<html><body style="word-wrap: break-word; -webkit-nbsp-mode: space; -webkit-line-break: after-white-space;" class="">Since we're running short on time, and the previous discussion thread diverged, here's my attempt to fix the Comparable protocol.<div class=""><br class=""></div><div class=""><b class="">Pull request:</b> <a href="https://github.com/apple/swift-evolution/pull/464" class="">https://github.com/apple/swift-evolution/pull/464</a></div><div class=""><div class=""><br class=""></div><div class="">TL;DR:</div><div class=""><br class=""></div><div class="">1. Equatable remains unchanged, while Comparable bloats a bit to support several use cases.</div><div class="">2. `a <=> b` is well-defined even if either value is NaN. Zero is equal to minus zero.</div><div class="">3. Types are not strictly required to become totally ordered, even if it's strongly recommended.</div><div class=""><br class=""></div><div class="">— — —</div><div class=""><br class=""></div><div class="">I simply can't see how a pure total order version of Comparable would fit the standard way floating point values are expected to behave. However, I think we can reach a satisfactory conclusion, one that involves no crashing in the standard library, which is what I previously suggested.</div><div class=""><br class=""></div><div class="">What I'm trying to fix is so that all operations listed in <a href="https://dl.dropboxusercontent.com/u/217402/Comparable.pdf" class="">https://dl.dropboxusercontent.com/u/217402/Comparable.pdf</a> abide to laws for types without incomparable values, and that types with weaker order can still work in <i class="">some</i> well-defined way outside their totally ordered range.<br class=""><div class=""><div class=""><br class=""></div><div class="">PS. Forgive me Robert, Jaden, and Harlan for not syncing with you, for time is tight. I can pull back or revise the proposal if you don't want to be involved.</div></div></div><div class=""><br class=""></div><div class="">— Pyry</div><div class=""><br class=""></div><div class=""><br class=""></div><div class=""><br class=""></div><div class=""><br class=""></div><div class=""><h1 style="box-sizing: border-box; margin-right: 0px; margin-bottom: 16px; margin-left: 0px; line-height: 1.25; padding-bottom: 0.3em; border-bottom-width: 1px; border-bottom-style: solid; border-bottom-color: rgb(238, 238, 238); color: rgb(51, 51, 51); font-family: -apple-system, BlinkMacSystemFont, 'Segoe UI', Roboto, Helvetica, Arial, sans-serif, 'Apple Color Emoji', 'Segoe UI Emoji', 'Segoe UI Symbol'; background-color: rgb(255, 255, 255); margin-top: 0px !important;" class="">Formalized Ordering</h1><ul style="box-sizing: border-box; padding-left: 2em; margin-top: 0px; margin-bottom: 16px; color: rgb(51, 51, 51); font-family: -apple-system, BlinkMacSystemFont, 'Segoe UI', Roboto, Helvetica, Arial, sans-serif, 'Apple Color Emoji', 'Segoe UI Emoji', 'Segoe UI Symbol'; font-size: 16px; background-color: rgb(255, 255, 255);" class=""><li style="box-sizing: border-box;" class="">Proposal: <a href="https://github.com/pyrtsa/swift-evolution/blob/ca89e7b3a1dffc99baa695a03544fcba75afd0f3/proposals/NNNN-filename.md" style="box-sizing: border-box; background-color: transparent; -webkit-text-decoration-skip: objects; color: rgb(64, 120, 192); text-decoration: none;" class="">SE-NNNN</a></li><li style="box-sizing: border-box; margin-top: 0.25em;" class="">Authors: <a href="https://github.com/codafi" style="box-sizing: border-box; background-color: transparent; -webkit-text-decoration-skip: objects; color: rgb(64, 120, 192); text-decoration: none;" class="">Robert Widmann</a>, <a href="https://github.com/jadengeller" style="box-sizing: border-box; background-color: transparent; -webkit-text-decoration-skip: objects; color: rgb(64, 120, 192); text-decoration: none;" class="">Jaden Geller</a>, <a href="https://github.com/harlanhaskins" style="box-sizing: border-box; background-color: transparent; -webkit-text-decoration-skip: objects; color: rgb(64, 120, 192); text-decoration: none;" class="">Harlan Haskins</a>, <a href="https://github.com/pyrtsa" style="box-sizing: border-box; background-color: transparent; -webkit-text-decoration-skip: objects; color: rgb(64, 120, 192); text-decoration: none;" class="">Pyry Jahkola</a></li><li style="box-sizing: border-box; margin-top: 0.25em;" class="">Status: <span style="box-sizing: border-box; font-weight: 600;" class="">Awaiting review</span></li><li style="box-sizing: border-box; margin-top: 0.25em;" class="">Review manager: TBD</li></ul><h2 style="box-sizing: border-box; margin-top: 24px; margin-bottom: 16px; line-height: 1.25; padding-bottom: 0.3em; border-bottom-width: 1px; border-bottom-style: solid; border-bottom-color: rgb(238, 238, 238); color: rgb(51, 51, 51); font-family: -apple-system, BlinkMacSystemFont, 'Segoe UI', Roboto, Helvetica, Arial, sans-serif, 'Apple Color Emoji', 'Segoe UI Emoji', 'Segoe UI Symbol'; background-color: rgb(255, 255, 255);" class=""><a id="user-content-introduction" class="anchor" href="https://github.com/pyrtsa/swift-evolution/blob/ca89e7b3a1dffc99baa695a03544fcba75afd0f3/proposals/NNNN-formalized-ordering.md#introduction" aria-hidden="true" style="box-sizing: border-box; background-color: transparent; -webkit-text-decoration-skip: objects; color: rgb(64, 120, 192); text-decoration: none; float: left; padding-right: 4px; margin-left: -20px; line-height: 1;"><svg aria-hidden="true" class="octicon octicon-link" height="16" version="1.1" viewBox="0 0 16 16" width="16"><path d="M4 9h1v1H4c-1.5 0-3-1.69-3-3.5S2.55 3 4 3h4c1.45 0 3 1.69 3 3.5 0 1.41-.91 2.72-2 3.25V8.59c.58-.45 1-1.27 1-2.09C10 5.22 8.98 4 8 4H4c-.98 0-2 1.22-2 2.5S3 9 4 9zm9-3h-1v1h1c1 0 2 1.22 2 2.5S13.98 12 13 12H9c-.98 0-2-1.22-2-2.5 0-.83.42-1.64 1-2.09V6.25c-1.09.53-2 1.84-2 3.25C6 11.31 7.55 13 9 13h4c1.45 0 3-1.69 3-3.5S14.5 6 13 6z"></path></svg></a>Introduction</h2><p style="box-sizing: border-box; margin-top: 0px; margin-bottom: 16px; color: rgb(51, 51, 51); font-family: -apple-system, BlinkMacSystemFont, 'Segoe UI', Roboto, Helvetica, Arial, sans-serif, 'Apple Color Emoji', 'Segoe UI Emoji', 'Segoe UI Symbol'; font-size: 16px; background-color: rgb(255, 255, 255);" class="">This proposal cleans up the semantics of ordering relations in the standard library. Our goal is to formalize the total ordering semantics of the <code style="box-sizing: border-box; font-family: Consolas, 'Liberation Mono', Menlo, Courier, monospace; font-size: 14px; padding: 0.2em 0px; margin: 0px; background-color: rgba(0, 0, 0, 0.0392157); border-top-left-radius: 3px; border-top-right-radius: 3px; border-bottom-right-radius: 3px; border-bottom-left-radius: 3px;" class="">Comparable</code> protocol and still provide accessible ordering definitions for types without total ordering semantics.</p><h2 style="box-sizing: border-box; margin-top: 24px; margin-bottom: 16px; line-height: 1.25; padding-bottom: 0.3em; border-bottom-width: 1px; border-bottom-style: solid; border-bottom-color: rgb(238, 238, 238); color: rgb(51, 51, 51); font-family: -apple-system, BlinkMacSystemFont, 'Segoe UI', Roboto, Helvetica, Arial, sans-serif, 'Apple Color Emoji', 'Segoe UI Emoji', 'Segoe UI Symbol'; background-color: rgb(255, 255, 255);" class=""><a id="user-content-motivation" class="anchor" href="https://github.com/pyrtsa/swift-evolution/blob/ca89e7b3a1dffc99baa695a03544fcba75afd0f3/proposals/NNNN-formalized-ordering.md#motivation" aria-hidden="true" style="box-sizing: border-box; background-color: transparent; -webkit-text-decoration-skip: objects; color: rgb(64, 120, 192); text-decoration: none; float: left; padding-right: 4px; margin-left: -20px; line-height: 1;"><svg aria-hidden="true" class="octicon octicon-link" height="16" version="1.1" viewBox="0 0 16 16" width="16"><path d="M4 9h1v1H4c-1.5 0-3-1.69-3-3.5S2.55 3 4 3h4c1.45 0 3 1.69 3 3.5 0 1.41-.91 2.72-2 3.25V8.59c.58-.45 1-1.27 1-2.09C10 5.22 8.98 4 8 4H4c-.98 0-2 1.22-2 2.5S3 9 4 9zm9-3h-1v1h1c1 0 2 1.22 2 2.5S13.98 12 13 12H9c-.98 0-2-1.22-2-2.5 0-.83.42-1.64 1-2.09V6.25c-1.09.53-2 1.84-2 3.25C6 11.31 7.55 13 9 13h4c1.45 0 3-1.69 3-3.5S14.5 6 13 6z"></path></svg></a>Motivation</h2><p style="box-sizing: border-box; margin-top: 0px; margin-bottom: 16px; color: rgb(51, 51, 51); font-family: -apple-system, BlinkMacSystemFont, 'Segoe UI', Roboto, Helvetica, Arial, sans-serif, 'Apple Color Emoji', 'Segoe UI Emoji', 'Segoe UI Symbol'; font-size: 16px; background-color: rgb(255, 255, 255);" class="">The standard comparison operators have an intuitive meaning to programmers. Swift encourages encoding that in an implementation of <code style="box-sizing: border-box; font-family: Consolas, 'Liberation Mono', Menlo, Courier, monospace; font-size: 14px; padding: 0.2em 0px; margin: 0px; background-color: rgba(0, 0, 0, 0.0392157); border-top-left-radius: 3px; border-top-right-radius: 3px; border-bottom-right-radius: 3px; border-bottom-left-radius: 3px;" class="">Comparable</code> that respects the rules of a <a href="https://en.wikipedia.org/wiki/Total_order" style="box-sizing: border-box; background-color: transparent; -webkit-text-decoration-skip: objects; color: rgb(64, 120, 192); text-decoration: none;" class="">total order</a>. The standard library takes advantage of these rules to provide consistent implementations for sorting and searching generic collections of <code style="box-sizing: border-box; font-family: Consolas, 'Liberation Mono', Menlo, Courier, monospace; font-size: 14px; padding: 0.2em 0px; margin: 0px; background-color: rgba(0, 0, 0, 0.0392157); border-top-left-radius: 3px; border-top-right-radius: 3px; border-bottom-right-radius: 3px; border-bottom-left-radius: 3px;" class="">Comparable</code> types.</p><p style="box-sizing: border-box; margin-top: 0px; margin-bottom: 16px; color: rgb(51, 51, 51); font-family: -apple-system, BlinkMacSystemFont, 'Segoe UI', Roboto, Helvetica, Arial, sans-serif, 'Apple Color Emoji', 'Segoe UI Emoji', 'Segoe UI Symbol'; font-size: 16px; background-color: rgb(255, 255, 255);" class="">Not all types behave so well in this framework, unfortunately. There are cases where the semantics of a total order cannot apply and still maintain the traditional definition of “comparison” over these types. Take, for example, sorting an array of <code style="box-sizing: border-box; font-family: Consolas, 'Liberation Mono', Menlo, Courier, monospace; font-size: 14px; padding: 0.2em 0px; margin: 0px; background-color: rgba(0, 0, 0, 0.0392157); border-top-left-radius: 3px; border-top-right-radius: 3px; border-bottom-right-radius: 3px; border-bottom-left-radius: 3px;" class="">Float</code> s. Today, <code style="box-sizing: border-box; font-family: Consolas, 'Liberation Mono', Menlo, Courier, monospace; font-size: 14px; padding: 0.2em 0px; margin: 0px; background-color: rgba(0, 0, 0, 0.0392157); border-top-left-radius: 3px; border-top-right-radius: 3px; border-bottom-right-radius: 3px; border-bottom-left-radius: 3px;" class="">Float</code> ‘s instance of <code style="box-sizing: border-box; font-family: Consolas, 'Liberation Mono', Menlo, Courier, monospace; font-size: 14px; padding: 0.2em 0px; margin: 0px; background-color: rgba(0, 0, 0, 0.0392157); border-top-left-radius: 3px; border-top-right-radius: 3px; border-bottom-right-radius: 3px; border-bottom-left-radius: 3px;" class="">Comparable</code> follows IEEE-754 and returns <code style="box-sizing: border-box; font-family: Consolas, 'Liberation Mono', Menlo, Courier, monospace; font-size: 14px; padding: 0.2em 0px; margin: 0px; background-color: rgba(0, 0, 0, 0.0392157); border-top-left-radius: 3px; border-top-right-radius: 3px; border-bottom-right-radius: 3px; border-bottom-left-radius: 3px;" class="">false</code> for all comparisons of <code style="box-sizing: border-box; font-family: Consolas, 'Liberation Mono', Menlo, Courier, monospace; font-size: 14px; padding: 0.2em 0px; margin: 0px; background-color: rgba(0, 0, 0, 0.0392157); border-top-left-radius: 3px; border-top-right-radius: 3px; border-bottom-right-radius: 3px; border-bottom-left-radius: 3px;" class="">NaN</code> . In order to sort this array, <code style="box-sizing: border-box; font-family: Consolas, 'Liberation Mono', Menlo, Courier, monospace; font-size: 14px; padding: 0.2em 0px; margin: 0px; background-color: rgba(0, 0, 0, 0.0392157); border-top-left-radius: 3px; border-top-right-radius: 3px; border-bottom-right-radius: 3px; border-bottom-left-radius: 3px;" class="">NaN</code> s are considered outside the domain of <code style="box-sizing: border-box; font-family: Consolas, 'Liberation Mono', Menlo, Courier, monospace; font-size: 14px; padding: 0.2em 0px; margin: 0px; background-color: rgba(0, 0, 0, 0.0392157); border-top-left-radius: 3px; border-top-right-radius: 3px; border-bottom-right-radius: 3px; border-bottom-left-radius: 3px;" class=""><</code> , and the order of a “sorted” array containing them is undefined.</p><p style="box-sizing: border-box; margin-top: 0px; margin-bottom: 16px; color: rgb(51, 51, 51); font-family: -apple-system, BlinkMacSystemFont, 'Segoe UI', Roboto, Helvetica, Arial, sans-serif, 'Apple Color Emoji', 'Segoe UI Emoji', 'Segoe UI Symbol'; font-size: 16px; background-color: rgb(255, 255, 255);" class="">In addition, generic algorithms in the Swift Standard Library that make use of the current <code style="box-sizing: border-box; font-family: Consolas, 'Liberation Mono', Menlo, Courier, monospace; font-size: 14px; padding: 0.2em 0px; margin: 0px; background-color: rgba(0, 0, 0, 0.0392157); border-top-left-radius: 3px; border-top-right-radius: 3px; border-bottom-right-radius: 3px; border-bottom-left-radius: 3px;" class="">Comparable</code> protocol may have to make twice as many comparisons to request the ordering of values with respect to each other than they should. Having a central operation to return information about the ordering of values once should provide a speedup for these operations.</p><p style="box-sizing: border-box; margin-top: 0px; margin-bottom: 16px; color: rgb(51, 51, 51); font-family: -apple-system, BlinkMacSystemFont, 'Segoe UI', Roboto, Helvetica, Arial, sans-serif, 'Apple Color Emoji', 'Segoe UI Emoji', 'Segoe UI Symbol'; font-size: 16px; background-color: rgb(255, 255, 255);" class="">In the interest of cleaning up the semantics of <code style="box-sizing: border-box; font-family: Consolas, 'Liberation Mono', Menlo, Courier, monospace; font-size: 14px; padding: 0.2em 0px; margin: 0px; background-color: rgba(0, 0, 0, 0.0392157); border-top-left-radius: 3px; border-top-right-radius: 3px; border-bottom-right-radius: 3px; border-bottom-left-radius: 3px;" class="">Comparable</code> types of all shapes and sizes and their uses in the Swift Standard Library, this proposal is going to re-arrange the requirements of the <code style="box-sizing: border-box; font-family: Consolas, 'Liberation Mono', Menlo, Courier, monospace; font-size: 14px; padding: 0.2em 0px; margin: 0px; background-color: rgba(0, 0, 0, 0.0392157); border-top-left-radius: 3px; border-top-right-radius: 3px; border-bottom-right-radius: 3px; border-bottom-left-radius: 3px;" class="">Comparable</code> and <code style="box-sizing: border-box; font-family: Consolas, 'Liberation Mono', Menlo, Courier, monospace; font-size: 14px; padding: 0.2em 0px; margin: 0px; background-color: rgba(0, 0, 0, 0.0392157); border-top-left-radius: 3px; border-top-right-radius: 3px; border-bottom-right-radius: 3px; border-bottom-left-radius: 3px;" class="">Equatable</code> protocols.</p><h2 style="box-sizing: border-box; margin-top: 24px; margin-bottom: 16px; line-height: 1.25; padding-bottom: 0.3em; border-bottom-width: 1px; border-bottom-style: solid; border-bottom-color: rgb(238, 238, 238); color: rgb(51, 51, 51); font-family: -apple-system, BlinkMacSystemFont, 'Segoe UI', Roboto, Helvetica, Arial, sans-serif, 'Apple Color Emoji', 'Segoe UI Emoji', 'Segoe UI Symbol'; background-color: rgb(255, 255, 255);" class=""><a id="user-content-proposed-solution" class="anchor" href="https://github.com/pyrtsa/swift-evolution/blob/ca89e7b3a1dffc99baa695a03544fcba75afd0f3/proposals/NNNN-formalized-ordering.md#proposed-solution" aria-hidden="true" style="box-sizing: border-box; background-color: transparent; -webkit-text-decoration-skip: objects; color: rgb(64, 120, 192); text-decoration: none; float: left; padding-right: 4px; margin-left: -20px; line-height: 1;"><svg aria-hidden="true" class="octicon octicon-link" height="16" version="1.1" viewBox="0 0 16 16" width="16"><path d="M4 9h1v1H4c-1.5 0-3-1.69-3-3.5S2.55 3 4 3h4c1.45 0 3 1.69 3 3.5 0 1.41-.91 2.72-2 3.25V8.59c.58-.45 1-1.27 1-2.09C10 5.22 8.98 4 8 4H4c-.98 0-2 1.22-2 2.5S3 9 4 9zm9-3h-1v1h1c1 0 2 1.22 2 2.5S13.98 12 13 12H9c-.98 0-2-1.22-2-2.5 0-.83.42-1.64 1-2.09V6.25c-1.09.53-2 1.84-2 3.25C6 11.31 7.55 13 9 13h4c1.45 0 3-1.69 3-3.5S14.5 6 13 6z"></path></svg></a>Proposed solution</h2><h3 style="box-sizing: border-box; margin-top: 24px; margin-bottom: 16px; font-size: 1.25em; line-height: 1.25; color: rgb(51, 51, 51); font-family: -apple-system, BlinkMacSystemFont, 'Segoe UI', Roboto, Helvetica, Arial, sans-serif, 'Apple Color Emoji', 'Segoe UI Emoji', 'Segoe UI Symbol'; background-color: rgb(255, 255, 255);" class=""><a id="user-content-equatable" class="anchor" href="https://github.com/pyrtsa/swift-evolution/blob/ca89e7b3a1dffc99baa695a03544fcba75afd0f3/proposals/NNNN-formalized-ordering.md#equatable" aria-hidden="true" style="box-sizing: border-box; background-color: transparent; -webkit-text-decoration-skip: objects; color: rgb(64, 120, 192); text-decoration: none; float: left; padding-right: 4px; margin-left: -20px; line-height: 1;"><svg aria-hidden="true" class="octicon octicon-link" height="16" version="1.1" viewBox="0 0 16 16" width="16"><path d="M4 9h1v1H4c-1.5 0-3-1.69-3-3.5S2.55 3 4 3h4c1.45 0 3 1.69 3 3.5 0 1.41-.91 2.72-2 3.25V8.59c.58-.45 1-1.27 1-2.09C10 5.22 8.98 4 8 4H4c-.98 0-2 1.22-2 2.5S3 9 4 9zm9-3h-1v1h1c1 0 2 1.22 2 2.5S13.98 12 13 12H9c-.98 0-2-1.22-2-2.5 0-.83.42-1.64 1-2.09V6.25c-1.09.53-2 1.84-2 3.25C6 11.31 7.55 13 9 13h4c1.45 0 3-1.69 3-3.5S14.5 6 13 6z"></path></svg></a>Equatable</h3><p style="box-sizing: border-box; margin-top: 0px; margin-bottom: 16px; color: rgb(51, 51, 51); font-family: -apple-system, BlinkMacSystemFont, 'Segoe UI', Roboto, Helvetica, Arial, sans-serif, 'Apple Color Emoji', 'Segoe UI Emoji', 'Segoe UI Symbol'; font-size: 16px; background-color: rgb(255, 255, 255);" class="">The interface of <code style="box-sizing: border-box; font-family: Consolas, 'Liberation Mono', Menlo, Courier, monospace; font-size: 14px; padding: 0.2em 0px; margin: 0px; background-color: rgba(0, 0, 0, 0.0392157); border-top-left-radius: 3px; border-top-right-radius: 3px; border-bottom-right-radius: 3px; border-bottom-left-radius: 3px;" class="">Equatable</code> remains unchanged under this proposal. Equatable types should still respect the equivalence laws of <em style="box-sizing: border-box;" class="">reflexivity</em> (<code style="box-sizing: border-box; font-family: Consolas, 'Liberation Mono', Menlo, Courier, monospace; font-size: 14px; padding: 0.2em 0px; margin: 0px; background-color: rgba(0, 0, 0, 0.0392157); border-top-left-radius: 3px; border-top-right-radius: 3px; border-bottom-right-radius: 3px; border-bottom-left-radius: 3px;" class="">a == a</code>), <em style="box-sizing: border-box;" class="">symmetry</em> (<code style="box-sizing: border-box; font-family: Consolas, 'Liberation Mono', Menlo, Courier, monospace; font-size: 14px; padding: 0.2em 0px; margin: 0px; background-color: rgba(0, 0, 0, 0.0392157); border-top-left-radius: 3px; border-top-right-radius: 3px; border-bottom-right-radius: 3px; border-bottom-left-radius: 3px;" class="">a == b</code> iff <code style="box-sizing: border-box; font-family: Consolas, 'Liberation Mono', Menlo, Courier, monospace; font-size: 14px; padding: 0.2em 0px; margin: 0px; background-color: rgba(0, 0, 0, 0.0392157); border-top-left-radius: 3px; border-top-right-radius: 3px; border-bottom-right-radius: 3px; border-bottom-left-radius: 3px;" class="">b == a</code>), and <em style="box-sizing: border-box;" class="">transitivity</em> (if <code style="box-sizing: border-box; font-family: Consolas, 'Liberation Mono', Menlo, Courier, monospace; font-size: 14px; padding: 0.2em 0px; margin: 0px; background-color: rgba(0, 0, 0, 0.0392157); border-top-left-radius: 3px; border-top-right-radius: 3px; border-bottom-right-radius: 3px; border-bottom-left-radius: 3px;" class="">a == b</code> and <code style="box-sizing: border-box; font-family: Consolas, 'Liberation Mono', Menlo, Courier, monospace; font-size: 14px; padding: 0.2em 0px; margin: 0px; background-color: rgba(0, 0, 0, 0.0392157); border-top-left-radius: 3px; border-top-right-radius: 3px; border-bottom-right-radius: 3px; border-bottom-left-radius: 3px;" class="">b == c</code>, then <code style="box-sizing: border-box; font-family: Consolas, 'Liberation Mono', Menlo, Courier, monospace; font-size: 14px; padding: 0.2em 0px; margin: 0px; background-color: rgba(0, 0, 0, 0.0392157); border-top-left-radius: 3px; border-top-right-radius: 3px; border-bottom-right-radius: 3px; border-bottom-left-radius: 3px;" class="">a == c</code>). Further, <code style="box-sizing: border-box; font-family: Consolas, 'Liberation Mono', Menlo, Courier, monospace; font-size: 14px; padding: 0.2em 0px; margin: 0px; background-color: rgba(0, 0, 0, 0.0392157); border-top-left-radius: 3px; border-top-right-radius: 3px; border-bottom-right-radius: 3px; border-bottom-left-radius: 3px;" class="">!=</code> remains a top-level binary operator for which <code style="box-sizing: border-box; font-family: Consolas, 'Liberation Mono', Menlo, Courier, monospace; font-size: 14px; padding: 0.2em 0px; margin: 0px; background-color: rgba(0, 0, 0, 0.0392157); border-top-left-radius: 3px; border-top-right-radius: 3px; border-bottom-right-radius: 3px; border-bottom-left-radius: 3px;" class="">a != b</code> iff <code style="box-sizing: border-box; font-family: Consolas, 'Liberation Mono', Menlo, Courier, monospace; font-size: 14px; padding: 0.2em 0px; margin: 0px; background-color: rgba(0, 0, 0, 0.0392157); border-top-left-radius: 3px; border-top-right-radius: 3px; border-bottom-right-radius: 3px; border-bottom-left-radius: 3px;" class="">!(a == b)</code>.</p><p style="box-sizing: border-box; margin-top: 0px; margin-bottom: 16px; color: rgb(51, 51, 51); font-family: -apple-system, BlinkMacSystemFont, 'Segoe UI', Roboto, Helvetica, Arial, sans-serif, 'Apple Color Emoji', 'Segoe UI Emoji', 'Segoe UI Symbol'; font-size: 16px; background-color: rgb(255, 255, 255);" class="">Types containing properties <em style="box-sizing: border-box;" class="">inessential to equality</em>, however, are allowed to retain their notion of identity. For example <code style="box-sizing: border-box; font-family: Consolas, 'Liberation Mono', Menlo, Courier, monospace; font-size: 14px; padding: 0.2em 0px; margin: 0px; background-color: rgba(0, 0, 0, 0.0392157); border-top-left-radius: 3px; border-top-right-radius: 3px; border-bottom-right-radius: 3px; border-bottom-left-radius: 3px;" class="">Array</code>'s <code style="box-sizing: border-box; font-family: Consolas, 'Liberation Mono', Menlo, Courier, monospace; font-size: 14px; padding: 0.2em 0px; margin: 0px; background-color: rgba(0, 0, 0, 0.0392157); border-top-left-radius: 3px; border-top-right-radius: 3px; border-bottom-right-radius: 3px; border-bottom-left-radius: 3px;" class="">capacity</code> isn't considered for equality; and <code style="box-sizing: border-box; font-family: Consolas, 'Liberation Mono', Menlo, Courier, monospace; font-size: 14px; padding: 0.2em 0px; margin: 0px; background-color: rgba(0, 0, 0, 0.0392157); border-top-left-radius: 3px; border-top-right-radius: 3px; border-bottom-right-radius: 3px; border-bottom-left-radius: 3px;" class="">-0.0 == 0.0</code> and <code style="box-sizing: border-box; font-family: Consolas, 'Liberation Mono', Menlo, Courier, monospace; font-size: 14px; padding: 0.2em 0px; margin: 0px; background-color: rgba(0, 0, 0, 0.0392157); border-top-left-radius: 3px; border-top-right-radius: 3px; border-bottom-right-radius: 3px; border-bottom-left-radius: 3px;" class="">"ä" == "a\u{308}"</code>, while <code style="box-sizing: border-box; font-family: Consolas, 'Liberation Mono', Menlo, Courier, monospace; font-size: 14px; padding: 0.2em 0px; margin: 0px; background-color: rgba(0, 0, 0, 0.0392157); border-top-left-radius: 3px; border-top-right-radius: 3px; border-bottom-right-radius: 3px; border-bottom-left-radius: 3px;" class="">(-0.0).sign != (0.0).sign</code> and <code style="box-sizing: border-box; font-family: Consolas, 'Liberation Mono', Menlo, Courier, monospace; font-size: 14px; padding: 0.2em 0px; margin: 0px; background-color: rgba(0, 0, 0, 0.0392157); border-top-left-radius: 3px; border-top-right-radius: 3px; border-bottom-right-radius: 3px; border-bottom-left-radius: 3px;" class="">"ä".utf8.count != "a\u{308}".utf8.count</code>.</p><p style="box-sizing: border-box; margin-top: 0px; margin-bottom: 16px; color: rgb(51, 51, 51); font-family: -apple-system, BlinkMacSystemFont, 'Segoe UI', Roboto, Helvetica, Arial, sans-serif, 'Apple Color Emoji', 'Segoe UI Emoji', 'Segoe UI Symbol'; font-size: 16px; background-color: rgb(255, 255, 255);" class="">IEEE-754 floating point numbers are allowed to break the reflexivity law by defining that <code style="box-sizing: border-box; font-family: Consolas, 'Liberation Mono', Menlo, Courier, monospace; font-size: 14px; padding: 0.2em 0px; margin: 0px; background-color: rgba(0, 0, 0, 0.0392157); border-top-left-radius: 3px; border-top-right-radius: 3px; border-bottom-right-radius: 3px; border-bottom-left-radius: 3px;" class="">.nan != x</code> for any value of <code style="box-sizing: border-box; font-family: Consolas, 'Liberation Mono', Menlo, Courier, monospace; font-size: 14px; padding: 0.2em 0px; margin: 0px; background-color: rgba(0, 0, 0, 0.0392157); border-top-left-radius: 3px; border-top-right-radius: 3px; border-bottom-right-radius: 3px; border-bottom-left-radius: 3px;" class="">x</code>, which is the standard behaviour documented in IEEE-754 and implemented the same way in other programming languages.</p><h3 style="box-sizing: border-box; margin-top: 24px; margin-bottom: 16px; font-size: 1.25em; line-height: 1.25; color: rgb(51, 51, 51); font-family: -apple-system, BlinkMacSystemFont, 'Segoe UI', Roboto, Helvetica, Arial, sans-serif, 'Apple Color Emoji', 'Segoe UI Emoji', 'Segoe UI Symbol'; background-color: rgb(255, 255, 255);" class=""><a id="user-content-comparable" class="anchor" href="https://github.com/pyrtsa/swift-evolution/blob/ca89e7b3a1dffc99baa695a03544fcba75afd0f3/proposals/NNNN-formalized-ordering.md#comparable" aria-hidden="true" style="box-sizing: border-box; background-color: transparent; -webkit-text-decoration-skip: objects; color: rgb(64, 120, 192); text-decoration: none; float: left; padding-right: 4px; margin-left: -20px; line-height: 1;"><svg aria-hidden="true" class="octicon octicon-link" height="16" version="1.1" viewBox="0 0 16 16" width="16"><path d="M4 9h1v1H4c-1.5 0-3-1.69-3-3.5S2.55 3 4 3h4c1.45 0 3 1.69 3 3.5 0 1.41-.91 2.72-2 3.25V8.59c.58-.45 1-1.27 1-2.09C10 5.22 8.98 4 8 4H4c-.98 0-2 1.22-2 2.5S3 9 4 9zm9-3h-1v1h1c1 0 2 1.22 2 2.5S13.98 12 13 12H9c-.98 0-2-1.22-2-2.5 0-.83.42-1.64 1-2.09V6.25c-1.09.53-2 1.84-2 3.25C6 11.31 7.55 13 9 13h4c1.45 0 3-1.69 3-3.5S14.5 6 13 6z"></path></svg></a>Comparable</h3><p style="box-sizing: border-box; margin-top: 0px; margin-bottom: 16px; color: rgb(51, 51, 51); font-family: -apple-system, BlinkMacSystemFont, 'Segoe UI', Roboto, Helvetica, Arial, sans-serif, 'Apple Color Emoji', 'Segoe UI Emoji', 'Segoe UI Symbol'; font-size: 16px; background-color: rgb(255, 255, 255);" class="">The <code style="box-sizing: border-box; font-family: Consolas, 'Liberation Mono', Menlo, Courier, monospace; font-size: 14px; padding: 0.2em 0px; margin: 0px; background-color: rgba(0, 0, 0, 0.0392157); border-top-left-radius: 3px; border-top-right-radius: 3px; border-bottom-right-radius: 3px; border-bottom-left-radius: 3px;" class="">Comparable</code> protocol will now require (without default implementation provided) a single operator definition: <code style="box-sizing: border-box; font-family: Consolas, 'Liberation Mono', Menlo, Courier, monospace; font-size: 14px; padding: 0.2em 0px; margin: 0px; background-color: rgba(0, 0, 0, 0.0392157); border-top-left-radius: 3px; border-top-right-radius: 3px; border-bottom-right-radius: 3px; border-bottom-left-radius: 3px;" class=""><=></code> — the comparison operator. From this, all other comparison operators will be derived so as to respect the total order semantics of <code style="box-sizing: border-box; font-family: Consolas, 'Liberation Mono', Menlo, Courier, monospace; font-size: 14px; padding: 0.2em 0px; margin: 0px; background-color: rgba(0, 0, 0, 0.0392157); border-top-left-radius: 3px; border-top-right-radius: 3px; border-bottom-right-radius: 3px; border-bottom-left-radius: 3px;" class="">Comparable</code>:</p><p style="box-sizing: border-box; margin-top: 0px; margin-bottom: 16px; color: rgb(51, 51, 51); font-family: -apple-system, BlinkMacSystemFont, 'Segoe UI', Roboto, Helvetica, Arial, sans-serif, 'Apple Color Emoji', 'Segoe UI Emoji', 'Segoe UI Symbol'; font-size: 16px; background-color: rgb(255, 255, 255);" class="">To maintain compatibility with IEEE-754, the interface of <code style="box-sizing: border-box; font-family: Consolas, 'Liberation Mono', Menlo, Courier, monospace; font-size: 14px; padding: 0.2em 0px; margin: 0px; background-color: rgba(0, 0, 0, 0.0392157); border-top-left-radius: 3px; border-top-right-radius: 3px; border-bottom-right-radius: 3px; border-bottom-left-radius: 3px;" class="">Comparable</code> also contains as customization points the operators <code style="box-sizing: border-box; font-family: Consolas, 'Liberation Mono', Menlo, Courier, monospace; font-size: 14px; padding: 0.2em 0px; margin: 0px; background-color: rgba(0, 0, 0, 0.0392157); border-top-left-radius: 3px; border-top-right-radius: 3px; border-bottom-right-radius: 3px; border-bottom-left-radius: 3px;" class=""><</code>, <code style="box-sizing: border-box; font-family: Consolas, 'Liberation Mono', Menlo, Courier, monospace; font-size: 14px; padding: 0.2em 0px; margin: 0px; background-color: rgba(0, 0, 0, 0.0392157); border-top-left-radius: 3px; border-top-right-radius: 3px; border-bottom-right-radius: 3px; border-bottom-left-radius: 3px;" class=""><=</code>, and <code style="box-sizing: border-box; font-family: Consolas, 'Liberation Mono', Menlo, Courier, monospace; font-size: 14px; padding: 0.2em 0px; margin: 0px; background-color: rgba(0, 0, 0, 0.0392157); border-top-left-radius: 3px; border-top-right-radius: 3px; border-bottom-right-radius: 3px; border-bottom-left-radius: 3px;" class="">==</code> (derived from <code style="box-sizing: border-box; font-family: Consolas, 'Liberation Mono', Menlo, Courier, monospace; font-size: 14px; padding: 0.2em 0px; margin: 0px; background-color: rgba(0, 0, 0, 0.0392157); border-top-left-radius: 3px; border-top-right-radius: 3px; border-bottom-right-radius: 3px; border-bottom-left-radius: 3px;" class="">Equatable</code>) as well as the static binary functions <code style="box-sizing: border-box; font-family: Consolas, 'Liberation Mono', Menlo, Courier, monospace; font-size: 14px; padding: 0.2em 0px; margin: 0px; background-color: rgba(0, 0, 0, 0.0392157); border-top-left-radius: 3px; border-top-right-radius: 3px; border-bottom-right-radius: 3px; border-bottom-left-radius: 3px;" class="">_min(_:_:)</code> and <code style="box-sizing: border-box; font-family: Consolas, 'Liberation Mono', Menlo, Courier, monospace; font-size: 14px; padding: 0.2em 0px; margin: 0px; background-color: rgba(0, 0, 0, 0.0392157); border-top-left-radius: 3px; border-top-right-radius: 3px; border-bottom-right-radius: 3px; border-bottom-left-radius: 3px;" class="">_max(_:_:)</code>. User-defined types are recommended against overriding the default implementations.</p><p style="box-sizing: border-box; margin-top: 0px; margin-bottom: 16px; color: rgb(51, 51, 51); font-family: -apple-system, BlinkMacSystemFont, 'Segoe UI', Roboto, Helvetica, Arial, sans-serif, 'Apple Color Emoji', 'Segoe UI Emoji', 'Segoe UI Symbol'; font-size: 16px; background-color: rgb(255, 255, 255);" class="">The uncustomizable top-level binary comparison operators <code style="box-sizing: border-box; font-family: Consolas, 'Liberation Mono', Menlo, Courier, monospace; font-size: 14px; padding: 0.2em 0px; margin: 0px; background-color: rgba(0, 0, 0, 0.0392157); border-top-left-radius: 3px; border-top-right-radius: 3px; border-bottom-right-radius: 3px; border-bottom-left-radius: 3px;" class="">a > b</code> and <code style="box-sizing: border-box; font-family: Consolas, 'Liberation Mono', Menlo, Courier, monospace; font-size: 14px; padding: 0.2em 0px; margin: 0px; background-color: rgba(0, 0, 0, 0.0392157); border-top-left-radius: 3px; border-top-right-radius: 3px; border-bottom-right-radius: 3px; border-bottom-left-radius: 3px;" class="">a >= b</code> are implemented as synonyms to <code style="box-sizing: border-box; font-family: Consolas, 'Liberation Mono', Menlo, Courier, monospace; font-size: 14px; padding: 0.2em 0px; margin: 0px; background-color: rgba(0, 0, 0, 0.0392157); border-top-left-radius: 3px; border-top-right-radius: 3px; border-bottom-right-radius: 3px; border-bottom-left-radius: 3px;" class="">b < a</code>and <code style="box-sizing: border-box; font-family: Consolas, 'Liberation Mono', Menlo, Courier, monospace; font-size: 14px; padding: 0.2em 0px; margin: 0px; background-color: rgba(0, 0, 0, 0.0392157); border-top-left-radius: 3px; border-top-right-radius: 3px; border-bottom-right-radius: 3px; border-bottom-left-radius: 3px;" class="">b <= a</code>, respectively.</p><h3 style="box-sizing: border-box; margin-top: 24px; margin-bottom: 16px; font-size: 1.25em; line-height: 1.25; color: rgb(51, 51, 51); font-family: -apple-system, BlinkMacSystemFont, 'Segoe UI', Roboto, Helvetica, Arial, sans-serif, 'Apple Color Emoji', 'Segoe UI Emoji', 'Segoe UI Symbol'; background-color: rgb(255, 255, 255);" class=""><a id="user-content-standard-library" class="anchor" href="https://github.com/pyrtsa/swift-evolution/blob/ca89e7b3a1dffc99baa695a03544fcba75afd0f3/proposals/NNNN-formalized-ordering.md#standard-library" aria-hidden="true" style="box-sizing: border-box; background-color: transparent; -webkit-text-decoration-skip: objects; color: rgb(64, 120, 192); text-decoration: none; float: left; padding-right: 4px; margin-left: -20px; line-height: 1;"><svg aria-hidden="true" class="octicon octicon-link" height="16" version="1.1" viewBox="0 0 16 16" width="16"><path d="M4 9h1v1H4c-1.5 0-3-1.69-3-3.5S2.55 3 4 3h4c1.45 0 3 1.69 3 3.5 0 1.41-.91 2.72-2 3.25V8.59c.58-.45 1-1.27 1-2.09C10 5.22 8.98 4 8 4H4c-.98 0-2 1.22-2 2.5S3 9 4 9zm9-3h-1v1h1c1 0 2 1.22 2 2.5S13.98 12 13 12H9c-.98 0-2-1.22-2-2.5 0-.83.42-1.64 1-2.09V6.25c-1.09.53-2 1.84-2 3.25C6 11.31 7.55 13 9 13h4c1.45 0 3-1.69 3-3.5S14.5 6 13 6z"></path></svg></a>Standard Library</h3><p style="box-sizing: border-box; margin-top: 0px; margin-bottom: 16px; color: rgb(51, 51, 51); font-family: -apple-system, BlinkMacSystemFont, 'Segoe UI', Roboto, Helvetica, Arial, sans-serif, 'Apple Color Emoji', 'Segoe UI Emoji', 'Segoe UI Symbol'; font-size: 16px; background-color: rgb(255, 255, 255);" class="">Unlike a previous revision of this proposal, standard library algorithms specific to <code style="box-sizing: border-box; font-family: Consolas, 'Liberation Mono', Menlo, Courier, monospace; font-size: 14px; padding: 0.2em 0px; margin: 0px; background-color: rgba(0, 0, 0, 0.0392157); border-top-left-radius: 3px; border-top-right-radius: 3px; border-bottom-right-radius: 3px; border-bottom-left-radius: 3px;" class="">FloatingPoint</code> remain unchanged.</p><p style="box-sizing: border-box; margin-top: 0px; margin-bottom: 16px; color: rgb(51, 51, 51); font-family: -apple-system, BlinkMacSystemFont, 'Segoe UI', Roboto, Helvetica, Arial, sans-serif, 'Apple Color Emoji', 'Segoe UI Emoji', 'Segoe UI Symbol'; font-size: 16px; background-color: rgb(255, 255, 255);" class="">Overloads of <code style="box-sizing: border-box; font-family: Consolas, 'Liberation Mono', Menlo, Courier, monospace; font-size: 14px; padding: 0.2em 0px; margin: 0px; background-color: rgba(0, 0, 0, 0.0392157); border-top-left-radius: 3px; border-top-right-radius: 3px; border-bottom-right-radius: 3px; border-bottom-left-radius: 3px;" class=""><=></code> for tuples of <code style="box-sizing: border-box; font-family: Consolas, 'Liberation Mono', Menlo, Courier, monospace; font-size: 14px; padding: 0.2em 0px; margin: 0px; background-color: rgba(0, 0, 0, 0.0392157); border-top-left-radius: 3px; border-top-right-radius: 3px; border-bottom-right-radius: 3px; border-bottom-left-radius: 3px;" class="">Comparable</code> elements are provided up to a library-defined arity.</p><p style="box-sizing: border-box; margin-top: 0px; margin-bottom: 16px; color: rgb(51, 51, 51); font-family: -apple-system, BlinkMacSystemFont, 'Segoe UI', Roboto, Helvetica, Arial, sans-serif, 'Apple Color Emoji', 'Segoe UI Emoji', 'Segoe UI Symbol'; font-size: 16px; background-color: rgb(255, 255, 255);" class="">The intent of this proposal is to later augment the standard library so that functions that take an ordering predicate <code style="box-sizing: border-box; font-family: Consolas, 'Liberation Mono', Menlo, Courier, monospace; font-size: 14px; padding: 0.2em 0px; margin: 0px; background-color: rgba(0, 0, 0, 0.0392157); border-top-left-radius: 3px; border-top-right-radius: 3px; border-bottom-right-radius: 3px; border-bottom-left-radius: 3px;" class="">by: (T, T) -> Bool</code> will have an overload <code style="box-sizing: border-box; font-family: Consolas, 'Liberation Mono', Menlo, Courier, monospace; font-size: 14px; padding: 0.2em 0px; margin: 0px; background-color: rgba(0, 0, 0, 0.0392157); border-top-left-radius: 3px; border-top-right-radius: 3px; border-bottom-right-radius: 3px; border-bottom-left-radius: 3px;" class="">ordering: (T, T) -> Ordering</code> that will provide a — potentially — more efficient implementation. A list of such functions is provided in Future directions.</p><h2 style="box-sizing: border-box; margin-top: 24px; margin-bottom: 16px; line-height: 1.25; padding-bottom: 0.3em; border-bottom-width: 1px; border-bottom-style: solid; border-bottom-color: rgb(238, 238, 238); color: rgb(51, 51, 51); font-family: -apple-system, BlinkMacSystemFont, 'Segoe UI', Roboto, Helvetica, Arial, sans-serif, 'Apple Color Emoji', 'Segoe UI Emoji', 'Segoe UI Symbol'; background-color: rgb(255, 255, 255);" class=""><a id="user-content-detailed-design" class="anchor" href="https://github.com/pyrtsa/swift-evolution/blob/ca89e7b3a1dffc99baa695a03544fcba75afd0f3/proposals/NNNN-formalized-ordering.md#detailed-design" aria-hidden="true" style="box-sizing: border-box; background-color: transparent; -webkit-text-decoration-skip: objects; color: rgb(64, 120, 192); text-decoration: none; float: left; padding-right: 4px; margin-left: -20px; line-height: 1;"><svg aria-hidden="true" class="octicon octicon-link" height="16" version="1.1" viewBox="0 0 16 16" width="16"><path d="M4 9h1v1H4c-1.5 0-3-1.69-3-3.5S2.55 3 4 3h4c1.45 0 3 1.69 3 3.5 0 1.41-.91 2.72-2 3.25V8.59c.58-.45 1-1.27 1-2.09C10 5.22 8.98 4 8 4H4c-.98 0-2 1.22-2 2.5S3 9 4 9zm9-3h-1v1h1c1 0 2 1.22 2 2.5S13.98 12 13 12H9c-.98 0-2-1.22-2-2.5 0-.83.42-1.64 1-2.09V6.25c-1.09.53-2 1.84-2 3.25C6 11.31 7.55 13 9 13h4c1.45 0 3-1.69 3-3.5S14.5 6 13 6z"></path></svg></a>Detailed design</h2><p style="box-sizing: border-box; margin-top: 0px; margin-bottom: 16px; color: rgb(51, 51, 51); font-family: -apple-system, BlinkMacSystemFont, 'Segoe UI', Roboto, Helvetica, Arial, sans-serif, 'Apple Color Emoji', 'Segoe UI Emoji', 'Segoe UI Symbol'; font-size: 16px; background-color: rgb(255, 255, 255);" class="">The <code style="box-sizing: border-box; font-family: Consolas, 'Liberation Mono', Menlo, Courier, monospace; font-size: 14px; padding: 0.2em 0px; margin: 0px; background-color: rgba(0, 0, 0, 0.0392157); border-top-left-radius: 3px; border-top-right-radius: 3px; border-bottom-right-radius: 3px; border-bottom-left-radius: 3px;" class="">Comparable</code> protocol will be amended by taking away <code style="box-sizing: border-box; font-family: Consolas, 'Liberation Mono', Menlo, Courier, monospace; font-size: 14px; padding: 0.2em 0px; margin: 0px; background-color: rgba(0, 0, 0, 0.0392157); border-top-left-radius: 3px; border-top-right-radius: 3px; border-bottom-right-radius: 3px; border-bottom-left-radius: 3px;" class="">></code> and <code style="box-sizing: border-box; font-family: Consolas, 'Liberation Mono', Menlo, Courier, monospace; font-size: 14px; padding: 0.2em 0px; margin: 0px; background-color: rgba(0, 0, 0, 0.0392157); border-top-left-radius: 3px; border-top-right-radius: 3px; border-bottom-right-radius: 3px; border-bottom-left-radius: 3px;" class="">>=</code>, adding customisation points <code style="box-sizing: border-box; font-family: Consolas, 'Liberation Mono', Menlo, Courier, monospace; font-size: 14px; padding: 0.2em 0px; margin: 0px; background-color: rgba(0, 0, 0, 0.0392157); border-top-left-radius: 3px; border-top-right-radius: 3px; border-bottom-right-radius: 3px; border-bottom-left-radius: 3px;" class="">_min(_:_:)</code>, and <code style="box-sizing: border-box; font-family: Consolas, 'Liberation Mono', Menlo, Courier, monospace; font-size: 14px; padding: 0.2em 0px; margin: 0px; background-color: rgba(0, 0, 0, 0.0392157); border-top-left-radius: 3px; border-top-right-radius: 3px; border-bottom-right-radius: 3px; border-bottom-left-radius: 3px;" class="">_max(_:_:)</code>, and introducing the ordering operator <code style="box-sizing: border-box; font-family: Consolas, 'Liberation Mono', Menlo, Courier, monospace; font-size: 14px; padding: 0.2em 0px; margin: 0px; background-color: rgba(0, 0, 0, 0.0392157); border-top-left-radius: 3px; border-top-right-radius: 3px; border-bottom-right-radius: 3px; border-bottom-left-radius: 3px;" class=""><=></code> that makes use of the <code style="box-sizing: border-box; font-family: Consolas, 'Liberation Mono', Menlo, Courier, monospace; font-size: 14px; padding: 0.2em 0px; margin: 0px; background-color: rgba(0, 0, 0, 0.0392157); border-top-left-radius: 3px; border-top-right-radius: 3px; border-bottom-right-radius: 3px; border-bottom-left-radius: 3px;" class="">Ordering</code> enum defined below.</p><div class="highlight highlight-source-swift" style="box-sizing: border-box; margin-bottom: 16px; color: rgb(51, 51, 51); font-family: -apple-system, BlinkMacSystemFont, 'Segoe UI', Roboto, Helvetica, Arial, sans-serif, 'Apple Color Emoji', 'Segoe UI Emoji', 'Segoe UI Symbol'; font-size: 16px; background-color: rgb(255, 255, 255);"><pre style="box-sizing: border-box; font-family: Consolas, 'Liberation Mono', Menlo, Courier, monospace; font-size: 14px; margin-top: 0px; margin-bottom: 0px; line-height: 1.45; word-wrap: normal; padding: 16px; overflow: auto; background-color: rgb(247, 247, 247); border-top-left-radius: 3px; border-top-right-radius: 3px; border-bottom-right-radius: 3px; border-bottom-left-radius: 3px; word-break: normal;" class=""><span class="pl-k" style="box-sizing: border-box; color: rgb(167, 29, 93);">enum</span> Ordering <span class="pl-k" style="box-sizing: border-box; color: rgb(167, 29, 93);">:</span> <span class="pl-c1" style="box-sizing: border-box; color: rgb(0, 134, 179);">Equatable</span> {
<span class="pl-k" style="box-sizing: border-box; color: rgb(167, 29, 93);">case</span> ascending
<span class="pl-k" style="box-sizing: border-box; color: rgb(167, 29, 93);">case</span> equal
<span class="pl-k" style="box-sizing: border-box; color: rgb(167, 29, 93);">case</span> descending
}
<span class="pl-k" style="box-sizing: border-box; color: rgb(167, 29, 93);">infix</span> <span class="pl-k" style="box-sizing: border-box; color: rgb(167, 29, 93);">operator</span> <span class="pl-k" style="box-sizing: border-box; color: rgb(167, 29, 93);"><=></span> { <span class="pl-k" style="box-sizing: border-box; color: rgb(167, 29, 93);">associativity</span> <span class="pl-k" style="box-sizing: border-box; color: rgb(167, 29, 93);">none</span> <span class="pl-k" style="box-sizing: border-box; color: rgb(167, 29, 93);">precedence</span> <span class="pl-c1" style="box-sizing: border-box; color: rgb(0, 134, 179);">130</span> }
<span class="pl-k" style="box-sizing: border-box; color: rgb(167, 29, 93);">public</span> <span class="pl-k" style="box-sizing: border-box; color: rgb(167, 29, 93);">protocol</span> <span class="pl-c1" style="box-sizing: border-box; color: rgb(0, 134, 179);">Comparable</span> <span class="pl-k" style="box-sizing: border-box; color: rgb(167, 29, 93);">:</span> <span class="pl-c1" style="box-sizing: border-box; color: rgb(0, 134, 179);">Equatable</span> {
<span class="pl-c" style="box-sizing: border-box; color: rgb(150, 152, 150);">// Implementation required:</span>
<span class="pl-k" style="box-sizing: border-box; color: rgb(167, 29, 93);">static</span> <span class="pl-k" style="box-sizing: border-box; color: rgb(167, 29, 93);">func</span> <span class="pl-en" style="box-sizing: border-box; color: rgb(121, 93, 163);"><=></span>(lhs: <span class="pl-k" style="box-sizing: border-box; color: rgb(167, 29, 93);">Self</span>, rhs: <span class="pl-k" style="box-sizing: border-box; color: rgb(167, 29, 93);">Self</span>) <span class="pl-k" style="box-sizing: border-box; color: rgb(167, 29, 93);">-></span> Ordering
<span class="pl-c" style="box-sizing: border-box; color: rgb(150, 152, 150);">// Default implementations provided:</span>
<span class="pl-k" style="box-sizing: border-box; color: rgb(167, 29, 93);">static</span> <span class="pl-k" style="box-sizing: border-box; color: rgb(167, 29, 93);">func</span> <span class="pl-en" style="box-sizing: border-box; color: rgb(121, 93, 163);">==</span> (lhs: <span class="pl-k" style="box-sizing: border-box; color: rgb(167, 29, 93);">Self</span>, rhs: <span class="pl-k" style="box-sizing: border-box; color: rgb(167, 29, 93);">Self</span>) <span class="pl-k" style="box-sizing: border-box; color: rgb(167, 29, 93);">-></span> <span class="pl-c1" style="box-sizing: border-box; color: rgb(0, 134, 179);">Bool</span> // derived from <span class="pl-c1" style="box-sizing: border-box; color: rgb(0, 134, 179);">Equatable</span>
<span class="pl-k" style="box-sizing: border-box; color: rgb(167, 29, 93);">static</span> <span class="pl-k" style="box-sizing: border-box; color: rgb(167, 29, 93);">func</span> <span class="pl-en" style="box-sizing: border-box; color: rgb(121, 93, 163);"><</span> (lhs: <span class="pl-k" style="box-sizing: border-box; color: rgb(167, 29, 93);">Self</span>, rhs: <span class="pl-k" style="box-sizing: border-box; color: rgb(167, 29, 93);">Self</span>) <span class="pl-k" style="box-sizing: border-box; color: rgb(167, 29, 93);">-></span> <span class="pl-c1" style="box-sizing: border-box; color: rgb(0, 134, 179);">Bool</span>
<span class="pl-k" style="box-sizing: border-box; color: rgb(167, 29, 93);">static</span> <span class="pl-k" style="box-sizing: border-box; color: rgb(167, 29, 93);">func</span> <span class="pl-en" style="box-sizing: border-box; color: rgb(121, 93, 163);"><=</span> (lhs: <span class="pl-k" style="box-sizing: border-box; color: rgb(167, 29, 93);">Self</span>, rhs: <span class="pl-k" style="box-sizing: border-box; color: rgb(167, 29, 93);">Self</span>) <span class="pl-k" style="box-sizing: border-box; color: rgb(167, 29, 93);">-></span> <span class="pl-c1" style="box-sizing: border-box; color: rgb(0, 134, 179);">Bool</span>
<span class="pl-k" style="box-sizing: border-box; color: rgb(167, 29, 93);">static</span> <span class="pl-k" style="box-sizing: border-box; color: rgb(167, 29, 93);">func</span> <span class="pl-en" style="box-sizing: border-box; color: rgb(121, 93, 163);">_min</span>(<span class="pl-en" style="box-sizing: border-box; color: rgb(121, 93, 163);">_</span> <span class="pl-smi" style="box-sizing: border-box;">lhs</span>: <span class="pl-k" style="box-sizing: border-box; color: rgb(167, 29, 93);">Self</span>, <span class="pl-en" style="box-sizing: border-box; color: rgb(121, 93, 163);">_</span> <span class="pl-smi" style="box-sizing: border-box;">rhs</span>: <span class="pl-k" style="box-sizing: border-box; color: rgb(167, 29, 93);">Self</span>) <span class="pl-k" style="box-sizing: border-box; color: rgb(167, 29, 93);">-></span> Self
<span class="pl-k" style="box-sizing: border-box; color: rgb(167, 29, 93);">static</span> <span class="pl-k" style="box-sizing: border-box; color: rgb(167, 29, 93);">func</span> <span class="pl-en" style="box-sizing: border-box; color: rgb(121, 93, 163);">_max</span>(<span class="pl-en" style="box-sizing: border-box; color: rgb(121, 93, 163);">_</span> <span class="pl-smi" style="box-sizing: border-box;">lhs</span>: <span class="pl-k" style="box-sizing: border-box; color: rgb(167, 29, 93);">Self</span>, <span class="pl-en" style="box-sizing: border-box; color: rgb(121, 93, 163);">_</span> <span class="pl-smi" style="box-sizing: border-box;">rhs</span>: <span class="pl-k" style="box-sizing: border-box; color: rgb(167, 29, 93);">Self</span>) <span class="pl-k" style="box-sizing: border-box; color: rgb(167, 29, 93);">-></span> Self
}</pre></div><p style="box-sizing: border-box; margin-top: 0px; margin-bottom: 16px; color: rgb(51, 51, 51); font-family: -apple-system, BlinkMacSystemFont, 'Segoe UI', Roboto, Helvetica, Arial, sans-serif, 'Apple Color Emoji', 'Segoe UI Emoji', 'Segoe UI Symbol'; font-size: 16px; background-color: rgb(255, 255, 255);" class="">The <code style="box-sizing: border-box; font-family: Consolas, 'Liberation Mono', Menlo, Courier, monospace; font-size: 14px; padding: 0.2em 0px; margin: 0px; background-color: rgba(0, 0, 0, 0.0392157); border-top-left-radius: 3px; border-top-right-radius: 3px; border-bottom-right-radius: 3px; border-bottom-left-radius: 3px;" class=""><=></code> operator defines a relationship between <code style="box-sizing: border-box; font-family: Consolas, 'Liberation Mono', Menlo, Courier, monospace; font-size: 14px; padding: 0.2em 0px; margin: 0px; background-color: rgba(0, 0, 0, 0.0392157); border-top-left-radius: 3px; border-top-right-radius: 3px; border-bottom-right-radius: 3px; border-bottom-left-radius: 3px;" class="">==</code> and <code style="box-sizing: border-box; font-family: Consolas, 'Liberation Mono', Menlo, Courier, monospace; font-size: 14px; padding: 0.2em 0px; margin: 0px; background-color: rgba(0, 0, 0, 0.0392157); border-top-left-radius: 3px; border-top-right-radius: 3px; border-bottom-right-radius: 3px; border-bottom-left-radius: 3px;" class=""><=></code> such that <code style="box-sizing: border-box; font-family: Consolas, 'Liberation Mono', Menlo, Courier, monospace; font-size: 14px; padding: 0.2em 0px; margin: 0px; background-color: rgba(0, 0, 0, 0.0392157); border-top-left-radius: 3px; border-top-right-radius: 3px; border-bottom-right-radius: 3px; border-bottom-left-radius: 3px;" class="">a == b</code> iff <code style="box-sizing: border-box; font-family: Consolas, 'Liberation Mono', Menlo, Courier, monospace; font-size: 14px; padding: 0.2em 0px; margin: 0px; background-color: rgba(0, 0, 0, 0.0392157); border-top-left-radius: 3px; border-top-right-radius: 3px; border-bottom-right-radius: 3px; border-bottom-left-radius: 3px;" class="">(a <=> b) == .equal</code>, unless <code style="box-sizing: border-box; font-family: Consolas, 'Liberation Mono', Menlo, Courier, monospace; font-size: 14px; padding: 0.2em 0px; margin: 0px; background-color: rgba(0, 0, 0, 0.0392157); border-top-left-radius: 3px; border-top-right-radius: 3px; border-bottom-right-radius: 3px; border-bottom-left-radius: 3px;" class="">Self</code> chooses to break the semantics in the way of IEEE-754. Likewise, it should hold that <code style="box-sizing: border-box; font-family: Consolas, 'Liberation Mono', Menlo, Courier, monospace; font-size: 14px; padding: 0.2em 0px; margin: 0px; background-color: rgba(0, 0, 0, 0.0392157); border-top-left-radius: 3px; border-top-right-radius: 3px; border-bottom-right-radius: 3px; border-bottom-left-radius: 3px;" class="">(a <=> b) == .ascending</code> iff <code style="box-sizing: border-box; font-family: Consolas, 'Liberation Mono', Menlo, Courier, monospace; font-size: 14px; padding: 0.2em 0px; margin: 0px; background-color: rgba(0, 0, 0, 0.0392157); border-top-left-radius: 3px; border-top-right-radius: 3px; border-bottom-right-radius: 3px; border-bottom-left-radius: 3px;" class="">a < b</code>, and <code style="box-sizing: border-box; font-family: Consolas, 'Liberation Mono', Menlo, Courier, monospace; font-size: 14px; padding: 0.2em 0px; margin: 0px; background-color: rgba(0, 0, 0, 0.0392157); border-top-left-radius: 3px; border-top-right-radius: 3px; border-bottom-right-radius: 3px; border-bottom-left-radius: 3px;" class="">(a <=> b) != .descending</code> iff <code style="box-sizing: border-box; font-family: Consolas, 'Liberation Mono', Menlo, Courier, monospace; font-size: 14px; padding: 0.2em 0px; margin: 0px; background-color: rgba(0, 0, 0, 0.0392157); border-top-left-radius: 3px; border-top-right-radius: 3px; border-bottom-right-radius: 3px; border-bottom-left-radius: 3px;" class="">a <= b</code>.</p><p style="box-sizing: border-box; margin-top: 0px; margin-bottom: 16px; color: rgb(51, 51, 51); font-family: -apple-system, BlinkMacSystemFont, 'Segoe UI', Roboto, Helvetica, Arial, sans-serif, 'Apple Color Emoji', 'Segoe UI Emoji', 'Segoe UI Symbol'; font-size: 16px; background-color: rgb(255, 255, 255);" class="">The <code style="box-sizing: border-box; font-family: Consolas, 'Liberation Mono', Menlo, Courier, monospace; font-size: 14px; padding: 0.2em 0px; margin: 0px; background-color: rgba(0, 0, 0, 0.0392157); border-top-left-radius: 3px; border-top-right-radius: 3px; border-bottom-right-radius: 3px; border-bottom-left-radius: 3px;" class="">_min(_:_:)</code> and <code style="box-sizing: border-box; font-family: Consolas, 'Liberation Mono', Menlo, Courier, monospace; font-size: 14px; padding: 0.2em 0px; margin: 0px; background-color: rgba(0, 0, 0, 0.0392157); border-top-left-radius: 3px; border-top-right-radius: 3px; border-bottom-right-radius: 3px; border-bottom-left-radius: 3px;" class="">_max(_:_:)</code> functions should return the lesser or greater of the two operands, respectively, while in case of equal arguments, <code style="box-sizing: border-box; font-family: Consolas, 'Liberation Mono', Menlo, Courier, monospace; font-size: 14px; padding: 0.2em 0px; margin: 0px; background-color: rgba(0, 0, 0, 0.0392157); border-top-left-radius: 3px; border-top-right-radius: 3px; border-bottom-right-radius: 3px; border-bottom-left-radius: 3px;" class="">_min(_:_:)</code> should favour the left-hand side and <code style="box-sizing: border-box; font-family: Consolas, 'Liberation Mono', Menlo, Courier, monospace; font-size: 14px; padding: 0.2em 0px; margin: 0px; background-color: rgba(0, 0, 0, 0.0392157); border-top-left-radius: 3px; border-top-right-radius: 3px; border-bottom-right-radius: 3px; border-bottom-left-radius: 3px;" class="">_max(_:_:)</code> the right-hand side to retain identity, as presently explained in <a href="https://github.com/apple/swift/blob/4614adc16168d612b6fc7e7a161dd5b6b34be704/stdlib/public/core/Algorithm.swift#L17-L20" style="box-sizing: border-box; background-color: transparent; -webkit-text-decoration-skip: objects; color: rgb(64, 120, 192); text-decoration: none;" class="">this comment</a>. Making them customization points of <code style="box-sizing: border-box; font-family: Consolas, 'Liberation Mono', Menlo, Courier, monospace; font-size: 14px; padding: 0.2em 0px; margin: 0px; background-color: rgba(0, 0, 0, 0.0392157); border-top-left-radius: 3px; border-top-right-radius: 3px; border-bottom-right-radius: 3px; border-bottom-left-radius: 3px;" class="">Comparable</code>, we get to fix their behaviour in the presense of unorderable values (<a href="https://bugs.swift.org/browse/SR-1011" style="box-sizing: border-box; background-color: transparent; -webkit-text-decoration-skip: objects; color: rgb(64, 120, 192); text-decoration: none;" class="">SR-1011</a>).</p><p style="box-sizing: border-box; margin-top: 0px; margin-bottom: 16px; color: rgb(51, 51, 51); font-family: -apple-system, BlinkMacSystemFont, 'Segoe UI', Roboto, Helvetica, Arial, sans-serif, 'Apple Color Emoji', 'Segoe UI Emoji', 'Segoe UI Symbol'; font-size: 16px; background-color: rgb(255, 255, 255);" class="">Most user types should only implement <code style="box-sizing: border-box; font-family: Consolas, 'Liberation Mono', Menlo, Courier, monospace; font-size: 14px; padding: 0.2em 0px; margin: 0px; background-color: rgba(0, 0, 0, 0.0392157); border-top-left-radius: 3px; border-top-right-radius: 3px; border-bottom-right-radius: 3px; border-bottom-left-radius: 3px;" class=""><=></code> and leave the other members of <code style="box-sizing: border-box; font-family: Consolas, 'Liberation Mono', Menlo, Courier, monospace; font-size: 14px; padding: 0.2em 0px; margin: 0px; background-color: rgba(0, 0, 0, 0.0392157); border-top-left-radius: 3px; border-top-right-radius: 3px; border-bottom-right-radius: 3px; border-bottom-left-radius: 3px;" class="">Equatable</code> and <code style="box-sizing: border-box; font-family: Consolas, 'Liberation Mono', Menlo, Courier, monospace; font-size: 14px; padding: 0.2em 0px; margin: 0px; background-color: rgba(0, 0, 0, 0.0392157); border-top-left-radius: 3px; border-top-right-radius: 3px; border-bottom-right-radius: 3px; border-bottom-left-radius: 3px;" class="">Comparable</code> to their default implementations. Note that even <code style="box-sizing: border-box; font-family: Consolas, 'Liberation Mono', Menlo, Courier, monospace; font-size: 14px; padding: 0.2em 0px; margin: 0px; background-color: rgba(0, 0, 0, 0.0392157); border-top-left-radius: 3px; border-top-right-radius: 3px; border-bottom-right-radius: 3px; border-bottom-left-radius: 3px;" class="">==</code> has a sane default implementation if <code style="box-sizing: border-box; font-family: Consolas, 'Liberation Mono', Menlo, Courier, monospace; font-size: 14px; padding: 0.2em 0px; margin: 0px; background-color: rgba(0, 0, 0, 0.0392157); border-top-left-radius: 3px; border-top-right-radius: 3px; border-bottom-right-radius: 3px; border-bottom-left-radius: 3px;" class="">Self</code> is made <code style="box-sizing: border-box; font-family: Consolas, 'Liberation Mono', Menlo, Courier, monospace; font-size: 14px; padding: 0.2em 0px; margin: 0px; background-color: rgba(0, 0, 0, 0.0392157); border-top-left-radius: 3px; border-top-right-radius: 3px; border-bottom-right-radius: 3px; border-bottom-left-radius: 3px;" class="">Comparable</code>:</p><div class="highlight highlight-source-swift" style="box-sizing: border-box; margin-bottom: 16px; color: rgb(51, 51, 51); font-family: -apple-system, BlinkMacSystemFont, 'Segoe UI', Roboto, Helvetica, Arial, sans-serif, 'Apple Color Emoji', 'Segoe UI Emoji', 'Segoe UI Symbol'; font-size: 16px; background-color: rgb(255, 255, 255);"><pre style="box-sizing: border-box; font-family: Consolas, 'Liberation Mono', Menlo, Courier, monospace; font-size: 14px; margin-top: 0px; margin-bottom: 0px; line-height: 1.45; word-wrap: normal; padding: 16px; overflow: auto; background-color: rgb(247, 247, 247); border-top-left-radius: 3px; border-top-right-radius: 3px; border-bottom-right-radius: 3px; border-bottom-left-radius: 3px; word-break: normal;" class=""><span class="pl-c" style="box-sizing: border-box; color: rgb(150, 152, 150);">// Default implementations, which should be used for most Comparable types:</span>
<span class="pl-k" style="box-sizing: border-box; color: rgb(167, 29, 93);">extension</span> <span class="pl-c1" style="box-sizing: border-box; color: rgb(0, 134, 179);">Comparable</span> {
<span class="pl-k" style="box-sizing: border-box; color: rgb(167, 29, 93);">static</span> <span class="pl-k" style="box-sizing: border-box; color: rgb(167, 29, 93);">func</span> <span class="pl-en" style="box-sizing: border-box; color: rgb(121, 93, 163);">==</span> (l: <span class="pl-k" style="box-sizing: border-box; color: rgb(167, 29, 93);">Self</span>, r: <span class="pl-k" style="box-sizing: border-box; color: rgb(167, 29, 93);">Self</span>) <span class="pl-k" style="box-sizing: border-box; color: rgb(167, 29, 93);">-></span> <span class="pl-c1" style="box-sizing: border-box; color: rgb(0, 134, 179);">Bool</span> { <span class="pl-k" style="box-sizing: border-box; color: rgb(167, 29, 93);">return</span> (l <span class="pl-k" style="box-sizing: border-box; color: rgb(167, 29, 93);"><=></span> r) <span class="pl-k" style="box-sizing: border-box; color: rgb(167, 29, 93);">==</span> <span class="pl-k" style="box-sizing: border-box; color: rgb(167, 29, 93);">.</span>equal }
<span class="pl-k" style="box-sizing: border-box; color: rgb(167, 29, 93);">static</span> <span class="pl-k" style="box-sizing: border-box; color: rgb(167, 29, 93);">func</span> <span class="pl-en" style="box-sizing: border-box; color: rgb(121, 93, 163);"><</span> (l: <span class="pl-k" style="box-sizing: border-box; color: rgb(167, 29, 93);">Self</span>, r: <span class="pl-k" style="box-sizing: border-box; color: rgb(167, 29, 93);">Self</span>) <span class="pl-k" style="box-sizing: border-box; color: rgb(167, 29, 93);">-></span> <span class="pl-c1" style="box-sizing: border-box; color: rgb(0, 134, 179);">Bool</span> { <span class="pl-k" style="box-sizing: border-box; color: rgb(167, 29, 93);">return</span> (l <span class="pl-k" style="box-sizing: border-box; color: rgb(167, 29, 93);"><=></span> r) <span class="pl-k" style="box-sizing: border-box; color: rgb(167, 29, 93);">==</span> <span class="pl-k" style="box-sizing: border-box; color: rgb(167, 29, 93);">.</span>ascending }
<span class="pl-k" style="box-sizing: border-box; color: rgb(167, 29, 93);">static</span> <span class="pl-k" style="box-sizing: border-box; color: rgb(167, 29, 93);">func</span> <span class="pl-en" style="box-sizing: border-box; color: rgb(121, 93, 163);"><=</span> (l: <span class="pl-k" style="box-sizing: border-box; color: rgb(167, 29, 93);">Self</span>, r: <span class="pl-k" style="box-sizing: border-box; color: rgb(167, 29, 93);">Self</span>) <span class="pl-k" style="box-sizing: border-box; color: rgb(167, 29, 93);">-></span> <span class="pl-c1" style="box-sizing: border-box; color: rgb(0, 134, 179);">Bool</span> { <span class="pl-k" style="box-sizing: border-box; color: rgb(167, 29, 93);">return</span> (l <span class="pl-k" style="box-sizing: border-box; color: rgb(167, 29, 93);"><=></span> r) <span class="pl-k" style="box-sizing: border-box; color: rgb(167, 29, 93);">!=</span> <span class="pl-k" style="box-sizing: border-box; color: rgb(167, 29, 93);">.</span>descending }
<span class="pl-k" style="box-sizing: border-box; color: rgb(167, 29, 93);">static</span> <span class="pl-k" style="box-sizing: border-box; color: rgb(167, 29, 93);">func</span> <span class="pl-en" style="box-sizing: border-box; color: rgb(121, 93, 163);">_min</span>(<span class="pl-en" style="box-sizing: border-box; color: rgb(121, 93, 163);">_</span> <span class="pl-smi" style="box-sizing: border-box;">l</span>: <span class="pl-k" style="box-sizing: border-box; color: rgb(167, 29, 93);">Self</span>, <span class="pl-en" style="box-sizing: border-box; color: rgb(121, 93, 163);">_</span> <span class="pl-smi" style="box-sizing: border-box;">r</span>: <span class="pl-k" style="box-sizing: border-box; color: rgb(167, 29, 93);">Self</span>) <span class="pl-k" style="box-sizing: border-box; color: rgb(167, 29, 93);">-></span> Self { <span class="pl-k" style="box-sizing: border-box; color: rgb(167, 29, 93);">return</span> r <span class="pl-k" style="box-sizing: border-box; color: rgb(167, 29, 93);"><</span> l <span class="pl-k" style="box-sizing: border-box; color: rgb(167, 29, 93);">?</span> r <span class="pl-k" style="box-sizing: border-box; color: rgb(167, 29, 93);">:</span> l }
<span class="pl-k" style="box-sizing: border-box; color: rgb(167, 29, 93);">static</span> <span class="pl-k" style="box-sizing: border-box; color: rgb(167, 29, 93);">func</span> <span class="pl-en" style="box-sizing: border-box; color: rgb(121, 93, 163);">_max</span>(<span class="pl-en" style="box-sizing: border-box; color: rgb(121, 93, 163);">_</span> <span class="pl-smi" style="box-sizing: border-box;">l</span>: <span class="pl-k" style="box-sizing: border-box; color: rgb(167, 29, 93);">Self</span>, <span class="pl-en" style="box-sizing: border-box; color: rgb(121, 93, 163);">_</span> <span class="pl-smi" style="box-sizing: border-box;">r</span>: <span class="pl-k" style="box-sizing: border-box; color: rgb(167, 29, 93);">Self</span>) <span class="pl-k" style="box-sizing: border-box; color: rgb(167, 29, 93);">-></span> Self { <span class="pl-k" style="box-sizing: border-box; color: rgb(167, 29, 93);">return</span> r <span class="pl-k" style="box-sizing: border-box; color: rgb(167, 29, 93);"><</span> l <span class="pl-k" style="box-sizing: border-box; color: rgb(167, 29, 93);">?</span> l <span class="pl-k" style="box-sizing: border-box; color: rgb(167, 29, 93);">:</span> r }
}
<span class="pl-c" style="box-sizing: border-box; color: rgb(150, 152, 150);">// Unoverridable top-level operators and functions for Comparable:</span>
<span class="pl-k" style="box-sizing: border-box; color: rgb(167, 29, 93);">public</span> <span class="pl-k" style="box-sizing: border-box; color: rgb(167, 29, 93);">func</span> <span class="pl-en" style="box-sizing: border-box; color: rgb(121, 93, 163);">></span> <T <span class="pl-k" style="box-sizing: border-box; color: rgb(167, 29, 93);">:</span> <span class="pl-c1" style="box-sizing: border-box; color: rgb(0, 134, 179);">Comparable</span>>(l: T, r: T) <span class="pl-k" style="box-sizing: border-box; color: rgb(167, 29, 93);">-></span> <span class="pl-c1" style="box-sizing: border-box; color: rgb(0, 134, 179);">Bool</span> { <span class="pl-k" style="box-sizing: border-box; color: rgb(167, 29, 93);">return</span> r <span class="pl-k" style="box-sizing: border-box; color: rgb(167, 29, 93);"><</span> l }
<span class="pl-k" style="box-sizing: border-box; color: rgb(167, 29, 93);">public</span> <span class="pl-k" style="box-sizing: border-box; color: rgb(167, 29, 93);">func</span> <span class="pl-en" style="box-sizing: border-box; color: rgb(121, 93, 163);">>=</span> <T <span class="pl-k" style="box-sizing: border-box; color: rgb(167, 29, 93);">:</span> <span class="pl-c1" style="box-sizing: border-box; color: rgb(0, 134, 179);">Comparable</span>>(l: T, r: T) <span class="pl-k" style="box-sizing: border-box; color: rgb(167, 29, 93);">-></span> <span class="pl-c1" style="box-sizing: border-box; color: rgb(0, 134, 179);">Bool</span> { <span class="pl-k" style="box-sizing: border-box; color: rgb(167, 29, 93);">return</span> r <span class="pl-k" style="box-sizing: border-box; color: rgb(167, 29, 93);"><=</span> l }
<span class="pl-k" style="box-sizing: border-box; color: rgb(167, 29, 93);">public</span> <span class="pl-k" style="box-sizing: border-box; color: rgb(167, 29, 93);">func</span> <span class="pl-en" style="box-sizing: border-box; color: rgb(121, 93, 163);">min</span><T <span class="pl-k" style="box-sizing: border-box; color: rgb(167, 29, 93);">:</span> <span class="pl-c1" style="box-sizing: border-box; color: rgb(0, 134, 179);">Comparable</span>>(<span class="pl-en" style="box-sizing: border-box; color: rgb(121, 93, 163);">_</span> <span class="pl-smi" style="box-sizing: border-box;">l</span>: T, <span class="pl-en" style="box-sizing: border-box; color: rgb(121, 93, 163);">_</span> <span class="pl-smi" style="box-sizing: border-box;">r</span>: T) <span class="pl-k" style="box-sizing: border-box; color: rgb(167, 29, 93);">-></span> T { <span class="pl-k" style="box-sizing: border-box; color: rgb(167, 29, 93);">return</span> T<span class="pl-k" style="box-sizing: border-box; color: rgb(167, 29, 93);">.</span>_min(l, r) }
<span class="pl-k" style="box-sizing: border-box; color: rgb(167, 29, 93);">public</span> <span class="pl-k" style="box-sizing: border-box; color: rgb(167, 29, 93);">func</span> <span class="pl-en" style="box-sizing: border-box; color: rgb(121, 93, 163);">max</span><T <span class="pl-k" style="box-sizing: border-box; color: rgb(167, 29, 93);">:</span> <span class="pl-c1" style="box-sizing: border-box; color: rgb(0, 134, 179);">Comparable</span>>(<span class="pl-en" style="box-sizing: border-box; color: rgb(121, 93, 163);">_</span> <span class="pl-smi" style="box-sizing: border-box;">l</span>: T, <span class="pl-en" style="box-sizing: border-box; color: rgb(121, 93, 163);">_</span> <span class="pl-smi" style="box-sizing: border-box;">r</span>: T) <span class="pl-k" style="box-sizing: border-box; color: rgb(167, 29, 93);">-></span> T { <span class="pl-k" style="box-sizing: border-box; color: rgb(167, 29, 93);">return</span> T<span class="pl-k" style="box-sizing: border-box; color: rgb(167, 29, 93);">.</span>_max(l, r) }</pre></div><h3 style="box-sizing: border-box; margin-top: 24px; margin-bottom: 16px; font-size: 1.25em; line-height: 1.25; color: rgb(51, 51, 51); font-family: -apple-system, BlinkMacSystemFont, 'Segoe UI', Roboto, Helvetica, Arial, sans-serif, 'Apple Color Emoji', 'Segoe UI Emoji', 'Segoe UI Symbol'; background-color: rgb(255, 255, 255);" class=""><a id="user-content-handling-of-floating-point-comparisons" class="anchor" href="https://github.com/pyrtsa/swift-evolution/blob/ca89e7b3a1dffc99baa695a03544fcba75afd0f3/proposals/NNNN-formalized-ordering.md#handling-of-floating-point-comparisons" aria-hidden="true" style="box-sizing: border-box; background-color: transparent; -webkit-text-decoration-skip: objects; color: rgb(64, 120, 192); text-decoration: none; float: left; padding-right: 4px; margin-left: -20px; line-height: 1;"><svg aria-hidden="true" class="octicon octicon-link" height="16" version="1.1" viewBox="0 0 16 16" width="16"><path d="M4 9h1v1H4c-1.5 0-3-1.69-3-3.5S2.55 3 4 3h4c1.45 0 3 1.69 3 3.5 0 1.41-.91 2.72-2 3.25V8.59c.58-.45 1-1.27 1-2.09C10 5.22 8.98 4 8 4H4c-.98 0-2 1.22-2 2.5S3 9 4 9zm9-3h-1v1h1c1 0 2 1.22 2 2.5S13.98 12 13 12H9c-.98 0-2-1.22-2-2.5 0-.83.42-1.64 1-2.09V6.25c-1.09.53-2 1.84-2 3.25C6 11.31 7.55 13 9 13h4c1.45 0 3-1.69 3-3.5S14.5 6 13 6z"></path></svg></a>Handling of floating point comparisons</h3><p style="box-sizing: border-box; margin-top: 0px; margin-bottom: 16px; color: rgb(51, 51, 51); font-family: -apple-system, BlinkMacSystemFont, 'Segoe UI', Roboto, Helvetica, Arial, sans-serif, 'Apple Color Emoji', 'Segoe UI Emoji', 'Segoe UI Symbol'; font-size: 16px; background-color: rgb(255, 255, 255);" class=""><em style="box-sizing: border-box;" class="">The following text is written in terms of <code style="box-sizing: border-box; font-family: Consolas, 'Liberation Mono', Menlo, Courier, monospace; font-size: 14px; padding: 0.2em 0px; margin: 0px; background-color: rgba(0, 0, 0, 0.0392157); border-top-left-radius: 3px; border-top-right-radius: 3px; border-bottom-right-radius: 3px; border-bottom-left-radius: 3px;" class="">Double</code> but other floating-point types (<code style="box-sizing: border-box; font-family: Consolas, 'Liberation Mono', Menlo, Courier, monospace; font-size: 14px; padding: 0.2em 0px; margin: 0px; background-color: rgba(0, 0, 0, 0.0392157); border-top-left-radius: 3px; border-top-right-radius: 3px; border-bottom-right-radius: 3px; border-bottom-left-radius: 3px;" class="">Float</code>, <code style="box-sizing: border-box; font-family: Consolas, 'Liberation Mono', Menlo, Courier, monospace; font-size: 14px; padding: 0.2em 0px; margin: 0px; background-color: rgba(0, 0, 0, 0.0392157); border-top-left-radius: 3px; border-top-right-radius: 3px; border-bottom-right-radius: 3px; border-bottom-left-radius: 3px;" class="">Float80</code>) are proposed the same treatment.</em></p><p style="box-sizing: border-box; margin-top: 0px; margin-bottom: 16px; color: rgb(51, 51, 51); font-family: -apple-system, BlinkMacSystemFont, 'Segoe UI', Roboto, Helvetica, Arial, sans-serif, 'Apple Color Emoji', 'Segoe UI Emoji', 'Segoe UI Symbol'; font-size: 16px; background-color: rgb(255, 255, 255);" class="">The IEEE-754 floating point specification has two oddities when it comes to orderability: there are two zeros (<code style="box-sizing: border-box; font-family: Consolas, 'Liberation Mono', Menlo, Courier, monospace; font-size: 14px; padding: 0.2em 0px; margin: 0px; background-color: rgba(0, 0, 0, 0.0392157); border-top-left-radius: 3px; border-top-right-radius: 3px; border-bottom-right-radius: 3px; border-bottom-left-radius: 3px;" class="">0.0</code> and <code style="box-sizing: border-box; font-family: Consolas, 'Liberation Mono', Menlo, Courier, monospace; font-size: 14px; padding: 0.2em 0px; margin: 0px; background-color: rgba(0, 0, 0, 0.0392157); border-top-left-radius: 3px; border-top-right-radius: 3px; border-bottom-right-radius: 3px; border-bottom-left-radius: 3px;" class="">-0.0</code>) which are considered equal to each other, and there are <em style="box-sizing: border-box;" class="">multiple</em> not-a-number values <code style="box-sizing: border-box; font-family: Consolas, 'Liberation Mono', Menlo, Courier, monospace; font-size: 14px; padding: 0.2em 0px; margin: 0px; background-color: rgba(0, 0, 0, 0.0392157); border-top-left-radius: 3px; border-top-right-radius: 3px; border-bottom-right-radius: 3px; border-bottom-left-radius: 3px;" class="">x</code> for which <code style="box-sizing: border-box; font-family: Consolas, 'Liberation Mono', Menlo, Courier, monospace; font-size: 14px; padding: 0.2em 0px; margin: 0px; background-color: rgba(0, 0, 0, 0.0392157); border-top-left-radius: 3px; border-top-right-radius: 3px; border-bottom-right-radius: 3px; border-bottom-left-radius: 3px;" class="">x.isNaN == true</code> and <code style="box-sizing: border-box; font-family: Consolas, 'Liberation Mono', Menlo, Courier, monospace; font-size: 14px; padding: 0.2em 0px; margin: 0px; background-color: rgba(0, 0, 0, 0.0392157); border-top-left-radius: 3px; border-top-right-radius: 3px; border-bottom-right-radius: 3px; border-bottom-left-radius: 3px;" class="">x != y</code> with any value of <code style="box-sizing: border-box; font-family: Consolas, 'Liberation Mono', Menlo, Courier, monospace; font-size: 14px; padding: 0.2em 0px; margin: 0px; background-color: rgba(0, 0, 0, 0.0392157); border-top-left-radius: 3px; border-top-right-radius: 3px; border-bottom-right-radius: 3px; border-bottom-left-radius: 3px;" class="">y</code>, even <code style="box-sizing: border-box; font-family: Consolas, 'Liberation Mono', Menlo, Courier, monospace; font-size: 14px; padding: 0.2em 0px; margin: 0px; background-color: rgba(0, 0, 0, 0.0392157); border-top-left-radius: 3px; border-top-right-radius: 3px; border-bottom-right-radius: 3px; border-bottom-left-radius: 3px;" class="">x</code> itself. (Remark: the most common NaN value is obtained by the static property <code style="box-sizing: border-box; font-family: Consolas, 'Liberation Mono', Menlo, Courier, monospace; font-size: 14px; padding: 0.2em 0px; margin: 0px; background-color: rgba(0, 0, 0, 0.0392157); border-top-left-radius: 3px; border-top-right-radius: 3px; border-bottom-right-radius: 3px; border-bottom-left-radius: 3px;" class="">Double.nan</code>.)</p><p style="box-sizing: border-box; margin-top: 0px; margin-bottom: 16px; color: rgb(51, 51, 51); font-family: -apple-system, BlinkMacSystemFont, 'Segoe UI', Roboto, Helvetica, Arial, sans-serif, 'Apple Color Emoji', 'Segoe UI Emoji', 'Segoe UI Symbol'; font-size: 16px; background-color: rgb(255, 255, 255);" class="">The interface of <code style="box-sizing: border-box; font-family: Consolas, 'Liberation Mono', Menlo, Courier, monospace; font-size: 14px; padding: 0.2em 0px; margin: 0px; background-color: rgba(0, 0, 0, 0.0392157); border-top-left-radius: 3px; border-top-right-radius: 3px; border-bottom-right-radius: 3px; border-bottom-left-radius: 3px;" class="">Comparable</code> is designed so that <code style="box-sizing: border-box; font-family: Consolas, 'Liberation Mono', Menlo, Courier, monospace; font-size: 14px; padding: 0.2em 0px; margin: 0px; background-color: rgba(0, 0, 0, 0.0392157); border-top-left-radius: 3px; border-top-right-radius: 3px; border-bottom-right-radius: 3px; border-bottom-left-radius: 3px;" class=""><=></code> alone is able to produce a total order among all possible <code style="box-sizing: border-box; font-family: Consolas, 'Liberation Mono', Menlo, Courier, monospace; font-size: 14px; padding: 0.2em 0px; margin: 0px; background-color: rgba(0, 0, 0, 0.0392157); border-top-left-radius: 3px; border-top-right-radius: 3px; border-bottom-right-radius: 3px; border-bottom-left-radius: 3px;" class="">Double</code>values, sorting negative NaNs less than any other values, and positive NaNs greater than any other. Otherwise, within the range of totally ordered floating point values, <code style="box-sizing: border-box; font-family: Consolas, 'Liberation Mono', Menlo, Courier, monospace; font-size: 14px; padding: 0.2em 0px; margin: 0px; background-color: rgba(0, 0, 0, 0.0392157); border-top-left-radius: 3px; border-top-right-radius: 3px; border-bottom-right-radius: 3px; border-bottom-left-radius: 3px;" class="">-Double.infinity ... Double.infinity</code>, the result of <code style="box-sizing: border-box; font-family: Consolas, 'Liberation Mono', Menlo, Courier, monospace; font-size: 14px; padding: 0.2em 0px; margin: 0px; background-color: rgba(0, 0, 0, 0.0392157); border-top-left-radius: 3px; border-top-right-radius: 3px; border-bottom-right-radius: 3px; border-bottom-left-radius: 3px;" class="">a <=> b</code> remains in full agreement with the laws of <code style="box-sizing: border-box; font-family: Consolas, 'Liberation Mono', Menlo, Courier, monospace; font-size: 14px; padding: 0.2em 0px; margin: 0px; background-color: rgba(0, 0, 0, 0.0392157); border-top-left-radius: 3px; border-top-right-radius: 3px; border-bottom-right-radius: 3px; border-bottom-left-radius: 3px;" class="">a < b</code>, <code style="box-sizing: border-box; font-family: Consolas, 'Liberation Mono', Menlo, Courier, monospace; font-size: 14px; padding: 0.2em 0px; margin: 0px; background-color: rgba(0, 0, 0, 0.0392157); border-top-left-radius: 3px; border-top-right-radius: 3px; border-bottom-right-radius: 3px; border-bottom-left-radius: 3px;" class="">a <= b</code>, and <code style="box-sizing: border-box; font-family: Consolas, 'Liberation Mono', Menlo, Courier, monospace; font-size: 14px; padding: 0.2em 0px; margin: 0px; background-color: rgba(0, 0, 0, 0.0392157); border-top-left-radius: 3px; border-top-right-radius: 3px; border-bottom-right-radius: 3px; border-bottom-left-radius: 3px;" class="">a == b</code>.</p><p style="box-sizing: border-box; margin-top: 0px; margin-bottom: 16px; color: rgb(51, 51, 51); font-family: -apple-system, BlinkMacSystemFont, 'Segoe UI', Roboto, Helvetica, Arial, sans-serif, 'Apple Color Emoji', 'Segoe UI Emoji', 'Segoe UI Symbol'; font-size: 16px; background-color: rgb(255, 255, 255);" class="">The suggested implementation of <code style="box-sizing: border-box; font-family: Consolas, 'Liberation Mono', Menlo, Courier, monospace; font-size: 14px; padding: 0.2em 0px; margin: 0px; background-color: rgba(0, 0, 0, 0.0392157); border-top-left-radius: 3px; border-top-right-radius: 3px; border-bottom-right-radius: 3px; border-bottom-left-radius: 3px;" class="">Double : Comparable</code> makes <code style="box-sizing: border-box; font-family: Consolas, 'Liberation Mono', Menlo, Courier, monospace; font-size: 14px; padding: 0.2em 0px; margin: 0px; background-color: rgba(0, 0, 0, 0.0392157); border-top-left-radius: 3px; border-top-right-radius: 3px; border-bottom-right-radius: 3px; border-bottom-left-radius: 3px;" class=""><=></code> distinguish between every different <code style="box-sizing: border-box; font-family: Consolas, 'Liberation Mono', Menlo, Courier, monospace; font-size: 14px; padding: 0.2em 0px; margin: 0px; background-color: rgba(0, 0, 0, 0.0392157); border-top-left-radius: 3px; border-top-right-radius: 3px; border-bottom-right-radius: 3px; border-bottom-left-radius: 3px;" class="">bitPattern</code>of NaN:</p><div class="highlight highlight-source-swift" style="box-sizing: border-box; margin-bottom: 16px; color: rgb(51, 51, 51); font-family: -apple-system, BlinkMacSystemFont, 'Segoe UI', Roboto, Helvetica, Arial, sans-serif, 'Apple Color Emoji', 'Segoe UI Emoji', 'Segoe UI Symbol'; font-size: 16px; background-color: rgb(255, 255, 255);"><pre style="box-sizing: border-box; font-family: Consolas, 'Liberation Mono', Menlo, Courier, monospace; font-size: 14px; margin-top: 0px; margin-bottom: 0px; line-height: 1.45; word-wrap: normal; padding: 16px; overflow: auto; background-color: rgb(247, 247, 247); border-top-left-radius: 3px; border-top-right-radius: 3px; border-bottom-right-radius: 3px; border-bottom-left-radius: 3px; word-break: normal;" class=""><span class="pl-k" style="box-sizing: border-box; color: rgb(167, 29, 93);">extension</span> <span class="pl-c1" style="box-sizing: border-box; color: rgb(0, 134, 179);">Double</span> <span class="pl-k" style="box-sizing: border-box; color: rgb(167, 29, 93);">:</span> <span class="pl-c1" style="box-sizing: border-box; color: rgb(0, 134, 179);">Comparable</span> {
<span class="pl-k" style="box-sizing: border-box; color: rgb(167, 29, 93);">public</span> <span class="pl-k" style="box-sizing: border-box; color: rgb(167, 29, 93);">static</span> <span class="pl-k" style="box-sizing: border-box; color: rgb(167, 29, 93);">func</span> <span class="pl-en" style="box-sizing: border-box; color: rgb(121, 93, 163);"><=></span> (l: <span class="pl-c1" style="box-sizing: border-box; color: rgb(0, 134, 179);">Double</span>, r: <span class="pl-c1" style="box-sizing: border-box; color: rgb(0, 134, 179);">Double</span>) <span class="pl-k" style="box-sizing: border-box; color: rgb(167, 29, 93);">-></span> Ordering {
<span class="pl-k" style="box-sizing: border-box; color: rgb(167, 29, 93);">func</span> <span class="pl-en" style="box-sizing: border-box; color: rgb(121, 93, 163);">ordinal</span>(<span class="pl-en" style="box-sizing: border-box; color: rgb(121, 93, 163);">_</span> <span class="pl-smi" style="box-sizing: border-box;">x</span>: <span class="pl-c1" style="box-sizing: border-box; color: rgb(0, 134, 179);">UInt64</span>) <span class="pl-k" style="box-sizing: border-box; color: rgb(167, 29, 93);">-></span> <span class="pl-c1" style="box-sizing: border-box; color: rgb(0, 134, 179);">UInt64</span> {
<span class="pl-k" style="box-sizing: border-box; color: rgb(167, 29, 93);">return</span> x <span class="pl-k" style="box-sizing: border-box; color: rgb(167, 29, 93);"><</span> 0x80000000_00000000 <span class="pl-k" style="box-sizing: border-box; color: rgb(167, 29, 93);">?</span> x <span class="pl-k" style="box-sizing: border-box; color: rgb(167, 29, 93);">+</span> 0x7fffffff_ffffffff <span class="pl-k" style="box-sizing: border-box; color: rgb(167, 29, 93);">:</span> <span class="pl-k" style="box-sizing: border-box; color: rgb(167, 29, 93);">~</span>x
}
<span class="pl-k" style="box-sizing: border-box; color: rgb(167, 29, 93);">return</span> ordinal(l<span class="pl-k" style="box-sizing: border-box; color: rgb(167, 29, 93);">.</span>bitPattern) <span class="pl-k" style="box-sizing: border-box; color: rgb(167, 29, 93);"><=></span> ordinal(r<span class="pl-k" style="box-sizing: border-box; color: rgb(167, 29, 93);">.</span>bitPattern)
}
<span class="pl-k" style="box-sizing: border-box; color: rgb(167, 29, 93);">public</span> <span class="pl-k" style="box-sizing: border-box; color: rgb(167, 29, 93);">static</span> <span class="pl-k" style="box-sizing: border-box; color: rgb(167, 29, 93);">func</span> <span class="pl-en" style="box-sizing: border-box; color: rgb(121, 93, 163);">==</span> (l: <span class="pl-c1" style="box-sizing: border-box; color: rgb(0, 134, 179);">Double</span>, r: <span class="pl-c1" style="box-sizing: border-box; color: rgb(0, 134, 179);">Double</span>) <span class="pl-k" style="box-sizing: border-box; color: rgb(167, 29, 93);">-></span> <span class="pl-c1" style="box-sizing: border-box; color: rgb(0, 134, 179);">Bool</span> { <span class="pl-k" style="box-sizing: border-box; color: rgb(167, 29, 93);">return</span> Builtin<span class="pl-k" style="box-sizing: border-box; color: rgb(167, 29, 93);">.</span>eq(l, r) }
<span class="pl-k" style="box-sizing: border-box; color: rgb(167, 29, 93);">public</span> <span class="pl-k" style="box-sizing: border-box; color: rgb(167, 29, 93);">static</span> <span class="pl-k" style="box-sizing: border-box; color: rgb(167, 29, 93);">func</span> <span class="pl-en" style="box-sizing: border-box; color: rgb(121, 93, 163);"><</span> (l: <span class="pl-c1" style="box-sizing: border-box; color: rgb(0, 134, 179);">Double</span>, r: <span class="pl-c1" style="box-sizing: border-box; color: rgb(0, 134, 179);">Double</span>) <span class="pl-k" style="box-sizing: border-box; color: rgb(167, 29, 93);">-></span> <span class="pl-c1" style="box-sizing: border-box; color: rgb(0, 134, 179);">Bool</span> { <span class="pl-k" style="box-sizing: border-box; color: rgb(167, 29, 93);">return</span> Builtin<span class="pl-k" style="box-sizing: border-box; color: rgb(167, 29, 93);">.</span>lt(l, r) }
<span class="pl-k" style="box-sizing: border-box; color: rgb(167, 29, 93);">public</span> <span class="pl-k" style="box-sizing: border-box; color: rgb(167, 29, 93);">static</span> <span class="pl-k" style="box-sizing: border-box; color: rgb(167, 29, 93);">func</span> <span class="pl-en" style="box-sizing: border-box; color: rgb(121, 93, 163);"><=</span> (l: <span class="pl-c1" style="box-sizing: border-box; color: rgb(0, 134, 179);">Double</span>, r: <span class="pl-c1" style="box-sizing: border-box; color: rgb(0, 134, 179);">Double</span>) <span class="pl-k" style="box-sizing: border-box; color: rgb(167, 29, 93);">-></span> <span class="pl-c1" style="box-sizing: border-box; color: rgb(0, 134, 179);">Bool</span> { <span class="pl-k" style="box-sizing: border-box; color: rgb(167, 29, 93);">return</span> Builtin<span class="pl-k" style="box-sizing: border-box; color: rgb(167, 29, 93);">.</span>le(l, r) }
<span class="pl-k" style="box-sizing: border-box; color: rgb(167, 29, 93);">public</span> <span class="pl-k" style="box-sizing: border-box; color: rgb(167, 29, 93);">static</span> <span class="pl-k" style="box-sizing: border-box; color: rgb(167, 29, 93);">func</span> <span class="pl-en" style="box-sizing: border-box; color: rgb(121, 93, 163);">_min</span>(l: <span class="pl-c1" style="box-sizing: border-box; color: rgb(0, 134, 179);">Double</span>, r: <span class="pl-c1" style="box-sizing: border-box; color: rgb(0, 134, 179);">Double</span>) <span class="pl-k" style="box-sizing: border-box; color: rgb(167, 29, 93);">-></span> <span class="pl-c1" style="box-sizing: border-box; color: rgb(0, 134, 179);">Double</span> { <span class="pl-k" style="box-sizing: border-box; color: rgb(167, 29, 93);">return</span> Builtin<span class="pl-k" style="box-sizing: border-box; color: rgb(167, 29, 93);">.</span>fmin(l, r) }
<span class="pl-k" style="box-sizing: border-box; color: rgb(167, 29, 93);">public</span> <span class="pl-k" style="box-sizing: border-box; color: rgb(167, 29, 93);">static</span> <span class="pl-k" style="box-sizing: border-box; color: rgb(167, 29, 93);">func</span> <span class="pl-en" style="box-sizing: border-box; color: rgb(121, 93, 163);">_max</span>(l: <span class="pl-c1" style="box-sizing: border-box; color: rgb(0, 134, 179);">Double</span>, r: <span class="pl-c1" style="box-sizing: border-box; color: rgb(0, 134, 179);">Double</span>) <span class="pl-k" style="box-sizing: border-box; color: rgb(167, 29, 93);">-></span> <span class="pl-c1" style="box-sizing: border-box; color: rgb(0, 134, 179);">Double</span> { <span class="pl-k" style="box-sizing: border-box; color: rgb(167, 29, 93);">return</span> Builtin<span class="pl-k" style="box-sizing: border-box; color: rgb(167, 29, 93);">.</span>fmax(l, r) }
}
<span class="pl-c" style="box-sizing: border-box; color: rgb(150, 152, 150);">// Likewise:</span>
<span class="pl-k" style="box-sizing: border-box; color: rgb(167, 29, 93);">extension</span> <span class="pl-c1" style="box-sizing: border-box; color: rgb(0, 134, 179);">Float</span> <span class="pl-k" style="box-sizing: border-box; color: rgb(167, 29, 93);">:</span> <span class="pl-c1" style="box-sizing: border-box; color: rgb(0, 134, 179);">Comparable</span> { <span class="pl-k" style="box-sizing: border-box; color: rgb(167, 29, 93);">...</span> }
<span class="pl-k" style="box-sizing: border-box; color: rgb(167, 29, 93);">extension</span> <span class="pl-c1" style="box-sizing: border-box; color: rgb(0, 134, 179);">Float80</span> <span class="pl-k" style="box-sizing: border-box; color: rgb(167, 29, 93);">:</span> <span class="pl-c1" style="box-sizing: border-box; color: rgb(0, 134, 179);">Comparable</span> { <span class="pl-k" style="box-sizing: border-box; color: rgb(167, 29, 93);">...</span> }</pre></div><h3 style="box-sizing: border-box; margin-top: 24px; margin-bottom: 16px; font-size: 1.25em; line-height: 1.25; color: rgb(51, 51, 51); font-family: -apple-system, BlinkMacSystemFont, 'Segoe UI', Roboto, Helvetica, Arial, sans-serif, 'Apple Color Emoji', 'Segoe UI Emoji', 'Segoe UI Symbol'; background-color: rgb(255, 255, 255);" class=""><a id="user-content-tuples-and-order-reversal" class="anchor" href="https://github.com/pyrtsa/swift-evolution/blob/ca89e7b3a1dffc99baa695a03544fcba75afd0f3/proposals/NNNN-formalized-ordering.md#tuples-and-order-reversal" aria-hidden="true" style="box-sizing: border-box; background-color: transparent; -webkit-text-decoration-skip: objects; color: rgb(64, 120, 192); text-decoration: none; float: left; padding-right: 4px; margin-left: -20px; line-height: 1;"><svg aria-hidden="true" class="octicon octicon-link" height="16" version="1.1" viewBox="0 0 16 16" width="16"><path d="M4 9h1v1H4c-1.5 0-3-1.69-3-3.5S2.55 3 4 3h4c1.45 0 3 1.69 3 3.5 0 1.41-.91 2.72-2 3.25V8.59c.58-.45 1-1.27 1-2.09C10 5.22 8.98 4 8 4H4c-.98 0-2 1.22-2 2.5S3 9 4 9zm9-3h-1v1h1c1 0 2 1.22 2 2.5S13.98 12 13 12H9c-.98 0-2-1.22-2-2.5 0-.83.42-1.64 1-2.09V6.25c-1.09.53-2 1.84-2 3.25C6 11.31 7.55 13 9 13h4c1.45 0 3-1.69 3-3.5S14.5 6 13 6z"></path></svg></a>Tuples and order reversal</h3><p style="box-sizing: border-box; margin-top: 0px; margin-bottom: 16px; color: rgb(51, 51, 51); font-family: -apple-system, BlinkMacSystemFont, 'Segoe UI', Roboto, Helvetica, Arial, sans-serif, 'Apple Color Emoji', 'Segoe UI Emoji', 'Segoe UI Symbol'; font-size: 16px; background-color: rgb(255, 255, 255);" class="">Due to missing language support, tuples of <code style="box-sizing: border-box; font-family: Consolas, 'Liberation Mono', Menlo, Courier, monospace; font-size: 14px; padding: 0.2em 0px; margin: 0px; background-color: rgba(0, 0, 0, 0.0392157); border-top-left-radius: 3px; border-top-right-radius: 3px; border-bottom-right-radius: 3px; border-bottom-left-radius: 3px;" class="">Comparable</code> elements cannot be <code style="box-sizing: border-box; font-family: Consolas, 'Liberation Mono', Menlo, Courier, monospace; font-size: 14px; padding: 0.2em 0px; margin: 0px; background-color: rgba(0, 0, 0, 0.0392157); border-top-left-radius: 3px; border-top-right-radius: 3px; border-bottom-right-radius: 3px; border-bottom-left-radius: 3px;" class="">Comparable</code> themselves, but in the spirit of <a href="https://github.com/apple/swift-evolution/blob/master/proposals/0015-tuple-comparison-operators.md" style="box-sizing: border-box; background-color: transparent; -webkit-text-decoration-skip: objects; color: rgb(64, 120, 192); text-decoration: none;" class="">SE-0015</a>, such tuples are given their overloads of <code style="box-sizing: border-box; font-family: Consolas, 'Liberation Mono', Menlo, Courier, monospace; font-size: 14px; padding: 0.2em 0px; margin: 0px; background-color: rgba(0, 0, 0, 0.0392157); border-top-left-radius: 3px; border-top-right-radius: 3px; border-bottom-right-radius: 3px; border-bottom-left-radius: 3px;" class=""><=></code> up to a standard library defined maximum arity:</p><div class="highlight highlight-source-swift" style="box-sizing: border-box; margin-bottom: 16px; color: rgb(51, 51, 51); font-family: -apple-system, BlinkMacSystemFont, 'Segoe UI', Roboto, Helvetica, Arial, sans-serif, 'Apple Color Emoji', 'Segoe UI Emoji', 'Segoe UI Symbol'; font-size: 16px; background-color: rgb(255, 255, 255);"><pre style="box-sizing: border-box; font-family: Consolas, 'Liberation Mono', Menlo, Courier, monospace; font-size: 14px; margin-top: 0px; margin-bottom: 0px; line-height: 1.45; word-wrap: normal; padding: 16px; overflow: auto; background-color: rgb(247, 247, 247); border-top-left-radius: 3px; border-top-right-radius: 3px; border-bottom-right-radius: 3px; border-bottom-left-radius: 3px; word-break: normal;" class=""><span class="pl-k" style="box-sizing: border-box; color: rgb(167, 29, 93);">public</span> <span class="pl-k" style="box-sizing: border-box; color: rgb(167, 29, 93);">func</span> <span class="pl-en" style="box-sizing: border-box; color: rgb(121, 93, 163);"><=></span> <A <span class="pl-k" style="box-sizing: border-box; color: rgb(167, 29, 93);">:</span> <span class="pl-c1" style="box-sizing: border-box; color: rgb(0, 134, 179);">Comparable</span>, B <span class="pl-k" style="box-sizing: border-box; color: rgb(167, 29, 93);">:</span> <span class="pl-c1" style="box-sizing: border-box; color: rgb(0, 134, 179);">Comparable</span>>(lhs: (A, B), rhs: (A, B)) <span class="pl-k" style="box-sizing: border-box; color: rgb(167, 29, 93);">-></span> Ordering {
<span class="pl-k" style="box-sizing: border-box; color: rgb(167, 29, 93);">let</span> a <span class="pl-k" style="box-sizing: border-box; color: rgb(167, 29, 93);">=</span> lhs<span class="pl-k" style="box-sizing: border-box; color: rgb(167, 29, 93);">.</span><span class="pl-c1" style="box-sizing: border-box; color: rgb(0, 134, 179);">0</span> <span class="pl-k" style="box-sizing: border-box; color: rgb(167, 29, 93);"><=></span> rhs<span class="pl-k" style="box-sizing: border-box; color: rgb(167, 29, 93);">.</span><span class="pl-c1" style="box-sizing: border-box; color: rgb(0, 134, 179);">0</span>
<span class="pl-k" style="box-sizing: border-box; color: rgb(167, 29, 93);">if</span> a <span class="pl-k" style="box-sizing: border-box; color: rgb(167, 29, 93);">!=</span> <span class="pl-k" style="box-sizing: border-box; color: rgb(167, 29, 93);">.</span>equal { <span class="pl-k" style="box-sizing: border-box; color: rgb(167, 29, 93);">return</span> a }
<span class="pl-k" style="box-sizing: border-box; color: rgb(167, 29, 93);">let</span> b <span class="pl-k" style="box-sizing: border-box; color: rgb(167, 29, 93);">=</span> lhs<span class="pl-k" style="box-sizing: border-box; color: rgb(167, 29, 93);">.</span><span class="pl-c1" style="box-sizing: border-box; color: rgb(0, 134, 179);">1</span> <span class="pl-k" style="box-sizing: border-box; color: rgb(167, 29, 93);"><=></span> rhs<span class="pl-k" style="box-sizing: border-box; color: rgb(167, 29, 93);">.</span><span class="pl-c1" style="box-sizing: border-box; color: rgb(0, 134, 179);">1</span>
<span class="pl-k" style="box-sizing: border-box; color: rgb(167, 29, 93);">if</span> b <span class="pl-k" style="box-sizing: border-box; color: rgb(167, 29, 93);">!=</span> <span class="pl-k" style="box-sizing: border-box; color: rgb(167, 29, 93);">.</span>equal { <span class="pl-k" style="box-sizing: border-box; color: rgb(167, 29, 93);">return</span> b }
<span class="pl-k" style="box-sizing: border-box; color: rgb(167, 29, 93);">return</span> <span class="pl-k" style="box-sizing: border-box; color: rgb(167, 29, 93);">.</span>equal
}
<span class="pl-c" style="box-sizing: border-box; color: rgb(150, 152, 150);">// Similarly for <A : Comparable, B : Comparable, C : Comparable>, etc.</span></pre></div><p style="box-sizing: border-box; margin-top: 0px; margin-bottom: 16px; color: rgb(51, 51, 51); font-family: -apple-system, BlinkMacSystemFont, 'Segoe UI', Roboto, Helvetica, Arial, sans-serif, 'Apple Color Emoji', 'Segoe UI Emoji', 'Segoe UI Symbol'; font-size: 16px; background-color: rgb(255, 255, 255);" class="">To simplify the reversal of a given ordering operation, two members of <code style="box-sizing: border-box; font-family: Consolas, 'Liberation Mono', Menlo, Courier, monospace; font-size: 14px; padding: 0.2em 0px; margin: 0px; background-color: rgba(0, 0, 0, 0.0392157); border-top-left-radius: 3px; border-top-right-radius: 3px; border-bottom-right-radius: 3px; border-bottom-left-radius: 3px;" class="">Ordering</code> are provided in an extension:</p><div class="highlight highlight-source-swift" style="box-sizing: border-box; margin-bottom: 16px; color: rgb(51, 51, 51); font-family: -apple-system, BlinkMacSystemFont, 'Segoe UI', Roboto, Helvetica, Arial, sans-serif, 'Apple Color Emoji', 'Segoe UI Emoji', 'Segoe UI Symbol'; font-size: 16px; background-color: rgb(255, 255, 255);"><pre style="box-sizing: border-box; font-family: Consolas, 'Liberation Mono', Menlo, Courier, monospace; font-size: 14px; margin-top: 0px; margin-bottom: 0px; line-height: 1.45; word-wrap: normal; padding: 16px; overflow: auto; background-color: rgb(247, 247, 247); border-top-left-radius: 3px; border-top-right-radius: 3px; border-bottom-right-radius: 3px; border-bottom-left-radius: 3px; word-break: normal;" class=""><span class="pl-k" style="box-sizing: border-box; color: rgb(167, 29, 93);">extension</span> Ordering {
<span class="pl-k" style="box-sizing: border-box; color: rgb(167, 29, 93);">public</span> <span class="pl-k" style="box-sizing: border-box; color: rgb(167, 29, 93);">static</span> <span class="pl-k" style="box-sizing: border-box; color: rgb(167, 29, 93);">func</span> <span class="pl-en" style="box-sizing: border-box; color: rgb(121, 93, 163);">reversing</span><T <span class="pl-k" style="box-sizing: border-box; color: rgb(167, 29, 93);">:</span> <span class="pl-c1" style="box-sizing: border-box; color: rgb(0, 134, 179);">Comparable</span>>(<span class="pl-en" style="box-sizing: border-box; color: rgb(121, 93, 163);">_</span> <span class="pl-smi" style="box-sizing: border-box;">ordering</span>: (T, T) <span class="pl-k" style="box-sizing: border-box; color: rgb(167, 29, 93);">-></span> Ordering)
<span class="pl-k" style="box-sizing: border-box; color: rgb(167, 29, 93);">-></span> (T, T) <span class="pl-k" style="box-sizing: border-box; color: rgb(167, 29, 93);">-></span> Ordering
{
<span class="pl-k" style="box-sizing: border-box; color: rgb(167, 29, 93);">return</span> { l, r <span class="pl-k" style="box-sizing: border-box; color: rgb(167, 29, 93);">in</span> ordering(r, l) }
}
<span class="pl-k" style="box-sizing: border-box; color: rgb(167, 29, 93);">public</span> <span class="pl-k" style="box-sizing: border-box; color: rgb(167, 29, 93);">var</span> reversed: Ordering {
<span class="pl-k" style="box-sizing: border-box; color: rgb(167, 29, 93);">switch</span> <span class="pl-k" style="box-sizing: border-box; color: rgb(167, 29, 93);">self</span> {
<span class="pl-k" style="box-sizing: border-box; color: rgb(167, 29, 93);">case</span> <span class="pl-k" style="box-sizing: border-box; color: rgb(167, 29, 93);">.</span>ascending: <span class="pl-k" style="box-sizing: border-box; color: rgb(167, 29, 93);">return</span> <span class="pl-k" style="box-sizing: border-box; color: rgb(167, 29, 93);">.</span>descending
<span class="pl-k" style="box-sizing: border-box; color: rgb(167, 29, 93);">case</span> <span class="pl-k" style="box-sizing: border-box; color: rgb(167, 29, 93);">.</span>equal: <span class="pl-k" style="box-sizing: border-box; color: rgb(167, 29, 93);">return</span> <span class="pl-k" style="box-sizing: border-box; color: rgb(167, 29, 93);">.</span>equal
<span class="pl-k" style="box-sizing: border-box; color: rgb(167, 29, 93);">case</span> <span class="pl-k" style="box-sizing: border-box; color: rgb(167, 29, 93);">.</span>descending: <span class="pl-k" style="box-sizing: border-box; color: rgb(167, 29, 93);">return</span> <span class="pl-k" style="box-sizing: border-box; color: rgb(167, 29, 93);">.</span>ascending
}
}
}</pre></div><h3 style="box-sizing: border-box; margin-top: 24px; margin-bottom: 16px; font-size: 1.25em; line-height: 1.25; color: rgb(51, 51, 51); font-family: -apple-system, BlinkMacSystemFont, 'Segoe UI', Roboto, Helvetica, Arial, sans-serif, 'Apple Color Emoji', 'Segoe UI Emoji', 'Segoe UI Symbol'; background-color: rgb(255, 255, 255);" class=""><a id="user-content-foundation" class="anchor" href="https://github.com/pyrtsa/swift-evolution/blob/ca89e7b3a1dffc99baa695a03544fcba75afd0f3/proposals/NNNN-formalized-ordering.md#foundation" aria-hidden="true" style="box-sizing: border-box; background-color: transparent; -webkit-text-decoration-skip: objects; color: rgb(64, 120, 192); text-decoration: none; float: left; padding-right: 4px; margin-left: -20px; line-height: 1;"><svg aria-hidden="true" class="octicon octicon-link" height="16" version="1.1" viewBox="0 0 16 16" width="16"><path d="M4 9h1v1H4c-1.5 0-3-1.69-3-3.5S2.55 3 4 3h4c1.45 0 3 1.69 3 3.5 0 1.41-.91 2.72-2 3.25V8.59c.58-.45 1-1.27 1-2.09C10 5.22 8.98 4 8 4H4c-.98 0-2 1.22-2 2.5S3 9 4 9zm9-3h-1v1h1c1 0 2 1.22 2 2.5S13.98 12 13 12H9c-.98 0-2-1.22-2-2.5 0-.83.42-1.64 1-2.09V6.25c-1.09.53-2 1.84-2 3.25C6 11.31 7.55 13 9 13h4c1.45 0 3-1.69 3-3.5S14.5 6 13 6z"></path></svg></a>Foundation</h3><p style="box-sizing: border-box; margin-top: 0px; margin-bottom: 16px; color: rgb(51, 51, 51); font-family: -apple-system, BlinkMacSystemFont, 'Segoe UI', Roboto, Helvetica, Arial, sans-serif, 'Apple Color Emoji', 'Segoe UI Emoji', 'Segoe UI Symbol'; font-size: 16px; background-color: rgb(255, 255, 255);" class="">In addition, <code style="box-sizing: border-box; font-family: Consolas, 'Liberation Mono', Menlo, Courier, monospace; font-size: 14px; padding: 0.2em 0px; margin: 0px; background-color: rgba(0, 0, 0, 0.0392157); border-top-left-radius: 3px; border-top-right-radius: 3px; border-bottom-right-radius: 3px; border-bottom-left-radius: 3px;" class="">Foundation</code> code will now bridge <code style="box-sizing: border-box; font-family: Consolas, 'Liberation Mono', Menlo, Courier, monospace; font-size: 14px; padding: 0.2em 0px; margin: 0px; background-color: rgba(0, 0, 0, 0.0392157); border-top-left-radius: 3px; border-top-right-radius: 3px; border-bottom-right-radius: 3px; border-bottom-left-radius: 3px;" class="">NSComparisonResult</code> to <code style="box-sizing: border-box; font-family: Consolas, 'Liberation Mono', Menlo, Courier, monospace; font-size: 14px; padding: 0.2em 0px; margin: 0px; background-color: rgba(0, 0, 0, 0.0392157); border-top-left-radius: 3px; border-top-right-radius: 3px; border-bottom-right-radius: 3px; border-bottom-left-radius: 3px;" class="">Ordering</code> allowing for a fluid, natural, and safe API.</p><h2 style="box-sizing: border-box; margin-top: 24px; margin-bottom: 16px; line-height: 1.25; padding-bottom: 0.3em; border-bottom-width: 1px; border-bottom-style: solid; border-bottom-color: rgb(238, 238, 238); color: rgb(51, 51, 51); font-family: -apple-system, BlinkMacSystemFont, 'Segoe UI', Roboto, Helvetica, Arial, sans-serif, 'Apple Color Emoji', 'Segoe UI Emoji', 'Segoe UI Symbol'; background-color: rgb(255, 255, 255);" class=""><a id="user-content-impact-on-existing-code" class="anchor" href="https://github.com/pyrtsa/swift-evolution/blob/ca89e7b3a1dffc99baa695a03544fcba75afd0f3/proposals/NNNN-formalized-ordering.md#impact-on-existing-code" aria-hidden="true" style="box-sizing: border-box; background-color: transparent; -webkit-text-decoration-skip: objects; color: rgb(64, 120, 192); text-decoration: none; float: left; padding-right: 4px; margin-left: -20px; line-height: 1;"><svg aria-hidden="true" class="octicon octicon-link" height="16" version="1.1" viewBox="0 0 16 16" width="16"><path d="M4 9h1v1H4c-1.5 0-3-1.69-3-3.5S2.55 3 4 3h4c1.45 0 3 1.69 3 3.5 0 1.41-.91 2.72-2 3.25V8.59c.58-.45 1-1.27 1-2.09C10 5.22 8.98 4 8 4H4c-.98 0-2 1.22-2 2.5S3 9 4 9zm9-3h-1v1h1c1 0 2 1.22 2 2.5S13.98 12 13 12H9c-.98 0-2-1.22-2-2.5 0-.83.42-1.64 1-2.09V6.25c-1.09.53-2 1.84-2 3.25C6 11.31 7.55 13 9 13h4c1.45 0 3-1.69 3-3.5S14.5 6 13 6z"></path></svg></a>Impact on existing code</h2><p style="box-sizing: border-box; margin-top: 0px; margin-bottom: 16px; color: rgb(51, 51, 51); font-family: -apple-system, BlinkMacSystemFont, 'Segoe UI', Roboto, Helvetica, Arial, sans-serif, 'Apple Color Emoji', 'Segoe UI Emoji', 'Segoe UI Symbol'; font-size: 16px; background-color: rgb(255, 255, 255);" class="">The biggest drawback of the proposed design is the large surface area of <code style="box-sizing: border-box; font-family: Consolas, 'Liberation Mono', Menlo, Courier, monospace; font-size: 14px; padding: 0.2em 0px; margin: 0px; background-color: rgba(0, 0, 0, 0.0392157); border-top-left-radius: 3px; border-top-right-radius: 3px; border-bottom-right-radius: 3px; border-bottom-left-radius: 3px;" class="">Comparable</code>'s interface, as well as the possibility of overriding the comparison operators by mistake. On the other hand, since the required <code style="box-sizing: border-box; font-family: Consolas, 'Liberation Mono', Menlo, Courier, monospace; font-size: 14px; padding: 0.2em 0px; margin: 0px; background-color: rgba(0, 0, 0, 0.0392157); border-top-left-radius: 3px; border-top-right-radius: 3px; border-bottom-right-radius: 3px; border-bottom-left-radius: 3px;" class=""><=></code> operator is new and affects all users porting their previously <code style="box-sizing: border-box; font-family: Consolas, 'Liberation Mono', Menlo, Courier, monospace; font-size: 14px; padding: 0.2em 0px; margin: 0px; background-color: rgba(0, 0, 0, 0.0392157); border-top-left-radius: 3px; border-top-right-radius: 3px; border-bottom-right-radius: 3px; border-bottom-left-radius: 3px;" class="">Comparable</code> data types to Swift 3, we can use documentation to suggest removing the redundant (and possibly faulty) implementations of other comparison operators.</p><p style="box-sizing: border-box; margin-top: 0px; margin-bottom: 16px; color: rgb(51, 51, 51); font-family: -apple-system, BlinkMacSystemFont, 'Segoe UI', Roboto, Helvetica, Arial, sans-serif, 'Apple Color Emoji', 'Segoe UI Emoji', 'Segoe UI Symbol'; font-size: 16px; background-color: rgb(255, 255, 255);" class="">Existing <code style="box-sizing: border-box; font-family: Consolas, 'Liberation Mono', Menlo, Courier, monospace; font-size: 14px; padding: 0.2em 0px; margin: 0px; background-color: rgba(0, 0, 0, 0.0392157); border-top-left-radius: 3px; border-top-right-radius: 3px; border-bottom-right-radius: 3px; border-bottom-left-radius: 3px;" class="">Equatable</code> but <span style="box-sizing: border-box; font-weight: 600;" class="">not</span> <code style="box-sizing: border-box; font-family: Consolas, 'Liberation Mono', Menlo, Courier, monospace; font-size: 14px; padding: 0.2em 0px; margin: 0px; background-color: rgba(0, 0, 0, 0.0392157); border-top-left-radius: 3px; border-top-right-radius: 3px; border-bottom-right-radius: 3px; border-bottom-left-radius: 3px;" class="">Comparable</code> types that define an equivalence relation with <code style="box-sizing: border-box; font-family: Consolas, 'Liberation Mono', Menlo, Courier, monospace; font-size: 14px; padding: 0.2em 0px; margin: 0px; background-color: rgba(0, 0, 0, 0.0392157); border-top-left-radius: 3px; border-top-right-radius: 3px; border-bottom-right-radius: 3px; border-bottom-left-radius: 3px;" class="">==</code> will remain unchanged.</p><p style="box-sizing: border-box; margin-top: 0px; margin-bottom: 16px; color: rgb(51, 51, 51); font-family: -apple-system, BlinkMacSystemFont, 'Segoe UI', Roboto, Helvetica, Arial, sans-serif, 'Apple Color Emoji', 'Segoe UI Emoji', 'Segoe UI Symbol'; font-size: 16px; background-color: rgb(255, 255, 255);" class="">Existing <code style="box-sizing: border-box; font-family: Consolas, 'Liberation Mono', Menlo, Courier, monospace; font-size: 14px; padding: 0.2em 0px; margin: 0px; background-color: rgba(0, 0, 0, 0.0392157); border-top-left-radius: 3px; border-top-right-radius: 3px; border-bottom-right-radius: 3px; border-bottom-left-radius: 3px;" class="">Comparable</code> types that define a total ordering with <code style="box-sizing: border-box; font-family: Consolas, 'Liberation Mono', Menlo, Courier, monospace; font-size: 14px; padding: 0.2em 0px; margin: 0px; background-color: rgba(0, 0, 0, 0.0392157); border-top-left-radius: 3px; border-top-right-radius: 3px; border-bottom-right-radius: 3px; border-bottom-left-radius: 3px;" class=""><</code> will need to implement <code style="box-sizing: border-box; font-family: Consolas, 'Liberation Mono', Menlo, Courier, monospace; font-size: 14px; padding: 0.2em 0px; margin: 0px; background-color: rgba(0, 0, 0, 0.0392157); border-top-left-radius: 3px; border-top-right-radius: 3px; border-bottom-right-radius: 3px; border-bottom-left-radius: 3px;" class=""><=></code> and should remove their existing implementation of any comparison operators, including <code style="box-sizing: border-box; font-family: Consolas, 'Liberation Mono', Menlo, Courier, monospace; font-size: 14px; padding: 0.2em 0px; margin: 0px; background-color: rgba(0, 0, 0, 0.0392157); border-top-left-radius: 3px; border-top-right-radius: 3px; border-bottom-right-radius: 3px; border-bottom-left-radius: 3px;" class="">==</code>. All other existing <code style="box-sizing: border-box; font-family: Consolas, 'Liberation Mono', Menlo, Courier, monospace; font-size: 14px; padding: 0.2em 0px; margin: 0px; background-color: rgba(0, 0, 0, 0.0392157); border-top-left-radius: 3px; border-top-right-radius: 3px; border-bottom-right-radius: 3px; border-bottom-left-radius: 3px;" class="">Comparable</code> types should implement <code style="box-sizing: border-box; font-family: Consolas, 'Liberation Mono', Menlo, Courier, monospace; font-size: 14px; padding: 0.2em 0px; margin: 0px; background-color: rgba(0, 0, 0, 0.0392157); border-top-left-radius: 3px; border-top-right-radius: 3px; border-bottom-right-radius: 3px; border-bottom-left-radius: 3px;" class=""><=></code> that provides a total ordering, or should drop their <code style="box-sizing: border-box; font-family: Consolas, 'Liberation Mono', Menlo, Courier, monospace; font-size: 14px; padding: 0.2em 0px; margin: 0px; background-color: rgba(0, 0, 0, 0.0392157); border-top-left-radius: 3px; border-top-right-radius: 3px; border-bottom-right-radius: 3px; border-bottom-left-radius: 3px;" class="">Comparable</code> conformance.</p><p style="box-sizing: border-box; margin-top: 0px; margin-bottom: 16px; color: rgb(51, 51, 51); font-family: -apple-system, BlinkMacSystemFont, 'Segoe UI', Roboto, Helvetica, Arial, sans-serif, 'Apple Color Emoji', 'Segoe UI Emoji', 'Segoe UI Symbol'; font-size: 16px; background-color: rgb(255, 255, 255);" class="">Before:</p><div class="highlight highlight-source-swift" style="box-sizing: border-box; margin-bottom: 16px; color: rgb(51, 51, 51); font-family: -apple-system, BlinkMacSystemFont, 'Segoe UI', Roboto, Helvetica, Arial, sans-serif, 'Apple Color Emoji', 'Segoe UI Emoji', 'Segoe UI Symbol'; font-size: 16px; background-color: rgb(255, 255, 255);"><pre style="box-sizing: border-box; font-family: Consolas, 'Liberation Mono', Menlo, Courier, monospace; font-size: 14px; margin-top: 0px; margin-bottom: 0px; line-height: 1.45; word-wrap: normal; padding: 16px; overflow: auto; background-color: rgb(247, 247, 247); border-top-left-radius: 3px; border-top-right-radius: 3px; border-bottom-right-radius: 3px; border-bottom-left-radius: 3px; word-break: normal;" class=""><span class="pl-k" style="box-sizing: border-box; color: rgb(167, 29, 93);">struct</span> Date: <span class="pl-c1" style="box-sizing: border-box; color: rgb(0, 134, 179);">Comparable</span> {
<span class="pl-k" style="box-sizing: border-box; color: rgb(167, 29, 93);">let</span> year: <span class="pl-c1" style="box-sizing: border-box; color: rgb(0, 134, 179);">Int</span>
<span class="pl-k" style="box-sizing: border-box; color: rgb(167, 29, 93);">let</span> month: <span class="pl-c1" style="box-sizing: border-box; color: rgb(0, 134, 179);">Int</span>
<span class="pl-k" style="box-sizing: border-box; color: rgb(167, 29, 93);">let</span> day: <span class="pl-c1" style="box-sizing: border-box; color: rgb(0, 134, 179);">Int</span>
}
<span class="pl-k" style="box-sizing: border-box; color: rgb(167, 29, 93);">func</span> <span class="pl-en" style="box-sizing: border-box; color: rgb(121, 93, 163);">==</span>(lhs: Date, rhs: Date) <span class="pl-k" style="box-sizing: border-box; color: rgb(167, 29, 93);">-></span> <span class="pl-c1" style="box-sizing: border-box; color: rgb(0, 134, 179);">Bool</span> {
<span class="pl-k" style="box-sizing: border-box; color: rgb(167, 29, 93);">return</span> lhs<span class="pl-k" style="box-sizing: border-box; color: rgb(167, 29, 93);">.</span>year <span class="pl-k" style="box-sizing: border-box; color: rgb(167, 29, 93);">==</span> rhs<span class="pl-k" style="box-sizing: border-box; color: rgb(167, 29, 93);">.</span>year
<span class="pl-k" style="box-sizing: border-box; color: rgb(167, 29, 93);">&&</span> lhs<span class="pl-k" style="box-sizing: border-box; color: rgb(167, 29, 93);">.</span>month <span class="pl-k" style="box-sizing: border-box; color: rgb(167, 29, 93);">==</span> rhs<span class="pl-k" style="box-sizing: border-box; color: rgb(167, 29, 93);">.</span>month
<span class="pl-k" style="box-sizing: border-box; color: rgb(167, 29, 93);">&&</span> lhs<span class="pl-k" style="box-sizing: border-box; color: rgb(167, 29, 93);">.</span>day <span class="pl-k" style="box-sizing: border-box; color: rgb(167, 29, 93);">==</span> rhs<span class="pl-k" style="box-sizing: border-box; color: rgb(167, 29, 93);">.</span>day
}
<span class="pl-k" style="box-sizing: border-box; color: rgb(167, 29, 93);">func</span> <span class="pl-en" style="box-sizing: border-box; color: rgb(121, 93, 163);"><</span>(lhs: Date, rhs: Date) <span class="pl-k" style="box-sizing: border-box; color: rgb(167, 29, 93);">-></span> <span class="pl-c1" style="box-sizing: border-box; color: rgb(0, 134, 179);">Bool</span> {
<span class="pl-k" style="box-sizing: border-box; color: rgb(167, 29, 93);">if</span> lhs<span class="pl-k" style="box-sizing: border-box; color: rgb(167, 29, 93);">.</span>year <span class="pl-k" style="box-sizing: border-box; color: rgb(167, 29, 93);">!=</span> rhs<span class="pl-k" style="box-sizing: border-box; color: rgb(167, 29, 93);">.</span>year {
<span class="pl-k" style="box-sizing: border-box; color: rgb(167, 29, 93);">return</span> lhs<span class="pl-k" style="box-sizing: border-box; color: rgb(167, 29, 93);">.</span>year <span class="pl-k" style="box-sizing: border-box; color: rgb(167, 29, 93);"><</span> rhs<span class="pl-k" style="box-sizing: border-box; color: rgb(167, 29, 93);">.</span>year
} <span class="pl-k" style="box-sizing: border-box; color: rgb(167, 29, 93);">else</span> <span class="pl-k" style="box-sizing: border-box; color: rgb(167, 29, 93);">if</span> lhs<span class="pl-k" style="box-sizing: border-box; color: rgb(167, 29, 93);">.</span>month <span class="pl-k" style="box-sizing: border-box; color: rgb(167, 29, 93);">!=</span> rhs<span class="pl-k" style="box-sizing: border-box; color: rgb(167, 29, 93);">.</span>month {
<span class="pl-k" style="box-sizing: border-box; color: rgb(167, 29, 93);">return</span> lhs<span class="pl-k" style="box-sizing: border-box; color: rgb(167, 29, 93);">.</span>month <span class="pl-k" style="box-sizing: border-box; color: rgb(167, 29, 93);"><</span> rhs<span class="pl-k" style="box-sizing: border-box; color: rgb(167, 29, 93);">.</span>month
} <span class="pl-k" style="box-sizing: border-box; color: rgb(167, 29, 93);">else</span> {
<span class="pl-k" style="box-sizing: border-box; color: rgb(167, 29, 93);">return</span> lhs<span class="pl-k" style="box-sizing: border-box; color: rgb(167, 29, 93);">.</span>day <span class="pl-k" style="box-sizing: border-box; color: rgb(167, 29, 93);"><</span> rhs<span class="pl-k" style="box-sizing: border-box; color: rgb(167, 29, 93);">.</span>day
}
}</pre></div><p style="box-sizing: border-box; margin-top: 0px; margin-bottom: 16px; color: rgb(51, 51, 51); font-family: -apple-system, BlinkMacSystemFont, 'Segoe UI', Roboto, Helvetica, Arial, sans-serif, 'Apple Color Emoji', 'Segoe UI Emoji', 'Segoe UI Symbol'; font-size: 16px; background-color: rgb(255, 255, 255);" class="">After, using the tuple overload of <code style="box-sizing: border-box; font-family: Consolas, 'Liberation Mono', Menlo, Courier, monospace; font-size: 14px; padding: 0.2em 0px; margin: 0px; background-color: rgba(0, 0, 0, 0.0392157); border-top-left-radius: 3px; border-top-right-radius: 3px; border-bottom-right-radius: 3px; border-bottom-left-radius: 3px;" class=""><=></code>:</p><div class="highlight highlight-source-swift" style="box-sizing: border-box; margin-bottom: 16px; color: rgb(51, 51, 51); font-family: -apple-system, BlinkMacSystemFont, 'Segoe UI', Roboto, Helvetica, Arial, sans-serif, 'Apple Color Emoji', 'Segoe UI Emoji', 'Segoe UI Symbol'; font-size: 16px; background-color: rgb(255, 255, 255);"><pre style="box-sizing: border-box; font-family: Consolas, 'Liberation Mono', Menlo, Courier, monospace; font-size: 14px; margin-top: 0px; margin-bottom: 0px; line-height: 1.45; word-wrap: normal; padding: 16px; overflow: auto; background-color: rgb(247, 247, 247); border-top-left-radius: 3px; border-top-right-radius: 3px; border-bottom-right-radius: 3px; border-bottom-left-radius: 3px; word-break: normal;" class=""><span class="pl-k" style="box-sizing: border-box; color: rgb(167, 29, 93);">struct</span> Date: <span class="pl-c1" style="box-sizing: border-box; color: rgb(0, 134, 179);">Comparable</span> {
<span class="pl-k" style="box-sizing: border-box; color: rgb(167, 29, 93);">let</span> year: <span class="pl-c1" style="box-sizing: border-box; color: rgb(0, 134, 179);">Int</span>
<span class="pl-k" style="box-sizing: border-box; color: rgb(167, 29, 93);">let</span> month: <span class="pl-c1" style="box-sizing: border-box; color: rgb(0, 134, 179);">Int</span>
<span class="pl-k" style="box-sizing: border-box; color: rgb(167, 29, 93);">let</span> day: <span class="pl-c1" style="box-sizing: border-box; color: rgb(0, 134, 179);">Int</span>
<span class="pl-k" style="box-sizing: border-box; color: rgb(167, 29, 93);">static</span> <span class="pl-k" style="box-sizing: border-box; color: rgb(167, 29, 93);">func</span> <span class="pl-en" style="box-sizing: border-box; color: rgb(121, 93, 163);"><=></span> (lhs: Date, rhs: Date) <span class="pl-k" style="box-sizing: border-box; color: rgb(167, 29, 93);">-></span> Ordering {
<span class="pl-k" style="box-sizing: border-box; color: rgb(167, 29, 93);">return</span> (lhs<span class="pl-k" style="box-sizing: border-box; color: rgb(167, 29, 93);">.</span>year, lhs<span class="pl-k" style="box-sizing: border-box; color: rgb(167, 29, 93);">.</span>month, lhs<span class="pl-k" style="box-sizing: border-box; color: rgb(167, 29, 93);">.</span>day)
<span class="pl-k" style="box-sizing: border-box; color: rgb(167, 29, 93);"><=></span> (rhs<span class="pl-k" style="box-sizing: border-box; color: rgb(167, 29, 93);">.</span>year, rhs<span class="pl-k" style="box-sizing: border-box; color: rgb(167, 29, 93);">.</span>month, rhs<span class="pl-k" style="box-sizing: border-box; color: rgb(167, 29, 93);">.</span>day)
}
<span class="pl-c" style="box-sizing: border-box; color: rgb(150, 152, 150);">// // Explicit version:</span>
<span class="pl-c" style="box-sizing: border-box; color: rgb(150, 152, 150);">// static func <=> (lhs: Date, rhs: Date) -> Ordering {</span>
<span class="pl-c" style="box-sizing: border-box; color: rgb(150, 152, 150);">// let yearResult = lhs.year <=> rhs.year</span>
<span class="pl-c" style="box-sizing: border-box; color: rgb(150, 152, 150);">// guard case .equal = yearResult else { return yearResult }</span>
<span class="pl-c" style="box-sizing: border-box; color: rgb(150, 152, 150);">// let monthResult = lhs.month <=> rhs.month</span>
<span class="pl-c" style="box-sizing: border-box; color: rgb(150, 152, 150);">// guard case .equal = monthResult else { return monthResult }</span>
<span class="pl-c" style="box-sizing: border-box; color: rgb(150, 152, 150);">// return lhs.day <=> rhs.day</span>
<span class="pl-c" style="box-sizing: border-box; color: rgb(150, 152, 150);">// }</span>
}</pre></div><h2 style="box-sizing: border-box; margin-top: 24px; margin-bottom: 16px; line-height: 1.25; padding-bottom: 0.3em; border-bottom-width: 1px; border-bottom-style: solid; border-bottom-color: rgb(238, 238, 238); color: rgb(51, 51, 51); font-family: -apple-system, BlinkMacSystemFont, 'Segoe UI', Roboto, Helvetica, Arial, sans-serif, 'Apple Color Emoji', 'Segoe UI Emoji', 'Segoe UI Symbol'; background-color: rgb(255, 255, 255);" class=""><a id="user-content-alternatives-considered" class="anchor" href="https://github.com/pyrtsa/swift-evolution/blob/ca89e7b3a1dffc99baa695a03544fcba75afd0f3/proposals/NNNN-formalized-ordering.md#alternatives-considered" aria-hidden="true" style="box-sizing: border-box; background-color: transparent; -webkit-text-decoration-skip: objects; color: rgb(64, 120, 192); text-decoration: none; float: left; padding-right: 4px; margin-left: -20px; line-height: 1;"><svg aria-hidden="true" class="octicon octicon-link" height="16" version="1.1" viewBox="0 0 16 16" width="16"><path d="M4 9h1v1H4c-1.5 0-3-1.69-3-3.5S2.55 3 4 3h4c1.45 0 3 1.69 3 3.5 0 1.41-.91 2.72-2 3.25V8.59c.58-.45 1-1.27 1-2.09C10 5.22 8.98 4 8 4H4c-.98 0-2 1.22-2 2.5S3 9 4 9zm9-3h-1v1h1c1 0 2 1.22 2 2.5S13.98 12 13 12H9c-.98 0-2-1.22-2-2.5 0-.83.42-1.64 1-2.09V6.25c-1.09.53-2 1.84-2 3.25C6 11.31 7.55 13 9 13h4c1.45 0 3-1.69 3-3.5S14.5 6 13 6z"></path></svg></a>Alternatives considered</h2><p style="box-sizing: border-box; margin-top: 0px; margin-bottom: 16px; color: rgb(51, 51, 51); font-family: -apple-system, BlinkMacSystemFont, 'Segoe UI', Roboto, Helvetica, Arial, sans-serif, 'Apple Color Emoji', 'Segoe UI Emoji', 'Segoe UI Symbol'; font-size: 16px; background-color: rgb(255, 255, 255);" class="">A previous design of this proposal suggested a strict total order upon <code style="box-sizing: border-box; font-family: Consolas, 'Liberation Mono', Menlo, Courier, monospace; font-size: 14px; padding: 0.2em 0px; margin: 0px; background-color: rgba(0, 0, 0, 0.0392157); border-top-left-radius: 3px; border-top-right-radius: 3px; border-bottom-right-radius: 3px; border-bottom-left-radius: 3px;" class="">Comparable</code>. While that would make generic algorithms more correct, the definition ended up fighting against the expected behaviour of floating point numbers.</p><p style="box-sizing: border-box; margin-top: 0px; margin-bottom: 16px; color: rgb(51, 51, 51); font-family: -apple-system, BlinkMacSystemFont, 'Segoe UI', Roboto, Helvetica, Arial, sans-serif, 'Apple Color Emoji', 'Segoe UI Emoji', 'Segoe UI Symbol'; font-size: 16px; background-color: rgb(255, 255, 255);" class="">An alternative design that better matches the existing arithmetic-related protocols in Swift is one that uses a member function.</p><div class="highlight highlight-source-swift" style="box-sizing: border-box; margin-bottom: 16px; color: rgb(51, 51, 51); font-family: -apple-system, BlinkMacSystemFont, 'Segoe UI', Roboto, Helvetica, Arial, sans-serif, 'Apple Color Emoji', 'Segoe UI Emoji', 'Segoe UI Symbol'; font-size: 16px; background-color: rgb(255, 255, 255);"><pre style="box-sizing: border-box; font-family: Consolas, 'Liberation Mono', Menlo, Courier, monospace; font-size: 14px; margin-top: 0px; margin-bottom: 0px; line-height: 1.45; word-wrap: normal; padding: 16px; overflow: auto; background-color: rgb(247, 247, 247); border-top-left-radius: 3px; border-top-right-radius: 3px; border-bottom-right-radius: 3px; border-bottom-left-radius: 3px; word-break: normal;" class=""><span class="pl-k" style="box-sizing: border-box; color: rgb(167, 29, 93);">public</span> <span class="pl-k" style="box-sizing: border-box; color: rgb(167, 29, 93);">protocol</span> <span class="pl-c1" style="box-sizing: border-box; color: rgb(0, 134, 179);">Comparable</span>: <span class="pl-c1" style="box-sizing: border-box; color: rgb(0, 134, 179);">Equatable</span> {
<span class="pl-k" style="box-sizing: border-box; color: rgb(167, 29, 93);">func</span> <span class="pl-en" style="box-sizing: border-box; color: rgb(121, 93, 163);">compare</span>(to: <span class="pl-k" style="box-sizing: border-box; color: rgb(167, 29, 93);">Self</span>) <span class="pl-k" style="box-sizing: border-box; color: rgb(167, 29, 93);">-></span> Ordering
}</pre></div><p style="box-sizing: border-box; margin-top: 0px; margin-bottom: 16px; color: rgb(51, 51, 51); font-family: -apple-system, BlinkMacSystemFont, 'Segoe UI', Roboto, Helvetica, Arial, sans-serif, 'Apple Color Emoji', 'Segoe UI Emoji', 'Segoe UI Symbol'; font-size: 16px; background-color: rgb(255, 255, 255);" class="">However, while this API does read better than an operator, we believe that this imposes a number of artificial restrictions (especially in light of <a href="https://github.com/apple/swift-evolution/blob/master/proposals/0091-improving-operators-in-protocols.md" style="box-sizing: border-box; background-color: transparent; -webkit-text-decoration-skip: objects; color: rgb(64, 120, 192); text-decoration: none;" class="">SE-0091</a>)</p><ol style="box-sizing: border-box; padding-left: 2em; margin-top: 0px; margin-bottom: 16px; color: rgb(51, 51, 51); font-family: -apple-system, BlinkMacSystemFont, 'Segoe UI', Roboto, Helvetica, Arial, sans-serif, 'Apple Color Emoji', 'Segoe UI Emoji', 'Segoe UI Symbol'; font-size: 16px; background-color: rgb(255, 255, 255);" class=""><li style="box-sizing: border-box;" class="">There is no way to use <code style="box-sizing: border-box; font-family: Consolas, 'Liberation Mono', Menlo, Courier, monospace; font-size: 14px; padding: 0.2em 0px; margin: 0px; background-color: rgba(0, 0, 0, 0.0392157); border-top-left-radius: 3px; border-top-right-radius: 3px; border-bottom-right-radius: 3px; border-bottom-left-radius: 3px;" class="">Comparable.compare</code> as a higher-order function in a non-generic context.</li><li style="box-sizing: border-box; margin-top: 0.25em;" class="">If a member is desired, it can be provided in a protocol extension and defined in terms of the ordering operator; to each according to their need.</li><li style="box-sizing: border-box; margin-top: 0.25em;" class="">The existing tuple overloads cannot be expressed with a member function.</li></ol><p style="box-sizing: border-box; margin-top: 0px; margin-bottom: 16px; color: rgb(51, 51, 51); font-family: -apple-system, BlinkMacSystemFont, 'Segoe UI', Roboto, Helvetica, Arial, sans-serif, 'Apple Color Emoji', 'Segoe UI Emoji', 'Segoe UI Symbol'; font-size: 16px; background-color: rgb(255, 255, 255);" class="">One other that Rust has adopted is the inclusion of <code style="box-sizing: border-box; font-family: Consolas, 'Liberation Mono', Menlo, Courier, monospace; font-size: 14px; padding: 0.2em 0px; margin: 0px; background-color: rgba(0, 0, 0, 0.0392157); border-top-left-radius: 3px; border-top-right-radius: 3px; border-bottom-right-radius: 3px; border-bottom-left-radius: 3px;" class="">PartialEquatable</code> and <code style="box-sizing: border-box; font-family: Consolas, 'Liberation Mono', Menlo, Courier, monospace; font-size: 14px; padding: 0.2em 0px; margin: 0px; background-color: rgba(0, 0, 0, 0.0392157); border-top-left-radius: 3px; border-top-right-radius: 3px; border-bottom-right-radius: 3px; border-bottom-left-radius: 3px;" class="">PartialComparable</code> as ancestors of their flavor of <code style="box-sizing: border-box; font-family: Consolas, 'Liberation Mono', Menlo, Courier, monospace; font-size: 14px; padding: 0.2em 0px; margin: 0px; background-color: rgba(0, 0, 0, 0.0392157); border-top-left-radius: 3px; border-top-right-radius: 3px; border-bottom-right-radius: 3px; border-bottom-left-radius: 3px;" class="">Equatable</code> and <code style="box-sizing: border-box; font-family: Consolas, 'Liberation Mono', Menlo, Courier, monospace; font-size: 14px; padding: 0.2em 0px; margin: 0px; background-color: rgba(0, 0, 0, 0.0392157); border-top-left-radius: 3px; border-top-right-radius: 3px; border-bottom-right-radius: 3px; border-bottom-left-radius: 3px;" class="">Comparable</code> . Having protocols to organize and catalogue types that can only guarantee partial equivalence and ordering relations is a good approach for modularity but clutters the standard library with two new protocols for which few useful algorithms could be written against.</p><h2 style="box-sizing: border-box; margin-top: 24px; margin-bottom: 16px; line-height: 1.25; padding-bottom: 0.3em; border-bottom-width: 1px; border-bottom-style: solid; border-bottom-color: rgb(238, 238, 238); color: rgb(51, 51, 51); font-family: -apple-system, BlinkMacSystemFont, 'Segoe UI', Roboto, Helvetica, Arial, sans-serif, 'Apple Color Emoji', 'Segoe UI Emoji', 'Segoe UI Symbol'; background-color: rgb(255, 255, 255);" class=""><a id="user-content-future-directions" class="anchor" href="https://github.com/pyrtsa/swift-evolution/blob/ca89e7b3a1dffc99baa695a03544fcba75afd0f3/proposals/NNNN-formalized-ordering.md#future-directions" aria-hidden="true" style="box-sizing: border-box; background-color: transparent; -webkit-text-decoration-skip: objects; color: rgb(64, 120, 192); text-decoration: none; float: left; padding-right: 4px; margin-left: -20px; line-height: 1;"><svg aria-hidden="true" class="octicon octicon-link" height="16" version="1.1" viewBox="0 0 16 16" width="16"><path d="M4 9h1v1H4c-1.5 0-3-1.69-3-3.5S2.55 3 4 3h4c1.45 0 3 1.69 3 3.5 0 1.41-.91 2.72-2 3.25V8.59c.58-.45 1-1.27 1-2.09C10 5.22 8.98 4 8 4H4c-.98 0-2 1.22-2 2.5S3 9 4 9zm9-3h-1v1h1c1 0 2 1.22 2 2.5S13.98 12 13 12H9c-.98 0-2-1.22-2-2.5 0-.83.42-1.64 1-2.09V6.25c-1.09.53-2 1.84-2 3.25C6 11.31 7.55 13 9 13h4c1.45 0 3-1.69 3-3.5S14.5 6 13 6z"></path></svg></a>Future directions</h2><p style="box-sizing: border-box; margin-top: 0px; margin-bottom: 16px; color: rgb(51, 51, 51); font-family: -apple-system, BlinkMacSystemFont, 'Segoe UI', Roboto, Helvetica, Arial, sans-serif, 'Apple Color Emoji', 'Segoe UI Emoji', 'Segoe UI Symbol'; font-size: 16px; background-color: rgb(255, 255, 255);" class="">That the default <code style="box-sizing: border-box; font-family: Consolas, 'Liberation Mono', Menlo, Courier, monospace; font-size: 14px; padding: 0.2em 0px; margin: 0px; background-color: rgba(0, 0, 0, 0.0392157); border-top-left-radius: 3px; border-top-right-radius: 3px; border-bottom-right-radius: 3px; border-bottom-left-radius: 3px;" class="">sort()</code> compares by <code style="box-sizing: border-box; font-family: Consolas, 'Liberation Mono', Menlo, Courier, monospace; font-size: 14px; padding: 0.2em 0px; margin: 0px; background-color: rgba(0, 0, 0, 0.0392157); border-top-left-radius: 3px; border-top-right-radius: 3px; border-bottom-right-radius: 3px; border-bottom-left-radius: 3px;" class=""><</code> and not <code style="box-sizing: border-box; font-family: Consolas, 'Liberation Mono', Menlo, Courier, monospace; font-size: 14px; padding: 0.2em 0px; margin: 0px; background-color: rgba(0, 0, 0, 0.0392157); border-top-left-radius: 3px; border-top-right-radius: 3px; border-bottom-right-radius: 3px; border-bottom-left-radius: 3px;" class=""><=></code> should be considered a bug to be fixed in a future version of Swift. Using <code style="box-sizing: border-box; font-family: Consolas, 'Liberation Mono', Menlo, Courier, monospace; font-size: 14px; padding: 0.2em 0px; margin: 0px; background-color: rgba(0, 0, 0, 0.0392157); border-top-left-radius: 3px; border-top-right-radius: 3px; border-bottom-right-radius: 3px; border-bottom-left-radius: 3px;" class=""><=></code> will make <code style="box-sizing: border-box; font-family: Consolas, 'Liberation Mono', Menlo, Courier, monospace; font-size: 14px; padding: 0.2em 0px; margin: 0px; background-color: rgba(0, 0, 0, 0.0392157); border-top-left-radius: 3px; border-top-right-radius: 3px; border-bottom-right-radius: 3px; border-bottom-left-radius: 3px;" class="">sort()</code> well-behaved in the presense of NaN. However, given that the current behaviour is to produce an unspecified order, the fix is additive and can be slipped past Swift 3.</p><p style="box-sizing: border-box; margin-top: 0px; margin-bottom: 16px; color: rgb(51, 51, 51); font-family: -apple-system, BlinkMacSystemFont, 'Segoe UI', Roboto, Helvetica, Arial, sans-serif, 'Apple Color Emoji', 'Segoe UI Emoji', 'Segoe UI Symbol'; font-size: 16px; background-color: rgb(255, 255, 255);" class="">With <code style="box-sizing: border-box; font-family: Consolas, 'Liberation Mono', Menlo, Courier, monospace; font-size: 14px; padding: 0.2em 0px; margin: 0px; background-color: rgba(0, 0, 0, 0.0392157); border-top-left-radius: 3px; border-top-right-radius: 3px; border-bottom-right-radius: 3px; border-bottom-left-radius: 3px;" class=""><=></code> in place, several present and future standard library algorithms involving a <code style="box-sizing: border-box; font-family: Consolas, 'Liberation Mono', Menlo, Courier, monospace; font-size: 14px; padding: 0.2em 0px; margin: 0px; background-color: rgba(0, 0, 0, 0.0392157); border-top-left-radius: 3px; border-top-right-radius: 3px; border-bottom-right-radius: 3px; border-bottom-left-radius: 3px;" class=""><T : Comparable></code> requirement will possibly benefit from knowing the total ordering of two operands at once. This is a list of possible such functions (taking <code style="box-sizing: border-box; font-family: Consolas, 'Liberation Mono', Menlo, Courier, monospace; font-size: 14px; padding: 0.2em 0px; margin: 0px; background-color: rgba(0, 0, 0, 0.0392157); border-top-left-radius: 3px; border-top-right-radius: 3px; border-bottom-right-radius: 3px; border-bottom-left-radius: 3px;" class="">Array</code> as example), to be proposed separately as an additive change:</p><div class="highlight highlight-source-swift" style="box-sizing: border-box; color: rgb(51, 51, 51); font-family: -apple-system, BlinkMacSystemFont, 'Segoe UI', Roboto, Helvetica, Arial, sans-serif, 'Apple Color Emoji', 'Segoe UI Emoji', 'Segoe UI Symbol'; font-size: 16px; background-color: rgb(255, 255, 255); margin-bottom: 0px !important;"><pre style="box-sizing: border-box; font-family: Consolas, 'Liberation Mono', Menlo, Courier, monospace; font-size: 14px; margin-top: 0px; margin-bottom: 0px; line-height: 1.45; word-wrap: normal; padding: 16px; overflow: auto; background-color: rgb(247, 247, 247); border-top-left-radius: 3px; border-top-right-radius: 3px; border-bottom-right-radius: 3px; border-bottom-left-radius: 3px; word-break: normal;" class=""><span class="pl-k" style="box-sizing: border-box; color: rgb(167, 29, 93);">extension</span> <span class="pl-c1" style="box-sizing: border-box; color: rgb(0, 134, 179);">Array</span> {
<span class="pl-c" style="box-sizing: border-box; color: rgb(150, 152, 150);">// Sorting</span>
<span class="pl-k" style="box-sizing: border-box; color: rgb(167, 29, 93);">mutating</span> <span class="pl-k" style="box-sizing: border-box; color: rgb(167, 29, 93);">func</span> <span class="pl-en" style="box-sizing: border-box; color: rgb(121, 93, 163);">sort</span>(ordering: <span class="pl-k" style="box-sizing: border-box; color: rgb(167, 29, 93);">@noescape</span> (Element, Element) throws <span class="pl-k" style="box-sizing: border-box; color: rgb(167, 29, 93);">-></span> Ordering) rethrows
<span class="pl-k" style="box-sizing: border-box; color: rgb(167, 29, 93);">func</span> <span class="pl-en" style="box-sizing: border-box; color: rgb(121, 93, 163);">sorted</span>(ordering: <span class="pl-k" style="box-sizing: border-box; color: rgb(167, 29, 93);">@noescape</span> (Element, Element) throws <span class="pl-k" style="box-sizing: border-box; color: rgb(167, 29, 93);">-></span> Ordering) rethrows -> [Element]
<span class="pl-k" style="box-sizing: border-box; color: rgb(167, 29, 93);">mutating</span> <span class="pl-k" style="box-sizing: border-box; color: rgb(167, 29, 93);">func</span> <span class="pl-en" style="box-sizing: border-box; color: rgb(121, 93, 163);">stableSort</span>(ordering: <span class="pl-k" style="box-sizing: border-box; color: rgb(167, 29, 93);">@noescape</span> (Element, Element) throws <span class="pl-k" style="box-sizing: border-box; color: rgb(167, 29, 93);">-></span> Ordering) rethrows
<span class="pl-k" style="box-sizing: border-box; color: rgb(167, 29, 93);">func</span> <span class="pl-en" style="box-sizing: border-box; color: rgb(121, 93, 163);">stableSorted</span>(ordering: <span class="pl-k" style="box-sizing: border-box; color: rgb(167, 29, 93);">@noescape</span> (Element, Element) throws <span class="pl-k" style="box-sizing: border-box; color: rgb(167, 29, 93);">-></span> Ordering) rethrows -> [Element]
<span class="pl-c" style="box-sizing: border-box; color: rgb(150, 152, 150);">/// Reorders the elements of the collection such that all the elements</span>
<span class="pl-c" style="box-sizing: border-box; color: rgb(150, 152, 150);">/// returning `.ascending` are moved to the start of the collection, and the</span>
<span class="pl-c" style="box-sizing: border-box; color: rgb(150, 152, 150);">/// elements returning `.descending` are moved to the end of the collection.</span>
<span class="pl-c" style="box-sizing: border-box; color: rgb(150, 152, 150);">/// - Returns: the range of elements for which `ordering(x) == .equal`.</span>
<span class="pl-k" style="box-sizing: border-box; color: rgb(167, 29, 93);">mutating</span> <span class="pl-k" style="box-sizing: border-box; color: rgb(167, 29, 93);">func</span> <span class="pl-en" style="box-sizing: border-box; color: rgb(121, 93, 163);">partition</span>(ordering: <span class="pl-k" style="box-sizing: border-box; color: rgb(167, 29, 93);">@noescape</span> (Iterator<span class="pl-k" style="box-sizing: border-box; color: rgb(167, 29, 93);">.</span>Element) throws <span class="pl-k" style="box-sizing: border-box; color: rgb(167, 29, 93);">-></span> Ordering) rethrows -> <span class="pl-c1" style="box-sizing: border-box; color: rgb(0, 134, 179);">Range</span><Index>
<span class="pl-c" style="box-sizing: border-box; color: rgb(150, 152, 150);">// Binary search</span>
<span class="pl-k" style="box-sizing: border-box; color: rgb(167, 29, 93);">func</span> <span class="pl-en" style="box-sizing: border-box; color: rgb(121, 93, 163);">bisectedIndex</span>(ordering: <span class="pl-k" style="box-sizing: border-box; color: rgb(167, 29, 93);">@noescape</span> (Element) throws <span class="pl-k" style="box-sizing: border-box; color: rgb(167, 29, 93);">-></span> Ordering) rethrows -> Index?
<span class="pl-k" style="box-sizing: border-box; color: rgb(167, 29, 93);">func</span> <span class="pl-en" style="box-sizing: border-box; color: rgb(121, 93, 163);">lowerBound</span>(ordering: <span class="pl-k" style="box-sizing: border-box; color: rgb(167, 29, 93);">@noescape</span> (Element) throws <span class="pl-k" style="box-sizing: border-box; color: rgb(167, 29, 93);">-></span> Ordering) rethrows -> Index
<span class="pl-k" style="box-sizing: border-box; color: rgb(167, 29, 93);">func</span> <span class="pl-en" style="box-sizing: border-box; color: rgb(121, 93, 163);">upperBound</span>(ordering: <span class="pl-k" style="box-sizing: border-box; color: rgb(167, 29, 93);">@noescape</span> (Element) throws <span class="pl-k" style="box-sizing: border-box; color: rgb(167, 29, 93);">-></span> Ordering) rethrows -> Index
<span class="pl-k" style="box-sizing: border-box; color: rgb(167, 29, 93);">func</span> <span class="pl-en" style="box-sizing: border-box; color: rgb(121, 93, 163);">equalRange</span>(ordering: <span class="pl-k" style="box-sizing: border-box; color: rgb(167, 29, 93);">@noescape</span> (Element) throws <span class="pl-k" style="box-sizing: border-box; color: rgb(167, 29, 93);">-></span> Ordering) rethrows -> <span class="pl-c1" style="box-sizing: border-box; color: rgb(0, 134, 179);">Range</span><Index>
}</pre></div><div class=""><br class=""></div></div></div></body></html>