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#![warn(missing_docs)] #![warn(missing_doc_code_examples)] //! # Prime Number Iterator and Calculations //! //! This library provides a structure for iterating through prime numbers //! as well as methods for calculating prime factors and classifying //! numbers as prime or composite. //! # Using this library //! //! Add the following to your `Cargo.toml` file //! ```toml //! [dependencies] //! elr_primes = "0.1.0" //! ``` //! //! # Examples //! //! Basic Usage: //! ```rust //! use elr_primes::Primes; //! //! // Provides an iterator for all prime numbers less than or equal to 1000 //! let mut p = Primes::new(1000); //! ``` //! //! Once the structure has been initiated, the `primes()` method provides an iterator //! for the prime numbers. //! //! ```rust //! # use elr_primes::Primes; //! let p = Primes::new(10); // Primes less than or equal to 10 //! let mut prime_iter = p.primes(); //! let primes: Vec<usize> = prime_iter.copied().collect(); //! let expected: [usize; 4] = [2, 3, 5, 7]; //! assert_eq!(primes, expected); //! ``` //! //! Since `primes()` returns an iterator, you can also use it to directly find a specific //! prime number. //! //! ```rust //! # use elr_primes::Primes; //! let p = Primes::new(100); // Primes less than or equal to 100 //! let n = 20; //! //! // Iterators are zero-based, so to get the 20th prime we need to search for the 19th //! match p.primes().nth(n - 1) { //! Some(x) => println!("The {}th prime is: {}", n, x), //! None => println!("The {}th prime is outside the current bounds", n) //! }; //! ``` //! //! Methods are also available to find the prime factors of a number, and whether a //! number is prime or composite. //! //! ```rust //! use elr_primes::{Primes, Primality}; //! let p = Primes::new(100); //! //! let n = 96; //! match p.factors(n) { //! Ok(factors) => println!("{:?}", factors), //! Err(_) => println!("Could not find all prime factors within the bounds"), //! }; //! //! let n = 23; //! match p.primality(n) { //! Primality::Prime => println!("{} is prime", n), //! Primality::Composite => println!("{} is composite", n), //! Primality::Unknown => println!("Primality of {} is undetermined", n), //! }; //! ``` use std::slice::Iter; use std::sync::mpsc; use std::thread; /// Vector of prime factor tuples. /// /// Factors are stored as a tuple, with the first entry being the prime value /// and the second entry being the exponent to raise the value to. /// /// # Example /// ```rust /// use elr_primes::Factors; /// /// let factors_of_18: Factors = vec![(2, 1), (3, 2)]; // 2^1 * 3^2 = 18 /// ``` pub type Factors = Vec<(usize, usize)>; /// Primality types for numbers. #[derive(Debug, PartialEq, Eq)] pub enum Primality { /// A number is prime Prime, /// A number is composite Composite, /// A number couldn't be classified as prime or composite /// with the current bound of primes Unknown, } /// Prime Iterator /// /// This provides an iterator over prime numbers up to a given maximum value. /// The inclusive upper bound for prime numbers is provided when the structure /// is instantiated. /// #[derive(Debug, PartialEq, Eq)] pub struct Primes { primes: Vec<usize>, bound: usize, } impl Primes { /// Create a new `Primes` instance. /// /// The maximum bound for prime numbers is passed as a parameter to `new()`. If the bound is /// less than 2, then the iterator will provide no primes. /// /// The method spawns threads to generate blocks of threads concurrently. /// /// # Example /// /// ```rust /// use elr_primes::Primes; /// /// // Create an iterator for primes that are less than or equal to 1000 /// let p = Primes::new(1000); /// ``` pub fn new(bound: usize) -> Self { let block = 500000; let mut primes = vec![]; let mut seed_primes = vec![]; if bound > 1 { let root = (bound as f64).sqrt() as usize; let mut sieve = vec![true; root + 1]; for i in 2..=root { if sieve[i] { seed_primes.push(i); for j in (i * i..=root).step_by(i) { sieve[j] = false; } } } let mut k = 0; let (tx, rx) = mpsc::channel(); while k * block <= bound { let t_k = k; let t_block = block; let t_bound = bound; let t_primes = seed_primes.clone(); let t_tx = mpsc::Sender::clone(&tx); thread::spawn(move || { let mut sieve = vec![true; t_block]; let start = t_k * t_block; for p in &t_primes { let start_index = (start + p - 1) / p; let start_index = if start_index > *p { start_index } else { *p } * *p - start; for j in (start_index..t_block).step_by(*p) { sieve[j] = false; } } if t_k == 0 { sieve[0] = false; sieve[1] = false; } let result = &mut sieve.iter().enumerate().filter_map(|(v, &p)| if p && v + start <= t_bound { Some(v + start) } else { None }).collect::<Vec<usize>>(); t_tx.send(result.clone()).unwrap(); }); k += 1; } drop(tx); for mut received in rx { primes.append(&mut received); } primes.sort(); } Primes { primes, bound } } /// Find the prime factors for a number. /// /// Returns a [`Factor`] type containing the factors for the number. /// /// # Errors /// /// If the the number has prime factors that are outside of the current bounds, /// a tuple is returned with the first element as a [`Factor`] type containing /// the in-bound factors found for the number, and the second element as the remainder /// value that could not be factored within the current bounds. /// /// [`Factor`]: type.Factors.html /// /// # Example /// /// ```rust /// # use elr_primes::Primes; /// let p = Primes::new(10); /// /// let factors = p.factors(40); /// assert!(factors.is_ok()); /// assert_eq!(factors.ok(), Some(vec![(2, 3), (5, 1)])); // 2^3 * 5^1 = 40 /// /// let factors = p.factors(429); /// assert!(factors.is_err()); /// assert_eq!(factors.err(), Some((vec![(3, 1)], 143))); // 3^1 is a prime factor of 429 /// // but the remainder 143 has no /// // factors in bounds /// ``` pub fn factors(&self, value: usize) -> Result<Factors, (Factors, usize)> { let mut value = value; let mut count: usize; let mut result = vec![]; for factor in &self.primes { count = 0; while value % factor == 0 { value /= factor; count += 1; } if count > 0 { result.push((*factor, count)); } } if value > 1 { if self.primality(value) != Primality::Prime { return Err((result, value)); } else { result.push((value, 1)); } } Ok(result) } /// Returns the primality of a number. /// /// This method tries to determine the primality of a given number through /// trial division of the primes that are less than the square root of the /// given number. /// /// Returns: /// * [`Primality::Composite`] - A prime was found that is a factor of the number /// * [`Primality::Prime`] - No prime was found that is a factor of the number, and the /// square root of the number is not greater than the current bounds /// * [`Primality::Unknown`] - No prime was found that is a factor of the number, but the /// square root fo the number is greater than the current bounds /// /// [`Primality::Composite`]: enum.Primality.html /// [`Primality::Prime`]: enum.Primality.html /// [`Primality::Unknown`]: enum.Primality.html /// /// # Example /// /// ```rust /// use elr_primes::{Primality, Primes}; /// /// let p = Primes::new(31); /// assert_eq!(p.primality(953), Primality::Prime); /// assert_eq!(p.primality(959), Primality::Composite); /// assert_eq!(p.primality(967), Primality::Unknown); // 967 is prime, but it's square root /// // is greater than the current bound /// // so it cannot be definitively known /// // as prime through trial division /// /// assert_eq!(p.primality(969), Primality::Composite); // The square root of 969 is also /// // greater than the current bound, but /// // it has a factor (3) that is within /// // the bounds, so it can be classified /// // as a composite number /// ``` pub fn primality(&self, value: usize) -> Primality { if value <= self.bound { return if self.primes.contains(&value) { Primality::Prime } else { Primality::Composite }; } let root = (value as f64).sqrt(); for prime in self.primes.iter().filter(|&x| *x as f64 <= root) { if value % prime == 0 { return Primality::Composite; } } if root > self.bound as f64 { return Primality::Unknown; } Primality::Prime } /// Returns an iterator for the bound prime numbers. /// /// # Example /// /// ```rust /// # use elr_primes::Primes; /// let p = Primes::new(100); /// /// // Print all of the primes below 100 /// for prime_value in p.primes() { /// println!("{}", prime_value); /// } /// ``` pub fn primes(&self) -> Iter<usize> { self.primes.iter() } } #[cfg(test)] mod tests { use super::{Factors, Primality, Primes}; #[test] fn generates_the_first_100_primes() { let p = Primes::new(541); // 541 is the 100th prime, so bounding here should include it let primes: Vec<usize> = p.primes().copied().collect(); assert_eq!( primes, vec![ 2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37, 41, 43, 47, 53, 59, 61, 67, 71, 73, 79, 83, 89, 97, 101, 103, 107, 109, 113, 127, 131, 137, 139, 149, 151, 157, 163, 167, 173, 179, 181, 191, 193, 197, 199, 211, 223, 227, 229, 233, 239, 241, 251, 257, 263, 269, 271, 277, 281, 283, 293, 307, 311, 313, 317, 331, 337, 347, 349, 353, 359, 367, 373, 379, 383, 389, 397, 401, 409, 419, 421, 431, 433, 439, 443, 449, 457, 461, 463, 467, 479, 487, 491, 499, 503, 509, 521, 523, 541, ] ); } #[test] fn no_primes_below_2() { let p = Primes::new(0); let primes: Vec<usize> = p.primes().copied().collect(); assert!(primes.is_empty()); let p = Primes::new(1); let primes: Vec<usize> = p.primes().copied().collect(); assert!(primes.is_empty()); let p = Primes::new(2); let primes: Vec<usize> = p.primes().copied().collect(); assert_eq!(primes, vec![2]); } #[test] fn prime_factorization() { let p = Primes::new(7); let expected: Factors = vec![(2, 1)]; assert_eq!(expected, p.factors(2).unwrap()); let expected: Factors = vec![(3, 1)]; assert_eq!(expected, p.factors(3).unwrap()); let expected: Factors = vec![(2, 2)]; assert_eq!(expected, p.factors(4).unwrap()); let expected: Factors = vec![(2, 3), (3, 2), (5, 1)]; assert_eq!(expected, p.factors(360).unwrap()); let expected: Factors = vec![(2, 1), (3, 2), (5, 3), (7, 4), (11, 1)]; assert_eq!(expected, p.factors(59424750).unwrap()); } #[test] fn composite_with_out_of_bound_factor() { let p = Primes::new(5); let expected: (Factors, usize) = (vec![(3, 1), (5, 1)], 29); assert_eq!(p.factors(435).err(), Some(expected)); let expected: (Factors, usize) = (vec![(2, 3), (3, 2), (5, 1)], 31); assert_eq!(p.factors(11160).err(), Some(expected)); } #[test] fn identifies_primes_within_bounds() { let p = Primes::new(2); assert_eq!(p.primality(2), Primality::Prime); assert_eq!(p.primality(4), Primality::Composite); assert_eq!(p.primality(5), Primality::Unknown); assert_eq!(p.primality(100_000_000), Primality::Composite); let p = Primes::new(31); assert_eq!(p.primality(3), Primality::Prime); assert_eq!(p.primality(953), Primality::Prime); assert_eq!(p.primality(959), Primality::Composite); assert_eq!(p.primality(967), Primality::Unknown); } }