# DiscreteFormatStyle A format style that transforms a continuous input into a discrete output and provides information about its discretization boundaries. ``` protocol DiscreteFormatStyle : FormatStyle ``` ## Overview Use this protocol to keep displays up to date if input changes continuously, or to iterate over all possible outputs of a [`FormatStyle`](/documentation/Foundation/FormatStyle) by obtaining the next discrete input in either direction from [`discreteInput(before:)`](/documentation/Foundation/DiscreteFormatStyle/discreteInput(before:)) or [`discreteInput(after:)`](/documentation/Foundation/DiscreteFormatStyle/discreteInput(after:)). ## Ordering of Inputs The ordering over [`FormatInput`](/documentation/Foundation/FormatStyle/FormatInput) defined by [`discreteInput(before:)`](/documentation/Foundation/DiscreteFormatStyle/discreteInput(before:)) / [`discreteInput(after:)`](/documentation/Foundation/DiscreteFormatStyle/discreteInput(after:)) must be consistent between the two functions. If [`FormatInput`](/documentation/Foundation/FormatStyle/FormatInput) conforms to the `Comparable` protocol, the format style’s ordering *should* be consistent with the canonical ordering defined via the `Comparable` conformance, i.e. it should hold that `discreteInput(before: x)! < x < discreteInput(after: x)!` where discrete inputs are not nil. ## Stepping through Discrete Input/Output Pairs One use case of this protocol is enumerating all discrete inputs of a format style and their respective outputs. While the [`discreteInput(before:)`](/documentation/Foundation/DiscreteFormatStyle/discreteInput(before:)) and [`discreteInput(after:)`](/documentation/Foundation/DiscreteFormatStyle/discreteInput(after:)) functions are the right tool for that, they do not give a guarantee that their respective return values actually produce an output that is different from the output produced by formatting the `input` value used when calling [`discreteInput(before:)`](/documentation/Foundation/DiscreteFormatStyle/discreteInput(before:)) / [`discreteInput(after:)`](/documentation/Foundation/DiscreteFormatStyle/discreteInput(after:)), they only provide a value that produces a different output for *most* inputs. E.g. when formatting a floating point value as an integer, we can get the next discrete input after `x` by calculating `floor(x + 1)`. However, when rounding toward zero, the whole interval (-1;1) formats as zero. It would be ok for a discrete format style to ignore that edge case and return `0` for the [`discreteInput(after:)`](/documentation/Foundation/DiscreteFormatStyle/discreteInput(after:)) a negative value greater than `-1`. Therefore, to enumerate all discrete input/output pairs, adjacent outputs must be deduplicated in order to guarantee no adjacent outputs are the same. The following example produces all discrete input/output pairs for inputs in a given `range` making sure adjacent outputs are unequal: ```swift extension DiscreteFormatStyle where FormatInput : Comparable, FormatOutput : Equatable { func enumerated( in range: ClosedRange ) -> [(input: FormatInput, output: FormatOutput)] { var input = range.lowerBound var output = format(input) var pairs = [(input: FormatInput, output: FormatOutput)]() pairs.append((input, output)) // get the next discretization bound while let nextInput = discreteInput(after: input), // check that it is still in the requested `range` nextInput <= range.upperBound { // get the respective formatted output let nextOutput = format(nextInput) // deduplicate based on the formatted output if nextOutput != output { pairs.append((nextInput, nextOutput)) } input = nextInput output = nextOutput } return pairs } } ``` ## Imperfect Discretization Boundaries In some scenarios, a format style cannot provide precise discretization boundaries in a performant manner. In those cases it must override [`input(before:)`](/documentation/Foundation/DiscreteFormatStyle/input(before:)) and [`input(after:)`](/documentation/Foundation/DiscreteFormatStyle/input(after:)) to reflect that. For any discretization boundary `x` returned by either [`discreteInput(before:)`](/documentation/Foundation/DiscreteFormatStyle/discreteInput(before:)) or [`discreteInput(after:)`](/documentation/Foundation/DiscreteFormatStyle/discreteInput(after:)) based on the original input `y`, all values representable in the [`FormatInput`](/documentation/Foundation/FormatStyle/FormatInput)strictly between `x` and the return value of `input(after: x)` or `input(before: x)`, respectively, are not guaranteed to produce the same formatted output as `y`. The following schematic shows an overview of the guarantees given by the protocol: ``` xB = discreteInput(before: y) y xA = discreteInput(after: y) | | | <-----+---+-------------------------+-------------------------+---+---> | | zB = input(after: xB) zA = input(before: xA) ``` - the formatted output for everything in `zB...zA` (including bounds) is **guaranteed** to be equal to `format(y)` - the formatted output for `xB` and lower is **most likely** different from `format(y)` - the formatted output for `xA` and higher is **most likely** different from `format(y)` - the formatted output between `xB` and `zB`, as well as `zA` and `xA` (excluding bounds) cannot be predicted ## Topics ### Instance Methods [`func discreteInput(after: Self.FormatInput) -> Self.FormatInput?`](/documentation/Foundation/DiscreteFormatStyle/discreteInput(after:)) The next discretization boundary after the given input. [`func discreteInput(before: Self.FormatInput) -> Self.FormatInput?`](/documentation/Foundation/DiscreteFormatStyle/discreteInput(before:)) The next discretization boundary before the given input. [`func input(after: Self.FormatInput) -> Self.FormatInput?`](/documentation/Foundation/DiscreteFormatStyle/input(after:)) The next input value after the given input. [`func input(before: Self.FormatInput) -> Self.FormatInput?`](/documentation/Foundation/DiscreteFormatStyle/input(before:)) The next input value before the given input. ## Relationships ### Conforming Types [`AnchoredRelativeFormatStyle`](/documentation/Foundation/Date/AnchoredRelativeFormatStyle) [`FormatStyle`](/documentation/Foundation/Date/FormatStyle) [`Attributed-swift.struct`](/documentation/Foundation/Date/FormatStyle/Attributed-swift.struct) [`Attributed-swift.struct`](/documentation/Foundation/Date/VerbatimFormatStyle/Attributed-swift.struct) [`VerbatimFormatStyle`](/documentation/Foundation/Date/VerbatimFormatStyle) [`ComponentsFormatStyle`](/documentation/Foundation/Date/ComponentsFormatStyle) ### Inherits From [`FormatStyle`](/documentation/Foundation/FormatStyle) [`Encodable`](/documentation/Swift/Encodable) [`Equatable`](/documentation/Swift/Equatable) [`Decodable`](/documentation/Swift/Decodable) [`Hashable`](/documentation/Swift/Hashable) --- Copyright © 2026 Apple Inc. 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