优化原生结果编码传输与浏览器缓存，记录八路性能基线

原生结果series通过字节索引直传，C端使用Ryu精确回读编码和64 KiB批量写出；网页采用Float64缓存和CSV工作线程，减少结果处理与保存等待。

补充八路AME曲线核查、全流程分阶段计时、独立编码基准和复现工具，固定后续优化采用修正八路及rtol=1e-8。C写出1.1808→0.1638 s，点击到可查看8.0100→6.9756 s。

验证：最终10项编码专项、29项相关后端回归通过；8份原生结果逐位一致，16次网页结果/CSV/刷新恢复通过。前端构建及缓存/CSV专项在本轮结果处理工作中通过。环境、原始大结果与临时构建不纳入Git。

native/encoding/ryu/LICENSE-Boost

@@ -0,0 +1,23 @@
+Boost Software License - Version 1.0 - August 17th, 2003
+
+Permission is hereby granted, free of charge, to any person or organization
+obtaining a copy of the software and accompanying documentation covered by
+this license (the "Software") to use, reproduce, display, distribute,
+execute, and transmit the Software, and to prepare derivative works of the
+Software, and to permit third-parties to whom the Software is furnished to
+do so, all subject to the following:
+
+The copyright notices in the Software and this entire statement, including
+the above license grant, this restriction and the following disclaimer,
+must be included in all copies of the Software, in whole or in part, and
+all derivative works of the Software, unless such copies or derivative
+works are solely in the form of machine-executable object code generated by
+a source language processor.
+
+THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, EXPRESS OR
+IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY,
+FITNESS FOR A PARTICULAR PURPOSE, TITLE AND NON-INFRINGEMENT. IN NO EVENT
+SHALL THE COPYRIGHT HOLDERS OR ANYONE DISTRIBUTING THE SOFTWARE BE LIABLE
+FOR ANY DAMAGES OR OTHER LIABILITY, WHETHER IN CONTRACT, TORT OR OTHERWISE,
+ARISING FROM, OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER
+DEALINGS IN THE SOFTWARE.

native/encoding/ryu/UPSTREAM.json

@@ -0,0 +1,58 @@
+{
+  "repository": "https://github.com/ulfjack/ryu",
+  "commit": "4c0618b0e44f7ef027ebae05d2cc7812048f7c8f",
+  "files": {
+    "ryu/d2s.c": {
+      "sha256": "d24323c7eb77d63f1e52c415212b50060b776f0883525d907d04954fcd48cf64",
+      "bytes": 17705,
+      "url": "https://raw.githubusercontent.com/ulfjack/ryu/4c0618b0e44f7ef027ebae05d2cc7812048f7c8f/ryu/d2s.c"
+    },
+    "ryu/ryu.h": {
+      "sha256": "b7feab0ba1df5e9ef3d602f386592ad152491405e49b408fb21c0e0e9e6bfb16",
+      "bytes": 1360,
+      "url": "https://raw.githubusercontent.com/ulfjack/ryu/4c0618b0e44f7ef027ebae05d2cc7812048f7c8f/ryu/ryu.h"
+    },
+    "ryu/common.h": {
+      "sha256": "0bbd71d26da6193e678d0776cf418f43f287c73d6fd6725353df0aadf70f2a19",
+      "bytes": 3648,
+      "url": "https://raw.githubusercontent.com/ulfjack/ryu/4c0618b0e44f7ef027ebae05d2cc7812048f7c8f/ryu/common.h"
+    },
+    "ryu/digit_table.h": {
+      "sha256": "8b782573abc0b8554d74163ae6c02f0beb5c30d1e63eaebdb0ddf2c98d817e01",
+      "bytes": 1745,
+      "url": "https://raw.githubusercontent.com/ulfjack/ryu/4c0618b0e44f7ef027ebae05d2cc7812048f7c8f/ryu/digit_table.h"
+    },
+    "ryu/d2s_intrinsics.h": {
+      "sha256": "1d05702f2edacce428223d4b43dd3095c1bd1f3ad30128ce1761d84356dddc7d",
+      "bytes": 13015,
+      "url": "https://raw.githubusercontent.com/ulfjack/ryu/4c0618b0e44f7ef027ebae05d2cc7812048f7c8f/ryu/d2s_intrinsics.h"
+    },
+    "ryu/d2s_full_table.h": {
+      "sha256": "2618f6e5fae6c4443899b184efe3d08295dd267dc9f1a994c983c7caca59ebe6",
+      "bytes": 34501,
+      "url": "https://raw.githubusercontent.com/ulfjack/ryu/4c0618b0e44f7ef027ebae05d2cc7812048f7c8f/ryu/d2s_full_table.h"
+    },
+    "ryu/d2s_small_table.h": {
+      "sha256": "54fec51f1c5eed786a8ce6de881b81582dd71f0812dcd4324b37396617bb0fa9",
+      "bytes": 7641,
+      "url": "https://raw.githubusercontent.com/ulfjack/ryu/4c0618b0e44f7ef027ebae05d2cc7812048f7c8f/ryu/d2s_small_table.h"
+    },
+    "LICENSE-Boost": {
+      "sha256": "c9bff75738922193e67fa726fa225535870d2aa1059f91452c411736284ad566",
+      "bytes": 1338,
+      "url": "https://raw.githubusercontent.com/ulfjack/ryu/4c0618b0e44f7ef027ebae05d2cc7812048f7c8f/LICENSE-Boost"
+    },
+    "LICENSE-Apache2": {
+      "sha256": "c71d239df91726fc519c6eb72d318ec65820627232b2f796219e87dcf35d0ab4",
+      "bytes": 11357,
+      "url": "https://raw.githubusercontent.com/ulfjack/ryu/4c0618b0e44f7ef027ebae05d2cc7812048f7c8f/LICENSE-Apache2"
+    },
+    "README.md": {
+      "sha256": "20572708ea26d19fd596f1c4a44097dbcb491cdf0517024d68bbb5d622d0ac93",
+      "bytes": 14930,
+      "url": "https://raw.githubusercontent.com/ulfjack/ryu/4c0618b0e44f7ef027ebae05d2cc7812048f7c8f/README.md"
+    }
+  },
+  "licenseSelected": "Boost Software License 1.0",
+  "layout": "Upstream ryu/*.h in native/include/ryu; unchanged ryu/d2s.c in native/encoding/ryu; no source edits."
+}

native/encoding/ryu/d2s.c

@@ -0,0 +1,509 @@
+// Copyright 2018 Ulf Adams
+//
+// The contents of this file may be used under the terms of the Apache License,
+// Version 2.0.
+//
+//    (See accompanying file LICENSE-Apache or copy at
+//     http://www.apache.org/licenses/LICENSE-2.0)
+//
+// Alternatively, the contents of this file may be used under the terms of
+// the Boost Software License, Version 1.0.
+//    (See accompanying file LICENSE-Boost or copy at
+//     https://www.boost.org/LICENSE_1_0.txt)
+//
+// Unless required by applicable law or agreed to in writing, this software
+// is distributed on an "AS IS" BASIS, WITHOUT WARRANTIES OR CONDITIONS OF ANY
+// KIND, either express or implied.
+
+// Runtime compiler options:
+// -DRYU_DEBUG Generate verbose debugging output to stdout.
+//
+// -DRYU_ONLY_64_BIT_OPS Avoid using uint128_t or 64-bit intrinsics. Slower,
+//     depending on your compiler.
+//
+// -DRYU_OPTIMIZE_SIZE Use smaller lookup tables. Instead of storing every
+//     required power of 5, only store every 26th entry, and compute
+//     intermediate values with a multiplication. This reduces the lookup table
+//     size by about 10x (only one case, and only double) at the cost of some
+//     performance. Currently requires MSVC intrinsics.
+
+#include "ryu/ryu.h"
+
+#include <assert.h>
+#include <stdbool.h>
+#include <stdint.h>
+#include <stdlib.h>
+#include <string.h>
+
+#ifdef RYU_DEBUG
+#include <inttypes.h>
+#include <stdio.h>
+#endif
+
+#include "ryu/common.h"
+#include "ryu/digit_table.h"
+#include "ryu/d2s_intrinsics.h"
+
+// Include either the small or the full lookup tables depending on the mode.
+#if defined(RYU_OPTIMIZE_SIZE)
+#include "ryu/d2s_small_table.h"
+#else
+#include "ryu/d2s_full_table.h"
+#endif
+
+#define DOUBLE_MANTISSA_BITS 52
+#define DOUBLE_EXPONENT_BITS 11
+#define DOUBLE_BIAS 1023
+
+static inline uint32_t decimalLength17(const uint64_t v) {
+  // This is slightly faster than a loop.
+  // The average output length is 16.38 digits, so we check high-to-low.
+  // Function precondition: v is not an 18, 19, or 20-digit number.
+  // (17 digits are sufficient for round-tripping.)
+  assert(v < 100000000000000000L);
+  if (v >= 10000000000000000L) { return 17; }
+  if (v >= 1000000000000000L) { return 16; }
+  if (v >= 100000000000000L) { return 15; }
+  if (v >= 10000000000000L) { return 14; }
+  if (v >= 1000000000000L) { return 13; }
+  if (v >= 100000000000L) { return 12; }
+  if (v >= 10000000000L) { return 11; }
+  if (v >= 1000000000L) { return 10; }
+  if (v >= 100000000L) { return 9; }
+  if (v >= 10000000L) { return 8; }
+  if (v >= 1000000L) { return 7; }
+  if (v >= 100000L) { return 6; }
+  if (v >= 10000L) { return 5; }
+  if (v >= 1000L) { return 4; }
+  if (v >= 100L) { return 3; }
+  if (v >= 10L) { return 2; }
+  return 1;
+}
+
+// A floating decimal representing m * 10^e.
+typedef struct floating_decimal_64 {
+  uint64_t mantissa;
+  // Decimal exponent's range is -324 to 308
+  // inclusive, and can fit in a short if needed.
+  int32_t exponent;
+} floating_decimal_64;
+
+static inline floating_decimal_64 d2d(const uint64_t ieeeMantissa, const uint32_t ieeeExponent) {
+  int32_t e2;
+  uint64_t m2;
+  if (ieeeExponent == 0) {
+    // We subtract 2 so that the bounds computation has 2 additional bits.
+    e2 = 1 - DOUBLE_BIAS - DOUBLE_MANTISSA_BITS - 2;
+    m2 = ieeeMantissa;
+  } else {
+    e2 = (int32_t) ieeeExponent - DOUBLE_BIAS - DOUBLE_MANTISSA_BITS - 2;
+    m2 = (1ull << DOUBLE_MANTISSA_BITS) | ieeeMantissa;
+  }
+  const bool even = (m2 & 1) == 0;
+  const bool acceptBounds = even;
+
+#ifdef RYU_DEBUG
+  printf("-> %" PRIu64 " * 2^%d\n", m2, e2 + 2);
+#endif
+
+  // Step 2: Determine the interval of valid decimal representations.
+  const uint64_t mv = 4 * m2;
+  // Implicit bool -> int conversion. True is 1, false is 0.
+  const uint32_t mmShift = ieeeMantissa != 0 || ieeeExponent <= 1;
+  // We would compute mp and mm like this:
+  // uint64_t mp = 4 * m2 + 2;
+  // uint64_t mm = mv - 1 - mmShift;
+
+  // Step 3: Convert to a decimal power base using 128-bit arithmetic.
+  uint64_t vr, vp, vm;
+  int32_t e10;
+  bool vmIsTrailingZeros = false;
+  bool vrIsTrailingZeros = false;
+  if (e2 >= 0) {
+    // I tried special-casing q == 0, but there was no effect on performance.
+    // This expression is slightly faster than max(0, log10Pow2(e2) - 1).
+    const uint32_t q = log10Pow2(e2) - (e2 > 3);
+    e10 = (int32_t) q;
+    const int32_t k = DOUBLE_POW5_INV_BITCOUNT + pow5bits((int32_t) q) - 1;
+    const int32_t i = -e2 + (int32_t) q + k;
+#if defined(RYU_OPTIMIZE_SIZE)
+    uint64_t pow5[2];
+    double_computeInvPow5(q, pow5);
+    vr = mulShiftAll64(m2, pow5, i, &vp, &vm, mmShift);
+#else
+    vr = mulShiftAll64(m2, DOUBLE_POW5_INV_SPLIT[q], i, &vp, &vm, mmShift);
+#endif
+#ifdef RYU_DEBUG
+    printf("%" PRIu64 " * 2^%d / 10^%u\n", mv, e2, q);
+    printf("V+=%" PRIu64 "\nV =%" PRIu64 "\nV-=%" PRIu64 "\n", vp, vr, vm);
+#endif
+    if (q <= 21) {
+      // This should use q <= 22, but I think 21 is also safe. Smaller values
+      // may still be safe, but it's more difficult to reason about them.
+      // Only one of mp, mv, and mm can be a multiple of 5, if any.
+      const uint32_t mvMod5 = ((uint32_t) mv) - 5 * ((uint32_t) div5(mv));
+      if (mvMod5 == 0) {
+        vrIsTrailingZeros = multipleOfPowerOf5(mv, q);
+      } else if (acceptBounds) {
+        // Same as min(e2 + (~mm & 1), pow5Factor(mm)) >= q
+        // <=> e2 + (~mm & 1) >= q && pow5Factor(mm) >= q
+        // <=> true && pow5Factor(mm) >= q, since e2 >= q.
+        vmIsTrailingZeros = multipleOfPowerOf5(mv - 1 - mmShift, q);
+      } else {
+        // Same as min(e2 + 1, pow5Factor(mp)) >= q.
+        vp -= multipleOfPowerOf5(mv + 2, q);
+      }
+    }
+  } else {
+    // This expression is slightly faster than max(0, log10Pow5(-e2) - 1).
+    const uint32_t q = log10Pow5(-e2) - (-e2 > 1);
+    e10 = (int32_t) q + e2;
+    const int32_t i = -e2 - (int32_t) q;
+    const int32_t k = pow5bits(i) - DOUBLE_POW5_BITCOUNT;
+    const int32_t j = (int32_t) q - k;
+#if defined(RYU_OPTIMIZE_SIZE)
+    uint64_t pow5[2];
+    double_computePow5(i, pow5);
+    vr = mulShiftAll64(m2, pow5, j, &vp, &vm, mmShift);
+#else
+    vr = mulShiftAll64(m2, DOUBLE_POW5_SPLIT[i], j, &vp, &vm, mmShift);
+#endif
+#ifdef RYU_DEBUG
+    printf("%" PRIu64 " * 5^%d / 10^%u\n", mv, -e2, q);
+    printf("%u %d %d %d\n", q, i, k, j);
+    printf("V+=%" PRIu64 "\nV =%" PRIu64 "\nV-=%" PRIu64 "\n", vp, vr, vm);
+#endif
+    if (q <= 1) {
+      // {vr,vp,vm} is trailing zeros if {mv,mp,mm} has at least q trailing 0 bits.
+      // mv = 4 * m2, so it always has at least two trailing 0 bits.
+      vrIsTrailingZeros = true;
+      if (acceptBounds) {
+        // mm = mv - 1 - mmShift, so it has 1 trailing 0 bit iff mmShift == 1.
+        vmIsTrailingZeros = mmShift == 1;
+      } else {
+        // mp = mv + 2, so it always has at least one trailing 0 bit.
+        --vp;
+      }
+    } else if (q < 63) { // TODO(ulfjack): Use a tighter bound here.
+      // We want to know if the full product has at least q trailing zeros.
+      // We need to compute min(p2(mv), p5(mv) - e2) >= q
+      // <=> p2(mv) >= q && p5(mv) - e2 >= q
+      // <=> p2(mv) >= q (because -e2 >= q)
+      vrIsTrailingZeros = multipleOfPowerOf2(mv, q);
+#ifdef RYU_DEBUG
+      printf("vr is trailing zeros=%s\n", vrIsTrailingZeros ? "true" : "false");
+#endif
+    }
+  }
+#ifdef RYU_DEBUG
+  printf("e10=%d\n", e10);
+  printf("V+=%" PRIu64 "\nV =%" PRIu64 "\nV-=%" PRIu64 "\n", vp, vr, vm);
+  printf("vm is trailing zeros=%s\n", vmIsTrailingZeros ? "true" : "false");
+  printf("vr is trailing zeros=%s\n", vrIsTrailingZeros ? "true" : "false");
+#endif
+
+  // Step 4: Find the shortest decimal representation in the interval of valid representations.
+  int32_t removed = 0;
+  uint8_t lastRemovedDigit = 0;
+  uint64_t output;
+  // On average, we remove ~2 digits.
+  if (vmIsTrailingZeros || vrIsTrailingZeros) {
+    // General case, which happens rarely (~0.7%).
+    for (;;) {
+      const uint64_t vpDiv10 = div10(vp);
+      const uint64_t vmDiv10 = div10(vm);
+      if (vpDiv10 <= vmDiv10) {
+        break;
+      }
+      const uint32_t vmMod10 = ((uint32_t) vm) - 10 * ((uint32_t) vmDiv10);
+      const uint64_t vrDiv10 = div10(vr);
+      const uint32_t vrMod10 = ((uint32_t) vr) - 10 * ((uint32_t) vrDiv10);
+      vmIsTrailingZeros &= vmMod10 == 0;
+      vrIsTrailingZeros &= lastRemovedDigit == 0;
+      lastRemovedDigit = (uint8_t) vrMod10;
+      vr = vrDiv10;
+      vp = vpDiv10;
+      vm = vmDiv10;
+      ++removed;
+    }
+#ifdef RYU_DEBUG
+    printf("V+=%" PRIu64 "\nV =%" PRIu64 "\nV-=%" PRIu64 "\n", vp, vr, vm);
+    printf("d-10=%s\n", vmIsTrailingZeros ? "true" : "false");
+#endif
+    if (vmIsTrailingZeros) {
+      for (;;) {
+        const uint64_t vmDiv10 = div10(vm);
+        const uint32_t vmMod10 = ((uint32_t) vm) - 10 * ((uint32_t) vmDiv10);
+        if (vmMod10 != 0) {
+          break;
+        }
+        const uint64_t vpDiv10 = div10(vp);
+        const uint64_t vrDiv10 = div10(vr);
+        const uint32_t vrMod10 = ((uint32_t) vr) - 10 * ((uint32_t) vrDiv10);
+        vrIsTrailingZeros &= lastRemovedDigit == 0;
+        lastRemovedDigit = (uint8_t) vrMod10;
+        vr = vrDiv10;
+        vp = vpDiv10;
+        vm = vmDiv10;
+        ++removed;
+      }
+    }
+#ifdef RYU_DEBUG
+    printf("%" PRIu64 " %d\n", vr, lastRemovedDigit);
+    printf("vr is trailing zeros=%s\n", vrIsTrailingZeros ? "true" : "false");
+#endif
+    if (vrIsTrailingZeros && lastRemovedDigit == 5 && vr % 2 == 0) {
+      // Round even if the exact number is .....50..0.
+      lastRemovedDigit = 4;
+    }
+    // We need to take vr + 1 if vr is outside bounds or we need to round up.
+    output = vr + ((vr == vm && (!acceptBounds || !vmIsTrailingZeros)) || lastRemovedDigit >= 5);
+  } else {
+    // Specialized for the common case (~99.3%). Percentages below are relative to this.
+    bool roundUp = false;
+    const uint64_t vpDiv100 = div100(vp);
+    const uint64_t vmDiv100 = div100(vm);
+    if (vpDiv100 > vmDiv100) { // Optimization: remove two digits at a time (~86.2%).
+      const uint64_t vrDiv100 = div100(vr);
+      const uint32_t vrMod100 = ((uint32_t) vr) - 100 * ((uint32_t) vrDiv100);
+      roundUp = vrMod100 >= 50;
+      vr = vrDiv100;
+      vp = vpDiv100;
+      vm = vmDiv100;
+      removed += 2;
+    }
+    // Loop iterations below (approximately), without optimization above:
+    // 0: 0.03%, 1: 13.8%, 2: 70.6%, 3: 14.0%, 4: 1.40%, 5: 0.14%, 6+: 0.02%
+    // Loop iterations below (approximately), with optimization above:
+    // 0: 70.6%, 1: 27.8%, 2: 1.40%, 3: 0.14%, 4+: 0.02%
+    for (;;) {
+      const uint64_t vpDiv10 = div10(vp);
+      const uint64_t vmDiv10 = div10(vm);
+      if (vpDiv10 <= vmDiv10) {
+        break;
+      }
+      const uint64_t vrDiv10 = div10(vr);
+      const uint32_t vrMod10 = ((uint32_t) vr) - 10 * ((uint32_t) vrDiv10);
+      roundUp = vrMod10 >= 5;
+      vr = vrDiv10;
+      vp = vpDiv10;
+      vm = vmDiv10;
+      ++removed;
+    }
+#ifdef RYU_DEBUG
+    printf("%" PRIu64 " roundUp=%s\n", vr, roundUp ? "true" : "false");
+    printf("vr is trailing zeros=%s\n", vrIsTrailingZeros ? "true" : "false");
+#endif
+    // We need to take vr + 1 if vr is outside bounds or we need to round up.
+    output = vr + (vr == vm || roundUp);
+  }
+  const int32_t exp = e10 + removed;
+
+#ifdef RYU_DEBUG
+  printf("V+=%" PRIu64 "\nV =%" PRIu64 "\nV-=%" PRIu64 "\n", vp, vr, vm);
+  printf("O=%" PRIu64 "\n", output);
+  printf("EXP=%d\n", exp);
+#endif
+
+  floating_decimal_64 fd;
+  fd.exponent = exp;
+  fd.mantissa = output;
+  return fd;
+}
+
+static inline int to_chars(const floating_decimal_64 v, const bool sign, char* const result) {
+  // Step 5: Print the decimal representation.
+  int index = 0;
+  if (sign) {
+    result[index++] = '-';
+  }
+
+  uint64_t output = v.mantissa;
+  const uint32_t olength = decimalLength17(output);
+
+#ifdef RYU_DEBUG
+  printf("DIGITS=%" PRIu64 "\n", v.mantissa);
+  printf("OLEN=%u\n", olength);
+  printf("EXP=%u\n", v.exponent + olength);
+#endif
+
+  // Print the decimal digits.
+  // The following code is equivalent to:
+  // for (uint32_t i = 0; i < olength - 1; ++i) {
+  //   const uint32_t c = output % 10; output /= 10;
+  //   result[index + olength - i] = (char) ('0' + c);
+  // }
+  // result[index] = '0' + output % 10;
+
+  uint32_t i = 0;
+  // We prefer 32-bit operations, even on 64-bit platforms.
+  // We have at most 17 digits, and uint32_t can store 9 digits.
+  // If output doesn't fit into uint32_t, we cut off 8 digits,
+  // so the rest will fit into uint32_t.
+  if ((output >> 32) != 0) {
+    // Expensive 64-bit division.
+    const uint64_t q = div1e8(output);
+    uint32_t output2 = ((uint32_t) output) - 100000000 * ((uint32_t) q);
+    output = q;
+
+    const uint32_t c = output2 % 10000;
+    output2 /= 10000;
+    const uint32_t d = output2 % 10000;
+    const uint32_t c0 = (c % 100) << 1;
+    const uint32_t c1 = (c / 100) << 1;
+    const uint32_t d0 = (d % 100) << 1;
+    const uint32_t d1 = (d / 100) << 1;
+    memcpy(result + index + olength - 1, DIGIT_TABLE + c0, 2);
+    memcpy(result + index + olength - 3, DIGIT_TABLE + c1, 2);
+    memcpy(result + index + olength - 5, DIGIT_TABLE + d0, 2);
+    memcpy(result + index + olength - 7, DIGIT_TABLE + d1, 2);
+    i += 8;
+  }
+  uint32_t output2 = (uint32_t) output;
+  while (output2 >= 10000) {
+#ifdef __clang__ // https://bugs.llvm.org/show_bug.cgi?id=38217
+    const uint32_t c = output2 - 10000 * (output2 / 10000);
+#else
+    const uint32_t c = output2 % 10000;
+#endif
+    output2 /= 10000;
+    const uint32_t c0 = (c % 100) << 1;
+    const uint32_t c1 = (c / 100) << 1;
+    memcpy(result + index + olength - i - 1, DIGIT_TABLE + c0, 2);
+    memcpy(result + index + olength - i - 3, DIGIT_TABLE + c1, 2);
+    i += 4;
+  }
+  if (output2 >= 100) {
+    const uint32_t c = (output2 % 100) << 1;
+    output2 /= 100;
+    memcpy(result + index + olength - i - 1, DIGIT_TABLE + c, 2);
+    i += 2;
+  }
+  if (output2 >= 10) {
+    const uint32_t c = output2 << 1;
+    // We can't use memcpy here: the decimal dot goes between these two digits.
+    result[index + olength - i] = DIGIT_TABLE[c + 1];
+    result[index] = DIGIT_TABLE[c];
+  } else {
+    result[index] = (char) ('0' + output2);
+  }
+
+  // Print decimal point if needed.
+  if (olength > 1) {
+    result[index + 1] = '.';
+    index += olength + 1;
+  } else {
+    ++index;
+  }
+
+  // Print the exponent.
+  result[index++] = 'E';
+  int32_t exp = v.exponent + (int32_t) olength - 1;
+  if (exp < 0) {
+    result[index++] = '-';
+    exp = -exp;
+  }
+
+  if (exp >= 100) {
+    const int32_t c = exp % 10;
+    memcpy(result + index, DIGIT_TABLE + 2 * (exp / 10), 2);
+    result[index + 2] = (char) ('0' + c);
+    index += 3;
+  } else if (exp >= 10) {
+    memcpy(result + index, DIGIT_TABLE + 2 * exp, 2);
+    index += 2;
+  } else {
+    result[index++] = (char) ('0' + exp);
+  }
+
+  return index;
+}
+
+static inline bool d2d_small_int(const uint64_t ieeeMantissa, const uint32_t ieeeExponent,
+  floating_decimal_64* const v) {
+  const uint64_t m2 = (1ull << DOUBLE_MANTISSA_BITS) | ieeeMantissa;
+  const int32_t e2 = (int32_t) ieeeExponent - DOUBLE_BIAS - DOUBLE_MANTISSA_BITS;
+
+  if (e2 > 0) {
+    // f = m2 * 2^e2 >= 2^53 is an integer.
+    // Ignore this case for now.
+    return false;
+  }
+
+  if (e2 < -52) {
+    // f < 1.
+    return false;
+  }
+
+  // Since 2^52 <= m2 < 2^53 and 0 <= -e2 <= 52: 1 <= f = m2 / 2^-e2 < 2^53.
+  // Test if the lower -e2 bits of the significand are 0, i.e. whether the fraction is 0.
+  const uint64_t mask = (1ull << -e2) - 1;
+  const uint64_t fraction = m2 & mask;
+  if (fraction != 0) {
+    return false;
+  }
+
+  // f is an integer in the range [1, 2^53).
+  // Note: mantissa might contain trailing (decimal) 0's.
+  // Note: since 2^53 < 10^16, there is no need to adjust decimalLength17().
+  v->mantissa = m2 >> -e2;
+  v->exponent = 0;
+  return true;
+}
+
+int d2s_buffered_n(double f, char* result) {
+  // Step 1: Decode the floating-point number, and unify normalized and subnormal cases.
+  const uint64_t bits = double_to_bits(f);
+
+#ifdef RYU_DEBUG
+  printf("IN=");
+  for (int32_t bit = 63; bit >= 0; --bit) {
+    printf("%d", (int) ((bits >> bit) & 1));
+  }
+  printf("\n");
+#endif
+
+  // Decode bits into sign, mantissa, and exponent.
+  const bool ieeeSign = ((bits >> (DOUBLE_MANTISSA_BITS + DOUBLE_EXPONENT_BITS)) & 1) != 0;
+  const uint64_t ieeeMantissa = bits & ((1ull << DOUBLE_MANTISSA_BITS) - 1);
+  const uint32_t ieeeExponent = (uint32_t) ((bits >> DOUBLE_MANTISSA_BITS) & ((1u << DOUBLE_EXPONENT_BITS) - 1));
+  // Case distinction; exit early for the easy cases.
+  if (ieeeExponent == ((1u << DOUBLE_EXPONENT_BITS) - 1u) || (ieeeExponent == 0 && ieeeMantissa == 0)) {
+    return copy_special_str(result, ieeeSign, ieeeExponent, ieeeMantissa);
+  }
+
+  floating_decimal_64 v;
+  const bool isSmallInt = d2d_small_int(ieeeMantissa, ieeeExponent, &v);
+  if (isSmallInt) {
+    // For small integers in the range [1, 2^53), v.mantissa might contain trailing (decimal) zeros.
+    // For scientific notation we need to move these zeros into the exponent.
+    // (This is not needed for fixed-point notation, so it might be beneficial to trim
+    // trailing zeros in to_chars only if needed - once fixed-point notation output is implemented.)
+    for (;;) {
+      const uint64_t q = div10(v.mantissa);
+      const uint32_t r = ((uint32_t) v.mantissa) - 10 * ((uint32_t) q);
+      if (r != 0) {
+        break;
+      }
+      v.mantissa = q;
+      ++v.exponent;
+    }
+  } else {
+    v = d2d(ieeeMantissa, ieeeExponent);
+  }
+
+  return to_chars(v, ieeeSign, result);
+}
+
+void d2s_buffered(double f, char* result) {
+  const int index = d2s_buffered_n(f, result);
+
+  // Terminate the string.
+  result[index] = '\0';
+}
+
+char* d2s(double f) {
+  char* const result = (char*) malloc(25);
+  d2s_buffered(f, result);
+  return result;
+}