Rework the std::iter::Step trait
Previous attempts: #43127#62886#68807
Tracking issue: #42168
This PR reworks the `Step` trait to be phrased in terms of the *successor* and *predecessor* operations. With this, `Step` hopefully has a consistent identity that can have a path towards stabilization. The proposed trait:
```rust
/// 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.
///
/// # Safety
///
/// This trait is `unsafe` because its implementation must be correct for
/// the safety of `unsafe trait TrustedLen` implementations, and the results
/// of using this trait can otherwise be trusted by `unsafe` code to be correct
/// and fulful the listed obligations.
pub unsafe trait Step: Clone + PartialOrd + Sized {
/// 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(&a, n) == Some(b)`
/// * `steps_between(&a, &b) == Some(n)` if and only if `Step::backward(&a, 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 wheen it would require more than `usize::MAX` steps to get to `b`
/// * `steps_between(&a, &b) == None` if `a > b`
fn steps_between(start: &Self, end: &Self) -> Option<usize>;
/// 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)`
fn forward_checked(start: Self, count: usize) -> Option<Self>;
/// 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`
fn forward(start: Self, count: usize) -> Self {
Step::forward_checked(start, count).expect("overflow in `Step::forward`")
}
/// 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)`
#[unstable(feature = "unchecked_math", reason = "niche optimization path", issue = "none")]
unsafe fn forward_unchecked(start: Self, count: usize) -> Self {
Step::forward(start, count)
}
/// 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::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)`
fn backward_checked(start: Self, count: usize) -> Option<Self>;
/// 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`
fn backward(start: Self, count: usize) -> Self {
Step::backward_checked(start, count).expect("overflow in `Step::backward`")
}
/// 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)`
#[unstable(feature = "unchecked_math", reason = "niche optimization path", issue = "none")]
unsafe fn backward_unchecked(start: Self, count: usize) -> Self {
Step::backward(start, count)
}
}
```
Note that all of these are associated functions and not callable via method syntax; the calling syntax is always `Step::forward(start, n)`. This version of the trait additionally changes the stepping functions to talk their arguments by value.
As opposed to previous attempts which provided a "step by one" method directly, this version of the trait only exposes "step by n". There are a few reasons for this:
- `Range*`, the primary consumer of `Step`, assumes that the "step by n" operation is cheap. If a single step function is provided, it will be a lot more enticing to implement "step by n" as n repeated calls to "step by one". While this is not strictly incorrect, this behavior would be surprising for anyone used to using `Range<{primitive integer}>`.
- With a trivial default impl, this can be easily added backwards-compatibly later.
- The debug-wrapping "step by n" needs to exist for `RangeFrom` to be consistent between "step by n" and "step by one" operation. (Note: the behavior is not changed by this PR, but making the behavior consistent is made tenable by this PR.)
Three "kinds" of step are provided: `_checked`, which returns an `Option` indicating attempted overflow; (unsuffixed), which provides "safe overflow" behavior (is allowed to panic, wrap, or saturate, depending on what is most convenient for a given type); and `_unchecked`, which is a version which assumes overflow does not happen.
Review is appreciated to check that:
- The invariants as described on the `Step` functions are enough to specify the "common sense" consistency for successor/predecessor.
- Implementation of `Step` functions is correct in the face of overflow and the edges of representable integers.
- Added tests of `Step` functions are asserting the correct behavior (and not just the implemented behavior).
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