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

// Copyright © 2024 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::traits::{
    OverflowingAddAssign, OverflowingAddMul, OverflowingAddMulAssign, UnsignedAbs,
};
use crate::num::basic::signeds::PrimitiveSigned;
use crate::num::basic::unsigneds::PrimitiveUnsigned;

fn overflowing_add_mul_unsigned<T: PrimitiveUnsigned>(x: T, y: T, z: T) -> (T, bool) {
    let (product, overflow_1) = y.overflowing_mul(z);
    let (result, overflow_2) = x.overflowing_add(product);
    (result, overflow_1 | overflow_2)
}

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

            /// Adds a number and the product of two other numbers.
            ///
            /// Returns a tuple containing the result and a boolean indicating whether an arithmetic
            /// overflow occured. If an overflow occurred, then the wrapped value is returned.
            ///
            /// # Worst-case complexity
            /// Constant time and additional memory.
            ///
            /// # Examples
            /// See [here](super::overflowing_add_mul#overflowing_add_mul).
            #[inline]
            fn overflowing_add_mul(self, y: $t, z: $t) -> ($t, bool) {
                overflowing_add_mul_unsigned(self, y, z)
            }
        }

        impl OverflowingAddMulAssign<$t> for $t {
            /// Adds a number and the product of two other numbers, in place.
            ///
            /// Returns a boolean indicating whether an arithmetic overflow occurred. If an overflow
            /// occurred, then the wrapped value is assigned.
            ///
            /// # Worst-case complexity
            /// Constant time and additional memory.
            ///
            /// # Examples
            /// See [here](super::overflowing_add_mul#overflowing_add_mul_assign).
            #[inline]
            fn overflowing_add_mul_assign(&mut self, y: $t, z: $t) -> bool {
                let (product, overflow) = y.overflowing_mul(z);
                self.overflowing_add_assign(product) | overflow
            }
        }
    };
}
apply_to_unsigneds!(impl_overflowing_add_mul_unsigned);

fn overflowing_add_mul_signed<
    U: PrimitiveUnsigned,
    S: PrimitiveSigned + UnsignedAbs<Output = U>,
>(
    x: S,
    y: S,
    z: S,
) -> (S, bool) {
    if y == S::ZERO || z == S::ZERO {
        return (x, false);
    }
    let x_sign = x >= S::ZERO;
    if x_sign == ((y >= S::ZERO) == (z >= S::ZERO)) {
        let (product, overflow_1) = y.overflowing_mul(z);
        let (result, overflow_2) = x.overflowing_add(product);
        (result, overflow_1 | overflow_2)
    } else {
        let result = x.wrapping_add(y.wrapping_mul(z));
        let overflow = {
            let x = x.unsigned_abs();
            match y.unsigned_abs().checked_mul(z.unsigned_abs()) {
                Some(product) => {
                    x < product
                        && if x_sign {
                            !x.wrapping_sub(product).get_highest_bit()
                        } else {
                            product.wrapping_sub(x).get_highest_bit()
                        }
                }
                None => true,
            }
        };
        (result, overflow)
    }
}

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

            /// Adds a number and the product of two other numbers.
            ///
            /// Returns a tuple containing the result and a boolean indicating whether an arithmetic
            /// overflow occurred. If an overflow occurred, then the wrapped value is returned.
            ///
            /// # Worst-case complexity
            /// Constant time and additional memory.
            ///
            /// # Examples
            /// See [here](super::overflowing_add_mul#overflowing_add_mul).
            #[inline]
            fn overflowing_add_mul(self, y: $t, z: $t) -> ($t, bool) {
                overflowing_add_mul_signed(self, y, z)
            }
        }

        impl OverflowingAddMulAssign<$t> for $t {
            /// Adds a number and the product of two other numbers, in place.
            ///
            /// Returns a boolean indicating whether an arithmetic overflow occurred. If an overflow
            /// occurred, then the wrapped value is assigned.
            ///
            /// # Worst-case complexity
            /// Constant time and additional memory.
            ///
            /// # Examples
            /// See [here](super::overflowing_add_mul#overflowing_add_mul_assign).
            #[inline]
            fn overflowing_add_mul_assign(&mut self, y: $t, z: $t) -> bool {
                let overflow;
                (*self, overflow) = self.overflowing_add_mul(y, z);
                overflow
            }
        }
    };
}
apply_to_signeds!(impl_overflowing_add_mul_signed);