1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37
38
39
40
41
42
43
44
45
46
47
48
49
50
51
52
53
54
55
56
57
58
59
60
61
62
63
64
65
66
67
68
69
70
71
72
73
74
75
76
77
78
79
80
81
82
83
84
85
86
87
88
89
90
91
92
93
94
95
96
97
98
99
100
101
102
103
104
105
106
107
108
109
110
111
112
113
114
115
116
117
118
119
120
121
122
123
124
125
126
127
128
129
130
131
132
133
134
135
136
137
138
139
140
141
142
143
144
145
146
147
148
149
150
151
152
153
154
155
156
157
158
159
160
161
162

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))
            }
    }
}