| // Copyright (c) Microsoft Corporation. |
| // SPDX-License-Identifier: Apache-2.0 WITH LLVM-exception |
| |
| #ifndef FLOATING_POINT_TEST_CASES_HPP |
| #define FLOATING_POINT_TEST_CASES_HPP |
| |
| #include <stdint.h> |
| #include <utility> |
| |
| constexpr std::pair<const char*, std::uint64_t> floating_point_test_cases_double[] = { |
| // Verify small exactly-representable integers: |
| {"1", 0x3FF0000000000000ULL}, |
| {"2", 0x4000000000000000ULL}, |
| {"3", 0x4008000000000000ULL}, |
| {"4", 0x4010000000000000ULL}, |
| {"5", 0x4014000000000000ULL}, |
| {"6", 0x4018000000000000ULL}, |
| {"7", 0x401C000000000000ULL}, |
| {"8", 0x4020000000000000ULL}, |
| |
| // Verify large exactly-representable integers: |
| {"9007199254740984", 0x433FFFFFFFFFFFF8ULL}, |
| {"9007199254740985", 0x433FFFFFFFFFFFF9ULL}, |
| {"9007199254740986", 0x433FFFFFFFFFFFFAULL}, |
| {"9007199254740987", 0x433FFFFFFFFFFFFBULL}, |
| {"9007199254740988", 0x433FFFFFFFFFFFFCULL}, |
| {"9007199254740989", 0x433FFFFFFFFFFFFDULL}, |
| {"9007199254740990", 0x433FFFFFFFFFFFFEULL}, |
| {"9007199254740991", 0x433FFFFFFFFFFFFFULL}, // 2^53 - 1 |
| |
| // Verify the smallest denormal values: |
| {"5.0e-324", 0x0000000000000001ULL}, |
| {"1.0e-323", 0x0000000000000002ULL}, |
| {"1.5e-323", 0x0000000000000003ULL}, |
| {"2.0e-323", 0x0000000000000004ULL}, |
| {"2.5e-323", 0x0000000000000005ULL}, |
| {"3.0e-323", 0x0000000000000006ULL}, |
| {"3.5e-323", 0x0000000000000007ULL}, |
| {"4.0e-323", 0x0000000000000008ULL}, |
| {"4.5e-323", 0x0000000000000009ULL}, |
| {"5.0e-323", 0x000000000000000AULL}, |
| {"5.5e-323", 0x000000000000000BULL}, |
| {"6.0e-323", 0x000000000000000CULL}, |
| {"6.5e-323", 0x000000000000000DULL}, |
| {"7.0e-323", 0x000000000000000EULL}, |
| {"7.5e-323", 0x000000000000000FULL}, |
| |
| // Verify the largest denormal values: |
| {"2.2250738585071935e-308", 0x000FFFFFFFFFFFF0ULL}, |
| {"2.2250738585071940e-308", 0x000FFFFFFFFFFFF1ULL}, |
| {"2.2250738585071945e-308", 0x000FFFFFFFFFFFF2ULL}, |
| {"2.2250738585071950e-308", 0x000FFFFFFFFFFFF3ULL}, |
| {"2.2250738585071955e-308", 0x000FFFFFFFFFFFF4ULL}, |
| {"2.2250738585071960e-308", 0x000FFFFFFFFFFFF5ULL}, |
| {"2.2250738585071964e-308", 0x000FFFFFFFFFFFF6ULL}, |
| {"2.2250738585071970e-308", 0x000FFFFFFFFFFFF7ULL}, |
| {"2.2250738585071974e-308", 0x000FFFFFFFFFFFF8ULL}, |
| {"2.2250738585071980e-308", 0x000FFFFFFFFFFFF9ULL}, |
| {"2.2250738585071984e-308", 0x000FFFFFFFFFFFFAULL}, |
| {"2.2250738585071990e-308", 0x000FFFFFFFFFFFFBULL}, |
| {"2.2250738585071994e-308", 0x000FFFFFFFFFFFFCULL}, |
| {"2.2250738585072000e-308", 0x000FFFFFFFFFFFFDULL}, |
| {"2.2250738585072004e-308", 0x000FFFFFFFFFFFFEULL}, |
| {"2.2250738585072010e-308", 0x000FFFFFFFFFFFFFULL}, |
| |
| // DevDiv#576315 "I/O library incorrect rounds floating point numbers on input" |
| // DevDiv#616647 "Visual C++ 11: iostream bug: incorrect input streaming of the smallest normal double and some |
| // denormals" |
| // DevDiv#730414 "iostreams is still misparsing floating-point" |
| // DevDiv#938627 "parsing float values using std::istream gives results inconsistent with sscanf() and with C++ |
| // compiler" |
| // DevDiv#961116 "floating point string conversion accuracy" |
| {"2.2250738585072014e-308", 0x0010000000000000ULL}, // DBL_MIN |
| {"1.7976931348623158e+308", 0x7FEFFFFFFFFFFFFFULL}, // DBL_MAX |
| {"4.26144921954407e-309", 0x00031076B2F00000ULL}, |
| {"179.9999999999999855", 0x40667FFFFFFFFFFFULL}, |
| {"4.1", 0x4010666666666666ULL}, |
| {"0.2288884", 0x3FCD4C37103785A8ULL}, |
| {"0.168", 0x3FC5810624DD2F1BULL}, |
| {"1.68", 0x3FFAE147AE147AE1ULL}, |
| {"16.80000001", 0x4030CCCCCCF7BFEBULL}, |
| |
| // Test cases from Rick Regan's article, "Incorrectly Rounded Conversions in Visual C++": |
| // https://www.exploringbinary.com/incorrectly-rounded-conversions-in-visual-c-plus-plus/ |
| |
| // Example 1: |
| {"9214843084008499", 0x43405E6CEC57761AULL}, |
| |
| // Example 2 (2^-1 + 2^-53 + 2^-54): |
| {"0.500000000000000166533453693773481063544750213623046875", 0x3FE0000000000002ULL}, |
| |
| // Example 3: |
| {"30078505129381147446200", 0x44997A3C7271B021ULL}, |
| |
| // Example 4: |
| {"1777820000000000000001", 0x4458180D5BAD2E3EULL}, |
| |
| // Example 5 (2^-1 + 2^-53 + 2^-54 + 2^-66): |
| {"0.500000000000000166547006220929549868969843373633921146392822265625", 0x3FE0000000000002ULL}, |
| |
| // Example 6 (2^-1 + 2^-53 + 2^-54 + 2^-65): |
| {"0.50000000000000016656055874808561867439493653364479541778564453125", 0x3FE0000000000002ULL}, |
| |
| // Example 7: |
| {"0.3932922657273", 0x3FD92BB352C4623AULL}, |
| |
| // The following test cases are taken from other articles on Rick Regan's |
| // Exploring Binary blog. These are conversions that other implementations |
| // were found to perform incorrectly. |
| |
| // https://www.exploringbinary.com/incorrectly-rounded-subnormal-conversions-in-java/ |
| // Example 1 (2^-1047 + 2^-1075, half-ulp above a power of two): |
| {"6.6312368714697582767853966302759672433990999473553031442499717587" |
| "362866301392654396180682007880487441059604205526018528897150063763" |
| "256665955396033303618005191075917832333584923372080578494993608994" |
| "251286407188566165030934449228547591599881603044399098682919739314" |
| "266256986631577498362522745234853124423586512070512924530832781161" |
| "439325697279187097860044978723221938561502254152119972830784963194" |
| "121246401117772161481107528151017752957198119743384519360959074196" |
| "224175384736794951486324803914359317679811223967034438033355297560" |
| "033532098300718322306892013830155987921841729099279241763393155074" |
| "022348361207309147831684007154624400538175927027662135590421159867" |
| "638194826541287705957668068727833491469671712939495988506756821156" |
| "96218943412532098591327667236328125E-316", |
| 0x0000000008000000ULL}, |
| |
| // Example 2 (2^-1058 - 2^-1075, half-ulp below a power of two): |
| {"3.2378839133029012895883524125015321748630376694231080599012970495" |
| "523019706706765657868357425877995578606157765598382834355143910841" |
| "531692526891905643964595773946180389283653051434639551003566966656" |
| "292020173313440317300443693602052583458034314716600326995807313009" |
| "548483639755486900107515300188817581841745696521731104736960227499" |
| "346384253806233697747365600089974040609674980283891918789639685754" |
| "392222064169814626901133425240027243859416510512935526014211553334" |
| "302252372915238433223313261384314778235911424088000307751706259156" |
| "707286570031519536642607698224949379518458015308952384398197084033" |
| "899378732414634842056080000272705311068273879077914449185347715987" |
| "501628125488627684932015189916680282517302999531439241685457086639" |
| "13273994694463908672332763671875E-319", |
| 0x0000000000010000ULL}, |
| |
| // Example 3 (2^-1027 + 2^-1066 + 2^-1075, half-ulp above a non-power of two): |
| {"6.9533558078476771059728052155218916902221198171459507544162056079" |
| "800301315496366888061157263994418800653863998640286912755395394146" |
| "528315847956685600829998895513577849614468960421131982842131079351" |
| "102171626549398024160346762138294097205837595404767869364138165416" |
| "212878432484332023692099166122496760055730227032447997146221165421" |
| "888377703760223711720795591258533828013962195524188394697705149041" |
| "926576270603193728475623010741404426602378441141744972109554498963" |
| "891803958271916028866544881824524095839813894427833770015054620157" |
| "450178487545746683421617594966617660200287528887833870748507731929" |
| "971029979366198762266880963149896457660004790090837317365857503352" |
| "620998601508967187744019647968271662832256419920407478943826987518" |
| "09812609536720628966577351093292236328125E-310", |
| 0x0000800000000100ULL}, |
| |
| // Example 4 (2^-1058 + 2^-1063 - 2^-1075, half-ulp below a non-power of two): |
| {"3.3390685575711885818357137012809439119234019169985217716556569973" |
| "284403145596153181688491490746626090999981130094655664268081703784" |
| "340657229916596426194677060348844249897410807907667784563321682004" |
| "646515939958173717821250106683466529959122339932545844611258684816" |
| "333436749050742710644097630907080178565840197768788124253120088123" |
| "262603630354748115322368533599053346255754042160606228586332807443" |
| "018924703005556787346899784768703698535494132771566221702458461669" |
| "916553215355296238706468887866375289955928004361779017462862722733" |
| "744717014529914330472578638646014242520247915673681950560773208853" |
| "293843223323915646452641434007986196650406080775491621739636492640" |
| "497383622906068758834568265867109610417379088720358034812416003767" |
| "05491726170293986797332763671875E-319", |
| 0x0000000000010800ULL}, |
| |
| // A number between 2^-1074 and 2^-1075, just slightly larger than 2^-1075. |
| // It has bit 1075 set (the denormal rounding bit), followed by 2506 zeroes, |
| // followed by one bits. It should round up to 2^-1074. |
| {"2.470328229206232720882843964341106861825299013071623822127928412503" |
| "37753635104375932649918180817996189898282347722858865463328355177969" |
| "89819938739800539093906315035659515570226392290858392449105184435931" |
| "80284993653615250031937045767824921936562366986365848075700158576926" |
| "99037063119282795585513329278343384093519780155312465972635795746227" |
| "66465272827220056374006485499977096599470454020828166226237857393450" |
| "73633900796776193057750674017632467360096895134053553745851666113422" |
| "37666786041621596804619144672918403005300575308490487653917113865916" |
| "46239524912623653881879636239373280423891018672348497668235089863388" |
| "58792562830275599565752445550725518931369083625477918694866799496832" |
| "40497058210285131854513962138377228261454376934125320985913276672363" |
| "28125001e-324", |
| 0x0000000000000001ULL}, |
| |
| // This value has a non-terminating binary fraction. It has a 0 at bit 54 followed by 120 ones. |
| {"1.8254370818746402660437411213933955878019332885742187", 0x3FFD34FD8378EA83ULL}, |
| |
| // https://www.exploringbinary.com/incorrect-decimal-to-floating-point-conversion-in-sqlite/ |
| {"1e-23", 0x3B282DB34012B251ULL}, |
| {"8.533e+68", 0x4E3FA69165A8EEA2ULL}, |
| {"4.1006e-184", 0x19DBE0D1C7EA60C9ULL}, |
| {"9.998e+307", 0x7FE1CC0A350CA87BULL}, |
| {"9.9538452227e-280", 0x0602117AE45CDE43ULL}, |
| {"6.47660115e-260", 0x0A1FDD9E333BADADULL}, |
| {"7.4e+47", 0x49E033D7ECA0ADEFULL}, |
| {"5.92e+48", 0x4A1033D7ECA0ADEFULL}, |
| {"7.35e+66", 0x4DD172B70EABABA9ULL}, |
| {"8.32116e+55", 0x4B8B2628393E02CDULL}, |
| }; |
| |
| constexpr std::pair<const char*, std::uint32_t> floating_point_test_cases_float[] = { |
| // Verify small exactly-representable integers: |
| {"1", 0x3F800000U}, |
| {"2", 0x40000000U}, |
| {"3", 0x40400000U}, |
| {"4", 0x40800000U}, |
| {"5", 0x40A00000U}, |
| {"6", 0x40C00000U}, |
| {"7", 0x40E00000U}, |
| {"8", 0x41000000U}, |
| |
| // Verify large exactly-representable integers: |
| {"16777208", 0x4B7FFFF8U}, |
| {"16777209", 0x4B7FFFF9U}, |
| {"16777210", 0x4B7FFFFAU}, |
| {"16777211", 0x4B7FFFFBU}, |
| {"16777212", 0x4B7FFFFCU}, |
| {"16777213", 0x4B7FFFFDU}, |
| {"16777214", 0x4B7FFFFEU}, |
| {"16777215", 0x4B7FFFFFU}, // 2^24 - 1 |
| |
| // Verify the smallest denormal values: |
| {"1.4012984643248170e-45", 0x00000001U}, |
| {"2.8025969286496340e-45", 0x00000002U}, |
| {"4.2038953929744510e-45", 0x00000003U}, |
| {"5.6051938572992680e-45", 0x00000004U}, |
| {"7.0064923216240850e-45", 0x00000005U}, |
| {"8.4077907859489020e-45", 0x00000006U}, |
| {"9.8090892502737200e-45", 0x00000007U}, |
| {"1.1210387714598537e-44", 0x00000008U}, |
| {"1.2611686178923354e-44", 0x00000009U}, |
| {"1.4012984643248170e-44", 0x0000000AU}, |
| {"1.5414283107572988e-44", 0x0000000BU}, |
| {"1.6815581571897805e-44", 0x0000000CU}, |
| {"1.8216880036222622e-44", 0x0000000DU}, |
| {"1.9618178500547440e-44", 0x0000000EU}, |
| {"2.1019476964872256e-44", 0x0000000FU}, |
| |
| // Verify the largest denormal values: |
| {"1.1754921087447446e-38", 0x007FFFF0U}, |
| {"1.1754922488745910e-38", 0x007FFFF1U}, |
| {"1.1754923890044375e-38", 0x007FFFF2U}, |
| {"1.1754925291342839e-38", 0x007FFFF3U}, |
| {"1.1754926692641303e-38", 0x007FFFF4U}, |
| {"1.1754928093939768e-38", 0x007FFFF5U}, |
| {"1.1754929495238232e-38", 0x007FFFF6U}, |
| {"1.1754930896536696e-38", 0x007FFFF7U}, |
| {"1.1754932297835160e-38", 0x007FFFF8U}, |
| {"1.1754933699133625e-38", 0x007FFFF9U}, |
| {"1.1754935100432089e-38", 0x007FFFFAU}, |
| {"1.1754936501730553e-38", 0x007FFFFBU}, |
| {"1.1754937903029018e-38", 0x007FFFFCU}, |
| {"1.1754939304327482e-38", 0x007FFFFDU}, |
| {"1.1754940705625946e-38", 0x007FFFFEU}, |
| {"1.1754942106924411e-38", 0x007FFFFFU}, |
| |
| // DevDiv#576315 "I/O library incorrect rounds floating point numbers on input" |
| // DevDiv#616647 "Visual C++ 11: iostream bug: incorrect input streaming of the smallest normal double and some |
| // denormals" |
| // DevDiv#730414 "iostreams is still misparsing floating-point" |
| // DevDiv#938627 "parsing float values using std::istream gives results inconsistent with sscanf() and with C++ |
| // compiler" |
| // DevDiv#961116 "floating point string conversion accuracy" |
| {"1.175494351e-38", 0x00800000U}, // FLT_MIN |
| {"3.402823466e+38", 0x7F7FFFFFU}, // FLT_MAX |
| {"179.9999999999999855", 0x43340000U}, |
| {"4.1", 0x40833333U}, |
| {"0.2288884", 0x3E6A61B9U}, |
| {"0.168", 0x3E2C0831U}, |
| {"1.68", 0x3FD70A3DU}, |
| {"16.80000001", 0x41866666U}, |
| }; |
| |
| #endif // FLOATING_POINT_TEST_CASES_HPP |