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 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. The scale of a numeric
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.
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 an “unconstrained numeric” column in which numeric values of any length can be stored, up to the implementation limits. 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 precision that can be explicitly specified in a NUMERIC
type declaration is 1000. An unconstrained NUMERIC
column 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 has several special values:
Infinity
-Infinity
NaN
These are adapted from the IEEE 754 standard, and represent “infinity”, “negative infinity”, and “not-a-number”, respectively. 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. The infinity values can alternatively be spelled inf
and -inf
.
The infinity values behave as per mathematical expectations. For example, Infinity
plus any finite value equals Infinity
, as does Infinity
plus Infinity
; but Infinity
minus Infinity
yields NaN
(not a number), because it has no well-defined interpretation. Note that an infinity can only be stored in an unconstrained numeric
column, because it notionally exceeds any finite precision limit.
The NaN
(not a number) value is used to represent undefined calculational results. In general, any operation with a NaN
input yields another NaN
. The only exception is when the operation's other inputs are such that the same output would be obtained if the NaN
were to be replaced by any finite or infinite numeric value; then, that output value is used for NaN
too. (An example of this principle is that NaN
raised to the zero power yields one.)
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. On all currently supported platforms, these types are 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 all currently supported platforms, the real
type has a range of around 1E-37 to 1E+37 with a precision of at least 6 decimal digits. The double precision
type 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.
By default, floating point values are output in text form in their shortest precise decimal representation; the decimal value produced is closer to the true stored binary value than to any other value representable in the same binary precision. (However, the output value is currently never exactly midway between two representable values, in order to avoid a widespread bug where input routines do not properly respect the round-to-nearest-even rule.) This value will use at most 17 significant decimal digits for float8
values, and at most 9 digits for float4
values.
This shortest-precise output format is much faster to generate than the historical rounded format.
For compatibility with output generated by older versions of PostgreSQL, and to allow the output precision to be reduced, the extra_float_digits parameter can be used to select rounded decimal output instead. Setting a value of 0 restores the previous default of rounding the value to 6 (for float4
) or 15 (for float8
) significant decimal digits. Setting a negative value reduces the number of digits further; for example -2 would round output to 4 or 13 digits respectively.
Any value of extra_float_digits greater than 0 selects the shortest-precise format.
Applications that wanted precise values have historically had to set extra_float_digits to 3 to obtain them. For maximum compatibility between versions, they should continue to do so.
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. 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. The infinity values can alternatively be spelled inf
and -inf
.
IEEE 754 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
.
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 AS integer; 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 9.17 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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