Handle numbers that do not fit narrow number types in the binary readers

With custom number types narrower than the values in a binary document,
for example basic_json<..., std::int32_t, std::uint32_t, float>, every
binary reader (CBOR, MessagePack, UBJSON, BJData, BSON, BON8) passed the
decoded number to the SAX interface with an implicit conversion: the
integer 5000000000 silently became 705032704, and a finite double such as
1e300 became infinity. The lexer handles the same values in JSON text: an
integer that fits neither integer type is stored as number_float_t, and a
finite number that overflows number_float_t is rejected with
out_of_range.406.

Pass every number read from binary input through three helpers that
apply the lexer's rules:
- emit_signed(): number_integer_t, else number_unsigned_t for a
  non-negative value, else number_float_t
- emit_unsigned(): number_unsigned_t, else number_float_t
- emit_float(): out_of_range.406 if a finite value overflows
  number_float_t; infinity and NaN are passed on

For consistency, a CBOR negative integer below the range of
number_integer_t is now stored as number_float_t, like a too small
integer in JSON text, instead of being rejected with parse_error.112.
With the default number types, this is the only change in behavior.

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

docs/mkdocs/docs/api/basic_json/number_float_t.md

@@ -55,6 +55,10 @@ This implementation does exactly follow this approach, as it uses double precisi
 smaller than `-1.79769313486232e+308` and values greater than `1.79769313486232e+308` will be stored as NaN internally
 and be serialized to `null`.
 
+During deserialization (from JSON text or any of the binary formats), a finite number that does not fit into
+`number_float_t` is rejected with [`out_of_range.406`](../../home/exceptions.md#jsonexceptionout_of_range406), for
+example a double-precision number in a binary format when `number_float_t` is `#!cpp float`.
+
 #### Storage
 
 Floating-point number values are stored directly inside a `basic_json` type.

docs/mkdocs/docs/api/basic_json/number_integer_t.md

@@ -47,8 +47,9 @@ With the default values for `NumberIntegerType` (`std::int64_t`), the default va
 
 When the default type is used, the maximal integer number that can be stored is `9223372036854775807` (INT64_MAX) and
 the minimal integer number that can be stored is `-9223372036854775808` (INT64_MIN). Integer numbers that are out of
-range will yield over/underflow when used in a constructor. During deserialization, too large or small integer numbers
-will automatically be stored as [`number_unsigned_t`](number_unsigned_t.md) or [`number_float_t`](number_float_t.md).
+range will yield over/underflow when used in a constructor. During deserialization (from JSON text or any of the binary
+formats), too large or small integer numbers will automatically be stored as [`number_unsigned_t`](number_unsigned_t.md)
+or [`number_float_t`](number_float_t.md).
 
 [RFC 8259](https://tools.ietf.org/html/rfc8259) further states:
 > Note that when such software is used, numbers that are integers and are in the range $[-2^{53}+1, 2^{53}-1]$ are

docs/mkdocs/docs/api/basic_json/number_unsigned_t.md

@@ -48,8 +48,9 @@ With the default values for `NumberUnsignedType` (`std::uint64_t`), the default
 
 When the default type is used, the maximal integer number that can be stored is `18446744073709551615` (UINT64_MAX) and
 the minimal integer number that can be stored is `0`. Integer numbers that are out of range will yield over/underflow
-when used in a constructor. During deserialization, too large or small integer numbers will automatically be stored
-as [`number_integer_t`](number_integer_t.md) or [`number_float_t`](number_float_t.md).
+when used in a constructor. During deserialization (from JSON text or any of the binary formats), too large or small
+integer numbers will automatically be stored as [`number_integer_t`](number_integer_t.md) or
+[`number_float_t`](number_float_t.md).
 
 [RFC 8259](https://tools.ietf.org/html/rfc8259) further states:
 > Note that when such software is used, numbers that are integers and are in the range $[-2^{53}+1, 2^{53}-1]$ are

docs/mkdocs/docs/features/binary_formats/cbor.md

@@ -168,9 +168,9 @@ The library maps CBOR types to JSON value types as follows:
 !!! warning "Negative integer overflow"
 
     CBOR negative integers (major type 1) are decoded as `-1 - n`. If the encoded magnitude `n` is too large for the
-    result to fit into `number_integer_t` (`std::int64_t` by default), parsing fails with a
-    [`parse_error.112`](../../home/exceptions.md#jsonexceptionparse_error112) exception rather than overflowing
-    silently.
+    result to fit into `number_integer_t` (`std::int64_t` by default), the result is stored as `number_float_t`, like
+    a too small integer in JSON text. For example, `-18446744073709551616` (`0x3B` followed by eight `0xFF` bytes) is
+    stored as `-1.8446744073709552e+19`.
 
 !!! warning "Object keys"
 

docs/mkdocs/docs/home/exceptions.md

@@ -331,9 +331,6 @@ An unexpected byte was read in a [binary format](../features/binary_formats/inde
     [json.exception.parse_error.112] parse error at byte 15: syntax error while parsing BSON binary: byte array length cannot be negative, is -1
     ```
     ```
-    [json.exception.parse_error.112] parse error at byte 9: syntax error while parsing CBOR value: negative integer overflow
-    ```
-    ```
     [json.exception.parse_error.112] parse error at byte 5: syntax error while parsing BSON document: document size 6 does not match the number of bytes read (5)
     ```
 
@@ -847,13 +844,18 @@ The JSON Patch operations 'remove' and 'add' cannot be applied to the root eleme
 
 ### json.exception.out_of_range.406
 
-A parsed number could not be stored as without changing it to NaN or INF.
+A parsed number could not be stored without changing it to NaN or INF. For the binary formats, this happens when a
+finite floating-point number does not fit into [`number_float_t`](../api/basic_json/number_float_t.md), for example a
+double-precision number when `number_float_t` is `#!cpp float`.
 
-!!! failure "Example message"
+!!! failure "Example messages"
 
     ```
     number overflow parsing '10E1000'
     ```
+    ```
+    [json.exception.out_of_range.406] syntax error while parsing CBOR value: number overflow
+    ```
 
 ### json.exception.out_of_range.407