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json/tests/src/float_hard_cases.hpp
Niels Lohmann b0db8653b6 Convert float and double with the library's own correctly rounded parser 
float, double, and long double where it is IEEE-754 binary64 (MSVC, Apple
arm64) are now converted by the library itself, correctly rounded and
independent of the locale and of the C and C++ libraries:

- The token is split into sign, significand w (at most 19 digits), and
  decimal exponent q, using the positions of the decimal point and the
  exponent that the scanners already recorded, so no character is
  classified again.
- Clinger's fast path where w and 10^|q| are exact.
- Eisel-Lemire otherwise, now templated for binary32 and binary64.
- For tokens with more than 19 digits whose w and w + 1 round differently,
  an exact big-integer comparison with the midpoint between the two
  candidates (the digit comparison of fast_float, simplified).

This replaces the separate token walks of Clinger's fast path and of
Eisel-Lemire, the significant-digit gate that avoided the former, and, for
float and double, std::from_chars and the locale-aware strtod. std::from_chars
and strtold remain only for other long double formats (x87, binary128,
double-double) and for types that are not IEEE-754. Values are bit-identical
to before wherever the previous conversion was correctly rounded; tokens
converted in a locale with a multi-byte decimal point are now also exact.
Overflow still gives out_of_range.406, underflow a signed zero.

convert_float() is the entry point for other parsers of JSON text: it
converts like the lexer, without allocation for binary32/binary64.

Tests: exact-bit tests for double and float (ties, subnormal and overflow
boundaries, huge exponents, more digits than any midpoint), Eisel-Lemire for
binary32, the round trips of 200,000 doubles and 100,000 floats without
declines, 508 generated hard cases with the expected bits of both formats
(float_hard_cases.hpp) through the converter and both scanners, and
JSON-level overflow/underflow checks for double and float. The locale tests
now check the values in a locale with a multi-byte decimal point.

Docs: the statements that parsing uses strtod/strtof/strtold; the fast_float
credit now names the digit comparison.

Signed-off-by: Niels Lohmann <mail@nlohmann.me>
2026-09-30 14:55:08 +02:00

600 lines
46 KiB
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// __ _____ _____ _____
// __| | __| | | | JSON for Modern C++ (supporting code)
// | | |__ | | | | | | version 3.12.0
// |_____|_____|_____|_|___| https://github.com/nlohmann/json
//
// SPDX-FileCopyrightText: 2013-2026 Niels Lohmann <https://nlohmann.me>
// SPDX-License-Identifier: MIT
#pragma once
#include <array> // array
#include <cstdint> // 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<hard_case, 508>& cases()
{
static const std::array<hard_case, 508> 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", 0xBFF0000000000000u, 0xBF800000u},
{"-1.00000000000000011103", 0xBFF0000000000001u, 0xBF800000u},
{"1.00000000000000011102230246251", 0x3FF0000000000000u, 0x3F800000u},
{"1.00000000000000011102230246252e0", 0x3FF0000000000001u, 0x3F800000u},
{"-0.999999999999999944488848768742172978818416595458984375", 0xBFF0000000000000u, 0xBF800000u},
{"-9.99999999999999944488848768742172978818416595458984376e-1", 0xBFF0000000000000u, 0xBF800000u},
{"999999999999999944488848768742172978818416595458984374e-54", 0x3FEFFFFFFFFFFFFFu, 0x3F800000u},
{"0.99999999999999994448884876874217297881841659545898437501", 0x3FF0000000000000u, 0x3F800000u},
{"9.99999999999999944488848768742172978818416595458984375000000000000000000001e-1", 0x3FF0000000000000u, 0x3F800000u},
{"-0.99999999999999994", 0xBFEFFFFFFFFFFFFFu, 0xBF800000u},
{"9.9999999999999995e-1", 0x3FF0000000000000u, 0x3F800000u},
{"9.999999999999999444e-1", 0x3FEFFFFFFFFFFFFFu, 0x3F800000u},
{"9999999999999999445e-19", 0x3FF0000000000000u, 0x3F800000u},
{"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, 0x3DCCCCCDu},
{"0.10000000000000001249", 0x3FB999999999999Au, 0x3DCCCCCDu},
{"1.00000000000000012491e-1", 0x3FB999999999999Bu, 0x3DCCCCCDu},
{"1.00000000000000012490009027033e-1", 0x3FB999999999999Au, 0x3DCCCCCDu},
{"100000000000000012490009027034e-30", 0x3FB999999999999Bu, 0x3DCCCCCDu},
{"2.45134755833537796875e14", 0x42EBDE5C4164D83Au, 0x575EF2E2u},
{"-245134755833537796876e-6", 0xC2EBDE5C4164D83Au, 0xD75EF2E2u},
{"-245134755833537.796874", 0xC2EBDE5C4164D839u, 0xD75EF2E2u},
{"2.4513475583353779687501e14", 0x42EBDE5C4164D83Au, 0x575EF2E2u},
{"245134755833537796875000000000000000000001e-27", 0x42EBDE5C4164D83Au, 0x575EF2E2u},
{"245134755833537.796875000000000000000000000000000000", 0x42EBDE5C4164D83Au, 0x575EF2E2u},
{"2.4513475583353779e14", 0x42EBDE5C4164D839u, 0x575EF2E2u},
{"2451347558335378e-1", 0x42EBDE5C4164D83Au, 0x575EF2E2u},
{"2451347558335377968e-4", 0x42EBDE5C4164D839u, 0x575EF2E2u},
{"245134755833537.7969", 0x42EBDE5C4164D83Au, 0x575EF2E2u},
{"245134755833537.79687", 0x42EBDE5C4164D839u, 0x575EF2E2u},
{"2.4513475583353779688e14", 0x42EBDE5C4164D83Au, 0x575EF2E2u},
{"181510327827821147441864013671875e-23", 0x41DB0C11CB91CE38u, 0x4ED8608Eu},
{"-1815103278.27821147441864013671876", 0xC1DB0C11CB91CE38u, 0xCED8608Eu},
{"1.81510327827821147441864013671874e9", 0x41DB0C11CB91CE37u, 0x4ED8608Eu},
{"18151032782782114744186401367187501e-25", 0x41DB0C11CB91CE38u, 0x4ED8608Eu},
{"1815103278.27821147441864013671875000000000000000000001", 0x41DB0C11CB91CE38u, 0x4ED8608Eu},
{"-1.81510327827821147441864013671875000000000000000000000000000000e9", 0xC1DB0C11CB91CE38u, 0xCED8608Eu},
{"18151032782782114e-7", 0x41DB0C11CB91CE37u, 0x4ED8608Eu},
{"1815103278.2782115", 0x41DB0C11CB91CE38u, 0x4ED8608Eu},
{"1815103278.278211474", 0x41DB0C11CB91CE37u, 0x4ED8608Eu},
{"-1.815103278278211475e9", 0xC1DB0C11CB91CE38u, 0xCED8608Eu},
{"1.8151032782782114744e9", 0x41DB0C11CB91CE37u, 0x4ED8608Eu},
{"-18151032782782114745e-10", 0xC1DB0C11CB91CE38u, 0xCED8608Eu},
{"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", 0x428D7210076CE2EFu, 0x546B9080u},
{"4.04696654991636694335937501e12", 0x428D7210076CE2F0u, 0x546B9080u},
{"4046966549916366943359375000000000000000000001e-33", 0x428D7210076CE2F0u, 0x546B9080u},
{"-4046966549916.366943359375000000000000000000000000000000", 0xC28D7210076CE2F0u, 0xD46B9080u},
{"4.0469665499163669e12", 0x428D7210076CE2EFu, 0x546B9080u},
{"4046966549916367e-3", 0x428D7210076CE2F0u, 0x546B9080u},
{"4046966549916366943e-6", 0x428D7210076CE2EFu, 0x546B9080u},
{"4046966549916.366944", 0x428D7210076CE2F0u, 0x546B9080u},
{"4046966549916.3669433", 0x428D7210076CE2EFu, 0x546B9080u},
{"4.0469665499163669434e12", 0x428D7210076CE2F0u, 0x546B9080u},
{"-4.04696654991636694335e12", 0xC28D7210076CE2EFu, 0xD46B9080u},
{"404696654991636694336e-8", 0x428D7210076CE2F0u, 0x546B9080u},
{"28093802557000874e154", 0x63529C3B77330BDBu, 0x7F800000u},
{"0.28093802557000875E+171", 0x63529C3B77330BDCu, 0x7F800000u},
{"0.2809380255700087447E+171", 0x63529C3B77330BDBu, 0x7F800000u},
{"2.809380255700087448e170", 0x63529C3B77330BDCu, 0x7F800000u},
{"2.8093802557000874472e170", 0x63529C3B77330BDBu, 0x7F800000u},
{"28093802557000874473e151", 0x63529C3B77330BDCu, 0x7F800000u},
{"280938025570008744728e150", 0x63529C3B77330BDBu, 0x7F800000u},
{"-0.280938025570008744729E+171", 0xE3529C3B77330BDCu, 0xFF800000u},
{"-0.280938025570008744728403667979E+171", 0xE3529C3B77330BDBu, 0xFF800000u},
{"2.8093802557000874472840366798e170", 0x63529C3B77330BDCu, 0x7F800000u},
{"0.39523280297734525e-154", 0x1FE0F51BF17FD374u, 0x00000000u},
{"-3.9523280297734526e-155", 0x9FE0F51BF17FD375u, 0x80000000u},
{"3.952328029773452547e-155", 0x1FE0F51BF17FD374u, 0x00000000u},
{"3952328029773452548e-173", 0x1FE0F51BF17FD375u, 0x00000000u},
{"-39523280297734525478e-174", 0x9FE0F51BF17FD374u, 0x80000000u},
{"0.39523280297734525479e-154", 0x1FE0F51BF17FD375u, 0x00000000u},
{"-0.395232802977345254787e-154", 0x9FE0F51BF17FD374u, 0x80000000u},
{"-3.95232802977345254788e-155", 0x9FE0F51BF17FD375u, 0x80000000u},
{"-3.95232802977345254787245825501e-155", 0x9FE0F51BF17FD374u, 0x80000000u},
{"395232802977345254787245825502e-184", 0x1FE0F51BF17FD375u, 0x00000000u},
{"-1.0790205420931879e-276", 0x86A3209CA6233255u, 0x80000000u},
{"-1079020542093188e-291", 0x86A3209CA6233256u, 0x80000000u},
{"-1079020542093187947e-294", 0x86A3209CA6233255u, 0x80000000u},
{"0.1079020542093187948e-275", 0x06A3209CA6233256u, 0x00000000u},
{"0.1079020542093187947e-275", 0x06A3209CA6233255u, 0x00000000u},
{"1.0790205420931879471e-276", 0x06A3209CA6233256u, 0x00000000u},
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{"1801462723903300515698039374612449137202929705381393432617187501e-79", 0x3CA9F63970000000u, 0x254FB1CCu},
{"18014627239033005e-32", 0x3CA9F63970000000u, 0x254FB1CBu},
{"0.00000000000000018014627239033006", 0x3CA9F63970000000u, 0x254FB1CCu},
{"0.0000000000000001801462723903300515", 0x3CA9F63970000000u, 0x254FB1CBu},
{"-1.801462723903300516e-16", 0xBCA9F63970000000u, 0xA54FB1CCu},
{"-1.8014627239033005156e-16", 0xBCA9F63970000000u, 0xA54FB1CBu},
{"18014627239033005157e-35", 0x3CA9F63970000000u, 0x254FB1CCu},
{"180146272390330051569e-36", 0x3CA9F63970000000u, 0x254FB1CBu},
{"-0.00000000000000018014627239033005157", 0xBCA9F63970000000u, 0xA54FB1CCu},
{"0.000000000000000180146272390330051569803937461", 0x3CA9F63970000000u, 0x254FB1CBu},
{"1.80146272390330051569803937462e-16", 0x3CA9F63970000000u, 0x254FB1CCu},
{"0.05534819327294826507568359375", 0x3FAC569930000000u, 0x3D62B4CAu},
{"-5.534819327294826507568359376e-2", 0xBFAC569930000000u, 0xBD62B4CAu},
{"5534819327294826507568359374e-29", 0x3FAC569930000000u, 0x3D62B4C9u},
{"-0.0553481932729482650756835937501", 0xBFAC569930000000u, 0xBD62B4CAu},
{"5.534819327294826507568359375000000000000000000001e-2", 0x3FAC569930000000u, 0x3D62B4CAu},
{"5534819327294826507568359375000000000000000000000000000000e-59", 0x3FAC569930000000u, 0x3D62B4CAu},
{"0.055348193272948265", 0x3FAC569930000000u, 0x3D62B4C9u},
{"5.5348193272948266e-2", 0x3FAC569930000000u, 0x3D62B4CAu},
{"5.534819327294826507e-2", 0x3FAC569930000000u, 0x3D62B4C9u},
{"5534819327294826508e-20", 0x3FAC569930000000u, 0x3D62B4CAu},
{"55348193272948265075e-21", 0x3FAC569930000000u, 0x3D62B4C9u},
{"-0.055348193272948265076", 0xBFAC569930000000u, 0xBD62B4CAu},
{"0.0553481932729482650756", 0x3FAC569930000000u, 0x3D62B4C9u},
{"-5.53481932729482650757e-2", 0xBFAC569930000000u, 0xBD62B4CAu},
{"5.179692133247783258005389047985340416e36", 0x478F2C9450000000u, 0x7C7964A2u},
{"5179692133247783258005389047985340417e0", 0x478F2C9450000000u, 0x7C7964A3u},
{"5179692133247783258005389047985340415", 0x478F2C9450000000u, 0x7C7964A2u},
{"-5.17969213324778325800538904798534041601e36", 0xC78F2C9450000000u, 0xFC7964A3u},
{"-5179692133247783258005389047985340416000000000000000000001e-21", 0xC78F2C9450000000u, 0xFC7964A3u},
{"-5179692133247783258005389047985340416.000000000000000000000000000000", 0xC78F2C9450000000u, 0xFC7964A2u},
{"5.1796921332477832e36", 0x478F2C9450000000u, 0x7C7964A2u},
{"51796921332477833e20", 0x478F2C9450000000u, 0x7C7964A3u},
{"-5179692133247783258e18", 0xC78F2C9450000000u, 0xFC7964A2u},
{"5179692133247783259000000000000000000", 0x478F2C9450000000u, 0x7C7964A3u},
{"5179692133247783258000000000000000000", 0x478F2C9450000000u, 0x7C7964A2u},
{"5.1796921332477832581e36", 0x478F2C9450000000u, 0x7C7964A3u},
{"-5.179692133247783258e36", 0xC78F2C9450000000u, 0xFC7964A2u},
{"-517969213324778325801e16", 0xC78F2C9450000000u, 0xFC7964A3u},
{"517969213324778325800538904798e7", 0x478F2C9450000000u, 0x7C7964A2u},
{"5179692133247783258005389047990000000", 0x478F2C9450000000u, 0x7C7964A3u},
{
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"8791414915891303962110687008643869459464552765720740782062174337998814106326732925355228688137214901"
"2981122451451889849057222307285255133155755015914397476397983411801999323962548289017107081850690630"
"6666559949382757725720157630626906633326475653000092458883164330377797918696120494973903778297049050"
"5108060994073026293712895895000358379996720725430436028407889577179615094551674824347103070260914462"
"1572289880258182545180325707018860872113128079512233426288368622321503775666622503982534335974568884"
"4239002654981983854879482922068947216898310996983658468140228542433306603398508864458040010349339704"
"2756718644338377048603786162277173854562306587467901408672332763671875e-307", 0x0010000000000000u, 0x00000000u
},
{
"2.22507385850720113605740979670913197593481954635164564802342610972482222202107694551652952390813508"
"7914149158913039621106870086438694594645527657207407820621743379988141063267329253552286881372149012"
"9811224514518898490572223072852551331557550159143974763979834118019993239625482890171070818506906306"
"6665599493827577257201576306269066333264756530000924588831643303777979186961204949739037782970490505"
"1080609940730262937128958950003583799967207254304360284078895771796150945516748243471030702609144621"
"5722898802581825451803257070188608721131280795122334262883686223215037756666225039825343359745688844"
"2390026549819838548794829220689472168983109969836584681402285424333066033985088644580400103493397042"
"756718644338377048603786162277173854562306587467901408672332763671875000000000000000000001e-308", 0x0010000000000000u, 0x00000000u
},
{
"0.11754942807573642917278829910357665133228589927589904276829631184250030649651730385585324256680905"
"8189392089843750000000000000000000000000000000000000000000000000000000000000000000000000000000000000"
"0000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000"
"0000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000"
"0000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000"
"0000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000"
"0000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000"
"00000000000000000000000000000000000000000000000000000000000000000e-37", 0x380FFFFFE0000000u, 0x00800000u
},
{
"1175494280757364291727882991035766513322858992758990427682963118425003064965173038558532425668090581"
"8939208984375000000000000000000000000000000000000000000000000000000000000000000000000000000000000000"
"0000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000"
"0000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000"
"0000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000"
"0000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000"
"0000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000"
"00000000000001e-751", 0x380FFFFFE0000000u, 0x00800000u
},
{"0", 0x0000000000000000u, 0x00000000u},
{"-0", 0x8000000000000000u, 0x80000000u},
{"0.0", 0x0000000000000000u, 0x00000000u},
{"-0.0", 0x8000000000000000u, 0x80000000u},
{"0e999999999999999999999", 0x0000000000000000u, 0x00000000u},
{"-0.000e-99999", 0x8000000000000000u, 0x80000000u},
{"1e-400", 0x0000000000000000u, 0x00000000u},
{"-1e-400", 0x8000000000000000u, 0x80000000u},
{"1e400", 0x7FF0000000000000u, 0x7F800000u},
{"-1e400", 0xFFF0000000000000u, 0xFF800000u},
{"1e-50", 0x358DEE7A4AD4B81Fu, 0x00000000u},
{"-1e-50", 0xB58DEE7A4AD4B81Fu, 0x80000000u},
{"1e39", 0x48078287F49C4A1Du, 0x7F800000u},
{"-1e39", 0xC8078287F49C4A1Du, 0xFF800000u},
{"1e99999999999999999999999999", 0x7FF0000000000000u, 0x7F800000u},
{"1e-99999999999999999999999999", 0x0000000000000000u, 0x00000000u},
{"1e0000000000000000000000000000000000000000308", 0x7FE1CCF385EBC8A0u, 0x7F800000u},
{"123456789012345678901234567890e-30", 0x3FBF9ADD3746F65Fu, 0x3DFCD6EAu},
{"18446744073709551615", 0x43F0000000000000u, 0x5F800000u},
{"18446744073709551616", 0x43F0000000000000u, 0x5F800000u},
{"-9223372036854775808", 0xC3E0000000000000u, 0xDF000000u},
{"-9223372036854775809", 0xC3E0000000000000u, 0xDF000000u},
}
};
return table;
}
} // namespace float_hard_cases
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