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_COMMON_H
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#define RYU_COMMON_H
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#include <assert.h>
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#include <stdint.h>
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#include <string.h>
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#if defined(_M_IX86) || defined(_M_ARM)
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#define RYU_32_BIT_PLATFORM
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#endif
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// Returns the number of decimal digits in v, which must not contain more than 9 digits.
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static inline uint32_t decimalLength9(const uint32_t v) {
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// Function precondition: v is not a 10-digit number.
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// (f2s: 9 digits are sufficient for round-tripping.)
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// (d2fixed: We print 9-digit blocks.)
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assert(v < 1000000000);
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if (v >= 100000000) { return 9; }
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if (v >= 10000000) { return 8; }
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if (v >= 1000000) { return 7; }
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if (v >= 100000) { return 6; }
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if (v >= 10000) { return 5; }
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if (v >= 1000) { return 4; }
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if (v >= 100) { return 3; }
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if (v >= 10) { return 2; }
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return 1;
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}
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// Returns e == 0 ? 1 : [log_2(5^e)]; requires 0 <= e <= 3528.
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static inline int32_t log2pow5(const int32_t e) {
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// This approximation works up to the point that the multiplication overflows at e = 3529.
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// If the multiplication were done in 64 bits, it would fail at 5^4004 which is just greater
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// than 2^9297.
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assert(e >= 0);
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assert(e <= 3528);
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return (int32_t) ((((uint32_t) e) * 1217359) >> 19);
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}
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// Returns e == 0 ? 1 : ceil(log_2(5^e)); requires 0 <= e <= 3528.
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static inline int32_t pow5bits(const int32_t e) {
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// This approximation works up to the point that the multiplication overflows at e = 3529.
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// If the multiplication were done in 64 bits, it would fail at 5^4004 which is just greater
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// than 2^9297.
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assert(e >= 0);
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assert(e <= 3528);
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return (int32_t) (((((uint32_t) e) * 1217359) >> 19) + 1);
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}
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// Returns e == 0 ? 1 : ceil(log_2(5^e)); requires 0 <= e <= 3528.
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static inline int32_t ceil_log2pow5(const int32_t e) {
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return log2pow5(e) + 1;
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}
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// Returns floor(log_10(2^e)); requires 0 <= e <= 1650.
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static inline uint32_t log10Pow2(const int32_t e) {
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// The first value this approximation fails for is 2^1651 which is just greater than 10^297.
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assert(e >= 0);
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assert(e <= 1650);
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return (((uint32_t) e) * 78913) >> 18;
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}
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// Returns floor(log_10(5^e)); requires 0 <= e <= 2620.
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static inline uint32_t log10Pow5(const int32_t e) {
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// The first value this approximation fails for is 5^2621 which is just greater than 10^1832.
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assert(e >= 0);
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assert(e <= 2620);
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return (((uint32_t) e) * 732923) >> 20;
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}
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static inline int copy_special_str(char * const result, const bool sign, const bool exponent, const bool mantissa) {
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if (mantissa) {
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memcpy(result, "NaN", 3);
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return 3;
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}
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if (sign) {
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result[0] = '-';
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}
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if (exponent) {
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memcpy(result + sign, "Infinity", 8);
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return sign + 8;
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}
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memcpy(result + sign, "0E0", 3);
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return sign + 3;
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}
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static inline uint32_t float_to_bits(const float f) {
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uint32_t bits = 0;
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memcpy(&bits, &f, sizeof(float));
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return bits;
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}
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static inline uint64_t double_to_bits(const double d) {
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uint64_t bits = 0;
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memcpy(&bits, &d, sizeof(double));
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return bits;
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}
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#endif // RYU_COMMON_H
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@@ -0,0 +1,367 @@
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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_FULL_TABLE_H
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#define RYU_D2S_FULL_TABLE_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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#define DOUBLE_POW5_INV_TABLE_SIZE 342
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#define DOUBLE_POW5_TABLE_SIZE 326
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static const uint64_t DOUBLE_POW5_INV_SPLIT[DOUBLE_POW5_INV_TABLE_SIZE][2] = {
|
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{ 1u, 2305843009213693952u }, { 11068046444225730970u, 1844674407370955161u },
|
||||
{ 5165088340638674453u, 1475739525896764129u }, { 7821419487252849886u, 1180591620717411303u },
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{ 8824922364862649494u, 1888946593147858085u }, { 7059937891890119595u, 1511157274518286468u },
|
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{ 13026647942995916322u, 1208925819614629174u }, { 9774590264567735146u, 1934281311383406679u },
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{ 11509021026396098440u, 1547425049106725343u }, { 16585914450600699399u, 1237940039285380274u },
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{ 15469416676735388068u, 1980704062856608439u }, { 16064882156130220778u, 1584563250285286751u },
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{ 9162556910162266299u, 1267650600228229401u }, { 7281393426775805432u, 2028240960365167042u },
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{ 7603720821608101175u, 2076918743413931051u }, { 2393627842544570617u, 1661534994731144841u },
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||||
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|
||||
{ 12584037722297574282u, 1378913065775496824u }, { 9066413911450387881u, 2206260905240794919u },
|
||||
{ 10942479943902220628u, 1765008724192635935u }, { 8753983955121776503u, 1412006979354108748u },
|
||||
{ 10317025513452932081u, 2259211166966573997u }, { 874922781278525018u, 1807368933573259198u },
|
||||
{ 8078635854506640661u, 1445895146858607358u }, { 13841606313089133175u, 1156716117486885886u },
|
||||
{ 14767872471458792434u, 1850745787979017418u }, { 746251532941302978u, 1480596630383213935u },
|
||||
{ 597001226353042382u, 1184477304306571148u }, { 15712597221132509104u, 1895163686890513836u },
|
||||
{ 8880728962164096960u, 1516130949512411069u }, { 10793931984473187891u, 1212904759609928855u },
|
||||
{ 17270291175157100626u, 1940647615375886168u }, { 2748186495899949531u, 1552518092300708935u },
|
||||
{ 2198549196719959625u, 1242014473840567148u }, { 18275073973719576693u, 1987223158144907436u },
|
||||
{ 10930710364233751031u, 1589778526515925949u }, { 12433917106128911148u, 1271822821212740759u },
|
||||
{ 8826220925580526867u, 2034916513940385215u }, { 7060976740464421494u, 1627933211152308172u },
|
||||
{ 16716827836597268165u, 1302346568921846537u }, { 11989529279587987770u, 2083754510274954460u },
|
||||
{ 9591623423670390216u, 1667003608219963568u }, { 15051996368420132820u, 1333602886575970854u },
|
||||
{ 13015147745246481542u, 2133764618521553367u }, { 3033420566713364587u, 1707011694817242694u },
|
||||
{ 6116085268112601993u, 1365609355853794155u }, { 9785736428980163188u, 2184974969366070648u },
|
||||
{ 15207286772667951197u, 1747979975492856518u }, { 1097782973908629988u, 1398383980394285215u },
|
||||
{ 1756452758253807981u, 2237414368630856344u }, { 5094511021344956708u, 1789931494904685075u },
|
||||
{ 4075608817075965366u, 1431945195923748060u }, { 6520974107321544586u, 2291112313477996896u },
|
||||
{ 1527430471115325346u, 1832889850782397517u }, { 12289990821117991246u, 1466311880625918013u },
|
||||
{ 17210690286378213644u, 1173049504500734410u }, { 9090360384495590213u, 1876879207201175057u },
|
||||
{ 18340334751822203140u, 1501503365760940045u }, { 14672267801457762512u, 1201202692608752036u },
|
||||
{ 16096930852848599373u, 1921924308174003258u }, { 1809498238053148529u, 1537539446539202607u },
|
||||
{ 12515645034668249793u, 1230031557231362085u }, { 1578287981759648052u, 1968050491570179337u },
|
||||
{ 12330676829633449412u, 1574440393256143469u }, { 13553890278448669853u, 1259552314604914775u },
|
||||
{ 3239480371808320148u, 2015283703367863641u }, { 17348979556414297411u, 1612226962694290912u },
|
||||
{ 6500486015647617283u, 1289781570155432730u }, { 10400777625036187652u, 2063650512248692368u },
|
||||
{ 15699319729512770768u, 1650920409798953894u }, { 16248804598352126938u, 1320736327839163115u },
|
||||
{ 7551343283653851484u, 2113178124542660985u }, { 6041074626923081187u, 1690542499634128788u },
|
||||
{ 12211557331022285596u, 1352433999707303030u }, { 1091747655926105338u, 2163894399531684849u },
|
||||
{ 4562746939482794594u, 1731115519625347879u }, { 7339546366328145998u, 1384892415700278303u },
|
||||
{ 8053925371383123274u, 2215827865120445285u }, { 6443140297106498619u, 1772662292096356228u },
|
||||
{ 12533209867169019542u, 1418129833677084982u }, { 5295740528502789974u, 2269007733883335972u },
|
||||
{ 15304638867027962949u, 1815206187106668777u }, { 4865013464138549713u, 1452164949685335022u },
|
||||
{ 14960057215536570740u, 1161731959748268017u }, { 9178696285890871890u, 1858771135597228828u },
|
||||
{ 14721654658196518159u, 1487016908477783062u }, { 4398626097073393881u, 1189613526782226450u },
|
||||
{ 7037801755317430209u, 1903381642851562320u }, { 5630241404253944167u, 1522705314281249856u },
|
||||
{ 814844308661245011u, 1218164251424999885u }, { 1303750893857992017u, 1949062802279999816u },
|
||||
{ 15800395974054034906u, 1559250241823999852u }, { 5261619149759407279u, 1247400193459199882u },
|
||||
{ 12107939454356961969u, 1995840309534719811u }, { 5997002748743659252u, 1596672247627775849u },
|
||||
{ 8486951013736837725u, 1277337798102220679u }, { 2511075177753209390u, 2043740476963553087u },
|
||||
{ 13076906586428298482u, 1634992381570842469u }, { 14150874083884549109u, 1307993905256673975u },
|
||||
{ 4194654460505726958u, 2092790248410678361u }, { 18113118827372222859u, 1674232198728542688u },
|
||||
{ 3422448617672047318u, 1339385758982834151u }, { 16543964232501006678u, 2143017214372534641u },
|
||||
{ 9545822571258895019u, 1714413771498027713u }, { 15015355686490936662u, 1371531017198422170u },
|
||||
{ 5577825024675947042u, 2194449627517475473u }, { 11840957649224578280u, 1755559702013980378u },
|
||||
{ 16851463748863483271u, 1404447761611184302u }, { 12204946739213931940u, 2247116418577894884u },
|
||||
{ 13453306206113055875u, 1797693134862315907u }, { 3383947335406624054u, 1438154507889852726u },
|
||||
{ 16482362180876329456u, 2301047212623764361u }, { 9496540929959153242u, 1840837770099011489u },
|
||||
{ 11286581558709232917u, 1472670216079209191u }, { 5339916432225476010u, 1178136172863367353u },
|
||||
{ 4854517476818851293u, 1885017876581387765u }, { 3883613981455081034u, 1508014301265110212u },
|
||||
{ 14174937629389795797u, 1206411441012088169u }, { 11611853762797942306u, 1930258305619341071u },
|
||||
{ 5600134195496443521u, 1544206644495472857u }, { 15548153800622885787u, 1235365315596378285u },
|
||||
{ 6430302007287065643u, 1976584504954205257u }, { 16212288050055383484u, 1581267603963364205u },
|
||||
{ 12969830440044306787u, 1265014083170691364u }, { 9683682259845159889u, 2024022533073106183u },
|
||||
{ 15125643437359948558u, 1619218026458484946u }, { 8411165935146048523u, 1295374421166787957u },
|
||||
{ 17147214310975587960u, 2072599073866860731u }, { 10028422634038560045u, 1658079259093488585u },
|
||||
{ 8022738107230848036u, 1326463407274790868u }, { 9147032156827446534u, 2122341451639665389u },
|
||||
{ 11006974540203867551u, 1697873161311732311u }, { 5116230817421183718u, 1358298529049385849u },
|
||||
{ 15564666937357714594u, 2173277646479017358u }, { 1383687105660440706u, 1738622117183213887u },
|
||||
{ 12174996128754083534u, 1390897693746571109u }, { 8411947361780802685u, 2225436309994513775u },
|
||||
{ 6729557889424642148u, 1780349047995611020u }, { 5383646311539713719u, 1424279238396488816u },
|
||||
{ 1235136468979721303u, 2278846781434382106u }, { 15745504434151418335u, 1823077425147505684u },
|
||||
{ 16285752362063044992u, 1458461940118004547u }, { 5649904260166615347u, 1166769552094403638u },
|
||||
{ 5350498001524674232u, 1866831283351045821u }, { 591049586477829062u, 1493465026680836657u },
|
||||
{ 11540886113407994219u, 1194772021344669325u }, { 18673707743239135u, 1911635234151470921u },
|
||||
{ 14772334225162232601u, 1529308187321176736u }, { 8128518565387875758u, 1223446549856941389u },
|
||||
{ 1937583260394870242u, 1957514479771106223u }, { 8928764237799716840u, 1566011583816884978u },
|
||||
{ 14521709019723594119u, 1252809267053507982u }, { 8477339172590109297u, 2004494827285612772u },
|
||||
{ 17849917782297818407u, 1603595861828490217u }, { 6901236596354434079u, 1282876689462792174u },
|
||||
{ 18420676183650915173u, 2052602703140467478u }, { 3668494502695001169u, 1642082162512373983u },
|
||||
{ 10313493231639821582u, 1313665730009899186u }, { 9122891541139893884u, 2101865168015838698u },
|
||||
{ 14677010862395735754u, 1681492134412670958u }, { 673562245690857633u, 1345193707530136767u }
|
||||
};
|
||||
|
||||
static const uint64_t DOUBLE_POW5_SPLIT[DOUBLE_POW5_TABLE_SIZE][2] = {
|
||||
{ 0u, 1152921504606846976u }, { 0u, 1441151880758558720u },
|
||||
{ 0u, 1801439850948198400u }, { 0u, 2251799813685248000u },
|
||||
{ 0u, 1407374883553280000u }, { 0u, 1759218604441600000u },
|
||||
{ 0u, 2199023255552000000u }, { 0u, 1374389534720000000u },
|
||||
{ 0u, 1717986918400000000u }, { 0u, 2147483648000000000u },
|
||||
{ 0u, 1342177280000000000u }, { 0u, 1677721600000000000u },
|
||||
{ 0u, 2097152000000000000u }, { 0u, 1310720000000000000u },
|
||||
{ 0u, 1638400000000000000u }, { 0u, 2048000000000000000u },
|
||||
{ 0u, 1280000000000000000u }, { 0u, 1600000000000000000u },
|
||||
{ 0u, 2000000000000000000u }, { 0u, 1250000000000000000u },
|
||||
{ 0u, 1562500000000000000u }, { 0u, 1953125000000000000u },
|
||||
{ 0u, 1220703125000000000u }, { 0u, 1525878906250000000u },
|
||||
{ 0u, 1907348632812500000u }, { 0u, 1192092895507812500u },
|
||||
{ 0u, 1490116119384765625u }, { 4611686018427387904u, 1862645149230957031u },
|
||||
{ 9799832789158199296u, 1164153218269348144u }, { 12249790986447749120u, 1455191522836685180u },
|
||||
{ 15312238733059686400u, 1818989403545856475u }, { 14528612397897220096u, 2273736754432320594u },
|
||||
{ 13692068767113150464u, 1421085471520200371u }, { 12503399940464050176u, 1776356839400250464u },
|
||||
{ 15629249925580062720u, 2220446049250313080u }, { 9768281203487539200u, 1387778780781445675u },
|
||||
{ 7598665485932036096u, 1734723475976807094u }, { 274959820560269312u, 2168404344971008868u },
|
||||
{ 9395221924704944128u, 1355252715606880542u }, { 2520655369026404352u, 1694065894508600678u },
|
||||
{ 12374191248137781248u, 2117582368135750847u }, { 14651398557727195136u, 1323488980084844279u },
|
||||
{ 13702562178731606016u, 1654361225106055349u }, { 3293144668132343808u, 2067951531382569187u },
|
||||
{ 18199116482078572544u, 1292469707114105741u }, { 8913837547316051968u, 1615587133892632177u },
|
||||
{ 15753982952572452864u, 2019483917365790221u }, { 12152082354571476992u, 1262177448353618888u },
|
||||
{ 15190102943214346240u, 1577721810442023610u }, { 9764256642163156992u, 1972152263052529513u },
|
||||
{ 17631875447420442880u, 1232595164407830945u }, { 8204786253993389888u, 1540743955509788682u },
|
||||
{ 1032610780636961552u, 1925929944387235853u }, { 2951224747111794922u, 1203706215242022408u },
|
||||
{ 3689030933889743652u, 1504632769052528010u }, { 13834660704216955373u, 1880790961315660012u },
|
||||
{ 17870034976990372916u, 1175494350822287507u }, { 17725857702810578241u, 1469367938527859384u },
|
||||
{ 3710578054803671186u, 1836709923159824231u }, { 26536550077201078u, 2295887403949780289u },
|
||||
{ 11545800389866720434u, 1434929627468612680u }, { 14432250487333400542u, 1793662034335765850u },
|
||||
{ 8816941072311974870u, 2242077542919707313u }, { 17039803216263454053u, 1401298464324817070u },
|
||||
{ 12076381983474541759u, 1751623080406021338u }, { 5872105442488401391u, 2189528850507526673u },
|
||||
{ 15199280947623720629u, 1368455531567204170u }, { 9775729147674874978u, 1710569414459005213u },
|
||||
{ 16831347453020981627u, 2138211768073756516u }, { 1296220121283337709u, 1336382355046097823u },
|
||||
{ 15455333206886335848u, 1670477943807622278u }, { 10095794471753144002u, 2088097429759527848u },
|
||||
{ 6309871544845715001u, 1305060893599704905u }, { 12499025449484531656u, 1631326116999631131u },
|
||||
{ 11012095793428276666u, 2039157646249538914u }, { 11494245889320060820u, 1274473528905961821u },
|
||||
{ 532749306367912313u, 1593091911132452277u }, { 5277622651387278295u, 1991364888915565346u },
|
||||
{ 7910200175544436838u, 1244603055572228341u }, { 14499436237857933952u, 1555753819465285426u },
|
||||
{ 8900923260467641632u, 1944692274331606783u }, { 12480606065433357876u, 1215432671457254239u },
|
||||
{ 10989071563364309441u, 1519290839321567799u }, { 9124653435777998898u, 1899113549151959749u },
|
||||
{ 8008751406574943263u, 1186945968219974843u }, { 5399253239791291175u, 1483682460274968554u },
|
||||
{ 15972438586593889776u, 1854603075343710692u }, { 759402079766405302u, 1159126922089819183u },
|
||||
{ 14784310654990170340u, 1448908652612273978u }, { 9257016281882937117u, 1811135815765342473u },
|
||||
{ 16182956370781059300u, 2263919769706678091u }, { 7808504722524468110u, 1414949856066673807u },
|
||||
{ 5148944884728197234u, 1768687320083342259u }, { 1824495087482858639u, 2210859150104177824u },
|
||||
{ 1140309429676786649u, 1381786968815111140u }, { 1425386787095983311u, 1727233711018888925u },
|
||||
{ 6393419502297367043u, 2159042138773611156u }, { 13219259225790630210u, 1349401336733506972u },
|
||||
{ 16524074032238287762u, 1686751670916883715u }, { 16043406521870471799u, 2108439588646104644u },
|
||||
{ 803757039314269066u, 1317774742903815403u }, { 14839754354425000045u, 1647218428629769253u },
|
||||
{ 4714634887749086344u, 2059023035787211567u }, { 9864175832484260821u, 1286889397367007229u },
|
||||
{ 16941905809032713930u, 1608611746708759036u }, { 2730638187581340797u, 2010764683385948796u },
|
||||
{ 10930020904093113806u, 1256727927116217997u }, { 18274212148543780162u, 1570909908895272496u },
|
||||
{ 4396021111970173586u, 1963637386119090621u }, { 5053356204195052443u, 1227273366324431638u },
|
||||
{ 15540067292098591362u, 1534091707905539547u }, { 14813398096695851299u, 1917614634881924434u },
|
||||
{ 13870059828862294966u, 1198509146801202771u }, { 12725888767650480803u, 1498136433501503464u },
|
||||
{ 15907360959563101004u, 1872670541876879330u }, { 14553786618154326031u, 1170419088673049581u },
|
||||
{ 4357175217410743827u, 1463023860841311977u }, { 10058155040190817688u, 1828779826051639971u },
|
||||
{ 7961007781811134206u, 2285974782564549964u }, { 14199001900486734687u, 1428734239102843727u },
|
||||
{ 13137066357181030455u, 1785917798878554659u }, { 11809646928048900164u, 2232397248598193324u },
|
||||
{ 16604401366885338411u, 1395248280373870827u }, { 16143815690179285109u, 1744060350467338534u },
|
||||
{ 10956397575869330579u, 2180075438084173168u }, { 6847748484918331612u, 1362547148802608230u },
|
||||
{ 17783057643002690323u, 1703183936003260287u }, { 17617136035325974999u, 2128979920004075359u },
|
||||
{ 17928239049719816230u, 1330612450002547099u }, { 17798612793722382384u, 1663265562503183874u },
|
||||
{ 13024893955298202172u, 2079081953128979843u }, { 5834715712847682405u, 1299426220705612402u },
|
||||
{ 16516766677914378815u, 1624282775882015502u }, { 11422586310538197711u, 2030353469852519378u },
|
||||
{ 11750802462513761473u, 1268970918657824611u }, { 10076817059714813937u, 1586213648322280764u },
|
||||
{ 12596021324643517422u, 1982767060402850955u }, { 5566670318688504437u, 1239229412751781847u },
|
||||
{ 2346651879933242642u, 1549036765939727309u }, { 7545000868343941206u, 1936295957424659136u },
|
||||
{ 4715625542714963254u, 1210184973390411960u }, { 5894531928393704067u, 1512731216738014950u },
|
||||
{ 16591536947346905892u, 1890914020922518687u }, { 17287239619732898039u, 1181821263076574179u },
|
||||
{ 16997363506238734644u, 1477276578845717724u }, { 2799960309088866689u, 1846595723557147156u },
|
||||
{ 10973347230035317489u, 1154122327223216972u }, { 13716684037544146861u, 1442652909029021215u },
|
||||
{ 12534169028502795672u, 1803316136286276519u }, { 11056025267201106687u, 2254145170357845649u },
|
||||
{ 18439230838069161439u, 1408840731473653530u }, { 13825666510731675991u, 1761050914342066913u },
|
||||
{ 3447025083132431277u, 2201313642927583642u }, { 6766076695385157452u, 1375821026829739776u },
|
||||
{ 8457595869231446815u, 1719776283537174720u }, { 10571994836539308519u, 2149720354421468400u },
|
||||
{ 6607496772837067824u, 1343575221513417750u }, { 17482743002901110588u, 1679469026891772187u },
|
||||
{ 17241742735199000331u, 2099336283614715234u }, { 15387775227926763111u, 1312085177259197021u },
|
||||
{ 5399660979626290177u, 1640106471573996277u }, { 11361262242960250625u, 2050133089467495346u },
|
||||
{ 11712474920277544544u, 1281333180917184591u }, { 10028907631919542777u, 1601666476146480739u },
|
||||
{ 7924448521472040567u, 2002083095183100924u }, { 14176152362774801162u, 1251301934489438077u },
|
||||
{ 3885132398186337741u, 1564127418111797597u }, { 9468101516160310080u, 1955159272639746996u },
|
||||
{ 15140935484454969608u, 1221974545399841872u }, { 479425281859160394u, 1527468181749802341u },
|
||||
{ 5210967620751338397u, 1909335227187252926u }, { 17091912818251750210u, 1193334516992033078u },
|
||||
{ 12141518985959911954u, 1491668146240041348u }, { 15176898732449889943u, 1864585182800051685u },
|
||||
{ 11791404716994875166u, 1165365739250032303u }, { 10127569877816206054u, 1456707174062540379u },
|
||||
{ 8047776328842869663u, 1820883967578175474u }, { 836348374198811271u, 2276104959472719343u },
|
||||
{ 7440246761515338900u, 1422565599670449589u }, { 13911994470321561530u, 1778206999588061986u },
|
||||
{ 8166621051047176104u, 2222758749485077483u }, { 2798295147690791113u, 1389224218428173427u },
|
||||
{ 17332926989895652603u, 1736530273035216783u }, { 17054472718942177850u, 2170662841294020979u },
|
||||
{ 8353202440125167204u, 1356664275808763112u }, { 10441503050156459005u, 1695830344760953890u },
|
||||
{ 3828506775840797949u, 2119787930951192363u }, { 86973725686804766u, 1324867456844495227u },
|
||||
{ 13943775212390669669u, 1656084321055619033u }, { 3594660960206173375u, 2070105401319523792u },
|
||||
{ 2246663100128858359u, 1293815875824702370u }, { 12031700912015848757u, 1617269844780877962u },
|
||||
{ 5816254103165035138u, 2021587305976097453u }, { 5941001823691840913u, 1263492066235060908u },
|
||||
{ 7426252279614801142u, 1579365082793826135u }, { 4671129331091113523u, 1974206353492282669u },
|
||||
{ 5225298841145639904u, 1233878970932676668u }, { 6531623551432049880u, 1542348713665845835u },
|
||||
{ 3552843420862674446u, 1927935892082307294u }, { 16055585193321335241u, 1204959932551442058u },
|
||||
{ 10846109454796893243u, 1506199915689302573u }, { 18169322836923504458u, 1882749894611628216u },
|
||||
{ 11355826773077190286u, 1176718684132267635u }, { 9583097447919099954u, 1470898355165334544u },
|
||||
{ 11978871809898874942u, 1838622943956668180u }, { 14973589762373593678u, 2298278679945835225u },
|
||||
{ 2440964573842414192u, 1436424174966147016u }, { 3051205717303017741u, 1795530218707683770u },
|
||||
{ 13037379183483547984u, 2244412773384604712u }, { 8148361989677217490u, 1402757983365377945u },
|
||||
{ 14797138505523909766u, 1753447479206722431u }, { 13884737113477499304u, 2191809349008403039u },
|
||||
{ 15595489723564518921u, 1369880843130251899u }, { 14882676136028260747u, 1712351053912814874u },
|
||||
{ 9379973133180550126u, 2140438817391018593u }, { 17391698254306313589u, 1337774260869386620u },
|
||||
{ 3292878744173340370u, 1672217826086733276u }, { 4116098430216675462u, 2090272282608416595u },
|
||||
{ 266718509671728212u, 1306420176630260372u }, { 333398137089660265u, 1633025220787825465u },
|
||||
{ 5028433689789463235u, 2041281525984781831u }, { 10060300083759496378u, 1275800953740488644u },
|
||||
{ 12575375104699370472u, 1594751192175610805u }, { 1884160825592049379u, 1993438990219513507u },
|
||||
{ 17318501580490888525u, 1245899368887195941u }, { 7813068920331446945u, 1557374211108994927u },
|
||||
{ 5154650131986920777u, 1946717763886243659u }, { 915813323278131534u, 1216698602428902287u },
|
||||
{ 14979824709379828129u, 1520873253036127858u }, { 9501408849870009354u, 1901091566295159823u },
|
||||
{ 12855909558809837702u, 1188182228934474889u }, { 2234828893230133415u, 1485227786168093612u },
|
||||
{ 2793536116537666769u, 1856534732710117015u }, { 8663489100477123587u, 1160334207943823134u },
|
||||
{ 1605989338741628675u, 1450417759929778918u }, { 11230858710281811652u, 1813022199912223647u },
|
||||
{ 9426887369424876662u, 2266277749890279559u }, { 12809333633531629769u, 1416423593681424724u },
|
||||
{ 16011667041914537212u, 1770529492101780905u }, { 6179525747111007803u, 2213161865127226132u },
|
||||
{ 13085575628799155685u, 1383226165704516332u }, { 16356969535998944606u, 1729032707130645415u },
|
||||
{ 15834525901571292854u, 2161290883913306769u }, { 2979049660840976177u, 1350806802445816731u },
|
||||
{ 17558870131333383934u, 1688508503057270913u }, { 8113529608884566205u, 2110635628821588642u },
|
||||
{ 9682642023980241782u, 1319147268013492901u }, { 16714988548402690132u, 1648934085016866126u },
|
||||
{ 11670363648648586857u, 2061167606271082658u }, { 11905663298832754689u, 1288229753919426661u },
|
||||
{ 1047021068258779650u, 1610287192399283327u }, { 15143834390605638274u, 2012858990499104158u },
|
||||
{ 4853210475701136017u, 1258036869061940099u }, { 1454827076199032118u, 1572546086327425124u },
|
||||
{ 1818533845248790147u, 1965682607909281405u }, { 3442426662494187794u, 1228551629943300878u },
|
||||
{ 13526405364972510550u, 1535689537429126097u }, { 3072948650933474476u, 1919611921786407622u },
|
||||
{ 15755650962115585259u, 1199757451116504763u }, { 15082877684217093670u, 1499696813895630954u },
|
||||
{ 9630225068416591280u, 1874621017369538693u }, { 8324733676974063502u, 1171638135855961683u },
|
||||
{ 5794231077790191473u, 1464547669819952104u }, { 7242788847237739342u, 1830684587274940130u },
|
||||
{ 18276858095901949986u, 2288355734093675162u }, { 16034722328366106645u, 1430222333808546976u },
|
||||
{ 1596658836748081690u, 1787777917260683721u }, { 6607509564362490017u, 2234722396575854651u },
|
||||
{ 1823850468512862308u, 1396701497859909157u }, { 6891499104068465790u, 1745876872324886446u },
|
||||
{ 17837745916940358045u, 2182346090406108057u }, { 4231062170446641922u, 1363966306503817536u },
|
||||
{ 5288827713058302403u, 1704957883129771920u }, { 6611034641322878003u, 2131197353912214900u },
|
||||
{ 13355268687681574560u, 1331998346195134312u }, { 16694085859601968200u, 1664997932743917890u },
|
||||
{ 11644235287647684442u, 2081247415929897363u }, { 4971804045566108824u, 1300779634956185852u },
|
||||
{ 6214755056957636030u, 1625974543695232315u }, { 3156757802769657134u, 2032468179619040394u },
|
||||
{ 6584659645158423613u, 1270292612261900246u }, { 17454196593302805324u, 1587865765327375307u },
|
||||
{ 17206059723201118751u, 1984832206659219134u }, { 6142101308573311315u, 1240520129162011959u },
|
||||
{ 3065940617289251240u, 1550650161452514949u }, { 8444111790038951954u, 1938312701815643686u },
|
||||
{ 665883850346957067u, 1211445438634777304u }, { 832354812933696334u, 1514306798293471630u },
|
||||
{ 10263815553021896226u, 1892883497866839537u }, { 17944099766707154901u, 1183052186166774710u },
|
||||
{ 13206752671529167818u, 1478815232708468388u }, { 16508440839411459773u, 1848519040885585485u },
|
||||
{ 12623618533845856310u, 1155324400553490928u }, { 15779523167307320387u, 1444155500691863660u },
|
||||
{ 1277659885424598868u, 1805194375864829576u }, { 1597074856780748586u, 2256492969831036970u },
|
||||
{ 5609857803915355770u, 1410308106144398106u }, { 16235694291748970521u, 1762885132680497632u },
|
||||
{ 1847873790976661535u, 2203606415850622041u }, { 12684136165428883219u, 1377254009906638775u },
|
||||
{ 11243484188358716120u, 1721567512383298469u }, { 219297180166231438u, 2151959390479123087u },
|
||||
{ 7054589765244976505u, 1344974619049451929u }, { 13429923224983608535u, 1681218273811814911u },
|
||||
{ 12175718012802122765u, 2101522842264768639u }, { 14527352785642408584u, 1313451776415480399u },
|
||||
{ 13547504963625622826u, 1641814720519350499u }, { 12322695186104640628u, 2052268400649188124u },
|
||||
{ 16925056528170176201u, 1282667750405742577u }, { 7321262604930556539u, 1603334688007178222u },
|
||||
{ 18374950293017971482u, 2004168360008972777u }, { 4566814905495150320u, 1252605225005607986u },
|
||||
{ 14931890668723713708u, 1565756531257009982u }, { 9441491299049866327u, 1957195664071262478u },
|
||||
{ 1289246043478778550u, 1223247290044539049u }, { 6223243572775861092u, 1529059112555673811u },
|
||||
{ 3167368447542438461u, 1911323890694592264u }, { 1979605279714024038u, 1194577431684120165u },
|
||||
{ 7086192618069917952u, 1493221789605150206u }, { 18081112809442173248u, 1866527237006437757u },
|
||||
{ 13606538515115052232u, 1166579523129023598u }, { 7784801107039039482u, 1458224403911279498u },
|
||||
{ 507629346944023544u, 1822780504889099373u }, { 5246222702107417334u, 2278475631111374216u },
|
||||
{ 3278889188817135834u, 1424047269444608885u }, { 8710297504448807696u, 1780059086805761106u }
|
||||
};
|
||||
|
||||
#endif // RYU_D2S_FULL_TABLE_H
|
||||
@@ -0,0 +1,357 @@
|
||||
// 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.
|
||||
#ifndef RYU_D2S_INTRINSICS_H
|
||||
#define RYU_D2S_INTRINSICS_H
|
||||
|
||||
#include <assert.h>
|
||||
#include <stdint.h>
|
||||
|
||||
// Defines RYU_32_BIT_PLATFORM if applicable.
|
||||
#include "ryu/common.h"
|
||||
|
||||
// ABSL avoids uint128_t on Win32 even if __SIZEOF_INT128__ is defined.
|
||||
// Let's do the same for now.
|
||||
#if defined(__SIZEOF_INT128__) && !defined(_MSC_VER) && !defined(RYU_ONLY_64_BIT_OPS)
|
||||
#define HAS_UINT128
|
||||
#elif defined(_MSC_VER) && !defined(RYU_ONLY_64_BIT_OPS) && defined(_M_X64)
|
||||
#define HAS_64_BIT_INTRINSICS
|
||||
#endif
|
||||
|
||||
#if defined(HAS_UINT128)
|
||||
typedef __uint128_t uint128_t;
|
||||
#endif
|
||||
|
||||
#if defined(HAS_64_BIT_INTRINSICS)
|
||||
|
||||
#include <intrin.h>
|
||||
|
||||
static inline uint64_t umul128(const uint64_t a, const uint64_t b, uint64_t* const productHi) {
|
||||
return _umul128(a, b, productHi);
|
||||
}
|
||||
|
||||
// Returns the lower 64 bits of (hi*2^64 + lo) >> dist, with 0 < dist < 64.
|
||||
static inline uint64_t shiftright128(const uint64_t lo, const uint64_t hi, const uint32_t dist) {
|
||||
// For the __shiftright128 intrinsic, the shift value is always
|
||||
// modulo 64.
|
||||
// In the current implementation of the double-precision version
|
||||
// of Ryu, the shift value is always < 64. (In the case
|
||||
// RYU_OPTIMIZE_SIZE == 0, the shift value is in the range [49, 58].
|
||||
// Otherwise in the range [2, 59].)
|
||||
// However, this function is now also called by s2d, which requires supporting
|
||||
// the larger shift range (TODO: what is the actual range?).
|
||||
// Check this here in case a future change requires larger shift
|
||||
// values. In this case this function needs to be adjusted.
|
||||
assert(dist < 64);
|
||||
return __shiftright128(lo, hi, (unsigned char) dist);
|
||||
}
|
||||
|
||||
#else // defined(HAS_64_BIT_INTRINSICS)
|
||||
|
||||
static inline uint64_t umul128(const uint64_t a, const uint64_t b, uint64_t* const productHi) {
|
||||
// The casts here help MSVC to avoid calls to the __allmul library function.
|
||||
const uint32_t aLo = (uint32_t)a;
|
||||
const uint32_t aHi = (uint32_t)(a >> 32);
|
||||
const uint32_t bLo = (uint32_t)b;
|
||||
const uint32_t bHi = (uint32_t)(b >> 32);
|
||||
|
||||
const uint64_t b00 = (uint64_t)aLo * bLo;
|
||||
const uint64_t b01 = (uint64_t)aLo * bHi;
|
||||
const uint64_t b10 = (uint64_t)aHi * bLo;
|
||||
const uint64_t b11 = (uint64_t)aHi * bHi;
|
||||
|
||||
const uint32_t b00Lo = (uint32_t)b00;
|
||||
const uint32_t b00Hi = (uint32_t)(b00 >> 32);
|
||||
|
||||
const uint64_t mid1 = b10 + b00Hi;
|
||||
const uint32_t mid1Lo = (uint32_t)(mid1);
|
||||
const uint32_t mid1Hi = (uint32_t)(mid1 >> 32);
|
||||
|
||||
const uint64_t mid2 = b01 + mid1Lo;
|
||||
const uint32_t mid2Lo = (uint32_t)(mid2);
|
||||
const uint32_t mid2Hi = (uint32_t)(mid2 >> 32);
|
||||
|
||||
const uint64_t pHi = b11 + mid1Hi + mid2Hi;
|
||||
const uint64_t pLo = ((uint64_t)mid2Lo << 32) | b00Lo;
|
||||
|
||||
*productHi = pHi;
|
||||
return pLo;
|
||||
}
|
||||
|
||||
static inline uint64_t shiftright128(const uint64_t lo, const uint64_t hi, const uint32_t dist) {
|
||||
// We don't need to handle the case dist >= 64 here (see above).
|
||||
assert(dist < 64);
|
||||
assert(dist > 0);
|
||||
return (hi << (64 - dist)) | (lo >> dist);
|
||||
}
|
||||
|
||||
#endif // defined(HAS_64_BIT_INTRINSICS)
|
||||
|
||||
#if defined(RYU_32_BIT_PLATFORM)
|
||||
|
||||
// Returns the high 64 bits of the 128-bit product of a and b.
|
||||
static inline uint64_t umulh(const uint64_t a, const uint64_t b) {
|
||||
// Reuse the umul128 implementation.
|
||||
// Optimizers will likely eliminate the instructions used to compute the
|
||||
// low part of the product.
|
||||
uint64_t hi;
|
||||
umul128(a, b, &hi);
|
||||
return hi;
|
||||
}
|
||||
|
||||
// On 32-bit platforms, compilers typically generate calls to library
|
||||
// functions for 64-bit divisions, even if the divisor is a constant.
|
||||
//
|
||||
// E.g.:
|
||||
// https://bugs.llvm.org/show_bug.cgi?id=37932
|
||||
// https://gcc.gnu.org/bugzilla/show_bug.cgi?id=17958
|
||||
// https://gcc.gnu.org/bugzilla/show_bug.cgi?id=37443
|
||||
//
|
||||
// The functions here perform division-by-constant using multiplications
|
||||
// in the same way as 64-bit compilers would do.
|
||||
//
|
||||
// NB:
|
||||
// The multipliers and shift values are the ones generated by clang x64
|
||||
// for expressions like x/5, x/10, etc.
|
||||
|
||||
static inline uint64_t div5(const uint64_t x) {
|
||||
return umulh(x, 0xCCCCCCCCCCCCCCCDu) >> 2;
|
||||
}
|
||||
|
||||
static inline uint64_t div10(const uint64_t x) {
|
||||
return umulh(x, 0xCCCCCCCCCCCCCCCDu) >> 3;
|
||||
}
|
||||
|
||||
static inline uint64_t div100(const uint64_t x) {
|
||||
return umulh(x >> 2, 0x28F5C28F5C28F5C3u) >> 2;
|
||||
}
|
||||
|
||||
static inline uint64_t div1e8(const uint64_t x) {
|
||||
return umulh(x, 0xABCC77118461CEFDu) >> 26;
|
||||
}
|
||||
|
||||
static inline uint64_t div1e9(const uint64_t x) {
|
||||
return umulh(x >> 9, 0x44B82FA09B5A53u) >> 11;
|
||||
}
|
||||
|
||||
static inline uint32_t mod1e9(const uint64_t x) {
|
||||
// Avoid 64-bit math as much as possible.
|
||||
// Returning (uint32_t) (x - 1000000000 * div1e9(x)) would
|
||||
// perform 32x64-bit multiplication and 64-bit subtraction.
|
||||
// x and 1000000000 * div1e9(x) are guaranteed to differ by
|
||||
// less than 10^9, so their highest 32 bits must be identical,
|
||||
// so we can truncate both sides to uint32_t before subtracting.
|
||||
// We can also simplify (uint32_t) (1000000000 * div1e9(x)).
|
||||
// We can truncate before multiplying instead of after, as multiplying
|
||||
// the highest 32 bits of div1e9(x) can't affect the lowest 32 bits.
|
||||
return ((uint32_t) x) - 1000000000 * ((uint32_t) div1e9(x));
|
||||
}
|
||||
|
||||
#else // defined(RYU_32_BIT_PLATFORM)
|
||||
|
||||
static inline uint64_t div5(const uint64_t x) {
|
||||
return x / 5;
|
||||
}
|
||||
|
||||
static inline uint64_t div10(const uint64_t x) {
|
||||
return x / 10;
|
||||
}
|
||||
|
||||
static inline uint64_t div100(const uint64_t x) {
|
||||
return x / 100;
|
||||
}
|
||||
|
||||
static inline uint64_t div1e8(const uint64_t x) {
|
||||
return x / 100000000;
|
||||
}
|
||||
|
||||
static inline uint64_t div1e9(const uint64_t x) {
|
||||
return x / 1000000000;
|
||||
}
|
||||
|
||||
static inline uint32_t mod1e9(const uint64_t x) {
|
||||
return (uint32_t) (x - 1000000000 * div1e9(x));
|
||||
}
|
||||
|
||||
#endif // defined(RYU_32_BIT_PLATFORM)
|
||||
|
||||
static inline uint32_t pow5Factor(uint64_t value) {
|
||||
const uint64_t m_inv_5 = 14757395258967641293u; // 5 * m_inv_5 = 1 (mod 2^64)
|
||||
const uint64_t n_div_5 = 3689348814741910323u; // #{ n | n = 0 (mod 2^64) } = 2^64 / 5
|
||||
uint32_t count = 0;
|
||||
for (;;) {
|
||||
assert(value != 0);
|
||||
value *= m_inv_5;
|
||||
if (value > n_div_5)
|
||||
break;
|
||||
++count;
|
||||
}
|
||||
return count;
|
||||
}
|
||||
|
||||
// Returns true if value is divisible by 5^p.
|
||||
static inline bool multipleOfPowerOf5(const uint64_t value, const uint32_t p) {
|
||||
// I tried a case distinction on p, but there was no performance difference.
|
||||
return pow5Factor(value) >= p;
|
||||
}
|
||||
|
||||
// Returns true if value is divisible by 2^p.
|
||||
static inline bool multipleOfPowerOf2(const uint64_t value, const uint32_t p) {
|
||||
assert(value != 0);
|
||||
assert(p < 64);
|
||||
// __builtin_ctzll doesn't appear to be faster here.
|
||||
return (value & ((1ull << p) - 1)) == 0;
|
||||
}
|
||||
|
||||
// We need a 64x128-bit multiplication and a subsequent 128-bit shift.
|
||||
// Multiplication:
|
||||
// The 64-bit factor is variable and passed in, the 128-bit factor comes
|
||||
// from a lookup table. We know that the 64-bit factor only has 55
|
||||
// significant bits (i.e., the 9 topmost bits are zeros). The 128-bit
|
||||
// factor only has 124 significant bits (i.e., the 4 topmost bits are
|
||||
// zeros).
|
||||
// Shift:
|
||||
// In principle, the multiplication result requires 55 + 124 = 179 bits to
|
||||
// represent. However, we then shift this value to the right by j, which is
|
||||
// at least j >= 115, so the result is guaranteed to fit into 179 - 115 = 64
|
||||
// bits. This means that we only need the topmost 64 significant bits of
|
||||
// the 64x128-bit multiplication.
|
||||
//
|
||||
// There are several ways to do this:
|
||||
// 1. Best case: the compiler exposes a 128-bit type.
|
||||
// We perform two 64x64-bit multiplications, add the higher 64 bits of the
|
||||
// lower result to the higher result, and shift by j - 64 bits.
|
||||
//
|
||||
// We explicitly cast from 64-bit to 128-bit, so the compiler can tell
|
||||
// that these are only 64-bit inputs, and can map these to the best
|
||||
// possible sequence of assembly instructions.
|
||||
// x64 machines happen to have matching assembly instructions for
|
||||
// 64x64-bit multiplications and 128-bit shifts.
|
||||
//
|
||||
// 2. Second best case: the compiler exposes intrinsics for the x64 assembly
|
||||
// instructions mentioned in 1.
|
||||
//
|
||||
// 3. We only have 64x64 bit instructions that return the lower 64 bits of
|
||||
// the result, i.e., we have to use plain C.
|
||||
// Our inputs are less than the full width, so we have three options:
|
||||
// a. Ignore this fact and just implement the intrinsics manually.
|
||||
// b. Split both into 31-bit pieces, which guarantees no internal overflow,
|
||||
// but requires extra work upfront (unless we change the lookup table).
|
||||
// c. Split only the first factor into 31-bit pieces, which also guarantees
|
||||
// no internal overflow, but requires extra work since the intermediate
|
||||
// results are not perfectly aligned.
|
||||
#if defined(HAS_UINT128)
|
||||
|
||||
// Best case: use 128-bit type.
|
||||
static inline uint64_t mulShift64(const uint64_t m, const uint64_t* const mul, const int32_t j) {
|
||||
const uint128_t b0 = ((uint128_t) m) * mul[0];
|
||||
const uint128_t b2 = ((uint128_t) m) * mul[1];
|
||||
return (uint64_t) (((b0 >> 64) + b2) >> (j - 64));
|
||||
}
|
||||
|
||||
static inline uint64_t mulShiftAll64(const uint64_t m, const uint64_t* const mul, const int32_t j,
|
||||
uint64_t* const vp, uint64_t* const vm, const uint32_t mmShift) {
|
||||
// m <<= 2;
|
||||
// uint128_t b0 = ((uint128_t) m) * mul[0]; // 0
|
||||
// uint128_t b2 = ((uint128_t) m) * mul[1]; // 64
|
||||
//
|
||||
// uint128_t hi = (b0 >> 64) + b2;
|
||||
// uint128_t lo = b0 & 0xffffffffffffffffull;
|
||||
// uint128_t factor = (((uint128_t) mul[1]) << 64) + mul[0];
|
||||
// uint128_t vpLo = lo + (factor << 1);
|
||||
// *vp = (uint64_t) ((hi + (vpLo >> 64)) >> (j - 64));
|
||||
// uint128_t vmLo = lo - (factor << mmShift);
|
||||
// *vm = (uint64_t) ((hi + (vmLo >> 64) - (((uint128_t) 1ull) << 64)) >> (j - 64));
|
||||
// return (uint64_t) (hi >> (j - 64));
|
||||
*vp = mulShift64(4 * m + 2, mul, j);
|
||||
*vm = mulShift64(4 * m - 1 - mmShift, mul, j);
|
||||
return mulShift64(4 * m, mul, j);
|
||||
}
|
||||
|
||||
#elif defined(HAS_64_BIT_INTRINSICS)
|
||||
|
||||
static inline uint64_t mulShift64(const uint64_t m, const uint64_t* const mul, const int32_t j) {
|
||||
// m is maximum 55 bits
|
||||
uint64_t high1; // 128
|
||||
const uint64_t low1 = umul128(m, mul[1], &high1); // 64
|
||||
uint64_t high0; // 64
|
||||
umul128(m, mul[0], &high0); // 0
|
||||
const uint64_t sum = high0 + low1;
|
||||
if (sum < high0) {
|
||||
++high1; // overflow into high1
|
||||
}
|
||||
return shiftright128(sum, high1, j - 64);
|
||||
}
|
||||
|
||||
static inline uint64_t mulShiftAll64(const uint64_t m, const uint64_t* const mul, const int32_t j,
|
||||
uint64_t* const vp, uint64_t* const vm, const uint32_t mmShift) {
|
||||
*vp = mulShift64(4 * m + 2, mul, j);
|
||||
*vm = mulShift64(4 * m - 1 - mmShift, mul, j);
|
||||
return mulShift64(4 * m, mul, j);
|
||||
}
|
||||
|
||||
#else // !defined(HAS_UINT128) && !defined(HAS_64_BIT_INTRINSICS)
|
||||
|
||||
static inline uint64_t mulShift64(const uint64_t m, const uint64_t* const mul, const int32_t j) {
|
||||
// m is maximum 55 bits
|
||||
uint64_t high1; // 128
|
||||
const uint64_t low1 = umul128(m, mul[1], &high1); // 64
|
||||
uint64_t high0; // 64
|
||||
umul128(m, mul[0], &high0); // 0
|
||||
const uint64_t sum = high0 + low1;
|
||||
if (sum < high0) {
|
||||
++high1; // overflow into high1
|
||||
}
|
||||
return shiftright128(sum, high1, j - 64);
|
||||
}
|
||||
|
||||
// This is faster if we don't have a 64x64->128-bit multiplication.
|
||||
static inline uint64_t mulShiftAll64(uint64_t m, const uint64_t* const mul, const int32_t j,
|
||||
uint64_t* const vp, uint64_t* const vm, const uint32_t mmShift) {
|
||||
m <<= 1;
|
||||
// m is maximum 55 bits
|
||||
uint64_t tmp;
|
||||
const uint64_t lo = umul128(m, mul[0], &tmp);
|
||||
uint64_t hi;
|
||||
const uint64_t mid = tmp + umul128(m, mul[1], &hi);
|
||||
hi += mid < tmp; // overflow into hi
|
||||
|
||||
const uint64_t lo2 = lo + mul[0];
|
||||
const uint64_t mid2 = mid + mul[1] + (lo2 < lo);
|
||||
const uint64_t hi2 = hi + (mid2 < mid);
|
||||
*vp = shiftright128(mid2, hi2, (uint32_t) (j - 64 - 1));
|
||||
|
||||
if (mmShift == 1) {
|
||||
const uint64_t lo3 = lo - mul[0];
|
||||
const uint64_t mid3 = mid - mul[1] - (lo3 > lo);
|
||||
const uint64_t hi3 = hi - (mid3 > mid);
|
||||
*vm = shiftright128(mid3, hi3, (uint32_t) (j - 64 - 1));
|
||||
} else {
|
||||
const uint64_t lo3 = lo + lo;
|
||||
const uint64_t mid3 = mid + mid + (lo3 < lo);
|
||||
const uint64_t hi3 = hi + hi + (mid3 < mid);
|
||||
const uint64_t lo4 = lo3 - mul[0];
|
||||
const uint64_t mid4 = mid3 - mul[1] - (lo4 > lo3);
|
||||
const uint64_t hi4 = hi3 - (mid4 > mid3);
|
||||
*vm = shiftright128(mid4, hi4, (uint32_t) (j - 64));
|
||||
}
|
||||
|
||||
return shiftright128(mid, hi, (uint32_t) (j - 64 - 1));
|
||||
}
|
||||
|
||||
#endif // HAS_64_BIT_INTRINSICS
|
||||
|
||||
#endif // RYU_D2S_INTRINSICS_H
|
||||
@@ -0,0 +1,186 @@
|
||||
// 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.
|
||||
#ifndef RYU_D2S_SMALL_TABLE_H
|
||||
#define RYU_D2S_SMALL_TABLE_H
|
||||
|
||||
#include <assert.h>
|
||||
|
||||
// Defines HAS_UINT128 and uint128_t if applicable.
|
||||
#include "ryu/d2s_intrinsics.h"
|
||||
|
||||
// These tables are generated by PrintDoubleLookupTable.
|
||||
#define DOUBLE_POW5_INV_BITCOUNT 125
|
||||
#define DOUBLE_POW5_BITCOUNT 125
|
||||
|
||||
static const uint64_t DOUBLE_POW5_INV_SPLIT2[15][2] = {
|
||||
{ 1u, 2305843009213693952u },
|
||||
{ 5955668970331000884u, 1784059615882449851u },
|
||||
{ 8982663654677661702u, 1380349269358112757u },
|
||||
{ 7286864317269821294u, 2135987035920910082u },
|
||||
{ 7005857020398200553u, 1652639921975621497u },
|
||||
{ 17965325103354776697u, 1278668206209430417u },
|
||||
{ 8928596168509315048u, 1978643211784836272u },
|
||||
{ 10075671573058298858u, 1530901034580419511u },
|
||||
{ 597001226353042382u, 1184477304306571148u },
|
||||
{ 1527430471115325346u, 1832889850782397517u },
|
||||
{ 12533209867169019542u, 1418129833677084982u },
|
||||
{ 5577825024675947042u, 2194449627517475473u },
|
||||
{ 11006974540203867551u, 1697873161311732311u },
|
||||
{ 10313493231639821582u, 1313665730009899186u },
|
||||
{ 12701016819766672773u, 2032799256770390445u }
|
||||
};
|
||||
static const uint32_t POW5_INV_OFFSETS[22] = {
|
||||
0x54544554, 0x04055545, 0x10041000, 0x00400414, 0x40010000, 0x41155555,
|
||||
0x00000454, 0x00010044, 0x40000000, 0x44000041, 0x50454450, 0x55550054,
|
||||
0x51655554, 0x40004000, 0x01000001, 0x00010500, 0x51515411, 0x05555554,
|
||||
0x50411500, 0x40040000, 0x05040110, 0x00000000
|
||||
};
|
||||
|
||||
static const uint64_t DOUBLE_POW5_SPLIT2[13][2] = {
|
||||
{ 0u, 1152921504606846976u },
|
||||
{ 0u, 1490116119384765625u },
|
||||
{ 1032610780636961552u, 1925929944387235853u },
|
||||
{ 7910200175544436838u, 1244603055572228341u },
|
||||
{ 16941905809032713930u, 1608611746708759036u },
|
||||
{ 13024893955298202172u, 2079081953128979843u },
|
||||
{ 6607496772837067824u, 1343575221513417750u },
|
||||
{ 17332926989895652603u, 1736530273035216783u },
|
||||
{ 13037379183483547984u, 2244412773384604712u },
|
||||
{ 1605989338741628675u, 1450417759929778918u },
|
||||
{ 9630225068416591280u, 1874621017369538693u },
|
||||
{ 665883850346957067u, 1211445438634777304u },
|
||||
{ 14931890668723713708u, 1565756531257009982u }
|
||||
};
|
||||
static const uint32_t POW5_OFFSETS[21] = {
|
||||
0x00000000, 0x00000000, 0x00000000, 0x00000000, 0x40000000, 0x59695995,
|
||||
0x55545555, 0x56555515, 0x41150504, 0x40555410, 0x44555145, 0x44504540,
|
||||
0x45555550, 0x40004000, 0x96440440, 0x55565565, 0x54454045, 0x40154151,
|
||||
0x55559155, 0x51405555, 0x00000105
|
||||
};
|
||||
|
||||
#define POW5_TABLE_SIZE 26
|
||||
static const uint64_t DOUBLE_POW5_TABLE[POW5_TABLE_SIZE] = {
|
||||
1ull, 5ull, 25ull, 125ull, 625ull, 3125ull, 15625ull, 78125ull, 390625ull,
|
||||
1953125ull, 9765625ull, 48828125ull, 244140625ull, 1220703125ull, 6103515625ull,
|
||||
30517578125ull, 152587890625ull, 762939453125ull, 3814697265625ull,
|
||||
19073486328125ull, 95367431640625ull, 476837158203125ull,
|
||||
2384185791015625ull, 11920928955078125ull, 59604644775390625ull,
|
||||
298023223876953125ull //, 1490116119384765625ull
|
||||
};
|
||||
|
||||
#if defined(HAS_UINT128)
|
||||
|
||||
// Computes 5^i in the form required by Ryu, and stores it in the given pointer.
|
||||
static inline void double_computePow5(const uint32_t i, uint64_t* const result) {
|
||||
const uint32_t base = i / POW5_TABLE_SIZE;
|
||||
const uint32_t base2 = base * POW5_TABLE_SIZE;
|
||||
const uint32_t offset = i - base2;
|
||||
const uint64_t* const mul = DOUBLE_POW5_SPLIT2[base];
|
||||
if (offset == 0) {
|
||||
result[0] = mul[0];
|
||||
result[1] = mul[1];
|
||||
return;
|
||||
}
|
||||
const uint64_t m = DOUBLE_POW5_TABLE[offset];
|
||||
const uint128_t b0 = ((uint128_t) m) * mul[0];
|
||||
const uint128_t b2 = ((uint128_t) m) * mul[1];
|
||||
const uint32_t delta = pow5bits(i) - pow5bits(base2);
|
||||
const uint128_t shiftedSum = (b0 >> delta) + (b2 << (64 - delta)) + ((POW5_OFFSETS[i / 16] >> ((i % 16) << 1)) & 3);
|
||||
result[0] = (uint64_t) shiftedSum;
|
||||
result[1] = (uint64_t) (shiftedSum >> 64);
|
||||
}
|
||||
|
||||
// Computes 5^-i in the form required by Ryu, and stores it in the given pointer.
|
||||
static inline void double_computeInvPow5(const uint32_t i, uint64_t* const result) {
|
||||
const uint32_t base = (i + POW5_TABLE_SIZE - 1) / POW5_TABLE_SIZE;
|
||||
const uint32_t base2 = base * POW5_TABLE_SIZE;
|
||||
const uint32_t offset = base2 - i;
|
||||
const uint64_t* const mul = DOUBLE_POW5_INV_SPLIT2[base]; // 1/5^base2
|
||||
if (offset == 0) {
|
||||
result[0] = mul[0];
|
||||
result[1] = mul[1];
|
||||
return;
|
||||
}
|
||||
const uint64_t m = DOUBLE_POW5_TABLE[offset]; // 5^offset
|
||||
const uint128_t b0 = ((uint128_t) m) * (mul[0] - 1);
|
||||
const uint128_t b2 = ((uint128_t) m) * mul[1]; // 1/5^base2 * 5^offset = 1/5^(base2-offset) = 1/5^i
|
||||
const uint32_t delta = pow5bits(base2) - pow5bits(i);
|
||||
assert(i / 16 < sizeof(POW5_INV_OFFSETS) / sizeof(POW5_INV_OFFSETS[0]));
|
||||
const uint128_t shiftedSum =
|
||||
((b0 >> delta) + (b2 << (64 - delta))) + 1 + ((POW5_INV_OFFSETS[i / 16] >> ((i % 16) << 1)) & 3);
|
||||
result[0] = (uint64_t) shiftedSum;
|
||||
result[1] = (uint64_t) (shiftedSum >> 64);
|
||||
}
|
||||
|
||||
#else // defined(HAS_UINT128)
|
||||
|
||||
// Computes 5^i in the form required by Ryu, and stores it in the given pointer.
|
||||
static inline void double_computePow5(const uint32_t i, uint64_t* const result) {
|
||||
const uint32_t base = i / POW5_TABLE_SIZE;
|
||||
const uint32_t base2 = base * POW5_TABLE_SIZE;
|
||||
const uint32_t offset = i - base2;
|
||||
const uint64_t* const mul = DOUBLE_POW5_SPLIT2[base];
|
||||
if (offset == 0) {
|
||||
result[0] = mul[0];
|
||||
result[1] = mul[1];
|
||||
return;
|
||||
}
|
||||
const uint64_t m = DOUBLE_POW5_TABLE[offset];
|
||||
uint64_t high1;
|
||||
const uint64_t low1 = umul128(m, mul[1], &high1);
|
||||
uint64_t high0;
|
||||
const uint64_t low0 = umul128(m, mul[0], &high0);
|
||||
const uint64_t sum = high0 + low1;
|
||||
if (sum < high0) {
|
||||
++high1; // overflow into high1
|
||||
}
|
||||
// high1 | sum | low0
|
||||
const uint32_t delta = pow5bits(i) - pow5bits(base2);
|
||||
result[0] = shiftright128(low0, sum, delta) + ((POW5_OFFSETS[i / 16] >> ((i % 16) << 1)) & 3);
|
||||
result[1] = shiftright128(sum, high1, delta);
|
||||
}
|
||||
|
||||
// Computes 5^-i in the form required by Ryu, and stores it in the given pointer.
|
||||
static inline void double_computeInvPow5(const uint32_t i, uint64_t* const result) {
|
||||
const uint32_t base = (i + POW5_TABLE_SIZE - 1) / POW5_TABLE_SIZE;
|
||||
const uint32_t base2 = base * POW5_TABLE_SIZE;
|
||||
const uint32_t offset = base2 - i;
|
||||
const uint64_t* const mul = DOUBLE_POW5_INV_SPLIT2[base]; // 1/5^base2
|
||||
if (offset == 0) {
|
||||
result[0] = mul[0];
|
||||
result[1] = mul[1];
|
||||
return;
|
||||
}
|
||||
const uint64_t m = DOUBLE_POW5_TABLE[offset];
|
||||
uint64_t high1;
|
||||
const uint64_t low1 = umul128(m, mul[1], &high1);
|
||||
uint64_t high0;
|
||||
const uint64_t low0 = umul128(m, mul[0] - 1, &high0);
|
||||
const uint64_t sum = high0 + low1;
|
||||
if (sum < high0) {
|
||||
++high1; // overflow into high1
|
||||
}
|
||||
// high1 | sum | low0
|
||||
const uint32_t delta = pow5bits(base2) - pow5bits(i);
|
||||
assert(i / 16 < sizeof(POW5_INV_OFFSETS) / sizeof(POW5_INV_OFFSETS[0]));
|
||||
result[0] = shiftright128(low0, sum, delta) + 1 + ((POW5_INV_OFFSETS[i / 16] >> ((i % 16) << 1)) & 3);
|
||||
result[1] = shiftright128(sum, high1, delta);
|
||||
}
|
||||
|
||||
#endif // defined(HAS_UINT128)
|
||||
|
||||
#endif // RYU_D2S_SMALL_TABLE_H
|
||||
@@ -0,0 +1,35 @@
|
||||
// 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.
|
||||
#ifndef RYU_DIGIT_TABLE_H
|
||||
#define RYU_DIGIT_TABLE_H
|
||||
|
||||
// A table of all two-digit numbers. This is used to speed up decimal digit
|
||||
// generation by copying pairs of digits into the final output.
|
||||
static const char DIGIT_TABLE[200] = {
|
||||
'0','0','0','1','0','2','0','3','0','4','0','5','0','6','0','7','0','8','0','9',
|
||||
'1','0','1','1','1','2','1','3','1','4','1','5','1','6','1','7','1','8','1','9',
|
||||
'2','0','2','1','2','2','2','3','2','4','2','5','2','6','2','7','2','8','2','9',
|
||||
'3','0','3','1','3','2','3','3','3','4','3','5','3','6','3','7','3','8','3','9',
|
||||
'4','0','4','1','4','2','4','3','4','4','4','5','4','6','4','7','4','8','4','9',
|
||||
'5','0','5','1','5','2','5','3','5','4','5','5','5','6','5','7','5','8','5','9',
|
||||
'6','0','6','1','6','2','6','3','6','4','6','5','6','6','6','7','6','8','6','9',
|
||||
'7','0','7','1','7','2','7','3','7','4','7','5','7','6','7','7','7','8','7','9',
|
||||
'8','0','8','1','8','2','8','3','8','4','8','5','8','6','8','7','8','8','8','9',
|
||||
'9','0','9','1','9','2','9','3','9','4','9','5','9','6','9','7','9','8','9','9'
|
||||
};
|
||||
|
||||
#endif // RYU_DIGIT_TABLE_H
|
||||
@@ -0,0 +1,46 @@
|
||||
// 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.
|
||||
#ifndef RYU_H
|
||||
#define RYU_H
|
||||
|
||||
#ifdef __cplusplus
|
||||
extern "C" {
|
||||
#endif
|
||||
|
||||
#include <inttypes.h>
|
||||
|
||||
int d2s_buffered_n(double f, char* result);
|
||||
void d2s_buffered(double f, char* result);
|
||||
char* d2s(double f);
|
||||
|
||||
int f2s_buffered_n(float f, char* result);
|
||||
void f2s_buffered(float f, char* result);
|
||||
char* f2s(float f);
|
||||
|
||||
int d2fixed_buffered_n(double d, uint32_t precision, char* result);
|
||||
void d2fixed_buffered(double d, uint32_t precision, char* result);
|
||||
char* d2fixed(double d, uint32_t precision);
|
||||
|
||||
int d2exp_buffered_n(double d, uint32_t precision, char* result);
|
||||
void d2exp_buffered(double d, uint32_t precision, char* result);
|
||||
char* d2exp(double d, uint32_t precision);
|
||||
|
||||
#ifdef __cplusplus
|
||||
}
|
||||
#endif
|
||||
|
||||
#endif // RYU_H
|
||||
Reference in new issue
Block a user