docs: make the diff() and patch() documentation accurate; add tests (#5939)

* Throw out_of_range.411 for JSON Patch add into a null parent (#5917)

Co-Authored-By: Claude Sonnet 5.5 <noreply@anthropic.com>
Claude-Session: https://claude.ai/code/session_01MKJf48vnGtTE25KscmjfaW
Signed-off-by: Niels Lohmann <niels.lohmann@gmail.com>

* 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>

---------

Signed-off-by: Niels Lohmann <niels.lohmann@gmail.com>
Signed-off-by: Niels Lohmann <mail@nlohmann.me>
Co-authored-by: Claude Sonnet 5.5 <noreply@anthropic.com>

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