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Trait Add

1.0.0 (const: unstable) · Source
pub trait Add<Rhs = Self> {
    type Output;

    // Required method
    const fn add(self, rhs: Rhs) -> Self::Output;
}
Expand description

The addition operator +.

Note that Rhs is Self by default, but this is not mandatory. For example, std::time::SystemTime implements Add<Duration>, which permits operations of the form SystemTime = SystemTime + Duration.

§Examples

§Addable points

use std::ops::Add;

#[derive(Debug, Copy, Clone, PartialEq)]
struct Point {
    x: i32,
    y: i32,
}

impl Add for Point {
    type Output = Self;

    fn add(self, other: Self) -> Self {
        Self {
            x: self.x + other.x,
            y: self.y + other.y,
        }
    }
}

assert_eq!(Point { x: 1, y: 0 } + Point { x: 2, y: 3 },
           Point { x: 3, y: 3 });

§Implementing Add with generics

Here is an example of the same Point struct implementing the Add trait using generics.

use std::ops::Add;

#[derive(Debug, Copy, Clone, PartialEq)]
struct Point<T> {
    x: T,
    y: T,
}

// Notice that the implementation uses the associated type `Output`.
impl<T: Add<Output = T>> Add for Point<T> {
    type Output = Self;

    fn add(self, other: Self) -> Self::Output {
        Self {
            x: self.x + other.x,
            y: self.y + other.y,
        }
    }
}

assert_eq!(Point { x: 1, y: 0 } + Point { x: 2, y: 3 },
           Point { x: 3, y: 3 });

Required Associated Types§

1.0.0 · Source

type Output

The resulting type after applying the + operator.

Required Methods§

1.0.0 · Source

const fn add(self, rhs: Rhs) -> Self::Output

Performs the + operation.

§Example
assert_eq!(12 + 1, 13);

Implementors§

1.0.0 (const: unstable) · Source§

impl Add for f16

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impl Add for f32

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impl Add for f64

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impl Add for f128

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impl Add for i8

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impl Add for i16

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impl Add for i32

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impl Add for i64

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impl Add for i128

1.0.0 (const: unstable) · Source§

impl Add for isize

1.0.0 (const: unstable) · Source§

impl Add for u8

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impl Add for u16

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impl Add for u32

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impl Add for u64

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impl Add for u128

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impl Add for usize

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impl Add for Assume

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impl Add for Saturating<i8>

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impl Add for Saturating<i16>

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impl Add for Saturating<i32>

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impl Add for Saturating<i64>

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impl Add for Saturating<i128>

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impl Add for Saturating<isize>

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impl Add for Saturating<u8>

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impl Add for Saturating<u16>

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impl Add for Saturating<u32>

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impl Add for Saturating<u64>

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impl Add for Saturating<u128>

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impl Add for Saturating<usize>

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impl Add for Wrapping<i8>

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impl Add for Wrapping<i16>

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impl Add for Wrapping<i32>

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impl Add for Wrapping<i64>

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impl Add for Wrapping<i128>

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impl Add for Wrapping<isize>

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impl Add for Wrapping<u8>

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impl Add for Wrapping<u16>

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impl Add for Wrapping<u32>

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impl Add for Wrapping<u64>

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impl Add for Wrapping<u128>

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impl Add for Wrapping<usize>

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impl Add for core::time::Duration

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impl Add for BigInt

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impl Add for num_bigint::biguint::BigUint

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impl Add for ATerm

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impl Add for BigUint

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type Output = BigUint

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impl Add for Duration

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type Output = Duration

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impl Add for EdwardsPoint

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type Output = EdwardsPoint

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impl Add for Field

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type Output = Field

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impl Add for FixedI64

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type Output = FixedI64

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impl Add for FixedI128

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type Output = FixedI128

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impl Add for FixedU64

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type Output = FixedU64

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impl Add for FixedU128

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type Output = FixedU128

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impl Add for Ieee32

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type Output = Ieee32

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impl Add for Ieee64

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type Output = Ieee64

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impl Add for PerU16

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type Output = PerU16

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impl Add for Perbill

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type Output = Perbill

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impl Add for Percent

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type Output = Percent

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impl Add for Permill

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type Output = Permill

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impl Add for Perquintill

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type Output = Perquintill

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impl Add for Rgb

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type Output = Rgb

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impl Add for RistrettoPoint

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type Output = RistrettoPoint

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impl Add for Scalar

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type Output = Scalar

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impl Add for Scalar

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type Output = Scalar

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impl Add for Timespec

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type Output = Timespec

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impl Add for Weight

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type Output = Weight

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impl Add<&f16> for &f16

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impl Add<&f16> for f16

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impl Add<&f32> for &f32

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impl Add<&f32> for f32

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impl Add<&f64> for &f64

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impl Add<&f64> for f64

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impl Add<&f128> for &f128

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impl Add<&f128> for f128

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impl Add<&i8> for &i8

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impl Add<&i8> for &BigInt

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impl Add<&i8> for i8

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impl Add<&i8> for BigInt

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impl Add<&i16> for &i16

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impl Add<&i16> for &BigInt

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impl Add<&i16> for i16

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impl Add<&i16> for BigInt

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impl Add<&i32> for &i32

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impl Add<&i32> for &BigInt

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impl Add<&i32> for i32

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impl Add<&i32> for BigInt

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impl Add<&i64> for &i64

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impl Add<&i64> for &BigInt

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impl Add<&i64> for i64

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impl Add<&i64> for BigInt

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impl Add<&i128> for &i128

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impl Add<&i128> for &BigInt

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impl Add<&i128> for i128

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impl Add<&i128> for BigInt

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impl Add<&isize> for &isize

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impl Add<&isize> for &BigInt

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impl Add<&isize> for isize

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impl Add<&isize> for BigInt

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impl Add<&str> for String

Implements the + operator for concatenating two strings.

This consumes the String on the left-hand side and re-uses its buffer (growing it if necessary). This is done to avoid allocating a new String and copying the entire contents on every operation, which would lead to O(n^2) running time when building an n-byte string by repeated concatenation.

The string on the right-hand side is only borrowed; its contents are copied into the returned String.

§Examples

Concatenating two Strings takes the first by value and borrows the second:

let a = String::from("hello");
let b = String::from(" world");
let c = a + &b;
// `a` is moved and can no longer be used here.

If you want to keep using the first String, you can clone it and append to the clone instead:

let a = String::from("hello");
let b = String::from(" world");
let c = a.clone() + &b;
// `a` is still valid here.

Concatenating &str slices can be done by converting the first to a String:

let a = "hello";
let b = " world";
let c = a.to_string() + b;
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impl Add<&u8> for &u8

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impl Add<&u8> for &BigInt

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impl Add<&u8> for &num_bigint::biguint::BigUint

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impl Add<&u8> for u8

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impl Add<&u8> for BigInt

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impl Add<&u8> for num_bigint::biguint::BigUint

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impl Add<&u16> for &u16

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impl Add<&u16> for &BigInt

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impl Add<&u16> for &num_bigint::biguint::BigUint

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impl Add<&u16> for u16

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impl Add<&u16> for BigInt

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impl Add<&u16> for num_bigint::biguint::BigUint

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impl Add<&u32> for &u32

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impl Add<&u32> for &BigInt

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impl Add<&u32> for &num_bigint::biguint::BigUint

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impl Add<&u32> for u32

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impl Add<&u32> for BigInt

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impl Add<&u32> for num_bigint::biguint::BigUint

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impl Add<&u64> for &u64

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impl Add<&u64> for &BigInt

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impl Add<&u64> for &num_bigint::biguint::BigUint

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impl Add<&u64> for u64

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impl Add<&u64> for BigInt

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impl Add<&u64> for num_bigint::biguint::BigUint

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impl Add<&u128> for &u128

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impl Add<&u128> for &BigInt

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impl Add<&u128> for &num_bigint::biguint::BigUint

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impl Add<&u128> for u128

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impl Add<&u128> for BigInt

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impl Add<&u128> for num_bigint::biguint::BigUint

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impl Add<&usize> for &usize

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impl Add<&usize> for &BigInt

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impl Add<&usize> for &num_bigint::biguint::BigUint

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impl Add<&usize> for usize

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impl Add<&usize> for BigInt

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impl Add<&usize> for num_bigint::biguint::BigUint

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impl Add<&Saturating<i8>> for &Saturating<i8>

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impl Add<&Saturating<i8>> for Saturating<i8>

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impl Add<&Saturating<i16>> for &Saturating<i16>

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impl Add<&Saturating<i16>> for Saturating<i16>

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impl Add<&Saturating<i32>> for &Saturating<i32>

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impl Add<&Saturating<i32>> for Saturating<i32>

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impl Add<&Saturating<i64>> for &Saturating<i64>

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impl Add<&Saturating<i64>> for Saturating<i64>

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impl Add<&Saturating<i128>> for &Saturating<i128>

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impl Add<&Saturating<i128>> for Saturating<i128>

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impl Add<&Saturating<isize>> for &Saturating<isize>

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impl Add<&Saturating<isize>> for Saturating<isize>

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impl Add<&Saturating<u8>> for &Saturating<u8>

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impl Add<&Saturating<u8>> for Saturating<u8>

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impl Add<&Saturating<u16>> for &Saturating<u16>

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impl Add<&Saturating<u16>> for Saturating<u16>

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impl Add<&Saturating<u32>> for &Saturating<u32>

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impl Add<&Saturating<u32>> for Saturating<u32>

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impl Add<&Saturating<u64>> for &Saturating<u64>

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impl Add<&Saturating<u64>> for Saturating<u64>

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impl Add<&Saturating<u128>> for &Saturating<u128>

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impl Add<&Saturating<u128>> for Saturating<u128>

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impl Add<&Saturating<usize>> for &Saturating<usize>

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impl Add<&Saturating<usize>> for Saturating<usize>

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impl Add<&Wrapping<i8>> for &Wrapping<i8>

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impl Add<&Wrapping<i8>> for Wrapping<i8>

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impl Add<&Wrapping<i16>> for &Wrapping<i16>

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impl Add<&Wrapping<i16>> for Wrapping<i16>

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impl Add<&Wrapping<i32>> for &Wrapping<i32>

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impl Add<&Wrapping<i32>> for Wrapping<i32>

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impl Add<&Wrapping<i64>> for &Wrapping<i64>

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impl Add<&Wrapping<i64>> for Wrapping<i64>

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impl Add<&Wrapping<i128>> for &Wrapping<i128>

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impl Add<&Wrapping<i128>> for Wrapping<i128>

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impl Add<&Wrapping<isize>> for &Wrapping<isize>

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impl Add<&Wrapping<isize>> for Wrapping<isize>

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impl Add<&Wrapping<u8>> for &Wrapping<u8>

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impl Add<&Wrapping<u8>> for Wrapping<u8>

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impl Add<&Wrapping<u16>> for &Wrapping<u16>

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impl Add<&Wrapping<u16>> for Wrapping<u16>

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impl Add<&Wrapping<u32>> for &Wrapping<u32>

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impl Add<&Wrapping<u32>> for Wrapping<u32>

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impl Add<&Wrapping<u64>> for &Wrapping<u64>

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impl Add<&Wrapping<u64>> for Wrapping<u64>

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impl Add<&Wrapping<u128>> for &Wrapping<u128>

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impl Add<&Wrapping<u128>> for Wrapping<u128>

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impl Add<&Wrapping<usize>> for &Wrapping<usize>

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impl Add<&Wrapping<usize>> for Wrapping<usize>

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impl Add<&BigInt> for &i8

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impl Add<&BigInt> for &i16

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impl Add<&BigInt> for &i32

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impl Add<&BigInt> for &i64

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impl Add<&BigInt> for &i128

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impl Add<&BigInt> for &isize

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impl Add<&BigInt> for &u8

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impl Add<&BigInt> for &u16

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impl Add<&BigInt> for &u32

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impl Add<&BigInt> for &u64

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impl Add<&BigInt> for &u128

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impl Add<&BigInt> for &usize

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impl Add<&BigInt> for &BigInt

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impl Add<&BigInt> for i8

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impl Add<&BigInt> for i16

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impl Add<&BigInt> for i32

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impl Add<&BigInt> for i64

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impl Add<&BigInt> for i128

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impl Add<&BigInt> for isize

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impl Add<&BigInt> for u8

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impl Add<&BigInt> for u16

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impl Add<&BigInt> for u32

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impl Add<&BigInt> for u64

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impl Add<&BigInt> for u128

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impl Add<&BigInt> for usize

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impl Add<&BigInt> for BigInt

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impl Add<&BigUint> for &u8

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impl Add<&BigUint> for &u16

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impl Add<&BigUint> for &u32

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impl Add<&BigUint> for &u64

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impl Add<&BigUint> for &u128

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impl Add<&BigUint> for &usize

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impl Add<&BigUint> for &num_bigint::biguint::BigUint

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impl Add<&BigUint> for u8

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impl Add<&BigUint> for u16

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impl Add<&BigUint> for u32

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impl Add<&BigUint> for u64

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impl Add<&BigUint> for u128

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impl Add<&BigUint> for usize

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impl Add<&BigUint> for num_bigint::biguint::BigUint

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impl Add<&Rgb> for &Rgb

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type Output = Rgb

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impl Add<&Rgb> for Rgb

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type Output = Rgb

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impl Add<i8> for &BigInt

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impl Add<i8> for BigInt

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impl Add<i16> for &BigInt

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impl Add<i16> for BigInt

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impl Add<i32> for &BigInt

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impl Add<i32> for BigInt

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impl Add<i64> for &BigInt

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impl Add<i64> for BigInt

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impl Add<i128> for &BigInt

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impl Add<i128> for BigInt

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impl Add<isize> for &BigInt

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impl Add<isize> for BigInt

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impl Add<u8> for &BigInt

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impl Add<u8> for &num_bigint::biguint::BigUint

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impl Add<u8> for BigInt

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impl Add<u8> for num_bigint::biguint::BigUint

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impl Add<u16> for &BigInt

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impl Add<u16> for &num_bigint::biguint::BigUint

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impl Add<u16> for BigInt

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impl Add<u16> for num_bigint::biguint::BigUint

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impl Add<u32> for &BigInt

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impl Add<u32> for &num_bigint::biguint::BigUint

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impl Add<u32> for BigInt

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impl Add<u32> for num_bigint::biguint::BigUint

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impl Add<u64> for &BigInt

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impl Add<u64> for &num_bigint::biguint::BigUint

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impl Add<u64> for BigInt

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impl Add<u64> for num_bigint::biguint::BigUint

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impl Add<u128> for &BigInt

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impl Add<u128> for &num_bigint::biguint::BigUint

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impl Add<u128> for BigInt

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impl Add<u128> for num_bigint::biguint::BigUint

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impl Add<usize> for &BigInt

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impl Add<usize> for &num_bigint::biguint::BigUint

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impl Add<usize> for BigInt

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impl Add<usize> for num_bigint::biguint::BigUint

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impl Add<Duration> for std::time::Instant

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impl Add<Duration> for SystemTime

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impl Add<Duration> for Date

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type Output = Date

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impl Add<Duration> for Duration

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type Output = Duration

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impl Add<Duration> for Instant

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type Output = Instant

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impl Add<Duration> for Instant

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type Output = Instant

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impl Add<Duration> for OffsetDateTime

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type Output = OffsetDateTime

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impl Add<Duration> for PrimitiveDateTime

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type Output = PrimitiveDateTime

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impl Add<Duration> for Time

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type Output = Time

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impl Add<BigInt> for &i8

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impl Add<BigInt> for &i16

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impl Add<BigInt> for &i32

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impl Add<BigInt> for &i64

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impl Add<BigInt> for &i128

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impl Add<BigInt> for &isize

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impl Add<BigInt> for &u8

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impl Add<BigInt> for &u16

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impl Add<BigInt> for &u32

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impl Add<BigInt> for &u64

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impl Add<BigInt> for &u128

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impl Add<BigInt> for &usize

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impl Add<BigInt> for &BigInt

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impl Add<BigInt> for i8

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impl Add<BigInt> for i16

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impl Add<BigInt> for i32

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impl Add<BigInt> for i64

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impl Add<BigInt> for i128

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impl Add<BigInt> for isize

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impl Add<BigInt> for u8

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impl Add<BigInt> for u16

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impl Add<BigInt> for u32

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impl Add<BigInt> for u64

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impl Add<BigInt> for u128

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impl Add<BigInt> for usize

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impl Add<BigUint> for &u8

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impl Add<BigUint> for &u16

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impl Add<BigUint> for &u32

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impl Add<BigUint> for &u64

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impl Add<BigUint> for &u128

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impl Add<BigUint> for &usize

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impl Add<BigUint> for &num_bigint::biguint::BigUint

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impl Add<BigUint> for u8

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impl Add<BigUint> for u16

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impl Add<BigUint> for u32

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impl Add<BigUint> for u64

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impl Add<BigUint> for u128

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impl Add<BigUint> for usize

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impl Add<B0> for UTerm

UTerm + B0 = UTerm

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impl Add<B1> for UTerm

UTerm + B1 = UInt<UTerm, B1>

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impl Add<Duration> for core::time::Duration

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type Output = Duration

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impl Add<Duration> for std::time::Instant

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impl Add<Duration> for SystemTime

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impl Add<Duration> for Date

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type Output = Date

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impl Add<Duration> for Instant

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type Output = Instant

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impl Add<Duration> for OffsetDateTime

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type Output = OffsetDateTime

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impl Add<Duration> for PrimitiveDateTime

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type Output = PrimitiveDateTime

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impl Add<Duration> for Time

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type Output = Time

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impl Add<Rgb> for &Rgb

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type Output = Rgb

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impl<'a> Add for Cow<'a, str>

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type Output = Cow<'a, str>

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impl<'a> Add<&'a str> for Cow<'a, str>

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type Output = Cow<'a, str>

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impl<'a> Add<f16> for &'a f16

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impl<'a> Add<f32> for &'a f32

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impl<'a> Add<f64> for &'a f64

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impl<'a> Add<f128> for &'a f128

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impl<'a> Add<i8> for &'a i8

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impl<'a> Add<i16> for &'a i16

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impl<'a> Add<i32> for &'a i32

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impl<'a> Add<i64> for &'a i64

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impl<'a> Add<i128> for &'a i128

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impl<'a> Add<isize> for &'a isize

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impl<'a> Add<u8> for &'a u8

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impl<'a> Add<u16> for &'a u16

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impl<'a> Add<u32> for &'a u32

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impl<'a> Add<u64> for &'a u64

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impl<'a> Add<u128> for &'a u128

1.0.0 · Source§

impl<'a> Add<usize> for &'a usize

1.74.0 · Source§

impl<'a> Add<Saturating<i8>> for &'a Saturating<i8>

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impl<'a> Add<Saturating<i16>> for &'a Saturating<i16>

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impl<'a> Add<Saturating<i32>> for &'a Saturating<i32>

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impl<'a> Add<Saturating<i64>> for &'a Saturating<i64>

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impl<'a> Add<Saturating<i128>> for &'a Saturating<i128>

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impl<'a> Add<Saturating<isize>> for &'a Saturating<isize>

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impl<'a> Add<Saturating<u8>> for &'a Saturating<u8>

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impl<'a> Add<Saturating<u16>> for &'a Saturating<u16>

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impl<'a> Add<Saturating<u32>> for &'a Saturating<u32>

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impl<'a> Add<Saturating<u64>> for &'a Saturating<u64>

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impl<'a> Add<Saturating<u128>> for &'a Saturating<u128>

1.74.0 · Source§

impl<'a> Add<Saturating<usize>> for &'a Saturating<usize>

1.14.0 · Source§

impl<'a> Add<Wrapping<i8>> for &'a Wrapping<i8>

1.14.0 · Source§

impl<'a> Add<Wrapping<i16>> for &'a Wrapping<i16>

1.14.0 · Source§

impl<'a> Add<Wrapping<i32>> for &'a Wrapping<i32>

1.14.0 · Source§

impl<'a> Add<Wrapping<i64>> for &'a Wrapping<i64>

1.14.0 · Source§

impl<'a> Add<Wrapping<i128>> for &'a Wrapping<i128>

1.14.0 · Source§

impl<'a> Add<Wrapping<isize>> for &'a Wrapping<isize>

1.14.0 · Source§

impl<'a> Add<Wrapping<u8>> for &'a Wrapping<u8>

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impl<'a> Add<Wrapping<u16>> for &'a Wrapping<u16>

1.14.0 · Source§

impl<'a> Add<Wrapping<u32>> for &'a Wrapping<u32>

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impl<'a> Add<Wrapping<u64>> for &'a Wrapping<u64>

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impl<'a> Add<Wrapping<u128>> for &'a Wrapping<u128>

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impl<'a> Add<Wrapping<usize>> for &'a Wrapping<usize>

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impl<'a> Add<EdwardsPoint> for &'a EdwardsPoint

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type Output = EdwardsPoint

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impl<'a> Add<RistrettoPoint> for &'a RistrettoPoint

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type Output = RistrettoPoint

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

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type Output = Scalar

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

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type Output = Field

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

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type Output = Scalar

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impl<'a, 'b> Add<&'b AffineNielsPoint> for &'a EdwardsPoint

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type Output = CompletedPoint

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

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type Output = EdwardsPoint

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impl<'a, 'b> Add<&'b ProjectiveNielsPoint> for &'a EdwardsPoint

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type Output = CompletedPoint

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

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type Output = RistrettoPoint

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

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type Output = Scalar

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impl<'a, 'b, F> Add<&'a DenseMultilinearExtension<F>> for &'b DenseMultilinearExtension<F>
where F: Field,

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type Output = DenseMultilinearExtension<F>

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impl<'a, 'b, F> Add<&'a DenseMultilinearExtension<F>> for &'b DenseMultilinearExtension<F>
where F: Field,

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type Output = DenseMultilinearExtension<F>

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impl<'a, 'b, F> Add<&'a DensePolynomial<F>> for &'b DensePolynomial<F>
where F: Field,

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type Output = DensePolynomial<F>

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impl<'a, 'b, F> Add<&'a DensePolynomial<F>> for &'b DensePolynomial<F>
where F: Field,

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type Output = DensePolynomial<F>

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impl<'a, 'b, F> Add<&'a SparseMultilinearExtension<F>> for &'b SparseMultilinearExtension<F>
where F: Field,

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type Output = SparseMultilinearExtension<F>

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impl<'a, 'b, F> Add<&'a SparseMultilinearExtension<F>> for &'b SparseMultilinearExtension<F>
where F: Field,

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type Output = SparseMultilinearExtension<F>

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impl<'a, 'b, F> Add<&'a SparsePolynomial<F>> for &'b DensePolynomial<F>
where F: Field,

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type Output = DensePolynomial<F>

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impl<'a, 'b, F> Add<&'a SparsePolynomial<F>> for &'b DensePolynomial<F>
where F: Field,

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type Output = DensePolynomial<F>

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impl<'a, 'b, F> Add<&'a SparsePolynomial<F>> for &'b SparsePolynomial<F>
where F: Field,

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type Output = SparsePolynomial<F>

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impl<'a, 'b, F> Add<&'a SparsePolynomial<F>> for &'b SparsePolynomial<F>
where F: Field,

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type Output = SparsePolynomial<F>

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impl<'a, 'b, F, D> Add<&'a Evaluations<F, D>> for &'b Evaluations<F, D>
where F: FftField, D: EvaluationDomain<F>,

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type Output = Evaluations<F, D>

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impl<'a, 'b, F, D> Add<&'a Evaluations<F, D>> for &'b Evaluations<F, D>
where F: FftField, D: EvaluationDomain<F>,

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type Output = Evaluations<F, D>

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impl<'a, 'b, F, T> Add<&'a SparsePolynomial<F, T>> for &'b SparsePolynomial<F, T>
where F: Field, T: Term,

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type Output = SparsePolynomial<F, T>

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impl<'a, 'b, F, T> Add<&'a SparsePolynomial<F, T>> for &'b SparsePolynomial<F, T>
where F: Field, T: Term,

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type Output = SparsePolynomial<F, T>

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impl<'a, 'b, P> Add<&'a CubicExtField<P>> for &'b CubicExtField<P>
where P: CubicExtConfig,

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type Output = CubicExtField<P>

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impl<'a, 'b, P> Add<&'a CubicExtField<P>> for &'b CubicExtField<P>
where P: CubicExtConfig,

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type Output = CubicExtField<P>

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impl<'a, 'b, P> Add<&'a PairingOutput<P>> for &'b PairingOutput<P>
where P: Pairing,

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type Output = PairingOutput<P>

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impl<'a, 'b, P> Add<&'a PairingOutput<P>> for &'b PairingOutput<P>
where P: Pairing,

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type Output = PairingOutput<P>

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impl<'a, 'b, P> Add<&'a Projective<P>> for &'b Projective<P>
where P: SWCurveConfig,

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type Output = Projective<P>

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impl<'a, 'b, P> Add<&'a Projective<P>> for &'b Projective<P>
where P: SWCurveConfig,

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type Output = Projective<P>

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impl<'a, 'b, P> Add<&'a Projective<P>> for &'b Projective<P>
where P: TECurveConfig,

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type Output = Projective<P>

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impl<'a, 'b, P> Add<&'a Projective<P>> for &'b Projective<P>
where P: TECurveConfig,

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type Output = Projective<P>

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impl<'a, 'b, P> Add<&'a QuadExtField<P>> for &'b QuadExtField<P>
where P: QuadExtConfig,

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type Output = QuadExtField<P>

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impl<'a, 'b, P> Add<&'a QuadExtField<P>> for &'b QuadExtField<P>
where P: QuadExtConfig,

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type Output = QuadExtField<P>

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impl<'a, 'b, P> Add<&'a mut CubicExtField<P>> for &'b CubicExtField<P>
where P: CubicExtConfig,

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type Output = CubicExtField<P>

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impl<'a, 'b, P> Add<&'a mut CubicExtField<P>> for &'b CubicExtField<P>
where P: CubicExtConfig,

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type Output = CubicExtField<P>

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impl<'a, 'b, P> Add<&'a mut PairingOutput<P>> for &'b PairingOutput<P>
where P: Pairing,

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type Output = PairingOutput<P>

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impl<'a, 'b, P> Add<&'a mut PairingOutput<P>> for &'b PairingOutput<P>
where P: Pairing,

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type Output = PairingOutput<P>

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impl<'a, 'b, P> Add<&'a mut Projective<P>> for &'b Projective<P>
where P: SWCurveConfig,

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type Output = Projective<P>

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impl<'a, 'b, P> Add<&'a mut Projective<P>> for &'b Projective<P>
where P: SWCurveConfig,

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type Output = Projective<P>

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impl<'a, 'b, P> Add<&'a mut Projective<P>> for &'b Projective<P>
where P: TECurveConfig,

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type Output = Projective<P>

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impl<'a, 'b, P> Add<&'a mut Projective<P>> for &'b Projective<P>
where P: TECurveConfig,

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type Output = Projective<P>

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impl<'a, 'b, P> Add<&'a mut QuadExtField<P>> for &'b QuadExtField<P>
where P: QuadExtConfig,

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type Output = QuadExtField<P>

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impl<'a, 'b, P> Add<&'a mut QuadExtField<P>> for &'b QuadExtField<P>
where P: QuadExtConfig,

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type Output = QuadExtField<P>

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impl<'a, 'b, P, const N: usize> Add<&'b Fp<P, N>> for &'a Fp<P, N>
where P: FpConfig<N>,

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type Output = Fp<P, N>

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impl<'a, 'b, P, const N: usize> Add<&'b Fp<P, N>> for &'a Fp<P, N>
where P: FpConfig<N>,

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type Output = Fp<P, N>

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impl<'a, F> Add<&'a DensePolynomial<F>> for DensePolynomial<F>
where F: Field,

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type Output = DensePolynomial<F>

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impl<'a, F> Add<DensePolynomial<F>> for &'a DensePolynomial<F>
where F: Field,

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type Output = DensePolynomial<F>

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impl<'a, P> Add<&'a CubicExtField<P>> for CubicExtField<P>
where P: CubicExtConfig,

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type Output = CubicExtField<P>

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impl<'a, P> Add<&'a CubicExtField<P>> for CubicExtField<P>
where P: CubicExtConfig,

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type Output = CubicExtField<P>

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impl<'a, P> Add<&'a PairingOutput<P>> for PairingOutput<P>
where P: Pairing,

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type Output = PairingOutput<P>

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impl<'a, P> Add<&'a PairingOutput<P>> for PairingOutput<P>
where P: Pairing,

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type Output = PairingOutput<P>

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impl<'a, P> Add<&'a Projective<P>> for Affine<P>
where P: SWCurveConfig,

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type Output = Projective<P>

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impl<'a, P> Add<&'a Projective<P>> for Affine<P>
where P: SWCurveConfig,

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type Output = Projective<P>

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impl<'a, P> Add<&'a Projective<P>> for Affine<P>
where P: TECurveConfig,

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type Output = Projective<P>

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impl<'a, P> Add<&'a Projective<P>> for Affine<P>
where P: TECurveConfig,

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type Output = Projective<P>

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impl<'a, P> Add<&'a Projective<P>> for Projective<P>
where P: SWCurveConfig,

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type Output = Projective<P>

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impl<'a, P> Add<&'a Projective<P>> for Projective<P>
where P: SWCurveConfig,

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type Output = Projective<P>

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impl<'a, P> Add<&'a Projective<P>> for Projective<P>
where P: TECurveConfig,

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type Output = Projective<P>

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impl<'a, P> Add<&'a Projective<P>> for Projective<P>
where P: TECurveConfig,

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type Output = Projective<P>

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impl<'a, P> Add<&'a QuadExtField<P>> for QuadExtField<P>
where P: QuadExtConfig,

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type Output = QuadExtField<P>

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impl<'a, P> Add<&'a QuadExtField<P>> for QuadExtField<P>
where P: QuadExtConfig,

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type Output = QuadExtField<P>

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impl<'a, P> Add<&'a mut CubicExtField<P>> for CubicExtField<P>
where P: CubicExtConfig,

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type Output = CubicExtField<P>

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impl<'a, P> Add<&'a mut CubicExtField<P>> for CubicExtField<P>
where P: CubicExtConfig,

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type Output = CubicExtField<P>

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impl<'a, P> Add<&'a mut PairingOutput<P>> for PairingOutput<P>
where P: Pairing,

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type Output = PairingOutput<P>

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impl<'a, P> Add<&'a mut PairingOutput<P>> for PairingOutput<P>
where P: Pairing,

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type Output = PairingOutput<P>

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impl<'a, P> Add<&'a mut Projective<P>> for Projective<P>
where P: SWCurveConfig,

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type Output = Projective<P>

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impl<'a, P> Add<&'a mut Projective<P>> for Projective<P>
where P: SWCurveConfig,

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type Output = Projective<P>

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impl<'a, P> Add<&'a mut Projective<P>> for Projective<P>
where P: TECurveConfig,

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type Output = Projective<P>

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impl<'a, P> Add<&'a mut Projective<P>> for Projective<P>
where P: TECurveConfig,

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type Output = Projective<P>

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impl<'a, P> Add<&'a mut QuadExtField<P>> for QuadExtField<P>
where P: QuadExtConfig,

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type Output = QuadExtField<P>

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impl<'a, P> Add<&'a mut QuadExtField<P>> for QuadExtField<P>
where P: QuadExtConfig,

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type Output = QuadExtField<P>

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impl<'a, P, const N: usize> Add<&'a Fp<P, N>> for Fp<P, N>
where P: FpConfig<N>,

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type Output = Fp<P, N>

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impl<'a, P, const N: usize> Add<&'a Fp<P, N>> for Fp<P, N>
where P: FpConfig<N>,

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type Output = Fp<P, N>

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impl<'a, P, const N: usize> Add<&'a mut Fp<P, N>> for Fp<P, N>
where P: FpConfig<N>,

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type Output = Fp<P, N>

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impl<'a, P, const N: usize> Add<&'a mut Fp<P, N>> for Fp<P, N>
where P: FpConfig<N>,

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type Output = Fp<P, N>

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impl<'a, T> Add<T> for &'a U128
where T: Into<U128>,

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type Output = U128

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impl<'a, T> Add<T> for &'a U256
where T: Into<U256>,

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type Output = U256

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impl<'a, T> Add<T> for &'a U512
where T: Into<U512>,

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type Output = U512

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impl<'b> Add<&'b EdwardsPoint> for EdwardsPoint

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type Output = EdwardsPoint

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impl<'b> Add<&'b RistrettoPoint> for RistrettoPoint

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type Output = RistrettoPoint

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

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type Output = Scalar

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impl<'b, P> Add<CubicExtField<P>> for &'b CubicExtField<P>
where P: CubicExtConfig,

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type Output = CubicExtField<P>

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impl<'b, P> Add<CubicExtField<P>> for &'b CubicExtField<P>
where P: CubicExtConfig,

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type Output = CubicExtField<P>

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impl<'b, P> Add<PairingOutput<P>> for &'b PairingOutput<P>
where P: Pairing,

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type Output = PairingOutput<P>

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impl<'b, P> Add<PairingOutput<P>> for &'b PairingOutput<P>
where P: Pairing,

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type Output = PairingOutput<P>

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impl<'b, P> Add<Projective<P>> for &'b Projective<P>
where P: SWCurveConfig,

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type Output = Projective<P>

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impl<'b, P> Add<Projective<P>> for &'b Projective<P>
where P: SWCurveConfig,

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type Output = Projective<P>

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impl<'b, P> Add<Projective<P>> for &'b Projective<P>
where P: TECurveConfig,

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type Output = Projective<P>

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impl<'b, P> Add<Projective<P>> for &'b Projective<P>
where P: TECurveConfig,

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type Output = Projective<P>

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impl<'b, P> Add<QuadExtField<P>> for &'b QuadExtField<P>
where P: QuadExtConfig,

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type Output = QuadExtField<P>

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impl<'b, P> Add<QuadExtField<P>> for &'b QuadExtField<P>
where P: QuadExtConfig,

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type Output = QuadExtField<P>

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impl<'lhs, 'rhs, T, const N: usize> Add<&'rhs Simd<T, N>> for &'lhs Simd<T, N>
where T: SimdElement, Simd<T, N>: Add<Output = Simd<T, N>>, LaneCount<N>: SupportedLaneCount,

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type Output = Simd<T, N>

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impl<Al, Vl, Ar, Vr> Add<TArr<Vr, Ar>> for TArr<Vl, Al>
where Al: Add<Ar>, Vl: Add<Vr>,

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type Output = TArr<<Vl as Add<Vr>>::Output, <Al as Add<Ar>>::Output>

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impl<E> Add for KzgCommitment<E>
where E: Pairing,

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type Output = KzgCommitment<E>

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impl<F> Add for DenseMultilinearExtension<F>
where F: Field,

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type Output = DenseMultilinearExtension<F>

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impl<F> Add for DenseMultilinearExtension<F>
where F: Field,

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type Output = DenseMultilinearExtension<F>

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impl<F> Add for DensePolynomial<F>
where F: Field,

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type Output = DensePolynomial<F>

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impl<F> Add for DensePolynomial<F>
where F: Field,

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type Output = DensePolynomial<F>

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impl<F> Add for SparseMultilinearExtension<F>
where F: Field,

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type Output = SparseMultilinearExtension<F>

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impl<F> Add for SparseMultilinearExtension<F>
where F: Field,

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type Output = SparseMultilinearExtension<F>

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impl<F> Add for SparsePolynomial<F>
where F: Field,

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type Output = SparsePolynomial<F>

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impl<F> Add for SparsePolynomial<F>
where F: Field,

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type Output = SparsePolynomial<F>

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impl<F, T> Add for SparsePolynomial<F, T>
where F: Field, T: Term,

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type Output = SparsePolynomial<F, T>

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impl<F, T> Add for SparsePolynomial<F, T>
where F: Field, T: Term,

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type Output = SparsePolynomial<F, T>

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impl<I> Add<I> for Z0
where I: Integer,

Z0 + I = I

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impl<P> Add for CubicExtField<P>
where P: CubicExtConfig,

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type Output = CubicExtField<P>

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impl<P> Add for CubicExtField<P>
where P: CubicExtConfig,

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type Output = CubicExtField<P>

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impl<P> Add for PairingOutput<P>
where P: Pairing,

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type Output = PairingOutput<P>

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impl<P> Add for PairingOutput<P>
where P: Pairing,

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type Output = PairingOutput<P>

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impl<P> Add for Projective<P>
where P: SWCurveConfig,

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type Output = Projective<P>

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impl<P> Add for Projective<P>
where P: SWCurveConfig,

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type Output = Projective<P>

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impl<P> Add for Projective<P>
where P: TECurveConfig,

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type Output = Projective<P>

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impl<P> Add for Projective<P>
where P: TECurveConfig,

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type Output = Projective<P>

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impl<P> Add for QuadExtField<P>
where P: QuadExtConfig,

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type Output = QuadExtField<P>

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impl<P> Add for QuadExtField<P>
where P: QuadExtConfig,

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type Output = QuadExtField<P>

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impl<P> Add<Projective<P>> for Affine<P>
where P: SWCurveConfig,

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type Output = Projective<P>

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impl<P> Add<Projective<P>> for Affine<P>
where P: SWCurveConfig,

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type Output = Projective<P>

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impl<P> Add<Projective<P>> for Affine<P>
where P: TECurveConfig,

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type Output = Projective<P>

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impl<P> Add<Projective<P>> for Affine<P>
where P: TECurveConfig,

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type Output = Projective<P>

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impl<P, T> Add<T> for Affine<P>
where P: SWCurveConfig, T: Borrow<Affine<P>>,

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type Output = Projective<P>

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impl<P, T> Add<T> for Affine<P>
where P: SWCurveConfig, T: Borrow<Affine<P>>,

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type Output = Projective<P>

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impl<P, T> Add<T> for Affine<P>
where P: TECurveConfig, T: Borrow<Affine<P>>,

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type Output = Projective<P>

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impl<P, T> Add<T> for Affine<P>
where P: TECurveConfig, T: Borrow<Affine<P>>,

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type Output = Projective<P>

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impl<P, T> Add<T> for Projective<P>
where P: SWCurveConfig, T: Borrow<Affine<P>>,

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type Output = Projective<P>

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impl<P, T> Add<T> for Projective<P>
where P: SWCurveConfig, T: Borrow<Affine<P>>,

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type Output = Projective<P>

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impl<P, T> Add<T> for Projective<P>
where P: TECurveConfig, T: Borrow<Affine<P>>,

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type Output = Projective<P>

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impl<P, T> Add<T> for Projective<P>
where P: TECurveConfig, T: Borrow<Affine<P>>,

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type Output = Projective<P>

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impl<P, const N: usize> Add for Fp<P, N>
where P: FpConfig<N>,

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type Output = Fp<P, N>

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impl<P, const N: usize> Add for Fp<P, N>
where P: FpConfig<N>,

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type Output = Fp<P, N>

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impl<T> Add<T> for U128
where T: Into<U128>,

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type Output = U128

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impl<T> Add<T> for U256
where T: Into<U256>,

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type Output = U256

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impl<T> Add<T> for U512
where T: Into<U512>,

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type Output = U512

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impl<T, D> Add for TypeWithDefault<T, D>
where T: Add<Output = T>, D: Get<T>,

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type Output = TypeWithDefault<T, D>

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impl<T, const N: usize> Add<&Simd<T, N>> for Simd<T, N>
where T: SimdElement, Simd<T, N>: Add<Output = Simd<T, N>>, LaneCount<N>: SupportedLaneCount,

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type Output = Simd<T, N>

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impl<T, const N: usize> Add<Simd<T, N>> for &Simd<T, N>
where T: SimdElement, Simd<T, N>: Add<Output = Simd<T, N>>, LaneCount<N>: SupportedLaneCount,

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type Output = Simd<T, N>

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impl<U> Add<B1> for UInt<U, B0>
where U: Unsigned,

UInt<U, B0> + B1 = UInt<U + B1>

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impl<U> Add<B1> for UInt<U, B1>
where U: Unsigned + Add<B1>, <U as Add<B1>>::Output: Unsigned,

UInt<U, B1> + B1 = UInt<U + B1, B0>

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type Output = UInt<<U as Add<B1>>::Output, B0>

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impl<U> Add<Z0> for NInt<U>
where U: Unsigned + NonZero,

NInt + Z0 = NInt

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impl<U> Add<Z0> for PInt<U>
where U: Unsigned + NonZero,

PInt + Z0 = PInt

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impl<U> Add<U> for UTerm
where U: Unsigned,

UTerm + U = U

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impl<U, B> Add<B0> for UInt<U, B>
where U: Unsigned, B: Bit,

U + B0 = U

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type Output = UInt<U, B>

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impl<U, B> Add<UTerm> for UInt<U, B>
where U: Unsigned, B: Bit,

UInt<U, B> + UTerm = UInt<U, B>

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type Output = UInt<U, B>

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impl<Ul, Ur> Add<NInt<Ur>> for NInt<Ul>
where Ul: Unsigned + NonZero + Add<Ur>, Ur: Unsigned + NonZero, <Ul as Add<Ur>>::Output: Unsigned + NonZero,

N(Ul) + N(Ur) = N(Ul + Ur)

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type Output = NInt<<Ul as Add<Ur>>::Output>

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impl<Ul, Ur> Add<NInt<Ur>> for PInt<Ul>
where Ul: Unsigned + NonZero + Cmp<Ur> + PrivateIntegerAdd<<Ul as Cmp<Ur>>::Output, Ur>, Ur: Unsigned + NonZero,

P(Ul) + N(Ur): We resolve this with our PrivateAdd

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type Output = <Ul as PrivateIntegerAdd<<Ul as Cmp<Ur>>::Output, Ur>>::Output

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impl<Ul, Ur> Add<PInt<Ur>> for NInt<Ul>
where Ul: Unsigned + NonZero, Ur: Unsigned + NonZero + Cmp<Ul> + PrivateIntegerAdd<<Ur as Cmp<Ul>>::Output, Ul>,

N(Ul) + P(Ur): We resolve this with our PrivateAdd

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type Output = <Ur as PrivateIntegerAdd<<Ur as Cmp<Ul>>::Output, Ul>>::Output

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impl<Ul, Ur> Add<PInt<Ur>> for PInt<Ul>
where Ul: Unsigned + NonZero + Add<Ur>, Ur: Unsigned + NonZero, <Ul as Add<Ur>>::Output: Unsigned + NonZero,

P(Ul) + P(Ur) = P(Ul + Ur)

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type Output = PInt<<Ul as Add<Ur>>::Output>

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impl<Ul, Ur> Add<UInt<Ur, B0>> for UInt<Ul, B0>
where Ul: Unsigned + Add<Ur>, Ur: Unsigned,

UInt<Ul, B0> + UInt<Ur, B0> = UInt<Ul + Ur, B0>

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type Output = UInt<<Ul as Add<Ur>>::Output, B0>

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impl<Ul, Ur> Add<UInt<Ur, B0>> for UInt<Ul, B1>
where Ul: Unsigned + Add<Ur>, Ur: Unsigned,

UInt<Ul, B1> + UInt<Ur, B0> = UInt<Ul + Ur, B1>

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type Output = UInt<<Ul as Add<Ur>>::Output, B1>

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impl<Ul, Ur> Add<UInt<Ur, B1>> for UInt<Ul, B0>
where Ul: Unsigned + Add<Ur>, Ur: Unsigned,

UInt<Ul, B0> + UInt<Ur, B1> = UInt<Ul + Ur, B1>

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type Output = UInt<<Ul as Add<Ur>>::Output, B1>

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impl<Ul, Ur> Add<UInt<Ur, B1>> for UInt<Ul, B1>
where Ul: Unsigned + Add<Ur>, Ur: Unsigned, <Ul as Add<Ur>>::Output: Add<B1>,

UInt<Ul, B1> + UInt<Ur, B1> = UInt<(Ul + Ur) + B1, B0>

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type Output = UInt<<<Ul as Add<Ur>>::Output as Add<B1>>::Output, B0>

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impl<const N: usize> Add for Simd<f32, N>

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impl<const N: usize> Add for Simd<f64, N>

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impl<const N: usize> Add for Simd<i8, N>

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impl<const N: usize> Add for Simd<i16, N>

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impl<const N: usize> Add for Simd<i32, N>

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impl<const N: usize> Add for Simd<i64, N>

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impl<const N: usize> Add for Simd<isize, N>

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impl<const N: usize> Add for Simd<u8, N>

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impl<const N: usize> Add for Simd<u16, N>

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impl<const N: usize> Add for Simd<u32, N>

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impl<const N: usize> Add for Simd<u64, N>

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impl<const N: usize> Add for Simd<usize, N>