Convert floats with Eisel-Lemire when std::from_chars is unavailable

Float tokens that Clinger's fast path cannot convert (e.g. the 17-digit coordinates of canada.json) went to strtod unless std::from_chars was available. It is not used in C++11/14, and not with libc++, which does not define __cpp_lib_to_chars. The Eisel-Lemire algorithm (after fast_float's compute_float) now converts them with integer arithmetic, correctly rounded for any token with at most 19 significant digits. Longer tokens are truncated; the result is used if w and w + 1 round alike, else strtod decides as before. Overflow still yields infinity (out_of_range.406). The table of powers of five (fast_float's) lives in pow5_table.hpp; a unit test recomputes every entry with big-integer arithmetic. Further tests: known values generated with Python (whose float() is correctly rounded), 200,000 round trips through to_chars, and the 128-bit multiplication and leading-zero count against big-integer references (both with and without a 128-bit type). Checked against strtod on 6.5 million tokens, among them 60,000 exact halfway cases: no difference. json::parse on canada.json: -8.6% (C++11), -7.6% (C++17, Apple clang); other files unchanged. Compile time of a TU including json.hpp: +0.7%. Signed-off-by: Niels Lohmann <mail@nlohmann.me>
2026-09-29 19:20:30 +00:00 · 2026-09-29 03:49:25 +02:00
8 changed files with 2006 additions and 8 deletions
@@ -21,6 +21,7 @@ cc_library(
        "include/nlohmann/adl_serializer.hpp",
        "include/nlohmann/byte_container_with_subtype.hpp",
        "include/nlohmann/detail/abi_macros.hpp",
+        "include/nlohmann/detail/bit_ops.hpp",
        "include/nlohmann/detail/conversions/from_json.hpp",
        "include/nlohmann/detail/conversions/to_chars.hpp",
        "include/nlohmann/detail/conversions/to_json.hpp",
@@ -33,6 +34,7 @@ cc_library(
        "include/nlohmann/detail/input/number_parse.hpp",
        "include/nlohmann/detail/input/parser.hpp",
        "include/nlohmann/detail/input/position_t.hpp",
+        "include/nlohmann/detail/input/pow5_table.hpp",
        "include/nlohmann/detail/input/string_scan.hpp",
        "include/nlohmann/detail/iterators/internal_iterator.hpp",
        "include/nlohmann/detail/iterators/iter_impl.hpp",
@@ -1395,6 +1395,7 @@ THE SOFTWARE IS PROVIDED “AS IS”, WITHOUT WARRANTY OF ANY KIND, EXPRESS OR I
 - The class contains a slightly modified version of the Grisu2 algorithm from Florian Loitsch which is licensed under the [MIT License](https://opensource.org/licenses/MIT) (see above). Copyright &copy; 2009 [Florian Loitsch](https://florian.loitsch.com/)
 - The class contains a copy of [Hedley](https://nemequ.github.io/hedley/) from Evan Nemerson which is licensed as [CC0-1.0](https://creativecommons.org/publicdomain/zero/1.0/).
 - The class contains parts of [Google Abseil](https://github.com/abseil/abseil-cpp) which is licensed under the [Apache 2.0 License](https://opensource.org/licenses/Apache-2.0).
+- The class contains an adapted version of the Eisel-Lemire algorithm and its table of powers of five from [fast_float](https://github.com/fastfloat/fast_float) by Daniel Lemire and contributors, which is available under the [MIT License](https://opensource.org/licenses/MIT) (used here), the Apache 2.0 License, and the Boost Software License. Copyright &copy; 2021 The fast_float authors

 <img align="right" src="https://git.fsfe.org/reuse/reuse-ci/raw/branch/master/reuse-horizontal.png" alt="REUSE Software">

@@ -19,3 +19,5 @@ The class contains the UTF-8 Decoder from Bjoern Hoehrmann which is licensed und
 The class contains a slightly modified version of the Grisu2 algorithm from Florian Loitsch which is licensed under the [MIT License](https://opensource.org/licenses/MIT) (see above). Copyright &copy; 2009 [Florian Loitsch](https://florian.loitsch.com/)

 The class contains a copy of [Hedley](https://nemequ.github.io/hedley/) from Evan Nemerson which is licensed as [CC0-1.0](https://creativecommons.org/publicdomain/zero/1.0/).
+
+The class contains an adapted version of the Eisel-Lemire algorithm and its table of powers of five from [fast_float](https://github.com/fastfloat/fast_float) by Daniel Lemire and contributors, which is available under the [MIT License](https://opensource.org/licenses/MIT) (used here), the Apache 2.0 License, and the Boost Software License. Copyright &copy; 2021 The fast_float authors
@@ -0,0 +1,81 @@
+//     __ _____ _____ _____
+//  __|  |   __|     |   | |  JSON for Modern C++
+// |  |  |__   |  |  | | | |  version 3.12.0
+// |_____|_____|_____|_|___|  https://github.com/nlohmann/json
+//
+// SPDX-FileCopyrightText: 2013-2026 Niels Lohmann <https://nlohmann.me>
+// SPDX-License-Identifier: MIT
+
+#pragma once
+
+#include <cstdint> // uint64_t
+
+#include <nlohmann/detail/abi_macros.hpp>
+
+// Portable bit-level helpers for the number and string scanners. They use
+// compiler builtins where available and plain C++ otherwise, so they need no
+// platform headers and work regardless of byte order.
+
+NLOHMANN_JSON_NAMESPACE_BEGIN
+namespace detail
+{
+
+/// number of leading zero bits of x (x != 0)
+inline int count_leading_zeros(std::uint64_t x) noexcept
+{
+#if defined(__GNUC__) || defined(__clang__)
+    return __builtin_clzll(x);
+#else
+    int n = 0;
+    for (int shift = 32; shift != 0; shift >>= 1)
+    {
+        if ((x >> (64 - shift)) == 0)
+        {
+            n += shift;
+            x <<= shift;
+        }
+    }
+    return n;
+#endif
+}
+
+/// the 128-bit product of two 64-bit numbers
+struct uint128_parts
+{
+    std::uint64_t low;
+    std::uint64_t high;
+};
+
+inline uint128_parts full_multiplication(std::uint64_t a, std::uint64_t b) noexcept
+{
+#if defined(__SIZEOF_INT128__)
+    __extension__ using uint128 = unsigned __int128;
+    const uint128 r = static_cast<uint128>(a) * b;
+    return {static_cast<std::uint64_t>(r), static_cast<std::uint64_t>(r >> 64u)};
+#else
+    const std::uint64_t a_lo = a & 0xFFFFFFFFu;
+    const std::uint64_t a_hi = a >> 32u;
+    const std::uint64_t b_lo = b & 0xFFFFFFFFu;
+    const std::uint64_t b_hi = b >> 32u;
+    const std::uint64_t lo_lo = a_lo * b_lo;
+    const std::uint64_t hi_lo = a_hi * b_lo;
+    const std::uint64_t lo_hi = a_lo * b_hi;
+    const std::uint64_t hi_hi = a_hi * b_hi;
+    const std::uint64_t cross = (lo_lo >> 32u) + (hi_lo & 0xFFFFFFFFu) + lo_hi;
+    return {(cross << 32u) | (lo_lo & 0xFFFFFFFFu), (hi_lo >> 32u) + (cross >> 32u) + hi_hi};
+#endif
+}
+
+/// eight bytes as a little-endian word (compilers fold this into one load on
+/// little-endian targets)
+inline std::uint64_t read_eight_bytes(const char* p) noexcept
+{
+    const auto* b = reinterpret_cast<const unsigned char*>(p); // NOLINT(cppcoreguidelines-pro-type-reinterpret-cast)
+    return static_cast<std::uint64_t>(b[0]) | (static_cast<std::uint64_t>(b[1]) << 8u)
+           | (static_cast<std::uint64_t>(b[2]) << 16u) | (static_cast<std::uint64_t>(b[3]) << 24u)
+           | (static_cast<std::uint64_t>(b[4]) << 32u) | (static_cast<std::uint64_t>(b[5]) << 40u)
+           | (static_cast<std::uint64_t>(b[6]) << 48u) | (static_cast<std::uint64_t>(b[7]) << 56u);
+}
+
+}  // namespace detail
+NLOHMANN_JSON_NAMESPACE_END
@@ -3,6 +3,7 @@
 // |  |  |__   |  |  | | | |  version 3.12.0
 // |_____|_____|_____|_|___|  https://github.com/nlohmann/json
 //
+// SPDX-FileCopyrightText: 2021 The fast_float authors <https://github.com/fastfloat/fast_float>
 // SPDX-FileCopyrightText: 2013-2026 Niels Lohmann <https://nlohmann.me>
 // SPDX-License-Identifier: MIT

@@ -14,9 +15,12 @@
 #include <cstddef> // size_t
 #include <cstdint> // int64_t, uint64_t
 #include <cstdlib> // strtof, strtod, strtold
+#include <cstring> // memcpy
 #include <limits> // numeric_limits
 #include <string> // string

+#include <nlohmann/detail/bit_ops.hpp>
+#include <nlohmann/detail/input/pow5_table.hpp>
 #include <nlohmann/detail/macro_scope.hpp>

 // std::from_chars lives in <charconv>, but being in C++17 mode does not
@@ -297,6 +301,233 @@ bool parse_float_from_chars(const char* first, const char* last, FloatType& out)
 #endif
 }

+/// whether the eight bytes of @a v (see read_eight_bytes()) are ASCII digits
+/// (after fast_float's is_made_of_eight_digits_fast)
+inline bool is_eight_digits(std::uint64_t v) noexcept
+{
+    return ((v & 0xF0F0F0F0F0F0F0F0u) | (((v + 0x0606060606060606u) & 0xF0F0F0F0F0F0F0F0u) >> 4u)) == 0x3333333333333333u;
+}
+
+/// the value of the eight ASCII digits in @a v (see read_eight_bytes()), three
+/// multiplications instead of eight (after simdjson and fast_float)
+inline std::uint32_t parse_eight_digits(std::uint64_t v) noexcept
+{
+    v = ((v & 0x0F0F0F0F0F0F0F0Fu) * 2561u) >> 8u;
+    v = ((v & 0x00FF00FF00FF00FFu) * 6553601u) >> 16u;
+    return static_cast<std::uint32_t>(((v & 0x0000FFFF0000FFFFu) * 42949672960001u) >> 32u);
+}
+
+/*!
+@brief the double nearest to w * 10^q (Eisel-Lemire)
+
+The algorithm of Daniel Lemire, "Number Parsing at a Gigabyte per Second"
+(Software: Practice and Experience, 2021), after fast_float's compute_float
+(used under the MIT license). With a 128-bit approximation of 5^q, the product
+is always sufficient to round correctly for w with at most 19 digits (Noble
+Mushtak and Daniel Lemire, "Fast number parsing without fallback", Software:
+Practice and Experience, 2023). Only integer arithmetic is used, so the result
+does not depend on the floating-point environment.
+
+@param[in] q  decimal exponent
+@param[in] w  significand, w != 0
+@return the IEEE-754 bits of the positive result (0 for underflow, infinity
+        for overflow)
+*/
+inline std::uint64_t eisel_lemire(std::int64_t q, std::uint64_t w) noexcept
+{
+    constexpr int mantissa_bits = 52;
+    constexpr std::uint64_t infinity = std::uint64_t{0x7FF} << mantissa_bits;
+    if (q < pow5_128_smallest_power)
+    {
+        return 0;
+    }
+    if (q > pow5_128_largest_power)
+    {
+        return infinity;
+    }
+
+    const int lz = count_leading_zeros(w);
+    w <<= static_cast<unsigned>(lz);
+    const auto index = static_cast<std::size_t>(2 * (q - pow5_128_smallest_power));
+    uint128_parts product = full_multiplication(w, pow5_128()[index]);
+    constexpr std::uint64_t precision_mask = 0xFFFFFFFFFFFFFFFFu >> (mantissa_bits + 3);
+    if ((product.high & precision_mask) == precision_mask)
+    {
+        // the lower bits may carry into the result: use the next 64 bits of 5^q
+        const uint128_parts second = full_multiplication(w, pow5_128()[index + 1]);
+        product.low += second.high;
+        if (second.high > product.low)
+        {
+            ++product.high;
+        }
+    }
+
+    const auto upperbit = static_cast<int>(product.high >> 63u);
+    const int shift = upperbit + 64 - mantissa_bits - 3;
+    std::uint64_t mantissa = product.high >> static_cast<unsigned>(shift);
+    // floor(log2(10^q)) + 63 + 1023, with log2(10) ~ 217706 / 2^16
+    std::int64_t power2 = (((152170 + 65536) * q) >> 16) + 63 + upperbit - lz + 1023;
+
+    if (power2 <= 0) // subnormal
+    {
+        if (-power2 + 1 >= 64)
+        {
+            return 0;
+        }
+        mantissa >>= static_cast<unsigned>(-power2 + 1);
+        mantissa += (mantissa & 1u);
+        mantissa >>= 1u;
+        // rounding up may produce the smallest normal number
+        power2 = (mantissa < (std::uint64_t{1} << mantissa_bits)) ? 0 : 1;
+        return mantissa | (static_cast<std::uint64_t>(power2) << mantissa_bits);
+    }
+
+    // a value exactly between two doubles rounds to even; this can only
+    // happen for small |q|, where 5^q is exact
+    if (product.low <= 1 && q >= -4 && q <= 23 && (mantissa & 3u) == 1
+            && (mantissa << static_cast<unsigned>(shift)) == product.high)
+    {
+        mantissa &= ~std::uint64_t{1};
+    }
+    mantissa += (mantissa & 1u);
+    mantissa >>= 1u;
+    if (mantissa >= (std::uint64_t{2} << mantissa_bits))
+    {
+        mantissa = std::uint64_t{1} << mantissa_bits;
+        ++power2;
+    }
+    mantissa &= ~(std::uint64_t{1} << mantissa_bits);
+    if (power2 >= 0x7FF)
+    {
+        return infinity;
+    }
+    return mantissa | (static_cast<std::uint64_t>(power2) << mantissa_bits);
+}
+
+/*!
+@brief parse a validated float token with the Eisel-Lemire algorithm
+
+The significand is accumulated eight digits at a time where possible. A token
+with more than 19 significant digits is truncated to w; the value then lies
+in [w, w + 1) * 10^q, and it is only returned if both ends round to the same
+double, which covers all but a few such tokens.
+
+@param[in]  first  pointer to the first character of the token
+@param[in]  last   pointer past the last character
+@param[out] out    the correctly rounded value on success (±infinity if it
+                   overflows, like strtod)
+@return true on success; false if strtod must decide
+*/
+inline bool parse_float_eisel_lemire(const char* first, const char* last, double& out) noexcept
+{
+    const char* p = first;
+    const bool negative = (p != last && *p == '-');
+    if (negative)
+    {
+        ++p;
+    }
+
+    std::uint64_t w = 0;
+    int digits = 0; // significant digits in w
+    std::int64_t exponent = 0;
+    bool truncated = false;
+    bool in_fraction = false;
+    for (;;)
+    {
+        // eight digits at a time, as long as they fit into w
+        while (w != 0 && digits <= 19 - 8 && last - p >= 8)
+        {
+            const std::uint64_t v = read_eight_bytes(p);
+            if (!is_eight_digits(v))
+            {
+                break;
+            }
+            w = (w * 100000000u) + parse_eight_digits(v);
+            digits += 8;
+            exponent -= in_fraction ? 8 : 0;
+            p += 8;
+        }
+        if (p == last)
+        {
+            break;
+        }
+        const char c = *p;
+        if (c >= '0' && c <= '9')
+        {
+            if (w == 0 && c == '0')
+            {
+                // leading zeros are not significant, but scale a fraction
+                exponent -= in_fraction ? 1 : 0;
+            }
+            else if (digits < 19)
+            {
+                w = (w * 10u) + static_cast<std::uint64_t>(c - '0');
+                ++digits;
+                exponent -= in_fraction ? 1 : 0;
+            }
+            else
+            {
+                // dropped: the value lies between w and w + 1 (in units of
+                // the last kept digit) unless all dropped digits are zero
+                truncated = truncated || c != '0';
+                exponent += in_fraction ? 0 : 1;
+            }
+            ++p;
+        }
+        else if (c == '.')
+        {
+            in_fraction = true;
+            ++p;
+        }
+        else
+        {
+            break; // 'e' or 'E'
+        }
+    }
+
+    if (p != last)
+    {
+        ++p; // 'e' or 'E'
+        bool exp_negative = false;
+        if (p != last && (*p == '-' || *p == '+'))
+        {
+            exp_negative = (*p == '-');
+            ++p;
+        }
+        std::int64_t exp_value = 0;
+        for (; p != last; ++p)
+        {
+            // saturate: any exponent beyond this under- or overflows anyway
+            if (exp_value < 100000)
+            {
+                exp_value = (exp_value * 10) + (*p - '0');
+            }
+        }
+        exponent += exp_negative ? -exp_value : exp_value;
+    }
+
+    std::uint64_t bits = 0;
+    if (w != 0)
+    {
+        bits = eisel_lemire(exponent, w);
+        if (truncated && (w + 1 == 0 || eisel_lemire(exponent, w + 1) != bits))
+        {
+            return false;
+        }
+    }
+    bits |= negative ? (std::uint64_t{1} << 63u) : 0u;
+    static_assert(sizeof(double) == sizeof(std::uint64_t), "double must have 64 bits");
+    std::memcpy(&out, &bits, sizeof(out));
+    return true;
+}
+
+/// Eisel-Lemire is only implemented for `double`
+template<typename FloatType>
+bool parse_float_eisel_lemire(const char* /*first*/, const char* /*last*/, FloatType& /*out*/) noexcept
+{
+    return false;
+}
+
 /*!
@brief check whether Clinger's fast path can still succeed for a float token

@@ -355,8 +586,9 @@ inline bool mantissa_fits_clinger(const char* token, std::size_t decimal_point_p
 /*!
@brief convert a validated float token without the C library, if possible

-Tries std::from_chars (when available) and then Clinger's exact fast path
-(double only), skipping the latter when it cannot succeed.
+Tries std::from_chars (when available), Clinger's exact fast path (double
+only, skipped when it cannot succeed), and the Eisel-Lemire algorithm (double
+only).

@param[in]  first                   pointer to the first character of the token
@param[in]  last                    pointer past the last character
@@ -379,8 +611,12 @@ bool convert_float_fast(const char* first, const char* last, std::size_t decimal
    // Skipping a fast path that cannot succeed is lossless and saves a full
    // extra pass over the token's bytes, which otherwise shows up on
    // high-precision inputs such as canada.json
-    return mantissa_fits_clinger(first, decimal_point_position, mantissa_end)
-           && parse_float_fast(first, last, value);
+    if (mantissa_fits_clinger(first, decimal_point_position, mantissa_end)
+            && parse_float_fast(first, last, value))
+    {
+        return true;
+    }
+    return parse_float_eisel_lemire(first, last, value);
 }

 /// std::strtof, std::strtod, or std::strtold, chosen by the type of @a f
@@ -0,0 +1,371 @@
+//     __ _____ _____ _____
+//  __|  |   __|     |   | |  JSON for Modern C++
+// |  |  |__   |  |  | | | |  version 3.12.0
+// |_____|_____|_____|_|___|  https://github.com/nlohmann/json
+//
+// SPDX-FileCopyrightText: 2021 The fast_float authors <https://github.com/fastfloat/fast_float>
+// SPDX-FileCopyrightText: 2013-2026 Niels Lohmann <https://nlohmann.me>
+// SPDX-License-Identifier: MIT
+
+#pragma once
+
+#include <array> // array
+#include <cstdint> // int64_t, uint64_t
+
+#include <nlohmann/detail/abi_macros.hpp>
+
+NLOHMANN_JSON_NAMESPACE_BEGIN
+namespace detail
+{
+
+/// the range of decimal exponents covered by pow5_128()
+constexpr std::int64_t pow5_128_smallest_power = -342;
+constexpr std::int64_t pow5_128_largest_power = 308;
+
+/*!
+@brief 128-bit approximations of 5^q for q in [-342, 308]
+
+Entry q (at index 2 * (q + 342)) holds the most significant 128 bits of 5^q,
+normalized so that the highest bit is set: for q >= 0 the truncated value, for
+q < 0 the value rounded up. This is the table of fast_float (Daniel Lemire and
+contributors, used under the MIT license), generated like its
+script/table_generation.py; unit-class_lexer.cpp recomputes every entry.
+*/
+inline const std::array<std::uint64_t, 1302>& pow5_128() noexcept
+{
+    static const std::array<std::uint64_t, 1302> table =
+    {
+        {
+            0xeef453d6923bd65au, 0x113faa2906a13b3fu, 0x9558b4661b6565f8u, 0x4ac7ca59a424c507u,
+            0xbaaee17fa23ebf76u, 0x5d79bcf00d2df649u, 0xe95a99df8ace6f53u, 0xf4d82c2c107973dcu,
+            0x91d8a02bb6c10594u, 0x79071b9b8a4be869u, 0xb64ec836a47146f9u, 0x9748e2826cdee284u,
+            0xe3e27a444d8d98b7u, 0xfd1b1b2308169b25u, 0x8e6d8c6ab0787f72u, 0xfe30f0f5e50e20f7u,
+            0xb208ef855c969f4fu, 0xbdbd2d335e51a935u, 0xde8b2b66b3bc4723u, 0xad2c788035e61382u,
+            0x8b16fb203055ac76u, 0x4c3bcb5021afcc31u, 0xaddcb9e83c6b1793u, 0xdf4abe242a1bbf3du,
+            0xd953e8624b85dd78u, 0xd71d6dad34a2af0du, 0x87d4713d6f33aa6bu, 0x8672648c40e5ad68u,
+            0xa9c98d8ccb009506u, 0x680efdaf511f18c2u, 0xd43bf0effdc0ba48u, 0x0212bd1b2566def2u,
+            0x84a57695fe98746du, 0x014bb630f7604b57u, 0xa5ced43b7e3e9188u, 0x419ea3bd35385e2du,
+            0xcf42894a5dce35eau, 0x52064cac828675b9u, 0x818995ce7aa0e1b2u, 0x7343efebd1940993u,
+            0xa1ebfb4219491a1fu, 0x1014ebe6c5f90bf8u, 0xca66fa129f9b60a6u, 0xd41a26e077774ef6u,
+            0xfd00b897478238d0u, 0x8920b098955522b4u, 0x9e20735e8cb16382u, 0x55b46e5f5d5535b0u,
+            0xc5a890362fddbc62u, 0xeb2189f734aa831du, 0xf712b443bbd52b7bu, 0xa5e9ec7501d523e4u,
+            0x9a6bb0aa55653b2du, 0x47b233c92125366eu, 0xc1069cd4eabe89f8u, 0x999ec0bb696e840au,
+            0xf148440a256e2c76u, 0xc00670ea43ca250du, 0x96cd2a865764dbcau, 0x380406926a5e5728u,
+            0xbc807527ed3e12bcu, 0xc605083704f5ecf2u, 0xeba09271e88d976bu, 0xf7864a44c633682eu,
+            0x93445b8731587ea3u, 0x7ab3ee6afbe0211du, 0xb8157268fdae9e4cu, 0x5960ea05bad82964u,
+            0xe61acf033d1a45dfu, 0x6fb92487298e33bdu, 0x8fd0c16206306babu, 0xa5d3b6d479f8e056u,
+            0xb3c4f1ba87bc8696u, 0x8f48a4899877186cu, 0xe0b62e2929aba83cu, 0x331acdabfe94de87u,
+            0x8c71dcd9ba0b4925u, 0x9ff0c08b7f1d0b14u, 0xaf8e5410288e1b6fu, 0x07ecf0ae5ee44dd9u,
+            0xdb71e91432b1a24au, 0xc9e82cd9f69d6150u, 0x892731ac9faf056eu, 0xbe311c083a225cd2u,
+            0xab70fe17c79ac6cau, 0x6dbd630a48aaf406u, 0xd64d3d9db981787du, 0x092cbbccdad5b108u,
+            0x85f0468293f0eb4eu, 0x25bbf56008c58ea5u, 0xa76c582338ed2621u, 0xaf2af2b80af6f24eu,
+            0xd1476e2c07286faau, 0x1af5af660db4aee1u, 0x82cca4db847945cau, 0x50d98d9fc890ed4du,
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+            0x867f59a9d4bed6c0u, 0x49ed8eabcccc485du, 0xa81f301449ee8c70u, 0x5c68f256bfff5a74u,
+            0xd226fc195c6a2f8cu, 0x73832eec6fff3111u, 0x83585d8fd9c25db7u, 0xc831fd53c5ff7eabu,
+            0xa42e74f3d032f525u, 0xba3e7ca8b77f5e55u, 0xcd3a1230c43fb26fu, 0x28ce1bd2e55f35ebu,
+            0x80444b5e7aa7cf85u, 0x7980d163cf5b81b3u, 0xa0555e361951c366u, 0xd7e105bcc332621fu,
+            0xc86ab5c39fa63440u, 0x8dd9472bf3fefaa7u, 0xfa856334878fc150u, 0xb14f98f6f0feb951u,
+            0x9c935e00d4b9d8d2u, 0x6ed1bf9a569f33d3u, 0xc3b8358109e84f07u, 0x0a862f80ec4700c8u,
+            0xf4a642e14c6262c8u, 0xcd27bb612758c0fau, 0x98e7e9cccfbd7dbdu, 0x8038d51cb897789cu,
+            0xbf21e44003acdd2cu, 0xe0470a63e6bd56c3u, 0xeeea5d5004981478u, 0x1858ccfce06cac74u,
+            0x95527a5202df0ccbu, 0x0f37801e0c43ebc8u, 0xbaa718e68396cffdu, 0xd30560258f54e6bau,
+            0xe950df20247c83fdu, 0x47c6b82ef32a2069u, 0x91d28b7416cdd27eu, 0x4cdc331d57fa5441u,
+            0xb6472e511c81471du, 0xe0133fe4adf8e952u, 0xe3d8f9e563a198e5u, 0x58180fddd97723a6u,
+            0x8e679c2f5e44ff8fu, 0x570f09eaa7ea7648u,
+        }
+    };
+    return table;
+}
+
+}  // namespace detail
+NLOHMANN_JSON_NAMESPACE_END
@@ -8487,6 +8487,7 @@ NLOHMANN_JSON_NAMESPACE_END
 // |  |  |__   |  |  | | | |  version 3.12.0
 // |_____|_____|_____|_|___|  https://github.com/nlohmann/json
 //
+// SPDX-FileCopyrightText: 2021 The fast_float authors <https://github.com/fastfloat/fast_float>
 // SPDX-FileCopyrightText: 2013-2026 Niels Lohmann <https://nlohmann.me>
 // SPDX-License-Identifier: MIT

@@ -8498,9 +8499,468 @@ NLOHMANN_JSON_NAMESPACE_END
 #include <cstddef> // size_t
 #include <cstdint> // int64_t, uint64_t
 #include <cstdlib> // strtof, strtod, strtold
+#include <cstring> // memcpy
 #include <limits> // numeric_limits
 #include <string> // string

+// #include <nlohmann/detail/bit_ops.hpp>
+//     __ _____ _____ _____
+//  __|  |   __|     |   | |  JSON for Modern C++
+// |  |  |__   |  |  | | | |  version 3.12.0
+// |_____|_____|_____|_|___|  https://github.com/nlohmann/json
+//
+// SPDX-FileCopyrightText: 2013-2026 Niels Lohmann <https://nlohmann.me>
+// SPDX-License-Identifier: MIT
+
+
+
+#include <cstdint> // uint64_t
+
+// #include <nlohmann/detail/abi_macros.hpp>
+
+
+// Portable bit-level helpers for the number and string scanners. They use
+// compiler builtins where available and plain C++ otherwise, so they need no
+// platform headers and work regardless of byte order.
+
+NLOHMANN_JSON_NAMESPACE_BEGIN
+namespace detail
+{
+
+/// number of leading zero bits of x (x != 0)
+inline int count_leading_zeros(std::uint64_t x) noexcept
+{
+#if defined(__GNUC__) || defined(__clang__)
+    return __builtin_clzll(x);
+#else
+    int n = 0;
+    for (int shift = 32; shift != 0; shift >>= 1)
+    {
+        if ((x >> (64 - shift)) == 0)
+        {
+            n += shift;
+            x <<= shift;
+        }
+    }
+    return n;
+#endif
+}
+
+/// the 128-bit product of two 64-bit numbers
+struct uint128_parts
+{
+    std::uint64_t low;
+    std::uint64_t high;
+};
+
+inline uint128_parts full_multiplication(std::uint64_t a, std::uint64_t b) noexcept
+{
+#if defined(__SIZEOF_INT128__)
+    __extension__ using uint128 = unsigned __int128;
+    const uint128 r = static_cast<uint128>(a) * b;
+    return {static_cast<std::uint64_t>(r), static_cast<std::uint64_t>(r >> 64u)};
+#else
+    const std::uint64_t a_lo = a & 0xFFFFFFFFu;
+    const std::uint64_t a_hi = a >> 32u;
+    const std::uint64_t b_lo = b & 0xFFFFFFFFu;
+    const std::uint64_t b_hi = b >> 32u;
+    const std::uint64_t lo_lo = a_lo * b_lo;
+    const std::uint64_t hi_lo = a_hi * b_lo;
+    const std::uint64_t lo_hi = a_lo * b_hi;
+    const std::uint64_t hi_hi = a_hi * b_hi;
+    const std::uint64_t cross = (lo_lo >> 32u) + (hi_lo & 0xFFFFFFFFu) + lo_hi;
+    return {(cross << 32u) | (lo_lo & 0xFFFFFFFFu), (hi_lo >> 32u) + (cross >> 32u) + hi_hi};
+#endif
+}
+
+/// eight bytes as a little-endian word (compilers fold this into one load on
+/// little-endian targets)
+inline std::uint64_t read_eight_bytes(const char* p) noexcept
+{
+    const auto* b = reinterpret_cast<const unsigned char*>(p); // NOLINT(cppcoreguidelines-pro-type-reinterpret-cast)
+    return static_cast<std::uint64_t>(b[0]) | (static_cast<std::uint64_t>(b[1]) << 8u)
+           | (static_cast<std::uint64_t>(b[2]) << 16u) | (static_cast<std::uint64_t>(b[3]) << 24u)
+           | (static_cast<std::uint64_t>(b[4]) << 32u) | (static_cast<std::uint64_t>(b[5]) << 40u)
+           | (static_cast<std::uint64_t>(b[6]) << 48u) | (static_cast<std::uint64_t>(b[7]) << 56u);
+}
+
+}  // namespace detail
+NLOHMANN_JSON_NAMESPACE_END
+
+// #include <nlohmann/detail/input/pow5_table.hpp>
+//     __ _____ _____ _____
+//  __|  |   __|     |   | |  JSON for Modern C++
+// |  |  |__   |  |  | | | |  version 3.12.0
+// |_____|_____|_____|_|___|  https://github.com/nlohmann/json
+//
+// SPDX-FileCopyrightText: 2021 The fast_float authors <https://github.com/fastfloat/fast_float>
+// SPDX-FileCopyrightText: 2013-2026 Niels Lohmann <https://nlohmann.me>
+// SPDX-License-Identifier: MIT
+
+
+
+#include <array> // array
+#include <cstdint> // int64_t, uint64_t
+
+// #include <nlohmann/detail/abi_macros.hpp>
+
+
+NLOHMANN_JSON_NAMESPACE_BEGIN
+namespace detail
+{
+
+/// the range of decimal exponents covered by pow5_128()
+constexpr std::int64_t pow5_128_smallest_power = -342;
+constexpr std::int64_t pow5_128_largest_power = 308;
+
+/*!
+@brief 128-bit approximations of 5^q for q in [-342, 308]
+
+Entry q (at index 2 * (q + 342)) holds the most significant 128 bits of 5^q,
+normalized so that the highest bit is set: for q >= 0 the truncated value, for
+q < 0 the value rounded up. This is the table of fast_float (Daniel Lemire and
+contributors, used under the MIT license), generated like its
+script/table_generation.py; unit-class_lexer.cpp recomputes every entry.
+*/
+inline const std::array<std::uint64_t, 1302>& pow5_128() noexcept
+{
+    static const std::array<std::uint64_t, 1302> table =
+    {
+        {
+            0xeef453d6923bd65au, 0x113faa2906a13b3fu, 0x9558b4661b6565f8u, 0x4ac7ca59a424c507u,
+            0xbaaee17fa23ebf76u, 0x5d79bcf00d2df649u, 0xe95a99df8ace6f53u, 0xf4d82c2c107973dcu,
+            0x91d8a02bb6c10594u, 0x79071b9b8a4be869u, 0xb64ec836a47146f9u, 0x9748e2826cdee284u,
+            0xe3e27a444d8d98b7u, 0xfd1b1b2308169b25u, 0x8e6d8c6ab0787f72u, 0xfe30f0f5e50e20f7u,
+            0xb208ef855c969f4fu, 0xbdbd2d335e51a935u, 0xde8b2b66b3bc4723u, 0xad2c788035e61382u,
+            0x8b16fb203055ac76u, 0x4c3bcb5021afcc31u, 0xaddcb9e83c6b1793u, 0xdf4abe242a1bbf3du,
+            0xd953e8624b85dd78u, 0xd71d6dad34a2af0du, 0x87d4713d6f33aa6bu, 0x8672648c40e5ad68u,
+            0xa9c98d8ccb009506u, 0x680efdaf511f18c2u, 0xd43bf0effdc0ba48u, 0x0212bd1b2566def2u,
+            0x84a57695fe98746du, 0x014bb630f7604b57u, 0xa5ced43b7e3e9188u, 0x419ea3bd35385e2du,
+            0xcf42894a5dce35eau, 0x52064cac828675b9u, 0x818995ce7aa0e1b2u, 0x7343efebd1940993u,
+            0xa1ebfb4219491a1fu, 0x1014ebe6c5f90bf8u, 0xca66fa129f9b60a6u, 0xd41a26e077774ef6u,
+            0xfd00b897478238d0u, 0x8920b098955522b4u, 0x9e20735e8cb16382u, 0x55b46e5f5d5535b0u,
+            0xc5a890362fddbc62u, 0xeb2189f734aa831du, 0xf712b443bbd52b7bu, 0xa5e9ec7501d523e4u,
+            0x9a6bb0aa55653b2du, 0x47b233c92125366eu, 0xc1069cd4eabe89f8u, 0x999ec0bb696e840au,
+            0xf148440a256e2c76u, 0xc00670ea43ca250du, 0x96cd2a865764dbcau, 0x380406926a5e5728u,
+            0xbc807527ed3e12bcu, 0xc605083704f5ecf2u, 0xeba09271e88d976bu, 0xf7864a44c633682eu,
+            0x93445b8731587ea3u, 0x7ab3ee6afbe0211du, 0xb8157268fdae9e4cu, 0x5960ea05bad82964u,
+            0xe61acf033d1a45dfu, 0x6fb92487298e33bdu, 0x8fd0c16206306babu, 0xa5d3b6d479f8e056u,
+            0xb3c4f1ba87bc8696u, 0x8f48a4899877186cu, 0xe0b62e2929aba83cu, 0x331acdabfe94de87u,
+            0x8c71dcd9ba0b4925u, 0x9ff0c08b7f1d0b14u, 0xaf8e5410288e1b6fu, 0x07ecf0ae5ee44dd9u,
+            0xdb71e91432b1a24au, 0xc9e82cd9f69d6150u, 0x892731ac9faf056eu, 0xbe311c083a225cd2u,
+            0xab70fe17c79ac6cau, 0x6dbd630a48aaf406u, 0xd64d3d9db981787du, 0x092cbbccdad5b108u,
+            0x85f0468293f0eb4eu, 0x25bbf56008c58ea5u, 0xa76c582338ed2621u, 0xaf2af2b80af6f24eu,
+            0xd1476e2c07286faau, 0x1af5af660db4aee1u, 0x82cca4db847945cau, 0x50d98d9fc890ed4du,
+            0xa37fce126597973cu, 0xe50ff107bab528a0u, 0xcc5fc196fefd7d0cu, 0x1e53ed49a96272c8u,
+            0xff77b1fcbebcdc4fu, 0x25e8e89c13bb0f7au, 0x9faacf3df73609b1u, 0x77b191618c54e9acu,
+            0xc795830d75038c1du, 0xd59df5b9ef6a2417u, 0xf97ae3d0d2446f25u, 0x4b0573286b44ad1du,
+            0x9becce62836ac577u, 0x4ee367f9430aec32u, 0xc2e801fb244576d5u, 0x229c41f793cda73fu,
+            0xf3a20279ed56d48au, 0x6b43527578c1110fu, 0x9845418c345644d6u, 0x830a13896b78aaa9u,
+            0xbe5691ef416bd60cu, 0x23cc986bc656d553u, 0xedec366b11c6cb8fu, 0x2cbfbe86b7ec8aa8u,
+            0x94b3a202eb1c3f39u, 0x7bf7d71432f3d6a9u, 0xb9e08a83a5e34f07u, 0xdaf5ccd93fb0cc53u,
+            0xe858ad248f5c22c9u, 0xd1b3400f8f9cff68u, 0x91376c36d99995beu, 0x23100809b9c21fa1u,
+            0xb58547448ffffb2du, 0xabd40a0c2832a78au, 0xe2e69915b3fff9f9u, 0x16c90c8f323f516cu,
+            0x8dd01fad907ffc3bu, 0xae3da7d97f6792e3u, 0xb1442798f49ffb4au, 0x99cd11cfdf41779cu,
+            0xdd95317f31c7fa1du, 0x40405643d711d583u, 0x8a7d3eef7f1cfc52u, 0x482835ea666b2572u,
+            0xad1c8eab5ee43b66u, 0xda3243650005eecfu, 0xd863b256369d4a40u, 0x90bed43e40076a82u,
+            0x873e4f75e2224e68u, 0x5a7744a6e804a291u, 0xa90de3535aaae202u, 0x711515d0a205cb36u,
+            0xd3515c2831559a83u, 0x0d5a5b44ca873e03u, 0x8412d9991ed58091u, 0xe858790afe9486c2u,
+            0xa5178fff668ae0b6u, 0x626e974dbe39a872u, 0xce5d73ff402d98e3u, 0xfb0a3d212dc8128fu,
+            0x80fa687f881c7f8eu, 0x7ce66634bc9d0b99u, 0xa139029f6a239f72u, 0x1c1fffc1ebc44e80u,
+            0xc987434744ac874eu, 0xa327ffb266b56220u, 0xfbe9141915d7a922u, 0x4bf1ff9f0062baa8u,
+            0x9d71ac8fada6c9b5u, 0x6f773fc3603db4a9u, 0xc4ce17b399107c22u, 0xcb550fb4384d21d3u,
+            0xf6019da07f549b2bu, 0x7e2a53a146606a48u, 0x99c102844f94e0fbu, 0x2eda7444cbfc426du,
+            0xc0314325637a1939u, 0xfa911155fefb5308u, 0xf03d93eebc589f88u, 0x793555ab7eba27cau,
+            0x96267c7535b763b5u, 0x4bc1558b2f3458deu, 0xbbb01b9283253ca2u, 0x9eb1aaedfb016f16u,
+            0xea9c227723ee8bcbu, 0x465e15a979c1cadcu, 0x92a1958a7675175fu, 0x0bfacd89ec191ec9u,
+            0xb749faed14125d36u, 0xcef980ec671f667bu, 0xe51c79a85916f484u, 0x82b7e12780e7401au,
+            0x8f31cc0937ae58d2u, 0xd1b2ecb8b0908810u, 0xb2fe3f0b8599ef07u, 0x861fa7e6dcb4aa15u,
+            0xdfbdcece67006ac9u, 0x67a791e093e1d49au, 0x8bd6a141006042bdu, 0xe0c8bb2c5c6d24e0u,
+            0xaecc49914078536du, 0x58fae9f773886e18u, 0xda7f5bf590966848u, 0xaf39a475506a899eu,
+            0x888f99797a5e012du, 0x6d8406c952429603u, 0xaab37fd7d8f58178u, 0xc8e5087ba6d33b83u,
+            0xd5605fcdcf32e1d6u, 0xfb1e4a9a90880a64u, 0x855c3be0a17fcd26u, 0x5cf2eea09a55067fu,
+            0xa6b34ad8c9dfc06fu, 0xf42faa48c0ea481eu, 0xd0601d8efc57b08bu, 0xf13b94daf124da26u,
+            0x823c12795db6ce57u, 0x76c53d08d6b70858u, 0xa2cb1717b52481edu, 0x54768c4b0c64ca6eu,
+            0xcb7ddcdda26da268u, 0xa9942f5dcf7dfd09u, 0xfe5d54150b090b02u, 0xd3f93b35435d7c4cu,
+            0x9efa548d26e5a6e1u, 0xc47bc5014a1a6dafu, 0xc6b8e9b0709f109au, 0x359ab6419ca1091bu,
+            0xf867241c8cc6d4c0u, 0xc30163d203c94b62u, 0x9b407691d7fc44f8u, 0x79e0de63425dcf1du,
+            0xc21094364dfb5636u, 0x985915fc12f542e4u, 0xf294b943e17a2bc4u, 0x3e6f5b7b17b2939du,
+            0x979cf3ca6cec5b5au, 0xa705992ceecf9c42u, 0xbd8430bd08277231u, 0x50c6ff782a838353u,
+            0xece53cec4a314ebdu, 0xa4f8bf5635246428u, 0x940f4613ae5ed136u, 0x871b7795e136be99u,
+            0xb913179899f68584u, 0x28e2557b59846e3fu, 0xe757dd7ec07426e5u, 0x331aeada2fe589cfu,
+            0x9096ea6f3848984fu, 0x3ff0d2c85def7621u, 0xb4bca50b065abe63u, 0x0fed077a756b53a9u,
+            0xe1ebce4dc7f16dfbu, 0xd3e8495912c62894u, 0x8d3360f09cf6e4bdu, 0x64712dd7abbbd95cu,
+            0xb080392cc4349decu, 0xbd8d794d96aacfb3u, 0xdca04777f541c567u, 0xecf0d7a0fc5583a0u,
+            0x89e42caaf9491b60u, 0xf41686c49db57244u, 0xac5d37d5b79b6239u, 0x311c2875c522ced5u,
+            0xd77485cb25823ac7u, 0x7d633293366b828bu, 0x86a8d39ef77164bcu, 0xae5dff9c02033197u,
+            0xa8530886b54dbdebu, 0xd9f57f830283fdfcu, 0xd267caa862a12d66u, 0xd072df63c324fd7bu,
+            0x8380dea93da4bc60u, 0x4247cb9e59f71e6du, 0xa46116538d0deb78u, 0x52d9be85f074e608u,
+            0xcd795be870516656u, 0x67902e276c921f8bu, 0x806bd9714632dff6u, 0x00ba1cd8a3db53b6u,
+            0xa086cfcd97bf97f3u, 0x80e8a40eccd228a4u, 0xc8a883c0fdaf7df0u, 0x6122cd128006b2cdu,
+            0xfad2a4b13d1b5d6cu, 0x796b805720085f81u, 0x9cc3a6eec6311a63u, 0xcbe3303674053bb0u,
+            0xc3f490aa77bd60fcu, 0xbedbfc4411068a9cu, 0xf4f1b4d515acb93bu, 0xee92fb5515482d44u,
+            0x991711052d8bf3c5u, 0x751bdd152d4d1c4au, 0xbf5cd54678eef0b6u, 0xd262d45a78a0635du,
+            0xef340a98172aace4u, 0x86fb897116c87c34u, 0x9580869f0e7aac0eu, 0xd45d35e6ae3d4da0u,
+            0xbae0a846d2195712u, 0x8974836059cca109u, 0xe998d258869facd7u, 0x2bd1a438703fc94bu,
+            0x91ff83775423cc06u, 0x7b6306a34627ddcfu, 0xb67f6455292cbf08u, 0x1a3bc84c17b1d542u,
+            0xe41f3d6a7377eecau, 0x20caba5f1d9e4a93u, 0x8e938662882af53eu, 0x547eb47b7282ee9cu,
+            0xb23867fb2a35b28du, 0xe99e619a4f23aa43u, 0xdec681f9f4c31f31u, 0x6405fa00e2ec94d4u,
+            0x8b3c113c38f9f37eu, 0xde83bc408dd3dd04u, 0xae0b158b4738705eu, 0x9624ab50b148d445u,
+            0xd98ddaee19068c76u, 0x3badd624dd9b0957u, 0x87f8a8d4cfa417c9u, 0xe54ca5d70a80e5d6u,
+            0xa9f6d30a038d1dbcu, 0x5e9fcf4ccd211f4cu, 0xd47487cc8470652bu, 0x7647c3200069671fu,
+            0x84c8d4dfd2c63f3bu, 0x29ecd9f40041e073u, 0xa5fb0a17c777cf09u, 0xf468107100525890u,
+            0xcf79cc9db955c2ccu, 0x7182148d4066eeb4u, 0x81ac1fe293d599bfu, 0xc6f14cd848405530u,
+            0xa21727db38cb002fu, 0xb8ada00e5a506a7cu, 0xca9cf1d206fdc03bu, 0xa6d90811f0e4851cu,
+            0xfd442e4688bd304au, 0x908f4a166d1da663u, 0x9e4a9cec15763e2eu, 0x9a598e4e043287feu,
+            0xc5dd44271ad3cdbau, 0x40eff1e1853f29fdu, 0xf7549530e188c128u, 0xd12bee59e68ef47cu,
+            0x9a94dd3e8cf578b9u, 0x82bb74f8301958ceu, 0xc13a148e3032d6e7u, 0xe36a52363c1faf01u,
+            0xf18899b1bc3f8ca1u, 0xdc44e6c3cb279ac1u, 0x96f5600f15a7b7e5u, 0x29ab103a5ef8c0b9u,
+            0xbcb2b812db11a5deu, 0x7415d448f6b6f0e7u, 0xebdf661791d60f56u, 0x111b495b3464ad21u,
+            0x936b9fcebb25c995u, 0xcab10dd900beec34u, 0xb84687c269ef3bfbu, 0x3d5d514f40eea742u,
+            0xe65829b3046b0afau, 0x0cb4a5a3112a5112u, 0x8ff71a0fe2c2e6dcu, 0x47f0e785eaba72abu,
+            0xb3f4e093db73a093u, 0x59ed216765690f56u, 0xe0f218b8d25088b8u, 0x306869c13ec3532cu,
+            0x8c974f7383725573u, 0x1e414218c73a13fbu, 0xafbd2350644eeacfu, 0xe5d1929ef90898fau,
+            0xdbac6c247d62a583u, 0xdf45f746b74abf39u, 0x894bc396ce5da772u, 0x6b8bba8c328eb783u,
+            0xab9eb47c81f5114fu, 0x066ea92f3f326564u, 0xd686619ba27255a2u, 0xc80a537b0efefebdu,
+            0x8613fd0145877585u, 0xbd06742ce95f5f36u, 0xa798fc4196e952e7u, 0x2c48113823b73704u,
+            0xd17f3b51fca3a7a0u, 0xf75a15862ca504c5u, 0x82ef85133de648c4u, 0x9a984d73dbe722fbu,
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+            0x802221226be55a64u, 0xc2494954da2c9789u, 0xa02aa96b06deb0fdu, 0xf2db9baa10b7bd6cu,
+            0xc83553c5c8965d3du, 0x6f92829494e5acc7u, 0xfa42a8b73abbf48cu, 0xcb772339ba1f17f9u,
+            0x9c69a97284b578d7u, 0xff2a760414536efbu, 0xc38413cf25e2d70du, 0xfef5138519684abau,
+            0xf46518c2ef5b8cd1u, 0x7eb258665fc25d69u, 0x98bf2f79d5993802u, 0xef2f773ffbd97a61u,
+            0xbeeefb584aff8603u, 0xaafb550ffacfd8fau, 0xeeaaba2e5dbf6784u, 0x95ba2a53f983cf38u,
+            0x952ab45cfa97a0b2u, 0xdd945a747bf26183u, 0xba756174393d88dfu, 0x94f971119aeef9e4u,
+            0xe912b9d1478ceb17u, 0x7a37cd5601aab85du, 0x91abb422ccb812eeu, 0xac62e055c10ab33au,
+            0xb616a12b7fe617aau, 0x577b986b314d6009u, 0xe39c49765fdf9d94u, 0xed5a7e85fda0b80bu,
+            0x8e41ade9fbebc27du, 0x14588f13be847307u, 0xb1d219647ae6b31cu, 0x596eb2d8ae258fc8u,
+            0xde469fbd99a05fe3u, 0x6fca5f8ed9aef3bbu, 0x8aec23d680043beeu, 0x25de7bb9480d5854u,
+            0xada72ccc20054ae9u, 0xaf561aa79a10ae6au, 0xd910f7ff28069da4u, 0x1b2ba1518094da04u,
+            0x87aa9aff79042286u, 0x90fb44d2f05d0842u, 0xa99541bf57452b28u, 0x353a1607ac744a53u,
+            0xd3fa922f2d1675f2u, 0x42889b8997915ce8u, 0x847c9b5d7c2e09b7u, 0x69956135febada11u,
+            0xa59bc234db398c25u, 0x43fab9837e699095u, 0xcf02b2c21207ef2eu, 0x94f967e45e03f4bbu,
+            0x8161afb94b44f57du, 0x1d1be0eebac278f5u, 0xa1ba1ba79e1632dcu, 0x6462d92a69731732u,
+            0xca28a291859bbf93u, 0x7d7b8f7503cfdcfeu, 0xfcb2cb35e702af78u, 0x5cda735244c3d43eu,
+            0x9defbf01b061adabu, 0x3a0888136afa64a7u, 0xc56baec21c7a1916u, 0x088aaa1845b8fdd0u,
+            0xf6c69a72a3989f5bu, 0x8aad549e57273d45u, 0x9a3c2087a63f6399u, 0x36ac54e2f678864bu,
+            0xc0cb28a98fcf3c7fu, 0x84576a1bb416a7ddu, 0xf0fdf2d3f3c30b9fu, 0x656d44a2a11c51d5u,
+            0x969eb7c47859e743u, 0x9f644ae5a4b1b325u, 0xbc4665b596706114u, 0x873d5d9f0dde1feeu,
+            0xeb57ff22fc0c7959u, 0xa90cb506d155a7eau, 0x9316ff75dd87cbd8u, 0x09a7f12442d588f2u,
+            0xb7dcbf5354e9beceu, 0x0c11ed6d538aeb2fu, 0xe5d3ef282a242e81u, 0x8f1668c8a86da5fau,
+            0x8fa475791a569d10u, 0xf96e017d694487bcu, 0xb38d92d760ec4455u, 0x37c981dcc395a9acu,
+            0xe070f78d3927556au, 0x85bbe253f47b1417u, 0x8c469ab843b89562u, 0x93956d7478ccec8eu,
+            0xaf58416654a6babbu, 0x387ac8d1970027b2u, 0xdb2e51bfe9d0696au, 0x06997b05fcc0319eu,
+            0x88fcf317f22241e2u, 0x441fece3bdf81f03u, 0xab3c2fddeeaad25au, 0xd527e81cad7626c3u,
+            0xd60b3bd56a5586f1u, 0x8a71e223d8d3b074u, 0x85c7056562757456u, 0xf6872d5667844e49u,
+            0xa738c6bebb12d16cu, 0xb428f8ac016561dbu, 0xd106f86e69d785c7u, 0xe13336d701beba52u,
+            0x82a45b450226b39cu, 0xecc0024661173473u, 0xa34d721642b06084u, 0x27f002d7f95d0190u,
+            0xcc20ce9bd35c78a5u, 0x31ec038df7b441f4u, 0xff290242c83396ceu, 0x7e67047175a15271u,
+            0x9f79a169bd203e41u, 0x0f0062c6e984d386u, 0xc75809c42c684dd1u, 0x52c07b78a3e60868u,
+            0xf92e0c3537826145u, 0xa7709a56ccdf8a82u, 0x9bbcc7a142b17ccbu, 0x88a66076400bb691u,
+            0xc2abf989935ddbfeu, 0x6acff893d00ea435u, 0xf356f7ebf83552feu, 0x0583f6b8c4124d43u,
+            0x98165af37b2153deu, 0xc3727a337a8b704au, 0xbe1bf1b059e9a8d6u, 0x744f18c0592e4c5cu,
+            0xeda2ee1c7064130cu, 0x1162def06f79df73u, 0x9485d4d1c63e8be7u, 0x8addcb5645ac2ba8u,
+            0xb9a74a0637ce2ee1u, 0x6d953e2bd7173692u, 0xe8111c87c5c1ba99u, 0xc8fa8db6ccdd0437u,
+            0x910ab1d4db9914a0u, 0x1d9c9892400a22a2u, 0xb54d5e4a127f59c8u, 0x2503beb6d00cab4bu,
+            0xe2a0b5dc971f303au, 0x2e44ae64840fd61du, 0x8da471a9de737e24u, 0x5ceaecfed289e5d2u,
+            0xb10d8e1456105dadu, 0x7425a83e872c5f47u, 0xdd50f1996b947518u, 0xd12f124e28f77719u,
+            0x8a5296ffe33cc92fu, 0x82bd6b70d99aaa6fu, 0xace73cbfdc0bfb7bu, 0x636cc64d1001550bu,
+            0xd8210befd30efa5au, 0x3c47f7e05401aa4eu, 0x8714a775e3e95c78u, 0x65acfaec34810a71u,
+            0xa8d9d1535ce3b396u, 0x7f1839a741a14d0du, 0xd31045a8341ca07cu, 0x1ede48111209a050u,
+            0x83ea2b892091e44du, 0x934aed0aab460432u, 0xa4e4b66b68b65d60u, 0xf81da84d5617853fu,
+            0xce1de40642e3f4b9u, 0x36251260ab9d668eu, 0x80d2ae83e9ce78f3u, 0xc1d72b7c6b426019u,
+            0xa1075a24e4421730u, 0xb24cf65b8612f81fu, 0xc94930ae1d529cfcu, 0xdee033f26797b627u,
+            0xfb9b7cd9a4a7443cu, 0x169840ef017da3b1u, 0x9d412e0806e88aa5u, 0x8e1f289560ee864eu,
+            0xc491798a08a2ad4eu, 0xf1a6f2bab92a27e2u, 0xf5b5d7ec8acb58a2u, 0xae10af696774b1dbu,
+            0x9991a6f3d6bf1765u, 0xacca6da1e0a8ef29u, 0xbff610b0cc6edd3fu, 0x17fd090a58d32af3u,
+            0xeff394dcff8a948eu, 0xddfc4b4cef07f5b0u, 0x95f83d0a1fb69cd9u, 0x4abdaf101564f98eu,
+            0xbb764c4ca7a4440fu, 0x9d6d1ad41abe37f1u, 0xea53df5fd18d5513u, 0x84c86189216dc5edu,
+            0x92746b9be2f8552cu, 0x32fd3cf5b4e49bb4u, 0xb7118682dbb66a77u, 0x3fbc8c33221dc2a1u,
+            0xe4d5e82392a40515u, 0x0fabaf3feaa5334au, 0x8f05b1163ba6832du, 0x29cb4d87f2a7400eu,
+            0xb2c71d5bca9023f8u, 0x743e20e9ef511012u, 0xdf78e4b2bd342cf6u, 0x914da9246b255416u,
+            0x8bab8eefb6409c1au, 0x1ad089b6c2f7548eu, 0xae9672aba3d0c320u, 0xa184ac2473b529b1u,
+            0xda3c0f568cc4f3e8u, 0xc9e5d72d90a2741eu, 0x8865899617fb1871u, 0x7e2fa67c7a658892u,
+            0xaa7eebfb9df9de8du, 0xddbb901b98feeab7u, 0xd51ea6fa85785631u, 0x552a74227f3ea565u,
+            0x8533285c936b35deu, 0xd53a88958f87275fu, 0xa67ff273b8460356u, 0x8a892abaf368f137u,
+            0xd01fef10a657842cu, 0x2d2b7569b0432d85u, 0x8213f56a67f6b29bu, 0x9c3b29620e29fc73u,
+            0xa298f2c501f45f42u, 0x8349f3ba91b47b8fu, 0xcb3f2f7642717713u, 0x241c70a936219a73u,
+            0xfe0efb53d30dd4d7u, 0xed238cd383aa0110u, 0x9ec95d1463e8a506u, 0xf4363804324a40aau,
+            0xc67bb4597ce2ce48u, 0xb143c6053edcd0d5u, 0xf81aa16fdc1b81dau, 0xdd94b7868e94050au,
+            0x9b10a4e5e9913128u, 0xca7cf2b4191c8326u, 0xc1d4ce1f63f57d72u, 0xfd1c2f611f63a3f0u,
+            0xf24a01a73cf2dccfu, 0xbc633b39673c8cecu, 0x976e41088617ca01u, 0xd5be0503e085d813u,
+            0xbd49d14aa79dbc82u, 0x4b2d8644d8a74e18u, 0xec9c459d51852ba2u, 0xddf8e7d60ed1219eu,
+            0x93e1ab8252f33b45u, 0xcabb90e5c942b503u, 0xb8da1662e7b00a17u, 0x3d6a751f3b936243u,
+            0xe7109bfba19c0c9du, 0x0cc512670a783ad4u, 0x906a617d450187e2u, 0x27fb2b80668b24c5u,
+            0xb484f9dc9641e9dau, 0xb1f9f660802dedf6u, 0xe1a63853bbd26451u, 0x5e7873f8a0396973u,
+            0x8d07e33455637eb2u, 0xdb0b487b6423e1e8u, 0xb049dc016abc5e5fu, 0x91ce1a9a3d2cda62u,
+            0xdc5c5301c56b75f7u, 0x7641a140cc7810fbu, 0x89b9b3e11b6329bau, 0xa9e904c87fcb0a9du,
+            0xac2820d9623bf429u, 0x546345fa9fbdcd44u, 0xd732290fbacaf133u, 0xa97c177947ad4095u,
+            0x867f59a9d4bed6c0u, 0x49ed8eabcccc485du, 0xa81f301449ee8c70u, 0x5c68f256bfff5a74u,
+            0xd226fc195c6a2f8cu, 0x73832eec6fff3111u, 0x83585d8fd9c25db7u, 0xc831fd53c5ff7eabu,
+            0xa42e74f3d032f525u, 0xba3e7ca8b77f5e55u, 0xcd3a1230c43fb26fu, 0x28ce1bd2e55f35ebu,
+            0x80444b5e7aa7cf85u, 0x7980d163cf5b81b3u, 0xa0555e361951c366u, 0xd7e105bcc332621fu,
+            0xc86ab5c39fa63440u, 0x8dd9472bf3fefaa7u, 0xfa856334878fc150u, 0xb14f98f6f0feb951u,
+            0x9c935e00d4b9d8d2u, 0x6ed1bf9a569f33d3u, 0xc3b8358109e84f07u, 0x0a862f80ec4700c8u,
+            0xf4a642e14c6262c8u, 0xcd27bb612758c0fau, 0x98e7e9cccfbd7dbdu, 0x8038d51cb897789cu,
+            0xbf21e44003acdd2cu, 0xe0470a63e6bd56c3u, 0xeeea5d5004981478u, 0x1858ccfce06cac74u,
+            0x95527a5202df0ccbu, 0x0f37801e0c43ebc8u, 0xbaa718e68396cffdu, 0xd30560258f54e6bau,
+            0xe950df20247c83fdu, 0x47c6b82ef32a2069u, 0x91d28b7416cdd27eu, 0x4cdc331d57fa5441u,
+            0xb6472e511c81471du, 0xe0133fe4adf8e952u, 0xe3d8f9e563a198e5u, 0x58180fddd97723a6u,
+            0x8e679c2f5e44ff8fu, 0x570f09eaa7ea7648u,
+        }
+    };
+    return table;
+}
+
+}  // namespace detail
+NLOHMANN_JSON_NAMESPACE_END
+
 // #include <nlohmann/detail/macro_scope.hpp>


@@ -8782,6 +9242,233 @@ bool parse_float_from_chars(const char* first, const char* last, FloatType& out)
 #endif
 }

+/// whether the eight bytes of @a v (see read_eight_bytes()) are ASCII digits
+/// (after fast_float's is_made_of_eight_digits_fast)
+inline bool is_eight_digits(std::uint64_t v) noexcept
+{
+    return ((v & 0xF0F0F0F0F0F0F0F0u) | (((v + 0x0606060606060606u) & 0xF0F0F0F0F0F0F0F0u) >> 4u)) == 0x3333333333333333u;
+}
+
+/// the value of the eight ASCII digits in @a v (see read_eight_bytes()), three
+/// multiplications instead of eight (after simdjson and fast_float)
+inline std::uint32_t parse_eight_digits(std::uint64_t v) noexcept
+{
+    v = ((v & 0x0F0F0F0F0F0F0F0Fu) * 2561u) >> 8u;
+    v = ((v & 0x00FF00FF00FF00FFu) * 6553601u) >> 16u;
+    return static_cast<std::uint32_t>(((v & 0x0000FFFF0000FFFFu) * 42949672960001u) >> 32u);
+}
+
+/*!
+@brief the double nearest to w * 10^q (Eisel-Lemire)
+
+The algorithm of Daniel Lemire, "Number Parsing at a Gigabyte per Second"
+(Software: Practice and Experience, 2021), after fast_float's compute_float
+(used under the MIT license). With a 128-bit approximation of 5^q, the product
+is always sufficient to round correctly for w with at most 19 digits (Noble
+Mushtak and Daniel Lemire, "Fast number parsing without fallback", Software:
+Practice and Experience, 2023). Only integer arithmetic is used, so the result
+does not depend on the floating-point environment.
+
+@param[in] q  decimal exponent
+@param[in] w  significand, w != 0
+@return the IEEE-754 bits of the positive result (0 for underflow, infinity
+        for overflow)
+*/
+inline std::uint64_t eisel_lemire(std::int64_t q, std::uint64_t w) noexcept
+{
+    constexpr int mantissa_bits = 52;
+    constexpr std::uint64_t infinity = std::uint64_t{0x7FF} << mantissa_bits;
+    if (q < pow5_128_smallest_power)
+    {
+        return 0;
+    }
+    if (q > pow5_128_largest_power)
+    {
+        return infinity;
+    }
+
+    const int lz = count_leading_zeros(w);
+    w <<= static_cast<unsigned>(lz);
+    const auto index = static_cast<std::size_t>(2 * (q - pow5_128_smallest_power));
+    uint128_parts product = full_multiplication(w, pow5_128()[index]);
+    constexpr std::uint64_t precision_mask = 0xFFFFFFFFFFFFFFFFu >> (mantissa_bits + 3);
+    if ((product.high & precision_mask) == precision_mask)
+    {
+        // the lower bits may carry into the result: use the next 64 bits of 5^q
+        const uint128_parts second = full_multiplication(w, pow5_128()[index + 1]);
+        product.low += second.high;
+        if (second.high > product.low)
+        {
+            ++product.high;
+        }
+    }
+
+    const auto upperbit = static_cast<int>(product.high >> 63u);
+    const int shift = upperbit + 64 - mantissa_bits - 3;
+    std::uint64_t mantissa = product.high >> static_cast<unsigned>(shift);
+    // floor(log2(10^q)) + 63 + 1023, with log2(10) ~ 217706 / 2^16
+    std::int64_t power2 = (((152170 + 65536) * q) >> 16) + 63 + upperbit - lz + 1023;
+
+    if (power2 <= 0) // subnormal
+    {
+        if (-power2 + 1 >= 64)
+        {
+            return 0;
+        }
+        mantissa >>= static_cast<unsigned>(-power2 + 1);
+        mantissa += (mantissa & 1u);
+        mantissa >>= 1u;
+        // rounding up may produce the smallest normal number
+        power2 = (mantissa < (std::uint64_t{1} << mantissa_bits)) ? 0 : 1;
+        return mantissa | (static_cast<std::uint64_t>(power2) << mantissa_bits);
+    }
+
+    // a value exactly between two doubles rounds to even; this can only
+    // happen for small |q|, where 5^q is exact
+    if (product.low <= 1 && q >= -4 && q <= 23 && (mantissa & 3u) == 1
+            && (mantissa << static_cast<unsigned>(shift)) == product.high)
+    {
+        mantissa &= ~std::uint64_t{1};
+    }
+    mantissa += (mantissa & 1u);
+    mantissa >>= 1u;
+    if (mantissa >= (std::uint64_t{2} << mantissa_bits))
+    {
+        mantissa = std::uint64_t{1} << mantissa_bits;
+        ++power2;
+    }
+    mantissa &= ~(std::uint64_t{1} << mantissa_bits);
+    if (power2 >= 0x7FF)
+    {
+        return infinity;
+    }
+    return mantissa | (static_cast<std::uint64_t>(power2) << mantissa_bits);
+}
+
+/*!
+@brief parse a validated float token with the Eisel-Lemire algorithm
+
+The significand is accumulated eight digits at a time where possible. A token
+with more than 19 significant digits is truncated to w; the value then lies
+in [w, w + 1) * 10^q, and it is only returned if both ends round to the same
+double, which covers all but a few such tokens.
+
+@param[in]  first  pointer to the first character of the token
+@param[in]  last   pointer past the last character
+@param[out] out    the correctly rounded value on success (±infinity if it
+                   overflows, like strtod)
+@return true on success; false if strtod must decide
+*/
+inline bool parse_float_eisel_lemire(const char* first, const char* last, double& out) noexcept
+{
+    const char* p = first;
+    const bool negative = (p != last && *p == '-');
+    if (negative)
+    {
+        ++p;
+    }
+
+    std::uint64_t w = 0;
+    int digits = 0; // significant digits in w
+    std::int64_t exponent = 0;
+    bool truncated = false;
+    bool in_fraction = false;
+    for (;;)
+    {
+        // eight digits at a time, as long as they fit into w
+        while (w != 0 && digits <= 19 - 8 && last - p >= 8)
+        {
+            const std::uint64_t v = read_eight_bytes(p);
+            if (!is_eight_digits(v))
+            {
+                break;
+            }
+            w = (w * 100000000u) + parse_eight_digits(v);
+            digits += 8;
+            exponent -= in_fraction ? 8 : 0;
+            p += 8;
+        }
+        if (p == last)
+        {
+            break;
+        }
+        const char c = *p;
+        if (c >= '0' && c <= '9')
+        {
+            if (w == 0 && c == '0')
+            {
+                // leading zeros are not significant, but scale a fraction
+                exponent -= in_fraction ? 1 : 0;
+            }
+            else if (digits < 19)
+            {
+                w = (w * 10u) + static_cast<std::uint64_t>(c - '0');
+                ++digits;
+                exponent -= in_fraction ? 1 : 0;
+            }
+            else
+            {
+                // dropped: the value lies between w and w + 1 (in units of
+                // the last kept digit) unless all dropped digits are zero
+                truncated = truncated || c != '0';
+                exponent += in_fraction ? 0 : 1;
+            }
+            ++p;
+        }
+        else if (c == '.')
+        {
+            in_fraction = true;
+            ++p;
+        }
+        else
+        {
+            break; // 'e' or 'E'
+        }
+    }
+
+    if (p != last)
+    {
+        ++p; // 'e' or 'E'
+        bool exp_negative = false;
+        if (p != last && (*p == '-' || *p == '+'))
+        {
+            exp_negative = (*p == '-');
+            ++p;
+        }
+        std::int64_t exp_value = 0;
+        for (; p != last; ++p)
+        {
+            // saturate: any exponent beyond this under- or overflows anyway
+            if (exp_value < 100000)
+            {
+                exp_value = (exp_value * 10) + (*p - '0');
+            }
+        }
+        exponent += exp_negative ? -exp_value : exp_value;
+    }
+
+    std::uint64_t bits = 0;
+    if (w != 0)
+    {
+        bits = eisel_lemire(exponent, w);
+        if (truncated && (w + 1 == 0 || eisel_lemire(exponent, w + 1) != bits))
+        {
+            return false;
+        }
+    }
+    bits |= negative ? (std::uint64_t{1} << 63u) : 0u;
+    static_assert(sizeof(double) == sizeof(std::uint64_t), "double must have 64 bits");
+    std::memcpy(&out, &bits, sizeof(out));
+    return true;
+}
+
+/// Eisel-Lemire is only implemented for `double`
+template<typename FloatType>
+bool parse_float_eisel_lemire(const char* /*first*/, const char* /*last*/, FloatType& /*out*/) noexcept
+{
+    return false;
+}
+
 /*!
@brief check whether Clinger's fast path can still succeed for a float token

@@ -8840,8 +9527,9 @@ inline bool mantissa_fits_clinger(const char* token, std::size_t decimal_point_p
 /*!
@brief convert a validated float token without the C library, if possible

-Tries std::from_chars (when available) and then Clinger's exact fast path
-(double only), skipping the latter when it cannot succeed.
+Tries std::from_chars (when available), Clinger's exact fast path (double
+only, skipped when it cannot succeed), and the Eisel-Lemire algorithm (double
+only).

@param[in]  first                   pointer to the first character of the token
@param[in]  last                    pointer past the last character
@@ -8864,8 +9552,12 @@ bool convert_float_fast(const char* first, const char* last, std::size_t decimal
    // Skipping a fast path that cannot succeed is lossless and saves a full
    // extra pass over the token's bytes, which otherwise shows up on
    // high-precision inputs such as canada.json
-    return mantissa_fits_clinger(first, decimal_point_position, mantissa_end)
-           && parse_float_fast(first, last, value);
+    if (mantissa_fits_clinger(first, decimal_point_position, mantissa_end)
+            && parse_float_fast(first, last, value))
+    {
+        return true;
+    }
+    return parse_float_eisel_lemire(first, last, value);
 }

 /// std::strtof, std::strtod, or std::strtold, chosen by the type of @a f
@@ -12,10 +12,14 @@
 #include <nlohmann/json.hpp>
 using nlohmann::json;

+#include <array> // array
 #include <cfloat> // FLT_EVAL_METHOD
+#include <cstdint> // uint32_t, uint64_t
 #include <cstdlib> // strtod
+#include <cstring> // memcpy
 #include <sstream> // stringstream
 #include <string> // string
+#include <utility> // pair
 #include <vector> // vector

 namespace
@@ -700,3 +704,612 @@ TEST_CASE("parse_float_fast declines what it cannot convert exactly")
    CHECK_FALSE(fast("1e23", out));
    CHECK_FALSE(fast("1e-23", out));
 }
+
+namespace
+{
+// arbitrary-precision unsigned integers, just enough to recompute the table of
+// powers of five (little-endian 32-bit limbs)
+using big_uint = std::vector<std::uint32_t>;
+
+void big_trim(big_uint& a)
+{
+    while (!a.empty() && a.back() == 0)
+    {
+        a.pop_back();
+    }
+}
+
+big_uint big_from(std::uint64_t high, std::uint64_t low)
+{
+    big_uint a = {static_cast<std::uint32_t>(low), static_cast<std::uint32_t>(low >> 32u),
+                  static_cast<std::uint32_t>(high), static_cast<std::uint32_t>(high >> 32u)
+                 };
+    big_trim(a);
+    return a;
+}
+
+big_uint big_mul(const big_uint& a, const big_uint& b)
+{
+    big_uint r(a.size() + b.size(), 0);
+    for (std::size_t i = 0; i < a.size(); ++i)
+    {
+        std::uint64_t carry = 0;
+        for (std::size_t j = 0; j < b.size(); ++j)
+        {
+            const std::uint64_t t = (static_cast<std::uint64_t>(a[i]) * b[j]) + r[i + j] + carry;
+            r[i + j] = static_cast<std::uint32_t>(t);
+            carry = t >> 32u;
+        }
+        r[i + b.size()] = static_cast<std::uint32_t>(carry);
+    }
+    big_trim(r);
+    return r;
+}
+
+big_uint big_shl(const big_uint& a, std::size_t s)
+{
+    big_uint r(s / 32, 0);
+    std::uint32_t carry = 0;
+    for (const std::uint32_t x : a)
+    {
+        const std::uint64_t t = static_cast<std::uint64_t>(x) << (s % 32);
+        r.push_back(static_cast<std::uint32_t>(t) | carry);
+        carry = static_cast<std::uint32_t>(t >> 32u);
+    }
+    r.push_back(carry);
+    big_trim(r);
+    return r;
+}
+
+// a + 1 (add) or a - 1 (!add, a > 0)
+big_uint big_step(big_uint a, bool add)
+{
+    for (auto& x : a)
+    {
+        const std::uint32_t old = x;
+        x = add ? x + 1 : x - 1;
+        if ((add && x > old) || (!add && x < old))
+        {
+            break;
+        }
+    }
+    if (add && (a.empty() || a.back() == 0))
+    {
+        a.push_back(1);
+    }
+    big_trim(a);
+    return a;
+}
+
+bool big_less_equal(const big_uint& a, const big_uint& b)
+{
+    if (a.size() != b.size())
+    {
+        return a.size() < b.size();
+    }
+    for (std::size_t i = a.size(); i-- > 0;)
+    {
+        if (a[i] != b[i])
+        {
+            return a[i] < b[i];
+        }
+    }
+    return true;
+}
+
+std::size_t big_bit_length(const big_uint& a)
+{
+    std::size_t n = a.size() * 32;
+    for (std::uint32_t top = a.back(); (top & 0x80000000u) == 0; top <<= 1u)
+    {
+        --n;
+    }
+    return n;
+}
+
+std::uint64_t bits_of(double d)
+{
+    std::uint64_t b = 0;
+    std::memcpy(&b, &d, sizeof(b));
+    return b;
+}
+
+bool eisel_lemire(const std::string& s, double& out)
+{
+    return nlohmann::detail::parse_float_eisel_lemire(s.data(), s.data() + s.size(), out);
+}
+
+// significant digits of a token, without trailing zeros
+std::size_t significant_digits(const std::string& s)
+{
+    std::string digits;
+    for (const char c : s)
+    {
+        if (c == 'e' || c == 'E')
+        {
+            break;
+        }
+        if (c >= '0' && c <= '9' && !(digits.empty() && c == '0'))
+        {
+            digits += c;
+        }
+    }
+    while (!digits.empty() && digits.back() == '0')
+    {
+        digits.pop_back();
+    }
+    return digits.size();
+}
+} // namespace
+
+TEST_CASE("Eisel-Lemire float conversion")
+{
+    SECTION("the table of powers of five")
+    {
+        // Recompute every entry the way fast_float's table_generation.py
+        // defines it, using only multiplications and comparisons: for q >= 0
+        // the most significant 128 bits of 5^q; for q < 0 floor(2^b / 5^-q) + 1
+        // for b = z + 127 (q >= -27), or that value for b = 2z + 128 cut to
+        // its most significant 128 bits (q < -27), where z is the bit length
+        // of 5^-q.
+        const auto& table = nlohmann::detail::pow5_128();
+        big_uint power5 = {1};
+        for (std::int64_t q = 0; q <= nlohmann::detail::pow5_128_largest_power; ++q)
+        {
+            const auto index = static_cast<std::size_t>(2 * (q - nlohmann::detail::pow5_128_smallest_power));
+            const big_uint entry = big_from(table[index], table[index + 1]);
+            const std::size_t bits = big_bit_length(power5);
+            if (bits <= 128)
+            {
+                CHECK(entry == big_shl(power5, 128 - bits));
+            }
+            else
+            {
+                // floor(5^q / 2^(bits - 128))
+                CHECK(big_less_equal(big_shl(entry, bits - 128), power5));
+                CHECK_FALSE(big_less_equal(big_shl(big_step(entry, true), bits - 128), power5));
+            }
+            power5 = big_mul(power5, {5});
+        }
+
+        power5 = {5};
+        for (std::int64_t q = -1; q >= nlohmann::detail::pow5_128_smallest_power; --q)
+        {
+            const auto index = static_cast<std::size_t>(2 * (q - nlohmann::detail::pow5_128_smallest_power));
+            const big_uint entry = big_from(table[index], table[index + 1]);
+            CHECK(big_bit_length(entry) == 128);
+            const std::size_t z = big_bit_length(power5);
+            const big_uint two_b = big_shl({1}, q >= -27 ? z + 127 : (2 * z) + 128);
+            // c = floor(2^b / p) + 1, stored as floor(c / 2^s):
+            // (entry * 2^s - 1) * p <= 2^b < ((entry + 1) * 2^s - 1) * p
+            const std::size_t s = q >= -27 ? 0 : z + 1;
+            CHECK(big_less_equal(big_mul(big_step(big_shl(entry, s), false), power5), two_b));
+            CHECK_FALSE(big_less_equal(big_mul(big_step(big_shl(big_step(entry, true), s), false), power5), two_b));
+            power5 = big_mul(power5, {5});
+        }
+    }
+
+    SECTION("128-bit products and leading zeros")
+    {
+        // whichever implementation the compiler gets (with or without a
+        // 128-bit integer type or a builtin)
+        std::uint64_t state = 42;
+        for (int i = 0; i < 10000; ++i)
+        {
+            state ^= state << 13u;
+            state ^= state >> 7u;
+            state ^= state << 17u;
+            const std::uint64_t a = state;
+            const std::uint64_t b = (state * 0x9E3779B97F4A7C15u) >> (i % 64);
+            const auto product = nlohmann::detail::full_multiplication(a, b);
+            CHECK(big_from(product.high, product.low) == big_mul(big_from(0, a), big_from(0, b)));
+
+            const int k = i % 64;
+            const std::uint64_t x = (std::uint64_t{1} << k) | (a & ((std::uint64_t{1} << k) - 1));
+            CHECK(nlohmann::detail::count_leading_zeros(x) == 63 - k);
+        }
+    }
+
+    SECTION("known values")
+    {
+        // Generated with Python, whose float() is correctly rounded:
+        //   cases = [<hard cases>, 2**53 + 2k + 1, 2**54 + 4k + 2, and exact midpoints
+        //            between neighbouring doubles, also 1e-60 above and below them]
+        //   print('{"%s", 0x%016xu},' % (s, struct.unpack('<Q', struct.pack('<d', float(s)))[0]))
+        const std::vector<std::pair<std::string, std::uint64_t>> known =
+        {
+            {"0", 0x0000000000000000u},
+            {"-0", 0x8000000000000000u},
+            {"0.0", 0x0000000000000000u},
+            {"-0.0", 0x8000000000000000u},
+            {"0e5", 0x0000000000000000u},
+            {"0.000e-9", 0x0000000000000000u},
+            {"1", 0x3ff0000000000000u},
+            {"-1", 0xbff0000000000000u},
+            {"0.1", 0x3fb999999999999au},
+            {"0.3", 0x3fd3333333333333u},
+            {"1.5", 0x3ff8000000000000u},
+            {"-2.5e-3", 0xbf647ae147ae147bu},
+            {"1e23", 0x44b52d02c7e14af6u},
+            {"1e22", 0x4480f0cf064dd592u},
+            {"8.98846567431158e307", 0x7fe0000000000000u},
+            {"2.2250738585072011e-308", 0x000fffffffffffffu},
+            {"2.2250738585072012e-308", 0x0010000000000000u},
+            {"2.2250738585072014e-308", 0x0010000000000000u},
+            {"4.9406564584124654e-324", 0x0000000000000001u},
+            {"2.4703282292062327e-324", 0x0000000000000000u},
+            {"2.4703282292062328e-324", 0x0000000000000001u},
+            {"1e-324", 0x0000000000000000u},
+            {"3e-324", 0x0000000000000001u},
+            {"1.7976931348623157e308", 0x7fefffffffffffffu},
+            {"1.7976931348623158e308", 0x7fefffffffffffffu},
+            {"1.7976931348623159e308", 0x7ff0000000000000u},
+            {"1e308", 0x7fe1ccf385ebc8a0u},
+            {"1e309", 0x7ff0000000000000u},
+            {"-1e400", 0xfff0000000000000u},
+            {"1e-400", 0x0000000000000000u},
+            {"9007199254740991", 0x433fffffffffffffu},
+            {"9007199254740992", 0x4340000000000000u},
+            {"9007199254740993", 0x4340000000000000u},
+            {"9007199254740995", 0x4340000000000002u},
+            {"18014398509481986", 0x4350000000000000u},
+            {"18014398509481990", 0x4350000000000002u},
+            {"7.2057594037927933e16", 0x4370000000000000u},
+            {"123456789012345678901234567890", 0x45f8ee90ff6c373eu},
+            {"1.000000000000000111", 0x3ff0000000000000u},
+            {"1.0000000000000001110223", 0x3ff0000000000000u},
+            {"1.00000000000000011102230246251565404236316680908203125", 0x3ff0000000000000u},
+            {"1.00000000000000011102230246251565404236316680908203126", 0x3ff0000000000001u},
+            {"0.00000000000000000000000000000000000000000000000000000000000001", 0x3310747ddddf22a8u},
+            {"100000000000000000000000000000000000000000000", 0x4911efc659cf7d4cu},
+            {"1234567890123456789", 0x43b12210f47de981u},
+            {"12345678901234567890", 0x43e56a95319d63e1u},
+            {"1234567890123456789.5", 0x43b12210f47de981u},
+            {"0.1234567890123456789012345", 0x3fbf9add3746f65fu},
+            {"4.4501477170144023e-308", 0x001fffffffffffffu},
+            {"2.4406961166466664e-309", 0x0001c14ae5310a48u},
+            {"5e-324", 0x0000000000000001u},
+            {"1.0e-307", 0x0031fa182c40c60du},
+            {"179769313486231570814527423731704356798070567525844996598917476803157260780028538760589558632766878171540458953514382464234321326889464182768467546703537516986049910576551282076245490090389328944075868508455133942304583236903222948165808559332123348274797826204144723168738177180919299881250404026184124858368", 0x7fefffffffffffffu},
+            {"4.9e-324", 0x0000000000000001u},
+            {"9007199254740993", 0x4340000000000000u},
+            {"18014398509481986", 0x4350000000000000u},
+            {"9007199254740995", 0x4340000000000002u},
+            {"18014398509481990", 0x4350000000000002u},
+            {"9007199254740997", 0x4340000000000002u},
+            {"18014398509481994", 0x4350000000000002u},
+            {"9007199254740999", 0x4340000000000004u},
+            {"18014398509481998", 0x4350000000000004u},
+            {"9007199254741001", 0x4340000000000004u},
+            {"18014398509482002", 0x4350000000000004u},
+            {"9007199254741003", 0x4340000000000006u},
+            {"18014398509482006", 0x4350000000000006u},
+            {"9007199254741005", 0x4340000000000006u},
+            {"18014398509482010", 0x4350000000000006u},
+            {"9007199254741007", 0x4340000000000008u},
+            {"18014398509482014", 0x4350000000000008u},
+            {"9007199254741009", 0x4340000000000008u},
+            {"18014398509482018", 0x4350000000000008u},
+            {"9007199254741011", 0x434000000000000au},
+            {"18014398509482022", 0x435000000000000au},
+            {"9007199254741013", 0x434000000000000au},
+            {"18014398509482026", 0x435000000000000au},
+            {"9007199254741015", 0x434000000000000cu},
+            {"18014398509482030", 0x435000000000000cu},
+            {"9007199254741017", 0x434000000000000cu},
+            {"18014398509482034", 0x435000000000000cu},
+            {"9007199254741019", 0x434000000000000eu},
+            {"18014398509482038", 0x435000000000000eu},
+            {"9007199254741021", 0x434000000000000eu},
+            {"18014398509482042", 0x435000000000000eu},
+            {"9007199254741023", 0x4340000000000010u},
+            {"18014398509482046", 0x4350000000000010u},
+            {"9007199254741025", 0x4340000000000010u},
+            {"18014398509482050", 0x4350000000000010u},
+            {"9007199254741027", 0x4340000000000012u},
+            {"18014398509482054", 0x4350000000000012u},
+            {"9007199254741029", 0x4340000000000012u},
+            {"18014398509482058", 0x4350000000000012u},
+            {"9007199254741031", 0x4340000000000014u},
+            {"18014398509482062", 0x4350000000000014u},
+            {"9007199254741033", 0x4340000000000014u},
+            {"18014398509482066", 0x4350000000000014u},
+            {"9007199254741035", 0x4340000000000016u},
+            {"18014398509482070", 0x4350000000000016u},
+            {"9007199254741037", 0x4340000000000016u},
+            {"18014398509482074", 0x4350000000000016u},
+            {"9007199254741039", 0x4340000000000018u},
+            {"18014398509482078", 0x4350000000000018u},
+            {"9007199254741041", 0x4340000000000018u},
+            {"18014398509482082", 0x4350000000000018u},
+            {"9007199254741043", 0x434000000000001au},
+            {"18014398509482086", 0x435000000000001au},
+            {"9007199254741045", 0x434000000000001au},
+            {"18014398509482090", 0x435000000000001au},
+            {"9007199254741047", 0x434000000000001cu},
+            {"18014398509482094", 0x435000000000001cu},
+            {"9007199254741049", 0x434000000000001cu},
+            {"18014398509482098", 0x435000000000001cu},
+            {"9007199254741051", 0x434000000000001eu},
+            {"18014398509482102", 0x435000000000001eu},
+            {"9007199254741053", 0x434000000000001eu},
+            {"18014398509482106", 0x435000000000001eu},
+            {"9007199254741055", 0x4340000000000020u},
+            {"18014398509482110", 0x4350000000000020u},
+            {"9007199254741057", 0x4340000000000020u},
+            {"18014398509482114", 0x4350000000000020u},
+            {"9007199254741059", 0x4340000000000022u},
+            {"18014398509482118", 0x4350000000000022u},
+            {"9007199254741061", 0x4340000000000022u},
+            {"18014398509482122", 0x4350000000000022u},
+            {"9007199254741063", 0x4340000000000024u},
+            {"18014398509482126", 0x4350000000000024u},
+            {"9007199254741065", 0x4340000000000024u},
+            {"18014398509482130", 0x4350000000000024u},
+            {"9007199254741067", 0x4340000000000026u},
+            {"18014398509482134", 0x4350000000000026u},
+            {"9007199254741069", 0x4340000000000026u},
+            {"18014398509482138", 0x4350000000000026u},
+            {"9007199254741071", 0x4340000000000028u},
+            {"18014398509482142", 0x4350000000000028u},
+            {"0.00000000000000000142055942108419951085063380808124102279024543292671443374397544090470546507276594638824462890625", 0x3c3a3466f662d406u},
+            {"0.000000000000000001420559421084199510850633808081241022790245432926714433743975440904705465072765946388244628906251", 0x3c3a3466f662d407u},
+            {"0.00000000000000000142055942108419951085063380808124102279024543292671443374397444090470546507276594638824462890625", 0x3c3a3466f662d406u},
+            {"8656.5250079159513916238211095333099365234375", 0x40c0e84333759a94u},
+            {"8656.52500791595139162382110953330993652343751", 0x40c0e84333759a94u},
+            {"8656.525007915951391623821109533309936523437499999999999999999", 0x40c0e84333759a93u},
+            {"13.07696731650454946560557800694368779659271240234375", 0x402a276842967ef0u},
+            {"13.076967316504549465605578006943687796592712402343751", 0x402a276842967ef0u},
+            {"13.07696731650454946560557800694368779659271240234374999999999", 0x402a276842967eefu},
+            {"74708253715391928", 0x437096ac2cc7ee5cu},
+            {"747082537153919281", 0x43a4bc5737f9e9f2u},
+            {"74708253715391927.99999999999999999999999999999999999999999999", 0x437096ac2cc7ee5bu},
+            {"1809802988.27203977108001708984375", 0x41daf7d9bb11691au},
+            {"1809802988.272039771080017089843751", 0x41daf7d9bb11691au},
+            {"1809802988.272039771080017089843749999999999999999999999999999", 0x41daf7d9bb116919u},
+            {"51.390809684186766759239617385901510715484619140625", 0x4049b2060d3e4568u},
+            {"51.3908096841867667592396173859015107154846191406251", 0x4049b2060d3e4569u},
+            {"51.39080968418676675923961738590151071548461914062499999999999", 0x4049b2060d3e4568u},
+            {"9999807412.59738445281982421875", 0x4202a0479da4c772u},
+            {"9999807412.597384452819824218751", 0x4202a0479da4c772u},
+            {"9999807412.597384452819824218749999999999999999999999999999999", 0x4202a0479da4c771u},
+            {"0.00000000023260971767101600534534272272645127367651785021962496102787554264068603515625", 0x3deff83a135dec10u},
+            {"0.000000000232609717671016005345342722726451273676517850219624961027875542640686035156251", 0x3deff83a135dec11u},
+            {"0.00000000023260971767101600534534272272645127367651785021962496102787544264068603515625", 0x3deff83a135dec10u},
+            {"0.000000000497610482021202508216234789619066523902457532813059515319764614105224609375", 0x3e01190730d1ec48u},
+            {"0.0000000004976104820212025082162347896190665239024575328130595153197646141052246093751", 0x3e01190730d1ec48u},
+            {"0.000000000497610482021202508216234789619066523902457532813059515319764514105224609375", 0x3e01190730d1ec47u},
+            {"0.0000000000291336422596533830691676779231223432149733287843673679162748157978057861328125", 0x3dc004321559736eu},
+            {"0.00000000002913364225965338306916767792312234321497332878436736791627481579780578613281251", 0x3dc004321559736fu},
+            {"0.0000000000291336422596533830691676779231223432149733287843673679162748057978057861328125", 0x3dc004321559736eu},
+            {"0.000000000000000039237155154865396441907405399546892080260012902422940561653064150959835387766361236572265625", 0x3c869e61cfa3b8a4u},
+            {"0.0000000000000000392371551548653964419074053995468920802600129024229405616530641509598353877663612365722656251", 0x3c869e61cfa3b8a5u},
+            {"0.000000000000000039237155154865396441907405399546892080260012902422940561653054150959835387766361236572265625", 0x3c869e61cfa3b8a4u},
+            {"0.00000000000000006496592863767266414092845207857846208631635335985395063307379359685000963509082794189453125", 0x3c92b9a3b219ee84u},
+            {"0.000000000000000064965928637672664140928452078578462086316353359853950633073793596850009635090827941894531251", 0x3c92b9a3b219ee85u},
+            {"0.00000000000000006496592863767266414092845207857846208631635335985395063307378359685000963509082794189453125", 0x3c92b9a3b219ee84u},
+            {"0.0000000000448169607439179753541822628688597626549217078917308754171244800090789794921875", 0x3dc8a36d2e8094dau},
+            {"0.00000000004481696074391797535418226286885976265492170789173087541712448000907897949218751", 0x3dc8a36d2e8094dau},
+            {"0.0000000000448169607439179753541822628688597626549217078917308754171244700090789794921875", 0x3dc8a36d2e8094d9u},
+            {"1800873890234250.875", 0x4319978a820cfe2cu},
+            {"1800873890234250.8751", 0x4319978a820cfe2cu},
+            {"1800873890234250.874999999999999999999999999999999999999999999", 0x4319978a820cfe2bu},
+            {"0.000023941132739153309216405436654628857695570331998169422149658203125", 0x3ef91aa61d42e0e0u},
+            {"0.0000239411327391533092164054366546288576955703319981694221496582031251", 0x3ef91aa61d42e0e1u},
+            {"0.000023941132739153309216405436654628857695570331998169422149658193125", 0x3ef91aa61d42e0e0u},
+            {"8339818978785937.5", 0x433da1056bb8ba92u},
+            {"8339818978785937.51", 0x433da1056bb8ba92u},
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+            {"283649145986385328", 0x438f7dcb29dae42eu},
+            {"2836491459863853281", 0x43c3ae9efa28ce9cu},
+            {"283649145986385327.9999999999999999999999999999999999999999999", 0x438f7dcb29dae42du},
+            {"0.0000000000000000004203729478287971874304476341685497759528753070014375965192388040492232903488911688327789306640625", 0x3c1f049ed78cb8a2u},
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+            {"0.00000000000000068304843500200357021582520000166071595321259251644419041582513277611471712589263916015625", 0x3cc89c02848f8654u},
+            {"0.00000000147705080029041786940146712084494760863773166192913777194917201995849609375", 0x3e1960235bc34d06u},
+            {"0.000000001477050800290417869401467120844947608637731661929137771949172019958496093751", 0x3e1960235bc34d06u},
+            {"0.00000000147705080029041786940146712084494760863773166192913777194917101995849609375", 0x3e1960235bc34d05u},
+            {"2164972979236447104", 0x43be0b87743fb524u},
+            {"21649729792364471041", 0x43f2c734a8a7d136u},
+            {"2164972979236447103.999999999999999999999999999999999999999999", 0x43be0b87743fb523u},
+            {"13124633159586767", 0x4347506464a469e8u},
+            {"131246331595867671", 0x437d247d7dcd8461u},
+            {"13124633159586766.99999999999999999999999999999999999999999999", 0x4347506464a469e7u},
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+            {"0.01727792833395616796388072344825559412129223346710205078125", 0x3f91b14e248c42c8u},
+            {"0.017277928333956167963880723448255594121292233467102050781251", 0x3f91b14e248c42c9u},
+            {"0.01727792833395616796388072344825559412129223346710205078124999", 0x3f91b14e248c42c8u},
+            {"0.00000000000003096211381890547702500862566064822950373937142376501441276559489779174327850341796875", 0x3d216e1c61130b22u},
+            {"0.000000000000030962113818905477025008625660648229503739371423765014412765594897791743278503417968751", 0x3d216e1c61130b22u},
+            {"0.00000000000003096211381890547702500862566064822950373937142376501441276558489779174327850341796875", 0x3d216e1c61130b21u},
+            {"0.0000000000000683414954481284270259359974108983284531919182025472281338807079009711742401123046875", 0x3d333c86137e5170u},
+            {"0.00000000000006834149544812842702593599741089832845319191820254722813388070790097117424011230468751", 0x3d333c86137e5170u},
+            {"0.0000000000000683414954481284270259359974108983284531919182025472281338806979009711742401123046875", 0x3d333c86137e516fu},
+            {"3237539054990129.75", 0x4327010c9aa36664u},
+            {"3237539054990129.751", 0x4327010c9aa36664u},
+            {"3237539054990129.749999999999999999999999999999999999999999999", 0x4327010c9aa36663u},
+            {"0.0000000000000105429301486355911969397173440055240907798901443814809653076736140064895153045654296875", 0x3d07bd95dfb8a1eeu},
+            {"0.00000000000001054293014863559119693971734400552409077989014438148096530767361400648951530456542968751", 0x3d07bd95dfb8a1eeu},
+            {"0.0000000000000105429301486355911969397173440055240907798901443814809653076636140064895153045654296875", 0x3d07bd95dfb8a1edu},
+            {"9460.2061893763575426419265568256378173828125", 0x40c27a1a6469da1eu},
+            {"9460.20618937635754264192655682563781738281251", 0x40c27a1a6469da1fu},
+            {"9460.206189376357542641926556825637817382812499999999999999999", 0x40c27a1a6469da1eu},
+            {"465000373656610.53125", 0x42fa6ea56179c228u},
+            {"465000373656610.531251", 0x42fa6ea56179c229u},
+            {"465000373656610.5312499999999999999999999999999999999999999999", 0x42fa6ea56179c228u},
+            {"0.000000000107709773707743713401260815383950956818093214195641849073581397533416748046875", 0x3ddd9b66c974bb14u},
+            {"0.0000000001077097737077437134012608153839509568180932141956418490735813975334167480468751", 0x3ddd9b66c974bb14u},
+            {"0.000000000107709773707743713401260815383950956818093214195641849073581297533416748046875", 0x3ddd9b66c974bb13u},
+            {"0.012083347821554271152300064073870089487172663211822509765625", 0x3f88bf277dc215f4u},
+            {"0.0120833478215542711523000640738700894871726632118225097656251", 0x3f88bf277dc215f5u},
+            {"0.01208334782155427115230006407387008948717266321182250976562499", 0x3f88bf277dc215f4u},
+            {"2309804058391724800", 0x43c0070946d098e2u},
+            {"23098040583917248001", 0x43f408cb9884bf1au},
+            {"2309804058391724799.999999999999999999999999999999999999999999", 0x43c0070946d098e1u},
+            {"0.000000000078286047058220682019445698291671103911937290575906445155851542949676513671875", 0x3dd584e40ca80638u},
+            {"0.0000000000782860470582206820194456982916711039119372905759064451558515429496765136718751", 0x3dd584e40ca80638u},
+            {"0.000000000078286047058220682019445698291671103911937290575906445155851532949676513671875", 0x3dd584e40ca80637u},
+            {"2940024994425.709228515625", 0x4285643929d3cdacu},
+            {"2940024994425.7092285156251", 0x4285643929d3cdadu},
+            {"2940024994425.709228515624999999999999999999999999999999999999", 0x4285643929d3cdacu},
+            {"9503358.427352792583405971527099609375", 0x4162204fcdacdfc4u},
+            {"9503358.4273527925834059715270996093751", 0x4162204fcdacdfc4u},
+            {"9503358.427352792583405971527099609374999999999999999999999999", 0x4162204fcdacdfc3u},
+            {"0.00005589147834433423614399101542193903924271580763161182403564453125", 0x3f0d4da092aa5d6au},
+            {"0.000055891478344334236143991015421939039242715807631611824035644531251", 0x3f0d4da092aa5d6bu},
+            {"0.00005589147834433423614399101542193903924271580763161182403564452125", 0x3f0d4da092aa5d6au},
+            {"0.0000000164797038506435664295103900420409737126448135313694365322589874267578125", 0x3e51b1e8107bd640u},
+            {"0.00000001647970385064356642951039004204097371264481353136943653225898742675781251", 0x3e51b1e8107bd641u},
+            {"0.0000000164797038506435664295103900420409737126448135313694365322589774267578125", 0x3e51b1e8107bd640u},
+            {"73055.7873927834807545877993106842041015625", 0x40f1d5fc99292ce2u},
+            {"73055.78739278348075458779931068420410156251", 0x40f1d5fc99292ce3u},
+            {"73055.78739278348075458779931068420410156249999999999999999999", 0x40f1d5fc99292ce2u},
+            {"0.00000000002558172364455232122427880575336067736115508441940846751094795763492584228515625", 0x3dbc209d7509115au},
+            {"0.000000000025581723644552321224278805753360677361155084419408467510947957634925842285156251", 0x3dbc209d7509115bu},
+            {"0.00000000002558172364455232122427880575336067736115508441940846751094794763492584228515625", 0x3dbc209d7509115au},
+            {"0.000000000854497507560657937804791333430312443020238077906469698064029216766357421875", 0x3e0d5c3d540cc0d2u},
+            {"0.0000000008544975075606579378047913334303124430202380779064696980640292167663574218751", 0x3e0d5c3d540cc0d2u},
+            {"0.000000000854497507560657937804791333430312443020238077906469698064029116766357421875", 0x3e0d5c3d540cc0d1u},
+            {"26671499731071461376", 0x43f722433b19970eu},
+            {"266714997310714613761", 0x442cead409dffcd2u},
+            {"26671499731071461375.99999999999999999999999999999999999999999", 0x43f722433b19970eu},
+            {"0.0000000002725195963972150049060368088050545186395989816219298518262803554534912109375", 0x3df2ba37271cf5f2u},
+            {"0.00000000027251959639721500490603680880505451863959898162192985182628035545349121093751", 0x3df2ba37271cf5f2u},
+            {"0.0000000002725195963972150049060368088050545186395989816219298518262802554534912109375", 0x3df2ba37271cf5f1u},
+            {"0.0000000000377224663702246439557904325637937886957218314165629635681398212909698486328125", 0x3dc4bcf7157af68eu},
+            {"0.00000000003772246637022464395579043256379378869572183141656296356813982129096984863281251", 0x3dc4bcf7157af68fu},
+            {"0.0000000000377224663702246439557904325637937886957218314165629635681398112909698486328125", 0x3dc4bcf7157af68eu},
+            {"0.00000000000000009977342762593364154535842258994910996905560208471673566688053824691451154649257659912109375", 0x3c9cc1fac312e2a6u},
+            {"0.000000000000000099773427625933641545358422589949109969055602084716735666880538246914511546492576599121093751", 0x3c9cc1fac312e2a6u},
+            {"0.00000000000000009977342762593364154535842258994910996905560208471673566688052824691451154649257659912109375", 0x3c9cc1fac312e2a5u},
+            {"0.0000000003146248171139977444431948290159907662133509376189977047033607959747314453125", 0x3df59ef03588a228u},
+            {"0.00000000031462481711399774444319482901599076621335093761899770470336079597473144531251", 0x3df59ef03588a229u},
+            {"0.0000000003146248171139977444431948290159907662133509376189977047033606959747314453125", 0x3df59ef03588a228u},
+            {"488899209263030304", 0x439b23acf64c5e80u},
+            {"4888992092630303041", 0x43d0f64c19efbb10u},
+            {"488899209263030303.9999999999999999999999999999999999999999999", 0x439b23acf64c5e80u},
+            {"1.88357157350592807620870416940306313335895538330078125", 0x3ffe231bf23e21acu},
+            {"1.883571573505928076208704169403063133358955383300781251", 0x3ffe231bf23e21adu},
+            {"1.883571573505928076208704169403063133358955383300781249999999", 0x3ffe231bf23e21acu},
+            {"0.0000000216458400594294836451424756990254139044083103726734407246112823486328125", 0x3e573df694e72fb8u},
+            {"0.00000002164584005942948364514247569902541390440831037267344072461128234863281251", 0x3e573df694e72fb9u},
+            {"0.0000000216458400594294836451424756990254139044083103726734407246112723486328125", 0x3e573df694e72fb8u},
+            {"5107.79271041116453488939441740512847900390625", 0x40b3f3caef11cb26u},
+            {"5107.792710411164534889394417405128479003906251", 0x40b3f3caef11cb27u},
+            {"5107.792710411164534889394417405128479003906249999999999999999", 0x40b3f3caef11cb26u},
+            {"734059.8035226609208621084690093994140625", 0x412666d79b67527cu},
+            {"734059.80352266092086210846900939941406251", 0x412666d79b67527du},
+            {"734059.8035226609208621084690093994140624999999999999999999999", 0x412666d79b67527cu},
+            {"61431562016722684", 0x436b47f5c40021e0u},
+            {"614315620167226841", 0x43a10cf99a80152cu},
+            {"61431562016722683.99999999999999999999999999999999999999999999", 0x436b47f5c40021dfu},
+            {"2.0060840449445034305853141631814651191234588623046875", 0x40000c75cab08326u},
+            {"2.00608404494450343058531416318146511912345886230468751", 0x40000c75cab08326u},
+            {"2.006084044944503430585314163181465119123458862304687499999999", 0x40000c75cab08325u},
+            {"0.0000001760623599453036952716420489480075861621344301966018974781036376953125", 0x3e87a174e55262cau},
+            {"0.00000017606235994530369527164204894800758616213443019660189747810363769531251", 0x3e87a174e55262cbu},
+            {"0.0000001760623599453036952716420489480075861621344301966018974781035376953125", 0x3e87a174e55262cau},
+            {"0.833085849636964581588216560703585855662822723388671875", 0x3feaa8a3a7de6fb6u},
+            {"0.8330858496369645815882165607035858556628227233886718751", 0x3feaa8a3a7de6fb6u},
+            {"0.8330858496369645815882165607035858556628227233886718749999999", 0x3feaa8a3a7de6fb5u},
+            {"45031428.4182307310402393341064453125", 0x418579002358895au},
+            {"45031428.41823073104023933410644531251", 0x418579002358895bu},
+            {"45031428.41823073104023933410644531249999999999999999999999999", 0x418579002358895au},
+            {"5003361733758455296", 0x43d15be0bf39dd24u},
+            {"50033617337584552961", 0x4405b2d8ef08546cu},
+            {"5003361733758455295.999999999999999999999999999999999999999999", 0x43d15be0bf39dd23u},
+        };
+
+        for (const auto& c : known)
+        {
+            CAPTURE(c.first);
+            double out = 0;
+            if (eisel_lemire(c.first, out))
+            {
+                CHECK(bits_of(out) == c.second);
+            }
+            else
+            {
+                // only tokens with more than 19 significant digits are left to
+                // strtod: those whose value lies too close to a tie
+                CHECK(significant_digits(c.first) > 19);
+            }
+        }
+    }
+
+    SECTION("round trip")
+    {
+        // every double written by to_chars and read back, also with trailing
+        // digits that make the token longer than 19 digits
+        std::uint64_t state = 5295;
+        std::size_t declined = 0;
+        for (int i = 0; i < 200000; ++i)
+        {
+            state ^= state << 13u;
+            state ^= state >> 7u;
+            state ^= state << 17u;
+            std::uint64_t b = state;
+            if ((b & 0x7FF0000000000000u) == 0x7FF0000000000000u)
+            {
+                continue; // infinity or NaN
+            }
+            if (i % 4 == 0)
+            {
+                b &= 0x800FFFFFFFFFFFFFu; // subnormals
+            }
+            double d = 0;
+            std::memcpy(&d, &b, sizeof(d));
+
+            std::array<char, 64> buffer{};
+            const char* end = nlohmann::detail::to_chars(buffer.data(), buffer.data() + buffer.size(), d);
+            const std::string token(buffer.data(), static_cast<std::size_t>(end - buffer.data()));
+            CAPTURE(token);
+            double out = 0;
+            REQUIRE(eisel_lemire(token, out));
+            CHECK(bits_of(out) == b);
+
+            // insert digits before the exponent: the value moves by far less
+            // than the distance to the rounding boundary, so it must not change
+            std::string longer = token;
+            const std::size_t e = longer.find('e');
+            const std::string extra = longer.find('.') == std::string::npos ? ".000000000000000000001" : "000000000000000000001";
+            longer.insert(e == std::string::npos ? longer.size() : e, extra);
+            CAPTURE(longer);
+            if (eisel_lemire(longer, out))
+            {
+                CHECK(bits_of(out) == b);
+            }
+            else
+            {
+                // w and w + 1 round differently: only when the value is very
+                // close to a rounding boundary
+                ++declined;
+            }
+        }
+        CHECK(declined < 1000); // 107 of the 200,000
+    }
+
+    SECTION("used by the lexer")
+    {
+        // 17 significant digits: beyond Clinger's fast path
+        CHECK(bits_of(json::parse("-65.613616999999977").get<double>()) == bits_of(-65.613616999999977));
+        CHECK(bits_of(json::parse("2.2250738585072011e-308").get<double>()) == 0x000FFFFFFFFFFFFFu);
+        CHECK(bits_of(json::parse("4.9406564584124654e-324").get<double>()) == 1u);
+        CHECK_THROWS_WITH_AS(json::parse("1.7976931348623159e308"),
+                             "[json.exception.out_of_range.406] number overflow parsing '1.7976931348623159e308'", json::out_of_range&);
+    }
+}