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

// Copyright (C) 2019-2022 Aleo Systems Inc.
// This file is part of the snarkVM library.

// The snarkVM library is free software: you can redistribute it and/or modify
// it under the terms of the GNU General Public License as published by
// the Free Software Foundation, either version 3 of the License, or
// (at your option) any later version.

// The snarkVM library is distributed in the hope that it will be useful,
// but WITHOUT ANY WARRANTY; without even the implied warranty of
// MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
// GNU General Public License for more details.

// You should have received a copy of the GNU General Public License
// along with the snarkVM library. If not, see <https://www.gnu.org/licenses/>.

use super::*;

impl<E: Environment> Inv for Field<E> {
    type Output = Self;

    fn inv(self) -> Self::Output {
        Self::inverse(&self)
    }
}

impl<E: Environment> Inv for &Field<E> {
    type Output = Field<E>;

    fn inv(self) -> Self::Output {
        self.inverse()
    }
}

impl<E: Environment> Inverse for Field<E> {
    type Output = Field<E>;

    fn inverse(&self) -> Self::Output {
        let inverse = witness!(|self| match self.inverse() {
            Ok(inverse) => inverse,
            _ => console::Field::zero(),
        });

        // Ensure `self` * `self^(-1)` == 1.
        E::enforce(|| (self, &inverse, E::one()));

        inverse
    }
}

impl<E: Environment> Metrics<dyn Inverse<Output = Field<E>>> for Field<E> {
    type Case = Mode;

    fn count(case: &Self::Case) -> Count {
        match case.is_constant() {
            true => Count::is(1, 0, 0, 0),
            false => Count::is(0, 0, 1, 1),
        }
    }
}

impl<E: Environment> OutputMode<dyn Inverse<Output = Field<E>>> for Field<E> {
    type Case = Mode;

    fn output_mode(case: &Self::Case) -> Mode {
        match case.is_constant() {
            true => Mode::Constant,
            false => Mode::Private,
        }
    }
}

#[cfg(test)]
mod tests {
    use super::*;
    use snarkvm_circuit_environment::Circuit;

    const ITERATIONS: u64 = 1_000;

    fn check_inverse(name: &str, mode: Mode) {
        for _ in 0..ITERATIONS {
            // Sample a random element.
            let given: console::Field<<Circuit as Environment>::Network> = Uniform::rand(&mut test_rng());
            // Compute it's inverse, or skip this iteration if it does not natively exist.
            if let Ok(expected) = given.inverse() {
                let candidate = Field::<Circuit>::new(mode, given);

                Circuit::scope(name, || {
                    let result = candidate.inverse();
                    assert_eq!(expected, result.eject_value());
                    assert_count!(Inverse(Field) => Field, &mode);
                    assert_output_mode!(Inverse(Field) => Field, &mode, result);
                });
                Circuit::reset();
            }
        }
    }

    #[test]
    fn test_inverse() {
        check_inverse("Constant", Mode::Constant);
        check_inverse("Public", Mode::Public);
        check_inverse("Private", Mode::Private);
    }

    #[test]
    fn test_zero_inverse_fails() {
        let zero = console::Field::<<Circuit as Environment>::Network>::zero();

        let result = std::panic::catch_unwind(|| Field::<Circuit>::zero().inverse());
        assert!(result.is_err());
        Circuit::reset();

        let result = std::panic::catch_unwind(|| Field::<Circuit>::new(Mode::Constant, zero).inverse());
        assert!(result.is_err());
        Circuit::reset();

        let candidate = Field::<Circuit>::new(Mode::Public, zero).inverse();
        assert_eq!(zero, candidate.eject_value());
        assert!(!Circuit::is_satisfied());
        Circuit::reset();

        let candidate = Field::<Circuit>::new(Mode::Private, zero).inverse();
        assert_eq!(zero, candidate.eject_value());
        assert!(!Circuit::is_satisfied());
        Circuit::reset();
    }
}