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dragonbox.cc
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// 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)
#include "dragonbox.h"
//--------------------------------------------------------------------------------------------------
// 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 <cassert>
#include <cstdint>
#include <cstring>
#include <limits>
#if defined(_MSC_VER)
#include <intrin.h>
#endif
#ifndef DRAGONBOX_ASSERT
#define DRAGONBOX_ASSERT(X) assert(X)
#endif
//==================================================================================================
//
//==================================================================================================
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;
}
namespace {
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;
}
};
} // namespace
//==================================================================================================
//
//==================================================================================================
// 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},
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{0xABFA45DA0EDBDE69, 0x0487DB9D17636892},
{0xD6F8D7509292D603, 0x45A9D2845D3C42B6},
{0x865B86925B9BC5C2, 0x0B8A2392BA45A9B2},
{0xA7F26836F282B732, 0x8E6CAC7768D7141E},
{0xD1EF0244AF2364FF, 0x3207D795430CD926},
{0x8335616AED761F1F, 0x7F44E6BD49E807B8},
{0xA402B9C5A8D3A6E7, 0x5F16206C9C6209A6},
{0xCD036837130890A1, 0x36DBA887C37A8C0F},
{0x802221226BE55A64, 0xC2494954DA2C9789},
{0xA02AA96B06DEB0FD, 0xF2DB9BAA10B7BD6C},
{0xC83553C5C8965D3D, 0x6F92829494E5ACC7},
{0xFA42A8B73ABBF48C, 0xCB772339BA1F17F9},
{0x9C69A97284B578D7, 0xFF2A760414536EFB},
{0xC38413CF25E2D70D, 0xFEF5138519684ABA},
{0xF46518C2EF5B8CD1, 0x7EB258665FC25D69},
{0x98BF2F79D5993802, 0xEF2F773FFBD97A61},
{0xBEEEFB584AFF8603, 0xAAFB550FFACFD8FA},
{0xEEAABA2E5DBF6784, 0x95BA2A53F983CF38},
{0x952AB45CFA97A0B2, 0xDD945A747BF26183},
{0xBA756174393D88DF, 0x94F971119AEEF9E4},
{0xE912B9D1478CEB17, 0x7A37CD5601AAB85D},
{0x91ABB422CCB812EE, 0xAC62E055C10AB33A},
{0xB616A12B7FE617AA, 0x577B986B314D6009},
{0xE39C49765FDF9D94, 0xED5A7E85FDA0B80B},
{0x8E41ADE9FBEBC27D, 0x14588F13BE847307},
{0xB1D219647AE6B31C, 0x596EB2D8AE258FC8},
{0xDE469FBD99A05FE3, 0x6FCA5F8ED9AEF3BB},
{0x8AEC23D680043BEE, 0x25DE7BB9480D5854},
{0xADA72CCC20054AE9, 0xAF561AA79A10AE6A},
{0xD910F7FF28069DA4, 0x1B2BA1518094DA04},
{0x87AA9AFF79042286, 0x90FB44D2F05D0842},
{0xA99541BF57452B28, 0x353A1607AC744A53},
{0xD3FA922F2D1675F2, 0x42889B8997915CE8},
{0x847C9B5D7C2E09B7, 0x69956135FEBADA11},
{0xA59BC234DB398C25, 0x43FAB9837E699095},
{0xCF02B2C21207EF2E, 0x94F967E45E03F4BB},
{0x8161AFB94B44F57D, 0x1D1BE0EEBAC278F5},
{0xA1BA1BA79E1632DC, 0x6462D92A69731732},
{0xCA28A291859BBF93, 0x7D7B8F7503CFDCFE},
{0xFCB2CB35E702AF78, 0x5CDA735244C3D43E},
{0x9DEFBF01B061ADAB, 0x3A0888136AFA64A7},
{0xC56BAEC21C7A1916, 0x088AAA1845B8FDD0},
{0xF6C69A72A3989F5B, 0x8AAD549E57273D45},
{0x9A3C2087A63F6399, 0x36AC54E2F678864B},
{0xC0CB28A98FCF3C7F, 0x84576A1BB416A7DD},
{0xF0FDF2D3F3C30B9F, 0x656D44A2A11C51D5},
{0x969EB7C47859E743, 0x9F644AE5A4B1B325},
{0xBC4665B596706114, 0x873D5D9F0DDE1FEE},
{0xEB57FF22FC0C7959, 0xA90CB506D155A7EA},
{0x9316FF75DD87CBD8, 0x09A7F12442D588F2},
{0xB7DCBF5354E9BECE, 0x0C11ED6D538AEB2F},
{0xE5D3EF282A242E81, 0x8F1668C8A86DA5FA},
{0x8FA475791A569D10, 0xF96E017D694487BC},
{0xB38D92D760EC4455, 0x37C981DCC395A9AC},
{0xE070F78D3927556A, 0x85BBE253F47B1417},
{0x8C469AB843B89562, 0x93956D7478CCEC8E},
{0xAF58416654A6BABB, 0x387AC8D1970027B2},
{0xDB2E51BFE9D0696A, 0x06997B05FCC0319E},
{0x88FCF317F22241E2, 0x441FECE3BDF81F03},
{0xAB3C2FDDEEAAD25A, 0xD527E81CAD7626C3},
{0xD60B3BD56A5586F1, 0x8A71E223D8D3B074},
{0x85C7056562757456, 0xF6872D5667844E49},
{0xA738C6BEBB12D16C, 0xB428F8AC016561DB},
{0xD106F86E69D785C7, 0xE13336D701BEBA52},
{0x82A45B450226B39C, 0xECC0024661173473},
{0xA34D721642B06084, 0x27F002D7F95D0190},
{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}, // 5^21
{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;