Incorrect division for values near zero.

[libbooze]

I am not certain what rounding can be done here, but I am pretty sure this is incorrect behavior and final result should be zero.

I have modified the library to make functions to get sig and exp public, no changes to library beside that. This was not necessary needed, but
I wanted to show issues is not just in printing.

code:

template<typename Dec>
void div_tiny()
{
    const auto display = [](const auto& val)
    {
        std::print("{:.40e}\n", val);
        if constexpr (boost::decimal::detail::impl::decimal_val_v<Dec> >= 128)
        {
            std::print("{}|{}  {}\n", val.full_significand().high, val.full_significand().low, val.biased_exponent());
        }
        else
        if constexpr(boost::decimal::detail::is_decimal_floating_point_v<Dec>)
        {
            std::print("{}  {}\n", val.full_significand(), val.biased_exponent());
        }
    };
    std::print("{}\n", boost::typeindex::type_id<Dec>().pretty_name());
    std::print("denorm_min: {:.20e}\n", std::numeric_limits<Dec>::denorm_min());
    const auto tiny = std::numeric_limits<Dec>::denorm_min() * Dec{7.0};
    display(tiny);
    const auto tiny2 = tiny/ Dec{2.0};
    display(tiny2);
    const auto tiny3 = tiny2/ Dec{3.0};
    display(tiny3);
    const auto tiny4 = tiny3/ Dec{5.0};
    display(tiny4);
    std::print("is zero {}\n\n", tiny4 == Dec{0.0});
}

float
denorm_min: 1.40129846432481707092e-45
9.8090892502737194964661070830294129189618e-45
5.6051938572992682836949183331596645251210e-45
1.4012984643248170709237295832899161312803e-45
0.0000000000000000000000000000000000000000e+00
is zero true

double
denorm_min: 4.94065645841246544177e-324
3.4584595208887258092359815500775496065554e-323
1.9762625833649861767062751714728854894602e-323
4.9406564584124654417656879286822137236506e-324
0.0000000000000000000000000000000000000000e+00
is zero true

boost::decimal::decimal32
denorm_min: 1.00000000000000000000e-101
inf
8388608  91
inf
8388608  91
inf
8388608  91
inf
8388608  91
is zero false

boost::decimal::decimal32_fast
denorm_min: 1.00000000000000000000e-95
7.0000000000000000000000000000000000000000e-95
7000000  -101
3.5000000000000000000000000000000000000000e-95
3500000  -101
1.1666670000000000000000000000000000000000e-95
1166667  -101
inf
18446744073709551615  -101
is zero false

boost::decimal::decimal64
denorm_min: 1.00000000000000000000e-398
inf
9007199254740992  370
inf
9007199254740992  370
inf
9007199254740992  370
inf
9007199254740992  370
is zero false

boost::decimal::decimal64_fast
denorm_min: 1.00000000000000000000e-383
7.0000000000000000000000000000000000000000e-383
7000000000000000  -398
3.5000000000000000000000000000000000000000e-383
3500000000000000  -398
1.1666666666666670000000000000000000000000e-383
1166666666666667  -398
inf
18446744073709551615  -398
is zero false

boost::decimal::decimal128
denorm_min: 1.00000000000000000000e-6176
7.0000000000000000000000000000000000000000e-6176
0|7  -6176
0.0000000000000000000000000000000000000000e+00
0|0  0
0.0000000000000000000000000000000000000000e+00
0|0  0
0.0000000000000000000000000000000000000000e+00
0|0  0
is zero true

boost::decimal::decimal128_fast
denorm_min: 1.00000000000000000000e-6143
7.0000000000000000000000000000000000000000e-6143
379470760369926|10180806172248899584  -6176
3.5000000000000000000000000000000000000000e-6143
189735380184963|5090403086124449792  -6176
1.1666666666666666666666666666666670000000e-6143
63245126728321|1696801028708149931  -6176
inf
18446744073709551613|18446744073709551615  -6176
is zero false

Although decimal128 prints is zero true I still believe it's division behavior is incorrect since it should not go to 0 after first division.

[mborland]

The fast types don't support denorms (https://github.com/cppalliance/decimal/blob/develop/include/boost/decimal/decimal32_fast.hpp#L1463) so we return min by convention: https://en.cppreference.com/w/cpp/types/numeric_limits/denorm_min. I'll look at other cases.

[libbooze]

The fast types don't support denorms (https://github.com/cppalliance/decimal/blob/develop/include/boost/decimal/decimal32_fast.hpp#L1463) so we return min by convention: https://en.cppreference.com/w/cpp/types/numeric_limits/denorm_min. I'll look at other cases.

Use of denorm_min is just to get tiny number. I could have manually constructed it but I think this way test is clearer. I believe bug is that end state of computation should be 0 in all cases.