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|
/* This code is a modified and condensed version of the ryu library, found at
* https://github.com/ulfjack/ryu. The formatting routine also mirrors some
* ideas taken from https://github.com/dtolnay/ryu, which was direct rust
* translation of the above (and has the same license as the above). That
* license is copied below.
*
* 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
#include <assert.h>
#include <stdbool.h>
#include <stdint.h>
#include <stdlib.h>
#include <string.h>
#include "common.h"
#include "itoa.h"
#define DOUBLE_MANTISSA_BITS 52
#define DOUBLE_EXPONENT_BITS 11
#define DOUBLE_BIAS 1023
#define DOUBLE_POW5_INV_BITCOUNT 125
#define DOUBLE_POW5_BITCOUNT 125
#define DOUBLE_POW5_INV_TABLE_SIZE 342
#define DOUBLE_POW5_TABLE_SIZE 326
static const uint64_t DOUBLE_POW5_INV_SPLIT[DOUBLE_POW5_INV_TABLE_SIZE][2] = {
{ 1u, 2305843009213693952u }, { 11068046444225730970u, 1844674407370955161u },
{ 5165088340638674453u, 1475739525896764129u }, { 7821419487252849886u, 1180591620717411303u },
{ 8824922364862649494u, 1888946593147858085u }, { 7059937891890119595u, 1511157274518286468u },
{ 13026647942995916322u, 1208925819614629174u }, { 9774590264567735146u, 1934281311383406679u },
{ 11509021026396098440u, 1547425049106725343u }, { 16585914450600699399u, 1237940039285380274u },
{ 15469416676735388068u, 1980704062856608439u }, { 16064882156130220778u, 1584563250285286751u },
{ 9162556910162266299u, 1267650600228229401u }, { 7281393426775805432u, 2028240960365167042u },
{ 16893161185646375315u, 1622592768292133633u }, { 2446482504291369283u, 1298074214633706907u },
{ 7603720821608101175u, 2076918743413931051u }, { 2393627842544570617u, 1661534994731144841u },
{ 16672297533003297786u, 1329227995784915872u }, { 11918280793837635165u, 2126764793255865396u },
{ 5845275820328197809u, 1701411834604692317u }, { 15744267100488289217u, 1361129467683753853u },
{ 3054734472329800808u, 2177807148294006166u }, { 17201182836831481939u, 1742245718635204932u },
{ 6382248639981364905u, 1393796574908163946u }, { 2832900194486363201u, 2230074519853062314u },
{ 5955668970331000884u, 1784059615882449851u }, { 1075186361522890384u, 1427247692705959881u },
{ 12788344622662355584u, 2283596308329535809u }, { 13920024512871794791u, 1826877046663628647u },
{ 3757321980813615186u, 1461501637330902918u }, { 10384555214134712795u, 1169201309864722334u },
{ 5547241898389809503u, 1870722095783555735u }, { 4437793518711847602u, 1496577676626844588u },
{ 10928932444453298728u, 1197262141301475670u }, { 17486291911125277965u, 1915619426082361072u },
{ 6610335899416401726u, 1532495540865888858u }, { 12666966349016942027u, 1225996432692711086u },
{ 12888448528943286597u, 1961594292308337738u }, { 17689456452638449924u, 1569275433846670190u },
{ 14151565162110759939u, 1255420347077336152u }, { 7885109000409574610u, 2008672555323737844u },
{ 9997436015069570011u, 1606938044258990275u }, { 7997948812055656009u, 1285550435407192220u },
{ 12796718099289049614u, 2056880696651507552u }, { 2858676849947419045u, 1645504557321206042u },
{ 13354987924183666206u, 1316403645856964833u }, { 17678631863951955605u, 2106245833371143733u },
{ 3074859046935833515u, 1684996666696914987u }, { 13527933681774397782u, 1347997333357531989u },
{ 10576647446613305481u, 2156795733372051183u }, { 15840015586774465031u, 1725436586697640946u },
{ 8982663654677661702u, 1380349269358112757u }, { 18061610662226169046u, 2208558830972980411u },
{ 10759939715039024913u, 1766847064778384329u }, { 12297300586773130254u, 1413477651822707463u },
{ 15986332124095098083u, 2261564242916331941u }, { 9099716884534168143u, 1809251394333065553u },
{ 14658471137111155161u, 1447401115466452442u }, { 4348079280205103483u, 1157920892373161954u },
{ 14335624477811986218u, 1852673427797059126u }, { 7779150767507678651u, 1482138742237647301u },
{ 2533971799264232598u, 1185710993790117841u }, { 15122401323048503126u, 1897137590064188545u },
{ 12097921058438802501u, 1517710072051350836u }, { 5988988032009131678u, 1214168057641080669u },
{ 16961078480698431330u, 1942668892225729070u }, { 13568862784558745064u, 1554135113780583256u },
{ 7165741412905085728u, 1243308091024466605u }, { 11465186260648137165u, 1989292945639146568u },
{ 16550846638002330379u, 1591434356511317254u }, { 16930026125143774626u, 1273147485209053803u },
{ 4951948911778577463u, 2037035976334486086u }, { 272210314680951647u, 1629628781067588869u },
{ 3907117066486671641u, 1303703024854071095u }, { 6251387306378674625u, 2085924839766513752u },
{ 16069156289328670670u, 1668739871813211001u }, { 9165976216721026213u, 1334991897450568801u },
{ 7286864317269821294u, 2135987035920910082u }, { 16897537898041588005u, 1708789628736728065u },
{ 13518030318433270404u, 1367031702989382452u }, { 6871453250525591353u, 2187250724783011924u },
{ 9186511415162383406u, 1749800579826409539u }, { 11038557946871817048u, 1399840463861127631u },
{ 10282995085511086630u, 2239744742177804210u }, { 8226396068408869304u, 1791795793742243368u },
{ 13959814484210916090u, 1433436634993794694u }, { 11267656730511734774u, 2293498615990071511u },
{ 5324776569667477496u, 1834798892792057209u }, { 7949170070475892320u, 1467839114233645767u },
{ 17427382500606444826u, 1174271291386916613u }, { 5747719112518849781u, 1878834066219066582u },
{ 15666221734240810795u, 1503067252975253265u }, { 12532977387392648636u, 1202453802380202612u },
{ 5295368560860596524u, 1923926083808324180u }, { 4236294848688477220u, 1539140867046659344u },
{ 7078384693692692099u, 1231312693637327475u }, { 11325415509908307358u, 1970100309819723960u },
{ 9060332407926645887u, 1576080247855779168u }, { 14626963555825137356u, 1260864198284623334u },
{ 12335095245094488799u, 2017382717255397335u }, { 9868076196075591040u, 1613906173804317868u },
{ 15273158586344293478u, 1291124939043454294u }, { 13369007293925138595u, 2065799902469526871u },
{ 7005857020398200553u, 1652639921975621497u }, { 16672732060544291412u, 1322111937580497197u },
{ 11918976037903224966u, 2115379100128795516u }, { 5845832015580669650u, 1692303280103036413u },
{ 12055363241948356366u, 1353842624082429130u }, { 841837113407818570u, 2166148198531886609u },
{ 4362818505468165179u, 1732918558825509287u }, { 14558301248600263113u, 1386334847060407429u },
{ 12225235553534690011u, 2218135755296651887u }, { 2401490813343931363u, 1774508604237321510u },
{ 1921192650675145090u, 1419606883389857208u }, { 17831303500047873437u, 2271371013423771532u },
{ 6886345170554478103u, 1817096810739017226u }, { 1819727321701672159u, 1453677448591213781u },
{ 16213177116328979020u, 1162941958872971024u }, { 14873036941900635463u, 1860707134196753639u },
{ 15587778368262418694u, 1488565707357402911u }, { 8780873879868024632u, 1190852565885922329u },
{ 2981351763563108441u, 1905364105417475727u }, { 13453127855076217722u, 1524291284333980581u },
{ 7073153469319063855u, 1219433027467184465u }, { 11317045550910502167u, 1951092843947495144u },
{ 12742985255470312057u, 1560874275157996115u }, { 10194388204376249646u, 1248699420126396892u },
{ 1553625868034358140u, 1997919072202235028u }, { 8621598323911307159u, 1598335257761788022u },
{ 17965325103354776697u, 1278668206209430417u }, { 13987124906400001422u, 2045869129935088668u },
{ 121653480894270168u, 1636695303948070935u }, { 97322784715416134u, 1309356243158456748u },
{ 14913111714512307107u, 2094969989053530796u }, { 8241140556867935363u, 1675975991242824637u },
{ 17660958889720079260u, 1340780792994259709u }, { 17189487779326395846u, 2145249268790815535u },
{ 13751590223461116677u, 1716199415032652428u }, { 18379969808252713988u, 1372959532026121942u },
{ 14650556434236701088u, 2196735251241795108u }, { 652398703163629901u, 1757388200993436087u },
{ 11589965406756634890u, 1405910560794748869u }, { 7475898206584884855u, 2249456897271598191u },
{ 2291369750525997561u, 1799565517817278553u }, { 9211793429904618695u, 1439652414253822842u },
{ 18428218302589300235u, 2303443862806116547u }, { 7363877012587619542u, 1842755090244893238u },
{ 13269799239553916280u, 1474204072195914590u }, { 10615839391643133024u, 1179363257756731672u },
{ 2227947767661371545u, 1886981212410770676u }, { 16539753473096738529u, 1509584969928616540u },
{ 13231802778477390823u, 1207667975942893232u }, { 6413489186596184024u, 1932268761508629172u },
{ 16198837793502678189u, 1545815009206903337u }, { 5580372605318321905u, 1236652007365522670u },
{ 8928596168509315048u, 1978643211784836272u }, { 18210923379033183008u, 1582914569427869017u },
{ 7190041073742725760u, 1266331655542295214u }, { 436019273762630246u, 2026130648867672343u },
{ 7727513048493924843u, 1620904519094137874u }, { 9871359253537050198u, 1296723615275310299u },
{ 4726128361433549347u, 2074757784440496479u }, { 7470251503888749801u, 1659806227552397183u },
{ 13354898832594820487u, 1327844982041917746u }, { 13989140502667892133u, 2124551971267068394u },
{ 14880661216876224029u, 1699641577013654715u }, { 11904528973500979224u, 1359713261610923772u },
{ 4289851098633925465u, 2175541218577478036u }, { 18189276137874781665u, 1740432974861982428u },
{ 3483374466074094362u, 1392346379889585943u }, { 1884050330976640656u, 2227754207823337509u },
{ 5196589079523222848u, 1782203366258670007u }, { 15225317707844309248u, 1425762693006936005u },
{ 5913764258841343181u, 2281220308811097609u }, { 8420360221814984868u, 1824976247048878087u },
{ 17804334621677718864u, 1459980997639102469u }, { 17932816512084085415u, 1167984798111281975u },
{ 10245762345624985047u, 1868775676978051161u }, { 4507261061758077715u, 1495020541582440929u },
{ 7295157664148372495u, 1196016433265952743u }, { 7982903447895485668u, 1913626293225524389u },
{ 10075671573058298858u, 1530901034580419511u }, { 4371188443704728763u, 1224720827664335609u },
{ 14372599139411386667u, 1959553324262936974u }, { 15187428126271019657u, 1567642659410349579u },
{ 15839291315758726049u, 1254114127528279663u }, { 3206773216762499739u, 2006582604045247462u },
{ 13633465017635730761u, 1605266083236197969u }, { 14596120828850494932u, 1284212866588958375u },
{ 4907049252451240275u, 2054740586542333401u }, { 236290587219081897u, 1643792469233866721u },
{ 14946427728742906810u, 1315033975387093376u }, { 16535586736504830250u, 2104054360619349402u },
{ 5849771759720043554u, 1683243488495479522u }, { 15747863852001765813u, 1346594790796383617u },
{ 10439186904235184007u, 2154551665274213788u }, { 15730047152871967852u, 1723641332219371030u },
{ 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 }
};
#if defined(_M_IX86) || defined(_M_ARM)
#define RYU_32_BIT_PLATFORM
#endif
#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;
}
#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;
}
#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
// Returns e == 0 ? 1 : ceil(log_2(5^e)); requires 0 <= e <= 3528.
static inline int32_t pow5bits(const int32_t e) {
// This approximation works up to the point that the multiplication overflows at e = 3529.
// If the multiplication were done in 64 bits, it would fail at 5^4004 which is just greater
// than 2^9297.
assert(e >= 0);
assert(e <= 3528);
return (int32_t) (((((uint32_t) e) * 1217359) >> 19) + 1);
}
// Returns floor(log_10(2^e)); requires 0 <= e <= 1650.
static inline uint32_t log10Pow2(const int32_t e) {
// The first value this approximation fails for is 2^1651 which is just greater than 10^297.
assert(e >= 0);
assert(e <= 1650);
return (((uint32_t) e) * 78913) >> 18;
}
// Returns floor(log_10(5^e)); requires 0 <= e <= 2620.
static inline uint32_t log10Pow5(const int32_t e) {
// The first value this approximation fails for is 5^2621 which is just greater than 10^1832.
assert(e >= 0);
assert(e <= 2620);
return (((uint32_t) e) * 732923) >> 20;
}
static inline uint64_t double_to_bits(const double d) {
uint64_t bits = 0;
memcpy(&bits, &d, sizeof(double));
return bits;
}
// 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;
// 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;
vr = mulShiftAll64(m2, DOUBLE_POW5_INV_SPLIT[q], i, &vp, &vm, mmShift);
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;
vr = mulShiftAll64(m2, DOUBLE_POW5_SPLIT[i], j, &vp, &vm, mmShift);
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);
}
}
// 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;
}
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;
}
}
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;
}
// 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;
floating_decimal_64 fd;
fd.exponent = exp;
fd.mantissa = output;
return fd;
}
static inline int
write_exponent(int32_t k, char* buf) {
int sign = k < 0;
if (sign) {
*buf++ = '-';
k = -k;
}
if (k >= 100) {
*buf++ = '0' + (k / 100);
k %= 100;
memcpy(buf, DIGIT_TABLE + (k * 2), 2);
return sign + 3;
}
else if (k >= 10) {
memcpy(buf, DIGIT_TABLE + (k * 2), 2);
return sign + 2;
}
else {
*buf = '0' + k;
return sign + 1;
}
}
/* Write a double to buf, requires 24 bytes of space */
static inline int
write_f64(double f, char* buf, bool allow_nonfinite) {
const uint64_t bits = double_to_bits(f);
const int sign = ((bits >> (DOUBLE_MANTISSA_BITS + DOUBLE_EXPONENT_BITS)) & 1) != 0;
const uint64_t ieee_mantissa = bits & ((1ull << DOUBLE_MANTISSA_BITS) - 1);
const uint32_t ieee_exponent = (uint32_t) ((bits >> DOUBLE_MANTISSA_BITS) & ((1u << DOUBLE_EXPONENT_BITS) - 1));
/* Serialize all non-finite numbers as null */
if (MS_UNLIKELY(ieee_exponent == ((1 << DOUBLE_EXPONENT_BITS) - 1))) {
if (MS_LIKELY(!allow_nonfinite)) {
memcpy(buf, "null", 4);
return 4;
}
else {
if (ieee_mantissa == 0) {
if (sign) {
memcpy(buf, "-inf", 4);
return 4;
}
memcpy(buf, "inf", 3);
return 3;
}
memcpy(buf, "nan", 3);
return 3;
}
}
if (sign) {
*buf++ = '-';
}
if (ieee_exponent == 0 && ieee_mantissa == 0) {
memcpy(buf, "0.0", 3);
return sign + 3;
}
floating_decimal_64 v = d2d(ieee_mantissa, ieee_exponent);
int length = write_u64(v.mantissa, buf) - buf;
int32_t k = v.exponent;
int32_t kk = length + k;
if (0 <= k && kk <= 16) {
/* XYZ00.0 */
memset(buf + length, '0', k + 2);
*(buf + kk) = '.';
return sign + kk + 2;
}
else if (0 < kk && kk <= 16) {
/* XY.Z */
memmove(buf + kk + 1, buf + kk, length - kk);
*(buf + kk) = '.';
return sign + length + 1;
}
else if (-5 < kk && kk <= 0) {
/* 0.0XYZ */
int offset = 2 - kk;
memmove(buf + offset, buf, length);
memset(buf, '0', offset);
*(buf + 1) = '.';
return sign + length + offset;
}
else {
/* X.YZe123 if length > 1 else Xe123 */
int offset = 0;
if (length > 1) {
offset = length;
memmove(buf + 2, buf + 1, length - 1);
*(buf + 1) = '.';
}
*(buf + offset + 1) = 'e';
return sign + offset + 2 + write_exponent(kk - 1, buf + offset + 2);
}
}
#endif // RYU_H
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