json_view: dump canada.json faster than yyjson (batched float decisions)

Dump of float tokens of 16 or 17 digits without an exponent (SIMD targets,
little-endian), in batches of up to 256 floats ahead of the walk, one loop
per step:
- the digits (16 bytes at a time) and the token's last four digits;
- locate_token(): Eisel-Lemire's product gives the double x, and x's position
  relative to the token is exact in a 64-bit fixed-point number (56 bits after
  the point of the token's last digit), with the radius of its interval;
- token_digits_1/2(), one loop per kind (g): the multiple of 10^g nearest to x
  if it is in the interval, else the multiple of 10^(g - 1) nearest to x, the
  digits that dump() (Zmij) writes. Exact ties between two candidates (like
  754570942.33984373, whose double is ...33984375) are left to the full
  conversion;
- the output is the token with its last four digits replaced; a rounding that
  carries further goes to the writer of Zmij's results.
The batch storage is on the heap (allocated by the first conversion), and a
pair of floats like [x, y] in a read-only document is written without a
frame. Reading: get<double>() converts such tokens with a lean Eisel-Lemire
(coordinate_float()).

Output is byte-identical to the previous writer: 10^9 generated tokens in one
array and 3 * 10^8 in arrays of 1 to 9 elements on Apple M1, 2.5 * 10^8 and
10^8 on x86-64 (all exponents, subnormals, 15-18 digits, exact binary
fractions and ties, near-short decimals); get<double>() equals json::parse
on 5 * 10^7 values.

compare.py --download, Apple M1 Max, clang 21, 30 rounds, two runs (and two
with aligned code: -falign-loops=64 -mllvm -align-all-functions=6); json_view,
and the factor of yyjson 0.13.0 over it:
- canada dump      3636 -> 1623 us (0.47x -> 1.06x; aligned 1.05x)
- canada traverse  2287 -> 1817 us (0.85x -> 1.07x; aligned 0.99x)
- canada patch     4628 -> 2735 us (0.80x -> 1.36x)
- canada update    4763 -> 2911 us (0.78x -> 1.28x)
Linux x86-64 (Haswell VPS, GCC 13, one run): canada dump 0.53x -> 0.72x,
traverse 0.89x -> 0.95x, patch 1.01x -> 1.17x, update 0.96x -> 1.13x.

Open: canada traverse in the aligned build (0.99x) and canada dump on x86-64
(0.72x) are still behind yyjson. Canada parse and select are about 2 % slower
in bench_view in both builds, with identical parser code (likely layout; the
corpus parse row is not slower). In the plain build only, rpc, status, and
twitter dump are 2-4 % slower (0-6 % faster in the aligned build).

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

include/nlohmann/detail/view/number.hpp

@@ -19,6 +19,7 @@
 #include <nlohmann/detail/view/macro_scope.hpp>
 #include <nlohmann/detail/view/node.hpp>
 #include <nlohmann/detail/view/scan.hpp>
+#include <nlohmann/detail/view/simd.hpp>
 
 NLOHMANN_JSON_NAMESPACE_BEGIN
 namespace detail
@@ -103,12 +104,56 @@ NLOHMANN_VIEW_NOINLINE FloatType float_value(const char* first, const node& n)
     return convert_float<FloatType>(first, last, dot, mantissa_end);
 }
 
+#if NLOHMANN_VIEW_VECTOR
+/*!
+@brief the value of the first 16 digits of a run of digits with a point after
+int_digits of them (or none, if int_digits >= 16)
+
+The 17 bytes at p are read at once: the bytes after the point move down by one,
+then pairs, quadruples, and octets of digits are combined by multiplications
+(after simdjson). The bytes [p, p + 32) must be readable. Bytes that are not
+digits (only in a damaged image loaded with image_check::bounds) give a wrong
+value, but no undefined behavior.
+*/
+NLOHMANN_VIEW_ALWAYS_INLINE std::uint64_t sixteen_digits(const unsigned char* p, unsigned int_digits) noexcept
+{
+#if NLOHMANN_VIEW_NEON
+    const uint8x16_t low = vld1q_u8(p);
+    const uint8x16_t index = vcombine_u8(vcreate_u8(0x0706050403020100u), vcreate_u8(0x0F0E0D0C0B0A0908u));
+    const uint8x16_t before_point = vcltq_u8(index, vdupq_n_u8(static_cast<std::uint8_t>(int_digits)));
+    const uint8x16_t digits = vsubq_u8(vbslq_u8(before_point, low, vextq_u8(low, vld1q_u8(p + 16), 1)), vdupq_n_u8('0'));
+    const uint16x8_t twos = vpaddlq_u8(vmulq_u8(digits, vreinterpretq_u8_u16(vdupq_n_u16(0x010A))));
+    const uint32x4_t fours = vpaddlq_u16(vmulq_u16(twos, vreinterpretq_u16_u32(vdupq_n_u32(0x00010064))));
+    const uint64x2_t eights = vpaddlq_u32(vmulq_u32(fours, vreinterpretq_u32_u64(vdupq_n_u64(0x0000000100002710u))));
+    return (vgetq_lane_u64(eights, 0) * 100000000u) + vgetq_lane_u64(eights, 1);
+#else
+    // NOLINTBEGIN(portability-simd-intrinsics)
+    const __m128i low = _mm_loadu_si128(static_cast<const __m128i*>(static_cast<const void*>(p))); // NOLINT(bugprone-casting-through-void)
+    const __m128i high = _mm_loadu_si128(static_cast<const __m128i*>(static_cast<const void*>(p + 16))); // NOLINT(bugprone-casting-through-void)
+    const __m128i before_point = _mm_cmpgt_epi8(_mm_set1_epi8(static_cast<char>(int_digits)), _mm_setr_epi8(0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15));
+    const __m128i moved = _mm_or_si128(_mm_srli_si128(low, 1), _mm_slli_si128(high, 15));
+    const __m128i digits = _mm_sub_epi8(_mm_or_si128(_mm_and_si128(before_point, low), _mm_andnot_si128(before_point, moved)), _mm_set1_epi8('0'));
+    // (16-bit lanes: SSE2 has no multiply-add of bytes)
+    const __m128i tens = _mm_setr_epi16(10, 1, 10, 1, 10, 1, 10, 1);
+    const __m128i twos = _mm_packs_epi32(_mm_madd_epi16(_mm_unpacklo_epi8(digits, _mm_setzero_si128()), tens),
+                                         _mm_madd_epi16(_mm_unpackhi_epi8(digits, _mm_setzero_si128()), tens));
+    const __m128i fours = _mm_madd_epi16(twos, _mm_setr_epi16(100, 1, 100, 1, 100, 1, 100, 1));
+    const __m128i eights = _mm_madd_epi16(_mm_packs_epi32(fours, fours), _mm_setr_epi16(10000, 1, 10000, 1, 10000, 1, 10000, 1));
+    const auto upper = static_cast<std::uint32_t>(_mm_cvtsi128_si32(eights));
+    const auto lower = static_cast<std::uint32_t>(_mm_cvtsi128_si32(_mm_srli_si128(eights, 4)));
+    // NOLINTEND(portability-simd-intrinsics)
+    return (std::uint64_t{upper} * 100000000u) + lower;
+#endif
+}
+#endif
+
 /*!
 @brief the digits of a float token with at most 19 digits, from its layout
 
 The digit layout recorded while parsing says where the integer digits, the
 fraction digits, and the exponent are, so the digits are read eight at a
-time without scanning.
+time without scanning (with SIMD, a token of 16 to 19 digits sixteen at a
+time).
 
 @param[in] p  first character of the token
 @param[in] e  end of the token
@@ -118,15 +163,34 @@ NLOHMANN_VIEW_ALWAYS_INLINE float_significand layout_decimal(const unsigned char
 {
     const bool negative = *p == '-';
     p += negative ? 1 : 0;
-    std::uint64_t w = parse_upto19(p, int_digits, limit);
+    std::uint64_t w = 0;
-    p += int_digits;
     std::int64_t q = 0;
-    if (frac_digits != 0)
+#if NLOHMANN_VIEW_VECTOR
+    const unsigned count = int_digits + frac_digits;
+    if (count >= 16 && limit - p >= 32)
     {
-        w = (w * int_pow10(frac_digits)) + parse_upto19(p + 1, frac_digits, limit);
+        // (the point, if any, follows the integer digits; the digits after
-        p += 1 + frac_digits;
+        // the first 16 are at most three)
+        w = sixteen_digits(p, int_digits);
+        for (unsigned i = 16; i < count; ++i)
+        {
+            w = (w * 10) + static_cast<std::uint64_t>(p[i + (i >= int_digits ? 1 : 0)] - '0');
+        }
+        p += count + (frac_digits != 0 ? 1 : 0);
         q = -static_cast<std::int64_t>(frac_digits);
     }
+    else
+#endif
+    {
+        w = parse_upto19(p, int_digits, limit);
+        p += int_digits;
+        if (frac_digits != 0)
+        {
+            w = (w * int_pow10(frac_digits)) + parse_upto19(p + 1, frac_digits, limit);
+            p += 1 + frac_digits;
+            q = -static_cast<std::int64_t>(frac_digits);
+        }
+    }
     if (p != e)
     {
         // [eE][+-]digits; huge exponents saturate (the parser rejected
@@ -161,12 +225,22 @@ NLOHMANN_VIEW_ALWAYS_INLINE float_significand layout_decimal(const unsigned char
 The result is correctly rounded by the lexer's conversion
 (detail::decimal_to_float(): Clinger's fast path where both operands are
 exact, else the Eisel-Lemire algorithm, which needs no fallback for up to 19
-digits), so it is the value parse() produces.
+digits), so it is the value parse() produces. Tokens of 16 or more digits go
+to Eisel-Lemire directly: the fast path takes few of them (none of 17 digits),
+and its check is a branch that data like GeoJSON coordinates mispredicts.
 */
 template<typename FloatType>
 NLOHMANN_VIEW_ALWAYS_INLINE FloatType layout_float(const unsigned char* p, const unsigned char* e, unsigned int_digits, unsigned frac_digits, const unsigned char* limit) noexcept
 {
-    return decimal_to_float<FloatType>(layout_decimal(p, e, int_digits, frac_digits, limit));
+    const float_significand d = layout_decimal(p, e, int_digits, frac_digits, limit);
+    if (int_digits + frac_digits >= 16)
+    {
+        using format = ieee_binary_format<std::numeric_limits<FloatType>::digits>;
+        native_float_t<FloatType> value{};
+        float_from_bits(eisel_lemire<format>(d.exponent, d.w) | (d.negative ? (std::uint64_t{1} << format::sign_bit()) : 0u), value);
+        return value;
+    }
+    return decimal_to_float<FloatType>(d);
 }
 
 /// the value of a float set by an edit: its token (the shortest round-trip
@@ -185,6 +259,80 @@ NLOHMANN_VIEW_NOINLINE FloatType edited_float(const char* token, const node& n)
     return float_value<FloatType>(token, n);
 }
 
+#if NLOHMANN_VIEW_VECTOR
+/// eisel_lemire() for the token w * 10^q of coordinate_float()
+template<typename Format>
+NLOHMANN_VIEW_ALWAYS_INLINE std::uint64_t coordinate_bits(std::int64_t q, std::uint64_t w, Format /*format*/) noexcept
+{
+    return eisel_lemire<Format>(q, w);
+}
+
+/*!
+@brief (binary64) eisel_lemire() without the cases that tokens of 16 or 17
+digits with 5 or more after the point cannot reach: a value of 0, a
+subnormal, an infinity, or a tie (q < -4)
+*/
+NLOHMANN_VIEW_ALWAYS_INLINE std::uint64_t coordinate_bits(std::int64_t q, std::uint64_t w, ieee_binary_format<53> format) noexcept
+{
+    if (NLOHMANN_VIEW_UNLIKELY(w == 0 || q > -5))
+    {
+        return eisel_lemire<ieee_binary_format<53>>(q, w);
+    }
+    static_cast<void>(format);
+    const int lz = count_leading_zeros(w);
+    const std::uint64_t normalized = w << static_cast<unsigned>(lz);
+    const auto index = static_cast<std::size_t>(2 * (q - pow5_128_smallest_power));
+    const uint128_parts product = full_multiplication(normalized, pow5_128()[index]);
+    std::uint64_t high = product.high;
+    if (NLOHMANN_VIEW_UNLIKELY((high & 0x1FFu) == 0x1FFu))
+    {
+        // (the lower bits may carry into the result)
+        const std::uint64_t second = full_multiplication(normalized, pow5_128()[index + 1]).high;
+        high += product.low + second < product.low ? 1u : 0u;
+    }
+    const auto upperbit = static_cast<unsigned>(high >> 63u);
+    std::uint64_t mantissa = high >> (upperbit + 9);
+    std::uint64_t power2 = static_cast<std::uint64_t>(((217706 * q) >> 16) + 63 + static_cast<std::int64_t>(upperbit) - lz + 1023);
+    mantissa = (mantissa + (mantissa & 1u)) >> 1u;
+    const bool carry = mantissa >= (std::uint64_t{2} << 52u);
+    mantissa = carry ? (std::uint64_t{1} << 52u) : mantissa;
+    power2 += carry ? 1u : 0u;
+    return (mantissa & ~(std::uint64_t{1} << 52u)) | (power2 << 52u);
+}
+
+/*!
+@brief (binary32 and binary64) the value of a float token of the source with
+16 or 17 digits, a point, and no exponent, the shape of most coordinates
+written with full precision; whether the token of n has this shape
+
+These tokens skip the general layout of layout_decimal(): no digits beyond
+the 17th, no exponent (and Eisel-Lemire directly, as in layout_float()).
+*/
+template<typename FloatType>
+NLOHMANN_VIEW_ALWAYS_INLINE bool coordinate_float(const document_data& d, const node& n, FloatType& value) noexcept
+{
+    const unsigned int_digits = n.extra & 0xFFu;
+    const unsigned frac_digits = n.extra >> 8u;
+    const unsigned count = int_digits + frac_digits;
+    const auto* const first = reinterpret_cast<const unsigned char*>(d.src + n.off); // NOLINT(cppcoreguidelines-pro-type-reinterpret-cast)
+    const unsigned negative = first[0] == '-' ? 1u : 0u;
+    if (count - 16u > 1u || frac_digits == 0 || n.len != negative + count + 1 || d.size - n.off < 33)
+    {
+        return false;
+    }
+    const unsigned char* const digits = first + negative;
+    const std::uint64_t w = sixteen_digits(digits, int_digits);
+    // (the 17th digit follows the point)
+    const std::uint64_t w17 = (w * 10) + static_cast<std::uint64_t>(digits[17] - '0');
+    using format = ieee_binary_format<std::numeric_limits<FloatType>::digits>;
+    native_float_t<FloatType> result{};
+    float_from_bits(coordinate_bits(-static_cast<std::int64_t>(frac_digits), count == 17 ? w17 : w, format{}) | (static_cast<std::uint64_t>(negative) << format::sign_bit()), result);
+    value = result;
+    return true;
+}
+
+#endif
+
 /// the value of the float token of a node, as parse() converts it; floats and
 /// doubles with at most 19 digits are converted from the digit layout
 template<typename FloatType>
@@ -200,6 +348,13 @@ FloatType float_value(const document_data& d, const node& n)
 template<typename FloatType>
 FloatType float_value(const document_data& d, const node& n, std::true_type /*binary32 or binary64*/)
 {
+#if NLOHMANN_VIEW_VECTOR
+    FloatType value {};
+    if (coordinate_float(d, n, value))
+    {
+        return value;
+    }
+#endif
     const unsigned int_digits = n.extra & 0xFFu;
     const unsigned frac_digits = n.extra >> 8u;
     if (NLOHMANN_VIEW_LIKELY(int_digits + frac_digits <= 19)) // (255 marks "many")

include/nlohmann/detail/view/serializer.hpp

@@ -14,7 +14,9 @@
 #include <cstddef> // size_t
 #include <cstdint> // uint8_t, uint32_t
 #include <cstring> // memcpy, memset
+#include <functional> // less
 #include <limits> // numeric_limits
+#include <memory> // unique_ptr
 #include <type_traits> // integral_constant
 #include <vector> // vector
 
@@ -384,6 +386,127 @@ struct depth_counter<false>
     }
 };
 
+/*!
+@brief where the double x nearest to a token w * 10^q lies, for 10^15 <= w <
+10^17 and -17 <= q <= -1 (Eisel-Lemire, then a fixed-point position)
+
+dump() writes the shortest decimal in the rounding interval of x (the closest
+one if there are several, see zmij::to_shortest()). Its digits are those of a
+multiple of 10^g of the token's last digit, with g = dec_exp + 1 - q for x's
+decimal exponent dec_exp: the multiple of 10^g nearest to x if it lies in the
+interval (at most one does), else the multiple of 10^(g - 1) nearest to x
+(see token_digits_1() and token_digits_2()). For g <= 0, the token itself is
+in the interval.
+
+The position is exact in a 64-bit fixed-point number with 56 bits after the
+point (of the token's last digit): x / 10^q = 2c * 5^-q / 2^t for x = c * 2^e2
+and t = q + 1 - e2, with at most 56 bits after the point here, and |x / 10^q -
+w| is at most half the spacing of the doubles, below 12 units. So only the low
+64 bits of 2c * 5^-q are needed. c and e2 come from Eisel-Lemire's product
+directly (as eisel_lemire() rounds it: no tie is possible for q < -4, and its
+second product is added where it can carry into the result).
+
+@param[out] offset  x / 10^q - w + 32, with 56 bits after the point
+@param[out] radius  half the spacing of the doubles at x, likewise (+ 1 if
+                    the interval is closed)
+@return g; 3 if the digits are not decided here (a power of two, whose
+        interval is not symmetric, or out of range)
+*/
+NLOHMANN_VIEW_ALWAYS_INLINE int locate_token(std::uint64_t w, int q, std::uint64_t& offset, std::uint64_t& radius) noexcept
+{
+    const int lz = count_leading_zeros(w);
+    const std::uint64_t normalized = w << static_cast<unsigned>(lz);
+    const auto index = static_cast<std::size_t>(2 * (q - pow5_128_smallest_power));
+    const uint128_parts product = full_multiplication(normalized, pow5_128()[index]);
+    std::uint64_t high = product.high;
+    if (NLOHMANN_VIEW_UNLIKELY((high & 0x1FFu) == 0x1FFu))
+    {
+        // (as eisel_lemire(): the lower bits may carry into the result)
+        const std::uint64_t second = full_multiplication(normalized, pow5_128()[index + 1]).high;
+        high += product.low + second < product.low ? 1u : 0u;
+    }
+    const auto upperbit = static_cast<unsigned>(high >> 63u);
+    const std::uint64_t mantissa = high >> (upperbit + 9);
+    const std::uint64_t c = (mantissa + (mantissa & 1u)) >> 1u;
+    // e2 as eisel_lemire() computes the exponent (log2(10) ~ 217706 / 2^16)
+    const int e2 = static_cast<int>((217706 * static_cast<std::int64_t>(q)) >> 16) + 63 + static_cast<int>(upperbit) - lz - 52;
+    const int t = q + 1 - e2;
+    const int g = ((e2 * 315653) >> 20) + 1 - q; // (dec_exp as in zmij::to_shortest(), for a regular x)
+    static const std::array<std::uint64_t, 17> fives = {{1u, 5u, 25u, 125u, 625u, 3125u, 15625u, 78125u, 390625u, 1953125u, 9765625u, 48828125u, 244140625u, 1220703125u, 6103515625u, 30517578125u, 152587890625u}};
+    const std::uint64_t five = fives[static_cast<std::size_t>(-q)]; // 5^-q
+    const unsigned s = static_cast<unsigned>(56 - t) & 63u;
+    offset = ((2 * c * five) << s) - (w << 56u) + (std::uint64_t{32} << 56u);
+    radius = (five << s) + ((c & 1u) == 0 ? 1u : 0u);
+    // (c = 2^52: a power of two; c = 2^53: rounded up to one. With 8 to 16
+    // fraction digits, as the batch's tokens have, t is in [15, 40] and g at
+    // most 2. x lies halfway between two candidates only if its distance from
+    // the token is a whole unit (g == 2) or a half (g == 1): such tokens are
+    // left to the full conversion)
+    const bool decided = c - ((std::uint64_t{1} << 52u) + 1) < (std::uint64_t{1} << 52u) - 1
+                         && (offset & ((std::uint64_t{1} << 55u) - 1)) != 0;
+    return decided ? g : 3;
+}
+
+/// the distance of a position (see locate_token()) from the biased point 32
+NLOHMANN_VIEW_ALWAYS_INLINE std::uint64_t biased_distance(std::uint64_t position) noexcept
+{
+    constexpr std::uint64_t center = std::uint64_t{32} << 56u;
+    return position >= center ? position - center : center - position;
+}
+
+/*!
+@brief (g == 1) the digits dump() writes for a token, from the position of its
+double (see locate_token()): the multiple of 10 nearest to x if it is in the
+interval, else w rounded to x (an exact tie between two candidates, like
+754570942.33984373, whose double is 754570942.33984375, is excluded by
+locate_token())
+
+With |x - w| at most the radius, which is below half the spacing of the
+candidates, the multiple of 10 nearest to x is w - r10 or the one above it.
+*/
+NLOHMANN_VIEW_ALWAYS_INLINE std::uint64_t token_digits_1(std::uint64_t w, std::uint64_t offset, std::uint64_t radius, std::uint64_t r10) noexcept
+{
+    constexpr std::uint64_t one = std::uint64_t{1} << 56u;
+    const std::uint64_t from = offset + (r10 * one); // x - (w - r10) (+ 32)
+    const bool up = from > 37 * one;                  // (nearer to the multiple above)
+    const bool shorter = biased_distance(from - (up ? 10 * one : 0)) < radius;
+    const std::uint64_t a = w - r10 + (up ? 10u : 0u);
+    const std::uint64_t b = w + ((offset + (one / 2)) >> 56u) - 32;                // w rounded to x
+    return shorter ? a : b;
+}
+
+/*!
+@brief (g == 2) the digits dump() writes for a token, as token_digits_1(): the
+multiple of 100 nearest to x if it is in the interval, else the multiple of 10
+nearest to x
+*/
+NLOHMANN_VIEW_ALWAYS_INLINE std::uint64_t token_digits_2(std::uint64_t w, std::uint64_t offset, std::uint64_t radius, std::uint64_t r10, std::uint64_t r100) noexcept
+{
+    constexpr std::uint64_t one = std::uint64_t{1} << 56u;
+    const std::uint64_t from = offset + (r100 * one);
+    const bool up = from > 82 * one;
+    const bool shorter = biased_distance(from - (up ? 100 * one : 0)) < radius;
+    const std::uint64_t a = w - r100 + (up ? 100u : 0u);
+    // x - (w - r10), in [-12, 21]: the multiple of 10 nearest to x is that one,
+    // or one or two above, or one below
+    const std::uint64_t y = offset + (r10 * one);
+    const std::uint64_t steps = (y > 37 * one ? 1u : 0u) + (y > 47 * one ? 1u : 0u);
+    const bool down = y < 27 * one;
+    const std::uint64_t b = w - r10 + (10 * steps) - (down ? 10u : 0u);
+    return shorter ? a : b;
+}
+
+/// the four ASCII digits of x < 10^4, the first in the lowest byte (as
+/// little-endian memory holds them)
+NLOHMANN_VIEW_ALWAYS_INLINE std::uint32_t four_digit_text(std::uint32_t x) noexcept
+{
+    const std::uint32_t ab = (x * 5243u) >> 19u; // x / 100
+    std::uint32_t v = ab | ((x - (ab * 100u)) << 16u);
+    const std::uint32_t a = ((v * 103u) >> 10u) & 0x000F000Fu; // / 10 per 16-bit lane
+    v = a | ((v - (a * 10u)) << 8u);
+    return v + 0x30303030u;
+}
+
 /// how the view's dump() writes a value
 struct dump_style
 {
@@ -711,6 +834,7 @@ class view_serializer
         std::array<frame, 32> buffer; // NOLINT(cppcoreguidelines-pro-type-member-init,hicpp-member-init): written before read
         std::vector<frame> heap;
         small_stack<frame> stack(buffer.data(), buffer.size(), heap);
+        float_batch batch;
         const char* const src = m_doc.src;
         const char* const src_end = src + m_doc.size;
         char* w = m_out.cursor();
@@ -850,7 +974,7 @@ class view_serializer
                     else if (enabled(fast_double::value))
                     {
                         room(64);
-                        w = write_double_at(w, *n);
+                        w = write_double_ahead(w, src, n, batch);
                     }
                     else
                     {
@@ -875,6 +999,20 @@ class view_serializer
                 case value_t::array:
                 {
                     const bool object = n->kind == static_cast<std::uint8_t>(value_t::object);
+                    // (read-only documents, compact output) a pair of floats,
+                    // like the coordinates of GeoJSON, without a frame
+                    if (!Editable && !Pretty && !SourceNumbers && enabled(fast_double::value) && n->next == 3 && n->len == 2
+                            && n[1].kind == static_cast<std::uint8_t>(value_t::number_float) && n[2].kind == static_cast<std::uint8_t>(value_t::number_float))
+                    {
+                        room(2 * 64);
+                        *w++ = '[';
+                        w = write_double_ahead(w, src, n + 1, batch);
+                        *w++ = ',';
+                        w = write_double_ahead(w, src, n + 2, batch);
+                        *w++ = ']';
+                        n += 2; // (the element before the next node)
+                        break;
+                    }
                     room(8);
                     if (n->len == 0)
                     {
@@ -984,6 +1122,247 @@ class view_serializer
         }
     }
 
+    /// (float_batch) the mark of digits whose rounding carried beyond the
+    /// token's last four (see mark())
+    static constexpr std::uint64_t carried() noexcept
+    {
+        return std::uint64_t{1} << 63u;
+    }
+
+    /// floats of 16 or 17 digits ahead of the walk, converted together (see
+    /// convert_ahead()), with their digits as mark() keeps them
+    struct float_batch
+    {
+        static constexpr std::size_t capacity() noexcept
+        {
+            return 256;
+        }
+        /// (on the heap, allocated by the first conversion: a frame of more
+        /// than a page made every dump of a small document slower)
+        struct entries
+        {
+            std::array<const node*, 256> at; // NOLINT(cppcoreguidelines-pro-type-member-init,hicpp-member-init): written before read
+            std::array<std::uint64_t, 256> digits; // NOLINT(cppcoreguidelines-pro-type-member-init,hicpp-member-init): written before read
+        };
+        std::unique_ptr<entries> storage{};
+        const node** at = nullptr;
+        std::uint64_t* digits = nullptr;
+        std::size_t count = 0;
+        std::size_t next = 0;
+        const node* scanned = nullptr; ///< where the last scan of the node array ended
+    };
+
+    /// (doubles) the float at n as dump() writes it, at w (64 bytes of room):
+    /// from the batch if it holds n
+    NLOHMANN_VIEW_ALWAYS_INLINE char* write_double_ahead(char* w, const char* src, const node* n, float_batch& batch)
+    {
+#if NLOHMANN_VIEW_VECTOR && NLOHMANN_VIEW_LITTLE_ENDIAN
+        // (digits 0: not written by the batch; carried(): rounding carried
+        // beyond the last four digits)
+        if (batch.next != batch.count && batch.at[batch.next] == n && batch.digits[batch.next] - 1 < carried() - 1)
+        {
+            return write_token_digits(w, src, *n, batch.digits[batch.next++]);
+        }
+        return write_double_beside(w, n, batch);
+#else
+        static_cast<void>(src);
+        static_cast<void>(batch);
+        return write_double_at(w, *n);
+#endif
+    }
+
+#if NLOHMANN_VIEW_VECTOR && NLOHMANN_VIEW_LITTLE_ENDIAN
+    /// write_double_ahead() for a float that is not the batch's next one (out
+    /// of line: the walk is faster with less code in its loop)
+    NLOHMANN_VIEW_NOINLINE char* write_double_beside(char* w, const node* n, float_batch& batch)
+    {
+        // (an editable document's walk can skip nodes of the array)
+        const std::less<const node*> before;
+        while (batch.next != batch.count && before(batch.at[batch.next], n))
+        {
+            ++batch.next;
+        }
+        if ((batch.next != batch.count && batch.at[batch.next] == n) || convert_ahead(n, batch))
+        {
+            const std::uint64_t digits = batch.digits[batch.next++];
+            if ((digits & carried()) != 0)
+            {
+                return write_carried_digits(w, *n, digits & ~carried());
+            }
+            if (digits != 0)
+            {
+                return write_token_digits(w, m_doc.src, *n, digits);
+            }
+        }
+        return write_double_at(w, *n);
+    }
+
+    /*!
+    @brief convert the floats of 16 or 17 digits among the next nodes of the
+    array at once; whether n is the first of them
+
+    Such tokens (like the coordinates of GeoJSON, written with 17 digits) are
+    written as the token with its last four digits replaced
+    (write_token_digits()). Each step (the digits, locate_token(),
+    token_digits_1/2()) is a long chain of dependent operations; one loop per
+    step over many floats lets the processor overlap the floats, which it does
+    not across the steps of one float (on Apple M1, one loop for the digits and
+    locate_token() made the dump of canada.json 12 % slower). Each node of the array
+    is scanned once; a node that the walk does not reach in order (in an
+    editable document) is written without the batch.
+    */
+    NLOHMANN_VIEW_NOINLINE bool convert_ahead(const node* n, float_batch& batch)
+    {
+        const std::less<const node*> before;
+        const node* const last = m_doc.nodes + m_doc.node_count;
+        if (before(n, batch.scanned) || before(n, m_doc.nodes) || !before(n, last))
+        {
+            return false;
+        }
+        const char* const src = m_doc.src;
+        const char* const src_end = src + m_doc.size;
+        const node* const stop = last - n > 1024 ? n + 1024 : last;
+        batch.count = 0;
+        batch.next = 0;
+        // the digits of each token (and its last four from the text)
+        std::array<std::uint64_t, 256> digits;     // NOLINT(cppcoreguidelines-pro-type-member-init,hicpp-member-init): written before read
+        std::array<int, 256> exponent;             // NOLINT(cppcoreguidelines-pro-type-member-init,hicpp-member-init): written before read
+        std::array<std::uint32_t, 256> last_four;  // NOLINT(cppcoreguidelines-pro-type-member-init,hicpp-member-init): written before read
+        const node* p = n;
+        if (!batch.storage)
+        {
+            batch.storage.reset(new typename float_batch::entries); // NOLINT(cppcoreguidelines-owning-memory,modernize-make-unique): C++11
+            batch.at = batch.storage->at.data();
+            batch.digits = batch.storage->digits.data();
+        }
+        for (; p != stop && batch.count != float_batch::capacity(); ++p)
+        {
+            // a token of the source: 16 or 17 digits, at least 8 after the
+            // point, no exponent, 32 bytes to read
+            const unsigned frac_digits = p->extra >> 8u;
+            const unsigned int_digits = p->extra & 0xFFu;
+            const unsigned count = int_digits + frac_digits;
+            if (p->kind == static_cast<std::uint8_t>(value_t::number_float) && (p->flags & node_flags::storage) == 0
+                    && count - 16u <= 1u && frac_digits >= 8 && src_end - (src + p->off) >= 33)
+            {
+                const auto* const token = reinterpret_cast<const unsigned char*>(src + p->off); // NOLINT(cppcoreguidelines-pro-type-reinterpret-cast)
+                const unsigned sign = token[0] == '-' ? 1 : 0;
+                const unsigned char* const first = token + sign;
+                const std::uint64_t w = sixteen_digits(first, int_digits);
+                // (the 17th digit follows the point; a token with an exponent
+                // gets digits outside the range of locate_token(), and is not
+                // written by the batch. A token 0.xxx with 16 significant
+                // digits is: its double is written as "0." and its digits too)
+                const std::uint64_t w17 = (w * 10) + static_cast<std::uint64_t>(first[17] - '0');
+                const std::size_t i = batch.count++;
+                batch.at[i] = p;
+                digits[i] = p->len != sign + count + 1 ? 0 : (count == 17 ? w17 : w);
+                exponent[i] = -static_cast<int>(frac_digits);
+                // (byte 0: the last digit, byte 1: the last two, bits 16-29: the last four)
+                std::uint32_t four = 0;
+                std::memcpy(&four, token + p->len - 4, 4);
+                four -= 0x30303030u;
+                const std::uint32_t pairs = ((four & 0x0F0F0F0Fu) * 2561u) >> 8u; // (byte 0, 2: the pairs)
+                last_four[i] = (four >> 24u) | ((pairs >> 16u & 0xFFu) << 8u) | ((((pairs & 0x00FF00FFu) * 6553601u) >> 16u) << 16u);
+            }
+        }
+        batch.scanned = p;
+        // the position of each double, and the floats of either kind
+        std::array<std::uint64_t, 256> offset; // NOLINT(cppcoreguidelines-pro-type-member-init,hicpp-member-init): written before read
+        std::array<std::uint64_t, 256> radius; // NOLINT(cppcoreguidelines-pro-type-member-init,hicpp-member-init): written before read
+        std::array<std::uint8_t, 256> kind_1;  // NOLINT(cppcoreguidelines-pro-type-member-init,hicpp-member-init): written before read
+        std::array<std::uint8_t, 256> kind_2;  // NOLINT(cppcoreguidelines-pro-type-member-init,hicpp-member-init): written before read
+        std::size_t count_1 = 0;
+        std::size_t count_2 = 0;
+        for (std::size_t i = 0; i != batch.count; ++i)
+        {
+            const std::uint64_t w = digits[i];
+            // (the range excludes the values of bytes that are not digits, only
+            // in a damaged image loaded with image_check::bounds)
+            const int g = w - 1000000000000000u < 99000000000000000u ? locate_token(w, exponent[i], offset[i], radius[i]) : 3;
+            batch.digits[i] = g <= 0 ? (last_four[i] >> 16u) + 1 : 0;
+            kind_1[count_1] = static_cast<std::uint8_t>(i);
+            count_1 += g == 1 ? 1 : 0;
+            kind_2[count_2] = static_cast<std::uint8_t>(i);
+            count_2 += g == 2 ? 1 : 0;
+        }
+        // the digits to write, in one loop per kind (see mark())
+        for (std::size_t k = 0; k != count_1; ++k)
+        {
+            const std::size_t i = kind_1[k];
+            const std::uint64_t s = token_digits_1(digits[i], offset[i], radius[i], last_four[i] & 0xFFu);
+            batch.digits[i] = mark(digits[i], s, last_four[i] >> 16u);
+        }
+        for (std::size_t k = 0; k != count_2; ++k)
+        {
+            const std::size_t i = kind_2[k];
+            const std::uint64_t s = token_digits_2(digits[i], offset[i], radius[i], last_four[i] & 0xFFu, (last_four[i] >> 8u) & 0xFFu);
+            batch.digits[i] = mark(digits[i], s, last_four[i] >> 16u);
+        }
+        return batch.count != 0 && batch.at[0] == n;
+    }
+
+    /*!
+    @brief a float token of 16 or 17 digits as dump() writes it, at w (64 bytes
+    of room), from the digits of its double (see locate_token()) whose
+    rounding carried beyond the token's last four digits
+
+    (like 43.42027299999999 -> 43.420273): the digits go to the writer of
+    Zmij's results as its 15 or 16 leading digits and one more, which omits
+    the trailing zeros.
+    */
+    NLOHMANN_VIEW_NOINLINE char* write_carried_digits(char* w, const node& n, std::uint64_t digits) const noexcept
+    {
+        const int exponent = -static_cast<int>(n.extra >> 8u);
+        const std::uint64_t leading = digits / 10;
+        const auto last = static_cast<unsigned char>(digits - (leading * 10));
+        const bool seventeen = digits >= 10000000000000000u;
+        *w = '-';
+        w += m_doc.src[n.off] == '-' ? 1 : 0;
+        return ::nlohmann::detail::dtoa_impl::write_shortest(w, seventeen ? ::nlohmann::detail::zmij::shortest_decimal{leading, exponent, last, last != 0}
+                : ::nlohmann::detail::zmij::shortest_decimal{digits, exponent - 1, 0, false});
+    }
+
+    /// the digits s of a token with the digits w and the last four digits
+    /// r4, as the batch keeps them: the new last four digits + 1 (only those
+    /// are written over the token's), or s marked if it differs from w beyond
+    /// them (0 stays for a float the batch does not write)
+    static std::uint64_t mark(std::uint64_t w, std::uint64_t s, std::uint64_t r4) noexcept
+    {
+        const std::uint64_t last = s - (w - r4);
+        return last < 10000 ? last + 1 : s | carried();
+    }
+
+    /*!
+    @brief a float token of 16 or 17 digits as dump() writes it, at w (64 bytes
+    of room): the token with its last four digits replaced by digits - 1 (see
+    mark(); the others are the token's), and without trailing zeros after the
+    point, but one
+    */
+    char* write_token_digits(char* w, const char* src, const node& n, std::uint64_t digits)
+    {
+        const char* const token = src + n.off;
+        std::memcpy(w, token, 32);
+        char* const end = w + n.len;
+        const std::uint32_t last = four_digit_text(static_cast<std::uint32_t>(digits - 1));
+        std::memcpy(end - 4, &last, 4);
+        // (the token's text before the new digits, from the source: reading
+        // the output back would wait for the stores)
+        std::uint64_t before = 0;
+        std::memcpy(&before, token + n.len - 12, 8);
+        const std::uint32_t last_zeros = last ^ 0x30303030u;
+        const std::uint64_t before_zeros = before ^ 0x3030303030303030u;
+        if (NLOHMANN_VIEW_UNLIKELY(last_zeros == 0 && before_zeros == 0))
+        {
+            return write_double_at(w, n); // (twelve or more trailing zeros)
+        }
+        const unsigned zeros = last_zeros != 0 ? static_cast<unsigned>(count_leading_zeros(last_zeros)) / 8 - 4
+                               : 4 + (static_cast<unsigned>(count_leading_zeros(before_zeros)) / 8);
+        const unsigned frac_digits = n.extra >> 8u;
+        return end - (zeros < frac_digits ? zeros : frac_digits - 1);
+    }
+#endif
+
     /// a float node as dump() writes it
     void write_float_node(const node& n)
     {

single_include/nlohmann/json_view.hpp

@@ -4605,6 +4605,8 @@ NLOHMANN_JSON_NAMESPACE_END
 
 // #include <nlohmann/detail/view/scan.hpp>
 
+// #include <nlohmann/detail/view/simd.hpp>
+
 
 NLOHMANN_JSON_NAMESPACE_BEGIN
 namespace detail
@@ -4689,12 +4691,56 @@ NLOHMANN_VIEW_NOINLINE FloatType float_value(const char* first, const node& n)
     return convert_float<FloatType>(first, last, dot, mantissa_end);
 }
 
+#if NLOHMANN_VIEW_VECTOR
+/*!
+@brief the value of the first 16 digits of a run of digits with a point after
+int_digits of them (or none, if int_digits >= 16)
+
+The 17 bytes at p are read at once: the bytes after the point move down by one,
+then pairs, quadruples, and octets of digits are combined by multiplications
+(after simdjson). The bytes [p, p + 32) must be readable. Bytes that are not
+digits (only in a damaged image loaded with image_check::bounds) give a wrong
+value, but no undefined behavior.
+*/
+NLOHMANN_VIEW_ALWAYS_INLINE std::uint64_t sixteen_digits(const unsigned char* p, unsigned int_digits) noexcept
+{
+#if NLOHMANN_VIEW_NEON
+    const uint8x16_t low = vld1q_u8(p);
+    const uint8x16_t index = vcombine_u8(vcreate_u8(0x0706050403020100u), vcreate_u8(0x0F0E0D0C0B0A0908u));
+    const uint8x16_t before_point = vcltq_u8(index, vdupq_n_u8(static_cast<std::uint8_t>(int_digits)));
+    const uint8x16_t digits = vsubq_u8(vbslq_u8(before_point, low, vextq_u8(low, vld1q_u8(p + 16), 1)), vdupq_n_u8('0'));
+    const uint16x8_t twos = vpaddlq_u8(vmulq_u8(digits, vreinterpretq_u8_u16(vdupq_n_u16(0x010A))));
+    const uint32x4_t fours = vpaddlq_u16(vmulq_u16(twos, vreinterpretq_u16_u32(vdupq_n_u32(0x00010064))));
+    const uint64x2_t eights = vpaddlq_u32(vmulq_u32(fours, vreinterpretq_u32_u64(vdupq_n_u64(0x0000000100002710u))));
+    return (vgetq_lane_u64(eights, 0) * 100000000u) + vgetq_lane_u64(eights, 1);
+#else
+    // NOLINTBEGIN(portability-simd-intrinsics)
+    const __m128i low = _mm_loadu_si128(static_cast<const __m128i*>(static_cast<const void*>(p))); // NOLINT(bugprone-casting-through-void)
+    const __m128i high = _mm_loadu_si128(static_cast<const __m128i*>(static_cast<const void*>(p + 16))); // NOLINT(bugprone-casting-through-void)
+    const __m128i before_point = _mm_cmpgt_epi8(_mm_set1_epi8(static_cast<char>(int_digits)), _mm_setr_epi8(0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15));
+    const __m128i moved = _mm_or_si128(_mm_srli_si128(low, 1), _mm_slli_si128(high, 15));
+    const __m128i digits = _mm_sub_epi8(_mm_or_si128(_mm_and_si128(before_point, low), _mm_andnot_si128(before_point, moved)), _mm_set1_epi8('0'));
+    // (16-bit lanes: SSE2 has no multiply-add of bytes)
+    const __m128i tens = _mm_setr_epi16(10, 1, 10, 1, 10, 1, 10, 1);
+    const __m128i twos = _mm_packs_epi32(_mm_madd_epi16(_mm_unpacklo_epi8(digits, _mm_setzero_si128()), tens),
+                                         _mm_madd_epi16(_mm_unpackhi_epi8(digits, _mm_setzero_si128()), tens));
+    const __m128i fours = _mm_madd_epi16(twos, _mm_setr_epi16(100, 1, 100, 1, 100, 1, 100, 1));
+    const __m128i eights = _mm_madd_epi16(_mm_packs_epi32(fours, fours), _mm_setr_epi16(10000, 1, 10000, 1, 10000, 1, 10000, 1));
+    const auto upper = static_cast<std::uint32_t>(_mm_cvtsi128_si32(eights));
+    const auto lower = static_cast<std::uint32_t>(_mm_cvtsi128_si32(_mm_srli_si128(eights, 4)));
+    // NOLINTEND(portability-simd-intrinsics)
+    return (std::uint64_t{upper} * 100000000u) + lower;
+#endif
+}
+#endif
+
 /*!
 @brief the digits of a float token with at most 19 digits, from its layout
 
 The digit layout recorded while parsing says where the integer digits, the
 fraction digits, and the exponent are, so the digits are read eight at a
-time without scanning.
+time without scanning (with SIMD, a token of 16 to 19 digits sixteen at a
+time).
 
 @param[in] p  first character of the token
 @param[in] e  end of the token
@@ -4704,15 +4750,34 @@ NLOHMANN_VIEW_ALWAYS_INLINE float_significand layout_decimal(const unsigned char
 {
     const bool negative = *p == '-';
     p += negative ? 1 : 0;
-    std::uint64_t w = parse_upto19(p, int_digits, limit);
+    std::uint64_t w = 0;
-    p += int_digits;
     std::int64_t q = 0;
-    if (frac_digits != 0)
+#if NLOHMANN_VIEW_VECTOR
+    const unsigned count = int_digits + frac_digits;
+    if (count >= 16 && limit - p >= 32)
     {
-        w = (w * int_pow10(frac_digits)) + parse_upto19(p + 1, frac_digits, limit);
+        // (the point, if any, follows the integer digits; the digits after
-        p += 1 + frac_digits;
+        // the first 16 are at most three)
+        w = sixteen_digits(p, int_digits);
+        for (unsigned i = 16; i < count; ++i)
+        {
+            w = (w * 10) + static_cast<std::uint64_t>(p[i + (i >= int_digits ? 1 : 0)] - '0');
+        }
+        p += count + (frac_digits != 0 ? 1 : 0);
         q = -static_cast<std::int64_t>(frac_digits);
     }
+    else
+#endif
+    {
+        w = parse_upto19(p, int_digits, limit);
+        p += int_digits;
+        if (frac_digits != 0)
+        {
+            w = (w * int_pow10(frac_digits)) + parse_upto19(p + 1, frac_digits, limit);
+            p += 1 + frac_digits;
+            q = -static_cast<std::int64_t>(frac_digits);
+        }
+    }
     if (p != e)
     {
         // [eE][+-]digits; huge exponents saturate (the parser rejected
@@ -4747,12 +4812,22 @@ NLOHMANN_VIEW_ALWAYS_INLINE float_significand layout_decimal(const unsigned char
 The result is correctly rounded by the lexer's conversion
 (detail::decimal_to_float(): Clinger's fast path where both operands are
 exact, else the Eisel-Lemire algorithm, which needs no fallback for up to 19
-digits), so it is the value parse() produces.
+digits), so it is the value parse() produces. Tokens of 16 or more digits go
+to Eisel-Lemire directly: the fast path takes few of them (none of 17 digits),
+and its check is a branch that data like GeoJSON coordinates mispredicts.
 */
 template<typename FloatType>
 NLOHMANN_VIEW_ALWAYS_INLINE FloatType layout_float(const unsigned char* p, const unsigned char* e, unsigned int_digits, unsigned frac_digits, const unsigned char* limit) noexcept
 {
-    return decimal_to_float<FloatType>(layout_decimal(p, e, int_digits, frac_digits, limit));
+    const float_significand d = layout_decimal(p, e, int_digits, frac_digits, limit);
+    if (int_digits + frac_digits >= 16)
+    {
+        using format = ieee_binary_format<std::numeric_limits<FloatType>::digits>;
+        native_float_t<FloatType> value{};
+        float_from_bits(eisel_lemire<format>(d.exponent, d.w) | (d.negative ? (std::uint64_t{1} << format::sign_bit()) : 0u), value);
+        return value;
+    }
+    return decimal_to_float<FloatType>(d);
 }
 
 /// the value of a float set by an edit: its token (the shortest round-trip
@@ -4771,6 +4846,80 @@ NLOHMANN_VIEW_NOINLINE FloatType edited_float(const char* token, const node& n)
     return float_value<FloatType>(token, n);
 }
 
+#if NLOHMANN_VIEW_VECTOR
+/// eisel_lemire() for the token w * 10^q of coordinate_float()
+template<typename Format>
+NLOHMANN_VIEW_ALWAYS_INLINE std::uint64_t coordinate_bits(std::int64_t q, std::uint64_t w, Format /*format*/) noexcept
+{
+    return eisel_lemire<Format>(q, w);
+}
+
+/*!
+@brief (binary64) eisel_lemire() without the cases that tokens of 16 or 17
+digits with 5 or more after the point cannot reach: a value of 0, a
+subnormal, an infinity, or a tie (q < -4)
+*/
+NLOHMANN_VIEW_ALWAYS_INLINE std::uint64_t coordinate_bits(std::int64_t q, std::uint64_t w, ieee_binary_format<53> format) noexcept
+{
+    if (NLOHMANN_VIEW_UNLIKELY(w == 0 || q > -5))
+    {
+        return eisel_lemire<ieee_binary_format<53>>(q, w);
+    }
+    static_cast<void>(format);
+    const int lz = count_leading_zeros(w);
+    const std::uint64_t normalized = w << static_cast<unsigned>(lz);
+    const auto index = static_cast<std::size_t>(2 * (q - pow5_128_smallest_power));
+    const uint128_parts product = full_multiplication(normalized, pow5_128()[index]);
+    std::uint64_t high = product.high;
+    if (NLOHMANN_VIEW_UNLIKELY((high & 0x1FFu) == 0x1FFu))
+    {
+        // (the lower bits may carry into the result)
+        const std::uint64_t second = full_multiplication(normalized, pow5_128()[index + 1]).high;
+        high += product.low + second < product.low ? 1u : 0u;
+    }
+    const auto upperbit = static_cast<unsigned>(high >> 63u);
+    std::uint64_t mantissa = high >> (upperbit + 9);
+    std::uint64_t power2 = static_cast<std::uint64_t>(((217706 * q) >> 16) + 63 + static_cast<std::int64_t>(upperbit) - lz + 1023);
+    mantissa = (mantissa + (mantissa & 1u)) >> 1u;
+    const bool carry = mantissa >= (std::uint64_t{2} << 52u);
+    mantissa = carry ? (std::uint64_t{1} << 52u) : mantissa;
+    power2 += carry ? 1u : 0u;
+    return (mantissa & ~(std::uint64_t{1} << 52u)) | (power2 << 52u);
+}
+
+/*!
+@brief (binary32 and binary64) the value of a float token of the source with
+16 or 17 digits, a point, and no exponent, the shape of most coordinates
+written with full precision; whether the token of n has this shape
+
+These tokens skip the general layout of layout_decimal(): no digits beyond
+the 17th, no exponent (and Eisel-Lemire directly, as in layout_float()).
+*/
+template<typename FloatType>
+NLOHMANN_VIEW_ALWAYS_INLINE bool coordinate_float(const document_data& d, const node& n, FloatType& value) noexcept
+{
+    const unsigned int_digits = n.extra & 0xFFu;
+    const unsigned frac_digits = n.extra >> 8u;
+    const unsigned count = int_digits + frac_digits;
+    const auto* const first = reinterpret_cast<const unsigned char*>(d.src + n.off); // NOLINT(cppcoreguidelines-pro-type-reinterpret-cast)
+    const unsigned negative = first[0] == '-' ? 1u : 0u;
+    if (count - 16u > 1u || frac_digits == 0 || n.len != negative + count + 1 || d.size - n.off < 33)
+    {
+        return false;
+    }
+    const unsigned char* const digits = first + negative;
+    const std::uint64_t w = sixteen_digits(digits, int_digits);
+    // (the 17th digit follows the point)
+    const std::uint64_t w17 = (w * 10) + static_cast<std::uint64_t>(digits[17] - '0');
+    using format = ieee_binary_format<std::numeric_limits<FloatType>::digits>;
+    native_float_t<FloatType> result{};
+    float_from_bits(coordinate_bits(-static_cast<std::int64_t>(frac_digits), count == 17 ? w17 : w, format{}) | (static_cast<std::uint64_t>(negative) << format::sign_bit()), result);
+    value = result;
+    return true;
+}
+
+#endif
+
 /// the value of the float token of a node, as parse() converts it; floats and
 /// doubles with at most 19 digits are converted from the digit layout
 template<typename FloatType>
@@ -4786,6 +4935,13 @@ FloatType float_value(const document_data& d, const node& n)
 template<typename FloatType>
 FloatType float_value(const document_data& d, const node& n, std::true_type /*binary32 or binary64*/)
 {
+#if NLOHMANN_VIEW_VECTOR
+    FloatType value {};
+    if (coordinate_float(d, n, value))
+    {
+        return value;
+    }
+#endif
     const unsigned int_digits = n.extra & 0xFFu;
     const unsigned frac_digits = n.extra >> 8u;
     if (NLOHMANN_VIEW_LIKELY(int_digits + frac_digits <= 19)) // (255 marks "many")
@@ -6357,7 +6513,9 @@ NLOHMANN_JSON_NAMESPACE_END
 #include <cstddef> // size_t
 #include <cstdint> // uint8_t, uint32_t
 #include <cstring> // memcpy, memset
+#include <functional> // less
 #include <limits> // numeric_limits
+#include <memory> // unique_ptr
 #include <type_traits> // integral_constant
 #include <vector> // vector
 
@@ -6732,6 +6890,127 @@ struct depth_counter<false>
     }
 };
 
+/*!
+@brief where the double x nearest to a token w * 10^q lies, for 10^15 <= w <
+10^17 and -17 <= q <= -1 (Eisel-Lemire, then a fixed-point position)
+
+dump() writes the shortest decimal in the rounding interval of x (the closest
+one if there are several, see zmij::to_shortest()). Its digits are those of a
+multiple of 10^g of the token's last digit, with g = dec_exp + 1 - q for x's
+decimal exponent dec_exp: the multiple of 10^g nearest to x if it lies in the
+interval (at most one does), else the multiple of 10^(g - 1) nearest to x
+(see token_digits_1() and token_digits_2()). For g <= 0, the token itself is
+in the interval.
+
+The position is exact in a 64-bit fixed-point number with 56 bits after the
+point (of the token's last digit): x / 10^q = 2c * 5^-q / 2^t for x = c * 2^e2
+and t = q + 1 - e2, with at most 56 bits after the point here, and |x / 10^q -
+w| is at most half the spacing of the doubles, below 12 units. So only the low
+64 bits of 2c * 5^-q are needed. c and e2 come from Eisel-Lemire's product
+directly (as eisel_lemire() rounds it: no tie is possible for q < -4, and its
+second product is added where it can carry into the result).
+
+@param[out] offset  x / 10^q - w + 32, with 56 bits after the point
+@param[out] radius  half the spacing of the doubles at x, likewise (+ 1 if
+                    the interval is closed)
+@return g; 3 if the digits are not decided here (a power of two, whose
+        interval is not symmetric, or out of range)
+*/
+NLOHMANN_VIEW_ALWAYS_INLINE int locate_token(std::uint64_t w, int q, std::uint64_t& offset, std::uint64_t& radius) noexcept
+{
+    const int lz = count_leading_zeros(w);
+    const std::uint64_t normalized = w << static_cast<unsigned>(lz);
+    const auto index = static_cast<std::size_t>(2 * (q - pow5_128_smallest_power));
+    const uint128_parts product = full_multiplication(normalized, pow5_128()[index]);
+    std::uint64_t high = product.high;
+    if (NLOHMANN_VIEW_UNLIKELY((high & 0x1FFu) == 0x1FFu))
+    {
+        // (as eisel_lemire(): the lower bits may carry into the result)
+        const std::uint64_t second = full_multiplication(normalized, pow5_128()[index + 1]).high;
+        high += product.low + second < product.low ? 1u : 0u;
+    }
+    const auto upperbit = static_cast<unsigned>(high >> 63u);
+    const std::uint64_t mantissa = high >> (upperbit + 9);
+    const std::uint64_t c = (mantissa + (mantissa & 1u)) >> 1u;
+    // e2 as eisel_lemire() computes the exponent (log2(10) ~ 217706 / 2^16)
+    const int e2 = static_cast<int>((217706 * static_cast<std::int64_t>(q)) >> 16) + 63 + static_cast<int>(upperbit) - lz - 52;
+    const int t = q + 1 - e2;
+    const int g = ((e2 * 315653) >> 20) + 1 - q; // (dec_exp as in zmij::to_shortest(), for a regular x)
+    static const std::array<std::uint64_t, 17> fives = {{1u, 5u, 25u, 125u, 625u, 3125u, 15625u, 78125u, 390625u, 1953125u, 9765625u, 48828125u, 244140625u, 1220703125u, 6103515625u, 30517578125u, 152587890625u}};
+    const std::uint64_t five = fives[static_cast<std::size_t>(-q)]; // 5^-q
+    const unsigned s = static_cast<unsigned>(56 - t) & 63u;
+    offset = ((2 * c * five) << s) - (w << 56u) + (std::uint64_t{32} << 56u);
+    radius = (five << s) + ((c & 1u) == 0 ? 1u : 0u);
+    // (c = 2^52: a power of two; c = 2^53: rounded up to one. With 8 to 16
+    // fraction digits, as the batch's tokens have, t is in [15, 40] and g at
+    // most 2. x lies halfway between two candidates only if its distance from
+    // the token is a whole unit (g == 2) or a half (g == 1): such tokens are
+    // left to the full conversion)
+    const bool decided = c - ((std::uint64_t{1} << 52u) + 1) < (std::uint64_t{1} << 52u) - 1
+                         && (offset & ((std::uint64_t{1} << 55u) - 1)) != 0;
+    return decided ? g : 3;
+}
+
+/// the distance of a position (see locate_token()) from the biased point 32
+NLOHMANN_VIEW_ALWAYS_INLINE std::uint64_t biased_distance(std::uint64_t position) noexcept
+{
+    constexpr std::uint64_t center = std::uint64_t{32} << 56u;
+    return position >= center ? position - center : center - position;
+}
+
+/*!
+@brief (g == 1) the digits dump() writes for a token, from the position of its
+double (see locate_token()): the multiple of 10 nearest to x if it is in the
+interval, else w rounded to x (an exact tie between two candidates, like
+754570942.33984373, whose double is 754570942.33984375, is excluded by
+locate_token())
+
+With |x - w| at most the radius, which is below half the spacing of the
+candidates, the multiple of 10 nearest to x is w - r10 or the one above it.
+*/
+NLOHMANN_VIEW_ALWAYS_INLINE std::uint64_t token_digits_1(std::uint64_t w, std::uint64_t offset, std::uint64_t radius, std::uint64_t r10) noexcept
+{
+    constexpr std::uint64_t one = std::uint64_t{1} << 56u;
+    const std::uint64_t from = offset + (r10 * one); // x - (w - r10) (+ 32)
+    const bool up = from > 37 * one;                  // (nearer to the multiple above)
+    const bool shorter = biased_distance(from - (up ? 10 * one : 0)) < radius;
+    const std::uint64_t a = w - r10 + (up ? 10u : 0u);
+    const std::uint64_t b = w + ((offset + (one / 2)) >> 56u) - 32;                // w rounded to x
+    return shorter ? a : b;
+}
+
+/*!
+@brief (g == 2) the digits dump() writes for a token, as token_digits_1(): the
+multiple of 100 nearest to x if it is in the interval, else the multiple of 10
+nearest to x
+*/
+NLOHMANN_VIEW_ALWAYS_INLINE std::uint64_t token_digits_2(std::uint64_t w, std::uint64_t offset, std::uint64_t radius, std::uint64_t r10, std::uint64_t r100) noexcept
+{
+    constexpr std::uint64_t one = std::uint64_t{1} << 56u;
+    const std::uint64_t from = offset + (r100 * one);
+    const bool up = from > 82 * one;
+    const bool shorter = biased_distance(from - (up ? 100 * one : 0)) < radius;
+    const std::uint64_t a = w - r100 + (up ? 100u : 0u);
+    // x - (w - r10), in [-12, 21]: the multiple of 10 nearest to x is that one,
+    // or one or two above, or one below
+    const std::uint64_t y = offset + (r10 * one);
+    const std::uint64_t steps = (y > 37 * one ? 1u : 0u) + (y > 47 * one ? 1u : 0u);
+    const bool down = y < 27 * one;
+    const std::uint64_t b = w - r10 + (10 * steps) - (down ? 10u : 0u);
+    return shorter ? a : b;
+}
+
+/// the four ASCII digits of x < 10^4, the first in the lowest byte (as
+/// little-endian memory holds them)
+NLOHMANN_VIEW_ALWAYS_INLINE std::uint32_t four_digit_text(std::uint32_t x) noexcept
+{
+    const std::uint32_t ab = (x * 5243u) >> 19u; // x / 100
+    std::uint32_t v = ab | ((x - (ab * 100u)) << 16u);
+    const std::uint32_t a = ((v * 103u) >> 10u) & 0x000F000Fu; // / 10 per 16-bit lane
+    v = a | ((v - (a * 10u)) << 8u);
+    return v + 0x30303030u;
+}
+
 /// how the view's dump() writes a value
 struct dump_style
 {
@@ -7059,6 +7338,7 @@ class view_serializer
         std::array<frame, 32> buffer; // NOLINT(cppcoreguidelines-pro-type-member-init,hicpp-member-init): written before read
         std::vector<frame> heap;
         small_stack<frame> stack(buffer.data(), buffer.size(), heap);
+        float_batch batch;
         const char* const src = m_doc.src;
         const char* const src_end = src + m_doc.size;
         char* w = m_out.cursor();
@@ -7198,7 +7478,7 @@ class view_serializer
                     else if (enabled(fast_double::value))
                     {
                         room(64);
-                        w = write_double_at(w, *n);
+                        w = write_double_ahead(w, src, n, batch);
                     }
                     else
                     {
@@ -7223,6 +7503,20 @@ class view_serializer
                 case value_t::array:
                 {
                     const bool object = n->kind == static_cast<std::uint8_t>(value_t::object);
+                    // (read-only documents, compact output) a pair of floats,
+                    // like the coordinates of GeoJSON, without a frame
+                    if (!Editable && !Pretty && !SourceNumbers && enabled(fast_double::value) && n->next == 3 && n->len == 2
+                            && n[1].kind == static_cast<std::uint8_t>(value_t::number_float) && n[2].kind == static_cast<std::uint8_t>(value_t::number_float))
+                    {
+                        room(2 * 64);
+                        *w++ = '[';
+                        w = write_double_ahead(w, src, n + 1, batch);
+                        *w++ = ',';
+                        w = write_double_ahead(w, src, n + 2, batch);
+                        *w++ = ']';
+                        n += 2; // (the element before the next node)
+                        break;
+                    }
                     room(8);
                     if (n->len == 0)
                     {
@@ -7332,6 +7626,247 @@ class view_serializer
         }
     }
 
+    /// (float_batch) the mark of digits whose rounding carried beyond the
+    /// token's last four (see mark())
+    static constexpr std::uint64_t carried() noexcept
+    {
+        return std::uint64_t{1} << 63u;
+    }
+
+    /// floats of 16 or 17 digits ahead of the walk, converted together (see
+    /// convert_ahead()), with their digits as mark() keeps them
+    struct float_batch
+    {
+        static constexpr std::size_t capacity() noexcept
+        {
+            return 256;
+        }
+        /// (on the heap, allocated by the first conversion: a frame of more
+        /// than a page made every dump of a small document slower)
+        struct entries
+        {
+            std::array<const node*, 256> at; // NOLINT(cppcoreguidelines-pro-type-member-init,hicpp-member-init): written before read
+            std::array<std::uint64_t, 256> digits; // NOLINT(cppcoreguidelines-pro-type-member-init,hicpp-member-init): written before read
+        };
+        std::unique_ptr<entries> storage{};
+        const node** at = nullptr;
+        std::uint64_t* digits = nullptr;
+        std::size_t count = 0;
+        std::size_t next = 0;
+        const node* scanned = nullptr; ///< where the last scan of the node array ended
+    };
+
+    /// (doubles) the float at n as dump() writes it, at w (64 bytes of room):
+    /// from the batch if it holds n
+    NLOHMANN_VIEW_ALWAYS_INLINE char* write_double_ahead(char* w, const char* src, const node* n, float_batch& batch)
+    {
+#if NLOHMANN_VIEW_VECTOR && NLOHMANN_VIEW_LITTLE_ENDIAN
+        // (digits 0: not written by the batch; carried(): rounding carried
+        // beyond the last four digits)
+        if (batch.next != batch.count && batch.at[batch.next] == n && batch.digits[batch.next] - 1 < carried() - 1)
+        {
+            return write_token_digits(w, src, *n, batch.digits[batch.next++]);
+        }
+        return write_double_beside(w, n, batch);
+#else
+        static_cast<void>(src);
+        static_cast<void>(batch);
+        return write_double_at(w, *n);
+#endif
+    }
+
+#if NLOHMANN_VIEW_VECTOR && NLOHMANN_VIEW_LITTLE_ENDIAN
+    /// write_double_ahead() for a float that is not the batch's next one (out
+    /// of line: the walk is faster with less code in its loop)
+    NLOHMANN_VIEW_NOINLINE char* write_double_beside(char* w, const node* n, float_batch& batch)
+    {
+        // (an editable document's walk can skip nodes of the array)
+        const std::less<const node*> before;
+        while (batch.next != batch.count && before(batch.at[batch.next], n))
+        {
+            ++batch.next;
+        }
+        if ((batch.next != batch.count && batch.at[batch.next] == n) || convert_ahead(n, batch))
+        {
+            const std::uint64_t digits = batch.digits[batch.next++];
+            if ((digits & carried()) != 0)
+            {
+                return write_carried_digits(w, *n, digits & ~carried());
+            }
+            if (digits != 0)
+            {
+                return write_token_digits(w, m_doc.src, *n, digits);
+            }
+        }
+        return write_double_at(w, *n);
+    }
+
+    /*!
+    @brief convert the floats of 16 or 17 digits among the next nodes of the
+    array at once; whether n is the first of them
+
+    Such tokens (like the coordinates of GeoJSON, written with 17 digits) are
+    written as the token with its last four digits replaced
+    (write_token_digits()). Each step (the digits, locate_token(),
+    token_digits_1/2()) is a long chain of dependent operations; one loop per
+    step over many floats lets the processor overlap the floats, which it does
+    not across the steps of one float (on Apple M1, one loop for the digits and
+    locate_token() made the dump of canada.json 12 % slower). Each node of the array
+    is scanned once; a node that the walk does not reach in order (in an
+    editable document) is written without the batch.
+    */
+    NLOHMANN_VIEW_NOINLINE bool convert_ahead(const node* n, float_batch& batch)
+    {
+        const std::less<const node*> before;
+        const node* const last = m_doc.nodes + m_doc.node_count;
+        if (before(n, batch.scanned) || before(n, m_doc.nodes) || !before(n, last))
+        {
+            return false;
+        }
+        const char* const src = m_doc.src;
+        const char* const src_end = src + m_doc.size;
+        const node* const stop = last - n > 1024 ? n + 1024 : last;
+        batch.count = 0;
+        batch.next = 0;
+        // the digits of each token (and its last four from the text)
+        std::array<std::uint64_t, 256> digits;     // NOLINT(cppcoreguidelines-pro-type-member-init,hicpp-member-init): written before read
+        std::array<int, 256> exponent;             // NOLINT(cppcoreguidelines-pro-type-member-init,hicpp-member-init): written before read
+        std::array<std::uint32_t, 256> last_four;  // NOLINT(cppcoreguidelines-pro-type-member-init,hicpp-member-init): written before read
+        const node* p = n;
+        if (!batch.storage)
+        {
+            batch.storage.reset(new typename float_batch::entries); // NOLINT(cppcoreguidelines-owning-memory,modernize-make-unique): C++11
+            batch.at = batch.storage->at.data();
+            batch.digits = batch.storage->digits.data();
+        }
+        for (; p != stop && batch.count != float_batch::capacity(); ++p)
+        {
+            // a token of the source: 16 or 17 digits, at least 8 after the
+            // point, no exponent, 32 bytes to read
+            const unsigned frac_digits = p->extra >> 8u;
+            const unsigned int_digits = p->extra & 0xFFu;
+            const unsigned count = int_digits + frac_digits;
+            if (p->kind == static_cast<std::uint8_t>(value_t::number_float) && (p->flags & node_flags::storage) == 0
+                    && count - 16u <= 1u && frac_digits >= 8 && src_end - (src + p->off) >= 33)
+            {
+                const auto* const token = reinterpret_cast<const unsigned char*>(src + p->off); // NOLINT(cppcoreguidelines-pro-type-reinterpret-cast)
+                const unsigned sign = token[0] == '-' ? 1 : 0;
+                const unsigned char* const first = token + sign;
+                const std::uint64_t w = sixteen_digits(first, int_digits);
+                // (the 17th digit follows the point; a token with an exponent
+                // gets digits outside the range of locate_token(), and is not
+                // written by the batch. A token 0.xxx with 16 significant
+                // digits is: its double is written as "0." and its digits too)
+                const std::uint64_t w17 = (w * 10) + static_cast<std::uint64_t>(first[17] - '0');
+                const std::size_t i = batch.count++;
+                batch.at[i] = p;
+                digits[i] = p->len != sign + count + 1 ? 0 : (count == 17 ? w17 : w);
+                exponent[i] = -static_cast<int>(frac_digits);
+                // (byte 0: the last digit, byte 1: the last two, bits 16-29: the last four)
+                std::uint32_t four = 0;
+                std::memcpy(&four, token + p->len - 4, 4);
+                four -= 0x30303030u;
+                const std::uint32_t pairs = ((four & 0x0F0F0F0Fu) * 2561u) >> 8u; // (byte 0, 2: the pairs)
+                last_four[i] = (four >> 24u) | ((pairs >> 16u & 0xFFu) << 8u) | ((((pairs & 0x00FF00FFu) * 6553601u) >> 16u) << 16u);
+            }
+        }
+        batch.scanned = p;
+        // the position of each double, and the floats of either kind
+        std::array<std::uint64_t, 256> offset; // NOLINT(cppcoreguidelines-pro-type-member-init,hicpp-member-init): written before read
+        std::array<std::uint64_t, 256> radius; // NOLINT(cppcoreguidelines-pro-type-member-init,hicpp-member-init): written before read
+        std::array<std::uint8_t, 256> kind_1;  // NOLINT(cppcoreguidelines-pro-type-member-init,hicpp-member-init): written before read
+        std::array<std::uint8_t, 256> kind_2;  // NOLINT(cppcoreguidelines-pro-type-member-init,hicpp-member-init): written before read
+        std::size_t count_1 = 0;
+        std::size_t count_2 = 0;
+        for (std::size_t i = 0; i != batch.count; ++i)
+        {
+            const std::uint64_t w = digits[i];
+            // (the range excludes the values of bytes that are not digits, only
+            // in a damaged image loaded with image_check::bounds)
+            const int g = w - 1000000000000000u < 99000000000000000u ? locate_token(w, exponent[i], offset[i], radius[i]) : 3;
+            batch.digits[i] = g <= 0 ? (last_four[i] >> 16u) + 1 : 0;
+            kind_1[count_1] = static_cast<std::uint8_t>(i);
+            count_1 += g == 1 ? 1 : 0;
+            kind_2[count_2] = static_cast<std::uint8_t>(i);
+            count_2 += g == 2 ? 1 : 0;
+        }
+        // the digits to write, in one loop per kind (see mark())
+        for (std::size_t k = 0; k != count_1; ++k)
+        {
+            const std::size_t i = kind_1[k];
+            const std::uint64_t s = token_digits_1(digits[i], offset[i], radius[i], last_four[i] & 0xFFu);
+            batch.digits[i] = mark(digits[i], s, last_four[i] >> 16u);
+        }
+        for (std::size_t k = 0; k != count_2; ++k)
+        {
+            const std::size_t i = kind_2[k];
+            const std::uint64_t s = token_digits_2(digits[i], offset[i], radius[i], last_four[i] & 0xFFu, (last_four[i] >> 8u) & 0xFFu);
+            batch.digits[i] = mark(digits[i], s, last_four[i] >> 16u);
+        }
+        return batch.count != 0 && batch.at[0] == n;
+    }
+
+    /*!
+    @brief a float token of 16 or 17 digits as dump() writes it, at w (64 bytes
+    of room), from the digits of its double (see locate_token()) whose
+    rounding carried beyond the token's last four digits
+
+    (like 43.42027299999999 -> 43.420273): the digits go to the writer of
+    Zmij's results as its 15 or 16 leading digits and one more, which omits
+    the trailing zeros.
+    */
+    NLOHMANN_VIEW_NOINLINE char* write_carried_digits(char* w, const node& n, std::uint64_t digits) const noexcept
+    {
+        const int exponent = -static_cast<int>(n.extra >> 8u);
+        const std::uint64_t leading = digits / 10;
+        const auto last = static_cast<unsigned char>(digits - (leading * 10));
+        const bool seventeen = digits >= 10000000000000000u;
+        *w = '-';
+        w += m_doc.src[n.off] == '-' ? 1 : 0;
+        return ::nlohmann::detail::dtoa_impl::write_shortest(w, seventeen ? ::nlohmann::detail::zmij::shortest_decimal{leading, exponent, last, last != 0}
+                : ::nlohmann::detail::zmij::shortest_decimal{digits, exponent - 1, 0, false});
+    }
+
+    /// the digits s of a token with the digits w and the last four digits
+    /// r4, as the batch keeps them: the new last four digits + 1 (only those
+    /// are written over the token's), or s marked if it differs from w beyond
+    /// them (0 stays for a float the batch does not write)
+    static std::uint64_t mark(std::uint64_t w, std::uint64_t s, std::uint64_t r4) noexcept
+    {
+        const std::uint64_t last = s - (w - r4);
+        return last < 10000 ? last + 1 : s | carried();
+    }
+
+    /*!
+    @brief a float token of 16 or 17 digits as dump() writes it, at w (64 bytes
+    of room): the token with its last four digits replaced by digits - 1 (see
+    mark(); the others are the token's), and without trailing zeros after the
+    point, but one
+    */
+    char* write_token_digits(char* w, const char* src, const node& n, std::uint64_t digits)
+    {
+        const char* const token = src + n.off;
+        std::memcpy(w, token, 32);
+        char* const end = w + n.len;
+        const std::uint32_t last = four_digit_text(static_cast<std::uint32_t>(digits - 1));
+        std::memcpy(end - 4, &last, 4);
+        // (the token's text before the new digits, from the source: reading
+        // the output back would wait for the stores)
+        std::uint64_t before = 0;
+        std::memcpy(&before, token + n.len - 12, 8);
+        const std::uint32_t last_zeros = last ^ 0x30303030u;
+        const std::uint64_t before_zeros = before ^ 0x3030303030303030u;
+        if (NLOHMANN_VIEW_UNLIKELY(last_zeros == 0 && before_zeros == 0))
+        {
+            return write_double_at(w, n); // (twelve or more trailing zeros)
+        }
+        const unsigned zeros = last_zeros != 0 ? static_cast<unsigned>(count_leading_zeros(last_zeros)) / 8 - 4
+                               : 4 + (static_cast<unsigned>(count_leading_zeros(before_zeros)) / 8);
+        const unsigned frac_digits = n.extra >> 8u;
+        return end - (zeros < frac_digits ? zeros : frac_digits - 1);
+    }
+#endif
+
     /// a float node as dump() writes it
     void write_float_node(const node& n)
     {

tests/src/unit-json_view_dump.cpp

@@ -150,6 +150,71 @@ TEST_CASE("json_view dump")
             CHECK(many_doc.root().dump() == json::parse(many_tokens).dump());
         }
 
+        // tokens of 16 and 17 digits without an exponent (like GeoJSON
+        // coordinates), which dump() converts in batches: doubles exactly
+        // halfway between two candidates for the shortest digits, random
+        // digits, and digits near a shorter decimal (...99999997,
+        // ...00000003), whose rounding carries; in pairs and among other
+        // values, so that the batches are interrupted; the last token near the
+        // end of the text
+        {
+            std::mt19937_64 tokens(5627); // NOLINT(cert-msc32-c,cert-msc51-cpp,bugprone-random-generator-seed)
+            const auto draw = [&tokens](std::size_t n)
+            {
+                const std::uint64_t r = tokens() % n;
+                return static_cast<std::size_t>(r);
+            };
+            std::string coordinates = "[754570942.33984373,257769445.56835938,858106901.94921875,97944964.876953125,"
+                                      "[0.5,1e-7],[1.5,-0.0,2.5],[1E2,12.5,0.1,3.25,4.5,5.75,6.125,7.0,8.5],[],[1.5],[1,2.5],[2.5,\"x\"],[[1.5],2.5],";
+            for (int i = 0; i < 20000; ++i)
+            {
+                const std::size_t length = 16 + draw(2);
+                std::string digits(1, static_cast<char>('1' + draw(9)));
+                const std::size_t kept = draw(3) == 0 ? length : 2 + draw(length - 3);
+                for (std::size_t k = 1; k < kept; ++k)
+                {
+                    digits += static_cast<char>('0' + draw(10));
+                }
+                digits += std::string(length - kept, draw(2) == 0 ? '9' : '0');
+                digits.back() = static_cast<char>('0' + draw(10));
+                const std::size_t point = 1 + draw(9);
+                const std::string token = (draw(2) == 0 ? "-" : "") + digits.substr(0, point) + "." + digits.substr(point);
+                coordinates += (i != 0 ? "," : "") + (draw(8) == 0 ? "{\"x\":" + token + ",\"s\":\"a\"}" : "[" + token + "," + token + "]");
+            }
+            coordinates += ",-65.613616999999977]";
+            const json_document parsed = json_document::parse(coordinates);
+            const ordered_json j = ordered_json::parse(coordinates);
+            CHECK(parsed.root().dump() == j.dump());
+            CHECK(parsed.root().dump(1) == j.dump(1));
+            CHECK(parsed.root().dump(-1, ' ', true) == j.dump(-1, ' ', true));
+            CHECK(parsed.root().back().get<double>() == j.back().get<double>());
+            CHECK(parsed.root().back().dump() == "-65.61361699999998");
+            std::size_t i = 0;
+            for (const json_view v : parsed.root())
+            {
+                const ordered_json& e = j[i++];
+                CHECK(v.dump() == e.dump());
+                if (v.is_array() && v.size() != 0 && v[0].is_number())
+                {
+                    CHECK(v[0].get<double>() == e[0].get<double>());
+                }
+            }
+
+            // an editable document: edits move some arrays, so that the walk
+            // leaves the order of the parsed nodes
+            ordered_json_editable_document editable = ordered_json_editable_document::parse(coordinates);
+            ordered_json expected = j;
+            for (std::size_t k = 0; k < 20000; k += 97)
+            {
+                if (expected[k].is_array())
+                {
+                    editable.push_back(editable.root()[k], ordered_json(1.5));
+                    expected[k].push_back(1.5);
+                }
+            }
+            CHECK(editable.root().dump() == expected.dump());
+        }
+
         // random doubles, written as parse() and dump() would
         std::mt19937_64 rng(1170); // NOLINT(cert-msc32-c,cert-msc51-cpp,bugprone-random-generator-seed)
         std::string many = "[";