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8.1. 数值类型

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数值类型包括二字节、四字节和八字节整数，四字节和八字节浮点数，以及可选精度的十进制数。表 8.2 列出了可用类型。

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表 8.2：数值类型

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\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n
名字存储大小说明范围
smallint2 字节小范围整数-32768 到 +32767
integer4 字节整数的常用选择-2147483648 到 +2147483647
bigint8 字节大范围整数-9223372036854775808 到 +9223372036854775807
decimal可变用户指定精度，精确小数点前最多 131072 位，小数点后最多 16383 位
numeric可变用户指定精度，精确小数点前最多 131072 位，小数点后最多 16383 位
real4 字节可变精度，不精确6 位十进制有效数字
double precision8 字节可变精度，不精确15 位十进制有效数字
smallserial2 字节小型自增整数1 至 32767
serial4 字节自增整数1 至 2147483647
bigserial8 字节大型自增整数1 至 9223372036854775807
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数值类型常量的语法见第 4.1.2 节。数值类型拥有完整的对应算术运算符和函数，更多信息见第 9 章。以下各节详细介绍这些类型。

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8.1.1. 整数类型

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smallint、integer 和 bigint 存储不含小数部分的整数，取值范围各不相同。尝试存储超出允许范围的值会报错。

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integer 是常用选择，在取值范围、存储大小和性能之间取得了最佳平衡。smallint 通常仅在磁盘空间非常紧张时使用；bigint 则用于 integer 范围不足的情况。

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SQL 仅规定了 integer（或 int）、smallint 和 bigint 这几种整数类型。类型名 int2、int4 和 int8 是扩展，一些其他 SQL 数据库系统也使用它们。

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8.1.2. 任意精度数值

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numeric 可以存储位数非常多的数值，尤其推荐用于货币金额和其他要求精确的数量。numeric 运算会在可能时产生精确结果，例如加法、减法和乘法。不过，与整数类型或下一节介绍的浮点类型相比，numeric 运算非常慢。

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下文使用以下术语：numeric 的精度是整个数值的有效数字总数，即小数点两侧数字的总位数；小数位数是小数点右侧小数部分的十进制数字位数。例如，23.5141 的精度为 6，小数位数为 4。整数可以视为小数位数为零。

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numeric 列的最大精度和最大小数位数都可以配置。声明 numeric 类型列时使用以下语法：

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NUMERIC(precision, scale)\n
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精度必须为正数，小数位数可以为正数或负数，见下文。也可以写为：

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NUMERIC(precision)\n
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选择小数位数为 0。指定：

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NUMERIC\n
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不指定精度或小数位数时，将创建一个“不受约束的 numeric”列，可存储任意长度的数值，但仍受实现上限约束。这类列不会将输入值强制转换为特定的小数位数，而声明了小数位数的 numeric 列会强制转换为该位数。（SQL 标准要求默认小数位数为 0，即强制采用整数精度。我们认为这样不太实用。如果需要兼容其他数据库，应始终显式指定精度和小数位数。）

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注意

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numeric 类型声明可显式指定的最大精度为 1000。未限定精度的 numeric 列受表 8.2 所述限制约束。

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如果待存储值的小数位数大于列声明的小数位数，系统会将该值舍入到指定的小数位数。随后，如果小数点左侧的位数超过声明精度减去声明小数位数的结果，就会报错。例如，声明为下列形式的列：

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NUMERIC(3, 1)\n
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会将值舍入到 1 位小数，并可存储 -99.9 至 99.9 之间的值，包含两端。

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从 PostgreSQL 15 开始，允许声明小数位数为负的 numeric 列。此时，数值会在小数点左侧进行舍入。精度仍表示未被舍入部分的最大位数。因此，声明为下列形式的列：

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NUMERIC(2, -3)\n
\n

会将值舍入到最接近的千位，并可存储 -99000 至 99000 之间的值，包含两端。还允许声明大于精度的小数位数。这样的列只能保存小数值，并要求小数点右侧紧接的零的位数，至少为声明的小数位数减去声明的精度。例如，声明为下列形式的列：

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NUMERIC(3, 5)\n
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会将值舍入到 5 位小数，并可存储 -0.00999 至 0.00999 之间的值，包含两端。

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注意

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PostgreSQL 允许 numeric 类型声明中的小数位数为 -1000 到 1000 之间的任意值。但 SQL 标准要求它介于 0 和精度之间。使用此范围以外的小数位数，可能无法移植到其他数据库系统。

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numeric 值在物理存储时不会保留多余的前导零或尾随零。因此，列声明的精度与小数位数是最大限制，而非固定分配的空间。（从这一点看，numeric 更像 varchar(n)，而非 char(n)。）实际存储每四位十进制数字需要两个字节，另加三到八个字节的开销。

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除普通数值外，numeric 类型还有几个特殊值：

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\nInfinity
\n-Infinity
\nNaN

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这些值取自 IEEE 754 标准，分别表示“正无穷”“负无穷”和“非数”。在 SQL 命令中将它们写成常量时，必须加引号，例如 UPDATE table SET x = '-Infinity'。输入识别时不区分大小写，无穷值也可写为 inf 和 -inf。

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无穷值遵循数学上的预期。例如，Infinity 加任意有限值仍为 Infinity，Infinity 加 Infinity 也如此；但 Infinity 减 Infinity 得到 NaN（非数），因为此运算没有明确的数学含义。无穷值只能存储在未限定精度的 numeric 列中，因为从概念上说，它超出了任何有限精度限制。

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NaN（非数）用于表示未定义的计算结果。通常，输入包含 NaN 的运算会产生另一个 NaN。唯一例外是：在其他输入不变的情况下，如果将 NaN 替换为任意有限或无限数值都会得到相同结果，那么对 NaN 也返回该结果。（例如，NaN 的零次方为一。）

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注意

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在“非数值”概念的大多数实现中，NaN 不被视为与任何其他数值相等（包括 NaN）。为了使数值能够排序并用于树形索引，PostgreSQL 将 NaN 值视为彼此相等，且大于所有非 NaN 值。

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decimal 和 numeric 等价，两者都属于 SQL 标准。

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舍入恰好处于中点的值时，numeric 向远离零的方向舍入，而 real 和 double precision 在大多数机器上向最近的偶数舍入。例如：

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SELECT x,\n  round(x::numeric) AS num_round,\n  round(x::double precision) AS dbl_round\nFROM generate_series(-3.5, 3.5, 1) as x;\n  x   | num_round | dbl_round\n------+-----------+-----------\n -3.5 |        -4 |        -4\n -2.5 |        -3 |        -2\n -1.5 |        -2 |        -2\n -0.5 |        -1 |        -0\n  0.5 |         1 |         0\n  1.5 |         2 |         2\n  2.5 |         3 |         2\n  3.5 |         4 |         4\n(8 rows)\n
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8.1.3. 浮点类型

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real 和 double precision 是非精确、可变精度的数值类型。在当前支持的所有平台上，在底层处理器、操作系统和编译器支持的范围内，它们分别实现 IEEE 754 二进制浮点运算标准的单精度和双精度格式。

\n

不精确意味着某些值无法精确转换为内部格式，只能存储为近似值，因此存储后再取出时可能出现细微差异。如何处理这些误差及其在计算中的传播，是数学和计算机科学中的一个完整分支，此处不作展开，仅说明以下几点：

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\n
    \n
  • 如果需要精确存储和计算（例如处理货币金额），请改用 numeric 类型。
    • \n
  • 如果要使用这些类型进行重要的复杂计算，尤其是依赖边界情况（无穷大、下溢）的特定行为时，应仔细评估其实现。
    • \n
  • 比较两个浮点值是否相等，结果可能并不总是符合预期。
    • \n
\n
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在当前支持的所有平台上，real 的取值范围约为 1E-37 到 1E+37，精度至少为 6 位十进制数字。double precision 的取值范围约为 1E-307 到 1E+308，精度至少为 15 位。值过大或过小都会报错；输入精度过高时可能发生舍入。过于接近零、无法表示为区别于零的数值时，会报下溢错误。

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默认情况下，浮点值以最短的精确十进制表示形式输出为文本；生成的十进制值与实际存储的二进制值之间的距离，小于它与相同二进制精度下任何其他可表示值之间的距离。（不过，目前输出值绝不会恰好位于两个可表示值的正中间，以避开输入例程未正确遵守舍入到最近偶数规则这一常见缺陷。）对于 float8 值，这种表示最多使用 17 位十进制有效数字；对于 float4 值，最多使用 9 位。

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\n

注意

\n

这种最短精确输出格式的生成速度，远高于历史上使用的舍入格式。

\n
\n

为兼容旧版 PostgreSQL 生成的输出，并允许降低输出精度，可以使用 extra_float_digits 参数改为选择舍入后的十进制输出。设置为 0 会恢复此前的默认行为，将值舍入为 6 位（float4）或 15 位（float8）十进制有效数字。负值会进一步减少位数；例如，-2 会分别将输出舍入为 4 位或 13 位。

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任何大于 0 的 extra_float_digits 值都会选择最短精确格式。

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\n

注意

\n

过去，需要精确值的应用必须将 extra_float_digits 设为 3 才能获得这些值。为了最大限度地兼容不同版本，它们应继续这样设置。

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\n

除普通数值外，浮点类型还有几个特殊值：

\n
\n


\nInfinity
\n-Infinity
\nNaN

\n
\n

这些值分别表示 IEEE 754 特殊值“正无穷”“负无穷”和“非数”。在 SQL 命令中将它们写成常量时，必须加引号，例如 UPDATE table SET x = '-Infinity'。输入识别时不区分大小写，无穷值也可写为 inf 和 -inf。

\n
\n

注意

\n

IEEE 754 规定，NaN 不应与任何其他浮点值相等（包括 NaN）。为了使浮点值能够排序并用于树形索引，PostgreSQL 将 NaN 值视为彼此相等，且大于所有非 NaN 值。

\n
\n

PostgreSQL 也支持 SQL 标准的 float 和 float(p) 记法来指定非精确数值类型。p 表示可接受的最小二进制位精度。float(1) 到 float(24) 选择 real 类型，float(25) 到 float(53) 选择 double precision。p 超出允许范围会报错；不指定精度的 float 等同于 double precision。

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\n
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8.1.4. 序列类型

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\n
\n
\n
\n

注意

\n

本节介绍 PostgreSQL 特有的自动递增列创建方法。另一种方法是使用 SQL 标准的标识列特性，参见第 5.3 节。

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\n

smallserial、serial 和 bigserial 并非真正的类型，而是用于创建唯一标识符列的便捷记法，类似于其他一些数据库支持的 AUTO_INCREMENT 属性。在当前实现中，指定：

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CREATE TABLE tablename (\n    colname SERIAL\n);\n
\n

等价于指定：

\n
CREATE SEQUENCE tablename_colname_seq AS integer;\nCREATE TABLE tablename (\n    colname integer NOT NULL DEFAULT nextval('tablename_colname_seq')\n);\nALTER SEQUENCE tablename_colname_seq OWNED BY tablename.colname;\n
\n

这样就创建了一个 integer 列，并安排由序列生成器提供默认值。NOT NULL 约束保证无法插入空值。（多数情况下还应增加 UNIQUE 或 PRIMARY KEY 约束，防止意外插入重复值，但系统不会自动添加。）最后，序列被标记为归该列所有，因此删除列或表时，序列也会被删除。

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\n

注意

\n

由于 smallserial、serial 和 bigserial 使用序列实现，即使从未删除任何行，列中出现的值序列也可能存在“空洞”或间隙。即便包含所分配值的行从未成功插入表列，从序列分配的值仍已被“用掉”。例如，插入事务回滚时就会发生这种情况。详见第 9.17 节的 nextval()。

\n
\n

要将序列的下一个值插入 serial 列，应让该列使用默认值。可以在 INSERT 的列列表中省略此列，也可以使用 DEFAULT 关键字。

\n

serial 与 serial4 等价，都会创建 integer 列。bigserial 与 serial8 的工作方式相同，只是创建 bigint 列。如果预计表的整个生命周期内使用的标识符超过 2^31 个，应使用 bigserial。smallserial 与 serial2 也采用相同方式，但创建 smallint 列。

\n

为 serial 列创建的序列会在所属列被删除时自动删除。也可以只删除序列而保留列，但这会强制移除列的默认值表达式。

\n
\n
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"oprkind": "b", "oprleft": "numeric", "oprname": "+", "oprrest": "-", "oprright": "numeric", "oprnegate": "0", "oprresult": "numeric", "oprcanhash": "f", "oprcanmerge": "f"}, {"oprcom": "0", "oprcode": "numeric_div", "oprjoin": "-", "oprkind": "b", "oprleft": "numeric", "oprname": "/", "oprrest": "-", "oprright": "numeric", "oprnegate": "0", "oprresult": "numeric", "oprcanhash": "f", "oprcanmerge": "f"}, {"oprcom": "<=(numeric,numeric)", "oprcode": "numeric_ge", "oprjoin": "scalargejoinsel", "oprkind": "b", "oprleft": "numeric", "oprname": ">=", "oprrest": "scalargesel", "oprright": "numeric", "oprnegate": "<(numeric,numeric)", "oprresult": "bool", "oprcanhash": "f", "oprcanmerge": "f"}, {"oprcom": "<(numeric,numeric)", "oprcode": "numeric_gt", "oprjoin": "scalargtjoinsel", "oprkind": "b", "oprleft": "numeric", "oprname": ">", "oprrest": "scalargtsel", "oprright": "numeric", "oprnegate": "<=(numeric,numeric)", "oprresult": "bool", "oprcanhash": "f", "oprcanmerge": "f"}, {"oprcom": 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