prime-factors
This commit is contained in:
parent
9624356fec
commit
ed09dd5590
5 changed files with 316 additions and 58 deletions
|
|
@ -1,48 +1,91 @@
|
|||
const PRIME_LEN: usize = 10_010;
|
||||
const LIMIT: usize = 106_000;
|
||||
|
||||
struct PrimeCache {
|
||||
primes: [u32; PRIME_LEN],
|
||||
}
|
||||
|
||||
impl PrimeCache {
|
||||
const fn new() -> Self {
|
||||
let mut primes = [0; PRIME_LEN];
|
||||
let mut sieve = [true; LIMIT];
|
||||
|
||||
sieve[0] = false;
|
||||
sieve[1] = false;
|
||||
|
||||
let mut i = 2;
|
||||
while i * i < LIMIT {
|
||||
if sieve[i] {
|
||||
let mut j = i * i;
|
||||
while j < LIMIT {
|
||||
sieve[j] = false;
|
||||
j += i;
|
||||
}
|
||||
}
|
||||
i += 1;
|
||||
}
|
||||
let mut num = 0;
|
||||
let mut j = 0;
|
||||
while num < LIMIT && j < PRIME_LEN {
|
||||
if sieve[num] {
|
||||
primes[j] = num as u32;
|
||||
j += 1;
|
||||
}
|
||||
num += 1;
|
||||
}
|
||||
Self { primes }
|
||||
}
|
||||
}
|
||||
|
||||
static CACHE: PrimeCache = PrimeCache::new();
|
||||
|
||||
pub fn nth(n: u32) -> u32 {
|
||||
let nth = n as usize;
|
||||
if nth >= PRIME_LEN {
|
||||
panic!("N more than comptime was calculated");
|
||||
let mut num = 1;
|
||||
for _ in 0..=n {
|
||||
loop {
|
||||
num += 1;
|
||||
if is_prime(num as u64) {
|
||||
break;
|
||||
}
|
||||
}
|
||||
}
|
||||
CACHE.primes[nth]
|
||||
num
|
||||
}
|
||||
|
||||
pub fn is_prime(n: u64) -> bool {
|
||||
if n < 2 {
|
||||
return false;
|
||||
}
|
||||
if n == 2 || n == 3 {
|
||||
return true;
|
||||
}
|
||||
if n % 2 == 0 {
|
||||
return false;
|
||||
}
|
||||
|
||||
let s = (n - 1).trailing_zeros();
|
||||
let d = (n - 1) >> s;
|
||||
|
||||
let witnesses = get_witnesses(n);
|
||||
|
||||
for &a in witnesses {
|
||||
if !miller_rabin_test(a, d, n, s) {
|
||||
return false;
|
||||
}
|
||||
}
|
||||
true
|
||||
}
|
||||
|
||||
fn get_witnesses(n: u64) -> &'static [u64] {
|
||||
const WITNESSES: &[(u64, &[u64])] = &[
|
||||
(2_046, &[2]),
|
||||
(1_373_652, &[2, 3]),
|
||||
(9_080_190, &[31, 73]),
|
||||
(25_326_000, &[2, 3, 5]),
|
||||
(4_759_123_140, &[2, 7, 61]),
|
||||
(1_112_004_669_632, &[2, 13, 23, 1662803]),
|
||||
(2_152_302_898_746, &[2, 3, 5, 7, 11]),
|
||||
(3_474_749_660_382, &[2, 3, 5, 7, 11, 13]),
|
||||
(341_550_071_728_320, &[2, 3, 5, 7, 11, 13, 17]),
|
||||
(3_825_123_056_546_413_050, &[2, 3, 5, 7, 11, 13, 17, 19, 23]),
|
||||
(u64::MAX, &[2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37]),
|
||||
];
|
||||
|
||||
WITNESSES
|
||||
.iter()
|
||||
.find(|(limit, _)| *limit >= n)
|
||||
.map(|(_, w)| *w)
|
||||
.unwrap()
|
||||
}
|
||||
|
||||
fn miller_rabin_test(a: u64, d: u64, n: u64, s: u32) -> bool {
|
||||
let mut x = mod_pow(a, d, n);
|
||||
if x == 1 || x == n - 1 {
|
||||
return true;
|
||||
}
|
||||
|
||||
for _ in 1..s {
|
||||
x = mod_mul(x, x, n);
|
||||
if x == n - 1 {
|
||||
return true;
|
||||
}
|
||||
}
|
||||
false
|
||||
}
|
||||
|
||||
#[inline]
|
||||
fn mod_mul(a: u64, b: u64, m: u64) -> u64 {
|
||||
((a as u128 * b as u128) % m as u128) as u64
|
||||
}
|
||||
|
||||
fn mod_pow(mut base: u64, mut exp: u64, m: u64) -> u64 {
|
||||
let mut res = 1;
|
||||
base %= m;
|
||||
while exp > 0 {
|
||||
if exp % 2 == 1 {
|
||||
res = mod_mul(res, base, m);
|
||||
}
|
||||
base = mod_mul(base, base, m);
|
||||
exp /= 2;
|
||||
}
|
||||
res
|
||||
}
|
||||
|
|
|
|||
82
rust/nth-prime/src/main.rs
Normal file
82
rust/nth-prime/src/main.rs
Normal file
|
|
@ -0,0 +1,82 @@
|
|||
fn main() {
|
||||
let n: u64 = std::env::args().nth(1)
|
||||
.and_then(|s| s.parse().ok())
|
||||
.unwrap_or(35);
|
||||
|
||||
println!("{} -> {}", n, if is_prime(n) { "prime" } else { "composite" });
|
||||
}
|
||||
|
||||
pub fn is_prime(n: u64) -> bool {
|
||||
if n < 2 { return false; }
|
||||
if n == 2 || n == 3 { return true; }
|
||||
if n % 2 == 0 { return false; }
|
||||
|
||||
let s = (n - 1).trailing_zeros();
|
||||
let d = (n - 1) >> s;
|
||||
|
||||
let witnesses = get_witnesses(n);
|
||||
|
||||
for &a in witnesses {
|
||||
if !miller_rabin_test(a, d, n, s) {
|
||||
return false;
|
||||
}
|
||||
}
|
||||
true
|
||||
}
|
||||
|
||||
// O(1) lookup based on input size
|
||||
fn get_witnesses(n: u64) -> &'static [u64] {
|
||||
const WITNESSES: &[(u64, &[u64])] = &[
|
||||
(2_046, &[2]),
|
||||
(1_373_652, &[2, 3]),
|
||||
(9_080_190, &[31, 73]),
|
||||
(25_326_000, &[2, 3, 5]),
|
||||
(4_759_123_140, &[2, 7, 61]),
|
||||
(1_112_004_669_632, &[2, 13, 23, 1662803]),
|
||||
(2_152_302_898_746, &[2, 3, 5, 7, 11]),
|
||||
(3_474_749_660_382, &[2, 3, 5, 7, 11, 13]),
|
||||
(341_550_071_728_320, &[2, 3, 5, 7, 11, 13, 17]),
|
||||
(3_825_123_056_546_413_050, &[2, 3, 5, 7, 11, 13, 17, 19, 23]),
|
||||
(u64::MAX, &[2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37]),
|
||||
];
|
||||
|
||||
WITNESSES.iter()
|
||||
.find(|(limit, _)| *limit >= n)
|
||||
.map(|(_, w)| *w)
|
||||
.unwrap()
|
||||
}
|
||||
|
||||
fn miller_rabin_test(a: u64, d: u64, n: u64, s: u32) -> bool {
|
||||
let mut x = mod_pow(a, d, n);
|
||||
if x == 1 || x == n - 1 {
|
||||
return true;
|
||||
}
|
||||
|
||||
for _ in 1..s {
|
||||
x = mod_mul(x, x, n);
|
||||
if x == n - 1 {
|
||||
return true;
|
||||
}
|
||||
}
|
||||
false
|
||||
}
|
||||
|
||||
// === Math Core ===
|
||||
|
||||
#[inline]
|
||||
fn mod_mul(a: u64, b: u64, m: u64) -> u64 {
|
||||
((a as u128 * b as u128) % m as u128) as u64
|
||||
}
|
||||
|
||||
fn mod_pow(mut base: u64, mut exp: u64, m: u64) -> u64 {
|
||||
let mut res = 1;
|
||||
base %= m;
|
||||
while exp > 0 {
|
||||
if exp % 2 == 1 {
|
||||
res = mod_mul(res, base, m);
|
||||
}
|
||||
base = mod_mul(base, base, m);
|
||||
exp /= 2;
|
||||
}
|
||||
res
|
||||
}
|
||||
115
rust/prime-factors/miller-rabin.rs
Normal file
115
rust/prime-factors/miller-rabin.rs
Normal file
|
|
@ -0,0 +1,115 @@
|
|||
pub fn nth(n: u32) -> u32 {
|
||||
let mut num = 1;
|
||||
for _ in 0..=n {
|
||||
loop {
|
||||
num += 1;
|
||||
if miller_rabin(num as u64) {
|
||||
break;
|
||||
}
|
||||
}
|
||||
}
|
||||
num
|
||||
}
|
||||
|
||||
fn miller_rabin(n: u64) -> bool {
|
||||
const HINT: &[u64] = &[2];
|
||||
|
||||
// we have a strict upper bound, so we can just use the witness
|
||||
// table of Pomerance, Selfridge & Wagstaff and Jeaschke to be as
|
||||
// efficient as possible, without having to fall back to
|
||||
// randomness. Additional limits from Feitsma and Galway complete
|
||||
// the entire range of `u64`. See also:
|
||||
// https://en.wikipedia.org/wiki/Miller%E2%80%93Rabin_primality_test#Testing_against_small_sets_of_bases
|
||||
const WITNESSES: &[(u64, &[u64])] = &[
|
||||
(2_046, HINT),
|
||||
(1_373_652, &[2, 3]),
|
||||
(9_080_190, &[31, 73]),
|
||||
(25_326_000, &[2, 3, 5]),
|
||||
(4_759_123_140, &[2, 7, 61]),
|
||||
(1_112_004_669_632, &[2, 13, 23, 1662803]),
|
||||
(2_152_302_898_746, &[2, 3, 5, 7, 11]),
|
||||
(3_474_749_660_382, &[2, 3, 5, 7, 11, 13]),
|
||||
(341_550_071_728_320, &[2, 3, 5, 7, 11, 13, 17]),
|
||||
(3_825_123_056_546_413_050, &[2, 3, 5, 7, 11, 13, 17, 19, 23]),
|
||||
(std::u64::MAX, &[2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37]),
|
||||
];
|
||||
|
||||
if n % 2 == 0 {
|
||||
return n == 2;
|
||||
}
|
||||
if n == 1 {
|
||||
return false;
|
||||
}
|
||||
|
||||
let mut d = n - 1;
|
||||
let mut s = 0;
|
||||
while d % 2 == 0 {
|
||||
d /= 2;
|
||||
s += 1
|
||||
}
|
||||
|
||||
let witnesses = WITNESSES
|
||||
.iter()
|
||||
.find(|&&(hi, _)| hi >= n)
|
||||
.map(|&(_, wtnss)| wtnss)
|
||||
.unwrap();
|
||||
'next_witness: for &a in witnesses.iter() {
|
||||
let mut power = mod_exp(a, d, n);
|
||||
assert!(power < n);
|
||||
if power == 1 || power == n - 1 {
|
||||
continue 'next_witness;
|
||||
}
|
||||
|
||||
for _r in 0..s {
|
||||
power = mod_sqr(power, n);
|
||||
assert!(power < n);
|
||||
if power == 1 {
|
||||
return false;
|
||||
}
|
||||
if power == n - 1 {
|
||||
continue 'next_witness;
|
||||
}
|
||||
}
|
||||
return false;
|
||||
}
|
||||
|
||||
true
|
||||
}
|
||||
|
||||
fn mod_mul_(a: u64, b: u64, m: u64) -> u64 {
|
||||
(u128::from(a) * u128::from(b) % u128::from(m)) as u64
|
||||
}
|
||||
|
||||
fn mod_mul(a: u64, b: u64, m: u64) -> u64 {
|
||||
match a.checked_mul(b) {
|
||||
Some(r) => {
|
||||
if r >= m {
|
||||
r % m
|
||||
} else {
|
||||
r
|
||||
}
|
||||
}
|
||||
None => mod_mul_(a, b, m),
|
||||
}
|
||||
}
|
||||
|
||||
fn mod_sqr(a: u64, m: u64) -> u64 {
|
||||
if a < (1 << 32) {
|
||||
let r = a * a;
|
||||
if r >= m { r % m } else { r }
|
||||
} else {
|
||||
mod_mul_(a, a, m)
|
||||
}
|
||||
}
|
||||
|
||||
fn mod_exp(mut x: u64, mut d: u64, n: u64) -> u64 {
|
||||
let mut ret: u64 = 1;
|
||||
while d != 0 {
|
||||
if d % 2 == 1 {
|
||||
ret = mod_mul(ret, x, n)
|
||||
}
|
||||
d /= 2;
|
||||
x = mod_sqr(x, n);
|
||||
}
|
||||
ret
|
||||
}
|
||||
|
|
@ -1,3 +1,32 @@
|
|||
pub fn factors(n: u64) -> Vec<u64> {
|
||||
todo!("This should calculate the prime factors of {n}")
|
||||
pub trait PrimeCollector {
|
||||
fn get_counted(&mut self, prime: u64) -> Vec<u64>;
|
||||
}
|
||||
|
||||
impl PrimeCollector for u64 {
|
||||
fn get_counted(&mut self, prime: u64) -> Vec<u64> {
|
||||
let mut res: Vec<_> = Vec::new();
|
||||
while 0 == *self % prime {
|
||||
*self /= prime;
|
||||
res.push(prime);
|
||||
}
|
||||
res
|
||||
}
|
||||
}
|
||||
|
||||
pub fn factors(n: u64) -> Vec<u64> {
|
||||
let mut res: Vec<_> = Vec::new();
|
||||
|
||||
let mut n_remained = n;
|
||||
let mut i = 2;
|
||||
while i * i <= n_remained {
|
||||
if n_remained % i == 0 {
|
||||
res.extend(n_remained.get_counted(i));
|
||||
}
|
||||
i += 1;
|
||||
}
|
||||
|
||||
if n_remained > 1 {
|
||||
res.push(n_remained);
|
||||
}
|
||||
res
|
||||
}
|
||||
|
|
|
|||
|
|
@ -8,7 +8,6 @@ fn no_factors() {
|
|||
}
|
||||
|
||||
#[test]
|
||||
#[ignore]
|
||||
fn prime_number() {
|
||||
let factors = factors(2);
|
||||
let expected = [2];
|
||||
|
|
@ -16,7 +15,6 @@ fn prime_number() {
|
|||
}
|
||||
|
||||
#[test]
|
||||
#[ignore]
|
||||
fn another_prime_number() {
|
||||
let factors = factors(3);
|
||||
let expected = [3];
|
||||
|
|
@ -24,7 +22,6 @@ fn another_prime_number() {
|
|||
}
|
||||
|
||||
#[test]
|
||||
#[ignore]
|
||||
fn square_of_a_prime() {
|
||||
let factors = factors(9);
|
||||
let expected = [3, 3];
|
||||
|
|
@ -32,7 +29,6 @@ fn square_of_a_prime() {
|
|||
}
|
||||
|
||||
#[test]
|
||||
#[ignore]
|
||||
fn product_of_first_prime() {
|
||||
let factors = factors(4);
|
||||
let expected = [2, 2];
|
||||
|
|
@ -40,7 +36,6 @@ fn product_of_first_prime() {
|
|||
}
|
||||
|
||||
#[test]
|
||||
#[ignore]
|
||||
fn cube_of_a_prime() {
|
||||
let factors = factors(8);
|
||||
let expected = [2, 2, 2];
|
||||
|
|
@ -48,7 +43,6 @@ fn cube_of_a_prime() {
|
|||
}
|
||||
|
||||
#[test]
|
||||
#[ignore]
|
||||
fn product_of_second_prime() {
|
||||
let factors = factors(27);
|
||||
let expected = [3, 3, 3];
|
||||
|
|
@ -56,7 +50,6 @@ fn product_of_second_prime() {
|
|||
}
|
||||
|
||||
#[test]
|
||||
#[ignore]
|
||||
fn product_of_third_prime() {
|
||||
let factors = factors(625);
|
||||
let expected = [5, 5, 5, 5];
|
||||
|
|
@ -64,7 +57,6 @@ fn product_of_third_prime() {
|
|||
}
|
||||
|
||||
#[test]
|
||||
#[ignore]
|
||||
fn product_of_first_and_second_prime() {
|
||||
let factors = factors(6);
|
||||
let expected = [2, 3];
|
||||
|
|
@ -72,7 +64,6 @@ fn product_of_first_and_second_prime() {
|
|||
}
|
||||
|
||||
#[test]
|
||||
#[ignore]
|
||||
fn product_of_primes_and_non_primes() {
|
||||
let factors = factors(12);
|
||||
let expected = [2, 2, 3];
|
||||
|
|
@ -80,7 +71,6 @@ fn product_of_primes_and_non_primes() {
|
|||
}
|
||||
|
||||
#[test]
|
||||
#[ignore]
|
||||
fn product_of_primes() {
|
||||
let factors = factors(901_255);
|
||||
let expected = [5, 17, 23, 461];
|
||||
|
|
@ -88,7 +78,6 @@ fn product_of_primes() {
|
|||
}
|
||||
|
||||
#[test]
|
||||
#[ignore]
|
||||
fn factors_include_a_large_prime() {
|
||||
let factors = factors(93_819_012_551);
|
||||
let expected = [11, 9_539, 894_119];
|
||||
|
|
|
|||
Loading…
Add table
Add a link
Reference in a new issue