# Trait std::iter::Step

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    pub trait Step: Clone + PartialOrd + Sized {
        // Required methods
        fn steps_between(start: &Self, end: &Self) -> Option<usize>;
        fn forward_checked(start: Self, count: usize) -> Option<Self>;
        fn backward_checked(start: Self, count: usize) -> Option<Self>;

        // Provided methods
        fn forward(start: Self, count: usize) -> Self { ... }
        unsafe fn forward_unchecked(start: Self, count: usize) -> Self { ... }
        fn backward(start: Self, count: usize) -> Self { ... }
        unsafe fn backward_unchecked(start: Self, count: usize) -> Self { ... }
    }

🔬This is a nightly-only experimental API. (`step_trait` #42168)
Expand description

Objects that have a notion of successor and predecessor operations.

The successor operation moves towards values that compare greater. The predecessor operation moves towards values that compare lesser.

## Required Methods§

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#### fn steps_between(start: &Self, end: &Self) -> Option<usize>

🔬This is a nightly-only experimental API. (`step_trait` #42168)

Returns the number of successor steps required to get from `start` to `end`.

Returns `None` if the number of steps would overflow `usize` (or is infinite, or if `end` would never be reached).

##### Invariants

For any `a`, `b`, and `n`:

- `steps_between(&a, &b) == Some(n)` if and only if `Step::forward_checked(&a, n) == Some(b)`
- `steps_between(&a, &b) == Some(n)` if and only if `Step::backward_checked(&b, n) == Some(a)`
- `steps_between(&a, &b) == Some(n)` only if `a <= b`
  - Corollary: `steps_between(&a, &b) == Some(0)` if and only if `a == b`
  - Note that `a <= b` does not imply `steps_between(&a, &b) != None`; this is the case when it would require more than `usize::MAX` steps to get to `b`
- `steps_between(&a, &b) == None` if `a > b`

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#### fn forward_checked(start: Self, count: usize) -> Option<Self>

🔬This is a nightly-only experimental API. (`step_trait` #42168)

Returns the value that would be obtained by taking the successor of `self` `count` times.

If this would overflow the range of values supported by `Self`, returns `None`.

##### Invariants

For any `a`, `n`, and `m`:

- `Step::forward_checked(a, n).and_then(|x| Step::forward_checked(x, m)) == Step::forward_checked(a, m).and_then(|x| Step::forward_checked(x, n))`

For any `a`, `n`, and `m` where `n + m` does not overflow:

- `Step::forward_checked(a, n).and_then(|x| Step::forward_checked(x, m)) == Step::forward_checked(a, n + m)`

For any `a` and `n`:

- `Step::forward_checked(a, n) == (0..n).try_fold(a, |x, _| Step::forward_checked(&x, 1))`
  - Corollary: `Step::forward_checked(&a, 0) == Some(a)`

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#### fn backward_checked(start: Self, count: usize) -> Option<Self>

🔬This is a nightly-only experimental API. (`step_trait` #42168)

Returns the value that would be obtained by taking the predecessor of `self` `count` times.

If this would overflow the range of values supported by `Self`, returns `None`.

##### Invariants

For any `a`, `n`, and `m`:

- `Step::backward_checked(a, n).and_then(|x| Step::backward_checked(x, m)) == n.checked_add(m).and_then(|x| Step::backward_checked(a, x))`
- `Step::backward_checked(a, n).and_then(|x| Step::backward_checked(x, m)) == try { Step::backward_checked(a, n.checked_add(m)?) }`

For any `a` and `n`:

- `Step::backward_checked(a, n) == (0..n).try_fold(a, |x, _| Step::backward_checked(&x, 1))`
  - Corollary: `Step::backward_checked(&a, 0) == Some(a)`

## Provided Methods§

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#### fn forward(start: Self, count: usize) -> Self

🔬This is a nightly-only experimental API. (`step_trait` #42168)

Returns the value that would be obtained by taking the successor of `self` `count` times.

If this would overflow the range of values supported by `Self`, this function is allowed to panic, wrap, or saturate. The suggested behavior is to panic when debug assertions are enabled, and to wrap or saturate otherwise.

Unsafe code should not rely on the correctness of behavior after overflow.

##### Invariants

For any `a`, `n`, and `m`, where no overflow occurs:

- `Step::forward(Step::forward(a, n), m) == Step::forward(a, n + m)`

For any `a` and `n`, where no overflow occurs:

- `Step::forward_checked(a, n) == Some(Step::forward(a, n))`
- `Step::forward(a, n) == (0..n).fold(a, |x, _| Step::forward(x, 1))`
  - Corollary: `Step::forward(a, 0) == a`
- `Step::forward(a, n) >= a`
- `Step::backward(Step::forward(a, n), n) == a`

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#### unsafe fn forward_unchecked(start: Self, count: usize) -> Self

🔬This is a nightly-only experimental API. (`step_trait` #42168)

Returns the value that would be obtained by taking the successor of `self` `count` times.

##### Safety

It is undefined behavior for this operation to overflow the range of values supported by `Self`. If you cannot guarantee that this will not overflow, use `forward` or `forward_checked` instead.

##### Invariants

For any `a`:

- if there exists `b` such that `b > a`, it is safe to call `Step::forward_unchecked(a, 1)`
- if there exists `b`, `n` such that `steps_between(&a, &b) == Some(n)`, it is safe to call `Step::forward_unchecked(a, m)` for any `m <= n`.

For any `a` and `n`, where no overflow occurs:

- `Step::forward_unchecked(a, n)` is equivalent to `Step::forward(a, n)`

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#### fn backward(start: Self, count: usize) -> Self

🔬This is a nightly-only experimental API. (`step_trait` #42168)

Returns the value that would be obtained by taking the predecessor of `self` `count` times.

If this would overflow the range of values supported by `Self`, this function is allowed to panic, wrap, or saturate. The suggested behavior is to panic when debug assertions are enabled, and to wrap or saturate otherwise.

Unsafe code should not rely on the correctness of behavior after overflow.

##### Invariants

For any `a`, `n`, and `m`, where no overflow occurs:

- `Step::backward(Step::backward(a, n), m) == Step::backward(a, n + m)`

For any `a` and `n`, where no overflow occurs:

- `Step::backward_checked(a, n) == Some(Step::backward(a, n))`
- `Step::backward(a, n) == (0..n).fold(a, |x, _| Step::backward(x, 1))`
  - Corollary: `Step::backward(a, 0) == a`
- `Step::backward(a, n) <= a`
- `Step::forward(Step::backward(a, n), n) == a`

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#### unsafe fn backward_unchecked(start: Self, count: usize) -> Self

🔬This is a nightly-only experimental API. (`step_trait` #42168)

Returns the value that would be obtained by taking the predecessor of `self` `count` times.

##### Safety

It is undefined behavior for this operation to overflow the range of values supported by `Self`. If you cannot guarantee that this will not overflow, use `backward` or `backward_checked` instead.

##### Invariants

For any `a`:

- if there exists `b` such that `b < a`, it is safe to call `Step::backward_unchecked(a, 1)`
- if there exists `b`, `n` such that `steps_between(&b, &a) == Some(n)`, it is safe to call `Step::backward_unchecked(a, m)` for any `m <= n`.

For any `a` and `n`, where no overflow occurs:

- `Step::backward_unchecked(a, n)` is equivalent to `Step::backward(a, n)`

## Object Safety§

This trait is not object safe.

## Implementors§

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### impl Step for AsciiChar

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### impl Step for char

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### impl Step for i8

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### impl Step for i16

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### impl Step for i32

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### impl Step for i64

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### impl Step for i128

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### impl Step for isize

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### impl Step for u8

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### impl Step for u16

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### impl Step for u32

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### impl Step for u64

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### impl Step for u128

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### impl Step for usize

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### impl Step for Ipv4Addr

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### impl Step for Ipv6Addr