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
163
164
165
166
167
168
169
170
171
172
173
174
175
176
177
178
179
180
181
182
183
184
185
186
187
188
189
190
191
192
193
194
195
196
197
198
199
200
201
202
203
204
205
206
207
208
209
210
211
212
213
214
215
216
217
218
219
220
221
222
223
224
225
226
227
228
229
230
231
232
use crate::prelude::*;
use std::{collections::VecDeque, vec};

/// A loosely-packed arbitrary base big int. 
/// See `Loose<BASE>` for implementation details.
pub type LooseInt<const BASE: usize> = BigInt<BASE, Loose<BASE>>;

/// A loosely-packed arbitrary base big int implementation. 
/// Supports any base from 2-u64::MAX. 
/// 
/// Each digit requires 8 bytes of storage, making this a somewhat space-inefficient 
/// implementation. however, the lack of additional complexity improves runtime efficiency on the
/// tightly-packed implementation.
/// 
/// ```
/// use big_int::prelude::*;
/// 
/// let a: LooseInt<10> = 593.into();
/// let b = a * 96.into();
/// assert_eq!(b, 56928.into());
/// ```
#[derive(Clone, Debug, PartialEq, Eq)]
pub struct Loose<const BASE: usize> {
    sign: Sign,
    digits: Vec<Digit>,
}

impl<const BASE: usize> Loose<BASE> {
    /// Create a new `Loose` int directly from a `Vec` of individual digits.
    ///
    /// Ensure the resulting int is properly normalized, and that no digits are greater than or
    /// equal to the base, to preserve soundness.
    ///
    /// To construct a negative int from raw parts, simply apply the negation
    /// operator (`-`) afterwards.
    ///
    /// ```
    /// use big_int::prelude::*;
    ///
    /// assert_eq!(
    ///     -BigInt(unsafe { Loose::<10>::from_raw_parts(vec![1, 5]) }),
    ///     (-15).into()
    /// );
    /// ```
    pub unsafe fn from_raw_parts(digits: Vec<Digit>) -> Self {
        let sign = Positive;
        Loose { sign, digits }
    }

    /// Extract the underlying digit Vec from the int.
    ///
    /// Can only be used to recreate the original int with the unsafe `from_raw_parts` fn.
    ///
    /// ```
    /// use big_int::prelude::*;
    ///
    /// assert_eq!(
    ///     LooseInt::<10>::from(539).0.digits(),
    ///     vec![5, 3, 9]
    /// );
    /// ```
    pub fn digits(self) -> Vec<Digit> {
        self.digits
    }
}

impl<const BASE: usize> BigIntImplementation<BASE> for Loose<BASE> {
    type Builder = LooseBuilder<{ BASE }>;

    fn len(&self) -> usize {
        self.digits.len()
    }

    fn get_digit(&self, digit: usize) -> Option<Digit> {
        self.digits.get(digit).copied()
    }

    /// ```
    /// use big_int::prelude::*;
    ///
    /// let mut a: Loose<10> = unsafe { Loose::from_raw_parts(vec![1, 2]) };
    /// a.set_digit(1, 0);
    /// assert_eq!(a, unsafe { Loose::from_raw_parts(vec![1, 0]) });
    /// ```
    fn set_digit(&mut self, digit: usize, value: Digit) {
        if let Some(digit) = self.digits.get_mut(digit) {
            *digit = value;
        }
    }

    fn zero() -> Self {
        let sign = Positive;
        let digits = vec![0];
        Loose { sign, digits }
    }

    fn with_sign(self, sign: Sign) -> Self {
        Loose { sign, ..self }
    }

    /// Return a normalized version of the int. Remove trailing zeros, and disable the parity flag
    /// if the resulting number is zero.
    ///
    /// ```
    /// use big_int::prelude::*;
    ///
    /// let n = BigInt(unsafe { Loose::<10>::from_raw_parts(vec![0, 0, 8, 3]) });
    /// assert_eq!(n.normalized(), 83.into());
    /// ```
    fn normalized(self) -> Self {
        match self.digits.iter().position(|digit| *digit != 0) {
            None => Self::zero(),
            Some(pos @ 1..) => Loose {
                digits: self.digits[pos..].to_vec(),
                ..self
            },
            _ => self,
        }
    }

    type DigitIterator<'a> = LooseIter<'a, BASE>;

    fn sign(&self) -> Sign {
        self.sign
    }

    fn set_sign(&mut self, sign: Sign) {
        self.sign = sign;
    }

    fn push_back(&mut self, digit: crate::Digit) {
        self.digits.push(digit);
    }

    unsafe fn push_front(&mut self, digit: crate::Digit) {
        self.digits.insert(0, digit);
    }

    fn shr_assign(&mut self, amount: usize) {
        self.digits =
            self.digits[..self.digits.len().checked_sub(amount).unwrap_or_default()].to_vec();
    }

    fn shl_assign(&mut self, amount: usize) {
        self.digits.extend(vec![0; amount]);
    }

    fn iter<'a>(&'a self) -> Self::DigitIterator<'a> {
        LooseIter {
            index: 0,
            back_index: self.len(),
            int: self,
        }
    }
}

pub struct LooseIter<'a, const BASE: usize> {
    index: usize,
    back_index: usize,
    int: &'a Loose<BASE>,
}

impl<const BASE: usize> Iterator for LooseIter<'_, BASE> {
    type Item = Digit;

    fn next(&mut self) -> Option<Self::Item> {
        (self.index < self.back_index)
            .then_some(&mut self.index)
            .and_then(|index| {
                *index += 1;
                self.int.digits.get(*index - 1)
            })
            .copied()
    }
}

impl<const BASE: usize> DoubleEndedIterator for LooseIter<'_, BASE> {
    fn next_back(&mut self) -> Option<Self::Item> {
        (self.back_index > self.index)
            .then_some(&mut self.back_index)
            .and_then(|index| {
                *index -= 1;
                self.int.digits.get(*index)
            })
            .copied()
    }
}

#[derive(Debug)]
pub struct LooseBuilder<const BASE: usize> {
    sign: Sign,
    digits: VecDeque<Digit>,
}

impl<const BASE: usize> BigIntBuilder<BASE> for LooseBuilder<BASE> {
    fn new() -> Self {
        LooseBuilder {
            sign: Positive,
            digits: VecDeque::new(),
        }
    }

    fn push_front(&mut self, digit: Digit) {
        self.digits.push_front(digit);
    }

    fn push_back(&mut self, digit: Digit) {
        self.digits.push_back(digit);
    }

    fn with_sign(self, sign: Sign) -> Self {
        LooseBuilder { sign, ..self }
    }

    fn is_empty(&self) -> bool {
        self.digits.is_empty()
    }
}

impl<const BASE: usize> Build<Loose<BASE>> for LooseBuilder<BASE> {
    fn build(self) -> Loose<BASE> {
        Loose::<BASE>::from(self).normalized()
    }
}

impl<const BASE: usize> From<LooseBuilder<BASE>> for Loose<BASE> {
    fn from(value: LooseBuilder<BASE>) -> Self {
        let sign = value.sign;
        let digits = value.digits.into();
        Loose { sign, digits }
    }
}