Mul in core::ops - Rust
Description: The multiplication operator `*`.

# Trait Mul

1.6.0 · Source

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

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

Expand description

The multiplication operator `*`.

Note that `Rhs` is `Self` by default, but this is not mandatory.

## §Examples

### §`Mul`tipliable rational numbers

    use std::ops::Mul;

    // By the fundamental theorem of arithmetic, rational numbers in lowest
    // terms are unique. So, by keeping `Rational`s in reduced form, we can
    // derive `Eq` and `PartialEq`.
    #[derive(Debug, Eq, PartialEq)]
    struct Rational {
        numerator: usize,
        denominator: usize,
    }

    impl Rational {
        fn new(numerator: usize, denominator: usize) -> Self {
            if denominator == 0 {
                panic!("Zero is an invalid denominator!");
            }

            // Reduce to lowest terms by dividing by the greatest common
            // divisor.
            let gcd = gcd(numerator, denominator);
            Self {
                numerator: numerator / gcd,
                denominator: denominator / gcd,
            }
        }
    }

    impl Mul for Rational {
        // The multiplication of rational numbers is a closed operation.
        type Output = Self;

        fn mul(self, rhs: Self) -> Self {
            let numerator = self.numerator * rhs.numerator;
            let denominator = self.denominator * rhs.denominator;
            Self::new(numerator, denominator)
        }
    }

    // Euclid's two-thousand-year-old algorithm for finding the greatest common
    // divisor.
    fn gcd(x: usize, y: usize) -> usize {
        let mut x = x;
        let mut y = y;
        while y != 0 {
            let t = y;
            y = x % y;
            x = t;
        }
        x
    }

    assert_eq!(Rational::new(1, 2), Rational::new(2, 4));
    assert_eq!(Rational::new(2, 3) * Rational::new(3, 4),
               Rational::new(1, 2));

### §Multiplying vectors by scalars as in linear algebra

    use std::ops::Mul;

    struct Scalar { value: usize }

    #[derive(Debug, PartialEq)]
    struct Vector { value: Vec<usize> }

    impl Mul<Scalar> for Vector {
        type Output = Self;

        fn mul(self, rhs: Scalar) -> Self::Output {
            Self { value: self.value.iter().map(|v| v * rhs.value).collect() }
        }
    }

    let vector = Vector { value: vec![2, 4, 6] };
    let scalar = Scalar { value: 3 };
    assert_eq!(vector * scalar, Vector { value: vec![6, 12, 18] });

## Required Associated Types§

1.0.0 · Source

#### type Output

The resulting type after applying the `*` operator.

## Required Methods§

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

Performs the `*` operation.

##### §Example

    assert_eq!(12 * 2, 24);

## Implementors§

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### impl Mul for f16

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#### type Output = f16

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### impl Mul for f32

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#### type Output = f32

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### impl Mul for f64

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#### type Output = f64

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### impl Mul for f128

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#### type Output = f128

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### impl Mul for i8

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#### type Output = i8

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### impl Mul for i16

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#### type Output = i16

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### impl Mul for i32

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#### type Output = i32

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### impl Mul for i64

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#### type Output = i64

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### impl Mul for i128

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#### type Output = i128

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### impl Mul for isize

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#### type Output = isize

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### impl Mul for u8

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#### type Output = u8

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### impl Mul for u16

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#### type Output = u16

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### impl Mul for u32

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#### type Output = u32

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### impl Mul for u64

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#### type Output = u64

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### impl Mul for u128

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#### type Output = u128

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### impl Mul for usize

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#### type Output = usize

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### impl Mul for Saturating<i8>

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#### type Output = Saturating<i8>

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### impl Mul for Saturating<i16>

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#### type Output = Saturating<i16>

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### impl Mul for Saturating<i32>

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#### type Output = Saturating<i32>

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### impl Mul for Saturating<i64>

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#### type Output = Saturating<i64>

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### impl Mul for Saturating<i128>

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#### type Output = Saturating<i128>

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### impl Mul for Saturating<isize>

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#### type Output = Saturating<isize>

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### impl Mul for Saturating<u8>

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#### type Output = Saturating<u8>

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### impl Mul for Saturating<u16>

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#### type Output = Saturating<u16>

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### impl Mul for Saturating<u32>

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#### type Output = Saturating<u32>

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### impl Mul for Saturating<u64>

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#### type Output = Saturating<u64>

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### impl Mul for Saturating<u128>

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#### type Output = Saturating<u128>

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### impl Mul for Saturating<usize>

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#### type Output = Saturating<usize>

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### impl Mul for Wrapping<i8>

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#### type Output = Wrapping<i8>

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### impl Mul for Wrapping<i16>

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#### type Output = Wrapping<i16>

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### impl Mul for Wrapping<i32>

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#### type Output = Wrapping<i32>

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### impl Mul for Wrapping<i64>

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#### type Output = Wrapping<i64>

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### impl Mul for Wrapping<i128>

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#### type Output = Wrapping<i128>

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### impl Mul for Wrapping<isize>

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#### type Output = Wrapping<isize>

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### impl Mul for Wrapping<u8>

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#### type Output = Wrapping<u8>

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### impl Mul for Wrapping<u16>

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#### type Output = Wrapping<u16>

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### impl Mul for Wrapping<u32>

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#### type Output = Wrapping<u32>

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### impl Mul for Wrapping<u64>

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#### type Output = Wrapping<u64>

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### impl Mul for Wrapping<u128>

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#### type Output = Wrapping<u128>

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### impl Mul for Wrapping<usize>

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#### type Output = Wrapping<usize>

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### impl Mul<&f16> for &f16

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#### type Output = <f16 as Mul>::Output

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### impl Mul<&f16> for f16

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#### type Output = <f16 as Mul>::Output

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### impl Mul<&f32> for &f32

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#### type Output = <f32 as Mul>::Output

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### impl Mul<&f32> for f32

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#### type Output = <f32 as Mul>::Output

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### impl Mul<&f64> for &f64

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#### type Output = <f64 as Mul>::Output

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### impl Mul<&f64> for f64

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#### type Output = <f64 as Mul>::Output

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### impl Mul<&f128> for &f128

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#### type Output = <f128 as Mul>::Output

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### impl Mul<&f128> for f128

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#### type Output = <f128 as Mul>::Output

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### impl Mul<&i8> for &i8

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#### type Output = <i8 as Mul>::Output

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### impl Mul<&i8> for i8

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#### type Output = <i8 as Mul>::Output

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### impl Mul<&i16> for &i16

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#### type Output = <i16 as Mul>::Output

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### impl Mul<&i16> for i16

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#### type Output = <i16 as Mul>::Output

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### impl Mul<&i32> for &i32

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#### type Output = <i32 as Mul>::Output

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### impl Mul<&i32> for i32

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#### type Output = <i32 as Mul>::Output

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### impl Mul<&i64> for &i64

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#### type Output = <i64 as Mul>::Output

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### impl Mul<&i64> for i64

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#### type Output = <i64 as Mul>::Output

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### impl Mul<&i128> for &i128

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#### type Output = <i128 as Mul>::Output

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### impl Mul<&i128> for i128

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#### type Output = <i128 as Mul>::Output

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### impl Mul<&isize> for &isize

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#### type Output = <isize as Mul>::Output

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### impl Mul<&isize> for isize

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#### type Output = <isize as Mul>::Output

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### impl Mul<&u8> for &u8

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#### type Output = <u8 as Mul>::Output

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### impl Mul<&u8> for u8

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#### type Output = <u8 as Mul>::Output

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### impl Mul<&u16> for &u16

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#### type Output = <u16 as Mul>::Output

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### impl Mul<&u16> for u16

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#### type Output = <u16 as Mul>::Output

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### impl Mul<&u32> for &u32

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#### type Output = <u32 as Mul>::Output

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### impl Mul<&u32> for u32

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#### type Output = <u32 as Mul>::Output

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### impl Mul<&u64> for &u64

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#### type Output = <u64 as Mul>::Output

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### impl Mul<&u64> for u64

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#### type Output = <u64 as Mul>::Output

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### impl Mul<&u128> for &u128

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#### type Output = <u128 as Mul>::Output

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### impl Mul<&u128> for u128

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#### type Output = <u128 as Mul>::Output

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### impl Mul<&usize> for &usize

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#### type Output = <usize as Mul>::Output

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### impl Mul<&usize> for usize

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#### type Output = <usize as Mul>::Output

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### impl Mul<&Saturating<i8>> for &Saturating<i8>

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#### type Output = <Saturating<i8> as Mul>::Output

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### impl Mul<&Saturating<i8>> for Saturating<i8>

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#### type Output = <Saturating<i8> as Mul>::Output

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### impl Mul<&Saturating<i16>> for &Saturating<i16>

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#### type Output = <Saturating<i16> as Mul>::Output

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### impl Mul<&Saturating<i16>> for Saturating<i16>

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#### type Output = <Saturating<i16> as Mul>::Output

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### impl Mul<&Saturating<i32>> for &Saturating<i32>

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#### type Output = <Saturating<i32> as Mul>::Output

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### impl Mul<&Saturating<i32>> for Saturating<i32>

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#### type Output = <Saturating<i32> as Mul>::Output

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### impl Mul<&Saturating<i64>> for &Saturating<i64>

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#### type Output = <Saturating<i64> as Mul>::Output

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### impl Mul<&Saturating<i64>> for Saturating<i64>

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#### type Output = <Saturating<i64> as Mul>::Output

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### impl Mul<&Saturating<i128>> for &Saturating<i128>

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#### type Output = <Saturating<i128> as Mul>::Output

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### impl Mul<&Saturating<i128>> for Saturating<i128>

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#### type Output = <Saturating<i128> as Mul>::Output

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### impl Mul<&Saturating<isize>> for &Saturating<isize>

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#### type Output = <Saturating<isize> as Mul>::Output

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### impl Mul<&Saturating<isize>> for Saturating<isize>

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#### type Output = <Saturating<isize> as Mul>::Output

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### impl Mul<&Saturating<u8>> for &Saturating<u8>

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#### type Output = <Saturating<u8> as Mul>::Output

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### impl Mul<&Saturating<u8>> for Saturating<u8>

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#### type Output = <Saturating<u8> as Mul>::Output

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### impl Mul<&Saturating<u16>> for &Saturating<u16>

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#### type Output = <Saturating<u16> as Mul>::Output

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### impl Mul<&Saturating<u16>> for Saturating<u16>

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#### type Output = <Saturating<u16> as Mul>::Output

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### impl Mul<&Saturating<u32>> for &Saturating<u32>

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#### type Output = <Saturating<u32> as Mul>::Output

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### impl Mul<&Saturating<u32>> for Saturating<u32>

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#### type Output = <Saturating<u32> as Mul>::Output

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### impl Mul<&Saturating<u64>> for &Saturating<u64>

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#### type Output = <Saturating<u64> as Mul>::Output

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### impl Mul<&Saturating<u64>> for Saturating<u64>

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#### type Output = <Saturating<u64> as Mul>::Output

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### impl Mul<&Saturating<u128>> for &Saturating<u128>

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#### type Output = <Saturating<u128> as Mul>::Output

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### impl Mul<&Saturating<u128>> for Saturating<u128>

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#### type Output = <Saturating<u128> as Mul>::Output

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### impl Mul<&Saturating<usize>> for &Saturating<usize>

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#### type Output = <Saturating<usize> as Mul>::Output

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### impl Mul<&Saturating<usize>> for Saturating<usize>

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#### type Output = <Saturating<usize> as Mul>::Output

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### impl Mul<&Wrapping<i8>> for &Wrapping<i8>

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#### type Output = <Wrapping<i8> as Mul>::Output

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### impl Mul<&Wrapping<i8>> for Wrapping<i8>

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#### type Output = <Wrapping<i8> as Mul>::Output

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### impl Mul<&Wrapping<i16>> for &Wrapping<i16>

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#### type Output = <Wrapping<i16> as Mul>::Output

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### impl Mul<&Wrapping<i16>> for Wrapping<i16>

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#### type Output = <Wrapping<i16> as Mul>::Output

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### impl Mul<&Wrapping<i32>> for &Wrapping<i32>

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#### type Output = <Wrapping<i32> as Mul>::Output

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### impl Mul<&Wrapping<i32>> for Wrapping<i32>

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#### type Output = <Wrapping<i32> as Mul>::Output

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### impl Mul<&Wrapping<i64>> for &Wrapping<i64>

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#### type Output = <Wrapping<i64> as Mul>::Output

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### impl Mul<&Wrapping<i64>> for Wrapping<i64>

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#### type Output = <Wrapping<i64> as Mul>::Output

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### impl Mul<&Wrapping<i128>> for &Wrapping<i128>

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#### type Output = <Wrapping<i128> as Mul>::Output

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### impl Mul<&Wrapping<i128>> for Wrapping<i128>

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#### type Output = <Wrapping<i128> as Mul>::Output

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### impl Mul<&Wrapping<isize>> for &Wrapping<isize>

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#### type Output = <Wrapping<isize> as Mul>::Output

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### impl Mul<&Wrapping<isize>> for Wrapping<isize>

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#### type Output = <Wrapping<isize> as Mul>::Output

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### impl Mul<&Wrapping<u8>> for &Wrapping<u8>

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#### type Output = <Wrapping<u8> as Mul>::Output

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### impl Mul<&Wrapping<u8>> for Wrapping<u8>

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#### type Output = <Wrapping<u8> as Mul>::Output

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### impl Mul<&Wrapping<u16>> for &Wrapping<u16>

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#### type Output = <Wrapping<u16> as Mul>::Output

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### impl Mul<&Wrapping<u16>> for Wrapping<u16>

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#### type Output = <Wrapping<u16> as Mul>::Output

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### impl Mul<&Wrapping<u32>> for &Wrapping<u32>

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#### type Output = <Wrapping<u32> as Mul>::Output

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### impl Mul<&Wrapping<u32>> for Wrapping<u32>

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#### type Output = <Wrapping<u32> as Mul>::Output

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### impl Mul<&Wrapping<u64>> for &Wrapping<u64>

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#### type Output = <Wrapping<u64> as Mul>::Output

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### impl Mul<&Wrapping<u64>> for Wrapping<u64>

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#### type Output = <Wrapping<u64> as Mul>::Output

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### impl Mul<&Wrapping<u128>> for &Wrapping<u128>

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#### type Output = <Wrapping<u128> as Mul>::Output

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### impl Mul<&Wrapping<u128>> for Wrapping<u128>

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#### type Output = <Wrapping<u128> as Mul>::Output

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### impl Mul<&Wrapping<usize>> for &Wrapping<usize>

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#### type Output = <Wrapping<usize> as Mul>::Output

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### impl Mul<&Wrapping<usize>> for Wrapping<usize>

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#### type Output = <Wrapping<usize> as Mul>::Output

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### impl Mul<u32> for Duration

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#### type Output = Duration

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### impl Mul<Duration> for u32

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#### type Output = Duration

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### impl<'a> Mul<f16> for &'a f16

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#### type Output = <f16 as Mul>::Output

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### impl<'a> Mul<f32> for &'a f32

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#### type Output = <f32 as Mul>::Output

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### impl<'a> Mul<f64> for &'a f64

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#### type Output = <f64 as Mul>::Output

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### impl<'a> Mul<f128> for &'a f128

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#### type Output = <f128 as Mul>::Output

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### impl<'a> Mul<i8> for &'a i8

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#### type Output = <i8 as Mul>::Output

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### impl<'a> Mul<i16> for &'a i16

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#### type Output = <i16 as Mul>::Output

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### impl<'a> Mul<i32> for &'a i32

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#### type Output = <i32 as Mul>::Output

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### impl<'a> Mul<i64> for &'a i64

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#### type Output = <i64 as Mul>::Output

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### impl<'a> Mul<i128> for &'a i128

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#### type Output = <i128 as Mul>::Output

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### impl<'a> Mul<isize> for &'a isize

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#### type Output = <isize as Mul>::Output

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### impl<'a> Mul<u8> for &'a u8

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#### type Output = <u8 as Mul>::Output

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### impl<'a> Mul<u16> for &'a u16

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#### type Output = <u16 as Mul>::Output

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### impl<'a> Mul<u32> for &'a u32

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#### type Output = <u32 as Mul>::Output

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### impl<'a> Mul<u64> for &'a u64

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#### type Output = <u64 as Mul>::Output

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### impl<'a> Mul<u128> for &'a u128

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#### type Output = <u128 as Mul>::Output

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### impl<'a> Mul<usize> for &'a usize

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#### type Output = <usize as Mul>::Output

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### impl<'a> Mul<Saturating<i8>> for &'a Saturating<i8>

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#### type Output = <Saturating<i8> as Mul>::Output

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### impl<'a> Mul<Saturating<i16>> for &'a Saturating<i16>

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#### type Output = <Saturating<i16> as Mul>::Output

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### impl<'a> Mul<Saturating<i32>> for &'a Saturating<i32>

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#### type Output = <Saturating<i32> as Mul>::Output

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### impl<'a> Mul<Saturating<i64>> for &'a Saturating<i64>

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#### type Output = <Saturating<i64> as Mul>::Output

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### impl<'a> Mul<Saturating<i128>> for &'a Saturating<i128>

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#### type Output = <Saturating<i128> as Mul>::Output

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### impl<'a> Mul<Saturating<isize>> for &'a Saturating<isize>

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#### type Output = <Saturating<isize> as Mul>::Output

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### impl<'a> Mul<Saturating<u8>> for &'a Saturating<u8>

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#### type Output = <Saturating<u8> as Mul>::Output

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### impl<'a> Mul<Saturating<u16>> for &'a Saturating<u16>

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#### type Output = <Saturating<u16> as Mul>::Output

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### impl<'a> Mul<Saturating<u32>> for &'a Saturating<u32>

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#### type Output = <Saturating<u32> as Mul>::Output

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### impl<'a> Mul<Saturating<u64>> for &'a Saturating<u64>

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#### type Output = <Saturating<u64> as Mul>::Output

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### impl<'a> Mul<Saturating<u128>> for &'a Saturating<u128>

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#### type Output = <Saturating<u128> as Mul>::Output

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### impl<'a> Mul<Saturating<usize>> for &'a Saturating<usize>

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#### type Output = <Saturating<usize> as Mul>::Output

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### impl<'a> Mul<Wrapping<i8>> for &'a Wrapping<i8>

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#### type Output = <Wrapping<i8> as Mul>::Output

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### impl<'a> Mul<Wrapping<i16>> for &'a Wrapping<i16>

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#### type Output = <Wrapping<i16> as Mul>::Output

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### impl<'a> Mul<Wrapping<i32>> for &'a Wrapping<i32>

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#### type Output = <Wrapping<i32> as Mul>::Output

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### impl<'a> Mul<Wrapping<i64>> for &'a Wrapping<i64>

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#### type Output = <Wrapping<i64> as Mul>::Output

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### impl<'a> Mul<Wrapping<i128>> for &'a Wrapping<i128>

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#### type Output = <Wrapping<i128> as Mul>::Output

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### impl<'a> Mul<Wrapping<isize>> for &'a Wrapping<isize>

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#### type Output = <Wrapping<isize> as Mul>::Output

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### impl<'a> Mul<Wrapping<u8>> for &'a Wrapping<u8>

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#### type Output = <Wrapping<u8> as Mul>::Output

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### impl<'a> Mul<Wrapping<u16>> for &'a Wrapping<u16>

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#### type Output = <Wrapping<u16> as Mul>::Output

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### impl<'a> Mul<Wrapping<u32>> for &'a Wrapping<u32>

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#### type Output = <Wrapping<u32> as Mul>::Output

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### impl<'a> Mul<Wrapping<u64>> for &'a Wrapping<u64>

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#### type Output = <Wrapping<u64> as Mul>::Output

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### impl<'a> Mul<Wrapping<u128>> for &'a Wrapping<u128>

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#### type Output = <Wrapping<u128> as Mul>::Output

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### impl<'a> Mul<Wrapping<usize>> for &'a Wrapping<usize>

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#### type Output = <Wrapping<usize> as Mul>::Output

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

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#### type Output = Simd<T, N>

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### impl<const N: usize> Mul for Simd<f32, N>
where f32: SimdElement, LaneCount<N>: SupportedLaneCount,

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#### type Output = Simd<f32, N>

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### impl<const N: usize> Mul for Simd<f64, N>
where f64: SimdElement, LaneCount<N>: SupportedLaneCount,

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#### type Output = Simd<f64, N>

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### impl<const N: usize> Mul for Simd<i8, N>
where i8: SimdElement, LaneCount<N>: SupportedLaneCount,

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#### type Output = Simd<i8, N>

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### impl<const N: usize> Mul for Simd<i16, N>
where i16: SimdElement, LaneCount<N>: SupportedLaneCount,

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#### type Output = Simd<i16, N>

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### impl<const N: usize> Mul for Simd<i32, N>
where i32: SimdElement, LaneCount<N>: SupportedLaneCount,

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#### type Output = Simd<i32, N>

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### impl<const N: usize> Mul for Simd<i64, N>
where i64: SimdElement, LaneCount<N>: SupportedLaneCount,

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#### type Output = Simd<i64, N>

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### impl<const N: usize> Mul for Simd<isize, N>
where isize: SimdElement, LaneCount<N>: SupportedLaneCount,

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#### type Output = Simd<isize, N>

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### impl<const N: usize> Mul for Simd<u8, N>
where u8: SimdElement, LaneCount<N>: SupportedLaneCount,

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#### type Output = Simd<u8, N>

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### impl<const N: usize> Mul for Simd<u16, N>
where u16: SimdElement, LaneCount<N>: SupportedLaneCount,

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#### type Output = Simd<u16, N>

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### impl<const N: usize> Mul for Simd<u32, N>
where u32: SimdElement, LaneCount<N>: SupportedLaneCount,

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#### type Output = Simd<u32, N>

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### impl<const N: usize> Mul for Simd<u64, N>
where u64: SimdElement, LaneCount<N>: SupportedLaneCount,

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#### type Output = Simd<u64, N>

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### impl<const N: usize> Mul for Simd<usize, N>
where usize: SimdElement, LaneCount<N>: SupportedLaneCount,

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#### type Output = Simd<usize, N>