src/Compilers/Core/CodeAnalysisTest/RealParserTests.cs - main - githubmirror/roslyn

src/Compilers/Core/CodeAnalysisTest/RealParserTests.cs
612 строк30 KB
Julien Couvreur
Warn for multiple blank lines in source (#65451)
17 ноя 2022, 22:55
17 ноя 2022, 22:55a8824e8
// Licensed to the .NET Foundation under one or more agreements.
// The .NET Foundation licenses this file to you under the MIT license.
// See the LICENSE file in the project root for more information.

#nullable disable

using System;
using System.Runtime.InteropServices;
using Xunit;

namespace Microsoft.CodeAnalysis.UnitTests
{
    public class RealParserTests
    {
        /// <summary>
        /// Test some specific floating-point literals that have been shown to be problematic
        /// in some implementation.
        /// </summary>
        [Fact]
        public static void TestTroublesomeDoubles()
        {
            //// https://msdn.microsoft.com/en-us/library/kfsatb94(v=vs.110).aspx
            CheckOneDouble("0.6822871999174", 0x3FE5D54BF743FD1Bul);

            //// Common problem numbers
            CheckOneDouble("2.2250738585072011e-308", 0x000FFFFFFFFFFFFFul);
            CheckOneDouble("2.2250738585072012e-308", 0x0010000000000000ul);

            //// http://www.exploringbinary.com/bigcomp-deciding-truncated-near-halfway-conversions/
            CheckOneDouble("1.3694713649464322631e-11", 0x3DAE1D703BB5749Dul);
            CheckOneDouble("9.3170532238714134438e+16", 0x4374B021AFD9F651ul);

            //// https://connect.microsoft.com/VisualStudio/feedback/details/914964/double-round-trip-conversion-via-a-string-is-not-safe
            CheckOneDouble("0.84551240822557006", 0x3FEB0E7009B61CE0ul);

            // This value has a non-terminating binary fraction.  It has a 0 at bit 54
            // followed by 120 ones.
            //// http://www.exploringbinary.com/a-bug-in-the-bigcomp-function-of-david-gays-strtod/
            CheckOneDouble("1.8254370818746402660437411213933955878019332885742187", 0x3FFD34FD8378EA83ul);

            //// http://www.exploringbinary.com/decimal-to-floating-point-needs-arbitrary-precision
            CheckOneDouble("7.8459735791271921e+65", 0x4D9DCD0089C1314Eul);
            CheckOneDouble("3.08984926168550152811e-32", 0x39640DE48676653Bul);

            //// other values from https://github.com/dotnet/roslyn/issues/4221
            CheckOneDouble("0.6822871999174000000", 0x3FE5D54BF743FD1Bul);
            CheckOneDouble("0.6822871999174000001", 0x3FE5D54BF743FD1Bul);

            // A handful of selected values for which double.Parse has been observed to produce an incorrect result
            CheckOneDouble("88.7448699245e+188", 0x675fde6aee647ed2ul);
            CheckOneDouble("02.0500496671303857e-88", 0x2dba19a3cf32cd7ful);
            CheckOneDouble("1.15362842193e193", 0x68043a6fcda86331ul);
            CheckOneDouble("65.9925719e-190", 0x18dd672e04e96a79ul);
            CheckOneDouble("0.4619024460e-158", 0x1f103c1e5abd7c87ul);
            CheckOneDouble("61.8391820096448e147", 0x5ed35849885ad12bul);
            CheckOneDouble("0.2e+127", 0x5a27a2ecc414a03ful);
            CheckOneDouble("0.8e+127", 0x5a47a2ecc414a03ful);
            CheckOneDouble("35.27614496323756e-307", 0x0083d141335ce6c7ul);
            CheckOneDouble("3.400034617466e190", 0x677e863a216ab367ul);
            CheckOneDouble("0.78393577148319e-254", 0x0b2d6d5379bc932dul);
            CheckOneDouble("0.947231e+100", 0x54b152a10483a38ful);
            CheckOneDouble("4.e126", 0x5a37a2ecc414a03ful);
            CheckOneDouble("6.235271922748e-165", 0x1dd6faeba4fc9f91ul);
            CheckOneDouble("3.497444198362024e-82", 0x2f053b8036dd4203ul);
            CheckOneDouble("8.e+126", 0x5a47a2ecc414a03ful);
            CheckOneDouble("10.027247729e+91", 0x53089cc2d930ed3ful);
            CheckOneDouble("4.6544819e-192", 0x18353c5d35ceaaadul);
            CheckOneDouble("5.e+125", 0x5a07a2ecc414a03ful);
            CheckOneDouble("6.96768e68", 0x4e39d8352ee997f9ul);
            CheckOneDouble("0.73433e-145", 0x21cd57b723dc17bful);
            CheckOneDouble("31.076044256878e259", 0x76043627aa7248dful);
            CheckOneDouble("0.8089124675e-201", 0x162fb3bf98f037f7ul);
            CheckOneDouble("88.7453407049700914e-144", 0x227150a674c218e3ul);
            CheckOneDouble("32.401089401e-65", 0x32c10fa88084d643ul);
            CheckOneDouble("0.734277884753e-209", 0x14834fdfb6248755ul);
            CheckOneDouble("8.3435e+153", 0x5fe3e9c5b617dc39ul);
            CheckOneDouble("30.379e-129", 0x25750ec799af9efful);
            CheckOneDouble("78.638509299e141", 0x5d99cb8c0a72cd05ul);
            CheckOneDouble("30.096884930e-42", 0x3784f976b4d47d63ul);

            //// values from http://www.icir.org/vern/papers/testbase-report.pdf table 1 (less than half ULP - round down)
            CheckOneDouble("69e+267", 0x77C0B7CB60C994DAul);
            CheckOneDouble("999e-026", 0x3B282782AFE1869Eul);
            CheckOneDouble("7861e-034", 0x39AFE3544145E9D8ul);
            CheckOneDouble("75569e-254", 0x0C35A462D91C6AB3ul);
            CheckOneDouble("928609e-261", 0x0AFBE2DD66200BEFul);
            CheckOneDouble("9210917e+080", 0x51FDA232347E6032ul);
            CheckOneDouble("84863171e+114", 0x59406E98F5EC8F37ul);
            CheckOneDouble("653777767e+273", 0x7A720223F2B3A881ul);
            CheckOneDouble("5232604057e-298", 0x041465B896C24520ul);
            CheckOneDouble("27235667517e-109", 0x2B77D41824D64FB2ul);
            CheckOneDouble("653532977297e-123", 0x28D925A0AABCDC68ul);
            CheckOneDouble("3142213164987e-294", 0x057D3409DFBCA26Ful);
            CheckOneDouble("46202199371337e-072", 0x33D28F9EDFBD341Ful);
            CheckOneDouble("231010996856685e-073", 0x33C28F9EDFBD341Ful);
            CheckOneDouble("9324754620109615e+212", 0x6F43AE60753AF6CAul);
            CheckOneDouble("78459735791271921e+049", 0x4D9DCD0089C1314Eul);
            CheckOneDouble("272104041512242479e+200", 0x6D13BBB4BF05F087ul);
            CheckOneDouble("6802601037806061975e+198", 0x6CF3BBB4BF05F087ul);
            CheckOneDouble("20505426358836677347e-221", 0x161012954B6AABBAul);
            CheckOneDouble("836168422905420598437e-234", 0x13B20403A628A9CAul);
            CheckOneDouble("4891559871276714924261e+222", 0x7286ECAF7694A3C7ul);

            //// values from http://www.icir.org/vern/papers/testbase-report.pdf table 2 (greater than half ULP - round up)
            CheckOneDouble("85e-037", 0x38A698CCDC60015Aul);
            CheckOneDouble("623e+100", 0x554640A62F3A83DFul);
            CheckOneDouble("3571e+263", 0x77462644C61D41AAul);
            CheckOneDouble("81661e+153", 0x60B7CA8E3D68578Eul);
            CheckOneDouble("920657e-023", 0x3C653A9985DBDE6Cul);
            CheckOneDouble("4603285e-024", 0x3C553A9985DBDE6Cul);
            CheckOneDouble("87575437e-309", 0x016E07320602056Cul);
            CheckOneDouble("245540327e+122", 0x5B01B6231E18C5CBul);
            CheckOneDouble("6138508175e+120", 0x5AE1B6231E18C5CBul);
            CheckOneDouble("83356057653e+193", 0x6A4544E6DAEE2A18ul);
            CheckOneDouble("619534293513e+124", 0x5C210C20303FE0F1ul);
            CheckOneDouble("2335141086879e+218", 0x6FC340A1C932C1EEul);
            CheckOneDouble("36167929443327e-159", 0x21BCE77C2B3328FCul);
            CheckOneDouble("609610927149051e-255", 0x0E104273B18918B1ul);
            CheckOneDouble("3743626360493413e-165", 0x20E8823A57ADBEF9ul);
            CheckOneDouble("94080055902682397e-242", 0x11364981E39E66CAul);
            CheckOneDouble("899810892172646163e+283", 0x7E6ADF51FA055E03ul);
            CheckOneDouble("7120190517612959703e+120", 0x5CC3220DCD5899FDul);
            CheckOneDouble("25188282901709339043e-252", 0x0FA4059AF3DB2A84ul);
            CheckOneDouble("308984926168550152811e-052", 0x39640DE48676653Bul);
            CheckOneDouble("6372891218502368041059e+064", 0x51C067047DBB38FEul);

            // http://www.exploringbinary.com/incorrect-decimal-to-floating-point-conversion-in-sqlite/
            CheckOneDouble("1e-23", 0x3B282DB34012B251ul);
            CheckOneDouble("8.533e+68", 0x4E3FA69165A8EEA2ul);
            CheckOneDouble("4.1006e-184", 0x19DBE0D1C7EA60C9ul);
            CheckOneDouble("9.998e+307", 0x7FE1CC0A350CA87Bul);
            CheckOneDouble("9.9538452227e-280", 0x0602117AE45CDE43ul);
            CheckOneDouble("6.47660115e-260", 0x0A1FDD9E333BADADul);
            CheckOneDouble("7.4e+47", 0x49E033D7ECA0ADEFul);
            CheckOneDouble("5.92e+48", 0x4A1033D7ECA0ADEFul);
            CheckOneDouble("7.35e+66", 0x4DD172B70EABABA9ul);
            CheckOneDouble("8.32116e+55", 0x4B8B2628393E02CDul);
        }

        /// <summary>
        /// Test round tripping for some specific floating-point values constructed to test the edge cases of conversion implementations.
        /// </summary>
        [Fact]
        public static void TestSpecificDoubles()
        {
            CheckOneDouble("0.0", 0x0000000000000000ul);

            // Verify the smallest denormals:
            for (ulong i = 0x0000000000000001ul; i != 0x0000000000000100ul; ++i)
            {
                TestRoundTripDouble(i);
            }

            // Verify the largest denormals and the smallest normals:
            for (ulong i = 0x000fffffffffff00ul; i != 0x0010000000000100ul; ++i)
            {
                TestRoundTripDouble(i);
            }

            // Verify the largest normals:
            for (ulong i = 0x7fefffffffffff00ul; i != 0x7ff0000000000000ul; ++i)
            {
                TestRoundTripDouble(i);
            }

            // Verify all representable powers of two and nearby values:
            for (int pow = -1022; pow <= 1023; pow++)
            {
                ulong twoToThePow = ((ulong)(pow + 1023)) << 52;
                TestRoundTripDouble(twoToThePow);
                TestRoundTripDouble(twoToThePow + 1);
                TestRoundTripDouble(twoToThePow - 1);
            }

            // Verify all representable powers of ten and nearby values:
            for (int pow = -323; pow <= 308; pow++)
            {
                var s = $"1.0e{pow}";
                double value;
                RealParser.TryParseDouble(s, out value);
                var tenToThePow = (ulong)BitConverter.DoubleToInt64Bits(value);
                CheckOneDouble(s, value);
                TestRoundTripDouble(tenToThePow + 1);
                TestRoundTripDouble(tenToThePow - 1);
            }

            // Verify a few large integer values:
            TestRoundTripDouble((double)long.MaxValue);
            TestRoundTripDouble((double)ulong.MaxValue);

            // Verify small and large exactly representable integers:
            CheckOneDouble("1", 0x3ff0000000000000);
            CheckOneDouble("2", 0x4000000000000000);
            CheckOneDouble("3", 0x4008000000000000);
            CheckOneDouble("4", 0x4010000000000000);
            CheckOneDouble("5", 0x4014000000000000);
            CheckOneDouble("6", 0x4018000000000000);
            CheckOneDouble("7", 0x401C000000000000);
            CheckOneDouble("8", 0x4020000000000000);

            CheckOneDouble("9007199254740984", 0x433ffffffffffff8);
            CheckOneDouble("9007199254740985", 0x433ffffffffffff9);
            CheckOneDouble("9007199254740986", 0x433ffffffffffffa);
            CheckOneDouble("9007199254740987", 0x433ffffffffffffb);
            CheckOneDouble("9007199254740988", 0x433ffffffffffffc);
            CheckOneDouble("9007199254740989", 0x433ffffffffffffd);
            CheckOneDouble("9007199254740990", 0x433ffffffffffffe);
            CheckOneDouble("9007199254740991", 0x433fffffffffffff); // 2^53 - 1

            // Verify the smallest and largest denormal values:
            CheckOneDouble("5.0e-324", 0x0000000000000001);
            CheckOneDouble("1.0e-323", 0x0000000000000002);
            CheckOneDouble("1.5e-323", 0x0000000000000003);
            CheckOneDouble("2.0e-323", 0x0000000000000004);
            CheckOneDouble("2.5e-323", 0x0000000000000005);
            CheckOneDouble("3.0e-323", 0x0000000000000006);
            CheckOneDouble("3.5e-323", 0x0000000000000007);
            CheckOneDouble("4.0e-323", 0x0000000000000008);
            CheckOneDouble("4.5e-323", 0x0000000000000009);
            CheckOneDouble("5.0e-323", 0x000000000000000a);
            CheckOneDouble("5.5e-323", 0x000000000000000b);
            CheckOneDouble("6.0e-323", 0x000000000000000c);
            CheckOneDouble("6.5e-323", 0x000000000000000d);
            CheckOneDouble("7.0e-323", 0x000000000000000e);
            CheckOneDouble("7.5e-323", 0x000000000000000f);

            CheckOneDouble("2.2250738585071935e-308", 0x000ffffffffffff0);
            CheckOneDouble("2.2250738585071940e-308", 0x000ffffffffffff1);
            CheckOneDouble("2.2250738585071945e-308", 0x000ffffffffffff2);
            CheckOneDouble("2.2250738585071950e-308", 0x000ffffffffffff3);
            CheckOneDouble("2.2250738585071955e-308", 0x000ffffffffffff4);
            CheckOneDouble("2.2250738585071960e-308", 0x000ffffffffffff5);
            CheckOneDouble("2.2250738585071964e-308", 0x000ffffffffffff6);
            CheckOneDouble("2.2250738585071970e-308", 0x000ffffffffffff7);
            CheckOneDouble("2.2250738585071974e-308", 0x000ffffffffffff8);
            CheckOneDouble("2.2250738585071980e-308", 0x000ffffffffffff9);
            CheckOneDouble("2.2250738585071984e-308", 0x000ffffffffffffa);
            CheckOneDouble("2.2250738585071990e-308", 0x000ffffffffffffb);
            CheckOneDouble("2.2250738585071994e-308", 0x000ffffffffffffc);
            CheckOneDouble("2.2250738585072000e-308", 0x000ffffffffffffd);
            CheckOneDouble("2.2250738585072004e-308", 0x000ffffffffffffe);
            CheckOneDouble("2.2250738585072010e-308", 0x000fffffffffffff);

            // Test cases from Rick Regan's article, "Incorrectly Rounded Conversions in Visual C++":
            //
            //     http://www.exploringbinary.com/incorrectly-rounded-conversions-in-visual-c-plus-plus/
            // 
            // Example 1:
            CheckOneDouble(
                "9214843084008499",
                0x43405e6cec57761a);

            // Example 2:
            CheckOneDouble(
                "0.500000000000000166533453693773481063544750213623046875",
                0x3fe0000000000002);

            // Example 3 (2^-1 + 2^-53 + 2^-54):
            CheckOneDouble(
                "30078505129381147446200",
                0x44997a3c7271b021);

            // Example 4:
            CheckOneDouble(
                "1777820000000000000001",
                0x4458180d5bad2e3e);

            // Example 5 (2^-1 + 2^-53 + 2^-54 + 2^-66):
            CheckOneDouble(
                "0.500000000000000166547006220929549868969843373633921146392822265625",
                0x3fe0000000000002);

            // Example 6 (2^-1 + 2^-53 + 2^-54 + 2^-65):
            CheckOneDouble(
                "0.50000000000000016656055874808561867439493653364479541778564453125",
                0x3fe0000000000002);

            // Example 7:
            CheckOneDouble(
                "0.3932922657273",
                0x3fd92bb352c4623a
                );

            // 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.

            // http://www.exploringbinary.com/nondeterministic-floating-point-conversions-in-java/
            // http://www.exploringbinary.com/incorrectly-rounded-subnormal-conversions-in-java/
            // Example 1 (2^-1047 + 2^-1075, half-ulp above a power of two):
            CheckOneDouble(
                "6.6312368714697582767853966302759672433990999473553031442499717587" +
                "362866301392654396180682007880487441059604205526018528897150063763" +
                "256665955396033303618005191075917832333584923372080578494993608994" +
                "251286407188566165030934449228547591599881603044399098682919739314" +
                "266256986631577498362522745234853124423586512070512924530832781161" +
                "439325697279187097860044978723221938561502254152119972830784963194" +
                "121246401117772161481107528151017752957198119743384519360959074196" +
                "224175384736794951486324803914359317679811223967034438033355297560" +
                "033532098300718322306892013830155987921841729099279241763393155074" +
                "022348361207309147831684007154624400538175927027662135590421159867" +
                "638194826541287705957668068727833491469671712939495988506756821156" +
                "96218943412532098591327667236328125E-316",
                0x0000000008000000);

            // Example 2 (2^-1058 - 2^-1075, half-ulp below a power of two):
            CheckOneDouble(
                "3.2378839133029012895883524125015321748630376694231080599012970495" +
                "523019706706765657868357425877995578606157765598382834355143910841" +
                "531692526891905643964595773946180389283653051434639551003566966656" +
                "292020173313440317300443693602052583458034314716600326995807313009" +
                "548483639755486900107515300188817581841745696521731104736960227499" +
                "346384253806233697747365600089974040609674980283891918789639685754" +
                "392222064169814626901133425240027243859416510512935526014211553334" +
                "302252372915238433223313261384314778235911424088000307751706259156" +
                "707286570031519536642607698224949379518458015308952384398197084033" +
                "899378732414634842056080000272705311068273879077914449185347715987" +
                "501628125488627684932015189916680282517302999531439241685457086639" +
                "13273994694463908672332763671875E-319",
                0x0000000000010000);

            // Example 3 (2^-1027 + 2^-1066 + 2^-1075, half-ulp above a non-power of two):
            CheckOneDouble(
                "6.9533558078476771059728052155218916902221198171459507544162056079" +
                "800301315496366888061157263994418800653863998640286912755395394146" +
                "528315847956685600829998895513577849614468960421131982842131079351" +
                "102171626549398024160346762138294097205837595404767869364138165416" +
                "212878432484332023692099166122496760055730227032447997146221165421" +
                "888377703760223711720795591258533828013962195524188394697705149041" +
                "926576270603193728475623010741404426602378441141744972109554498963" +
                "891803958271916028866544881824524095839813894427833770015054620157" +
                "450178487545746683421617594966617660200287528887833870748507731929" +
                "971029979366198762266880963149896457660004790090837317365857503352" +
                "620998601508967187744019647968271662832256419920407478943826987518" +
                "09812609536720628966577351093292236328125E-310",
                0x0000800000000100
                );

            // Example 4 (2^-1058 + 2^-1063 + 2^-1075, half-ulp below a non-power of two):
            CheckOneDouble(
                "3.3390685575711885818357137012809439119234019169985217716556569973" +
                "284403145596153181688491490746626090999981130094655664268081703784" +
                "340657229916596426194677060348844249897410807907667784563321682004" +
                "646515939958173717821250106683466529959122339932545844611258684816" +
                "333436749050742710644097630907080178565840197768788124253120088123" +
                "262603630354748115322368533599053346255754042160606228586332807443" +
                "018924703005556787346899784768703698535494132771566221702458461669" +
                "916553215355296238706468887866375289955928004361779017462862722733" +
                "744717014529914330472578638646014242520247915673681950560773208853" +
                "293843223323915646452641434007986196650406080775491621739636492640" +
                "497383622906068758834568265867109610417379088720358034812416003767" +
                "05491726170293986797332763671875E-319",
                0x0000000000010800
                );

            // http://www.exploringbinary.com/gays-strtod-returns-zero-for-inputs-just-above-2-1075/
            // A number between 2^-2074 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.
            CheckOneDouble(
                "2.470328229206232720882843964341106861825299013071623822127928412503" +
                "37753635104375932649918180817996189898282347722858865463328355177969" +
                "89819938739800539093906315035659515570226392290858392449105184435931" +
                "80284993653615250031937045767824921936562366986365848075700158576926" +
                "99037063119282795585513329278343384093519780155312465972635795746227" +
                "66465272827220056374006485499977096599470454020828166226237857393450" +
                "73633900796776193057750674017632467360096895134053553745851666113422" +
                "37666786041621596804619144672918403005300575308490487653917113865916" +
                "46239524912623653881879636239373280423891018672348497668235089863388" +
                "58792562830275599565752445550725518931369083625477918694866799496832" +
                "40497058210285131854513962138377228261454376934125320985913276672363" +
                "28125001e-324",
                0x0000000000000001);

            CheckOneDouble("1.0e-99999999999999999999", 0.0);
            CheckOneDouble("0e-99999999999999999999", 0.0);
            CheckOneDouble("0e99999999999999999999", 0.0);
        }

        private static void TestRoundTripDouble(ulong bits)
        {
            double d = BitConverter.Int64BitsToDouble((long)bits);
            if (double.IsInfinity(d) || double.IsNaN(d)) return;
            string s = InvariantToString(d);
            CheckOneDouble(s, bits);
        }

        private static string InvariantToString(object o)
        {
            return string.Format(System.Globalization.CultureInfo.InvariantCulture, "{0:G17}", o);
        }

        private static void TestRoundTripDouble(double d)
        {
            string s = InvariantToString(d);
            CheckOneDouble(s, d);
        }

        private static void CheckOneDouble(string s, ulong expectedBits)
        {
            CheckOneDouble(s, BitConverter.Int64BitsToDouble((long)expectedBits));
        }

        private static void CheckOneDouble(string s, double expected)
        {
            double actual;
            if (!RealParser.TryParseDouble(s, out actual)) actual = 1.0 / 0.0;
            if (!actual.Equals(expected))
            {
                throw new Exception($@"
Error for double input ""{s}""
   expected {InvariantToString(expected)}
   actual {InvariantToString(actual)}");
            }
        }

        // ============ test some floats ============

        [Fact]
        public static void TestSpecificFloats()
        {
            CheckOneFloat(" 0.0", 0x00000000);

            // Verify the smallest denormals:
            for (uint i = 0x00000001; i != 0x00000100; ++i)
            {
                TestRoundTripFloat(i);
            }

            // Verify the largest denormals and the smallest normals:
            for (uint i = 0x007fff00; i != 0x00800100; ++i)
            {
                TestRoundTripFloat(i);
            }

            // Verify the largest normals:
            for (uint i = 0x7f7fff00; i != 0x7f800000; ++i)
            {
                TestRoundTripFloat(i);
            }

            // Verify all representable powers of two and nearby values:
            for (int i = -1022; i != 1023; ++i)
            {
                float f;
                try
                {
                    f = (float)Math.Pow(2.0, i);
                }
                catch (OverflowException)
                {
                    continue;
                }
                if (f == 0) continue;
                uint bits = FloatToInt32Bits(f);
                TestRoundTripFloat(bits - 1);
                TestRoundTripFloat(bits);
                TestRoundTripFloat(bits + 1);
            }

            // Verify all representable powers of ten and nearby values:
            for (int i = -50; i <= 40; ++i)
            {
                float f;
                try
                {
                    f = (float)Math.Pow(10.0, i);
                }
                catch (OverflowException)
                {
                    continue;
                }
                if (f == 0) continue;
                uint bits = FloatToInt32Bits(f);
                TestRoundTripFloat(bits - 1);
                TestRoundTripFloat(bits);
                TestRoundTripFloat(bits + 1);
            }

            TestRoundTripFloat((float)int.MaxValue);
            TestRoundTripFloat((float)uint.MaxValue);

            // Verify small and large exactly representable integers:
            CheckOneFloat("1", 0x3f800000);
            CheckOneFloat("2", 0x40000000);
            CheckOneFloat("3", 0x40400000);
            CheckOneFloat("4", 0x40800000);
            CheckOneFloat("5", 0x40A00000);
            CheckOneFloat("6", 0x40C00000);
            CheckOneFloat("7", 0x40E00000);
            CheckOneFloat("8", 0x41000000);
            CheckOneFloat("16777208", 0x4b7ffff8);
            CheckOneFloat("16777209", 0x4b7ffff9);
            CheckOneFloat("16777210", 0x4b7ffffa);
            CheckOneFloat("16777211", 0x4b7ffffb);
            CheckOneFloat("16777212", 0x4b7ffffc);
            CheckOneFloat("16777213", 0x4b7ffffd);
            CheckOneFloat("16777214", 0x4b7ffffe);
            CheckOneFloat("16777215", 0x4b7fffff); // 2^24 - 1    // Verify the smallest and largest denormal values:
            CheckOneFloat("1.4012984643248170e-45", 0x00000001);
            CheckOneFloat("2.8025969286496340e-45", 0x00000002);
            CheckOneFloat("4.2038953929744510e-45", 0x00000003);
            CheckOneFloat("5.6051938572992680e-45", 0x00000004);
            CheckOneFloat("7.0064923216240850e-45", 0x00000005);
            CheckOneFloat("8.4077907859489020e-45", 0x00000006);
            CheckOneFloat("9.8090892502737200e-45", 0x00000007);
            CheckOneFloat("1.1210387714598537e-44", 0x00000008);
            CheckOneFloat("1.2611686178923354e-44", 0x00000009);
            CheckOneFloat("1.4012984643248170e-44", 0x0000000a);
            CheckOneFloat("1.5414283107572988e-44", 0x0000000b);
            CheckOneFloat("1.6815581571897805e-44", 0x0000000c);
            CheckOneFloat("1.8216880036222622e-44", 0x0000000d);
            CheckOneFloat("1.9618178500547440e-44", 0x0000000e);
            CheckOneFloat("2.1019476964872256e-44", 0x0000000f);

            CheckOneFloat("1.1754921087447446e-38", 0x007ffff0);
            CheckOneFloat("1.1754922488745910e-38", 0x007ffff1);
            CheckOneFloat("1.1754923890044375e-38", 0x007ffff2);
            CheckOneFloat("1.1754925291342839e-38", 0x007ffff3);
            CheckOneFloat("1.1754926692641303e-38", 0x007ffff4);
            CheckOneFloat("1.1754928093939768e-38", 0x007ffff5);
            CheckOneFloat("1.1754929495238232e-38", 0x007ffff6);
            CheckOneFloat("1.1754930896536696e-38", 0x007ffff7);
            CheckOneFloat("1.1754932297835160e-38", 0x007ffff8);
            CheckOneFloat("1.1754933699133625e-38", 0x007ffff9);
            CheckOneFloat("1.1754935100432089e-38", 0x007ffffa);
            CheckOneFloat("1.1754936501730553e-38", 0x007ffffb);
            CheckOneFloat("1.1754937903029018e-38", 0x007ffffc);
            CheckOneFloat("1.1754939304327482e-38", 0x007ffffd);
            CheckOneFloat("1.1754940705625946e-38", 0x007ffffe);
            CheckOneFloat("1.1754942106924411e-38", 0x007fffff);

            // This number is exactly representable and should not be rounded in any
            // mode:
            // 0.1111111111111111111111100
            //                          ^
            CheckOneFloat("0.99999988079071044921875", 0x3f7ffffe);

            // This number is below the halfway point between two representable values
            // so it should round down in nearest mode:
            // 0.11111111111111111111111001
            //                          ^
            CheckOneFloat("0.99999989569187164306640625", 0x3f7ffffe);

            // This number is exactly halfway between two representable values, so it
            // should round to even in nearest mode:
            // 0.1111111111111111111111101
            //                          ^
            CheckOneFloat("0.9999999105930328369140625", 0x3f7ffffe);

            // This number is above the halfway point between two representable values
            // so it should round up in nearest mode:
            // 0.11111111111111111111111011
            //                          ^
            CheckOneFloat("0.99999992549419403076171875", 0x3f7fffff);
        }

        private static void TestRoundTripFloat(uint bits)
        {
            float d = Int32BitsToFloat(bits);
            if (float.IsInfinity(d) || float.IsNaN(d)) return;
            string s = InvariantToString(d);
            CheckOneFloat(s, bits);
        }

        private static void TestRoundTripFloat(float d)
        {
            string s = InvariantToString(d);
            if (s != "NaN" && s != "Infinity") CheckOneFloat(s, d);
        }

        private static void CheckOneFloat(string s, uint expectedBits)
        {
            CheckOneFloat(s, Int32BitsToFloat(expectedBits));
        }

        private static void CheckOneFloat(string s, float expected)
        {
            float actual;
            if (!RealParser.TryParseFloat(s, out actual)) actual = 1.0f / 0.0f;
            if (!actual.Equals(expected))
            {
                throw new Exception($@"Error for float input ""{s}""
   expected {InvariantToString(expected)}
   actual {InvariantToString(actual)}");
            }
        }

        private static uint FloatToInt32Bits(float f)
        {
            var bits = default(FloatUnion);
            bits.FloatData = f;
            return bits.IntData;
        }

        private static float Int32BitsToFloat(uint i)
        {
            var bits = default(FloatUnion);
            bits.IntData = i;
            return bits.FloatData;
        }

        [StructLayout(LayoutKind.Explicit)]
        private struct FloatUnion
        {
            [FieldOffset(0)]
            public uint IntData;
            [FieldOffset(0)]
            public float FloatData;
        }
    }
}