Add test to find last prime before 10^9.

I don't know why yet, but this seems to be the near optimal sieve size
when testing with the benchmarking script. It's equal to `1024^2 * 10`.

.gitignore

@@ -1,2 +1,3 @@
 /target
 /indivisible.1.gz
+callgrind.out.*

README.md

@@ -1,38 +1,29 @@
 # Indivisible
 
-Indivisible is an optimized prime number generator and tester written in Rust.
+Indivisible is an optimized prime number generator and tester.
 
 ## Build & Installation
 
-To build the project you will require the Rust compiler and build
-system, `cargo`. At which point you simply run `cargo build` in the root
-directory of the project. To create an optimized release build append
-the `--release` flag to the previous command.
+Build a binary release using the following command:
 
-Once a release build has been compiled, you may install Indivisible and
-the manpage documentation by running the `install` script. In a similar
-manner, you can run the `uninstall` script to remove the previously
-installed binary and documentation.
+```console
+$ cargo build -r
+```
 
-## Usage
+Once compiled, you can install it using the `install` script. By default this
+will install to `/usr/local/{bin,share}`, but you can optionally change the
+`PREFIX` used as follows:
 
-The purpose of Indivisible is to find the nth prime and all the primes
-before it. The basic usage is `indivisible <n>` where `n` is the ordinal
-of the prime you'd like to find. To display all primes before `n`, you
-can run verbose mode by using the `--verbose` or simply `-v` option.
+```console
+$ PREFIX="~/.local" ./install
+```
 
-Since Indivisible generates primes using previously computed primes, you
-can also import prime numbers previously computed with the `--import` or
-`-i` option. To store already computed primes you are expected to use
-piping like any UNIX user would expect. Here is an example:
+Additionally there is an `uninstall` script available. If you have used a custom
+`PREFIX` this must also be specified to uninstall in the same manner. To see
+where you've installed it you can always use the following command:
 
-```bash
-# store first 100 primes in ./primes
-indivisible -v 100 > ./primes
-# appends next 400 primes
-indivisible -i ./primes -v 500 >> ./primes
-# display the 600th prime
-indivisible -i ./primes 600
+```console
+$ which indivisible
 ```
 
 ## Legacy

benchmark.sh

@@ -0,0 +1,45 @@
+#!/bin/bash
+
+EXE="./target/release/indivisible"
+OPTIONS=()
+TRIALS=20
+
+if ! [ -f "$EXE" ]
+then
+	>&2 echo "Release build not available. Please run 'cargo build -r'."
+	exit 1
+fi
+
+if ! command -v calc &>/dev/null
+then
+	>&2 echo "Missing 'calc' program. Please install it for this script."
+	exit 1
+fi
+
+while getopts "t:s:" opt
+do
+	case "$opt" in
+		s)
+			OPTIONS=("${OPTIONS[@]}" -s "$OPTARG")
+			;;
+		t)
+			TRIALS="$OPTARG"
+			;;
+		*)
+			>&2 echo "Uknown option $opt"
+			exit 1
+			;;
+	esac
+done
+
+echo "Calculating primes up to 1,000,000,000"
+TOTAL="0"
+for _ in $(seq "$TRIALS")
+do
+	TIME=$(command time -f "%e" "$EXE" "${OPTIONS[@]}" 1000000000 2>&1 >/dev/null)
+	TOTAL=$(calc "$TOTAL + $TIME")
+done
+
+AVG=$(calc "$TOTAL / $TRIALS")
+
+echo "Average time: ${AVG}s"

indivisible.1

@@ -6,7 +6,9 @@ indivisible \- prime number generator and tester
 [\fIOPTIONS\fR] <\fIn\fR>
 
 .SH "DESCRIPTION"
-Indivisible is a program for working with prime numbers. Its default behaviour will attempt to find the \fInth\fR prime.
+Indivisible is a program for working with prime numbers. It can either generate
+primes up to a limit \fIn\fR or test to see if \fIn\fR is a prime. It makes use
+of a segmented sieve of Eratosthenes.
 
 .SH "OPTIONS"
 .TP
@@ -19,6 +21,9 @@ Import prime numbers from \fIFILE\fR
 \fB\-t\fR, \fB\-\-test\fR
 Test if n is a prime instead of generation
 .TP
+\fB\-s\fR, \fB\-\-sieve\fR <\fISIZE\fR>
+Set a custom sieve size
+.TP
 \fB\-v\fR, \fB\-\-verbose\fR
 Print all found primes
 .TP

src/main.rs

@@ -16,13 +16,14 @@
  * along with this program.  If not, see <http://www.gnu.org/licenses/>.
  */
 
-use std::collections::VecDeque;
 use std::fs::File;
 use std::io::{BufRead, BufReader};
 use std::path::PathBuf;
 use std::process;
 use structopt::StructOpt;
 
+mod worker;
+
 #[derive(StructOpt)]
 #[structopt(about = "A prime number generator and tester.")]
 struct Opt {
@@ -32,26 +33,28 @@ struct Opt {
 	import:Option<PathBuf>,
 	#[structopt(short, long, help = "Test if num is prime instead of generation")]
 	test:bool,
-	#[structopt(help = "Ordinal of the prime to generate or number to test for primality")]
-	num:u64,
-	#[structopt(short, long, name = "n", default_value = "1", help = "Number of threads to spawn")]
-	jobs:u64,
+	#[structopt(help = "Max of the prime to generate or number to test for primality")]
+	num:usize,
+	#[structopt(short, long, name = "SIZE", default_value = "10485760", help = "Set a custom sieve size")]
+	sieve:usize,
+	//#[structopt(short, long, name = "n", default_value = "1", help = "Number of threads to spawn")]
+	//jobs:u64,
 }
 
 fn main() {
 	let opts = Opt::from_args();
-
-	let mut prime_list = VecDeque::<u64>::new();
-	let mut arr = Vec::new();
-	for _ in 0..=opts.num {
-		arr.push(false);
-	}
+	let mut prime_list = Vec::new();
 
 	if opts.import.is_some() {
 		let in_file = File::open(opts.import.unwrap()).unwrap();
 		let reader = BufReader::new(in_file);
 		for p in reader.lines().into_iter() {
-			prime_list.push_back(p.unwrap().parse().unwrap());
+			let prime:u64 = p.unwrap().parse().unwrap();
+			if (prime as usize) > opts.num {
+				break;
+			}
+
+			prime_list.push(prime);
 		}
 	}
 
@@ -59,57 +62,32 @@ fn main() {
 		eprintln!("Invalid value for num: {}", opts.num);
 		process::exit(1);
 	}
-	if opts.num > 2 {
-		arr[2] = true;
+
+	let mut start:usize = if prime_list.is_empty() {
+		2
+	} else {
+		(*prime_list.last().unwrap() + 1) as usize
+	};
+	while start < opts.num {
+		let end = if start + opts.sieve < opts.num {
+			start + opts.sieve
+		} else {
+			opts.num + 1
+		};
+		let mut new_primes = worker::work_segment(&prime_list, start, end);
+
+		if opts.verbose {
+			for p in &new_primes {
+				println!("{}", *p);
 			}
-	if opts.num > 3 {
-		arr[3] = true;
+		}
+		prime_list.append(&mut new_primes);
+
+		start += opts.sieve;
 	}
 
-	for x in 1..=(f64::sqrt(opts.num as f64) as u64 + 1) {
-		for y in 1..=(f64::sqrt(opts.num as f64) as u64 + 1) {
-			let n1 = ((4 * x * x) + (y * y)) as usize;
-			if n1 <= (opts.num as usize) && (n1 % 12 == 1 || n1 % 12 == 5) {
-				arr[n1] = !arr[n1];
-			}
-
-			let n2 = ((3 * x * x) + (y * y)) as usize;
-			if n2 <= (opts.num as usize) && n2 % 12 == 7 {
-				arr[n2] = !arr[n2];
-			}
-
-			let n3 = ((3 * x * x) - (y * y)) as usize;
-			if x > y && n3 <= (opts.num as usize) && n3 % 12 == 11 {
-				arr[n3] = !arr[n3];
-			}
-		}
-	}
-
-	for i in 5..=(f64::sqrt(opts.num as f64) as u64 + 1) as usize {
-		if !arr[i as usize] {
-			continue;
-		}
-
-		let mut j = i * i;
-		while j <= (opts.num as usize) {
-			arr[j] = false;
-			j += i * i;
-		}
-	}
-
-	for i in 2..=(opts.num as usize) {
-		if arr[i] {
-			if opts.verbose && !opts.test {
-				println!("{}", i);
-			}
-			prime_list.push_back(i as u64);
-		}
-	}
-
-	if !opts.verbose && !opts.test {
-		println!("{}", prime_list.back().unwrap());
-	} else if opts.test {
-		if *prime_list.back().unwrap() == opts.num {
+	if opts.test {
+		if *prime_list.last().unwrap() == (opts.num as u64) {
 			if opts.verbose {
 				println!("{} is prime", opts.num);
 			}
@@ -120,5 +98,7 @@ fn main() {
 			}
 			process::exit(1);
 		}
+	} else if !opts.verbose {
+		println!("{}", prime_list.last().unwrap());
 	}
 }

src/worker.rs

@@ -0,0 +1,66 @@
+/*
+ * Copyright (C) 2025  Nicolás Ortega Froysa <nicolas@ortegas.org>
+ * Author: Nicolás Ortega Froysa <nicolas@ortegas.org>
+ *
+ * This program is free software: you can redistribute it and/or modify
+ * it under the terms of the GNU General Public License as published by
+ * the Free Software Foundation, either version 3 of the License, or
+ * (at your option) any later version.
+ *
+ * This program is distributed in the hope that it will be useful,
+ * but WITHOUT ANY WARRANTY; without even the implied warranty of
+ * MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the
+ * GNU General Public License for more details.
+ *
+ * You should have received a copy of the GNU General Public License
+ * along with this program.  If not, see <http://www.gnu.org/licenses/>.
+ */
+
+/**
+ * @brief Work on a segment.
+ *
+ * @param known_primes:&Vec<u64> List of known primes at least until sqrt(end).
+ * @param start:usize Beginning of the segment (inclusive).
+ * @param end:usize End of the segment (exclusive).
+ *
+ * @return List of primes found in segment.
+ */
+pub fn work_segment(known_primes:&Vec<u64>, start:usize, end:usize) -> Vec<u64> {
+	let mut sieve = vec![true; end - start];
+	let mut found_primes = Vec::new();
+
+	let sqrt_end = f64::sqrt(end as f64) as usize;
+
+	for p in known_primes {
+		let prime = *p as usize;
+		if prime > sqrt_end {
+			break;
+		}
+
+		let modu = start % prime;
+		let mut mult = if modu == 0 {
+			start
+		} else {
+			start + prime - modu
+		};
+		while mult < end {
+			sieve[mult - start] = false;
+			mult += prime;
+		}
+	}
+
+	for i in 0..(end - start) {
+		if sieve[i] {
+			let prime = i + start;
+			found_primes.push(prime as u64);
+
+			let mut mult = prime * prime;
+			while mult < end {
+				sieve[mult - start] = false;
+				mult += prime;
+			}
+		}
+	}
+
+	found_primes
+}

test.sh

@@ -17,9 +17,12 @@ fi
 tests=0
 passed=0
 
+## TEST
 ((tests++))
-echo -n "${tests}: Find 5th prime number..."
-if [[ $("$BINARY" 5) == 11 ]]
+echo -n "${tests}: Find all prime numbers before 70..."
+expect="2 3 5 7 11 13 17 19 23 29 31 37 41 43 47 53 59 61 67 "
+
+if [ "$("$BINARY" -v 70 | tr '\n' ' ')" = "$expect" ]
 then
 	echo " pass"
 	((passed++))
@@ -27,6 +30,20 @@ else
 	echo " FAIL"
 fi
 
+## TEST
+((tests++))
+echo -n "${tests}: Find last prime before 1,000,000,000..."
+expect="999999937"
+
+if [ "$("$BINARY" 1000000000)" = "$expect" ]
+then
+	echo " pass"
+	((passed++))
+else
+	echo " FAIL"
+fi
+
+## TEST
 ((tests++))
 echo -n "${tests}: 11 is prime..."
 if "$BINARY" -t 11
@@ -37,6 +54,7 @@ else
 	echo " FAIL"
 fi
 
+## TEST
 ((tests++))
 echo -n "${tests}: 9 is not prime..."
 if ! "$BINARY" -t 9
@@ -47,4 +65,10 @@ else
 	echo " FAIL"
 fi
 
+## RESULTS
 echo "Results: $passed/$tests"
+
+if [ $passed -ne $tests ]
+then
+	exit 1
+fi