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

// Copyright © 2024 Mikhail Hogrefe
//
// Uses code adopted from the FLINT Library.
//
//      Copyright © 2010 William Hart
//
//      Copyright © 2021 Fredrik Johansson
//
// 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::traits::{ModAdd, ModAddAssign};
use crate::num::basic::unsigneds::PrimitiveUnsigned;

fn mod_add<T: PrimitiveUnsigned>(x: T, y: T, m: T) -> T {
    assert!(x < m, "x must be reduced mod m, but {x} >= {m}");
    assert!(y < m, "y must be reduced mod m, but {y} >= {m}");
    let neg = m - x;
    if neg > y {
        x + y
    } else {
        y - neg
    }
}

fn mod_add_assign<T: PrimitiveUnsigned>(x: &mut T, y: T, m: T) {
    assert!(*x < m, "x must be reduced mod m, but {x} >= {m}");
    assert!(y < m, "y must be reduced mod m, but {y} >= {m}");
    let neg = m - *x;
    if neg > y {
        *x += y;
    } else {
        *x = y - neg;
    }
}

macro_rules! impl_mod_add {
    ($t:ident) => {
        impl ModAdd<$t> for $t {
            type Output = $t;

            /// Adds two numbers modulo a third number $m$. The inputs must be already reduced
            /// modulo $m$.
            ///
            /// $f(x, y, m) = z$, where $x, y, z < m$ and $x + y \equiv z \mod m$.
            ///
            /// # Worst-case complexity
            /// Constant time and additional memory.
            ///
            /// # Panics
            /// Panics if `self` or `other` are greater than or equal to `m`.
            ///
            /// # Examples
            /// See [here](super::mod_add#mod_add).
            ///
            /// This is equivalent to `nmod_add` from `nmod.h`, FLINT 2.7.1.
            #[inline]
            fn mod_add(self, other: $t, m: $t) -> $t {
                mod_add(self, other, m)
            }
        }

        impl ModAddAssign<$t> for $t {
            /// Adds two numbers modulo a third number $m$, in place. The inputs must be already
            /// reduced modulo $m$.
            ///
            /// $x \gets z$, where $x, y, z < m$ and $x + y \equiv z \mod m$.
            ///
            /// # Worst-case complexity
            /// Constant time and additional memory.
            ///
            /// # Panics
            /// Panics if `self` or `other` are greater than or equal to `m`.
            ///
            /// # Examples
            /// See [here](super::mod_add#mod_add_assign).
            ///
            /// This is equivalent to `nmod_add` from `nmod.h`, FLINT 2.7.1, where the result is
            /// assigned to `a`.
            #[inline]
            fn mod_add_assign(&mut self, other: $t, m: $t) {
                mod_add_assign(self, other, m);
            }
        }
    };
}
apply_to_unsigneds!(impl_mod_add);