malachite_q/conversion/digits/
power_of_2_digits.rs

1// Copyright © 2025 Mikhail Hogrefe
2//
3// This file is part of Malachite.
4//
5// Malachite is free software: you can redistribute it and/or modify it under the terms of the GNU
6// Lesser General Public License (LGPL) as published by the Free Software Foundation; either version
7// 3 of the License, or (at your option) any later version. See <https://www.gnu.org/licenses/>.
8
9use crate::Rational;
10use alloc::vec::Vec;
11use malachite_base::num::arithmetic::traits::{Abs, Floor, UnsignedAbs};
12use malachite_base::num::conversion::traits::PowerOf2Digits;
13use malachite_nz::natural::Natural;
14
15/// Represents the base-$2^k$ digits of the fractional portion of a [`Rational`] number.
16///
17/// See [`power_of_2_digits`](Rational::power_of_2_digits) for more information.
18#[derive(Clone, Debug, Eq, PartialEq)]
19pub struct RationalPowerOf2Digits {
20    log_base: u64,
21    remainder: Rational,
22}
23
24impl Iterator for RationalPowerOf2Digits {
25    type Item = Natural;
26
27    fn next(&mut self) -> Option<Natural> {
28        if self.remainder == 0u32 {
29            None
30        } else {
31            self.remainder <<= self.log_base;
32            let digit = (&self.remainder).floor().unsigned_abs();
33            self.remainder -= Rational::from(&digit);
34            Some(digit)
35        }
36    }
37}
38
39impl Rational {
40    /// Returns the base-$2^k$ digits of a [`Rational`].
41    ///
42    /// The output has two components. The first is a [`Vec`] of the digits of the integer portion
43    /// of the [`Rational`], least- to most-significant. The second is an iterator of the digits of
44    /// the fractional portion.
45    ///
46    /// The output is in its simplest form: the integer-portion digits do not end with a zero, and
47    /// the fractional-portion digits do not end with infinitely many zeros or $(2^k-1)$s.
48    ///
49    /// If the [`Rational`] has a small denominator, it may be more efficient to use
50    /// [`to_power_of_2_digits`](Rational::to_power_of_2_digits) or
51    /// [`into_power_of_2_digits`](Rational::into_power_of_2_digits) instead. These functions
52    /// compute the entire repeating portion of the repeating digits.
53    ///
54    /// For example, consider these two expressions:
55    /// - `Rational::from_signeds(1, 7).power_of_2_digits(1).1.nth(1000)`
56    /// - `Rational::from_signeds(1, 7).into_power_of_2_digits(1).1[1000]`
57    ///
58    /// Both get the thousandth digit after the binary point of `1/7`. The first way explicitly
59    /// calculates each bit after the binary point, whereas the second way determines that `1/7` is
60    /// `0.(001)`, with the `001` repeating, and takes `1000 % 3 == 1` to determine that the
61    /// thousandth bit is 0. But when the [`Rational`] has a large denominator, the second way is
62    /// less efficient.
63    ///
64    /// # Worst-case complexity per iteration
65    /// $T(n) = O(n \log n \log\log n)$
66    ///
67    /// $M(n) = O(n \log n)$
68    ///
69    /// where $T$ is time, $M$ is additional memory, and $n$ is `max(self.significant_bits(),
70    /// base)`.
71    ///
72    /// # Panics
73    /// Panics if `log_base` is zero.
74    ///
75    /// # Examples
76    /// ```
77    /// use malachite_base::iterators::prefix_to_string;
78    /// use malachite_base::strings::ToDebugString;
79    /// use malachite_q::Rational;
80    ///
81    /// let (before_point, after_point) = Rational::from(3u32).power_of_2_digits(1);
82    /// assert_eq!(before_point.to_debug_string(), "[1, 1]");
83    /// assert_eq!(prefix_to_string(after_point, 10), "[]");
84    ///
85    /// let (before_point, after_point) = Rational::from_signeds(22, 7).power_of_2_digits(1);
86    /// assert_eq!(before_point.to_debug_string(), "[1, 1]");
87    /// assert_eq!(
88    ///     prefix_to_string(after_point, 10),
89    ///     "[0, 0, 1, 0, 0, 1, 0, 0, 1, 0, ...]"
90    /// );
91    ///
92    /// let (before_point, after_point) = Rational::from_signeds(22, 7).power_of_2_digits(10);
93    /// assert_eq!(before_point.to_debug_string(), "[3]");
94    /// assert_eq!(
95    ///     prefix_to_string(after_point, 10),
96    ///     "[146, 292, 585, 146, 292, 585, 146, 292, 585, 146, ...]"
97    /// );
98    /// ```
99    pub fn power_of_2_digits(&self, log_base: u64) -> (Vec<Natural>, RationalPowerOf2Digits) {
100        let mut remainder = self.abs();
101        let floor = (&remainder).floor().unsigned_abs();
102        remainder -= Self::from(&floor);
103        (
104            floor.to_power_of_2_digits_asc(log_base),
105            RationalPowerOf2Digits {
106                log_base,
107                remainder,
108            },
109        )
110    }
111}
malachite_q/conversion/digits/power_of_2_digits.rs

malachite_q/conversion/digits/
power_of_2_digits.rs
