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ryu_64.cc
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// Copyright 2020 Ulf Adams
// 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 "ryu_64.h"
#if defined(__has_include) && __has_include(<version>)
#include <version>
#else
#include <cassert>
#endif
#if defined(__cpp_lib_to_chars)
#define HAS_CHARCONV() 1
#else
#define HAS_CHARCONV() 0
#endif
//#undef NDEBUG
#include <cassert>
#include <climits>
#include <cstdint>
#include <cstdlib>
#include <cstring>
#include <limits>
#if HAS_CHARCONV()
#include <charconv>
#else
#include <string>
#endif
#if _MSC_VER
#include <intrin.h>
#endif
#ifndef RYU_ASSERT
#define RYU_ASSERT(X) assert(X)
#endif
#ifndef RYU_NEVER_INLINE
#if _MSC_VER
#define RYU_NEVER_INLINE __declspec(noinline) inline
#elif __GNUC__
#define RYU_NEVER_INLINE __attribute__((noinline)) inline
#else
#define RYU_NEVER_INLINE inline
#endif
#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 int32_t MaxIeeeExponent = 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 = bits_type{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
//==================================================================================================
//
//==================================================================================================
static inline int32_t Max(int32_t x, int32_t y)
{
return y < x ? x : y;
}
// Returns floor(x / 2^n).
static inline int32_t FloorDivPow2(int32_t x, int32_t n)
{
#if 0
// Technically, right-shift of negative integers is implementation defined...
// Should easily be optimized into SAR (or equivalent) instruction.
return x < 0 ? ~(~x >> n) : (x >> n);
#else
return x >> n;
#endif
}
static inline int32_t FloorLog2Pow5(int32_t e)
{
RYU_ASSERT(e >= -1764);
RYU_ASSERT(e <= 1763);
return FloorDivPow2(e * 1217359, 19);
}
static inline int32_t FloorLog10Pow2(int32_t e)
{
RYU_ASSERT(e >= -2620);
RYU_ASSERT(e <= 2620);
return FloorDivPow2(e * 315653, 20);
}
static inline int32_t FloorLog10Pow5(int32_t e)
{
RYU_ASSERT(e >= -2620);
RYU_ASSERT(e <= 2620);
return FloorDivPow2(e * 732923, 20);
}
static inline uint32_t Lo32(uint64_t x)
{
return static_cast<uint32_t>(x & 0xFFFFFFFFu);
}
//[[maybe_unused]]
static inline uint32_t Hi32(uint64_t x)
{
return static_cast<uint32_t>(x >> 32);
}
//==================================================================================================
// ToDecimal
//
// Double-precision implementation
//==================================================================================================
// Constant data = 10'656 (+ 400) bytes
static constexpr int32_t BitsPerPow5_Double = 128;
namespace {
struct uint64x2 {
uint64_t hi;
uint64_t lo;
};
}
static inline uint64x2 ComputePow5_Double(int32_t k)
{
// Let e = FloorLog2Pow5(k) + 1 - BitsPerPow5_Double
// For k < 0, stores 5^k in the form: ceil(2^-e / 5^-k)
// For k >= 0, stores 5^k in the form: floor( 5^k / 2^e )
static constexpr int32_t MinDecExp = -340;
static constexpr int32_t MaxDecExp = 325;
static constexpr uint64x2 Pow5[MaxDecExp - MinDecExp + 1] = {
{0xBAAEE17FA23EBF76, 0x5D79BCF00D2DF64A}, // e = -917, k = -340
{0xE95A99DF8ACE6F53, 0xF4D82C2C107973DD}, // e = -915, k = -339
{0x91D8A02BB6C10594, 0x79071B9B8A4BE86A}, // e = -912, k = -338
{0xB64EC836A47146F9, 0x9748E2826CDEE285}, // e = -910, k = -337
{0xE3E27A444D8D98B7, 0xFD1B1B2308169B26}, // e = -908, k = -336
{0x8E6D8C6AB0787F72, 0xFE30F0F5E50E20F8}, // e = -905, k = -335
{0xB208EF855C969F4F, 0xBDBD2D335E51A936}, // e = -903, k = -334
{0xDE8B2B66B3BC4723, 0xAD2C788035E61383}, // e = -901, k = -333
{0x8B16FB203055AC76, 0x4C3BCB5021AFCC32}, // e = -898, k = -332
{0xADDCB9E83C6B1793, 0xDF4ABE242A1BBF3E}, // e = -896, k = -331
{0xD953E8624B85DD78, 0xD71D6DAD34A2AF0E}, // e = -894, k = -330
{0x87D4713D6F33AA6B, 0x8672648C40E5AD69}, // e = -891, k = -329
{0xA9C98D8CCB009506, 0x680EFDAF511F18C3}, // e = -889, k = -328
{0xD43BF0EFFDC0BA48, 0x0212BD1B2566DEF3}, // e = -887, k = -327
{0x84A57695FE98746D, 0x014BB630F7604B58}, // e = -884, k = -326
{0xA5CED43B7E3E9188, 0x419EA3BD35385E2E}, // e = -882, k = -325
{0xCF42894A5DCE35EA, 0x52064CAC828675BA}, // e = -880, k = -324
{0x818995CE7AA0E1B2, 0x7343EFEBD1940994}, // e = -877, k = -323
{0xA1EBFB4219491A1F, 0x1014EBE6C5F90BF9}, // e = -875, k = -322
{0xCA66FA129F9B60A6, 0xD41A26E077774EF7}, // e = -873, k = -321
{0xFD00B897478238D0, 0x8920B098955522B5}, // e = -871, k = -320
{0x9E20735E8CB16382, 0x55B46E5F5D5535B1}, // e = -868, k = -319
{0xC5A890362FDDBC62, 0xEB2189F734AA831E}, // e = -866, k = -318
{0xF712B443BBD52B7B, 0xA5E9EC7501D523E5}, // e = -864, k = -317
{0x9A6BB0AA55653B2D, 0x47B233C92125366F}, // e = -861, k = -316
{0xC1069CD4EABE89F8, 0x999EC0BB696E840B}, // e = -859, k = -315
{0xF148440A256E2C76, 0xC00670EA43CA250E}, // e = -857, k = -314
{0x96CD2A865764DBCA, 0x380406926A5E5729}, // e = -854, k = -313
{0xBC807527ED3E12BC, 0xC605083704F5ECF3}, // e = -852, k = -312
{0xEBA09271E88D976B, 0xF7864A44C633682F}, // e = -850, k = -311
{0x93445B8731587EA3, 0x7AB3EE6AFBE0211E}, // e = -847, k = -310
{0xB8157268FDAE9E4C, 0x5960EA05BAD82965}, // e = -845, k = -309
{0xE61ACF033D1A45DF, 0x6FB92487298E33BE}, // e = -843, k = -308
{0x8FD0C16206306BAB, 0xA5D3B6D479F8E057}, // e = -840, k = -307
{0xB3C4F1BA87BC8696, 0x8F48A4899877186D}, // e = -838, k = -306
{0xE0B62E2929ABA83C, 0x331ACDABFE94DE88}, // e = -836, k = -305
{0x8C71DCD9BA0B4925, 0x9FF0C08B7F1D0B15}, // e = -833, k = -304
{0xAF8E5410288E1B6F, 0x07ECF0AE5EE44DDA}, // e = -831, k = -303
{0xDB71E91432B1A24A, 0xC9E82CD9F69D6151}, // e = -829, k = -302
{0x892731AC9FAF056E, 0xBE311C083A225CD3}, // e = -826, k = -301
{0xAB70FE17C79AC6CA, 0x6DBD630A48AAF407}, // e = -824, k = -300
{0xD64D3D9DB981787D, 0x092CBBCCDAD5B109}, // e = -822, k = -299
{0x85F0468293F0EB4E, 0x25BBF56008C58EA6}, // e = -819, k = -298
{0xA76C582338ED2621, 0xAF2AF2B80AF6F24F}, // e = -817, k = -297
{0xD1476E2C07286FAA, 0x1AF5AF660DB4AEE2}, // e = -815, k = -296
{0x82CCA4DB847945CA, 0x50D98D9FC890ED4E}, // e = -812, k = -295
{0xA37FCE126597973C, 0xE50FF107BAB528A1}, // e = -810, k = -294
{0xCC5FC196FEFD7D0C, 0x1E53ED49A96272C9}, // e = -808, k = -293
{0xFF77B1FCBEBCDC4F, 0x25E8E89C13BB0F7B}, // e = -806, k = -292
{0x9FAACF3DF73609B1, 0x77B191618C54E9AD}, // e = -803, k = -291
{0xC795830D75038C1D, 0xD59DF5B9EF6A2418}, // e = -801, k = -290
{0xF97AE3D0D2446F25, 0x4B0573286B44AD1E}, // e = -799, k = -289
{0x9BECCE62836AC577, 0x4EE367F9430AEC33}, // e = -796, k = -288
{0xC2E801FB244576D5, 0x229C41F793CDA740}, // e = -794, k = -287
{0xF3A20279ED56D48A, 0x6B43527578C11110}, // e = -792, k = -286
{0x9845418C345644D6, 0x830A13896B78AAAA}, // e = -789, k = -285
{0xBE5691EF416BD60C, 0x23CC986BC656D554}, // e = -787, k = -284
{0xEDEC366B11C6CB8F, 0x2CBFBE86B7EC8AA9}, // e = -785, k = -283
{0x94B3A202EB1C3F39, 0x7BF7D71432F3D6AA}, // e = -782, k = -282
{0xB9E08A83A5E34F07, 0xDAF5CCD93FB0CC54}, // e = -780, k = -281
{0xE858AD248F5C22C9, 0xD1B3400F8F9CFF69}, // e = -778, k = -280
{0x91376C36D99995BE, 0x23100809B9C21FA2}, // e = -775, k = -279
{0xB58547448FFFFB2D, 0xABD40A0C2832A78B}, // e = -773, k = -278
{0xE2E69915B3FFF9F9, 0x16C90C8F323F516D}, // e = -771, k = -277
{0x8DD01FAD907FFC3B, 0xAE3DA7D97F6792E4}, // e = -768, k = -276
{0xB1442798F49FFB4A, 0x99CD11CFDF41779D}, // e = -766, k = -275
{0xDD95317F31C7FA1D, 0x40405643D711D584}, // e = -764, k = -274
{0x8A7D3EEF7F1CFC52, 0x482835EA666B2573}, // e = -761, k = -273
{0xAD1C8EAB5EE43B66, 0xDA3243650005EED0}, // e = -759, k = -272
{0xD863B256369D4A40, 0x90BED43E40076A83}, // e = -757, k = -271
{0x873E4F75E2224E68, 0x5A7744A6E804A292}, // e = -754, k = -270
{0xA90DE3535AAAE202, 0x711515D0A205CB37}, // e = -752, k = -269
{0xD3515C2831559A83, 0x0D5A5B44CA873E04}, // e = -750, k = -268
{0x8412D9991ED58091, 0xE858790AFE9486C3}, // e = -747, k = -267
{0xA5178FFF668AE0B6, 0x626E974DBE39A873}, // e = -745, k = -266
{0xCE5D73FF402D98E3, 0xFB0A3D212DC81290}, // e = -743, k = -265
{0x80FA687F881C7F8E, 0x7CE66634BC9D0B9A}, // e = -740, k = -264
{0xA139029F6A239F72, 0x1C1FFFC1EBC44E81}, // e = -738, k = -263
{0xC987434744AC874E, 0xA327FFB266B56221}, // e = -736, k = -262
{0xFBE9141915D7A922, 0x4BF1FF9F0062BAA9}, // e = -734, k = -261
{0x9D71AC8FADA6C9B5, 0x6F773FC3603DB4AA}, // e = -731, k = -260
{0xC4CE17B399107C22, 0xCB550FB4384D21D4}, // e = -729, k = -259
{0xF6019DA07F549B2B, 0x7E2A53A146606A49}, // e = -727, k = -258
{0x99C102844F94E0FB, 0x2EDA7444CBFC426E}, // e = -724, k = -257
{0xC0314325637A1939, 0xFA911155FEFB5309}, // e = -722, k = -256
{0xF03D93EEBC589F88, 0x793555AB7EBA27CB}, // e = -720, k = -255
{0x96267C7535B763B5, 0x4BC1558B2F3458DF}, // e = -717, k = -254
{0xBBB01B9283253CA2, 0x9EB1AAEDFB016F17}, // e = -715, k = -253
{0xEA9C227723EE8BCB, 0x465E15A979C1CADD}, // e = -713, k = -252
{0x92A1958A7675175F, 0x0BFACD89EC191ECA}, // e = -710, k = -251
{0xB749FAED14125D36, 0xCEF980EC671F667C}, // e = -708, k = -250
{0xE51C79A85916F484, 0x82B7E12780E7401B}, // e = -706, k = -249
{0x8F31CC0937AE58D2, 0xD1B2ECB8B0908811}, // e = -703, k = -248
{0xB2FE3F0B8599EF07, 0x861FA7E6DCB4AA16}, // e = -701, k = -247
{0xDFBDCECE67006AC9, 0x67A791E093E1D49B}, // e = -699, k = -246
{0x8BD6A141006042BD, 0xE0C8BB2C5C6D24E1}, // e = -696, k = -245
{0xAECC49914078536D, 0x58FAE9F773886E19}, // e = -694, k = -244
{0xDA7F5BF590966848, 0xAF39A475506A899F}, // e = -692, k = -243
{0x888F99797A5E012D, 0x6D8406C952429604}, // e = -689, k = -242
{0xAAB37FD7D8F58178, 0xC8E5087BA6D33B84}, // e = -687, k = -241
{0xD5605FCDCF32E1D6, 0xFB1E4A9A90880A65}, // e = -685, k = -240
{0x855C3BE0A17FCD26, 0x5CF2EEA09A550680}, // e = -682, k = -239
{0xA6B34AD8C9DFC06F, 0xF42FAA48C0EA481F}, // e = -680, k = -238
{0xD0601D8EFC57B08B, 0xF13B94DAF124DA27}, // e = -678, k = -237
{0x823C12795DB6CE57, 0x76C53D08D6B70859}, // e = -675, k = -236
{0xA2CB1717B52481ED, 0x54768C4B0C64CA6F}, // e = -673, k = -235
{0xCB7DDCDDA26DA268, 0xA9942F5DCF7DFD0A}, // e = -671, k = -234
{0xFE5D54150B090B02, 0xD3F93B35435D7C4D}, // e = -669, k = -233
{0x9EFA548D26E5A6E1, 0xC47BC5014A1A6DB0}, // e = -666, k = -232
{0xC6B8E9B0709F109A, 0x359AB6419CA1091C}, // e = -664, k = -231
{0xF867241C8CC6D4C0, 0xC30163D203C94B63}, // e = -662, k = -230
{0x9B407691D7FC44F8, 0x79E0DE63425DCF1E}, // e = -659, k = -229
{0xC21094364DFB5636, 0x985915FC12F542E5}, // e = -657, k = -228
{0xF294B943E17A2BC4, 0x3E6F5B7B17B2939E}, // e = -655, k = -227
{0x979CF3CA6CEC5B5A, 0xA705992CEECF9C43}, // e = -652, k = -226
{0xBD8430BD08277231, 0x50C6FF782A838354}, // e = -650, k = -225
{0xECE53CEC4A314EBD, 0xA4F8BF5635246429}, // e = -648, k = -224
{0x940F4613AE5ED136, 0x871B7795E136BE9A}, // e = -645, k = -223
{0xB913179899F68584, 0x28E2557B59846E40}, // e = -643, k = -222
{0xE757DD7EC07426E5, 0x331AEADA2FE589D0}, // e = -641, k = -221
{0x9096EA6F3848984F, 0x3FF0D2C85DEF7622}, // e = -638, k = -220
{0xB4BCA50B065ABE63, 0x0FED077A756B53AA}, // e = -636, k = -219
{0xE1EBCE4DC7F16DFB, 0xD3E8495912C62895}, // e = -634, k = -218
{0x8D3360F09CF6E4BD, 0x64712DD7ABBBD95D}, // e = -631, k = -217
{0xB080392CC4349DEC, 0xBD8D794D96AACFB4}, // e = -629, k = -216
{0xDCA04777F541C567, 0xECF0D7A0FC5583A1}, // e = -627, k = -215
{0x89E42CAAF9491B60, 0xF41686C49DB57245}, // e = -624, k = -214
{0xAC5D37D5B79B6239, 0x311C2875C522CED6}, // e = -622, k = -213
{0xD77485CB25823AC7, 0x7D633293366B828C}, // e = -620, k = -212
{0x86A8D39EF77164BC, 0xAE5DFF9C02033198}, // e = -617, k = -211
{0xA8530886B54DBDEB, 0xD9F57F830283FDFD}, // e = -615, k = -210
{0xD267CAA862A12D66, 0xD072DF63C324FD7C}, // e = -613, k = -209
{0x8380DEA93DA4BC60, 0x4247CB9E59F71E6E}, // e = -610, k = -208
{0xA46116538D0DEB78, 0x52D9BE85F074E609}, // e = -608, k = -207
{0xCD795BE870516656, 0x67902E276C921F8C}, // e = -606, k = -206
{0x806BD9714632DFF6, 0x00BA1CD8A3DB53B7}, // e = -603, k = -205
{0xA086CFCD97BF97F3, 0x80E8A40ECCD228A5}, // e = -601, k = -204
{0xC8A883C0FDAF7DF0, 0x6122CD128006B2CE}, // e = -599, k = -203
{0xFAD2A4B13D1B5D6C, 0x796B805720085F82}, // e = -597, k = -202
{0x9CC3A6EEC6311A63, 0xCBE3303674053BB1}, // e = -594, k = -201
{0xC3F490AA77BD60FC, 0xBEDBFC4411068A9D}, // e = -592, k = -200
{0xF4F1B4D515ACB93B, 0xEE92FB5515482D45}, // e = -590, k = -199
{0x991711052D8BF3C5, 0x751BDD152D4D1C4B}, // e = -587, k = -198
{0xBF5CD54678EEF0B6, 0xD262D45A78A0635E}, // e = -585, k = -197
{0xEF340A98172AACE4, 0x86FB897116C87C35}, // e = -583, k = -196
{0x9580869F0E7AAC0E, 0xD45D35E6AE3D4DA1}, // e = -580, k = -195
{0xBAE0A846D2195712, 0x8974836059CCA10A}, // e = -578, k = -194
{0xE998D258869FACD7, 0x2BD1A438703FC94C}, // e = -576, k = -193
{0x91FF83775423CC06, 0x7B6306A34627DDD0}, // e = -573, k = -192
{0xB67F6455292CBF08, 0x1A3BC84C17B1D543}, // e = -571, k = -191
{0xE41F3D6A7377EECA, 0x20CABA5F1D9E4A94}, // e = -569, k = -190
{0x8E938662882AF53E, 0x547EB47B7282EE9D}, // e = -566, k = -189
{0xB23867FB2A35B28D, 0xE99E619A4F23AA44}, // e = -564, k = -188
{0xDEC681F9F4C31F31, 0x6405FA00E2EC94D5}, // e = -562, k = -187
{0x8B3C113C38F9F37E, 0xDE83BC408DD3DD05}, // e = -559, k = -186
{0xAE0B158B4738705E, 0x9624AB50B148D446}, // e = -557, k = -185
{0xD98DDAEE19068C76, 0x3BADD624DD9B0958}, // e = -555, k = -184
{0x87F8A8D4CFA417C9, 0xE54CA5D70A80E5D7}, // e = -552, k = -183
{0xA9F6D30A038D1DBC, 0x5E9FCF4CCD211F4D}, // e = -550, k = -182
{0xD47487CC8470652B, 0x7647C32000696720}, // e = -548, k = -181
{0x84C8D4DFD2C63F3B, 0x29ECD9F40041E074}, // e = -545, k = -180
{0xA5FB0A17C777CF09, 0xF468107100525891}, // e = -543, k = -179
{0xCF79CC9DB955C2CC, 0x7182148D4066EEB5}, // e = -541, k = -178
{0x81AC1FE293D599BF, 0xC6F14CD848405531}, // e = -538, k = -177
{0xA21727DB38CB002F, 0xB8ADA00E5A506A7D}, // e = -536, k = -176
{0xCA9CF1D206FDC03B, 0xA6D90811F0E4851D}, // e = -534, k = -175
{0xFD442E4688BD304A, 0x908F4A166D1DA664}, // e = -532, k = -174
{0x9E4A9CEC15763E2E, 0x9A598E4E043287FF}, // e = -529, k = -173
{0xC5DD44271AD3CDBA, 0x40EFF1E1853F29FE}, // e = -527, k = -172
{0xF7549530E188C128, 0xD12BEE59E68EF47D}, // e = -525, k = -171
{0x9A94DD3E8CF578B9, 0x82BB74F8301958CF}, // e = -522, k = -170
{0xC13A148E3032D6E7, 0xE36A52363C1FAF02}, // e = -520, k = -169
{0xF18899B1BC3F8CA1, 0xDC44E6C3CB279AC2}, // e = -518, k = -168
{0x96F5600F15A7B7E5, 0x29AB103A5EF8C0BA}, // e = -515, k = -167
{0xBCB2B812DB11A5DE, 0x7415D448F6B6F0E8}, // e = -513, k = -166
{0xEBDF661791D60F56, 0x111B495B3464AD22}, // e = -511, k = -165
{0x936B9FCEBB25C995, 0xCAB10DD900BEEC35}, // e = -508, k = -164
{0xB84687C269EF3BFB, 0x3D5D514F40EEA743}, // e = -506, k = -163
{0xE65829B3046B0AFA, 0x0CB4A5A3112A5113}, // e = -504, k = -162
{0x8FF71A0FE2C2E6DC, 0x47F0E785EABA72AC}, // e = -501, k = -161
{0xB3F4E093DB73A093, 0x59ED216765690F57}, // e = -499, k = -160
{0xE0F218B8D25088B8, 0x306869C13EC3532D}, // e = -497, k = -159
{0x8C974F7383725573, 0x1E414218C73A13FC}, // e = -494, k = -158
{0xAFBD2350644EEACF, 0xE5D1929EF90898FB}, // e = -492, k = -157
{0xDBAC6C247D62A583, 0xDF45F746B74ABF3A}, // e = -490, k = -156
{0x894BC396CE5DA772, 0x6B8BBA8C328EB784}, // e = -487, k = -155
{0xAB9EB47C81F5114F, 0x066EA92F3F326565}, // e = -485, k = -154
{0xD686619BA27255A2, 0xC80A537B0EFEFEBE}, // e = -483, k = -153
{0x8613FD0145877585, 0xBD06742CE95F5F37}, // e = -480, k = -152
{0xA798FC4196E952E7, 0x2C48113823B73705}, // e = -478, k = -151
{0xD17F3B51FCA3A7A0, 0xF75A15862CA504C6}, // e = -476, k = -150
{0x82EF85133DE648C4, 0x9A984D73DBE722FC}, // e = -473, k = -149
{0xA3AB66580D5FDAF5, 0xC13E60D0D2E0EBBB}, // e = -471, k = -148
{0xCC963FEE10B7D1B3, 0x318DF905079926A9}, // e = -469, k = -147
{0xFFBBCFE994E5C61F, 0xFDF17746497F7053}, // e = -467, k = -146
{0x9FD561F1FD0F9BD3, 0xFEB6EA8BEDEFA634}, // e = -464, k = -145
{0xC7CABA6E7C5382C8, 0xFE64A52EE96B8FC1}, // e = -462, k = -144
{0xF9BD690A1B68637B, 0x3DFDCE7AA3C673B1}, // e = -460, k = -143
{0x9C1661A651213E2D, 0x06BEA10CA65C084F}, // e = -457, k = -142
{0xC31BFA0FE5698DB8, 0x486E494FCFF30A63}, // e = -455, k = -141
{0xF3E2F893DEC3F126, 0x5A89DBA3C3EFCCFB}, // e = -453, k = -140
{0x986DDB5C6B3A76B7, 0xF89629465A75E01D}, // e = -450, k = -139
{0xBE89523386091465, 0xF6BBB397F1135824}, // e = -448, k = -138
{0xEE2BA6C0678B597F, 0x746AA07DED582E2D}, // e = -446, k = -137
{0x94DB483840B717EF, 0xA8C2A44EB4571CDD}, // e = -443, k = -136
{0xBA121A4650E4DDEB, 0x92F34D62616CE414}, // e = -441, k = -135
{0xE896A0D7E51E1566, 0x77B020BAF9C81D18}, // e = -439, k = -134
{0x915E2486EF32CD60, 0x0ACE1474DC1D122F}, // e = -436, k = -133
{0xB5B5ADA8AAFF80B8, 0x0D819992132456BB}, // e = -434, k = -132
{0xE3231912D5BF60E6, 0x10E1FFF697ED6C6A}, // e = -432, k = -131
{0x8DF5EFABC5979C8F, 0xCA8D3FFA1EF463C2}, // e = -429, k = -130
{0xB1736B96B6FD83B3, 0xBD308FF8A6B17CB3}, // e = -427, k = -129
{0xDDD0467C64BCE4A0, 0xAC7CB3F6D05DDBDF}, // e = -425, k = -128
{0x8AA22C0DBEF60EE4, 0x6BCDF07A423AA96C}, // e = -422, k = -127
{0xAD4AB7112EB3929D, 0x86C16C98D2C953C7}, // e = -420, k = -126
{0xD89D64D57A607744, 0xE871C7BF077BA8B8}, // e = -418, k = -125
{0x87625F056C7C4A8B, 0x11471CD764AD4973}, // e = -415, k = -124
{0xA93AF6C6C79B5D2D, 0xD598E40D3DD89BD0}, // e = -413, k = -123
{0xD389B47879823479, 0x4AFF1D108D4EC2C4}, // e = -411, k = -122
{0x843610CB4BF160CB, 0xCEDF722A585139BB}, // e = -408, k = -121
{0xA54394FE1EEDB8FE, 0xC2974EB4EE658829}, // e = -406, k = -120
{0xCE947A3DA6A9273E, 0x733D226229FEEA33}, // e = -404, k = -119
{0x811CCC668829B887, 0x0806357D5A3F5260}, // e = -401, k = -118
{0xA163FF802A3426A8, 0xCA07C2DCB0CF26F8}, // e = -399, k = -117
{0xC9BCFF6034C13052, 0xFC89B393DD02F0B6}, // e = -397, k = -116
{0xFC2C3F3841F17C67, 0xBBAC2078D443ACE3}, // e = -395, k = -115
{0x9D9BA7832936EDC0, 0xD54B944B84AA4C0E}, // e = -392, k = -114
{0xC5029163F384A931, 0x0A9E795E65D4DF12}, // e = -390, k = -113
{0xF64335BCF065D37D, 0x4D4617B5FF4A16D6}, // e = -388, k = -112
{0x99EA0196163FA42E, 0x504BCED1BF8E4E46}, // e = -385, k = -111
{0xC06481FB9BCF8D39, 0xE45EC2862F71E1D7}, // e = -383, k = -110
{0xF07DA27A82C37088, 0x5D767327BB4E5A4D}, // e = -381, k = -109
{0x964E858C91BA2655, 0x3A6A07F8D510F870}, // e = -378, k = -108
{0xBBE226EFB628AFEA, 0x890489F70A55368C}, // e = -376, k = -107
{0xEADAB0ABA3B2DBE5, 0x2B45AC74CCEA842F}, // e = -374, k = -106
{0x92C8AE6B464FC96F, 0x3B0B8BC90012929E}, // e = -371, k = -105
{0xB77ADA0617E3BBCB, 0x09CE6EBB40173745}, // e = -369, k = -104
{0xE55990879DDCAABD, 0xCC420A6A101D0516}, // e = -367, k = -103
{0x8F57FA54C2A9EAB6, 0x9FA946824A12232E}, // e = -364, k = -102
{0xB32DF8E9F3546564, 0x47939822DC96ABFA}, // e = -362, k = -101
{0xDFF9772470297EBD, 0x59787E2B93BC56F8}, // e = -360, k = -100
{0x8BFBEA76C619EF36, 0x57EB4EDB3C55B65B}, // e = -357, k = -99
{0xAEFAE51477A06B03, 0xEDE622920B6B23F2}, // e = -355, k = -98
{0xDAB99E59958885C4, 0xE95FAB368E45ECEE}, // e = -353, k = -97
{0x88B402F7FD75539B, 0x11DBCB0218EBB415}, // e = -350, k = -96
{0xAAE103B5FCD2A881, 0xD652BDC29F26A11A}, // e = -348, k = -95
{0xD59944A37C0752A2, 0x4BE76D3346F04960}, // e = -346, k = -94
{0x857FCAE62D8493A5, 0x6F70A4400C562DDC}, // e = -343, k = -93
{0xA6DFBD9FB8E5B88E, 0xCB4CCD500F6BB953}, // e = -341, k = -92
{0xD097AD07A71F26B2, 0x7E2000A41346A7A8}, // e = -339, k = -91
{0x825ECC24C873782F, 0x8ED400668C0C28C9}, // e = -336, k = -90
{0xA2F67F2DFA90563B, 0x728900802F0F32FB}, // e = -334, k = -89
{0xCBB41EF979346BCA, 0x4F2B40A03AD2FFBA}, // e = -332, k = -88
{0xFEA126B7D78186BC, 0xE2F610C84987BFA9}, // e = -330, k = -87
{0x9F24B832E6B0F436, 0x0DD9CA7D2DF4D7CA}, // e = -327, k = -86
{0xC6EDE63FA05D3143, 0x91503D1C79720DBC}, // e = -325, k = -85
{0xF8A95FCF88747D94, 0x75A44C6397CE912B}, // e = -323, k = -84
{0x9B69DBE1B548CE7C, 0xC986AFBE3EE11ABB}, // e = -320, k = -83
{0xC24452DA229B021B, 0xFBE85BADCE996169}, // e = -318, k = -82
{0xF2D56790AB41C2A2, 0xFAE27299423FB9C4}, // e = -316, k = -81
{0x97C560BA6B0919A5, 0xDCCD879FC967D41B}, // e = -313, k = -80
{0xBDB6B8E905CB600F, 0x5400E987BBC1C921}, // e = -311, k = -79
{0xED246723473E3813, 0x290123E9AAB23B69}, // e = -309, k = -78
{0x9436C0760C86E30B, 0xF9A0B6720AAF6522}, // e = -306, k = -77
{0xB94470938FA89BCE, 0xF808E40E8D5B3E6A}, // e = -304, k = -76
{0xE7958CB87392C2C2, 0xB60B1D1230B20E05}, // e = -302, k = -75
{0x90BD77F3483BB9B9, 0xB1C6F22B5E6F48C3}, // e = -299, k = -74
{0xB4ECD5F01A4AA828, 0x1E38AEB6360B1AF4}, // e = -297, k = -73
{0xE2280B6C20DD5232, 0x25C6DA63C38DE1B1}, // e = -295, k = -72
{0x8D590723948A535F, 0x579C487E5A38AD0F}, // e = -292, k = -71
{0xB0AF48EC79ACE837, 0x2D835A9DF0C6D852}, // e = -290, k = -70
{0xDCDB1B2798182244, 0xF8E431456CF88E66}, // e = -288, k = -69
{0x8A08F0F8BF0F156B, 0x1B8E9ECB641B5900}, // e = -285, k = -68
{0xAC8B2D36EED2DAC5, 0xE272467E3D222F40}, // e = -283, k = -67
{0xD7ADF884AA879177, 0x5B0ED81DCC6ABB10}, // e = -281, k = -66
{0x86CCBB52EA94BAEA, 0x98E947129FC2B4EA}, // e = -278, k = -65
{0xA87FEA27A539E9A5, 0x3F2398D747B36225}, // e = -276, k = -64
{0xD29FE4B18E88640E, 0x8EEC7F0D19A03AAE}, // e = -274, k = -63
{0x83A3EEEEF9153E89, 0x1953CF68300424AD}, // e = -271, k = -62
{0xA48CEAAAB75A8E2B, 0x5FA8C3423C052DD8}, // e = -269, k = -61
{0xCDB02555653131B6, 0x3792F412CB06794E}, // e = -267, k = -60
{0x808E17555F3EBF11, 0xE2BBD88BBEE40BD1}, // e = -264, k = -59
{0xA0B19D2AB70E6ED6, 0x5B6ACEAEAE9D0EC5}, // e = -262, k = -58
{0xC8DE047564D20A8B, 0xF245825A5A445276}, // e = -260, k = -57
{0xFB158592BE068D2E, 0xEED6E2F0F0D56713}, // e = -258, k = -56
{0x9CED737BB6C4183D, 0x55464DD69685606C}, // e = -255, k = -55
{0xC428D05AA4751E4C, 0xAA97E14C3C26B887}, // e = -253, k = -54
{0xF53304714D9265DF, 0xD53DD99F4B3066A9}, // e = -251, k = -53
{0x993FE2C6D07B7FAB, 0xE546A8038EFE402A}, // e = -248, k = -52
{0xBF8FDB78849A5F96, 0xDE98520472BDD034}, // e = -246, k = -51
{0xEF73D256A5C0F77C, 0x963E66858F6D4441}, // e = -244, k = -50
{0x95A8637627989AAD, 0xDDE7001379A44AA9}, // e = -241, k = -49
{0xBB127C53B17EC159, 0x5560C018580D5D53}, // e = -239, k = -48
{0xE9D71B689DDE71AF, 0xAAB8F01E6E10B4A7}, // e = -237, k = -47
{0x9226712162AB070D, 0xCAB3961304CA70E9}, // e = -234, k = -46
{0xB6B00D69BB55C8D1, 0x3D607B97C5FD0D23}, // e = -232, k = -45
{0xE45C10C42A2B3B05, 0x8CB89A7DB77C506B}, // e = -230, k = -44
{0x8EB98A7A9A5B04E3, 0x77F3608E92ADB243}, // e = -227, k = -43
{0xB267ED1940F1C61C, 0x55F038B237591ED4}, // e = -225, k = -42
{0xDF01E85F912E37A3, 0x6B6C46DEC52F6689}, // e = -223, k = -41
{0x8B61313BBABCE2C6, 0x2323AC4B3B3DA016}, // e = -220, k = -40
{0xAE397D8AA96C1B77, 0xABEC975E0A0D081B}, // e = -218, k = -39
{0xD9C7DCED53C72255, 0x96E7BD358C904A22}, // e = -216, k = -38
{0x881CEA14545C7575, 0x7E50D64177DA2E55}, // e = -213, k = -37
{0xAA242499697392D2, 0xDDE50BD1D5D0B9EA}, // e = -211, k = -36
{0xD4AD2DBFC3D07787, 0x955E4EC64B44E865}, // e = -209, k = -35
{0x84EC3C97DA624AB4, 0xBD5AF13BEF0B113F}, // e = -206, k = -34
{0xA6274BBDD0FADD61, 0xECB1AD8AEACDD58F}, // e = -204, k = -33
{0xCFB11EAD453994BA, 0x67DE18EDA5814AF3}, // e = -202, k = -32
{0x81CEB32C4B43FCF4, 0x80EACF948770CED8}, // e = -199, k = -31
{0xA2425FF75E14FC31, 0xA1258379A94D028E}, // e = -197, k = -30
{0xCAD2F7F5359A3B3E, 0x096EE45813A04331}, // e = -195, k = -29
{0xFD87B5F28300CA0D, 0x8BCA9D6E188853FD}, // e = -193, k = -28
{0x9E74D1B791E07E48, 0x775EA264CF55347E}, // e = -190, k = -27
{0xC612062576589DDA, 0x95364AFE032A819E}, // e = -188, k = -26
{0xF79687AED3EEC551, 0x3A83DDBD83F52205}, // e = -186, k = -25
{0x9ABE14CD44753B52, 0xC4926A9672793543}, // e = -183, k = -24
{0xC16D9A0095928A27, 0x75B7053C0F178294}, // e = -181, k = -23
{0xF1C90080BAF72CB1, 0x5324C68B12DD6339}, // e = -179, k = -22
{0x971DA05074DA7BEE, 0xD3F6FC16EBCA5E04}, // e = -176, k = -21
{0xBCE5086492111AEA, 0x88F4BB1CA6BCF585}, // e = -174, k = -20
{0xEC1E4A7DB69561A5, 0x2B31E9E3D06C32E6}, // e = -172, k = -19
{0x9392EE8E921D5D07, 0x3AFF322E62439FD0}, // e = -169, k = -18
{0xB877AA3236A4B449, 0x09BEFEB9FAD487C3}, // e = -167, k = -17
{0xE69594BEC44DE15B, 0x4C2EBE687989A9B4}, // e = -165, k = -16
{0x901D7CF73AB0ACD9, 0x0F9D37014BF60A11}, // e = -162, k = -15
{0xB424DC35095CD80F, 0x538484C19EF38C95}, // e = -160, k = -14
{0xE12E13424BB40E13, 0x2865A5F206B06FBA}, // e = -158, k = -13
{0x8CBCCC096F5088CB, 0xF93F87B7442E45D4}, // e = -155, k = -12
{0xAFEBFF0BCB24AAFE, 0xF78F69A51539D749}, // e = -153, k = -11
{0xDBE6FECEBDEDD5BE, 0xB573440E5A884D1C}, // e = -151, k = -10
{0x89705F4136B4A597, 0x31680A88F8953031}, // e = -148, k = -9
{0xABCC77118461CEFC, 0xFDC20D2B36BA7C3E}, // e = -146, k = -8
{0xD6BF94D5E57A42BC, 0x3D32907604691B4D}, // e = -144, k = -7
{0x8637BD05AF6C69B5, 0xA63F9A49C2C1B110}, // e = -141, k = -6
{0xA7C5AC471B478423, 0x0FCF80DC33721D54}, // e = -139, k = -5
{0xD1B71758E219652B, 0xD3C36113404EA4A9}, // e = -137, k = -4
{0x83126E978D4FDF3B, 0x645A1CAC083126EA}, // e = -134, k = -3
{0xA3D70A3D70A3D70A, 0x3D70A3D70A3D70A4}, // e = -132, k = -2
{0xCCCCCCCCCCCCCCCC, 0xCCCCCCCCCCCCCCCD}, // e = -130, k = -1
{0x8000000000000000, 0x0000000000000000}, // e = -127, k = 0
{0xA000000000000000, 0x0000000000000000}, // e = -125, k = 1
{0xC800000000000000, 0x0000000000000000}, // e = -123, k = 2
{0xFA00000000000000, 0x0000000000000000}, // e = -121, k = 3
{0x9C40000000000000, 0x0000000000000000}, // e = -118, k = 4
{0xC350000000000000, 0x0000000000000000}, // e = -116, k = 5
{0xF424000000000000, 0x0000000000000000}, // e = -114, k = 6
{0x9896800000000000, 0x0000000000000000}, // e = -111, k = 7
{0xBEBC200000000000, 0x0000000000000000}, // e = -109, k = 8
{0xEE6B280000000000, 0x0000000000000000}, // e = -107, k = 9
{0x9502F90000000000, 0x0000000000000000}, // e = -104, k = 10
{0xBA43B74000000000, 0x0000000000000000}, // e = -102, k = 11
{0xE8D4A51000000000, 0x0000000000000000}, // e = -100, k = 12
{0x9184E72A00000000, 0x0000000000000000}, // e = -97, k = 13
{0xB5E620F480000000, 0x0000000000000000}, // e = -95, k = 14
{0xE35FA931A0000000, 0x0000000000000000}, // e = -93, k = 15
{0x8E1BC9BF04000000, 0x0000000000000000}, // e = -90, k = 16
{0xB1A2BC2EC5000000, 0x0000000000000000}, // e = -88, k = 17
{0xDE0B6B3A76400000, 0x0000000000000000}, // e = -86, k = 18
{0x8AC7230489E80000, 0x0000000000000000}, // e = -83, k = 19
{0xAD78EBC5AC620000, 0x0000000000000000}, // e = -81, k = 20
{0xD8D726B7177A8000, 0x0000000000000000}, // e = -79, k = 21
{0x878678326EAC9000, 0x0000000000000000}, // e = -76, k = 22
{0xA968163F0A57B400, 0x0000000000000000}, // e = -74, k = 23
{0xD3C21BCECCEDA100, 0x0000000000000000}, // e = -72, k = 24
{0x84595161401484A0, 0x0000000000000000}, // e = -69, k = 25
{0xA56FA5B99019A5C8, 0x0000000000000000}, // e = -67, k = 26
{0xCECB8F27F4200F3A, 0x0000000000000000}, // e = -65, k = 27
{0x813F3978F8940984, 0x4000000000000000}, // e = -62, k = 28
{0xA18F07D736B90BE5, 0x5000000000000000}, // e = -60, k = 29
{0xC9F2C9CD04674EDE, 0xA400000000000000}, // e = -58, k = 30
{0xFC6F7C4045812296, 0x4D00000000000000}, // e = -56, k = 31
{0x9DC5ADA82B70B59D, 0xF020000000000000}, // e = -53, k = 32
{0xC5371912364CE305, 0x6C28000000000000}, // e = -51, k = 33
{0xF684DF56C3E01BC6, 0xC732000000000000}, // e = -49, k = 34
{0x9A130B963A6C115C, 0x3C7F400000000000}, // e = -46, k = 35
{0xC097CE7BC90715B3, 0x4B9F100000000000}, // e = -44, k = 36
{0xF0BDC21ABB48DB20, 0x1E86D40000000000}, // e = -42, k = 37
{0x96769950B50D88F4, 0x1314448000000000}, // e = -39, k = 38
{0xBC143FA4E250EB31, 0x17D955A000000000}, // e = -37, k = 39
{0xEB194F8E1AE525FD, 0x5DCFAB0800000000}, // e = -35, k = 40
{0x92EFD1B8D0CF37BE, 0x5AA1CAE500000000}, // e = -32, k = 41
{0xB7ABC627050305AD, 0xF14A3D9E40000000}, // e = -30, k = 42
{0xE596B7B0C643C719, 0x6D9CCD05D0000000}, // e = -28, k = 43
{0x8F7E32CE7BEA5C6F, 0xE4820023A2000000}, // e = -25, k = 44
{0xB35DBF821AE4F38B, 0xDDA2802C8A800000}, // e = -23, k = 45
{0xE0352F62A19E306E, 0xD50B2037AD200000}, // e = -21, k = 46
{0x8C213D9DA502DE45, 0x4526F422CC340000}, // e = -18, k = 47
{0xAF298D050E4395D6, 0x9670B12B7F410000}, // e = -16, k = 48
{0xDAF3F04651D47B4C, 0x3C0CDD765F114000}, // e = -14, k = 49
{0x88D8762BF324CD0F, 0xA5880A69FB6AC800}, // e = -11, k = 50
{0xAB0E93B6EFEE0053, 0x8EEA0D047A457A00}, // e = -9, k = 51
{0xD5D238A4ABE98068, 0x72A4904598D6D880}, // e = -7, k = 52
{0x85A36366EB71F041, 0x47A6DA2B7F864750}, // e = -4, k = 53
{0xA70C3C40A64E6C51, 0x999090B65F67D924}, // e = -2, k = 54
{0xD0CF4B50CFE20765, 0xFFF4B4E3F741CF6D}, // e = 0, k = 55
{0x82818F1281ED449F, 0xBFF8F10E7A8921A4}, // e = 3, k = 56
{0xA321F2D7226895C7, 0xAFF72D52192B6A0D}, // e = 5, k = 57
{0xCBEA6F8CEB02BB39, 0x9BF4F8A69F764490}, // e = 7, k = 58
{0xFEE50B7025C36A08, 0x02F236D04753D5B4}, // e = 9, k = 59
{0x9F4F2726179A2245, 0x01D762422C946590}, // e = 12, k = 60
{0xC722F0EF9D80AAD6, 0x424D3AD2B7B97EF5}, // e = 14, k = 61
{0xF8EBAD2B84E0D58B, 0xD2E0898765A7DEB2}, // e = 16, k = 62
{0x9B934C3B330C8577, 0x63CC55F49F88EB2F}, // e = 19, k = 63
{0xC2781F49FFCFA6D5, 0x3CBF6B71C76B25FB}, // e = 21, k = 64
{0xF316271C7FC3908A, 0x8BEF464E3945EF7A}, // e = 23, k = 65
{0x97EDD871CFDA3A56, 0x97758BF0E3CBB5AC}, // e = 26, k = 66
{0xBDE94E8E43D0C8EC, 0x3D52EEED1CBEA317}, // e = 28, k = 67
{0xED63A231D4C4FB27, 0x4CA7AAA863EE4BDD}, // e = 30, k = 68
{0x945E455F24FB1CF8, 0x8FE8CAA93E74EF6A}, // e = 33, k = 69
{0xB975D6B6EE39E436, 0xB3E2FD538E122B44}, // e = 35, k = 70
{0xE7D34C64A9C85D44, 0x60DBBCA87196B616}, // e = 37, k = 71
{0x90E40FBEEA1D3A4A, 0xBC8955E946FE31CD}, // e = 40, k = 72
{0xB51D13AEA4A488DD, 0x6BABAB6398BDBE41}, // e = 42, k = 73
{0xE264589A4DCDAB14, 0xC696963C7EED2DD1}, // e = 44, k = 74
{0x8D7EB76070A08AEC, 0xFC1E1DE5CF543CA2}, // e = 47, k = 75
{0xB0DE65388CC8ADA8, 0x3B25A55F43294BCB}, // e = 49, k = 76
{0xDD15FE86AFFAD912, 0x49EF0EB713F39EBE}, // e = 51, k = 77
{0x8A2DBF142DFCC7AB, 0x6E3569326C784337}, // e = 54, k = 78
{0xACB92ED9397BF996, 0x49C2C37F07965404}, // e = 56, k = 79
{0xD7E77A8F87DAF7FB, 0xDC33745EC97BE906}, // e = 58, k = 80
{0x86F0AC99B4E8DAFD, 0x69A028BB3DED71A3}, // e = 61, k = 81
{0xA8ACD7C0222311BC, 0xC40832EA0D68CE0C}, // e = 63, k = 82
{0xD2D80DB02AABD62B, 0xF50A3FA490C30190}, // e = 65, k = 83
{0x83C7088E1AAB65DB, 0x792667C6DA79E0FA}, // e = 68, k = 84
{0xA4B8CAB1A1563F52, 0x577001B891185938}, // e = 70, k = 85
{0xCDE6FD5E09ABCF26, 0xED4C0226B55E6F86}, // e = 72, k = 86
{0x80B05E5AC60B6178, 0x544F8158315B05B4}, // e = 75, k = 87
{0xA0DC75F1778E39D6, 0x696361AE3DB1C721}, // e = 77, k = 88
{0xC913936DD571C84C, 0x03BC3A19CD1E38E9}, // e = 79, k = 89
{0xFB5878494ACE3A5F, 0x04AB48A04065C723}, // e = 81, k = 90
{0x9D174B2DCEC0E47B, 0x62EB0D64283F9C76}, // e = 84, k = 91
{0xC45D1DF942711D9A, 0x3BA5D0BD324F8394}, // e = 86, k = 92
{0xF5746577930D6500, 0xCA8F44EC7EE36479}, // e = 88, k = 93
{0x9968BF6ABBE85F20, 0x7E998B13CF4E1ECB}, // e = 91, k = 94
{0xBFC2EF456AE276E8, 0x9E3FEDD8C321A67E}, // e = 93, k = 95
{0xEFB3AB16C59B14A2, 0xC5CFE94EF3EA101E}, // e = 95, k = 96
{0x95D04AEE3B80ECE5, 0xBBA1F1D158724A12}, // e = 98, k = 97
{0xBB445DA9CA61281F, 0x2A8A6E45AE8EDC97}, // e = 100, k = 98
{0xEA1575143CF97226, 0xF52D09D71A3293BD}, // e = 102, k = 99
{0x924D692CA61BE758, 0x593C2626705F9C56}, // e = 105, k = 100
{0xB6E0C377CFA2E12E, 0x6F8B2FB00C77836C}, // e = 107, k = 101
{0xE498F455C38B997A, 0x0B6DFB9C0F956447}, // e = 109, k = 102
{0x8EDF98B59A373FEC, 0x4724BD4189BD5EAC}, // e = 112, k = 103
{0xB2977EE300C50FE7, 0x58EDEC91EC2CB657}, // e = 114, k = 104
{0xDF3D5E9BC0F653E1, 0x2F2967B66737E3ED}, // e = 116, k = 105
{0x8B865B215899F46C, 0xBD79E0D20082EE74}, // e = 119, k = 106
{0xAE67F1E9AEC07187, 0xECD8590680A3AA11}, // e = 121, k = 107
{0xDA01EE641A708DE9, 0xE80E6F4820CC9495}, // e = 123, k = 108
{0x884134FE908658B2, 0x3109058D147FDCDD}, // e = 126, k = 109
{0xAA51823E34A7EEDE, 0xBD4B46F0599FD415}, // e = 128, k = 110
{0xD4E5E2CDC1D1EA96, 0x6C9E18AC7007C91A}, // e = 130, k = 111
{0x850FADC09923329E, 0x03E2CF6BC604DDB0}, // e = 133, k = 112
{0xA6539930BF6BFF45, 0x84DB8346B786151C}, // e = 135, k = 113
{0xCFE87F7CEF46FF16, 0xE612641865679A63}, // e = 137, k = 114
{0x81F14FAE158C5F6E, 0x4FCB7E8F3F60C07E}, // e = 140, k = 115
{0xA26DA3999AEF7749, 0xE3BE5E330F38F09D}, // e = 142, k = 116
{0xCB090C8001AB551C, 0x5CADF5BFD3072CC5}, // e = 144, k = 117
{0xFDCB4FA002162A63, 0x73D9732FC7C8F7F6}, // e = 146, k = 118
{0x9E9F11C4014DDA7E, 0x2867E7FDDCDD9AFA}, // e = 149, k = 119
{0xC646D63501A1511D, 0xB281E1FD541501B8}, // e = 151, k = 120
{0xF7D88BC24209A565, 0x1F225A7CA91A4226}, // e = 153, k = 121
{0x9AE757596946075F, 0x3375788DE9B06958}, // e = 156, k = 122
{0xC1A12D2FC3978937, 0x0052D6B1641C83AE}, // e = 158, k = 123
{0xF209787BB47D6B84, 0xC0678C5DBD23A49A}, // e = 160, k = 124
{0x9745EB4D50CE6332, 0xF840B7BA963646E0}, // e = 163, k = 125
{0xBD176620A501FBFF, 0xB650E5A93BC3D898}, // e = 165, k = 126
{0xEC5D3FA8CE427AFF, 0xA3E51F138AB4CEBE}, // e = 167, k = 127
{0x93BA47C980E98CDF, 0xC66F336C36B10137}, // e = 170, k = 128
{0xB8A8D9BBE123F017, 0xB80B0047445D4184}, // e = 172, k = 129
{0xE6D3102AD96CEC1D, 0xA60DC059157491E5}, // e = 174, k = 130
{0x9043EA1AC7E41392, 0x87C89837AD68DB2F}, // e = 177, k = 131
{0xB454E4A179DD1877, 0x29BABE4598C311FB}, // e = 179, k = 132
{0xE16A1DC9D8545E94, 0xF4296DD6FEF3D67A}, // e = 181, k = 133
{0x8CE2529E2734BB1D, 0x1899E4A65F58660C}, // e = 184, k = 134
{0xB01AE745B101E9E4, 0x5EC05DCFF72E7F8F}, // e = 186, k = 135
{0xDC21A1171D42645D, 0x76707543F4FA1F73}, // e = 188, k = 136
{0x899504AE72497EBA, 0x6A06494A791C53A8}, // e = 191, k = 137
{0xABFA45DA0EDBDE69, 0x0487DB9D17636892}, // e = 193, k = 138
{0xD6F8D7509292D603, 0x45A9D2845D3C42B6}, // e = 195, k = 139
{0x865B86925B9BC5C2, 0x0B8A2392BA45A9B2}, // e = 198, k = 140
{0xA7F26836F282B732, 0x8E6CAC7768D7141E}, // e = 200, k = 141
{0xD1EF0244AF2364FF, 0x3207D795430CD926}, // e = 202, k = 142
{0x8335616AED761F1F, 0x7F44E6BD49E807B8}, // e = 205, k = 143
{0xA402B9C5A8D3A6E7, 0x5F16206C9C6209A6}, // e = 207, k = 144
{0xCD036837130890A1, 0x36DBA887C37A8C0F}, // e = 209, k = 145
{0x802221226BE55A64, 0xC2494954DA2C9789}, // e = 212, k = 146
{0xA02AA96B06DEB0FD, 0xF2DB9BAA10B7BD6C}, // e = 214, k = 147
{0xC83553C5C8965D3D, 0x6F92829494E5ACC7}, // e = 216, k = 148
{0xFA42A8B73ABBF48C, 0xCB772339BA1F17F9}, // e = 218, k = 149
{0x9C69A97284B578D7, 0xFF2A760414536EFB}, // e = 221, k = 150
{0xC38413CF25E2D70D, 0xFEF5138519684ABA}, // e = 223, k = 151
{0xF46518C2EF5B8CD1, 0x7EB258665FC25D69}, // e = 225, k = 152
{0x98BF2F79D5993802, 0xEF2F773FFBD97A61}, // e = 228, k = 153
{0xBEEEFB584AFF8603, 0xAAFB550FFACFD8FA}, // e = 230, k = 154
{0xEEAABA2E5DBF6784, 0x95BA2A53F983CF38}, // e = 232, k = 155
{0x952AB45CFA97A0B2, 0xDD945A747BF26183}, // e = 235, k = 156
{0xBA756174393D88DF, 0x94F971119AEEF9E4}, // e = 237, k = 157
{0xE912B9D1478CEB17, 0x7A37CD5601AAB85D}, // e = 239, k = 158
{0x91ABB422CCB812EE, 0xAC62E055C10AB33A}, // e = 242, k = 159
{0xB616A12B7FE617AA, 0x577B986B314D6009}, // e = 244, k = 160
{0xE39C49765FDF9D94, 0xED5A7E85FDA0B80B}, // e = 246, k = 161
{0x8E41ADE9FBEBC27D, 0x14588F13BE847307}, // e = 249, k = 162
{0xB1D219647AE6B31C, 0x596EB2D8AE258FC8}, // e = 251, k = 163
{0xDE469FBD99A05FE3, 0x6FCA5F8ED9AEF3BB}, // e = 253, k = 164
{0x8AEC23D680043BEE, 0x25DE7BB9480D5854}, // e = 256, k = 165
{0xADA72CCC20054AE9, 0xAF561AA79A10AE6A}, // e = 258, k = 166
{0xD910F7FF28069DA4, 0x1B2BA1518094DA04}, // e = 260, k = 167
{0x87AA9AFF79042286, 0x90FB44D2F05D0842}, // e = 263, k = 168
{0xA99541BF57452B28, 0x353A1607AC744A53}, // e = 265, k = 169
{0xD3FA922F2D1675F2, 0x42889B8997915CE8}, // e = 267, k = 170
{0x847C9B5D7C2E09B7, 0x69956135FEBADA11}, // e = 270, k = 171
{0xA59BC234DB398C25, 0x43FAB9837E699095}, // e = 272, k = 172
{0xCF02B2C21207EF2E, 0x94F967E45E03F4BB}, // e = 274, k = 173
{0x8161AFB94B44F57D, 0x1D1BE0EEBAC278F5}, // e = 277, k = 174
{0xA1BA1BA79E1632DC, 0x6462D92A69731732}, // e = 279, k = 175
{0xCA28A291859BBF93, 0x7D7B8F7503CFDCFE}, // e = 281, k = 176
{0xFCB2CB35E702AF78, 0x5CDA735244C3D43E}, // e = 283, k = 177
{0x9DEFBF01B061ADAB, 0x3A0888136AFA64A7}, // e = 286, k = 178
{0xC56BAEC21C7A1916, 0x088AAA1845B8FDD0}, // e = 288, k = 179
{0xF6C69A72A3989F5B, 0x8AAD549E57273D45}, // e = 290, k = 180
{0x9A3C2087A63F6399, 0x36AC54E2F678864B}, // e = 293, k = 181
{0xC0CB28A98FCF3C7F, 0x84576A1BB416A7DD}, // e = 295, k = 182
{0xF0FDF2D3F3C30B9F, 0x656D44A2A11C51D5}, // e = 297, k = 183
{0x969EB7C47859E743, 0x9F644AE5A4B1B325}, // e = 300, k = 184
{0xBC4665B596706114, 0x873D5D9F0DDE1FEE}, // e = 302, k = 185
{0xEB57FF22FC0C7959, 0xA90CB506D155A7EA}, // e = 304, k = 186
{0x9316FF75DD87CBD8, 0x09A7F12442D588F2}, // e = 307, k = 187
{0xB7DCBF5354E9BECE, 0x0C11ED6D538AEB2F}, // e = 309, k = 188
{0xE5D3EF282A242E81, 0x8F1668C8A86DA5FA}, // e = 311, k = 189
{0x8FA475791A569D10, 0xF96E017D694487BC}, // e = 314, k = 190
{0xB38D92D760EC4455, 0x37C981DCC395A9AC}, // e = 316, k = 191
{0xE070F78D3927556A, 0x85BBE253F47B1417}, // e = 318, k = 192
{0x8C469AB843B89562, 0x93956D7478CCEC8E}, // e = 321, k = 193
{0xAF58416654A6BABB, 0x387AC8D1970027B2}, // e = 323, k = 194
{0xDB2E51BFE9D0696A, 0x06997B05FCC0319E}, // e = 325, k = 195
{0x88FCF317F22241E2, 0x441FECE3BDF81F03}, // e = 328, k = 196
{0xAB3C2FDDEEAAD25A, 0xD527E81CAD7626C3}, // e = 330, k = 197
{0xD60B3BD56A5586F1, 0x8A71E223D8D3B074}, // e = 332, k = 198
{0x85C7056562757456, 0xF6872D5667844E49}, // e = 335, k = 199
{0xA738C6BEBB12D16C, 0xB428F8AC016561DB}, // e = 337, k = 200
{0xD106F86E69D785C7, 0xE13336D701BEBA52}, // e = 339, k = 201
{0x82A45B450226B39C, 0xECC0024661173473}, // e = 342, k = 202
{0xA34D721642B06084, 0x27F002D7F95D0190}, // e = 344, k = 203
{0xCC20CE9BD35C78A5, 0x31EC038DF7B441F4}, // e = 346, k = 204
{0xFF290242C83396CE, 0x7E67047175A15271}, // e = 348, k = 205
{0x9F79A169BD203E41, 0x0F0062C6E984D386}, // e = 351, k = 206
{0xC75809C42C684DD1, 0x52C07B78A3E60868}, // e = 353, k = 207
{0xF92E0C3537826145, 0xA7709A56CCDF8A82}, // e = 355, k = 208
{0x9BBCC7A142B17CCB, 0x88A66076400BB691}, // e = 358, k = 209
{0xC2ABF989935DDBFE, 0x6ACFF893D00EA435}, // e = 360, k = 210
{0xF356F7EBF83552FE, 0x0583F6B8C4124D43}, // e = 362, k = 211
{0x98165AF37B2153DE, 0xC3727A337A8B704A}, // e = 365, k = 212
{0xBE1BF1B059E9A8D6, 0x744F18C0592E4C5C}, // e = 367, k = 213
{0xEDA2EE1C7064130C, 0x1162DEF06F79DF73}, // e = 369, k = 214
{0x9485D4D1C63E8BE7, 0x8ADDCB5645AC2BA8}, // e = 372, k = 215
{0xB9A74A0637CE2EE1, 0x6D953E2BD7173692}, // e = 374, k = 216
{0xE8111C87C5C1BA99, 0xC8FA8DB6CCDD0437}, // e = 376, k = 217
{0x910AB1D4DB9914A0, 0x1D9C9892400A22A2}, // e = 379, k = 218
{0xB54D5E4A127F59C8, 0x2503BEB6D00CAB4B}, // e = 381, k = 219
{0xE2A0B5DC971F303A, 0x2E44AE64840FD61D}, // e = 383, k = 220
{0x8DA471A9DE737E24, 0x5CEAECFED289E5D2}, // e = 386, k = 221
{0xB10D8E1456105DAD, 0x7425A83E872C5F47}, // e = 388, k = 222
{0xDD50F1996B947518, 0xD12F124E28F77719}, // e = 390, k = 223
{0x8A5296FFE33CC92F, 0x82BD6B70D99AAA6F}, // e = 393, k = 224
{0xACE73CBFDC0BFB7B, 0x636CC64D1001550B}, // e = 395, k = 225
{0xD8210BEFD30EFA5A, 0x3C47F7E05401AA4E}, // e = 397, k = 226
{0x8714A775E3E95C78, 0x65ACFAEC34810A71}, // e = 400, k = 227
{0xA8D9D1535CE3B396, 0x7F1839A741A14D0D}, // e = 402, k = 228
{0xD31045A8341CA07C, 0x1EDE48111209A050}, // e = 404, k = 229
{0x83EA2B892091E44D, 0x934AED0AAB460432}, // e = 407, k = 230
{0xA4E4B66B68B65D60, 0xF81DA84D5617853F}, // e = 409, k = 231
{0xCE1DE40642E3F4B9, 0x36251260AB9D668E}, // e = 411, k = 232
{0x80D2AE83E9CE78F3, 0xC1D72B7C6B426019}, // e = 414, k = 233
{0xA1075A24E4421730, 0xB24CF65B8612F81F}, // e = 416, k = 234
{0xC94930AE1D529CFC, 0xDEE033F26797B627}, // e = 418, k = 235
{0xFB9B7CD9A4A7443C, 0x169840EF017DA3B1}, // e = 420, k = 236
{0x9D412E0806E88AA5, 0x8E1F289560EE864E}, // e = 423, k = 237
{0xC491798A08A2AD4E, 0xF1A6F2BAB92A27E2}, // e = 425, k = 238
{0xF5B5D7EC8ACB58A2, 0xAE10AF696774B1DB}, // e = 427, k = 239
{0x9991A6F3D6BF1765, 0xACCA6DA1E0A8EF29}, // e = 430, k = 240
{0xBFF610B0CC6EDD3F, 0x17FD090A58D32AF3}, // e = 432, k = 241
{0xEFF394DCFF8A948E, 0xDDFC4B4CEF07F5B0}, // e = 434, k = 242
{0x95F83D0A1FB69CD9, 0x4ABDAF101564F98E}, // e = 437, k = 243
{0xBB764C4CA7A4440F, 0x9D6D1AD41ABE37F1}, // e = 439, k = 244
{0xEA53DF5FD18D5513, 0x84C86189216DC5ED}, // e = 441, k = 245
{0x92746B9BE2F8552C, 0x32FD3CF5B4E49BB4}, // e = 444, k = 246
{0xB7118682DBB66A77, 0x3FBC8C33221DC2A1}, // e = 446, k = 247
{0xE4D5E82392A40515, 0x0FABAF3FEAA5334A}, // e = 448, k = 248
{0x8F05B1163BA6832D, 0x29CB4D87F2A7400E}, // e = 451, k = 249
{0xB2C71D5BCA9023F8, 0x743E20E9EF511012}, // e = 453, k = 250
{0xDF78E4B2BD342CF6, 0x914DA9246B255416}, // e = 455, k = 251
{0x8BAB8EEFB6409C1A, 0x1AD089B6C2F7548E}, // e = 458, k = 252
{0xAE9672ABA3D0C320, 0xA184AC2473B529B1}, // e = 460, k = 253
{0xDA3C0F568CC4F3E8, 0xC9E5D72D90A2741E}, // e = 462, k = 254
{0x8865899617FB1871, 0x7E2FA67C7A658892}, // e = 465, k = 255
{0xAA7EEBFB9DF9DE8D, 0xDDBB901B98FEEAB7}, // e = 467, k = 256
{0xD51EA6FA85785631, 0x552A74227F3EA565}, // e = 469, k = 257
{0x8533285C936B35DE, 0xD53A88958F87275F}, // e = 472, k = 258
{0xA67FF273B8460356, 0x8A892ABAF368F137}, // e = 474, k = 259
{0xD01FEF10A657842C, 0x2D2B7569B0432D85}, // e = 476, k = 260
{0x8213F56A67F6B29B, 0x9C3B29620E29FC73}, // e = 479, k = 261
{0xA298F2C501F45F42, 0x8349F3BA91B47B8F}, // e = 481, k = 262
{0xCB3F2F7642717713, 0x241C70A936219A73}, // e = 483, k = 263
{0xFE0EFB53D30DD4D7, 0xED238CD383AA0110}, // e = 485, k = 264
{0x9EC95D1463E8A506, 0xF4363804324A40AA}, // e = 488, k = 265
{0xC67BB4597CE2CE48, 0xB143C6053EDCD0D5}, // e = 490, k = 266
{0xF81AA16FDC1B81DA, 0xDD94B7868E94050A}, // e = 492, k = 267
{0x9B10A4E5E9913128, 0xCA7CF2B4191C8326}, // e = 495, k = 268
{0xC1D4CE1F63F57D72, 0xFD1C2F611F63A3F0}, // e = 497, k = 269
{0xF24A01A73CF2DCCF, 0xBC633B39673C8CEC}, // e = 499, k = 270
{0x976E41088617CA01, 0xD5BE0503E085D813}, // e = 502, k = 271
{0xBD49D14AA79DBC82, 0x4B2D8644D8A74E18}, // e = 504, k = 272
{0xEC9C459D51852BA2, 0xDDF8E7D60ED1219E}, // e = 506, k = 273
{0x93E1AB8252F33B45, 0xCABB90E5C942B503}, // e = 509, k = 274
{0xB8DA1662E7B00A17, 0x3D6A751F3B936243}, // e = 511, k = 275
{0xE7109BFBA19C0C9D, 0x0CC512670A783AD4}, // e = 513, k = 276
{0x906A617D450187E2, 0x27FB2B80668B24C5}, // e = 516, k = 277
{0xB484F9DC9641E9DA, 0xB1F9F660802DEDF6}, // e = 518, k = 278
{0xE1A63853BBD26451, 0x5E7873F8A0396973}, // e = 520, k = 279
{0x8D07E33455637EB2, 0xDB0B487B6423E1E8}, // e = 523, k = 280
{0xB049DC016ABC5E5F, 0x91CE1A9A3D2CDA62}, // e = 525, k = 281
{0xDC5C5301C56B75F7, 0x7641A140CC7810FB}, // e = 527, k = 282
{0x89B9B3E11B6329BA, 0xA9E904C87FCB0A9D}, // e = 530, k = 283
{0xAC2820D9623BF429, 0x546345FA9FBDCD44}, // e = 532, k = 284
{0xD732290FBACAF133, 0xA97C177947AD4095}, // e = 534, k = 285
{0x867F59A9D4BED6C0, 0x49ED8EABCCCC485D}, // e = 537, k = 286
{0xA81F301449EE8C70, 0x5C68F256BFFF5A74}, // e = 539, k = 287
{0xD226FC195C6A2F8C, 0x73832EEC6FFF3111}, // e = 541, k = 288
{0x83585D8FD9C25DB7, 0xC831FD53C5FF7EAB}, // e = 544, k = 289
{0xA42E74F3D032F525, 0xBA3E7CA8B77F5E55}, // e = 546, k = 290
{0xCD3A1230C43FB26F, 0x28CE1BD2E55F35EB}, // e = 548, k = 291
{0x80444B5E7AA7CF85, 0x7980D163CF5B81B3}, // e = 551, k = 292
{0xA0555E361951C366, 0xD7E105BCC332621F}, // e = 553, k = 293
{0xC86AB5C39FA63440, 0x8DD9472BF3FEFAA7}, // e = 555, k = 294
{0xFA856334878FC150, 0xB14F98F6F0FEB951}, // e = 557, k = 295
{0x9C935E00D4B9D8D2, 0x6ED1BF9A569F33D3}, // e = 560, k = 296
{0xC3B8358109E84F07, 0x0A862F80EC4700C8}, // e = 562, k = 297
{0xF4A642E14C6262C8, 0xCD27BB612758C0FA}, // e = 564, k = 298
{0x98E7E9CCCFBD7DBD, 0x8038D51CB897789C}, // e = 567, k = 299
{0xBF21E44003ACDD2C, 0xE0470A63E6BD56C3}, // e = 569, k = 300
{0xEEEA5D5004981478, 0x1858CCFCE06CAC74}, // e = 571, k = 301
{0x95527A5202DF0CCB, 0x0F37801E0C43EBC8}, // e = 574, k = 302
{0xBAA718E68396CFFD, 0xD30560258F54E6BA}, // e = 576, k = 303
{0xE950DF20247C83FD, 0x47C6B82EF32A2069}, // e = 578, k = 304
{0x91D28B7416CDD27E, 0x4CDC331D57FA5441}, // e = 581, k = 305
{0xB6472E511C81471D, 0xE0133FE4ADF8E952}, // e = 583, k = 306
{0xE3D8F9E563A198E5, 0x58180FDDD97723A6}, // e = 585, k = 307
{0x8E679C2F5E44FF8F, 0x570F09EAA7EA7648}, // e = 588, k = 308
{0xB201833B35D63F73, 0x2CD2CC6551E513DA}, // e = 590, k = 309
{0xDE81E40A034BCF4F, 0xF8077F7EA65E58D1}, // e = 592, k = 310
{0x8B112E86420F6191, 0xFB04AFAF27FAF782}, // e = 595, k = 311
{0xADD57A27D29339F6, 0x79C5DB9AF1F9B563}, // e = 597, k = 312
{0xD94AD8B1C7380874, 0x18375281AE7822BC}, // e = 599, k = 313
{0x87CEC76F1C830548, 0x8F2293910D0B15B5}, // e = 602, k = 314
{0xA9C2794AE3A3C69A, 0xB2EB3875504DDB22}, // e = 604, k = 315
{0xD433179D9C8CB841, 0x5FA60692A46151EB}, // e = 606, k = 316
{0x849FEEC281D7F328, 0xDBC7C41BA6BCD333}, // e = 609, k = 317
{0xA5C7EA73224DEFF3, 0x12B9B522906C0800}, // e = 611, k = 318
{0xCF39E50FEAE16BEF, 0xD768226B34870A00}, // e = 613, k = 319
{0x81842F29F2CCE375, 0xE6A1158300D46640}, // e = 616, k = 320
{0xA1E53AF46F801C53, 0x60495AE3C1097FD0}, // e = 618, k = 321
{0xCA5E89B18B602368, 0x385BB19CB14BDFC4}, // e = 620, k = 322
{0xFCF62C1DEE382C42, 0x46729E03DD9ED7B5}, // e = 622, k = 323
{0x9E19DB92B4E31BA9, 0x6C07A2C26A8346D1}, // e = 625, k = 324
{0xC5A05277621BE293, 0xC7098B7305241885}, // e = 627, k = 325
};
RYU_ASSERT(k >= MinDecExp);
RYU_ASSERT(k <= MaxDecExp);
return Pow5[static_cast<unsigned>(k - MinDecExp)];
}
#if defined(__SIZEOF_INT128__)
static inline uint64_t MulShift(uint64_t m, const uint64x2* mul, int32_t j)
{
__extension__ using uint128_t = unsigned __int128;
RYU_ASSERT(j >= 64 + 1);
RYU_ASSERT(j <= 64 + 127);
const uint128_t b0 = uint128_t{m} * mul->lo;
const uint128_t b2 = uint128_t{m} * mul->hi;
#if 1
const int32_t shift = j - 64;
#else
RYU_ASSERT(j <= 64 + 63);
// We need shift = j - 64 here.
// Since 64 < j < 128, this is equivalent to shift = (j - 64) % 64 = j % 64.
// When written as shift = j & 63, clang can optimize the 128-bit shift into
// a simple funnel shift.
const int32_t shift = j & 63;
#endif
return static_cast<uint64_t>((b2 + static_cast<uint64_t>(b0 >> 64)) >> shift);
}
#elif defined(_MSC_VER) && defined(_M_X64)
static inline uint64_t MulShift(uint64_t m, const uint64x2* mul, int32_t j)
{
RYU_ASSERT(j >= 64 + 1);
RYU_ASSERT(j <= 64 + 127);
uint64_t b0_hi;
uint64_t b0_lo = _umul128(m, mul->lo, &b0_hi);
uint64_t b2_hi;
uint64_t b2_lo = _umul128(m, mul->hi, &b2_hi);
static_cast<void>(b0_lo);
// b2 + (b0 >> 64)
// b2_lo += b0_hi;
// b2_hi += b2_lo < b0_hi;
_addcarry_u64(_addcarry_u64(0, b2_lo, b0_hi, &b2_lo), b2_hi, 0, &b2_hi);
#if 1
const int32_t shift = j - 64;
const uint64_t l = __shiftright128(b2_lo, b2_hi, static_cast<unsigned char>(shift));
const uint64_t h = __ull_rshift(b2_hi, shift);
return (shift & 64) ? h : l;
#else
RYU_ASSERT(j <= 64 + 63);
// We need shift = j - 64 here.
// For the __shiftright128 intrinsic, the shift value is always modulo 64.
// Since (j - 64) % 64 = j, we can simply use j here.
return __shiftright128(b2_lo, b2_hi, static_cast<unsigned char>(j));
#endif
}
#else
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};
}
static inline uint64_t ShiftRight128(uint64_t lo, uint64_t hi, int32_t n)
{
// For the __shiftright128 intrinsic, the shift value is always modulo 64.
// In the current implementation of the double-precision version of Ryu, the
// shift value is always < 64.
// Check this here in case a future change requires larger shift values. In
// this case this function needs to be adjusted.
RYU_ASSERT(n >= 1);
RYU_ASSERT(n <= 63);
const int32_t lshift = -n & 63;
const int32_t rshift = n;
return (hi << lshift) | (lo >> rshift);
}
static inline uint64_t MulShift(uint64_t m, const uint64x2* mul, int32_t j)
{
RYU_ASSERT(j >= 65);
RYU_ASSERT(j <= 64 + 96 - 1);
auto b0 = Mul128(m, mul->lo);
auto b2 = Mul128(m, mul->hi);
// b2 + (b0 >> 64)
b2.lo += b0.hi;
b2.hi += b2.lo < b0.hi;
#if 1
const int32_t shift = j - 64; // [0, 128)
// NB:
// shift >= 64 ==> 0 <= shift - 64 <= 31 (use 32-bit intrinsics?)
return shift <= 63 ? ShiftRight128(b2.lo, b2.hi, shift) : b2.hi >> (shift - 64);
#else
RYU_ASSERT(j <= 64 + 63);
const int32_t shift = j - 64;
return ShiftRight128(b2.lo, b2.hi, shift);
#endif
}
#endif
static inline void MulPow5DivPow2_Double(uint64_t u, uint64_t v, uint64_t w, int32_t e5, int32_t e2, uint64_t& a, uint64_t& b, uint64_t& c)
{
// j >= 121 and m has at most 53 + 2 = 55 bits.
// The product along with the subsequent shift therefore requires
// 55 + 128 - 121 = 62 bits.
const auto k = FloorLog2Pow5(e5) + 1 - BitsPerPow5_Double;
const auto j = e2 - k;
RYU_ASSERT(j >= BitsPerPow5_Double - 7); // 121 - 64 = 57
RYU_ASSERT(j <= BitsPerPow5_Double - 1); // 127 - 64 = 63
const auto pow5 = ComputePow5_Double(e5);
a = MulShift(u, &pow5, j);