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><DIV
CLASS="SECT1"
><H1
CLASS="SECT1"
><A
NAME="DATATYPE-NUMERIC"
>8.1. Numeric Types</A
></H1
><P
>    Numeric types consist of two-, four-, and eight-byte integers,
    four- and eight-byte floating-point numbers, and selectable-precision
    decimals.  <A
HREF="datatype-numeric.html#DATATYPE-NUMERIC-TABLE"
>Table 8-2</A
> lists the
    available types.
   </P
><DIV
CLASS="TABLE"
><A
NAME="DATATYPE-NUMERIC-TABLE"
></A
><P
><B
>Table 8-2. Numeric Types</B
></P
><TABLE
BORDER="1"
CLASS="CALSTABLE"
><COL><COL><COL><COL><THEAD
><TR
><TH
>Name</TH
><TH
>Storage Size</TH
><TH
>Description</TH
><TH
>Range</TH
></TR
></THEAD
><TBODY
><TR
><TD
><TT
CLASS="TYPE"
>smallint</TT
></TD
><TD
>2 bytes</TD
><TD
>small-range integer</TD
><TD
>-32768 to +32767</TD
></TR
><TR
><TD
><TT
CLASS="TYPE"
>integer</TT
></TD
><TD
>4 bytes</TD
><TD
>typical choice for integer</TD
><TD
>-2147483648 to +2147483647</TD
></TR
><TR
><TD
><TT
CLASS="TYPE"
>bigint</TT
></TD
><TD
>8 bytes</TD
><TD
>large-range integer</TD
><TD
>-9223372036854775808 to +9223372036854775807</TD
></TR
><TR
><TD
><TT
CLASS="TYPE"
>decimal</TT
></TD
><TD
>variable</TD
><TD
>user-specified precision, exact</TD
><TD
>up to 131072 digits before the decimal point; up to 16383 digits after the decimal point</TD
></TR
><TR
><TD
><TT
CLASS="TYPE"
>numeric</TT
></TD
><TD
>variable</TD
><TD
>user-specified precision, exact</TD
><TD
>up to 131072 digits before the decimal point; up to 16383 digits after the decimal point</TD
></TR
><TR
><TD
><TT
CLASS="TYPE"
>real</TT
></TD
><TD
>4 bytes</TD
><TD
>variable-precision, inexact</TD
><TD
>6 decimal digits precision</TD
></TR
><TR
><TD
><TT
CLASS="TYPE"
>double precision</TT
></TD
><TD
>8 bytes</TD
><TD
>variable-precision, inexact</TD
><TD
>15 decimal digits precision</TD
></TR
><TR
><TD
><TT
CLASS="TYPE"
>smallserial</TT
></TD
><TD
>2 bytes</TD
><TD
>small autoincrementing integer</TD
><TD
>1 to 32767</TD
></TR
><TR
><TD
><TT
CLASS="TYPE"
>serial</TT
></TD
><TD
>4 bytes</TD
><TD
>autoincrementing integer</TD
><TD
>1 to 2147483647</TD
></TR
><TR
><TD
><TT
CLASS="TYPE"
>bigserial</TT
></TD
><TD
>8 bytes</TD
><TD
>large autoincrementing integer</TD
><TD
>1 to 9223372036854775807</TD
></TR
></TBODY
></TABLE
></DIV
><P
>    The syntax of constants for the numeric types is described in
    <A
HREF="sql-syntax-lexical.html#SQL-SYNTAX-CONSTANTS"
>Section 4.1.2</A
>.  The numeric types have a
    full set of corresponding arithmetic operators and
    functions. Refer to <A
HREF="functions.html"
>Chapter 9</A
> for more
    information.  The following sections describe the types in detail.
   </P
><DIV
CLASS="SECT2"
><H2
CLASS="SECT2"
><A
NAME="DATATYPE-INT"
>8.1.1. Integer Types</A
></H2
><P
>     The types <TT
CLASS="TYPE"
>smallint</TT
>, <TT
CLASS="TYPE"
>integer</TT
>, and
     <TT
CLASS="TYPE"
>bigint</TT
> store whole numbers, that is, numbers without
     fractional components, of various ranges.  Attempts to store
     values outside of the allowed range will result in an error.
    </P
><P
>     The type <TT
CLASS="TYPE"
>integer</TT
> is the common choice, as it offers
     the best balance between range, storage size, and performance.
     The <TT
CLASS="TYPE"
>smallint</TT
> type is generally only used if disk
     space is at a premium.  The <TT
CLASS="TYPE"
>bigint</TT
> type is designed to be
     used when the range of the <TT
CLASS="TYPE"
>integer</TT
> type is insufficient.
    </P
><P
>     <ACRONYM
CLASS="ACRONYM"
>SQL</ACRONYM
> only specifies the integer types
     <TT
CLASS="TYPE"
>integer</TT
> (or <TT
CLASS="TYPE"
>int</TT
>),
     <TT
CLASS="TYPE"
>smallint</TT
>, and <TT
CLASS="TYPE"
>bigint</TT
>.  The
     type names <TT
CLASS="TYPE"
>int2</TT
>, <TT
CLASS="TYPE"
>int4</TT
>, and
     <TT
CLASS="TYPE"
>int8</TT
> are extensions, which are also used by some
     other <ACRONYM
CLASS="ACRONYM"
>SQL</ACRONYM
> database systems.
    </P
></DIV
><DIV
CLASS="SECT2"
><H2
CLASS="SECT2"
><A
NAME="DATATYPE-NUMERIC-DECIMAL"
>8.1.2. Arbitrary Precision Numbers</A
></H2
><P
>     The type <TT
CLASS="TYPE"
>numeric</TT
> can store numbers with a
     very large number of digits and perform calculations exactly. It is
     especially recommended for storing monetary amounts and other
     quantities where exactness is required. However, arithmetic on
     <TT
CLASS="TYPE"
>numeric</TT
> values is very slow compared to the integer
     types, or to the floating-point types described in the next section.
    </P
><P
>     We use the following terms below:  The
     <I
CLASS="FIRSTTERM"
>scale</I
> of a <TT
CLASS="TYPE"
>numeric</TT
> is the
     count of decimal digits in the fractional part, to the right of
     the decimal point.  The <I
CLASS="FIRSTTERM"
>precision</I
> of a
     <TT
CLASS="TYPE"
>numeric</TT
> is the total count of significant digits in
     the whole number, that is, the number of digits to both sides of
     the decimal point.  So the number 23.5141 has a precision of 6
     and a scale of 4.  Integers can be considered to have a scale of
     zero.
    </P
><P
>     Both the maximum precision and the maximum scale of a
     <TT
CLASS="TYPE"
>numeric</TT
> column can be
     configured.  To declare a column of type <TT
CLASS="TYPE"
>numeric</TT
> use
     the syntax:
</P><PRE
CLASS="PROGRAMLISTING"
>NUMERIC(<TT
CLASS="REPLACEABLE"
><I
>precision</I
></TT
>, <TT
CLASS="REPLACEABLE"
><I
>scale</I
></TT
>)</PRE
><P>
     The precision must be positive, the scale zero or positive.
     Alternatively:
</P><PRE
CLASS="PROGRAMLISTING"
>NUMERIC(<TT
CLASS="REPLACEABLE"
><I
>precision</I
></TT
>)</PRE
><P>
     selects a scale of 0.  Specifying:
</P><PRE
CLASS="PROGRAMLISTING"
>NUMERIC</PRE
><P>
     without any precision or scale creates a column in which numeric
     values of any precision and scale can be stored, up to the
     implementation limit on precision.  A column of this kind will
     not coerce input values to any particular scale, whereas
     <TT
CLASS="TYPE"
>numeric</TT
> columns with a declared scale will coerce
     input values to that scale.  (The <ACRONYM
CLASS="ACRONYM"
>SQL</ACRONYM
> standard
     requires a default scale of 0, i.e., coercion to integer
     precision.  We find this a bit useless.  If you're concerned
     about portability, always specify the precision and scale
     explicitly.)
    </P
><DIV
CLASS="NOTE"
><BLOCKQUOTE
CLASS="NOTE"
><P
><B
>Note: </B
>      The maximum allowed precision when explicitly specified in the
      type declaration is 1000; <TT
CLASS="TYPE"
>NUMERIC</TT
> without a specified
      precision is subject to the limits described in <A
HREF="datatype-numeric.html#DATATYPE-NUMERIC-TABLE"
>Table 8-2</A
>.
     </P
></BLOCKQUOTE
></DIV
><P
>     If the scale of a value to be stored is greater than the declared
     scale of the column, the system will round the value to the specified
     number of fractional digits.  Then, if the number of digits to the
     left of the decimal point exceeds the declared precision minus the
     declared scale, an error is raised.
    </P
><P
>     Numeric values are physically stored without any extra leading or
     trailing zeroes.  Thus, the declared precision and scale of a column
     are maximums, not fixed allocations.  (In this sense the <TT
CLASS="TYPE"
>numeric</TT
>
     type is more akin to <TT
CLASS="TYPE"
>varchar(<TT
CLASS="REPLACEABLE"
><I
>n</I
></TT
>)</TT
>
     than to <TT
CLASS="TYPE"
>char(<TT
CLASS="REPLACEABLE"
><I
>n</I
></TT
>)</TT
>.)  The actual storage
     requirement is two bytes for each group of four decimal digits,
     plus three to eight bytes overhead.
    </P
><P
>     In addition to ordinary numeric values, the <TT
CLASS="TYPE"
>numeric</TT
>
     type allows the special value <TT
CLASS="LITERAL"
>NaN</TT
>, meaning
     <SPAN
CLASS="QUOTE"
>"not-a-number"</SPAN
>.  Any operation on <TT
CLASS="LITERAL"
>NaN</TT
>
     yields another <TT
CLASS="LITERAL"
>NaN</TT
>.  When writing this value
     as a constant in an SQL command, you must put quotes around it,
     for example <TT
CLASS="LITERAL"
>UPDATE table SET x = 'NaN'</TT
>.  On input,
     the string <TT
CLASS="LITERAL"
>NaN</TT
> is recognized in a case-insensitive manner.
    </P
><DIV
CLASS="NOTE"
><BLOCKQUOTE
CLASS="NOTE"
><P
><B
>Note: </B
>      In most implementations of the <SPAN
CLASS="QUOTE"
>"not-a-number"</SPAN
> concept,
      <TT
CLASS="LITERAL"
>NaN</TT
> is not considered equal to any other numeric
      value (including <TT
CLASS="LITERAL"
>NaN</TT
>).  In order to allow
      <TT
CLASS="TYPE"
>numeric</TT
> values to be sorted and used in tree-based
      indexes, <SPAN
CLASS="PRODUCTNAME"
>PostgreSQL</SPAN
> treats <TT
CLASS="LITERAL"
>NaN</TT
>
      values as equal, and greater than all non-<TT
CLASS="LITERAL"
>NaN</TT
>
      values.
     </P
></BLOCKQUOTE
></DIV
><P
>     The types <TT
CLASS="TYPE"
>decimal</TT
> and <TT
CLASS="TYPE"
>numeric</TT
> are
     equivalent.  Both types are part of the <ACRONYM
CLASS="ACRONYM"
>SQL</ACRONYM
>
     standard.
    </P
></DIV
><DIV
CLASS="SECT2"
><H2
CLASS="SECT2"
><A
NAME="DATATYPE-FLOAT"
>8.1.3. Floating-Point Types</A
></H2
><P
>     The data types <TT
CLASS="TYPE"
>real</TT
> and <TT
CLASS="TYPE"
>double
     precision</TT
> are inexact, variable-precision numeric types.
     In practice, these types are usually implementations of
     <ACRONYM
CLASS="ACRONYM"
>IEEE</ACRONYM
> Standard 754 for Binary Floating-Point
     Arithmetic (single and double precision, respectively), to the
     extent that the underlying processor, operating system, and
     compiler support it.
    </P
><P
>     Inexact means that some values cannot be converted exactly to the
     internal format and are stored as approximations, so that storing
     and retrieving a value might show slight discrepancies.
     Managing these errors and how they propagate through calculations
     is the subject of an entire branch of mathematics and computer
     science and will not be discussed here, except for the
     following points:
     <P
></P
></P><UL
><LI
><P
>        If you require exact storage and calculations (such as for
        monetary amounts), use the <TT
CLASS="TYPE"
>numeric</TT
> type instead.
       </P
></LI
><LI
><P
>        If you want to do complicated calculations with these types
        for anything important, especially if you rely on certain
        behavior in boundary cases (infinity, underflow), you should
        evaluate the implementation carefully.
       </P
></LI
><LI
><P
>        Comparing two floating-point values for equality might not
        always work as expected.
       </P
></LI
></UL
><P>
    </P
><P
>     On most platforms, the <TT
CLASS="TYPE"
>real</TT
> type has a range of at least
     1E-37 to 1E+37 with a precision of at least 6 decimal digits.  The
     <TT
CLASS="TYPE"
>double precision</TT
> type typically has a range of around
     1E-307 to 1E+308 with a precision of at least 15 digits.  Values that
     are too large or too small will cause an error.  Rounding might
     take place if the precision of an input number is too high.
     Numbers too close to zero that are not representable as distinct
     from zero will cause an underflow error.
    </P
><DIV
CLASS="NOTE"
><BLOCKQUOTE
CLASS="NOTE"
><P
><B
>Note: </B
>      The <A
HREF="runtime-config-client.html#GUC-EXTRA-FLOAT-DIGITS"
>extra_float_digits</A
> setting controls the
      number of extra significant digits included when a floating point
      value is converted to text for output.  With the default value of
      <TT
CLASS="LITERAL"
>0</TT
>, the output is the same on every platform
      supported by PostgreSQL.  Increasing it will produce output that
      more accurately represents the stored value, but may be unportable.
     </P
></BLOCKQUOTE
></DIV
><P
>     In addition to ordinary numeric values, the floating-point types
     have several special values:
<P
CLASS="LITERALLAYOUT"
><TT
CLASS="LITERAL"
>Infinity</TT
><br>
<TT
CLASS="LITERAL"
>-Infinity</TT
><br>
<TT
CLASS="LITERAL"
>NaN</TT
></P
>
     These represent the IEEE 754 special values
     <SPAN
CLASS="QUOTE"
>"infinity"</SPAN
>, <SPAN
CLASS="QUOTE"
>"negative infinity"</SPAN
>, and
     <SPAN
CLASS="QUOTE"
>"not-a-number"</SPAN
>, respectively.  (On a machine whose
     floating-point arithmetic does not follow IEEE 754, these values
     will probably not work as expected.)  When writing these values
     as constants in an SQL command, you must put quotes around them,
     for example <TT
CLASS="LITERAL"
>UPDATE table SET x = 'Infinity'</TT
>.  On input,
     these strings are recognized in a case-insensitive manner.
    </P
><DIV
CLASS="NOTE"
><BLOCKQUOTE
CLASS="NOTE"
><P
><B
>Note: </B
>      IEEE754 specifies that <TT
CLASS="LITERAL"
>NaN</TT
> should not compare equal
      to any other floating-point value (including <TT
CLASS="LITERAL"
>NaN</TT
>).
      In order to allow floating-point values to be sorted and used
      in tree-based indexes, <SPAN
CLASS="PRODUCTNAME"
>PostgreSQL</SPAN
> treats
      <TT
CLASS="LITERAL"
>NaN</TT
> values as equal, and greater than all
      non-<TT
CLASS="LITERAL"
>NaN</TT
> values.
     </P
></BLOCKQUOTE
></DIV
><P
>     <SPAN
CLASS="PRODUCTNAME"
>PostgreSQL</SPAN
> also supports the SQL-standard
     notations <TT
CLASS="TYPE"
>float</TT
> and
     <TT
CLASS="TYPE"
>float(<TT
CLASS="REPLACEABLE"
><I
>p</I
></TT
>)</TT
> for specifying
     inexact numeric types.  Here, <TT
CLASS="REPLACEABLE"
><I
>p</I
></TT
> specifies
     the minimum acceptable precision in <SPAN
CLASS="emphasis"
><I
CLASS="EMPHASIS"
>binary</I
></SPAN
> digits.
     <SPAN
CLASS="PRODUCTNAME"
>PostgreSQL</SPAN
> accepts
     <TT
CLASS="TYPE"
>float(1)</TT
> to <TT
CLASS="TYPE"
>float(24)</TT
> as selecting the
     <TT
CLASS="TYPE"
>real</TT
> type, while
     <TT
CLASS="TYPE"
>float(25)</TT
> to <TT
CLASS="TYPE"
>float(53)</TT
> select
     <TT
CLASS="TYPE"
>double precision</TT
>.  Values of <TT
CLASS="REPLACEABLE"
><I
>p</I
></TT
>
     outside the allowed range draw an error.
     <TT
CLASS="TYPE"
>float</TT
> with no precision specified is taken to mean
     <TT
CLASS="TYPE"
>double precision</TT
>.
    </P
><DIV
CLASS="NOTE"
><BLOCKQUOTE
CLASS="NOTE"
><P
><B
>Note: </B
>      Prior to <SPAN
CLASS="PRODUCTNAME"
>PostgreSQL</SPAN
> 7.4, the precision in
      <TT
CLASS="TYPE"
>float(<TT
CLASS="REPLACEABLE"
><I
>p</I
></TT
>)</TT
> was taken to mean
      so many <SPAN
CLASS="emphasis"
><I
CLASS="EMPHASIS"
>decimal</I
></SPAN
> digits.  This has been corrected to match the SQL
      standard, which specifies that the precision is measured in binary
      digits.  The assumption that <TT
CLASS="TYPE"
>real</TT
> and
      <TT
CLASS="TYPE"
>double precision</TT
> have exactly 24 and 53 bits in the
      mantissa respectively is correct for IEEE-standard floating point
      implementations.  On non-IEEE platforms it might be off a little, but
      for simplicity the same ranges of <TT
CLASS="REPLACEABLE"
><I
>p</I
></TT
> are used
      on all platforms.
     </P
></BLOCKQUOTE
></DIV
></DIV
><DIV
CLASS="SECT2"
><H2
CLASS="SECT2"
><A
NAME="DATATYPE-SERIAL"
>8.1.4. Serial Types</A
></H2
><P
>     The data types <TT
CLASS="TYPE"
>smallserial</TT
>, <TT
CLASS="TYPE"
>serial</TT
> and
     <TT
CLASS="TYPE"
>bigserial</TT
> are not true types, but merely
     a notational convenience for creating unique identifier columns
     (similar to the <TT
CLASS="LITERAL"
>AUTO_INCREMENT</TT
> property
     supported by some other databases). In the current
     implementation, specifying:

</P><PRE
CLASS="PROGRAMLISTING"
>CREATE TABLE <TT
CLASS="REPLACEABLE"
><I
>tablename</I
></TT
> (
    <TT
CLASS="REPLACEABLE"
><I
>colname</I
></TT
> SERIAL
);</PRE
><P>

     is equivalent to specifying:

</P><PRE
CLASS="PROGRAMLISTING"
>CREATE SEQUENCE <TT
CLASS="REPLACEABLE"
><I
>tablename</I
></TT
>_<TT
CLASS="REPLACEABLE"
><I
>colname</I
></TT
>_seq;
CREATE TABLE <TT
CLASS="REPLACEABLE"
><I
>tablename</I
></TT
> (
    <TT
CLASS="REPLACEABLE"
><I
>colname</I
></TT
> integer NOT NULL DEFAULT nextval('<TT
CLASS="REPLACEABLE"
><I
>tablename</I
></TT
>_<TT
CLASS="REPLACEABLE"
><I
>colname</I
></TT
>_seq')
);
ALTER SEQUENCE <TT
CLASS="REPLACEABLE"
><I
>tablename</I
></TT
>_<TT
CLASS="REPLACEABLE"
><I
>colname</I
></TT
>_seq OWNED BY <TT
CLASS="REPLACEABLE"
><I
>tablename</I
></TT
>.<TT
CLASS="REPLACEABLE"
><I
>colname</I
></TT
>;</PRE
><P>

     Thus, we have created an integer column and arranged for its default
     values to be assigned from a sequence generator.  A <TT
CLASS="LITERAL"
>NOT NULL</TT
>
     constraint is applied to ensure that a null value cannot be
     inserted.  (In most cases you would also want to attach a
     <TT
CLASS="LITERAL"
>UNIQUE</TT
> or <TT
CLASS="LITERAL"
>PRIMARY KEY</TT
> constraint to prevent
     duplicate values from being inserted by accident, but this is
     not automatic.)  Lastly, the sequence is marked as <SPAN
CLASS="QUOTE"
>"owned by"</SPAN
>
     the column, so that it will be dropped if the column or table is dropped.
    </P
><DIV
CLASS="NOTE"
><BLOCKQUOTE
CLASS="NOTE"
><P
><B
>Note: </B
>        Because <TT
CLASS="TYPE"
>smallserial</TT
>, <TT
CLASS="TYPE"
>serial</TT
> and
        <TT
CLASS="TYPE"
>bigserial</TT
> are implemented using sequences, there may
        be "holes" or gaps in the sequence of values which appears in the
        column, even if no rows are ever deleted.  A value allocated
        from the sequence is still "used up" even if a row containing that
        value is never successfully inserted into the table column.  This
        may happen, for example, if the inserting transaction rolls back.
        See <TT
CLASS="LITERAL"
>nextval()</TT
> in <A
HREF="functions-sequence.html"
>Section 9.16</A
>
        for details.
      </P
></BLOCKQUOTE
></DIV
><DIV
CLASS="NOTE"
><BLOCKQUOTE
CLASS="NOTE"
><P
><B
>Note: </B
>      Prior to <SPAN
CLASS="PRODUCTNAME"
>PostgreSQL</SPAN
> 7.3, <TT
CLASS="TYPE"
>serial</TT
>
      implied <TT
CLASS="LITERAL"
>UNIQUE</TT
>.  This is no longer automatic.  If
      you wish a serial column to have a unique constraint or be a
      primary key, it must now be specified, just like
      any other data type.
     </P
></BLOCKQUOTE
></DIV
><P
>     To insert the next value of the sequence into the <TT
CLASS="TYPE"
>serial</TT
>
     column, specify that the <TT
CLASS="TYPE"
>serial</TT
>
     column should be assigned its default value. This can be done
     either by excluding the column from the list of columns in
     the <TT
CLASS="COMMAND"
>INSERT</TT
> statement, or through the use of
     the <TT
CLASS="LITERAL"
>DEFAULT</TT
> key word.
    </P
><P
>     The type names <TT
CLASS="TYPE"
>serial</TT
> and <TT
CLASS="TYPE"
>serial4</TT
> are
     equivalent: both create <TT
CLASS="TYPE"
>integer</TT
> columns.  The type
     names <TT
CLASS="TYPE"
>bigserial</TT
> and <TT
CLASS="TYPE"
>serial8</TT
> work
     the same way, except that they create a <TT
CLASS="TYPE"
>bigint</TT
>
     column.  <TT
CLASS="TYPE"
>bigserial</TT
> should be used if you anticipate
     the use of more than 2<SUP
>31</SUP
> identifiers over the
     lifetime of the table. The type names <TT
CLASS="TYPE"
>smallserial</TT
> and
     <TT
CLASS="TYPE"
>serial2</TT
> also work the same way, except that they
     create a <TT
CLASS="TYPE"
>smallint</TT
> column.
    </P
><P
>     The sequence created for a <TT
CLASS="TYPE"
>serial</TT
> column is
     automatically dropped when the owning column is dropped.
     You can drop the sequence without dropping the column, but this
     will force removal of the column default expression.
    </P
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