/*
 * ********** REFERENCE **********
 * URL: https://github.com/abolz/Drachennest
 * Section: src/dragonbox.cc
 */

#define DIY_SIGNIFICAND_SIZE        64                  /* Symbol: 1 bit, Exponent, 11 bits, Mantissa, 52 bits */
#define DP_SIGNIFICAND_SIZE         52                  /* Mantissa, 52 bits */
#define DP_EXPONENT_OFFSET          0x3FF               /* Exponent offset is 0x3FF */
#define DP_EXPONENT_MAX             0x7FF               /* Max Exponent value */
#define DP_EXPONENT_MASK            0x7FF0000000000000  /* Exponent Mask, 11 bits */
#define DP_SIGNIFICAND_MASK         0x000FFFFFFFFFFFFF  /* Mantissa Mask, 52 bits */
#define DP_HIDDEN_BIT               0x0010000000000000  /* Integer bit for Mantissa */

typedef struct {
    uint64_t f;
    int32_t e;
} diy_fp_t;

typedef struct {
    uint64_t hi;
    uint64_t lo;
} uint64x2;

static inline uint64x2 compute_pow10_double(int32_t k)
{
#define MIN_K   -292
#define MAX_K    326
    static const uint64x2 pow10_lut[MAX_K - MIN_K + 1] = {
        {0xFF77B1FCBEBCDC4F, 0x25E8E89C13BB0F7B},
        {0x9FAACF3DF73609B1, 0x77B191618C54E9AD},
        {0xC795830D75038C1D, 0xD59DF5B9EF6A2418},
        {0xF97AE3D0D2446F25, 0x4B0573286B44AD1E},
        {0x9BECCE62836AC577, 0x4EE367F9430AEC33},
        {0xC2E801FB244576D5, 0x229C41F793CDA740},
        {0xF3A20279ED56D48A, 0x6B43527578C11110},
        {0x9845418C345644D6, 0x830A13896B78AAAA},
        {0xBE5691EF416BD60C, 0x23CC986BC656D554},
        {0xEDEC366B11C6CB8F, 0x2CBFBE86B7EC8AA9},
        {0x94B3A202EB1C3F39, 0x7BF7D71432F3D6AA},
        {0xB9E08A83A5E34F07, 0xDAF5CCD93FB0CC54},
        {0xE858AD248F5C22C9, 0xD1B3400F8F9CFF69},
        {0x91376C36D99995BE, 0x23100809B9C21FA2},
        {0xB58547448FFFFB2D, 0xABD40A0C2832A78B},
        {0xE2E69915B3FFF9F9, 0x16C90C8F323F516D},
        {0x8DD01FAD907FFC3B, 0xAE3DA7D97F6792E4},
        {0xB1442798F49FFB4A, 0x99CD11CFDF41779D},
        {0xDD95317F31C7FA1D, 0x40405643D711D584},
        {0x8A7D3EEF7F1CFC52, 0x482835EA666B2573},
        {0xAD1C8EAB5EE43B66, 0xDA3243650005EED0},
        {0xD863B256369D4A40, 0x90BED43E40076A83},
        {0x873E4F75E2224E68, 0x5A7744A6E804A292},
        {0xA90DE3535AAAE202, 0x711515D0A205CB37},
        {0xD3515C2831559A83, 0x0D5A5B44CA873E04},
        {0x8412D9991ED58091, 0xE858790AFE9486C3},
        {0xA5178FFF668AE0B6, 0x626E974DBE39A873},
        {0xCE5D73FF402D98E3, 0xFB0A3D212DC81290},
        {0x80FA687F881C7F8E, 0x7CE66634BC9D0B9A},
        {0xA139029F6A239F72, 0x1C1FFFC1EBC44E81},
        {0xC987434744AC874E, 0xA327FFB266B56221},
        {0xFBE9141915D7A922, 0x4BF1FF9F0062BAA9},
        {0x9D71AC8FADA6C9B5, 0x6F773FC3603DB4AA},
        {0xC4CE17B399107C22, 0xCB550FB4384D21D4},
        {0xF6019DA07F549B2B, 0x7E2A53A146606A49},
        {0x99C102844F94E0FB, 0x2EDA7444CBFC426E},
        {0xC0314325637A1939, 0xFA911155FEFB5309},
        {0xF03D93EEBC589F88, 0x793555AB7EBA27CB},
        {0x96267C7535B763B5, 0x4BC1558B2F3458DF},
        {0xBBB01B9283253CA2, 0x9EB1AAEDFB016F17},
        {0xEA9C227723EE8BCB, 0x465E15A979C1CADD},
        {0x92A1958A7675175F, 0x0BFACD89EC191ECA},
        {0xB749FAED14125D36, 0xCEF980EC671F667C},
        {0xE51C79A85916F484, 0x82B7E12780E7401B},
        {0x8F31CC0937AE58D2, 0xD1B2ECB8B0908811},
        {0xB2FE3F0B8599EF07, 0x861FA7E6DCB4AA16},
        {0xDFBDCECE67006AC9, 0x67A791E093E1D49B},
        {0x8BD6A141006042BD, 0xE0C8BB2C5C6D24E1},
        {0xAECC49914078536D, 0x58FAE9F773886E19},
        {0xDA7F5BF590966848, 0xAF39A475506A899F},
        {0x888F99797A5E012D, 0x6D8406C952429604},
        {0xAAB37FD7D8F58178, 0xC8E5087BA6D33B84},
        {0xD5605FCDCF32E1D6, 0xFB1E4A9A90880A65},
        {0x855C3BE0A17FCD26, 0x5CF2EEA09A550680},
        {0xA6B34AD8C9DFC06F, 0xF42FAA48C0EA481F},
        {0xD0601D8EFC57B08B, 0xF13B94DAF124DA27},
        {0x823C12795DB6CE57, 0x76C53D08D6B70859},
        {0xA2CB1717B52481ED, 0x54768C4B0C64CA6F},
        {0xCB7DDCDDA26DA268, 0xA9942F5DCF7DFD0A},
        {0xFE5D54150B090B02, 0xD3F93B35435D7C4D},
        {0x9EFA548D26E5A6E1, 0xC47BC5014A1A6DB0},
        {0xC6B8E9B0709F109A, 0x359AB6419CA1091C},
        {0xF867241C8CC6D4C0, 0xC30163D203C94B63},
        {0x9B407691D7FC44F8, 0x79E0DE63425DCF1E},
        {0xC21094364DFB5636, 0x985915FC12F542E5},
        {0xF294B943E17A2BC4, 0x3E6F5B7B17B2939E},
        {0x979CF3CA6CEC5B5A, 0xA705992CEECF9C43},
        {0xBD8430BD08277231, 0x50C6FF782A838354},
        {0xECE53CEC4A314EBD, 0xA4F8BF5635246429},
        {0x940F4613AE5ED136, 0x871B7795E136BE9A},
        {0xB913179899F68584, 0x28E2557B59846E40},
        {0xE757DD7EC07426E5, 0x331AEADA2FE589D0},
        {0x9096EA6F3848984F, 0x3FF0D2C85DEF7622},
        {0xB4BCA50B065ABE63, 0x0FED077A756B53AA},
        {0xE1EBCE4DC7F16DFB, 0xD3E8495912C62895},
        {0x8D3360F09CF6E4BD, 0x64712DD7ABBBD95D},
        {0xB080392CC4349DEC, 0xBD8D794D96AACFB4},
        {0xDCA04777F541C567, 0xECF0D7A0FC5583A1},
        {0x89E42CAAF9491B60, 0xF41686C49DB57245},
        {0xAC5D37D5B79B6239, 0x311C2875C522CED6},
        {0xD77485CB25823AC7, 0x7D633293366B828C},
        {0x86A8D39EF77164BC, 0xAE5DFF9C02033198},
        {0xA8530886B54DBDEB, 0xD9F57F830283FDFD},
        {0xD267CAA862A12D66, 0xD072DF63C324FD7C},
        {0x8380DEA93DA4BC60, 0x4247CB9E59F71E6E},
        {0xA46116538D0DEB78, 0x52D9BE85F074E609},
        {0xCD795BE870516656, 0x67902E276C921F8C},
        {0x806BD9714632DFF6, 0x00BA1CD8A3DB53B7},
        {0xA086CFCD97BF97F3, 0x80E8A40ECCD228A5},
        {0xC8A883C0FDAF7DF0, 0x6122CD128006B2CE},
        {0xFAD2A4B13D1B5D6C, 0x796B805720085F82},
        {0x9CC3A6EEC6311A63, 0xCBE3303674053BB1},
        {0xC3F490AA77BD60FC, 0xBEDBFC4411068A9D},
        {0xF4F1B4D515ACB93B, 0xEE92FB5515482D45},
        {0x991711052D8BF3C5, 0x751BDD152D4D1C4B},
        {0xBF5CD54678EEF0B6, 0xD262D45A78A0635E},
        {0xEF340A98172AACE4, 0x86FB897116C87C35},
        {0x9580869F0E7AAC0E, 0xD45D35E6AE3D4DA1},
        {0xBAE0A846D2195712, 0x8974836059CCA10A},
        {0xE998D258869FACD7, 0x2BD1A438703FC94C},
        {0x91FF83775423CC06, 0x7B6306A34627DDD0},
        {0xB67F6455292CBF08, 0x1A3BC84C17B1D543},
        {0xE41F3D6A7377EECA, 0x20CABA5F1D9E4A94},
        {0x8E938662882AF53E, 0x547EB47B7282EE9D},
        {0xB23867FB2A35B28D, 0xE99E619A4F23AA44},
        {0xDEC681F9F4C31F31, 0x6405FA00E2EC94D5},
        {0x8B3C113C38F9F37E, 0xDE83BC408DD3DD05},
        {0xAE0B158B4738705E, 0x9624AB50B148D446},
        {0xD98DDAEE19068C76, 0x3BADD624DD9B0958},
        {0x87F8A8D4CFA417C9, 0xE54CA5D70A80E5D7},
        {0xA9F6D30A038D1DBC, 0x5E9FCF4CCD211F4D},
        {0xD47487CC8470652B, 0x7647C32000696720},
        {0x84C8D4DFD2C63F3B, 0x29ECD9F40041E074},
        {0xA5FB0A17C777CF09, 0xF468107100525891},
        {0xCF79CC9DB955C2CC, 0x7182148D4066EEB5},
        {0x81AC1FE293D599BF, 0xC6F14CD848405531},
        {0xA21727DB38CB002F, 0xB8ADA00E5A506A7D},
        {0xCA9CF1D206FDC03B, 0xA6D90811F0E4851D},
        {0xFD442E4688BD304A, 0x908F4A166D1DA664},
        {0x9E4A9CEC15763E2E, 0x9A598E4E043287FF},
        {0xC5DD44271AD3CDBA, 0x40EFF1E1853F29FE},
        {0xF7549530E188C128, 0xD12BEE59E68EF47D},
        {0x9A94DD3E8CF578B9, 0x82BB74F8301958CF},
        {0xC13A148E3032D6E7, 0xE36A52363C1FAF02},
        {0xF18899B1BC3F8CA1, 0xDC44E6C3CB279AC2},
        {0x96F5600F15A7B7E5, 0x29AB103A5EF8C0BA},
        {0xBCB2B812DB11A5DE, 0x7415D448F6B6F0E8},
        {0xEBDF661791D60F56, 0x111B495B3464AD22},
        {0x936B9FCEBB25C995, 0xCAB10DD900BEEC35},
        {0xB84687C269EF3BFB, 0x3D5D514F40EEA743},
        {0xE65829B3046B0AFA, 0x0CB4A5A3112A5113},
        {0x8FF71A0FE2C2E6DC, 0x47F0E785EABA72AC},
        {0xB3F4E093DB73A093, 0x59ED216765690F57},
        {0xE0F218B8D25088B8, 0x306869C13EC3532D},
        {0x8C974F7383725573, 0x1E414218C73A13FC},
        {0xAFBD2350644EEACF, 0xE5D1929EF90898FB},
        {0xDBAC6C247D62A583, 0xDF45F746B74ABF3A},
        {0x894BC396CE5DA772, 0x6B8BBA8C328EB784},
        {0xAB9EB47C81F5114F, 0x066EA92F3F326565},
        {0xD686619BA27255A2, 0xC80A537B0EFEFEBE},
        {0x8613FD0145877585, 0xBD06742CE95F5F37},
        {0xA798FC4196E952E7, 0x2C48113823B73705},
        {0xD17F3B51FCA3A7A0, 0xF75A15862CA504C6},
        {0x82EF85133DE648C4, 0x9A984D73DBE722FC},
        {0xA3AB66580D5FDAF5, 0xC13E60D0D2E0EBBB},
        {0xCC963FEE10B7D1B3, 0x318DF905079926A9},
        {0xFFBBCFE994E5C61F, 0xFDF17746497F7053},
        {0x9FD561F1FD0F9BD3, 0xFEB6EA8BEDEFA634},
        {0xC7CABA6E7C5382C8, 0xFE64A52EE96B8FC1},
        {0xF9BD690A1B68637B, 0x3DFDCE7AA3C673B1},
        {0x9C1661A651213E2D, 0x06BEA10CA65C084F},
        {0xC31BFA0FE5698DB8, 0x486E494FCFF30A63},
        {0xF3E2F893DEC3F126, 0x5A89DBA3C3EFCCFB},
        {0x986DDB5C6B3A76B7, 0xF89629465A75E01D},
        {0xBE89523386091465, 0xF6BBB397F1135824},
        {0xEE2BA6C0678B597F, 0x746AA07DED582E2D},
        {0x94DB483840B717EF, 0xA8C2A44EB4571CDD},
        {0xBA121A4650E4DDEB, 0x92F34D62616CE414},
        {0xE896A0D7E51E1566, 0x77B020BAF9C81D18},
        {0x915E2486EF32CD60, 0x0ACE1474DC1D122F},
        {0xB5B5ADA8AAFF80B8, 0x0D819992132456BB},
        {0xE3231912D5BF60E6, 0x10E1FFF697ED6C6A},
        {0x8DF5EFABC5979C8F, 0xCA8D3FFA1EF463C2},
        {0xB1736B96B6FD83B3, 0xBD308FF8A6B17CB3},
        {0xDDD0467C64BCE4A0, 0xAC7CB3F6D05DDBDF},
        {0x8AA22C0DBEF60EE4, 0x6BCDF07A423AA96C},
        {0xAD4AB7112EB3929D, 0x86C16C98D2C953C7},
        {0xD89D64D57A607744, 0xE871C7BF077BA8B8},
        {0x87625F056C7C4A8B, 0x11471CD764AD4973},
        {0xA93AF6C6C79B5D2D, 0xD598E40D3DD89BD0},
        {0xD389B47879823479, 0x4AFF1D108D4EC2C4},
        {0x843610CB4BF160CB, 0xCEDF722A585139BB},
        {0xA54394FE1EEDB8FE, 0xC2974EB4EE658829},
        {0xCE947A3DA6A9273E, 0x733D226229FEEA33},
        {0x811CCC668829B887, 0x0806357D5A3F5260},
        {0xA163FF802A3426A8, 0xCA07C2DCB0CF26F8},
        {0xC9BCFF6034C13052, 0xFC89B393DD02F0B6},
        {0xFC2C3F3841F17C67, 0xBBAC2078D443ACE3},
        {0x9D9BA7832936EDC0, 0xD54B944B84AA4C0E},
        {0xC5029163F384A931, 0x0A9E795E65D4DF12},
        {0xF64335BCF065D37D, 0x4D4617B5FF4A16D6},
        {0x99EA0196163FA42E, 0x504BCED1BF8E4E46},
        {0xC06481FB9BCF8D39, 0xE45EC2862F71E1D7},
        {0xF07DA27A82C37088, 0x5D767327BB4E5A4D},
        {0x964E858C91BA2655, 0x3A6A07F8D510F870},
        {0xBBE226EFB628AFEA, 0x890489F70A55368C},
        {0xEADAB0ABA3B2DBE5, 0x2B45AC74CCEA842F},
        {0x92C8AE6B464FC96F, 0x3B0B8BC90012929E},
        {0xB77ADA0617E3BBCB, 0x09CE6EBB40173745},
        {0xE55990879DDCAABD, 0xCC420A6A101D0516},
        {0x8F57FA54C2A9EAB6, 0x9FA946824A12232E},
        {0xB32DF8E9F3546564, 0x47939822DC96ABFA},
        {0xDFF9772470297EBD, 0x59787E2B93BC56F8},
        {0x8BFBEA76C619EF36, 0x57EB4EDB3C55B65B},
        {0xAEFAE51477A06B03, 0xEDE622920B6B23F2},
        {0xDAB99E59958885C4, 0xE95FAB368E45ECEE},
        {0x88B402F7FD75539B, 0x11DBCB0218EBB415},
        {0xAAE103B5FCD2A881, 0xD652BDC29F26A11A},
        {0xD59944A37C0752A2, 0x4BE76D3346F04960},
        {0x857FCAE62D8493A5, 0x6F70A4400C562DDC},
        {0xA6DFBD9FB8E5B88E, 0xCB4CCD500F6BB953},
        {0xD097AD07A71F26B2, 0x7E2000A41346A7A8},
        {0x825ECC24C873782F, 0x8ED400668C0C28C9},
        {0xA2F67F2DFA90563B, 0x728900802F0F32FB},
        {0xCBB41EF979346BCA, 0x4F2B40A03AD2FFBA},
        {0xFEA126B7D78186BC, 0xE2F610C84987BFA9},
        {0x9F24B832E6B0F436, 0x0DD9CA7D2DF4D7CA},
        {0xC6EDE63FA05D3143, 0x91503D1C79720DBC},
        {0xF8A95FCF88747D94, 0x75A44C6397CE912B},
        {0x9B69DBE1B548CE7C, 0xC986AFBE3EE11ABB},
        {0xC24452DA229B021B, 0xFBE85BADCE996169},
        {0xF2D56790AB41C2A2, 0xFAE27299423FB9C4},
        {0x97C560BA6B0919A5, 0xDCCD879FC967D41B},
        {0xBDB6B8E905CB600F, 0x5400E987BBC1C921},
        {0xED246723473E3813, 0x290123E9AAB23B69},
        {0x9436C0760C86E30B, 0xF9A0B6720AAF6522},
        {0xB94470938FA89BCE, 0xF808E40E8D5B3E6A},
        {0xE7958CB87392C2C2, 0xB60B1D1230B20E05},
        {0x90BD77F3483BB9B9, 0xB1C6F22B5E6F48C3},
        {0xB4ECD5F01A4AA828, 0x1E38AEB6360B1AF4},
        {0xE2280B6C20DD5232, 0x25C6DA63C38DE1B1},
        {0x8D590723948A535F, 0x579C487E5A38AD0F},
        {0xB0AF48EC79ACE837, 0x2D835A9DF0C6D852},
        {0xDCDB1B2798182244, 0xF8E431456CF88E66},
        {0x8A08F0F8BF0F156B, 0x1B8E9ECB641B5900},
        {0xAC8B2D36EED2DAC5, 0xE272467E3D222F40},
        {0xD7ADF884AA879177, 0x5B0ED81DCC6ABB10},
        {0x86CCBB52EA94BAEA, 0x98E947129FC2B4EA},
        {0xA87FEA27A539E9A5, 0x3F2398D747B36225},
        {0xD29FE4B18E88640E, 0x8EEC7F0D19A03AAE},
        {0x83A3EEEEF9153E89, 0x1953CF68300424AD},
        {0xA48CEAAAB75A8E2B, 0x5FA8C3423C052DD8},
        {0xCDB02555653131B6, 0x3792F412CB06794E},
        {0x808E17555F3EBF11, 0xE2BBD88BBEE40BD1},
        {0xA0B19D2AB70E6ED6, 0x5B6ACEAEAE9D0EC5},
        {0xC8DE047564D20A8B, 0xF245825A5A445276},
        {0xFB158592BE068D2E, 0xEED6E2F0F0D56713},
        {0x9CED737BB6C4183D, 0x55464DD69685606C},
        {0xC428D05AA4751E4C, 0xAA97E14C3C26B887},
        {0xF53304714D9265DF, 0xD53DD99F4B3066A9},
        {0x993FE2C6D07B7FAB, 0xE546A8038EFE402A},
        {0xBF8FDB78849A5F96, 0xDE98520472BDD034},
        {0xEF73D256A5C0F77C, 0x963E66858F6D4441},
        {0x95A8637627989AAD, 0xDDE7001379A44AA9},
        {0xBB127C53B17EC159, 0x5560C018580D5D53},
        {0xE9D71B689DDE71AF, 0xAAB8F01E6E10B4A7},
        {0x9226712162AB070D, 0xCAB3961304CA70E9},
        {0xB6B00D69BB55C8D1, 0x3D607B97C5FD0D23},
        {0xE45C10C42A2B3B05, 0x8CB89A7DB77C506B},
        {0x8EB98A7A9A5B04E3, 0x77F3608E92ADB243},
        {0xB267ED1940F1C61C, 0x55F038B237591ED4},
        {0xDF01E85F912E37A3, 0x6B6C46DEC52F6689},
        {0x8B61313BBABCE2C6, 0x2323AC4B3B3DA016},
        {0xAE397D8AA96C1B77, 0xABEC975E0A0D081B},
        {0xD9C7DCED53C72255, 0x96E7BD358C904A22},
        {0x881CEA14545C7575, 0x7E50D64177DA2E55},
        {0xAA242499697392D2, 0xDDE50BD1D5D0B9EA},
        {0xD4AD2DBFC3D07787, 0x955E4EC64B44E865},
        {0x84EC3C97DA624AB4, 0xBD5AF13BEF0B113F},
        {0xA6274BBDD0FADD61, 0xECB1AD8AEACDD58F},
        {0xCFB11EAD453994BA, 0x67DE18EDA5814AF3},
        {0x81CEB32C4B43FCF4, 0x80EACF948770CED8},
        {0xA2425FF75E14FC31, 0xA1258379A94D028E},
        {0xCAD2F7F5359A3B3E, 0x096EE45813A04331},
        {0xFD87B5F28300CA0D, 0x8BCA9D6E188853FD},
        {0x9E74D1B791E07E48, 0x775EA264CF55347E},
        {0xC612062576589DDA, 0x95364AFE032A819E},
        {0xF79687AED3EEC551, 0x3A83DDBD83F52205},
        {0x9ABE14CD44753B52, 0xC4926A9672793543},
        {0xC16D9A0095928A27, 0x75B7053C0F178294},
        {0xF1C90080BAF72CB1, 0x5324C68B12DD6339},
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        {0x976E41088617CA01, 0xD5BE0503E085D813},
        {0xBD49D14AA79DBC82, 0x4B2D8644D8A74E18},
        {0xEC9C459D51852BA2, 0xDDF8E7D60ED1219E},
        {0x93E1AB8252F33B45, 0xCABB90E5C942B503},
        {0xB8DA1662E7B00A17, 0x3D6A751F3B936243},
        {0xE7109BFBA19C0C9D, 0x0CC512670A783AD4},
        {0x906A617D450187E2, 0x27FB2B80668B24C5},
        {0xB484F9DC9641E9DA, 0xB1F9F660802DEDF6},
        {0xE1A63853BBD26451, 0x5E7873F8A0396973},
        {0x8D07E33455637EB2, 0xDB0B487B6423E1E8},
        {0xB049DC016ABC5E5F, 0x91CE1A9A3D2CDA62},
        {0xDC5C5301C56B75F7, 0x7641A140CC7810FB},
        {0x89B9B3E11B6329BA, 0xA9E904C87FCB0A9D},
        {0xAC2820D9623BF429, 0x546345FA9FBDCD44},
        {0xD732290FBACAF133, 0xA97C177947AD4095},
        {0x867F59A9D4BED6C0, 0x49ED8EABCCCC485D},
        {0xA81F301449EE8C70, 0x5C68F256BFFF5A74},
        {0xD226FC195C6A2F8C, 0x73832EEC6FFF3111},
        {0x83585D8FD9C25DB7, 0xC831FD53C5FF7EAB},
        {0xA42E74F3D032F525, 0xBA3E7CA8B77F5E55},
        {0xCD3A1230C43FB26F, 0x28CE1BD2E55F35EB},
        {0x80444B5E7AA7CF85, 0x7980D163CF5B81B3},
        {0xA0555E361951C366, 0xD7E105BCC332621F},
        {0xC86AB5C39FA63440, 0x8DD9472BF3FEFAA7},
        {0xFA856334878FC150, 0xB14F98F6F0FEB951},
        {0x9C935E00D4B9D8D2, 0x6ED1BF9A569F33D3},
        {0xC3B8358109E84F07, 0x0A862F80EC4700C8},
        {0xF4A642E14C6262C8, 0xCD27BB612758C0FA},
        {0x98E7E9CCCFBD7DBD, 0x8038D51CB897789C},
        {0xBF21E44003ACDD2C, 0xE0470A63E6BD56C3},
        {0xEEEA5D5004981478, 0x1858CCFCE06CAC74},
        {0x95527A5202DF0CCB, 0x0F37801E0C43EBC8},
        {0xBAA718E68396CFFD, 0xD30560258F54E6BA},
        {0xE950DF20247C83FD, 0x47C6B82EF32A2069},
        {0x91D28B7416CDD27E, 0x4CDC331D57FA5441},
        {0xB6472E511C81471D, 0xE0133FE4ADF8E952},
        {0xE3D8F9E563A198E5, 0x58180FDDD97723A6},
        {0x8E679C2F5E44FF8F, 0x570F09EAA7EA7648},
        {0xB201833B35D63F73, 0x2CD2CC6551E513DA},
        {0xDE81E40A034BCF4F, 0xF8077F7EA65E58D1},
        {0x8B112E86420F6191, 0xFB04AFAF27FAF782},
        {0xADD57A27D29339F6, 0x79C5DB9AF1F9B563},
        {0xD94AD8B1C7380874, 0x18375281AE7822BC},
        {0x87CEC76F1C830548, 0x8F2293910D0B15B5},
        {0xA9C2794AE3A3C69A, 0xB2EB3875504DDB22},
        {0xD433179D9C8CB841, 0x5FA60692A46151EB},
        {0x849FEEC281D7F328, 0xDBC7C41BA6BCD333},
        {0xA5C7EA73224DEFF3, 0x12B9B522906C0800},
        {0xCF39E50FEAE16BEF, 0xD768226B34870A00},
        {0x81842F29F2CCE375, 0xE6A1158300D46640},
        {0xA1E53AF46F801C53, 0x60495AE3C1097FD0},
        {0xCA5E89B18B602368, 0x385BB19CB14BDFC4},
        {0xFCF62C1DEE382C42, 0x46729E03DD9ED7B5},
        {0x9E19DB92B4E31BA9, 0x6C07A2C26A8346D1},
        {0xC5A05277621BE293, 0xC7098B7305241885},
        {0xF70867153AA2DB38, 0xB8CBEE4FC66D1EA7},
    };

    return pow10_lut[k - MIN_K];
}

static inline bool multiple_of_pow2(uint64_t value, int32_t e2)
{
    /* Return whether value is divisible by 2^e2 */
    return (value & (((uint64_t)1 << e2) - 1)) == 0 && e2 < 64;
}

static inline bool multiple_of_pow5(uint64_t value, int32_t e5)
{
    struct mul_cmp {
        uint64_t mul;
        uint64_t cmp;
    };

    /* Return whether value is divisible by 5^e5 */
    static struct mul_cmp mod5_lut[] = {
        {0x0000000000000001u, 0xFFFFFFFFFFFFFFFFu}, // 5^0
        {0xCCCCCCCCCCCCCCCDu, 0x3333333333333333u}, // 5^1
        {0x8F5C28F5C28F5C29u, 0x0A3D70A3D70A3D70u}, // 5^2
        {0x1CAC083126E978D5u, 0x020C49BA5E353F7Cu}, // 5^3
        {0xD288CE703AFB7E91u, 0x0068DB8BAC710CB2u}, // 5^4
        {0x5D4E8FB00BCBE61Du, 0x0014F8B588E368F0u}, // 5^5
        {0x790FB65668C26139u, 0x000431BDE82D7B63u}, // 5^6
        {0xE5032477AE8D46A5u, 0x0000D6BF94D5E57Au}, // 5^7
        {0xC767074B22E90E21u, 0x00002AF31DC46118u}, // 5^8
        {0x8E47CE423A2E9C6Du, 0x0000089705F4136Bu}, // 5^9
        {0x4FA7F60D3ED61F49u, 0x000001B7CDFD9D7Bu}, // 5^10
        {0x0FEE64690C913975u, 0x00000057F5FF85E5u}, // 5^11
        {0x3662E0E1CF503EB1u, 0x000000119799812Du}, // 5^12
        {0xA47A2CF9F6433FBDu, 0x0000000384B84D09u}, // 5^13
        {0x54186F653140A659u, 0x00000000B424DC35u}, // 5^14
        {0x7738164770402145u, 0x0000000024075F3Du}, // 5^15
        {0xE4A4D1417CD9A041u, 0x000000000734ACA5u}, // 5^16
        {0xC75429D9E5C5200Du, 0x000000000170EF54u}, // 5^17
        {0xC1773B91FAC10669u, 0x000000000049C977u}, // 5^18
        {0x26B172506559CE15u, 0x00000000000EC1E4u}, // 5^19
        {0xD489E3A9ADDEC2D1u, 0x000000000002F394u}, // 5^20
        {0x90E860BB892C8D5Du, 0x000000000000971Du}, // 5^21
        {0x502E79BF1B6F4F79u, 0x0000000000001E39u}, // 5^22
        {0xDCD618596BE30FE5u, 0x000000000000060Bu}, // 5^23
        {0x2C2AD1AB7BFA3661u, 0x0000000000000135u}, // 5^24
    };

    /* The range of e5 is [0, 24] */
    const struct mul_cmp m5 = mod5_lut[e5];
    return value * m5.mul <= m5.cmp;
}

static inline bool is_integral_end_point(uint64_t two_f, int32_t e2, int32_t minus_k)
{
    if (e2 < -2)
        return false;
    if (e2 <= 9)
        return true;
    if (e2 <= 86)
        return multiple_of_pow5(two_f, minus_k);
    return false;
}

static inline bool is_integral_mid_point(uint64_t two_f, int32_t e2, int32_t minus_k)
{
    if (e2 < -4)
        return multiple_of_pow2(two_f, minus_k - e2 + 1);
    if (e2 <= 9)
        return true;
    if (e2 <= 86)
        return multiple_of_pow5(two_f, minus_k);
    return false;
}

static inline int32_t floor_log2_pow10(int32_t e)
{
    /* The range of e is [-1233, 1233] */
    return ((e * 1741647) >> 19);
}

static inline int32_t floor_log10_pow2(int32_t e)
{
    /* The range of e is [-1500, 1500] */
    return ((e * 1262611) >> 22);
}

static inline int32_t floor_log10_threequarters_pow2(int32_t e)
{
    /* The range of e is [-1500, 1500] */
    return ((e * 1262611 - 524031) >> 22);
}

static inline uint64x2 mul128_calc(uint64_t x, uint64_t y)
{
    uint64x2 r;
#if defined(_MSC_VER) && defined(_M_AMD64)
    r.lo = _umul128(x, y, &r.hi);
#elif (__GNUC__ > 4 || (__GNUC__ == 4 && __GNUC_MINOR__ >= 6) || __clang_major__ >= 9) && (__WORDSIZE == 64)
    __extension__ typedef unsigned __int128 uint128;
    const uint128 p = (uint128)x * (uint128)y;
    r.hi = (uint64_t)(p >> 64);
    r.lo = (uint64_t)p;
#else
    const uint64_t M32 = 0XFFFFFFFF;
    const uint64_t a = x >> 32;
    const uint64_t b = x & M32;
    const uint64_t c = y >> 32;
    const uint64_t d = y & M32;

    const uint64_t ac = a * c;
    const uint64_t bc = b * c;
    const uint64_t ad = a * d;
    const uint64_t bd = b * d;

    const uint64_t mid1 = ad + (bd >> 32);
    const uint64_t mid2 = bc + (mid1 & M32);

    r.hi = ac + (mid1 >> 32) + (mid2 >> 32);
    r.lo = (bd & M32) | (mid2 & M32) << 32;
#endif
    return r;
}

static inline uint64_t mul128_shift(uint64_t x, uint64x2 y)
{
    /* Return (x * y) / 2^128 */
    uint64x2 p1 = mul128_calc(x, y.hi);
    uint64x2 p0 = mul128_calc(x, y.lo);

    p1.lo += p0.hi;
    p1.hi += p1.lo < p0.hi;
    return p1.hi;
}

static inline bool compute_parity(uint64_t two_f, uint64x2 pow10, int32_t minus_1)
{
    /* The range of minus_1 is [1, 63] */
    const uint64_t mid = two_f * pow10.hi + mul128_calc(two_f, pow10.lo).hi;
    return (mid & ((uint64_t)1 << (64 - minus_1))) != 0;
}

static inline uint32_t compute_delta(uint64x2 pow10, int32_t minus_1)
{
    /* The range of minus_1 is [0, 63] */
    return (uint32_t)(pow10.hi >> (63 - minus_1));
}

static inline void dragonbox_convert_asymmetric(diy_fp_t *v)
{
    int32_t e = v->e;
    const int32_t minus_k = floor_log10_threequarters_pow2(e);
    const int32_t minus_1 = e + floor_log2_pow10(-minus_k);
    const uint64x2 pow10  = compute_pow10_double(-minus_k);
    uint64_t lower        = (pow10.hi - (pow10.hi >> (DP_SIGNIFICAND_SIZE + 2))) >> (63 - DP_SIGNIFICAND_SIZE - minus_1);
    uint64_t upper        = (pow10.hi + (pow10.hi >> (DP_SIGNIFICAND_SIZE + 1))) >> (63 - DP_SIGNIFICAND_SIZE - minus_1);
    /*
     * If we don't accept the left endpoint (but we do!)
     * or if the left endpoint is not an integer, increase it
     */
    lower += !(2 <= e && e <= 3);

    /* Try bigger divisor */
    uint64_t q = upper / 10;
    if ((q << 1) + (q << 3) >= lower) {
        v->f = q;
        v->e = minus_k + 1;
    } else {
        /* Otherwise, compute the round-up of y */
        q = ((pow10.hi >> (63 - (DP_SIGNIFICAND_SIZE + 1) - minus_1)) + 1) >> 1;
        /* When tie occurs, choose one of them according to the rule */
        if (e == -77) {
            q -= (q & (uint64_t)1); /* Round to even. */
        } else {
            q += (q < lower);
        }

        v->f = q;
        v->e = minus_k;
    }
}

static inline void dragonbox_convert(diy_fp_t *v)
{
#define KAPPA_VALUE     2
#define SMALL_DIVISOR   100
#define BIG_DIVISOR     1000

    uint64_t f = v->f;
    int32_t e = v->e;
    int32_t kappa_plus = 0;
    const bool is_even = !(f & (uint64_t)1);

    const int32_t minus_k = floor_log10_pow2(e) - KAPPA_VALUE;
    const int32_t minus_1 = e + floor_log2_pow10(-minus_k); /* The range of e is [6, 9] */
    const uint64x2 pow10 = compute_pow10_double(-minus_k);
    const uint32_t delta = compute_delta(pow10, minus_1); /* The range of delta is [100, 999] */
    const uint64_t two_fc = (f << 1);
    const uint64_t two_fl = two_fc - 1;
    const uint64_t two_fr = two_fc + 1; /* 54 bits */
    const uint64_t zi = mul128_shift(two_fr << minus_1, pow10); // 2 mulx

    uint64_t q = zi / BIG_DIVISOR;
    uint32_t r = (uint32_t)zi - BIG_DIVISOR * (uint32_t)q; /* The range of r is [0, 999] */

    if (r < delta) {
        if (r != 0 || is_even || !is_integral_end_point(two_fr, e, minus_k)) {
            kappa_plus = 1;
            goto end;
        }

        /* q can't be 0 */
        --q;
        r = BIG_DIVISOR;
    } else if (r == delta) {
        if ((is_even && is_integral_end_point(two_fl, e, minus_k)) || compute_parity(two_fl, pow10, minus_1)) {
            kappa_plus = 1;
            goto end;
        }
    }
    q = (q << 1) + (q << 3);

    const uint32_t dist = r - (delta >> 1) + (SMALL_DIVISOR >> 1);
    const uint32_t dist_q = dist / 100;
    q += dist_q;

    if (dist == dist_q * 100)
    {
        if (compute_parity(two_fc, pow10, minus_1) != ((dist & 1) != 0)) {
            --q;
        } else if ((q & (uint64_t)1) && is_integral_mid_point(two_fc, e, minus_k)) {
            --q;
        }
    }

end:
    v->f = q;
    v->e = minus_k + KAPPA_VALUE + kappa_plus;
}

#if !FAST_FILL_DIGITS_EXISTED
#define FAST_FILL_DIGITS_EXISTED  1
static const char ch_100_lut[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',
};

static const uint8_t tz_100_lut[100] = {
    2, 0, 0, 0, 0, 0, 0, 0, 0, 0,
    1, 0, 0, 0, 0, 0, 0, 0, 0, 0,
    1, 0, 0, 0, 0, 0, 0, 0, 0, 0,
    1, 0, 0, 0, 0, 0, 0, 0, 0, 0,
    1, 0, 0, 0, 0, 0, 0, 0, 0, 0,
    1, 0, 0, 0, 0, 0, 0, 0, 0, 0,
    1, 0, 0, 0, 0, 0, 0, 0, 0, 0,
    1, 0, 0, 0, 0, 0, 0, 0, 0, 0,
    1, 0, 0, 0, 0, 0, 0, 0, 0, 0,
    1, 0, 0, 0, 0, 0, 0, 0, 0, 0,
};

#define FAST_DIV10(n)       (ch_100_lut[(n) << 1] - '0')                    /* 0 <= n < 100 */
#define FAST_DIV100(n)      (((n) * 5243) >> 19)                            /* 0 <= n < 10000 */
#define FAST_DIV10000(n)    ((uint32_t)(((uint64_t)(n) * 109951163) >> 40)) /* 0 <= n < 100000000 */

static inline int32_t fill_1_4_digits(char *buffer, uint32_t digits, int32_t *ptz)
{
    char *s = buffer;

    if (digits < 100) {
        if (digits >= 10) {
            *ptz = tz_100_lut[digits];
            memcpy(s, &ch_100_lut[digits<<1], 2);
            s += 2;
        } else {
            *ptz = 0;
            *s++ = digits + '0';
        }
    } else {
        uint32_t q = FAST_DIV100(digits);
        uint32_t r = digits - q * 100;

        if (q >= 10) {
            *ptz = tz_100_lut[q];
            memcpy(s, &ch_100_lut[q<<1], 2);
            s += 2;
        } else {
            *ptz = 0;
            *s++ = q + '0';
        }

        if (!r) {
            *ptz += 2;
            memset(s, '0', 2);
            s += 2;
        } else {
            *ptz = tz_100_lut[r];
            memcpy(s, &ch_100_lut[r<<1], 2);
            s += 2;
        }
    }

    return s - buffer;
}

static inline int32_t fill_t_4_digits(char *buffer, uint32_t digits, int32_t *ptz)
{
    char *s = buffer;
    uint32_t q = FAST_DIV100(digits);
    uint32_t r = digits - q * 100;

    memcpy(s, &ch_100_lut[q<<1], 2);
    memcpy(s + 2, &ch_100_lut[r<<1], 2);

    if (!r) {
        *ptz = tz_100_lut[q] + 2;
    } else {
        *ptz = tz_100_lut[r];
    }

    return 4;
}

static inline int32_t fill_1_8_digits(char *buffer, uint32_t digits, int32_t *ptz)
{
    char *s = buffer;

    if (digits < 10000) {
        return fill_1_4_digits(s, digits, ptz);
    } else {
        uint32_t q = FAST_DIV10000(digits);
        uint32_t r = digits - q * 10000;

        s += fill_1_4_digits(s, q, ptz);
        if (!r) {
            *ptz += 4;
            memset(s, '0', 4);
            s += 4;
        } else {
            s += fill_t_4_digits(s, r, ptz);
        }
    }

    return s - buffer;
}

static inline int32_t fill_t_8_digits(char *buffer, uint32_t digits, int32_t *ptz)
{
    char *s = buffer;

    if (digits < 10000) {
        memset(s, '0', 4);
        fill_t_4_digits(s + 4, digits, ptz);
    } else {
        uint32_t q = FAST_DIV10000(digits);
        uint32_t r = digits - q * 10000;

        fill_t_4_digits(s, q, ptz);
        if (!r) {
            memset(s + 4, '0', 4);
            *ptz += 4;
        } else {
            fill_t_4_digits(s + 4, r, ptz);
        }
    }

    return 8;
}

static inline int32_t fill_1_16_digits(char *buffer, uint64_t digits, int32_t *ptz)
{
    char *s = buffer;

    if (digits < 100000000llu) {
        return fill_1_8_digits(s, (uint32_t)digits, ptz);
    } else {
        uint32_t q = (uint32_t)(digits / 100000000);
        uint32_t r = (uint32_t)(digits - (uint64_t)q * 100000000);

        s += fill_1_8_digits(s, q, ptz);
        if (!r) {
            *ptz += 8;
            memset(s, '0', 8);
            s += 8;
        } else {
            s += fill_t_8_digits(s, r, ptz);
        }
    }

    return s - buffer;
}

static inline int32_t fill_t_16_digits(char *buffer, uint64_t digits, int32_t *ptz)
{
    char *s = buffer;

    if (digits < 100000000llu) {
        memset(s, '0', 8);
        fill_t_8_digits(s + 8, digits, ptz);
    } else {
        uint32_t q = (uint32_t)(digits / 100000000);
        uint32_t r = (uint32_t)(digits - (uint64_t)q * 100000000);

        fill_t_8_digits(s, q, ptz);
        if (!r) {
            memset(s + 8, '0', 8);
            *ptz += 8;
        } else {
            fill_t_8_digits(s + 8, r, ptz);
        }
    }

    return 16;
}
#endif

static inline int32_t fill_significand(char *buffer, uint64_t digits, int32_t *ptz)
{
    char *s = buffer;

    if (digits < 10000000000000000llu) {
        return fill_1_16_digits(s, digits, ptz);
    } else {
        uint32_t q = (uint32_t)(digits / 10000000000000000llu);
        uint64_t r = (digits - (uint64_t)q * 10000000000000000llu);

        *s++ = q + '0';
        if (!r) {
            memset(s, '0', 16);
            s += 16;
            *ptz = 16;
        } else {
            s += fill_t_16_digits(s, r, ptz);
        }
    }

    return s - buffer;
}

static inline int32_t fill_exponent(int32_t K, char* buffer)
{
    int32_t i = 0, k = 0;

    if (K < 0) {
        buffer[i++] = '-';
        K = -K;
    } else {
        buffer[i++] = '+';
    }

    if (K < 100) {
        if (K < 10) {
            buffer[i++] = '0' + K;
        } else {
            memcpy(&buffer[i], &ch_100_lut[K<<1], 2);
            i += 2;
        }
    } else {
        k = FAST_DIV100(K);
        K -= k * 100;
        buffer[i++] = '0' + k;
        memcpy(&buffer[i], &ch_100_lut[K<<1], 2);
        i += 2;
    }

    return i;
}

static inline char* dragonbox_format(char* buffer, uint64_t digits, int32_t decimal_exponent)
{
    int32_t num_digits, vnum_digits, trailing_zeros, decimal_point;

    num_digits = fill_significand(buffer, digits, &trailing_zeros);
    vnum_digits = num_digits - trailing_zeros;
    decimal_point = num_digits + decimal_exponent;

    switch (decimal_point) {
    case -6: case -5: case -4: case -3: case -2: case -1: case 0:
         /* 0.[000]digits */
        memmove(buffer + 2 - decimal_point, buffer, vnum_digits);
        memset(buffer, '0', 2 - decimal_point);
        buffer[1] = '.';
        buffer += 2 - decimal_point + vnum_digits;
        break;

    case 1: case 2: case 3: case 4: case 5: case 6: case 7: case 8: case 9:
    case 10: case 11: case 12: case 13: case 14: case 15: case 16: case 17:
        if (decimal_point < vnum_digits) {
            /* dig.its */
            memmove(buffer + 1 + decimal_point, buffer + decimal_point, vnum_digits - decimal_point);
            buffer[decimal_point] = '.';
            buffer += vnum_digits + 1;
        } else {
            /* digits[000] */
            buffer += decimal_point;
            memcpy(buffer, ".0", 2);
            buffer += 2;
        }
        break;

    default:
        if (vnum_digits == 1) {
            /* dE+123 */
            ++buffer;
        } else {
            /* d.igitsE+123 */
            memmove(buffer + 2, buffer + 1, vnum_digits - 1);
            buffer[1] = '.';
            buffer += vnum_digits + 1;
        }
        *buffer++ = 'e';
        buffer += fill_exponent(decimal_point - 1, buffer);
        break;
    }

    *buffer = '\0';
    return buffer;
}

static int dragonbox_dtoa(double value, char* buffer)
{
    diy_fp_t v;
    char *s = buffer;
    union {double d; uint64_t n;} u = {.d = value};
    int signbit = u.n >> (DIY_SIGNIFICAND_SIZE - 1);
    int exponent = (u.n & DP_EXPONENT_MASK) >> DP_SIGNIFICAND_SIZE; /* Exponent */
    uint64_t significand = u.n & DP_SIGNIFICAND_MASK; /* Mantissa */

    if (signbit) {
        *s++ = '-';
    }

    switch (exponent) {
    case DP_EXPONENT_MAX:
        if (significand) {
            memcpy(buffer, "nan", 4);
            return 3;
        } else {
            memcpy(s, "inf", 4);
            return signbit + 3;
        }
        break;
    case 0:
        if (!significand) {
            /* no-normalized double */
            v.f = significand; /* Non-normalized double doesn't have a extra integer bit for Mantissa */
            v.e = 1 - DP_EXPONENT_OFFSET - DP_SIGNIFICAND_SIZE; /* Fixed Exponent: -1022, divisor of Mantissa: pow(2,52) */
            dragonbox_convert(&v);
        } else {
            memcpy(s, "0.0", 4);
            return signbit + 3;
        }
        break;

    default:
        /* normalized double */
        v.f = significand + DP_HIDDEN_BIT; /* Normalized double has a extra integer bit for Mantissa */
        v.e = exponent - DP_EXPONENT_OFFSET - DP_SIGNIFICAND_SIZE; /* Exponent offset: -1023, divisor of Mantissa: pow(2,52) */

        if (0 <= -v.e && -v.e <= DP_SIGNIFICAND_SIZE && ((v.f & (((uint64_t)1 << -v.e) - 1)) == 0)) {
            /* small integer. */
            v.f >>= -v.e;
            v.e = 0;
        } else if (significand == 0 && exponent > 1) {
            /* Shorter interval case; proceed like Schubfach. */
            dragonbox_convert_asymmetric(&v);
        } else {
            dragonbox_convert(&v);
        }
        break;
    }

    s = dragonbox_format(s, v.f, v.e);
    return s - buffer;
}