// Advances the solar system by one timestep by first updating the
+/// velocities and then integrating the positions using the updated velocities.
+///
+/// Note: the `diff` & `mag` arrays are effectively scratch space. They're
+/// provided as arguments to avoid re-zeroing them every time `advance` is
+/// called.
+fn advance(mut bodies: &mut [Planet; N_BODIES], dt: f64,
+ diff: &mut [Vec3; N_PAIRS], mag: &mut [f64; N_PAIRS]) {
+ update_velocities(bodies, dt, diff, mag);
+ for body in bodies.iter_mut() {
+ body.pos = body.pos + body.vel * dt;
+ }
+}
+
+/// Computes the total energy of the solar system.
+fn energy(bodies: &[Planet; N_BODIES]) -> f64 {
let mut e = 0.0;
let mut bodies = bodies.iter();
- loop {
- let bi = match bodies.next() {
- Some(bi) => bi,
- None => break
- };
- e += (bi.vx * bi.vx + bi.vy * bi.vy + bi.vz * bi.vz) * bi.mass / 2.0;
- for bj in bodies.clone() {
- let dx = bi.x - bj.x;
- let dy = bi.y - bj.y;
- let dz = bi.z - bj.z;
- let dist = (dx * dx + dy * dy + dz * dz).sqrt();
- e -= bi.mass * bj.mass / dist;
- }
+ while let Some(bi) = bodies.next() {
+ e += bi.vel.squared_norm() * bi.mass / 2.0
+ - bi.mass * bodies.clone()
+ .map(|bj| bj.mass / (bi.pos - bj.pos).norm())
+ .fold(0.0, |a, b| a + b);
}
e
}
-fn offset_momentum(bodies: &mut [Planet;N_BODIES]) {
- let mut px = 0.0;
- let mut py = 0.0;
- let mut pz = 0.0;
- for bi in bodies.iter() {
- px += bi.vx * bi.mass;
- py += bi.vy * bi.mass;
- pz += bi.vz * bi.mass;
- }
- let sun = &mut bodies[0];
- sun.vx = - px / SOLAR_MASS;
- sun.vy = - py / SOLAR_MASS;
- sun.vz = - pz / SOLAR_MASS;
+/// Offsets the sun's velocity to make the overall momentum of the system zero.
+fn offset_momentum(bodies: &mut [Planet; N_BODIES]) {
+ let p = bodies.iter().fold(Vec3::zero(), |v, b| v + b.vel * b.mass);
+ bodies[0].vel = p * (-1.0 / bodies[0].mass);
}
fn main() {
.unwrap_or(1000)
};
let mut bodies = BODIES;
+ let mut diff = [Vec3::zero(); N_PAIRS];
+ let mut mag = [0.0f64; N_PAIRS];
offset_momentum(&mut bodies);
println!("{:.9}", energy(&bodies));
- advance(&mut bodies, 0.01, n);
+ for _ in (0..n) {
+ advance(&mut bodies, 0.01, &mut diff, &mut mag);
+ }
println!("{:.9}", energy(&bodies));
}
projects / rust.git / commitdiff