279 lines · plain
1// Copyright (c) Microsoft Corporation.2// SPDX-License-Identifier: Apache-2.0 WITH LLVM-exception3 4#ifndef FLOATING_POINT_TEST_CASES_HPP5#define FLOATING_POINT_TEST_CASES_HPP6 7#include <stdint.h>8#include <utility>9 10constexpr std::pair<const char*, std::uint64_t> floating_point_test_cases_double[] = {11 // Verify small exactly-representable integers:12 {"1", 0x3FF0000000000000ULL},13 {"2", 0x4000000000000000ULL},14 {"3", 0x4008000000000000ULL},15 {"4", 0x4010000000000000ULL},16 {"5", 0x4014000000000000ULL},17 {"6", 0x4018000000000000ULL},18 {"7", 0x401C000000000000ULL},19 {"8", 0x4020000000000000ULL},20 21 // Verify large exactly-representable integers:22 {"9007199254740984", 0x433FFFFFFFFFFFF8ULL},23 {"9007199254740985", 0x433FFFFFFFFFFFF9ULL},24 {"9007199254740986", 0x433FFFFFFFFFFFFAULL},25 {"9007199254740987", 0x433FFFFFFFFFFFFBULL},26 {"9007199254740988", 0x433FFFFFFFFFFFFCULL},27 {"9007199254740989", 0x433FFFFFFFFFFFFDULL},28 {"9007199254740990", 0x433FFFFFFFFFFFFEULL},29 {"9007199254740991", 0x433FFFFFFFFFFFFFULL}, // 2^53 - 130 31 // Verify the smallest denormal values:32 {"5.0e-324", 0x0000000000000001ULL},33 {"1.0e-323", 0x0000000000000002ULL},34 {"1.5e-323", 0x0000000000000003ULL},35 {"2.0e-323", 0x0000000000000004ULL},36 {"2.5e-323", 0x0000000000000005ULL},37 {"3.0e-323", 0x0000000000000006ULL},38 {"3.5e-323", 0x0000000000000007ULL},39 {"4.0e-323", 0x0000000000000008ULL},40 {"4.5e-323", 0x0000000000000009ULL},41 {"5.0e-323", 0x000000000000000AULL},42 {"5.5e-323", 0x000000000000000BULL},43 {"6.0e-323", 0x000000000000000CULL},44 {"6.5e-323", 0x000000000000000DULL},45 {"7.0e-323", 0x000000000000000EULL},46 {"7.5e-323", 0x000000000000000FULL},47 48 // Verify the largest denormal values:49 {"2.2250738585071935e-308", 0x000FFFFFFFFFFFF0ULL},50 {"2.2250738585071940e-308", 0x000FFFFFFFFFFFF1ULL},51 {"2.2250738585071945e-308", 0x000FFFFFFFFFFFF2ULL},52 {"2.2250738585071950e-308", 0x000FFFFFFFFFFFF3ULL},53 {"2.2250738585071955e-308", 0x000FFFFFFFFFFFF4ULL},54 {"2.2250738585071960e-308", 0x000FFFFFFFFFFFF5ULL},55 {"2.2250738585071964e-308", 0x000FFFFFFFFFFFF6ULL},56 {"2.2250738585071970e-308", 0x000FFFFFFFFFFFF7ULL},57 {"2.2250738585071974e-308", 0x000FFFFFFFFFFFF8ULL},58 {"2.2250738585071980e-308", 0x000FFFFFFFFFFFF9ULL},59 {"2.2250738585071984e-308", 0x000FFFFFFFFFFFFAULL},60 {"2.2250738585071990e-308", 0x000FFFFFFFFFFFFBULL},61 {"2.2250738585071994e-308", 0x000FFFFFFFFFFFFCULL},62 {"2.2250738585072000e-308", 0x000FFFFFFFFFFFFDULL},63 {"2.2250738585072004e-308", 0x000FFFFFFFFFFFFEULL},64 {"2.2250738585072010e-308", 0x000FFFFFFFFFFFFFULL},65 66 // DevDiv#576315 "I/O library incorrect rounds floating point numbers on input"67 // DevDiv#616647 "Visual C++ 11: iostream bug: incorrect input streaming of the smallest normal double and some68 // denormals"69 // DevDiv#730414 "iostreams is still misparsing floating-point"70 // DevDiv#938627 "parsing float values using std::istream gives results inconsistent with sscanf() and with C++71 // compiler"72 // DevDiv#961116 "floating point string conversion accuracy"73 {"2.2250738585072014e-308", 0x0010000000000000ULL}, // DBL_MIN74 {"1.7976931348623158e+308", 0x7FEFFFFFFFFFFFFFULL}, // DBL_MAX75 {"4.26144921954407e-309", 0x00031076B2F00000ULL},76 {"179.9999999999999855", 0x40667FFFFFFFFFFFULL},77 {"4.1", 0x4010666666666666ULL},78 {"0.2288884", 0x3FCD4C37103785A8ULL},79 {"0.168", 0x3FC5810624DD2F1BULL},80 {"1.68", 0x3FFAE147AE147AE1ULL},81 {"16.80000001", 0x4030CCCCCCF7BFEBULL},82 83 // Test cases from Rick Regan's article, "Incorrectly Rounded Conversions in Visual C++":84 // https://www.exploringbinary.com/incorrectly-rounded-conversions-in-visual-c-plus-plus/85 86 // Example 1:87 {"9214843084008499", 0x43405E6CEC57761AULL},88 89 // Example 2 (2^-1 + 2^-53 + 2^-54):90 {"0.500000000000000166533453693773481063544750213623046875", 0x3FE0000000000002ULL},91 92 // Example 3:93 {"30078505129381147446200", 0x44997A3C7271B021ULL},94 95 // Example 4:96 {"1777820000000000000001", 0x4458180D5BAD2E3EULL},97 98 // Example 5 (2^-1 + 2^-53 + 2^-54 + 2^-66):99 {"0.500000000000000166547006220929549868969843373633921146392822265625", 0x3FE0000000000002ULL},100 101 // Example 6 (2^-1 + 2^-53 + 2^-54 + 2^-65):102 {"0.50000000000000016656055874808561867439493653364479541778564453125", 0x3FE0000000000002ULL},103 104 // Example 7:105 {"0.3932922657273", 0x3FD92BB352C4623AULL},106 107 // The following test cases are taken from other articles on Rick Regan's108 // Exploring Binary blog. These are conversions that other implementations109 // were found to perform incorrectly.110 111 // https://www.exploringbinary.com/incorrectly-rounded-subnormal-conversions-in-java/112 // Example 1 (2^-1047 + 2^-1075, half-ulp above a power of two):113 {"6.6312368714697582767853966302759672433990999473553031442499717587"114 "362866301392654396180682007880487441059604205526018528897150063763"115 "256665955396033303618005191075917832333584923372080578494993608994"116 "251286407188566165030934449228547591599881603044399098682919739314"117 "266256986631577498362522745234853124423586512070512924530832781161"118 "439325697279187097860044978723221938561502254152119972830784963194"119 "121246401117772161481107528151017752957198119743384519360959074196"120 "224175384736794951486324803914359317679811223967034438033355297560"121 "033532098300718322306892013830155987921841729099279241763393155074"122 "022348361207309147831684007154624400538175927027662135590421159867"123 "638194826541287705957668068727833491469671712939495988506756821156"124 "96218943412532098591327667236328125E-316",125 0x0000000008000000ULL},126 127 // Example 2 (2^-1058 - 2^-1075, half-ulp below a power of two):128 {"3.2378839133029012895883524125015321748630376694231080599012970495"129 "523019706706765657868357425877995578606157765598382834355143910841"130 "531692526891905643964595773946180389283653051434639551003566966656"131 "292020173313440317300443693602052583458034314716600326995807313009"132 "548483639755486900107515300188817581841745696521731104736960227499"133 "346384253806233697747365600089974040609674980283891918789639685754"134 "392222064169814626901133425240027243859416510512935526014211553334"135 "302252372915238433223313261384314778235911424088000307751706259156"136 "707286570031519536642607698224949379518458015308952384398197084033"137 "899378732414634842056080000272705311068273879077914449185347715987"138 "501628125488627684932015189916680282517302999531439241685457086639"139 "13273994694463908672332763671875E-319",140 0x0000000000010000ULL},141 142 // Example 3 (2^-1027 + 2^-1066 + 2^-1075, half-ulp above a non-power of two):143 {"6.9533558078476771059728052155218916902221198171459507544162056079"144 "800301315496366888061157263994418800653863998640286912755395394146"145 "528315847956685600829998895513577849614468960421131982842131079351"146 "102171626549398024160346762138294097205837595404767869364138165416"147 "212878432484332023692099166122496760055730227032447997146221165421"148 "888377703760223711720795591258533828013962195524188394697705149041"149 "926576270603193728475623010741404426602378441141744972109554498963"150 "891803958271916028866544881824524095839813894427833770015054620157"151 "450178487545746683421617594966617660200287528887833870748507731929"152 "971029979366198762266880963149896457660004790090837317365857503352"153 "620998601508967187744019647968271662832256419920407478943826987518"154 "09812609536720628966577351093292236328125E-310",155 0x0000800000000100ULL},156 157 // Example 4 (2^-1058 + 2^-1063 - 2^-1075, half-ulp below a non-power of two):158 {"3.3390685575711885818357137012809439119234019169985217716556569973"159 "284403145596153181688491490746626090999981130094655664268081703784"160 "340657229916596426194677060348844249897410807907667784563321682004"161 "646515939958173717821250106683466529959122339932545844611258684816"162 "333436749050742710644097630907080178565840197768788124253120088123"163 "262603630354748115322368533599053346255754042160606228586332807443"164 "018924703005556787346899784768703698535494132771566221702458461669"165 "916553215355296238706468887866375289955928004361779017462862722733"166 "744717014529914330472578638646014242520247915673681950560773208853"167 "293843223323915646452641434007986196650406080775491621739636492640"168 "497383622906068758834568265867109610417379088720358034812416003767"169 "05491726170293986797332763671875E-319",170 0x0000000000010800ULL},171 172 // A number between 2^-1074 and 2^-1075, just slightly larger than 2^-1075.173 // It has bit 1075 set (the denormal rounding bit), followed by 2506 zeroes,174 // followed by one bits. It should round up to 2^-1074.175 {"2.470328229206232720882843964341106861825299013071623822127928412503"176 "37753635104375932649918180817996189898282347722858865463328355177969"177 "89819938739800539093906315035659515570226392290858392449105184435931"178 "80284993653615250031937045767824921936562366986365848075700158576926"179 "99037063119282795585513329278343384093519780155312465972635795746227"180 "66465272827220056374006485499977096599470454020828166226237857393450"181 "73633900796776193057750674017632467360096895134053553745851666113422"182 "37666786041621596804619144672918403005300575308490487653917113865916"183 "46239524912623653881879636239373280423891018672348497668235089863388"184 "58792562830275599565752445550725518931369083625477918694866799496832"185 "40497058210285131854513962138377228261454376934125320985913276672363"186 "28125001e-324",187 0x0000000000000001ULL},188 189 // This value has a non-terminating binary fraction. It has a 0 at bit 54 followed by 120 ones.190 {"1.8254370818746402660437411213933955878019332885742187", 0x3FFD34FD8378EA83ULL},191 192 // https://www.exploringbinary.com/incorrect-decimal-to-floating-point-conversion-in-sqlite/193 {"1e-23", 0x3B282DB34012B251ULL},194 {"8.533e+68", 0x4E3FA69165A8EEA2ULL},195 {"4.1006e-184", 0x19DBE0D1C7EA60C9ULL},196 {"9.998e+307", 0x7FE1CC0A350CA87BULL},197 {"9.9538452227e-280", 0x0602117AE45CDE43ULL},198 {"6.47660115e-260", 0x0A1FDD9E333BADADULL},199 {"7.4e+47", 0x49E033D7ECA0ADEFULL},200 {"5.92e+48", 0x4A1033D7ECA0ADEFULL},201 {"7.35e+66", 0x4DD172B70EABABA9ULL},202 {"8.32116e+55", 0x4B8B2628393E02CDULL},203};204 205constexpr std::pair<const char*, std::uint32_t> floating_point_test_cases_float[] = {206 // Verify small exactly-representable integers:207 {"1", 0x3F800000U},208 {"2", 0x40000000U},209 {"3", 0x40400000U},210 {"4", 0x40800000U},211 {"5", 0x40A00000U},212 {"6", 0x40C00000U},213 {"7", 0x40E00000U},214 {"8", 0x41000000U},215 216 // Verify large exactly-representable integers:217 {"16777208", 0x4B7FFFF8U},218 {"16777209", 0x4B7FFFF9U},219 {"16777210", 0x4B7FFFFAU},220 {"16777211", 0x4B7FFFFBU},221 {"16777212", 0x4B7FFFFCU},222 {"16777213", 0x4B7FFFFDU},223 {"16777214", 0x4B7FFFFEU},224 {"16777215", 0x4B7FFFFFU}, // 2^24 - 1225 226 // Verify the smallest denormal values:227 {"1.4012984643248170e-45", 0x00000001U},228 {"2.8025969286496340e-45", 0x00000002U},229 {"4.2038953929744510e-45", 0x00000003U},230 {"5.6051938572992680e-45", 0x00000004U},231 {"7.0064923216240850e-45", 0x00000005U},232 {"8.4077907859489020e-45", 0x00000006U},233 {"9.8090892502737200e-45", 0x00000007U},234 {"1.1210387714598537e-44", 0x00000008U},235 {"1.2611686178923354e-44", 0x00000009U},236 {"1.4012984643248170e-44", 0x0000000AU},237 {"1.5414283107572988e-44", 0x0000000BU},238 {"1.6815581571897805e-44", 0x0000000CU},239 {"1.8216880036222622e-44", 0x0000000DU},240 {"1.9618178500547440e-44", 0x0000000EU},241 {"2.1019476964872256e-44", 0x0000000FU},242 243 // Verify the largest denormal values:244 {"1.1754921087447446e-38", 0x007FFFF0U},245 {"1.1754922488745910e-38", 0x007FFFF1U},246 {"1.1754923890044375e-38", 0x007FFFF2U},247 {"1.1754925291342839e-38", 0x007FFFF3U},248 {"1.1754926692641303e-38", 0x007FFFF4U},249 {"1.1754928093939768e-38", 0x007FFFF5U},250 {"1.1754929495238232e-38", 0x007FFFF6U},251 {"1.1754930896536696e-38", 0x007FFFF7U},252 {"1.1754932297835160e-38", 0x007FFFF8U},253 {"1.1754933699133625e-38", 0x007FFFF9U},254 {"1.1754935100432089e-38", 0x007FFFFAU},255 {"1.1754936501730553e-38", 0x007FFFFBU},256 {"1.1754937903029018e-38", 0x007FFFFCU},257 {"1.1754939304327482e-38", 0x007FFFFDU},258 {"1.1754940705625946e-38", 0x007FFFFEU},259 {"1.1754942106924411e-38", 0x007FFFFFU},260 261 // DevDiv#576315 "I/O library incorrect rounds floating point numbers on input"262 // DevDiv#616647 "Visual C++ 11: iostream bug: incorrect input streaming of the smallest normal double and some263 // denormals"264 // DevDiv#730414 "iostreams is still misparsing floating-point"265 // DevDiv#938627 "parsing float values using std::istream gives results inconsistent with sscanf() and with C++266 // compiler"267 // DevDiv#961116 "floating point string conversion accuracy"268 {"1.175494351e-38", 0x00800000U}, // FLT_MIN269 {"3.402823466e+38", 0x7F7FFFFFU}, // FLT_MAX270 {"179.9999999999999855", 0x43340000U},271 {"4.1", 0x40833333U},272 {"0.2288884", 0x3E6A61B9U},273 {"0.168", 0x3E2C0831U},274 {"1.68", 0x3FD70A3DU},275 {"16.80000001", 0x41866666U},276};277 278#endif // FLOATING_POINT_TEST_CASES_HPP279