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
// Copyright © 2026 Mikhail Hogrefe
//
// This file is part of Malachite.
//
// Malachite is free software: you can redistribute it and/or modify it under the terms of the GNU
// Lesser General Public License (LGPL) as published by the Free Software Foundation; either version
// 3 of the License, or (at your option) any later version. See <https://www.gnu.org/licenses/>.
use crate::num::arithmetic::mul_add_mul::{
Wide, mul_add_mul_wide_signed, mul_add_mul_wide_unsigned,
};
use crate::num::arithmetic::traits::{
OverflowingMulSubMul, OverflowingMulSubMulAssign, WrappingMulSubMul,
};
macro_rules! impl_overflowing_mul_sub_mul {
($t:ident, $wide:ident) => {
impl OverflowingMulSubMul for $t {
type Output = $t;
/// Subtracts the product of one pair of numbers from the product of another.
///
/// Returns a tuple of the result along with a boolean indicating whether an arithmetic
/// overflow occurred. If an overflow occurred, then the wrapped result is returned.
///
/// $$
/// f(x, y, z, w) = (xy - zw \\mod 2^W, m),
/// $$
/// where $W$ is `Self::WIDTH` and $m$ is true if and only if $xy - zw$ is not
/// representable.
///
/// # Worst-case complexity
/// Constant time and additional memory.
///
/// # Examples
/// See [here](super::overflowing_mul_sub_mul#overflowing_mul_sub_mul).
#[inline]
fn overflowing_mul_sub_mul(self, y: $t, z: $t, w: $t) -> ($t, bool) {
(
self.wrapping_mul_sub_mul(y, z, w),
!matches!($wide(self, y, z, w, true), Wide::Fits(_)),
)
}
}
impl OverflowingMulSubMulAssign for $t {
/// Subtracts the product of one pair of numbers from the product of another, in place.
///
/// Returns a boolean indicating whether an arithmetic overflow occurred. If an overflow
/// occurred, then the wrapped result is assigned.
///
/// $$
/// x \\gets xy - zw \\mod 2^W,
/// $$
/// where $W$ is `Self::WIDTH`; the return value is true if and only if $xy - zw$ is not
/// representable.
///
/// # Worst-case complexity
/// Constant time and additional memory.
///
/// # Examples
/// See [here](super::overflowing_mul_sub_mul#overflowing_mul_sub_mul_assign).
#[inline]
fn overflowing_mul_sub_mul_assign(&mut self, y: $t, z: $t, w: $t) -> bool {
let (result, overflow) = self.overflowing_mul_sub_mul(y, z, w);
*self = result;
overflow
}
}
};
}
macro_rules! impl_overflowing_mul_sub_mul_unsigned {
($t:ident) => {
impl_overflowing_mul_sub_mul!($t, mul_add_mul_wide_unsigned);
};
}
apply_to_unsigneds!(impl_overflowing_mul_sub_mul_unsigned);
macro_rules! impl_overflowing_mul_sub_mul_signed {
($t:ident) => {
impl_overflowing_mul_sub_mul!($t, mul_add_mul_wide_signed);
};
}
apply_to_signeds!(impl_overflowing_mul_sub_mul_signed);