Trait Sub

pub trait Sub<Rhs = Self> {
    type Output;

    // Required method
    fn sub(self, rhs: Rhs) -> Self::Output;
}

The subtraction operator -.

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

Examples

Subtractable points

use std::ops::Sub;

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

impl Sub for Point {
    type Output = Self;

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

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

Implementing Sub with generics

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

use std::ops::Sub;

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

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

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

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

Required Associated Types

type Output

The resulting type after applying the - operator.

Required Methods

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

Performs the - operation.

Example

assert_eq!(12 - 1, 11);

Implementors

impl Sub for f16

type Output = f16

impl Sub for f32

type Output = f32

impl Sub for f64

type Output = f64

impl Sub for f128

type Output = f128

impl Sub for i8

type Output = i8

impl Sub for i16

type Output = i16

impl Sub for i32

type Output = i32

impl Sub for i64

type Output = i64

impl Sub for i128

type Output = i128

impl Sub for isize

type Output = isize

impl Sub for u8

type Output = u8

impl Sub for u16

type Output = u16

impl Sub for u32

type Output = u32

impl Sub for u64

type Output = u64

impl Sub for u128

type Output = u128

impl Sub for usize

type Output = usize

impl Sub for Assume

type Output = Assume

impl Sub for Saturating<i8>

type Output = Saturating<i8>

impl Sub for Saturating<i16>

type Output = Saturating<i16>

impl Sub for Saturating<i32>

type Output = Saturating<i32>

impl Sub for Saturating<i64>

type Output = Saturating<i64>

impl Sub for Saturating<i128>

type Output = Saturating<i128>

impl Sub for Saturating<isize>

type Output = Saturating<isize>

impl Sub for Saturating<u8>

type Output = Saturating<u8>

impl Sub for Saturating<u16>

type Output = Saturating<u16>

impl Sub for Saturating<u32>

type Output = Saturating<u32>

impl Sub for Saturating<u64>

type Output = Saturating<u64>

impl Sub for Saturating<u128>

type Output = Saturating<u128>

impl Sub for Saturating<usize>

type Output = Saturating<usize>

impl Sub for Wrapping<i8>

type Output = Wrapping<i8>

impl Sub for Wrapping<i16>

type Output = Wrapping<i16>

impl Sub for Wrapping<i32>

type Output = Wrapping<i32>

impl Sub for Wrapping<i64>

type Output = Wrapping<i64>

impl Sub for Wrapping<i128>

type Output = Wrapping<i128>

impl Sub for Wrapping<isize>

type Output = Wrapping<isize>

impl Sub for Wrapping<u8>

type Output = Wrapping<u8>

impl Sub for Wrapping<u16>

type Output = Wrapping<u16>

impl Sub for Wrapping<u32>

type Output = Wrapping<u32>

impl Sub for Wrapping<u64>

type Output = Wrapping<u64>

impl Sub for Wrapping<u128>

type Output = Wrapping<u128>

impl Sub for Wrapping<usize>

type Output = Wrapping<usize>

impl Sub for Duration

type Output = Duration

impl Sub for Instant

type Output = Duration

impl Sub for BigInt

type Output = BigInt

impl Sub for BigUint

type Output = BigUint

impl Sub for ATerm

type Output = ATerm

impl Sub for Z0

Z0 - Z0 = Z0

type Output = Z0

impl Sub for UTerm

UTerm - UTerm = UTerm

type Output = UTerm

impl Sub<&f16> for &f16

type Output = <f16 as Sub>::Output

impl Sub<&f16> for f16

type Output = <f16 as Sub>::Output

impl Sub<&f32> for &f32

type Output = <f32 as Sub>::Output

impl Sub<&f32> for f32

type Output = <f32 as Sub>::Output

impl Sub<&f64> for &f64

type Output = <f64 as Sub>::Output

impl Sub<&f64> for f64

type Output = <f64 as Sub>::Output

impl Sub<&f128> for &f128

type Output = <f128 as Sub>::Output

impl Sub<&f128> for f128

type Output = <f128 as Sub>::Output

impl Sub<&i8> for &i8

type Output = <i8 as Sub>::Output

impl Sub<&i8> for &BigInt

type Output = BigInt

impl Sub<&i8> for i8

type Output = <i8 as Sub>::Output

impl Sub<&i8> for BigInt

type Output = BigInt

impl Sub<&i16> for &i16

type Output = <i16 as Sub>::Output

impl Sub<&i16> for &BigInt

type Output = BigInt

impl Sub<&i16> for i16

type Output = <i16 as Sub>::Output

impl Sub<&i16> for BigInt

type Output = BigInt

impl Sub<&i32> for &i32

type Output = <i32 as Sub>::Output

impl Sub<&i32> for &BigInt

type Output = BigInt

impl Sub<&i32> for i32

type Output = <i32 as Sub>::Output

impl Sub<&i32> for BigInt

type Output = BigInt

impl Sub<&i64> for &i64

type Output = <i64 as Sub>::Output

impl Sub<&i64> for &BigInt

type Output = BigInt

impl Sub<&i64> for i64

type Output = <i64 as Sub>::Output

impl Sub<&i64> for BigInt

type Output = BigInt

impl Sub<&i128> for &i128

type Output = <i128 as Sub>::Output

impl Sub<&i128> for &BigInt

type Output = BigInt

impl Sub<&i128> for i128

type Output = <i128 as Sub>::Output

impl Sub<&i128> for BigInt

type Output = BigInt

impl Sub<&isize> for &isize

type Output = <isize as Sub>::Output

impl Sub<&isize> for &BigInt

type Output = BigInt

impl Sub<&isize> for isize

type Output = <isize as Sub>::Output

impl Sub<&isize> for BigInt

type Output = BigInt

impl Sub<&u8> for &u8

type Output = <u8 as Sub>::Output

impl Sub<&u8> for &BigInt

type Output = BigInt

impl Sub<&u8> for &BigUint

type Output = BigUint

impl Sub<&u8> for u8

type Output = <u8 as Sub>::Output

impl Sub<&u8> for BigInt

type Output = BigInt

impl Sub<&u8> for BigUint

type Output = BigUint

impl Sub<&u16> for &u16

type Output = <u16 as Sub>::Output

impl Sub<&u16> for &BigInt

type Output = BigInt

impl Sub<&u16> for &BigUint

type Output = BigUint

impl Sub<&u16> for u16

type Output = <u16 as Sub>::Output

impl Sub<&u16> for BigInt

type Output = BigInt

impl Sub<&u16> for BigUint

type Output = BigUint

impl Sub<&u32> for &u32

type Output = <u32 as Sub>::Output

impl Sub<&u32> for &BigInt

type Output = BigInt

impl Sub<&u32> for &BigUint

type Output = BigUint

impl Sub<&u32> for u32

type Output = <u32 as Sub>::Output

impl Sub<&u32> for BigInt

type Output = BigInt

impl Sub<&u32> for BigUint

type Output = BigUint

impl Sub<&u64> for &u64

type Output = <u64 as Sub>::Output

impl Sub<&u64> for &BigInt

type Output = BigInt

impl Sub<&u64> for &BigUint

type Output = BigUint

impl Sub<&u64> for u64

type Output = <u64 as Sub>::Output

impl Sub<&u64> for BigInt

type Output = BigInt

impl Sub<&u64> for BigUint

type Output = BigUint

impl Sub<&u128> for &u128

type Output = <u128 as Sub>::Output

impl Sub<&u128> for &BigInt

type Output = BigInt

impl Sub<&u128> for &BigUint

type Output = BigUint

impl Sub<&u128> for u128

type Output = <u128 as Sub>::Output

impl Sub<&u128> for BigInt

type Output = BigInt

impl Sub<&u128> for BigUint

type Output = BigUint

impl Sub<&usize> for &usize

type Output = <usize as Sub>::Output

impl Sub<&usize> for &BigInt

type Output = BigInt

impl Sub<&usize> for &BigUint

type Output = BigUint

impl Sub<&usize> for usize

type Output = <usize as Sub>::Output

impl Sub<&usize> for BigInt

type Output = BigInt

impl Sub<&usize> for BigUint

type Output = BigUint

impl Sub<&Saturating<i8>> for &Saturating<i8>

type Output = <Saturating<i8> as Sub>::Output

impl Sub<&Saturating<i8>> for Saturating<i8>

type Output = <Saturating<i8> as Sub>::Output

impl Sub<&Saturating<i16>> for &Saturating<i16>

type Output = <Saturating<i16> as Sub>::Output

impl Sub<&Saturating<i16>> for Saturating<i16>

type Output = <Saturating<i16> as Sub>::Output

impl Sub<&Saturating<i32>> for &Saturating<i32>

type Output = <Saturating<i32> as Sub>::Output

impl Sub<&Saturating<i32>> for Saturating<i32>

type Output = <Saturating<i32> as Sub>::Output

impl Sub<&Saturating<i64>> for &Saturating<i64>

type Output = <Saturating<i64> as Sub>::Output

impl Sub<&Saturating<i64>> for Saturating<i64>

type Output = <Saturating<i64> as Sub>::Output

impl Sub<&Saturating<i128>> for &Saturating<i128>

type Output = <Saturating<i128> as Sub>::Output

impl Sub<&Saturating<i128>> for Saturating<i128>

type Output = <Saturating<i128> as Sub>::Output

impl Sub<&Saturating<isize>> for &Saturating<isize>

type Output = <Saturating<isize> as Sub>::Output

impl Sub<&Saturating<isize>> for Saturating<isize>

type Output = <Saturating<isize> as Sub>::Output

impl Sub<&Saturating<u8>> for &Saturating<u8>

type Output = <Saturating<u8> as Sub>::Output

impl Sub<&Saturating<u8>> for Saturating<u8>

type Output = <Saturating<u8> as Sub>::Output

impl Sub<&Saturating<u16>> for &Saturating<u16>

type Output = <Saturating<u16> as Sub>::Output

impl Sub<&Saturating<u16>> for Saturating<u16>

type Output = <Saturating<u16> as Sub>::Output

impl Sub<&Saturating<u32>> for &Saturating<u32>

type Output = <Saturating<u32> as Sub>::Output

impl Sub<&Saturating<u32>> for Saturating<u32>

type Output = <Saturating<u32> as Sub>::Output

impl Sub<&Saturating<u64>> for &Saturating<u64>

type Output = <Saturating<u64> as Sub>::Output

impl Sub<&Saturating<u64>> for Saturating<u64>

type Output = <Saturating<u64> as Sub>::Output

impl Sub<&Saturating<u128>> for &Saturating<u128>

type Output = <Saturating<u128> as Sub>::Output

impl Sub<&Saturating<u128>> for Saturating<u128>

type Output = <Saturating<u128> as Sub>::Output

impl Sub<&Saturating<usize>> for &Saturating<usize>

type Output = <Saturating<usize> as Sub>::Output

impl Sub<&Saturating<usize>> for Saturating<usize>

type Output = <Saturating<usize> as Sub>::Output

impl Sub<&Wrapping<i8>> for &Wrapping<i8>

type Output = <Wrapping<i8> as Sub>::Output

impl Sub<&Wrapping<i8>> for Wrapping<i8>

type Output = <Wrapping<i8> as Sub>::Output

impl Sub<&Wrapping<i16>> for &Wrapping<i16>

type Output = <Wrapping<i16> as Sub>::Output

impl Sub<&Wrapping<i16>> for Wrapping<i16>

type Output = <Wrapping<i16> as Sub>::Output

impl Sub<&Wrapping<i32>> for &Wrapping<i32>

type Output = <Wrapping<i32> as Sub>::Output

impl Sub<&Wrapping<i32>> for Wrapping<i32>

type Output = <Wrapping<i32> as Sub>::Output

impl Sub<&Wrapping<i64>> for &Wrapping<i64>

type Output = <Wrapping<i64> as Sub>::Output

impl Sub<&Wrapping<i64>> for Wrapping<i64>

type Output = <Wrapping<i64> as Sub>::Output

impl Sub<&Wrapping<i128>> for &Wrapping<i128>

type Output = <Wrapping<i128> as Sub>::Output

impl Sub<&Wrapping<i128>> for Wrapping<i128>

type Output = <Wrapping<i128> as Sub>::Output

impl Sub<&Wrapping<isize>> for &Wrapping<isize>

type Output = <Wrapping<isize> as Sub>::Output

impl Sub<&Wrapping<isize>> for Wrapping<isize>

type Output = <Wrapping<isize> as Sub>::Output

impl Sub<&Wrapping<u8>> for &Wrapping<u8>

type Output = <Wrapping<u8> as Sub>::Output

impl Sub<&Wrapping<u8>> for Wrapping<u8>

type Output = <Wrapping<u8> as Sub>::Output

impl Sub<&Wrapping<u16>> for &Wrapping<u16>

type Output = <Wrapping<u16> as Sub>::Output

impl Sub<&Wrapping<u16>> for Wrapping<u16>

type Output = <Wrapping<u16> as Sub>::Output

impl Sub<&Wrapping<u32>> for &Wrapping<u32>

type Output = <Wrapping<u32> as Sub>::Output

impl Sub<&Wrapping<u32>> for Wrapping<u32>

type Output = <Wrapping<u32> as Sub>::Output

impl Sub<&Wrapping<u64>> for &Wrapping<u64>

type Output = <Wrapping<u64> as Sub>::Output

impl Sub<&Wrapping<u64>> for Wrapping<u64>

type Output = <Wrapping<u64> as Sub>::Output

impl Sub<&Wrapping<u128>> for &Wrapping<u128>

type Output = <Wrapping<u128> as Sub>::Output

impl Sub<&Wrapping<u128>> for Wrapping<u128>

type Output = <Wrapping<u128> as Sub>::Output

impl Sub<&Wrapping<usize>> for &Wrapping<usize>

type Output = <Wrapping<usize> as Sub>::Output

impl Sub<&Wrapping<usize>> for Wrapping<usize>

type Output = <Wrapping<usize> as Sub>::Output

impl Sub<&BigInt> for &i8

type Output = BigInt

impl Sub<&BigInt> for &i16

type Output = BigInt

impl Sub<&BigInt> for &i32

type Output = BigInt

impl Sub<&BigInt> for &i64

type Output = BigInt

impl Sub<&BigInt> for &i128

type Output = BigInt

impl Sub<&BigInt> for &isize

type Output = BigInt

impl Sub<&BigInt> for &u8

type Output = BigInt

impl Sub<&BigInt> for &u16

type Output = BigInt

impl Sub<&BigInt> for &u32

type Output = BigInt

impl Sub<&BigInt> for &u64

type Output = BigInt

impl Sub<&BigInt> for &u128

type Output = BigInt

impl Sub<&BigInt> for &usize

type Output = BigInt

impl Sub<&BigInt> for &BigInt

type Output = BigInt

impl Sub<&BigInt> for i8

type Output = BigInt

impl Sub<&BigInt> for i16

type Output = BigInt

impl Sub<&BigInt> for i32

type Output = BigInt

impl Sub<&BigInt> for i64

type Output = BigInt

impl Sub<&BigInt> for i128

type Output = BigInt

impl Sub<&BigInt> for isize

type Output = BigInt

impl Sub<&BigInt> for u8

type Output = BigInt

impl Sub<&BigInt> for u16

type Output = BigInt

impl Sub<&BigInt> for u32

type Output = BigInt

impl Sub<&BigInt> for u64

type Output = BigInt

impl Sub<&BigInt> for u128

type Output = BigInt

impl Sub<&BigInt> for usize

type Output = BigInt

impl Sub<&BigInt> for BigInt

type Output = BigInt

impl Sub<&BigUint> for &u8

type Output = BigUint

impl Sub<&BigUint> for &u16

type Output = BigUint

impl Sub<&BigUint> for &u32

type Output = BigUint

impl Sub<&BigUint> for &u64

type Output = BigUint

impl Sub<&BigUint> for &u128

type Output = BigUint

impl Sub<&BigUint> for &usize

type Output = BigUint

impl Sub<&BigUint> for &BigUint

type Output = BigUint

impl Sub<&BigUint> for u8

type Output = BigUint

impl Sub<&BigUint> for u16

type Output = BigUint

impl Sub<&BigUint> for u32

type Output = BigUint

impl Sub<&BigUint> for u64

type Output = BigUint

impl Sub<&BigUint> for u128

type Output = BigUint

impl Sub<&BigUint> for usize

type Output = BigUint

impl Sub<&BigUint> for BigUint

type Output = BigUint

impl Sub<i8> for &BigInt

type Output = BigInt

impl Sub<i8> for BigInt

type Output = BigInt

impl Sub<i16> for &BigInt

type Output = BigInt

impl Sub<i16> for BigInt

type Output = BigInt

impl Sub<i32> for &BigInt

type Output = BigInt

impl Sub<i32> for BigInt

type Output = BigInt

impl Sub<i64> for &BigInt

type Output = BigInt

impl Sub<i64> for BigInt

type Output = BigInt

impl Sub<i128> for &BigInt

type Output = BigInt

impl Sub<i128> for BigInt

type Output = BigInt

impl Sub<isize> for &BigInt

type Output = BigInt

impl Sub<isize> for BigInt

type Output = BigInt

impl Sub<u8> for &BigInt

type Output = BigInt

impl Sub<u8> for &BigUint

type Output = BigUint

impl Sub<u8> for BigInt

type Output = BigInt

impl Sub<u8> for BigUint

type Output = BigUint

impl Sub<u16> for &BigInt

type Output = BigInt

impl Sub<u16> for &BigUint

type Output = BigUint

impl Sub<u16> for BigInt

type Output = BigInt

impl Sub<u16> for BigUint

type Output = BigUint

impl Sub<u32> for &BigInt

type Output = BigInt

impl Sub<u32> for &BigUint

type Output = BigUint

impl Sub<u32> for BigInt

type Output = BigInt

impl Sub<u32> for BigUint

type Output = BigUint

impl Sub<u64> for &BigInt

type Output = BigInt

impl Sub<u64> for &BigUint

type Output = BigUint

impl Sub<u64> for BigInt

type Output = BigInt

impl Sub<u64> for BigUint

type Output = BigUint

impl Sub<u128> for &BigInt

type Output = BigInt

impl Sub<u128> for &BigUint

type Output = BigUint

impl Sub<u128> for BigInt

type Output = BigInt

impl Sub<u128> for BigUint

type Output = BigUint

impl Sub<usize> for &BigInt

type Output = BigInt

impl Sub<usize> for &BigUint

type Output = BigUint

impl Sub<usize> for BigInt

type Output = BigInt

impl Sub<usize> for BigUint

type Output = BigUint

impl Sub<Duration> for Instant

type Output = Instant

impl Sub<Duration> for SystemTime

type Output = SystemTime

impl Sub<BigInt> for &i8

type Output = BigInt

impl Sub<BigInt> for &i16

type Output = BigInt

impl Sub<BigInt> for &i32

type Output = BigInt

impl Sub<BigInt> for &i64

type Output = BigInt

impl Sub<BigInt> for &i128

type Output = BigInt

impl Sub<BigInt> for &isize

type Output = BigInt

impl Sub<BigInt> for &u8

type Output = BigInt

impl Sub<BigInt> for &u16

type Output = BigInt

impl Sub<BigInt> for &u32

type Output = BigInt

impl Sub<BigInt> for &u64

type Output = BigInt

impl Sub<BigInt> for &u128

type Output = BigInt

impl Sub<BigInt> for &usize

type Output = BigInt

impl Sub<BigInt> for &BigInt

type Output = BigInt

impl Sub<BigInt> for i8

type Output = BigInt

impl Sub<BigInt> for i16

type Output = BigInt

impl Sub<BigInt> for i32

type Output = BigInt

impl Sub<BigInt> for i64

type Output = BigInt

impl Sub<BigInt> for i128

type Output = BigInt

impl Sub<BigInt> for isize

type Output = BigInt

impl Sub<BigInt> for u8

type Output = BigInt

impl Sub<BigInt> for u16

type Output = BigInt

impl Sub<BigInt> for u32

type Output = BigInt

impl Sub<BigInt> for u64

type Output = BigInt

impl Sub<BigInt> for u128

type Output = BigInt

impl Sub<BigInt> for usize

type Output = BigInt

impl Sub<BigUint> for &u8

type Output = BigUint

impl Sub<BigUint> for &u16

type Output = BigUint

impl Sub<BigUint> for &u32

type Output = BigUint

impl Sub<BigUint> for &u64

type Output = BigUint

impl Sub<BigUint> for &u128

type Output = BigUint

impl Sub<BigUint> for &usize

type Output = BigUint

impl Sub<BigUint> for &BigUint

type Output = BigUint

impl Sub<BigUint> for u8

type Output = BigUint

impl Sub<BigUint> for u16

type Output = BigUint

impl Sub<BigUint> for u32

type Output = BigUint

impl Sub<BigUint> for u64

type Output = BigUint

impl Sub<BigUint> for u128

type Output = BigUint

impl Sub<BigUint> for usize

type Output = BigUint

impl Sub<B0> for UTerm

UTerm - B0 = Term

type Output = UTerm

impl Sub<B1> for UInt<UTerm, B1>

UInt<UTerm, B1> - B1 = UTerm

type Output = UTerm

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

type Output = <f16 as Sub>::Output

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

type Output = <f32 as Sub>::Output

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

type Output = <f64 as Sub>::Output

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

type Output = <f128 as Sub>::Output

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

type Output = <i8 as Sub>::Output

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

type Output = <i16 as Sub>::Output

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

type Output = <i32 as Sub>::Output

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

type Output = <i64 as Sub>::Output

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

type Output = <i128 as Sub>::Output

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

type Output = <isize as Sub>::Output

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

type Output = <u8 as Sub>::Output

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

type Output = <u16 as Sub>::Output

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

type Output = <u32 as Sub>::Output

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

type Output = <u64 as Sub>::Output

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

type Output = <u128 as Sub>::Output

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

type Output = <usize as Sub>::Output

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

type Output = <Saturating<i8> as Sub>::Output

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

type Output = <Saturating<i16> as Sub>::Output

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

type Output = <Saturating<i32> as Sub>::Output

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

type Output = <Saturating<i64> as Sub>::Output

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

type Output = <Saturating<i128> as Sub>::Output

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

type Output = <Saturating<isize> as Sub>::Output

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

type Output = <Saturating<u8> as Sub>::Output

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

type Output = <Saturating<u16> as Sub>::Output

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

type Output = <Saturating<u32> as Sub>::Output

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

type Output = <Saturating<u64> as Sub>::Output

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

type Output = <Saturating<u128> as Sub>::Output

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

type Output = <Saturating<usize> as Sub>::Output

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

type Output = <Wrapping<i8> as Sub>::Output

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

type Output = <Wrapping<i16> as Sub>::Output

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

type Output = <Wrapping<i32> as Sub>::Output

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

type Output = <Wrapping<i64> as Sub>::Output

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

type Output = <Wrapping<i128> as Sub>::Output

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

type Output = <Wrapping<isize> as Sub>::Output

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

type Output = <Wrapping<u8> as Sub>::Output

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

type Output = <Wrapping<u16> as Sub>::Output

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

type Output = <Wrapping<u32> as Sub>::Output

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

type Output = <Wrapping<u64> as Sub>::Output

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

type Output = <Wrapping<u128> as Sub>::Output

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

type Output = <Wrapping<usize> as Sub>::Output

impl<'a, 'b, F> Sub<&'a Evaluations<F>> for &'b Evaluations<F>

where F: PrimeField,

type Output = Evaluations<F>

impl<'a, 'b, F> Sub<&'a DensePolynomial<F>> for &'b DensePolynomial<F>

where F: Field,

type Output = DensePolynomial<F>

impl<'a, F> Sub<&'a SparsePolynomial<F>> for DensePolynomial<F>

where F: Field,

type Output = DensePolynomial<F>

impl<'a, F> Sub<&'a LinearCombination<F>> for snarkvm_algorithms::r1cs::linear_combination::LinearCombination<F>

where F: Field,

type Output = LinearCombination<F>

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

where F: Field,

type Output = LinearCombination<F>

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

where P: ShortWeierstrassParameters,

type Output = Projective<P>

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

where P: TwistedEdwardsParameters,

type Output = Projective<P>

impl<'a, P> Sub<&'a Fp2<P>> for Fp2<P>

where P: Fp2Parameters,

type Output = Fp2<P>

impl<'a, P> Sub<&'a Fp6<P>> for Fp6<P>

where P: Fp6Parameters,

type Output = Fp6<P>

impl<'a, P> Sub<&'a Fp12<P>> for Fp12<P>

where P: Fp12Parameters,

type Output = Fp12<P>

impl<'a, P> Sub<&'a Fp256<P>> for Fp256<P>

where P: Fp256Parameters,

type Output = Fp256<P>

impl<'a, P> Sub<&'a Fp384<P>> for Fp384<P>

where P: Fp384Parameters,

type Output = Fp384<P>

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

where P: ShortWeierstrassParameters,

type Output = Projective<P>

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

where P: TwistedEdwardsParameters,

type Output = Projective<P>

impl<'a, P> Sub<&'a mut Fp2<P>> for Fp2<P>

where P: Fp2Parameters,

type Output = Fp2<P>

impl<'a, P> Sub<&'a mut Fp6<P>> for Fp6<P>

where P: Fp6Parameters,

type Output = Fp6<P>

impl<'a, P> Sub<&'a mut Fp12<P>> for Fp12<P>

where P: Fp12Parameters,

type Output = Fp12<P>

impl<'a, P> Sub<&'a mut Fp256<P>> for Fp256<P>

where P: Fp256Parameters,

type Output = Fp256<P>

impl<'a, P> Sub<&'a mut Fp384<P>> for Fp384<P>

where P: Fp384Parameters,

type Output = Fp384<P>

impl<'lhs, 'rhs, T, const N: usize> Sub<&'rhs Simd<T, N>> for &'lhs Simd<T, N>

where T: SimdElement, Simd<T, N>: Sub<Output = Simd<T, N>>, LaneCount<N>: SupportedLaneCount,

type Output = Simd<T, N>

impl<E> Sub for Field<E>

where E: Environment,

type Output = Field<E>

impl<E> Sub for Group<E>

where E: Environment,

type Output = Group<E>

impl<E> Sub for Scalar<E>

where E: Environment,

type Output = Scalar<E>

impl<E> Sub<&Field<E>> for Field<E>

where E: Environment,

type Output = Field<E>

impl<E> Sub<&Group<E>> for Group<E>

where E: Environment,

type Output = Group<E>

impl<E> Sub<&Scalar<E>> for Scalar<E>

where E: Environment,

type Output = Scalar<E>

impl<E, I> Sub for Integer<E, I>

where E: Environment, I: IntegerType,

type Output = Integer<E, I>

impl<E, I> Sub<&Integer<E, I>> for Integer<E, I>

where E: Environment, I: IntegerType,

type Output = Integer<E, I>

impl<F> Sub for snarkvm_algorithms::r1cs::linear_combination::LinearCombination<F>

where F: Field,

type Output = LinearCombination<F>

impl<F> Sub<&LinearCombination<F>> for &snarkvm_algorithms::r1cs::linear_combination::LinearCombination<F>

where F: Field,

type Output = LinearCombination<F>

impl<F> Sub<(F, &LinearCombination<F>)> for &snarkvm_algorithms::r1cs::linear_combination::LinearCombination<F>

where F: Field,

type Output = LinearCombination<F>

impl<F> Sub<(F, LinearCombination<F>)> for &snarkvm_algorithms::r1cs::linear_combination::LinearCombination<F>

where F: Field,

type Output = LinearCombination<F>

impl<F> Sub<(F, LinearCombination<F>)> for snarkvm_algorithms::r1cs::linear_combination::LinearCombination<F>

where F: Field,

type Output = LinearCombination<F>

impl<F> Sub<(F, Variable)> for snarkvm_algorithms::r1cs::linear_combination::LinearCombination<F>

where F: Field,

type Output = LinearCombination<F>

impl<F> Sub<LinearCombination<F>> for &snarkvm_algorithms::r1cs::linear_combination::LinearCombination<F>

where F: Field,

type Output = LinearCombination<F>

impl<F> Sub<Variable> for snarkvm_algorithms::r1cs::linear_combination::LinearCombination<F>

where F: Field,

type Output = LinearCombination<F>

impl<F: PrimeField> Sub for Variable<F>

type Output = LinearCombination<F>

impl<F: PrimeField> Sub for snarkvm_circuit_environment::helpers::linear_combination::LinearCombination<F>

type Output = LinearCombination<F>

impl<F: PrimeField> Sub<&Variable<F>> for &Variable<F>

type Output = LinearCombination<F>

impl<F: PrimeField> Sub<&Variable<F>> for Variable<F>

type Output = LinearCombination<F>

impl<F: PrimeField> Sub<&Variable<F>> for snarkvm_circuit_environment::helpers::linear_combination::LinearCombination<F>

type Output = LinearCombination<F>

impl<F: PrimeField> Sub<&LinearCombination<F>> for &Variable<F>

type Output = LinearCombination<F>

impl<F: PrimeField> Sub<&LinearCombination<F>> for &snarkvm_circuit_environment::helpers::linear_combination::LinearCombination<F>

type Output = LinearCombination<F>

impl<F: PrimeField> Sub<&LinearCombination<F>> for Variable<F>

type Output = LinearCombination<F>

impl<F: PrimeField> Sub<&LinearCombination<F>> for snarkvm_circuit_environment::helpers::linear_combination::LinearCombination<F>

type Output = LinearCombination<F>

impl<F: PrimeField> Sub<Variable<F>> for &Variable<F>

type Output = LinearCombination<F>

impl<F: PrimeField> Sub<Variable<F>> for &snarkvm_circuit_environment::helpers::linear_combination::LinearCombination<F>

type Output = LinearCombination<F>

impl<F: PrimeField> Sub<Variable<F>> for snarkvm_circuit_environment::helpers::linear_combination::LinearCombination<F>

type Output = LinearCombination<F>

impl<F: PrimeField> Sub<LinearCombination<F>> for &Variable<F>

type Output = LinearCombination<F>

impl<F: PrimeField> Sub<LinearCombination<F>> for &snarkvm_circuit_environment::helpers::linear_combination::LinearCombination<F>

type Output = LinearCombination<F>

impl<F: PrimeField> Sub<LinearCombination<F>> for Variable<F>

type Output = LinearCombination<F>

impl<O> Sub for F32<O>

where O: ByteOrder,

type Output = F32<O>

impl<O> Sub for F64<O>

where O: ByteOrder,

type Output = F64<O>

impl<O> Sub for I16<O>

where O: ByteOrder,

type Output = I16<O>

impl<O> Sub for I32<O>

where O: ByteOrder,

type Output = I32<O>

impl<O> Sub for I64<O>

where O: ByteOrder,

type Output = I64<O>

impl<O> Sub for I128<O>

where O: ByteOrder,

type Output = I128<O>

impl<O> Sub for U16<O>

where O: ByteOrder,

type Output = U16<O>

impl<O> Sub for U32<O>

where O: ByteOrder,

type Output = U32<O>

impl<O> Sub for U64<O>

where O: ByteOrder,

type Output = U64<O>

impl<O> Sub for U128<O>

where O: ByteOrder,

type Output = U128<O>

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

where P: ShortWeierstrassParameters,

type Output = Projective<P>

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

where P: TwistedEdwardsParameters,

type Output = Projective<P>

impl<P> Sub for Fp2<P>

where P: Fp2Parameters,

type Output = Fp2<P>

impl<P> Sub for Fp6<P>

where P: Fp6Parameters,

type Output = Fp6<P>

impl<P> Sub for Fp12<P>

where P: Fp12Parameters,

type Output = Fp12<P>

impl<P> Sub for Fp256<P>

where P: Fp256Parameters,

type Output = Fp256<P>

impl<P> Sub for Fp384<P>

where P: Fp384Parameters,

type Output = Fp384<P>

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

where P: ShortWeierstrassParameters,

type Output = Projective<P>

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

where P: TwistedEdwardsParameters,

type Output = Projective<P>

impl<P> Sub<&&Fp2<P>> for Fp2<P>

where P: Fp2Parameters,

type Output = Fp2<P>

impl<P> Sub<&&Fp6<P>> for Fp6<P>

where P: Fp6Parameters,

type Output = Fp6<P>

impl<P> Sub<&&Fp12<P>> for Fp12<P>

where P: Fp12Parameters,

type Output = Fp12<P>

impl<P> Sub<&&Fp256<P>> for Fp256<P>

where P: Fp256Parameters,

type Output = Fp256<P>

impl<P> Sub<&&Fp384<P>> for Fp384<P>

where P: Fp384Parameters,

type Output = Fp384<P>

impl<T, A> Sub<&BTreeSet<T, A>> for &BTreeSet<T, A>

where T: Ord + Clone, A: Allocator + Clone,

type Output = BTreeSet<T, A>

impl<T, S1, S2> Sub<&IndexSet<T, S2>> for &IndexSet<T, S1>

where T: Eq + Hash + Clone, S1: BuildHasher + Default, S2: BuildHasher,

type Output = IndexSet<T, S1>

impl<T, S> Sub<&HashSet<T, S>> for &std::collections::hash::set::HashSet<T, S>

where T: Eq + Hash + Clone, S: BuildHasher + Default,

type Output = HashSet<T, S>

impl<T, S> Sub<&HashSet<T, S>> for &hashbrown::set::HashSet<T, S>

where T: Eq + Hash + Clone, S: BuildHasher + Default,

type Output = HashSet<T, S>

impl<T, S, A> Sub<&HashSet<T, S, A>> for &hashbrown::set::HashSet<T, S, A>

where T: Eq + Hash + Clone, S: BuildHasher + Default, A: Allocator + Default,

type Output = HashSet<T, S, A>

impl<T, const N: usize> Sub<&Simd<T, N>> for Simd<T, N>

where T: SimdElement, Simd<T, N>: Sub<Output = Simd<T, N>>, LaneCount<N>: SupportedLaneCount,

type Output = Simd<T, N>

impl<T, const N: usize> Sub<Simd<T, N>> for &Simd<T, N>

where T: SimdElement, Simd<T, N>: Sub<Output = Simd<T, N>>, LaneCount<N>: SupportedLaneCount,

type Output = Simd<T, N>

impl<U> Sub<B1> for UInt<U, B0>

where U: Unsigned + Sub<B1>, <U as Sub<B1>>::Output: Unsigned,

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

type Output = UInt<<U as Sub<B1>>::Output, B1>

impl<U> Sub<NInt<U>> for Z0

where U: Unsigned + NonZero,

Z0 - N = P

type Output = PInt<U>

impl<U> Sub<PInt<U>> for Z0

where U: Unsigned + NonZero,

Z0 - P = N

type Output = NInt<U>

impl<U> Sub<Z0> for NInt<U>

where U: Unsigned + NonZero,

NInt - Z0 = NInt

type Output = NInt<U>

impl<U> Sub<Z0> for PInt<U>

where U: Unsigned + NonZero,

PInt - Z0 = PInt

type Output = PInt<U>

impl<U, B> Sub<B0> for UInt<U, B>

where U: Unsigned, B: Bit,

UInt - B0 = UInt

type Output = UInt<U, B>

impl<U, B> Sub<B1> for UInt<UInt<U, B>, B1>

where U: Unsigned, B: Bit,

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

type Output = UInt<UInt<U, B>, B0>

impl<Ul, Bl, Ur> Sub<Ur> for UInt<Ul, Bl>

where Ul: Unsigned, Bl: Bit, Ur: Unsigned, UInt<Ul, Bl>: PrivateSub<Ur>, <UInt<Ul, Bl> as PrivateSub<Ur>>::Output: Trim,

Subtracting unsigned integers. We just do our PrivateSub and then Trim the output.

type Output = <<UInt<Ul, Bl> as PrivateSub<Ur>>::Output as Trim>::Output

impl<Ul, Ur> Sub<NInt<Ur>> for NInt<Ul>

where Ul: Unsigned + NonZero, Ur: Unsigned + NonZero + Cmp<Ul> + PrivateIntegerAdd<<Ur as Cmp<Ul>>::Output, Ul>,

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

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

impl<Ul, Ur> Sub<NInt<Ur>> for PInt<Ul>

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

P(Ul) - N(Ur) = P(Ul + Ur)

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

impl<Ul, Ur> Sub<PInt<Ur>> for NInt<Ul>

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

N(Ul) - P(Ur) = N(Ul + Ur)

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

impl<Ul, Ur> Sub<PInt<Ur>> for PInt<Ul>

where Ul: Unsigned + NonZero + Cmp<Ur> + PrivateIntegerAdd<<Ul as Cmp<Ur>>::Output, Ur>, Ur: Unsigned + NonZero,

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

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

impl<Vl, Al, Vr, Ar> Sub<TArr<Vr, Ar>> for TArr<Vl, Al>

where Vl: Sub<Vr>, Al: Sub<Ar>,

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

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

where f32: SimdElement, LaneCount<N>: SupportedLaneCount,

type Output = Simd<f32, N>

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

where f64: SimdElement, LaneCount<N>: SupportedLaneCount,

type Output = Simd<f64, N>

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

where i8: SimdElement, LaneCount<N>: SupportedLaneCount,

type Output = Simd<i8, N>

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

where i16: SimdElement, LaneCount<N>: SupportedLaneCount,

type Output = Simd<i16, N>

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

where i32: SimdElement, LaneCount<N>: SupportedLaneCount,

type Output = Simd<i32, N>

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

where i64: SimdElement, LaneCount<N>: SupportedLaneCount,

type Output = Simd<i64, N>

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

where isize: SimdElement, LaneCount<N>: SupportedLaneCount,

type Output = Simd<isize, N>

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

where u8: SimdElement, LaneCount<N>: SupportedLaneCount,

type Output = Simd<u8, N>

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

where u16: SimdElement, LaneCount<N>: SupportedLaneCount,

type Output = Simd<u16, N>

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

where u32: SimdElement, LaneCount<N>: SupportedLaneCount,

type Output = Simd<u32, N>

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

where u64: SimdElement, LaneCount<N>: SupportedLaneCount,

type Output = Simd<u64, N>

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

where usize: SimdElement, LaneCount<N>: SupportedLaneCount,

type Output = Simd<usize, N>