Add

Trait Add 

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

    // Required method
    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

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

Performs the + operation.

§Example
assert_eq!(12 + 1, 13);

Trait Implementations§

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

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type Case = (Mode, Mode)

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

Returns the number of constants, public inputs, private inputs, and constraints.
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impl<E> OutputMode<dyn Add<Scalar<E>, Output = Scalar<E>>> for Scalar<E>
where E: Environment,

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type Case = (Mode, Mode)

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

Returns the mode of the output.

Implementors§

1.0.0 (const: unstable) · Source§

impl Add for f16

1.0.0 (const: unstable) · Source§

impl Add for f32

1.0.0 (const: unstable) · Source§

impl Add for f64

1.0.0 (const: unstable) · Source§

impl Add for f128

1.0.0 (const: unstable) · Source§

impl Add for i8

1.0.0 (const: unstable) · Source§

impl Add for i16

1.0.0 (const: unstable) · Source§

impl Add for i32

1.0.0 (const: unstable) · Source§

impl Add for i64

1.0.0 (const: unstable) · Source§

impl Add for i128

1.0.0 (const: unstable) · Source§

impl Add for isize

1.0.0 (const: unstable) · Source§

impl Add for u8

1.0.0 (const: unstable) · Source§

impl Add for u16

1.0.0 (const: unstable) · Source§

impl Add for u32

1.0.0 (const: unstable) · Source§

impl Add for u64

1.0.0 (const: unstable) · Source§

impl Add for u128

1.0.0 (const: unstable) · Source§

impl Add for usize

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impl Add for Assume

1.74.0 (const: unstable) · Source§

impl Add for Saturating<i8>

1.74.0 (const: unstable) · Source§

impl Add for Saturating<i16>

1.74.0 (const: unstable) · Source§

impl Add for Saturating<i32>

1.74.0 (const: unstable) · Source§

impl Add for Saturating<i64>

1.74.0 (const: unstable) · Source§

impl Add for Saturating<i128>

1.74.0 (const: unstable) · Source§

impl Add for Saturating<isize>

1.74.0 (const: unstable) · Source§

impl Add for Saturating<u8>

1.74.0 (const: unstable) · Source§

impl Add for Saturating<u16>

1.74.0 (const: unstable) · Source§

impl Add for Saturating<u32>

1.74.0 (const: unstable) · Source§

impl Add for Saturating<u64>

1.74.0 (const: unstable) · Source§

impl Add for Saturating<u128>

1.74.0 (const: unstable) · Source§

impl Add for Saturating<usize>

1.0.0 (const: unstable) · Source§

impl Add for Wrapping<i8>

1.0.0 (const: unstable) · Source§

impl Add for Wrapping<i16>

1.0.0 (const: unstable) · Source§

impl Add for Wrapping<i32>

1.0.0 (const: unstable) · Source§

impl Add for Wrapping<i64>

1.0.0 (const: unstable) · Source§

impl Add for Wrapping<i128>

1.0.0 (const: unstable) · Source§

impl Add for Wrapping<isize>

1.0.0 (const: unstable) · Source§

impl Add for Wrapping<u8>

1.0.0 (const: unstable) · Source§

impl Add for Wrapping<u16>

1.0.0 (const: unstable) · Source§

impl Add for Wrapping<u32>

1.0.0 (const: unstable) · Source§

impl Add for Wrapping<u64>

1.0.0 (const: unstable) · Source§

impl Add for Wrapping<u128>

1.0.0 (const: unstable) · Source§

impl Add for Wrapping<usize>

1.3.0 (const: unstable) · Source§

impl Add for core::time::Duration

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impl Add for BigInt

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impl Add for BigUint

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impl Add for AsciiSet

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impl Add for Timespec

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impl Add for Count

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impl Add for time::duration::Duration

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impl Add for ATerm

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impl Add for LengthHint

1.0.0 (const: unstable) · Source§

impl Add<&f16> for &f16

1.0.0 (const: unstable) · Source§

impl Add<&f16> for f16

1.0.0 (const: unstable) · Source§

impl Add<&f32> for &f32

1.0.0 (const: unstable) · Source§

impl Add<&f32> for f32

1.0.0 (const: unstable) · Source§

impl Add<&f64> for &f64

1.0.0 (const: unstable) · Source§

impl Add<&f64> for f64

1.0.0 (const: unstable) · Source§

impl Add<&f128> for &f128

1.0.0 (const: unstable) · Source§

impl Add<&f128> for f128

1.0.0 (const: unstable) · Source§

impl Add<&i8> for &i8

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impl Add<&i8> for &BigInt

1.0.0 (const: unstable) · Source§

impl Add<&i8> for i8

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impl Add<&i8> for BigInt

1.0.0 (const: unstable) · Source§

impl Add<&i16> for &i16

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impl Add<&i16> for &BigInt

1.0.0 (const: unstable) · Source§

impl Add<&i16> for i16

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impl Add<&i16> for BigInt

1.0.0 (const: unstable) · Source§

impl Add<&i32> for &i32

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impl Add<&i32> for &BigInt

1.0.0 (const: unstable) · Source§

impl Add<&i32> for i32

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impl Add<&i32> for BigInt

1.0.0 (const: unstable) · Source§

impl Add<&i64> for &i64

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impl Add<&i64> for &BigInt

1.0.0 (const: unstable) · Source§

impl Add<&i64> for i64

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impl Add<&i64> for BigInt

1.0.0 (const: unstable) · Source§

impl Add<&i128> for &i128

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impl Add<&i128> for &BigInt

1.0.0 (const: unstable) · Source§

impl Add<&i128> for i128

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impl Add<&i128> for BigInt

1.0.0 (const: unstable) · Source§

impl Add<&isize> for &isize

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impl Add<&isize> for &BigInt

1.0.0 (const: unstable) · Source§

impl Add<&isize> for isize

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impl Add<&isize> for BigInt

1.0.0 · Source§

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;
1.0.0 (const: unstable) · Source§

impl Add<&u8> for &u8

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impl Add<&u8> for &BigInt

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impl Add<&u8> for &BigUint

1.0.0 (const: unstable) · Source§

impl Add<&u8> for u8

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impl Add<&u8> for BigInt

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impl Add<&u8> for BigUint

1.0.0 (const: unstable) · Source§

impl Add<&u16> for &u16

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impl Add<&u16> for &BigInt

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impl Add<&u16> for &BigUint

1.0.0 (const: unstable) · Source§

impl Add<&u16> for u16

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impl Add<&u16> for BigInt

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impl Add<&u16> for BigUint

1.0.0 (const: unstable) · Source§

impl Add<&u32> for &u32

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impl Add<&u32> for &BigInt

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impl Add<&u32> for &BigUint

1.0.0 (const: unstable) · Source§

impl Add<&u32> for u32

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impl Add<&u32> for BigInt

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impl Add<&u32> for BigUint

1.0.0 (const: unstable) · Source§

impl Add<&u64> for &u64

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impl Add<&u64> for &BigInt

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impl Add<&u64> for &BigUint

1.0.0 (const: unstable) · Source§

impl Add<&u64> for u64

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impl Add<&u64> for BigInt

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impl Add<&u64> for BigUint

1.0.0 (const: unstable) · Source§

impl Add<&u128> for &u128

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impl Add<&u128> for &BigInt

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impl Add<&u128> for &BigUint

1.0.0 (const: unstable) · Source§

impl Add<&u128> for u128

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impl Add<&u128> for BigInt

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impl Add<&u128> for BigUint

1.0.0 (const: unstable) · Source§

impl Add<&usize> for &usize

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impl Add<&usize> for &BigInt

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impl Add<&usize> for &BigUint

1.0.0 (const: unstable) · Source§

impl Add<&usize> for usize

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impl Add<&usize> for BigInt

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impl Add<&usize> for BigUint

1.74.0 (const: unstable) · Source§

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

1.74.0 (const: unstable) · Source§

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

1.74.0 (const: unstable) · Source§

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

1.74.0 (const: unstable) · Source§

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

1.74.0 (const: unstable) · Source§

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

1.74.0 (const: unstable) · Source§

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

1.74.0 (const: unstable) · Source§

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

1.74.0 (const: unstable) · Source§

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

1.74.0 (const: unstable) · Source§

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

1.74.0 (const: unstable) · Source§

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

1.74.0 (const: unstable) · Source§

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

1.74.0 (const: unstable) · Source§

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

1.74.0 (const: unstable) · Source§

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

1.74.0 (const: unstable) · Source§

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

1.74.0 (const: unstable) · Source§

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

1.74.0 (const: unstable) · Source§

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

1.74.0 (const: unstable) · Source§

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

1.74.0 (const: unstable) · Source§

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

1.74.0 (const: unstable) · Source§

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

1.74.0 (const: unstable) · Source§

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

1.74.0 (const: unstable) · Source§

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

1.74.0 (const: unstable) · Source§

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

1.74.0 (const: unstable) · Source§

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

1.74.0 (const: unstable) · Source§

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

1.14.0 (const: unstable) · Source§

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

1.14.0 (const: unstable) · Source§

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

1.14.0 (const: unstable) · Source§

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

1.14.0 (const: unstable) · Source§

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

1.14.0 (const: unstable) · Source§

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

1.14.0 (const: unstable) · Source§

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

1.14.0 (const: unstable) · Source§

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

1.14.0 (const: unstable) · Source§

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

1.14.0 (const: unstable) · Source§

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

1.14.0 (const: unstable) · Source§

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

1.14.0 (const: unstable) · Source§

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

1.14.0 (const: unstable) · Source§

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

1.14.0 (const: unstable) · Source§

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

1.14.0 (const: unstable) · Source§

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

1.14.0 (const: unstable) · Source§

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

1.14.0 (const: unstable) · Source§

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

1.14.0 (const: unstable) · Source§

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

1.14.0 (const: unstable) · Source§

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

1.14.0 (const: unstable) · Source§

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

1.14.0 (const: unstable) · Source§

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

1.14.0 (const: unstable) · Source§

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

1.14.0 (const: unstable) · Source§

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

1.14.0 (const: unstable) · Source§

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

1.14.0 (const: unstable) · Source§

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 &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 BigUint

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impl Add<&BigNumRef> for &BigNumRef

1.0.0 (const: unstable) · Source§

impl Add<f16> for &f16

1.0.0 (const: unstable) · Source§

impl Add<f32> for &f32

1.0.0 (const: unstable) · Source§

impl Add<f64> for &f64

1.0.0 (const: unstable) · Source§

impl Add<f128> for &f128

1.0.0 (const: unstable) · Source§

impl Add<i8> for &i8

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impl Add<i8> for &BigInt

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impl Add<i8> for BigInt

1.0.0 (const: unstable) · Source§

impl Add<i16> for &i16

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impl Add<i16> for &BigInt

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impl Add<i16> for BigInt

1.0.0 (const: unstable) · Source§

impl Add<i32> for &i32

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impl Add<i32> for &BigInt

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impl Add<i32> for BigInt

1.0.0 (const: unstable) · Source§

impl Add<i64> for &i64

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impl Add<i64> for &BigInt

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impl Add<i64> for BigInt

1.0.0 (const: unstable) · Source§

impl Add<i128> for &i128

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impl Add<i128> for &BigInt

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impl Add<i128> for BigInt

1.0.0 (const: unstable) · Source§

impl Add<isize> for &isize

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impl Add<isize> for &BigInt

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impl Add<isize> for BigInt

1.0.0 (const: unstable) · Source§

impl Add<u8> for &u8

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impl Add<u8> for &BigInt

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impl Add<u8> for &BigUint

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impl Add<u8> for BigInt

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impl Add<u8> for BigUint

1.0.0 (const: unstable) · Source§

impl Add<u16> for &u16

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impl Add<u16> for &BigInt

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impl Add<u16> for &BigUint

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impl Add<u16> for BigInt

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impl Add<u16> for BigUint

1.0.0 (const: unstable) · Source§

impl Add<u32> for &u32

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impl Add<u32> for &BigInt

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impl Add<u32> for &BigUint

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impl Add<u32> for BigInt

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impl Add<u32> for BigUint

1.0.0 (const: unstable) · Source§

impl Add<u64> for &u64

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impl Add<u64> for &BigInt

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impl Add<u64> for &BigUint

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impl Add<u64> for BigInt

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impl Add<u64> for BigUint

1.0.0 (const: unstable) · Source§

impl Add<u128> for &u128

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impl Add<u128> for &BigInt

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impl Add<u128> for &BigUint

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impl Add<u128> for BigInt

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impl Add<u128> for BigUint

1.0.0 (const: unstable) · Source§

impl Add<usize> for &usize

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impl Add<usize> for &BigInt

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impl Add<usize> for &BigUint

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impl Add<usize> for BigInt

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impl Add<usize> for BigUint

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impl Add<usize> for LengthHint

1.74.0 (const: unstable) · Source§

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

1.74.0 (const: unstable) · Source§

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

1.74.0 (const: unstable) · Source§

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

1.74.0 (const: unstable) · Source§

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

1.74.0 (const: unstable) · Source§

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

1.74.0 (const: unstable) · Source§

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

1.74.0 (const: unstable) · Source§

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

1.74.0 (const: unstable) · Source§

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

1.74.0 (const: unstable) · Source§

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

1.74.0 (const: unstable) · Source§

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

1.74.0 (const: unstable) · Source§

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

1.74.0 (const: unstable) · Source§

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

1.14.0 (const: unstable) · Source§

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

1.14.0 (const: unstable) · Source§

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

1.14.0 (const: unstable) · Source§

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

1.14.0 (const: unstable) · Source§

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

1.14.0 (const: unstable) · Source§

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

1.14.0 (const: unstable) · Source§

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

1.14.0 (const: unstable) · Source§

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

1.14.0 (const: unstable) · Source§

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

1.14.0 (const: unstable) · Source§

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

1.14.0 (const: unstable) · Source§

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

1.14.0 (const: unstable) · Source§

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

1.14.0 (const: unstable) · Source§

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

1.8.0 · Source§

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

1.8.0 · Source§

impl Add<Duration> for SystemTime

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impl Add<Duration> for Date

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

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impl Add<Duration> for OffsetDateTime

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impl Add<Duration> for PrimitiveDateTime

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impl Add<Duration> for Time

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impl Add<Duration> for UtcDateTime

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impl Add<Duration> for tokio::time::instant::Instant

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

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impl Add<Duration> for PrimitiveDateTime

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impl Add<Duration> for Time

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impl Add<Duration> for UtcDateTime

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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>

1.14.0 · Source§

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, 'b> Add<&'b BigNum> for &'a BigNum

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impl<'a, 'b> Add<&'b BigNum> for &'a BigNumRef

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impl<'a, 'b> Add<&'b BigNumRef> for &'a BigNum

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impl<'a, 'b, F> Add<&'a Evaluations<F>> for &'b Evaluations<F>
where F: PrimeField,

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

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impl<'a, E> Add<&'a KZGRandomness<E>> for KZGRandomness<E>
where E: PairingEngine,

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impl<'a, E> Add<(<E as PairingEngine>::Fr, &'a KZGRandomness<E>)> for KZGRandomness<E>
where E: PairingEngine,

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

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impl<'a, F> Add<&'a LinearCombination<F>> for snarkvm_algorithms::r1cs::linear_combination::LinearCombination<F>
where F: Field,

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impl<'a, F> Add<(F, &'a ConstraintVariable<F>)> for ConstraintVariable<F>
where F: Field,

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impl<'a, F> Add<(F, &'a LinearCombination<F>)> for snarkvm_algorithms::r1cs::linear_combination::LinearCombination<F>
where F: Field,

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impl<'a, P> Add<&'a Projective<P>> for snarkvm_curves::templates::short_weierstrass_jacobian::projective::Projective<P>

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impl<'a, P> Add<&'a Projective<P>> for snarkvm_curves::templates::twisted_edwards_extended::projective::Projective<P>

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impl<'a, P> Add<&'a Fp2<P>> for Fp2<P>
where P: Fp2Parameters,

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impl<'a, P> Add<&'a Fp6<P>> for Fp6<P>
where P: Fp6Parameters,

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impl<'a, P> Add<&'a Fp12<P>> for Fp12<P>
where P: Fp12Parameters,

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impl<'a, P> Add<&'a Fp256<P>> for Fp256<P>
where P: Fp256Parameters,

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impl<'a, P> Add<&'a Fp384<P>> for Fp384<P>
where P: Fp384Parameters,

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impl<'a, P> Add<&'a mut Projective<P>> for snarkvm_curves::templates::short_weierstrass_jacobian::projective::Projective<P>

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impl<'a, P> Add<&'a mut Projective<P>> for snarkvm_curves::templates::twisted_edwards_extended::projective::Projective<P>

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impl<'a, P> Add<&'a mut Fp2<P>> for Fp2<P>
where P: Fp2Parameters,

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impl<'a, P> Add<&'a mut Fp6<P>> for Fp6<P>
where P: Fp6Parameters,

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impl<'a, P> Add<&'a mut Fp12<P>> for Fp12<P>
where P: Fp12Parameters,

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impl<'a, P> Add<&'a mut Fp256<P>> for Fp256<P>
where P: Fp256Parameters,

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impl<'a, P> Add<&'a mut Fp384<P>> for Fp384<P>
where P: Fp384Parameters,

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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 snarkvm_debug::prelude::Field<E>
where E: Environment,

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impl<E> Add for snarkvm_debug::prelude::Group<E>
where E: Environment,

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impl<E> Add for snarkvm_debug::prelude::Scalar<E>
where E: Environment,

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

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impl<E> Add for snarkvm_circuit_types_group::Group<E>
where E: Environment,

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impl<E> Add for snarkvm_circuit_types_scalar::Scalar<E>
where E: Environment,

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

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impl<E> Add<&Group<E>> for snarkvm_debug::prelude::Group<E>
where E: Environment,

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impl<E> Add<&Scalar<E>> for snarkvm_debug::prelude::Scalar<E>
where E: Environment,

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

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

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impl<E> Add<&Group<E>> for &snarkvm_circuit_types_group::Group<E>
where E: Environment,

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impl<E> Add<&Group<E>> for snarkvm_circuit_types_group::Group<E>
where E: Environment,

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impl<E> Add<&Scalar<E>> for &snarkvm_circuit_types_scalar::Scalar<E>
where E: Environment,

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impl<E> Add<&Scalar<E>> for snarkvm_circuit_types_scalar::Scalar<E>
where E: Environment,

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

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impl<E> Add<Scalar<E>> for &snarkvm_circuit_types_scalar::Scalar<E>
where E: Environment,

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impl<E, I> Add for snarkvm_debug::prelude::integers::Integer<E, I>
where E: Environment, I: IntegerType,

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type Output = Integer<E, I>

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impl<E, I> Add for snarkvm_circuit_types_integers::Integer<E, I>
where E: Environment, I: IntegerType,

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type Output = Integer<E, I>

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impl<E, I> Add<&Integer<E, I>> for snarkvm_debug::prelude::integers::Integer<E, I>
where E: Environment, I: IntegerType,

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type Output = Integer<E, I>

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impl<E, I> Add<&Integer<E, I>> for &snarkvm_circuit_types_integers::Integer<E, I>
where E: Environment, I: IntegerType,

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type Output = Integer<E, I>

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impl<E, I> Add<&Integer<E, I>> for snarkvm_circuit_types_integers::Integer<E, I>
where E: Environment, I: IntegerType,

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type Output = Integer<E, I>

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impl<E, I> Add<Integer<E, I>> for &snarkvm_circuit_types_integers::Integer<E, I>
where E: Environment, I: IntegerType,

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type Output = Integer<E, I>

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impl<F> Add for Variable<F>
where F: PrimeField,

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impl<F> Add for snarkvm_algorithms::r1cs::linear_combination::LinearCombination<F>
where F: Field,

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impl<F> Add for snarkvm_circuit_environment::helpers::linear_combination::LinearCombination<F>
where F: PrimeField,

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impl<F> Add<&ConstraintVariable<F>> for &ConstraintVariable<F>
where F: Field,

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impl<F> Add<&Variable<F>> for &Variable<F>
where F: PrimeField,

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impl<F> Add<&Variable<F>> for Variable<F>
where F: PrimeField,

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impl<F> Add<&Variable<F>> for snarkvm_circuit_environment::helpers::linear_combination::LinearCombination<F>
where F: PrimeField,

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impl<F> Add<&LinearCombination<F>> for &snarkvm_algorithms::r1cs::linear_combination::LinearCombination<F>
where F: Field,

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impl<F> Add<&LinearCombination<F>> for &Variable<F>
where F: PrimeField,

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impl<F> Add<&LinearCombination<F>> for &snarkvm_circuit_environment::helpers::linear_combination::LinearCombination<F>
where F: PrimeField,

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impl<F> Add<&LinearCombination<F>> for Variable<F>
where F: PrimeField,

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impl<F> Add<&LinearCombination<F>> for snarkvm_circuit_environment::helpers::linear_combination::LinearCombination<F>
where F: PrimeField,

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impl<F> Add<(F, &LinearCombination<F>)> for &snarkvm_algorithms::r1cs::linear_combination::LinearCombination<F>
where F: Field,

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impl<F> Add<(F, LinearCombination<F>)> for &snarkvm_algorithms::r1cs::linear_combination::LinearCombination<F>
where F: Field,

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impl<F> Add<(F, LinearCombination<F>)> for snarkvm_algorithms::r1cs::linear_combination::LinearCombination<F>
where F: Field,

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impl<F> Add<(F, Variable)> for ConstraintVariable<F>
where F: Field,

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impl<F> Add<(F, Variable)> for snarkvm_algorithms::r1cs::linear_combination::LinearCombination<F>
where F: Field,

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impl<F> Add<Variable<F>> for &Variable<F>
where F: PrimeField,

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impl<F> Add<Variable<F>> for &snarkvm_circuit_environment::helpers::linear_combination::LinearCombination<F>
where F: PrimeField,

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impl<F> Add<Variable<F>> for snarkvm_circuit_environment::helpers::linear_combination::LinearCombination<F>
where F: PrimeField,

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impl<F> Add<LinearCombination<F>> for &ConstraintVariable<F>
where F: Field,

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impl<F> Add<LinearCombination<F>> for &snarkvm_algorithms::r1cs::linear_combination::LinearCombination<F>
where F: Field,

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impl<F> Add<LinearCombination<F>> for ConstraintVariable<F>
where F: Field,

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impl<F> Add<Variable> for ConstraintVariable<F>
where F: Field,

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impl<F> Add<Variable> for snarkvm_algorithms::r1cs::linear_combination::LinearCombination<F>
where F: Field,

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impl<F> Add<LinearCombination<F>> for &Variable<F>
where F: PrimeField,

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impl<F> Add<LinearCombination<F>> for &snarkvm_circuit_environment::helpers::linear_combination::LinearCombination<F>
where F: PrimeField,

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impl<F> Add<LinearCombination<F>> for Variable<F>
where F: PrimeField,

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

Z0 + I = I

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impl<O> Add for F32<O>
where O: ByteOrder,

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impl<O> Add for F64<O>
where O: ByteOrder,

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impl<O> Add for I16<O>
where O: ByteOrder,

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impl<O> Add for I32<O>
where O: ByteOrder,

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impl<O> Add for I64<O>
where O: ByteOrder,

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impl<O> Add for I128<O>
where O: ByteOrder,

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impl<O> Add for Isize<O>
where O: ByteOrder,

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impl<O> Add for U16<O>
where O: ByteOrder,

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impl<O> Add for U32<O>
where O: ByteOrder,

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impl<O> Add for U64<O>
where O: ByteOrder,

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impl<O> Add for U128<O>
where O: ByteOrder,

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impl<O> Add for Usize<O>
where O: ByteOrder,

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impl<O> Add<f32> for F32<O>
where O: ByteOrder,

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impl<O> Add<f64> for F64<O>
where O: ByteOrder,

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impl<O> Add<i16> for I16<O>
where O: ByteOrder,

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impl<O> Add<i32> for I32<O>
where O: ByteOrder,

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impl<O> Add<i64> for I64<O>
where O: ByteOrder,

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impl<O> Add<i128> for I128<O>
where O: ByteOrder,

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impl<O> Add<isize> for Isize<O>
where O: ByteOrder,

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impl<O> Add<u16> for U16<O>
where O: ByteOrder,

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impl<O> Add<u32> for U32<O>
where O: ByteOrder,

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impl<O> Add<u64> for U64<O>
where O: ByteOrder,

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impl<O> Add<u128> for U128<O>
where O: ByteOrder,

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impl<O> Add<usize> for Usize<O>
where O: ByteOrder,

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impl<O> Add<F32<O>> for f32
where O: ByteOrder,

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impl<O> Add<F64<O>> for f64
where O: ByteOrder,

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impl<O> Add<I16<O>> for i16
where O: ByteOrder,

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impl<O> Add<I32<O>> for i32
where O: ByteOrder,

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impl<O> Add<I64<O>> for i64
where O: ByteOrder,

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impl<O> Add<I128<O>> for i128
where O: ByteOrder,

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impl<O> Add<Isize<O>> for isize
where O: ByteOrder,

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impl<O> Add<U16<O>> for u16
where O: ByteOrder,

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impl<O> Add<U32<O>> for u32
where O: ByteOrder,

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impl<O> Add<U64<O>> for u64
where O: ByteOrder,

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impl<O> Add<U128<O>> for u128
where O: ByteOrder,

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impl<O> Add<Usize<O>> for usize
where O: ByteOrder,

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impl<P> Add for snarkvm_curves::templates::short_weierstrass_jacobian::projective::Projective<P>

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impl<P> Add for snarkvm_curves::templates::twisted_edwards_extended::projective::Projective<P>

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impl<P> Add for Fp2<P>
where P: Fp2Parameters,

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impl<P> Add for Fp6<P>
where P: Fp6Parameters,

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impl<P> Add for Fp12<P>
where P: Fp12Parameters,

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impl<P> Add for Fp256<P>
where P: Fp256Parameters,

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impl<P> Add for Fp384<P>
where P: Fp384Parameters,

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impl<P> Add<&&Projective<P>> for snarkvm_curves::templates::short_weierstrass_jacobian::projective::Projective<P>

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impl<P> Add<&&Projective<P>> for snarkvm_curves::templates::twisted_edwards_extended::projective::Projective<P>

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impl<P> Add<&&Fp2<P>> for Fp2<P>
where P: Fp2Parameters,

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impl<P> Add<&&Fp6<P>> for Fp6<P>
where P: Fp6Parameters,

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impl<P> Add<&&Fp12<P>> for Fp12<P>
where P: Fp12Parameters,

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impl<P> Add<&&Fp256<P>> for Fp256<P>
where P: Fp256Parameters,

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impl<P> Add<&&Fp384<P>> for Fp384<P>
where P: Fp384Parameters,

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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<V> Add for Measurement<V>
where V: Display + Ord + Add<Output = V> + Sub<Output = V> + Copy + Mul<Output = V> + Debug,

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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>