polkadot_sdk_frame::arithmetic

Trait One

pub trait One: Sized + Mul<Output = Self> {
    // Required method
    fn one() -> Self;

    // Provided methods
    fn set_one(&mut self) { ... }
    fn is_one(&self) -> bool
       where Self: PartialEq { ... }
}

Expand description

Defines a multiplicative identity element for Self.

§Laws

a * 1 = a       ∀ a ∈ Self
1 * a = a       ∀ a ∈ Self

Required Methods§

fn one() -> Self

Returns the multiplicative identity element of Self, 1.

§Purity

This function should return the same result at all times regardless of external mutable state, for example values stored in TLS or in static muts.

Provided Methods§

fn set_one(&mut self)

Sets self to the multiplicative identity element of Self, 1.

fn is_one(&self) -> bool
where Self: PartialEq,

Returns true if self is equal to the multiplicative identity.

For performance reasons, it’s best to implement this manually. After a semver bump, this method will be required, and the where Self: PartialEq bound will be removed.

Dyn Compatibility§

This trait is not dyn compatible.

In older versions of Rust, dyn compatibility was called "object safety", so this trait is not object safe.

Implementations on Foreign Types§

impl One for f32

fn one() -> f32

fn is_one(&self) -> bool

impl One for f64

fn one() -> f64

fn is_one(&self) -> bool

impl One for i8

fn one() -> i8

fn is_one(&self) -> bool

impl One for i16

fn one() -> i16

fn is_one(&self) -> bool

impl One for i32

fn one() -> i32

fn is_one(&self) -> bool

impl One for i64

fn one() -> i64

fn is_one(&self) -> bool

impl One for i128

fn one() -> i128

fn is_one(&self) -> bool

impl One for isize

fn one() -> isize

fn is_one(&self) -> bool

impl One for u8

fn one() -> u8

fn is_one(&self) -> bool

impl One for u16

fn one() -> u16

fn is_one(&self) -> bool

impl One for u32

fn one() -> u32

fn is_one(&self) -> bool

impl One for u64

fn one() -> u64

fn is_one(&self) -> bool

impl One for u128

fn one() -> u128

fn is_one(&self) -> bool

impl One for usize

fn one() -> usize

fn is_one(&self) -> bool

impl One for BigInt

fn one() -> BigInt

fn set_one(&mut self)

fn is_one(&self) -> bool

impl One for BigUint

fn one() -> BigUint

fn set_one(&mut self)

fn is_one(&self) -> bool

impl One for AutoSimd<[f32; 2]>

fn one() -> AutoSimd<[f32; 2]>

impl One for AutoSimd<[f32; 4]>

fn one() -> AutoSimd<[f32; 4]>

impl One for AutoSimd<[f32; 8]>

fn one() -> AutoSimd<[f32; 8]>

impl One for AutoSimd<[f32; 16]>

fn one() -> AutoSimd<[f32; 16]>

impl One for AutoSimd<[f64; 2]>

fn one() -> AutoSimd<[f64; 2]>

impl One for AutoSimd<[f64; 4]>

fn one() -> AutoSimd<[f64; 4]>

impl One for AutoSimd<[f64; 8]>

fn one() -> AutoSimd<[f64; 8]>

impl One for AutoSimd<[i8; 2]>

fn one() -> AutoSimd<[i8; 2]>

impl One for AutoSimd<[i8; 4]>

fn one() -> AutoSimd<[i8; 4]>

impl One for AutoSimd<[i8; 8]>

fn one() -> AutoSimd<[i8; 8]>

impl One for AutoSimd<[i8; 16]>

fn one() -> AutoSimd<[i8; 16]>

impl One for AutoSimd<[i8; 32]>

fn one() -> AutoSimd<[i8; 32]>

impl One for AutoSimd<[i16; 2]>

fn one() -> AutoSimd<[i16; 2]>

impl One for AutoSimd<[i16; 4]>

fn one() -> AutoSimd<[i16; 4]>

impl One for AutoSimd<[i16; 8]>

fn one() -> AutoSimd<[i16; 8]>

impl One for AutoSimd<[i16; 16]>

fn one() -> AutoSimd<[i16; 16]>

impl One for AutoSimd<[i16; 32]>

fn one() -> AutoSimd<[i16; 32]>

impl One for AutoSimd<[i32; 2]>

fn one() -> AutoSimd<[i32; 2]>

impl One for AutoSimd<[i32; 4]>

fn one() -> AutoSimd<[i32; 4]>

impl One for AutoSimd<[i32; 8]>

fn one() -> AutoSimd<[i32; 8]>

impl One for AutoSimd<[i32; 16]>

fn one() -> AutoSimd<[i32; 16]>

impl One for AutoSimd<[i64; 2]>

fn one() -> AutoSimd<[i64; 2]>

impl One for AutoSimd<[i64; 4]>

fn one() -> AutoSimd<[i64; 4]>

impl One for AutoSimd<[i64; 8]>

fn one() -> AutoSimd<[i64; 8]>

impl One for AutoSimd<[i128; 1]>

fn one() -> AutoSimd<[i128; 1]>

impl One for AutoSimd<[i128; 2]>

fn one() -> AutoSimd<[i128; 2]>

impl One for AutoSimd<[i128; 4]>

fn one() -> AutoSimd<[i128; 4]>

impl One for AutoSimd<[isize; 2]>

fn one() -> AutoSimd<[isize; 2]>

impl One for AutoSimd<[isize; 4]>

fn one() -> AutoSimd<[isize; 4]>

impl One for AutoSimd<[isize; 8]>

fn one() -> AutoSimd<[isize; 8]>

impl One for AutoSimd<[u8; 2]>

fn one() -> AutoSimd<[u8; 2]>

impl One for AutoSimd<[u8; 4]>

fn one() -> AutoSimd<[u8; 4]>

impl One for AutoSimd<[u8; 8]>

fn one() -> AutoSimd<[u8; 8]>

impl One for AutoSimd<[u8; 16]>

fn one() -> AutoSimd<[u8; 16]>

impl One for AutoSimd<[u8; 32]>

fn one() -> AutoSimd<[u8; 32]>

impl One for AutoSimd<[u16; 2]>

fn one() -> AutoSimd<[u16; 2]>

impl One for AutoSimd<[u16; 4]>

fn one() -> AutoSimd<[u16; 4]>

impl One for AutoSimd<[u16; 8]>

fn one() -> AutoSimd<[u16; 8]>

impl One for AutoSimd<[u16; 16]>

fn one() -> AutoSimd<[u16; 16]>

impl One for AutoSimd<[u16; 32]>

fn one() -> AutoSimd<[u16; 32]>

impl One for AutoSimd<[u32; 2]>

fn one() -> AutoSimd<[u32; 2]>

impl One for AutoSimd<[u32; 4]>

fn one() -> AutoSimd<[u32; 4]>

impl One for AutoSimd<[u32; 8]>

fn one() -> AutoSimd<[u32; 8]>

impl One for AutoSimd<[u32; 16]>

fn one() -> AutoSimd<[u32; 16]>

impl One for AutoSimd<[u64; 2]>

fn one() -> AutoSimd<[u64; 2]>

impl One for AutoSimd<[u64; 4]>

fn one() -> AutoSimd<[u64; 4]>

impl One for AutoSimd<[u64; 8]>

fn one() -> AutoSimd<[u64; 8]>

impl One for AutoSimd<[u128; 1]>

fn one() -> AutoSimd<[u128; 1]>

impl One for AutoSimd<[u128; 2]>

fn one() -> AutoSimd<[u128; 2]>

impl One for AutoSimd<[u128; 4]>

fn one() -> AutoSimd<[u128; 4]>

impl One for AutoSimd<[usize; 2]>

fn one() -> AutoSimd<[usize; 2]>

impl One for AutoSimd<[usize; 4]>

fn one() -> AutoSimd<[usize; 4]>

impl One for AutoSimd<[usize; 8]>

fn one() -> AutoSimd<[usize; 8]>

impl One for U128

fn one() -> U128

impl One for WideF32x4

fn one() -> WideF32x4

impl One for WideF32x8

fn one() -> WideF32x8

impl One for WideF64x4

fn one() -> WideF64x4

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

fn one() -> CubicExtField<P>

fn is_one(&self) -> bool

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

fn one() -> CubicExtField<P>

fn is_one(&self) -> bool

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

fn one() -> QuadExtField<P>

fn is_one(&self) -> bool

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

fn one() -> QuadExtField<P>

fn is_one(&self) -> bool

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

fn one() -> Fp<P, N>

fn is_one(&self) -> bool

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

fn one() -> Fp<P, N>

fn is_one(&self) -> bool

impl<T> One for Wrapping<T>
where T: One, Wrapping<T>: Mul<Output = Wrapping<T>>,

fn set_one(&mut self)

fn one() -> Wrapping<T>

impl<T> One for Unit<DualQuaternion<T>>
where T: SimdRealField, <T as SimdValue>::Element: SimdRealField,

fn one() -> Unit<DualQuaternion<T>>

impl<T> One for Unit<Quaternion<T>>
where T: SimdRealField, <T as SimdValue>::Element: SimdRealField,

fn one() -> Unit<Quaternion<T>>

impl<T> One for Unit<Complex<T>>
where T: SimdRealField, <T as SimdValue>::Element: SimdRealField,

fn one() -> Unit<Complex<T>>

impl<T> One for DualQuaternion<T>
where T: SimdRealField, <T as SimdValue>::Element: SimdRealField,

fn one() -> DualQuaternion<T>

impl<T> One for Quaternion<T>
where T: SimdRealField, <T as SimdValue>::Element: SimdRealField,

fn one() -> Quaternion<T>

impl<T> One for Complex<T>
where T: Clone + Num,

fn one() -> Complex<T>

fn is_one(&self) -> bool

fn set_one(&mut self)

impl<T> One for Ratio<T>
where T: Clone + Integer,

fn one() -> Ratio<T>

fn is_one(&self) -> bool

fn set_one(&mut self)

impl<T, C, const D: usize> One for Transform<T, C, D>
where T: RealField, C: TCategory, Const<D>: DimNameAdd<Const<1>>, DefaultAllocator: Allocator<T, <Const<D> as DimNameAdd<Const<1>>>::Output, <Const<D> as DimNameAdd<Const<1>>>::Output>,

fn one() -> Transform<T, C, D>

Creates a new identity transform.

impl<T, D> One for Matrix<T, D, D, <DefaultAllocator as Allocator<T, D, D>>::Buffer>
where D: DimName, T: Scalar + Zero + One + ClosedMul + ClosedAdd, DefaultAllocator: Allocator<T, D, D>,

fn one() -> Matrix<T, D, D, <DefaultAllocator as Allocator<T, D, D>>::Buffer>

impl<T, D> One for TypeWithDefault<T, D>
where T: One, D: Get<T>,

fn one() -> TypeWithDefault<T, D>

impl<T, R, const D: usize> One for Isometry<T, R, D>
where T: SimdRealField, R: AbstractRotation<T, D>, <T as SimdValue>::Element: SimdRealField,

fn one() -> Isometry<T, R, D>

Creates a new identity isometry.

impl<T, R, const D: usize> One for Similarity<T, R, D>
where T: SimdRealField, <T as SimdValue>::Element: SimdRealField, R: AbstractRotation<T, D>,

fn one() -> Similarity<T, R, D>

Creates a new identity similarity.

impl<T, const D: usize> One for Rotation<T, D>
where T: Scalar + Zero + One + ClosedAdd + ClosedMul,

fn one() -> Rotation<T, D>

impl<T, const D: usize> One for Scale<T, D>
where T: Scalar + One + ClosedMul,

fn one() -> Scale<T, D>

impl<T, const D: usize> One for Translation<T, D>
where T: Scalar + Zero + ClosedAdd,

fn one() -> Translation<T, D>

Implementors§

impl One for U256

impl One for U512

impl One for polkadot_sdk_frame::arithmetic::biguint::BigUint

impl One for FixedI64

impl One for FixedI128

impl One for FixedU64

impl One for FixedU128

impl One for PerU16

impl One for Perbill

impl One for Percent

impl One for Permill

impl One for Perquintill