docs: make the diff() and patch() documentation accurate; add tests

Document the exceptions to the diff round-trip invariant (NaN, discarded
values, number types), the path parameter, non-minimal patches, array and
object operation order, the ordered_json fallback, binary values in
serialized patches, the real complexity, duplicate member names in
operations, test on missing paths, and the exact out_of_range.403 message.
Add tests for these behaviors.

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

docs/mkdocs/docs/api/basic_json/diff.md

@@ -2,17 +2,27 @@
 
 ```cpp
 static basic_json diff(const basic_json& source,
-                       const basic_json& target);
+                       const basic_json& target,
+                       const string_t& path = "");
 ```
 
 Creates a [JSON Patch](http://jsonpatch.com) so that value `source` can be changed into the value `target` by calling
 [`patch`](patch.md) function.
 
-For two JSON values `source` and `target`, the following code always yields `#!cpp true`:
+For two JSON values `source` and `target`, the following code yields `#!cpp true`:
 ```cpp
 source.patch(diff(source, target)) == target;
 ```
 
+The equality holds up to [`operator==`](operator_eq.md), so it has the following exceptions:
+
+- A value that is not equal to itself cannot round-trip. This applies to `NaN` (also nested in an array or object) and
+  to [discarded](is_discarded.md) values: `diff` emits a `replace` operation for them. A `NaN` in the patch is
+  serialized as `#!json null`, so a patch that was dumped and parsed again would set `#!json null`.
+- Numbers that compare equal produce no operation, even if their types or signs differ: `diff(1, 1.0)`,
+  `diff(1u, 1)` (unsigned and signed integer) and `diff(0.0, -0.0)` all return `#!json []`. The patched value is then
+  the `source` and keeps its number type.
+
 ## Parameters
 
 `source` (in)
@@ -21,6 +31,12 @@ source.patch(diff(source, target)) == target;
 `target` (in)
 :   JSON value to compare against
 
+`path` (in)
+:   a prefix that is put verbatim in front of the `path` member of every operation (default: `""`, which addresses the
+    root of the value). The prefix is neither escaped nor validated: `#!cpp diff(1, 2, "abc")` yields an operation with
+    the `path` `abc`, which is not a valid JSON Pointer. Use it with a valid JSON Pointer such as `/root` and escape
+    `~` and `/` in its reference tokens (see [JSON Pointer](../../features/json_pointer.md)).
+
 ## Return value
 
 a JSON patch to convert the `source` to `target`
@@ -31,11 +47,32 @@ Strong guarantee: `source` and `target` are never modified.
 
 ## Complexity
 
-Linear in the lengths of `source` and `target`.
+Linear in the total number of values (including nested ones) in `source` and `target`, times the cost of a key-based
+object operation (looking up a key in an object): logarithmic for [`json`](../json.md), and linear for
+[`ordered_json`](../ordered_json.md) (see [`ordered_map` complexity](../ordered_map.md#complexity)). For
+`ordered_json`, diffing two objects with `n` and `m` members therefore takes O((n+m)²) when their keys do not line up
+(e.g., a key was added or the keys are in a different order). The size of the patch is proportional to the number of
+operations times the length of their paths, so a small change deep inside a value yields a long `path`.
 
 ## Notes
 
-Currently, only `remove`, `add`, and `replace` operations are generated.
+- Currently, only `remove`, `add`, and `replace` operations are generated.
+- The patch is correct, but not guaranteed to be minimal. For instance, `diff([1,2,3], [0,1,2,3])` yields three
+  `replace` operations and one `add` operation instead of a single insertion.
+- Differences between two arrays are reported index by index. Elements that were added at the end of the array are added
+  with `add` operations on the path `/-` (appended in order), and elements that were removed are removed with `remove`
+  operations from the highest index down to the lowest, so that the remaining indices stay valid.
+- For objects, the operations for the members of `source` come first (`replace`, `remove`, or the operations for nested
+  values, in the iteration order of `source`), followed by `add` operations for the members that only `target` has.
+- For [`ordered_json`](../ordered_json.md), objects with the same keys in a different order are different. As a patch
+  cannot reorder members, `diff` removes all keys of the `source` object and adds them again in the order of the
+  `target`.
+- If `source` and `target` differ as a whole (e.g., different types), the patch consists of a single `replace`
+  operation for the root of the value, i.e., with the `path` `""` (or the given `path` prefix).
+- The `value` members of the patch hold copies of values of `target`. A [binary](../../features/binary_values.md) value
+  has no JSON representation: when a patch that contains one is serialized, it becomes an object such as
+  `#!json {"bytes":[1,3],"subtype":null}`, so a parsed patch no longer holds a binary value (and would set that object
+  instead).
           
 ## Examples
 

docs/mkdocs/docs/api/basic_json/patch.md

@@ -40,7 +40,7 @@ Strong guarantee: if an exception is thrown, there are no changes in the JSON va
   where an existing element is required (the "path" of "replace", the "from" of "move" and "copy"); example:
   `"array index '-' (3) is out of range"`.
 - Throws [`out_of_range.403`](../../home/exceptions.md#jsonexceptionout_of_range403) if a JSON pointer inside the patch
-  could not be resolved successfully in the current JSON value; example: `"key baz not found"`.
+  could not be resolved successfully in the current JSON value; example: `"key 'baz' not found"`.
 - Throws [`out_of_range.404`](../../home/exceptions.md#jsonexceptionout_of_range404) if a reference token of a JSON
   pointer inside the patch cannot be resolved, e.g., `-` in a "remove" operation or `1a` for an array; example:
   `"unresolved reference token '-'"`.
@@ -53,7 +53,10 @@ Strong guarantee: if an exception is thrown, there are no changes in the JSON va
 - Throws [`out_of_range.414`](../../home/exceptions.md#jsonexceptionout_of_range414) if a "move" operation's "from"
   location is a proper prefix of its "path" location.
 - Throws [`other_error.501`](../../home/exceptions.md#jsonexceptionother_error501) if "test" operation was
-  unsuccessful.
+  unsuccessful. A "test" operation whose "path" does not exist is unsuccessful, too: the failed lookup is reported as a
+  failed test, even if the operation has no "value" member (which would otherwise be
+  [`parse_error.105`](../../home/exceptions.md#jsonexceptionparse_error105)). Which of the two errors is reported for
+  this combination depends on the order in which the operands of a comparison are evaluated, so do not rely on it.
 
 ## Complexity
 
@@ -65,6 +68,10 @@ the JSON value, the complexity can usually be neglected.
 The application of a patch is atomic: Either all operations succeed and the patched document is returned or an exception
 is thrown. In any case, the original value is not changed: the patch is applied to a copy of the value.
 
+Duplicate member names inside an operation object are resolved by the parser before the patch is applied (the last one
+is kept, see [`object_t`](object_t.md#behavior)), so `#!json {"op": "add", "op": "remove", "path": "/a"}` is a
+`remove` operation.
+
 ## Examples
 
 ??? example "Example: apply a JSON patch"
@@ -108,6 +115,7 @@ is thrown. In any case, the original value is not changed: the patch is applied
 - Added in version 2.0.0.
 - Added [`out_of_range.411`](../../home/exceptions.md#jsonexceptionout_of_range411) and stopped relying on an internal assertion when an "add" operation's
   target location has a non-object/non-array parent in version 3.13.0.
+  This includes a `null` parent, which was previously silently converted to an object, in version 3.13.0.
 - Added [`out_of_range.413`](../../home/exceptions.md#jsonexceptionout_of_range413) and stopped silently ignoring a "remove" operation whose target
   location has a non-object/non-array parent in version 3.13.0.
 - Added [`out_of_range.414`](../../home/exceptions.md#jsonexceptionout_of_range414) and rejected a "move" operation whose "from" location is a proper

docs/mkdocs/docs/api/basic_json/patch_inplace.md

@@ -36,7 +36,7 @@ No guarantees, value may be corrupted by an unsuccessful patch operation.
   where an existing element is required (the "path" of "replace", the "from" of "move" and "copy"); example:
   `"array index '-' (3) is out of range"`.
 - Throws [`out_of_range.403`](../../home/exceptions.md#jsonexceptionout_of_range403) if a JSON pointer inside the patch
-  could not be resolved successfully in the current JSON value; example: `"key baz not found"`.
+  could not be resolved successfully in the current JSON value; example: `"key 'baz' not found"`.
 - Throws [`out_of_range.404`](../../home/exceptions.md#jsonexceptionout_of_range404) if a reference token of a JSON
   pointer inside the patch cannot be resolved, e.g., `-` in a "remove" operation or `1a` for an array; example:
   `"unresolved reference token '-'"`.
@@ -49,7 +49,10 @@ No guarantees, value may be corrupted by an unsuccessful patch operation.
 - Throws [`out_of_range.414`](../../home/exceptions.md#jsonexceptionout_of_range414) if a "move" operation's "from"
   location is a proper prefix of its "path" location.
 - Throws [`other_error.501`](../../home/exceptions.md#jsonexceptionother_error501) if "test" operation was
-  unsuccessful.
+  unsuccessful. A "test" operation whose "path" does not exist is unsuccessful, too: the failed lookup is reported as a
+  failed test, even if the operation has no "value" member (which would otherwise be
+  [`parse_error.105`](../../home/exceptions.md#jsonexceptionparse_error105)). Which of the two errors is reported for
+  this combination depends on the order in which the operands of a comparison are evaluated, so do not rely on it.
 
 ## Complexity
 
@@ -62,6 +65,10 @@ Unlike [`patch`](patch.md), `patch_inplace` applies the operation "in place" and
 That makes it faster for large documents by avoiding the copy. However, the JSON value might be corrupted if the
 function throws an exception.
 
+Duplicate member names inside an operation object are resolved by the parser before the patch is applied (the last one
+is kept, see [`object_t`](object_t.md#behavior)), so `#!json {"op": "add", "op": "remove", "path": "/a"}` is a
+`remove` operation.
+
 ## Examples
 
 ??? example "Example: apply a JSON patch in place"
@@ -106,6 +113,7 @@ function throws an exception.
 - Added in version 3.11.0.
 - Added [`out_of_range.411`](../../home/exceptions.md#jsonexceptionout_of_range411) and stopped relying on an internal assertion when an "add" operation's
   target location has a non-object/non-array parent in version 3.13.0.
+  This includes a `null` parent, which was previously silently converted to an object, in version 3.13.0.
 - Added [`out_of_range.413`](../../home/exceptions.md#jsonexceptionout_of_range413) and stopped silently ignoring a "remove" operation whose target
   location has a non-object/non-array parent in version 3.13.0.
 - Added [`out_of_range.414`](../../home/exceptions.md#jsonexceptionout_of_range414) and rejected a "move" operation whose "from" location is a proper

docs/mkdocs/docs/features/json_patch.md

@@ -13,6 +13,12 @@ to the current JSON value by executing all operations from the patch, yielding t
     If the document is large and the original value is no longer needed,
     [`patch_inplace`](../api/basic_json/patch_inplace.md) applies the same operations in place instead.
 
+!!! note "Duplicate member names"
+
+    Duplicate member names inside an operation object are resolved by the parser before the patch is applied (the last
+    one is kept, see [`object_t`](../api/basic_json/object_t.md#behavior)), so
+    `#!json {"op": "add", "op": "remove", "path": "/a"}` is a `remove` operation.
+
 ??? example "Example: apply a JSON Patch"
 
     The following code shows how a JSON patch is applied to a value.
@@ -41,12 +47,23 @@ flowchart LR
 
 !!! success "Invariant"
 
-    For two JSON values *source* and *target*, the following code yields always true:
+    For two JSON values *source* and *target*, the following code yields true:
 
     ```cpp
     source.patch(diff(source, target)) == target;
     ```
 
+    The equality holds up to [`operator==`](../api/basic_json/operator_eq.md), with these exceptions:
+
+    - `NaN` and [discarded](../api/basic_json/is_discarded.md) values are not equal to themselves, so the invariant
+      cannot hold for them. `diff` emits a `replace` operation for such a value, and a `NaN` in a patch is serialized
+      as `#!json null`.
+    - Numbers that compare equal produce no operation even if their types differ: `diff(1, 1.0)`, `diff(1u, 1)`, and
+      `diff(0.0, -0.0)` return `#!json []`, so the patched value keeps the number type of *source*.
+    - A [binary value](binary_values.md) in a patch is serialized as an object
+      (`#!json {"bytes":[...],"subtype":null}`), so a patch that was dumped and parsed again no longer holds a binary
+      value.
+
 ??? example "Example: create a JSON Patch from the difference of two values"
 
     The following code shows how a JSON patch is created as a diff for two JSON values.

docs/mkdocs/docs/home/exceptions.md

@@ -1100,6 +1100,8 @@ A JSON Patch `add` operation cannot be applied because the target location's par
 
     This exception was added in version 3.13.0. Before that, this situation hit an internal assertion (aborting the program in debug builds) or was silently ignored when assertions were disabled.
 
+    A `null` parent is rejected as well. Before version 3.13.0, an `add` into a `null` parent silently converted it to an object (e.g., `add` at `/foo/bar` turned `{"foo":null}` into `{"foo":{"bar":1}}`).
+
 ### json.exception.out_of_range.412
 
 BSON stores the length of documents, arrays, strings, and binary values in a signed 32-bit integer, and MessagePack

include/nlohmann/json.hpp

@@ -7003,7 +7003,6 @@ public:
 
             switch (parent.m_data.m_type)
             {
-                case value_t::null:
                 case value_t::object:
                 {
                     // use operator[] to add value
@@ -7035,6 +7034,7 @@ public:
 
                 // the parent of an "add" target must be an object or array
                 // (see #4292)
+                case value_t::null:
                 case value_t::string:
                 case value_t::boolean:
                 case value_t::number_integer:

single_include/nlohmann/json.hpp

@@ -42793,7 +42793,6 @@ public:
 
             switch (parent.m_data.m_type)
             {
-                case value_t::null:
                 case value_t::object:
                 {
                     // use operator[] to add value
@@ -42825,6 +42824,7 @@ public:
 
                 // the parent of an "add" target must be an object or array
                 // (see #4292)
+                case value_t::null:
                 case value_t::string:
                 case value_t::boolean:
                 case value_t::number_integer:

tests/src/unit-json_patch.cpp

@@ -15,6 +15,7 @@ using nlohmann::json;
 #endif
 
 #include <fstream>
+#include <limits>
 #include <string>
 #include <vector>
 #include "make_test_data_available.hpp"
@@ -490,7 +491,9 @@ TEST_CASE("JSON patch")
         }
 
         // A.13. Invalid JSON Patch Document
-        // not applicable
+        // not applicable: the library cannot tell the duplicate "op" members
+        // apart, because the parser resolves them (the last one is kept); see
+        // "duplicate member names in an operation" below
 
         SECTION("A.14. Escape Ordering")
         {
@@ -1515,6 +1518,24 @@ TEST_CASE("JSON patch - add to a primitive parent (regression #4292)")
 #endif
     }
 
+    SECTION("null parent")
+    {
+        json const doc = {{"foo", nullptr}};
+        json const patch = {{{"op", "add"}, {"path", "/foo/bar"}, {"value", 1}}};
+#if JSON_DIAGNOSTICS
+        CHECK_THROWS_WITH_AS(doc.patch(patch), "[json.exception.out_of_range.411] (/foo) cannot add value: the JSON Patch 'add' target's parent is of type null, but must be an object or array", json::out_of_range&);
+#else
+        CHECK_THROWS_WITH_AS(doc.patch(patch), "[json.exception.out_of_range.411] cannot add value: the JSON Patch 'add' target's parent is of type null, but must be an object or array", json::out_of_range&);
+#endif
+    }
+
+    SECTION("null document")
+    {
+        json const doc = nullptr;
+        json const patch = {{{"op", "add"}, {"path", "/-"}, {"value", 1}}};
+        CHECK_THROWS_WITH_AS(doc.patch(patch), "[json.exception.out_of_range.411] cannot add value: the JSON Patch 'add' target's parent is of type null, but must be an object or array", json::out_of_range&);
+    }
+
     SECTION("number parent")
     {
         json const doc = {{"foo", 1}};
@@ -2103,3 +2124,204 @@ TEST_CASE_TEMPLATE("JSON patch - diff round trip on hand-made documents", Json,
         roundtrip(Json(1), Json::parse("[1]"));
     }
 }
+
+TEST_CASE("JSON patch - behavior documented in the API reference")
+{
+    SECTION("duplicate member names in an operation")
+    {
+        // RFC 6902, A.13: the parser resolves the duplicates (the last one
+        // is kept), so this is a "remove" and not an "add"
+        const json patch = json::parse(R"([{"op": "add", "op": "remove", "path": "/a"}])");
+        CHECK(patch == json::parse(R"([{"op": "remove", "path": "/a"}])"));
+        CHECK(json({{"a", 1}, {"b", 2}}).patch(patch) == json({{"b", 2}}));
+    }
+
+    SECTION("add with a leading zero in an array index")
+    {
+        const json patch = R"([{"op": "add", "path": "/01", "value": 1}])"_json;
+        json doc = json::array();
+#if !defined(JSON_NOEXCEPTION)
+        CHECK_THROWS_AS(doc.patch(patch), json::parse_error&);
+        CHECK_THROWS_AS(doc.patch_inplace(patch), json::parse_error&);
+#endif
+        CHECK(doc == json::array());
+    }
+
+    SECTION("test compares numbers by value")
+    {
+        const json doc = R"({"a": 1, "b": 0, "c": 1.5})"_json;
+        CHECK(doc.patch(R"([{"op": "test", "path": "/a", "value": 1.0}])"_json) == doc);
+        CHECK(doc.patch(R"([{"op": "test", "path": "/b", "value": -0.0}])"_json) == doc);
+        CHECK(doc.patch(R"([{"op": "test", "path": "/c", "value": 1.5}])"_json) == doc);
+        CHECK_THROWS_AS(doc.patch(R"([{"op": "test", "path": "/a", "value": 2}])"_json), json::other_error&);
+        CHECK_THROWS_AS(doc.patch(R"([{"op": "test", "path": "/a", "value": "1"}])"_json), json::other_error&);
+    }
+
+    SECTION("test ignores the order of object members, but not the order of array elements")
+    {
+        const json doc = R"({"o": {"x": 1, "y": 2}, "a": [1, 2]})"_json;
+        CHECK(doc.patch(R"([{"op": "test", "path": "/o", "value": {"y": 2, "x": 1}}])"_json) == doc);
+        CHECK(doc.patch(R"([{"op": "test", "path": "/a", "value": [1, 2]}])"_json) == doc);
+        CHECK_THROWS_AS(doc.patch(R"([{"op": "test", "path": "/a", "value": [2, 1]}])"_json), json::other_error&);
+    }
+
+    SECTION("test on a path that does not exist")
+    {
+        const json doc = R"({"a": 1})"_json;
+        // with a "value" member, the failed lookup is a failed test
+        CHECK_THROWS_AS(doc.patch(R"([{"op": "test", "path": "/b", "value": 1}])"_json), json::other_error&);
+        CHECK_THROWS_AS(doc.patch(R"([{"op": "test", "path": "/b", "value": null}])"_json), json::other_error&);
+        // without it, an exception is thrown, too; which one depends on the
+        // order of evaluation of the operands of ==, so it is not checked
+        CHECK_THROWS(doc.patch(R"([{"op": "test", "path": "/b"}])"_json));
+    }
+
+    SECTION("patch() has the strong guarantee")
+    {
+        const json doc = R"({"a": [1, 2], "o": {"k": "v"}})"_json;
+        const json before = doc;
+
+        const std::vector<json> failing =
+        {
+            // remove of a member that does not exist
+            R"([{"op": "add", "path": "/n", "value": 1}, {"op": "remove", "path": "/missing"}])"_json,
+            // replace of a member that does not exist
+            R"([{"op": "remove", "path": "/a/0"}, {"op": "replace", "path": "/missing", "value": 1}])"_json,
+            // move from a member that does not exist
+            R"([{"op": "add", "path": "/n", "value": 1}, {"op": "move", "from": "/missing", "path": "/m"}])"_json,
+            // copy from a member that does not exist
+            R"([{"op": "add", "path": "/n", "value": 1}, {"op": "copy", "from": "/missing", "path": "/m"}])"_json,
+            // out-of-range array index
+            R"([{"op": "add", "path": "/n", "value": 1}, {"op": "add", "path": "/a/5", "value": 1}])"_json,
+            // failing test after a successful operation
+            R"([{"op": "remove", "path": "/o"}, {"op": "test", "path": "/a", "value": []}])"_json,
+        };
+        for (const auto& patch : failing)
+        {
+            CAPTURE(patch.dump())
+            CHECK_THROWS_AS(doc.patch(patch), json::exception&);
+            CHECK(doc == before);
+
+            json copy = doc;
+            CHECK_THROWS_AS(copy.patch(patch), json::exception&);
+            CHECK(copy == before);
+        }
+    }
+}
+
+TEST_CASE("JSON patch - diff behavior documented in the API reference")
+{
+    SECTION("path is a verbatim prefix")
+    {
+        // not escaped and not validated
+        CHECK(json::diff(1, 2) == R"([{"op": "replace", "path": "", "value": 2}])"_json);
+        CHECK(json::diff(1, 2, "abc") == R"([{"op": "replace", "path": "abc", "value": 2}])"_json);
+        CHECK(json::diff(1, 2, "/root") == R"([{"op": "replace", "path": "/root", "value": 2}])"_json);
+        // an escaped token in a non-root prefix is kept as given
+        CHECK(json::diff(R"({"a": 1})"_json, R"({"a": 2})"_json, "/x~1y/~0")
+              == R"([{"op": "replace", "path": "/x~1y/~0/a", "value": 2}])"_json);
+        CHECK(json::diff(R"({"a": 1})"_json, R"({"a": 2})"_json, "/p")
+              == R"([{"op": "replace", "path": "/p/a", "value": 2}])"_json);
+    }
+
+    SECTION("keys are escaped in the paths")
+    {
+        const json source = json::object();
+        const json target =
+        {
+            {"", 0}, {"/", 1}, {"~", 2}, {"~1", 3}, {"~01", 4}
+        };
+        const json patch = json::diff(source, target);
+        REQUIRE(patch.size() == 5);
+
+        // the order of the operations is not checked
+        json paths = json::object();
+        for (const auto& op : patch)
+        {
+            CHECK(op["op"] == "add");
+            paths[op["path"].get<std::string>()] = op["value"];
+        }
+        CHECK(paths == json({{"/", 0}, {"/~1", 1}, {"/~0", 2}, {"/~01", 3}, {"/~001", 4}}));
+        CHECK(source.patch(patch) == target);
+    }
+
+    SECTION("NaN is not equal to itself")
+    {
+        const json nan = std::numeric_limits<json::number_float_t>::quiet_NaN();
+        const json patch = json::diff(nan, nan);
+        CHECK(patch.size() == 1);
+        CHECK(patch[0]["op"] == "replace");
+        CHECK(patch[0]["path"] == "");
+        CHECK(patch[0]["value"].is_number_float());
+        CHECK(nan.patch(patch) != nan);
+
+        // a NaN in a patch is serialized as null
+        CHECK(json::parse(patch.dump())[0]["value"].is_null());
+
+        const json nested = {{"a", {1, nan}}};
+        const json nested_patch = json::diff(nested, nested);
+        CHECK(nested_patch.size() == 1);
+        CHECK(nested_patch[0]["path"] == "/a/1");
+
+        // infinity is equal to itself
+        const json inf = std::numeric_limits<json::number_float_t>::infinity();
+        CHECK(json::diff(inf, inf).empty());
+    }
+
+    SECTION("discarded values are not equal to themselves")
+    {
+        const json discarded(json::value_t::discarded);
+        const json patch = json::diff(discarded, discarded);
+        CHECK(patch.size() == 1);
+        CHECK(patch[0]["op"] == "replace");
+        CHECK(patch[0]["path"] == "");
+        CHECK(patch[0]["value"].is_discarded());
+        CHECK(discarded.patch(patch) != discarded);
+    }
+
+    SECTION("numbers that compare equal produce no operation")
+    {
+        CHECK(json::diff(json(1), json(1.0)).empty());
+        CHECK(json::diff(json(1.0), json(1)).empty());
+        CHECK(json::diff(json(1U), json(1)).empty());
+        CHECK(json::diff(json(1), json(1U)).empty());
+        CHECK(json::diff(json(0.0), json(-0.0)).empty());
+
+        // the patched value keeps the number type of the source
+        const json source = 1;
+        const json patched = source.patch(json::diff(source, json(1.0)));
+        CHECK(patched.is_number_integer());
+        CHECK(patched == json(1.0));
+
+        // different values are replaced
+        CHECK(json::diff(json(1), json(2.0)) == R"([{"op": "replace", "path": "", "value": 2.0}])"_json);
+        CHECK(json::diff(json(1), json(-1)) == R"([{"op": "replace", "path": "", "value": -1}])"_json);
+        CHECK(json::diff(json(1.0), json(1.5)) == R"([{"op": "replace", "path": "", "value": 1.5}])"_json);
+        CHECK(json::diff(json(1), json("1")) == R"([{"op": "replace", "path": "", "value": "1"}])"_json);
+    }
+
+    SECTION("binary values")
+    {
+        const json a = json::binary({1, 2});
+        const json b = json::binary({1, 3});
+        CHECK(json::diff(a, a).empty());
+
+        const json patch = json::diff(a, b);
+        CHECK(patch.size() == 1);
+        CHECK(patch[0]["op"] == "replace");
+        CHECK(patch[0]["path"] == "");
+        CHECK(patch[0]["value"].is_binary());
+        CHECK(a.patch(patch) == b);
+
+        // serialized, the binary value is an object
+        const json parsed = json::parse(patch.dump());
+        CHECK(parsed[0]["value"].is_object());
+        CHECK(parsed[0]["value"] == R"({"bytes": [1, 3], "subtype": null})"_json);
+    }
+
+    SECTION("a difference as a whole is a replace of the root")
+    {
+        CHECK(json::diff(json::array({1}), json::object()) == R"([{"op": "replace", "path": "", "value": {}}])"_json);
+        CHECK(json::diff(json(nullptr), json::array()) == R"([{"op": "replace", "path": "", "value": []}])"_json);
+    }
+}