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8.1.1. Integer Types

8.1.2. Arbitrary Precision Numbers

8.1.3. Floating-Point Types

8.1.4. Serial Types

Table 8.2. Numeric Types

The typessmallint,integer, andbigint 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 typeinteger is the common choice, as it offers the best balance between range, storage size, and performance. Thesmallint type is generally only used if disk space is at a premium. Thebigint type is designed to be used when the range of theinteger type is insufficient.

SQL only specifies the integer typesinteger (orint),smallint, andbigint. The type namesint2,int4, andint8 are extensions, which are also used by some otherSQL database systems.

The typenumeric 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 withnumeric values yield exact results where possible, e.g., addition, subtraction, multiplication. However, calculations onnumeric 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: Theprecision of anumeric is the total count of significant digits in the whole number, that is, the number of digits to both sides of the decimal point. Thescale of anumeric 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 anumeric column can be configured. To declare a column of typenumeric use the syntax:

NUMERIC(precision,scale)

The precision must be positive, while the scale may be positive or negative (see below). 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, whereasnumeric columns with a declared scale will coerce input values to that scale. (TheSQL 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.)

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. For example, a column declared as

NUMERIC(3, 1)

will round values to 1 decimal place and can store values between -99.9 and 99.9, inclusive.

Beginning inPostgreSQL 15, it is allowed to declare anumeric column with a negative scale. Then values will be rounded to the left of the decimal point. The precision still represents the maximum number of non-rounded digits. Thus, a column declared as

NUMERIC(2, -3)

will round values to the nearest thousand and can store values between -99000 and 99000, inclusive. It is also allowed to declare a scale larger than the declared precision. Such a column can only hold fractional values, and it requires the number of zero digits just to the right of the decimal point to be at least the declared scale minus the declared precision. For example, a column declared as

NUMERIC(3, 5)

will round values to 5 decimal places and can store values between -0.00999 and 0.00999, inclusive.

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 thenumeric type is more akin tovarchar(n) than tochar(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, thenumeric type has several special values:

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 exampleUPDATE table SET x = '-Infinity'. On input, these strings are recognized in a case-insensitive manner. The infinity values can alternatively be spelledinf and-inf.

The infinity values behave as per mathematical expectations. For example,Infinity plus any finite value equalsInfinity, as doesInfinity plusInfinity; butInfinity minusInfinity yieldsNaN (not a number), because it has no well-defined interpretation. Note that an infinity can only be stored in an unconstrainednumeric column, because it notionally exceeds any finite precision limit.

TheNaN (not a number) value is used to represent undefined calculational results. In general, any operation with aNaN input yields anotherNaN. The only exception is when the operation's other inputs are such that the same output would be obtained if theNaN were to be replaced by any finite or infinite numeric value; then, that output value is used forNaN too. (An example of this principle is thatNaN raised to the zero power yields one.)

The typesdecimal andnumeric are equivalent. Both types are part of theSQL standard.

When rounding values, thenumeric type rounds ties away from zero, while (on most machines) thereal anddouble 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_roundFROM 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 typesreal anddouble precision are inexact, variable-precision numeric types. On all currently supported platforms, these types are implementations ofIEEE 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:

On all currently supported platforms, thereal type has a range of around 1E-37 to 1E+37 with a precision of at least 6 decimal digits. Thedouble 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 neverexactly 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 forfloat8 values, and at most 9 digits forfloat4 values.

For compatibility with output generated by older versions ofPostgreSQL, and to allow the output precision to be reduced, theextra_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 (forfloat4) or 15 (forfloat8) 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 ofextra_float_digits greater than 0 selects the shortest-precise format.

In addition to ordinary numeric values, the floating-point types have several special values:

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 exampleUPDATE table SET x = '-Infinity'. On input, these strings are recognized in a case-insensitive manner. The infinity values can alternatively be spelledinf and-inf.

PostgreSQL also supports the SQL-standard notationsfloat andfloat(p) for specifying inexact numeric types. Here,p specifies the minimum acceptable precision inbinary digits.PostgreSQL acceptsfloat(1) tofloat(24) as selecting thereal type, whilefloat(25) tofloat(53) selectdouble precision. Values ofp outside the allowed range draw an error.float with no precision specified is taken to meandouble precision.

The data typessmallserial,serial andbigserial are not true types, but merely a notational convenience for creating unique identifier columns (similar to theAUTO_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. ANOT NULL constraint is applied to ensure that a null value cannot be inserted. (In most cases you would also want to attach aUNIQUE orPRIMARY 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.

To insert the next value of the sequence into theserial column, specify that theserial column should be assigned its default value. This can be done either by excluding the column from the list of columns in theINSERT statement, or through the use of theDEFAULT key word.

The type namesserial andserial4 are equivalent: both createinteger columns. The type namesbigserial andserial8 work the same way, except that they create abigint column.bigserial should be used if you anticipate the use of more than 2³¹ identifiers over the lifetime of the table. The type namessmallserial andserial2 also work the same way, except that they create asmallint column.

The sequence created for aserial 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.