Optimize intersectAttrs performance

Always traverse the shortest set.

src/libexpr/primops.cc

@@ -2448,12 +2448,62 @@ static void prim_intersectAttrs(EvalState & state, const PosIdx pos, Value * * a
     state.forceAttrs(*args[0], pos);
     state.forceAttrs(*args[1], pos);
 
-    auto attrs = state.buildBindings(std::min(args[0]->attrs->size(), args[1]->attrs->size()));
+    Bindings &left = *args[0]->attrs;
+    Bindings &right = *args[1]->attrs;
 
-    for (auto & i : *args[0]->attrs) {
-        Bindings::iterator j = args[1]->attrs->find(i.name);
-        if (j != args[1]->attrs->end())
-            attrs.insert(*j);
+    auto attrs = state.buildBindings(std::min(left.size(), right.size()));
+
+    // The current implementation has good asymptotic complexity and is reasonably
+    // simple. Further optimization may be possible, but does not seem productive,
+    // considering the state of eval performance in 2022.
+    //
+    // I have looked for reusable and/or standard solutions and these are my
+    // findings:
+    //
+    // STL
+    // ===
+    // std::set_intersection is not suitable, as it only performs a simultaneous
+    // linear scan; not taking advantage of random access. This is O(n + m), so
+    // linear in the largest set, which is not acceptable for callPackage in Nixpkgs.
+    //
+    // Simultaneous scan, with alternating simple binary search
+    // ===
+    // One alternative algorithm scans the attrsets simultaneously, jumping
+    // forward using `lower_bound` in case of inequality. This should perform
+    // well on very similar sets, having a local and predictable access pattern.
+    // On dissimilar sets, it seems to need more comparisons than the current
+    // algorithm, as few consecutive attrs match. `lower_bound` could take
+    // advantage of the decreasing remaining search space, but this causes
+    // the medians to move, which can mean that they don't stay in the cache
+    // like they would with the current naive `find`.
+    //
+    // Double binary search
+    // ===
+    // The optimal algorithm may be "Double binary search", which doesn't
+    // scan at all, but rather divides both sets simultaneously.
+    // See "Fast Intersection Algorithms for Sorted Sequences" by Baeza-Yates et al.
+    // https://cs.uwaterloo.ca/~ajsaling/papers/intersection_alg_app10.pdf
+    // The only downsides I can think of are not having a linear access pattern
+    // for similar sets, and having to maintain a more intricate algorithm.
+    //
+    // Adaptive
+    // ===
+    // Finally one could run try a simultaneous scan, count misses and fall back
+    // to double binary search when the counter hit some threshold and/or ratio.
+
+    if (left.size() < right.size()) {
+        for (auto & l : left) {
+            Bindings::iterator r = right.find(l.name);
+            if (r != right.end())
+                attrs.insert(*r);
+        }
+    }
+    else {
+        for (auto & r : right) {
+            Bindings::iterator l = left.find(r.name);
+            if (l != left.end())
+                attrs.insert(r);
+        }
     }
 
     v.mkAttrs(attrs.alreadySorted());
@@ -2465,6 +2515,8 @@ static RegisterPrimOp primop_intersectAttrs({
     .doc = R"(
       Return a set consisting of the attributes in the set *e2* which have the
       same name as some attribute in *e1*.
+
+      Performs in O(*n* log *m*) where *n* is the size of the smaller set and *m* the larger set's size.
     )",
     .fun = prim_intersectAttrs,
 });

tests/lang/eval-okay-intersectAttrs.exp

@@ -0,0 +1 @@
+[ { } { a = 1; } { a = 1; } { a = "a"; } { m = 1; } { m = "m"; } { n = 1; } { n = "n"; } { n = 1; p = 2; } { n = "n"; p = "p"; } { n = 1; p = 2; } { n = "n"; p = "p"; } { a = "a"; b = "b"; c = "c"; d = "d"; e = "e"; f = "f"; g = "g"; h = "h"; i = "i"; j = "j"; k = "k"; l = "l"; m = "m"; n = "n"; o = "o"; p = "p"; q = "q"; r = "r"; s = "s"; t = "t"; u = "u"; v = "v"; w = "w"; x = "x"; y = "y"; z = "z"; } true ]

tests/lang/eval-okay-intersectAttrs.nix

@@ -0,0 +1,50 @@
+let
+  alphabet =
+  { a = "a";
+    b = "b";
+    c = "c";
+    d = "d";
+    e = "e";
+    f = "f";
+    g = "g";
+    h = "h";
+    i = "i";
+    j = "j";
+    k = "k";
+    l = "l";
+    m = "m";
+    n = "n";
+    o = "o";
+    p = "p";
+    q = "q";
+    r = "r";
+    s = "s";
+    t = "t";
+    u = "u";
+    v = "v";
+    w = "w";
+    x = "x";
+    y = "y";
+    z = "z";
+  };
+  foo = {
+    inherit (alphabet) f o b a r z q u x;
+    aa = throw "aa";
+  };
+  alphabetFail = builtins.mapAttrs throw alphabet;
+in
+[ (builtins.intersectAttrs { a = abort "l1"; } { b = abort "r1"; })
+  (builtins.intersectAttrs { a = abort "l2"; } { a = 1; })
+  (builtins.intersectAttrs alphabetFail { a = 1; })
+  (builtins.intersectAttrs  { a = abort "laa"; } alphabet)
+  (builtins.intersectAttrs alphabetFail { m = 1; })
+  (builtins.intersectAttrs  { m = abort "lam"; } alphabet)
+  (builtins.intersectAttrs alphabetFail { n = 1; })
+  (builtins.intersectAttrs  { n = abort "lan"; } alphabet)
+  (builtins.intersectAttrs alphabetFail { n = 1; p = 2; })
+  (builtins.intersectAttrs  { n = abort "lan2"; p = abort "lap"; } alphabet)
+  (builtins.intersectAttrs alphabetFail { n = 1; p = 2; })
+  (builtins.intersectAttrs  { n = abort "lan2"; p = abort "lap"; } alphabet)
+  (builtins.intersectAttrs alphabetFail alphabet)
+  (builtins.intersectAttrs alphabet foo == builtins.intersectAttrs foo alphabet)
+]