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use crate::num::basic::unsigneds::PrimitiveUnsigned;
use crate::num::conversion::traits::{ExactFrom, WrappingFrom};
use crate::num::factorization::prime_sieve::{
id_to_n, limbs_prime_sieve_size, limbs_prime_sieve_u64,
};
use crate::num::factorization::traits::Primes;
use crate::num::logic::traits::TrailingZeros;
use alloc::vec::Vec;
use core::marker::PhantomData;
// This differs from the identically-named function in malachite-nz; this one returns None if there
// are no more false bits.
fn limbs_index_of_next_false_bit<T: PrimitiveUnsigned>(xs: &[T], start: u64) -> Option<u64> {
let starting_index = usize::exact_from(start >> T::LOG_WIDTH);
if starting_index >= xs.len() {
return None;
}
if let Some(result) = xs[starting_index].index_of_next_false_bit(start & T::WIDTH_MASK) {
if result != T::WIDTH {
return Some((u64::wrapping_from(starting_index) << T::LOG_WIDTH) + result);
}
}
if starting_index == xs.len() - 1 {
return None;
}
let false_index = starting_index
+ 1
+ xs[starting_index + 1..]
.iter()
.take_while(|&&y| y == T::MAX)
.count();
if false_index == xs.len() {
None
} else {
Some(
(u64::exact_from(false_index) << T::LOG_WIDTH)
+ TrailingZeros::trailing_zeros(!xs[false_index]),
)
}
}
/// An iterator over that generates all primes less than a given value.
///
/// This `struct` is created by [`Primes::primes_less_than`] and
/// [`Primes::primes_less_than_or_equal_to`]; see their documentation for more.
#[derive(Clone, Debug)]
pub struct PrimesLessThanIterator<T: PrimitiveUnsigned> {
i: u8,
j: u64,
sieve: Vec<u64>,
phantom: PhantomData<*const T>,
}
impl<T: PrimitiveUnsigned> PrimesLessThanIterator<T> {
fn new(n: T) -> PrimesLessThanIterator<T> {
let n: u64 = n.saturating_into();
let mut sieve;
if n < 5 {
sieve = Vec::with_capacity(0);
} else {
sieve = alloc::vec![0; limbs_prime_sieve_size::<u64>(n)];
limbs_prime_sieve_u64(&mut sieve, n);
}
PrimesLessThanIterator {
i: 0,
j: n,
sieve,
phantom: PhantomData,
}
}
}
impl<T: PrimitiveUnsigned> Iterator for PrimesLessThanIterator<T> {
type Item = T;
fn next(&mut self) -> Option<T> {
match self.i {
0 => {
if self.j < 2 {
None
} else {
self.i = 1;
Some(T::TWO)
}
}
1 => {
if self.j == 2 {
None
} else {
self.i = 2;
self.j = 0;
Some(T::from(3u8))
}
}
_ => {
self.j = limbs_index_of_next_false_bit(&self.sieve, self.j)? + 1;
Some(T::exact_from(id_to_n(self.j)))
}
}
}
}
/// An iterator over that generates all primes.
///
/// This `struct` is created by [`Primes::primes`]; see its documentation for more.
#[derive(Clone, Debug)]
pub struct PrimesIterator<T: PrimitiveUnsigned> {
limit: T,
xs: PrimesLessThanIterator<T>,
}
impl<T: PrimitiveUnsigned> PrimesIterator<T> {
fn new() -> PrimesIterator<T> {
let limit = T::saturating_from(256u16);
PrimesIterator {
limit,
xs: PrimesLessThanIterator::new(limit),
}
}
}
impl<T: PrimitiveUnsigned> Iterator for PrimesIterator<T> {
type Item = T;
fn next(&mut self) -> Option<T> {
loop {
let p = self.xs.next();
if p.is_some() {
return p;
} else if self.limit == T::MAX {
return None;
} else {
self.limit.saturating_mul_assign(T::TWO);
let j = self.xs.j;
self.xs = T::primes_less_than_or_equal_to(&self.limit);
self.xs.i = 3;
self.xs.j = j;
}
}
}
}
macro_rules! impl_primes {
($t:ident) => {
impl Primes for $t {
type I = PrimesIterator<$t>;
type LI = PrimesLessThanIterator<$t>;
/// Returns an iterator that generates all primes less than a given value.
///
/// The iterator produced by `primes_less_than(n)` generates the same primes as the
/// iterator produced by `primes().take_while(|&p| p < n)`, but the latter would be
/// slower because it doesn't know in advance how large its prime sieve should be, and
/// might have to create larger and larger prime sieves.
///
/// # Worst-case complexity (amortized)
/// $T(i) = O(\log \log i)$
///
/// $M(i) = O(1)$
///
/// where $T$ is time, $M$ is additional memory, and $i$ is the iteration index.
///
/// # Examples
/// See [here](super::primes#primes_less_than).
#[inline]
fn primes_less_than(n: &$t) -> PrimesLessThanIterator<$t> {
PrimesLessThanIterator::new(n.saturating_sub(1))
}
/// Returns an iterator that generates all primes less than or equal to a given value.
///
/// The iterator produced by `primes_less_than_or_equal_to(n)` generates the same primes
/// as the iterator produced by `primes().take_while(|&p| p <= n)`, but the latter would
/// be slower because it doesn't know in advance how large its prime sieve should be,
/// and might have to create larger and larger prime sieves.
///
/// # Worst-case complexity (amortized)
/// $T(i) = O(\log \log i)$
///
/// $M(i) = O(1)$
///
/// where $T$ is time, $M$ is additional memory, and $i$ is the iteration index.
///
/// # Examples
/// See [here](super::primes#primes_less_than_or_equal_to).
#[inline]
fn primes_less_than_or_equal_to(&n: &$t) -> PrimesLessThanIterator<$t> {
PrimesLessThanIterator::new(n)
}
/// Returns all primes that fit into the specified type.
///
/// The iterator produced by `primes(n)` generates the same primes as the iterator
/// produced by `primes_less_than_or_equal_to(T::MAX)`. If you really need to generate
/// _every_ prime, and `T` is `u32` or smaller, then you should use the latter, as it
/// will allocate all the needed memory at once. If `T` is `u64` or larger, or if you
/// probably don't need every prime, then `primes()` will be faster as it won't allocate
/// too much memory right away.
///
/// # Worst-case complexity (amortized)
/// $T(i) = O(\log \log i)$
///
/// $M(i) = O(1)$
///
/// where $T$ is time, $M$ is additional memory, and $i$ is the iteration index.
///
/// # Examples
/// See [here](super::primes#primes).
#[inline]
fn primes() -> PrimesIterator<$t> {
PrimesIterator::new()
}
}
};
}
apply_to_unsigneds!(impl_primes);