pub struct Scalar { /* private fields */ }
Expand description

The Scalar struct holds an integer \(s < 2^{255} \) which represents an element of \(\mathbb Z / \ell\).

Implementations§

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impl Scalar

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pub fn from_bytes_mod_order(bytes: [u8; 32]) -> Scalar

Construct a Scalar by reducing a 256-bit little-endian integer modulo the group order \( \ell \).

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pub fn from_bytes_mod_order_wide(input: &[u8; 64]) -> Scalar

Construct a Scalar by reducing a 512-bit little-endian integer modulo the group order \( \ell \).

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pub fn from_canonical_bytes(bytes: [u8; 32]) -> CtOption<Scalar>

Attempt to construct a Scalar from a canonical byte representation.

Return
  • Some(s), where s is the Scalar corresponding to bytes, if bytes is a canonical byte representation;
  • None if bytes is not a canonical byte representation.
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pub const fn from_bits(bytes: [u8; 32]) -> Scalar

Construct a Scalar from the low 255 bits of a 256-bit integer.

This function is intended for applications like X25519 which require specific bit-patterns when performing scalar multiplication.

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pub const fn from_bits_clamped(bytes: [u8; 32]) -> Scalar

Construct a Scalar from the low 255 bits of a little-endian 256-bit integer clamping it’s value to be in range

n ∈ 2^254 + 8*{0, 1, 2, 3, . . ., 2^251 − 1}

Explanation of clamping

For Curve25519, h = 8, and multiplying by 8 is the same as a binary left-shift by 3 bits. If you take a secret scalar value between 2^251 and 2^252 – 1 and left-shift by 3 bits then you end up with a 255-bit number with the most significant bit set to 1 and the least-significant three bits set to 0.

The Curve25519 clamping operation takes an arbitrary 256-bit random value and clears the most-significant bit (making it a 255-bit number), sets the next bit, and then clears the 3 least-significant bits. In other words, it directly creates a scalar value that is in the right form and pre-multiplied by the cofactor.

See https://neilmadden.blog/2020/05/28/whats-the-curve25519-clamping-all-about/ for details

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impl Scalar

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pub const ZERO: Self = _

The scalar \( 0 \).

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pub const ONE: Self = _

The scalar \( 1 \).

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pub fn random<R: CryptoRngCore + ?Sized>(rng: &mut R) -> Self

Available on crate feature rand_core only.

Return a Scalar chosen uniformly at random using a user-provided RNG.

Inputs
  • rng: any RNG which implements CryptoRngCore (i.e. CryptoRng + RngCore) interface.
Returns

A random scalar within ℤ/lℤ.

Example
use curve25519_dalek::scalar::Scalar;

use rand_core::OsRng;

let mut csprng = OsRng;
let a: Scalar = Scalar::random(&mut csprng);
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pub fn hash_from_bytes<D>(input: &[u8]) -> Scalarwhere
    D: Digest<OutputSize = U64> + Default,

Available on crate feature digest only.

Hash a slice of bytes into a scalar.

Takes a type parameter D, which is any Digest producing 64 bytes (512 bits) of output.

Convenience wrapper around from_hash.

Example
use sha2::Sha512;

let msg = "To really appreciate architecture, you may even need to commit a murder";
let s = Scalar::hash_from_bytes::<Sha512>(msg.as_bytes());
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pub fn from_hash<D>(hash: D) -> Scalarwhere
    D: Digest<OutputSize = U64>,

Available on crate feature digest only.

Construct a scalar from an existing Digest instance.

Use this instead of hash_from_bytes if it is more convenient to stream data into the Digest than to pass a single byte slice.

Example
use curve25519_dalek::digest::Update;

use sha2::Digest;
use sha2::Sha512;

let mut h = Sha512::new()
    .chain("To really appreciate architecture, you may even need to commit a murder.")
    .chain("While the programs used for The Manhattan Transcripts are of the most extreme")
    .chain("nature, they also parallel the most common formula plot: the archetype of")
    .chain("murder. Other phantasms were occasionally used to underline the fact that")
    .chain("perhaps all architecture, rather than being about functional standards, is")
    .chain("about love and death.");

let s = Scalar::from_hash(h);

println!("{:?}", s.to_bytes());
assert!(s == Scalar::from_bits([ 21,  88, 208, 252,  63, 122, 210, 152,
                                154,  38,  15,  23,  16, 167,  80, 150,
                                192, 221,  77, 226,  62,  25, 224, 148,
                                239,  48, 176,  10, 185,  69, 168,  11, ]));
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pub const fn to_bytes(&self) -> [u8; 32]

Convert this Scalar to its underlying sequence of bytes.

Example
use curve25519_dalek::scalar::Scalar;

let s: Scalar = Scalar::ZERO;

assert!(s.to_bytes() == [0u8; 32]);
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pub const fn as_bytes(&self) -> &[u8; 32]

View the little-endian byte encoding of the integer representing this Scalar.

Example
use curve25519_dalek::scalar::Scalar;

let s: Scalar = Scalar::ZERO;

assert!(s.as_bytes() == &[0u8; 32]);
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pub fn invert(&self) -> Scalar

Given a nonzero Scalar, compute its multiplicative inverse.

Warning

self MUST be nonzero. If you cannot prove that this is the case, you SHOULD NOT USE THIS FUNCTION.

Returns

The multiplicative inverse of the this Scalar.

Example
use curve25519_dalek::scalar::Scalar;

// x = 2238329342913194256032495932344128051776374960164957527413114840482143558222
let X: Scalar = Scalar::from_bytes_mod_order([
        0x4e, 0x5a, 0xb4, 0x34, 0x5d, 0x47, 0x08, 0x84,
        0x59, 0x13, 0xb4, 0x64, 0x1b, 0xc2, 0x7d, 0x52,
        0x52, 0xa5, 0x85, 0x10, 0x1b, 0xcc, 0x42, 0x44,
        0xd4, 0x49, 0xf4, 0xa8, 0x79, 0xd9, 0xf2, 0x04,
    ]);
// 1/x = 6859937278830797291664592131120606308688036382723378951768035303146619657244
let XINV: Scalar = Scalar::from_bytes_mod_order([
        0x1c, 0xdc, 0x17, 0xfc, 0xe0, 0xe9, 0xa5, 0xbb,
        0xd9, 0x24, 0x7e, 0x56, 0xbb, 0x01, 0x63, 0x47,
        0xbb, 0xba, 0x31, 0xed, 0xd5, 0xa9, 0xbb, 0x96,
        0xd5, 0x0b, 0xcd, 0x7a, 0x3f, 0x96, 0x2a, 0x0f,
    ]);

let inv_X: Scalar = X.invert();
assert!(XINV == inv_X);
let should_be_one: Scalar = &inv_X * &X;
assert!(should_be_one == Scalar::ONE);
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pub fn batch_invert(inputs: &mut [Scalar]) -> Scalar

Available on crate feature alloc only.

Given a slice of nonzero (possibly secret) Scalars, compute their inverses in a batch.

Return

Each element of inputs is replaced by its inverse.

The product of all inverses is returned.

Warning

All input Scalars MUST be nonzero. If you cannot prove that this is the case, you SHOULD NOT USE THIS FUNCTION.

Example
let mut scalars = [
    Scalar::from(3u64),
    Scalar::from(5u64),
    Scalar::from(7u64),
    Scalar::from(11u64),
];

let allinv = Scalar::batch_invert(&mut scalars);

assert_eq!(allinv, Scalar::from(3*5*7*11u64).invert());
assert_eq!(scalars[0], Scalar::from(3u64).invert());
assert_eq!(scalars[1], Scalar::from(5u64).invert());
assert_eq!(scalars[2], Scalar::from(7u64).invert());
assert_eq!(scalars[3], Scalar::from(11u64).invert());
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pub fn reduce(&self) -> Scalar

Reduce this Scalar modulo \(\ell\).

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pub fn is_canonical(&self) -> Choice

Check whether this Scalar is the canonical representative mod \(\ell\).

// 2^255 - 1, since `from_bits` clears the high bit
let _2_255_minus_1 = Scalar::from_bits([0xff;32]);
assert!(! bool::from(_2_255_minus_1.is_canonical()));

let reduced = _2_255_minus_1.reduce();
assert!(bool::from(reduced.is_canonical()));

Trait Implementations§

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impl<'a, 'b> Add<&'b Scalar> for &'a Scalar

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type Output = Scalar

The resulting type after applying the + operator.
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fn add(self, _rhs: &'b Scalar) -> Scalar

Performs the + operation. Read more
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impl<'b> Add<&'b Scalar> for Scalar

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type Output = Scalar

The resulting type after applying the + operator.
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fn add(self, rhs: &'b Scalar) -> Scalar

Performs the + operation. Read more
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impl<'a> Add<Scalar> for &'a Scalar

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type Output = Scalar

The resulting type after applying the + operator.
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fn add(self, rhs: Scalar) -> Scalar

Performs the + operation. Read more
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impl Add<Scalar> for Scalar

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type Output = Scalar

The resulting type after applying the + operator.
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fn add(self, rhs: Scalar) -> Scalar

Performs the + operation. Read more
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impl<'b> AddAssign<&'b Scalar> for Scalar

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fn add_assign(&mut self, _rhs: &'b Scalar)

Performs the += operation. Read more
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impl AddAssign<Scalar> for Scalar

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fn add_assign(&mut self, rhs: Scalar)

Performs the += operation. Read more
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impl Clone for Scalar

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fn clone(&self) -> Scalar

Returns a copy of the value. Read more
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fn clone_from(&mut self, source: &Self)

Performs copy-assignment from source. Read more
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impl ConditionallySelectable for Scalar

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fn conditional_select(a: &Self, b: &Self, choice: Choice) -> Self

Select a or b according to choice. Read more
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fn conditional_assign(&mut self, other: &Self, choice: Choice)

Conditionally assign other to self, according to choice. Read more
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fn conditional_swap(a: &mut Self, b: &mut Self, choice: Choice)

Conditionally swap self and other if choice == 1; otherwise, reassign both unto themselves. Read more
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impl ConstantTimeEq for Scalar

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fn ct_eq(&self, other: &Self) -> Choice

Determine if two items are equal. Read more
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impl Debug for Scalar

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

Formats the value using the given formatter. Read more
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impl Default for Scalar

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fn default() -> Scalar

Returns the “default value” for a type. Read more
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impl<'de> Deserialize<'de> for Scalar

Available on crate feature serde only.
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fn deserialize<D>(deserializer: D) -> Result<Self, D::Error>where
    D: Deserializer<'de>,

Deserialize this value from the given Serde deserializer. Read more
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impl From<u128> for Scalar

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fn from(x: u128) -> Scalar

Converts to this type from the input type.
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impl From<u16> for Scalar

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fn from(x: u16) -> Scalar

Converts to this type from the input type.
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impl From<u32> for Scalar

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fn from(x: u32) -> Scalar

Converts to this type from the input type.
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impl From<u64> for Scalar

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fn from(x: u64) -> Scalar

Construct a scalar from the given u64.

Inputs

An u64 to convert to a Scalar.

Returns

A Scalar corresponding to the input u64.

Example
use curve25519_dalek::scalar::Scalar;

let fourtytwo = Scalar::from(42u64);
let six = Scalar::from(6u64);
let seven = Scalar::from(7u64);

assert!(fourtytwo == six * seven);
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impl From<u8> for Scalar

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fn from(x: u8) -> Scalar

Converts to this type from the input type.
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impl Hash for Scalar

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fn hash<__H: Hasher>(&self, state: &mut __H)

Feeds this value into the given Hasher. Read more
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fn hash_slice<H>(data: &[Self], state: &mut H)where
    H: Hasher,
    Self: Sized,

Feeds a slice of this type into the given Hasher. Read more
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impl Index<usize> for Scalar

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fn index(&self, _index: usize) -> &u8

Index the bytes of the representative for this Scalar. Mutation is not permitted.

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type Output = u8

The returned type after indexing.
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impl<'a, 'b> Mul<&'a EdwardsBasepointTable> for &'b Scalar

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fn mul(self, basepoint_table: &'a EdwardsBasepointTable) -> EdwardsPoint

Construct an EdwardsPoint from a Scalar \(a\) by computing the multiple \(aB\) of this basepoint \(B\).

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type Output = EdwardsPoint

The resulting type after applying the * operator.
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impl<'a, 'b> Mul<&'a EdwardsBasepointTableRadix128> for &'b Scalar

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fn mul(self, basepoint_table: &'a EdwardsBasepointTableRadix128) -> EdwardsPoint

Construct an EdwardsPoint from a Scalar \(a\) by computing the multiple \(aB\) of this basepoint \(B\).

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type Output = EdwardsPoint

The resulting type after applying the * operator.
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impl<'a, 'b> Mul<&'a EdwardsBasepointTableRadix256> for &'b Scalar

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fn mul(self, basepoint_table: &'a EdwardsBasepointTableRadix256) -> EdwardsPoint

Construct an EdwardsPoint from a Scalar \(a\) by computing the multiple \(aB\) of this basepoint \(B\).

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type Output = EdwardsPoint

The resulting type after applying the * operator.
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impl<'a, 'b> Mul<&'a EdwardsBasepointTableRadix32> for &'b Scalar

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fn mul(self, basepoint_table: &'a EdwardsBasepointTableRadix32) -> EdwardsPoint

Construct an EdwardsPoint from a Scalar \(a\) by computing the multiple \(aB\) of this basepoint \(B\).

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type Output = EdwardsPoint

The resulting type after applying the * operator.
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impl<'a, 'b> Mul<&'a EdwardsBasepointTableRadix64> for &'b Scalar

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fn mul(self, basepoint_table: &'a EdwardsBasepointTableRadix64) -> EdwardsPoint

Construct an EdwardsPoint from a Scalar \(a\) by computing the multiple \(aB\) of this basepoint \(B\).

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type Output = EdwardsPoint

The resulting type after applying the * operator.
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impl<'a, 'b> Mul<&'a RistrettoBasepointTable> for &'b Scalar

Available on crate feature precomputed-tables only.
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type Output = RistrettoPoint

The resulting type after applying the * operator.
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fn mul(self, basepoint_table: &'a RistrettoBasepointTable) -> RistrettoPoint

Performs the * operation. Read more
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impl<'a, 'b> Mul<&'b EdwardsPoint> for &'a Scalar

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fn mul(self, point: &'b EdwardsPoint) -> EdwardsPoint

Scalar multiplication: compute scalar * self.

For scalar multiplication of a basepoint, EdwardsBasepointTable is approximately 4x faster.

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type Output = EdwardsPoint

The resulting type after applying the * operator.
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impl<'b> Mul<&'b EdwardsPoint> for Scalar

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type Output = EdwardsPoint

The resulting type after applying the * operator.
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fn mul(self, rhs: &'b EdwardsPoint) -> EdwardsPoint

Performs the * operation. Read more
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impl<'a, 'b> Mul<&'b MontgomeryPoint> for &'a Scalar

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type Output = MontgomeryPoint

The resulting type after applying the * operator.
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fn mul(self, point: &'b MontgomeryPoint) -> MontgomeryPoint

Performs the * operation. Read more
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impl<'b> Mul<&'b MontgomeryPoint> for Scalar

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type Output = MontgomeryPoint

The resulting type after applying the * operator.
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fn mul(self, rhs: &'b MontgomeryPoint) -> MontgomeryPoint

Performs the * operation. Read more
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impl<'a, 'b> Mul<&'b RistrettoPoint> for &'a Scalar

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fn mul(self, point: &'b RistrettoPoint) -> RistrettoPoint

Scalar multiplication: compute self * scalar.

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type Output = RistrettoPoint

The resulting type after applying the * operator.
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impl<'b> Mul<&'b RistrettoPoint> for Scalar

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type Output = RistrettoPoint

The resulting type after applying the * operator.
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fn mul(self, rhs: &'b RistrettoPoint) -> RistrettoPoint

Performs the * operation. Read more
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impl<'a, 'b> Mul<&'b Scalar> for &'a EdwardsBasepointTable

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fn mul(self, scalar: &'b Scalar) -> EdwardsPoint

Construct an EdwardsPoint from a Scalar \(a\) by computing the multiple \(aB\) of this basepoint \(B\).

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type Output = EdwardsPoint

The resulting type after applying the * operator.
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impl<'a, 'b> Mul<&'b Scalar> for &'a EdwardsBasepointTableRadix128

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fn mul(self, scalar: &'b Scalar) -> EdwardsPoint

Construct an EdwardsPoint from a Scalar \(a\) by computing the multiple \(aB\) of this basepoint \(B\).

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type Output = EdwardsPoint

The resulting type after applying the * operator.
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impl<'a, 'b> Mul<&'b Scalar> for &'a EdwardsBasepointTableRadix256

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fn mul(self, scalar: &'b Scalar) -> EdwardsPoint

Construct an EdwardsPoint from a Scalar \(a\) by computing the multiple \(aB\) of this basepoint \(B\).

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type Output = EdwardsPoint

The resulting type after applying the * operator.
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impl<'a, 'b> Mul<&'b Scalar> for &'a EdwardsBasepointTableRadix32

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fn mul(self, scalar: &'b Scalar) -> EdwardsPoint

Construct an EdwardsPoint from a Scalar \(a\) by computing the multiple \(aB\) of this basepoint \(B\).

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type Output = EdwardsPoint

The resulting type after applying the * operator.
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impl<'a, 'b> Mul<&'b Scalar> for &'a EdwardsBasepointTableRadix64

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fn mul(self, scalar: &'b Scalar) -> EdwardsPoint

Construct an EdwardsPoint from a Scalar \(a\) by computing the multiple \(aB\) of this basepoint \(B\).

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type Output = EdwardsPoint

The resulting type after applying the * operator.
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impl<'a, 'b> Mul<&'b Scalar> for &'a EdwardsPoint

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fn mul(self, scalar: &'b Scalar) -> EdwardsPoint

Scalar multiplication: compute scalar * self.

For scalar multiplication of a basepoint, EdwardsBasepointTable is approximately 4x faster.

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type Output = EdwardsPoint

The resulting type after applying the * operator.
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impl<'a, 'b> Mul<&'b Scalar> for &'a MontgomeryPoint

Multiply this MontgomeryPoint by a Scalar.

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fn mul(self, scalar: &'b Scalar) -> MontgomeryPoint

Given self \( = u_0(P) \), and a Scalar \(n\), return \( u_0([n]P) \).

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type Output = MontgomeryPoint

The resulting type after applying the * operator.
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impl<'a, 'b> Mul<&'b Scalar> for &'a RistrettoBasepointTable

Available on crate feature precomputed-tables only.
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type Output = RistrettoPoint

The resulting type after applying the * operator.
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fn mul(self, scalar: &'b Scalar) -> RistrettoPoint

Performs the * operation. Read more
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impl<'a, 'b> Mul<&'b Scalar> for &'a RistrettoPoint

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fn mul(self, scalar: &'b Scalar) -> RistrettoPoint

Scalar multiplication: compute scalar * self.

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type Output = RistrettoPoint

The resulting type after applying the * operator.
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impl<'a, 'b> Mul<&'b Scalar> for &'a Scalar

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type Output = Scalar

The resulting type after applying the * operator.
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fn mul(self, _rhs: &'b Scalar) -> Scalar

Performs the * operation. Read more
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impl<'b> Mul<&'b Scalar> for EdwardsPoint

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type Output = EdwardsPoint

The resulting type after applying the * operator.
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fn mul(self, rhs: &'b Scalar) -> EdwardsPoint

Performs the * operation. Read more
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impl<'b> Mul<&'b Scalar> for MontgomeryPoint

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type Output = MontgomeryPoint

The resulting type after applying the * operator.
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fn mul(self, rhs: &'b Scalar) -> MontgomeryPoint

Performs the * operation. Read more
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impl<'b> Mul<&'b Scalar> for RistrettoPoint

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type Output = RistrettoPoint

The resulting type after applying the * operator.
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fn mul(self, rhs: &'b Scalar) -> RistrettoPoint

Performs the * operation. Read more
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impl<'b> Mul<&'b Scalar> for Scalar

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type Output = Scalar

The resulting type after applying the * operator.
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fn mul(self, rhs: &'b Scalar) -> Scalar

Performs the * operation. Read more
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impl<'a> Mul<EdwardsPoint> for &'a Scalar

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type Output = EdwardsPoint

The resulting type after applying the * operator.
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fn mul(self, rhs: EdwardsPoint) -> EdwardsPoint

Performs the * operation. Read more
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impl Mul<EdwardsPoint> for Scalar

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type Output = EdwardsPoint

The resulting type after applying the * operator.
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fn mul(self, rhs: EdwardsPoint) -> EdwardsPoint

Performs the * operation. Read more
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impl<'a> Mul<MontgomeryPoint> for &'a Scalar

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type Output = MontgomeryPoint

The resulting type after applying the * operator.
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fn mul(self, rhs: MontgomeryPoint) -> MontgomeryPoint

Performs the * operation. Read more
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impl Mul<MontgomeryPoint> for Scalar

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type Output = MontgomeryPoint

The resulting type after applying the * operator.
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fn mul(self, rhs: MontgomeryPoint) -> MontgomeryPoint

Performs the * operation. Read more
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impl<'a> Mul<RistrettoPoint> for &'a Scalar

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type Output = RistrettoPoint

The resulting type after applying the * operator.
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fn mul(self, rhs: RistrettoPoint) -> RistrettoPoint

Performs the * operation. Read more
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impl Mul<RistrettoPoint> for Scalar

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type Output = RistrettoPoint

The resulting type after applying the * operator.
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fn mul(self, rhs: RistrettoPoint) -> RistrettoPoint

Performs the * operation. Read more
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impl<'a> Mul<Scalar> for &'a EdwardsPoint

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type Output = EdwardsPoint

The resulting type after applying the * operator.
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fn mul(self, rhs: Scalar) -> EdwardsPoint

Performs the * operation. Read more
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impl<'a> Mul<Scalar> for &'a MontgomeryPoint

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type Output = MontgomeryPoint

The resulting type after applying the * operator.
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fn mul(self, rhs: Scalar) -> MontgomeryPoint

Performs the * operation. Read more
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impl<'a> Mul<Scalar> for &'a RistrettoPoint

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type Output = RistrettoPoint

The resulting type after applying the * operator.
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fn mul(self, rhs: Scalar) -> RistrettoPoint

Performs the * operation. Read more
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impl<'a> Mul<Scalar> for &'a Scalar

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type Output = Scalar

The resulting type after applying the * operator.
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fn mul(self, rhs: Scalar) -> Scalar

Performs the * operation. Read more
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impl Mul<Scalar> for EdwardsPoint

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type Output = EdwardsPoint

The resulting type after applying the * operator.
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fn mul(self, rhs: Scalar) -> EdwardsPoint

Performs the * operation. Read more
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impl Mul<Scalar> for MontgomeryPoint

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type Output = MontgomeryPoint

The resulting type after applying the * operator.
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fn mul(self, rhs: Scalar) -> MontgomeryPoint

Performs the * operation. Read more
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impl Mul<Scalar> for RistrettoPoint

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type Output = RistrettoPoint

The resulting type after applying the * operator.
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fn mul(self, rhs: Scalar) -> RistrettoPoint

Performs the * operation. Read more
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impl Mul<Scalar> for Scalar

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type Output = Scalar

The resulting type after applying the * operator.
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fn mul(self, rhs: Scalar) -> Scalar

Performs the * operation. Read more
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impl<'b> MulAssign<&'b Scalar> for EdwardsPoint

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fn mul_assign(&mut self, scalar: &'b Scalar)

Performs the *= operation. Read more
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impl<'b> MulAssign<&'b Scalar> for MontgomeryPoint

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fn mul_assign(&mut self, scalar: &'b Scalar)

Performs the *= operation. Read more
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impl<'b> MulAssign<&'b Scalar> for RistrettoPoint

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fn mul_assign(&mut self, scalar: &'b Scalar)

Performs the *= operation. Read more
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impl<'b> MulAssign<&'b Scalar> for Scalar

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fn mul_assign(&mut self, _rhs: &'b Scalar)

Performs the *= operation. Read more
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impl MulAssign<Scalar> for EdwardsPoint

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fn mul_assign(&mut self, rhs: Scalar)

Performs the *= operation. Read more
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impl MulAssign<Scalar> for MontgomeryPoint

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fn mul_assign(&mut self, rhs: Scalar)

Performs the *= operation. Read more
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impl MulAssign<Scalar> for RistrettoPoint

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fn mul_assign(&mut self, rhs: Scalar)

Performs the *= operation. Read more
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impl MulAssign<Scalar> for Scalar

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fn mul_assign(&mut self, rhs: Scalar)

Performs the *= operation. Read more
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impl<'a> Neg for &'a Scalar

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type Output = Scalar

The resulting type after applying the - operator.
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fn neg(self) -> Scalar

Performs the unary - operation. Read more
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impl Neg for Scalar

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type Output = Scalar

The resulting type after applying the - operator.
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fn neg(self) -> Scalar

Performs the unary - operation. Read more
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impl PartialEq<Scalar> for Scalar

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fn eq(&self, other: &Self) -> bool

This method tests for self and other values to be equal, and is used by ==.
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fn ne(&self, other: &Rhs) -> bool

This method tests for !=. The default implementation is almost always sufficient, and should not be overridden without very good reason.
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impl<T> Product<T> for Scalarwhere
    T: Borrow<Scalar>,

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fn product<I>(iter: I) -> Selfwhere
    I: Iterator<Item = T>,

Method which takes an iterator and generates Self from the elements by multiplying the items.
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impl Serialize for Scalar

Available on crate feature serde only.
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fn serialize<S>(&self, serializer: S) -> Result<S::Ok, S::Error>where
    S: Serializer,

Serialize this value into the given Serde serializer. Read more
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impl<'a, 'b> Sub<&'b Scalar> for &'a Scalar

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type Output = Scalar

The resulting type after applying the - operator.
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fn sub(self, rhs: &'b Scalar) -> Scalar

Performs the - operation. Read more
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impl<'b> Sub<&'b Scalar> for Scalar

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type Output = Scalar

The resulting type after applying the - operator.
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fn sub(self, rhs: &'b Scalar) -> Scalar

Performs the - operation. Read more
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impl<'a> Sub<Scalar> for &'a Scalar

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type Output = Scalar

The resulting type after applying the - operator.
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fn sub(self, rhs: Scalar) -> Scalar

Performs the - operation. Read more
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impl Sub<Scalar> for Scalar

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type Output = Scalar

The resulting type after applying the - operator.
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fn sub(self, rhs: Scalar) -> Scalar

Performs the - operation. Read more
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impl<'b> SubAssign<&'b Scalar> for Scalar

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fn sub_assign(&mut self, _rhs: &'b Scalar)

Performs the -= operation. Read more
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impl SubAssign<Scalar> for Scalar

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fn sub_assign(&mut self, rhs: Scalar)

Performs the -= operation. Read more
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impl<T> Sum<T> for Scalarwhere
    T: Borrow<Scalar>,

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fn sum<I>(iter: I) -> Selfwhere
    I: Iterator<Item = T>,

Method which takes an iterator and generates Self from the elements by “summing up” the items.
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impl Zeroize for Scalar

Available on crate feature zeroize only.
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fn zeroize(&mut self)

Zero out this object from memory using Rust intrinsics which ensure the zeroization operation is not “optimized away” by the compiler.
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impl Copy for Scalar

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impl Eq for Scalar

Auto Trait Implementations§

Blanket Implementations§

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impl<T> Any for Twhere
    T: 'static + ?Sized,

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fn type_id(&self) -> TypeId

Gets the TypeId of self. Read more
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impl<T> Borrow<T> for Twhere
    T: ?Sized,

const: unstable · source§

fn borrow(&self) -> &T

Immutably borrows from an owned value. Read more
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impl<T> BorrowMut<T> for Twhere
    T: ?Sized,

const: unstable · source§

fn borrow_mut(&mut self) -> &mut T

Mutably borrows from an owned value. Read more
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impl<T, U> Cast<U> for Twhere
    U: FromCast<T>,

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fn cast(self) -> U

Numeric cast from self to T.
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impl<T> ConditionallyNegatable for Twhere
    T: ConditionallySelectable,
    &'a T: for<'a> Neg<Output = T>,

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fn conditional_negate(&mut self, choice: Choice)

Negate self if choice == Choice(1); otherwise, leave it unchanged. Read more
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impl<T> From<T> for T

const: unstable · source§

fn from(t: T) -> T

Returns the argument unchanged.

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impl<T> FromBits<T> for T

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fn from_bits(t: T) -> T

Safe lossless bitwise transmute from T to Self.
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impl<T> FromCast<T> for T

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fn from_cast(t: T) -> T

Numeric cast from T to Self.
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impl<T, U> Into<U> for Twhere
    U: From<T>,

const: unstable · source§

fn into(self) -> U

Calls U::from(self).

That is, this conversion is whatever the implementation of From<T> for U chooses to do.

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impl<T, U> IntoBits<U> for Twhere
    U: FromBits<T>,

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fn into_bits(self) -> U

Safe lossless bitwise transmute from self to T.
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impl<T> Same<T> for T

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type Output = T

Should always be Self
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impl<T> ToOwned for Twhere
    T: Clone,

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type Owned = T

The resulting type after obtaining ownership.
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fn to_owned(&self) -> T

Creates owned data from borrowed data, usually by cloning. Read more
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fn clone_into(&self, target: &mut T)

Uses borrowed data to replace owned data, usually by cloning. Read more
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impl<T, U> TryFrom<U> for Twhere
    U: Into<T>,

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type Error = Infallible

The type returned in the event of a conversion error.
const: unstable · source§

fn try_from(value: U) -> Result<T, <T as TryFrom<U>>::Error>

Performs the conversion.
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impl<T, U> TryInto<U> for Twhere
    U: TryFrom<T>,

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type Error = <U as TryFrom<T>>::Error

The type returned in the event of a conversion error.
const: unstable · source§

fn try_into(self) -> Result<U, <U as TryFrom<T>>::Error>

Performs the conversion.
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impl<T> DeserializeOwned for Twhere
    T: for<'de> Deserialize<'de>,