ruint 1.18.0

Unsigned integer type with const-generic bit length
Documentation 
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
233
234
235
236
237
238
239
240
241
242
243
244
245
246
247
248
249
250
251
252
253
254
255
256
257
258
259
260
261
262
263
264
265
266
267
268
269
270
271
272
273
274
275
276
277
278
279
280
281
282
283
284
285
286
287
288

#![allow(clippy::module_name_repetitions)]

use crate::algorithms::{DoubleWord, borrowing_sub};

/// ⚠️ Computes `result += a * b` and checks for overflow.
#[doc = crate::algorithms::unstable_warning!()]
/// Arrays are in little-endian order. All arrays can be arbitrary sized.
///
/// # Algorithm
///
/// Trims zeros from inputs, then uses the schoolbook multiplication algorithm.
/// It takes the shortest input as the outer loop.
///
/// # Examples
///
/// ```
/// # use ruint::algorithms::addmul;
/// let mut result = [0];
/// let overflow = addmul(&mut result, &[3], &[4]);
/// assert_eq!(overflow, false);
/// assert_eq!(result, [12]);
/// ```
#[inline(always)]
pub fn addmul(mut lhs: &mut [u64], mut a: &[u64], mut b: &[u64]) -> bool {
    // Trim zeros from `a`
    while let [0, rest @ ..] = a {
        a = rest;
        if let [_, rest @ ..] = lhs {
            lhs = rest;
        }
    }
    a = super::trim_end_zeros(a);
    if a.is_empty() {
        return false;
    }

    // Trim zeros from `b`
    while let [0, rest @ ..] = b {
        b = rest;
        if let [_, rest @ ..] = lhs {
            lhs = rest;
        }
    }
    b = super::trim_end_zeros(b);
    if b.is_empty() {
        return false;
    }

    if lhs.is_empty() {
        return true;
    }

    let (a, b) = if b.len() > a.len() { (b, a) } else { (a, b) };

    // Iterate over limbs of `b` and add partial products to `lhs`.
    let mut overflow = false;
    for &b in b {
        if lhs.len() >= a.len() {
            let (target, rest) = lhs.split_at_mut(a.len());
            let carry = addmul_nx1(target, a, b);
            let carry = add_nx1(rest, carry);
            overflow |= carry != 0;
        } else {
            overflow = true;
            if lhs.is_empty() {
                break;
            }
            addmul_nx1(lhs, &a[..lhs.len()], b);
        }
        lhs = &mut lhs[1..];
    }
    overflow
}

const ADDMUL_N_SMALL_LIMIT: usize = 8;

/// ⚠️ Computes wrapping `result += a * b`, with a fast-path for when all inputs
/// are the same length and small enough.
#[doc = crate::algorithms::unstable_warning!()]
/// See [`addmul`] for more details.
#[inline(always)]
pub fn addmul_n(lhs: &mut [u64], a: &[u64], b: &[u64]) {
    let n = lhs.len();
    if n <= ADDMUL_N_SMALL_LIMIT && a.len() == n && b.len() == n {
        addmul_n_small(lhs, a, b);
    } else {
        let _ = addmul(lhs, a, b);
    }
}

#[inline(always)]
fn addmul_n_small(lhs: &mut [u64], a: &[u64], b: &[u64]) {
    let n = lhs.len();
    assume!(n <= ADDMUL_N_SMALL_LIMIT);
    assume!(a.len() == n);
    assume!(b.len() == n);

    for j in 0..n {
        let mut carry = 0;
        // Widening multiply-accumulate for all but the last position.
        let i = n - j - 1;
        for i in 0..i {
            (lhs[j + i], carry) = u128::muladd2(a[i], b[j], carry, lhs[j + i]).split();
        }
        // Last position: the carry out is discarded (it would go beyond n
        // limbs), so use truncated arithmetic to reduce register pressure.
        lhs[j + i] = (a[i].wrapping_mul(b[j]))
            .wrapping_add(lhs[j + i])
            .wrapping_add(carry);
    }
}

/// ⚠️ Computes `lhs += a` and returns the carry.
#[doc = crate::algorithms::unstable_warning!()]
#[inline(always)]
pub fn add_nx1(lhs: &mut [u64], mut a: u64) -> u64 {
    if a == 0 {
        return 0;
    }
    for lhs in lhs {
        (*lhs, a) = u128::add(*lhs, a).split();
        if a == 0 {
            return 0;
        }
    }
    a
}

/// ⚠️ Computes `lhs *= a` and returns the carry.
#[doc = crate::algorithms::unstable_warning!()]
#[inline(always)]
pub fn mul_nx1(lhs: &mut [u64], a: u64) -> u64 {
    let mut carry = 0;
    for lhs in lhs {
        (*lhs, carry) = u128::muladd(*lhs, a, carry).split();
    }
    carry
}

/// ⚠️ Computes `lhs += a * b` and returns the carry.
#[doc = crate::algorithms::unstable_warning!()]
/// Requires `lhs.len() == a.len()`.
///
/// $$
/// \begin{aligned}
/// \mathsf{lhs'} &= \mod{\mathsf{lhs} + \mathsf{a} ⋅ \mathsf{b}}_{2^{64⋅N}}
/// \\\\ \mathsf{carry} &= \floor{\frac{\mathsf{lhs} + \mathsf{a} ⋅ \mathsf{b}
/// }{2^{64⋅N}}} \end{aligned}
/// $$
#[inline(always)]
pub fn addmul_nx1(lhs: &mut [u64], a: &[u64], b: u64) -> u64 {
    assume!(lhs.len() == a.len());
    let mut carry = 0;
    for i in 0..a.len() {
        (lhs[i], carry) = u128::muladd2(a[i], b, carry, lhs[i]).split();
    }
    carry
}

/// ⚠️ Computes `lhs -= a * b` and returns the borrow.
#[doc = crate::algorithms::unstable_warning!()]
/// Requires `lhs.len() == a.len()`.
///
/// $$
/// \begin{aligned}
/// \mathsf{lhs'} &= \mod{\mathsf{lhs} - \mathsf{a} ⋅ \mathsf{b}}_{2^{64⋅N}}
/// \\\\ \mathsf{borrow} &= \floor{\frac{\mathsf{a} ⋅ \mathsf{b} -
/// \mathsf{lhs}}{2^{64⋅N}}} \end{aligned}
/// $$
// OPT: `carry` and `borrow` can probably be merged into a single var.
#[inline(always)]
pub fn submul_nx1(lhs: &mut [u64], a: &[u64], b: u64) -> u64 {
    assume!(lhs.len() == a.len());
    let mut carry = 0;
    let mut borrow = false;
    for i in 0..a.len() {
        // Compute product limbs
        let limb;
        (limb, carry) = u128::muladd(a[i], b, carry).split();

        // Subtract
        (lhs[i], borrow) = borrowing_sub(lhs[i], limb, borrow);
    }
    borrow as u64 + carry
}

#[cfg(test)]
mod tests {
    use super::*;
    use proptest::{collection, num::u64, proptest};

    #[allow(clippy::cast_possible_truncation)] // Intentional truncation.
    fn addmul_ref(result: &mut [u64], a: &[u64], b: &[u64]) -> bool {
        let mut overflow = 0;
        for (i, a) in a.iter().copied().enumerate() {
            let mut result = result.iter_mut().skip(i);
            let mut b = b.iter().copied();
            let mut carry = 0_u128;
            loop {
                match (result.next(), b.next()) {
                    // Partial product.
                    (Some(result), Some(b)) => {
                        carry += u128::from(*result) + u128::from(a) * u128::from(b);
                        *result = carry as u64;
                        carry >>= 64;
                    }
                    // Carry propagation.
                    (Some(result), None) => {
                        carry += u128::from(*result);
                        *result = carry as u64;
                        carry >>= 64;
                    }
                    // Excess product.
                    (None, Some(b)) => {
                        carry += u128::from(a) * u128::from(b);
                        overflow |= carry as u64;
                        carry >>= 64;
                    }
                    // Fin.
                    (None, None) => {
                        break;
                    }
                }
            }
            overflow |= carry as u64;
        }
        overflow != 0
    }

    #[test]
    fn test_addmul() {
        let any_vec = collection::vec(u64::ANY, 0..10);
        proptest!(|(mut lhs in &any_vec, a in &any_vec, b in &any_vec)| {
            // Reference
            let mut ref_lhs = lhs.clone();
            let ref_overflow = addmul_ref(&mut ref_lhs, &a, &b);

            // Test
            let overflow = addmul(&mut lhs, &a, &b);
            assert_eq!(lhs, ref_lhs);
            assert_eq!(overflow, ref_overflow);
        });
    }

    fn test_vals(lhs: &[u64], rhs: &[u64], expected: &[u64], expected_overflow: bool) {
        let mut result = vec![0; expected.len()];
        let overflow = addmul(&mut result, lhs, rhs);
        assert_eq!(overflow, expected_overflow);
        assert_eq!(result, expected);
    }

    #[test]
    fn test_empty() {
        test_vals(&[], &[], &[], false);
        test_vals(&[], &[1], &[], false);
        test_vals(&[1], &[], &[], false);
        test_vals(&[1], &[1], &[], true);
        test_vals(&[], &[], &[0], false);
        test_vals(&[], &[1], &[0], false);
        test_vals(&[1], &[], &[0], false);
        test_vals(&[1], &[1], &[1], false);
    }

    #[test]
    fn test_submul_nx1() {
        let mut lhs = [
            15520854688669198950,
            13760048731709406392,
            14363314282014368551,
            13263184899940581802,
        ];
        let a = [
            7955980792890017645,
            6297379555503105007,
            2473663400150304794,
            18362433840513668572,
        ];
        let b = 17275533833223164845;
        let borrow = submul_nx1(&mut lhs, &a, b);
        assert_eq!(lhs, [
            2427453526388035261,
            7389014268281543265,
            6670181329660292018,
            8411211985208067428
        ]);
        assert_eq!(borrow, 17196576577663999042);
    }
}