Function grisu2_digit_gen

Source/Utils/json.hpp:14920–15153

! Generates V = buffer * 10^decimal_exponent, such that M- <= V <= M+. M- and M+ must be normalized and share the same exponent -60 <= e <= -32. */

            M- and M+ must be normalized and share the same exponent -60 <= e <= -32.
            */
            inline void grisu2_digit_gen(char* buffer, int& length, int& decimal_exponent,
                diyfp M_minus, diyfp w, diyfp M_plus)
            {
                static_assert(kAlpha >= -60, "internal error");
                static_assert(kGamma <= -32, "internal error");

                // Generates the digits (and the exponent) of a decimal floating-point
                // number V = buffer * 10^decimal_exponent in the range [M-, M+]. The diyfp's
                // w, M- and M+ share the same exponent e, which satisfies alpha <= e <= gamma.
                //
                //               <--------------------------- delta ---->
                //                                  <---- dist --------->
                // --------------[------------------+-------------------]--------------
                //               M-                 w                   M+
                //
                // Grisu2 generates the digits of M+ from left to right and stops as soon as
                // V is in [M-,M+].

                JSON_ASSERT(M_plus.e >= kAlpha);
                JSON_ASSERT(M_plus.e <= kGamma);

                std::uint64_t delta = diyfp::sub(M_plus, M_minus).f; // (significand of (M+ - M-), implicit exponent is e)
                std::uint64_t dist = diyfp::sub(M_plus, w).f; // (significand of (M+ - w ), implicit exponent is e)

                // Split M+ = f * 2^e into two parts p1 and p2 (note: e < 0):
                //
                //      M+ = f * 2^e
                //         = ((f div 2^-e) * 2^-e + (f mod 2^-e)) * 2^e
                //         = ((p1        ) * 2^-e + (p2        )) * 2^e
                //         = p1 + p2 * 2^e

                const diyfp one(std::uint64_t{ 1 } << -M_plus.e, M_plus.e);

                auto p1 = static_cast<std::uint32_t>(M_plus.f >> -one.e); // p1 = f div 2^-e (Since -e >= 32, p1 fits into a 32-bit int.)
                std::uint64_t p2 = M_plus.f & (one.f - 1);                    // p2 = f mod 2^-e

                // 1)
                //
                // Generate the digits of the integral part p1 = d[n-1]...d[1]d[0]

                JSON_ASSERT(p1 > 0);

                std::uint32_t pow10;
                const int k = find_largest_pow10(p1, pow10);

                //      10^(k-1) <= p1 < 10^k, pow10 = 10^(k-1)
                //
                //      p1 = (p1 div 10^(k-1)) * 10^(k-1) + (p1 mod 10^(k-1))
                //         = (d[k-1]         ) * 10^(k-1) + (p1 mod 10^(k-1))
                //
                //      M+ = p1                                             + p2 * 2^e
                //         = d[k-1] * 10^(k-1) + (p1 mod 10^(k-1))          + p2 * 2^e
                //         = d[k-1] * 10^(k-1) + ((p1 mod 10^(k-1)) * 2^-e + p2) * 2^e
                //         = d[k-1] * 10^(k-1) + (                         rest) * 2^e
                //
                // Now generate the digits d[n] of p1 from left to right (n = k-1,...,0)
                //
                //      p1 = d[k-1]...d[n] * 10^n + d[n-1]...d[0]