Report an empty array for UBJSON [$N#<n>] instead of n elements (#6079)

* Report an empty array for UBJSON `[$N#<n>` instead of n elements

A no-op (N) is not a value, so an optimized array of type N holds no
element whatever count it declares. The reader skipped the elements but
still passed the declared count to the SAX parser: a handler was told
start_array(n) and no element followed, and the DOM parser reserved
min(n, 16384) values (256 KB) for an array that stays empty. Nine bytes
(`[$N#l 0x7FFFFFFF`) therefore committed 256 KB: 2000 of them in one
input, 18 KB, committed 512 MB of heap (capacity 163,840,000 values for
the 10000 arrays of the original probe: 2.6 GB for 70 KB of input).
Untouched pages keep the resident size small, but the commit charge and
a 32-bit address space are consumed.

The reader now announces 0 elements for an optimized array of type N.
The loop that skips the elements is unchanged (it never ran). A count
that does not fit into std::size_t is still rejected by the count
reader; a count that is too large for the array type of the DOM (before:
out_of_range.408 "excessive array size" from the DOM handler) is
accepted now, because the array is empty.

Behaviour change: sax_parse reports start_array(0) for `[$N#n` (before:
n); from_ubjson no longer throws out_of_range.408 for an N-typed array
whose count exceeds the maximum size of the array type.

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

* Clarify the reservation note for announced array counts

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

---------

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

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

docs/mkdocs/docs/api/basic_json/from_ubjson.md

@@ -89,8 +89,10 @@ Strong guarantee: if an exception is thrown, there are no changes in the JSON va
 - Throws [out_of_range.406](../../home/exceptions.md#jsonexceptionout_of_range406) if a high-precision number, or a
   float64 when `number_float_t` is `float`, does not fit into `number_float_t`
 - Throws [out_of_range.408](../../home/exceptions.md#jsonexceptionout_of_range408) if the count of an optimized
-  container exceeds the capacity of the container (or of `std::size_t`), or if an optimized array of `Z`, `T`, or `F` has
+  container exceeds the capacity of the container (or of `std::size_t`; an array of type `N` is empty, so only the
-  more than 1,048,576 elements
+  latter applies to it), if an optimized array of `Z`, `T`, or `F` has more than 1,048,576 elements, or if the
+  optimized arrays of `Z`, `T`, and `F` in the input together have more than 1,048,576 elements plus 4 for every byte
+  read so far
 
 ## Complexity
 
@@ -132,6 +134,9 @@ Linear in the size of the input.
 - Extended container support (1) to include types with lvalue-only ADL `begin`/`end` (matching `std::begin`/`std::end` semantics) in version 3.13.0.
 - Extended overload (2) to accept heterogeneous iterator+sentinel pairs (C++20 ranges support) in version 3.13.0.
 - Added `error_handler` parameter in version 3.13.0.
+- Report `start_array(0)` to a SAX handler for an optimized array of type `N` (`[$N#n`), whatever its count, in version
+  3.13.0.
+- Limited the total number of elements of optimized arrays of `Z`, `T`, and `F` in one input in version 3.13.0.
 
 !!! warning "Deprecation"
 

docs/mkdocs/docs/api/basic_json/operator_ge.md

@@ -60,14 +60,6 @@ Linear.
       2. Comparing a `NaN` with another `NaN`.
       3. Comparing a `NaN` and any other number.
 
-    For arrays and objects, the elements are compared in order. If the comparison reaches a `NaN` and a number (or
-    another `NaN`) before any other difference, the result depends on the language standard. Before C++20, the pair
-    counts as equivalent and the following elements (or the sizes) decide: for instance, `[NaN] < [1, NaN]` and
-    `[1] <= [NaN]` are `#!cpp true`. Since C++20, the whole comparison is unordered, and `<`, `<=`, `>`, and `>=` all
-    yield `#!cpp false`. Otherwise (for example `[1, NaN] < [2, NaN]`, or objects whose keys differ), the result is the
-    same for all language standards. The same program can therefore order such values differently when it is compiled
-    with a different language standard.
-
 !!! note "Operator overload resolution"
 
     Since C++20 overload resolution will consider the _rewritten candidate_ generated from

docs/mkdocs/docs/api/basic_json/operator_gt.md

@@ -60,14 +60,6 @@ Linear.
       2. Comparing a `NaN` with another `NaN`.
       3. Comparing a `NaN` and any other number.
 
-    For arrays and objects, the elements are compared in order. If the comparison reaches a `NaN` and a number (or
-    another `NaN`) before any other difference, the result depends on the language standard. Before C++20, the pair
-    counts as equivalent and the following elements (or the sizes) decide: for instance, `[NaN] < [1, NaN]` and
-    `[1] <= [NaN]` are `#!cpp true`. Since C++20, the whole comparison is unordered, and `<`, `<=`, `>`, and `>=` all
-    yield `#!cpp false`. Otherwise (for example `[1, NaN] < [2, NaN]`, or objects whose keys differ), the result is the
-    same for all language standards. The same program can therefore order such values differently when it is compiled
-    with a different language standard.
-
 !!! note "Operator overload resolution"
 
     Since C++20 overload resolution will consider the _rewritten candidate_ generated from

docs/mkdocs/docs/api/basic_json/operator_le.md

@@ -61,14 +61,6 @@ Linear.
       2. Comparing a `NaN` with another `NaN`.
       3. Comparing a `NaN` and any other number.
 
-    For arrays and objects, the elements are compared in order. If the comparison reaches a `NaN` and a number (or
-    another `NaN`) before any other difference, the result depends on the language standard. Before C++20, the pair
-    counts as equivalent and the following elements (or the sizes) decide: for instance, `[NaN] < [1, NaN]` and
-    `[1] <= [NaN]` are `#!cpp true`. Since C++20, the whole comparison is unordered, and `<`, `<=`, `>`, and `>=` all
-    yield `#!cpp false`. Otherwise (for example `[1, NaN] < [2, NaN]`, or objects whose keys differ), the result is the
-    same for all language standards. The same program can therefore order such values differently when it is compiled
-    with a different language standard.
-
 !!! note "Operator overload resolution"
 
     Since C++20 overload resolution will consider the _rewritten candidate_ generated from

docs/mkdocs/docs/api/basic_json/operator_lt.md

@@ -71,14 +71,6 @@ Linear.
       2. Comparing a `NaN` with another `NaN`.
       3. Comparing a `NaN` and any other number.
 
-    For arrays and objects, the elements are compared in order. If the comparison reaches a `NaN` and a number (or
-    another `NaN`) before any other difference, the result depends on the language standard. Before C++20, the pair
-    counts as equivalent and the following elements (or the sizes) decide: for instance, `[NaN] < [1, NaN]` and
-    `[1] <= [NaN]` are `#!cpp true`. Since C++20, the whole comparison is unordered, and `<`, `<=`, `>`, and `>=` all
-    yield `#!cpp false`. Otherwise (for example `[1, NaN] < [2, NaN]`, or objects whose keys differ), the result is the
-    same for all language standards. The same program can therefore order such values differently when it is compiled
-    with a different language standard.
-
 !!! note "Operator overload resolution"
 
     Since C++20 overload resolution will consider the _rewritten candidate_ generated from

docs/mkdocs/docs/api/basic_json/operator_spaceship.md

@@ -55,10 +55,6 @@ Linear.
         1. Comparing a `NaN` with itself.
         2. Comparing a `NaN` with another `NaN`.
         3. Comparing a `NaN` and any other number.
-    - For arrays and objects, the elements are compared in order. If the comparison reaches a `NaN` and a number (or
-      another `NaN`) before any other difference, the result is `std::partial_ordering::unordered`. (Without C++20, the
-      comparison operators `<`, `<=`, `>`, and `>=` use the comparison of the containers, which treats such a pair as
-      equivalent; see [**operator<**](operator_lt.md).)
 
 ## Examples
 

docs/mkdocs/docs/api/basic_json/parse.md

@@ -130,13 +130,11 @@ outside of a string, invalid) byte; see the [FAQ entry](../../home/faq.md#nul-by
 
     Contiguous inputs (strings, string views, vectors, arrays, pointer ranges) are the fastest to parse. A
     `#!cpp std::istream` comes close: the parser scans the characters its stream buffer holds in bulk, without reading
-    ahead, so the stream is left exactly where it would be after reading one character at a time. With glibc
+    ahead, so the stream is left exactly where it would be after reading one character at a time. A `#!cpp FILE*` is
-    and the Apple C library, the characters the `#!cpp FILE` holds in its buffer are scanned in bulk like a stream's;
+    read one character at a time, but the file is locked only once, so other threads that use the same `FILE` object
-    elsewhere a `#!cpp FILE*` is read one character at a time. Where the C library has unlocked stdio functions, the
+    wait until parsing is done. See [input sources and performance](../../features/parsing/index.md#input-sources-and-performance),
-    file is locked only once, so other threads that use the same `FILE` object wait until parsing is done, unless
+    [`JSON_DISABLE_STREAM_BULK_SCAN`](../macros/json_disable_stream_bulk_scan.md), and
-    [`JSON_DISABLE_UNLOCKED_FILE_IO`](../macros/json_disable_unlocked_file_io.md) is defined to `1`. See
+    [`JSON_DISABLE_UNLOCKED_FILE_IO`](../macros/json_disable_unlocked_file_io.md).
-    [input sources and performance](../../features/parsing/index.md#input-sources-and-performance) and
-    [`JSON_DISABLE_STREAM_BULK_SCAN`](../macros/json_disable_stream_bulk_scan.md).
 
 ## Examples
 

docs/mkdocs/docs/api/basic_json/sax_parse.md

@@ -124,10 +124,9 @@ consumer `sax` has a super-linear complexity.
 
 A UTF-8 byte order mark is silently ignored.
 
-When reading from a `#!c FILE*` where the C library has unlocked stdio functions, the file is locked while it is parsed,
+When reading from a `#!c FILE*`, the file is locked while it is parsed. The lock is recursive, so the SAX handler may
-unless [`JSON_DISABLE_UNLOCKED_FILE_IO`](../macros/json_disable_unlocked_file_io.md) is defined to `1`.
+use the same file with stdio functions, but it must not wait for another thread that uses the same `FILE` object; see
-The lock is recursive, so the SAX handler may use the same file with stdio functions, but it must not wait for another
+[`JSON_DISABLE_UNLOCKED_FILE_IO`](../macros/json_disable_unlocked_file_io.md).
-thread that uses the same `FILE` object.
 
 ## Examples
 

docs/mkdocs/docs/api/basic_json/to_ubjson.md

@@ -117,5 +117,8 @@ Linear in the size of the JSON value `j`.
 - Added `error_handler` parameter in version 3.13.0. Its default, `keep`, writes the bytes of a string or object key
   that is not valid UTF-8 unchanged, as before; `strict` (the default if
   [`JSON_STRICT_BINARY_UTF8`](../macros/json_strict_binary_utf8.md) is enabled) throws `type_error.316`.
+- Writes arrays of `Z`, `T`, or `F` without the `$` type annotation (`[#n Z Z ...`) once their elements in one call
+  add up to more than 1,048,576, in version 3.13.0, so that `from_ubjson` can read the output back. Such output is
+  larger: 270,000 rows of 100 `null` values take 26.8 MB instead of 1.35 MB.
 - Throws `type_error.321` for a discarded value since version 3.13.0; previously, a discarded value nested in an
   array or object was silently skipped, producing invalid UBJSON.

docs/mkdocs/docs/features/binary_formats/bjdata.md

@@ -88,6 +88,7 @@ The library uses the following mapping from JSON values types to BJData types ac
 | number_integer  | 65536..2147483647                         | int32       | `l`                                                                     |
 | number_integer  | 2147483648..4294967295                    | uint32      | `m`                                                                     |
 | number_integer  | 4294967296..9223372036854775807           | int64       | `L`                                                                     |
+| number_integer  | 9223372036854775808..18446744073709551615 | uint64      | `M`                                                                     |
 | number_unsigned | 0..127                                    | int8        | `i`                                                                     |
 | number_unsigned | 128..255                                  | uint8       | `U`                                                                     |
 | number_unsigned | 256..32767                                | int16       | `I`                                                                     |

docs/mkdocs/docs/features/binary_formats/messagepack.md

@@ -61,7 +61,7 @@ specification:
 | number_integer  | 128..255                                 | uint 8           | 0xCC       |
 | number_integer  | 256..65535                               | uint 16          | 0xCD       |
 | number_integer  | 65536..4294967295                        | uint 32          | 0xCE       |
-| number_integer  | 4294967296..9223372036854775807          | uint 64          | 0xCF       |
+| number_integer  | 4294967296..18446744073709551615         | uint 64          | 0xCF       |
 | number_unsigned | 0..127                                   | positive fixint  | 0x00..0x7F |
 | number_unsigned | 128..255                                 | uint 8           | 0xCC       |
 | number_unsigned | 256..65535                               | uint 16          | 0xCD       |

docs/mkdocs/docs/features/binary_formats/ubjson.md

@@ -122,9 +122,18 @@ The library uses the following mapping from JSON values types to UBJSON types ac
     already is the value. Its declared count is therefore the only thing that decides how much memory the receiving side
     allocates, and a handful of bytes can describe billions of elements. `from_ubjson` rejects such an array with
     [`out_of_range.408`](../../home/exceptions.md#jsonexceptionout_of_range408) when the count exceeds 1,048,576
-    (`1 << 20`), and `to_ubjson` writes longer arrays of these types in the counted but untyped form: the `$` type marker is
+    (`1 << 20`), or when the counts of all such arrays in the input add up to more than 1,048,576 plus 4 for every byte
-    dropped, the `#` count is kept, and every element is written with its own marker (`[#l 1048577 Z Z ...`), so any value
+    read so far. `to_ubjson` therefore writes an array of these types in the counted but untyped form when it is longer
-    it produces can be read back. Objects and untyped counted arrays are not subject to this limit.
+    than that, or when it would bring the total of the typed arrays written so far above 1,048,576: the `$` type marker
+    is dropped, the `#` count is kept, and every element is written with its own marker (`[#l 1048577 Z Z ...`), so
+    everything it produces can be read back. Only input from another encoder, or written by version 3.12.0 and earlier of
+    this library, can exceed the limit: for example, 1,100 rows of 1,000 `null` values or 210,000 rows of 25, each with
+    a `$Z` annotation. Version 3.12.0 writes such a row in 5 bytes (6 above 255 elements), so rows of 20 or fewer such
+    values are never rejected. Objects and untyped counted arrays are not subject to this limit.
+
+    An optimized array of type `N` (no-op) is empty whatever its count is, because a no-op is not a value. Its count is
+    not passed on: `sax_parse` reports `start_array(0)` (versions before 3.13.0 reported the declared count), and the DOM
+    parser reserves nothing for it.
 
 !!! info "Binary values"
 
@@ -180,10 +189,11 @@ The library maps UBJSON types to JSON value types as follows:
 
     Every well-formed UBJSON value can be converted to a JSON value, with these exceptions: a high-precision number
     outside the range of `number_float_t` ([`out_of_range.406`](../../home/exceptions.md#jsonexceptionout_of_range406)),
-    an optimized array of `Z`, `T`, or `F` with more than 1,048,576 elements, and a count that exceeds the capacity of the
+    optimized arrays of `Z`, `T`, or `F` with more elements than the limit allows (1,048,576 plus 4 per byte read),
-    container ([`out_of_range.408`](../../home/exceptions.md#jsonexceptionout_of_range408)). High-precision numbers that
+    and a count that exceeds the capacity of the container
-    do not fit an integer type are stored as floating-point numbers and may lose precision. Ill-formed input is rejected
+    ([`out_of_range.408`](../../home/exceptions.md#jsonexceptionout_of_range408)). High-precision numbers that do not
-    with a parse error.
+    fit an integer type are stored as floating-point numbers and may lose precision. Ill-formed input is rejected with a
+    parse error.
 
 !!! info "Duplicate object keys"
 

docs/mkdocs/docs/features/parsing/index.md

@@ -77,15 +77,9 @@ them faster than others:
 |--------------------------------------------------------------------------------------------|------------------------------------------------------------------------------------|
 | strings, string views, string literals, contiguous containers, pointer or iterator ranges over contiguous memory | the whole input is scanned in bulk: runs of string characters, numbers, and indentation are recognized several bytes at a time |
 | `#!cpp std::istream` (`#!cpp std::ifstream`, `#!cpp std::istringstream`, ...)            | the characters the stream buffer holds are scanned in bulk like a string; the stream buffer is asked for more when they are used up |
-| `#!cpp FILE*`                                                                              | with glibc and the Apple C library, the characters the `FILE` holds in its buffer are scanned in bulk like a stream's; elsewhere one character at a time; where the C library has unlocked stdio functions, the file is locked once for the whole parse |
+| `#!cpp FILE*`                                                                              | with glibc and the Apple C library, the characters the `FILE` holds in its buffer are scanned in bulk like a stream's; elsewhere one character at a time; the file is locked once for the whole parse |
 | other iterator ranges (e.g., `#!cpp std::list<char>`, `#!cpp std::istreambuf_iterator<char>`), wide strings | one character at a time                                                             |
 
-Defining [`JSON_DISABLE_STREAM_BULK_SCAN`](../../api/macros/json_disable_stream_bulk_scan.md) to `1` turns off the bulk
-scan of a stream buffer, so a `#!cpp std::istream` is read one character at a time. Defining
-[`JSON_DISABLE_UNLOCKED_FILE_IO`](../../api/macros/json_disable_unlocked_file_io.md) to `1` makes a `#!cpp FILE*` read
-every character with `std::fgetc`, without locking the file for the whole parse and without the bulk scan of its buffer
-(which `JSON_DISABLE_STREAM_BULK_SCAN` does not affect). Neither changes any result.
-
 Input in one block of memory is read even faster with the default options (no
 [parser callback](../../api/basic_json/parser_callback_t.md), no comments, no trailing commas, and for `sax_parse()`
 `strict = true`): `parse()`, `accept()`, and `sax_parse()` then read the grammar and the tokens in one loop over the

docs/mkdocs/docs/features/parsing/untrusted_input.md

@@ -72,10 +72,22 @@ For the binary formats, an announced size is never trusted outright:
   (reported as a parse error) instead of triggering an oversized allocation.
 - When an array announces its number of elements and the array container supports `reserve()` (as `#!cpp std::vector`,
   the default, does), the library reserves storage for at most 16384 of them upfront, regardless of how large the
-  announced count is; further elements still grow the container normally as they are read.
+  announced count is; further elements still grow the container normally as they are read. A truncated input whose
+  count is larger than its remaining bytes therefore reserves at most that much before the parse error is reported.
+  Every array element takes at least one byte of input, except in the [UBJSON](../binary_formats/ubjson.md) arrays of
+  type `Z`, `T` or `F` described below.
 - An announced array or object size that exceeds what the target container could ever hold (its `max_size()`) is
   rejected immediately as [`out_of_range.408`](../../home/exceptions.md#jsonexceptionout_of_range408), without
   attempting to allocate anything.
+- A UBJSON array of the no-op type (`[$N#<n>`) is empty whatever count it declares: a SAX handler is told
+  `start_array(0)` and the DOM parser reserves nothing.
+- A UBJSON array of type `Z`, `T` or `F` has no payload, so its announced count is not bounded by the input. One array
+  may announce at most 1,048,576 elements, and all such arrays of one input together may contain at most 1,048,576
+  elements plus 4 for every byte read so far (checked when each array's header has been read); beyond that the input is
+  rejected as [`out_of_range.408`](../../home/exceptions.md#jsonexceptionout_of_range408). For a DOM that bounds the memory these
+  arrays can need to about 80 bytes per byte of input plus about 33 MB for the first 1,048,576 elements; a SAX handler
+  receives at most that many events. Every other optimized array element, and every UBJSON object member (it has a
+  key), takes at least one byte of input.
 
 ## Strings
 

docs/mkdocs/docs/features/performance.md

@@ -27,13 +27,9 @@ A `#!cpp std::istream` (including `#!cpp std::ifstream`) gets the same bulk scan
 characters its stream buffer already holds (the *get area*) and asks the stream buffer for more only when they are used
 up. Nothing is read ahead, so the stream is left exactly where it would be after reading one character at a time, and
 [`operator>>`](../api/operator_gtgt.md) can still read several values from one stream. A stream buffer without a get
-area is read one character at a time. Where the C library has unlocked stdio functions, a `#!cpp FILE*` is locked once
+area is read one character at a time. A `#!cpp FILE*` is locked once per parse instead of once per character, and with
-per parse instead of once per character, and with glibc and the Apple C library, the characters in its buffer are
+glibc and the Apple C library, the characters in its buffer are scanned in bulk as a stream's get area is. See
-scanned in bulk as a stream's get area is.
+[input sources and performance](parsing/index.md#input-sources-and-performance) for the full table. Parsing from a
-[`JSON_DISABLE_STREAM_BULK_SCAN`](../api/macros/json_disable_stream_bulk_scan.md) turns off the bulk scan of streams, and
-[`JSON_DISABLE_UNLOCKED_FILE_IO`](../api/macros/json_disable_unlocked_file_io.md) both the single lock and the bulk scan
-of a `#!cpp FILE*`. See [input sources and performance](parsing/index.md#input-sources-and-performance) for the full
-table. Parsing from a
 stream takes about 1.15 to 1.45 times as long as parsing an equivalent `#!cpp std::string`, which `parse()` reads with
 a parser of its own (see there).
 

docs/mkdocs/docs/home/exceptions.md

@@ -1050,11 +1050,17 @@ The size of an array or object in a [binary format](../features/binary_formats/i
 the size following `#` for [UBJSON](../features/binary_formats/ubjson.md)/[BJData](../features/binary_formats/bjdata.md),
 or the encoded length for [CBOR](../features/binary_formats/cbor.md).
 
-The exception is also thrown for a [UBJSON](../features/binary_formats/ubjson.md) array of a type that is encoded by its
+The exception is also thrown for [UBJSON](../features/binary_formats/ubjson.md) arrays of a type that is encoded by
-marker alone (`Z`, `T` or `F`) whose declared count exceeds 1,048,576 (`1 << 20`). Such an array has no payload, so its
+its marker alone (`Z`, `T` or `F`). Such an array has no payload, so its count alone decides how much memory is
-count alone decides how much memory is allocated, and a handful of bytes would otherwise describe billions of values.
+allocated, and a handful of bytes would otherwise describe billions of values. It is thrown if the declared count of one
-[`to_ubjson`](../api/basic_json/to_ubjson.md) writes longer arrays of these types without the `$` type annotation (the `#`
+array exceeds 1,048,576 (`1 << 20`), and if the counts of all such arrays read so far in one input add up to more than
-count and one marker per element are kept), so any value it produces can still be read back.
+1,048,576 plus 4 for every byte of the input read when the header of the last array has been read.
+[`to_ubjson`](../api/basic_json/to_ubjson.md) writes an array of these types without the `$` type annotation (the `#`
+count and one marker per element are kept) when it is longer, or when it would bring the total of the typed arrays
+written so far above 1,048,576, so everything it produces can be read back. Only input written by another encoder, or
+by version 3.12.0 and earlier of this library, can exceed the limit: for example, 1,100 rows of 1,000 `null` values or
+210,000 rows of 25, each with a `$Z` annotation. Version 3.12.0 writes such a row in 5 bytes (6 above 255 elements),
+so rows of 20 or fewer such values are never rejected.
 
 !!! failure "Example messages"
 
@@ -1070,6 +1076,9 @@ count and one marker per element are kept), so any value it produces can still b
     ```
     [json.exception.out_of_range.408] syntax error while parsing UBJSON size: excessive array size
     ```
+    ```
+    [json.exception.out_of_range.408] syntax error while parsing UBJSON size: excessive number of elements without payload
+    ```
 
 ### json.exception.out_of_range.409
 

include/nlohmann/detail/input/binary_reader.hpp

@@ -73,13 +73,46 @@ the input.
 
 This is a sanity bound rather than a security boundary, and it is far above
 any container met in practice. @ref binary_writer falls back to the
-unoptimized encoding for longer containers, so that a value serialized by
+unoptimized encoding for longer containers, and for containers that together
-this library can always be read back.
+with the ones before them would exceed @ref valueless_elements_base, so that a
+value serialized by this library can always be read back.
 
 @sa https://github.com/nlohmann/json/issues/2793
 */
 JSON_INLINE_VARIABLE constexpr std::size_t max_valueless_container_size = 1 << 20;
 
+/*!
+@brief number of elements of valueless UBJSON containers accepted on top of
+       @ref valueless_elements_per_byte
+
+The limit @ref max_valueless_container_size applies to each container on its
+own, so on its own it lets 9 bytes announce 1048576 values, and every further
+9 bytes another 1048576. The elements of all containers of a valueless type
+in one input are therefore added up, and the sum must stay below this base
+plus @ref valueless_elements_per_byte for every byte read so far. The base is
+the per-container limit, so a container that was accepted on its own before
+the sum was introduced is still accepted at the start of an input.
+*/
+JSON_INLINE_VARIABLE constexpr std::size_t valueless_elements_base = max_valueless_container_size;
+
+/*!
+@brief number of elements of valueless UBJSON containers accepted per byte of
+       input, in addition to @ref valueless_elements_base
+
+An element of a value that has a payload costs at least one byte of input.
+Valueless elements are accepted at a rate of 4 per byte. A value takes 16
+bytes of memory in a DOM, so these arrays add about 80 bytes of memory per
+byte of input (measured: 77; one `Z` per byte needs about 32), beyond what the
+same bytes cost anyway, plus the base. This bounds the arrays of valueless
+type, not the memory of a whole document. Containers written by
+@ref binary_writer never need more than the base, because it writes an array
+in the unoptimized form once the typed arrays written so far and this one add
+up to more than that. The rate matters for input written by other encoders and
+by versions before 3.13.0 only; in the data this was measured on, no input has
+more than 0.17 elements per byte.
+*/
+JSON_INLINE_VARIABLE constexpr std::size_t valueless_elements_per_byte = 4;
+
 ///////////////////
 // binary reader //
 ///////////////////
@@ -3700,6 +3733,37 @@ class binary_reader
         return emit_unsigned(number);
     }
 
+    /*!
+    @brief add the elements of a container of a valueless type to the total of
+           the input and check the total against the input read so far
+
+    A container of type 'Z', 'T' or 'F' has no payload, so its elements are the
+    only ones for which the input does not bound the count. The check is made
+    once per container, not per element.
+
+    @param[in] count  number of elements the container declares; at most
+                      @ref max_valueless_container_size
+    @return false if the total is more than @ref valueless_elements_base plus
+            @ref valueless_elements_per_byte for every byte read so far; the
+            total is not changed then
+    */
+    bool charge_valueless_elements(const std::size_t count) noexcept
+    {
+        // the limit saturates instead of overflowing when size_t is 32 bits
+        // wide and a very large input has been read; valueless_elements
+        // never exceeds the limit, so the difference cannot underflow
+        constexpr std::size_t max_size = (std::numeric_limits<std::size_t>::max)();
+        const std::size_t limit = chars_read <= (max_size - valueless_elements_base) / valueless_elements_per_byte
+                                  ? valueless_elements_base + (valueless_elements_per_byte * chars_read)
+                                  : max_size;
+        if (JSON_HEDLEY_UNLIKELY(count > limit - valueless_elements))
+        {
+            return false;
+        }
+        valueless_elements += count;
+        return true;
+    }
+
     /*!
     @return whether array creation completed
     */
@@ -3785,24 +3849,27 @@ class binary_reader
             // declared count alone decides how much is allocated; the check is
             // made before the start event so that no container is opened that
             // is then abandoned. See @ref max_valueless_container_size.
-            if (JSON_HEDLEY_UNLIKELY((size_and_type.second == 'Z' || size_and_type.second == 'T' || size_and_type.second == 'F')
+            if (JSON_HEDLEY_UNLIKELY(size_and_type.second == 'Z' || size_and_type.second == 'T' || size_and_type.second == 'F'))
-                                     && size_and_type.first > max_valueless_container_size))
             {
-                return out_of_range_error(exception_id::container_too_large, "excessive array size", "size");
+                if (JSON_HEDLEY_UNLIKELY(size_and_type.first > max_valueless_container_size))
+                {
+                    return out_of_range_error(exception_id::container_too_large, "excessive array size", "size");
+                }
+                if (JSON_HEDLEY_UNLIKELY(!charge_valueless_elements(size_and_type.first)))
+                {
+                    return out_of_range_error(exception_id::container_too_large, "excessive number of elements without payload", "size");
+                }
             }
 
-            if (JSON_HEDLEY_UNLIKELY(!enter_array(size_and_type.first, size_and_type.second)))
+            // a no-op is not a value, so an array of them is empty whatever
+            // count it declares: the SAX parser is told so, instead of being
+            // made to reserve storage for a count that no input backs
+            const std::size_t announced = size_and_type.second == 'N' ? 0 : size_and_type.first;
+            if (JSON_HEDLEY_UNLIKELY(!enter_array(announced, size_and_type.second)))
             {
                 return false;
             }
 
-            if (size_and_type.second == 'N')
-            {
-                // a no-op is not a value, so a container of them holds none;
-                // the declared size has already been passed to the SAX parser
-                container_stack.back().remaining = 0;
-            }
-
             return size_and_type.second == 0
                    || parse_ubjson_typed_run(container_stack.back().remaining, size_and_type.second, std::integral_constant<bool, bulk_scan> {});
         }
@@ -5114,6 +5181,10 @@ class binary_reader
     /// the number of characters read
     std::size_t chars_read = 0;
 
+    /// UBJSON: the sum of the element counts of the containers of a valueless
+    /// type read so far; see @ref charge_valueless_elements
+    std::size_t valueless_elements = 0;
+
     /// whether we can assume little endianness
     const bool is_little_endian = little_endianness();
 

include/nlohmann/detail/output/binary_writer.hpp

@@ -1204,20 +1204,27 @@ class binary_writer
 
             // an optimized array of a valueless type carries no payload, so a
             // reader has nothing but the declared count to bound the allocation
-            // by and refuses an excessive one. Write the unoptimized form for
+            // by. It refuses one array of more than max_valueless_container_size
-            // those, at one byte per element, so the result can be read back.
+            // elements, and all such arrays of one input together when they add
-            // Objects are not affected: every element is preceded by its key.
+            // up to more than valueless_elements_base plus a number per byte
-            const bool valueless_type = (first_prefix == 'Z' || first_prefix == 'T' || first_prefix == 'F');
+            // read. Write the unoptimized form, at one byte per element, for
-            const bool excessive_valueless = IsArray
+            // an array that would exceed the base with the arrays written so
-                                             && valueless_type
+            // far, so that the result can be read back: the limit of a reader
-                                             && size > detail::max_valueless_container_size;
+            // is never below the base. Objects are not affected: every element
-
+            // is preceded by its key.
-            if (same_prefix && !excessive_valueless
+            if (same_prefix && !(use_bjdata && is_bjdata_excluded_type_marker(first_prefix)))
-                    && !(use_bjdata && is_bjdata_excluded_type_marker(first_prefix)))
             {
-                prefix_required = false;
+                const bool valueless_type = IsArray && (first_prefix == 'Z' || first_prefix == 'T' || first_prefix == 'F');
-                oa.write_character(to_char_type('$'));
+                if (!valueless_type || size <= detail::valueless_elements_base - valueless_elements_written)
-                oa.write_character(first_prefix);
+                {
+                    prefix_required = false;
+                    oa.write_character(to_char_type('$'));
+                    oa.write_character(first_prefix);
+                    if (valueless_type)
+                    {
+                        valueless_elements_written += size;
+                    }
+                }
             }
         }
 
@@ -5441,6 +5448,10 @@ class binary_writer
     /// how to treat a string value or object key that is not valid UTF-8
     /// (CBOR, MessagePack, UBJSON, BJData, and BSON; not BON8)
     const error_handler_t error_handler = binary_writer_default_error_handler();
+
+    /// UBJSON: the number of elements written so far in optimized arrays of a
+    /// valueless type, which a reader adds up and bounds
+    std::size_t valueless_elements_written = 0;
 };
 
 }  // namespace detail

single_include/nlohmann/json.hpp

@@ -18352,13 +18352,46 @@ the input.
 
 This is a sanity bound rather than a security boundary, and it is far above
 any container met in practice. @ref binary_writer falls back to the
-unoptimized encoding for longer containers, so that a value serialized by
+unoptimized encoding for longer containers, and for containers that together
-this library can always be read back.
+with the ones before them would exceed @ref valueless_elements_base, so that a
+value serialized by this library can always be read back.
 
 @sa https://github.com/nlohmann/json/issues/2793
 */
 JSON_INLINE_VARIABLE constexpr std::size_t max_valueless_container_size = 1 << 20;
 
+/*!
+@brief number of elements of valueless UBJSON containers accepted on top of
+       @ref valueless_elements_per_byte
+
+The limit @ref max_valueless_container_size applies to each container on its
+own, so on its own it lets 9 bytes announce 1048576 values, and every further
+9 bytes another 1048576. The elements of all containers of a valueless type
+in one input are therefore added up, and the sum must stay below this base
+plus @ref valueless_elements_per_byte for every byte read so far. The base is
+the per-container limit, so a container that was accepted on its own before
+the sum was introduced is still accepted at the start of an input.
+*/
+JSON_INLINE_VARIABLE constexpr std::size_t valueless_elements_base = max_valueless_container_size;
+
+/*!
+@brief number of elements of valueless UBJSON containers accepted per byte of
+       input, in addition to @ref valueless_elements_base
+
+An element of a value that has a payload costs at least one byte of input.
+Valueless elements are accepted at a rate of 4 per byte. A value takes 16
+bytes of memory in a DOM, so these arrays add about 80 bytes of memory per
+byte of input (measured: 77; one `Z` per byte needs about 32), beyond what the
+same bytes cost anyway, plus the base. This bounds the arrays of valueless
+type, not the memory of a whole document. Containers written by
+@ref binary_writer never need more than the base, because it writes an array
+in the unoptimized form once the typed arrays written so far and this one add
+up to more than that. The rate matters for input written by other encoders and
+by versions before 3.13.0 only; in the data this was measured on, no input has
+more than 0.17 elements per byte.
+*/
+JSON_INLINE_VARIABLE constexpr std::size_t valueless_elements_per_byte = 4;
+
 ///////////////////
 // binary reader //
 ///////////////////
@@ -21979,6 +22012,37 @@ class binary_reader
         return emit_unsigned(number);
     }
 
+    /*!
+    @brief add the elements of a container of a valueless type to the total of
+           the input and check the total against the input read so far
+
+    A container of type 'Z', 'T' or 'F' has no payload, so its elements are the
+    only ones for which the input does not bound the count. The check is made
+    once per container, not per element.
+
+    @param[in] count  number of elements the container declares; at most
+                      @ref max_valueless_container_size
+    @return false if the total is more than @ref valueless_elements_base plus
+            @ref valueless_elements_per_byte for every byte read so far; the
+            total is not changed then
+    */
+    bool charge_valueless_elements(const std::size_t count) noexcept
+    {
+        // the limit saturates instead of overflowing when size_t is 32 bits
+        // wide and a very large input has been read; valueless_elements
+        // never exceeds the limit, so the difference cannot underflow
+        constexpr std::size_t max_size = (std::numeric_limits<std::size_t>::max)();
+        const std::size_t limit = chars_read <= (max_size - valueless_elements_base) / valueless_elements_per_byte
+                                  ? valueless_elements_base + (valueless_elements_per_byte * chars_read)
+                                  : max_size;
+        if (JSON_HEDLEY_UNLIKELY(count > limit - valueless_elements))
+        {
+            return false;
+        }
+        valueless_elements += count;
+        return true;
+    }
+
     /*!
     @return whether array creation completed
     */
@@ -22064,24 +22128,27 @@ class binary_reader
             // declared count alone decides how much is allocated; the check is
             // made before the start event so that no container is opened that
             // is then abandoned. See @ref max_valueless_container_size.
-            if (JSON_HEDLEY_UNLIKELY((size_and_type.second == 'Z' || size_and_type.second == 'T' || size_and_type.second == 'F')
+            if (JSON_HEDLEY_UNLIKELY(size_and_type.second == 'Z' || size_and_type.second == 'T' || size_and_type.second == 'F'))
-                                     && size_and_type.first > max_valueless_container_size))
             {
-                return out_of_range_error(exception_id::container_too_large, "excessive array size", "size");
+                if (JSON_HEDLEY_UNLIKELY(size_and_type.first > max_valueless_container_size))
+                {
+                    return out_of_range_error(exception_id::container_too_large, "excessive array size", "size");
+                }
+                if (JSON_HEDLEY_UNLIKELY(!charge_valueless_elements(size_and_type.first)))
+                {
+                    return out_of_range_error(exception_id::container_too_large, "excessive number of elements without payload", "size");
+                }
             }
 
-            if (JSON_HEDLEY_UNLIKELY(!enter_array(size_and_type.first, size_and_type.second)))
+            // a no-op is not a value, so an array of them is empty whatever
+            // count it declares: the SAX parser is told so, instead of being
+            // made to reserve storage for a count that no input backs
+            const std::size_t announced = size_and_type.second == 'N' ? 0 : size_and_type.first;
+            if (JSON_HEDLEY_UNLIKELY(!enter_array(announced, size_and_type.second)))
             {
                 return false;
             }
 
-            if (size_and_type.second == 'N')
-            {
-                // a no-op is not a value, so a container of them holds none;
-                // the declared size has already been passed to the SAX parser
-                container_stack.back().remaining = 0;
-            }
-
             return size_and_type.second == 0
                    || parse_ubjson_typed_run(container_stack.back().remaining, size_and_type.second, std::integral_constant<bool, bulk_scan> {});
         }
@@ -23393,6 +23460,10 @@ class binary_reader
     /// the number of characters read
     std::size_t chars_read = 0;
 
+    /// UBJSON: the sum of the element counts of the containers of a valueless
+    /// type read so far; see @ref charge_valueless_elements
+    std::size_t valueless_elements = 0;
+
     /// whether we can assume little endianness
     const bool is_little_endian = little_endianness();
 
@@ -30546,20 +30617,27 @@ class binary_writer
 
             // an optimized array of a valueless type carries no payload, so a
             // reader has nothing but the declared count to bound the allocation
-            // by and refuses an excessive one. Write the unoptimized form for
+            // by. It refuses one array of more than max_valueless_container_size
-            // those, at one byte per element, so the result can be read back.
+            // elements, and all such arrays of one input together when they add
-            // Objects are not affected: every element is preceded by its key.
+            // up to more than valueless_elements_base plus a number per byte
-            const bool valueless_type = (first_prefix == 'Z' || first_prefix == 'T' || first_prefix == 'F');
+            // read. Write the unoptimized form, at one byte per element, for
-            const bool excessive_valueless = IsArray
+            // an array that would exceed the base with the arrays written so
-                                             && valueless_type
+            // far, so that the result can be read back: the limit of a reader
-                                             && size > detail::max_valueless_container_size;
+            // is never below the base. Objects are not affected: every element
-
+            // is preceded by its key.
-            if (same_prefix && !excessive_valueless
+            if (same_prefix && !(use_bjdata && is_bjdata_excluded_type_marker(first_prefix)))
-                    && !(use_bjdata && is_bjdata_excluded_type_marker(first_prefix)))
             {
-                prefix_required = false;
+                const bool valueless_type = IsArray && (first_prefix == 'Z' || first_prefix == 'T' || first_prefix == 'F');
-                oa.write_character(to_char_type('$'));
+                if (!valueless_type || size <= detail::valueless_elements_base - valueless_elements_written)
-                oa.write_character(first_prefix);
+                {
+                    prefix_required = false;
+                    oa.write_character(to_char_type('$'));
+                    oa.write_character(first_prefix);
+                    if (valueless_type)
+                    {
+                        valueless_elements_written += size;
+                    }
+                }
             }
         }
 
@@ -34783,6 +34861,10 @@ class binary_writer
     /// how to treat a string value or object key that is not valid UTF-8
     /// (CBOR, MessagePack, UBJSON, BJData, and BSON; not BON8)
     const error_handler_t error_handler = binary_writer_default_error_handler();
+
+    /// UBJSON: the number of elements written so far in optimized arrays of a
+    /// valueless type, which a reader adds up and bounds
+    std::size_t valueless_elements_written = 0;
 };
 
 }  // namespace detail

tests/src/unit-ubjson.cpp

@@ -19,8 +19,12 @@
 #include <nlohmann/json.hpp>
 using nlohmann::json;
 
+#include <cstdio>
 #include <iostream>
+#include <sstream>
+#include <utility>
 #include <fstream>
+#include <limits>
 #include <list>
 #include <set>
 #include "make_test_data_available.hpp"
@@ -2436,6 +2440,341 @@ TEST_CASE("UBJSON optimized arrays of a valueless type are bounded")
     }
 }
 
+namespace
+{
+/// SAX consumer that counts the values and keeps the id of a parse error
+struct ValuelessEventCounter : public nlohmann::json_sax<json>
+{
+    bool null() override
+    {
+        return ++values < stop_after;
+    }
+    bool boolean(bool /*val*/) override
+    {
+        return ++values < stop_after;
+    }
+    bool number_integer(json::number_integer_t /*val*/) override
+    {
+        ++values;
+        return true;
+    }
+    bool number_unsigned(json::number_unsigned_t /*val*/) override
+    {
+        ++values;
+        return true;
+    }
+    bool number_float(json::number_float_t /*val*/, const std::string& /*s*/) override
+    {
+        ++values;
+        return true;
+    }
+    bool string(std::string& /*val*/) override
+    {
+        ++values;
+        return true;
+    }
+    bool binary(json::binary_t& /*val*/) override
+    {
+        ++values;
+        return true;
+    }
+    bool start_object(std::size_t /*elements*/) override
+    {
+        return true;
+    }
+    bool key(std::string& /*val*/) override
+    {
+        return true;
+    }
+    bool end_object() override
+    {
+        return true;
+    }
+    bool start_array(std::size_t /*elements*/) override
+    {
+        return true;
+    }
+    bool end_array() override
+    {
+        return true;
+    }
+    bool parse_error(std::size_t /*position*/, const std::string& /*last_token*/, const json::exception& ex) override
+    {
+        error_id = ex.id;
+        return false;
+    }
+
+    /// the handler refuses the value that makes this many
+    std::size_t stop_after = (std::numeric_limits<std::size_t>::max)();
+    std::size_t values = 0;
+    int error_id = 0;
+};
+
+/// appends `[$<marker>#l<count>` (nine bytes) to @a v
+void append_valueless_array(std::vector<std::uint8_t>& v, const char marker, const std::uint32_t count)
+{
+    v.push_back('[');
+    v.push_back('$');
+    v.push_back(static_cast<std::uint8_t>(marker));
+    v.push_back('#');
+    v.push_back('l');
+    v.push_back(static_cast<std::uint8_t>(count >> 24));
+    v.push_back(static_cast<std::uint8_t>(count >> 16));
+    v.push_back(static_cast<std::uint8_t>(count >> 8));
+    v.push_back(static_cast<std::uint8_t>(count));
+}
+
+/// `[` followed by one `[$<marker>#l<count>` per entry of @a counts and `]`
+std::vector<std::uint8_t> valueless_arrays(const char marker, const std::vector<std::uint32_t>& counts)
+{
+    std::vector<std::uint8_t> v = {'['};
+    for (const auto count : counts)
+    {
+        append_valueless_array(v, marker, count);
+    }
+    v.push_back(']');
+    return v;
+}
+} // namespace
+
+TEST_CASE("UBJSON the valueless elements of a whole input are bounded")
+{
+    // The per-container limit alone let nine bytes (`[$Z#l` and a count of
+    // 1048576) announce a million values, and every further nine bytes another
+    // million. The elements of all containers of type 'Z', 'T' or 'F' in one
+    // input are now added up: they may not exceed 1048576 plus 4 for every
+    // byte read when the container's header has been read.
+    //
+    // The tests count events with a SAX handler where they can: building and
+    // comparing values of a million elements is what makes them slow under
+    // Valgrind, so there is one rejection and one round trip with a DOM.
+    json _;
+    const char* const budget_message = "[json.exception.out_of_range.408] syntax error while parsing UBJSON size: excessive number of elements without payload";
+
+    // two arrays that exceed the limit: the second one, with its header read
+    // at byte 19, may hold 4 * 19 = 76 values on top of the base of 1048576
+    const std::uint32_t over_first = 524288;
+    const std::uint32_t over_second = 1048576 + 76 - over_first + 1;
+
+    SECTION("the input of the original report is rejected")
+    {
+        // 362 bytes (40 arrays of 1048576 values) used to allocate 661 MB; the
+        // second array is the one that is refused
+        const auto input = valueless_arrays('Z', {over_first, over_second});
+        CHECK_THROWS_WITH_AS(_ = json::from_ubjson(input), budget_message, json::out_of_range&);
+    }
+
+    SECTION("every input adapter applies the budget")
+    {
+        const auto input = valueless_arrays('Z', {over_first, over_second});
+
+        // stream; not strict, which does not matter
+        std::stringstream stream;
+        stream.write(reinterpret_cast<const char*>(input.data()), static_cast<std::streamsize>(input.size()));
+        ValuelessEventCounter from_stream;
+        CHECK(!json::sax_parse(stream, &from_stream, json::input_format_t::ubjson, false));
+        CHECK(from_stream.error_id == 408);
+
+        // a container that is not contiguous; the counts of arrays of
+        // different types are added up
+        std::vector<std::uint8_t> mixed = {'['};
+        append_valueless_array(mixed, 'T', over_first);
+        append_valueless_array(mixed, 'F', over_second);
+        mixed.push_back(']');
+        const std::list<std::uint8_t> as_list(mixed.begin(), mixed.end());
+        ValuelessEventCounter from_list;
+        CHECK(!json::sax_parse(as_list.begin(), as_list.end(), &from_list, json::input_format_t::ubjson));
+        CHECK(from_list.error_id == 408);
+        CHECK(from_list.values == over_first);
+
+        // FILE*
+        FILE* const file = std::tmpfile(); // NOLINT(cppcoreguidelines-owning-memory)
+        REQUIRE(file != nullptr);
+        CHECK(std::fwrite(input.data(), 1, input.size(), file) == input.size());
+        std::rewind(file);
+        ValuelessEventCounter from_file;
+        CHECK(!json::sax_parse(file, &from_file, json::input_format_t::ubjson));
+        CHECK(from_file.error_id == 408);
+        std::fclose(file); // NOLINT(cert-err33-c,cppcoreguidelines-owning-memory)
+    }
+
+    SECTION("the limit is exact and the bytes read raise it")
+    {
+        // [ [$Z#l 524288] [$U#l 4096 + 4096 bytes] [$Z#l count] ]: chars_read
+        // is 1 + 9 + (9 + 4096) + 9 = 4124 when the last header has been read,
+        // so the last array may hold 4 * 4124 = 16496 values on top of the
+        // base of 1048576 less the 524288 of the first array
+        const std::uint32_t last_allowed = 1048576 + 16496 - 524288;
+        for (const std::uint32_t count :
+                {
+                    last_allowed, last_allowed + 1
+                })
+        {
+            CAPTURE(count)
+            std::vector<std::uint8_t> input = {'['};
+            append_valueless_array(input, 'Z', 524288);
+            input.insert(input.end(), {'[', '$', 'U', '#', 'l', 0x00, 0x00, 0x10, 0x00});
+            input.insert(input.end(), 4096, 0x01);
+            append_valueless_array(input, 'Z', count);
+            input.push_back(']');
+            ValuelessEventCounter sax;
+            const bool accepted = count == last_allowed;
+            CHECK(json::sax_parse(input, &sax, json::input_format_t::ubjson) == accepted);
+            CHECK(sax.error_id == (accepted ? 0 : 408));
+            CHECK(sax.values == 524288u + 4096u + (accepted ? count : 0u));
+        }
+
+        // an array of 1048576 values on its own is accepted as before
+        const std::vector<std::uint8_t> single = {'[', '$', 'Z', '#', 'l', 0x00, 0x10, 0x00, 0x00};
+        // (the handler ends the parse at the first value, so that the million
+        // values are not read)
+        ValuelessEventCounter sax;
+        sax.stop_after = 1;
+        CHECK(!json::sax_parse(single, &sax, json::input_format_t::ubjson));
+        CHECK(sax.error_id == 0);
+        CHECK(sax.values == 1);
+    }
+
+    SECTION("to_ubjson writes the typed form up to the base only")
+    {
+        // 1048 rows of 1000 values fit under the base of 1048576, the 1049th
+        // would not: its elements are written one by one. Written all typed,
+        // 1100 rows of 6 bytes would be refused by a reader (1075 rows are the
+        // most it accepts). The rows hold null, true or false, and the
+        // fallback does not depend on which
+        std::vector<std::uint8_t> encoded;
+        {
+            json table = json::array();
+            for (int row = 0; row < 1100; ++row)
+            {
+                const json cell = row % 3 == 0 ? json(nullptr) : json(row % 3 == 1);
+                table.push_back(json(1000, cell));
+            }
+            encoded = json::to_ubjson(table, true, true);
+        }
+        // outer array: `[$[#I` and the count (7 bytes), then 1048 typed rows of 6
+        // bytes (`$Z#I` and two bytes) and 52 rows of `#I`, two bytes, and 1000 `Z`
+        CHECK(encoded.size() == 7 + (1048 * 6) + (52 * (4 + 1000)));
+
+        // the output is read back
+        ValuelessEventCounter sax;
+        CHECK(json::sax_parse(encoded, &sax, json::input_format_t::ubjson));
+        CHECK(sax.error_id == 0);
+        CHECK(sax.values == 1100u * 1000u);
+    }
+
+    SECTION("BJData is not affected")
+    {
+        // BJData has no optimized arrays of these types, and the writer does
+        // not charge them
+        json table = json::array();
+        for (int row = 0; row < 3; ++row)
+        {
+            table.push_back(json(10, nullptr));
+        }
+        const auto encoded = json::to_bjdata(table, true, true);
+        CHECK(json::from_bjdata(encoded) == table);
+
+        const std::vector<std::uint8_t> input = {'[', '$', 'Z', '#', 'l', 0x00, 0x10, 0x00, 0x00};
+        CHECK_THROWS_AS(_ = json::from_bjdata(input), json::parse_error&);
+    }
+
+    SECTION("an object of a valueless type needs a key for every value")
+    {
+        // an object member costs a key, so the count is bounded by the input
+        // and is not charged to the budget
+        const std::vector<std::uint8_t> input = {'{', '$', 'Z', '#', 'l', 0x00, 0x10, 0x00, 0x00};
+        ValuelessEventCounter sax;
+        CHECK(!json::sax_parse(input, &sax, json::input_format_t::ubjson));
+        CHECK(sax.error_id == 110);
+        CHECK(sax.values == 0);
+    }
+}
+
+TEST_CASE("UBJSON an optimized array of no-ops is empty whatever its count")
+{
+    // A no-op ('N') is not a value, so `[$N#<n>` is an array without elements
+    // for every n. The count used to be passed on to the SAX parser, which
+    // told it to expect n elements, and the DOM parser reserved storage for
+    // them: 16384 values (256 KB) for a count of 2^31 in 9 bytes of input.
+    SECTION("the SAX parser is told that the array is empty")
+    {
+        for (const std::vector<std::uint8_t>& input :
+                {
+                    std::vector<std::uint8_t> {'[', '$', 'N', '#', 'i', 2},
+                    std::vector<std::uint8_t> {'[', '$', 'N', '#', 'I', 0x7F, 0xFF},
+                    std::vector<std::uint8_t> {'[', '$', 'N', '#', 'l', 0x7F, 0xFF, 0xFF, 0xFF},
+                    std::vector<std::uint8_t> {'[', '$', 'N', '#', 'i', 0}
+                })
+        {
+            SaxEventLogger logger;
+            CHECK(json::sax_parse(input, &logger, json::input_format_t::ubjson));
+            CHECK(logger.events == std::vector<std::string>({"start_array(0)", "end_array()"}));
+        }
+
+        // between other values, the next value is read as usual
+        const std::vector<std::uint8_t> nested = {'[', '[', '$', 'N', '#', 'l', 0x7F, 0xFF, 0xFF, 0xFF, 'T', '[', '$', 'N', '#', 'i', 3, ']'};
+        SaxEventLogger logger;
+        CHECK(json::sax_parse(nested, &logger, json::input_format_t::ubjson));
+        CHECK(logger.events == std::vector<std::string>({"start_array()", "start_array(0)", "end_array()", "boolean(true)", "start_array(0)", "end_array()", "end_array()"}));
+    }
+
+    SECTION("the DOM parser reserves nothing")
+    {
+        // 2000 arrays of 9 bytes that announce 2^31 elements each: with a
+        // reservation of 16384 values per array this took about 500 MB
+        std::vector<std::uint8_t> input = {'['};
+        for (int i = 0; i < 2000; ++i)
+        {
+            input.insert(input.end(), {'[', '$', 'N', '#', 'l', 0x7F, 0xFF, 0xFF, 0xFF});
+        }
+        input.push_back(']');
+
+        const json j = json::from_ubjson(input);
+        REQUIRE(j.size() == 2000);
+        std::size_t capacity = 0;
+        for (const auto& element : j)
+        {
+            CHECK(element.is_array());
+            CHECK(element.empty());
+            capacity += element.get_ref<const json::array_t&>().capacity();
+        }
+        CHECK(capacity == 0);
+
+        // the 7-byte form inside an optimized array of arrays
+        std::vector<std::uint8_t> typed = {'[', '$', '[', '#', 'I', 0x07, 0xD0};
+        for (int i = 0; i < 2000; ++i)
+        {
+            typed.insert(typed.end(), {'$', 'N', '#', 'I', 0x7F, 0xFF});
+        }
+        const json k = json::from_ubjson(typed);
+        REQUIRE(k.size() == 2000);
+        capacity = 0;
+        for (const auto& element : k)
+        {
+            CHECK(element.empty());
+            capacity += element.get_ref<const json::array_t&>().capacity();
+        }
+        CHECK(capacity == 0);
+    }
+
+    SECTION("a count that no container could hold is no longer an error")
+    {
+        // the array is empty, so nothing has to fit: 0x7FFFFFFF used to be
+        // reported as out_of_range.408 where it exceeds the maximum size of
+        // an array, and is accepted now
+        const std::vector<std::uint8_t> input = {'[', '$', 'N', '#', 'l', 0x7F, 0xFF, 0xFF, 0xFF};
+        CHECK(json::from_ubjson(input) == json::array());
+
+        // a count that does not fit into std::size_t still is
+#if SIZE_MAX == 0xffffffff
+        const std::vector<std::uint8_t> too_large = {'[', '$', 'N', '#', 'L', 0x00, 0x00, 0x00, 0x01, 0x00, 0x00, 0x00, 0x00};
+        json _;
+        CHECK_THROWS_AS(_ = json::from_ubjson(too_large), json::out_of_range&);
+#endif
+    }
+}
+
 TEST_CASE("issue #5405 - array reserve for definite-length UBJSON arrays")
 {
 #if !defined(JSON_NOEXCEPTION)