Macro primes_segment

macro_rules! primes_segment {
    ($n:expr; < $lim:expr) => { ... };
    ($n:expr; >= $lim:expr) => { ... };
}

Generate arrays of large prime numbers without having to store all primes from 2 and up in the result, and thus potentially the binary.

Calls primes_geq or primes_lt, and automatically computes the memory requirement of the sieve.

Compute N primes larger than or equal to some limit as primes_segment!(N; >= LIMIT), and N primes less than some limit as primes_segment!(N; < LIMIT).

Estimates the sieve size as isqrt(upper_limit) + 1 for primes_lt and as isqrt(lower_limit) + 1 + N for primes_geq. This may overestimate the memory requirement for primes_geq.

Example

const N: usize = 3;
const LIMIT: u64 = 5_000_000_031;

const PRIMES_GEQ: Result<[u64; N], GenerationError> = primes_segment!(N; >= LIMIT);
const PRIMES_LT: Result<[u64; N], GenerationError> = primes_segment!(N; < LIMIT);

// Can also be used at runtime:
let primes_geq = primes_segment!(N; >= LIMIT);

assert_eq!(PRIMES_GEQ, primes_geq);
assert_eq!(PRIMES_GEQ, Ok([5000000039, 5000000059, 5000000063]));
assert_eq!(PRIMES_LT, Ok([4999999903, 4999999937, 5000000029]));

Errors

Has the same error behaviour as primes_geq and primes_lt, with the exception that it sets MEM such that the sieve doesn’t run out of memory.