| // Copyright 2020 Junekey Jeon |
| // Copyright 2020 Alexander Bolz |
| // |
| // Distributed under the Boost Software License, Version 1.0. |
| // (See accompanying file LICENSE_1_0.txt or copy at https://www.boost.org/LICENSE_1_0.txt) |
| |
| //-------------------------------------------------------------------------------------------------- |
| // This file contains an implementation of Junekey Jeon's Dragonbox algorithm. |
| // |
| // It is a simplified version of the reference implementation found here: |
| // https://github.com/jk-jeon/dragonbox |
| // |
| // The reference implementation also works with single-precision floating-point numbers and |
| // has options to configure the rounding mode. |
| //-------------------------------------------------------------------------------------------------- |
| |
| #include <cstdint> |
| #include <cstring> |
| #include <limits> |
| #if defined(_MSC_VER) |
| #include <intrin.h> |
| #endif |
| |
| #ifndef DRAGONBOX_ASSERT |
| #define DRAGONBOX_ASSERT(X) |
| #endif |
| |
| namespace dragonbox { |
| namespace { |
| |
| //================================================================================================== |
| // |
| //================================================================================================== |
| |
| template <typename Dest, typename Source> |
| static inline Dest ReinterpretBits(Source source) |
| { |
| static_assert(sizeof(Dest) == sizeof(Source), "size mismatch"); |
| |
| Dest dest; |
| std::memcpy(&dest, &source, sizeof(Source)); |
| return dest; |
| } |
| |
| struct Double |
| { |
| static_assert(std::numeric_limits<double>::is_iec559 |
| && std::numeric_limits<double>::digits == 53 |
| && std::numeric_limits<double>::max_exponent == 1024, |
| "IEEE-754 double-precision implementation required"); |
| |
| using value_type = double; |
| using bits_type = uint64_t; |
| |
| // static constexpr int32_t MaxDigits10 = std::numeric_limits<value_type>::max_digits10; |
| static constexpr int32_t SignificandSize = std::numeric_limits<value_type>::digits; // = p (includes the hidden bit) |
| static constexpr int32_t ExponentBias = std::numeric_limits<value_type>::max_exponent - 1 + (SignificandSize - 1); |
| // static constexpr int32_t MaxExponent = std::numeric_limits<value_type>::max_exponent - 1 - (SignificandSize - 1); |
| // static constexpr int32_t MinExponent = std::numeric_limits<value_type>::min_exponent - 1 - (SignificandSize - 1); |
| static constexpr bits_type MaxIeeeExponent = bits_type{2 * std::numeric_limits<value_type>::max_exponent - 1}; |
| static constexpr bits_type HiddenBit = bits_type{1} << (SignificandSize - 1); // = 2^(p-1) |
| static constexpr bits_type SignificandMask = HiddenBit - 1; // = 2^(p-1) - 1 |
| static constexpr bits_type ExponentMask = MaxIeeeExponent << (SignificandSize - 1); |
| static constexpr bits_type SignMask = ~(~bits_type{0} >> 1); |
| |
| bits_type bits; |
| |
| explicit Double(bits_type bits_) : bits(bits_) {} |
| explicit Double(value_type value) : bits(ReinterpretBits<bits_type>(value)) {} |
| |
| bits_type PhysicalSignificand() const { |
| return bits & SignificandMask; |
| } |
| |
| bits_type PhysicalExponent() const { |
| return (bits & ExponentMask) >> (SignificandSize - 1); |
| } |
| |
| bool IsFinite() const { |
| return (bits & ExponentMask) != ExponentMask; |
| } |
| |
| bool IsInf() const { |
| return (bits & ExponentMask) == ExponentMask && (bits & SignificandMask) == 0; |
| } |
| |
| bool IsNaN() const { |
| return (bits & ExponentMask) == ExponentMask && (bits & SignificandMask) != 0; |
| } |
| |
| bool IsZero() const { |
| return (bits & ~SignMask) == 0; |
| } |
| |
| bool SignBit() const { |
| return (bits & SignMask) != 0; |
| } |
| }; |
| |
| //================================================================================================== |
| // |
| //================================================================================================== |
| |
| // Returns floor(x / 2^n). |
| // |
| // Technically, right-shift of negative integers is implementation defined... |
| // Should easily be optimized into SAR (or equivalent) instruction. |
| static inline int32_t FloorDivPow2(int32_t x, int32_t n) |
| { |
| #if 0 |
| return x < 0 ? ~(~x >> n) : (x >> n); |
| #else |
| return x >> n; |
| #endif |
| } |
| |
| static inline int32_t FloorLog2Pow10(int32_t e) |
| { |
| DRAGONBOX_ASSERT(e >= -1233); |
| DRAGONBOX_ASSERT(e <= 1233); |
| return FloorDivPow2(e * 1741647, 19); |
| } |
| |
| static inline int32_t FloorLog10Pow2(int32_t e) |
| { |
| DRAGONBOX_ASSERT(e >= -1500); |
| DRAGONBOX_ASSERT(e <= 1500); |
| return FloorDivPow2(e * 1262611, 22); |
| } |
| |
| static inline int32_t FloorLog10ThreeQuartersPow2(int32_t e) |
| { |
| DRAGONBOX_ASSERT(e >= -1500); |
| DRAGONBOX_ASSERT(e <= 1500); |
| return FloorDivPow2(e * 1262611 - 524031, 22); |
| } |
| |
| //================================================================================================== |
| // |
| //================================================================================================== |
| |
| namespace { |
| struct uint64x2 { |
| uint64_t hi; |
| uint64_t lo; |
| }; |
| } |
| |
| static inline uint64x2 ComputePow10(int32_t k) |
| { |
| static constexpr int32_t kMin = -292; |
| static constexpr int32_t kMax = 326; |
| static constexpr uint64x2 Pow10[kMax - kMin + 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}, |
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| {0xCC20CE9BD35C78A5, 0x31EC038DF7B441F4}, |
| {0xFF290242C83396CE, 0x7E67047175A15271}, |
| {0x9F79A169BD203E41, 0x0F0062C6E984D386}, |
| {0xC75809C42C684DD1, 0x52C07B78A3E60868}, |
| {0xF92E0C3537826145, 0xA7709A56CCDF8A82}, |
| {0x9BBCC7A142B17CCB, 0x88A66076400BB691}, |
| {0xC2ABF989935DDBFE, 0x6ACFF893D00EA435}, |
| {0xF356F7EBF83552FE, 0x0583F6B8C4124D43}, |
| {0x98165AF37B2153DE, 0xC3727A337A8B704A}, |
| {0xBE1BF1B059E9A8D6, 0x744F18C0592E4C5C}, |
| {0xEDA2EE1C7064130C, 0x1162DEF06F79DF73}, |
| {0x9485D4D1C63E8BE7, 0x8ADDCB5645AC2BA8}, |
| {0xB9A74A0637CE2EE1, 0x6D953E2BD7173692}, |
| {0xE8111C87C5C1BA99, 0xC8FA8DB6CCDD0437}, |
| {0x910AB1D4DB9914A0, 0x1D9C9892400A22A2}, |
| {0xB54D5E4A127F59C8, 0x2503BEB6D00CAB4B}, |
| {0xE2A0B5DC971F303A, 0x2E44AE64840FD61D}, |
| {0x8DA471A9DE737E24, 0x5CEAECFED289E5D2}, |
| {0xB10D8E1456105DAD, 0x7425A83E872C5F47}, |
| {0xDD50F1996B947518, 0xD12F124E28F77719}, |
| {0x8A5296FFE33CC92F, 0x82BD6B70D99AAA6F}, |
| {0xACE73CBFDC0BFB7B, 0x636CC64D1001550B}, |
| {0xD8210BEFD30EFA5A, 0x3C47F7E05401AA4E}, |
| {0x8714A775E3E95C78, 0x65ACFAEC34810A71}, |
| {0xA8D9D1535CE3B396, 0x7F1839A741A14D0D}, |
| {0xD31045A8341CA07C, 0x1EDE48111209A050}, |
| {0x83EA2B892091E44D, 0x934AED0AAB460432}, |
| {0xA4E4B66B68B65D60, 0xF81DA84D5617853F}, |
| {0xCE1DE40642E3F4B9, 0x36251260AB9D668E}, |
| {0x80D2AE83E9CE78F3, 0xC1D72B7C6B426019}, |
| {0xA1075A24E4421730, 0xB24CF65B8612F81F}, |
| {0xC94930AE1D529CFC, 0xDEE033F26797B627}, |
| {0xFB9B7CD9A4A7443C, 0x169840EF017DA3B1}, |
| {0x9D412E0806E88AA5, 0x8E1F289560EE864E}, |
| {0xC491798A08A2AD4E, 0xF1A6F2BAB92A27E2}, |
| {0xF5B5D7EC8ACB58A2, 0xAE10AF696774B1DB}, |
| {0x9991A6F3D6BF1765, 0xACCA6DA1E0A8EF29}, |
| {0xBFF610B0CC6EDD3F, 0x17FD090A58D32AF3}, |
| {0xEFF394DCFF8A948E, 0xDDFC4B4CEF07F5B0}, |
| {0x95F83D0A1FB69CD9, 0x4ABDAF101564F98E}, |
| {0xBB764C4CA7A4440F, 0x9D6D1AD41ABE37F1}, |
| {0xEA53DF5FD18D5513, 0x84C86189216DC5ED}, |
| {0x92746B9BE2F8552C, 0x32FD3CF5B4E49BB4}, |
| {0xB7118682DBB66A77, 0x3FBC8C33221DC2A1}, |
| {0xE4D5E82392A40515, 0x0FABAF3FEAA5334A}, |
| {0x8F05B1163BA6832D, 0x29CB4D87F2A7400E}, |
| {0xB2C71D5BCA9023F8, 0x743E20E9EF511012}, |
| {0xDF78E4B2BD342CF6, 0x914DA9246B255416}, |
| {0x8BAB8EEFB6409C1A, 0x1AD089B6C2F7548E}, |
| {0xAE9672ABA3D0C320, 0xA184AC2473B529B1}, |
| {0xDA3C0F568CC4F3E8, 0xC9E5D72D90A2741E}, |
| {0x8865899617FB1871, 0x7E2FA67C7A658892}, |
| {0xAA7EEBFB9DF9DE8D, 0xDDBB901B98FEEAB7}, |
| {0xD51EA6FA85785631, 0x552A74227F3EA565}, |
| {0x8533285C936B35DE, 0xD53A88958F87275F}, |
| {0xA67FF273B8460356, 0x8A892ABAF368F137}, |
| {0xD01FEF10A657842C, 0x2D2B7569B0432D85}, |
| {0x8213F56A67F6B29B, 0x9C3B29620E29FC73}, |
| {0xA298F2C501F45F42, 0x8349F3BA91B47B8F}, |
| {0xCB3F2F7642717713, 0x241C70A936219A73}, |
| {0xFE0EFB53D30DD4D7, 0xED238CD383AA0110}, |
| {0x9EC95D1463E8A506, 0xF4363804324A40AA}, |
| {0xC67BB4597CE2CE48, 0xB143C6053EDCD0D5}, |
| {0xF81AA16FDC1B81DA, 0xDD94B7868E94050A}, |
| {0x9B10A4E5E9913128, 0xCA7CF2B4191C8326}, |
| {0xC1D4CE1F63F57D72, 0xFD1C2F611F63A3F0}, |
| {0xF24A01A73CF2DCCF, 0xBC633B39673C8CEC}, |
| {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}, |
| }; |
| |
| DRAGONBOX_ASSERT(k >= kMin); |
| DRAGONBOX_ASSERT(k <= kMax); |
| return Pow10[static_cast<uint32_t>(k - kMin)]; |
| } |
| |
| // Returns whether value is divisible by 2^e2 |
| static inline bool MultipleOfPow2(uint64_t value, int32_t e2) |
| { |
| DRAGONBOX_ASSERT(e2 >= 0); |
| return e2 < 64 && (value & ((uint64_t{1} << e2) - 1)) == 0; |
| } |
| |
| // Returns whether value is divisible by 5^e5 |
| static inline bool MultipleOfPow5(uint64_t value, int32_t e5) |
| { |
| struct MulCmp { |
| uint64_t mul; |
| uint64_t cmp; |
| }; |
| |
| static constexpr MulCmp Mod5[] = { |
| {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}, // 5^21char* buffer, double value |
| {0x502E79BF1B6F4F79u, 0x0000000000001E39u}, // 5^22 |
| {0xDCD618596BE30FE5u, 0x000000000000060Bu}, // 5^23 |
| {0x2C2AD1AB7BFA3661u, 0x0000000000000135u}, // 5^24 |
| }; |
| |
| DRAGONBOX_ASSERT(e5 >= 0); |
| DRAGONBOX_ASSERT(e5 <= 24); |
| const MulCmp m5 = Mod5[static_cast<unsigned>(e5)]; |
| |
| return value * m5.mul <= m5.cmp; |
| } |
| |
| namespace { |
| struct FloatingDecimal64 { |
| uint64_t significand; |
| int32_t exponent; |
| }; |
| } |
| |
| static inline FloatingDecimal64 ToDecimal64_asymmetric_interval(int32_t e2) |
| { |
| // NB: |
| // accept_lower_endpoint = true |
| // accept_upper_endpoint = true |
| |
| static constexpr int32_t P = Double::SignificandSize; |
| |
| // Compute k and beta |
| const int32_t minus_k = FloorLog10ThreeQuartersPow2(e2); |
| const int32_t beta_minus_1 = e2 + FloorLog2Pow10(-minus_k); |
| |
| // Compute xi and zi |
| const uint64x2 pow10 = ComputePow10(-minus_k); |
| |
| const uint64_t lower_endpoint = (pow10.hi - (pow10.hi >> (P + 1))) >> (64 - P - beta_minus_1); |
| const uint64_t upper_endpoint = (pow10.hi + (pow10.hi >> (P + 0))) >> (64 - P - beta_minus_1); |
| |
| // If we don't accept the left endpoint (but we do!) or |
| // if the left endpoint is not an integer, increase it |
| const bool lower_endpoint_is_integer = (2 <= e2 && e2 <= 3); |
| |
| const uint64_t xi = lower_endpoint + !lower_endpoint_is_integer; |
| const uint64_t zi = upper_endpoint; |
| |
| // Try bigger divisor |
| uint64_t q = zi / 10; |
| if (q * 10 >= xi) |
| { |
| return {q, minus_k + 1}; |
| } |
| |
| // Otherwise, compute the round-up of y |
| q = ((pow10.hi >> (64 - (P + 1) - beta_minus_1)) + 1) / 2; |
| |
| // When tie occurs, choose one of them according to the rule |
| if (e2 == -77) |
| { |
| q -= (q % 2 != 0); // Round to even. |
| } |
| else |
| { |
| q += (q < xi); |
| } |
| |
| return {q, minus_k}; |
| } |
| |
| static inline uint32_t ComputeDelta(uint64x2 pow10, int32_t beta_minus_1) |
| { |
| DRAGONBOX_ASSERT(beta_minus_1 >= 0); |
| DRAGONBOX_ASSERT(beta_minus_1 <= 63); |
| return static_cast<uint32_t>(pow10.hi >> (64 - 1 - beta_minus_1)); |
| } |
| |
| #if defined(__SIZEOF_INT128__) |
| static inline uint64x2 Mul128(uint64_t x, uint64_t y) // 1 mulx |
| { |
| __extension__ using uint128_t = unsigned __int128; |
| |
| const uint128_t p = uint128_t{x} * y; |
| |
| const uint64_t hi = static_cast<uint64_t>(p >> 64); |
| const uint64_t lo = static_cast<uint64_t>(p); |
| return {hi, lo}; |
| } |
| #elif defined(_MSC_VER) && defined(_M_X64) |
| static inline uint64x2 Mul128(uint64_t x, uint64_t y) |
| { |
| uint64_t hi = 0; |
| uint64_t lo = _umul128(x, y, &hi); |
| return {hi, lo}; |
| } |
| #else |
| static inline uint32_t Lo32(uint64_t x) |
| { |
| return static_cast<uint32_t>(x); |
| } |
| |
| static inline uint32_t Hi32(uint64_t x) |
| { |
| return static_cast<uint32_t>(x >> 32); |
| } |
| |
| static inline uint64x2 Mul128(uint64_t a, uint64_t b) |
| { |
| const uint64_t b00 = uint64_t{Lo32(a)} * Lo32(b); |
| const uint64_t b01 = uint64_t{Lo32(a)} * Hi32(b); |
| const uint64_t b10 = uint64_t{Hi32(a)} * Lo32(b); |
| const uint64_t b11 = uint64_t{Hi32(a)} * Hi32(b); |
| |
| const uint64_t mid1 = b10 + Hi32(b00); |
| const uint64_t mid2 = b01 + Lo32(mid1); |
| |
| const uint64_t hi = b11 + Hi32(mid1) + Hi32(mid2); |
| const uint64_t lo = Lo32(b00) | uint64_t{Lo32(mid2)} << 32; |
| return {hi, lo}; |
| } |
| #endif |
| |
| // Returns (x * y) / 2^128 |
| static inline uint64_t MulShift(uint64_t x, uint64x2 y) // 2 mulx |
| { |
| uint64x2 p1 = Mul128(x, y.hi); |
| uint64x2 p0 = Mul128(x, y.lo); |
| p1.lo += p0.hi; |
| p1.hi += p1.lo < p0.hi; |
| return p1.hi; |
| } |
| |
| static inline bool MulParity(uint64_t two_f, uint64x2 pow10, int32_t beta_minus_1) // 1 mulx, 1 mul |
| { |
| DRAGONBOX_ASSERT(beta_minus_1 >= 1); |
| DRAGONBOX_ASSERT(beta_minus_1 <= 63); |
| |
| const uint64_t p01 = two_f * pow10.hi; |
| const uint64_t p10 = Mul128(two_f, pow10.lo).hi; |
| const uint64_t mid = p01 + p10; |
| |
| return (mid & (uint64_t{1} << (64 - beta_minus_1))) != 0; |
| } |
| |
| static inline bool IsIntegralEndpoint(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 MultipleOfPow5(two_f, minus_k); |
| |
| return false; |
| } |
| |
| static inline bool IsIntegralMidpoint(uint64_t two_f, int32_t e2, int32_t minus_k) |
| { |
| if (e2 < -4) |
| return MultipleOfPow2(two_f, minus_k - e2 + 1); |
| if (e2 <= 9) |
| return true; |
| if (e2 <= 86) |
| return MultipleOfPow5(two_f, minus_k); |
| |
| return false; |
| } |
| |
| static inline FloatingDecimal64 ToDecimal64(const uint64_t ieee_significand, const uint64_t ieee_exponent) |
| { |
| static constexpr int32_t Kappa = 2; |
| static constexpr uint32_t BigDivisor = 1000; // 10^(kappa + 1) |
| static constexpr uint32_t SmallDivisor = 100; // 10^(kappa) |
| |
| // |
| // Step 1: |
| // integer promotion & Schubfach multiplier calculation. |
| // |
| |
| uint64_t m2; |
| int32_t e2; |
| if (ieee_exponent != 0) |
| { |
| m2 = Double::HiddenBit | ieee_significand; |
| e2 = static_cast<int32_t>(ieee_exponent) - Double::ExponentBias; |
| |
| if /*unlikely*/ (0 <= -e2 && -e2 < Double::SignificandSize && MultipleOfPow2(m2, -e2)) |
| { |
| // Small integer. |
| return {m2 >> -e2, 0}; |
| } |
| |
| if /*unlikely*/ (ieee_significand == 0 && ieee_exponent > 1) |
| { |
| // Shorter interval case; proceed like Schubfach. |
| return ToDecimal64_asymmetric_interval(e2); |
| } |
| } |
| else |
| { |
| // Subnormal case; interval is always regular. |
| m2 = ieee_significand; |
| e2 = 1 - Double::ExponentBias; |
| } |
| |
| const bool is_even = (m2 % 2 == 0); |
| const bool accept_lower = is_even; |
| const bool accept_upper = is_even; |
| |
| // Compute k and beta. |
| const int32_t minus_k = FloorLog10Pow2(e2) - Kappa; |
| const int32_t beta_minus_1 = e2 + FloorLog2Pow10(-minus_k); |
| DRAGONBOX_ASSERT(beta_minus_1 >= 6); |
| DRAGONBOX_ASSERT(beta_minus_1 <= 9); |
| |
| const uint64x2 pow10 = ComputePow10(-minus_k); |
| |
| // Compute delta |
| // 10^kappa <= delta < 10^(kappa + 1) |
| // 100 <= delta < 1000 |
| const uint32_t delta = ComputeDelta(pow10, beta_minus_1); |
| DRAGONBOX_ASSERT(delta >= SmallDivisor); |
| DRAGONBOX_ASSERT(delta < BigDivisor ); |
| |
| const uint64_t two_fl = 2 * m2 - 1; |
| const uint64_t two_fc = 2 * m2; |
| const uint64_t two_fr = 2 * m2 + 1; // (54 bits) |
| |
| // Compute zi |
| // (54 + 9 = 63 bits) |
| const uint64_t zi = MulShift(two_fr << beta_minus_1, pow10); // 2 mulx |
| |
| // |
| // Step 2: |
| // Try larger divisor. |
| // |
| |
| uint64_t q = zi / BigDivisor; |
| // uint64_t q = Mul128(zi, 0x83126E978D4FDF3Cu).hi >> 9; // 1 mulx |
| uint32_t r = static_cast<uint32_t>(zi) - BigDivisor * static_cast<uint32_t>(q); // r = zi % BigDivisor |
| // 0 <= r < 1000 |
| |
| if /*likely ~50% ?!*/ (r < delta) |
| { |
| // Exclude the right endpoint if necessary |
| if /*likely*/ (r != 0 || accept_upper || !IsIntegralEndpoint(two_fr, e2, minus_k)) |
| { |
| return {q, minus_k + Kappa + 1}; |
| } |
| |
| DRAGONBOX_ASSERT(q != 0); |
| --q; |
| r = BigDivisor; |
| } |
| else if /*unlikely*/ (r == delta) |
| { |
| // Compare fractional parts. |
| // Check conditions in the order different from the paper |
| // to take advantage of short-circuiting |
| if ((accept_lower && IsIntegralEndpoint(two_fl, e2, minus_k)) || MulParity(two_fl, pow10, beta_minus_1)) // 1 mulx, 1 mul |
| { |
| return {q, minus_k + Kappa + 1}; |
| } |
| } |
| else /*likely ~50% ?!*/ // (r > deltai) |
| { |
| } |
| |
| // |
| // Step 3: |
| // Find the significand with the smaller divisor |
| // |
| |
| q *= 10; // 1 hmul |
| |
| // 0 <= r <= 1000 |
| |
| const uint32_t dist = r - (delta / 2) + (SmallDivisor / 2); |
| |
| const uint32_t dist_q = dist / 100; // 1 mul |
| // const uint32_t dist_r = dist % 100; |
| q += dist_q; |
| |
| // if /*likely*/ (dist_r == 0) |
| if /*likely*/ (dist == dist_q * 100) // 1 mul32 |
| { |
| // const bool approx_y_parity = ((dist ^ (SmallDivisor / 2)) & 1) != 0; |
| const bool approx_y_parity = (dist & 1) != 0; |
| |
| // Check z^(f) >= epsilon^(f) |
| // We have either yi == zi - epsiloni or yi == (zi - epsiloni) - 1, |
| // where yi == zi - epsiloni if and only if z^(f) >= epsilon^(f) |
| // Since there are only 2 possibilities, we only need to care about the |
| // parity. Also, zi and r should have the same parity since the divisor |
| // is an even number |
| if /*likely*/ (MulParity(two_fc, pow10, beta_minus_1) != approx_y_parity) // 1 mulx, 1 mul |
| { |
| --q; |
| } |
| // If z^(f) >= epsilon^(f), we might have a tie |
| // when z^(f) == epsilon^(f), or equivalently, when y is an integer |
| else if (q % 2 != 0 && IsIntegralMidpoint(two_fc, e2, minus_k)) |
| { |
| --q; |
| } |
| } |
| |
| return {q, minus_k + Kappa}; |
| } |
| |
| //================================================================================================== |
| // ToChars |
| //================================================================================================== |
| |
| static inline void Utoa_2Digits(char* buf, uint32_t digits) |
| { |
| static constexpr char Digits100[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', |
| }; |
| |
| DRAGONBOX_ASSERT(digits <= 99); |
| std::memcpy(buf, &Digits100[2 * digits], 2 * sizeof(char)); |
| } |
| |
| static inline int32_t TrailingZeros_2Digits(uint32_t digits) |
| { |
| static constexpr int8_t TrailingZeros100[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, |
| }; |
| |
| DRAGONBOX_ASSERT(digits <= 99); |
| return TrailingZeros100[digits]; |
| } |
| |
| static inline int32_t Utoa_8Digits_skip_trailing_zeros(char* buf, uint32_t digits) |
| { |
| DRAGONBOX_ASSERT(digits >= 1); |
| DRAGONBOX_ASSERT(digits <= 99999999); |
| |
| const uint32_t q = digits / 10000; |
| const uint32_t r = digits % 10000; |
| |
| const uint32_t qH = q / 100; |
| const uint32_t qL = q % 100; |
| Utoa_2Digits(buf + 0, qH); |
| Utoa_2Digits(buf + 2, qL); |
| |
| if (r == 0) |
| { |
| return TrailingZeros_2Digits(qL == 0 ? qH : qL) + (qL == 0 ? 6 : 4); |
| } |
| else |
| { |
| const uint32_t rH = r / 100; |
| const uint32_t rL = r % 100; |
| Utoa_2Digits(buf + 4, rH); |
| Utoa_2Digits(buf + 6, rL); |
| |
| return TrailingZeros_2Digits(rL == 0 ? rH : rL) + (rL == 0 ? 2 : 0); |
| } |
| } |
| |
| static inline int32_t PrintDecimalDigitsBackwards(char* buf, uint64_t output64) |
| { |
| int32_t tz = 0; // number of trailing zeros removed. |
| int32_t nd = 0; // number of decimal digits processed. |
| |
| // At most 17 digits remaining |
| |
| if (output64 >= 100000000) |
| { |
| const uint64_t q = output64 / 100000000; |
| const uint32_t r = static_cast<uint32_t>(output64 % 100000000); |
| output64 = q; |
| buf -= 8; |
| if (r != 0) |
| { |
| tz = Utoa_8Digits_skip_trailing_zeros(buf, r); |
| DRAGONBOX_ASSERT(tz >= 0); |
| DRAGONBOX_ASSERT(tz <= 7); |
| } |
| else |
| { |
| tz = 8; |
| } |
| nd = 8; |
| } |
| |
| // At most 9 digits remaining. |
| DRAGONBOX_ASSERT(output64 <= UINT32_MAX); |
| uint32_t output = static_cast<uint32_t>(output64); |
| |
| if (output >= 10000) |
| { |
| const uint32_t q = output / 10000; |
| const uint32_t r = output % 10000; |
| output = q; |
| buf -= 4; |
| if (r != 0) |
| { |
| const uint32_t rH = r / 100; |
| const uint32_t rL = r % 100; |
| Utoa_2Digits(buf + 0, rH); |
| Utoa_2Digits(buf + 2, rL); |
| if (tz == nd) |
| { |
| tz += TrailingZeros_2Digits(rL == 0 ? rH : rL) + (rL == 0 ? 2 : 0); |
| } |
| } |
| else |
| { |
| if (tz == nd) |
| tz += 4; |
| else |
| std::memset(buf, '0', 4); // (actually not required...) |
| } |
| nd += 4; |
| } |
| |
| // At most 5 digits remaining. |
| |
| if (output >= 100) |
| { |
| const uint32_t q = output / 100; |
| const uint32_t r = output % 100; |
| output = q; |
| buf -= 2; |
| Utoa_2Digits(buf, r); |
| if (tz == nd) |
| { |
| tz += TrailingZeros_2Digits(r); |
| } |
| nd += 2; |
| |
| if (output >= 100) |
| { |
| const uint32_t q = output / 100; |
| const uint32_t r = output % 100; |
| output = q; |
| buf -= 2; |
| Utoa_2Digits(buf, r); |
| if (tz == nd) |
| { |
| tz += TrailingZeros_2Digits(r); |
| } |
| nd += 2; |
| } |
| } |
| |
| // At most 2 digits remaining. |
| |
| DRAGONBOX_ASSERT(output >= 1); |
| DRAGONBOX_ASSERT(output <= 99); |
| |
| if (output >= 10) |
| { |
| const uint32_t q = output; |
| buf -= 2; |
| Utoa_2Digits(buf, q); |
| if (tz == nd) |
| { |
| tz += TrailingZeros_2Digits(q); |
| } |
| // nd += 2; |
| } |
| else |
| { |
| const uint32_t q = output; |
| DRAGONBOX_ASSERT(q >= 1); |
| DRAGONBOX_ASSERT(q <= 9); |
| *--buf = static_cast<char>('0' + q); |
| } |
| |
| return tz; |
| } |
| |
| static inline int32_t DecimalLength(uint64_t v) |
| { |
| DRAGONBOX_ASSERT(v >= 1); |
| DRAGONBOX_ASSERT(v <= 99999999999999999ull); |
| |
| if (static_cast<uint32_t>(v >> 32) != 0) |
| { |
| if (v >= 10000000000000000ull) { return 17; } |
| if (v >= 1000000000000000ull) { return 16; } |
| if (v >= 100000000000000ull) { return 15; } |
| if (v >= 10000000000000ull) { return 14; } |
| if (v >= 1000000000000ull) { return 13; } |
| if (v >= 100000000000ull) { return 12; } |
| if (v >= 10000000000ull) { return 11; } |
| return 10; |
| } |
| |
| const uint32_t v32 = static_cast<uint32_t>(v); |
| if (v32 >= 1000000000u) { return 10; } |
| if (v32 >= 100000000u) { return 9; } |
| if (v32 >= 10000000u) { return 8; } |
| if (v32 >= 1000000u) { return 7; } |
| if (v32 >= 100000u) { return 6; } |
| if (v32 >= 10000u) { return 5; } |
| if (v32 >= 1000u) { return 4; } |
| if (v32 >= 100u) { return 3; } |
| if (v32 >= 10u) { return 2; } |
| return 1; |
| } |
| |
| static inline char* FormatDigits(char* buffer, uint64_t digits, int32_t decimal_exponent, bool force_trailing_dot_zero = false) |
| { |
| static constexpr int32_t MinFixedDecimalPoint = -6; |
| static constexpr int32_t MaxFixedDecimalPoint = 17; |
| static_assert(MinFixedDecimalPoint <= -1, "internal error"); |
| static_assert(MaxFixedDecimalPoint >= 17, "internal error"); |
| |
| DRAGONBOX_ASSERT(digits >= 1); |
| DRAGONBOX_ASSERT(digits <= 99999999999999999ull); |
| DRAGONBOX_ASSERT(decimal_exponent >= -999); |
| DRAGONBOX_ASSERT(decimal_exponent <= 999); |
| |
| int32_t num_digits = DecimalLength(digits); |
| const int32_t decimal_point = num_digits + decimal_exponent; |
| |
| const bool use_fixed = MinFixedDecimalPoint <= decimal_point && decimal_point <= MaxFixedDecimalPoint; |
| |
| // Prepare the buffer. |
| // Avoid calling memset/memcpy with variable arguments below... |
| |
| std::memset(buffer + 0, '0', 16); |
| std::memset(buffer + 16, '0', 16); |
| static_assert(MinFixedDecimalPoint >= -30, "internal error"); |
| static_assert(MaxFixedDecimalPoint <= 32, "internal error"); |
| |
| int32_t decimal_digits_position; |
| if (use_fixed) |
| { |
| if (decimal_point <= 0) |
| { |
| // 0.[000]digits |
| decimal_digits_position = 2 - decimal_point; |
| } |
| else |
| { |
| // dig.its |
| // digits[000] |
| decimal_digits_position = 0; |
| } |
| } |
| else |
| { |
| // dE+123 or d.igitsE+123 |
| decimal_digits_position = 1; |
| } |
| |
| char* digits_end = buffer + decimal_digits_position + num_digits; |
| |
| const int32_t tz = PrintDecimalDigitsBackwards(digits_end, digits); |
| digits_end -= tz; |
| num_digits -= tz; |
| // decimal_exponent += tz; // => decimal_point unchanged. |
| |
| if (use_fixed) |
| { |
| if (decimal_point <= 0) |
| { |
| // 0.[000]digits |
| buffer[1] = '.'; |
| buffer = digits_end; |
| } |
| else if (decimal_point < num_digits) |
| { |
| // dig.its |
| #if defined(_MSC_VER) && !defined(__clang__) |
| // VC does not inline the memmove call below. (Even if compiled with /arch:AVX2.) |
| // However, memcpy will be inlined. |
| uint8_t tmp[16]; |
| char* const src = buffer + decimal_point; |
| char* const dst = src + 1; |
| std::memcpy(tmp, src, 16); |
| std::memcpy(dst, tmp, 16); |
| #else |
| std::memmove(buffer + decimal_point + 1, buffer + decimal_point, 16); |
| #endif |
| buffer[decimal_point] = '.'; |
| buffer = digits_end + 1; |
| } |
| else |
| { |
| // digits[000] |
| buffer += decimal_point; |
| if (force_trailing_dot_zero) |
| { |
| std::memcpy(buffer, ".0", 2); |
| buffer += 2; |
| } |
| } |
| } |
| else |
| { |
| // Copy the first digit one place to the left. |
| buffer[0] = buffer[1]; |
| if (num_digits == 1) |
| { |
| // dE+123 |
| ++buffer; |
| } |
| else |
| { |
| // d.igitsE+123 |
| buffer[1] = '.'; |
| buffer = digits_end; |
| } |
| |
| const int32_t scientific_exponent = decimal_point - 1; |
| // SF_ASSERT(scientific_exponent != 0); |
| |
| std::memcpy(buffer, scientific_exponent < 0 ? "e-" : "e+", 2); |
| buffer += 2; |
| |
| const uint32_t k = static_cast<uint32_t>(scientific_exponent < 0 ? -scientific_exponent : scientific_exponent); |
| if (k < 10) |
| { |
| *buffer++ = static_cast<char>('0' + k); |
| } |
| else if (k < 100) |
| { |
| Utoa_2Digits(buffer, k); |
| buffer += 2; |
| } |
| else |
| { |
| const uint32_t q = k / 100; |
| const uint32_t r = k % 100; |
| *buffer++ = static_cast<char>('0' + q); |
| Utoa_2Digits(buffer, r); |
| buffer += 2; |
| } |
| } |
| |
| return buffer; |
| } |
| |
| static inline char* ToChars(char* buffer, double value, bool force_trailing_dot_zero = false) |
| { |
| const Double v(value); |
| |
| const uint64_t significand = v.PhysicalSignificand(); |
| const uint64_t exponent = v.PhysicalExponent(); |
| |
| // if (exponent != Double::MaxIeeeExponent) // [[likely]] |
| // { |
| // // Finite |
| |
| buffer[0] = '-'; |
| buffer += v.SignBit(); |
| |
| // if (exponent != 0 || significand != 0) // [[likely]] |
| // { |
| // // != 0 |
| // |
| const auto dec = ToDecimal64(significand, exponent); |
| return FormatDigits(buffer, dec.significand, dec.exponent, force_trailing_dot_zero); |
| // } |
| // else |
| // { |
| // std::memcpy(buffer, "0.0 ", 4); |
| // buffer += force_trailing_dot_zero ? 3 : 1; |
| // return buffer; |
| // } |
| // } |
| // |
| // if (significand == 0) |
| // { |
| // buffer[0] = '-'; |
| // buffer += v.SignBit(); |
| // |
| // std::memcpy(buffer, "inf ", 4); |
| // return buffer + 3; |
| // } |
| // else |
| // { |
| // std::memcpy(buffer, "nan ", 4); |
| // return buffer + 3; |
| // } |
| } |
| |
| //================================================================================================== |
| // |
| //================================================================================================== |
| |
| char* Dtoa(char* buffer, double value) |
| { |
| return ToChars(buffer, value, true); |
| } |
| |
| } // namespace |
| } // dragonbox |
