// __ _____ _____ _____ // __| | __| | | | JSON for Modern C++ (supporting code) // | | |__ | | | | | | version 3.12.0 // |_____|_____|_____|_|___| https://github.com/nlohmann/json // // SPDX-FileCopyrightText: 2013-2026 Niels Lohmann // SPDX-License-Identifier: MIT #pragma once #include // array #include // uint32_t, uint64_t // Number tokens that are hard to round correctly, with the IEEE-754 binary64 // and binary32 bits of their correctly rounded values (ties to even; infinity // for an overflow, a signed zero for an underflow). // // For doubles and floats around 0, the smallest normal number, 1, 2^24, 2^53, // 0.1, and the largest finite number, and for random ones, the exact midpoint // m to the next number gives: m, m with one unit more and less in the last // digit, m with "01" and "0...01" appended, m with trailing zeros, and m cut // after 17 to 30 digits (rounded down and up, so that the rounding is decided // after the 19th digit), in fixed and exponent notation, 30% of them negative. // Tokens longer than 80 characters are left out, except for four of 700 digits // and more. Zeros, underflow, overflow, huge exponents, and integers beyond 64 // bits complete the set. Of the 508 tokens, 134 (as double) and 150 (as // float) need the exact comparison with the midpoint (detail::digit_comparison()). // // The expected bits were computed with exact rational arithmetic in Python // (fractions.Fraction) and cross-checked with Python's float(); strtod_l and // strtof_l of Apple's libc and of glibc agree. Generated by // compact_hard_cases.py 5 (with hard_cases.py), see the pull request that // added this file. namespace float_hard_cases { struct hard_case { const char* token; std::uint64_t bits64; std::uint32_t bits32; }; inline const std::array& cases() { static const std::array table = { { {"-2.4703282292062327e-324", 0x8000000000000000u, 0x80000000u}, {"24703282292062328e-340", 0x0000000000000001u, 0x00000000u}, {"247032822920623272e-341", 0x0000000000000000u, 0x00000000u}, {"-0.2470328229206232721e-323", 0x8000000000000001u, 0x80000000u}, {"-0.24703282292062327208e-323", 0x8000000000000000u, 0x80000000u}, {"-2.4703282292062327209e-324", 0x8000000000000001u, 0x80000000u}, {"2.47032822920623272088e-324", 0x0000000000000000u, 0x00000000u}, {"247032822920623272089e-344", 0x0000000000000001u, 0x00000000u}, {"-247032822920623272088284396434e-353", 0x8000000000000000u, 0x80000000u}, {"0.247032822920623272088284396435e-323", 0x0000000000000001u, 0x00000000u}, {"-74109846876186981e-340", 0x8000000000000001u, 0x80000000u}, {"0.74109846876186982e-323", 0x0000000000000002u, 0x00000000u}, {"-0.7410984687618698162e-323", 0x8000000000000001u, 0x80000000u}, {"-7.410984687618698163e-324", 0x8000000000000002u, 0x80000000u}, {"7.4109846876186981626e-324", 0x0000000000000001u, 0x00000000u}, {"-74109846876186981627e-343", 0x8000000000000002u, 0x80000000u}, {"-741098468761869816264e-344", 0x8000000000000001u, 0x80000000u}, {"0.741098468761869816265e-323", 0x0000000000000002u, 0x00000000u}, {"0.741098468761869816264853189302e-323", 0x0000000000000001u, 0x00000000u}, {"-7.41098468761869816264853189303e-324", 0x8000000000000002u, 0x80000000u}, {"0.22250738585072006e-307", 0x000FFFFFFFFFFFFEu, 0x00000000u}, {"2.2250738585072007e-308", 0x000FFFFFFFFFFFFFu, 0x00000000u}, {"2.225073858507200641e-308", 0x000FFFFFFFFFFFFEu, 0x00000000u}, {"-2225073858507200642e-326", 0x800FFFFFFFFFFFFFu, 0x80000000u}, {"22250738585072006419e-327", 0x000FFFFFFFFFFFFEu, 0x00000000u}, {"0.2225073858507200642e-307", 0x000FFFFFFFFFFFFFu, 0x00000000u}, {"0.222507385850720064199e-307", 0x000FFFFFFFFFFFFEu, 0x00000000u}, {"2.225073858507200642e-308", 0x000FFFFFFFFFFFFFu, 0x00000000u}, {"-2.22507385850720064199176395546e-308", 0x800FFFFFFFFFFFFEu, 0x80000000u}, {"222507385850720064199176395547e-337", 0x000FFFFFFFFFFFFFu, 0x00000000u}, {"-2.2250738585072011e-308", 0x800FFFFFFFFFFFFFu, 0x80000000u}, {"-22250738585072012e-324", 0x8010000000000000u, 0x80000000u}, {"-2225073858507201136e-326", 0x800FFFFFFFFFFFFFu, 0x80000000u}, {"0.2225073858507201137e-307", 0x0010000000000000u, 0x00000000u}, {"0.2225073858507201136e-307", 0x000FFFFFFFFFFFFFu, 0x00000000u}, {"-2.2250738585072011361e-308", 0x8010000000000000u, 0x80000000u}, {"2.22507385850720113605e-308", 0x000FFFFFFFFFFFFFu, 0x00000000u}, {"222507385850720113606e-328", 0x0010000000000000u, 0x00000000u}, {"22250738585072011360574097967e-336", 0x000FFFFFFFFFFFFFu, 0x00000000u}, {"0.222507385850720113605740979671e-307", 0x0010000000000000u, 0x00000000u}, {"22250738585072016e-324", 0x0010000000000000u, 0x00000000u}, {"0.22250738585072017e-307", 0x0010000000000001u, 0x00000000u}, {"0.222507385850720163e-307", 0x0010000000000000u, 0x00000000u}, {"2.225073858507201631e-308", 0x0010000000000001u, 0x00000000u}, {"-2.2250738585072016301e-308", 0x8010000000000000u, 0x80000000u}, {"22250738585072016302e-327", 0x0010000000000001u, 0x00000000u}, {"-222507385850720163012e-328", 0x8010000000000000u, 0x80000000u}, {"0.222507385850720163013e-307", 0x0010000000000001u, 0x00000000u}, {"0.222507385850720163012305563795e-307", 0x0010000000000000u, 0x00000000u}, {"-2.22507385850720163012305563796e-308", 0x8010000000000001u, 0x80000000u}, {"0.17976931348623156E+309", 0x7FEFFFFFFFFFFFFEu, 0x7F800000u}, {"1.7976931348623157e308", 0x7FEFFFFFFFFFFFFFu, 0x7F800000u}, {"1.797693134862315608e308", 0x7FEFFFFFFFFFFFFEu, 0x7F800000u}, {"-1797693134862315609e290", 0xFFEFFFFFFFFFFFFFu, 0xFF800000u}, {"-17976931348623156083e289", 0xFFEFFFFFFFFFFFFEu, 0xFF800000u}, {"-0.17976931348623156084E+309", 0xFFEFFFFFFFFFFFFFu, 0xFF800000u}, {"0.179769313486231560835E+309", 0x7FEFFFFFFFFFFFFEu, 0x7F800000u}, {"-1.79769313486231560836e308", 0xFFEFFFFFFFFFFFFFu, 0xFF800000u}, {"1.79769313486231560835325876058e308", 0x7FEFFFFFFFFFFFFEu, 0x7F800000u}, {"179769313486231560835325876059e279", 0x7FEFFFFFFFFFFFFFu, 0x7F800000u}, {"1.7976931348623158e308", 0x7FEFFFFFFFFFFFFFu, 0x7F800000u}, {"17976931348623159e292", 0x7FF0000000000000u, 0x7F800000u}, {"1797693134862315807e290", 0x7FEFFFFFFFFFFFFFu, 0x7F800000u}, {"0.1797693134862315808E+309", 0x7FF0000000000000u, 0x7F800000u}, {"0.17976931348623158079E+309", 0x7FEFFFFFFFFFFFFFu, 0x7F800000u}, {"-1.797693134862315808e308", 0xFFF0000000000000u, 0xFF800000u}, {"1.79769313486231580793e308", 0x7FEFFFFFFFFFFFFFu, 0x7F800000u}, {"179769313486231580794e288", 0x7FF0000000000000u, 0x7F800000u}, {"179769313486231580793728971405e279", 0x7FEFFFFFFFFFFFFFu, 0x7F800000u}, {"-0.179769313486231580793728971406E+309", 0xFFF0000000000000u, 0xFF800000u}, {"100000000000000011102230246251565404236316680908203125e-53", 0x3FF0000000000000u, 0x3F800000u}, {"-1.00000000000000011102230246251565404236316680908203126", 0xBFF0000000000001u, 0xBF800000u}, {"1.00000000000000011102230246251565404236316680908203124e0", 0x3FF0000000000000u, 0x3F800000u}, {"10000000000000001110223024625156540423631668090820312501e-55", 0x3FF0000000000001u, 0x3F800000u}, {"1.00000000000000011102230246251565404236316680908203125000000000000000000001", 0x3FF0000000000001u, 0x3F800000u}, {"10000000000000001e-16", 0x3FF0000000000000u, 0x3F800000u}, {"1.0000000000000002", 0x3FF0000000000001u, 0x3F800000u}, {"1.000000000000000111", 0x3FF0000000000000u, 0x3F800000u}, {"1.000000000000000112e0", 0x3FF0000000000001u, 0x3F800000u}, {"1.000000000000000111e0", 0x3FF0000000000000u, 0x3F800000u}, {"-10000000000000001111e-19", 0xBFF0000000000001u, 0xBF800000u}, {"-100000000000000011102e-20", 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{"99999999999999994448e-20", 0x3FEFFFFFFFFFFFFFu, 0x3F800000u}, {"-0.99999999999999994449", 0xBFF0000000000000u, 0xBF800000u}, {"0.999999999999999944488", 0x3FEFFFFFFFFFFFFFu, 0x3F800000u}, {"-9.99999999999999944489e-1", 0xBFF0000000000000u, 0xBF800000u}, {"9.99999999999999944488848768742e-1", 0x3FEFFFFFFFFFFFFFu, 0x3F800000u}, {"999999999999999944488848768743e-30", 0x3FF0000000000000u, 0x3F800000u}, {"-9.007199254740993e15", 0xC340000000000000u, 0xDA000000u}, {"9007199254740994e0", 0x4340000000000001u, 0x5A000000u}, {"9007199254740992", 0x4340000000000000u, 0x5A000000u}, {"9.00719925474099301e15", 0x4340000000000001u, 0x5A000000u}, {"9007199254740993000000000000000000001e-21", 0x4340000000000001u, 0x5A000000u}, {"-9007199254740993.000000000000000000000000000000", 0xC340000000000000u, 0xDA000000u}, {"90071992547409915e-1", 0x4340000000000000u, 0x5A000000u}, {"-9007199254740991.6", 0xC340000000000000u, 0xDA000000u}, {"9.0071992547409914e15", 0x433FFFFFFFFFFFFFu, 0x5A000000u}, {"-9007199254740991501e-3", 0xC340000000000000u, 0xDA000000u}, {"9007199254740991.5000000000000000000001", 0x4340000000000000u, 0x5A000000u}, {"9.0071992547409915000000000000000000000000000000e15", 0x4340000000000000u, 0x5A000000u}, {"0.100000000000000012490009027033011079765856266021728515625", 0x3FB999999999999Au, 0x3DCCCCCDu}, {"1.00000000000000012490009027033011079765856266021728515626e-1", 0x3FB999999999999Bu, 0x3DCCCCCDu}, {"100000000000000012490009027033011079765856266021728515624e-57", 0x3FB999999999999Au, 0x3DCCCCCDu}, {"0.10000000000000001249000902703301107976585626602172851562501", 0x3FB999999999999Bu, 0x3DCCCCCDu}, {"0.10000000000000001", 0x3FB999999999999Au, 0x3DCCCCCDu}, {"1.0000000000000002e-1", 0x3FB999999999999Bu, 0x3DCCCCCDu}, {"-1.000000000000000124e-1", 0xBFB999999999999Au, 0xBDCCCCCDu}, {"1000000000000000125e-19", 0x3FB999999999999Bu, 0x3DCCCCCDu}, {"-10000000000000001249e-20", 0xBFB999999999999Au, 0xBDCCCCCDu}, {"0.1000000000000000125", 0x3FB999999999999Bu, 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{"181510327827821147441e-11", 0x41DB0C11CB91CE37u, 0x4ED8608Eu}, {"1815103278.27821147442", 0x41DB0C11CB91CE38u, 0x4ED8608Eu}, {"1815103278.27821147441864013671", 0x41DB0C11CB91CE37u, 0x4ED8608Eu}, {"1.81510327827821147441864013672e9", 0x41DB0C11CB91CE38u, 0x4ED8608Eu}, {"3809325632181785344", 0x43CA6EB8BD69FE2Au, 0x5E5375C6u}, {"3.809325632181785345e18", 0x43CA6EB8BD69FE2Au, 0x5E5375C6u}, {"3809325632181785343e0", 0x43CA6EB8BD69FE29u, 0x5E5375C6u}, {"3809325632181785344.01", 0x43CA6EB8BD69FE2Au, 0x5E5375C6u}, {"3.809325632181785344000000000000000000001e18", 0x43CA6EB8BD69FE2Au, 0x5E5375C6u}, {"3809325632181785344000000000000000000000000000000e-30", 0x43CA6EB8BD69FE2Au, 0x5E5375C6u}, {"3809325632181785300", 0x43CA6EB8BD69FE29u, 0x5E5375C6u}, {"3.8093256321817854e18", 0x43CA6EB8BD69FE2Au, 0x5E5375C6u}, {"4.046966549916366943359375e12", 0x428D7210076CE2F0u, 0x546B9080u}, {"4046966549916366943359376e-12", 0x428D7210076CE2F0u, 0x546B9080u}, {"4046966549916.366943359374", 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{"18446744073709551616", 0x43F0000000000000u, 0x5F800000u}, {"-9223372036854775808", 0xC3E0000000000000u, 0xDF000000u}, {"-9223372036854775809", 0xC3E0000000000000u, 0xDF000000u}, } }; return table; } } // namespace float_hard_cases