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/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"