MySQL科学计数法展示解惑

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作者：好好先生

一、问题引入

今天遇到一个很奇怪的问题，在MySQL客户端输入，用不同科学计数法表示的数值，展示效果却截然不同：

mysql> select 1e+14,1e+15;
+-----------------+-------+
| 1e+14           | 1e+15 |
+-----------------+-------+
| 100000000000000 |  1e15 |
+-----------------+-------+

为什么都是用科学计数法，一个是用完全展开的形式表示，另外一个却变成用科学计数法来表示？

二、代码跟踪

我们知道，在MySQL中解析这类科学计数法的标识token，是通过BISON来进行词法和语法解析的，并最终转成Item类型，Item构造初始化的堆栈如下所示：

#0  Item_float::init (this=0x7fffe844e8c0, str_arg=0xe7f312c00e0f8 <error: Cannot access memory at address 0xe7f312c00e0f8>, length=21845) at /home/greatdb/sql/item.cc:7216
#1  0x0000555559260095 in Item_float::Item_float (this=0x7fff2c00dad8, pos=..., str_arg=0x7fff2c00dac8 "1.234e-14", length=9) at /home/greatdb/sql/item.h:5237
#2  0x00005555592503af in MYSQLparse (YYTHD=0x7fff2c001040, parse_tree=0x7fffe84506b0) at /home/greatdb/sql/sql_yacc.yy:16616
#3  0x0000555558ea2410 in THD::sql_parser (this=0x7fff2c001040) at /home/greatdb/sql/sql_class.cc:3149
#4  0x0000555558fe8126 in parse_sql (thd=0x7fff2c001040, parser_state=0x7fffe8450990, creation_ctx=0x0) at /home/greatdb/sql/sql_parse.cc:7391
#5  0x0000555558fe1f16 in dispatch_sql_command (thd=0x7fff2c001040, parser_state=0x7fffe8450990, update_userstat=false) at /home/greatdb/sql/sql_parse.cc:5293
#6  0x0000555558fd7969 in dispatch_command (thd=0x7fff2c001040, com_data=0x7fffe8451b70, command=COM_QUERY) at /home/greatdb/sql/sql_parse.cc:1994
#7  0x0000555558fd5cd9 in do_command (thd=0x7fff2c001040) at /home/greatdb/sql/sql_parse.cc:1442
#8  0x00005555591fffc6 in handle_connection (arg=0x555560992ff0) at /home/greatdb/sql/conn_handler/connection_handler_per_thread.cc:307
#9  0x000055555ae2314b in pfs_spawn_thread (arg=0x5555608507a0) at /home/greatdb/storage/perfschema/pfs.cc:2899
#10 0x00007ffff77c3609 in start_thread (arg=<optimized out>) at pthread_create.c:477
#11 0x00007ffff76e8133 in clone () at ../sysdeps/unix/sysv/linux/x86_64/clone.S:95

我们仔细看下面这个函数的实现：

void Item_float::init(const char *str_arg, uint length) {
  int error;
  const char *end_not_used;
  //经过观察，我们发现：不管是1e+14还是1e+15，这里把字符串转成浮点数，都是完全展开形式。
  //即1e+14展开为100000000000000
  //1e+15展开为1000000000000000
  //说明至少到目前为止，没有触发展示差异的原因。
  value = my_strntod(&my_charset_bin, str_arg, length, &end_not_used, &error);
  if (error) {
    char tmp[NAME_LEN + 1];
    snprintf(tmp, sizeof(tmp), "%.*s", length, str_arg);
    my_error(ER_ILLEGAL_VALUE_FOR_TYPE, MYF(0), "double", tmp);
  }
  presentation.copy(str_arg, length);
  item_name.copy(str_arg, length);
  set_data_type(MYSQL_TYPE_DOUBLE);
  decimals = (uint8)nr_of_decimals(str_arg, str_arg + length);
  max_length = length;
  fixed = true;
}

接着我们继续查看Item处理结果的堆栈信息：

#0  my_gcvt (x=100000000000000, type=MY_GCVT_ARG_DOUBLE, width=342, to=0x7fffe844ec60 "\033", error=0x0) at /home/greatdb/strings/dtoa.cc:428
#1  0x00005555594ba4d5 in floating_point_to_text (value=100000000000000, decimals=31, gcvt_arg_type=MY_GCVT_ARG_DOUBLE, buffer=0x7fffe844ec60 "\033") at /home/greatdb/sql/protocol_classic.cc:3539
#2  0x00005555594ba53d in store_floating_point (value=100000000000000, decimals=31, zerofill=0, gcvt_arg_type=MY_GCVT_ARG_DOUBLE, packet=0x7fff2c003148) at /home/greatdb/sql/protocol_classic.cc:3558
#3  0x00005555594ba703 in Protocol_text::store_double (this=0x7fff2c005600, from=100000000000000, decimals=31, zerofill=0) at /home/greatdb/sql/protocol_classic.cc:3579
#4  0x0000555558aa2260 in Item::send (this=0x7fff2c021f90, protocol=0x7fff2c005600, buffer=0x7fffe844ef00) at /home/greatdb/sql/item.cc:7625
#5  0x0000555558ea1886 in THD::send_result_set_row (this=0x7fff2c001040, row_items=const mem_root_deque<Item*> & = {...}) at /home/greatdb/sql/sql_class.cc:2975
#6  0x0000555558ddbf7d in Query_result_send::send_data (this=0x7fff2c022c88, thd=0x7fff2c001040, items=const mem_root_deque<Item*> & = {...}) at /home/greatdb/sql/query_result.cc:109
#7  0x000055555912c6e3 in Query_expression::ExecuteIteratorQuery (this=0x7fff2c021408, thd=0x7fff2c001040) at /home/greatdb/sql/sql_union.cc:1282
#8  0x000055555912ca74 in Query_expression::execute (this=0x7fff2c021408, thd=0x7fff2c001040) at /home/greatdb/sql/sql_union.cc:1342
#9  0x0000555559069670 in Sql_cmd_dml::execute_inner (this=0x7fff2c022c50, thd=0x7fff2c001040) at /home/greatdb/sql/sql_select.cc:827
#10 0x00005555590689ec in Sql_cmd_dml::execute (this=0x7fff2c022c50, thd=0x7fff2c001040) at /home/greatdb/sql/sql_select.cc:580
#11 0x0000555558fe0324 in mysql_execute_command (thd=0x7fff2c001040, first_level=true) at /home/greatdb/sql/sql_parse.cc:4788
#12 0x0000555558fe24bb in dispatch_sql_command (thd=0x7fff2c001040, parser_state=0x7fffe8450990, update_userstat=false) at /home/greatdb/sql/sql_parse.cc:5393
#13 0x0000555558fd7969 in dispatch_command (thd=0x7fff2c001040, com_data=0x7fffe8451b70, command=COM_QUERY) at /home/greatdb/sql/sql_parse.cc:1994
#14 0x0000555558fd5cd9 in do_command (thd=0x7fff2c001040) at /home/greatdb/sql/sql_parse.cc:1442
#15 0x00005555591fffc6 in handle_connection (arg=0x555560992ff0) at /home/greatdb/sql/conn_handler/connection_handler_per_thread.cc:307
#16 0x000055555ae2314b in pfs_spawn_thread (arg=0x5555608507a0) at /home/greatdb/storage/perfschema/pfs.cc:2899
#17 0x00007ffff77c3609 in start_thread (arg=<optimized out>) at pthread_create.c:477
#18 0x00007ffff76e8133 in clone () at ../sysdeps/unix/sysv/linux/x86_64/clone.S:95

我们发现不管是1e+14还是1e+15，最终都会进入到my_gcvt这个函数里面，此函数大概的功能是把一个浮点数类型转成对应的字符串类型输出。现在我们来看该函数的关键逻辑实现：

//1、x表示要转换的浮点数
//2、width表示展示宽度。具体来说：MySQL其实对数据库返回的每一个列的最大宽度是有要求的。如果浮点数是完全展开的情况，那就有可能超过这个展示的最大宽度，这里固定取值342
//3、to表示存放转换后浮点数x对应的字符数组指针
size_t my_gcvt(double x, my_gcvt_arg_type type, int width, char *to,
               bool *error) {
  int decpt, sign, len, exp_len;
  char *res, *src, *end, *dst = to, *dend = dst + width;
  char buf[DTOA_BUFF_SIZE];
  bool have_space, force_e_format;
  assert(width > 0 && to != nullptr);
 ...
 //这里主要是为了计算浮点数x的存储的小数点位置decpt。
 //比如100000000000000，得到的decpt为15
 //1000000000000000，得到的decpt为16
  res =
      dtoa(x, 4, type == MY_GCVT_ARG_DOUBLE ? width : std::min(width, FLT_DIG),
           &decpt, &sign, &end, buf, sizeof(buf));
 ...
 //have_space为真表示，浮点数完全展开的形式对应的长度，符合MySQL列展示最大宽度的要求。
 //下面这个判断的逻辑主要是说：
 //浮点数的展示宽度足够或者展示宽度不足的情况下，继续判断小数点位置decpt是否介于[-MAX_DECPT_FOR_F_FORMAT + 1,MAX_DECPT_FOR_F_FORMAT]之间。
 //跟踪一下代码的宏定义，很容易发现MAX_DECPT_FOR_F_FORMAT定义的长度就是15。
 //那这样就是说decpt介于[-14,15]之间的时候，也是符合要求的。
  if ((have_space ||
       /*
         Not enough space, let's see if the 'f' format provides the most number
         of significant digits.
       */
       ((decpt <= width &&
         (decpt >= -1 || (decpt == -2 && (len > 1 || !force_e_format)))) &&
        !force_e_format)) &&

      /*
        Use the 'e' format in some cases even if we have enough space for the
        'f' one. See comment for MAX_DECPT_FOR_F_FORMAT.
      */
      (!have_space || (decpt >= -MAX_DECPT_FOR_F_FORMAT + 1 &&
                       (decpt <= MAX_DECPT_FOR_F_FORMAT || len > decpt)))) {
  //如果符合这个条件的要求，那浮点数x就按照'f' format，即非科学计数法，完全展开形式处理。
  //1e+14的decpt取值为15，介于[-14,15]区间，故按照完全展开形式处理。
  ...
 }else{
  //否则浮点数x按照'e' format，即科学计数法表示。
  //1e+15的decpt取值为16，超出[-14,15]区间，故按照科学计数法形式处理。
  ...
 }
}