Function grisu2

examples/server/json.hpp:17611–17662

*/
JSON_HEDLEY_NON_NULL(1)
inline void grisu2(char* buf, int& len, int& decimal_exponent,
                   diyfp m_minus, diyfp v, diyfp m_plus)
{
    JSON_ASSERT(m_plus.e == m_minus.e);
    JSON_ASSERT(m_plus.e == v.e);

    //  --------(-----------------------+-----------------------)--------    (A)
    //          m-                      v                       m+
    //
    //  --------------------(-----------+-----------------------)--------    (B)
    //                      m-          v                       m+
    //
    // First scale v (and m- and m+) such that the exponent is in the range
    // [alpha, gamma].

    const cached_power cached = get_cached_power_for_binary_exponent(m_plus.e);

    const diyfp c_minus_k(cached.f, cached.e); // = c ~= 10^-k

    // The exponent of the products is = v.e + c_minus_k.e + q and is in the range [alpha,gamma]
    const diyfp w       = diyfp::mul(v,       c_minus_k);
    const diyfp w_minus = diyfp::mul(m_minus, c_minus_k);
    const diyfp w_plus  = diyfp::mul(m_plus,  c_minus_k);

    //  ----(---+---)---------------(---+---)---------------(---+---)----
    //          w-                      w                       w+
    //          = c*m-                  = c*v                   = c*m+
    //
    // diyfp::mul rounds its result and c_minus_k is approximated too. w, w- and
    // w+ are now off by a small amount.
    // In fact:
    //
    //      w - v * 10^k < 1 ulp
    //
    // To account for this inaccuracy, add resp. subtract 1 ulp.
    //
    //  --------+---[---------------(---+---)---------------]---+--------
    //          w-  M-                  w                   M+  w+
    //
    // Now any number in [M-, M+] (bounds included) will round to w when input,
    // regardless of how the input rounding algorithm breaks ties.
    //
    // And digit_gen generates the shortest possible such number in [M-, M+].
    // Note that this does not mean that Grisu2 always generates the shortest
    // possible number in the interval (m-, m+).
    const diyfp M_minus(w_minus.f + 1, w_minus.e);
    const diyfp M_plus (w_plus.f  - 1, w_plus.e );

    decimal_exponent = -cached.k; // = -(-k) = k

    grisu2_digit_gen(buf, len, decimal_exponent, M_minus, w, M_plus);
}

/*!
v = buf * 10^decimal_exponent