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
141
142
143
144
145
146
147
148
149
150
151
152
153
154
155
156
157
158
159
160
161
162
163
164
165
166
167
168
169
170
171
172
173
174
175
176
177
178
179
180
181
182
183
184
185
186
187
188
189
190
191
192
193
194
195
196
197
//! Definition of linear combinations.

use curve25519_dalek::scalar::Scalar;
use std::iter::FromIterator;
use std::ops::{Add, Mul, Neg, Sub};

/// Represents a variable in a constraint system.
#[derive(Copy, Clone, Debug)]
pub enum Variable {
    /// Represents an external input specified by a commitment.
    Committed(usize),
    /// Represents the left input of a multiplication gate.
    MultiplierLeft(usize),
    /// Represents the right input of a multiplication gate.
    MultiplierRight(usize),
    /// Represents the output of a multiplication gate.
    MultiplierOutput(usize),
    /// Represents the constant 1.
    One(),
}

impl From<Variable> for LinearCombination {
    fn from(v: Variable) -> LinearCombination {
        LinearCombination {
            terms: vec![(v, Scalar::one())],
        }
    }
}

impl<S: Into<Scalar>> From<S> for LinearCombination {
    fn from(s: S) -> LinearCombination {
        LinearCombination {
            terms: vec![(Variable::One(), s.into())],
        }
    }
}

// Arithmetic on variables produces linear combinations

impl Neg for Variable {
    type Output = LinearCombination;

    fn neg(self) -> Self::Output {
        -LinearCombination::from(self)
    }
}

impl<L: Into<LinearCombination>> Add<L> for Variable {
    type Output = LinearCombination;

    fn add(self, other: L) -> Self::Output {
        LinearCombination::from(self) + other.into()
    }
}

impl<L: Into<LinearCombination>> Sub<L> for Variable {
    type Output = LinearCombination;

    fn sub(self, other: L) -> Self::Output {
        LinearCombination::from(self) - other.into()
    }
}

impl<S: Into<Scalar>> Mul<S> for Variable {
    type Output = LinearCombination;

    fn mul(self, other: S) -> Self::Output {
        LinearCombination {
            terms: vec![(self, other.into())],
        }
    }
}

// Arithmetic on scalars with variables produces linear combinations

impl Add<Variable> for Scalar {
    type Output = LinearCombination;

    fn add(self, other: Variable) -> Self::Output {
        LinearCombination {
            terms: vec![(Variable::One(), self), (other, Scalar::one())],
        }
    }
}

impl Sub<Variable> for Scalar {
    type Output = LinearCombination;

    fn sub(self, other: Variable) -> Self::Output {
        LinearCombination {
            terms: vec![(Variable::One(), self), (other, -Scalar::one())],
        }
    }
}

impl Mul<Variable> for Scalar {
    type Output = LinearCombination;

    fn mul(self, other: Variable) -> Self::Output {
        LinearCombination {
            terms: vec![(other, self)],
        }
    }
}

/// Represents a linear combination of
/// [`Variables`](::r1cs::Variable).  Each term is represented by a
/// `(Variable, Scalar)` pair.
#[derive(Clone, Debug)]
pub struct LinearCombination {
    pub(super) terms: Vec<(Variable, Scalar)>,
}

impl Default for LinearCombination {
    fn default() -> Self {
        LinearCombination { terms: Vec::new() }
    }
}

impl FromIterator<(Variable, Scalar)> for LinearCombination {
    fn from_iter<T>(iter: T) -> Self
    where
        T: IntoIterator<Item = (Variable, Scalar)>,
    {
        LinearCombination {
            terms: iter.into_iter().collect(),
        }
    }
}

impl<'a> FromIterator<&'a (Variable, Scalar)> for LinearCombination {
    fn from_iter<T>(iter: T) -> Self
    where
        T: IntoIterator<Item = &'a (Variable, Scalar)>,
    {
        LinearCombination {
            terms: iter.into_iter().cloned().collect(),
        }
    }
}

// Arithmetic on linear combinations

impl<L: Into<LinearCombination>> Add<L> for LinearCombination {
    type Output = Self;

    fn add(mut self, rhs: L) -> Self::Output {
        self.terms.extend(rhs.into().terms.iter().cloned());
        LinearCombination { terms: self.terms }
    }
}

impl<L: Into<LinearCombination>> Sub<L> for LinearCombination {
    type Output = Self;

    fn sub(mut self, rhs: L) -> Self::Output {
        self.terms
            .extend(rhs.into().terms.iter().map(|(var, coeff)| (*var, -coeff)));
        LinearCombination { terms: self.terms }
    }
}

impl Mul<LinearCombination> for Scalar {
    type Output = LinearCombination;

    fn mul(self, other: LinearCombination) -> Self::Output {
        let out_terms = other
            .terms
            .into_iter()
            .map(|(var, scalar)| (var, scalar * self))
            .collect();
        LinearCombination { terms: out_terms }
    }
}

impl Neg for LinearCombination {
    type Output = Self;

    fn neg(mut self) -> Self::Output {
        for (_, s) in self.terms.iter_mut() {
            *s = -*s
        }
        self
    }
}

impl<S: Into<Scalar>> Mul<S> for LinearCombination {
    type Output = Self;

    fn mul(mut self, other: S) -> Self::Output {
        let other = other.into();
        for (_, s) in self.terms.iter_mut() {
            *s *= other
        }
        self
    }
}