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
(colname
SERIAL );
is equivalent to specifying:
CREATE SEQUENCEtablename
_colname
_seq; CREATE TABLEtablename
(colname
integer 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
2^{31} 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.
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