[deps] cargo update

[code] remove unnecessary reference
[fix] but primes behind an Arc
2025-05-29 11:33:43 +02:00 · 2024-09-28 12:59:31 +02:00 · 2024-09-28 12:57:29 +02:00 · 2024-09-12 20:35:23 +02:00
5 changed files with 167 additions and 502 deletions
@@ -3,184 +3,23 @@
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@@ -1,10 +1,10 @@
 [package]
 name = "hcn"
-version = "1.0.0"
-edition = "2024"
+version = "1.0.0-multithread"
+edition = "2021"

 [dependencies]
-clap = { version = "4", features = ["derive"] }
+itertools = "0.14"

 [lints.rust]
 unsafe_code = "forbid"
@@ -1,72 +0,0 @@
-# hcn
-
-Find highly composite numbers up to a search limit.
-
-```bash
-cargo run --release -- [SEARCH_LIMIT]
-```
-
-If no limit is given, the default is `1_000_000_000`.
-Use `--help` to see the generated command-line help and `--version` to print
-the package version.
-
-## Structure
-
- `src/main.rs`
-  - Command-line interface: parses the optional `SEARCH_LIMIT` argument with
-    `clap` and rejects non-positive limits before the search starts.
-  - Search setup: defines the default limit and the fixed prime list used for
-    candidate generation.
-  - Candidate generation: recursively builds only exponent sequences that can
-    produce highly composite record candidates.
-  - Record filtering: sorts candidates and prints each new divisor-count record.
-
-## Algorithm
-
-A number with prime factorization
-
-```text
-n = 2^a * 3^b * 5^c * ...
-```
-
-has
-
-```text
-(a + 1) * (b + 1) * (c + 1) * ...
-```
-
-divisors.
-
-The exact primes do not affect the divisor count; only the exponents do.
-For a fixed exponent list, the smallest possible number is made by putting the
-largest exponent on the smallest prime:
-
-```text
-a >= b >= c >= ...
-```
-
-If a larger exponent appears on a larger prime, swapping those two exponents
-keeps the divisor count unchanged but makes the number smaller.
-
-So a highly composite number cannot have that shape. If it did, the smaller
-swapped number would already have the same number of divisors, so the original
-number would not be the first record.
-
-That means record candidates are only numbers like:
-
-```text
-2^a * 3^b * 5^c * ...  where a >= b >= c >= ...
-```
-
-All other numbers are redundant for finding new records.
-
-The program:
-
-1. Recursively generates numbers from the first primes.
-2. Only tries exponent sequences where each exponent is no larger than the
-   previous one.
-3. Stops a branch as soon as the number exceeds the search limit.
-4. Computes the divisor count directly from the exponents.
-5. Sorts candidates by number and prints each new divisor-count record.
-
-This avoids factoring every number in the range.
@@ -1,278 +1,126 @@
-use std::{num::NonZeroU64, time::Instant};
+mod sieve;

-use clap::Parser;
+use std::{
+    collections::HashMap,
+    env,
+    sync::Arc,
+    thread::{self, available_parallelism},
+    time::Instant,
+};

-const DEFAULT_SEARCH_LIMIT: u64 = 1_000_000_000;
-const FIRST_PRIMES: &[u64] = &[2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31];
+use itertools::Itertools as _;
+use sieve::get_primes;

-#[derive(Debug, Parser)]
-#[command(version, about = "Find highly composite numbers up to a search limit")]
-struct Cli {
-    #[arg(value_name = "SEARCH_LIMIT", default_value_t = NonZeroU64::new(DEFAULT_SEARCH_LIMIT).expect("default search limit is non-zero"))]
-    search_limit: NonZeroU64,
+const MAX_SIEVED_PRIMES: usize = 100_000_000;
+
+fn count_prime_factor_exponent(prime: u64, mut nr: u64) -> u64 {
+    let mut count = 0;
+
+    while nr % prime == 0 {
+        nr /= prime;
+        count += 1;
    }

-#[derive(Clone, Copy, Debug, Eq, PartialEq)]
-struct Candidate {
-    nr: u64,
-    divisors: u64,
+    count
 }

-fn max_exponent(limit: u64) -> u64 {
-    let mut exponent = 0;
-    let mut nr = 1_u64;
+fn prime_factors(nr: u64, primes: &[u64]) -> u64 {
+    let mut num_teilers = 1;

-    while let Some(next_nr) = nr.checked_mul(2) {
-        if next_nr > limit {
+    // safety: nr <= 2.pow(53) must be fulfilled,
+    //         otherwise we have a precision loss
+    assert!(nr <= 2u64.pow(53));
+    #[allow(
+        clippy::cast_sign_loss,
+        clippy::cast_possible_truncation,
+        clippy::cast_precision_loss
+    )]
+    let nr_sqrt = (nr as f64).sqrt().ceil() as u64;
+
+    for prime in primes {
+        if *prime > nr_sqrt {
            break;
        }

-        nr = next_nr;
-        exponent += 1;
-    }
-
-    exponent
-}
-
-fn collect_hcn_candidates(
-    limit: u64,
-    prime_idx: usize,
-    max_exponent: u64,
-    nr: u64,
-    divisors: u64,
-    candidates: &mut Vec<Candidate>,
-) {
-    let Some(&prime) = FIRST_PRIMES.get(prime_idx) else {
-        return;
-    };
-
-    let mut next_nr = nr;
-
-    for exponent in 1..=max_exponent {
-        let Some(multiplied_nr) = next_nr.checked_mul(prime) else {
-            break;
-        };
-
-        if multiplied_nr > limit {
-            break;
-        }
-
-        next_nr = multiplied_nr;
-        let next_divisors = divisors * (exponent + 1);
-
-        candidates.push(Candidate {
-            nr: next_nr,
-            divisors: next_divisors,
-        });
-
-        collect_hcn_candidates(
-            limit,
-            prime_idx + 1,
-            exponent,
-            next_nr,
-            next_divisors,
-            candidates,
-        );
+        let count = count_prime_factor_exponent(*prime, nr);
+        if count > 0 {
+            num_teilers *= count + 1;
        }
    }

-fn has_enough_primes(limit: u64) -> bool {
-    let mut primorial = 1_u64;
-
-    for &prime in FIRST_PRIMES {
-        let Some(next_primorial) = primorial.checked_mul(prime) else {
-            return true;
-        };
-
-        if next_primorial > limit {
-            return true;
+    num_teilers
 }

-        primorial = next_primorial;
+fn the_thread(mut start: u64, end: u64, primes: &[u64]) -> HashMap<u64, u64> {
+    let mut max_teilers = 0;
+    let mut max_teilers_hashmap = HashMap::new();
+
+    let mut step_size = 10;
+
+    if start == 0 {
+        start = 2;
+        step_size = 2;
    }

-    false
-}
-
-fn hcn_records(limit: u64) -> Vec<Candidate> {
-    assert!(
-        has_enough_primes(limit),
-        "not enough primes for search limit"
-    );
-
-    let mut candidates = Vec::new();
-    collect_hcn_candidates(limit, 0, max_exponent(limit), 1, 1, &mut candidates);
-    candidates.sort_unstable_by_key(|candidate| candidate.nr);
-
-    let mut records = Vec::new();
-    let mut max_divisors = 0;
-
-    for candidate in candidates {
-        if candidate.divisors > max_divisors {
-            records.push(candidate);
-            max_divisors = candidate.divisors;
+    for nr in (start..=end).step_by(step_size) {
+        let teilers = prime_factors(nr, primes);
+        if teilers > max_teilers {
+            max_teilers = teilers;
+            max_teilers_hashmap.insert(nr, teilers);
        }
    }

-    records
+    max_teilers_hashmap
+}
+
+fn calculate_chunk_bounds(i: usize, num_threads: usize, max_nr: usize) -> (usize, usize) {
+    let chunk_size = max_nr / num_threads;
+    let start = i * chunk_size;
+    let end = ((i + 1) * chunk_size).min(max_nr);
+    (start, end)
 }

 fn main() {
-    let search_limit = Cli::parse().search_limit.get();
+    let max_nr = env::args()
+        .nth(1)
+        .expect("Usage: hcn <max_nr>")
+        .parse::<usize>()
+        .expect("Invalid max_nr");

    let start = Instant::now();
-    let records = hcn_records(search_limit);
+    println!("Precalculating primes...");
+    let primes = get_primes(MAX_SIEVED_PRIMES);
+    println!("{} primes. Took {:?}", primes.len(), start.elapsed());

-    for Candidate { nr, divisors } in records {
-        println!("{nr}: {divisors} ({:?} since start)", start.elapsed());
+    let primes = Arc::new(primes);
+
+    #[allow(clippy::unwrap_used)]
+    let num_threads = available_parallelism().unwrap().get();
+    let mut threads = Vec::with_capacity(num_threads);
+
+    let now = Instant::now();
+    for i in 0..num_threads {
+        let (start, end) = calculate_chunk_bounds(i, num_threads, max_nr);
+        let primes = primes.clone();
+        threads.push(thread::spawn(move || {
+            the_thread(start as u64, end as u64, &primes)
+        }));
+    }
+
+    let mut results = HashMap::new();
+    for thread in threads {
+        let thread_result = thread.join().expect("Thread failed to join (panicked?)");
+        results.extend(thread_result);
+    }
+
+    let mut max_teilers = 0;
+
+    for (nr, teilers) in results.into_iter().sorted() {
+        if teilers > max_teilers {
+            println!("{nr}: {teilers}");
+            max_teilers = teilers;
        }
    }

-#[cfg(test)]
-mod tests {
-    use clap::Parser;
-
-    use super::{Candidate, Cli, DEFAULT_SEARCH_LIMIT, hcn_records, max_exponent};
-
-    fn count_divisors(mut nr: u64) -> u64 {
-        let mut divisor_count = 1;
-        let mut divisor = 2;
-
-        while divisor * divisor <= nr {
-            let mut exponent = 0;
-
-            while nr.is_multiple_of(divisor) {
-                nr /= divisor;
-                exponent += 1;
-            }
-
-            if exponent > 0 {
-                divisor_count *= exponent + 1;
-            }
-
-            divisor += if divisor == 2 { 1 } else { 2 };
-        }
-
-        if nr > 1 {
-            divisor_count *= 2;
-        }
-
-        divisor_count
-    }
-
-    fn brute_force_hcn_records(limit: u64) -> Vec<Candidate> {
-        let mut records = Vec::new();
-        let mut max_divisors = 0;
-
-        for nr in 2..=limit {
-            let divisors = count_divisors(nr);
-
-            if divisors > max_divisors {
-                records.push(Candidate { nr, divisors });
-                max_divisors = divisors;
-            }
-        }
-
-        records
-    }
-
-    #[test]
-    fn max_exponent_counts_powers_of_two_up_to_limit() {
-        assert_eq!(max_exponent(1), 0);
-        assert_eq!(max_exponent(2), 1);
-        assert_eq!(max_exponent(3), 1);
-        assert_eq!(max_exponent(16), 4);
-    }
-
-    #[test]
-    fn finds_highly_composite_records_up_to_one_thousand() {
-        let records = hcn_records(1_000);
-
-        assert_eq!(
-            records,
-            vec![
-                Candidate { nr: 2, divisors: 2 },
-                Candidate { nr: 4, divisors: 3 },
-                Candidate { nr: 6, divisors: 4 },
-                Candidate {
-                    nr: 12,
-                    divisors: 6,
-                },
-                Candidate {
-                    nr: 24,
-                    divisors: 8,
-                },
-                Candidate {
-                    nr: 36,
-                    divisors: 9,
-                },
-                Candidate {
-                    nr: 48,
-                    divisors: 10,
-                },
-                Candidate {
-                    nr: 60,
-                    divisors: 12,
-                },
-                Candidate {
-                    nr: 120,
-                    divisors: 16,
-                },
-                Candidate {
-                    nr: 180,
-                    divisors: 18,
-                },
-                Candidate {
-                    nr: 240,
-                    divisors: 20,
-                },
-                Candidate {
-                    nr: 360,
-                    divisors: 24,
-                },
-                Candidate {
-                    nr: 720,
-                    divisors: 30,
-                },
-                Candidate {
-                    nr: 840,
-                    divisors: 32,
-                },
-            ],
-        );
-    }
-
-    #[test]
-    fn matches_brute_force_records_up_to_ten_thousand() {
-        assert_eq!(hcn_records(10_000), brute_force_hcn_records(10_000));
-    }
-
-    #[test]
-    fn parses_default_search_limit_without_arg() {
-        assert_eq!(
-            Cli::try_parse_from(["hcn"])
-                .expect("CLI should parse without an explicit search limit")
-                .search_limit
-                .get(),
-            DEFAULT_SEARCH_LIMIT
-        );
-    }
-
-    #[test]
-    fn parses_search_limit_arg() {
-        assert_eq!(
-            Cli::try_parse_from(["hcn", "42000"])
-                .expect("CLI should parse an explicit search limit")
-                .search_limit
-                .get(),
-            42_000
-        );
-    }
-
-    #[test]
-    fn rejects_invalid_search_limit_arg() {
-        assert!(Cli::try_parse_from(["hcn", "nope"]).is_err());
-        assert!(Cli::try_parse_from(["hcn", "0"]).is_err());
-        assert!(Cli::try_parse_from(["hcn", "100", "200"]).is_err());
-    }
+    println!("Took {:?}", now.elapsed());
 }
@@ -0,0 +1,50 @@
+pub fn get_primes(max_nr: usize) -> Vec<u64> {
+    let mut sieve = vec![true; max_nr + 1];
+
+    let mut primes = Vec::with_capacity(1_000_000);
+
+    sieve[0] = false;
+    sieve[1] = false;
+
+    let mut nr = 2;
+    primes.push(2);
+
+    loop {
+        check_off_multiples_of_nr(nr, &mut sieve);
+
+        if find_next_prime(&mut nr, &mut sieve).is_none() {
+            break;
+        }
+
+        primes.push(nr);
+    }
+
+    primes
+}
+
+fn find_next_prime(nr: &mut u64, sieve: &mut [bool]) -> Option<u64> {
+    let start_idx = usize::try_from(*nr).ok()? + 1;
+
+    if let Some((idx, _)) = sieve
+        .iter()
+        .enumerate()
+        .skip(start_idx)
+        .find(|(_, &is_prime)| is_prime)
+    {
+        *nr = idx as u64;
+        return Some(*nr);
+    }
+
+    None
+}
+
+#[allow(clippy::unwrap_used)]
+fn check_off_multiples_of_nr(nr: u64, sieve: &mut [bool]) {
+    let nr = usize::try_from(nr).unwrap();
+
+    sieve
+        .iter_mut()
+        .skip(nr.checked_mul(2).unwrap())
+        .step_by(nr)
+        .for_each(|nr| *nr = false);
+}
Author	SHA1	Message	Date
ddidderr	dc82024ed0	[deps] cargo update	2025-05-29 11:33:43 +02:00
ddidderr	fd36faae13	[code] remove unnecessary reference	2024-09-28 12:59:31 +02:00
ddidderr	490c53a280	[fix] but primes behind an Arc - don't clone primes for every thread, instead put it behind an Arc (atomic reference counted) - print the pure calculation time at the end of the program - don't show thread debug prints	2024-09-28 12:57:29 +02:00
ddidderr	939e239b36	[feature] use multiple threads to calculate chunks in parallel	2024-09-12 20:35:23 +02:00