Add benchmarks for SAX parsing, value operations, JSON Pointer, and conversions

The benchmark suite covered only parsing, serialization, and the binary formats.
Add benchmarks for SAX parsing without building values, copying, destroying,
comparing and iterating documents, flatten()/unflatten() (also for ordered_json),
diff() and patch(), JSON Pointer parsing, printing and lookup, and conversions
from and to standard containers. They use only API that 3.12.0 also has, so
releases can be compared on them.

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

include/nlohmann/detail/conversions/zmij.hpp

@@ -184,10 +184,7 @@ JSON_HEDLEY_ALWAYS_INLINE shortest_decimal to_shortest(std::uint64_t bits) noexc
     const uint128_parts p10 = pow10(-dec_exp - 1);
     const uint128_parts p = umul192_hi128(p10.high, p10.low, bin_sig << static_cast<unsigned>(shift));
     std::uint64_t integral = p.high >> static_cast<unsigned>(extra_shift);
-    // (no casts in the shifts: MSVC 2015 warns C4554 on them despite the parentheses)
-    constexpr unsigned fractional_low_shift = static_cast<unsigned>(extra_shift);
-    constexpr unsigned fractional_high_shift = 64u - fractional_low_shift;
-    const std::uint64_t fractional = (p.high << fractional_high_shift) | (p.low >> fractional_low_shift);
+    const std::uint64_t fractional = (p.high << static_cast<unsigned>(64 - extra_shift)) | (p.low >> static_cast<unsigned>(extra_shift));
     std::uint64_t digit = 0;
     bool round_up = false;
     bool round_down = false;

single_include/nlohmann/json.hpp

@@ -25874,10 +25874,7 @@ JSON_HEDLEY_ALWAYS_INLINE shortest_decimal to_shortest(std::uint64_t bits) noexc
     const uint128_parts p10 = pow10(-dec_exp - 1);
     const uint128_parts p = umul192_hi128(p10.high, p10.low, bin_sig << static_cast<unsigned>(shift));
     std::uint64_t integral = p.high >> static_cast<unsigned>(extra_shift);
-    // (no casts in the shifts: MSVC 2015 warns C4554 on them despite the parentheses)
-    constexpr unsigned fractional_low_shift = static_cast<unsigned>(extra_shift);
-    constexpr unsigned fractional_high_shift = 64u - fractional_low_shift;
-    const std::uint64_t fractional = (p.high << fractional_high_shift) | (p.low >> fractional_low_shift);
+    const std::uint64_t fractional = (p.high << static_cast<unsigned>(64 - extra_shift)) | (p.low >> static_cast<unsigned>(extra_shift));
     std::uint64_t digit = 0;
     bool round_up = false;
     bool round_down = false;

tests/benchmarks/README.md

@@ -16,6 +16,13 @@ Micro-benchmarks for parsing, serialization and the binary formats, written with
 | `FromBinaryBuffer`, `FromBinaryFile` | read CBOR, MessagePack, UBJSON, BJData and BSON from a buffer or a `FILE*` |
 | `FromBinaryShape` | read deeply nested, container-heavy and scalar-heavy documents in every binary format |
 | `FromCborChunkedString` | read CBOR strings split into indefinite-length chunks |
+| `SaxParse` | parse with a SAX handler that only counts events, so no values are built |
+| `Copy`, `Destroy`, `Equal`, `Iterate` | copy, destroy, or compare a parsed document, or visit every value with range-based `for` loops |
+| `Flatten`, `FlattenOrdered`, `Unflatten` | `flatten()` for `json` and `ordered_json`, and `unflatten()` |
+| `Diff`, `Patch` | `diff()` against the document with every eighth scalar changed, and applying that patch |
+| `JsonPointerParse`, `JsonPointerToString`, `JsonPointerAt`, `JsonPointerContains` | the JSON pointers of every scalar in a document: parse them from strings, turn them back into strings, look them up with `at()` and `contains()` |
+| `GetVectorInt`, `GetVectorDouble`, `GetMap` | `get<std::vector<std::int64_t>>()`, `get<std::vector<double>>()` and `get<std::map<std::string, json>>()` on large arrays and a large flat object |
+| `ToJsonStrings` | create a `json` array from a `std::vector` of 100,000 strings, copied or moved |
 
 The input files are those of [nativejson-benchmark](https://github.com/miloyip/nativejson-benchmark) (`canada`,
 `citm_catalog`, `twitter`), a large `jeopardy` file, and number-heavy files (`floats`, `signed_ints`, ...).

tests/benchmarks/src/benchmarks.cpp

@@ -8,8 +8,11 @@
 
 #include <benchmark/benchmark.h>
 #include <nlohmann/json.hpp>
+#include <cstdint>
 #include <fstream>
+#include <map>
 #include <numeric>
+#include <string>
 #include <vector>
 #include <test_data.hpp>
 
@@ -621,4 +624,524 @@ static void FromCborChunkedString(benchmark::State& state, const std::size_t chu
 
 BENCHMARK_CAPTURE(FromCborChunkedString, 10000 chunks, 10000);
 
+//////////////////////////////////////////////////////////////////////////////
+// SAX-parse JSON from string
+//
+// sax_parse() with a handler that does next to nothing runs the lexer and
+// parser without building values, so the gap to ParseString above is the cost
+// of building the DOM.
+//////////////////////////////////////////////////////////////////////////////
+
+static std::string read_file(const char* filename)
+{
+    std::ifstream f(filename);
+    return std::string((std::istreambuf_iterator<char>(f)), std::istreambuf_iterator<char>());
+}
+
+static json load_json(const char* filename)
+{
+    return json::parse(read_file(filename));
+}
+
+/// SAX handler that only counts the events, so that the handler costs next to nothing
+class counting_sax : public nlohmann::json_sax<json>
+{
+  public:
+    std::size_t events = 0;
+
+    bool null() override
+    {
+        return count();
+    }
+    bool boolean(bool /*val*/) override
+    {
+        return count();
+    }
+    bool number_integer(number_integer_t /*val*/) override
+    {
+        return count();
+    }
+    bool number_unsigned(number_unsigned_t /*val*/) override
+    {
+        return count();
+    }
+    bool number_float(number_float_t /*val*/, const string_t& /*s*/) override
+    {
+        return count();
+    }
+    bool string(string_t& /*val*/) override
+    {
+        return count();
+    }
+    bool binary(binary_t& /*val*/) override
+    {
+        return count();
+    }
+    bool start_object(std::size_t /*elements*/) override
+    {
+        return count();
+    }
+    bool key(string_t& /*val*/) override
+    {
+        return count();
+    }
+    bool end_object() override
+    {
+        return count();
+    }
+    bool start_array(std::size_t /*elements*/) override
+    {
+        return count();
+    }
+    bool end_array() override
+    {
+        return count();
+    }
+    bool parse_error(std::size_t /*position*/, const std::string& /*last_token*/, const json::exception& /*ex*/) override
+    {
+        return false;
+    }
+
+  private:
+    bool count()
+    {
+        ++events;
+        return true;
+    }
+};
+
+static void SaxParse(benchmark::State& state, const char* filename)
+{
+    const std::string str = read_file(filename);
+
+    for (auto _ : state)
+    {
+        counting_sax sax;
+        bool result = json::sax_parse(str, &sax);
+        benchmark::DoNotOptimize(result);
+        benchmark::DoNotOptimize(sax.events);
+    }
+
+    state.SetBytesProcessed(state.iterations() * str.size());
+}
+BENCHMARK_CAPTURE(SaxParse, canada,       TEST_DATA_DIRECTORY "/nativejson-benchmark/canada.json");
+BENCHMARK_CAPTURE(SaxParse, citm_catalog, TEST_DATA_DIRECTORY "/nativejson-benchmark/citm_catalog.json");
+BENCHMARK_CAPTURE(SaxParse, twitter,      TEST_DATA_DIRECTORY "/nativejson-benchmark/twitter.json");
+
+//////////////////////////////////////////////////////////////////////////////
+// work with values: copy, destroy, compare, iterate
+//
+// The parsed test files stand in for a document an application keeps around.
+// Each benchmark times one whole-document operation; setup and cleanup run
+// outside the timed section.
+//////////////////////////////////////////////////////////////////////////////
+
+static void Copy(benchmark::State& state, const char* filename)
+{
+    const json j = load_json(filename);
+
+    for (auto _ : state)
+    {
+        auto* copy = new json(j);
+
+        state.PauseTiming();
+        delete copy;
+        state.ResumeTiming();
+    }
+}
+BENCHMARK_CAPTURE(Copy, canada,       TEST_DATA_DIRECTORY "/nativejson-benchmark/canada.json");
+BENCHMARK_CAPTURE(Copy, citm_catalog, TEST_DATA_DIRECTORY "/nativejson-benchmark/citm_catalog.json");
+BENCHMARK_CAPTURE(Copy, twitter,      TEST_DATA_DIRECTORY "/nativejson-benchmark/twitter.json");
+
+static void Destroy(benchmark::State& state, const char* filename)
+{
+    const json j = load_json(filename);
+
+    for (auto _ : state)
+    {
+        state.PauseTiming();
+        auto* copy = new json(j);
+        state.ResumeTiming();
+
+        delete copy;
+    }
+}
+BENCHMARK_CAPTURE(Destroy, canada,       TEST_DATA_DIRECTORY "/nativejson-benchmark/canada.json");
+BENCHMARK_CAPTURE(Destroy, citm_catalog, TEST_DATA_DIRECTORY "/nativejson-benchmark/citm_catalog.json");
+BENCHMARK_CAPTURE(Destroy, twitter,      TEST_DATA_DIRECTORY "/nativejson-benchmark/twitter.json");
+
+static void Equal(benchmark::State& state, const char* filename)
+{
+    // two separate values, so that the comparison cannot stop at identical addresses
+    const json j = load_json(filename);
+    const json copy = j;
+
+    for (auto _ : state)
+    {
+        bool result = (j == copy);
+        benchmark::DoNotOptimize(result);
+    }
+}
+BENCHMARK_CAPTURE(Equal, canada,       TEST_DATA_DIRECTORY "/nativejson-benchmark/canada.json");
+BENCHMARK_CAPTURE(Equal, citm_catalog, TEST_DATA_DIRECTORY "/nativejson-benchmark/citm_catalog.json");
+BENCHMARK_CAPTURE(Equal, twitter,      TEST_DATA_DIRECTORY "/nativejson-benchmark/twitter.json");
+
+/// visit every value with range-based for loops, as client code walks a document
+static std::size_t count_values(const json& j)
+{
+    std::size_t result = 1;
+    if (j.is_structured())
+    {
+        for (const auto& element : j)
+        {
+            result += count_values(element);
+        }
+    }
+    return result;
+}
+
+static void Iterate(benchmark::State& state, const char* filename)
+{
+    const json j = load_json(filename);
+
+    for (auto _ : state)
+    {
+        std::size_t result = count_values(j);
+        benchmark::DoNotOptimize(result);
+    }
+
+    state.SetItemsProcessed(state.iterations() * static_cast<std::int64_t>(count_values(j)));
+}
+BENCHMARK_CAPTURE(Iterate, canada,       TEST_DATA_DIRECTORY "/nativejson-benchmark/canada.json");
+BENCHMARK_CAPTURE(Iterate, citm_catalog, TEST_DATA_DIRECTORY "/nativejson-benchmark/citm_catalog.json");
+BENCHMARK_CAPTURE(Iterate, twitter,      TEST_DATA_DIRECTORY "/nativejson-benchmark/twitter.json");
+
+//////////////////////////////////////////////////////////////////////////////
+// flatten and unflatten
+//////////////////////////////////////////////////////////////////////////////
+
+static void Flatten(benchmark::State& state, const char* filename)
+{
+    const json j = load_json(filename);
+
+    for (auto _ : state)
+    {
+        json flat = j.flatten();
+        benchmark::DoNotOptimize(flat);
+    }
+}
+BENCHMARK_CAPTURE(Flatten, canada,       TEST_DATA_DIRECTORY "/nativejson-benchmark/canada.json");
+BENCHMARK_CAPTURE(Flatten, citm_catalog, TEST_DATA_DIRECTORY "/nativejson-benchmark/citm_catalog.json");
+BENCHMARK_CAPTURE(Flatten, twitter,      TEST_DATA_DIRECTORY "/nativejson-benchmark/twitter.json");
+
+// ordered_json objects look keys up linearly, which flatten() used to do for
+// every value; canada (330,000 values in one flat object) is left out, as it
+// would take minutes with such versions
+static void FlattenOrdered(benchmark::State& state, const char* filename)
+{
+    const nlohmann::ordered_json j = nlohmann::ordered_json::parse(read_file(filename));
+
+    for (auto _ : state)
+    {
+        nlohmann::ordered_json flat = j.flatten();
+        benchmark::DoNotOptimize(flat);
+    }
+}
+BENCHMARK_CAPTURE(FlattenOrdered, citm_catalog, TEST_DATA_DIRECTORY "/nativejson-benchmark/citm_catalog.json");
+BENCHMARK_CAPTURE(FlattenOrdered, twitter,      TEST_DATA_DIRECTORY "/nativejson-benchmark/twitter.json");
+
+static void Unflatten(benchmark::State& state, const char* filename)
+{
+    const json flat = load_json(filename).flatten();
+
+    for (auto _ : state)
+    {
+        json j = flat.unflatten();
+        benchmark::DoNotOptimize(j);
+    }
+}
+BENCHMARK_CAPTURE(Unflatten, canada,       TEST_DATA_DIRECTORY "/nativejson-benchmark/canada.json");
+BENCHMARK_CAPTURE(Unflatten, citm_catalog, TEST_DATA_DIRECTORY "/nativejson-benchmark/citm_catalog.json");
+BENCHMARK_CAPTURE(Unflatten, twitter,      TEST_DATA_DIRECTORY "/nativejson-benchmark/twitter.json");
+
+//////////////////////////////////////////////////////////////////////////////
+// diff and patch
+//
+// The target is the document with every eighth scalar changed, so the patch
+// has one "replace" operation per changed value and the structure stays the
+// same.
+//////////////////////////////////////////////////////////////////////////////
+
+static void change_every_eighth_scalar(json& j, std::size_t& counter)
+{
+    if (j.is_structured())
+    {
+        for (auto& element : j)
+        {
+            change_every_eighth_scalar(element, counter);
+        }
+        return;
+    }
+
+    if (++counter % 8 != 0)
+    {
+        return;
+    }
+
+    switch (j.type())
+    {
+        case json::value_t::number_integer:
+            j = j.get<json::number_integer_t>() + 1;
+            break;
+        case json::value_t::number_unsigned:
+            j = j.get<json::number_unsigned_t>() + 1;
+            break;
+        case json::value_t::number_float:
+            j = j.get<json::number_float_t>() + 0.5;
+            break;
+        case json::value_t::string:
+            j = j.get<std::string>() + "!";
+            break;
+        case json::value_t::boolean:
+            j = !j.get<bool>();
+            break;
+        case json::value_t::null:
+        case json::value_t::object:
+        case json::value_t::array:
+        case json::value_t::binary:
+        case json::value_t::discarded:
+        default:
+            j = 0;
+            break;
+    }
+}
+
+static json changed_copy(const json& j)
+{
+    json result = j;
+    std::size_t counter = 0;
+    change_every_eighth_scalar(result, counter);
+    return result;
+}
+
+static void Diff(benchmark::State& state, const char* filename)
+{
+    const json source = load_json(filename);
+    const json target = changed_copy(source);
+
+    for (auto _ : state)
+    {
+        json patch = json::diff(source, target);
+        benchmark::DoNotOptimize(patch);
+    }
+
+    state.SetItemsProcessed(state.iterations() * static_cast<std::int64_t>(json::diff(source, target).size()));
+}
+BENCHMARK_CAPTURE(Diff, canada,       TEST_DATA_DIRECTORY "/nativejson-benchmark/canada.json");
+BENCHMARK_CAPTURE(Diff, citm_catalog, TEST_DATA_DIRECTORY "/nativejson-benchmark/citm_catalog.json");
+BENCHMARK_CAPTURE(Diff, twitter,      TEST_DATA_DIRECTORY "/nativejson-benchmark/twitter.json");
+
+static void Patch(benchmark::State& state, const char* filename)
+{
+    const json source = load_json(filename);
+    const json patch = json::diff(source, changed_copy(source));
+
+    for (auto _ : state)
+    {
+        json result = source.patch(patch);
+        benchmark::DoNotOptimize(result);
+    }
+
+    state.SetItemsProcessed(state.iterations() * static_cast<std::int64_t>(patch.size()));
+}
+BENCHMARK_CAPTURE(Patch, canada,       TEST_DATA_DIRECTORY "/nativejson-benchmark/canada.json");
+BENCHMARK_CAPTURE(Patch, citm_catalog, TEST_DATA_DIRECTORY "/nativejson-benchmark/citm_catalog.json");
+BENCHMARK_CAPTURE(Patch, twitter,      TEST_DATA_DIRECTORY "/nativejson-benchmark/twitter.json");
+
+//////////////////////////////////////////////////////////////////////////////
+// JSON Pointer
+//
+// The pointers are those of every scalar in the document, i.e., the keys of
+// its flattened form.
+//////////////////////////////////////////////////////////////////////////////
+
+static std::vector<std::string> pointer_strings(const json& j)
+{
+    std::vector<std::string> result;
+    const json flat = j.flatten();
+    result.reserve(flat.size());
+    for (auto it = flat.begin(); it != flat.end(); ++it)
+    {
+        result.push_back(it.key());
+    }
+    return result;
+}
+
+static std::vector<json::json_pointer> pointers(const json& j)
+{
+    const std::vector<std::string> strings = pointer_strings(j);
+    std::vector<json::json_pointer> result;
+    result.reserve(strings.size());
+    for (const auto& s : strings)
+    {
+        result.emplace_back(s);
+    }
+    return result;
+}
+
+static void JsonPointerParse(benchmark::State& state, const char* filename)
+{
+    const std::vector<std::string> strings = pointer_strings(load_json(filename));
+
+    for (auto _ : state)
+    {
+        for (const auto& s : strings)
+        {
+            json::json_pointer ptr(s);
+            benchmark::DoNotOptimize(ptr);
+        }
+    }
+
+    state.SetItemsProcessed(state.iterations() * static_cast<std::int64_t>(strings.size()));
+}
+BENCHMARK_CAPTURE(JsonPointerParse, citm_catalog, TEST_DATA_DIRECTORY "/nativejson-benchmark/citm_catalog.json");
+BENCHMARK_CAPTURE(JsonPointerParse, twitter,      TEST_DATA_DIRECTORY "/nativejson-benchmark/twitter.json");
+
+static void JsonPointerToString(benchmark::State& state, const char* filename)
+{
+    const std::vector<json::json_pointer> ptrs = pointers(load_json(filename));
+
+    for (auto _ : state)
+    {
+        for (const auto& ptr : ptrs)
+        {
+            std::string s = ptr.to_string();
+            benchmark::DoNotOptimize(s);
+        }
+    }
+
+    state.SetItemsProcessed(state.iterations() * static_cast<std::int64_t>(ptrs.size()));
+}
+BENCHMARK_CAPTURE(JsonPointerToString, citm_catalog, TEST_DATA_DIRECTORY "/nativejson-benchmark/citm_catalog.json");
+BENCHMARK_CAPTURE(JsonPointerToString, twitter,      TEST_DATA_DIRECTORY "/nativejson-benchmark/twitter.json");
+
+static void JsonPointerAt(benchmark::State& state, const char* filename)
+{
+    const json j = load_json(filename);
+    const std::vector<json::json_pointer> ptrs = pointers(j);
+
+    for (auto _ : state)
+    {
+        for (const auto& ptr : ptrs)
+        {
+            const json& value = j.at(ptr);
+            benchmark::DoNotOptimize(&value);
+        }
+    }
+
+    state.SetItemsProcessed(state.iterations() * static_cast<std::int64_t>(ptrs.size()));
+}
+BENCHMARK_CAPTURE(JsonPointerAt, citm_catalog, TEST_DATA_DIRECTORY "/nativejson-benchmark/citm_catalog.json");
+BENCHMARK_CAPTURE(JsonPointerAt, twitter,      TEST_DATA_DIRECTORY "/nativejson-benchmark/twitter.json");
+
+static void JsonPointerContains(benchmark::State& state, const char* filename)
+{
+    const json j = load_json(filename);
+    const std::vector<json::json_pointer> ptrs = pointers(j);
+
+    for (auto _ : state)
+    {
+        for (const auto& ptr : ptrs)
+        {
+            bool result = j.contains(ptr);
+            benchmark::DoNotOptimize(result);
+        }
+    }
+
+    state.SetItemsProcessed(state.iterations() * static_cast<std::int64_t>(ptrs.size()));
+}
+BENCHMARK_CAPTURE(JsonPointerContains, citm_catalog, TEST_DATA_DIRECTORY "/nativejson-benchmark/citm_catalog.json");
+BENCHMARK_CAPTURE(JsonPointerContains, twitter,      TEST_DATA_DIRECTORY "/nativejson-benchmark/twitter.json");
+
+//////////////////////////////////////////////////////////////////////////////
+// conversions from and to C++ containers
+//////////////////////////////////////////////////////////////////////////////
+
+static void GetVectorInt(benchmark::State& state, const char* filename)
+{
+    const json j = load_json(filename);
+
+    for (auto _ : state)
+    {
+        auto v = j.get<std::vector<std::int64_t>>();
+        benchmark::DoNotOptimize(v);
+    }
+
+    state.SetItemsProcessed(state.iterations() * static_cast<std::int64_t>(j.size()));
+}
+BENCHMARK_CAPTURE(GetVectorInt, signed_ints, TEST_DATA_DIRECTORY "/regression/signed_ints.json");
+
+static void GetVectorDouble(benchmark::State& state, const char* filename)
+{
+    const json j = load_json(filename);
+
+    for (auto _ : state)
+    {
+        auto v = j.get<std::vector<double>>();
+        benchmark::DoNotOptimize(v);
+    }
+
+    state.SetItemsProcessed(state.iterations() * static_cast<std::int64_t>(j.size()));
+}
+BENCHMARK_CAPTURE(GetVectorDouble, floats, TEST_DATA_DIRECTORY "/regression/floats.json");
+
+// a large flat object: the flattened document, one member per scalar
+static void GetMap(benchmark::State& state, const char* filename)
+{
+    const json j = load_json(filename).flatten();
+
+    for (auto _ : state)
+    {
+        auto m = j.get<std::map<std::string, json>>();
+        benchmark::DoNotOptimize(m);
+    }
+
+    state.SetItemsProcessed(state.iterations() * static_cast<std::int64_t>(j.size()));
+}
+BENCHMARK_CAPTURE(GetMap, citm_catalog, TEST_DATA_DIRECTORY "/nativejson-benchmark/citm_catalog.json");
+
+/// 100,000 strings, each too long for the small string optimization
+static std::vector<std::string> make_strings()
+{
+    std::vector<std::string> result;
+    result.reserve(100000);
+    for (std::size_t i = 0; i < 100000; ++i)
+    {
+        result.push_back("a string that does not fit in place: " + std::to_string(i));
+    }
+    return result;
+}
+
+static void ToJsonStrings(benchmark::State& state, const bool move)
+{
+    const std::vector<std::string> strings = make_strings();
+
+    for (auto _ : state)
+    {
+        state.PauseTiming();
+        std::vector<std::string> input = strings;
+        state.ResumeTiming();
+
+        auto* j = move ? new json(std::move(input)) : new json(input);
+
+        state.PauseTiming();
+        delete j;
+        state.ResumeTiming();
+    }
+
+    state.SetItemsProcessed(state.iterations() * static_cast<std::int64_t>(strings.size()));
+}
+BENCHMARK_CAPTURE(ToJsonStrings, copy, false);
+BENCHMARK_CAPTURE(ToJsonStrings, move, true);
+
 BENCHMARK_MAIN();

tests/src/unit-to_chars.cpp

@@ -21,8 +21,11 @@ using nlohmann::detail::dtoa_impl::reinterpret_bits;
 #include <cstdint>
 #include <cstdio>
 #include <cstdlib>
+#include <iomanip>
 #include <limits>
+#include <locale>
 #include <random>
+#include <sstream>
 #include <string>
 #include <utility>
 #include <vector>
@@ -686,13 +689,20 @@ void check_shortest(double v)
     const std::string& digits = de.first;
     if (digits.size() > 1)
     {
-        // the decimals of one digit fewer next to the value: v lies within
-        // half a unit of the last digit of text, so the closest ones are the
-        // truncated digits and their successor
-        // (not a stream with std::setprecision(digits.size() - 2): the
-        // standard library of MSVC 2017 ignores a precision of 0)
-        const std::string m = digits.substr(0, digits.size() - 1);
-        const int e = de.second + 1;
+        // the decimals of one digit fewer next to the value
+        // (a stream rather than snprintf("%.*e"), whose output GCC cannot bound)
+        std::ostringstream shorter;
+        shorter.imbue(std::locale::classic());
+        shorter << std::scientific << std::setprecision(static_cast<int>(digits.size()) - 2) << v;
+        const auto near = digits_and_exponent(shorter.str());
+        // as an integer with digits.size() - 1 digits
+        std::string m = near.first;
+        int e = near.second;
+        while (m.size() < digits.size() - 1)
+        {
+            m += '0';
+            --e;
+        }
         const std::uint64_t mid = std::stoull(m);
         for (const std::uint64_t candidate :
                 {