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// Copyright 2018 - 2023 Ulf Adams
// Copyright 2023 Matt Borland
// Distributed under the Boost Software License, Version 1.0.
// https://www.boost.org/LICENSE_1_0.txt
#ifndef BOOST_CHARCONV_DETAIL_RYU_GENERIC_128_HPP
#define BOOST_CHARCONV_DETAIL_RYU_GENERIC_128_HPP
#include <boost/charconv/detail/config.hpp>
#include <boost/charconv/detail/integer_search_trees.hpp>
#include <boost/charconv/detail/emulated128.hpp>
#include <cstdint>
#define BOOST_CHARCONV_POW5_TABLE_SIZE 56
#define BOOST_CHARCONV_POW5_BITCOUNT 249
#define BOOST_CHARCONV_POW5_INV_BITCOUNT 249
namespace boost { namespace charconv { namespace detail { namespace ryu {
#ifdef BOOST_CHARCONV_HAS_INT128
using unsigned_128_type = boost::uint128_type;
#else
using unsigned_128_type = uint128;
#endif
// These tables are ~4.5 kByte total, compared to ~160 kByte for the full tables.
//
// There's no way to define 128-bit constants in C, so we use little-endian
// pairs of 64-bit constants.
#if (!defined(BOOST_MSVC) || BOOST_MSVC != 1900)
template <bool b>
struct ryu_tables_template
#else
struct ryu_tables
#endif
{
static constexpr uint64_t GENERIC_POW5_TABLE[BOOST_CHARCONV_POW5_TABLE_SIZE][2] = {
{1u, 0u},
{5u, 0u},
{25u, 0u},
{125u, 0u},
{625u, 0u},
{3125u, 0u},
{15625u, 0u},
{78125u, 0u},
{390625u, 0u},
{1953125u, 0u},
{9765625u, 0u},
{48828125u, 0u},
{244140625u, 0u},
{1220703125u, 0u},
{6103515625u, 0u},
{30517578125u, 0u},
{152587890625u, 0u},
{762939453125u, 0u},
{3814697265625u, 0u},
{19073486328125u, 0u},
{95367431640625u, 0u},
{476837158203125u, 0u},
{2384185791015625u, 0u},
{11920928955078125u, 0u},
{59604644775390625u, 0u},
{298023223876953125u, 0u},
{1490116119384765625u, 0u},
{7450580596923828125u, 0u},
{359414837200037393u, 2u},
{1797074186000186965u, 10u},
{8985370930000934825u, 50u},
{8033366502585570893u, 252u},
{3273344365508751233u, 1262u},
{16366721827543756165u, 6310u},
{8046632842880574361u, 31554u},
{3339676066983768573u, 157772u},
{16698380334918842865u, 788860u},
{9704925379756007861u, 3944304u},
{11631138751360936073u, 19721522u},
{2815461535676025517u, 98607613u},
{14077307678380127585u, 493038065u},
{15046306170771983077u, 2465190328u},
{1444554559021708921u, 12325951644u},
{7222772795108544605u, 61629758220u},
{17667119901833171409u, 308148791101u},
{14548623214327650581u, 1540743955509u},
{17402883850509598057u, 7703719777548u},
{13227442957709783821u, 38518598887744u},
{10796982567420264257u, 192592994438723u},
{17091424689682218053u, 962964972193617u},
{11670147153572883801u, 4814824860968089u},
{3010503546735764157u, 24074124304840448u},
{15052517733678820785u, 120370621524202240u},
{1475612373555897461u, 601853107621011204u},
{7378061867779487305u, 3009265538105056020u},
{18443565265187884909u, 15046327690525280101u}
};
static constexpr uint64_t GENERIC_POW5_SPLIT[89][4] = {
{0u, 0u, 0u, 72057594037927936u},
{0u, 5206161169240293376u, 4575641699882439235u, 73468396926392969u},
{3360510775605221349u, 6983200512169538081u, 4325643253124434363u, 74906821675075173u},
{11917660854915489451u, 9652941469841108803u, 946308467778435600u, 76373409087490117u},
{1994853395185689235u, 16102657350889591545u, 6847013871814915412u, 77868710555449746u},
{958415760277438274u, 15059347134713823592u, 7329070255463483331u, 79393288266368765u},
{2065144883315240188u, 7145278325844925976u, 14718454754511147343u, 80947715414629833u},
{8980391188862868935u, 13709057401304208685u, 8230434828742694591u, 82532576417087045u},
{432148644612782575u, 7960151582448466064u, 12056089168559840552u, 84148467132788711u},
{484109300864744403u, 15010663910730448582u, 16824949663447227068u, 85795995087002057u},
{14793711725276144220u, 16494403799991899904u, 10145107106505865967u, 87475779699624060u},
{15427548291869817042u, 12330588654550505203u, 13980791795114552342u, 89188452518064298u},
{9979404135116626552u, 13477446383271537499u, 14459862802511591337u, 90934657454687378u},
{12385121150303452775u, 9097130814231585614u, 6523855782339765207u, 92715051028904201u},
{1822931022538209743u, 16062974719797586441u, 3619180286173516788u, 94530302614003091u},
{12318611738248470829u, 13330752208259324507u, 10986694768744162601u, 96381094688813589u},
{13684493829640282333u, 7674802078297225834u, 15208116197624593182u, 98268123094297527u},
{5408877057066295332u, 6470124174091971006u, 15112713923117703147u, 100192097295163851u},
{11407083166564425062u, 18189998238742408185u, 4337638702446708282u, 102153740646605557u},
{4112405898036935485u, 924624216579956435u, 14251108172073737125u, 104153790666259019u},
{16996739107011444789u, 10015944118339042475u, 2395188869672266257u, 106192999311487969u},
{4588314690421337879u, 5339991768263654604u, 15441007590670620066u, 108272133262096356u},
{2286159977890359825u, 14329706763185060248u, 5980012964059367667u, 110391974208576409u},
{9654767503237031099u, 11293544302844823188u, 11739932712678287805u, 112553319146000238u},
{11362964448496095896u, 7990659682315657680u, 251480263940996374u, 114756980673665505u},
{1423410421096377129u, 14274395557581462179u, 16553482793602208894u, 117003787300607788u},
{2070444190619093137u, 11517140404712147401u, 11657844572835578076u, 119294583757094535u},
{7648316884775828921u, 15264332483297977688u, 247182277434709002u, 121630231312217685u},
{17410896758132241352u, 10923914482914417070u, 13976383996795783649u, 124011608097704390u},
{9542674537907272703u, 3079432708831728956u, 14235189590642919676u, 126439609438067572u},
{10364666969937261816u, 8464573184892924210u, 12758646866025101190u, 128915148187220428u},
{14720354822146013883u, 11480204489231511423u, 7449876034836187038u, 131439155071681461u},
{1692907053653558553u, 17835392458598425233u, 1754856712536736598u, 134012579040499057u},
{5620591334531458755u, 11361776175667106627u, 13350215315297937856u, 136636387622027174u},
{17455759733928092601u, 10362573084069962561u, 11246018728801810510u, 139311567287686283u},
{2465404073814044982u, 17694822665274381860u, 1509954037718722697u, 142039123822846312u},
{2152236053329638369u, 11202280800589637091u, 16388426812920420176u, 72410041352485523u},
{17319024055671609028u, 10944982848661280484u, 2457150158022562661u, 73827744744583080u},
{17511219308535248024u, 5122059497846768077u, 2089605804219668451u, 75273205100637900u},
{10082673333144031533u, 14429008783411894887u, 12842832230171903890u, 76746965869337783u},
{16196653406315961184u, 10260180891682904501u, 10537411930446752461u, 78249581139456266u},
{15084422041749743389u, 234835370106753111u, 16662517110286225617u, 79781615848172976u},
{8199644021067702606u, 3787318116274991885u, 7438130039325743106u, 81343645993472659u},
{12039493937039359765u, 9773822153580393709u, 5945428874398357806u, 82936258850702722u},
{984543865091303961u, 7975107621689454830u, 6556665988501773347u, 84560053193370726u},
{9633317878125234244u, 16099592426808915028u, 9706674539190598200u, 86215639518264828u},
{6860695058870476186u, 4471839111886709592u, 7828342285492709568u, 87903640274981819u},
{14583324717644598331u, 4496120889473451238u, 5290040788305728466u, 89624690099949049u},
{18093669366515003715u, 12879506572606942994u, 18005739787089675377u, 91379436055028227u},
{17997493966862379937u, 14646222655265145582u, 10265023312844161858u, 93168537870790806u},
{12283848109039722318u, 11290258077250314935u, 9878160025624946825u, 94992668194556404u},
{8087752761883078164u, 5262596608437575693u, 11093553063763274413u, 96852512843287537u},
{15027787746776840781u, 12250273651168257752u, 9290470558712181914u, 98748771061435726u},
{15003915578366724489u, 2937334162439764327u, 5404085603526796602u, 100682155783835929u},
{5225610465224746757u, 14932114897406142027u, 2774647558180708010u, 102653393903748137u},
{17112957703385190360u, 12069082008339002412u, 3901112447086388439u, 104663226546146909u},
{4062324464323300238u, 3992768146772240329u, 15757196565593695724u, 106712409346361594u},
{5525364615810306701u, 11855206026704935156u, 11344868740897365300u, 108801712734172003u},
{9274143661888462646u, 4478365862348432381u, 18010077872551661771u, 110931922223466333u},
{12604141221930060148u, 8930937759942591500u, 9382183116147201338u, 113103838707570263u},
{14513929377491886653u, 1410646149696279084u, 587092196850797612u, 115318278760358235u},
{2226851524999454362u, 7717102471110805679u, 7187441550995571734u, 117576074943260147u},
{5527526061344932763u, 2347100676188369132u, 16976241418824030445u, 119878076118278875u},
{6088479778147221611u, 17669593130014777580u, 10991124207197663546u, 122225147767136307u},
{11107734086759692041u, 3391795220306863431u, 17233960908859089158u, 124618172316667879u},
{7913172514655155198u, 17726879005381242552u, 641069866244011540u, 127058049470587962u},
{12596991768458713949u, 15714785522479904446u, 6035972567136116512u, 129545696547750811u},
{16901996933781815980u, 4275085211437148707u, 14091642539965169063u, 132082048827034281u},
{7524574627987869240u, 15661204384239316051u, 2444526454225712267u, 134668059898975949u},
{8199251625090479942u, 6803282222165044067u, 16064817666437851504u, 137304702024293857u},
{4453256673338111920u, 15269922543084434181u, 3139961729834750852u, 139992966499426682u},
{15841763546372731299u, 3013174075437671812u, 4383755396295695606u, 142733864029230733u},
{9771896230907310329u, 4900659362437687569u, 12386126719044266361u, 72764212553486967u},
{9420455527449565190u, 1859606122611023693u, 6555040298902684281u, 74188850200884818u},
{5146105983135678095u, 2287300449992174951u, 4325371679080264751u, 75641380576797959u},
{11019359372592553360u, 8422686425957443718u, 7175176077944048210u, 77122349788024458u},
{11005742969399620716u, 4132174559240043701u, 9372258443096612118u, 78632314633490790u},
{8887589641394725840u, 8029899502466543662u, 14582206497241572853u, 80171842813591127u},
{360247523705545899u, 12568341805293354211u, 14653258284762517866u, 81741513143625247u},
{12314272731984275834u, 4740745023227177044u, 6141631472368337539u, 83341915771415304u},
{441052047733984759u, 7940090120939869826u, 11750200619921094248u, 84973652399183278u},
{3436657868127012749u, 9187006432149937667u, 16389726097323041290u, 86637336509772529u},
{13490220260784534044u, 15339072891382896702u, 8846102360835316895u, 88333593597298497u},
{4125672032094859833u, 158347675704003277u, 10592598512749774447u, 90063061402315272u},
{12189928252974395775u, 2386931199439295891u, 7009030566469913276u, 91826390151586454u},
{9256479608339282969u, 2844900158963599229u, 11148388908923225596u, 93624242802550437u},
{11584393507658707408u, 2863659090805147914u, 9873421561981063551u, 95457295292572042u},
{13984297296943171390u, 1931468383973130608u, 12905719743235082319u, 97326236793074198u},
{5837045222254987499u, 10213498696735864176u, 14893951506257020749u, 99231769968645227u}
};
// Unfortunately, the results are sometimes off by one or two. We use an additional
// lookup table to store those cases and adjust the result.
static constexpr uint64_t POW5_ERRORS[156] = {
0x0000000000000000u, 0x0000000000000000u, 0x0000000000000000u, 0x9555596400000000u,
0x65a6569525565555u, 0x4415551445449655u, 0x5105015504144541u, 0x65a69969a6965964u,
0x5054955969959656u, 0x5105154515554145u, 0x4055511051591555u, 0x5500514455550115u,
0x0041140014145515u, 0x1005440545511051u, 0x0014405450411004u, 0x0414440010500000u,
0x0044000440010040u, 0x5551155000004001u, 0x4554555454544114u, 0x5150045544005441u,
0x0001111400054501u, 0x6550955555554554u, 0x1504159645559559u, 0x4105055141454545u,
0x1411541410405454u, 0x0415555044545555u, 0x0014154115405550u, 0x1540055040411445u,
0x0000000500000000u, 0x5644000000000000u, 0x1155555591596555u, 0x0410440054569565u,
0x5145100010010005u, 0x0555041405500150u, 0x4141450455140450u, 0x0000000144000140u,
0x5114004001105410u, 0x4444100404005504u, 0x0414014410001015u, 0x5145055155555015u,
0x0141041444445540u, 0x0000100451541414u, 0x4105041104155550u, 0x0500501150451145u,
0x1001050000004114u, 0x5551504400141045u, 0x5110545410151454u, 0x0100001400004040u,
0x5040010111040000u, 0x0140000150541100u, 0x4400140400104110u, 0x5011014405545004u,
0x0000000044155440u, 0x0000000010000000u, 0x1100401444440001u, 0x0040401010055111u,
0x5155155551405454u, 0x0444440015514411u, 0x0054505054014101u, 0x0451015441115511u,
0x1541411401140551u, 0x4155104514445110u, 0x4141145450145515u, 0x5451445055155050u,
0x4400515554110054u, 0x5111145104501151u, 0x565a655455500501u, 0x5565555555525955u,
0x0550511500405695u, 0x4415504051054544u, 0x6555595965555554u, 0x0100915915555655u,
0x5540001510001001u, 0x5450051414000544u, 0x1405010555555551u, 0x5555515555644155u,
0x5555055595496555u, 0x5451045004415000u, 0x5450510144040144u, 0x5554155555556455u,
0x5051555495415555u, 0x5555554555555545u, 0x0000000010005455u, 0x4000005000040000u,
0x5565555555555954u, 0x5554559555555505u, 0x9645545495552555u, 0x4000400055955564u,
0x0040000000000001u, 0x4004100100000000u, 0x5540040440000411u, 0x4565555955545644u,
0x1140659549651556u, 0x0100000410010000u, 0x5555515400004001u, 0x5955545555155255u,
0x5151055545505556u, 0x5051454510554515u, 0x0501500050415554u, 0x5044154005441005u,
0x1455445450550455u, 0x0010144055144545u, 0x0000401100000004u, 0x1050145050000010u,
0x0415004554011540u, 0x1000510100151150u, 0x0100040400001144u, 0x0000000000000000u,
0x0550004400000100u, 0x0151145041451151u, 0x0000400400005450u, 0x0000100044010004u,
0x0100054100050040u, 0x0504400005410010u, 0x4011410445500105u, 0x0000404000144411u,
0x0101504404500000u, 0x0000005044400400u, 0x0000000014000100u, 0x0404440414000000u,
0x5554100410000140u, 0x4555455544505555u, 0x5454105055455455u, 0x0115454155454015u,
0x4404110000045100u, 0x4400001100101501u, 0x6596955956966a94u, 0x0040655955665965u,
0x5554144400100155u, 0xa549495401011041u, 0x5596555565955555u, 0x5569965959549555u,
0x969565a655555456u, 0x0000001000000000u, 0x0000000040000140u, 0x0000040100000000u,
0x1415454400000000u, 0x5410415411454114u, 0x0400040104000154u, 0x0504045000000411u,
0x0000001000000010u, 0x5554000000001040u, 0x5549155551556595u, 0x1455541055515555u,
0x0510555454554541u, 0x9555555555540455u, 0x6455456555556465u, 0x4524565555654514u,
0x5554655255559545u, 0x9555455441155556u, 0x0000000051515555u, 0x0010005040000550u,
0x5044044040000000u, 0x1045040440010500u, 0x0000400000040000u, 0x0000000000000000u
};
static constexpr uint64_t GENERIC_POW5_INV_SPLIT[89][4] = {
{0u, 0u, 0u, 144115188075855872u},
{1573859546583440065u, 2691002611772552616u, 6763753280790178510u, 141347765182270746u},
{12960290449513840412u, 12345512957918226762u, 18057899791198622765u, 138633484706040742u},
{7615871757716765416u, 9507132263365501332u, 4879801712092008245u, 135971326161092377u},
{7869961150745287587u, 5804035291554591636u, 8883897266325833928u, 133360288657597085u},
{2942118023529634767u, 15128191429820565086u, 10638459445243230718u, 130799390525667397u},
{14188759758411913794u, 5362791266439207815u, 8068821289119264054u, 128287668946279217u},
{7183196927902545212u, 1952291723540117099u, 12075928209936341512u, 125824179589281448u},
{5672588001402349748u, 17892323620748423487u, 9874578446960390364u, 123407996258356868u},
{4442590541217566325u, 4558254706293456445u, 10343828952663182727u, 121038210542800766u},
{3005560928406962566u, 2082271027139057888u, 13961184524927245081u, 118713931475986426u},
{13299058168408384786u, 17834349496131278595u, 9029906103900731664u, 116434285200389047u},
{5414878118283973035u, 13079825470227392078u, 17897304791683760280u, 114198414639042157u},
{14609755883382484834u, 14991702445765844156u, 3269802549772755411u, 112005479173303009u},
{15967774957605076027u, 2511532636717499923u, 16221038267832563171u, 109854654326805788u},
{9269330061621627145u, 3332501053426257392u, 16223281189403734630u, 107745131455483836u},
{16739559299223642282u, 1873986623300664530u, 6546709159471442872u, 105676117443544318u},
{17116435360051202055u, 1359075105581853924u, 2038341371621886470u, 103646834405281051u},
{17144715798009627550u, 3201623802661132408u, 9757551605154622431u, 101656519392613377u},
{17580479792687825857u, 6546633380567327312u, 15099972427870912398u, 99704424108241124u},
{9726477118325522902u, 14578369026754005435u, 11728055595254428803u, 97789814624307808u},
{134593949518343635u, 5715151379816901985u, 1660163707976377376u, 95911971106466306u},
{5515914027713859358u, 7124354893273815720u, 5548463282858794077u, 94070187543243255u},
{6188403395862945512u, 5681264392632320838u, 15417410852121406654u, 92263771480600430u},
{15908890877468271457u, 10398888261125597540u, 4817794962769172309u, 90492043761593298u},
{1413077535082201005u, 12675058125384151580u, 7731426132303759597u, 88754338271028867u},
{1486733163972670293u, 11369385300195092554u, 11610016711694864110u, 87050001685026843u},
{8788596583757589684u, 3978580923851924802u, 9255162428306775812u, 85378393225389919u},
{7203518319660962120u, 15044736224407683725u, 2488132019818199792u, 83738884418690858u},
{4004175967662388707u, 18236988667757575407u, 15613100370957482671u, 82130858859985791u},
{18371903370586036463u, 53497579022921640u, 16465963977267203307u, 80553711981064899u},
{10170778323887491315u, 1999668801648976001u, 10209763593579456445u, 79006850823153334u},
{17108131712433974546u, 16825784443029944237u, 2078700786753338945u, 77489693813976938u},
{17221789422665858532u, 12145427517550446164u, 5391414622238668005u, 76001670549108934u},
{4859588996898795878u, 1715798948121313204u, 3950858167455137171u, 74542221577515387u},
{13513469241795711526u, 631367850494860526u, 10517278915021816160u, 73110798191218799u},
{11757513142672073111u, 2581974932255022228u, 17498959383193606459u, 143413724438001539u},
{14524355192525042817u, 5640643347559376447u, 1309659274756813016u, 140659771648132296u},
{2765095348461978538u, 11021111021896007722u, 3224303603779962366u, 137958702611185230u},
{12373410389187981037u, 13679193545685856195u, 11644609038462631561u, 135309501808182158u},
{12813176257562780151u, 3754199046160268020u, 9954691079802960722u, 132711173221007413u},
{17557452279667723458u, 3237799193992485824u, 17893947919029030695u, 130162739957935629u},
{14634200999559435155u, 4123869946105211004u, 6955301747350769239u, 127663243886350468u},
{2185352760627740240u, 2864813346878886844u, 13049218671329690184u, 125211745272516185u},
{6143438674322183002u, 10464733336980678750u, 6982925169933978309u, 122807322428266620u},
{1099509117817174576u, 10202656147550524081u, 754997032816608484u, 120449071364478757u},
{2410631293559367023u, 17407273750261453804u, 15307291918933463037u, 118136105451200587u},
{12224968375134586697u, 1664436604907828062u, 11506086230137787358u, 115867555084305488u},
{3495926216898000888u, 18392536965197424288u, 10992889188570643156u, 113642567358547782u},
{8744506286256259680u, 3966568369496879937u, 18342264969761820037u, 111460305746896569u},
{7689600520560455039u, 5254331190877624630u, 9628558080573245556u, 109319949786027263u},
{11862637625618819436u, 3456120362318976488u, 14690471063106001082u, 107220694767852583u},
{5697330450030126444u, 12424082405392918899u, 358204170751754904u, 105161751436977040u},
{11257457505097373622u, 15373192700214208870u, 671619062372033814u, 103142345693961148u},
{16850355018477166700u, 1913910419361963966u, 4550257919755970531u, 101161718304283822u},
{9670835567561997011u, 10584031339132130638u, 3060560222974851757u, 99219124612893520u},
{7698686577353054710u, 11689292838639130817u, 11806331021588878241u, 97313834264240819u},
{12233569599615692137u, 3347791226108469959u, 10333904326094451110u, 95445130927687169u},
{13049400362825383933u, 17142621313007799680u, 3790542585289224168u, 93612312028186576u},
{12430457242474442072u, 5625077542189557960u, 14765055286236672238u, 91814688482138969u},
{4759444137752473128u, 2230562561567025078u, 4954443037339580076u, 90051584438315940u},
{7246913525170274758u, 8910297835195760709u, 4015904029508858381u, 88322337023761438u},
{12854430245836432067u, 8135139748065431455u, 11548083631386317976u, 86626296094571907u},
{4848827254502687803u, 4789491250196085625u, 3988192420450664125u, 84962823991462151u},
{7435538409611286684u, 904061756819742353u, 14598026519493048444u, 83331295300025028u},
{11042616160352530997u, 8948390828345326218u, 10052651191118271927u, 81731096615594853u},
{11059348291563778943u, 11696515766184685544u, 3783210511290897367u, 80161626312626082u},
{7020010856491885826u, 5025093219346041680u, 8960210401638911765u, 78622294318500592u},
{17732844474490699984u, 7820866704994446502u, 6088373186798844243u, 77112521891678506u},
{688278527545590501u, 3045610706602776618u, 8684243536999567610u, 75631741404109150u},
{2734573255120657297u, 3903146411440697663u, 9470794821691856713u, 74179396127820347u},
{15996457521023071259u, 4776627823451271680u, 12394856457265744744u, 72754940025605801u},
{13492065758834518331u, 7390517611012222399u, 1630485387832860230u, 142715675091463768u},
{13665021627282055864u, 9897834675523659302u, 17907668136755296849u, 139975126841173266u},
{9603773719399446181u, 10771916301484339398u, 10672699855989487527u, 137287204938390542u},
{3630218541553511265u, 8139010004241080614u, 2876479648932814543u, 134650898807055963u},
{8318835909686377084u, 9525369258927993371u, 2796120270400437057u, 132065217277054270u},
{11190003059043290163u, 12424345635599592110u, 12539346395388933763u, 129529188211565064u},
{8701968833973242276u, 820569587086330727u, 2315591597351480110u, 127041858141569228u},
{5115113890115690487u, 16906305245394587826u, 9899749468931071388u, 124602291907373862u},
{15543535488939245974u, 10945189844466391399u, 3553863472349432246u, 122209572307020975u},
{7709257252608325038u, 1191832167690640880u, 15077137020234258537u, 119862799751447719u},
{7541333244210021737u, 9790054727902174575u, 5160944773155322014u, 117561091926268545u},
{12297384708782857832u, 1281328873123467374u, 4827925254630475769u, 115303583460052092u},
{13243237906232367265u, 15873887428139547641u, 3607993172301799599u, 113089425598968120u},
{11384616453739611114u, 15184114243769211033u, 13148448124803481057u, 110917785887682141u},
{17727970963596660683u, 1196965221832671990u, 14537830463956404138u, 108787847856377790u},
{17241367586707330931u, 8880584684128262874u, 11173506540726547818u, 106698810713789254u},
{7184427196661305643u, 14332510582433188173u, 14230167953789677901u, 104649889046128358u}
};
static constexpr uint64_t POW5_INV_ERRORS[154] = {
0x1144155514145504u, 0x0000541555401141u, 0x0000000000000000u, 0x0154454000000000u,
0x4114105515544440u, 0x0001001111500415u, 0x4041411410011000u, 0x5550114515155014u,
0x1404100041554551u, 0x0515000450404410u, 0x5054544401140004u, 0x5155501005555105u,
0x1144141000105515u, 0x0541500000500000u, 0x1104105540444140u, 0x4000015055514110u,
0x0054010450004005u, 0x4155515404100005u, 0x5155145045155555u, 0x1511555515440558u,
0x5558544555515555u, 0x0000000000000010u, 0x5004000000000050u, 0x1415510100000010u,
0x4545555444514500u, 0x5155151555555551u, 0x1441540144044554u, 0x5150104045544400u,
0x5450545401444040u, 0x5554455045501400u, 0x4655155555555145u, 0x1000010055455055u,
0x1000004000055004u, 0x4455405104000005u, 0x4500114504150545u, 0x0000000014000000u,
0x5450000000000000u, 0x5514551511445555u, 0x4111501040555451u, 0x4515445500054444u,
0x5101500104100441u, 0x1545115155545055u, 0x0000000000000000u, 0x1554000000100000u,
0x5555545595551555u, 0x5555051851455955u, 0x5555555555555559u, 0x0000400011001555u,
0x0000004400040000u, 0x5455511555554554u, 0x5614555544115445u, 0x6455156145555155u,
0x5455855455415455u, 0x5515555144555545u, 0x0114400000145155u, 0x0000051000450511u,
0x4455154554445100u, 0x4554150141544455u, 0x65955555559a5965u, 0x5555555854559559u,
0x9569654559616595u, 0x1040044040005565u, 0x1010010500011044u, 0x1554015545154540u,
0x4440555401545441u, 0x1014441450550105u, 0x4545400410504145u, 0x5015111541040151u,
0x5145051154000410u, 0x1040001044545044u, 0x4001400000151410u, 0x0540000044040000u,
0x0510555454411544u, 0x0400054054141550u, 0x1001041145001100u, 0x0000000140000000u,
0x0000000014100000u, 0x1544005454000140u, 0x4050055505445145u, 0x0011511104504155u,
0x5505544415045055u, 0x1155154445515554u, 0x0000000000004555u, 0x0000000000000000u,
0x5101010510400004u, 0x1514045044440400u, 0x5515519555515555u, 0x4554545441555545u,
0x1551055955551515u, 0x0150000011505515u, 0x0044005040400000u, 0x0004001004010050u,
0x0000051004450414u, 0x0114001101001144u, 0x0401000001000001u, 0x4500010001000401u,
0x0004100000005000u, 0x0105000441101100u, 0x0455455550454540u, 0x5404050144105505u,
0x4101510540555455u, 0x1055541411451555u, 0x5451445110115505u, 0x1154110010101545u,
0x1145140450054055u, 0x5555565415551554u, 0x1550559555555555u, 0x5555541545045141u,
0x4555455450500100u, 0x5510454545554555u, 0x1510140115045455u, 0x1001050040111510u,
0x5555454555555504u, 0x9954155545515554u, 0x6596656555555555u, 0x0140410051555559u,
0x0011104010001544u, 0x965669659a680501u, 0x5655a55955556955u, 0x4015111014404514u,
0x1414155554505145u, 0x0540040011051404u, 0x1010000000015005u, 0x0010054050004410u,
0x5041104014000100u, 0x4440010500100001u, 0x1155510504545554u, 0x0450151545115541u,
0x4000100400110440u, 0x1004440010514440u, 0x0000115050450000u, 0x0545404455541500u,
0x1051051555505101u, 0x5505144554544144u, 0x4550545555515550u, 0x0015400450045445u,
0x4514155400554415u, 0x4555055051050151u, 0x1511441450001014u, 0x4544554510404414u,
0x4115115545545450u, 0x5500541555551555u, 0x5550010544155015u, 0x0144414045545500u,
0x4154050001050150u, 0x5550511111000145u, 0x1114504055000151u, 0x5104041101451040u,
0x0010501401051441u, 0x0010501450504401u, 0x4554585440044444u, 0x5155555951450455u,
0x0040000400105555u, 0x0000000000000001u,
};
};
#if defined(BOOST_NO_CXX17_INLINE_VARIABLES) && (!defined(BOOST_MSVC) || BOOST_MSVC != 1900)
template <bool b> constexpr uint64_t ryu_tables_template<b>::GENERIC_POW5_TABLE[BOOST_CHARCONV_POW5_TABLE_SIZE][2];
template <bool b> constexpr uint64_t ryu_tables_template<b>::GENERIC_POW5_SPLIT[89][4];
template <bool b> constexpr uint64_t ryu_tables_template<b>::GENERIC_POW5_INV_SPLIT[89][4];
template <bool b> constexpr uint64_t ryu_tables_template<b>::POW5_ERRORS[156];
template <bool b> constexpr uint64_t ryu_tables_template<b>::POW5_INV_ERRORS[154];
#endif
#if (!defined(BOOST_MSVC) || BOOST_MSVC != 1900)
using ryu_tables = ryu_tables_template<true>;
#endif
// Returns e == 0 ? 1 : ceil(log_2(5^e)); requires 0 <= e <= 32768.
static BOOST_CHARCONV_CXX14_CONSTEXPR uint32_t pow5bits(const uint32_t e) noexcept
{
BOOST_CHARCONV_ASSERT(e <= 1 << 15);
return static_cast<uint32_t>(((e * UINT64_C(163391164108059)) >> 46) + 1);
}
static BOOST_CHARCONV_CXX14_CONSTEXPR
void mul_128_256_shift(
const uint64_t* const a, const uint64_t* const b,
const uint32_t shift, const uint32_t corr,
uint64_t* const result) noexcept
{
BOOST_CHARCONV_ASSERT(shift > 0);
BOOST_CHARCONV_ASSERT(shift < 256);
const unsigned_128_type b00 = static_cast<unsigned_128_type>(a[0]) * b[0]; // 0
const unsigned_128_type b01 = static_cast<unsigned_128_type>(a[0]) * b[1]; // 64
const unsigned_128_type b02 = static_cast<unsigned_128_type>(a[0]) * b[2]; // 128
const unsigned_128_type b03 = static_cast<unsigned_128_type>(a[0]) * b[3]; // 196
const unsigned_128_type b10 = static_cast<unsigned_128_type>(a[1]) * b[0]; // 64
const unsigned_128_type b11 = static_cast<unsigned_128_type>(a[1]) * b[1]; // 128
const unsigned_128_type b12 = static_cast<unsigned_128_type>(a[1]) * b[2]; // 196
const unsigned_128_type b13 = static_cast<unsigned_128_type>(a[1]) * b[3]; // 256
const unsigned_128_type s0 = b00; // 0 x
const unsigned_128_type s1 = b01 + b10; // 64 x
const unsigned_128_type c1 = s1 < b01; // 196 x
const unsigned_128_type s2 = b02 + b11; // 128 x
const unsigned_128_type c2 = s2 < b02; // 256 x
const unsigned_128_type s3 = b03 + b12; // 196 x
const unsigned_128_type c3 = s3 < b03; // 324 x
const unsigned_128_type p0 = s0 + (s1 << 64); // 0
const unsigned_128_type d0 = p0 < b00; // 128
const unsigned_128_type q1 = s2 + (s1 >> 64) + (s3 << 64); // 128
const unsigned_128_type d1 = q1 < s2; // 256
const unsigned_128_type p1 = q1 + (c1 << 64) + d0; // 128
const unsigned_128_type d2 = p1 < q1; // 256
const unsigned_128_type p2 = b13 + (s3 >> 64) + c2 + (c3 << 64) + d1 + d2; // 256
if (shift < 128)
{
const unsigned_128_type r0 = corr + ((p0 >> shift) | (p1 << (128 - shift)));
const unsigned_128_type r1 = ((p1 >> shift) | (p2 << (128 - shift))) + (r0 < corr);
result[0] = static_cast<uint64_t>(r0);
result[1] = static_cast<uint64_t>(r0 >> 64);
result[2] = static_cast<uint64_t>(r1);
result[3] = static_cast<uint64_t>(r1 >> 64);
}
else if (shift == 128)
{
const unsigned_128_type r0 = corr + p1;
const unsigned_128_type r1 = p2 + (r0 < corr);
result[0] = static_cast<uint64_t>(r0);
result[1] = static_cast<uint64_t>(r0 >> 64);
result[2] = static_cast<uint64_t>(r1);
result[3] = static_cast<uint64_t>(r1 >> 64);
}
else
{
const unsigned_128_type r0 = corr + ((p1 >> (shift - 128)) | (p2 << (256 - shift)));
const unsigned_128_type r1 = (p2 >> (shift - 128)) + (r0 < corr);
result[0] = static_cast<uint64_t>(r0);
result[1] = static_cast<uint64_t>(r0 >> 64);
result[2] = static_cast<uint64_t>(r1);
result[3] = static_cast<uint64_t>(r1 >> 64);
}
}
// Computes 5^i in the form required by Ryu, and stores it in the given pointer.
static BOOST_CXX14_CONSTEXPR void generic_computePow5(const uint32_t i, uint64_t* const result) noexcept
{
const uint32_t base = i / BOOST_CHARCONV_POW5_TABLE_SIZE;
const uint32_t base2 = base * BOOST_CHARCONV_POW5_TABLE_SIZE;
const uint64_t* const mul = ryu_tables::GENERIC_POW5_SPLIT[base];
if (i == base2)
{
result[0] = mul[0];
result[1] = mul[1];
result[2] = mul[2];
result[3] = mul[3];
}
else
{
const uint32_t offset = i - base2;
const uint64_t* const m = ryu_tables::GENERIC_POW5_TABLE[offset];
const uint32_t delta = pow5bits(i) - pow5bits(base2);
const uint32_t corr = static_cast<uint32_t>((ryu_tables::POW5_ERRORS[i / 32] >> (2 * (i % 32))) & 3);
mul_128_256_shift(m, mul, delta, corr, result);
}
}
// Computes 5^-i in the form required by Ryu, and stores it in the given pointer.
static BOOST_CXX14_CONSTEXPR void generic_computeInvPow5(const uint32_t i, uint64_t* const result) noexcept
{
const uint32_t base = (i + BOOST_CHARCONV_POW5_TABLE_SIZE - 1) / BOOST_CHARCONV_POW5_TABLE_SIZE;
const uint32_t base2 = base * BOOST_CHARCONV_POW5_TABLE_SIZE;
const uint64_t* const mul = ryu_tables::GENERIC_POW5_INV_SPLIT[base]; // 1/5^base2
if (i == base2)
{
result[0] = mul[0] + 1;
result[1] = mul[1];
result[2] = mul[2];
result[3] = mul[3];
}
else
{
const uint32_t offset = base2 - i;
const uint64_t* const m = ryu_tables::GENERIC_POW5_TABLE[offset]; // 5^offset
const uint32_t delta = pow5bits(base2) - pow5bits(i);
const uint32_t corr = static_cast<uint32_t>((ryu_tables::POW5_INV_ERRORS[i / 32] >> (2 * (i % 32))) & 3) + UINT32_C(1);
mul_128_256_shift(m, mul, delta, corr, result);
}
}
static BOOST_CXX14_CONSTEXPR uint32_t pow5Factor(unsigned_128_type value) noexcept
{
for (uint32_t count = 0; value > 0; ++count)
{
if (value % 5 != 0)
{
return count;
}
value /= 5;
}
return 0;
}
// Returns true if value is divisible by 5^p.
static BOOST_CHARCONV_CXX14_CONSTEXPR bool multipleOfPowerOf5(const unsigned_128_type value, const uint32_t p) noexcept
{
// 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 BOOST_CHARCONV_CXX14_CONSTEXPR bool multipleOfPowerOf2(const unsigned_128_type value, const uint32_t p) noexcept
{
return (value & ((static_cast<unsigned_128_type>(1) << p) - 1)) == 0;
}
static BOOST_CHARCONV_CXX14_CONSTEXPR
unsigned_128_type mulShift(const unsigned_128_type m, const uint64_t* const mul, const int32_t j) noexcept
{
BOOST_CHARCONV_ASSERT(j > 128);
uint64_t a[2] {};
a[0] = static_cast<uint64_t>(m);
a[1] = static_cast<uint64_t>(m >> 64);
uint64_t result[4] {};
mul_128_256_shift(a, mul, static_cast<uint32_t>(j), 0, result);
return (static_cast<unsigned_128_type>(result[1]) << 64) | result[0];
}
// Returns floor(log_10(2^e)).
static BOOST_CHARCONV_CXX14_CONSTEXPR uint32_t log10Pow2(const int32_t e) noexcept
{
// The first value this approximation fails for is 2^1651 which is just greater than 10^297.
BOOST_CHARCONV_ASSERT(e >= 0);
BOOST_CHARCONV_ASSERT(e <= 1 << 15);
return static_cast<uint32_t>((static_cast<uint64_t>(e) * UINT64_C(169464822037455)) >> 49);
}
// Returns floor(log_10(5^e)).
static BOOST_CHARCONV_CXX14_CONSTEXPR uint32_t log10Pow5(const int32_t e) noexcept
{
// The first value this approximation fails for is 5^2621 which is just greater than 10^1832.
assert(e >= 0);
assert(e <= 1 << 15);
return static_cast<uint32_t>((static_cast<uint64_t>(e) * UINT64_C(196742565691928)) >> 48);
}
}}}} // Namespaces
#endif // BOOST_CHARCONV_DETAIL_RYU_GENERIC_128_HPP
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