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use malachite_base::num::arithmetic::traits::{CheckedLogBase2, Pow};
use malachite_base::num::basic::traits::One;
use malachite_base::num::conversion::traits::{Digits, ExactFrom};
use malachite_base::rational_sequences::RationalSequence;
use malachite_nz::natural::Natural;
use Rational;
impl Rational {
/// Converts base-$b$ digits to a [`Rational`]. The inputs are taken by value.
///
/// The input consists of the digits of the integer portion of the [`Rational`] and the digits
/// of the fractional portion. The integer-portion digits are ordered from least- to
/// most-significant, and the fractional-portion digits from most- to least.
///
/// The fractional-portion digits may end in infinitely many zeros or $(b-1)$s; these are
/// handled correctly.
///
/// # Worst-case complexity
/// $T(n, m) = O(nm \log (nm)^2 \log\log (nm))$
///
/// $M(n, m) = O(nm \log (nm))$
///
/// where $T$ is time, $M$ is additional memory, $n$ is
/// `max(before_point.len(), after_point.component_len())`, and $m$ is
/// `base.significant_bits()`.
///
/// # Panics
/// Panics if `base` is less than 2.
///
/// # Examples
/// ```
/// extern crate malachite_base;
/// extern crate malachite_nz;
///
/// use malachite_base::rational_sequences::RationalSequence;
/// use malachite_base::vecs::vec_from_str;
/// use malachite_nz::natural::Natural;
/// use malachite_q::Rational;
///
/// let before_point = vec_from_str("[3]").unwrap();
/// let after_point = RationalSequence::from_vecs(
/// Vec::new(),
/// vec_from_str("[1, 4, 2, 8, 5, 7]").unwrap(),
/// );
/// assert_eq!(
/// Rational::from_digits(&Natural::from(10u32), before_point, after_point).to_string(),
/// "22/7"
/// );
///
/// // 21.34565656...
/// let before_point = vec_from_str("[1, 2]").unwrap();
/// let after_point = RationalSequence::from_vecs(
/// vec_from_str("[3, 4]").unwrap(),
/// vec_from_str("[5, 6]").unwrap(),
/// );
/// assert_eq!(
/// Rational::from_digits(&Natural::from(10u32), before_point, after_point).to_string(),
/// "105661/4950"
/// );
/// ```
pub fn from_digits(
base: &Natural,
before_point: Vec<Natural>,
after_point: RationalSequence<Natural>,
) -> Rational {
if let Some(log_base) = base.checked_log_base_2() {
return Rational::from_power_of_2_digits(log_base, before_point, after_point);
}
let (non_repeating, repeating) = after_point.into_vecs();
let r_len = u64::exact_from(repeating.len());
let nr_len = u64::exact_from(non_repeating.len());
let nr = Natural::from_digits_asc(base, non_repeating.into_iter().rev()).unwrap();
let r = Natural::from_digits_asc(base, repeating.into_iter().rev()).unwrap();
let floor =
Rational::from(Natural::from_digits_asc(base, before_point.into_iter()).unwrap());
floor
+ if r == 0u32 {
Rational::from_naturals(nr, base.pow(nr_len))
} else {
(Rational::from_naturals(r, base.pow(r_len) - Natural::ONE) + Rational::from(nr))
/ Rational::from(base.pow(nr_len))
}
}
/// Converts base-$b$ digits to a [`Rational`]. The inputs are taken by reference.
///
/// The input consists of the digits of the integer portion of the [`Rational`] and the digits
/// of the fractional portion. The integer-portion digits are ordered from least- to
/// most-significant, and the fractional-portion digits from most- to least.
///
/// The fractional-portion digits may end in infinitely many zeros or $(b-1)$s; these are
/// handled correctly.
///
/// # Worst-case complexity
/// $T(n, m) = O(nm \log (nm)^2 \log\log (nm))$
///
/// $M(n, m) = O(nm \log (nm))$
///
/// where $T$ is time, $M$ is additional memory, $n$ is
/// `max(before_point.len(), after_point.component_len())`, and $m$ is
/// `base.significant_bits()`.
///
/// # Panics
/// Panics if `base` is less than 2.
///
/// # Examples
/// ```
/// extern crate malachite_base;
/// extern crate malachite_nz;
///
/// use malachite_base::rational_sequences::RationalSequence;
/// use malachite_base::vecs::vec_from_str;
/// use malachite_nz::natural::Natural;
/// use malachite_q::Rational;
///
/// let before_point = vec_from_str("[3]").unwrap();
/// let after_point = RationalSequence::from_vecs(
/// Vec::new(),
/// vec_from_str("[1, 4, 2, 8, 5, 7]").unwrap(),
/// );
/// assert_eq!(
/// Rational::from_digits_ref(&Natural::from(10u32), &before_point, &after_point)
/// .to_string(),
/// "22/7"
/// );
///
/// // 21.34565656...
/// let before_point = vec_from_str("[1, 2]").unwrap();
/// let after_point = RationalSequence::from_vecs(
/// vec_from_str("[3, 4]").unwrap(),
/// vec_from_str("[5, 6]").unwrap(),
/// );
/// assert_eq!(
/// Rational::from_digits_ref(&Natural::from(10u32), &before_point, &after_point)
/// .to_string(),
/// "105661/4950"
/// );
/// ```
pub fn from_digits_ref(
base: &Natural,
before_point: &[Natural],
after_point: &RationalSequence<Natural>,
) -> Rational {
if let Some(log_base) = base.checked_log_base_2() {
return Rational::from_power_of_2_digits_ref(log_base, before_point, after_point);
}
let (non_repeating, repeating) = after_point.to_vecs();
let r_len = u64::exact_from(repeating.len());
let nr_len = u64::exact_from(non_repeating.len());
let nr = Natural::from_digits_asc(base, non_repeating.into_iter().rev()).unwrap();
let r = Natural::from_digits_asc(base, repeating.into_iter().rev()).unwrap();
let floor =
Rational::from(Natural::from_digits_asc(base, before_point.iter().cloned()).unwrap());
floor
+ if r == 0u32 {
Rational::from_naturals(nr, base.pow(nr_len))
} else {
(Rational::from_naturals(r, base.pow(r_len) - Natural::ONE) + Rational::from(nr))
/ Rational::from(base.pow(nr_len))
}
}
}