Numeric types consist of two-, four-, and eight-byte integers, four- and eight-byte floating-point numbers, and selectable-precision decimals. Table 8.2 lists the available types.
Table 8.2. Numeric Types
| Name | Storage Size | Description | Range | 
|---|---|---|---|
| smallint | 2 bytes | small-range integer | -32768 to +32767 | 
| integer | 4 bytes | typical choice for integer | -2147483648 to +2147483647 | 
| bigint | 8 bytes | large-range integer | -9223372036854775808 to +9223372036854775807 | 
| decimal | variable | user-specified precision, exact | up to 131072 digits before the decimal point; up to 16383 digits after the decimal point | 
| numeric | variable | user-specified precision, exact | up to 131072 digits before the decimal point; up to 16383 digits after the decimal point | 
| real | 4 bytes | variable-precision, inexact | 6 decimal digits precision | 
| double precision | 8 bytes | variable-precision, inexact | 15 decimal digits precision | 
| smallserial | 2 bytes | small autoincrementing integer | 1 to 32767 | 
| serial | 4 bytes | autoincrementing integer | 1 to 2147483647 | 
| bigserial | 8 bytes | large autoincrementing integer | 1 to 9223372036854775807 | 
The syntax of constants for the numeric types is described in Section 4.1.2. The numeric types have a full set of corresponding arithmetic operators and functions. Refer to Chapter 9 for more information. The following sections describe the types in detail.
     The types smallint, integer, and
     bigint 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.
    
     The type integer is the common choice, as it offers
     the best balance between range, storage size, and performance.
     The smallint type is generally only used if disk
     space is at a premium.  The bigint type is designed to be
     used when the range of the integer type is insufficient.
    
     SQL only specifies the integer types
     integer (or int),
     smallint, and bigint.  The
     type names int2, int4, and
     int8 are extensions, which are also used by some
     other SQL database systems.
    
     The type numeric 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 numeric values yield exact
     results where possible, e.g.  addition, subtraction, multiplication.
     However, calculations on numeric values are very slow
     compared to the integer types, or to the floating-point types
     described in the next section.
    
     We use the following terms below:  The
     scale of a numeric is the
     count of decimal digits in the fractional part, to the right of
     the decimal point.  The precision of a
     numeric 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.
    
     Both the maximum precision and the maximum scale of a
     numeric column can be
     configured.  To declare a column of type numeric use
     the syntax:
NUMERIC(precision,scale)
The precision must be positive, the scale zero or positive. Alternatively:
NUMERIC(precision)selects a scale of 0. Specifying:
NUMERIC
     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
     numeric columns with a declared scale will coerce
     input values to that scale.  (The SQL 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.)
    
      The maximum allowed precision when explicitly specified in the
      type declaration is 1000; NUMERIC without a specified
      precision is subject to the limits described in Table 8.2.
     
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.
     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 numeric
     type is more akin to varchar(
     than to n)char(.)  The actual storage
     requirement is two bytes for each group of four decimal digits,
     plus three to eight bytes overhead.
    n)
     In addition to ordinary numeric values, the numeric
     type allows the special value NaN, meaning
     “not-a-number”.  Any operation on NaN
     yields another NaN.  When writing this value
     as a constant in an SQL command, you must put quotes around it,
     for example UPDATE table SET x = 'NaN'.  On input,
     the string NaN is recognized in a case-insensitive manner.
    
      In most implementations of the “not-a-number” concept,
      NaN is not considered equal to any other numeric
      value (including NaN).  In order to allow
      numeric values to be sorted and used in tree-based
      indexes, PostgreSQL treats NaN
      values as equal, and greater than all non-NaN
      values.
     
     The types decimal and numeric are
     equivalent.  Both types are part of the SQL
     standard.
    
     When rounding values, the numeric type rounds ties away
     from zero, while (on most machines) the real
     and double precision types round ties to the nearest even
     number.  For example:
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)
     The data types real and double
     precision are inexact, variable-precision numeric types.
     In practice, these types are usually implementations of
     IEEE 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.
    
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:
        If you require exact storage and calculations (such as for
        monetary amounts), use the numeric type instead.
       
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.
Comparing two floating-point values for equality might not always work as expected.
     On most platforms, the real type has a range of at least
     1E-37 to 1E+37 with a precision of at least 6 decimal digits.  The
     double precision 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.
    
      The extra_float_digits 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
      0, 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.
     
In addition to ordinary numeric values, the floating-point types have several special values:
Infinity
-Infinity
NaN
     These represent the IEEE 754 special values
     “infinity”, “negative infinity”, and
     “not-a-number”, 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 UPDATE table SET x = '-Infinity'.  On input,
     these strings are recognized in a case-insensitive manner.
    
      IEEE754 specifies that NaN should not compare equal
      to any other floating-point value (including NaN).
      In order to allow floating-point values to be sorted and used
      in tree-based indexes, PostgreSQL treats
      NaN values as equal, and greater than all
      non-NaN values.
     
     PostgreSQL also supports the SQL-standard
     notations float and
     float( for specifying
     inexact numeric types.  Here, p)p specifies
     the minimum acceptable precision in binary digits.
     PostgreSQL accepts
     float(1) to float(24) as selecting the
     real type, while
     float(25) to float(53) select
     double precision.  Values of p
     outside the allowed range draw an error.
     float with no precision specified is taken to mean
     double precision.
    
      The assumption that real and
      double precision 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 p are used
      on all platforms.
     
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 CREATE TABLE.
     The data types smallserial, serial and
     bigserial are not true types, but merely
     a notational convenience for creating unique identifier columns
     (similar to the AUTO_INCREMENT property
     supported by some other databases). In the current
     implementation, specifying:
CREATE TABLEtablename(colnameSERIAL );
is equivalent to specifying:
CREATE SEQUENCEtablename_colname_seq; CREATE TABLEtablename(colnameinteger NOT NULL DEFAULT nextval('tablename_colname_seq') ); ALTER SEQUENCEtablename_colname_seq OWNED BYtablename.colname;
     Thus, we have created an integer column and arranged for its default
     values to be assigned from a sequence generator.  A NOT NULL
     constraint is applied to ensure that a null value cannot be
     inserted.  (In most cases you would also want to attach a
     UNIQUE or PRIMARY KEY constraint to prevent
     duplicate values from being inserted by accident, but this is
     not automatic.)  Lastly, the sequence is marked as “owned by”
     the column, so that it will be dropped if the column or table is dropped.
    
        Because smallserial, serial and
        bigserial 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 nextval() in Section 9.16
        for details.
      
     To insert the next value of the sequence into the serial
     column, specify that the serial
     column should be assigned its default value. This can be done
     either by excluding the column from the list of columns in
     the INSERT statement, or through the use of
     the DEFAULT key word.
    
     The type names serial and serial4 are
     equivalent: both create integer columns.  The type
     names bigserial and serial8 work
     the same way, except that they create a bigint
     column.  bigserial should be used if you anticipate
     the use of more than 231 identifiers over the
     lifetime of the table. The type names smallserial and
     serial2 also work the same way, except that they
     create a smallint column.
    
     The sequence created for a serial 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.