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Use much simpler and more readable trial division

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This commit is contained in:
Avery Winters 2024-11-06 12:59:36 -06:00
parent 0f87a7d30b
commit f1c6438b80
Signed by: avery
SSH key fingerprint: SHA256:eesvLB5MMqHLZrAMFt6kEhqJWnASMLcET6Sgmw0FqZI
1 changed files with 9 additions and 78 deletions
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87
rust/nth-prime/src/lib.rs
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@ -1,83 +1,14 @@
pub fn nth(mut n: u32) -> u32 { pub fn nth(n: u32) -> u32 {
let upper_bound = upper_bound_nth_prime(n); (2..)
let upper_bound: usize = upper_bound as usize + 1; .filter(|&x| is_prime(x))
let len = upper_bound.div_ceil(8); .nth(n as usize)
let mut bytes = vec![u8::MAX; len]; .expect("at least n 32-bit integers are prime")
let mask = (1 << 0) | (1 << 1);
bytes[0] &= !mask;
let bound: f64 = upper_bound as f64;
let bound = bound.sqrt();
let bound: usize = bound as usize;
for i in 2..=bound {
let mask = 1 << (i % 8);
let byte = bytes[i / 8];
if byte & mask != 0u8 {
let start = i * i;
for j in (start..=upper_bound).step_by(i.try_into().unwrap()) {
let mask = 1 << (j % 8);
bytes[j / 8] &= !mask;
}
}
}
for (i, byte) in bytes.iter().enumerate() {
let count = byte.count_ones();
if count >= n {
for j in 0..8 {
let mask = 1 << j;
if byte & mask != 0u8 {
if n == 0 {
return (8 * i + j) as u32;
}
n -= 1;
}
}
} else {
n -= count;
}
}
unreachable!()
} }
fn upper_bound_nth_prime(n: u32) -> u32 { fn is_prime(n: u32) -> bool {
// For small prime counts, the upper bound estimate is not big enough. (2..=isqrt(n)).all(|x| n % x != 0)
// Hardcode it to the 6th prime (13).
if n < 6 {
return 13;
}
let mut low = n;
let mut high = u32::MAX - 1;
while low < high {
let mid = low + (high - low) / 2;
let guess = {
let mid: f64 = mid.into();
mid / mid.ln()
};
if guess > n.into() {
high = mid - 1;
} else {
low = mid + 1;
}
}
high + 1
} }
#[cfg(test)] fn isqrt(n: u32) -> u32 {
mod test { (n as f64).sqrt() as u32
use crate::upper_bound_nth_prime;
#[test]
fn greater_first_20() {
let primes = [
2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37, 41, 43, 47, 53, 59, 61, 67, 71,
];
for (i, &p) in primes.iter().enumerate() {
let i = i.try_into().unwrap();
let upper_bound = upper_bound_nth_prime(i);
assert!(upper_bound >= p, "{upper_bound} < {p}");
}
}
} }