primal-slowsieve-0.3.1/.cargo_vcs_info.json0000644000000001560000000000100143410ustar { "git": { "sha1": "ebd1ba9d75e865d94a1d47c3451c5c14acf8183a" }, "path_in_vcs": "primal-slowsieve" }primal-slowsieve-0.3.1/Cargo.toml0000644000000023320000000000100123350ustar # THIS FILE IS AUTOMATICALLY GENERATED BY CARGO # # When uploading crates to the registry Cargo will automatically # "normalize" Cargo.toml files for maximal compatibility # with all versions of Cargo and also rewrite `path` dependencies # to registry (e.g., crates.io) dependencies. # # If you are reading this file be aware that the original Cargo.toml # will likely look very different (and much more reasonable). # See Cargo.toml.orig for the original contents. [package] edition = "2018" name = "primal-slowsieve" version = "0.3.1" authors = ["Huon Wilson "] description = """ A simple sieve of Eratosthenes designed for testing faster sieves. You probably want `primal-sieve`, or even just `primal` itself. """ homepage = "https://github.com/huonw/primal" documentation = "http://docs.rs/primal-slowsieve/" keywords = [ "math", "mathematics", "primes", "number-theory", ] license = "MIT OR Apache-2.0" repository = "https://github.com/huonw/primal" [[bench]] name = "bench" harness = false [dependencies.primal-bit] version = "0.3" [dependencies.primal-estimate] version = "0.3" [dev-dependencies.criterion] version = "0.3.4" features = ["html_reports"] [features] slow_tests = [] unstable = [] primal-slowsieve-0.3.1/Cargo.toml.orig000064400000000000000000000014561046102023000160240ustar 00000000000000[package] name = "primal-slowsieve" version = "0.3.1" authors = ["Huon Wilson "] edition = "2018" homepage = "https://github.com/huonw/primal" repository = "https://github.com/huonw/primal" documentation = "http://docs.rs/primal-slowsieve/" license = "MIT OR Apache-2.0" keywords = ["math", "mathematics", "primes", "number-theory"] description = """ A simple sieve of Eratosthenes designed for testing faster sieves. You probably want `primal-sieve`, or even just `primal` itself. """ [dependencies] primal-bit = { path = "../primal-bit", version = "0.3" } primal-estimate = { path = "../primal-estimate", version = "0.3" } [dev-dependencies] criterion = { version = "0.3.4", features = ["html_reports"] } [[bench]] name = "bench" harness = false [features] unstable = [] slow_tests = [] primal-slowsieve-0.3.1/LICENSE-APACHE000064400000000000000000000251371046102023000150630ustar 00000000000000 Apache License Version 2.0, January 2004 http://www.apache.org/licenses/ TERMS AND CONDITIONS FOR USE, REPRODUCTION, AND DISTRIBUTION 1. Definitions. "License" shall mean the terms and conditions for use, reproduction, and distribution as defined by Sections 1 through 9 of this document. "Licensor" shall mean the copyright owner or entity authorized by the copyright owner that is granting the License. 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See the License for the specific language governing permissions and limitations under the License. primal-slowsieve-0.3.1/LICENSE-MIT000064400000000000000000000020361046102023000145640ustar 00000000000000Copyright (c) 2014 Huon Wilson Permission is hereby granted, free of charge, to any person obtaining a copy of this software and associated documentation files (the "Software"), to deal in the Software without restriction, including without limitation the rights to use, copy, modify, merge, publish, distribute, sublicense, and/or sell copies of the Software, and to permit persons to whom the Software is furnished to do so, subject to the following conditions: The above copyright notice and this permission notice shall be included in all copies or substantial portions of the Software. THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, EXPRESS OR IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY, FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. IN NO EVENT SHALL THE AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING FROM, OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER DEALINGS IN THE SOFTWARE.primal-slowsieve-0.3.1/benches/bench.rs000064400000000000000000000014271046102023000161670ustar 00000000000000#[macro_use] extern crate criterion; use criterion::Criterion; use primal_slowsieve::Primes; const SIZES: [usize; 4] = [100, 10_000, 100_000, 1_000_000]; fn sieve(c: &mut Criterion) { let mut group = c.benchmark_group("Primes::sieve"); for i in &SIZES { group.bench_with_input(i.to_string(), i, |b, upto: &usize| { b.iter(|| Primes::sieve(*upto)) }); } group.finish(); } fn primes(c: &mut Criterion) { let mut group = c.benchmark_group("Primes::primes"); for i in &SIZES { group.bench_with_input(i.to_string(), i, |b, upto: &usize| { let s = Primes::sieve(*upto); b.iter(|| s.primes().count()) }); } group.finish(); } criterion_group!(benches, sieve, primes); criterion_main!(benches); primal-slowsieve-0.3.1/src/lib.rs000064400000000000000000000303571046102023000150420ustar 00000000000000//! Sieve small numbers. //! //! This is designed to be used via the `primal` crate. use primal_bit::BitVec; use std::{iter, cmp}; /// Stores information about primes up to some limit. /// /// This uses at least `limit / 16 + O(1)` bytes of storage. #[derive(Debug)] pub struct Primes { // This only stores odd numbers, since even numbers are mostly // non-prime. // // This indicates which numbers are composite. v: BitVec } /// Iterator over the primes stored in a sieve. #[derive(Clone)] pub struct PrimeIterator<'a> { two: bool, iter: iter::Enumerate>, } impl Primes { /// Construct a `Primes` via a sieve up to at least `limit`. /// /// This stores all primes less than `limit` (and possibly some /// more), allowing for very efficient iteration and primality /// testing below this, and guarantees that all numbers up to /// `limit^2` can be factorised. pub fn sieve(limit: usize) -> Primes { // having this out-of-line like this is faster (130 us/iter // vs. 111 us/iter on sieve_large), and using a manual while // rather than a `range_step` is a similar speedup. #[inline(never)] fn filter(is_prime: &mut BitVec, limit: usize, p: usize) { let mut zero = p * p / 2; while zero < limit / 2 { is_prime.set(zero, true); zero += p; } } // bad stuff happens for very small bounds. let limit = cmp::max(10, limit); let mut is_prime = BitVec::from_elem((limit + 1) / 2, false); // 1 isn't prime is_prime.set(0, true); // multiples of 3 aren't prime (3 is handled separately, so // the ticking works properly) filter(&mut is_prime, limit, 3); let bound = (limit as f64).sqrt() as usize + 1; // skip 2. let mut check = 2; let mut tick = if check % 3 == 1 {2} else {1}; while check <= bound { if !is_prime[check] { filter(&mut is_prime, limit, 2 * check + 1) } check += tick; tick = 3 - tick; } Primes { v: is_prime } } /// The largest number stored. pub fn upper_bound(&self) -> usize { self.v.len() * 2 } /// Check if `n` is prime, possibly failing if `n` is larger than /// the upper bound of this Primes instance. pub fn is_prime(&self, n: usize) -> bool { if n % 2 == 0 { // 2 is the evenest prime. n == 2 } else { assert!(n <= self.upper_bound()); !self.v[n / 2] } } /// Iterator over the primes stored in this map. pub fn primes(&self) -> PrimeIterator<'_> { PrimeIterator { two: true, iter: self.v.iter().enumerate() } } /// Factorise `n` into (prime, exponent) pairs. /// /// Returns `Err((leftover, partial factorisation))` if `n` cannot /// be fully factored, or if `n` is zero (`leftover == 0`). A /// number can not be completely factored if and only if the prime /// factors of `n` are too large for this sieve, that is, if there /// is /// /// - a prime factor larger than `U^2`, or /// - more than one prime factor between `U` and `U^2` /// /// where `U` is the upper bound of the primes stored in this /// sieve. /// /// Notably, any number between `U` and `U^2` can always be fully /// factored, since these numbers are guaranteed to only have zero /// or one prime factors larger than `U`. pub fn factor(&self, mut n: usize) -> Result, (usize, Vec<(usize, usize)>)> { if n == 0 { return Err((0, vec![])) } let mut ret = Vec::new(); for p in self.primes() { if n == 1 { break } let mut count = 0; while n % p == 0 { n /= p; count += 1; } if count > 0 { ret.push((p,count)); } } if n != 1 { let b = self.upper_bound(); if b * b >= n { // n is not divisible by anything from 1..=sqrt(n), so // must be prime itself! (That is, even though we // don't know this prime specifically, we can infer // that it must be prime.) ret.push((n, 1)); } else { // large factors :( return Err((n, ret)) } } Ok(ret) } /// Count the primes upto and including `n`. /// /// # Panics /// /// `count_upto` panics if `n > self.upper_bound()`. pub fn count_upto(&self, n: usize) -> usize { if n < 2 { return 0 } assert!(n <= self.upper_bound()); let bit = (n + 1) / 2; 1 + (bit - self.v.count_ones_before(bit)) } } impl<'a> Iterator for PrimeIterator<'a> { type Item = usize; #[inline] fn next(&mut self) -> Option { if self.two { self.two = false; Some(2) } else { for (i, is_not_prime) in &mut self.iter { if !is_not_prime { return Some(2 * i + 1) } } None } } fn size_hint(&self) -> (usize, Option) { let mut iter = self.clone(); // TODO: this doesn't run in constant time, is it super-bad? match (iter.next(), iter.next_back()) { (Some(lo), Some(hi)) => { let (below_hi, above_hi) = primal_estimate::prime_pi(hi as u64); let (below_lo, above_lo) = primal_estimate::prime_pi(lo as u64); ((below_hi - cmp::min(above_lo, below_hi)) as usize, Some((above_hi - below_lo + 1) as usize)) } (Some(_), None) => (1, Some(1)), (None, _) => (0, Some(0)) } } } impl<'a> DoubleEndedIterator for PrimeIterator<'a> { #[inline] fn next_back(&mut self) -> Option { loop { match self.iter.next_back() { Some((i, false)) => return Some(2 * i + 1), Some((_, true)) => {/* continue */} None if self.two => { self.two = false; return Some(2) } None => return None } } } } #[cfg(test)] mod tests { use super::Primes; #[test] fn is_prime() { let primes = Primes::sieve(1000); let tests = [ (0, false), (1, false), (2, true), (3, true), (4, false), (5, true), (6, false), (7, true), (8, false), (9, false), (10, false), (11, true) ]; for &(n, expected) in tests.iter() { assert_eq!(primes.is_prime(n), expected); } } #[test] fn upper_bound() { for i in 1..1000 { let primes = Primes::sieve(i); assert!(primes.upper_bound() >= i); } let range = if cfg!(feature = "slow_tests") { 1..200 } else { 100..120 }; for i in range { let i = i * 10000; let primes = Primes::sieve(i); assert!(primes.upper_bound() >= i); } } #[test] fn primes_iterator() { let primes = Primes::sieve(50); let mut expected = [2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37, 41, 43, 47]; assert_eq!(primes.primes().collect::>(), expected); expected.reverse(); assert_eq!(primes.primes().rev().collect::>(), expected); } #[test] fn factor() { let primes = Primes::sieve(1000); let tests: &[(usize, &[(usize, usize)])] = &[ (1, &[]), (2, &[(2_usize, 1)]), (3, &[(3, 1)]), (4, &[(2, 2)]), (5, &[(5, 1)]), (6, &[(2, 1), (3, 1)]), (7, &[(7, 1)]), (8, &[(2, 3)]), (9, &[(3, 2)]), (10, &[(2, 1), (5, 1)]), (2*2*2*2*2 * 3*3*3*3*3, &[(2, 5), (3,5)]), (2*3*5*7*11*13*17*19, &[(2,1), (3,1), (5,1), (7,1), (11,1), (13,1), (17,1), (19,1)]), // a factor larger than that stored in the map (7561, &[(7561, 1)]), (2*7561, &[(2, 1), (7561, 1)]), (4*5*7561, &[(2, 2), (5,1), (7561, 1)]), ]; for &(n, expected) in tests.iter() { assert_eq!(primes.factor(n), Ok(expected.to_vec())); } } #[test] fn factor_compare() { let short = Primes::sieve(30); let long = Primes::sieve(10000); let short_lim = short.upper_bound() * short.upper_bound() + 1; // every number less than bound^2 can be factored (since they // always have a factor <= bound). for n in 0..short_lim { assert_eq!(short.factor(n), long.factor(n)) } // larger numbers can only sometimes be factored 'next_n: for n in short_lim..10000 { let possible = short.factor(n); let real = long.factor(n).ok().unwrap(); let mut seen_small = None; for (this_idx, &(p,i)) in real.iter().enumerate() { let last_short_prime = if p >= short_lim { this_idx } else if p > short.upper_bound() { match seen_small { Some(idx) => idx, None if i > 1 => this_idx, None => { // we can cope with one seen_small = Some(this_idx); continue } } } else { // small enough continue }; // break into the two parts let (low, hi) = real.split_at(last_short_prime); let leftover = hi.iter().fold(1, |x, &(p, i)| x * p.pow(i as u32)); assert_eq!(possible, Err((leftover, low.to_vec()))); continue 'next_n; } // if we're here, we know that everything should match assert_eq!(possible, Ok(real)) } } #[test] fn factor_failures() { let primes = Primes::sieve(30); assert_eq!(primes.factor(0), Err((0, vec![]))); // can only handle one large factor assert_eq!(primes.factor(31 * 31), Err((31 * 31, vec![]))); assert_eq!(primes.factor(2 * 3 * 31 * 31), Err((31 * 31, vec![(2, 1), (3, 1)]))); // prime that's too large (bigger than 30*30). assert_eq!(primes.factor(7561), Err((7561, vec![]))); assert_eq!(primes.factor(2 * 3 * 7561), Err((7561, vec![(2, 1), (3, 1)]))); } #[test] fn size_hint() { let mut i = 0; while i < 1000 { let sieve = Primes::sieve(i); let mut primes = sieve.primes(); // check the size hint at each and every iteration loop { let (lo, hi) = primes.size_hint(); let copy = primes.clone(); let len = copy.count(); let next = primes.next(); assert!(lo <= len && len <= hi.unwrap(), "found failing size_hint for {:?} to {}, should satisfy: {} <= {} <= {:?}", next, i, lo, len, hi); if next.is_none() { break } } i += 100; } } #[test] fn count_upto() { let (limit, mult) = if cfg!(feature = "slow_tests") { (2_000_000, 19_998) } else { (200_000, 1_998) }; let sieve = Primes::sieve(limit); for i in (0..20).chain((0..100).map(|n| n * mult + 1)) { let val = sieve.count_upto(i); let true_ = sieve.primes().take_while(|p| *p <= i).count(); assert!(val == true_, "failed for {}, true {}, computed {}", i, true_, val) } } }