<p dir="ltr">Sets and maps don't inherently have orderings, but Set and Map do. I think you could still make an argument for retaining the constraint, but it's a thin one. It is possible to imagine that there could be some *other* Ord-based representation of sets and maps for which having the ordering directly available would lead to more efficient splits. Retaining the constraint could then be seen as forward compatibility with such a hypothetical reimplementation.</p>
<div class="gmail_quote">On Mar 7, 2016 7:26 PM, "Dan Burton" <<a href="mailto:danburton.email@gmail.com">danburton.email@gmail.com</a>> wrote:<br type="attribution"><blockquote class="gmail_quote" style="margin:0 0 0 .8ex;border-left:1px #ccc solid;padding-left:1ex"><div dir="ltr">I would prefer that the Ord constraint be retained in the type signature, even if not used in the implementation. Sets and Maps conceptually do not have an ordering; the Ord constraint indicates in which order one is sequencing the values.</div><div class="gmail_extra"><br clear="all"><div><div>-- Dan Burton</div></div>
<br><div class="gmail_quote">On Mon, Mar 7, 2016 at 4:14 PM, Gabriel Gonzalez <span dir="ltr"><<a href="mailto:gabriel439@gmail.com" target="_blank">gabriel439@gmail.com</a>></span> wrote:<br><blockquote class="gmail_quote" style="margin:0 0 0 .8ex;border-left:1px #ccc solid;padding-left:1ex"><div style="word-wrap:break-word">I would like to propose adding `take`/`drop`/`splitAt` to both `Data.Map` and `Data.Set` as originally requested in:<div><br></div><div><a href="https://github.com/haskell/containers/issues/135" target="_blank">https://github.com/haskell/containers/issues/135</a></div><div><br></div><div>The motivation behind this proposal is three-fold:</div><div><br></div><div>* for convenience - these functions are commonly used to implement pagination or previews of maps/sets</div><div>* for type accuracy - the public API impose an unnecessary `Ord` constraint</div><div>* for efficiency - these can be implemented more efficiently using the internal API</div><div><br></div><div>Currently the only way you can implement this functionality via the public API is to use `lookupIndex`/`elemAt` + `split`. For example, one way to implement `Data.Set.take` is:<blockquote style="margin:0 0 0 40px;border:none;padding:0px"><br></blockquote><blockquote style="margin:0 0 0 40px;border:none;padding:0px"><div style="margin:0px;font-size:11px;line-height:normal;font-family:Menlo">take :: Ord a => Int -> Set a -> Set a</div><div style="margin:0px;font-size:11px;line-height:normal;font-family:Menlo">take n m</div><div style="margin:0px;font-size:11px;line-height:normal;font-family:Menlo"> | n < 0 = empty</div><div style="margin:0px;font-size:11px;line-height:normal;font-family:Menlo"> | size m <= n = m</div><div style="margin:0px;font-size:11px;line-height:normal;font-family:Menlo"> | otherwise = lt</div><div style="margin:0px;font-size:11px;line-height:normal;font-family:Menlo"> where</div><div style="margin:0px;font-size:11px;line-height:normal;font-family:Menlo"> (lt, _) = split k m</div><div style="margin:0px;font-size:11px;line-height:normal;font-family:Menlo"> k = elemAt n m</div><div style="margin:0px;font-size:11px;line-height:normal;font-family:Menlo"><div style="margin:0px;line-height:normal">{-# INLINE take #-}</div></div></blockquote><div><div><br></div><div>This implementation incurs an unnecessary `Ord` constraint due to a roundabout way of computing `take`: this extracts the element at the given index and then works backwards from the element’s value to partition the set using O(log N) comparisons. We could eliminate all of the comparisons by using the internal API.</div><div><br></div><div>Intuitively, we expect that the performance of `Data.Set.take` would benefit from avoiding those unnecessary comparisons and also avoiding traversing the `Set`’s spine twice. So I tested that hypothesis by implementing `take` via the internal API like this:</div></div></div><div><br></div><blockquote style="margin:0 0 0 40px;border:none;padding:0px"><div><div style="margin:0px;font-size:11px;line-height:normal;font-family:Menlo">take :: Int -> Set a -> Set a</div></div><div><div style="margin:0px;font-size:11px;line-height:normal;font-family:Menlo">take n0 s0 = go s0 n0</div></div><div><div style="margin:0px;font-size:11px;line-height:normal;font-family:Menlo"> where</div></div><div><div style="margin:0px;font-size:11px;line-height:normal;font-family:Menlo"> go s@(Bin sz x l r) n =</div></div><div><div style="margin:0px;font-size:11px;line-height:normal;font-family:Menlo"> if sz <= n</div></div><div><div style="margin:0px;font-size:11px;line-height:normal;font-family:Menlo"> then s</div></div><div><div style="margin:0px;font-size:11px;line-height:normal;font-family:Menlo"> else</div></div><div><div style="margin:0px;font-size:11px;line-height:normal;font-family:Menlo"> let sl = size l</div></div><div><div style="margin:0px;font-size:11px;line-height:normal;font-family:Menlo"> in if n <= sl</div></div><div><div style="margin:0px;font-size:11px;line-height:normal;font-family:Menlo"> then go l n</div></div><div><div style="margin:0px;font-size:11px;line-height:normal;font-family:Menlo"> else link x l (go r $! n - sl)</div></div><div><div style="margin:0px;font-size:11px;line-height:normal;font-family:Menlo"> go Tip _ = Tip</div></div><div><div style="margin:0px;font-size:11px;line-height:normal;font-family:Menlo">{-# INLINE take #-}</div></div></blockquote><div><br></div><div>I then added the following benchmark to `benchmarks/Set.hs`:</div><div><br></div><blockquote style="margin:0 0 0 40px;border:none;padding:0px"><div><div style="margin:0px;font-size:11px;line-height:normal;font-family:Menlo"><b>diff --git a/benchmarks/Set.hs b/benchmarks/Set.hs</b></div></div><div><div style="margin:0px;font-size:11px;line-height:normal;font-family:Menlo"><b>index 3a6e8aa..03c99fb 100644</b></div></div><div><div style="margin:0px;font-size:11px;line-height:normal;font-family:Menlo"><b>--- a/benchmarks/Set.hs</b></div></div><div><div style="margin:0px;font-size:11px;line-height:normal;font-family:Menlo"><b>+++ b/benchmarks/Set.hs</b></div></div><div><div style="margin:0px;font-size:11px;line-height:normal;font-family:Menlo;color:rgb(52,187,199)">@@ -31,6 +31,7 @@<span style="color:#000000"> main = do</span></div></div><div><div style="margin:0px;font-size:11px;line-height:normal;font-family:Menlo"> , bench "union" $ whnf (S.union s_even) s_odd</div></div><div><div style="margin:0px;font-size:11px;line-height:normal;font-family:Menlo"> , bench "difference" $ whnf (S.difference s) s_even</div></div><div><div style="margin:0px;font-size:11px;line-height:normal;font-family:Menlo"> , bench "intersection" $ whnf (S.intersection s) s_even</div></div><div><div style="margin:0px;font-size:11px;line-height:normal;font-family:Menlo;color:rgb(52,189,38)">+ , bench "take" $ whnf (S.take (2^11)) s</div></div><div><div style="margin:0px;font-size:11px;line-height:normal;font-family:Menlo"> , bench "fromList" $ whnf S.fromList elems</div></div><div><div style="margin:0px;font-size:11px;line-height:normal;font-family:Menlo"> , bench "fromList-desc" $ whnf S.fromList (reverse elems)</div></div><div><div style="margin:0px;font-size:11px;line-height:normal;font-family:Menlo"> , bench "fromAscList" $ whnf S.fromAscList elems</div></div></blockquote><div><br></div><div>Here is the performance on my machine when implementing `take` via the public API:</div><div><br></div><blockquote style="margin:0 0 0 40px;border:none;padding:0px"><div><div style="margin:0px;font-size:11px;line-height:normal;font-family:Menlo">benchmarking take</div></div><div><div style="margin:0px;font-size:11px;line-height:normal;font-family:Menlo">time 272.8 ns (266.7 ns .. 278.1 ns)</div></div><div><div style="margin:0px;font-size:11px;line-height:normal;font-family:Menlo"> 0.997 R² (0.996 R² .. 0.998 R²)</div></div><div><div style="margin:0px;font-size:11px;line-height:normal;font-family:Menlo">mean 266.3 ns (261.8 ns .. 270.8 ns)</div></div><div><div style="margin:0px;font-size:11px;line-height:normal;font-family:Menlo">std dev 15.44 ns (13.26 ns .. 18.95 ns)</div></div><div><div style="margin:0px;font-size:11px;line-height:normal;font-family:Menlo">variance introduced by outliers: 75% (severely inflated)</div></div></blockquote><div><br></div><div><div>… and the performance improved by 61% from using the internal API:</div></div><div><br></div><blockquote style="margin:0 0 0 40px;border:none;padding:0px"><div style="margin:0px;font-size:11px;line-height:normal;font-family:Menlo"><div style="margin:0px;line-height:normal">benchmarking take</div><div style="margin:0px;line-height:normal">time 169.2 ns (166.1 ns .. 172.6 ns)</div><div style="margin:0px;line-height:normal"> 0.997 R² (0.996 R² .. 0.998 R²)</div><div style="margin:0px;line-height:normal">mean 172.1 ns (169.4 ns .. 175.4 ns)</div><div style="margin:0px;line-height:normal">std dev 10.68 ns (8.420 ns .. 15.34 ns)</div><div style="margin:0px;line-height:normal">variance introduced by outliers: 78% (severely inflated)</div></div></blockquote><div><br></div><div>… and I’m guessing (but haven’t tested) that the performance gap would only increase the more expensive the comparison function gets.</div><div><br></div><div>I haven’t performed comparative performance testing for `drop`/`splitAt` nor have I tested `Map` (because the benchmarks take a while for me to build and run) but I can perform those additional comparisons upon requests if people feel they are necessary.</div><div><br></div><div>I haven’t yet written up a full patch since the maintainer asked me to first run this proposal by the libraries mailing list to assess whether it would be wise to expand the `containers` API to include these utilities.</div><div><br></div><div>The deadline for discussion is two weeks.</div></div><br>_______________________________________________<br>
Libraries mailing list<br>
<a href="mailto:Libraries@haskell.org" target="_blank">Libraries@haskell.org</a><br>
<a href="http://mail.haskell.org/cgi-bin/mailman/listinfo/libraries" rel="noreferrer" target="_blank">http://mail.haskell.org/cgi-bin/mailman/listinfo/libraries</a><br>
<br></blockquote></div><br></div>
<br>_______________________________________________<br>
Libraries mailing list<br>
<a href="mailto:Libraries@haskell.org">Libraries@haskell.org</a><br>
<a href="http://mail.haskell.org/cgi-bin/mailman/listinfo/libraries" rel="noreferrer" target="_blank">http://mail.haskell.org/cgi-bin/mailman/listinfo/libraries</a><br>
<br></blockquote></div>