Struct snarkvm_circuit::Field

pub struct Field<E>where
    E: Environment,{ /* private fields */ }

Trait Implementations

impl<E> Add<&Field<E>> for &Field<E>where E: Environment,

type Output = Field<E>

The resulting type after applying the + operator.

fn add(self, other: &Field<E>) -> <&Field<E> as Add<&Field<E>>>::Output

Performs the + operation.

impl<E> Add<&Field<E>> for Field<E>where E: Environment,

type Output = Field<E>

The resulting type after applying the + operator.

fn add(self, other: &Field<E>) -> <Field<E> as Add<&Field<E>>>::Output

Performs the + operation.

impl<E> Add<Field<E>> for &Field<E>where E: Environment,

type Output = Field<E>

The resulting type after applying the + operator.

fn add(self, other: Field<E>) -> <&Field<E> as Add<Field<E>>>::Output

Performs the + operation.

impl<E> Add<Field<E>> for Field<E>where E: Environment,

type Output = Field<E>

The resulting type after applying the + operator.

fn add(self, other: Field<E>) -> <Field<E> as Add<Field<E>>>::Output

Performs the + operation.

impl<E> AddAssign<&Field<E>> for Field<E>where E: Environment,

fn add_assign(&mut self, other: &Field<E>)

Performs the += operation.

impl<E> AddAssign<Field<E>> for Field<E>where E: Environment,

fn add_assign(&mut self, other: Field<E>)

Performs the += operation.

impl<E> Clone for Field<E>where E: Clone + Environment, <E as Environment>::BaseField: Clone,

fn clone(&self) -> Field<E>

Returns a copy of the value.

fn clone_from(&mut self, source: &Self)

Performs copy-assignment from source.

impl<E> Compare<Field<E>> for Field<E>where E: Environment,

fn is_less_than( &self, other: &Field<E> ) -> <Field<E> as Compare<Field<E>>>::Output

Returns true if self is less than other.

fn is_greater_than( &self, other: &Field<E> ) -> <Field<E> as Compare<Field<E>>>::Output

Returns true if self is greater than other.

fn is_less_than_or_equal( &self, other: &Field<E> ) -> <Field<E> as Compare<Field<E>>>::Output

Returns true if self is less than or equal to other.

fn is_greater_than_or_equal( &self, other: &Field<E> ) -> <Field<E> as Compare<Field<E>>>::Output

Returns true if self is greater than or equal to other.

type Output = Boolean<E>

impl<E> Debug for Field<E>where E: Environment,

fn fmt(&self, f: &mut Formatter<'_>) -> Result<(), Error>

Formats the value using the given formatter.

impl<E> Display for Field<E>where E: Environment,

fn fmt(&self, f: &mut Formatter<'_>) -> Result<(), Error>

Formats the value using the given formatter.

impl<E> Div<&Field<E>> for &Field<E>where E: Environment,

type Output = Field<E>

The resulting type after applying the / operator.

fn div(self, other: &Field<E>) -> <&Field<E> as Div<&Field<E>>>::Output

Performs the / operation.

impl<E> Div<&Field<E>> for Field<E>where E: Environment,

type Output = Field<E>

The resulting type after applying the / operator.

fn div(self, other: &Field<E>) -> <Field<E> as Div<&Field<E>>>::Output

Performs the / operation.

impl<E> Div<Field<E>> for &Field<E>where E: Environment,

type Output = Field<E>

The resulting type after applying the / operator.

fn div(self, other: Field<E>) -> <&Field<E> as Div<Field<E>>>::Output

Performs the / operation.

impl<E> Div<Field<E>> for Field<E>where E: Environment,

type Output = Field<E>

The resulting type after applying the / operator.

fn div(self, other: Field<E>) -> <Field<E> as Div<Field<E>>>::Output

Performs the / operation.

impl<E> DivAssign<&Field<E>> for Field<E>where E: Environment,

fn div_assign(&mut self, other: &Field<E>)

Performs the /= operation.

impl<E> DivAssign<Field<E>> for Field<E>where E: Environment,

fn div_assign(&mut self, other: Field<E>)

Performs the /= operation.

impl<E> DivUnchecked<Field<E>> for Field<E>where E: Environment,

type Output = Field<E>

fn div_unchecked(&self, rhs: &Rhs) -> Self::Output

impl<E> Double for Field<E>where E: Environment,

type Output = Field<E>

fn double(&self) -> <Field<E> as Double>::Output

impl<E> Eject for Field<E>where E: Environment,

fn eject_mode(&self) -> Mode

Ejects the mode of the field circuit.

fn eject_value(&self) -> <Field<E> as Eject>::Primitive

Ejects the field circuit as a console field.

type Primitive = Field<<E as Environment>::Network>

fn eject(&self) -> (Mode, Self::Primitive)

Ejects the mode and primitive value of the circuit type.

fn is_constant(&self) -> bool

Returns true if the circuit is a constant.

fn is_public(&self) -> bool

Returns true if the circuit is a public.

fn is_private(&self) -> bool

Returns true if the circuit is a private.

impl<E> Equal<Field<E>> for Field<E>where E: Environment,

fn is_equal(&self, other: &Field<E>) -> <Field<E> as Equal<Field<E>>>::Output

Returns true if self and other are equal.

This method costs 3 constraints.

fn is_not_equal( &self, other: &Field<E> ) -> <Field<E> as Equal<Field<E>>>::Output

Returns true if self and other are not equal.

This method constructs a boolean that indicates if self and other are not equal to each other.

This method costs 3 constraints.

type Output = Boolean<E>

impl<E> From<&Address<E>> for Field<E>where E: Environment,

fn from(value: &Address<E>) -> Field<E>

Returns the x-coordinate of the affine group element in the address.

impl<E> From<&Field<E>> for Address<E>where E: Environment,

fn from(value: &Field<E>) -> Address<E>

Initializes an address from the x-coordinate of an affine group element.

impl<E> From<&Field<E>> for LinearCombination<<E as Environment>::BaseField>where E: Environment,

fn from(field: &Field<E>) -> LinearCombination<<E as Environment>::BaseField>

Converts to this type from the input type.

impl<E> From<&LinearCombination<<E as Environment>::BaseField>> for Field<E>where E: Environment,

fn from( linear_combination: &LinearCombination<<E as Environment>::BaseField> ) -> Field<E>

Converts to this type from the input type.

impl<E> From<Address<E>> for Field<E>where E: Environment,

fn from(value: Address<E>) -> Field<E>

Returns the x-coordinate of the affine group element in the address.

impl<E> From<Field<E>> for Address<E>where E: Environment,

fn from(value: Field<E>) -> Address<E>

Initializes an address from the x-coordinate of an affine group element.

impl<E> From<Field<E>> for LinearCombination<<E as Environment>::BaseField>where E: Environment,

fn from(field: Field<E>) -> LinearCombination<<E as Environment>::BaseField>

Converts to this type from the input type.

impl<E> From<LinearCombination<<E as Environment>::BaseField>> for Field<E>where E: Environment,

fn from( linear_combination: LinearCombination<<E as Environment>::BaseField> ) -> Field<E>

Converts to this type from the input type.

impl<E> FromBits for Field<E>where E: Environment,

fn from_bits_le(bits_le: &[<Field<E> as FromBits>::Boolean]) -> Field<E>

Initializes a new base field element from a list of little-endian bits.

• If bits_le is longer than E::BaseField::size_in_bits(), the excess bits are enforced to be 0s.
• If bits_le is shorter than E::BaseField::size_in_bits(), it is padded with 0s up to base field size.

fn from_bits_be(bits_be: &[<Field<E> as FromBits>::Boolean]) -> Field<E>

Initializes a new base field element from a list of big-endian bits without leading zeros.

type Boolean = Boolean<E>

impl<E> FromBoolean for Field<E>where E: Environment,

fn from_boolean(boolean: &<Field<E> as FromBoolean>::Boolean) -> Field<E>

Initializes a base field from a boolean.

type Boolean = Boolean<E>

impl<E> FromStr for Field<E>where E: Environment,

fn from_str(string: &str) -> Result<Field<E>, Error>

Parses a string into a field circuit.

type Err = Error

The associated error which can be returned from parsing.

impl<E> Inject for Field<E>where E: Environment,

fn new(mode: Mode, field: <Field<E> as Inject>::Primitive) -> Field<E>

Initializes a field circuit from a console field.

type Primitive = Field<<E as Environment>::Network>

fn constant(value: Self::Primitive) -> Selfwhere Self: Sized,

Initializes a constant of the given primitive value.

impl<E> Inv for &Field<E>where E: Environment,

type Output = Field<E>

The result after applying the operator.

fn inv(self) -> <&Field<E> as Inv>::Output

Returns the multiplicative inverse of self.

impl<E> Inv for Field<E>where E: Environment,

type Output = Field<E>

The result after applying the operator.

fn inv(self) -> <Field<E> as Inv>::Output

Returns the multiplicative inverse of self.

impl<E> Inverse for Field<E>where E: Environment,

type Output = Field<E>

fn inverse(&self) -> <Field<E> as Inverse>::Output

impl<E> Metrics<dyn Add<Field<E>, Output = Field<E>>> for Field<E>where E: Environment,

type Case = (Mode, Mode)

fn count( _case: &<Field<E> as Metrics<dyn Add<Field<E>, Output = Field<E>>>>::Case ) -> Count

Returns the number of constants, public inputs, private inputs, and constraints.

impl<E> Metrics<dyn Div<Field<E>, Output = Field<E>>> for Field<E>where E: Environment,

type Case = (Mode, Mode)

fn count( case: &<Field<E> as Metrics<dyn Div<Field<E>, Output = Field<E>>>>::Case ) -> Count

Returns the number of constants, public inputs, private inputs, and constraints.

impl<E> Metrics<dyn DivUnchecked<Field<E>, Output = Field<E>>> for Field<E>where E: Environment,

type Case = (Mode, Mode)

fn count( case: &<Field<E> as Metrics<dyn DivUnchecked<Field<E>, Output = Field<E>>>>::Case ) -> Count

Returns the number of constants, public inputs, private inputs, and constraints.

impl<E> Metrics<dyn Double<Output = Field<E>>> for Field<E>where E: Environment,

type Case = Mode

fn count( _parameter: &<Field<E> as Metrics<dyn Double<Output = Field<E>>>>::Case ) -> Count

Returns the number of constants, public inputs, private inputs, and constraints.

impl<E> Metrics<dyn Equal<Field<E>, Output = Boolean<E>>> for Field<E>where E: Environment,

type Case = (Mode, Mode)

fn count( case: &<Field<E> as Metrics<dyn Equal<Field<E>, Output = Boolean<E>>>>::Case ) -> Count

Returns the number of constants, public inputs, private inputs, and constraints.

impl<E> Metrics<dyn FromBits<Boolean = Boolean<E>>> for Field<E>where E: Environment,

type Case = Vec<Mode, Global>

fn count( _modes: &<Field<E> as Metrics<dyn FromBits<Boolean = Boolean<E>>>>::Case ) -> Count

Returns the number of constants, public inputs, private inputs, and constraints.

impl<E> Metrics<dyn FromBoolean<Boolean = Boolean<E>>> for Field<E>where E: Environment,

type Case = ()

fn count( _case: &<Field<E> as Metrics<dyn FromBoolean<Boolean = Boolean<E>>>>::Case ) -> Count

Returns the number of constants, public inputs, private inputs, and constraints.

impl<E> Metrics<dyn Inverse<Output = Field<E>>> for Field<E>where E: Environment,

type Case = Mode

fn count( case: &<Field<E> as Metrics<dyn Inverse<Output = Field<E>>>>::Case ) -> Count

Returns the number of constants, public inputs, private inputs, and constraints.

impl<E> Metrics<dyn Mul<Field<E>, Output = Field<E>>> for Field<E>where E: Environment,

type Case = (Mode, Mode)

fn count( case: &<Field<E> as Metrics<dyn Mul<Field<E>, Output = Field<E>>>>::Case ) -> Count

Returns the number of constants, public inputs, private inputs, and constraints.

impl<E> Metrics<dyn Neg<Output = Field<E>>> for Field<E>where E: Environment,

type Case = Mode

fn count( _case: &<Field<E> as Metrics<dyn Neg<Output = Field<E>>>>::Case ) -> Count

Returns the number of constants, public inputs, private inputs, and constraints.

impl<E> Metrics<dyn One<Boolean = Boolean<E>>> for Field<E>where E: Environment,

type Case = ()

fn count( _parameter: &<Field<E> as Metrics<dyn One<Boolean = Boolean<E>>>>::Case ) -> Count

Returns the number of constants, public inputs, private inputs, and constraints.

impl<E> Metrics<dyn Pow<Field<E>, Output = Field<E>>> for Field<E>where E: Environment,

type Case = (CircuitType<Field<E>>, CircuitType<Field<E>>)

fn count( case: &<Field<E> as Metrics<dyn Pow<Field<E>, Output = Field<E>>>>::Case ) -> Count

Returns the number of constants, public inputs, private inputs, and constraints.

impl<E> Metrics<dyn Square<Output = Field<E>>> for Field<E>where E: Environment,

type Case = Mode

fn count( case: &<Field<E> as Metrics<dyn Square<Output = Field<E>>>>::Case ) -> Count

Returns the number of constants, public inputs, private inputs, and constraints.

impl<E> Metrics<dyn SquareRoot<Output = Field<E>>> for Field<E>where E: Environment,

type Case = Mode

fn count( case: &<Field<E> as Metrics<dyn SquareRoot<Output = Field<E>>>>::Case ) -> Count

Returns the number of constants, public inputs, private inputs, and constraints.

impl<E> Metrics<dyn Sub<Field<E>, Output = Field<E>>> for Field<E>where E: Environment,

type Case = (Mode, Mode)

fn count( _case: &<Field<E> as Metrics<dyn Sub<Field<E>, Output = Field<E>>>>::Case ) -> Count

Returns the number of constants, public inputs, private inputs, and constraints.

impl<E> Metrics<dyn Ternary<Output = Field<E>, Boolean = Boolean<E>>> for Field<E>where E: Environment,

type Case = (Mode, Mode, Mode)

fn count( case: &<Field<E> as Metrics<dyn Ternary<Output = Field<E>, Boolean = Boolean<E>>>>::Case ) -> Count

Returns the number of constants, public inputs, private inputs, and constraints.

impl<E> Metrics<dyn ToBits<Boolean = Boolean<E>>> for Field<E>where E: Environment,

type Case = Mode

fn count( case: &<Field<E> as Metrics<dyn ToBits<Boolean = Boolean<E>>>>::Case ) -> Count

Returns the number of constants, public inputs, private inputs, and constraints.

impl<E> Metrics<dyn ToLowerBits<Boolean = Boolean<E>>> for Field<E>where E: Environment,

type Case = (Mode, u64)

fn count( case: &<Field<E> as Metrics<dyn ToLowerBits<Boolean = Boolean<E>>>>::Case ) -> Count

Returns the number of constants, public inputs, private inputs, and constraints.

impl<E> Metrics<dyn ToUpperBits<Boolean = Boolean<E>>> for Field<E>where E: Environment,

type Case = (Mode, u64)

fn count( case: &<Field<E> as Metrics<dyn ToUpperBits<Boolean = Boolean<E>>>>::Case ) -> Count

Returns the number of constants, public inputs, private inputs, and constraints.

impl<E> Metrics<dyn Zero<Boolean = Boolean<E>>> for Field<E>where E: Environment,

type Case = ()

fn count( _parameter: &<Field<E> as Metrics<dyn Zero<Boolean = Boolean<E>>>>::Case ) -> Count

Returns the number of constants, public inputs, private inputs, and constraints.

impl<E> Mul<&Field<E>> for &Field<E>where E: Environment,

type Output = Field<E>

The resulting type after applying the * operator.

fn mul(self, other: &Field<E>) -> <&Field<E> as Mul<&Field<E>>>::Output

Performs the * operation.

impl<E> Mul<&Field<E>> for Field<E>where E: Environment,

type Output = Field<E>

The resulting type after applying the * operator.

fn mul(self, other: &Field<E>) -> <Field<E> as Mul<&Field<E>>>::Output

Performs the * operation.

impl<E> Mul<Field<E>> for &Field<E>where E: Environment,

type Output = Field<E>

The resulting type after applying the * operator.

fn mul(self, other: Field<E>) -> <&Field<E> as Mul<Field<E>>>::Output

Performs the * operation.

impl<E> Mul<Field<E>> for Field<E>where E: Environment,

type Output = Field<E>

The resulting type after applying the * operator.

fn mul(self, other: Field<E>) -> <Field<E> as Mul<Field<E>>>::Output

Performs the * operation.

impl<E> MulAssign<&Field<E>> for Field<E>where E: Environment,

fn mul_assign(&mut self, other: &Field<E>)

Performs the *= operation.

impl<E> MulAssign<Field<E>> for Field<E>where E: Environment,

fn mul_assign(&mut self, other: Field<E>)

Performs the *= operation.

impl<E> Neg for &Field<E>where E: Environment,

fn neg(self) -> <&Field<E> as Neg>::Output

Performs the unary - operation.

type Output = Field<E>

The resulting type after applying the - operator.

impl<E> Neg for Field<E>where E: Environment,

fn neg(self) -> <Field<E> as Neg>::Output

Performs the unary - operation.

type Output = Field<E>

The resulting type after applying the - operator.

impl<E> One for Field<E>where E: Environment,

type Boolean = Boolean<E>

fn one() -> Field<E>

Returns a new one constant.

fn is_one(&self) -> <Field<E> as One>::Boolean

Returns true if self is one.

impl<E> OutputMode<dyn Add<Field<E>, Output = Field<E>>> for Field<E>where E: Environment,

type Case = (CircuitType<Field<E>>, CircuitType<Field<E>>)

fn output_mode( case: &<Field<E> as OutputMode<dyn Add<Field<E>, Output = Field<E>>>>::Case ) -> Mode

Returns the mode of the output.

impl<E> OutputMode<dyn Div<Field<E>, Output = Field<E>>> for Field<E>where E: Environment,

type Case = (CircuitType<Field<E>>, CircuitType<Field<E>>)

fn output_mode( case: &<Field<E> as OutputMode<dyn Div<Field<E>, Output = Field<E>>>>::Case ) -> Mode

Returns the mode of the output.

impl<E> OutputMode<dyn DivUnchecked<Field<E>, Output = Field<E>>> for Field<E>where E: Environment,

type Case = (CircuitType<Field<E>>, CircuitType<Field<E>>)

fn output_mode( case: &<Field<E> as OutputMode<dyn DivUnchecked<Field<E>, Output = Field<E>>>>::Case ) -> Mode

Returns the mode of the output.

impl<E> OutputMode<dyn Double<Output = Field<E>>> for Field<E>where E: Environment,

type Case = Mode

fn output_mode( input: &<Field<E> as OutputMode<dyn Double<Output = Field<E>>>>::Case ) -> Mode

Returns the mode of the output.

impl<E> OutputMode<dyn Equal<Field<E>, Output = Boolean<E>>> for Field<E>where E: Environment,

type Case = (Mode, Mode)

fn output_mode( case: &<Field<E> as OutputMode<dyn Equal<Field<E>, Output = Boolean<E>>>>::Case ) -> Mode

Returns the mode of the output.

impl<E> OutputMode<dyn FromBits<Boolean = Boolean<E>>> for Field<E>where E: Environment,

type Case = Vec<Mode, Global>

fn output_mode( case: &<Field<E> as OutputMode<dyn FromBits<Boolean = Boolean<E>>>>::Case ) -> Mode

Returns the mode of the output.

impl<E> OutputMode<dyn FromBoolean<Boolean = Boolean<E>>> for Field<E>where E: Environment,

type Case = Mode

fn output_mode( case: &<Field<E> as OutputMode<dyn FromBoolean<Boolean = Boolean<E>>>>::Case ) -> Mode

Returns the mode of the output.

impl<E> OutputMode<dyn Inverse<Output = Field<E>>> for Field<E>where E: Environment,

type Case = Mode

fn output_mode( case: &<Field<E> as OutputMode<dyn Inverse<Output = Field<E>>>>::Case ) -> Mode

Returns the mode of the output.

impl<E> OutputMode<dyn Mul<Field<E>, Output = Field<E>>> for Field<E>where E: Environment,

type Case = (CircuitType<Field<E>>, CircuitType<Field<E>>)

fn output_mode( case: &<Field<E> as OutputMode<dyn Mul<Field<E>, Output = Field<E>>>>::Case ) -> Mode

Returns the mode of the output.

impl<E> OutputMode<dyn Neg<Output = Field<E>>> for Field<E>where E: Environment,

type Case = Mode

fn output_mode( case: &<Field<E> as OutputMode<dyn Neg<Output = Field<E>>>>::Case ) -> Mode

Returns the mode of the output.

impl<E> OutputMode<dyn One<Boolean = Boolean<E>>> for Field<E>where E: Environment,

type Case = ()

fn output_mode( _input: &<Field<E> as OutputMode<dyn One<Boolean = Boolean<E>>>>::Case ) -> Mode

Returns the mode of the output.

impl<E> OutputMode<dyn Pow<Field<E>, Output = Field<E>>> for Field<E>where E: Environment,

type Case = (CircuitType<Field<E>>, CircuitType<Field<E>>)

fn output_mode( case: &<Field<E> as OutputMode<dyn Pow<Field<E>, Output = Field<E>>>>::Case ) -> Mode

Returns the mode of the output.

impl<E> OutputMode<dyn Square<Output = Field<E>>> for Field<E>where E: Environment,

type Case = Mode

fn output_mode( input: &<Field<E> as OutputMode<dyn Square<Output = Field<E>>>>::Case ) -> Mode

Returns the mode of the output.

impl<E> OutputMode<dyn SquareRoot<Output = Field<E>>> for Field<E>where E: Environment,

type Case = Mode

fn output_mode( case: &<Field<E> as OutputMode<dyn SquareRoot<Output = Field<E>>>>::Case ) -> Mode

Returns the mode of the output.

impl<E> OutputMode<dyn Sub<Field<E>, Output = Field<E>>> for Field<E>where E: Environment,

type Case = (CircuitType<Field<E>>, CircuitType<Field<E>>)

fn output_mode( case: &<Field<E> as OutputMode<dyn Sub<Field<E>, Output = Field<E>>>>::Case ) -> Mode

Returns the mode of the output.

impl<E> OutputMode<dyn Ternary<Output = Field<E>, Boolean = Boolean<E>>> for Field<E>where E: Environment,

type Case = (CircuitType<Boolean<E>>, Mode, Mode)

fn output_mode( parameter: &<Field<E> as OutputMode<dyn Ternary<Output = Field<E>, Boolean = Boolean<E>>>>::Case ) -> Mode

Returns the mode of the output.

impl<E> OutputMode<dyn ToBits<Boolean = Boolean<E>>> for Field<E>where E: Environment,

type Case = Mode

fn output_mode( case: &<Field<E> as OutputMode<dyn ToBits<Boolean = Boolean<E>>>>::Case ) -> Mode

Returns the mode of the output.

impl<E> OutputMode<dyn ToLowerBits<Boolean = Boolean<E>>> for Field<E>where E: Environment,

type Case = Mode

fn output_mode( case: &<Field<E> as OutputMode<dyn ToLowerBits<Boolean = Boolean<E>>>>::Case ) -> Mode

Returns the mode of the output.

impl<E> OutputMode<dyn ToUpperBits<Boolean = Boolean<E>>> for Field<E>where E: Environment,

type Case = Mode

fn output_mode( case: &<Field<E> as OutputMode<dyn ToUpperBits<Boolean = Boolean<E>>>>::Case ) -> Mode

Returns the mode of the output.

impl<E> OutputMode<dyn Zero<Boolean = Boolean<E>>> for Field<E>where E: Environment,

type Case = ()

fn output_mode( _input: &<Field<E> as OutputMode<dyn Zero<Boolean = Boolean<E>>>>::Case ) -> Mode

Returns the mode of the output.

impl<E> Parser for Field<E>where E: Environment,

fn parse(string: &str) -> Result<(&str, Field<E>), Err<VerboseError<&str>>>

Parses a string into a field circuit.

impl<E> Pow<&Field<E>> for &Field<E>where E: Environment,

type Output = Field<E>

The result after applying the operator.

fn pow(self, exponent: &Field<E>) -> <&Field<E> as Pow<&Field<E>>>::Output

Returns self to the power rhs.

impl<E> Pow<&Field<E>> for Field<E>where E: Environment,

type Output = Field<E>

The result after applying the operator.

fn pow(self, exponent: &Field<E>) -> <Field<E> as Pow<&Field<E>>>::Output

Returns self to the power rhs.

impl<E> Pow<Field<E>> for &Field<E>where E: Environment,

type Output = Field<E>

The result after applying the operator.

fn pow(self, exponent: Field<E>) -> <&Field<E> as Pow<Field<E>>>::Output

Returns self to the power rhs.

impl<E> Pow<Field<E>> for Field<E>where E: Environment,

type Output = Field<E>

The result after applying the operator.

fn pow(self, exponent: Field<E>) -> <Field<E> as Pow<Field<E>>>::Output

Returns self to the power rhs.

impl<E> Square for Field<E>where E: Environment,

type Output = Field<E>

fn square(&self) -> <Field<E> as Square>::Output

impl<E> SquareRoot for Field<E>where E: Environment,

type Output = Field<E>

fn square_root(&self) -> <Field<E> as SquareRoot>::Output

impl<E> Sub<&Field<E>> for &Field<E>where E: Environment,

type Output = Field<E>

The resulting type after applying the - operator.

fn sub(self, other: &Field<E>) -> <&Field<E> as Sub<&Field<E>>>::Output

Performs the - operation.

impl<E> Sub<&Field<E>> for Field<E>where E: Environment,

type Output = Field<E>

The resulting type after applying the - operator.

fn sub(self, other: &Field<E>) -> <Field<E> as Sub<&Field<E>>>::Output

Performs the - operation.

impl<E> Sub<Field<E>> for &Field<E>where E: Environment,

type Output = Field<E>

The resulting type after applying the - operator.

fn sub(self, other: Field<E>) -> <&Field<E> as Sub<Field<E>>>::Output

Performs the - operation.

impl<E> Sub<Field<E>> for Field<E>where E: Environment,

type Output = Field<E>

The resulting type after applying the - operator.

fn sub(self, other: Field<E>) -> <Field<E> as Sub<Field<E>>>::Output

Performs the - operation.

impl<E> SubAssign<&Field<E>> for Field<E>where E: Environment,

fn sub_assign(&mut self, other: &Field<E>)

Performs the -= operation.

impl<E> SubAssign<Field<E>> for Field<E>where E: Environment,

fn sub_assign(&mut self, other: Field<E>)

Performs the -= operation.

impl<E> Ternary for Field<E>where E: Environment,

fn ternary( condition: &<Field<E> as Ternary>::Boolean, first: &Field<E>, second: &Field<E> ) -> <Field<E> as Ternary>::Output

Returns first if condition is true, otherwise returns second.

type Boolean = Boolean<E>

type Output = Field<E>

impl<E> ToBits for &Field<E>where E: Environment,

fn to_bits_le(&self) -> Vec<<&Field<E> as ToBits>::Boolean, Global>

Outputs the unique, minimal little-endian bit representation of self without trailing zeros.

fn to_bits_be(&self) -> Vec<<&Field<E> as ToBits>::Boolean, Global>

Outputs the unique, minimal big-endian bit representation of self without leading zeros.

type Boolean = Boolean<E>

impl<E> ToBits for Field<E>where E: Environment,

fn to_bits_le(&self) -> Vec<<Field<E> as ToBits>::Boolean, Global>

Outputs the little-endian bit representation of self without trailing zeros.

fn to_bits_be(&self) -> Vec<<Field<E> as ToBits>::Boolean, Global>

Outputs the big-endian bit representation of self without leading zeros.

type Boolean = Boolean<E>

impl<E> ToLowerBits for Field<E>where E: Environment,

fn to_lower_bits_le( &self, k: usize ) -> Vec<<Field<E> as ToLowerBits>::Boolean, Global>

Outputs the lower k bits of an n-bit field element in little-endian representation. Enforces that the upper n - k bits are zero.

fn to_lower_bits_be( &self, k: usize ) -> Vec<<Field<E> as ToLowerBits>::Boolean, Global>

Outputs the lower k bits of an n-bit field element in big-endian representation. Enforces that the upper n - k bits are zero.

type Boolean = Boolean<E>

impl<E> ToUpperBits for Field<E>where E: Environment,

fn to_upper_bits_le( &self, k: usize ) -> Vec<<Field<E> as ToUpperBits>::Boolean, Global>

Outputs the upper k bits of an n-bit field element in little-endian representation. Enforces that the lower n - k bits are zero.

fn to_upper_bits_be( &self, k: usize ) -> Vec<<Field<E> as ToUpperBits>::Boolean, Global>

Outputs the upper k bits of an n-bit field element in big-endian representation. Enforces that the lower n - k bits are zero.

type Boolean = Boolean<E>

impl<E> TypeName for Field<E>where E: Environment,

fn type_name() -> &'static str

Returns the type name of the circuit as a string.

impl<E> Zero for Field<E>where E: Environment,

type Boolean = Boolean<E>

fn zero() -> Field<E>

Returns a new zero constant.

fn is_zero(&self) -> <Field<E> as Zero>::Boolean

Returns true if self is zero.

impl<E> FieldTrait for Field<E>where E: Environment,