<div dir="ltr">See, your design still takes as given that floating point values require more than one type of comparison, however these are spelled. I continue to think that we do not need to go down this road, and that we can make things work with each type being comparable in exactly one way.<div><br></div><div>The only wrinkle is that some floating point values are unordered with respect to each other. While IEEE talks about different ways to think about what a floating point value _represents_, it actually describes only one type of comparison. And we have already nailed down what a floating point value represents in Swift: it models a real value (level 1 representation).<div class="gmail_extra"><br></div><div class="gmail_extra"><br><div class="gmail_quote">On Sun, Apr 16, 2017 at 11:49 AM, Karl Wagner via swift-evolution <span dir="ltr"><<a href="mailto:swift-evolution@swift.org" target="_blank">swift-evolution@swift.org</a>></span> wrote:<br><blockquote class="gmail_quote" style="margin:0px 0px 0px 0.8ex;border-left-width:1px;border-left-style:solid;border-left-color:rgb(204,204,204);padding-left:1ex"><div style="word-wrap:break-word"><div><div class="gmail-h5"><br><div><blockquote type="cite"><div>On 16 Apr 2017, at 18:35, Karl Wagner <<a href="mailto:karl.swift@springsup.com" target="_blank">karl.swift@springsup.com</a>> wrote:</div><br class="gmail-m_8904624953561823771Apple-interchange-newline"><div><div style="font-family:helvetica;font-size:12px;font-style:normal;font-variant-caps:normal;font-weight:normal;letter-spacing:normal;text-align:start;text-indent:0px;text-transform:none;white-space:normal;word-spacing:0px"><blockquote type="cite"><div><br class="gmail-m_8904624953561823771Apple-interchange-newline">On 16 Apr 2017, at 05:32, Dave Abrahams via swift-evolution <<a href="mailto:swift-evolution@swift.org" target="_blank">swift-evolution@swift.org</a>> wrote:</div><br class="gmail-m_8904624953561823771Apple-interchange-newline"><div><br style="font-family:helvetica;font-size:12px;font-style:normal;font-variant-caps:normal;font-weight:normal;letter-spacing:normal;text-align:start;text-indent:0px;text-transform:none;white-space:normal;word-spacing:0px"><span style="font-family:helvetica;font-size:12px;font-style:normal;font-variant-caps:normal;font-weight:normal;letter-spacing:normal;text-align:start;text-indent:0px;text-transform:none;white-space:normal;word-spacing:0px;float:none;display:inline">on Sat Apr 15 2017, Xiaodi Wu <</span><a href="mailto:swift-evolution@swift.org" style="font-family:helvetica;font-size:12px;font-style:normal;font-variant-caps:normal;font-weight:normal;letter-spacing:normal;text-align:start;text-indent:0px;text-transform:none;white-space:normal;word-spacing:0px" target="_blank">swift-evolution@swift.org</a><span style="font-family:helvetica;font-size:12px;font-style:normal;font-variant-caps:normal;font-weight:normal;letter-spacing:normal;text-align:start;text-indent:0px;text-transform:none;white-space:normal;word-spacing:0px;float:none;display:inline">> wrote:</span><br style="font-family:helvetica;font-size:12px;font-style:normal;font-variant-caps:normal;font-weight:normal;letter-spacing:normal;text-align:start;text-indent:0px;text-transform:none;white-space:normal;word-spacing:0px"><br style="font-family:helvetica;font-size:12px;font-style:normal;font-variant-caps:normal;font-weight:normal;letter-spacing:normal;text-align:start;text-indent:0px;text-transform:none;white-space:normal;word-spacing:0px"><blockquote type="cite" style="font-family:helvetica;font-size:12px;font-style:normal;font-variant-caps:normal;font-weight:normal;letter-spacing:normal;text-align:start;text-indent:0px;text-transform:none;white-space:normal;word-spacing:0px">On Sat, Apr 15, 2017 at 3:12 PM, Dave Abrahams via swift-evolution <<br><a href="mailto:swift-evolution@swift.org" target="_blank">swift-evolution@swift.org</a>> wrote:<br><br><blockquote type="cite"><br>on Thu Apr 13 2017, Xiaodi Wu <<a href="mailto:swift-evolution@swift.org" target="_blank">swift-evolution@swift.org</a>> wrote:<br><br><blockquote type="cite">Getting this sorted out is definitely a worthwhile effort. I do have<br>thoughts about this proposal:<br><br>I continue to have reservations about an identical spelling (e.g. `==`)<br>giving two different answers with the same values of the same type,<br>depending on the generic context. It is a very *clever* design, but it is<br>also a very *subtle* behavior that I can see leading to much confusion<br></blockquote>and<br><blockquote type="cite">befuddlement for any user who is not well versed *both* in the<br></blockquote>intricacies<br><blockquote type="cite">of IEEE floating point *and* in the intricacies of Swift.<br></blockquote><br>I can't help but think that the concern over confusion here is not<br>informed by any realistic situations. Please describe<br><br></blockquote><br>To be clear, I'm not claiming that my concerns about the proposal outweigh<br>my enthusiasm for it.<br><br>But here, the confusion I'm concerned about stems from the essential<br>conclusion by the proposal authors that types (including, but not<br>necessarily only limited to FP types) which are ordinarily compared in a<br>way that treats certain "special values" differently must also present an<br>alternative notion of comparison that accounts for all possible<br>values.<span class="gmail-m_8904624953561823771Apple-converted-space"> </span><br></blockquote><br style="font-family:helvetica;font-size:12px;font-style:normal;font-variant-caps:normal;font-weight:normal;letter-spacing:normal;text-align:start;text-indent:0px;text-transform:none;white-space:normal;word-spacing:0px"><span style="font-family:helvetica;font-size:12px;font-style:normal;font-variant-caps:normal;font-weight:normal;letter-spacing:normal;text-align:start;text-indent:0px;text-transform:none;white-space:normal;word-spacing:0px;float:none;display:inline">That may be a conclusion, but it's not an assumption. For example, it's</span><br style="font-family:helvetica;font-size:12px;font-style:normal;font-variant-caps:normal;font-weight:normal;letter-spacing:normal;text-align:start;text-indent:0px;text-transform:none;white-space:normal;word-spacing:0px"><span style="font-family:helvetica;font-size:12px;font-style:normal;font-variant-caps:normal;font-weight:normal;letter-spacing:normal;text-align:start;text-indent:0px;text-transform:none;white-space:normal;word-spacing:0px;float:none;display:inline">totally reasonable that there is a value of Int (i.e. 0) for which the</span><br style="font-family:helvetica;font-size:12px;font-style:normal;font-variant-caps:normal;font-weight:normal;letter-spacing:normal;text-align:start;text-indent:0px;text-transform:none;white-space:normal;word-spacing:0px"><span style="font-family:helvetica;font-size:12px;font-style:normal;font-variant-caps:normal;font-weight:normal;letter-spacing:normal;text-align:start;text-indent:0px;text-transform:none;white-space:normal;word-spacing:0px;float:none;display:inline">requirements of division don't hold. We say that 0 is outside the</span><br style="font-family:helvetica;font-size:12px;font-style:normal;font-variant-caps:normal;font-weight:normal;letter-spacing:normal;text-align:start;text-indent:0px;text-transform:none;white-space:normal;word-spacing:0px"><span style="font-family:helvetica;font-size:12px;font-style:normal;font-variant-caps:normal;font-weight:normal;letter-spacing:normal;text-align:start;text-indent:0px;text-transform:none;white-space:normal;word-spacing:0px;float:none;display:inline">domain of / when used as a divisor, and we tried to get away with saying</span><br style="font-family:helvetica;font-size:12px;font-style:normal;font-variant-caps:normal;font-weight:normal;letter-spacing:normal;text-align:start;text-indent:0px;text-transform:none;white-space:normal;word-spacing:0px"><span style="font-family:helvetica;font-size:12px;font-style:normal;font-variant-caps:normal;font-weight:normal;letter-spacing:normal;text-align:start;text-indent:0px;text-transform:none;white-space:normal;word-spacing:0px;float:none;display:inline">that NaN was outside the domain of ==. However, it's also reasonable to</span><br style="font-family:helvetica;font-size:12px;font-style:normal;font-variant-caps:normal;font-weight:normal;letter-spacing:normal;text-align:start;text-indent:0px;text-transform:none;white-space:normal;word-spacing:0px"><span style="font-family:helvetica;font-size:12px;font-style:normal;font-variant-caps:normal;font-weight:normal;letter-spacing:normal;text-align:start;text-indent:0px;text-transform:none;white-space:normal;word-spacing:0px;float:none;display:inline">trap on integer division by zero.</span><br style="font-family:helvetica;font-size:12px;font-style:normal;font-variant-caps:normal;font-weight:normal;letter-spacing:normal;text-align:start;text-indent:0px;text-transform:none;white-space:normal;word-spacing:0px"><br style="font-family:helvetica;font-size:12px;font-style:normal;font-variant-caps:normal;font-weight:normal;letter-spacing:normal;text-align:start;text-indent:0px;text-transform:none;white-space:normal;word-spacing:0px"><span style="font-family:helvetica;font-size:12px;font-style:normal;font-variant-caps:normal;font-weight:normal;letter-spacing:normal;text-align:start;text-indent:0px;text-transform:none;white-space:normal;word-spacing:0px;float:none;display:inline">What we have is a situation where values that “misbehave” when given</span><br style="font-family:helvetica;font-size:12px;font-style:normal;font-variant-caps:normal;font-weight:normal;letter-spacing:normal;text-align:start;text-indent:0px;text-transform:none;white-space:normal;word-spacing:0px"><span style="font-family:helvetica;font-size:12px;font-style:normal;font-variant-caps:normal;font-weight:normal;letter-spacing:normal;text-align:start;text-indent:0px;text-transform:none;white-space:normal;word-spacing:0px;float:none;display:inline">IEEE semantics occur in normal code and are expected to interoperate</span><br style="font-family:helvetica;font-size:12px;font-style:normal;font-variant-caps:normal;font-weight:normal;letter-spacing:normal;text-align:start;text-indent:0px;text-transform:none;white-space:normal;word-spacing:0px"><span style="font-family:helvetica;font-size:12px;font-style:normal;font-variant-caps:normal;font-weight:normal;letter-spacing:normal;text-align:start;text-indent:0px;text-transform:none;white-space:normal;word-spacing:0px;float:none;display:inline">with other floating point values under normal circumstances (such as</span><br style="font-family:helvetica;font-size:12px;font-style:normal;font-variant-caps:normal;font-weight:normal;letter-spacing:normal;text-align:start;text-indent:0px;text-transform:none;white-space:normal;word-spacing:0px"><span style="font-family:helvetica;font-size:12px;font-style:normal;font-variant-caps:normal;font-weight:normal;letter-spacing:normal;text-align:start;text-indent:0px;text-transform:none;white-space:normal;word-spacing:0px;float:none;display:inline">when sorting), and not only interoperate but give reasonable results.</span><br style="font-family:helvetica;font-size:12px;font-style:normal;font-variant-caps:normal;font-weight:normal;letter-spacing:normal;text-align:start;text-indent:0px;text-transform:none;white-space:normal;word-spacing:0px"><br style="font-family:helvetica;font-size:12px;font-style:normal;font-variant-caps:normal;font-weight:normal;letter-spacing:normal;text-align:start;text-indent:0px;text-transform:none;white-space:normal;word-spacing:0px"><span style="font-family:helvetica;font-size:12px;font-style:normal;font-variant-caps:normal;font-weight:normal;letter-spacing:normal;text-align:start;text-indent:0px;text-transform:none;white-space:normal;word-spacing:0px;float:none;display:inline">Now, having thought about this a bit more myself, here is a real case</span><br style="font-family:helvetica;font-size:12px;font-style:normal;font-variant-caps:normal;font-weight:normal;letter-spacing:normal;text-align:start;text-indent:0px;text-transform:none;white-space:normal;word-spacing:0px"><span style="font-family:helvetica;font-size:12px;font-style:normal;font-variant-caps:normal;font-weight:normal;letter-spacing:normal;text-align:start;text-indent:0px;text-transform:none;white-space:normal;word-spacing:0px;float:none;display:inline">where confusion might occur:</span><br style="font-family:helvetica;font-size:12px;font-style:normal;font-variant-caps:normal;font-weight:normal;letter-spacing:normal;text-align:start;text-indent:0px;text-transform:none;white-space:normal;word-spacing:0px"><br style="font-family:helvetica;font-size:12px;font-style:normal;font-variant-caps:normal;font-weight:normal;letter-spacing:normal;text-align:start;text-indent:0px;text-transform:none;white-space:normal;word-spacing:0px"><span style="font-family:helvetica;font-size:12px;font-style:normal;font-variant-caps:normal;font-weight:normal;letter-spacing:normal;text-align:start;text-indent:0px;text-transform:none;white-space:normal;word-spacing:0px;float:none;display:inline"> if values.contains(.NaN) {</span><br style="font-family:helvetica;font-size:12px;font-style:normal;font-variant-caps:normal;font-weight:normal;letter-spacing:normal;text-align:start;text-indent:0px;text-transform:none;white-space:normal;word-spacing:0px"><span style="font-family:helvetica;font-size:12px;font-style:normal;font-variant-caps:normal;font-weight:normal;letter-spacing:normal;text-align:start;text-indent:0px;text-transform:none;white-space:normal;word-spacing:0px;float:none;display:inline"> print(values.filter { $0 != .NaN }) // Surprise, NaN is printed!</span><br style="font-family:helvetica;font-size:12px;font-style:normal;font-variant-caps:normal;font-weight:normal;letter-spacing:normal;text-align:start;text-indent:0px;text-transform:none;white-space:normal;word-spacing:0px"><span style="font-family:helvetica;font-size:12px;font-style:normal;font-variant-caps:normal;font-weight:normal;letter-spacing:normal;text-align:start;text-indent:0px;text-transform:none;white-space:normal;word-spacing:0px;float:none;display:inline"> }</span><br style="font-family:helvetica;font-size:12px;font-style:normal;font-variant-caps:normal;font-weight:normal;letter-spacing:normal;text-align:start;text-indent:0px;text-transform:none;white-space:normal;word-spacing:0px"><br style="font-family:helvetica;font-size:12px;font-style:normal;font-variant-caps:normal;font-weight:normal;letter-spacing:normal;text-align:start;text-indent:0px;text-transform:none;white-space:normal;word-spacing:0px"><span style="font-family:helvetica;font-size:12px;font-style:normal;font-variant-caps:normal;font-weight:normal;letter-spacing:normal;text-align:start;text-indent:0px;text-transform:none;white-space:normal;word-spacing:0px;float:none;display:inline">I find this result truly loathsome, but it seems to me that the only</span><br style="font-family:helvetica;font-size:12px;font-style:normal;font-variant-caps:normal;font-weight:normal;letter-spacing:normal;text-align:start;text-indent:0px;text-transform:none;white-space:normal;word-spacing:0px"><span style="font-family:helvetica;font-size:12px;font-style:normal;font-variant-caps:normal;font-weight:normal;letter-spacing:normal;text-align:start;text-indent:0px;text-transform:none;white-space:normal;word-spacing:0px;float:none;display:inline">reasonable cure is giving == equivalence relation semantics under all</span><br style="font-family:helvetica;font-size:12px;font-style:normal;font-variant-caps:normal;font-weight:normal;letter-spacing:normal;text-align:start;text-indent:0px;text-transform:none;white-space:normal;word-spacing:0px"><span style="font-family:helvetica;font-size:12px;font-style:normal;font-variant-caps:normal;font-weight:normal;letter-spacing:normal;text-align:start;text-indent:0px;text-transform:none;white-space:normal;word-spacing:0px;float:none;display:inline">circumstances.</span><br style="font-family:helvetica;font-size:12px;font-style:normal;font-variant-caps:normal;font-weight:normal;letter-spacing:normal;text-align:start;text-indent:0px;text-transform:none;white-space:normal;word-spacing:0px"></div></blockquote></div><div style="font-family:helvetica;font-size:12px;font-style:normal;font-variant-caps:normal;font-weight:normal;letter-spacing:normal;text-align:start;text-indent:0px;text-transform:none;white-space:normal;word-spacing:0px"><br></div><div style="font-family:helvetica;font-size:12px;font-style:normal;font-variant-caps:normal;font-weight:normal;letter-spacing:normal;text-align:start;text-indent:0px;text-transform:none;white-space:normal;word-spacing:0px">The thing that’s bad about it is that we silently pick different operators for different contexts. With Swift’s heavy use of abstraction layering, you often can’t really tell what the context is (if it even has meaning at all).</div><div style="font-family:helvetica;font-size:12px;font-style:normal;font-variant-caps:normal;font-weight:normal;letter-spacing:normal;text-align:start;text-indent:0px;text-transform:none;white-space:normal;word-spacing:0px"><br></div><div style="font-family:helvetica;font-size:12px;font-style:normal;font-variant-caps:normal;font-weight:normal;letter-spacing:normal;text-align:start;text-indent:0px;text-transform:none;white-space:normal;word-spacing:0px">I’ve been thinking about Swift architectural patterns, and one pattern that I think of as being a good fit for the language is this idea of wrapping operations on protocol-types as generic structs (for example, the way we do FilterCollection, LazyMapCollection, and he various String views in the standard library), providing transformed “views” of the object with a common base protocol (which will hopefully get optimised away). I wonder if we couldn’t apply a similar idea here…</div><div style="font-family:helvetica;font-size:12px;font-style:normal;font-variant-caps:normal;font-weight:normal;letter-spacing:normal;text-align:start;text-indent:0px;text-transform:none;white-space:normal;word-spacing:0px"><br></div><div style="font-family:helvetica;font-size:12px;font-style:normal;font-variant-caps:normal;font-weight:normal;letter-spacing:normal;text-align:start;text-indent:0px;text-transform:none;white-space:normal;word-spacing:0px">So basically, every FloatingPoint will expose another pseudo-FloatingPoint type which differs from its base object only in its interpretation of “Comparable” operators. The type-system would enforce that you are comparing them consistently.</div><div style="font-family:helvetica;font-size:12px;font-style:normal;font-variant-caps:normal;font-weight:normal;letter-spacing:normal;text-align:start;text-indent:0px;text-transform:none;white-space:normal;word-spacing:0px"><br></div><blockquote style="font-family:helvetica;font-size:12px;font-style:normal;font-variant-caps:normal;font-weight:normal;letter-spacing:normal;text-align:start;text-indent:0px;text-transform:none;white-space:normal;word-spacing:0px;margin:0px 0px 0px 40px;border:none;padding:0px"><div><font face="Courier">protocol FloatingPoint: Comparable {</font></div><div><font face="Courier"><br></font></div><div><font face="Courier"> /// A FloatingPoint with comparison quirks</font></div><div><font face="Courier"> ///</font></div><div><font face="Courier"> associatedtype StandardComparable: FloatingPoint</font></div><div><font face="Courier"> var comparable: StandardComparable { get }</font></div><div><font face="Courier"><br></font></div><div><font face="Courier"> /// A FloatingPoint which compares according to IEEE level <whatever></font></div><div><font face="Courier"> ///</font></div><div><font face="Courier"> associatedtype IEEEComparable: FloatingPoint = Self</font></div><div><font face="Courier"> var ieeeComparable: IEEEComparable { get }</font></div><div><font face="Courier">}</font></div><div><font face="Courier">extension FloatingPoint where IEEEComparable == Self {</font></div><div><font face="Courier"> var ieeeComparable: Self { return self }</font></div><div><font face="Courier">}</font></div><div><font face="Courier"><br></font></div><div><font face="Courier">struct Float: FloatingPoint {</font></div><div><font face="Courier"> /* IEEE comparison */ </font></div><div><font face="Courier"> static func compare(_: Float, to: Float) -> ComparisonResult { ... }</font></div><div><font face="Courier"><br></font></div><div><font face="Courier"> /* Quirky Float where .Nan == .Nan, +0.0 == -0.0 etc... */</font></div><div><font face="Courier"> struct StandardComparable: FloatingPoint {</font></div><div><font face="Courier"> static func compare(_: StandardComparable, to: StandardComparable) -> ComparisonResult { ... }</font></div><div><font face="Courier"> }</font></div><div><font face="Courier"> var comparable: StandardComparable { return StandardComparable(self) }</font></div><div><font face="Courier">}</font></div></blockquote><div style="font-family:helvetica;font-size:12px;font-style:normal;font-variant-caps:normal;font-weight:normal;letter-spacing:normal;text-align:start;text-indent:0px;text-transform:none;white-space:normal;word-spacing:0px"><br></div><div style="font-family:helvetica;font-size:12px;font-style:normal;font-variant-caps:normal;font-weight:normal;letter-spacing:normal;text-align:start;text-indent:0px;text-transform:none;white-space:normal;word-spacing:0px">The idea is that the invisible context-sensitive comparison quirks would become visible:</div><div style="font-family:helvetica;font-size:12px;font-style:normal;font-variant-caps:normal;font-weight:normal;letter-spacing:normal;text-align:start;text-indent:0px;text-transform:none;white-space:normal;word-spacing:0px"><br></div><blockquote style="font-family:helvetica;font-size:12px;font-style:normal;font-variant-caps:normal;font-weight:normal;letter-spacing:normal;text-align:start;text-indent:0px;text-transform:none;white-space:normal;word-spacing:0px;margin:0px 0px 0px 40px;border:none;padding:0px"><div><font face="Courier">if values.contains(.NaN) { // uses IEEE rules, so is always false</font></div><div><font face="Courier"> print(values.filter { $0 != .NaN })</font></div><div><font face="Courier">}</font></div><div><font face="Courier"><br></font></div><div><font face="Courier">if values.contains(where: { $0.comparable == .NaN }) { // opt-in to stdlib quirks</font></div><div><font face="Courier"> print(values.filter { $0.comparable != .NaN }) // no NaNs</font></div><div><font face="Courier">}</font></div></blockquote><div style="font-family:helvetica;font-size:12px;font-style:normal;font-variant-caps:normal;font-weight:normal;letter-spacing:normal;text-align:start;text-indent:0px;text-transform:none;white-space:normal;word-spacing:0px"><br></div><div style="font-family:helvetica;font-size:12px;font-style:normal;font-variant-caps:normal;font-weight:normal;letter-spacing:normal;text-align:start;text-indent:0px;text-transform:none;white-space:normal;word-spacing:0px">- Karl</div></div></blockquote></div><br></div></div><div>Oh, and:</div><div><br></div><div>Float.StandardComparable.<wbr>IEEEComparable = Float, and</div><div>Float.StandardComparable.<wbr>StandardComparable = Self</div><div><br></div><div>...so they wouldn’t recurse. You could just flip between views with “.comparable” or “.ieeeComparable”.</div><div><br></div><div>- Karl</div><div><br></div></div><br>______________________________<wbr>_________________<br>
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