<html><head><meta http-equiv="Content-Type" content="text/html charset=utf-8"></head><body style="word-wrap: break-word; -webkit-nbsp-mode: space; -webkit-line-break: after-white-space;" class=""><div class="">Hi Pyry —</div><div class=""><br class=""></div><div class="">Dave and I spent some time discussing the details of how this applies to floating point earlier today. We’re now in agreement that <=> should treat -0 and +0 as distinct, and treat all NaNs as .equal. There are three motivating considerations:</div><div class=""><br class=""></div><div class="">1. Although -0 and +0 are “IEEE 754 equal”, there is no computation that can produce both of them. In the parlance of IEEE 754, for any rounding mode, the sets of real values that round to them are disjoint. Because of this, if -0 and +0 appear as members of a set, or as keys in a dictionary, they necessarily are the result of distinct computations or data.</div><div class=""><br class=""></div><div class="">2. Substitutability. Adopting these semantics means that if `x <=> y` is `.equal`, `f(x) <=> f(y)` is also `.equal` for any computation `f(x)` that depends on the represented value (as opposed to the encoding) of its argument.</div><div class=""><br class=""></div><div class="">3. 754 defines four “specification levels”, or models:</div><div class=""><br class=""></div><div class=""><span class="Apple-tab-span" style="white-space:pre"> </span>- Level 1: The two-point compactification of the reals, or “extended real numbers”.</div><div class=""><span class="Apple-tab-span" style="white-space:pre"> </span>- Level 2: The set of representable floating-point data: {-inf … -0} union { 0 … inf } union { NaN }.</div><div class=""><span class="Apple-tab-span" style="white-space:pre"> </span>- Level 3: The set of representations of floating-point data: sign-exponent-significand triples, +/-inf, qNaN, sNaN.</div><div class=""><span class="Apple-tab-span" style="white-space:pre"> </span>- Level 4: Floating-point encodings (bit patterns).</div><div class=""><br class=""></div><div class="">The `<=>` semantics we propose constitute a total order on level 2, which is the computable model closest to the (reasonably familiar) extended real numbers. Treating -0 and +0 as .equal would put us in a bit of a no-man’s land between levels 1 and 2.</div><div class=""><br class=""></div><div class="">Thanks,</div><div class="">– Steve</div><div class=""><br class=""></div><div><blockquote type="cite" class=""><div class="">On Jul 25, 2016, at 7:41 AM, Pyry Jahkola <<a href="mailto:pyry.jahkola@iki.fi" class="">pyry.jahkola@iki.fi</a>> wrote:</div><br class="Apple-interchange-newline"><div class=""><div 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></div></div></blockquote></div><br class=""></body></html>