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。
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// Copyright 2018 Ulf Adams
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//
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// The contents of this file may be used under the terms of the Apache License,
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// Version 2.0.
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//
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// (See accompanying file LICENSE-Apache or copy at
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// http://www.apache.org/licenses/LICENSE-2.0)
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//
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// Alternatively, the contents of this file may be used under the terms of
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// the Boost Software License, Version 1.0.
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// (See accompanying file LICENSE-Boost or copy at
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// https://www.boost.org/LICENSE_1_0.txt)
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//
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// Unless required by applicable law or agreed to in writing, this software
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// is distributed on an "AS IS" BASIS, WITHOUT WARRANTIES OR CONDITIONS OF ANY
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// KIND, either express or implied.
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#ifndef RYU_D2S_SMALL_TABLE_H
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#define RYU_D2S_SMALL_TABLE_H
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#include <assert.h>
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// Defines HAS_UINT128 and uint128_t if applicable.
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#include "ryu/d2s_intrinsics.h"
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// These tables are generated by PrintDoubleLookupTable.
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#define DOUBLE_POW5_INV_BITCOUNT 125
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#define DOUBLE_POW5_BITCOUNT 125
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static const uint64_t DOUBLE_POW5_INV_SPLIT2[15][2] = {
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{ 1u, 2305843009213693952u },
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{ 5955668970331000884u, 1784059615882449851u },
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{ 8982663654677661702u, 1380349269358112757u },
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{ 7286864317269821294u, 2135987035920910082u },
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{ 7005857020398200553u, 1652639921975621497u },
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{ 17965325103354776697u, 1278668206209430417u },
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{ 8928596168509315048u, 1978643211784836272u },
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{ 10075671573058298858u, 1530901034580419511u },
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{ 597001226353042382u, 1184477304306571148u },
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{ 1527430471115325346u, 1832889850782397517u },
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{ 12533209867169019542u, 1418129833677084982u },
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{ 5577825024675947042u, 2194449627517475473u },
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{ 11006974540203867551u, 1697873161311732311u },
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{ 10313493231639821582u, 1313665730009899186u },
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{ 12701016819766672773u, 2032799256770390445u }
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};
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static const uint32_t POW5_INV_OFFSETS[22] = {
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0x54544554, 0x04055545, 0x10041000, 0x00400414, 0x40010000, 0x41155555,
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0x00000454, 0x00010044, 0x40000000, 0x44000041, 0x50454450, 0x55550054,
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0x51655554, 0x40004000, 0x01000001, 0x00010500, 0x51515411, 0x05555554,
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0x50411500, 0x40040000, 0x05040110, 0x00000000
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};
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static const uint64_t DOUBLE_POW5_SPLIT2[13][2] = {
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{ 0u, 1152921504606846976u },
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{ 0u, 1490116119384765625u },
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{ 1032610780636961552u, 1925929944387235853u },
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{ 7910200175544436838u, 1244603055572228341u },
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{ 16941905809032713930u, 1608611746708759036u },
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{ 13024893955298202172u, 2079081953128979843u },
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{ 6607496772837067824u, 1343575221513417750u },
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{ 17332926989895652603u, 1736530273035216783u },
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{ 13037379183483547984u, 2244412773384604712u },
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{ 1605989338741628675u, 1450417759929778918u },
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{ 9630225068416591280u, 1874621017369538693u },
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{ 665883850346957067u, 1211445438634777304u },
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{ 14931890668723713708u, 1565756531257009982u }
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};
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static const uint32_t POW5_OFFSETS[21] = {
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0x00000000, 0x00000000, 0x00000000, 0x00000000, 0x40000000, 0x59695995,
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0x55545555, 0x56555515, 0x41150504, 0x40555410, 0x44555145, 0x44504540,
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0x45555550, 0x40004000, 0x96440440, 0x55565565, 0x54454045, 0x40154151,
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0x55559155, 0x51405555, 0x00000105
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};
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#define POW5_TABLE_SIZE 26
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static const uint64_t DOUBLE_POW5_TABLE[POW5_TABLE_SIZE] = {
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1ull, 5ull, 25ull, 125ull, 625ull, 3125ull, 15625ull, 78125ull, 390625ull,
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1953125ull, 9765625ull, 48828125ull, 244140625ull, 1220703125ull, 6103515625ull,
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30517578125ull, 152587890625ull, 762939453125ull, 3814697265625ull,
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19073486328125ull, 95367431640625ull, 476837158203125ull,
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2384185791015625ull, 11920928955078125ull, 59604644775390625ull,
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298023223876953125ull //, 1490116119384765625ull
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};
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#if defined(HAS_UINT128)
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// Computes 5^i in the form required by Ryu, and stores it in the given pointer.
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static inline void double_computePow5(const uint32_t i, uint64_t* const result) {
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const uint32_t base = i / POW5_TABLE_SIZE;
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const uint32_t base2 = base * POW5_TABLE_SIZE;
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const uint32_t offset = i - base2;
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const uint64_t* const mul = DOUBLE_POW5_SPLIT2[base];
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if (offset == 0) {
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result[0] = mul[0];
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result[1] = mul[1];
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return;
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}
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const uint64_t m = DOUBLE_POW5_TABLE[offset];
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const uint128_t b0 = ((uint128_t) m) * mul[0];
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const uint128_t b2 = ((uint128_t) m) * mul[1];
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const uint32_t delta = pow5bits(i) - pow5bits(base2);
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const uint128_t shiftedSum = (b0 >> delta) + (b2 << (64 - delta)) + ((POW5_OFFSETS[i / 16] >> ((i % 16) << 1)) & 3);
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result[0] = (uint64_t) shiftedSum;
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result[1] = (uint64_t) (shiftedSum >> 64);
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}
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// Computes 5^-i in the form required by Ryu, and stores it in the given pointer.
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static inline void double_computeInvPow5(const uint32_t i, uint64_t* const result) {
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const uint32_t base = (i + POW5_TABLE_SIZE - 1) / POW5_TABLE_SIZE;
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const uint32_t base2 = base * POW5_TABLE_SIZE;
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const uint32_t offset = base2 - i;
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const uint64_t* const mul = DOUBLE_POW5_INV_SPLIT2[base]; // 1/5^base2
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if (offset == 0) {
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result[0] = mul[0];
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result[1] = mul[1];
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return;
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}
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const uint64_t m = DOUBLE_POW5_TABLE[offset]; // 5^offset
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const uint128_t b0 = ((uint128_t) m) * (mul[0] - 1);
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const uint128_t b2 = ((uint128_t) m) * mul[1]; // 1/5^base2 * 5^offset = 1/5^(base2-offset) = 1/5^i
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const uint32_t delta = pow5bits(base2) - pow5bits(i);
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assert(i / 16 < sizeof(POW5_INV_OFFSETS) / sizeof(POW5_INV_OFFSETS[0]));
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const uint128_t shiftedSum =
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((b0 >> delta) + (b2 << (64 - delta))) + 1 + ((POW5_INV_OFFSETS[i / 16] >> ((i % 16) << 1)) & 3);
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result[0] = (uint64_t) shiftedSum;
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result[1] = (uint64_t) (shiftedSum >> 64);
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}
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#else // defined(HAS_UINT128)
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// Computes 5^i in the form required by Ryu, and stores it in the given pointer.
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static inline void double_computePow5(const uint32_t i, uint64_t* const result) {
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const uint32_t base = i / POW5_TABLE_SIZE;
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const uint32_t base2 = base * POW5_TABLE_SIZE;
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const uint32_t offset = i - base2;
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const uint64_t* const mul = DOUBLE_POW5_SPLIT2[base];
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if (offset == 0) {
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result[0] = mul[0];
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result[1] = mul[1];
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return;
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}
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const uint64_t m = DOUBLE_POW5_TABLE[offset];
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uint64_t high1;
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const uint64_t low1 = umul128(m, mul[1], &high1);
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uint64_t high0;
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const uint64_t low0 = umul128(m, mul[0], &high0);
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const uint64_t sum = high0 + low1;
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if (sum < high0) {
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++high1; // overflow into high1
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}
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// high1 | sum | low0
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const uint32_t delta = pow5bits(i) - pow5bits(base2);
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result[0] = shiftright128(low0, sum, delta) + ((POW5_OFFSETS[i / 16] >> ((i % 16) << 1)) & 3);
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result[1] = shiftright128(sum, high1, delta);
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}
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// Computes 5^-i in the form required by Ryu, and stores it in the given pointer.
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static inline void double_computeInvPow5(const uint32_t i, uint64_t* const result) {
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const uint32_t base = (i + POW5_TABLE_SIZE - 1) / POW5_TABLE_SIZE;
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const uint32_t base2 = base * POW5_TABLE_SIZE;
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const uint32_t offset = base2 - i;
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const uint64_t* const mul = DOUBLE_POW5_INV_SPLIT2[base]; // 1/5^base2
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if (offset == 0) {
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result[0] = mul[0];
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result[1] = mul[1];
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return;
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}
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const uint64_t m = DOUBLE_POW5_TABLE[offset];
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uint64_t high1;
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const uint64_t low1 = umul128(m, mul[1], &high1);
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uint64_t high0;
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const uint64_t low0 = umul128(m, mul[0] - 1, &high0);
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const uint64_t sum = high0 + low1;
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if (sum < high0) {
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++high1; // overflow into high1
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}
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// high1 | sum | low0
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const uint32_t delta = pow5bits(base2) - pow5bits(i);
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assert(i / 16 < sizeof(POW5_INV_OFFSETS) / sizeof(POW5_INV_OFFSETS[0]));
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result[0] = shiftright128(low0, sum, delta) + 1 + ((POW5_INV_OFFSETS[i / 16] >> ((i % 16) << 1)) & 3);
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result[1] = shiftright128(sum, high1, delta);
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}
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#endif // defined(HAS_UINT128)
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#endif // RYU_D2S_SMALL_TABLE_H
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