elliptic_curve::ops

Trait Sub

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

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

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§

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type Output

The resulting type after applying the - operator.

Required Methods§

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

Performs the - operation.

§Example
assert_eq!(12 - 1, 11);

Implementors§

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impl Sub for f16

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impl Sub for f32

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impl Sub for f64

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impl Sub for f128

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impl Sub for i8

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impl Sub for i16

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impl Sub for i32

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impl Sub for i64

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impl Sub for i128

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impl Sub for isize

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impl Sub for u8

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impl Sub for u16

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impl Sub for u32

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impl Sub for u64

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impl Sub for u128

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impl Sub for usize

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impl Sub for Checked<Limb>

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impl Sub for crypto_bigint::wrapping::Wrapping<Limb>

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impl Sub for Length

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impl Sub for ATerm

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impl Sub for UTerm

UTerm - UTerm = UTerm

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impl Sub for Z0

Z0 - Z0 = Z0

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impl Sub for Assume

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impl Sub for Saturating<i8>

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impl Sub for Saturating<i16>

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impl Sub for Saturating<i32>

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impl Sub for Saturating<i64>

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impl Sub for Saturating<i128>

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impl Sub for Saturating<isize>

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impl Sub for Saturating<u8>

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impl Sub for Saturating<u16>

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impl Sub for Saturating<u32>

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impl Sub for Saturating<u64>

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impl Sub for Saturating<u128>

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impl Sub for Saturating<usize>

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impl Sub for core::num::wrapping::Wrapping<i8>

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impl Sub for core::num::wrapping::Wrapping<i16>

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impl Sub for core::num::wrapping::Wrapping<i32>

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impl Sub for core::num::wrapping::Wrapping<i64>

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impl Sub for core::num::wrapping::Wrapping<i128>

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impl Sub for core::num::wrapping::Wrapping<isize>

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impl Sub for core::num::wrapping::Wrapping<u8>

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impl Sub for core::num::wrapping::Wrapping<u16>

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impl Sub for core::num::wrapping::Wrapping<u32>

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impl Sub for core::num::wrapping::Wrapping<u64>

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impl Sub for core::num::wrapping::Wrapping<u128>

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impl Sub for core::num::wrapping::Wrapping<usize>

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impl Sub for Duration

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impl Sub for Instant

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impl Sub<&f16> for &f16

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impl Sub<&f16> for f16

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impl Sub<&f32> for &f32

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impl Sub<&f32> for f32

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impl Sub<&f64> for &f64

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impl Sub<&f64> for f64

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impl Sub<&f128> for &f128

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impl Sub<&f128> for f128

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impl Sub<&i8> for &i8

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impl Sub<&i8> for i8

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impl Sub<&i16> for &i16

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impl Sub<&i16> for i16

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impl Sub<&i32> for &i32

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impl Sub<&i32> for i32

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impl Sub<&i64> for &i64

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impl Sub<&i64> for i64

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impl Sub<&i128> for &i128

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impl Sub<&i128> for i128

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impl Sub<&isize> for &isize

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impl Sub<&isize> for isize

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impl Sub<&u8> for &u8

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impl Sub<&u8> for u8

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impl Sub<&u16> for &u16

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impl Sub<&u16> for u16

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impl Sub<&u32> for &u32

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impl Sub<&u32> for u32

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impl Sub<&u64> for &u64

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impl Sub<&u64> for u64

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impl Sub<&u128> for &u128

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impl Sub<&u128> for u128

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impl Sub<&usize> for &usize

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impl Sub<&usize> for usize

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impl Sub<&Checked<Limb>> for &Checked<Limb>

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impl Sub<&Checked<Limb>> for Checked<Limb>

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impl Sub<&Wrapping<Limb>> for &crypto_bigint::wrapping::Wrapping<Limb>

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impl Sub<&Wrapping<Limb>> for crypto_bigint::wrapping::Wrapping<Limb>

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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impl Sub<&Wrapping<i8>> for &core::num::wrapping::Wrapping<i8>

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impl Sub<&Wrapping<i8>> for core::num::wrapping::Wrapping<i8>

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impl Sub<&Wrapping<i16>> for &core::num::wrapping::Wrapping<i16>

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impl Sub<&Wrapping<i16>> for core::num::wrapping::Wrapping<i16>

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impl Sub<&Wrapping<i32>> for &core::num::wrapping::Wrapping<i32>

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impl Sub<&Wrapping<i32>> for core::num::wrapping::Wrapping<i32>

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impl Sub<&Wrapping<i64>> for &core::num::wrapping::Wrapping<i64>

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impl Sub<&Wrapping<i64>> for core::num::wrapping::Wrapping<i64>

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impl Sub<&Wrapping<i128>> for &core::num::wrapping::Wrapping<i128>

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impl Sub<&Wrapping<i128>> for core::num::wrapping::Wrapping<i128>

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impl Sub<&Wrapping<isize>> for &core::num::wrapping::Wrapping<isize>

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impl Sub<&Wrapping<isize>> for core::num::wrapping::Wrapping<isize>

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impl Sub<&Wrapping<u8>> for &core::num::wrapping::Wrapping<u8>

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impl Sub<&Wrapping<u8>> for core::num::wrapping::Wrapping<u8>

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impl Sub<&Wrapping<u16>> for &core::num::wrapping::Wrapping<u16>

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impl Sub<&Wrapping<u16>> for core::num::wrapping::Wrapping<u16>

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impl Sub<&Wrapping<u32>> for &core::num::wrapping::Wrapping<u32>

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impl Sub<&Wrapping<u32>> for core::num::wrapping::Wrapping<u32>

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impl Sub<&Wrapping<u64>> for &core::num::wrapping::Wrapping<u64>

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impl Sub<&Wrapping<u64>> for core::num::wrapping::Wrapping<u64>

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impl Sub<&Wrapping<u128>> for &core::num::wrapping::Wrapping<u128>

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impl Sub<&Wrapping<u128>> for core::num::wrapping::Wrapping<u128>

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impl Sub<&Wrapping<usize>> for &core::num::wrapping::Wrapping<usize>

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impl Sub<&Wrapping<usize>> for core::num::wrapping::Wrapping<usize>

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impl Sub<Checked<Limb>> for &Checked<Limb>

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impl Sub<Wrapping<Limb>> for &crypto_bigint::wrapping::Wrapping<Limb>

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impl Sub<Length> for Result<Length, Error>

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impl Sub<B0> for UTerm

UTerm - B0 = Term

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

UInt<UTerm, B1> - B1 = UTerm

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impl Sub<Duration> for Instant

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impl Sub<Duration> for SystemTime

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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impl<'a> Sub<Wrapping<i8>> for &'a core::num::wrapping::Wrapping<i8>

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impl<'a> Sub<Wrapping<i16>> for &'a core::num::wrapping::Wrapping<i16>

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impl<'a> Sub<Wrapping<i32>> for &'a core::num::wrapping::Wrapping<i32>

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impl<'a> Sub<Wrapping<i64>> for &'a core::num::wrapping::Wrapping<i64>

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impl<'a> Sub<Wrapping<i128>> for &'a core::num::wrapping::Wrapping<i128>

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impl<'a> Sub<Wrapping<isize>> for &'a core::num::wrapping::Wrapping<isize>

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impl<'a> Sub<Wrapping<u8>> for &'a core::num::wrapping::Wrapping<u8>

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impl<'a> Sub<Wrapping<u16>> for &'a core::num::wrapping::Wrapping<u16>

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impl<'a> Sub<Wrapping<u32>> for &'a core::num::wrapping::Wrapping<u32>

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impl<'a> Sub<Wrapping<u64>> for &'a core::num::wrapping::Wrapping<u64>

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impl<'a> Sub<Wrapping<u128>> for &'a core::num::wrapping::Wrapping<u128>

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impl<'a> Sub<Wrapping<usize>> for &'a core::num::wrapping::Wrapping<usize>

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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,

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type Output = Simd<T, N>

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impl<C> Sub for ScalarPrimitive<C>
where C: Curve,

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impl<C> Sub<&ScalarPrimitive<C>> for ScalarPrimitive<C>
where C: Curve,

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impl<MOD, const LIMBS: usize> Sub for Residue<MOD, LIMBS>
where MOD: ResidueParams<LIMBS>,

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type Output = Residue<MOD, LIMBS>

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impl<MOD, const LIMBS: usize> Sub<&Residue<MOD, LIMBS>> for &Residue<MOD, LIMBS>
where MOD: ResidueParams<LIMBS>,

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type Output = Residue<MOD, LIMBS>

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impl<MOD, const LIMBS: usize> Sub<&Residue<MOD, LIMBS>> for Residue<MOD, LIMBS>
where MOD: ResidueParams<LIMBS>,

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type Output = Residue<MOD, LIMBS>

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impl<MOD, const LIMBS: usize> Sub<Residue<MOD, LIMBS>> for &Residue<MOD, LIMBS>
where MOD: ResidueParams<LIMBS>,

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type Output = Residue<MOD, LIMBS>

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impl<T, A> Sub<&BTreeSet<T, A>> for &BTreeSet<T, A>
where T: Ord + Clone, A: Allocator + Clone,

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impl<T, S> Sub<&HashSet<T, S>> for &HashSet<T, S>
where T: Eq + Hash + Clone, S: BuildHasher + Default,

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type Output = HashSet<T, S>

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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,

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type Output = Simd<T, N>

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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,

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type Output = Simd<T, N>

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

Z0 - N = P

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

Z0 - P = N

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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>

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

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

NInt - Z0 = NInt

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

PInt - Z0 = PInt

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

UInt - B0 = UInt

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type Output = UInt<U, B>

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impl<U, B> Sub<B1> for UInt<UInt<U, B>, B1>
where U: Unsigned, B: Bit,

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

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

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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.

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

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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

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

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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)

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

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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)

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

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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

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

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

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

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impl<const LIMBS: usize> Sub for Checked<Uint<LIMBS>>

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type Output = Checked<Uint<LIMBS>>

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impl<const LIMBS: usize> Sub for DynResidue<LIMBS>

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impl<const LIMBS: usize> Sub for crypto_bigint::wrapping::Wrapping<Uint<LIMBS>>

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impl<const LIMBS: usize> Sub<&Checked<Uint<LIMBS>>> for &Checked<Uint<LIMBS>>

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type Output = Checked<Uint<LIMBS>>

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impl<const LIMBS: usize> Sub<&Checked<Uint<LIMBS>>> for Checked<Uint<LIMBS>>

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type Output = Checked<Uint<LIMBS>>

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impl<const LIMBS: usize> Sub<&DynResidue<LIMBS>> for &DynResidue<LIMBS>

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impl<const LIMBS: usize> Sub<&DynResidue<LIMBS>> for DynResidue<LIMBS>

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impl<const LIMBS: usize> Sub<&Wrapping<Uint<LIMBS>>> for &crypto_bigint::wrapping::Wrapping<Uint<LIMBS>>

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impl<const LIMBS: usize> Sub<&Wrapping<Uint<LIMBS>>> for crypto_bigint::wrapping::Wrapping<Uint<LIMBS>>

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impl<const LIMBS: usize> Sub<Checked<Uint<LIMBS>>> for &Checked<Uint<LIMBS>>

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type Output = Checked<Uint<LIMBS>>

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impl<const LIMBS: usize> Sub<DynResidue<LIMBS>> for &DynResidue<LIMBS>

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impl<const LIMBS: usize> Sub<Wrapping<Uint<LIMBS>>> for &crypto_bigint::wrapping::Wrapping<Uint<LIMBS>>

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

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

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

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

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

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

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

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

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

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

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

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