diff --git a/cmake/download_test_data.cmake b/cmake/download_test_data.cmake
index fe95235f..b023d8b4 100644
--- a/cmake/download_test_data.cmake
+++ b/cmake/download_test_data.cmake
@@ -1,7 +1,7 @@
 find_package(Git)
 
 set(JSON_TEST_DATA_URL     https://github.com/nlohmann/json_test_data)
-set(JSON_TEST_DATA_VERSION 2.0.0)
+set(JSON_TEST_DATA_VERSION 3.0.0)
 
 # target to download test data
 add_custom_target(download_test_data
diff --git a/doc/mkdocs/docs/features/binary_formats/messagepack.md b/doc/mkdocs/docs/features/binary_formats/messagepack.md
index ed061056..3e041bb7 100644
--- a/doc/mkdocs/docs/features/binary_formats/messagepack.md
+++ b/doc/mkdocs/docs/features/binary_formats/messagepack.md
@@ -31,7 +31,8 @@ number_unsigned | 128..255                          | uint 8           | 0xCC
 number_unsigned | 256..65535                        | uint 16          | 0xCD
 number_unsigned | 65536..4294967295                 | uint 32          | 0xCE
 number_unsigned | 4294967296..18446744073709551615  | uint 64          | 0xCF
-number_float    | *any value*                       | float 64         | 0xCB
+number_float    | *any value representable by a float*     | float 32  | 0xCA
+number_float    | *any value NOT representable by a float* | float 64  | 0xCB
 string          | *length*: 0..31                   | fixstr           | 0xA0..0xBF
 string          | *length*: 32..255                 | str 8            | 0xD9
 string          | *length*: 256..65535              | str 16           | 0xDA
@@ -61,10 +62,6 @@ binary          | *size*: 65536..4294967295         | bin 32           | 0xC6
 	  - arrays with more than 4294967295 elements
 	  - objects with more than 4294967295 elements
 
-!!! info "Unused MessagePack types"
-
-	The following MessagePack types are not used in the conversion: float 32 (0xCA)
-
 !!! info "NaN/infinity handling"
 
 	If NaN or Infinity are stored inside a JSON number, they are serialized properly. function which serializes NaN or Infinity to `null`.
diff --git a/include/nlohmann/detail/output/binary_writer.hpp b/include/nlohmann/detail/output/binary_writer.hpp
index 269df0d5..7289da3d 100644
--- a/include/nlohmann/detail/output/binary_writer.hpp
+++ b/include/nlohmann/detail/output/binary_writer.hpp
@@ -28,6 +28,7 @@ class binary_writer
 {
     using string_t = typename BasicJsonType::string_t;
     using binary_t = typename BasicJsonType::binary_t;
+    using number_float_t = typename BasicJsonType::number_float_t;
 
   public:
     /*!
@@ -194,18 +195,7 @@ class binary_writer
                 }
                 else
                 {
-                    if (static_cast<double>(j.m_value.number_float) >= static_cast<double>(std::numeric_limits<float>::lowest()) and
-                            static_cast<double>(j.m_value.number_float) <= static_cast<double>((std::numeric_limits<float>::max)()) and
-                            static_cast<double>(static_cast<float>(j.m_value.number_float)) == static_cast<double>(j.m_value.number_float))
-                    {
-                        oa->write_character(get_cbor_float_prefix(static_cast<float>(j.m_value.number_float)));
-                        write_number(static_cast<float>(j.m_value.number_float));
-                    }
-                    else
-                    {
-                        oa->write_character(get_cbor_float_prefix(j.m_value.number_float));
-                        write_number(j.m_value.number_float);
-                    }
+                    write_compact_float(j.m_value.number_float, detail::input_format_t::cbor);
                 }
                 break;
             }
@@ -504,8 +494,7 @@ class binary_writer
 
             case value_t::number_float:
             {
-                oa->write_character(get_msgpack_float_prefix(j.m_value.number_float));
-                write_number(j.m_value.number_float);
+                write_compact_float(j.m_value.number_float, detail::input_format_t::msgpack);
                 break;
             }
 
@@ -1518,6 +1507,26 @@ class binary_writer
         oa->write_characters(vec.data(), sizeof(NumberType));
     }
 
+    void write_compact_float(const number_float_t n, detail::input_format_t format)
+    {
+        if (static_cast<double>(n) >= static_cast<double>(std::numeric_limits<float>::lowest()) and
+                static_cast<double>(n) <= static_cast<double>((std::numeric_limits<float>::max)()) and
+                static_cast<double>(static_cast<float>(n)) == static_cast<double>(n))
+        {
+            oa->write_character(format == detail::input_format_t::cbor
+                                ? get_cbor_float_prefix(static_cast<float>(n))
+                                : get_msgpack_float_prefix(static_cast<float>(n)));
+            write_number(static_cast<float>(n));
+        }
+        else
+        {
+            oa->write_character(format == detail::input_format_t::cbor
+                                ? get_cbor_float_prefix(n)
+                                : get_msgpack_float_prefix(n));
+            write_number(n);
+        }
+    }
+
   public:
     // The following to_char_type functions are implement the conversion
     // between uint8_t and CharType. In case CharType is not unsigned,
diff --git a/include/nlohmann/json.hpp b/include/nlohmann/json.hpp
index 409a6e79..790ecd4b 100644
--- a/include/nlohmann/json.hpp
+++ b/include/nlohmann/json.hpp
@@ -7040,7 +7040,8 @@ class basic_json
     number_unsigned | 256..65535                        | uint 16          | 0xCD
     number_unsigned | 65536..4294967295                 | uint 32          | 0xCE
     number_unsigned | 4294967296..18446744073709551615  | uint 64          | 0xCF
-    number_float    | *any value*                       | float 64         | 0xCB
+    number_float    | *any value representable by a float*     | float 32 | 0xCA
+    number_float    | *any value NOT representable by a float* | float 64 | 0xCB
     string          | *length*: 0..31                   | fixstr           | 0xA0..0xBF
     string          | *length*: 32..255                 | str 8            | 0xD9
     string          | *length*: 256..65535              | str 16           | 0xDA
@@ -7064,9 +7065,6 @@ class basic_json
           - arrays with more than 4294967295 elements
           - objects with more than 4294967295 elements
 
-    @note The following MessagePack types are not used in the conversion:
-          - float 32 (0xCA)
-
     @note Any MessagePack output created @ref to_msgpack can be successfully
           parsed by @ref from_msgpack.
 
diff --git a/single_include/nlohmann/json.hpp b/single_include/nlohmann/json.hpp
index cc822a54..33d0c357 100644
--- a/single_include/nlohmann/json.hpp
+++ b/single_include/nlohmann/json.hpp
@@ -12238,6 +12238,7 @@ class binary_writer
 {
     using string_t = typename BasicJsonType::string_t;
     using binary_t = typename BasicJsonType::binary_t;
+    using number_float_t = typename BasicJsonType::number_float_t;
 
   public:
     /*!
@@ -12404,18 +12405,7 @@ class binary_writer
                 }
                 else
                 {
-                    if (static_cast<double>(j.m_value.number_float) >= static_cast<double>(std::numeric_limits<float>::lowest()) and
-                            static_cast<double>(j.m_value.number_float) <= static_cast<double>((std::numeric_limits<float>::max)()) and
-                            static_cast<double>(static_cast<float>(j.m_value.number_float)) == static_cast<double>(j.m_value.number_float))
-                    {
-                        oa->write_character(get_cbor_float_prefix(static_cast<float>(j.m_value.number_float)));
-                        write_number(static_cast<float>(j.m_value.number_float));
-                    }
-                    else
-                    {
-                        oa->write_character(get_cbor_float_prefix(j.m_value.number_float));
-                        write_number(j.m_value.number_float);
-                    }
+                    write_compact_float(j.m_value.number_float, detail::input_format_t::cbor);
                 }
                 break;
             }
@@ -12714,8 +12704,7 @@ class binary_writer
 
             case value_t::number_float:
             {
-                oa->write_character(get_msgpack_float_prefix(j.m_value.number_float));
-                write_number(j.m_value.number_float);
+                write_compact_float(j.m_value.number_float, detail::input_format_t::msgpack);
                 break;
             }
 
@@ -13728,6 +13717,26 @@ class binary_writer
         oa->write_characters(vec.data(), sizeof(NumberType));
     }
 
+    void write_compact_float(const number_float_t n, detail::input_format_t format)
+    {
+        if (static_cast<double>(n) >= static_cast<double>(std::numeric_limits<float>::lowest()) and
+                static_cast<double>(n) <= static_cast<double>((std::numeric_limits<float>::max)()) and
+                static_cast<double>(static_cast<float>(n)) == static_cast<double>(n))
+        {
+            oa->write_character(format == detail::input_format_t::cbor
+                                ? get_cbor_float_prefix(static_cast<float>(n))
+                                : get_msgpack_float_prefix(static_cast<float>(n)));
+            write_number(static_cast<float>(n));
+        }
+        else
+        {
+            oa->write_character(format == detail::input_format_t::cbor
+                                ? get_cbor_float_prefix(n)
+                                : get_msgpack_float_prefix(n));
+            write_number(n);
+        }
+    }
+
   public:
     // The following to_char_type functions are implement the conversion
     // between uint8_t and CharType. In case CharType is not unsigned,
@@ -22821,7 +22830,8 @@ class basic_json
     number_unsigned | 256..65535                        | uint 16          | 0xCD
     number_unsigned | 65536..4294967295                 | uint 32          | 0xCE
     number_unsigned | 4294967296..18446744073709551615  | uint 64          | 0xCF
-    number_float    | *any value*                       | float 64         | 0xCB
+    number_float    | *any value representable by a float*     | float 32 | 0xCA
+    number_float    | *any value NOT representable by a float* | float 64 | 0xCB
     string          | *length*: 0..31                   | fixstr           | 0xA0..0xBF
     string          | *length*: 32..255                 | str 8            | 0xD9
     string          | *length*: 256..65535              | str 16           | 0xDA
@@ -22845,9 +22855,6 @@ class basic_json
           - arrays with more than 4294967295 elements
           - objects with more than 4294967295 elements
 
-    @note The following MessagePack types are not used in the conversion:
-          - float 32 (0xCA)
-
     @note Any MessagePack output created @ref to_msgpack can be successfully
           parsed by @ref from_msgpack.
 
diff --git a/test/src/unit-msgpack.cpp b/test/src/unit-msgpack.cpp
index 2744a67b..5baecf02 100644
--- a/test/src/unit-msgpack.cpp
+++ b/test/src/unit-msgpack.cpp
@@ -783,6 +783,40 @@ TEST_CASE("MessagePack")
                     CHECK(json::from_msgpack(result) == v);
                     CHECK(json::from_msgpack(result, true, false) == j);
                 }
+
+                SECTION("1.0")
+                {
+                    double v = 1.0;
+                    json j = v;
+                    std::vector<uint8_t> expected =
+                    {
+                        0xca, 0x3f, 0x80, 0x00, 0x00
+                    };
+                    const auto result = json::to_msgpack(j);
+                    CHECK(result == expected);
+
+                    // roundtrip
+                    CHECK(json::from_msgpack(result) == j);
+                    CHECK(json::from_msgpack(result) == v);
+                    CHECK(json::from_msgpack(result, true, false) == j);
+                }
+
+                SECTION("128.128")
+                {
+                    double v = 128.1280059814453125;
+                    json j = v;
+                    std::vector<uint8_t> expected =
+                    {
+                        0xca, 0x43, 0x00, 0x20, 0xc5
+                    };
+                    const auto result = json::to_msgpack(j);
+                    CHECK(result == expected);
+
+                    // roundtrip
+                    CHECK(json::from_msgpack(result) == j);
+                    CHECK(json::from_msgpack(result) == v);
+                    CHECK(json::from_msgpack(result, true, false) == j);
+                }
             }
         }