Rework the std::iter::Step trait

Previous attempts: rust-lang#43127 rust-lang#62886 rust-lang#68807
Tracking issue: rust-lang#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).

Rework the std::iter::Step trait

Previous attempts: rust-lang#43127 rust-lang#62886 rust-lang#68807
Tracking issue: rust-lang#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).

Tested on commit rust-lang/rust@ed084b0.
Direct link to PR: <rust-lang/rust#69659>

💔 rls on windows: test-pass → build-fail (cc @Xanewok).
💔 rls on linux: test-pass → build-fail (cc @Xanewok).
💔 rustfmt on windows: test-pass → build-fail (cc @topecongiro).
💔 rustfmt on linux: test-pass → build-fail (cc @topecongiro).

Resolve overflow behavior for RangeFrom

This specifies a documented unspecified implementation detail of `RangeFrom` and makes it consistently implement the specified behavior.

Specifically, `(u8::MAX).next()` is defined to cause an overflow, and resolve that overflow in the same manner as the `Step::forward` implementation.

The inconsistency that has existed is `<RangeFrom as Iterator>::nth`. The existing behavior should be plain to see after rust-lang#69659: the skipping part previously always panicked if it caused an overflow, but the final step (to set up the state for further iteration) has always been debug-checked.

The inconsistency, then, is that `RangeFrom::nth` does not implement the same behavior as the naive (and default) implementation of just calling `next` multiple times. This PR aligns `RangeFrom::nth` to have identical behavior to the naive implementation. It also lines up with the standard behavior of primitive math in Rust everywhere else in the language: debug checked overflow.

cc @Amanieu

---

Followup to rust-lang#69659. Closes rust-lang#25708 (by documenting the panic as intended).

The documentation wording is preliminary and can probably be improved.

This will probably need an FCP, as it changes observable stable behavior.

Resolve overflow behavior for RangeFrom

This specifies a documented unspecified implementation detail of `RangeFrom` and makes it consistently implement the specified behavior.

Specifically, `(u8::MAX).next()` is defined to cause an overflow, and resolve that overflow in the same manner as the `Step::forward` implementation.

The inconsistency that has existed is `<RangeFrom as Iterator>::nth`. The existing behavior should be plain to see after rust-lang#69659: the skipping part previously always panicked if it caused an overflow, but the final step (to set up the state for further iteration) has always been debug-checked.

The inconsistency, then, is that `RangeFrom::nth` does not implement the same behavior as the naive (and default) implementation of just calling `next` multiple times. This PR aligns `RangeFrom::nth` to have identical behavior to the naive implementation. It also lines up with the standard behavior of primitive math in Rust everywhere else in the language: debug checked overflow.

cc @Amanieu

---

Followup to rust-lang#69659. Closes rust-lang#25708 (by documenting the panic as intended).

The documentation wording is preliminary and can probably be improved.

This will probably need an FCP, as it changes observable stable behavior.