| //===--- Stride.swift.gyb - Components for stride(...) iteration ----------===// |
| // |
| // This source file is part of the Swift.org open source project |
| // |
| // Copyright (c) 2014 - 2017 Apple Inc. and the Swift project authors |
| // Licensed under Apache License v2.0 with Runtime Library Exception |
| // |
| // See https://swift.org/LICENSE.txt for license information |
| // See https://swift.org/CONTRIBUTORS.txt for the list of Swift project authors |
| // |
| //===----------------------------------------------------------------------===// |
| |
| /// A type representing continuous, one-dimensional values that can be offset |
| /// and measured. |
| /// |
| /// You can use a type that conforms to the `Strideable` protocol with the |
| /// `stride(from:to:by:)` and `stride(from:through:by:)` functions. For |
| /// example, you can use `stride(from:to:by:)` to iterate over an |
| /// interval of floating-point values: |
| /// |
| /// for radians in stride(from: 0.0, to: .pi * 2, by: .pi / 2) { |
| /// let degrees = Int(radians * 180 / .pi) |
| /// print("Degrees: \(degrees), radians: \(radians)") |
| /// } |
| /// // Degrees: 0, radians: 0.0 |
| /// // Degrees: 90, radians: 1.5707963267949 |
| /// // Degrees: 180, radians: 3.14159265358979 |
| /// // Degrees: 270, radians: 4.71238898038469 |
| /// |
| /// The last parameter of these functions is of the associated `Stride` |
| /// type---the type that represents the distance between any two instances of |
| /// the `Strideable` type. |
| /// |
| /// Types that have an integer `Stride` can be used as the boundaries of a |
| /// countable range or as the lower bound of an iterable one-sided range. For |
| /// example, you can iterate over a range of `Int` and use sequence and |
| /// collection methods. |
| /// |
| /// var sum = 0 |
| /// for x in 1...100 { |
| /// sum += x |
| /// } |
| /// // sum == 5050 |
| /// |
| /// let digits = (0..<10).map(String.init) |
| /// // ["0", "1", "2", "3", "4", "5", "6", "7", "8", "9"] |
| /// |
| /// Conforming to the Strideable Protocol |
| /// ===================================== |
| /// |
| /// To add `Strideable` conformance to a custom type, choose a `Stride` type |
| /// that can represent the distance between two instances and implement the |
| /// `advanced(by:)` and `distance(to:)` methods. For example, this |
| /// hypothetical `Date` type stores its value as the number of days before or |
| /// after January 1, 2000: |
| /// |
| /// struct Date: Equatable, CustomStringConvertible { |
| /// var daysAfterY2K: Int |
| /// |
| /// var description: String { |
| /// // ... |
| /// } |
| /// } |
| /// |
| /// The `Stride` type for `Date` is `Int`, inferred from the parameter and |
| /// return types of `advanced(by:)` and `distance(to:)`: |
| /// |
| /// extension Date: Strideable { |
| /// func advanced(by n: Int) -> Date { |
| /// var result = self |
| /// result.daysAfterY2K += n |
| /// return result |
| /// } |
| /// |
| /// func distance(to other: Date) -> Int { |
| /// return other.daysAfterY2K - self.daysAfterY2K |
| /// } |
| /// } |
| /// |
| /// The `Date` type can now be used with the `stride(from:to:by:)` and |
| /// `stride(from:through:by:)` functions and as the bounds of an iterable |
| /// range. |
| /// |
| /// let startDate = Date(daysAfterY2K: 0) // January 1, 2000 |
| /// let endDate = Date(daysAfterY2K: 15) // January 16, 2000 |
| /// |
| /// for date in stride(from: startDate, to: endDate, by: 7) { |
| /// print(date) |
| /// } |
| /// // January 1, 2000 |
| /// // January 8, 2000 |
| /// // January 15, 2000 |
| /// |
| /// - Important: The `Strideable` protocol provides default implementations for |
| /// the equal-to (`==`) and less-than (`<`) operators that depend on the |
| /// `Stride` type's implementations. If a type conforming to `Strideable` is |
| /// its own `Stride` type, it must provide concrete implementations of the |
| /// two operators to avoid infinite recursion. |
| public protocol Strideable : Comparable { |
| /// A type that represents the distance between two values. |
| associatedtype Stride : SignedNumeric, Comparable |
| |
| /// Returns the distance from this value to the given value, expressed as a |
| /// stride. |
| /// |
| /// If this type's `Stride` type conforms to `BinaryInteger`, then for two |
| /// values `x` and `y`, and a distance `n = x.distance(to: y)`, |
| /// `x.advanced(by: n) == y`. Using this method with types that have a |
| /// noninteger `Stride` may result in an approximation. |
| /// |
| /// - Parameter other: The value to calculate the distance to. |
| /// - Returns: The distance from this value to `other`. |
| /// |
| /// - Complexity: O(1) |
| func distance(to other: Self) -> Stride |
| |
| /// Returns a value that is offset the specified distance from this value. |
| /// |
| /// Use the `advanced(by:)` method in generic code to offset a value by a |
| /// specified distance. If you're working directly with numeric values, use |
| /// the addition operator (`+`) instead of this method. |
| /// |
| /// func addOne<T: Strideable>(to x: T) -> T |
| /// where T.Stride : ExpressibleByIntegerLiteral |
| /// { |
| /// return x.advanced(by: 1) |
| /// } |
| /// |
| /// let x = addOne(to: 5) |
| /// // x == 6 |
| /// let y = addOne(to: 3.5) |
| /// // y = 4.5 |
| /// |
| /// If this type's `Stride` type conforms to `BinaryInteger`, then for a |
| /// value `x`, a distance `n`, and a value `y = x.advanced(by: n)`, |
| /// `x.distance(to: y) == n`. Using this method with types that have a |
| /// noninteger `Stride` may result in an approximation. |
| /// |
| /// - Parameter n: The distance to advance this value. |
| /// - Returns: A value that is offset from this value by `n`. |
| /// |
| /// - Complexity: O(1) |
| func advanced(by n: Stride) -> Self |
| |
| /// `_step` is an implementation detail of Strideable; do not use it directly. |
| static func _step( |
| after current: (index: Int?, value: Self), |
| from start: Self, by distance: Self.Stride |
| ) -> (index: Int?, value: Self) |
| |
| associatedtype _DisabledRangeIndex = Never |
| } |
| |
| extension Strideable { |
| @inlinable |
| public static func < (x: Self, y: Self) -> Bool { |
| return x.distance(to: y) > 0 |
| } |
| |
| @inlinable |
| public static func == (x: Self, y: Self) -> Bool { |
| return x.distance(to: y) == 0 |
| } |
| } |
| |
| //===----------------------------------------------------------------------===// |
| |
| %{ |
| # Strideable used to provide + and - unconditionally. With the updated |
| # collection indexing model of Swift 3 this became unnecessary for integer |
| # types, and was deprecated, as it was a way to write mixed-type arithmetic |
| # expressions, that are otherwise are not allowed. |
| }% |
| % for Base, VersionInfo in [ |
| % ('Strideable where Self : _Pointer', None), |
| % ('Strideable', 'deprecated: 3, obsoleted: 4'), |
| % ]: |
| % Availability = '@available(swift, %s, message: "Please use explicit type conversions or Strideable methods for mixed-type arithmetics.")' % (VersionInfo) if VersionInfo else '' |
| |
| extension ${Base} { |
| @inlinable // FIXME(sil-serialize-all) |
| @_transparent |
| ${Availability} |
| public static func + (lhs: Self, rhs: Self.Stride) -> Self { |
| return lhs.advanced(by: rhs) |
| } |
| |
| @inlinable // FIXME(sil-serialize-all) |
| @_transparent |
| ${Availability} |
| public static func + (lhs: Self.Stride, rhs: Self) -> Self { |
| return rhs.advanced(by: lhs) |
| } |
| |
| @inlinable // FIXME(sil-serialize-all) |
| @_transparent |
| ${Availability} |
| public static func - (lhs: Self, rhs: Self.Stride) -> Self { |
| return lhs.advanced(by: -rhs) |
| } |
| |
| @inlinable // FIXME(sil-serialize-all) |
| @_transparent |
| ${Availability} |
| public static func - (lhs: Self, rhs: Self) -> Self.Stride { |
| return rhs.distance(to: lhs) |
| } |
| |
| @inlinable // FIXME(sil-serialize-all) |
| @_transparent |
| ${Availability} |
| public static func += (lhs: inout Self, rhs: Self.Stride) { |
| lhs = lhs.advanced(by: rhs) |
| } |
| |
| @inlinable // FIXME(sil-serialize-all) |
| @_transparent |
| ${Availability} |
| public static func -= (lhs: inout Self, rhs: Self.Stride) { |
| lhs = lhs.advanced(by: -rhs) |
| } |
| } |
| |
| % end |
| |
| //===----------------------------------------------------------------------===// |
| |
| extension Strideable { |
| @inlinable |
| public static func _step( |
| after current: (index: Int?, value: Self), |
| from start: Self, by distance: Self.Stride |
| ) -> (index: Int?, value: Self) { |
| return (nil, current.value.advanced(by: distance)) |
| } |
| } |
| |
| extension Strideable where Stride : FloatingPoint { |
| @inlinable |
| public static func _step( |
| after current: (index: Int?, value: Self), |
| from start: Self, by distance: Self.Stride |
| ) -> (index: Int?, value: Self) { |
| if let i = current.index { |
| // When Stride is a floating-point type, we should avoid accumulating |
| // rounding error from repeated addition. |
| return (i + 1, start.advanced(by: Stride(i + 1) * distance)) |
| } |
| return (nil, current.value.advanced(by: distance)) |
| } |
| } |
| |
| extension Strideable where Self : FloatingPoint, Self == Stride { |
| @inlinable |
| public static func _step( |
| after current: (index: Int?, value: Self), |
| from start: Self, by distance: Self.Stride |
| ) -> (index: Int?, value: Self) { |
| if let i = current.index { |
| // When both Self and Stride are the same floating-point type, we should |
| // take advantage of fused multiply-add (where supported) to eliminate |
| // intermediate rounding error. |
| return (i + 1, start.addingProduct(Stride(i + 1), distance)) |
| } |
| return (nil, current.value.advanced(by: distance)) |
| } |
| } |
| |
| /// An iterator for a `StrideTo` instance. |
| @_fixed_layout |
| public struct StrideToIterator<Element : Strideable> { |
| @usableFromInline |
| internal let _start: Element |
| |
| @usableFromInline |
| internal let _end: Element |
| |
| @usableFromInline |
| internal let _stride: Element.Stride |
| |
| @usableFromInline |
| internal var _current: (index: Int?, value: Element) |
| |
| @inlinable |
| internal init(_start: Element, end: Element, stride: Element.Stride) { |
| self._start = _start |
| _end = end |
| _stride = stride |
| _current = (0, _start) |
| } |
| } |
| |
| extension StrideToIterator: IteratorProtocol { |
| /// Advances to the next element and returns it, or `nil` if no next element |
| /// exists. |
| /// |
| /// Once `nil` has been returned, all subsequent calls return `nil`. |
| @inlinable |
| public mutating func next() -> Element? { |
| let result = _current.value |
| if _stride > 0 ? result >= _end : result <= _end { |
| return nil |
| } |
| _current = Element._step(after: _current, from: _start, by: _stride) |
| return result |
| } |
| } |
| |
| // FIXME: should really be a Collection, as it is multipass |
| /// A sequence of values formed by striding over a half-open interval. |
| /// |
| /// Use the `stride(from:to:by:)` function to create `StrideTo` instances. |
| @_fixed_layout |
| public struct StrideTo<Element : Strideable> { |
| @usableFromInline |
| internal let _start: Element |
| |
| @usableFromInline |
| internal let _end: Element |
| |
| @usableFromInline |
| internal let _stride: Element.Stride |
| |
| @inlinable |
| internal init(_start: Element, end: Element, stride: Element.Stride) { |
| _precondition(stride != 0, "Stride size must not be zero") |
| // At start, striding away from end is allowed; it just makes for an |
| // already-empty Sequence. |
| self._start = _start |
| self._end = end |
| self._stride = stride |
| } |
| } |
| |
| extension StrideTo: Sequence { |
| /// Returns an iterator over the elements of this sequence. |
| /// |
| /// - Complexity: O(1). |
| @inlinable |
| public func makeIterator() -> StrideToIterator<Element> { |
| return StrideToIterator(_start: _start, end: _end, stride: _stride) |
| } |
| |
| // FIXME(conditional-conformances): this is O(N) instead of O(1), leaving it |
| // here until a proper Collection conformance is possible |
| @inlinable |
| public var underestimatedCount: Int { |
| var it = self.makeIterator() |
| var count = 0 |
| while it.next() != nil { |
| count += 1 |
| } |
| return count |
| } |
| |
| @inlinable |
| public func _preprocessingPass<R>( |
| _ preprocess: () throws -> R |
| ) rethrows -> R? { |
| return try preprocess() |
| } |
| |
| @inlinable |
| public func _customContainsEquatableElement( |
| _ element: Element |
| ) -> Bool? { |
| if element < _start || _end <= element { |
| return false |
| } |
| return nil |
| } |
| } |
| |
| extension StrideTo: CustomReflectable { |
| @inlinable // FIXME(sil-serialize-all) |
| public var customMirror: Mirror { |
| return Mirror(self, children: ["from": _start, "to": _end, "by": _stride]) |
| } |
| } |
| |
| // FIXME(conditional-conformances): This does not yet compile (SR-6474). |
| #if false |
| extension StrideTo : RandomAccessCollection |
| where Element.Stride : BinaryInteger { |
| public typealias Index = Int |
| public typealias SubSequence = Slice<StrideTo<Element>> |
| public typealias Indices = Range<Int> |
| |
| @inlinable |
| public var startIndex: Index { return 0 } |
| |
| @inlinable |
| public var endIndex: Index { return count } |
| |
| @inlinable |
| public var count: Int { |
| let distance = _start.distance(to: _end) |
| guard distance != 0 && (distance < 0) == (_stride < 0) else { return 0 } |
| return Int((distance - 1) / _stride) + 1 |
| } |
| |
| public subscript(position: Index) -> Element { |
| _failEarlyRangeCheck(position, bounds: startIndex..<endIndex) |
| return _start.advanced(by: Element.Stride(position) * _stride) |
| } |
| |
| public subscript(bounds: Range<Index>) -> Slice<StrideTo<Element>> { |
| _failEarlyRangeCheck(bounds, bounds: startIndex ..< endIndex) |
| return Slice(base: self, bounds: bounds) |
| } |
| |
| @inlinable |
| public func index(before i: Index) -> Index { |
| _failEarlyRangeCheck(i, bounds: startIndex + 1...endIndex) |
| return i - 1 |
| } |
| |
| @inlinable |
| public func index(after i: Index) -> Index { |
| _failEarlyRangeCheck(i, bounds: startIndex - 1..<endIndex) |
| return i + 1 |
| } |
| } |
| #endif |
| |
| /// Returns a sequence from a starting value to, but not including, an end |
| /// value, stepping by the specified amount. |
| /// |
| /// You can use this function to stride over values of any type that conforms |
| /// to the `Strideable` protocol, such as integers or floating-point types. |
| /// Starting with `start`, each successive value of the sequence adds `stride` |
| /// until the next value would be equal to or beyond `end`. |
| /// |
| /// for radians in stride(from: 0.0, to: .pi * 2, by: .pi / 2) { |
| /// let degrees = Int(radians * 180 / .pi) |
| /// print("Degrees: \(degrees), radians: \(radians)") |
| /// } |
| /// // Degrees: 0, radians: 0.0 |
| /// // Degrees: 90, radians: 1.5707963267949 |
| /// // Degrees: 180, radians: 3.14159265358979 |
| /// // Degrees: 270, radians: 4.71238898038469 |
| /// |
| /// You can use `stride(from:to:by:)` to create a sequence that strides upward |
| /// or downward. Pass a negative value as `stride` to create a sequence from a |
| /// higher start to a lower end: |
| /// |
| /// for countdown in stride(from: 3, to: 0, by: -1) { |
| /// print("\(countdown)...") |
| /// } |
| /// // 3... |
| /// // 2... |
| /// // 1... |
| /// |
| /// If you pass a value as `stride` that moves away from `end`, the sequence |
| /// contains no values. |
| /// |
| /// for x in stride(from: 0, to: 10, by: -1) { |
| /// print(x) |
| /// } |
| /// // Nothing is printed. |
| /// |
| /// - Parameters: |
| /// - start: The starting value to use for the sequence. If the sequence |
| /// contains any values, the first one is `start`. |
| /// - end: An end value to limit the sequence. `end` is never an element of |
| /// the resulting sequence. |
| /// - stride: The amount to step by with each iteration. A positive `stride` |
| /// iterates upward; a negative `stride` iterates downward. |
| /// - Returns: A sequence from `start` toward, but not including, `end`. Each |
| /// value in the sequence steps by `stride`. |
| @inlinable |
| public func stride<T>( |
| from start: T, to end: T, by stride: T.Stride |
| ) -> StrideTo<T> { |
| return StrideTo(_start: start, end: end, stride: stride) |
| } |
| |
| /// An iterator for a `StrideThrough` instance. |
| @_fixed_layout |
| public struct StrideThroughIterator<Element : Strideable> { |
| @usableFromInline |
| internal let _start: Element |
| |
| @usableFromInline |
| internal let _end: Element |
| |
| @usableFromInline |
| internal let _stride: Element.Stride |
| |
| @usableFromInline |
| internal var _current: (index: Int?, value: Element) |
| |
| @usableFromInline |
| internal var _didReturnEnd: Bool = false |
| |
| @inlinable |
| internal init(_start: Element, end: Element, stride: Element.Stride) { |
| self._start = _start |
| _end = end |
| _stride = stride |
| _current = (0, _start) |
| } |
| } |
| |
| extension StrideThroughIterator: IteratorProtocol { |
| /// Advances to the next element and returns it, or `nil` if no next element |
| /// exists. |
| /// |
| /// Once `nil` has been returned, all subsequent calls return `nil`. |
| @inlinable |
| public mutating func next() -> Element? { |
| let result = _current.value |
| if _stride > 0 ? result >= _end : result <= _end { |
| // This check is needed because if we just changed the above operators |
| // to > and <, respectively, we might advance current past the end |
| // and throw it out of bounds (e.g. above Int.max) unnecessarily. |
| if result == _end && !_didReturnEnd { |
| _didReturnEnd = true |
| return result |
| } |
| return nil |
| } |
| _current = Element._step(after: _current, from: _start, by: _stride) |
| return result |
| } |
| } |
| |
| // FIXME: should really be a Collection, as it is multipass |
| /// A sequence of values formed by striding over a closed interval. |
| /// |
| /// Use the `stride(from:through:by:)` function to create `StrideThrough` |
| /// instances. |
| @_fixed_layout |
| public struct StrideThrough<Element: Strideable> { |
| @usableFromInline |
| internal let _start: Element |
| @usableFromInline |
| internal let _end: Element |
| @usableFromInline |
| internal let _stride: Element.Stride |
| |
| @inlinable |
| internal init(_start: Element, end: Element, stride: Element.Stride) { |
| _precondition(stride != 0, "Stride size must not be zero") |
| self._start = _start |
| self._end = end |
| self._stride = stride |
| } |
| } |
| |
| extension StrideThrough: Sequence { |
| /// Returns an iterator over the elements of this sequence. |
| /// |
| /// - Complexity: O(1). |
| @inlinable |
| public func makeIterator() -> StrideThroughIterator<Element> { |
| return StrideThroughIterator(_start: _start, end: _end, stride: _stride) |
| } |
| |
| // FIXME(conditional-conformances): this is O(N) instead of O(1), leaving it |
| // here until a proper Collection conformance is possible |
| @inlinable |
| public var underestimatedCount: Int { |
| var it = self.makeIterator() |
| var count = 0 |
| while it.next() != nil { |
| count += 1 |
| } |
| return count |
| } |
| |
| @inlinable |
| public func _preprocessingPass<R>( |
| _ preprocess: () throws -> R |
| ) rethrows -> R? { |
| return try preprocess() |
| } |
| |
| @inlinable |
| public func _customContainsEquatableElement( |
| _ element: Element |
| ) -> Bool? { |
| if element < _start || _end < element { |
| return false |
| } |
| return nil |
| } |
| } |
| |
| extension StrideThrough: CustomReflectable { |
| @inlinable // FIXME(sil-serialize-all) |
| public var customMirror: Mirror { |
| return Mirror(self, |
| children: ["from": _start, "through": _end, "by": _stride]) |
| } |
| } |
| |
| // FIXME(conditional-conformances): This does not yet compile (SR-6474). |
| #if false |
| extension StrideThrough : RandomAccessCollection |
| where Element.Stride : BinaryInteger { |
| public typealias Index = ClosedRangeIndex<Int> |
| public typealias SubSequence = Slice<StrideThrough<Element>> |
| |
| @inlinable |
| public var startIndex: Index { |
| let distance = _start.distance(to: _end) |
| return distance == 0 || (distance < 0) == (_stride < 0) |
| ? ClosedRangeIndex(0) |
| : ClosedRangeIndex() |
| } |
| |
| @inlinable |
| public var endIndex: Index { return ClosedRangeIndex() } |
| |
| @inlinable |
| public var count: Int { |
| let distance = _start.distance(to: _end) |
| guard distance != 0 else { return 1 } |
| guard (distance < 0) == (_stride < 0) else { return 0 } |
| return Int(distance / _stride) + 1 |
| } |
| |
| public subscript(position: Index) -> Element { |
| let offset = Element.Stride(position._dereferenced) * _stride |
| return _start.advanced(by: offset) |
| } |
| |
| public subscript(bounds: Range<Index>) -> Slice<StrideThrough<Element>> { |
| return Slice(base: self, bounds: bounds) |
| } |
| |
| @inlinable |
| public func index(before i: Index) -> Index { |
| switch i._value { |
| case .inRange(let n): |
| _precondition(n > 0, "Incrementing past start index") |
| return ClosedRangeIndex(n - 1) |
| case .pastEnd: |
| _precondition(_end >= _start, "Incrementing past start index") |
| return ClosedRangeIndex(count - 1) |
| } |
| } |
| |
| @inlinable |
| public func index(after i: Index) -> Index { |
| switch i._value { |
| case .inRange(let n): |
| return n == (count - 1) |
| ? ClosedRangeIndex() |
| : ClosedRangeIndex(n + 1) |
| case .pastEnd: |
| _preconditionFailure("Incrementing past end index") |
| } |
| } |
| } |
| #endif |
| |
| /// Returns a sequence from a starting value toward, and possibly including, an end |
| /// value, stepping by the specified amount. |
| /// |
| /// You can use this function to stride over values of any type that conforms |
| /// to the `Strideable` protocol, such as integers or floating-point types. |
| /// Starting with `start`, each successive value of the sequence adds `stride` |
| /// until the next value would be beyond `end`. |
| /// |
| /// for radians in stride(from: 0.0, through: .pi * 2, by: .pi / 2) { |
| /// let degrees = Int(radians * 180 / .pi) |
| /// print("Degrees: \(degrees), radians: \(radians)") |
| /// } |
| /// // Degrees: 0, radians: 0.0 |
| /// // Degrees: 90, radians: 1.5707963267949 |
| /// // Degrees: 180, radians: 3.14159265358979 |
| /// // Degrees: 270, radians: 4.71238898038469 |
| /// // Degrees: 360, radians: 6.28318530717959 |
| /// |
| /// You can use `stride(from:through:by:)` to create a sequence that strides |
| /// upward or downward. Pass a negative value as `stride` to create a sequence |
| /// from a higher start to a lower end: |
| /// |
| /// for countdown in stride(from: 3, through: 1, by: -1) { |
| /// print("\(countdown)...") |
| /// } |
| /// // 3... |
| /// // 2... |
| /// // 1... |
| /// |
| /// The value you pass as `end` is not guaranteed to be included in the |
| /// sequence. If stepping from `start` by `stride` does not produce `end`, |
| /// the last value in the sequence will be one step before going beyond `end`. |
| /// |
| /// for multipleOfThree in stride(from: 3, through: 10, by: 3) { |
| /// print(multipleOfThree) |
| /// } |
| /// // 3 |
| /// // 6 |
| /// // 9 |
| /// |
| /// If you pass a value as `stride` that moves away from `end`, the sequence |
| /// contains no values. |
| /// |
| /// for x in stride(from: 0, through: 10, by: -1) { |
| /// print(x) |
| /// } |
| /// // Nothing is printed. |
| /// |
| /// - Parameters: |
| /// - start: The starting value to use for the sequence. If the sequence |
| /// contains any values, the first one is `start`. |
| /// - end: An end value to limit the sequence. `end` is an element of |
| /// the resulting sequence if and only if it can be produced from `start` |
| /// using steps of `stride`. |
| /// - stride: The amount to step by with each iteration. A positive `stride` |
| /// iterates upward; a negative `stride` iterates downward. |
| /// - Returns: A sequence from `start` toward, and possibly including, `end`. |
| /// Each value in the sequence is separated by `stride`. |
| @inlinable |
| public func stride<T>( |
| from start: T, through end: T, by stride: T.Stride |
| ) -> StrideThrough<T> { |
| return StrideThrough(_start: start, end: end, stride: stride) |
| } |