Trait GateInstructions 

pub trait GateInstructions<F: ScalarField> {
    // Required methods
    fn pow_of_two(&self) -> &[F];
    fn inner_product<QA>(
        &self,
        ctx: &mut Context<F>,
        a: impl IntoIterator<Item = QA>,
        b: impl IntoIterator<Item = QuantumCell<F>>,
    ) -> AssignedValue<F>
       where QA: Into<QuantumCell<F>>;
    fn inner_product_left_last<QA>(
        &self,
        ctx: &mut Context<F>,
        a: impl IntoIterator<Item = QA>,
        b: impl IntoIterator<Item = QuantumCell<F>>,
    ) -> (AssignedValue<F>, AssignedValue<F>)
       where QA: Into<QuantumCell<F>>;
    fn inner_product_left<QA>(
        &self,
        ctx: &mut Context<F>,
        a: impl IntoIterator<Item = QA>,
        b: impl IntoIterator<Item = QuantumCell<F>>,
    ) -> (AssignedValue<F>, Vec<AssignedValue<F>>)
       where QA: Into<QuantumCell<F>>;
    fn inner_product_with_sums<'thread, QA>(
        &self,
        ctx: &'thread mut Context<F>,
        a: impl IntoIterator<Item = QA>,
        b: impl IntoIterator<Item = QuantumCell<F>>,
    ) -> Box<dyn Iterator<Item = AssignedValue<F>> + 'thread>
       where QA: Into<QuantumCell<F>>;
    fn sum_products_with_coeff_and_var(
        &self,
        ctx: &mut Context<F>,
        values: impl IntoIterator<Item = (F, QuantumCell<F>, QuantumCell<F>)>,
        var: QuantumCell<F>,
    ) -> AssignedValue<F>;
    fn select(
        &self,
        ctx: &mut Context<F>,
        a: impl Into<QuantumCell<F>>,
        b: impl Into<QuantumCell<F>>,
        sel: impl Into<QuantumCell<F>>,
    ) -> AssignedValue<F>;
    fn or_and(
        &self,
        ctx: &mut Context<F>,
        a: impl Into<QuantumCell<F>>,
        b: impl Into<QuantumCell<F>>,
        c: impl Into<QuantumCell<F>>,
    ) -> AssignedValue<F>;
    fn num_to_bits(
        &self,
        ctx: &mut Context<F>,
        a: AssignedValue<F>,
        range_bits: usize,
    ) -> Vec<AssignedValue<F>>;
    fn pow_var(
        &self,
        ctx: &mut Context<F>,
        a: AssignedValue<F>,
        exp: AssignedValue<F>,
        max_bits: usize,
    ) -> AssignedValue<F>;

    // Provided methods
    fn add(
        &self,
        ctx: &mut Context<F>,
        a: impl Into<QuantumCell<F>>,
        b: impl Into<QuantumCell<F>>,
    ) -> AssignedValue<F> { ... }
    fn inc(
        &self,
        ctx: &mut Context<F>,
        a: impl Into<QuantumCell<F>>,
    ) -> AssignedValue<F> { ... }
    fn sub(
        &self,
        ctx: &mut Context<F>,
        a: impl Into<QuantumCell<F>>,
        b: impl Into<QuantumCell<F>>,
    ) -> AssignedValue<F> { ... }
    fn dec(
        &self,
        ctx: &mut Context<F>,
        a: impl Into<QuantumCell<F>>,
    ) -> AssignedValue<F> { ... }
    fn sub_mul(
        &self,
        ctx: &mut Context<F>,
        a: impl Into<QuantumCell<F>>,
        b: impl Into<QuantumCell<F>>,
        c: impl Into<QuantumCell<F>>,
    ) -> AssignedValue<F> { ... }
    fn neg(
        &self,
        ctx: &mut Context<F>,
        a: impl Into<QuantumCell<F>>,
    ) -> AssignedValue<F> { ... }
    fn mul(
        &self,
        ctx: &mut Context<F>,
        a: impl Into<QuantumCell<F>>,
        b: impl Into<QuantumCell<F>>,
    ) -> AssignedValue<F> { ... }
    fn mul_add(
        &self,
        ctx: &mut Context<F>,
        a: impl Into<QuantumCell<F>>,
        b: impl Into<QuantumCell<F>>,
        c: impl Into<QuantumCell<F>>,
    ) -> AssignedValue<F> { ... }
    fn mul_not(
        &self,
        ctx: &mut Context<F>,
        a: impl Into<QuantumCell<F>>,
        b: impl Into<QuantumCell<F>>,
    ) -> AssignedValue<F> { ... }
    fn assert_bit(&self, ctx: &mut Context<F>, x: AssignedValue<F>) { ... }
    fn div_unsafe(
        &self,
        ctx: &mut Context<F>,
        a: impl Into<QuantumCell<F>>,
        b: impl Into<QuantumCell<F>>,
    ) -> AssignedValue<F> { ... }
    fn assert_is_const(
        &self,
        ctx: &mut Context<F>,
        a: &AssignedValue<F>,
        constant: &F,
    ) { ... }
    fn sum<Q>(
        &self,
        ctx: &mut Context<F>,
        a: impl IntoIterator<Item = Q>,
    ) -> AssignedValue<F>
       where Q: Into<QuantumCell<F>> { ... }
    fn partial_sums<'thread, Q>(
        &self,
        ctx: &'thread mut Context<F>,
        a: impl IntoIterator<Item = Q>,
    ) -> Box<dyn Iterator<Item = AssignedValue<F>> + 'thread>
       where Q: Into<QuantumCell<F>> { ... }
    fn accumulated_product<QA, QB>(
        &self,
        ctx: &mut Context<F>,
        a: impl IntoIterator<Item = QA>,
        b: impl IntoIterator<Item = QB>,
    ) -> Vec<AssignedValue<F>>
       where QA: Into<QuantumCell<F>>,
             QB: Into<QuantumCell<F>> { ... }
    fn or(
        &self,
        ctx: &mut Context<F>,
        a: impl Into<QuantumCell<F>>,
        b: impl Into<QuantumCell<F>>,
    ) -> AssignedValue<F> { ... }
    fn and(
        &self,
        ctx: &mut Context<F>,
        a: impl Into<QuantumCell<F>>,
        b: impl Into<QuantumCell<F>>,
    ) -> AssignedValue<F> { ... }
    fn not(
        &self,
        ctx: &mut Context<F>,
        a: impl Into<QuantumCell<F>>,
    ) -> AssignedValue<F> { ... }
    fn bits_to_indicator(
        &self,
        ctx: &mut Context<F>,
        bits: &[AssignedValue<F>],
    ) -> Vec<AssignedValue<F>> { ... }
    fn idx_to_indicator(
        &self,
        ctx: &mut Context<F>,
        idx: impl Into<QuantumCell<F>>,
        len: usize,
    ) -> Vec<AssignedValue<F>> { ... }
    fn select_by_indicator<Q>(
        &self,
        ctx: &mut Context<F>,
        a: impl IntoIterator<Item = Q>,
        indicator: impl IntoIterator<Item = AssignedValue<F>>,
    ) -> AssignedValue<F>
       where Q: Into<QuantumCell<F>> { ... }
    fn select_from_idx<Q>(
        &self,
        ctx: &mut Context<F>,
        cells: impl IntoIterator<Item = Q>,
        idx: impl Into<QuantumCell<F>>,
    ) -> AssignedValue<F>
       where Q: Into<QuantumCell<F>> { ... }
    fn select_array_by_indicator<AR, AV>(
        &self,
        ctx: &mut Context<F>,
        array2d: &[AR],
        indicator: &[AssignedValue<F>],
    ) -> Vec<AssignedValue<F>>
       where AR: AsRef<[AV]>,
             AV: AsRef<AssignedValue<F>> { ... }
    fn is_zero(
        &self,
        ctx: &mut Context<F>,
        a: AssignedValue<F>,
    ) -> AssignedValue<F> { ... }
    fn is_equal(
        &self,
        ctx: &mut Context<F>,
        a: impl Into<QuantumCell<F>>,
        b: impl Into<QuantumCell<F>>,
    ) -> AssignedValue<F> { ... }
    fn lagrange_and_eval(
        &self,
        ctx: &mut Context<F>,
        coords: &[(AssignedValue<F>, AssignedValue<F>)],
        x: AssignedValue<F>,
    ) -> (AssignedValue<F>, AssignedValue<F>) { ... }
}

Trait that defines basic arithmetic operations for a gate.

Required Methods

fn pow_of_two(&self) -> &[F]

Returns a slice of the ScalarField field elements 2^i for i in 0..F::NUM_BITS.

fn inner_product<QA>( &self, ctx: &mut Context<F>, a: impl IntoIterator<Item = QA>, b: impl IntoIterator<Item = QuantumCell<F>>, ) -> AssignedValue<F>

where QA: Into<QuantumCell<F>>,

Constrains and returns the inner product of <a, b>.

Assumes ‘a’ and ‘b’ are the same length.

• ctx: Context to add the constraints to
• a: Iterator of QuantumCell values
• b: Iterator of QuantumCell values to take inner product of a by

fn inner_product_left_last<QA>( &self, ctx: &mut Context<F>, a: impl IntoIterator<Item = QA>, b: impl IntoIterator<Item = QuantumCell<F>>, ) -> (AssignedValue<F>, AssignedValue<F>)

where QA: Into<QuantumCell<F>>,

Returns the inner product of <a, b> and the last element of a after it has been assigned.

NOT encouraged for general usage. This is a low-level function, where you want to avoid first assigning a and then copying the last element into the correct cell for this computation.

Assumes ‘a’ and ‘b’ are the same length.

• ctx: Context of the circuit
• a: Iterator of QuantumCells
• b: Iterator of QuantumCells to take inner product of a by

fn inner_product_left<QA>( &self, ctx: &mut Context<F>, a: impl IntoIterator<Item = QA>, b: impl IntoIterator<Item = QuantumCell<F>>, ) -> (AssignedValue<F>, Vec<AssignedValue<F>>)

where QA: Into<QuantumCell<F>>,

Returns (<a,b>, a_assigned). See inner_product for more details.

NOT encouraged for general usage. This is a low-level function, useful for when you want to simultaneously compute an inner product while assigning private witnesses for the first time. This avoids first assigning a and then copying into the correct cells for this computation. We do not return the assignments of a in inner_product as an optimization to avoid the memory allocation of having to collect the vectors.

Assumes ‘a’ and ‘b’ are the same length.

fn inner_product_with_sums<'thread, QA>( &self, ctx: &'thread mut Context<F>, a: impl IntoIterator<Item = QA>, b: impl IntoIterator<Item = QuantumCell<F>>, ) -> Box<dyn Iterator<Item = AssignedValue<F>> + 'thread>

where QA: Into<QuantumCell<F>>,

Calculates and constrains the inner product.

Returns the assignment trace where output[i] has the running sum sum_{j=0..=i} a[j] * b[j].

Assumes ‘a’ and ‘b’ are the same length.

• ctx: Context to add the constraints to
• a: Iterator of QuantumCell values
• b: Iterator of QuantumCell values to calculate the partial sums of the inner product of a by.

fn sum_products_with_coeff_and_var( &self, ctx: &mut Context<F>, values: impl IntoIterator<Item = (F, QuantumCell<F>, QuantumCell<F>)>, var: QuantumCell<F>, ) -> AssignedValue<F>

Constrains and returns the sum of products of coeff * (a * b) defined in values plus a variable var e.g. x = var + values[0].0 * (values[0].1 * values[0].2) + values[1].0 * (values[1].1 * values[1].2) + ... + values[n].0 * (values[n].1 * values[n].2).

• ctx: Context to add the constraints to.
• values: Iterator of tuples (coeff, a, b) where coeff is a field element, a and b are QuantumCell’s.
• var: QuantumCell that represents the value of a variable added to the sum.

fn select( &self, ctx: &mut Context<F>, a: impl Into<QuantumCell<F>>, b: impl Into<QuantumCell<F>>, sel: impl Into<QuantumCell<F>>, ) -> AssignedValue<F>

Constrains and returns sel ? a : b assuming sel is boolean.

Defines a vertical gate of form | 1 - sel | sel | 1 | a | 1 - sel | sel | 1 | b | out |, where out = sel * a + (1 - sel) * b.

• ctx: Context to add the constraints to.
• a: QuantumCell that contains a boolean value.
• b: QuantumCell that contains a boolean value.
• sel: QuantumCell that contains a boolean value.

fn or_and( &self, ctx: &mut Context<F>, a: impl Into<QuantumCell<F>>, b: impl Into<QuantumCell<F>>, c: impl Into<QuantumCell<F>>, ) -> AssignedValue<F>

Constains and returns a || (b && c), assuming a, b and c are boolean.

Defines a vertical gate of form | 1 - b c | b | c | 1 | a - 1 | 1 - b c | out | a - 1 | 1 | 1 | a |, where out = a + b * c - a * b * c.

• ctx: Context to add the constraints to.
• a: QuantumCell that contains a boolean value.
• b: QuantumCell that contains a boolean value.
• c: QuantumCell that contains a boolean value.

fn num_to_bits( &self, ctx: &mut Context<F>, a: AssignedValue<F>, range_bits: usize, ) -> Vec<AssignedValue<F>>

Constrains and returns little-endian bit vector representation of a.

Assumes range_bits >= bit_length(a).

• a: QuantumCell of the value to convert
• range_bits: range of bits needed to represent a

fn pow_var( &self, ctx: &mut Context<F>, a: AssignedValue<F>, exp: AssignedValue<F>, max_bits: usize, ) -> AssignedValue<F>

Constrains and computes aexp where both a, exp are witnesses. The exponent is computed in the native field F.

Constrains that exp has at most max_bits bits.

Provided Methods

fn add( &self, ctx: &mut Context<F>, a: impl Into<QuantumCell<F>>, b: impl Into<QuantumCell<F>>, ) -> AssignedValue<F>

Constrains and returns a + b * 1 = out.

Defines a vertical gate of form | a | b | 1 | a + b | where (a + b) = out.

• ctx: Context to add the constraints to
• a: QuantumCell value
• b: QuantumCell value to add to ’a`

fn inc( &self, ctx: &mut Context<F>, a: impl Into<QuantumCell<F>>, ) -> AssignedValue<F>

Constrains and returns out = a + 1.

• ctx: Context to add the constraints to
• a: QuantumCell value

fn sub( &self, ctx: &mut Context<F>, a: impl Into<QuantumCell<F>>, b: impl Into<QuantumCell<F>>, ) -> AssignedValue<F>

Constrains and returns a + b * (-1) = out.

Defines a vertical gate of form | a - b | b | 1 | a |, where (a - b) = out.

• ctx: Context to add the constraints to
• a: QuantumCell value
• b: QuantumCell value to subtract from ‘a’

fn dec( &self, ctx: &mut Context<F>, a: impl Into<QuantumCell<F>>, ) -> AssignedValue<F>

Constrains and returns out = a - 1.

• ctx: Context to add the constraints to
• a: QuantumCell value

fn sub_mul( &self, ctx: &mut Context<F>, a: impl Into<QuantumCell<F>>, b: impl Into<QuantumCell<F>>, c: impl Into<QuantumCell<F>>, ) -> AssignedValue<F>

Constrains and returns a - b * c = out.

Defines a vertical gate of form | a - b * c | b | c | a |, where (a - b * c) = out.

• ctx: Context to add the constraints to
• a: QuantumCell value to subtract ‘b * c’ from
• b: QuantumCell value
• c: QuantumCell value

fn neg( &self, ctx: &mut Context<F>, a: impl Into<QuantumCell<F>>, ) -> AssignedValue<F>

Constrains and returns a * (-1) = out.

Defines a vertical gate of form | a | -a | 1 | 0 |, where (-a) = out.

• ctx: the Context to add the constraints to
• a: QuantumCell value to negate

fn mul( &self, ctx: &mut Context<F>, a: impl Into<QuantumCell<F>>, b: impl Into<QuantumCell<F>>, ) -> AssignedValue<F>

Constrains and returns 0 + a * b = out.

Defines a vertical gate of form | 0 | a | b | a * b |, where (a * b) = out.

• ctx: Context to add the constraints to
• a: QuantumCell value
• b: QuantumCell value to multiply ‘a’ by

fn mul_add( &self, ctx: &mut Context<F>, a: impl Into<QuantumCell<F>>, b: impl Into<QuantumCell<F>>, c: impl Into<QuantumCell<F>>, ) -> AssignedValue<F>

Constrains and returns a * b + c = out.

Defines a vertical gate of form | c | a | b | a * b + c |, where (a * b + c) = out.

• ctx: Context to add the constraints to
• a: QuantumCell value
• b: QuantumCell value to multiply ‘a’ by
• c: QuantumCell value to add to ‘a * b’

fn mul_not( &self, ctx: &mut Context<F>, a: impl Into<QuantumCell<F>>, b: impl Into<QuantumCell<F>>, ) -> AssignedValue<F>

Constrains and returns (1 - a) * b = b - a * b.

Defines a vertical gate of form | (1 - a) * b | a | b | b |, where (1 - a) * b = out.

• ctx: Context to add the constraints to
• a: QuantumCell value
• b: QuantumCell value to multiply ‘a’ by

fn assert_bit(&self, ctx: &mut Context<F>, x: AssignedValue<F>)

Constrains that x is boolean (e.g. 0 or 1).

Defines a vertical gate of form | 0 | x | x | x |.

• ctx: Context to add the constraints to
• x: QuantumCell value to constrain

fn div_unsafe( &self, ctx: &mut Context<F>, a: impl Into<QuantumCell<F>>, b: impl Into<QuantumCell<F>>, ) -> AssignedValue<F>

Constrains and returns a / b = out.

Defines a vertical gate of form | 0 | a / b | b | a |, where a / b = out.

Assumes b != 0.

• ctx: Context to add the constraints to
• a: QuantumCell value
• b: QuantumCell value to divide ‘a’ by

fn assert_is_const( &self, ctx: &mut Context<F>, a: &AssignedValue<F>, constant: &F, )

Constrains that a is equal to constant value.

• ctx: Context to add the constraints to
• a: QuantumCell value
• constant: constant value to constrain a to be equal to

fn sum<Q>( &self, ctx: &mut Context<F>, a: impl IntoIterator<Item = Q>, ) -> AssignedValue<F>

where Q: Into<QuantumCell<F>>,

Constrains and returns the sum of QuantumCell’s in iterator a.

• ctx: Context to add the constraints to
• a: Iterator of QuantumCell values to sum

fn partial_sums<'thread, Q>( &self, ctx: &'thread mut Context<F>, a: impl IntoIterator<Item = Q>, ) -> Box<dyn Iterator<Item = AssignedValue<F>> + 'thread>

where Q: Into<QuantumCell<F>>,

Calculates and constrains the sum of the elements of a.

Returns the assignment trace where output[i] has the running sum sum_{j=0..=i} a[j].

• ctx: Context to add the constraints to
• a: Iterator of QuantumCell values to sum

fn accumulated_product<QA, QB>( &self, ctx: &mut Context<F>, a: impl IntoIterator<Item = QA>, b: impl IntoIterator<Item = QB>, ) -> Vec<AssignedValue<F>>

where QA: Into<QuantumCell<F>>, QB: Into<QuantumCell<F>>,

Calculates and constrains the accumulated product of ‘a’ and ‘b’ i.e. x_i = b_1 * (a_1...a_{i - 1}) + b_2 * (a_2...a_{i - 1}) + ... + b_i

Returns the assignment trace where output[i] is the running accumulated product x_i.

Assumes ‘a’ and ‘b’ are the same length.

• ctx: Context to add the constraints to
• a: Iterator of QuantumCell values
• b: Iterator of QuantumCell values to take the accumulated product of a by

fn or( &self, ctx: &mut Context<F>, a: impl Into<QuantumCell<F>>, b: impl Into<QuantumCell<F>>, ) -> AssignedValue<F>

Constrains and returns a || b, assuming a and b are boolean.

Defines a vertical gate of form | 1 - b | 1 | b | 1 | b | a | 1 - b | out |, where out = a + b - a * b.

• ctx: Context to add the constraints to.
• a: QuantumCell that contains a boolean value.
• b: QuantumCell that contains a boolean value.

fn and( &self, ctx: &mut Context<F>, a: impl Into<QuantumCell<F>>, b: impl Into<QuantumCell<F>>, ) -> AssignedValue<F>

Constrains and returns a & b, assumeing a and b are boolean.

Defines a vertical gate of form | 0 | a | b | out |, where out = a * b.

• ctx: Context to add the constraints to.
• a: QuantumCell that contains a boolean value.
• b: QuantumCell that contains a boolean value.

fn not( &self, ctx: &mut Context<F>, a: impl Into<QuantumCell<F>>, ) -> AssignedValue<F>

Constrains and returns !a assumeing a is boolean.

Defines a vertical gate of form | 1 - a | a | 1 | 1 |, where 1 - a = out.

• ctx: Context to add the constraints to.
• a: QuantumCell that contains a boolean value.

fn bits_to_indicator( &self, ctx: &mut Context<F>, bits: &[AssignedValue<F>], ) -> Vec<AssignedValue<F>>

Constrains and returns an indicator vector from a slice of boolean values, where output[idx] = 1 iff idx = (the number represented by bits in binary little endian), otherwise output[idx] = 0.

• ctx: Context to add the constraints to
• bits: slice of QuantumCell’s that contains boolean values

Assumptions

• bits is non-empty

fn idx_to_indicator( &self, ctx: &mut Context<F>, idx: impl Into<QuantumCell<F>>, len: usize, ) -> Vec<AssignedValue<F>>

Constrains and returns a Vec indicator of length len, where indicator[i] == 1 if i == idx otherwise 0, if idx >= len then indicator is all zeros.

Assumes len is greater than 0.

• ctx: Context to add the constraints to
• idx: QuantumCell index of the indicator vector to be set to 1
• len: length of the indicator vector

fn select_by_indicator<Q>( &self, ctx: &mut Context<F>, a: impl IntoIterator<Item = Q>, indicator: impl IntoIterator<Item = AssignedValue<F>>, ) -> AssignedValue<F>

where Q: Into<QuantumCell<F>>,

Constrains the inner product of a and indicator and returns a[idx] (e.g. the value of a at idx).

Assumes that a and indicator are non-empty iterators of the same length, the values of indicator are boolean, and that indicator has at most one 1 bit.

• ctx: Context to add the constraints to
• a: Iterator of QuantumCell’s that contains field elements
• indicator: Iterator of AssignedValue’s where indicator[i] == 1 if i == idx, otherwise 0

fn select_from_idx<Q>( &self, ctx: &mut Context<F>, cells: impl IntoIterator<Item = Q>, idx: impl Into<QuantumCell<F>>, ) -> AssignedValue<F>

where Q: Into<QuantumCell<F>>,

Constrains and returns cells[idx] if idx < cells.len(), otherwise return 0.

Assumes that cells and idx are non-empty iterators of the same length.

• ctx: Context to add the constraints to
• cells: Iterator of QuantumCells to select from
• idx: QuantumCell with value idx where idx is the index of the cell to be selected

fn select_array_by_indicator<AR, AV>( &self, ctx: &mut Context<F>, array2d: &[AR], indicator: &[AssignedValue<F>], ) -> Vec<AssignedValue<F>>

where AR: AsRef<[AV]>, AV: AsRef<AssignedValue<F>>,

array2d is an array of fixed length arrays. Assumes:

• array2d.len() == indicator.len()
• array2d[i].len() == array2d[j].len() for all i,j.
• the values of indicator are boolean and that indicator has at most one 1 bit.
• the lengths of array2d and indicator are the same.

Returns the “dot product” of array2d with indicator as a fixed length (1d) array of length array2d[0].len().

fn is_zero(&self, ctx: &mut Context<F>, a: AssignedValue<F>) -> AssignedValue<F>

Constrains that a cell is equal to 0 and returns 1 if a = 0, otherwise 0.

Defines a vertical gate of form | out | a | inv | 1 | 0 | a | out | 0 |, where out = 1 if a = 0, otherwise out = 0.

• ctx: Context to add the constraints to
• a: QuantumCell value to be constrained

fn is_equal( &self, ctx: &mut Context<F>, a: impl Into<QuantumCell<F>>, b: impl Into<QuantumCell<F>>, ) -> AssignedValue<F>

Constrains that the value of two cells are equal: b - a = 0, returns 1 if a = b, otherwise 0.

• ctx: Context to add the constraints to
• a: QuantumCell value
• b: QuantumCell value to compare to a

fn lagrange_and_eval( &self, ctx: &mut Context<F>, coords: &[(AssignedValue<F>, AssignedValue<F>)], x: AssignedValue<F>, ) -> (AssignedValue<F>, AssignedValue<F>)

Performs and constrains Lagrange interpolation on coords and evaluates the resulting polynomial at x.

Given pairs coords[i] = (x_i, y_i), let f be the unique degree len(coords) - 1 polynomial such that f(x_i) = y_i for all i.

Returns: (f(x), Prod_i(x - x_i))

• ctx: Context to add the constraints to
• coords: immutable reference to a slice of tuples of AssignedValues representing the points to interpolate over such that coords[i] = (x_i, y_i)
• x: x-coordinate of the point to evaluate f at

Assumptions

• coords is non-empty

Dyn Compatibility

This trait is not dyn compatible.

In older versions of Rust, dyn compatibility was called "object safety", so this trait is not object safe.

Implementors

impl<F: ScalarField> GateInstructions<F> for GateChip<F>