pub trait Step: Sized + Clone + PartialOrd {
// 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 { ... }
}
step_trait
)std
only.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§
sourcefn steps_between(start: &Self, end: &Self) -> Option<usize>
🔬This is a nightly-only experimental API. (step_trait
)
fn steps_between(start: &Self, end: &Self) -> Option<usize>
step_trait
)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 ifStep::forward_checked(&a, n) == Some(b)
steps_between(&a, &b) == Some(n)
if and only ifStep::backward_checked(&b, n) == Some(a)
steps_between(&a, &b) == Some(n)
only ifa <= b
- Corollary:
steps_between(&a, &b) == Some(0)
if and only ifa == b
- Note that
a <= b
does not implysteps_between(&a, &b) != None
; this is the case when it would require more thanusize::MAX
steps to get tob
- Corollary:
steps_between(&a, &b) == None
ifa > b
sourcefn forward_checked(start: Self, count: usize) -> Option<Self>
🔬This is a nightly-only experimental API. (step_trait
)
fn forward_checked(start: Self, count: usize) -> Option<Self>
step_trait
)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))
Step::forward_checked(a, n).and_then(|x| Step::forward_checked(x, m)) == try { Step::forward_checked(a, n.checked_add(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)
- Corollary:
sourcefn backward_checked(start: Self, count: usize) -> Option<Self>
🔬This is a nightly-only experimental API. (step_trait
)
fn backward_checked(start: Self, count: usize) -> Option<Self>
step_trait
)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)
- Corollary:
Provided Methods§
sourcefn forward(start: Self, count: usize) -> Self
🔬This is a nightly-only experimental API. (step_trait
)
fn forward(start: Self, count: usize) -> Self
step_trait
)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
- Corollary:
Step::forward(a, n) >= a
Step::backward(Step::forward(a, n), n) == a
sourceunsafe fn forward_unchecked(start: Self, count: usize) -> Self
🔬This is a nightly-only experimental API. (step_trait
)
unsafe fn forward_unchecked(start: Self, count: usize) -> Self
step_trait
)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 thatb > a
, it is safe to callStep::forward_unchecked(a, 1)
- if there exists
b
,n
such thatsteps_between(&a, &b) == Some(n)
, it is safe to callStep::forward_unchecked(a, m)
for anym <= n
.- Corollary:
Step::forward_unchecked(a, 0)
is always safe.
- Corollary:
For any a
and n
, where no overflow occurs:
Step::forward_unchecked(a, n)
is equivalent toStep::forward(a, n)
sourcefn backward(start: Self, count: usize) -> Self
🔬This is a nightly-only experimental API. (step_trait
)
fn backward(start: Self, count: usize) -> Self
step_trait
)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
- Corollary:
Step::backward(a, n) <= a
Step::forward(Step::backward(a, n), n) == a
sourceunsafe fn backward_unchecked(start: Self, count: usize) -> Self
🔬This is a nightly-only experimental API. (step_trait
)
unsafe fn backward_unchecked(start: Self, count: usize) -> Self
step_trait
)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 thatb < a
, it is safe to callStep::backward_unchecked(a, 1)
- if there exists
b
,n
such thatsteps_between(&b, &a) == Some(n)
, it is safe to callStep::backward_unchecked(a, m)
for anym <= n
.- Corollary:
Step::backward_unchecked(a, 0)
is always safe.
- Corollary:
For any a
and n
, where no overflow occurs:
Step::backward_unchecked(a, n)
is equivalent toStep::backward(a, n)