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## 8.1. Numeric Types

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.

### 8.1.1. Integer Types

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.

### 8.1.2. Arbitrary Precision Numbers

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 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.)

### Note

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(``n`

)

.) The actual storage
requirement is two bytes for each group of four decimal digits,
plus three to eight bytes overhead.
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.

### Note

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)

### 8.1.3. Floating-Point Types

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.

### Note

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.

### Note

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.

### Note

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*)

*specifies the minimum acceptable precision in*

`p`

*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 *outside the allowed range draw an error.*

`p`

`float`

with no precision specified is taken to mean
`double precision`

.
### 8.1.4. Serial Types

### Note

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 TABLE(`tablename`

SERIAL );`colname`

is equivalent to specifying:

CREATE SEQUENCE_`tablename`

_seq AS integer; CREATE TABLE`colname`

(`tablename`

integer NOT NULL DEFAULT nextval('`colname`

_`tablename`

_seq') ); ALTER SEQUENCE`colname`

_`tablename`

_seq OWNED BY`colname`

.`tablename`

;`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.

### Note

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.