plonky2/src/gadgets/arithmetic.rs

use crate::circuit_builder::CircuitBuilder;
use crate::field::field::Field;
use crate::gates::arithmetic::ArithmeticGate;
use crate::target::Target;
use crate::wire::Wire;
use crate::generator::SimpleGenerator;
use crate::witness::PartialWitness;

impl<F: Field> CircuitBuilder<F> {
    pub fn neg(&mut self, x: Target) -> Target {
        let neg_one = self.neg_one();
        self.mul(x, neg_one)
    }

    /// Computes `const_0 * multiplicand_0 * multiplicand_1 + const_1 * addend`.
    pub fn arithmetic(
        &mut self,
        const_0: F,
        multiplicand_0: Target,
        multiplicand_1: Target,
        const_1: F,
        addend: Target,
    ) -> Target {
        // See if we can determine the result without adding an `ArithmeticGate`.
        if let Some(result) = self.arithmetic_special_cases(
            const_0, multiplicand_0, multiplicand_1, const_1, addend) {
            return result;
        }

        let gate = self.add_gate(ArithmeticGate::new(), vec![const_0, const_1]);

        let wire_multiplicand_0 = Wire {
            gate,
            input: ArithmeticGate::WIRE_MULTIPLICAND_0,
        };
        let wire_multiplicand_1 = Wire {
            gate,
            input: ArithmeticGate::WIRE_MULTIPLICAND_1,
        };
        let wire_addend = Wire {
            gate,
            input: ArithmeticGate::WIRE_ADDEND,
        };
        let wire_output = Wire {
            gate,
            input: ArithmeticGate::WIRE_OUTPUT,
        };

        self.route(multiplicand_0, Target::Wire(wire_multiplicand_0));
        self.route(multiplicand_1, Target::Wire(wire_multiplicand_1));
        self.route(addend, Target::Wire(wire_addend));
        Target::Wire(wire_output)
    }

    /// Checks for special cases where the value of
    /// `const_0 * multiplicand_0 * multiplicand_1 + const_1 * addend`
    /// can be determined without adding an `ArithmeticGate`.
    fn arithmetic_special_cases(
        &mut self,
        const_0: F,
        multiplicand_0: Target,
        multiplicand_1: Target,
        const_1: F,
        addend: Target,
    ) -> Option<Target> {
        let zero = self.zero();

        let mul_0_const = self.target_as_constant(multiplicand_0);
        let mul_1_const = self.target_as_constant(multiplicand_1);
        let addend_const = self.target_as_constant(addend);

        let first_term_zero = const_0 == F::ZERO || multiplicand_0 == zero || multiplicand_1 == zero;
        let second_term_zero = const_1 == F::ZERO || addend == zero;

        // If both terms are constant, return their (constant) sum.
        let first_term_const = if first_term_zero {
            Some(F::ZERO)
        } else if let (Some(x), Some(y)) = (mul_0_const, mul_1_const) {
            Some(const_0 * x * y)
        } else {
            None
        };
        let second_term_const = if second_term_zero {
            Some(F::ZERO)
        } else {
            addend_const.map(|x| const_1 * x)
        };
        if let (Some(x), Some(y)) = (first_term_const, second_term_const) {
            return Some(self.constant(x + y));
        }

        if first_term_zero {
            if const_1.is_one() {
                return Some(addend);
            }
        }

        if second_term_zero {
            if let Some(x) = mul_0_const {
                if (const_0 * x).is_one() {
                    return Some(multiplicand_1);
                }
            }
            if let Some(x) = mul_1_const {
                if (const_1 * x).is_one() {
                    return Some(multiplicand_0);
                }
            }
        }

        None
    }

    pub fn add(&mut self, x: Target, y: Target) -> Target {
        let one = self.one();
        // x + y = 1 * x * 1 + 1 * y
        self.arithmetic(F::ONE, x, one, F::ONE, y)
    }

    pub fn add_many(&mut self, terms: &[Target]) -> Target {
        let mut sum = self.zero();
        for term in terms {
            sum = self.add(sum, *term);
        }
        sum
    }

    pub fn sub(&mut self, x: Target, y: Target) -> Target {
        let one = self.one();
        // x - y = 1 * x * 1 + (-1) * y
        self.arithmetic(F::ONE, x, one, F::NEG_ONE, y)
    }

    pub fn mul(&mut self, x: Target, y: Target) -> Target {
        // x * y = 1 * x * y + 0 * x
        self.arithmetic(F::ONE, x, y, F::ZERO, x)
    }

    pub fn mul_many(&mut self, terms: &[Target]) -> Target {
        let mut product = self.one();
        for term in terms {
            product = self.mul(product, *term);
        }
        product
    }

    /// Computes `q = x / y` by witnessing `q` and requiring that `q * y = x`. This can be unsafe in
    /// some cases, as it allows `0 / 0 = <anything>`.
    pub fn div_unsafe(&mut self, x: Target, y: Target) -> Target {
        // Check for special cases where we can determine the result without an `ArithmeticGate`.
        let zero = self.zero();
        let one = self.one();
        if x == zero {
            return zero;
        }
        if y == one {
            return x;
        }
        if let (Some(x_const), Some(y_const)) = (self.target_as_constant(x), self.target_as_constant(y)) {
            return self.constant(x_const / y_const);
        }

        // Add an `ArithmeticGate` to compute `q * y`.
        let gate = self.add_gate(ArithmeticGate::new(), vec![F::ONE, F::ZERO]);

        let wire_multiplicand_0 = Wire { gate, input: ArithmeticGate::WIRE_MULTIPLICAND_0 };
        let wire_multiplicand_1 = Wire { gate, input: ArithmeticGate::WIRE_MULTIPLICAND_1 };
        let wire_addend = Wire { gate, input: ArithmeticGate::WIRE_ADDEND };
        let wire_output = Wire { gate, input: ArithmeticGate::WIRE_OUTPUT };

        let q = Target::Wire(wire_multiplicand_0);
        self.add_generator(QuotientGenerator {
            numerator: x,
            denominator: y,
            quotient: q,
        });

        self.route(y, Target::Wire(wire_multiplicand_1));

        // This can be anything, since the whole second term has a weight of zero.
        self.route(zero, Target::Wire(wire_addend));

        let q_y = Target::Wire(wire_output);
        self.assert_equal(q_y, x);

        q
    }
}

struct QuotientGenerator {
    numerator: Target,
    denominator: Target,
    quotient: Target,
}

impl<F: Field> SimpleGenerator<F> for QuotientGenerator {
    fn dependencies(&self) -> Vec<Target> {
        vec![self.numerator, self.denominator]
    }

    fn run_once(&self, witness: &PartialWitness<F>) -> PartialWitness<F> {
        let num = witness.get_target(self.numerator);
        let den = witness.get_target(self.denominator);
        PartialWitness::singleton_target(self.quotient, num / den)
    }
}