Struct Scalar 

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

Implementations

impl<E> Scalar<E>

where E: Environment,

pub fn from_field_lossy(field: &Field<E>) -> Scalar<E>

Casts a scalar from a base field, with lossy truncation.

This method is commonly used by hash-to-scalar algorithms, where the hash output does not need to preserve the full base field.

Trait Implementations

impl<E> Add<&Scalar<E>> for &Scalar<E>

where E: Environment,

type Output = Scalar<E>

The resulting type after applying the + operator.

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

Performs the + operation.

impl<E> Add<&Scalar<E>> for Scalar<E>

where E: Environment,

type Output = Scalar<E>

The resulting type after applying the + operator.

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

Performs the + operation.

impl<E> Add<Scalar<E>> for &Scalar<E>

where E: Environment,

type Output = Scalar<E>

The resulting type after applying the + operator.

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

Performs the + operation.

impl<E> Add for Scalar<E>

where E: Environment,

type Output = Scalar<E>

The resulting type after applying the + operator.

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

Performs the + operation.

impl<E> AddAssign<&Scalar<E>> for Scalar<E>

where E: Environment,

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

Performs the += operation.

impl<E> AddAssign for Scalar<E>

where E: Environment,

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

Performs the += operation.

impl<E> Cast<Address<E>> for Scalar<E>

where E: Environment,

fn cast(&self) -> Address<E>

Casts a Scalar to an Address.

This operation converts the scalar to a field element, and then attempts to recover the group element by treating the field element as an x-coordinate. The group element is then converted to an address.

To cast arbitrary scalars to addresses, use Scalar::cast_lossy.

impl<E> Cast<Boolean<E>> for Scalar<E>

where E: Environment,

fn cast(&self) -> Boolean<E>

Casts a Scalar to a Boolean, if the scalar is zero or one.

To cast arbitrary scalars to booleans, use Scalar::cast_lossy.

impl<E> Cast<Field<E>> for Scalar<E>

where E: Environment,

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

Casts a Scalar to a Field.

impl<E> Cast<Group<E>> for Scalar<E>

where E: Environment,

fn cast(&self) -> Group<E>

Casts a Scalar to a Group.

This operation converts the scalar to a field element, and then attempts to recover the group element by treating the field element as an x-coordinate.

To cast arbitrary scalars to groups, use Scalar::cast_lossy.

impl<E, I> Cast<Integer<E, I>> for Scalar<E>

where E: Environment, I: IntegerType,

fn cast(&self) -> Integer<E, I>

Casts a Scalar to an Integer, if the scalar is in the range of the integer.

To cast arbitrary scalars to integers, via truncation, use Scalar::cast_lossy.

impl<E> Cast<Scalar<E>> for Boolean<E>

where E: Environment,

fn cast(&self) -> Scalar<E>

Casts a Boolean to a Scalar.

impl<E> Cast<Scalar<E>> for Field<E>

where E: Environment,

fn cast(&self) -> Scalar<E>

Casts a Field to a Scalar, if the field element is in the scalar’s range.

To cast arbitrary field elements to scalars, use Field::cast_lossy.

impl<E, I> Cast<Scalar<E>> for Integer<E, I>

where E: Environment, I: IntegerType,

fn cast(&self) -> Scalar<E>

Casts an Integer to a Scalar.

impl<E> Cast for Scalar<E>

where E: Environment,

fn cast(&self) -> Scalar<E>

Casts a Scalar to a Scalar.

impl<E> CastLossy<Address<E>> for Scalar<E>

where E: Environment,

fn cast_lossy(&self) -> Address<E>

Casts a Scalar to an Address.

This operation converts the scalar into a field element, and then attempts to recover the group element to construct the address. See the documentation of Field::cast_lossy on the Group type for more details.

impl<E> CastLossy<Boolean<E>> for Scalar<E>

where E: Environment,

fn cast_lossy(&self) -> Boolean<E>

Casts a Scalar to a Boolean, with lossy truncation. This operation returns the least significant bit of the scalar.

impl<E> CastLossy<Field<E>> for Scalar<E>

where E: Environment,

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

Casts a Scalar to a Field. This operation is always lossless.

impl<E> CastLossy<Group<E>> for Scalar<E>

where E: Environment,

fn cast_lossy(&self) -> Group<E>

Casts a Scalar to a Group.

This operation converts the scalar into a field element, and then attempts to recover the group element. See the documentation of Field::cast_lossy on the Group type for more details.

impl<E, I> CastLossy<Integer<E, I>> for Scalar<E>

where E: Environment, I: IntegerType,

fn cast_lossy(&self) -> Integer<E, I>

Casts a Scalar to an Integer, with lossy truncation.

impl<E> CastLossy<Scalar<E>> for Boolean<E>

where E: Environment,

fn cast_lossy(&self) -> Scalar<E>

Casts a Boolean to a Scalar. This is safe because casting from a boolean to any other type is always lossless.

impl<E> CastLossy<Scalar<E>> for Field<E>

where E: Environment,

fn cast_lossy(&self) -> Scalar<E>

Casts a Field to a Scalar, with lossy truncation. This operation truncates the field to a scalar.

impl<E, I> CastLossy<Scalar<E>> for Integer<E, I>

where E: Environment, I: IntegerType,

fn cast_lossy(&self) -> Scalar<E>

Casts an Integer to a Scalar. This is safe because casting from an integer to a scalar is always lossless.

impl<E> CastLossy for Scalar<E>

where E: Environment,

fn cast_lossy(&self) -> Scalar<E>

Casts a Scalar to a Scalar. This is an identity cast, so it is always lossless.

impl<E> Clone for Scalar<E>

where E: Clone + Environment,

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

Returns a duplicate of the value.

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

Performs copy-assignment from source.

impl<E> Compare for Scalar<E>

where E: Environment,

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

Returns true if self is less than other.

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

Returns true if self is greater than other.

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

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

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

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

type Output = Boolean<E>

impl<E> Debug for Scalar<E>

where E: Environment,

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

Formats the value using the given formatter.

impl<E> Display for Scalar<E>

where E: Environment,

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

Formats the value using the given formatter.

impl<E> Eject for Scalar<E>

where E: Environment,

fn eject_mode(&self) -> Mode

Ejects the mode of the scalar.

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

Ejects the scalar circuit as a console scalar.

type Primitive = Scalar<<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 for Scalar<E>

where E: Environment,

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

Returns true if self and other are equal.

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

Returns true if self and other are not equal.

type Output = Boolean<E>

impl<E> From<&Scalar<E>> for LinearCombination<<E as Environment>::BaseField>

where E: Environment,

fn from(scalar: &Scalar<E>) -> LinearCombination<<E as Environment>::BaseField>

Converts to this type from the input type.

impl<A> From<Scalar<A>> for Literal<A>

where A: Aleo,

fn from(value: Scalar<A>) -> Literal<A>

Converts to this type from the input type.

impl<E> From<Scalar<E>> for LinearCombination<<E as Environment>::BaseField>

where E: Environment,

fn from(scalar: Scalar<E>) -> LinearCombination<<E as Environment>::BaseField>

Converts to this type from the input type.

impl<E> FromBits for Scalar<E>

where E: Environment,

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

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

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

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

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

type Boolean = Boolean<E>

impl<E> FromField for Scalar<E>

where E: Environment,

fn from_field(field: <Scalar<E> as FromField>::Field) -> Scalar<E>

Casts a scalar from a base field element.

This method guarantees the following:

1. If the field element is larger than the scalar field modulus, then the operation will fail.
2. If the field element is smaller than the scalar field modulus, then the operation will succeed.
   • This is particularly useful for the case where a user called, Scalar::from_field(scalar.to_field()), and the scalar bit representation is between size_in_data_bits < bits.len() < size_in_bits.

type Field = Field<E>

impl<E> FromStr for Scalar<E>

where E: Environment,

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

Parses a string into a scalar circuit.

type Err = Error

The associated error which can be returned from parsing.

impl<E> Inject for Scalar<E>

where E: Environment,

fn new(mode: Mode, scalar: <Scalar<E> as Inject>::Primitive) -> Scalar<E>

Initializes a scalar circuit from a console scalar.

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

fn constant(value: Self::Primitive) -> Self

where Self: Sized,

Initializes a constant of the given primitive value.

impl<E> Metrics<dyn Add<Scalar<E>, Output = Scalar<E>>> for Scalar<E>

where E: Environment,

type Case = (Mode, Mode)

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

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

impl<E> Mul<&Group<E>> for &Scalar<E>

where E: Environment,

type Output = Group<E>

The resulting type after applying the * operator.

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

Performs the * operation.

impl<E> Mul<&Group<E>> for Scalar<E>

where E: Environment,

type Output = Group<E>

The resulting type after applying the * operator.

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

Performs the * operation.

impl<E> Mul<&Scalar<E>> for &Group<E>

where E: Environment,

type Output = Group<E>

The resulting type after applying the * operator.

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

Performs the * operation.

impl<E> Mul<&Scalar<E>> for Group<E>

where E: Environment,

type Output = Group<E>

The resulting type after applying the * operator.

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

Performs the * operation.

impl<E> Mul<Group<E>> for &Scalar<E>

where E: Environment,

type Output = Group<E>

The resulting type after applying the * operator.

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

Performs the * operation.

impl<E> Mul<Group<E>> for Scalar<E>

where E: Environment,

type Output = Group<E>

The resulting type after applying the * operator.

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

Performs the * operation.

impl<E> Mul<Scalar<E>> for &Group<E>

where E: Environment,

type Output = Group<E>

The resulting type after applying the * operator.

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

Performs the * operation.

impl<E> Mul<Scalar<E>> for Group<E>

where E: Environment,

type Output = Group<E>

The resulting type after applying the * operator.

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

Performs the * operation.

impl<E> MulAssign<&Scalar<E>> for Group<E>

where E: Environment,

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

Performs the *= operation.

impl<E> MulAssign<Scalar<E>> for Group<E>

where E: Environment,

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

Performs the *= operation.

impl<E> One for Scalar<E>

where E: Environment,

type Boolean = Boolean<E>

fn one() -> Scalar<E>

Returns a new one constant.

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

Returns true if self is one.

impl<E> OutputMode<dyn Add<Scalar<E>, Output = Scalar<E>>> for Scalar<E>

where E: Environment,

type Case = (Mode, Mode)

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

Returns the mode of the output.

impl<E> Parser for Scalar<E>

where E: Environment,

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

Parses a string into a scalar circuit.

impl<E> Ternary for Scalar<E>

where E: Environment,

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

Returns first if condition is true, otherwise returns second.

type Boolean = Boolean<E>

type Output = Scalar<E>

impl<E> ToBits for &Scalar<E>

where E: Environment,

fn write_bits_le(&self, vec: &mut Vec<<&Scalar<E> as ToBits>::Boolean>)

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

fn write_bits_be(&self, vec: &mut Vec<<&Scalar<E> as ToBits>::Boolean>)

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

type Boolean = Boolean<E>

fn to_bits_le(&self) -> Vec<Self::Boolean>

Returns the little-endian bits of the circuit.

fn to_bits_be(&self) -> Vec<Self::Boolean>

Returns the big-endian bits of the circuit.

impl<E> ToBits for Scalar<E>

where E: Environment,

fn write_bits_le(&self, vec: &mut Vec<<Scalar<E> as ToBits>::Boolean>)

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

fn write_bits_be(&self, vec: &mut Vec<<Scalar<E> as ToBits>::Boolean>)

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

type Boolean = Boolean<E>

fn to_bits_le(&self) -> Vec<Self::Boolean>

Returns the little-endian bits of the circuit.

fn to_bits_be(&self) -> Vec<Self::Boolean>

Returns the big-endian bits of the circuit.

impl<E> ToField for Scalar<E>

where E: Environment,

fn to_field(&self) -> <Scalar<E> as ToField>::Field

Casts a scalar field element into a base field element.

type Field = Field<E>

impl<E> ToFields for Scalar<E>

where E: Environment,

fn to_fields(&self) -> Vec<<Scalar<E> as ToFields>::Field>

Casts a scalar into a list of base fields.

type Field = Field<E>

impl<E> TypeName for Scalar<E>

where E: Environment,

fn type_name() -> &'static str

Returns the type name of the circuit as a string.

impl<E> Zero for Scalar<E>

where E: Environment,

type Boolean = Boolean<E>

fn zero() -> Scalar<E>

Returns a new zero constant.

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

Returns true if self is zero.

impl<E> GroupTrait<Scalar<E>> for Group<E>

where E: Environment,

impl<E> ScalarTrait for Scalar<E>

where E: Environment,