4cbbb340ad
* benches/generators.rs: standardize thread_rng benchmarks * Remove cfgs from examples * Remove ReadRng * Add ThreadRng::reseed and doc to use * Remove fork protection from ReseedingRng; remove libc dep * Enable ReseedingRng without std * Move ReseedingRng up; remove module rand::rngs::adapter
81 lines
3.1 KiB
Rust
81 lines
3.1 KiB
Rust
// Copyright 2018 Developers of the Rand project.
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// Copyright 2013-2018 The Rust Project Developers.
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//
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// Licensed under the Apache License, Version 2.0 <LICENSE-APACHE or
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// https://www.apache.org/licenses/LICENSE-2.0> or the MIT license
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// <LICENSE-MIT or https://opensource.org/licenses/MIT>, at your
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// option. This file may not be copied, modified, or distributed
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// except according to those terms.
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//! # Monte Carlo estimation of π with a chosen seed and rayon for parallelism
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//!
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//! Imagine that we have a square with sides of length 2 and a unit circle
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//! (radius = 1), both centered at the origin. The areas are:
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//!
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//! ```text
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//! area of circle = πr² = π * r * r = π
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//! area of square = 2² = 4
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//! ```
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//!
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//! The circle is entirely within the square, so if we sample many points
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//! randomly from the square, roughly π / 4 of them should be inside the circle.
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//!
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//! We can use the above fact to estimate the value of π: pick many points in
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//! the square at random, calculate the fraction that fall within the circle,
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//! and multiply this fraction by 4.
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//!
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//! Note on determinism:
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//! It's slightly tricky to build a parallel simulation using Rayon
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//! which is both efficient *and* reproducible.
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//!
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//! Rayon's ParallelIterator api does not guarantee that the work will be
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//! batched into identical batches on every run, so we can't simply use
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//! map_init to construct one RNG per Rayon batch.
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//!
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//! Instead, we do our own batching, so that a Rayon work item becomes a
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//! batch. Then we can fix our rng stream to the batched work item.
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//! Batching amortizes the cost of constructing the Rng from a fixed seed
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//! over BATCH_SIZE trials. Manually batching also turns out to be faster
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//! for the nondeterministic version of this program as well.
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use rand::distributions::{Distribution, Uniform};
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use rand_chacha::{rand_core::SeedableRng, ChaCha8Rng};
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use rayon::prelude::*;
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static SEED: u64 = 0;
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static BATCH_SIZE: u64 = 10_000;
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static BATCHES: u64 = 1000;
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fn main() {
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let range = Uniform::new(-1.0f64, 1.0).unwrap();
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let in_circle = (0..BATCHES)
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.into_par_iter()
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.map(|i| {
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let mut rng = ChaCha8Rng::seed_from_u64(SEED);
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// We chose ChaCha because it's fast, has suitable statistical properties for simulation,
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// and because it supports this set_stream() api, which lets us choose a different stream
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// per work item. ChaCha supports 2^64 independent streams.
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rng.set_stream(i);
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let mut count = 0;
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for _ in 0..BATCH_SIZE {
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let a = range.sample(&mut rng);
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let b = range.sample(&mut rng);
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if a * a + b * b <= 1.0 {
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count += 1;
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}
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}
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count
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})
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.sum::<usize>();
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// assert this is deterministic
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assert_eq!(in_circle, 7852263);
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// prints something close to 3.14159...
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println!(
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"π is approximately {}",
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4. * (in_circle as f64) / ((BATCH_SIZE * BATCHES) as f64)
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);
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}
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