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
// 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::integer::Integer;
use crate::integer_vector::IntegerVector;
use malachite_base::num::arithmetic::traits::ElementProduct;
impl ElementProduct for IntegerVector {
type Output = Integer;
/// Returns the product of the elements of an [`IntegerVector`], taking the vector by reference.
///
/// The 0-dimensional vector has no elements, and their product is 1. The elements are
/// multiplied in a balanced tree, so that the operands of each multiplication have similar
/// sizes, and multiplication stops as soon as a zero element is found.
///
/// $$
/// f(v) = \prod_i v_i.
/// $$
///
/// # Worst-case complexity
/// $T(n) = O(n (\log n)^2 \log\log n)$
///
/// $M(n) = O(n \log n)$
///
/// where $T$ is time, $M$ is additional memory, and $n$ is the total number of bits of the
/// elements.
///
/// # Examples
/// ```
/// use core::str::FromStr;
/// use malachite_base::num::arithmetic::traits::ElementProduct;
/// use malachite_nz::integer_vector::IntegerVector;
///
/// assert_eq!(
/// IntegerVector::from_str("(2, -3, 7)")
/// .unwrap()
/// .to_element_product(),
/// -42
/// );
/// assert_eq!(
/// IntegerVector::from_str("()").unwrap().to_element_product(),
/// 1
/// );
/// ```
///
/// This is equivalent to `_fmpz_vec_prod` from `fmpz_vec/prod.c`, FLINT 3.6.0.
#[inline]
fn to_element_product(&self) -> Integer {
self.elements.iter().product()
}
/// Returns the product of the elements of an [`IntegerVector`], taking the vector by value.
///
/// The 0-dimensional vector has no elements, and their product is 1. The elements are
/// multiplied in a balanced tree, so that the operands of each multiplication have similar
/// sizes, and multiplication stops as soon as a zero element is found.
///
/// $$
/// f(v) = \prod_i v_i.
/// $$
///
/// # Worst-case complexity
/// $T(n) = O(n (\log n)^2 \log\log n)$
///
/// $M(n) = O(n \log n)$
///
/// where $T$ is time, $M$ is additional memory, and $n$ is the total number of bits of the
/// elements.
///
/// # Examples
/// ```
/// use core::str::FromStr;
/// use malachite_base::num::arithmetic::traits::ElementProduct;
/// use malachite_nz::integer_vector::IntegerVector;
///
/// assert_eq!(
/// IntegerVector::from_str("(2, -3, 7)")
/// .unwrap()
/// .into_element_product(),
/// -42
/// );
/// assert_eq!(
/// IntegerVector::from_str("()")
/// .unwrap()
/// .into_element_product(),
/// 1
/// );
/// ```
///
/// This is equivalent to `_fmpz_vec_prod` from `fmpz_vec/prod.c`, FLINT 3.6.0.
#[inline]
fn into_element_product(self) -> Integer {
self.elements.into_iter().product()
}
}