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schubfach_64.cc
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// 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 "schubfach_64.h"
//--------------------------------------------------------------------------------------------------
// This file contains an implementation of the Schubfach algorithm as described in
//
// [1] Raffaello Giulietti, "The Schubfach way to render doubles",
// https://drive.google.com/open?id=1luHhyQF9zKlM8yJ1nebU0OgVYhfC6CBN
//--------------------------------------------------------------------------------------------------
#include <cassert>
#include <cstdint>
#include <cstdlib>
#include <cstring>
#include <limits>
#if _MSC_VER
#include <intrin.h>
#endif
#ifndef SF_ASSERT
#define SF_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
}
// Returns floor(log_10(2^e))
// static inline int32_t FloorLog10Pow2(int32_t e)
// {
// SF_ASSERT(e >= -1500);
// SF_ASSERT(e <= 1500);
// return FloorDivPow2(e * 1262611, 22);
// }
// Returns floor(log_10(3/4 2^e))
// static inline int32_t FloorLog10ThreeQuartersPow2(int32_t e)
// {
// SF_ASSERT(e >= -1500);
// SF_ASSERT(e <= 1500);
// return FloorDivPow2(e * 1262611 - 524031, 22);
// }
// Returns floor(log_2(10^e))
static inline int32_t FloorLog2Pow10(int32_t e)
{
SF_ASSERT(e >= -1233);
SF_ASSERT(e <= 1233);
return FloorDivPow2(e * 1741647, 19);
}
//==================================================================================================
//
//==================================================================================================
namespace {
struct uint64x2 {
uint64_t hi;
uint64_t lo;
};
}
static inline uint64x2 ComputePow10_Double(int32_t k)
{
// There are unique beta and r such that 10^k = beta 2^r and
// 2^127 <= beta < 2^128, namely r = floor(log_2 10^k) - 127 and
// beta = 2^-r 10^k.
// Let g = ceil(beta), so (g-1) 2^r < 10^k <= g 2^r, with the latter
// value being a pretty good overestimate for 10^k.
// NB: Since for all the required exponents k, we have g < 2^128,
// all constants can be stored in 128-bit integers.
static constexpr int32_t kMin = -292;
static constexpr int32_t kMax = 324;
static constexpr uint64x2 g[kMax - kMin + 1] = {
{0xFF77B1FCBEBCDC4F, 0x25E8E89C13BB0F7B}, // -292
{0x9FAACF3DF73609B1, 0x77B191618C54E9AD}, // -291
{0xC795830D75038C1D, 0xD59DF5B9EF6A2418}, // -290
{0xF97AE3D0D2446F25, 0x4B0573286B44AD1E}, // -289
{0x9BECCE62836AC577, 0x4EE367F9430AEC33}, // -288
{0xC2E801FB244576D5, 0x229C41F793CDA740}, // -287
{0xF3A20279ED56D48A, 0x6B43527578C11110}, // -286
{0x9845418C345644D6, 0x830A13896B78AAAA}, // -285
{0xBE5691EF416BD60C, 0x23CC986BC656D554}, // -284
{0xEDEC366B11C6CB8F, 0x2CBFBE86B7EC8AA9}, // -283
{0x94B3A202EB1C3F39, 0x7BF7D71432F3D6AA}, // -282
{0xB9E08A83A5E34F07, 0xDAF5CCD93FB0CC54}, // -281
{0xE858AD248F5C22C9, 0xD1B3400F8F9CFF69}, // -280
{0x91376C36D99995BE, 0x23100809B9C21FA2}, // -279
{0xB58547448FFFFB2D, 0xABD40A0C2832A78B}, // -278
{0xE2E69915B3FFF9F9, 0x16C90C8F323F516D}, // -277
{0x8DD01FAD907FFC3B, 0xAE3DA7D97F6792E4}, // -276
{0xB1442798F49FFB4A, 0x99CD11CFDF41779D}, // -275
{0xDD95317F31C7FA1D, 0x40405643D711D584}, // -274
{0x8A7D3EEF7F1CFC52, 0x482835EA666B2573}, // -273
{0xAD1C8EAB5EE43B66, 0xDA3243650005EED0}, // -272
{0xD863B256369D4A40, 0x90BED43E40076A83}, // -271
{0x873E4F75E2224E68, 0x5A7744A6E804A292}, // -270
{0xA90DE3535AAAE202, 0x711515D0A205CB37}, // -269
{0xD3515C2831559A83, 0x0D5A5B44CA873E04}, // -268
{0x8412D9991ED58091, 0xE858790AFE9486C3}, // -267
{0xA5178FFF668AE0B6, 0x626E974DBE39A873}, // -266
{0xCE5D73FF402D98E3, 0xFB0A3D212DC81290}, // -265
{0x80FA687F881C7F8E, 0x7CE66634BC9D0B9A}, // -264
{0xA139029F6A239F72, 0x1C1FFFC1EBC44E81}, // -263
{0xC987434744AC874E, 0xA327FFB266B56221}, // -262
{0xFBE9141915D7A922, 0x4BF1FF9F0062BAA9}, // -261
{0x9D71AC8FADA6C9B5, 0x6F773FC3603DB4AA}, // -260
{0xC4CE17B399107C22, 0xCB550FB4384D21D4}, // -259
{0xF6019DA07F549B2B, 0x7E2A53A146606A49}, // -258
{0x99C102844F94E0FB, 0x2EDA7444CBFC426E}, // -257
{0xC0314325637A1939, 0xFA911155FEFB5309}, // -256
{0xF03D93EEBC589F88, 0x793555AB7EBA27CB}, // -255
{0x96267C7535B763B5, 0x4BC1558B2F3458DF}, // -254
{0xBBB01B9283253CA2, 0x9EB1AAEDFB016F17}, // -253
{0xEA9C227723EE8BCB, 0x465E15A979C1CADD}, // -252
{0x92A1958A7675175F, 0x0BFACD89EC191ECA}, // -251
{0xB749FAED14125D36, 0xCEF980EC671F667C}, // -250
{0xE51C79A85916F484, 0x82B7E12780E7401B}, // -249
{0x8F31CC0937AE58D2, 0xD1B2ECB8B0908811}, // -248
{0xB2FE3F0B8599EF07, 0x861FA7E6DCB4AA16}, // -247
{0xDFBDCECE67006AC9, 0x67A791E093E1D49B}, // -246
{0x8BD6A141006042BD, 0xE0C8BB2C5C6D24E1}, // -245
{0xAECC49914078536D, 0x58FAE9F773886E19}, // -244
{0xDA7F5BF590966848, 0xAF39A475506A899F}, // -243
{0x888F99797A5E012D, 0x6D8406C952429604}, // -242
{0xAAB37FD7D8F58178, 0xC8E5087BA6D33B84}, // -241
{0xD5605FCDCF32E1D6, 0xFB1E4A9A90880A65}, // -240
{0x855C3BE0A17FCD26, 0x5CF2EEA09A550680}, // -239
{0xA6B34AD8C9DFC06F, 0xF42FAA48C0EA481F}, // -238
{0xD0601D8EFC57B08B, 0xF13B94DAF124DA27}, // -237
{0x823C12795DB6CE57, 0x76C53D08D6B70859}, // -236
{0xA2CB1717B52481ED, 0x54768C4B0C64CA6F}, // -235
{0xCB7DDCDDA26DA268, 0xA9942F5DCF7DFD0A}, // -234
{0xFE5D54150B090B02, 0xD3F93B35435D7C4D}, // -233
{0x9EFA548D26E5A6E1, 0xC47BC5014A1A6DB0}, // -232
{0xC6B8E9B0709F109A, 0x359AB6419CA1091C}, // -231
{0xF867241C8CC6D4C0, 0xC30163D203C94B63}, // -230
{0x9B407691D7FC44F8, 0x79E0DE63425DCF1E}, // -229
{0xC21094364DFB5636, 0x985915FC12F542E5}, // -228
{0xF294B943E17A2BC4, 0x3E6F5B7B17B2939E}, // -227
{0x979CF3CA6CEC5B5A, 0xA705992CEECF9C43}, // -226
{0xBD8430BD08277231, 0x50C6FF782A838354}, // -225
{0xECE53CEC4A314EBD, 0xA4F8BF5635246429}, // -224
{0x940F4613AE5ED136, 0x871B7795E136BE9A}, // -223
{0xB913179899F68584, 0x28E2557B59846E40}, // -222
{0xE757DD7EC07426E5, 0x331AEADA2FE589D0}, // -221
{0x9096EA6F3848984F, 0x3FF0D2C85DEF7622}, // -220
{0xB4BCA50B065ABE63, 0x0FED077A756B53AA}, // -219
{0xE1EBCE4DC7F16DFB, 0xD3E8495912C62895}, // -218
{0x8D3360F09CF6E4BD, 0x64712DD7ABBBD95D}, // -217
{0xB080392CC4349DEC, 0xBD8D794D96AACFB4}, // -216
{0xDCA04777F541C567, 0xECF0D7A0FC5583A1}, // -215
{0x89E42CAAF9491B60, 0xF41686C49DB57245}, // -214
{0xAC5D37D5B79B6239, 0x311C2875C522CED6}, // -213
{0xD77485CB25823AC7, 0x7D633293366B828C}, // -212
{0x86A8D39EF77164BC, 0xAE5DFF9C02033198}, // -211
{0xA8530886B54DBDEB, 0xD9F57F830283FDFD}, // -210
{0xD267CAA862A12D66, 0xD072DF63C324FD7C}, // -209
{0x8380DEA93DA4BC60, 0x4247CB9E59F71E6E}, // -208
{0xA46116538D0DEB78, 0x52D9BE85F074E609}, // -207
{0xCD795BE870516656, 0x67902E276C921F8C}, // -206
{0x806BD9714632DFF6, 0x00BA1CD8A3DB53B7}, // -205
{0xA086CFCD97BF97F3, 0x80E8A40ECCD228A5}, // -204
{0xC8A883C0FDAF7DF0, 0x6122CD128006B2CE}, // -203
{0xFAD2A4B13D1B5D6C, 0x796B805720085F82}, // -202
{0x9CC3A6EEC6311A63, 0xCBE3303674053BB1}, // -201
{0xC3F490AA77BD60FC, 0xBEDBFC4411068A9D}, // -200
{0xF4F1B4D515ACB93B, 0xEE92FB5515482D45}, // -199
{0x991711052D8BF3C5, 0x751BDD152D4D1C4B}, // -198
{0xBF5CD54678EEF0B6, 0xD262D45A78A0635E}, // -197
{0xEF340A98172AACE4, 0x86FB897116C87C35}, // -196
{0x9580869F0E7AAC0E, 0xD45D35E6AE3D4DA1}, // -195
{0xBAE0A846D2195712, 0x8974836059CCA10A}, // -194
{0xE998D258869FACD7, 0x2BD1A438703FC94C}, // -193
{0x91FF83775423CC06, 0x7B6306A34627DDD0}, // -192
{0xB67F6455292CBF08, 0x1A3BC84C17B1D543}, // -191
{0xE41F3D6A7377EECA, 0x20CABA5F1D9E4A94}, // -190
{0x8E938662882AF53E, 0x547EB47B7282EE9D}, // -189
{0xB23867FB2A35B28D, 0xE99E619A4F23AA44}, // -188
{0xDEC681F9F4C31F31, 0x6405FA00E2EC94D5}, // -187
{0x8B3C113C38F9F37E, 0xDE83BC408DD3DD05}, // -186
{0xAE0B158B4738705E, 0x9624AB50B148D446}, // -185
{0xD98DDAEE19068C76, 0x3BADD624DD9B0958}, // -184
{0x87F8A8D4CFA417C9, 0xE54CA5D70A80E5D7}, // -183
{0xA9F6D30A038D1DBC, 0x5E9FCF4CCD211F4D}, // -182
{0xD47487CC8470652B, 0x7647C32000696720}, // -181
{0x84C8D4DFD2C63F3B, 0x29ECD9F40041E074}, // -180
{0xA5FB0A17C777CF09, 0xF468107100525891}, // -179
{0xCF79CC9DB955C2CC, 0x7182148D4066EEB5}, // -178
{0x81AC1FE293D599BF, 0xC6F14CD848405531}, // -177
{0xA21727DB38CB002F, 0xB8ADA00E5A506A7D}, // -176
{0xCA9CF1D206FDC03B, 0xA6D90811F0E4851D}, // -175
{0xFD442E4688BD304A, 0x908F4A166D1DA664}, // -174
{0x9E4A9CEC15763E2E, 0x9A598E4E043287FF}, // -173
{0xC5DD44271AD3CDBA, 0x40EFF1E1853F29FE}, // -172
{0xF7549530E188C128, 0xD12BEE59E68EF47D}, // -171
{0x9A94DD3E8CF578B9, 0x82BB74F8301958CF}, // -170
{0xC13A148E3032D6E7, 0xE36A52363C1FAF02}, // -169
{0xF18899B1BC3F8CA1, 0xDC44E6C3CB279AC2}, // -168
{0x96F5600F15A7B7E5, 0x29AB103A5EF8C0BA}, // -167
{0xBCB2B812DB11A5DE, 0x7415D448F6B6F0E8}, // -166
{0xEBDF661791D60F56, 0x111B495B3464AD22}, // -165
{0x936B9FCEBB25C995, 0xCAB10DD900BEEC35}, // -164
{0xB84687C269EF3BFB, 0x3D5D514F40EEA743}, // -163
{0xE65829B3046B0AFA, 0x0CB4A5A3112A5113}, // -162
{0x8FF71A0FE2C2E6DC, 0x47F0E785EABA72AC}, // -161
{0xB3F4E093DB73A093, 0x59ED216765690F57}, // -160
{0xE0F218B8D25088B8, 0x306869C13EC3532D}, // -159
{0x8C974F7383725573, 0x1E414218C73A13FC}, // -158
{0xAFBD2350644EEACF, 0xE5D1929EF90898FB}, // -157
{0xDBAC6C247D62A583, 0xDF45F746B74ABF3A}, // -156
{0x894BC396CE5DA772, 0x6B8BBA8C328EB784}, // -155
{0xAB9EB47C81F5114F, 0x066EA92F3F326565}, // -154
{0xD686619BA27255A2, 0xC80A537B0EFEFEBE}, // -153
{0x8613FD0145877585, 0xBD06742CE95F5F37}, // -152
{0xA798FC4196E952E7, 0x2C48113823B73705}, // -151
{0xD17F3B51FCA3A7A0, 0xF75A15862CA504C6}, // -150
{0x82EF85133DE648C4, 0x9A984D73DBE722FC}, // -149
{0xA3AB66580D5FDAF5, 0xC13E60D0D2E0EBBB}, // -148
{0xCC963FEE10B7D1B3, 0x318DF905079926A9}, // -147
{0xFFBBCFE994E5C61F, 0xFDF17746497F7053}, // -146
{0x9FD561F1FD0F9BD3, 0xFEB6EA8BEDEFA634}, // -145
{0xC7CABA6E7C5382C8, 0xFE64A52EE96B8FC1}, // -144
{0xF9BD690A1B68637B, 0x3DFDCE7AA3C673B1}, // -143
{0x9C1661A651213E2D, 0x06BEA10CA65C084F}, // -142
{0xC31BFA0FE5698DB8, 0x486E494FCFF30A63}, // -141
{0xF3E2F893DEC3F126, 0x5A89DBA3C3EFCCFB}, // -140
{0x986DDB5C6B3A76B7, 0xF89629465A75E01D}, // -139
{0xBE89523386091465, 0xF6BBB397F1135824}, // -138
{0xEE2BA6C0678B597F, 0x746AA07DED582E2D}, // -137
{0x94DB483840B717EF, 0xA8C2A44EB4571CDD}, // -136
{0xBA121A4650E4DDEB, 0x92F34D62616CE414}, // -135
{0xE896A0D7E51E1566, 0x77B020BAF9C81D18}, // -134
{0x915E2486EF32CD60, 0x0ACE1474DC1D122F}, // -133
{0xB5B5ADA8AAFF80B8, 0x0D819992132456BB}, // -132
{0xE3231912D5BF60E6, 0x10E1FFF697ED6C6A}, // -131
{0x8DF5EFABC5979C8F, 0xCA8D3FFA1EF463C2}, // -130
{0xB1736B96B6FD83B3, 0xBD308FF8A6B17CB3}, // -129
{0xDDD0467C64BCE4A0, 0xAC7CB3F6D05DDBDF}, // -128
{0x8AA22C0DBEF60EE4, 0x6BCDF07A423AA96C}, // -127
{0xAD4AB7112EB3929D, 0x86C16C98D2C953C7}, // -126
{0xD89D64D57A607744, 0xE871C7BF077BA8B8}, // -125
{0x87625F056C7C4A8B, 0x11471CD764AD4973}, // -124
{0xA93AF6C6C79B5D2D, 0xD598E40D3DD89BD0}, // -123
{0xD389B47879823479, 0x4AFF1D108D4EC2C4}, // -122
{0x843610CB4BF160CB, 0xCEDF722A585139BB}, // -121
{0xA54394FE1EEDB8FE, 0xC2974EB4EE658829}, // -120
{0xCE947A3DA6A9273E, 0x733D226229FEEA33}, // -119
{0x811CCC668829B887, 0x0806357D5A3F5260}, // -118
{0xA163FF802A3426A8, 0xCA07C2DCB0CF26F8}, // -117
{0xC9BCFF6034C13052, 0xFC89B393DD02F0B6}, // -116
{0xFC2C3F3841F17C67, 0xBBAC2078D443ACE3}, // -115
{0x9D9BA7832936EDC0, 0xD54B944B84AA4C0E}, // -114
{0xC5029163F384A931, 0x0A9E795E65D4DF12}, // -113
{0xF64335BCF065D37D, 0x4D4617B5FF4A16D6}, // -112
{0x99EA0196163FA42E, 0x504BCED1BF8E4E46}, // -111
{0xC06481FB9BCF8D39, 0xE45EC2862F71E1D7}, // -110
{0xF07DA27A82C37088, 0x5D767327BB4E5A4D}, // -109
{0x964E858C91BA2655, 0x3A6A07F8D510F870}, // -108
{0xBBE226EFB628AFEA, 0x890489F70A55368C}, // -107
{0xEADAB0ABA3B2DBE5, 0x2B45AC74CCEA842F}, // -106
{0x92C8AE6B464FC96F, 0x3B0B8BC90012929E}, // -105
{0xB77ADA0617E3BBCB, 0x09CE6EBB40173745}, // -104
{0xE55990879DDCAABD, 0xCC420A6A101D0516}, // -103
{0x8F57FA54C2A9EAB6, 0x9FA946824A12232E}, // -102
{0xB32DF8E9F3546564, 0x47939822DC96ABFA}, // -101
{0xDFF9772470297EBD, 0x59787E2B93BC56F8}, // -100
{0x8BFBEA76C619EF36, 0x57EB4EDB3C55B65B}, // -99
{0xAEFAE51477A06B03, 0xEDE622920B6B23F2}, // -98
{0xDAB99E59958885C4, 0xE95FAB368E45ECEE}, // -97
{0x88B402F7FD75539B, 0x11DBCB0218EBB415}, // -96
{0xAAE103B5FCD2A881, 0xD652BDC29F26A11A}, // -95
{0xD59944A37C0752A2, 0x4BE76D3346F04960}, // -94
{0x857FCAE62D8493A5, 0x6F70A4400C562DDC}, // -93
{0xA6DFBD9FB8E5B88E, 0xCB4CCD500F6BB953}, // -92
{0xD097AD07A71F26B2, 0x7E2000A41346A7A8}, // -91
{0x825ECC24C873782F, 0x8ED400668C0C28C9}, // -90
{0xA2F67F2DFA90563B, 0x728900802F0F32FB}, // -89
{0xCBB41EF979346BCA, 0x4F2B40A03AD2FFBA}, // -88
{0xFEA126B7D78186BC, 0xE2F610C84987BFA9}, // -87
{0x9F24B832E6B0F436, 0x0DD9CA7D2DF4D7CA}, // -86
{0xC6EDE63FA05D3143, 0x91503D1C79720DBC}, // -85
{0xF8A95FCF88747D94, 0x75A44C6397CE912B}, // -84
{0x9B69DBE1B548CE7C, 0xC986AFBE3EE11ABB}, // -83
{0xC24452DA229B021B, 0xFBE85BADCE996169}, // -82
{0xF2D56790AB41C2A2, 0xFAE27299423FB9C4}, // -81
{0x97C560BA6B0919A5, 0xDCCD879FC967D41B}, // -80
{0xBDB6B8E905CB600F, 0x5400E987BBC1C921}, // -79
{0xED246723473E3813, 0x290123E9AAB23B69}, // -78
{0x9436C0760C86E30B, 0xF9A0B6720AAF6522}, // -77
{0xB94470938FA89BCE, 0xF808E40E8D5B3E6A}, // -76
{0xE7958CB87392C2C2, 0xB60B1D1230B20E05}, // -75
{0x90BD77F3483BB9B9, 0xB1C6F22B5E6F48C3}, // -74
{0xB4ECD5F01A4AA828, 0x1E38AEB6360B1AF4}, // -73
{0xE2280B6C20DD5232, 0x25C6DA63C38DE1B1}, // -72
{0x8D590723948A535F, 0x579C487E5A38AD0F}, // -71
{0xB0AF48EC79ACE837, 0x2D835A9DF0C6D852}, // -70
{0xDCDB1B2798182244, 0xF8E431456CF88E66}, // -69
{0x8A08F0F8BF0F156B, 0x1B8E9ECB641B5900}, // -68
{0xAC8B2D36EED2DAC5, 0xE272467E3D222F40}, // -67
{0xD7ADF884AA879177, 0x5B0ED81DCC6ABB10}, // -66
{0x86CCBB52EA94BAEA, 0x98E947129FC2B4EA}, // -65
{0xA87FEA27A539E9A5, 0x3F2398D747B36225}, // -64
{0xD29FE4B18E88640E, 0x8EEC7F0D19A03AAE}, // -63
{0x83A3EEEEF9153E89, 0x1953CF68300424AD}, // -62
{0xA48CEAAAB75A8E2B, 0x5FA8C3423C052DD8}, // -61
{0xCDB02555653131B6, 0x3792F412CB06794E}, // -60
{0x808E17555F3EBF11, 0xE2BBD88BBEE40BD1}, // -59
{0xA0B19D2AB70E6ED6, 0x5B6ACEAEAE9D0EC5}, // -58
{0xC8DE047564D20A8B, 0xF245825A5A445276}, // -57
{0xFB158592BE068D2E, 0xEED6E2F0F0D56713}, // -56
{0x9CED737BB6C4183D, 0x55464DD69685606C}, // -55
{0xC428D05AA4751E4C, 0xAA97E14C3C26B887}, // -54
{0xF53304714D9265DF, 0xD53DD99F4B3066A9}, // -53
{0x993FE2C6D07B7FAB, 0xE546A8038EFE402A}, // -52
{0xBF8FDB78849A5F96, 0xDE98520472BDD034}, // -51
{0xEF73D256A5C0F77C, 0x963E66858F6D4441}, // -50
{0x95A8637627989AAD, 0xDDE7001379A44AA9}, // -49
{0xBB127C53B17EC159, 0x5560C018580D5D53}, // -48
{0xE9D71B689DDE71AF, 0xAAB8F01E6E10B4A7}, // -47
{0x9226712162AB070D, 0xCAB3961304CA70E9}, // -46
{0xB6B00D69BB55C8D1, 0x3D607B97C5FD0D23}, // -45
{0xE45C10C42A2B3B05, 0x8CB89A7DB77C506B}, // -44
{0x8EB98A7A9A5B04E3, 0x77F3608E92ADB243}, // -43
{0xB267ED1940F1C61C, 0x55F038B237591ED4}, // -42
{0xDF01E85F912E37A3, 0x6B6C46DEC52F6689}, // -41
{0x8B61313BBABCE2C6, 0x2323AC4B3B3DA016}, // -40
{0xAE397D8AA96C1B77, 0xABEC975E0A0D081B}, // -39
{0xD9C7DCED53C72255, 0x96E7BD358C904A22}, // -38
{0x881CEA14545C7575, 0x7E50D64177DA2E55}, // -37
{0xAA242499697392D2, 0xDDE50BD1D5D0B9EA}, // -36
{0xD4AD2DBFC3D07787, 0x955E4EC64B44E865}, // -35
{0x84EC3C97DA624AB4, 0xBD5AF13BEF0B113F}, // -34
{0xA6274BBDD0FADD61, 0xECB1AD8AEACDD58F}, // -33
{0xCFB11EAD453994BA, 0x67DE18EDA5814AF3}, // -32
{0x81CEB32C4B43FCF4, 0x80EACF948770CED8}, // -31
{0xA2425FF75E14FC31, 0xA1258379A94D028E}, // -30
{0xCAD2F7F5359A3B3E, 0x096EE45813A04331}, // -29
{0xFD87B5F28300CA0D, 0x8BCA9D6E188853FD}, // -28
{0x9E74D1B791E07E48, 0x775EA264CF55347E}, // -27
{0xC612062576589DDA, 0x95364AFE032A819E}, // -26
{0xF79687AED3EEC551, 0x3A83DDBD83F52205}, // -25
{0x9ABE14CD44753B52, 0xC4926A9672793543}, // -24
{0xC16D9A0095928A27, 0x75B7053C0F178294}, // -23
{0xF1C90080BAF72CB1, 0x5324C68B12DD6339}, // -22
{0x971DA05074DA7BEE, 0xD3F6FC16EBCA5E04}, // -21
{0xBCE5086492111AEA, 0x88F4BB1CA6BCF585}, // -20
{0xEC1E4A7DB69561A5, 0x2B31E9E3D06C32E6}, // -19
{0x9392EE8E921D5D07, 0x3AFF322E62439FD0}, // -18
{0xB877AA3236A4B449, 0x09BEFEB9FAD487C3}, // -17
{0xE69594BEC44DE15B, 0x4C2EBE687989A9B4}, // -16
{0x901D7CF73AB0ACD9, 0x0F9D37014BF60A11}, // -15
{0xB424DC35095CD80F, 0x538484C19EF38C95}, // -14
{0xE12E13424BB40E13, 0x2865A5F206B06FBA}, // -13
{0x8CBCCC096F5088CB, 0xF93F87B7442E45D4}, // -12
{0xAFEBFF0BCB24AAFE, 0xF78F69A51539D749}, // -11
{0xDBE6FECEBDEDD5BE, 0xB573440E5A884D1C}, // -10
{0x89705F4136B4A597, 0x31680A88F8953031}, // -9
{0xABCC77118461CEFC, 0xFDC20D2B36BA7C3E}, // -8
{0xD6BF94D5E57A42BC, 0x3D32907604691B4D}, // -7
{0x8637BD05AF6C69B5, 0xA63F9A49C2C1B110}, // -6
{0xA7C5AC471B478423, 0x0FCF80DC33721D54}, // -5
{0xD1B71758E219652B, 0xD3C36113404EA4A9}, // -4
{0x83126E978D4FDF3B, 0x645A1CAC083126EA}, // -3
{0xA3D70A3D70A3D70A, 0x3D70A3D70A3D70A4}, // -2
{0xCCCCCCCCCCCCCCCC, 0xCCCCCCCCCCCCCCCD}, // -1
{0x8000000000000000, 0x0000000000000000}, // 0
{0xA000000000000000, 0x0000000000000000}, // 1
{0xC800000000000000, 0x0000000000000000}, // 2
{0xFA00000000000000, 0x0000000000000000}, // 3
{0x9C40000000000000, 0x0000000000000000}, // 4
{0xC350000000000000, 0x0000000000000000}, // 5
{0xF424000000000000, 0x0000000000000000}, // 6
{0x9896800000000000, 0x0000000000000000}, // 7
{0xBEBC200000000000, 0x0000000000000000}, // 8
{0xEE6B280000000000, 0x0000000000000000}, // 9
{0x9502F90000000000, 0x0000000000000000}, // 10
{0xBA43B74000000000, 0x0000000000000000}, // 11
{0xE8D4A51000000000, 0x0000000000000000}, // 12
{0x9184E72A00000000, 0x0000000000000000}, // 13
{0xB5E620F480000000, 0x0000000000000000}, // 14
{0xE35FA931A0000000, 0x0000000000000000}, // 15
{0x8E1BC9BF04000000, 0x0000000000000000}, // 16
{0xB1A2BC2EC5000000, 0x0000000000000000}, // 17
{0xDE0B6B3A76400000, 0x0000000000000000}, // 18
{0x8AC7230489E80000, 0x0000000000000000}, // 19
{0xAD78EBC5AC620000, 0x0000000000000000}, // 20
{0xD8D726B7177A8000, 0x0000000000000000}, // 21
{0x878678326EAC9000, 0x0000000000000000}, // 22
{0xA968163F0A57B400, 0x0000000000000000}, // 23
{0xD3C21BCECCEDA100, 0x0000000000000000}, // 24
{0x84595161401484A0, 0x0000000000000000}, // 25
{0xA56FA5B99019A5C8, 0x0000000000000000}, // 26
{0xCECB8F27F4200F3A, 0x0000000000000000}, // 27
{0x813F3978F8940984, 0x4000000000000000}, // 28
{0xA18F07D736B90BE5, 0x5000000000000000}, // 29
{0xC9F2C9CD04674EDE, 0xA400000000000000}, // 30
{0xFC6F7C4045812296, 0x4D00000000000000}, // 31
{0x9DC5ADA82B70B59D, 0xF020000000000000}, // 32
{0xC5371912364CE305, 0x6C28000000000000}, // 33
{0xF684DF56C3E01BC6, 0xC732000000000000}, // 34
{0x9A130B963A6C115C, 0x3C7F400000000000}, // 35
{0xC097CE7BC90715B3, 0x4B9F100000000000}, // 36
{0xF0BDC21ABB48DB20, 0x1E86D40000000000}, // 37
{0x96769950B50D88F4, 0x1314448000000000}, // 38
{0xBC143FA4E250EB31, 0x17D955A000000000}, // 39
{0xEB194F8E1AE525FD, 0x5DCFAB0800000000}, // 40
{0x92EFD1B8D0CF37BE, 0x5AA1CAE500000000}, // 41
{0xB7ABC627050305AD, 0xF14A3D9E40000000}, // 42
{0xE596B7B0C643C719, 0x6D9CCD05D0000000}, // 43
{0x8F7E32CE7BEA5C6F, 0xE4820023A2000000}, // 44
{0xB35DBF821AE4F38B, 0xDDA2802C8A800000}, // 45
{0xE0352F62A19E306E, 0xD50B2037AD200000}, // 46
{0x8C213D9DA502DE45, 0x4526F422CC340000}, // 47
{0xAF298D050E4395D6, 0x9670B12B7F410000}, // 48
{0xDAF3F04651D47B4C, 0x3C0CDD765F114000}, // 49
{0x88D8762BF324CD0F, 0xA5880A69FB6AC800}, // 50
{0xAB0E93B6EFEE0053, 0x8EEA0D047A457A00}, // 51
{0xD5D238A4ABE98068, 0x72A4904598D6D880}, // 52
{0x85A36366EB71F041, 0x47A6DA2B7F864750}, // 53
{0xA70C3C40A64E6C51, 0x999090B65F67D924}, // 54
{0xD0CF4B50CFE20765, 0xFFF4B4E3F741CF6D}, // 55
{0x82818F1281ED449F, 0xBFF8F10E7A8921A5}, // 56
{0xA321F2D7226895C7, 0xAFF72D52192B6A0E}, // 57
{0xCBEA6F8CEB02BB39, 0x9BF4F8A69F764491}, // 58
{0xFEE50B7025C36A08, 0x02F236D04753D5B5}, // 59
{0x9F4F2726179A2245, 0x01D762422C946591}, // 60
{0xC722F0EF9D80AAD6, 0x424D3AD2B7B97EF6}, // 61
{0xF8EBAD2B84E0D58B, 0xD2E0898765A7DEB3}, // 62
{0x9B934C3B330C8577, 0x63CC55F49F88EB30}, // 63
{0xC2781F49FFCFA6D5, 0x3CBF6B71C76B25FC}, // 64
{0xF316271C7FC3908A, 0x8BEF464E3945EF7B}, // 65
{0x97EDD871CFDA3A56, 0x97758BF0E3CBB5AD}, // 66
{0xBDE94E8E43D0C8EC, 0x3D52EEED1CBEA318}, // 67
{0xED63A231D4C4FB27, 0x4CA7AAA863EE4BDE}, // 68
{0x945E455F24FB1CF8, 0x8FE8CAA93E74EF6B}, // 69
{0xB975D6B6EE39E436, 0xB3E2FD538E122B45}, // 70
{0xE7D34C64A9C85D44, 0x60DBBCA87196B617}, // 71
{0x90E40FBEEA1D3A4A, 0xBC8955E946FE31CE}, // 72
{0xB51D13AEA4A488DD, 0x6BABAB6398BDBE42}, // 73
{0xE264589A4DCDAB14, 0xC696963C7EED2DD2}, // 74
{0x8D7EB76070A08AEC, 0xFC1E1DE5CF543CA3}, // 75
{0xB0DE65388CC8ADA8, 0x3B25A55F43294BCC}, // 76
{0xDD15FE86AFFAD912, 0x49EF0EB713F39EBF}, // 77
{0x8A2DBF142DFCC7AB, 0x6E3569326C784338}, // 78
{0xACB92ED9397BF996, 0x49C2C37F07965405}, // 79
{0xD7E77A8F87DAF7FB, 0xDC33745EC97BE907}, // 80
{0x86F0AC99B4E8DAFD, 0x69A028BB3DED71A4}, // 81
{0xA8ACD7C0222311BC, 0xC40832EA0D68CE0D}, // 82
{0xD2D80DB02AABD62B, 0xF50A3FA490C30191}, // 83
{0x83C7088E1AAB65DB, 0x792667C6DA79E0FB}, // 84
{0xA4B8CAB1A1563F52, 0x577001B891185939}, // 85
{0xCDE6FD5E09ABCF26, 0xED4C0226B55E6F87}, // 86
{0x80B05E5AC60B6178, 0x544F8158315B05B5}, // 87
{0xA0DC75F1778E39D6, 0x696361AE3DB1C722}, // 88
{0xC913936DD571C84C, 0x03BC3A19CD1E38EA}, // 89
{0xFB5878494ACE3A5F, 0x04AB48A04065C724}, // 90
{0x9D174B2DCEC0E47B, 0x62EB0D64283F9C77}, // 91
{0xC45D1DF942711D9A, 0x3BA5D0BD324F8395}, // 92
{0xF5746577930D6500, 0xCA8F44EC7EE3647A}, // 93
{0x9968BF6ABBE85F20, 0x7E998B13CF4E1ECC}, // 94
{0xBFC2EF456AE276E8, 0x9E3FEDD8C321A67F}, // 95
{0xEFB3AB16C59B14A2, 0xC5CFE94EF3EA101F}, // 96
{0x95D04AEE3B80ECE5, 0xBBA1F1D158724A13}, // 97
{0xBB445DA9CA61281F, 0x2A8A6E45AE8EDC98}, // 98
{0xEA1575143CF97226, 0xF52D09D71A3293BE}, // 99
{0x924D692CA61BE758, 0x593C2626705F9C57}, // 100
{0xB6E0C377CFA2E12E, 0x6F8B2FB00C77836D}, // 101
{0xE498F455C38B997A, 0x0B6DFB9C0F956448}, // 102
{0x8EDF98B59A373FEC, 0x4724BD4189BD5EAD}, // 103
{0xB2977EE300C50FE7, 0x58EDEC91EC2CB658}, // 104
{0xDF3D5E9BC0F653E1, 0x2F2967B66737E3EE}, // 105
{0x8B865B215899F46C, 0xBD79E0D20082EE75}, // 106
{0xAE67F1E9AEC07187, 0xECD8590680A3AA12}, // 107
{0xDA01EE641A708DE9, 0xE80E6F4820CC9496}, // 108
{0x884134FE908658B2, 0x3109058D147FDCDE}, // 109
{0xAA51823E34A7EEDE, 0xBD4B46F0599FD416}, // 110
{0xD4E5E2CDC1D1EA96, 0x6C9E18AC7007C91B}, // 111
{0x850FADC09923329E, 0x03E2CF6BC604DDB1}, // 112
{0xA6539930BF6BFF45, 0x84DB8346B786151D}, // 113
{0xCFE87F7CEF46FF16, 0xE612641865679A64}, // 114
{0x81F14FAE158C5F6E, 0x4FCB7E8F3F60C07F}, // 115
{0xA26DA3999AEF7749, 0xE3BE5E330F38F09E}, // 116
{0xCB090C8001AB551C, 0x5CADF5BFD3072CC6}, // 117
{0xFDCB4FA002162A63, 0x73D9732FC7C8F7F7}, // 118
{0x9E9F11C4014DDA7E, 0x2867E7FDDCDD9AFB}, // 119
{0xC646D63501A1511D, 0xB281E1FD541501B9}, // 120
{0xF7D88BC24209A565, 0x1F225A7CA91A4227}, // 121
{0x9AE757596946075F, 0x3375788DE9B06959}, // 122
{0xC1A12D2FC3978937, 0x0052D6B1641C83AF}, // 123
{0xF209787BB47D6B84, 0xC0678C5DBD23A49B}, // 124
{0x9745EB4D50CE6332, 0xF840B7BA963646E1}, // 125
{0xBD176620A501FBFF, 0xB650E5A93BC3D899}, // 126
{0xEC5D3FA8CE427AFF, 0xA3E51F138AB4CEBF}, // 127
{0x93BA47C980E98CDF, 0xC66F336C36B10138}, // 128
{0xB8A8D9BBE123F017, 0xB80B0047445D4185}, // 129
{0xE6D3102AD96CEC1D, 0xA60DC059157491E6}, // 130
{0x9043EA1AC7E41392, 0x87C89837AD68DB30}, // 131
{0xB454E4A179DD1877, 0x29BABE4598C311FC}, // 132
{0xE16A1DC9D8545E94, 0xF4296DD6FEF3D67B}, // 133
{0x8CE2529E2734BB1D, 0x1899E4A65F58660D}, // 134
{0xB01AE745B101E9E4, 0x5EC05DCFF72E7F90}, // 135
{0xDC21A1171D42645D, 0x76707543F4FA1F74}, // 136
{0x899504AE72497EBA, 0x6A06494A791C53A9}, // 137
{0xABFA45DA0EDBDE69, 0x0487DB9D17636893}, // 138
{0xD6F8D7509292D603, 0x45A9D2845D3C42B7}, // 139
{0x865B86925B9BC5C2, 0x0B8A2392BA45A9B3}, // 140
{0xA7F26836F282B732, 0x8E6CAC7768D7141F}, // 141
{0xD1EF0244AF2364FF, 0x3207D795430CD927}, // 142
{0x8335616AED761F1F, 0x7F44E6BD49E807B9}, // 143
{0xA402B9C5A8D3A6E7, 0x5F16206C9C6209A7}, // 144
{0xCD036837130890A1, 0x36DBA887C37A8C10}, // 145
{0x802221226BE55A64, 0xC2494954DA2C978A}, // 146
{0xA02AA96B06DEB0FD, 0xF2DB9BAA10B7BD6D}, // 147
{0xC83553C5C8965D3D, 0x6F92829494E5ACC8}, // 148
{0xFA42A8B73ABBF48C, 0xCB772339BA1F17FA}, // 149
{0x9C69A97284B578D7, 0xFF2A760414536EFC}, // 150
{0xC38413CF25E2D70D, 0xFEF5138519684ABB}, // 151
{0xF46518C2EF5B8CD1, 0x7EB258665FC25D6A}, // 152
{0x98BF2F79D5993802, 0xEF2F773FFBD97A62}, // 153
{0xBEEEFB584AFF8603, 0xAAFB550FFACFD8FB}, // 154
{0xEEAABA2E5DBF6784, 0x95BA2A53F983CF39}, // 155
{0x952AB45CFA97A0B2, 0xDD945A747BF26184}, // 156
{0xBA756174393D88DF, 0x94F971119AEEF9E5}, // 157
{0xE912B9D1478CEB17, 0x7A37CD5601AAB85E}, // 158
{0x91ABB422CCB812EE, 0xAC62E055C10AB33B}, // 159
{0xB616A12B7FE617AA, 0x577B986B314D600A}, // 160
{0xE39C49765FDF9D94, 0xED5A7E85FDA0B80C}, // 161
{0x8E41ADE9FBEBC27D, 0x14588F13BE847308}, // 162
{0xB1D219647AE6B31C, 0x596EB2D8AE258FC9}, // 163
{0xDE469FBD99A05FE3, 0x6FCA5F8ED9AEF3BC}, // 164
{0x8AEC23D680043BEE, 0x25DE7BB9480D5855}, // 165
{0xADA72CCC20054AE9, 0xAF561AA79A10AE6B}, // 166
{0xD910F7FF28069DA4, 0x1B2BA1518094DA05}, // 167
{0x87AA9AFF79042286, 0x90FB44D2F05D0843}, // 168
{0xA99541BF57452B28, 0x353A1607AC744A54}, // 169
{0xD3FA922F2D1675F2, 0x42889B8997915CE9}, // 170
{0x847C9B5D7C2E09B7, 0x69956135FEBADA12}, // 171
{0xA59BC234DB398C25, 0x43FAB9837E699096}, // 172
{0xCF02B2C21207EF2E, 0x94F967E45E03F4BC}, // 173
{0x8161AFB94B44F57D, 0x1D1BE0EEBAC278F6}, // 174
{0xA1BA1BA79E1632DC, 0x6462D92A69731733}, // 175
{0xCA28A291859BBF93, 0x7D7B8F7503CFDCFF}, // 176
{0xFCB2CB35E702AF78, 0x5CDA735244C3D43F}, // 177
{0x9DEFBF01B061ADAB, 0x3A0888136AFA64A8}, // 178
{0xC56BAEC21C7A1916, 0x088AAA1845B8FDD1}, // 179
{0xF6C69A72A3989F5B, 0x8AAD549E57273D46}, // 180
{0x9A3C2087A63F6399, 0x36AC54E2F678864C}, // 181
{0xC0CB28A98FCF3C7F, 0x84576A1BB416A7DE}, // 182
{0xF0FDF2D3F3C30B9F, 0x656D44A2A11C51D6}, // 183
{0x969EB7C47859E743, 0x9F644AE5A4B1B326}, // 184
{0xBC4665B596706114, 0x873D5D9F0DDE1FEF}, // 185
{0xEB57FF22FC0C7959, 0xA90CB506D155A7EB}, // 186
{0x9316FF75DD87CBD8, 0x09A7F12442D588F3}, // 187
{0xB7DCBF5354E9BECE, 0x0C11ED6D538AEB30}, // 188
{0xE5D3EF282A242E81, 0x8F1668C8A86DA5FB}, // 189
{0x8FA475791A569D10, 0xF96E017D694487BD}, // 190
{0xB38D92D760EC4455, 0x37C981DCC395A9AD}, // 191
{0xE070F78D3927556A, 0x85BBE253F47B1418}, // 192
{0x8C469AB843B89562, 0x93956D7478CCEC8F}, // 193
{0xAF58416654A6BABB, 0x387AC8D1970027B3}, // 194
{0xDB2E51BFE9D0696A, 0x06997B05FCC0319F}, // 195
{0x88FCF317F22241E2, 0x441FECE3BDF81F04}, // 196
{0xAB3C2FDDEEAAD25A, 0xD527E81CAD7626C4}, // 197
{0xD60B3BD56A5586F1, 0x8A71E223D8D3B075}, // 198
{0x85C7056562757456, 0xF6872D5667844E4A}, // 199
{0xA738C6BEBB12D16C, 0xB428F8AC016561DC}, // 200
{0xD106F86E69D785C7, 0xE13336D701BEBA53}, // 201
{0x82A45B450226B39C, 0xECC0024661173474}, // 202
{0xA34D721642B06084, 0x27F002D7F95D0191}, // 203
{0xCC20CE9BD35C78A5, 0x31EC038DF7B441F5}, // 204
{0xFF290242C83396CE, 0x7E67047175A15272}, // 205
{0x9F79A169BD203E41, 0x0F0062C6E984D387}, // 206
{0xC75809C42C684DD1, 0x52C07B78A3E60869}, // 207
{0xF92E0C3537826145, 0xA7709A56CCDF8A83}, // 208
{0x9BBCC7A142B17CCB, 0x88A66076400BB692}, // 209
{0xC2ABF989935DDBFE, 0x6ACFF893D00EA436}, // 210
{0xF356F7EBF83552FE, 0x0583F6B8C4124D44}, // 211
{0x98165AF37B2153DE, 0xC3727A337A8B704B}, // 212
{0xBE1BF1B059E9A8D6, 0x744F18C0592E4C5D}, // 213
{0xEDA2EE1C7064130C, 0x1162DEF06F79DF74}, // 214
{0x9485D4D1C63E8BE7, 0x8ADDCB5645AC2BA9}, // 215
{0xB9A74A0637CE2EE1, 0x6D953E2BD7173693}, // 216
{0xE8111C87C5C1BA99, 0xC8FA8DB6CCDD0438}, // 217
{0x910AB1D4DB9914A0, 0x1D9C9892400A22A3}, // 218
{0xB54D5E4A127F59C8, 0x2503BEB6D00CAB4C}, // 219
{0xE2A0B5DC971F303A, 0x2E44AE64840FD61E}, // 220
{0x8DA471A9DE737E24, 0x5CEAECFED289E5D3}, // 221
{0xB10D8E1456105DAD, 0x7425A83E872C5F48}, // 222
{0xDD50F1996B947518, 0xD12F124E28F7771A}, // 223
{0x8A5296FFE33CC92F, 0x82BD6B70D99AAA70}, // 224
{0xACE73CBFDC0BFB7B, 0x636CC64D1001550C}, // 225
{0xD8210BEFD30EFA5A, 0x3C47F7E05401AA4F}, // 226
{0x8714A775E3E95C78, 0x65ACFAEC34810A72}, // 227
{0xA8D9D1535CE3B396, 0x7F1839A741A14D0E}, // 228
{0xD31045A8341CA07C, 0x1EDE48111209A051}, // 229
{0x83EA2B892091E44D, 0x934AED0AAB460433}, // 230
{0xA4E4B66B68B65D60, 0xF81DA84D56178540}, // 231
{0xCE1DE40642E3F4B9, 0x36251260AB9D668F}, // 232
{0x80D2AE83E9CE78F3, 0xC1D72B7C6B42601A}, // 233
{0xA1075A24E4421730, 0xB24CF65B8612F820}, // 234
{0xC94930AE1D529CFC, 0xDEE033F26797B628}, // 235
{0xFB9B7CD9A4A7443C, 0x169840EF017DA3B2}, // 236
{0x9D412E0806E88AA5, 0x8E1F289560EE864F}, // 237
{0xC491798A08A2AD4E, 0xF1A6F2BAB92A27E3}, // 238
{0xF5B5D7EC8ACB58A2, 0xAE10AF696774B1DC}, // 239
{0x9991A6F3D6BF1765, 0xACCA6DA1E0A8EF2A}, // 240
{0xBFF610B0CC6EDD3F, 0x17FD090A58D32AF4}, // 241
{0xEFF394DCFF8A948E, 0xDDFC4B4CEF07F5B1}, // 242
{0x95F83D0A1FB69CD9, 0x4ABDAF101564F98F}, // 243
{0xBB764C4CA7A4440F, 0x9D6D1AD41ABE37F2}, // 244
{0xEA53DF5FD18D5513, 0x84C86189216DC5EE}, // 245
{0x92746B9BE2F8552C, 0x32FD3CF5B4E49BB5}, // 246
{0xB7118682DBB66A77, 0x3FBC8C33221DC2A2}, // 247
{0xE4D5E82392A40515, 0x0FABAF3FEAA5334B}, // 248
{0x8F05B1163BA6832D, 0x29CB4D87F2A7400F}, // 249
{0xB2C71D5BCA9023F8, 0x743E20E9EF511013}, // 250
{0xDF78E4B2BD342CF6, 0x914DA9246B255417}, // 251
{0x8BAB8EEFB6409C1A, 0x1AD089B6C2F7548F}, // 252
{0xAE9672ABA3D0C320, 0xA184AC2473B529B2}, // 253
{0xDA3C0F568CC4F3E8, 0xC9E5D72D90A2741F}, // 254
{0x8865899617FB1871, 0x7E2FA67C7A658893}, // 255
{0xAA7EEBFB9DF9DE8D, 0xDDBB901B98FEEAB8}, // 256
{0xD51EA6FA85785631, 0x552A74227F3EA566}, // 257
{0x8533285C936B35DE, 0xD53A88958F872760}, // 258
{0xA67FF273B8460356, 0x8A892ABAF368F138}, // 259
{0xD01FEF10A657842C, 0x2D2B7569B0432D86}, // 260
{0x8213F56A67F6B29B, 0x9C3B29620E29FC74}, // 261
{0xA298F2C501F45F42, 0x8349F3BA91B47B90}, // 262
{0xCB3F2F7642717713, 0x241C70A936219A74}, // 263
{0xFE0EFB53D30DD4D7, 0xED238CD383AA0111}, // 264
{0x9EC95D1463E8A506, 0xF4363804324A40AB}, // 265
{0xC67BB4597CE2CE48, 0xB143C6053EDCD0D6}, // 266
{0xF81AA16FDC1B81DA, 0xDD94B7868E94050B}, // 267
{0x9B10A4E5E9913128, 0xCA7CF2B4191C8327}, // 268
{0xC1D4CE1F63F57D72, 0xFD1C2F611F63A3F1}, // 269
{0xF24A01A73CF2DCCF, 0xBC633B39673C8CED}, // 270
{0x976E41088617CA01, 0xD5BE0503E085D814}, // 271
{0xBD49D14AA79DBC82, 0x4B2D8644D8A74E19}, // 272
{0xEC9C459D51852BA2, 0xDDF8E7D60ED1219F}, // 273
{0x93E1AB8252F33B45, 0xCABB90E5C942B504}, // 274
{0xB8DA1662E7B00A17, 0x3D6A751F3B936244}, // 275
{0xE7109BFBA19C0C9D, 0x0CC512670A783AD5}, // 276
{0x906A617D450187E2, 0x27FB2B80668B24C6}, // 277
{0xB484F9DC9641E9DA, 0xB1F9F660802DEDF7}, // 278
{0xE1A63853BBD26451, 0x5E7873F8A0396974}, // 279
{0x8D07E33455637EB2, 0xDB0B487B6423E1E9}, // 280
{0xB049DC016ABC5E5F, 0x91CE1A9A3D2CDA63}, // 281
{0xDC5C5301C56B75F7, 0x7641A140CC7810FC}, // 282
{0x89B9B3E11B6329BA, 0xA9E904C87FCB0A9E}, // 283
{0xAC2820D9623BF429, 0x546345FA9FBDCD45}, // 284
{0xD732290FBACAF133, 0xA97C177947AD4096}, // 285
{0x867F59A9D4BED6C0, 0x49ED8EABCCCC485E}, // 286
{0xA81F301449EE8C70, 0x5C68F256BFFF5A75}, // 287
{0xD226FC195C6A2F8C, 0x73832EEC6FFF3112}, // 288
{0x83585D8FD9C25DB7, 0xC831FD53C5FF7EAC}, // 289
{0xA42E74F3D032F525, 0xBA3E7CA8B77F5E56}, // 290
{0xCD3A1230C43FB26F, 0x28CE1BD2E55F35EC}, // 291
{0x80444B5E7AA7CF85, 0x7980D163CF5B81B4}, // 292
{0xA0555E361951C366, 0xD7E105BCC3326220}, // 293
{0xC86AB5C39FA63440, 0x8DD9472BF3FEFAA8}, // 294
{0xFA856334878FC150, 0xB14F98F6F0FEB952}, // 295
{0x9C935E00D4B9D8D2, 0x6ED1BF9A569F33D4}, // 296
{0xC3B8358109E84F07, 0x0A862F80EC4700C9}, // 297
{0xF4A642E14C6262C8, 0xCD27BB612758C0FB}, // 298
{0x98E7E9CCCFBD7DBD, 0x8038D51CB897789D}, // 299
{0xBF21E44003ACDD2C, 0xE0470A63E6BD56C4}, // 300
{0xEEEA5D5004981478, 0x1858CCFCE06CAC75}, // 301
{0x95527A5202DF0CCB, 0x0F37801E0C43EBC9}, // 302
{0xBAA718E68396CFFD, 0xD30560258F54E6BB}, // 303
{0xE950DF20247C83FD, 0x47C6B82EF32A206A}, // 304
{0x91D28B7416CDD27E, 0x4CDC331D57FA5442}, // 305
{0xB6472E511C81471D, 0xE0133FE4ADF8E953}, // 306
{0xE3D8F9E563A198E5, 0x58180FDDD97723A7}, // 307
{0x8E679C2F5E44FF8F, 0x570F09EAA7EA7649}, // 308
{0xB201833B35D63F73, 0x2CD2CC6551E513DB}, // 309
{0xDE81E40A034BCF4F, 0xF8077F7EA65E58D2}, // 310
{0x8B112E86420F6191, 0xFB04AFAF27FAF783}, // 311
{0xADD57A27D29339F6, 0x79C5DB9AF1F9B564}, // 312
{0xD94AD8B1C7380874, 0x18375281AE7822BD}, // 313
{0x87CEC76F1C830548, 0x8F2293910D0B15B6}, // 314
{0xA9C2794AE3A3C69A, 0xB2EB3875504DDB23}, // 315
{0xD433179D9C8CB841, 0x5FA60692A46151EC}, // 316
{0x849FEEC281D7F328, 0xDBC7C41BA6BCD334}, // 317
{0xA5C7EA73224DEFF3, 0x12B9B522906C0801}, // 318
{0xCF39E50FEAE16BEF, 0xD768226B34870A01}, // 319
{0x81842F29F2CCE375, 0xE6A1158300D46641}, // 320
{0xA1E53AF46F801C53, 0x60495AE3C1097FD1}, // 321
{0xCA5E89B18B602368, 0x385BB19CB14BDFC5}, // 322
{0xFCF62C1DEE382C42, 0x46729E03DD9ED7B6}, // 323
{0x9E19DB92B4E31BA9, 0x6C07A2C26A8346D2}, // 324
};
SF_ASSERT(k >= kMin);
SF_ASSERT(k <= kMax);
return g[static_cast<uint32_t>(k - kMin)];
}
#if defined(__SIZEOF_INT128__)
static inline uint64_t RoundToOdd(uint64x2 g, uint64_t cp)
{
__extension__ using uint128_t = unsigned __int128;
const uint128_t x = uint128_t{cp} * g.lo;
const uint128_t y = uint128_t{cp} * g.hi + static_cast<uint64_t>(x >> 64);
const uint64_t y0 = static_cast<uint64_t>(y);
const uint64_t y1 = static_cast<uint64_t>(y >> 64);
return y1 | (y0 > 1);
}
#elif defined(_MSC_VER) && defined(_M_X64)
static inline uint64_t RoundToOdd(uint64x2 g, uint64_t cp)
{
uint64_t x1 = 0;
uint64_t x0 = _umul128(g.lo, cp, &x1);
uint64_t y1 = 0;
uint64_t y0 = _umul128(g.hi, cp, &y1);
static_cast<void>(x0);
// y0 += x1;
// y1 += y0 < x1;
_addcarry_u64(_addcarry_u64(0, y0, x1, &y0), y1, 0, &y1);
return y1 | (y0 > 1);
}
#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};
}
static inline uint64_t RoundToOdd(uint64x2 g, uint64_t cp)
{
uint64_t x = Mul128(g.lo, cp).hi;
uint64x2 y = Mul128(g.hi, cp);
y.lo += x;
y.hi += y.lo < x;
return y.hi | (y.lo > 1);
}
#endif
// Returns whether value is divisible by 2^e2
static inline bool MultipleOfPow2(uint64_t value, int32_t e2)
{
SF_ASSERT(e2 >= 0);
SF_ASSERT(e2 <= 63);
return (value & ((uint64_t{1} << e2) - 1)) == 0;
}
namespace {
struct FloatingDecimal64 {
uint64_t digits; // num_digits <= 17
int32_t exponent;
};
}
static inline FloatingDecimal64 ToDecimal64(uint64_t ieee_significand, uint64_t ieee_exponent)
{
uint64_t c;
int32_t q;
if (ieee_exponent != 0)
{
c = Double::HiddenBit | ieee_significand;
q = static_cast<int32_t>(ieee_exponent) - Double::ExponentBias;
if (0 <= -q && -q < Double::SignificandSize && MultipleOfPow2(c, -q))
{
return {c >> -q, 0};
}
}
else
{
c = ieee_significand;
q = 1 - Double::ExponentBias;
}
const bool is_even = (c % 2 == 0);
const bool accept_lower = is_even;
const bool accept_upper = is_even;
const bool lower_boundary_is_closer = (ieee_significand == 0 && ieee_exponent > 1);
// const int32_t qb = q - 2;
const uint64_t cbl = 4 * c - 2 + lower_boundary_is_closer;
const uint64_t cb = 4 * c;
const uint64_t cbr = 4 * c + 2;
// (q * 1262611 ) >> 22 == floor(log_10( 2^q))
// (q * 1262611 - 524031) >> 22 == floor(log_10(3/4 2^q))
SF_ASSERT(q >= -1500);
SF_ASSERT(q <= 1500);
const int32_t k = FloorDivPow2(q * 1262611 - (lower_boundary_is_closer ? 524031 : 0), 22);
const int32_t h = q + FloorLog2Pow10(-k) + 1;
SF_ASSERT(h >= 1);
SF_ASSERT(h <= 4);
const uint64x2 pow10 = ComputePow10_Double(-k);
const uint64_t vbl = RoundToOdd(pow10, cbl << h);
const uint64_t vb = RoundToOdd(pow10, cb << h);
const uint64_t vbr = RoundToOdd(pow10, cbr << h);
const uint64_t lower = vbl + !accept_lower;
const uint64_t upper = vbr - !accept_upper;
// See Figure 4 in [1].
// And the modifications in Figure 6.
const uint64_t s = vb / 4; // NB: 4 * s == vb & ~3 == vb & -4
if (s >= 10) // vb >= 40
{
const uint64_t sp = s / 10; // = vb / 40
const bool up_inside = lower <= 40 * sp;
const bool wp_inside = 40 * sp + 40 <= upper;
// if (up_inside || wp_inside) // NB: At most one of u' and w' is in R_v.
if (up_inside != wp_inside)
{
return {sp + wp_inside, k + 1};
}
}
const bool u_inside = lower <= 4 * s;
const bool w_inside = 4 * s + 4 <= upper;
if (u_inside != w_inside)
{
return {s + w_inside, k};
}
// NB: s & 1 == vb & 0x4
const uint64_t mid = 4 * s + 2; // = 2(s + t)
const bool round_up = vb > mid || (vb == mid && (s & 1) != 0);
return {s + round_up, k};
}
//==================================================================================================
// 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',
};
SF_ASSERT(digits <= 99);
std::memcpy(buf, &Digits100[2 * digits], 2);
}
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,
};
SF_ASSERT(digits <= 99);
return TrailingZeros100[digits];
}
static inline int32_t Utoa_8Digits_skip_trailing_zeros(char* buf, uint32_t digits)
{
SF_ASSERT(digits >= 1);
SF_ASSERT(digits <= 99999999);