path: root/include/jsoncons_ext/bson/bson_decimal128.hpp

#ifndef JSONCONS_BSON_BSON_DECIMAL128_HPP
#define JSONCONS_BSON_BSON_DECIMAL128_HPP

/*
 *  Implements decimal128_to_chars and decimal128_from_chars
 *  
 *  Based on the libjson functions bson_decimal128_to_string
 *  and bson_decimal128_from_string_w_len, available at
 *  https://github.com/mongodb/mongo-c-driver/blob/master/src/libbson/src/bson/bson-decimal128.h
 *  and https://github.com/mongodb/mongo-c-driver/blob/master/src/libbson/src/bson/bson-decimal128.c
 *  
*/

/*
 * Copyright 2015 MongoDB, Inc.
 *
 * Licensed under the Apache License, Version 2.0 (the "License");
 * you may not use this file except in compliance with the License.
 * You may obtain a copy of the License at
 *
 *   http://www.apache.org/licenses/LICENSE-2.0
 *
 * Unless required by applicable law or agreed to in writing, software
 * distributed under the License is distributed on an "AS IS" BASIS,
 * WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
 * See the License for the specific language governing permissions and
 * limitations under the License.
 */

#include <stdlib.h>
#include <string.h>
#include <cstring>
#include <ctype.h>
#include <system_error>
#include <algorithm>
#include <jsoncons/config/jsoncons_config.hpp>

namespace jsoncons { namespace bson {

    struct decimal128_to_chars_result 
    {
        char* ptr;
        std::errc ec;
    };

    struct decimal128_from_chars_result 
    {
        const char* ptr;
        std::errc ec;
    };

/**
 * BSON_DECIMAL128_STRING:
 *
 * The length of a decimal128 string (with null terminator).
 *
 * 1  for the sign
 * 35 for digits and radix
 * 2  for exponent indicator and sign
 * 4  for exponent digits
 */
#define BSON_DECIMAL128_STRING 43

    struct TP1 
    { 
        uint64_t low; 
        uint64_t high; 

        constexpr TP1() : low(0), high(0) {}
        constexpr TP1(uint64_t hi, uint64_t lo) : low(lo), high(hi) {}
    };
    struct TP2 
    { 
        uint64_t high; 
        uint64_t low; 

        constexpr TP2() : high(0), low(0) {}
        constexpr TP2(uint64_t hi, uint64_t lo) : high(hi), low(lo) {}
    };

    typedef std::conditional<
        jsoncons::endian::native == jsoncons::endian::little,
        TP1,
        TP2
    >::type decimal128_t;

    inline
    bool operator==(const decimal128_t& lhs, const decimal128_t& rhs)
    {
       return lhs.high == rhs.high && lhs.low == rhs.low;
    }   

    inline
    bool operator!=(const decimal128_t& lhs, const decimal128_t& rhs)
    {
       return !(lhs == rhs);
    }   

    struct decimal128_limits
    {
        // The length of a decimal128 string (without null terminator).
        //
        // 1  for the sign
        // 35 for digits and radix
        // 2  for exponent indicator and sign
        // 4  for exponent digits
        static constexpr int buf_size = 42;  
        static constexpr int exponent_max = 6111;
        static constexpr int exponent_min = -6176;
        static constexpr int exponent_bias = 6176;
        static constexpr int max_digits = 34;

        static constexpr decimal128_t nan() {return decimal128_t(0x7c00000000000000ull, 0);}
        static constexpr decimal128_t infinity() {return decimal128_t(0x7800000000000000ull, 0);}
        static constexpr decimal128_t neg_infinity() {return decimal128_t(0x7800000000000000ull + 0x8000000000000000ull, 0);}
    };

    inline
    bool is_nan(decimal128_t dec) { return dec == decimal128_limits::nan(); }

    inline
    bool is_inf(decimal128_t dec) { return dec == decimal128_limits::infinity(); }

    inline
    bool is_neg_inf(decimal128_t dec) { return dec == decimal128_limits::neg_infinity(); }

    /**
     * bson_uint128_t:
     *
     * This struct represents a 128 bit integer.
     */
    typedef struct {
       uint32_t parts[4]; /* 32-bit words stored high to low. */
    } bson_uint128_t;

    typedef struct {
       uint64_t high, low;
    } bson_uint128_6464_t;

    namespace detail {
    
        /**
         *------------------------------------------------------------------------------
         *
         * bson_uint128_divide1B --
         *
         *    This function divides a #bson_uint128_t by 1000000000 (1 billion) and
         *    computes the quotient and remainder.
         *
         *    The remainder will contain 9 decimal digits for conversion to string.
         *
         * @value     The #bson_uint128_t operand.
         * @quotient  A pointer to store the #bson_uint128_t quotient.
         * @rem       A pointer to store the #uint64_t remainder.
         *
         * Returns:
         *    The quotient at @quotient and the remainder at @rem.
         *
         * Side effects:
         *    None.
         *
         *------------------------------------------------------------------------------
         */

        inline
        void bson_uint128_divide1B (bson_uint128_t value,     /* IN */
                                     bson_uint128_t *quotient, /* OUT */
                                     uint32_t *rem)             /* OUT */
        {
            const uint32_t DIVISOR = 1000 * 1000 * 1000;
            uint64_t _rem = 0;
            int i = 0;
            
            if (!value.parts[0] && !value.parts[1] && !value.parts[2] &&
                !value.parts[3]) {
               *quotient = value;
               *rem = 0;
               return;
            }
            
            for (i = 0; i <= 3; i++) {
               _rem <<= 32; /* Adjust remainder to match value of next dividend */
               _rem += value.parts[i]; /* Add the divided to _rem */
               value.parts[i] = (uint32_t) (_rem / DIVISOR);
               _rem %= DIVISOR; /* Store the remainder */
            }
            
            *quotient = value;
            *rem = (uint32_t) _rem;
        }

        /**
         *-------------------------------------------------------------------------
         *
         * mul64x64 --
         *
         *    This function multiplies two &uint64_t into a &bson_uint128_6464_t.
         *
         * Returns:
         *    The product of @left and @right.
         *
         * Side Effects:
         *    None.
         *
         *-------------------------------------------------------------------------
         */

        inline
        void mul_64x64 (uint64_t left,                 /* IN */
                        uint64_t right,                /* IN */
                        bson_uint128_6464_t *product) /* OUT */
        {
            uint64_t left_high, left_low, right_high, right_low, product_high,
               product_mid, product_mid2, product_low;
            bson_uint128_6464_t rt = {0,0};
 
            if (!left && !right) {
               *product = rt;
               return;
            }
 
            left_high = left >> 32;
            left_low = (uint32_t) left;
            right_high = right >> 32;
            right_low = (uint32_t) right;
 
            product_high = left_high * right_high;
            product_mid = left_high * right_low;
            product_mid2 = left_low * right_high;
            product_low = left_low * right_low;
 
            product_high += product_mid >> 32;
            product_mid = (uint32_t) product_mid + product_mid2 + (product_low >> 32);
 
            product_high = product_high + (product_mid >> 32);
            product_low = (product_mid << 32) + (uint32_t) product_low;
 
            rt.high = product_high;
            rt.low = product_low;
            *product = rt;
        }

        /**
         *------------------------------------------------------------------------------
         *
         * dec128_tolower --
         *
         *    This function converts the ASCII character @c to lowercase.  It is locale
         *    insensitive (unlike the stdlib tolower).
         *
         * Returns:
         *    The lowercased character.
         */

        inline
        char dec128_tolower (char c)
        {
           if (isupper (c)) {
              c += 32;
           }

           return c;
        }

        /**
         *------------------------------------------------------------------------------
         *
         * dec128_istreq --
         *
         *    This function compares the null-terminated *ASCII* strings @a and @b
         *    for case-insensitive equality.
         *
         * Returns:
         *    true if the strings are equal, false otherwise.
         */

        inline
        bool dec128_istreq (const char* a, const char* lasta,
                            const char* b, const char* lastb)
        {
            while (!(a == lasta && b == lastb)) 
            {
               // strings are different lengths
               if (a == lasta || b == lastb) 
               {
                  return false;
               }
         
               if (dec128_tolower (*a) != dec128_tolower (*b)) {
                  return false;
               }
         
               a++;
               b++;
            }
         
            return true;
        }

    } // namespace detail


    /**
     *------------------------------------------------------------------------------
     *
     * decimal128_to_chars --
     *
     *    This function converts a BID formatted decimal128 value to string,
     *    accepting a &decimal128_t as @dec.  The string is stored at @str.
     *
     * @dec : The BID formatted decimal to convert.
     * @str : The output decimal128 string. At least %BSON_DECIMAL128_STRING
     *characters.
     *
     * Returns:
     *    None.
     *
     * Side effects:
     *    None.
     *
     *------------------------------------------------------------------------------
     */

    inline
    decimal128_to_chars_result decimal128_to_chars(char* first, char* last, const decimal128_t& dec)
    {
        const std::string bson_decimal128_inf = "Infinity";
        const std::string bson_decimal128_nan = "NaN";

        const uint32_t combination_mask = 0x1f;   /* Extract least significant 5 bits */
        const uint32_t exponent_mask = 0x3fff;    /* Extract least significant 14 bits */
        const uint32_t combination_infinity = 30; /* Value of combination field for Inf */
        const uint32_t combination_nan = 31;      /* Value of combination field for NaN */
        const uint32_t exponent_bias = 6176;      /* decimal128 exponent bias */

        char* str_out = first;      /* output pointer in string */
        char significand_str[35]; /* decoded significand digits */

        /* Note: bits in this routine are referred to starting at 0, */
        /* from the sign bit, towards the coefficient. */
        uint32_t high;                   /* bits 0 - 31 */
        uint32_t midh;                   /* bits 32 - 63 */
        uint32_t midl;                   /* bits 64 - 95 */
        uint32_t low;                    /* bits 96 - 127 */
        uint32_t combination;            /* bits 1 - 5 */
        uint32_t biased_exponent;        /* decoded biased exponent (14 bits) */
        uint32_t significand_digits = 0; /* the number of significand digits */
        uint32_t significand[36] = {0};  /* the base-10 digits in the significand */
        uint32_t *significand_read = significand; /* read pointer into significand */
        int32_t exponent;                         /* unbiased exponent */
        int32_t scientific_exponent; /* the exponent if scientific notation is
                                      * used */
        bool is_zero = false;        /* true if the number is zero */
 
        uint8_t significand_msb; /* the most signifcant significand bits (50-46) */
        bson_uint128_t
           significand128; /* temporary storage for significand decoding */
 
        memset (significand_str, 0, sizeof (significand_str));
 
        if ((int64_t) dec.high < 0) { /* negative */
           *(str_out++) = '-';
        }
 
        low = (uint32_t) dec.low, midl = (uint32_t) (dec.low >> 32),
        midh = (uint32_t) dec.high, high = (uint32_t) (dec.high >> 32);
 
        /* Decode combination field and exponent */
        combination = (high >> 26) & combination_mask;
 
        if (JSONCONS_UNLIKELY ((combination >> 3) == 3)) {
           /* Check for 'special' values */
           if (combination == combination_infinity) { /* Infinity */
               if (last-str_out >= static_cast<ptrdiff_t >(bson_decimal128_inf.size())) 
               {
                   std::memcpy(str_out, bson_decimal128_inf.data(), bson_decimal128_inf.size());
                   str_out += bson_decimal128_inf.size();
               }
               *str_out = 0;
              //strcpy_s (str_out, last-str_out, bson_decimal128_inf.c_str());
              return decimal128_to_chars_result{str_out, std::errc()};
           } else if (combination == combination_nan) { /* NaN */
               /* first, not str_out, to erase the sign */
               str_out = first;
               if (last-str_out >= static_cast<ptrdiff_t >(bson_decimal128_nan.size())) 
               {
                   std::memcpy(str_out, bson_decimal128_nan.data(), bson_decimal128_nan.size());
                   str_out += bson_decimal128_nan.size();
               }
               *str_out = 0;
              //strcpy_s (first, last-first, bson_decimal128_nan.c_str());
              /* we don't care about the NaN payload. */
               return decimal128_to_chars_result{str_out, std::errc()};
           } else {
              biased_exponent = (high >> 15) & exponent_mask;
              significand_msb = 0x8 + ((high >> 14) & 0x1);
           }
        } else {
           significand_msb = (high >> 14) & 0x7;
           biased_exponent = (high >> 17) & exponent_mask;
        }
 
        exponent = biased_exponent - exponent_bias;
        /* Create string of significand digits */
 
        /* Convert the 114-bit binary number represented by */
        /* (high, midh, midl, low) to at most 34 decimal */
        /* digits through modulo and division. */
        significand128.parts[0] = (high & 0x3fff) + ((significand_msb & 0xf) << 14);
        significand128.parts[1] = midh;
        significand128.parts[2] = midl;
        significand128.parts[3] = low;
 
        if (significand128.parts[0] == 0 && significand128.parts[1] == 0 &&
            significand128.parts[2] == 0 && significand128.parts[3] == 0) {
           is_zero = true;
        } else if (significand128.parts[0] >= (1 << 17)) {
           /* The significand is non-canonical or zero.
            * In order to preserve compatibility with the densely packed decimal
            * format, the maximum value for the significand of decimal128 is
            * 1e34 - 1.  If the value is greater than 1e34 - 1, the IEEE 754
            * standard dictates that the significand is interpreted as zero.
            */
           is_zero = true;
        } else {
           for (int k = 3; k >= 0; k--) {
              uint32_t least_digits = 0;
              detail::bson_uint128_divide1B (
                 significand128, &significand128, &least_digits);
 
              /* We now have the 9 least significant digits (in base 2). */
              /* Convert and output to string. */
              if (!least_digits) {
                 continue;
              }
 
              for (int j = 8; j >= 0; j--) {
                 significand[k * 9 + j] = least_digits % 10;
                 least_digits /= 10;
              }
           }
        }
 
        /* Output format options: */
        /* Scientific - [-]d.dddE(+/-)dd or [-]dE(+/-)dd */
        /* Regular    - ddd.ddd */
 
        if (is_zero) {
           significand_digits = 1;
           *significand_read = 0;
        } else {
           significand_digits = 36;
           while (!(*significand_read)) {
              significand_digits--;
              significand_read++;
           }
        }
 
        scientific_exponent = significand_digits - 1 + exponent;
 
        /* The scientific exponent checks are dictated by the string conversion
         * specification and are somewhat arbitrary cutoffs.
         *
         * We must check exponent > 0, because if this is the case, the number
         * has trailing zeros.  However, we *cannot* output these trailing zeros,
         * because doing so would change the precision of the value, and would
         * change stored data if the string converted number is round tripped.
         */
        if (scientific_exponent < -6 || exponent > 0) {
           /* Scientific format */
           *(str_out++) = char(*(significand_read++)) + '0';
           significand_digits--;
 
           if (significand_digits) {
              *(str_out++) = '.';
           }
 
           for (std::size_t i = 0; i < significand_digits && (str_out - first) < 36; i++) {
              *(str_out++) = char(*(significand_read++)) + '0';
           }
           /* Exponent */
           *(str_out++) = 'E';

           std::string s;
           if (scientific_exponent >= 0) {
               s.push_back('+');
           }
           jsoncons::detail::from_integer(scientific_exponent, s);
           if (str_out + s.size() < last) 
           {
               std::memcpy(str_out, s.data(), s.size());
           }
           else
           {
               return decimal128_to_chars_result{str_out, std::errc::value_too_large};
           }
           str_out += s.size();
        } else {
           /* Regular format with no decimal place */
           if (exponent >= 0) {
              for (std::size_t i = 0; i < significand_digits && (str_out - first) < 36; i++) {
                 *(str_out++) = char(*(significand_read++)) + '0';
              }
           } else {
              int32_t radix_position = significand_digits + exponent;
 
              if (radix_position > 0) { /* non-zero digits before radix */
                 for (int32_t i = 0;
                      i < radix_position && (str_out < last);
                      i++) {
                    *(str_out++) = char(*(significand_read++)) + '0';
                 }
              } else { /* leading zero before radix point */
                 *(str_out++) = '0';
              }
 
              *(str_out++) = '.';
              while (radix_position++ < 0) { /* add leading zeros after radix */
                 *(str_out++) = '0';
              }
 
              for (std::size_t i = 0;
                   (i < significand_digits - (std::max) (radix_position - 1, 0)) &&
                   (str_out < last);
                   i++) {
                 *(str_out++) = char(*(significand_read++)) + '0';
              }
           }
        }
        return decimal128_to_chars_result{str_out, std::errc()};
    }



    /**
     *------------------------------------------------------------------------------
     *
     * bson_decimal128_from_string_w_len --
     *
     *    This function converts @string in the format [+-]ddd[.]ddd[E][+-]dddd to
     *    decimal128.  Out of range values are converted to +/-Infinity.  Invalid
     *    strings are converted to NaN. @len is the length of the string, or -1
     *    meaning the string is null-terminated.
     *
     *    If more digits are provided than the available precision allows,
     *    round to the nearest expressable decimal128 with ties going to even will
     *    occur.
     *
     *    Note: @string must be ASCII only!
     *
     * Returns:
     *    true on success, or false on failure. @dec will be NaN if @str was invalid
     *    The &decimal128_t converted from @string at @dec.
     *
     * Side effects:
     *    None.
     *
     *------------------------------------------------------------------------------
     */

    inline
    decimal128_from_chars_result decimal128_from_chars(const char* first, const char* last, decimal128_t& dec) 
    {
        const string_view inf_str = "inf";
        const string_view infinity_str = "infinity";
        const string_view nan_str = "nan";

        ptrdiff_t len = last - first;

        bson_uint128_6464_t significand = {0,0};
 
        const char* str_read = first; /* Read pointer for consuming str. */
 
        /* Parsing state tracking */
        bool is_negative = false;
        bool saw_radix = false;
        bool includes_sign = false; /* True if the input first contains a sign. */
        bool found_nonzero = false;
 
        size_t significant_digits = 0; /* Total number of significant digits
                                        * (no leading or trailing zero) */
        size_t ndigits_read = 0;       /* Total number of significand digits read */
        size_t ndigits = 0;        /* Total number of digits (no leading zeros) */
        size_t radix_position = 0; /* The number of the digits after radix */
        size_t first_nonzero = 0;  /* The index of the first non-zero in *str* */
 
        uint16_t digits[decimal128_limits::max_digits] = {0};
        uint16_t ndigits_stored = 0;      /* The number of digits in digits */
        uint16_t *digits_insert = digits; /* Insertion pointer for digits */
        size_t first_digit = 0;           /* The index of the first non-zero digit */
        size_t last_digit = 0;            /* The index of the last digit */
 
        int32_t exponent = 0;
        uint64_t significand_high = 0; /* The high 17 digits of the significand */
        uint64_t significand_low = 0;  /* The low 17 digits of the significand */
        uint16_t biased_exponent = 0;  /* The biased exponent */
 
        dec.high = 0;
        dec.low = 0;
 
        if (*str_read == '+' || *str_read == '-') {
           is_negative = *(str_read++) == '-';
           includes_sign = true;
        }

        /* Check for Infinity or NaN */
        if (!isdigit (*str_read) && *str_read != '.') {
           if (detail::dec128_istreq (str_read, last, inf_str.data(), inf_str.data()+inf_str.length()) ||
               detail::dec128_istreq (str_read, last, infinity_str.data(), infinity_str.data()+infinity_str.length())) 
           {
               dec = is_negative ? decimal128_limits::neg_infinity() : decimal128_limits::infinity();
              return decimal128_from_chars_result{str_read,std::errc()};
           } else if (detail::dec128_istreq (str_read, last, nan_str.data(), nan_str.data()+nan_str.length())) {
              dec = decimal128_limits::nan();
              return decimal128_from_chars_result{str_read,std::errc()};
           }
 
           dec = decimal128_limits::nan();
           return decimal128_from_chars_result{str_read,std::errc::invalid_argument};
        }
 
        /* Read digits */
        while (((isdigit (*str_read) || *str_read == '.')) &&
               (len == -1 || str_read < first + len)) {
           if (*str_read == '.') {
              if (saw_radix) {
                 dec = decimal128_limits::nan();
                 return decimal128_from_chars_result{str_read,std::errc::invalid_argument};
              }
 
              saw_radix = true;
              str_read++;
              continue;
           }
 
           if (ndigits_stored < 34) {
              if (*str_read != '0' || found_nonzero) {
                 if (!found_nonzero) {
                    first_nonzero = ndigits_read;
                 }
 
                 found_nonzero = true;
                 *(digits_insert++) = *(str_read) - '0'; /* Only store 34 digits */
                 ndigits_stored++;
              }
           }
 
           if (found_nonzero) {
              ndigits++;
           }
 
           if (saw_radix) {
              radix_position++;
           }
 
           ndigits_read++;
           str_read++;
        }
 
        if (saw_radix && !ndigits_read) {
           dec = decimal128_limits::nan();
           return decimal128_from_chars_result{str_read,std::errc::invalid_argument};
        }
 
        /* Read exponent if exists */
        if (*str_read == 'e' || *str_read == 'E') {
           ++str_read;
           if (*str_read == '+') {
               ++str_read;
           }
           auto result = jsoncons::detail::to_integer(str_read, last - str_read, exponent);
           if (result.ec != jsoncons::detail::to_integer_errc()) 
           {
               dec = decimal128_limits::nan();
               return decimal128_from_chars_result{str_read,std::errc::invalid_argument};
           }
           str_read = result.ptr;
        }

        if ((len == -1 || str_read < first + len) && *str_read) {
           dec = decimal128_limits::nan();
           return decimal128_from_chars_result{str_read,std::errc::invalid_argument};
        }
 
        /* Done reading input. */
        /* Find first non-zero digit in digits */
        first_digit = 0;
 
        if (!ndigits_stored) { /* value is zero */
           first_digit = 0;
           last_digit = 0;
           digits[0] = 0;
           ndigits = 1;
           ndigits_stored = 1;
           significant_digits = 0;
        } else {
           last_digit = ndigits_stored - 1;
           significant_digits = ndigits;
           /* Mark trailing zeros as non-significant */
           while (first[first_nonzero + significant_digits - 1 + includes_sign +
                         saw_radix] == '0') {
              significant_digits--;
           }
        }
 
 
        /* Normalization of exponent */
        /* Correct exponent based on radix position, and shift significand as needed
         */
        /* to represent user input */
 
        /* Overflow prevention */
        if (exponent <= static_cast<int32_t>(radix_position) && static_cast<int32_t>(radix_position) - exponent > (1 << 14)) {
           exponent = decimal128_limits::exponent_min;
        } else {
           exponent -= static_cast<int32_t>(radix_position);
        }
 
        /* Attempt to normalize the exponent */
        while (exponent > decimal128_limits::exponent_max) {
           /* Shift exponent to significand and decrease */
           last_digit++;
 
           if (last_digit - first_digit > decimal128_limits::max_digits) {
              /* The exponent is too great to shift into the significand. */
              if (significant_digits == 0) {
                 /* Value is zero, we are allowed to clamp the exponent. */
                 exponent = decimal128_limits::exponent_max;
                 break;
              }
 
              /* Overflow is not permitted, error. */
              dec = decimal128_limits::nan();
              return decimal128_from_chars_result{str_read,std::errc::invalid_argument};
           }
 
           exponent--;
        }
 
        while (exponent < decimal128_limits::exponent_min || ndigits_stored < ndigits) {
           /* Shift last digit */
           if (last_digit == 0) {
              /* underflow is not allowed, but zero clamping is */
              if (significant_digits == 0) {
                 exponent = decimal128_limits::exponent_min;
                 break;
              }
 
              dec = decimal128_limits::nan();
              return decimal128_from_chars_result{str_read,std::errc::invalid_argument};
           }
 
           if (ndigits_stored < ndigits) {
              if (first[ndigits - 1 + includes_sign + saw_radix] - '0' != 0 &&
                  significant_digits != 0) {
                 dec = decimal128_limits::nan();
                 return decimal128_from_chars_result{str_read,std::errc::invalid_argument};
              }
 
              ndigits--; /* adjust to match digits not stored */
           } else {
              if (digits[last_digit] != 0) {
                 /* Inexact rounding is not allowed. */
                 dec = decimal128_limits::nan();
                 return decimal128_from_chars_result{str_read,std::errc::invalid_argument};
              }
 
 
              last_digit--; /* adjust to round */
           }
 
           if (exponent < decimal128_limits::exponent_max) {
              exponent++;
           } else {
              dec = decimal128_limits::nan();
              return decimal128_from_chars_result{str_read,std::errc::invalid_argument};
           }
        }
 
        /* Round */
        /* We've normalized the exponent, but might still need to round. */
        if (last_digit - first_digit + 1 < significant_digits) {
           uint8_t round_digit;
 
           /* There are non-zero digits after last_digit that need rounding. */
           /* We round to nearest, ties to even */
           round_digit =
              first[first_nonzero + last_digit + includes_sign + saw_radix + 1] -
              '0';
 
           if (round_digit != 0) {
              /* Inexact (non-zero) rounding is not allowed */
              dec = decimal128_limits::nan();
              return decimal128_from_chars_result{str_read,std::errc::invalid_argument};
           }
        }
 
        /* Encode significand */
        significand_high = 0,   /* The high 17 digits of the significand */
           significand_low = 0; /* The low 17 digits of the significand */
 
        if (significant_digits == 0) { /* read a zero */
           significand_high = 0;
           significand_low = 0;
        } else if (last_digit - first_digit < 17) {
           size_t d_idx = first_digit;
           significand_low = digits[d_idx++];
 
           for (; d_idx <= last_digit; d_idx++) {
              significand_low *= 10;
              significand_low += digits[d_idx];
              significand_high = 0;
           }
        } else {
           size_t d_idx = first_digit;
           significand_high = digits[d_idx++];
 
           for (; d_idx <= last_digit - 17; d_idx++) {
              significand_high *= 10;
              significand_high += digits[d_idx];
           }
 
           significand_low = digits[d_idx++];
 
           for (; d_idx <= last_digit; d_idx++) {
              significand_low *= 10;
              significand_low += digits[d_idx];
           }
        }
 
        detail::mul_64x64 (significand_high, 100000000000000000ull, &significand);
        significand.low += significand_low;
 
        if (significand.low < significand_low) {
           significand.high += 1;
        }
 
 
        biased_exponent = static_cast<uint16_t>(exponent + static_cast<int32_t>(decimal128_limits::exponent_bias));
 
        /* Encode combination, exponent, and significand. */
        if ((significand.high >> 49) & 1) {
           /* Encode '11' into bits 1 to 3 */
           dec.high |= (0x3ull << 61);
           dec.high |= (biased_exponent & 0x3fffull) << 47;
           dec.high |= significand.high & 0x7fffffffffffull;
        } else {
           dec.high |= (biased_exponent & 0x3fffull) << 49;
           dec.high |= significand.high & 0x1ffffffffffffull;
        }
 
        dec.low = significand.low;
 
        /* Encode sign */
        if (is_negative) {
           dec.high |= 0x8000000000000000ull;
        }
 
        return decimal128_from_chars_result{str_read,std::errc()};
    }

} // namespace bson
} // namespace jsoncons

#endif