pub struct Field<E: Environment> { /* private fields */ }
Implementations§
Source§impl<E: Environment> Field<E>
impl<E: Environment> Field<E>
Sourcepub fn even_square_root(&self) -> Self
pub fn even_square_root(&self) -> Self
Returns the square root of self
, where the least significant bit of the square root is zero.
Source§impl<E: Environment> Field<E>
impl<E: Environment> Field<E>
Sourcepub fn square_roots_flagged_nondeterministic(&self) -> (Self, Self, Boolean<E>)
pub fn square_roots_flagged_nondeterministic(&self) -> (Self, Self, Boolean<E>)
Returns both square roots of self
and a Boolean
flag, which is set iff self
is not a square.
If self
is a non-zero square,
- the first field result is the positive root (i.e. closer to 0)
- the second field result is the negative root (i.e. closer to the prime)
- the flag is 0
If self
is 0,
- both field results are 0
- the flag is 0
If self
is not a square,
- both field results are 0
- the flag is 1
Note that the constraints do not impose an ordering on the two roots returned by this function;
this is what the nondeterministic
part of this function name refers to.
Trait Implementations§
Source§impl<E: Environment> Add for Field<E>
impl<E: Environment> Add for Field<E>
Source§impl<E: Environment> AddAssign<&Field<E>> for Field<E>
impl<E: Environment> AddAssign<&Field<E>> for Field<E>
Source§fn add_assign(&mut self, other: &Field<E>)
fn add_assign(&mut self, other: &Field<E>)
+=
operation. Read moreSource§impl<E: Environment> AddAssign for Field<E>
impl<E: Environment> AddAssign for Field<E>
Source§fn add_assign(&mut self, other: Field<E>)
fn add_assign(&mut self, other: Field<E>)
+=
operation. Read moreSource§impl<E: Environment> Compare for Field<E>
impl<E: Environment> Compare for Field<E>
Source§fn is_less_than(&self, other: &Self) -> Self::Output
fn is_less_than(&self, other: &Self) -> Self::Output
Returns true
if self
is less than other
.
Source§fn is_greater_than(&self, other: &Self) -> Self::Output
fn is_greater_than(&self, other: &Self) -> Self::Output
Returns true
if self
is greater than other
.
Source§fn is_less_than_or_equal(&self, other: &Self) -> Self::Output
fn is_less_than_or_equal(&self, other: &Self) -> Self::Output
Returns true
if self
is less than or equal to other
.
Source§fn is_greater_than_or_equal(&self, other: &Self) -> Self::Output
fn is_greater_than_or_equal(&self, other: &Self) -> Self::Output
Returns true
if self
is greater than or equal to other
.
type Output = Boolean<E>
Source§impl<E: Environment> Debug for Field<E>
impl<E: Environment> Debug for Field<E>
Source§impl<E: Environment> Default for Field<E>
impl<E: Environment> Default for Field<E>
Source§impl<E: Environment> Display for Field<E>
impl<E: Environment> Display for Field<E>
Source§impl<E: Environment> Div for Field<E>
impl<E: Environment> Div for Field<E>
Source§impl<E: Environment> DivAssign<&Field<E>> for Field<E>
impl<E: Environment> DivAssign<&Field<E>> for Field<E>
Source§fn div_assign(&mut self, other: &Self)
fn div_assign(&mut self, other: &Self)
/=
operation. Read moreSource§impl<E: Environment> DivAssign for Field<E>
impl<E: Environment> DivAssign for Field<E>
Source§fn div_assign(&mut self, other: Self)
fn div_assign(&mut self, other: Self)
/=
operation. Read moreSource§impl<E: Environment> DivUnchecked for Field<E>
impl<E: Environment> DivUnchecked for Field<E>
Source§impl<E: Environment> Double for Field<E>
impl<E: Environment> Double for Field<E>
Source§impl<E: Environment> Eject for Field<E>
impl<E: Environment> Eject for Field<E>
Source§fn eject_mode(&self) -> Mode
fn eject_mode(&self) -> Mode
Ejects the mode of the field circuit.
Source§fn eject_value(&self) -> Self::Primitive
fn eject_value(&self) -> Self::Primitive
Ejects the field circuit as a console field.
type Primitive = Field<<E as Environment>::Network>
Source§fn eject(&self) -> (Mode, Self::Primitive)
fn eject(&self) -> (Mode, Self::Primitive)
Source§fn is_constant(&self) -> bool
fn is_constant(&self) -> bool
true
if the circuit is a constant.Source§fn is_private(&self) -> bool
fn is_private(&self) -> bool
true
if the circuit is a private.Source§impl<E: Environment> Equal for Field<E>
impl<E: Environment> Equal for Field<E>
Source§fn is_equal(&self, other: &Self) -> Self::Output
fn is_equal(&self, other: &Self) -> Self::Output
Returns true
if self
and other
are equal.
This method costs 2 constraints.
Source§fn is_not_equal(&self, other: &Self) -> Self::Output
fn is_not_equal(&self, other: &Self) -> Self::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 2 constraints.
type Output = Boolean<E>
Source§impl<E: Environment> From<&Field<E>> for LinearCombination<E::BaseField>
impl<E: Environment> From<&Field<E>> for LinearCombination<E::BaseField>
Source§impl<E: Environment> From<&LinearCombination<<E as Environment>::BaseField>> for Field<E>
impl<E: Environment> From<&LinearCombination<<E as Environment>::BaseField>> for Field<E>
Source§fn from(linear_combination: &LinearCombination<E::BaseField>) -> Self
fn from(linear_combination: &LinearCombination<E::BaseField>) -> Self
Source§impl<E: Environment> From<Field<E>> for LinearCombination<E::BaseField>
impl<E: Environment> From<Field<E>> for LinearCombination<E::BaseField>
Source§impl<E: Environment> From<LinearCombination<<E as Environment>::BaseField>> for Field<E>
impl<E: Environment> From<LinearCombination<<E as Environment>::BaseField>> for Field<E>
Source§fn from(linear_combination: LinearCombination<E::BaseField>) -> Self
fn from(linear_combination: LinearCombination<E::BaseField>) -> Self
Source§impl<E: Environment> FromBits for Field<E>
impl<E: Environment> FromBits for Field<E>
Source§fn from_bits_le(bits_le: &[Self::Boolean]) -> Self
fn from_bits_le(bits_le: &[Self::Boolean]) -> Self
Initializes a new base field element from a list of little-endian bits.
- If
bits_le
is longer thanE::BaseField::size_in_bits()
, the excess bits are enforced to be0
s. - If
bits_le
is shorter thanE::BaseField::size_in_bits()
, it is padded with0
s up to base field size.
Source§fn from_bits_be(bits_be: &[Self::Boolean]) -> Self
fn from_bits_be(bits_be: &[Self::Boolean]) -> Self
Initializes a new base field element from a list of big-endian bits without leading zeros.
type Boolean = Boolean<E>
Source§impl<E: Environment> FromBoolean for Field<E>
impl<E: Environment> FromBoolean for Field<E>
Source§impl<E: Environment> FromStr for Field<E>
impl<E: Environment> FromStr for Field<E>
Source§impl<E: Environment> Inject for Field<E>
impl<E: Environment> Inject for Field<E>
Source§impl<E: Environment> Inv for &Field<E>
impl<E: Environment> Inv for &Field<E>
Source§impl<E: Environment> Inv for Field<E>
impl<E: Environment> Inv for Field<E>
Source§impl<E: Environment> Inverse for Field<E>
impl<E: Environment> Inverse for Field<E>
Source§impl<E: Environment> Metrics<dyn DivUnchecked<Field<E>, Output = Field<E>>> for Field<E>
impl<E: Environment> Metrics<dyn DivUnchecked<Field<E>, Output = Field<E>>> for Field<E>
Source§impl<E: Environment> Metrics<dyn FromBoolean<Boolean = Boolean<E>>> for Field<E>
impl<E: Environment> Metrics<dyn FromBoolean<Boolean = Boolean<E>>> for Field<E>
Source§impl<E: Environment> Metrics<dyn SquareRoot<Output = Field<E>>> for Field<E>
impl<E: Environment> Metrics<dyn SquareRoot<Output = Field<E>>> for Field<E>
Source§impl<E: Environment> Metrics<dyn Ternary<Boolean = Boolean<E>, Output = Field<E>>> for Field<E>
impl<E: Environment> Metrics<dyn Ternary<Boolean = Boolean<E>, Output = Field<E>>> for Field<E>
Source§impl<E: Environment> Metrics<dyn ToLowerBits<Boolean = Boolean<E>>> for Field<E>
impl<E: Environment> Metrics<dyn ToLowerBits<Boolean = Boolean<E>>> for Field<E>
Source§impl<E: Environment> Metrics<dyn ToUpperBits<Boolean = Boolean<E>>> for Field<E>
impl<E: Environment> Metrics<dyn ToUpperBits<Boolean = Boolean<E>>> for Field<E>
Source§impl<E: Environment> Mul for Field<E>
impl<E: Environment> Mul for Field<E>
Source§impl<E: Environment> MulAssign<&Field<E>> for Field<E>
impl<E: Environment> MulAssign<&Field<E>> for Field<E>
Source§fn mul_assign(&mut self, other: &Field<E>)
fn mul_assign(&mut self, other: &Field<E>)
*=
operation. Read moreSource§impl<E: Environment> MulAssign for Field<E>
impl<E: Environment> MulAssign for Field<E>
Source§fn mul_assign(&mut self, other: Field<E>)
fn mul_assign(&mut self, other: Field<E>)
*=
operation. Read moreSource§impl<E: Environment> Neg for &Field<E>
impl<E: Environment> Neg for &Field<E>
Source§impl<E: Environment> Neg for Field<E>
impl<E: Environment> Neg for Field<E>
Source§impl<E: Environment> One for Field<E>
impl<E: Environment> One for Field<E>
Source§impl<E: Environment> OutputMode<dyn Add<Field<E>, Output = Field<E>>> for Field<E>
impl<E: Environment> OutputMode<dyn Add<Field<E>, Output = Field<E>>> for Field<E>
type Case = (CircuitType<Field<E>>, CircuitType<Field<E>>)
Source§fn output_mode(case: &Self::Case) -> Mode
fn output_mode(case: &Self::Case) -> Mode
Source§impl<E: Environment> OutputMode<dyn Div<Field<E>, Output = Field<E>>> for Field<E>
impl<E: Environment> OutputMode<dyn Div<Field<E>, Output = Field<E>>> for Field<E>
type Case = (CircuitType<Field<E>>, CircuitType<Field<E>>)
Source§fn output_mode(case: &Self::Case) -> Mode
fn output_mode(case: &Self::Case) -> Mode
Source§impl<E: Environment> OutputMode<dyn DivUnchecked<Field<E>, Output = Field<E>>> for Field<E>
impl<E: Environment> OutputMode<dyn DivUnchecked<Field<E>, Output = Field<E>>> for Field<E>
type Case = (CircuitType<Field<E>>, CircuitType<Field<E>>)
Source§fn output_mode(case: &Self::Case) -> Mode
fn output_mode(case: &Self::Case) -> Mode
Source§impl<E: Environment> OutputMode<dyn Double<Output = Field<E>>> for Field<E>
impl<E: Environment> OutputMode<dyn Double<Output = Field<E>>> for Field<E>
Source§impl<E: Environment> OutputMode<dyn Equal<Field<E>, Output = Boolean<E>>> for Field<E>
impl<E: Environment> OutputMode<dyn Equal<Field<E>, Output = Boolean<E>>> for Field<E>
Source§impl<E: Environment> OutputMode<dyn FromBits<Boolean = Boolean<E>>> for Field<E>
impl<E: Environment> OutputMode<dyn FromBits<Boolean = Boolean<E>>> for Field<E>
Source§impl<E: Environment> OutputMode<dyn FromBoolean<Boolean = Boolean<E>>> for Field<E>
impl<E: Environment> OutputMode<dyn FromBoolean<Boolean = Boolean<E>>> for Field<E>
Source§impl<E: Environment> OutputMode<dyn Inverse<Output = Field<E>>> for Field<E>
impl<E: Environment> OutputMode<dyn Inverse<Output = Field<E>>> for Field<E>
Source§impl<E: Environment> OutputMode<dyn Mul<Field<E>, Output = Field<E>>> for Field<E>
impl<E: Environment> OutputMode<dyn Mul<Field<E>, Output = Field<E>>> for Field<E>
type Case = (CircuitType<Field<E>>, CircuitType<Field<E>>)
Source§fn output_mode(case: &Self::Case) -> Mode
fn output_mode(case: &Self::Case) -> Mode
Source§impl<E: Environment> OutputMode<dyn Neg<Output = Field<E>>> for Field<E>
impl<E: Environment> OutputMode<dyn Neg<Output = Field<E>>> for Field<E>
Source§impl<E: Environment> OutputMode<dyn One<Boolean = Boolean<E>>> for Field<E>
impl<E: Environment> OutputMode<dyn One<Boolean = Boolean<E>>> for Field<E>
Source§impl<E: Environment> OutputMode<dyn Pow<Field<E>, Output = Field<E>>> for Field<E>
impl<E: Environment> OutputMode<dyn Pow<Field<E>, Output = Field<E>>> for Field<E>
type Case = (CircuitType<Field<E>>, CircuitType<Field<E>>)
Source§fn output_mode(case: &Self::Case) -> Mode
fn output_mode(case: &Self::Case) -> Mode
Source§impl<E: Environment> OutputMode<dyn Square<Output = Field<E>>> for Field<E>
impl<E: Environment> OutputMode<dyn Square<Output = Field<E>>> for Field<E>
Source§impl<E: Environment> OutputMode<dyn SquareRoot<Output = Field<E>>> for Field<E>
impl<E: Environment> OutputMode<dyn SquareRoot<Output = Field<E>>> for Field<E>
Source§impl<E: Environment> OutputMode<dyn Sub<Field<E>, Output = Field<E>>> for Field<E>
impl<E: Environment> OutputMode<dyn Sub<Field<E>, Output = Field<E>>> for Field<E>
type Case = (CircuitType<Field<E>>, CircuitType<Field<E>>)
Source§fn output_mode(case: &Self::Case) -> Mode
fn output_mode(case: &Self::Case) -> Mode
Source§impl<E: Environment> OutputMode<dyn Ternary<Boolean = Boolean<E>, Output = Field<E>>> for Field<E>
impl<E: Environment> OutputMode<dyn Ternary<Boolean = Boolean<E>, Output = Field<E>>> for Field<E>
Source§impl<E: Environment> OutputMode<dyn ToBits<Boolean = Boolean<E>>> for Field<E>
impl<E: Environment> OutputMode<dyn ToBits<Boolean = Boolean<E>>> for Field<E>
Source§impl<E: Environment> OutputMode<dyn ToLowerBits<Boolean = Boolean<E>>> for Field<E>
impl<E: Environment> OutputMode<dyn ToLowerBits<Boolean = Boolean<E>>> for Field<E>
Source§impl<E: Environment> OutputMode<dyn ToUpperBits<Boolean = Boolean<E>>> for Field<E>
impl<E: Environment> OutputMode<dyn ToUpperBits<Boolean = Boolean<E>>> for Field<E>
Source§impl<E: Environment> OutputMode<dyn Zero<Boolean = Boolean<E>>> for Field<E>
impl<E: Environment> OutputMode<dyn Zero<Boolean = Boolean<E>>> for Field<E>
Source§impl<E: Environment> Parser for Field<E>
impl<E: Environment> Parser for Field<E>
Source§fn parse(string: &str) -> ParserResult<'_, Self>
fn parse(string: &str) -> ParserResult<'_, Self>
Parses a string into a field circuit.
Source§impl<E: Environment> Square for Field<E>
impl<E: Environment> Square for Field<E>
Source§impl<E: Environment> SquareRoot for Field<E>
impl<E: Environment> SquareRoot for Field<E>
Source§impl<E: Environment> Sub for Field<E>
impl<E: Environment> Sub for Field<E>
Source§impl<E: Environment> SubAssign<&Field<E>> for Field<E>
impl<E: Environment> SubAssign<&Field<E>> for Field<E>
Source§fn sub_assign(&mut self, other: &Field<E>)
fn sub_assign(&mut self, other: &Field<E>)
-=
operation. Read moreSource§impl<E: Environment> SubAssign for Field<E>
impl<E: Environment> SubAssign for Field<E>
Source§fn sub_assign(&mut self, other: Field<E>)
fn sub_assign(&mut self, other: Field<E>)
-=
operation. Read moreSource§impl<E: Environment> Ternary for Field<E>
impl<E: Environment> Ternary for Field<E>
Source§impl<E: Environment> ToBits for &Field<E>
impl<E: Environment> ToBits for &Field<E>
Source§fn write_bits_le(&self, vec: &mut Vec<Self::Boolean>)
fn write_bits_le(&self, vec: &mut Vec<Self::Boolean>)
Outputs the unique, minimal little-endian bit representation of self
without trailing zeros.
Source§fn write_bits_be(&self, vec: &mut Vec<Self::Boolean>)
fn write_bits_be(&self, vec: &mut Vec<Self::Boolean>)
Outputs the unique, minimal big-endian bit representation of self
without leading zeros.
type Boolean = Boolean<E>
Source§fn to_bits_le(&self) -> Vec<Self::Boolean>
fn to_bits_le(&self) -> Vec<Self::Boolean>
Source§fn to_bits_be(&self) -> Vec<Self::Boolean>
fn to_bits_be(&self) -> Vec<Self::Boolean>
Source§impl<E: Environment> ToBits for Field<E>
impl<E: Environment> ToBits for Field<E>
Source§fn write_bits_le(&self, vec: &mut Vec<Self::Boolean>)
fn write_bits_le(&self, vec: &mut Vec<Self::Boolean>)
Outputs the little-endian bit representation of self
without trailing zeros.
Source§fn write_bits_be(&self, vec: &mut Vec<Self::Boolean>)
fn write_bits_be(&self, vec: &mut Vec<Self::Boolean>)
Outputs the big-endian bit representation of self
without leading zeros.
type Boolean = Boolean<E>
Source§fn to_bits_le(&self) -> Vec<Self::Boolean>
fn to_bits_le(&self) -> Vec<Self::Boolean>
Source§fn to_bits_be(&self) -> Vec<Self::Boolean>
fn to_bits_be(&self) -> Vec<Self::Boolean>
Source§impl<E: Environment> ToLowerBits for Field<E>
impl<E: Environment> ToLowerBits for Field<E>
Source§fn to_lower_bits_le(&self, k: usize) -> Vec<Self::Boolean>
fn to_lower_bits_le(&self, k: usize) -> Vec<Self::Boolean>
Outputs the lower k
bits of an n
-bit field element in little-endian representation.
Enforces that the upper n - k
bits are zero.
Source§fn to_lower_bits_be(&self, k: usize) -> Vec<Self::Boolean>
fn to_lower_bits_be(&self, k: usize) -> Vec<Self::Boolean>
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>
Source§impl<E: Environment> ToUpperBits for Field<E>
impl<E: Environment> ToUpperBits for Field<E>
Source§fn to_upper_bits_le(&self, k: usize) -> Vec<Self::Boolean>
fn to_upper_bits_le(&self, k: usize) -> Vec<Self::Boolean>
Outputs the upper k
bits of an n
-bit field element in little-endian representation.
Enforces that the lower n - k
bits are zero.
Source§fn to_upper_bits_be(&self, k: usize) -> Vec<Self::Boolean>
fn to_upper_bits_be(&self, k: usize) -> Vec<Self::Boolean>
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>
Source§impl<E: Environment> TypeName for Field<E>
impl<E: Environment> TypeName for Field<E>
Source§impl<E: Environment> Zero for Field<E>
impl<E: Environment> Zero for Field<E>
impl<E: Environment> FieldTrait for Field<E>
Auto Trait Implementations§
impl<E> !Freeze for Field<E>
impl<E> RefUnwindSafe for Field<E>
impl<E> !Send for Field<E>
impl<E> !Sync for Field<E>
impl<E> Unpin for Field<E>
impl<E> UnwindSafe for Field<E>
Blanket Implementations§
Source§impl<T> BorrowMut<T> for Twhere
T: ?Sized,
impl<T> BorrowMut<T> for Twhere
T: ?Sized,
Source§fn borrow_mut(&mut self) -> &mut T
fn borrow_mut(&mut self) -> &mut T
Source§impl<T> CloneToUninit for Twhere
T: Clone,
impl<T> CloneToUninit for Twhere
T: Clone,
Source§impl<T> IntoEither for T
impl<T> IntoEither for T
Source§fn into_either(self, into_left: bool) -> Either<Self, Self>
fn into_either(self, into_left: bool) -> Either<Self, Self>
self
into a Left
variant of Either<Self, Self>
if into_left
is true
.
Converts self
into a Right
variant of Either<Self, Self>
otherwise. Read moreSource§fn into_either_with<F>(self, into_left: F) -> Either<Self, Self>
fn into_either_with<F>(self, into_left: F) -> Either<Self, Self>
self
into a Left
variant of Either<Self, Self>
if into_left(&self)
returns true
.
Converts self
into a Right
variant of Either<Self, Self>
otherwise. Read more