compute_boundaries()

template<typename FloatType >

boundaries nlohmann::detail::dtoa_impl::compute_boundaries

(

FloatType

value

)

Compute the (normalized) diyfp representing the input number 'value' and its boundaries.

Precondition

value must be finite and positive

Definition at line 15709 of file json.hpp.

{
    JSON_ASSERT(std::isfinite(value));
    JSON_ASSERT(value > 0);
    // Convert the IEEE representation into a diyfp.
    //
    // If v is denormal:
    //      value = 0.F * 2^(1 - bias) = (          F) * 2^(1 - bias - (p-1))
    // If v is normalized:
    //      value = 1.F * 2^(E - bias) = (2^(p-1) + F) * 2^(E - bias - (p-1))
    static_assert(std::numeric_limits<FloatType>::is_iec559,
                  "internal error: dtoa_short requires an IEEE-754 floating-point implementation");
    constexpr int      kPrecision = std::numeric_limits<FloatType>::digits; // = p (includes the hidden bit)
    constexpr int      kBias      = std::numeric_limits<FloatType>::max_exponent - 1 + (kPrecision - 1);
    constexpr int      kMinExp    = 1 - kBias;
    constexpr std::uint64_t kHiddenBit = std::uint64_t{1} << (kPrecision - 1); // = 2^(p-1)
    using bits_type = typename std::conditional<kPrecision == 24, std::uint32_t, std::uint64_t >::type;
    const auto bits = static_cast<std::uint64_t>(reinterpret_bits<bits_type>(value));
    const std::uint64_t E = bits >> (kPrecision - 1);
    const std::uint64_t F = bits & (kHiddenBit - 1);
    const bool is_denormal = E == 0;
    const diyfp v = is_denormal
                    ? diyfp(F, kMinExp)
                    : diyfp(F + kHiddenBit, static_cast<int>(E) - kBias);
    // Compute the boundaries m- and m+ of the floating-point value
    // v = f * 2^e.
    //
    // Determine v- and v+, the floating-point predecessor and successor if v,
    // respectively.
    //
    //      v- = v - 2^e        if f != 2^(p-1) or e == e_min                (A)
    //         = v - 2^(e-1)    if f == 2^(p-1) and e > e_min                (B)
    //
    //      v+ = v + 2^e
    //
    // Let m- = (v- + v) / 2 and m+ = (v + v+) / 2. All real numbers _strictly_
    // between m- and m+ round to v, regardless of how the input rounding
    // algorithm breaks ties.
    //
    //      ---+-------------+-------------+-------------+-------------+---  (A)
    //         v-            m-            v             m+            v+
    //
    //      -----------------+------+------+-------------+-------------+---  (B)
    //                       v-     m-     v             m+            v+
    const bool lower_boundary_is_closer = F == 0 && E > 1;
    const diyfp m_plus = diyfp(2 * v.f + 1, v.e - 1);
    const diyfp m_minus = lower_boundary_is_closer
                          ? diyfp(4 * v.f - 1, v.e - 2)  // (B)
                          : diyfp(2 * v.f - 1, v.e - 1); // (A)
    // Determine the normalized w+ = m+.
    const diyfp w_plus = diyfp::normalize(m_plus);
    // Determine w- = m- such that e_(w-) = e_(w+).
    const diyfp w_minus = diyfp::normalize_to(m_minus, w_plus.e);
    return {diyfp::normalize(v), w_minus, w_plus};
}