Resume patch operations from the common prefix in constant time per step

patch() and patch_inplace() keep the values along the previously resolved
pointer, so that the next operation resumes from the prefix the two paths
have in common. To find the resume point, each cached step was tested from the
deepest upwards with a memcmp over its whole prefix. If two paths shared a
prefix and the previous path continued for D more tokens, the search compared
D prefixes of that length: for two "test" operations whose paths share n
tokens and continue for n more, the time was quadratic in n (3.12.0 was
linear).

With more than 16 cached steps, the length of the common prefix of the two
paths is now computed once, and the deepest cached step that ends within it,
at a token boundary of the new path, is taken. Steps that are skipped are
dropped from the cache, so the search is amortized constant per token. With
fewer steps, which is the usual case, they are compared as before, as that
is cheaper for short paths. The operations, and which values stay valid after
them, are unchanged.

Measurements (Apple clang -O2, arm64), patch_inplace() of two "test"
operations whose paths share n tokens and continue for n more:

  n          25k    50k    100k    200k
  before    42 ms  182 ms 1194 ms 5433 ms
  after      0 ms    2 ms    4 ms    8 ms
  3.12.0     3 ms    5 ms   10 ms   19 ms

Patches of ordinary documents (diff() then patch(), and many short
operations): within 0.5 % of before in instructions retired (canada, citm_catalog,
twitter, mesh, update-center, many short synthetic operations).

Signed-off-by: Niels Lohmann <mail@nlohmann.me>

.github/dependabot.yml

@@ -67,4 +67,3 @@ updates:
       - dependency-name: mcp
       - dependency-name: boltons
       - dependency-name: "opentelemetry-*"
-      - dependency-name: importlib-metadata

.github/workflows/codeql-analysis.yml

@@ -38,7 +38,7 @@ jobs:
 
     # Initializes the CodeQL tools for scanning.
     - name: Initialize CodeQL
-      uses: github/codeql-action/init@33d7b85da1a04171e211befe2c739303b9a4c066 # v4.39.3
+      uses: github/codeql-action/init@1fc58d04a4d4374f921bdac573c3811c240f9c26 # v4.39.2
       with:
         languages: c-cpp
         # Analyze the sources without compiling them. Autobuild compiled the
@@ -47,4 +47,4 @@ jobs:
         build-mode: none
 
     - name: Perform CodeQL Analysis
-      uses: github/codeql-action/analyze@33d7b85da1a04171e211befe2c739303b9a4c066 # v4.39.3
+      uses: github/codeql-action/analyze@1fc58d04a4d4374f921bdac573c3811c240f9c26 # v4.39.2

.github/workflows/flawfinder.yml

@@ -48,6 +48,6 @@ jobs:
           output: 'flawfinder_results.sarif'
 
       - name: Upload analysis results to GitHub Security tab
-        uses: github/codeql-action/upload-sarif@33d7b85da1a04171e211befe2c739303b9a4c066 # v4.39.3
+        uses: github/codeql-action/upload-sarif@1fc58d04a4d4374f921bdac573c3811c240f9c26 # v4.39.2
         with:
           sarif_file: ${{github.workspace}}/flawfinder_results.sarif

.github/workflows/scorecards.yml

@@ -80,6 +80,6 @@ jobs:
 
       # Upload the results to GitHub's code scanning dashboard.
       - name: "Upload to code-scanning"
-        uses: github/codeql-action/upload-sarif@33d7b85da1a04171e211befe2c739303b9a4c066 # v4.39.3
+        uses: github/codeql-action/upload-sarif@1fc58d04a4d4374f921bdac573c3811c240f9c26 # v4.39.2
         with:
           sarif_file: results.sarif

.github/workflows/semgrep.yml

@@ -65,7 +65,7 @@ jobs:
 
       # Upload SARIF file generated in previous step
       - name: Upload SARIF file
-        uses: github/codeql-action/upload-sarif@33d7b85da1a04171e211befe2c739303b9a4c066 # v4.39.3
+        uses: github/codeql-action/upload-sarif@1fc58d04a4d4374f921bdac573c3811c240f9c26 # v4.39.2
         with:
           sarif_file: semgrep.sarif
         if: always()

cmake/requirements/requirements-semgrep.txt

@@ -391,9 +391,9 @@ httpx-sse==0.4.3 \
 idna==3.20 \
     --hash=sha256:a7db850025b95ded1eae8a46181a1a6c56c92c96f0e2b005d9ff8dc0210cab44 \
     --hash=sha256:ab7ae7122974553370f0bdb919e1a960b2cd1bc1ef0276416d896db81c14582c
-importlib-metadata==8.7.1 \
+importlib-metadata==10.1.0 \
-    --hash=sha256:49fef1ae6440c182052f407c8d34a68f72efc36db9ca90dc0113398f2fdde8bb \
+    --hash=sha256:82b04047fa09792c1a8cfeddfe08bec79e4b13c29c8469b0d3949860f61017e8 \
-    --hash=sha256:5a1f80bf1daa489495071efbb095d75a634cf28a8bc299581244063b53176151
+    --hash=sha256:cf45ce66a929c64e994185a809c04840d0501db17e663810d993d0f4829265c7
 jsonschema==4.25.1 \
     --hash=sha256:3fba0169e345c7175110351d456342c364814cfcf3b964ba4587f22915230a63 \
     --hash=sha256:e4a9655ce0da0c0b67a085847e00a3a51449e1157f4f75e9fb5aa545e122eb85

include/nlohmann/detail/json_pointer.hpp

@@ -1091,6 +1091,32 @@ class json_pointer
         }
     };
 
+    /*!
+    @brief the number of the deepest step of the previous path that is a prefix of the new one
+
+    Comparing every one of many steps with the beginning of the path would take
+    quadratic time. Instead, the length of the common beginning of the two paths
+    is computed once: a step whose prefix is not longer is a prefix of the new
+    path, too. For few steps, which is the usual case, @ref resolve_plain
+    compares them, which is cheaper.
+    */
+    template<typename Steps>
+    JSON_HEDLEY_NEVER_INLINE static std::size_t deepest_shared_step(const string_t& path, const std::size_t length, const string_t& previous, const Steps& steps) noexcept
+    {
+        const std::size_t same = common_prefix_length(path.data(), previous.data(), (std::min)(length, previous.size()));
+        std::size_t depth = steps.size();
+        for (; depth > 1; --depth)
+        {
+            // a step ends at a token boundary of the previous path
+            const std::size_t prefix = steps[depth - 1].first;
+            if (prefix <= same && (prefix == length || path[prefix] == '/'))
+            {
+                break;
+            }
+        }
+        return depth;
+    }
+
     /*!
     @brief resolve a plain JSON pointer without building its reference tokens
 
@@ -1119,6 +1145,12 @@ class json_pointer
         if (cache.path != nullptr && !steps.empty() && steps[0].second == root)
         {
             const string_t& previous = *cache.path;
+            if (JSON_HEDLEY_UNLIKELY(steps.size() > 16))
+            {
+                depth = deepest_shared_step(path, length, previous, steps);
+            }
+            else
+            {
                 for (depth = steps.size(); depth > 1; --depth)
                 {
                     // a step ends at a token boundary of the previous path
@@ -1128,6 +1160,7 @@ class json_pointer
                         break;
                     }
                 }
+            }
             steps.resize(depth);
         }
         else

single_include/nlohmann/json.hpp

@@ -27266,6 +27266,32 @@ class json_pointer
         }
     };
 
+    /*!
+    @brief the number of the deepest step of the previous path that is a prefix of the new one
+
+    Comparing every one of many steps with the beginning of the path would take
+    quadratic time. Instead, the length of the common beginning of the two paths
+    is computed once: a step whose prefix is not longer is a prefix of the new
+    path, too. For few steps, which is the usual case, @ref resolve_plain
+    compares them, which is cheaper.
+    */
+    template<typename Steps>
+    JSON_HEDLEY_NEVER_INLINE static std::size_t deepest_shared_step(const string_t& path, const std::size_t length, const string_t& previous, const Steps& steps) noexcept
+    {
+        const std::size_t same = common_prefix_length(path.data(), previous.data(), (std::min)(length, previous.size()));
+        std::size_t depth = steps.size();
+        for (; depth > 1; --depth)
+        {
+            // a step ends at a token boundary of the previous path
+            const std::size_t prefix = steps[depth - 1].first;
+            if (prefix <= same && (prefix == length || path[prefix] == '/'))
+            {
+                break;
+            }
+        }
+        return depth;
+    }
+
     /*!
     @brief resolve a plain JSON pointer without building its reference tokens
 
@@ -27294,6 +27320,12 @@ class json_pointer
         if (cache.path != nullptr && !steps.empty() && steps[0].second == root)
         {
             const string_t& previous = *cache.path;
+            if (JSON_HEDLEY_UNLIKELY(steps.size() > 16))
+            {
+                depth = deepest_shared_step(path, length, previous, steps);
+            }
+            else
+            {
                 for (depth = steps.size(); depth > 1; --depth)
                 {
                     // a step ends at a token boundary of the previous path
@@ -27303,6 +27335,7 @@ class json_pointer
                         break;
                     }
                 }
+            }
             steps.resize(depth);
         }
         else

tests/src/unit-json_patch.cpp

@@ -14,9 +14,12 @@ using nlohmann::json;
     using namespace nlohmann::literals; // NOLINT(google-build-using-namespace)
 #endif
 
+#include <algorithm>
 #include <cstddef>
+#include <ctime>
 #include <fstream>
 #include <limits>
+#include <random>
 #include <string>
 #include <utility>
 #include <vector>
@@ -2551,3 +2554,419 @@ TEST_CASE("JSON patch - diff of leaf values below the bound of the recursive des
     CHECK(object_patch.size() == 2);
     CHECK(object_source.patch(object_patch) == object_target);
 }
+
+namespace
+{
+// all pointers to values below `value` (not to `value` itself)
+void collect_pointers(const json& value, const std::string& path, std::vector<std::string>& pointers)
+{
+    if (value.is_object())
+    {
+        for (const auto& element : value.items())
+        {
+            std::string child = path;
+            child += '/';
+            for (const char c : element.key())
+            {
+                if (c == '~')
+                {
+                    child += "~0";
+                }
+                else if (c == '/')
+                {
+                    child += "~1";
+                }
+                else
+                {
+                    child += c;
+                }
+            }
+            pointers.push_back(child);
+            collect_pointers(element.value(), child, pointers);
+        }
+    }
+    else if (value.is_array())
+    {
+        for (std::size_t i = 0; i < value.size(); ++i)
+        {
+            std::string child = path;
+            child += '/';
+            child += std::to_string(i);
+            pointers.push_back(child);
+            collect_pointers(value[i], child, pointers);
+        }
+    }
+}
+
+// a random document of at most `depth` levels, with the names as keys
+json random_document(std::mt19937& gen, const std::vector<std::string>& names, const int depth)
+{
+    const int kind = std::uniform_int_distribution<int>(0, 9)(gen);
+    if (depth == 0 || kind < 2)
+    {
+        return std::uniform_int_distribution<int>(0, 3)(gen);
+    }
+    const int size = std::uniform_int_distribution<int>(1, 3)(gen);
+    json result = kind < 6 ? json::array() : json::object();
+    for (int i = 0; i < size; ++i)
+    {
+        if (kind < 6)
+        {
+            result.push_back(random_document(gen, names, depth - 1));
+        }
+        else
+        {
+            result[names[std::uniform_int_distribution<std::size_t>(0, names.size() - 1)(gen)]] = random_document(gen, names, depth - 1);
+        }
+    }
+    return result;
+}
+
+// the strings, one after the other
+std::string concat(std::string first, const std::string& second, const std::string& third = std::string())
+{
+    first += second;
+    first += third;
+    return first;
+}
+
+// the best of five times in seconds that std::clock() measures to apply the patch
+double patch_cpu_time(json& doc, const json& patch)
+{
+    double best = 1e30;
+    for (int i = 0; i < 5; ++i)
+    {
+        const std::clock_t start = std::clock();
+        doc.patch_inplace(patch);
+        best = (std::min)(best, static_cast<double>(std::clock() - start) / static_cast<double>(CLOCKS_PER_SEC));
+    }
+    return best;
+}
+} // namespace
+
+TEST_CASE("JSON patch - consecutive operations with paths that share a prefix")
+{
+    SECTION("tokens that start the same way")
+    {
+        const json doc = {{"a", {{"bc", {{"x", 1}}}, {"b", {{"x", 2}}}, {"b2", 3}}}};
+
+        // the second path shares "/a/b" with the first, but not the token "bc"
+        const json patch = json::parse(R"([
+            {"op": "test", "path": "/a/bc/x", "value": 1},
+            {"op": "test", "path": "/a/b/x", "value": 2},
+            {"op": "test", "path": "/a/bc/x", "value": 1},
+            {"op": "test", "path": "/a/b2", "value": 3},
+            {"op": "test", "path": "/a/b/x", "value": 2}
+        ])");
+        CHECK(doc.patch(patch) == doc);
+
+        json inplace = doc;
+        inplace.patch_inplace(patch);
+        CHECK(inplace == doc);
+
+        // a path that is a prefix of the previous one, and the other way round
+        const json prefixes = json::parse(R"([
+            {"op": "test", "path": "/a/bc/x", "value": 1},
+            {"op": "test", "path": "/a/bc", "value": {"x": 1}},
+            {"op": "test", "path": "/a/bc/x", "value": 1},
+            {"op": "test", "path": "/a", "value": {"bc": {"x": 1}, "b": {"x": 2}, "b2": 3}},
+            {"op": "test", "path": "/a/b/x", "value": 2},
+            {"op": "test", "path": "", "value": {"a": {"bc": {"x": 1}, "b": {"x": 2}, "b2": 3}}}
+        ])");
+        CHECK(doc.patch(prefixes) == doc);
+    }
+
+    SECTION("operations above a path that was resolved before")
+    {
+        const json doc = json::parse(R"({"a": [{"b": [1, 2, 3]}, {"b": [4, 5, 6]}], "c": {"d": {"e": 7}}})");
+
+        // an element inserted before the elements of an array moves them
+        CHECK(doc.patch(json::parse(R"([
+            {"op": "test", "path": "/a/0/b/2", "value": 3},
+            {"op": "add", "path": "/a/0", "value": {"b": [9]}},
+            {"op": "test", "path": "/a/1/b/2", "value": 3},
+            {"op": "test", "path": "/a/0/b/0", "value": 9},
+            {"op": "test", "path": "/a/2/b/0", "value": 4}
+        ])")) == json::parse(R"({"a": [{"b": [9]}, {"b": [1, 2, 3]}, {"b": [4, 5, 6]}], "c": {"d": {"e": 7}}})"));
+
+        // an element removed from the front
+        CHECK(doc.patch(json::parse(R"([
+            {"op": "test", "path": "/a/1/b/2", "value": 6},
+            {"op": "remove", "path": "/a/0"},
+            {"op": "test", "path": "/a/0/b/2", "value": 6},
+            {"op": "replace", "path": "/a/0/b/2", "value": 60},
+            {"op": "test", "path": "/a/0/b/2", "value": 60}
+        ])")) == json::parse(R"({"a": [{"b": [4, 5, 60]}], "c": {"d": {"e": 7}}})"));
+
+        // a value replaced above the path that was resolved before
+        CHECK(doc.patch(json::parse(R"([
+            {"op": "test", "path": "/c/d/e", "value": 7},
+            {"op": "replace", "path": "/c/d", "value": {"e": 8, "f": {"g": 9}}},
+            {"op": "test", "path": "/c/d/e", "value": 8},
+            {"op": "test", "path": "/c/d/f/g", "value": 9},
+            {"op": "remove", "path": "/c/d/f"},
+            {"op": "add", "path": "/c/d/f", "value": [1]},
+            {"op": "test", "path": "/c/d/f/0", "value": 1}
+        ])")) == json::parse(R"({"a": [{"b": [1, 2, 3]}, {"b": [4, 5, 6]}], "c": {"d": {"e": 8, "f": [1]}}})"));
+
+#if !defined(JSON_NOEXCEPTION)
+        // a value removed above the path that was resolved before is gone
+        const json removed = json::parse(R"([
+            {"op": "test", "path": "/c/d/e", "value": 7},
+            {"op": "remove", "path": "/c/d"},
+            {"op": "test", "path": "/c/d/e", "value": 7}
+        ])");
+        CHECK_THROWS_AS(doc.patch(removed), json::other_error&);
+        json inplace = doc;
+        CHECK_THROWS_AS(inplace.patch_inplace(removed), json::other_error&);
+
+        const json emptied = json::parse(R"([
+            {"op": "test", "path": "/a/1/b/2", "value": 6},
+            {"op": "remove", "path": "/a/1"},
+            {"op": "test", "path": "/a/1/b/2", "value": 6}
+        ])");
+        CHECK_THROWS_AS(doc.patch(emptied), json::other_error&);
+#endif
+    }
+
+    SECTION("paths with more than 16 tokens")
+    {
+        // 40 levels, with an array at the bottom and a second branch at level 20
+        std::string prefix20;
+        std::string prefix40;
+        json doc = {{"leaf", {1, 2, 3}}};
+        for (int i = 40; i > 0; --i)
+        {
+            if (i == 20)
+            {
+                doc["other"] = {{"x", 5}};
+            }
+            doc = {{"n", doc}};
+        }
+        for (int i = 1; i <= 40; ++i)
+        {
+            prefix40 += "/n";
+            if (i == 20)
+            {
+                prefix20 = prefix40;
+            }
+        }
+
+        const auto op = [](const char* name, const std::string & path, const json & value)
+        {
+            return json({{"op", name}, {"path", path}, {"value", value}});
+        };
+        const json patch =
+        {
+            op("test", concat(prefix40, "/leaf/2"), 3),
+            op("test", concat(prefix20, "/other/x"), 5),
+            op("test", concat(prefix40, "/leaf/0"), 1),
+            op("add", concat(prefix40, "/leaf/0"), 0),
+            op("test", concat(prefix40, "/leaf/3"), 3),
+            op("replace", concat(prefix20, "/other"), {{"x", 6}}),
+            op("test", concat(prefix20, "/other/x"), 6),
+            op("test", concat(prefix40, "/leaf/1"), 1),
+            {{"op", "remove"}, {"path", concat(prefix20, "/other")}},
+            op("test", concat(prefix40, "/leaf/1"), 1)
+        };
+        json expected = doc;
+        for (const auto& operation : patch)
+        {
+            expected = expected.patch(json::array({operation}));
+        }
+        CHECK(doc.patch(patch) == expected);
+        json inplace = doc;
+        inplace.patch_inplace(patch);
+        CHECK(inplace == expected);
+        CHECK(expected[json::json_pointer(concat(prefix40, "/leaf"))] == json({0, 1, 2, 3}));
+        CHECK(!expected[json::json_pointer(prefix20)].contains("other"));
+
+#if !defined(JSON_NOEXCEPTION)
+        // the value that was resolved before is gone with the member that held it
+        const json gone =
+        {
+            op("test", concat(prefix40, "/leaf/2"), 3),
+            {{"op", "remove"}, {"path", prefix20}},
+            op("test", concat(prefix40, "/leaf/2"), 3)
+        };
+        CHECK_THROWS_AS(doc.patch(gone), json::other_error&);
+#endif
+    }
+
+    SECTION("random sequences of operations give the same result as one operation at a time")
+    {
+        std::mt19937 gen(20261110); // NOLINT(cert-msc32-c,cert-msc51-cpp,bugprone-random-generator-seed): reproducible
+        const std::vector<std::string> names = {"a", "b", "ab", "abc", "a/b", "a~b", "1", "10", "token_longer_than_eight_bytes"};
+        const auto pick = [&gen](const std::size_t n)
+        {
+            return std::uniform_int_distribution<std::size_t>(0, n - 1)(gen);
+        };
+
+        for (int round = 0; round < 300; ++round)
+        {
+            const json start = random_document(gen, names, 7);
+            json current = start;
+            json patch = json::array();
+            std::string previous;
+
+            for (int step = 0; step < 25; ++step)
+            {
+                std::vector<std::string> pointers;
+                collect_pointers(current, "", pointers);
+                if (pointers.empty())
+                {
+                    break;
+                }
+
+                // most of the time, stay below a part of the previous path
+                std::vector<std::string> candidates;
+                if (!previous.empty() && pick(10) < 8)
+                {
+                    std::string prefix = previous;
+                    const std::size_t cut = prefix.find('/', 1 + pick(prefix.size()));
+                    prefix = prefix.substr(0, cut == std::string::npos ? prefix.size() : cut);
+                    for (const auto& p : pointers)
+                    {
+                        if (p.compare(0, prefix.size(), prefix) == 0)
+                        {
+                            candidates.push_back(p);
+                        }
+                    }
+                }
+                if (candidates.empty())
+                {
+                    candidates = pointers;
+                }
+                const std::string path = candidates[pick(candidates.size())];
+                const json::json_pointer pointer(path);
+
+                json operation;
+                switch (pick(5))
+                {
+                    case 0:
+                        operation = {{"op", "test"}, {"path", path}, {"value", current[pointer]}};
+                        break;
+                    case 1:
+                        operation = {{"op", "replace"}, {"path", path}, {"value", static_cast<int>(pick(100))}};
+                        break;
+                    case 2:
+                        operation = {{"op", "remove"}, {"path", path}};
+                        break;
+                    default:
+                    {
+                        // add below an array or object, which may be the root
+                        const json::json_pointer parent_pointer = pick(4) == 0 ? json::json_pointer() : pointer;
+                        const std::string parent_path = parent_pointer.to_string();
+                        const json& parent = current[parent_pointer];
+                        std::string token = "-";
+                        if (parent.is_array())
+                        {
+                            token = pick(3) == 0 ? "-" : std::to_string(pick(parent.size() + 1));
+                        }
+                        else if (parent.is_object())
+                        {
+                            token = pick(2) == 0 ? "new" : "ab";
+                        }
+                        else
+                        {
+                            // a primitive parent: replace it instead
+                            operation = {{"op", "replace"}, {"path", parent_path}, {"value", json::array({1, 2})}};
+                            break;
+                        }
+                        operation = {{"op", "add"}, {"path", concat(parent_path, "/", token)}, {"value", json::object({{"k", {1, 2}}})}};
+                        break;
+                    }
+                }
+                if (operation["path"].get<std::string>().empty())
+                {
+                    continue;
+                }
+
+                // one operation at a time: the cache is empty at the start of each
+                current = current.patch(json::array({operation}));
+                patch.push_back(operation);
+                previous = operation["path"].get<std::string>();
+            }
+
+            CHECK(start.patch(patch) == current);
+            json inplace = start;
+            inplace.patch_inplace(patch);
+            CHECK(inplace == current);
+
+            // the same for a type that keeps the order of the members, which makes
+            // objects that were built in a different order unequal: leave out the
+            // tests of structured values
+            json without_tests = json::array();
+            for (const auto& operation : patch)
+            {
+                if (operation["op"] != "test" || !operation["value"].is_structured())
+                {
+                    without_tests.push_back(operation);
+                }
+            }
+            const nlohmann::ordered_json ordered_patch = without_tests;
+            nlohmann::ordered_json ordered_inplace = start;
+            ordered_inplace.patch_inplace(ordered_patch);
+            CHECK(json(ordered_inplace) == current);
+        }
+    }
+}
+
+TEST_CASE("JSON patch - time is linear for long paths that share a prefix")
+{
+    // The time of the patch is compared with the time of a patch that is
+    // linear for sure, because a bound in seconds would depend on the machine:
+    // both test the same two values at the end of paths with 2n tokens. The
+    // second path of the first patch shares n tokens with the first one and
+    // continues for n tokens: the ratio is 1 to 2, and about 60 when every
+    // step is compared with the start of the path. The time that std::clock()
+    // measures is mostly the time of the processor, which a busy machine does
+    // not inflate (on MSVC, it is the time that has passed).
+    constexpr std::size_t n = 25000;
+
+    const auto nest = [](const std::size_t depth, const std::string & inner)
+    {
+        std::string text;
+        for (std::size_t i = 0; i < depth; ++i)
+        {
+            text += "{\"a\":";
+        }
+        text += inner;
+        text.append(depth, '}');
+        return text;
+    };
+    std::string as;
+    for (std::size_t i = 0; i < n; ++i)
+    {
+        as += "/a";
+    }
+    const std::string deep = nest(n, "1");
+    std::string members = "{\"x\":";
+    members += deep;
+    members += ",\"y\":";
+    members += deep;
+    members += "}";
+    json doc = json::parse(nest(n, members));
+
+    const auto test_op = [](const std::string & path)
+    {
+        return json({{"op", "test"}, {"path", path}, {"value", 1}});
+    };
+    const json shared = json::array({test_op(concat(as, "/x", as)), test_op(concat(as, "/y", as))});
+    const json same = json::array({test_op(concat(as, "/x", as)), test_op(concat(as, "/x", as))});
+
+    // the operations do not change the document, which is too deep to copy;
+    // a busy machine may spoil one comparison, hardly two
+    bool linear = false;
+    double t_shared = 0;
+    double t_same = 0;
+    for (int attempt = 0; attempt < 2 && !linear; ++attempt)
+    {
+        t_shared = patch_cpu_time(doc, shared);
+        t_same = (std::max)(patch_cpu_time(doc, same), 1e-3);
+        linear = t_shared < 10 * t_same;
+    }
+    CAPTURE(t_shared)
+    CAPTURE(t_same)
+    CHECK(linear);
+}