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<!DOCTYPE html PUBLIC "-//W3C//DTD XHTML 1.0 Transitional//EN" "http://www.w3.org/TR/xhtml1/DTD/xhtml1-transitional.dtd"><html xmlns="http://www.w3.org/1999/xhtml"><head><meta http-equiv="Content-Type" content="text/html; charset=UTF-8" /><title>8.1. Numeric Types</title><link rel="stylesheet" type="text/css" href="stylesheet.css" /><link rev="made" href="pgsql-docs@lists.postgresql.org" /><meta name="generator" content="DocBook XSL Stylesheets Vsnapshot" /><link rel="prev" href="datatype.html" title="Chapter 8. Data Types" /><link rel="next" href="datatype-money.html" title="8.2. Monetary Types" /></head><body><div xmlns="http://www.w3.org/TR/xhtml1/transitional" class="navheader"><table width="100%" summary="Navigation header"><tr><th colspan="5" align="center">8.1. Numeric Types</th></tr><tr><td width="10%" align="left"><a accesskey="p" href="datatype.html" title="Chapter 8. Data Types">Prev</a> </td><td width="10%" align="left"><a accesskey="u" href="datatype.html" title="Chapter 8. Data Types">Up</a></td><th width="60%" align="center">Chapter 8. Data Types</th><td width="10%" align="right"><a accesskey="h" href="index.html" title="PostgreSQL 11.5 Documentation">Home</a></td><td width="10%" align="right"> <a accesskey="n" href="datatype-money.html" title="8.2. Monetary Types">Next</a></td></tr></table><hr></hr></div><div class="sect1" id="DATATYPE-NUMERIC"><div class="titlepage"><div><div><h2 class="title" style="clear: both">8.1. Numeric Types</h2></div></div></div><div class="toc"><dl class="toc"><dt><span class="sect2"><a href="datatype-numeric.html#DATATYPE-INT">8.1.1. Integer Types</a></span></dt><dt><span class="sect2"><a href="datatype-numeric.html#DATATYPE-NUMERIC-DECIMAL">8.1.2. Arbitrary Precision Numbers</a></span></dt><dt><span class="sect2"><a href="datatype-numeric.html#DATATYPE-FLOAT">8.1.3. Floating-Point Types</a></span></dt><dt><span class="sect2"><a href="datatype-numeric.html#DATATYPE-SERIAL">8.1.4. Serial Types</a></span></dt></dl></div><a id="id-1.5.7.9.2" class="indexterm"></a><p>
    Numeric types consist of two-, four-, and eight-byte integers,
    four- and eight-byte floating-point numbers, and selectable-precision
    decimals.  <a class="xref" href="datatype-numeric.html#DATATYPE-NUMERIC-TABLE" title="Table 8.2. Numeric Types">Table 8.2</a> lists the
    available types.
   </p><div class="table" id="DATATYPE-NUMERIC-TABLE"><p class="title"><strong>Table 8.2. Numeric Types</strong></p><div class="table-contents"><table class="table" summary="Numeric Types" border="1"><colgroup><col /><col /><col /><col /></colgroup><thead><tr><th>Name</th><th>Storage Size</th><th>Description</th><th>Range</th></tr></thead><tbody><tr><td><code class="type">smallint</code></td><td>2 bytes</td><td>small-range integer</td><td>-32768 to +32767</td></tr><tr><td><code class="type">integer</code></td><td>4 bytes</td><td>typical choice for integer</td><td>-2147483648 to +2147483647</td></tr><tr><td><code class="type">bigint</code></td><td>8 bytes</td><td>large-range integer</td><td>-9223372036854775808 to +9223372036854775807</td></tr><tr><td><code class="type">decimal</code></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><code class="type">numeric</code></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><code class="type">real</code></td><td>4 bytes</td><td>variable-precision, inexact</td><td>6 decimal digits precision</td></tr><tr><td><code class="type">double precision</code></td><td>8 bytes</td><td>variable-precision, inexact</td><td>15 decimal digits precision</td></tr><tr><td><code class="type">smallserial</code></td><td>2 bytes</td><td>small autoincrementing integer</td><td>1 to 32767</td></tr><tr><td><code class="type">serial</code></td><td>4 bytes</td><td>autoincrementing integer</td><td>1 to 2147483647</td></tr><tr><td><code class="type">bigserial</code></td><td>8 bytes</td><td>large autoincrementing integer</td><td>1 to 9223372036854775807</td></tr></tbody></table></div></div><br class="table-break" /><p>
    The syntax of constants for the numeric types is described in
    <a class="xref" href="sql-syntax-lexical.html#SQL-SYNTAX-CONSTANTS" title="4.1.2. Constants">Section 4.1.2</a>.  The numeric types have a
    full set of corresponding arithmetic operators and
    functions. Refer to <a class="xref" href="functions.html" title="Chapter 9. Functions and Operators">Chapter 9</a> for more
    information.  The following sections describe the types in detail.
   </p><div class="sect2" id="DATATYPE-INT"><div class="titlepage"><div><div><h3 class="title">8.1.1. Integer Types</h3></div></div></div><a id="id-1.5.7.9.6.2" class="indexterm"></a><a id="id-1.5.7.9.6.3" class="indexterm"></a><a id="id-1.5.7.9.6.4" class="indexterm"></a><a id="id-1.5.7.9.6.5" class="indexterm"></a><a id="id-1.5.7.9.6.6" class="indexterm"></a><a id="id-1.5.7.9.6.7" class="indexterm"></a><p>
     The types <code class="type">smallint</code>, <code class="type">integer</code>, and
     <code class="type">bigint</code> 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 <code class="type">integer</code> is the common choice, as it offers
     the best balance between range, storage size, and performance.
     The <code class="type">smallint</code> type is generally only used if disk
     space is at a premium.  The <code class="type">bigint</code> type is designed to be
     used when the range of the <code class="type">integer</code> type is insufficient.
    </p><p>
     <acronym class="acronym">SQL</acronym> only specifies the integer types
     <code class="type">integer</code> (or <code class="type">int</code>),
     <code class="type">smallint</code>, and <code class="type">bigint</code>.  The
     type names <code class="type">int2</code>, <code class="type">int4</code>, and
     <code class="type">int8</code> are extensions, which are also used by some
     other <acronym class="acronym">SQL</acronym> database systems.
    </p></div><div class="sect2" id="DATATYPE-NUMERIC-DECIMAL"><div class="titlepage"><div><div><h3 class="title">8.1.2. Arbitrary Precision Numbers</h3></div></div></div><a id="id-1.5.7.9.7.2" class="indexterm"></a><a id="id-1.5.7.9.7.3" class="indexterm"></a><a id="id-1.5.7.9.7.4" class="indexterm"></a><p>
     The type <code class="type">numeric</code> can store numbers with a
     very large number of digits. It is especially recommended for
     storing monetary amounts and other quantities where exactness is
     required.  Calculations with <code class="type">numeric</code> values yield exact
     results where possible, e.g.  addition, subtraction, multiplication.
     However, calculations on <code class="type">numeric</code> values are 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
     <em class="firstterm">precision</em> of a <code class="type">numeric</code>
     is the total count of significant digits in the whole number,
     that is, the number of digits to both sides of the decimal point.
     The <em class="firstterm">scale</em> of a <code class="type">numeric</code> is the
     count of decimal digits in the fractional part, to the right 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
     <code class="type">numeric</code> column can be
     configured.  To declare a column of type <code class="type">numeric</code> use
     the syntax:
</p><pre class="programlisting">
NUMERIC(<em class="replaceable"><code>precision</code></em>, <em class="replaceable"><code>scale</code></em>)
</pre><p>
     The precision must be positive, the scale zero or positive.
     Alternatively:
</p><pre class="programlisting">
NUMERIC(<em class="replaceable"><code>precision</code></em>)
</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
     <code class="type">numeric</code> 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"><h3 class="title">Note</h3><p>
      The maximum allowed precision when explicitly specified in the
      type declaration is 1000; <code class="type">NUMERIC</code> without a specified
      precision is subject to the limits described in <a class="xref" href="datatype-numeric.html#DATATYPE-NUMERIC-TABLE" title="Table 8.2. Numeric Types">Table 8.2</a>.
     </p></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 <code class="type">numeric</code>
     type is more akin to <code class="type">varchar(<em class="replaceable"><code>n</code></em>)</code>
     than to <code class="type">char(<em class="replaceable"><code>n</code></em>)</code>.)  The actual storage
     requirement is two bytes for each group of four decimal digits,
     plus three to eight bytes overhead.
    </p><a id="id-1.5.7.9.7.11" class="indexterm"></a><a id="id-1.5.7.9.7.12" class="indexterm"></a><p>
     In addition to ordinary numeric values, the <code class="type">numeric</code>
     type allows the special value <code class="literal">NaN</code>, meaning
     <span class="quote">“<span class="quote">not-a-number</span>”</span>.  Any operation on <code class="literal">NaN</code>
     yields another <code class="literal">NaN</code>.  When writing this value
     as a constant in an SQL command, you must put quotes around it,
     for example <code class="literal">UPDATE table SET x = 'NaN'</code>.  On input,
     the string <code class="literal">NaN</code> is recognized in a case-insensitive manner.
    </p><div class="note"><h3 class="title">Note</h3><p>
      In most implementations of the <span class="quote">“<span class="quote">not-a-number</span>”</span> concept,
      <code class="literal">NaN</code> is not considered equal to any other numeric
      value (including <code class="literal">NaN</code>).  In order to allow
      <code class="type">numeric</code> values to be sorted and used in tree-based
      indexes, <span class="productname">PostgreSQL</span> treats <code class="literal">NaN</code>
      values as equal, and greater than all non-<code class="literal">NaN</code>
      values.
     </p></div><p>
     The types <code class="type">decimal</code> and <code class="type">numeric</code> are
     equivalent.  Both types are part of the <acronym class="acronym">SQL</acronym>
     standard.
    </p><p>
     When rounding values, the <code class="type">numeric</code> type rounds ties away
     from zero, while (on most machines) the <code class="type">real</code>
     and <code class="type">double precision</code> types round ties to the nearest even
     number.  For example:

</p><pre class="programlisting">
SELECT x,
  round(x::numeric) AS num_round,
  round(x::double precision) AS dbl_round
FROM generate_series(-3.5, 3.5, 1) as x;
  x   | num_round | dbl_round
------+-----------+-----------
 -3.5 |        -4 |        -4
 -2.5 |        -3 |        -2
 -1.5 |        -2 |        -2
 -0.5 |        -1 |        -0
  0.5 |         1 |         0
  1.5 |         2 |         2
  2.5 |         3 |         2
  3.5 |         4 |         4
(8 rows)
</pre><p>
    </p></div><div class="sect2" id="DATATYPE-FLOAT"><div class="titlepage"><div><div><h3 class="title">8.1.3. Floating-Point Types</h3></div></div></div><a id="id-1.5.7.9.8.2" class="indexterm"></a><a id="id-1.5.7.9.8.3" class="indexterm"></a><a id="id-1.5.7.9.8.4" class="indexterm"></a><a id="id-1.5.7.9.8.5" class="indexterm"></a><a id="id-1.5.7.9.8.6" class="indexterm"></a><p>
     The data types <code class="type">real</code> and <code class="type">double
     precision</code> 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><div class="itemizedlist"><ul class="itemizedlist" style="list-style-type: disc; "><li class="listitem"><p>
        If you require exact storage and calculations (such as for
        monetary amounts), use the <code class="type">numeric</code> type instead.
       </p></li><li class="listitem"><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 class="listitem"><p>
        Comparing two floating-point values for equality might not
        always work as expected.
       </p></li></ul></div><p>
    </p><p>
     On most platforms, the <code class="type">real</code> type has a range of at least
     1E-37 to 1E+37 with a precision of at least 6 decimal digits.  The
     <code class="type">double precision</code> 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"><h3 class="title">Note</h3><p>
      The <a class="xref" 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
      <code class="literal">0</code>, 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></div><a id="id-1.5.7.9.8.11" class="indexterm"></a><p>
     In addition to ordinary numeric values, the floating-point types
     have several special values:
</p><div class="literallayout"><p><br />
<code class="literal">Infinity</code><br />
<code class="literal">-Infinity</code><br />
<code class="literal">NaN</code><br />
</p></div><p>
     These represent the IEEE 754 special values
     <span class="quote">“<span class="quote">infinity</span>”</span>, <span class="quote">“<span class="quote">negative infinity</span>”</span>, and
     <span class="quote">“<span class="quote">not-a-number</span>”</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 <code class="literal">UPDATE table SET x = '-Infinity'</code>.  On input,
     these strings are recognized in a case-insensitive manner.
    </p><div class="note"><h3 class="title">Note</h3><p>
      IEEE754 specifies that <code class="literal">NaN</code> should not compare equal
      to any other floating-point value (including <code class="literal">NaN</code>).
      In order to allow floating-point values to be sorted and used
      in tree-based indexes, <span class="productname">PostgreSQL</span> treats
      <code class="literal">NaN</code> values as equal, and greater than all
      non-<code class="literal">NaN</code> values.
     </p></div><p>
     <span class="productname">PostgreSQL</span> also supports the SQL-standard
     notations <code class="type">float</code> and
     <code class="type">float(<em class="replaceable"><code>p</code></em>)</code> for specifying
     inexact numeric types.  Here, <em class="replaceable"><code>p</code></em> specifies
     the minimum acceptable precision in <span class="emphasis"><em>binary</em></span> digits.
     <span class="productname">PostgreSQL</span> accepts
     <code class="type">float(1)</code> to <code class="type">float(24)</code> as selecting the
     <code class="type">real</code> type, while
     <code class="type">float(25)</code> to <code class="type">float(53)</code> select
     <code class="type">double precision</code>.  Values of <em class="replaceable"><code>p</code></em>
     outside the allowed range draw an error.
     <code class="type">float</code> with no precision specified is taken to mean
     <code class="type">double precision</code>.
    </p><div class="note"><h3 class="title">Note</h3><p>
      The assumption that <code class="type">real</code> and
      <code class="type">double precision</code> 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 <em class="replaceable"><code>p</code></em> are used
      on all platforms.
     </p></div></div><div class="sect2" id="DATATYPE-SERIAL"><div class="titlepage"><div><div><h3 class="title">8.1.4. Serial Types</h3></div></div></div><a id="id-1.5.7.9.9.2" class="indexterm"></a><a id="id-1.5.7.9.9.3" class="indexterm"></a><a id="id-1.5.7.9.9.4" class="indexterm"></a><a id="id-1.5.7.9.9.5" class="indexterm"></a><a id="id-1.5.7.9.9.6" class="indexterm"></a><a id="id-1.5.7.9.9.7" class="indexterm"></a><a id="id-1.5.7.9.9.8" class="indexterm"></a><a id="id-1.5.7.9.9.9" class="indexterm"></a><div class="note"><h3 class="title">Note</h3><p>
      This section describes a PostgreSQL-specific way to create an
      autoincrementing column.  Another way is to use the SQL-standard
      identity column feature, described at <a class="xref" href="sql-createtable.html" title="CREATE TABLE"><span class="refentrytitle">CREATE TABLE</span></a>.
     </p></div><p>
     The data types <code class="type">smallserial</code>, <code class="type">serial</code> and
     <code class="type">bigserial</code> are not true types, but merely
     a notational convenience for creating unique identifier columns
     (similar to the <code class="literal">AUTO_INCREMENT</code> property
     supported by some other databases). In the current
     implementation, specifying:

</p><pre class="programlisting">
CREATE TABLE <em class="replaceable"><code>tablename</code></em> (
    <em class="replaceable"><code>colname</code></em> SERIAL
);
</pre><p>

     is equivalent to specifying:

</p><pre class="programlisting">
CREATE SEQUENCE <em class="replaceable"><code>tablename</code></em>_<em class="replaceable"><code>colname</code></em>_seq AS integer;
CREATE TABLE <em class="replaceable"><code>tablename</code></em> (
    <em class="replaceable"><code>colname</code></em> integer NOT NULL DEFAULT nextval('<em class="replaceable"><code>tablename</code></em>_<em class="replaceable"><code>colname</code></em>_seq')
);
ALTER SEQUENCE <em class="replaceable"><code>tablename</code></em>_<em class="replaceable"><code>colname</code></em>_seq OWNED BY <em class="replaceable"><code>tablename</code></em>.<em class="replaceable"><code>colname</code></em>;
</pre><p>

     Thus, we have created an integer column and arranged for its default
     values to be assigned from a sequence generator.  A <code class="literal">NOT NULL</code>
     constraint is applied to ensure that a null value cannot be
     inserted.  (In most cases you would also want to attach a
     <code class="literal">UNIQUE</code> or <code class="literal">PRIMARY KEY</code> constraint to prevent
     duplicate values from being inserted by accident, but this is
     not automatic.)  Lastly, the sequence is marked as <span class="quote">“<span class="quote">owned by</span>”</span>
     the column, so that it will be dropped if the column or table is dropped.
    </p><div class="note"><h3 class="title">Note</h3><p>
        Because <code class="type">smallserial</code>, <code class="type">serial</code> and
        <code class="type">bigserial</code> 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 <code class="literal">nextval()</code> in <a class="xref" href="functions-sequence.html" title="9.16. Sequence Manipulation Functions">Section 9.16</a>
        for details.
      </p></div><p>
     To insert the next value of the sequence into the <code class="type">serial</code>
     column, specify that the <code class="type">serial</code>
     column should be assigned its default value. This can be done
     either by excluding the column from the list of columns in
     the <code class="command">INSERT</code> statement, or through the use of
     the <code class="literal">DEFAULT</code> key word.
    </p><p>
     The type names <code class="type">serial</code> and <code class="type">serial4</code> are
     equivalent: both create <code class="type">integer</code> columns.  The type
     names <code class="type">bigserial</code> and <code class="type">serial8</code> work
     the same way, except that they create a <code class="type">bigint</code>
     column.  <code class="type">bigserial</code> 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 <code class="type">smallserial</code> and
     <code class="type">serial2</code> also work the same way, except that they
     create a <code class="type">smallint</code> column.
    </p><p>
     The sequence created for a <code class="type">serial</code> 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></div></div><div class="navfooter"><hr /><table width="100%" summary="Navigation footer"><tr><td width="40%" align="left"><a accesskey="p" href="datatype.html">Prev</a> </td><td width="20%" align="center"><a accesskey="u" href="datatype.html">Up</a></td><td width="40%" align="right"> <a accesskey="n" href="datatype-money.html">Next</a></td></tr><tr><td width="40%" align="left" valign="top">Chapter 8. Data Types </td><td width="20%" align="center"><a accesskey="h" href="index.html">Home</a></td><td width="40%" align="right" valign="top"> 8.2. Monetary Types</td></tr></table></div></body></html>