# Impala mathematical functions

Mathematical functions, or arithmetic functions, perform numeric calculations that are typically more complex than basic addition, subtraction, multiplication, and division. For example, these functions include trigonometric, logarithmic, and base conversion operations.

Related information:

The mathematical functions operate mainly on these data types:
• INT
• BIGINT
• SMALLINT
• TINYINT
• DOUBLE
• FLOAT
• DECIMAL
For the operators that perform the standard operations such as addition, subtraction, multiplication, and division, see Arithmetic operators.

Functions that perform bitwise operations are explained in Impala bit functions.

Function reference:

Impala supports the following mathematical functions:

ABS(numeric_type a)
Purpose: Returns the absolute value of the argument.

Return type: Same as the input value

Usage notes: Use this function to ensure all return values are positive. This is different than the `positive()` function, which returns its argument unchanged (even if the argument was negative).

ACOS(DOUBLE a)
Purpose: Returns the arccosine of the argument.

Return type: `DOUBLE`

ASIN(DOUBLE a)
Purpose: Returns the arcsine of the argument.

Return type: `DOUBLE`

ATAN(DOUBLE a)
Purpose: Returns the arctangent of the argument.

Return type: `DOUBLE`

ATAN(DOUBLE a, DOUBLE b)
Purpose: Returns the arctangent of the two arguments, with the signs of the arguments used to determine the quadrant of the result.

Return type: `DOUBLE`

BIN(BIGINT a)
Purpose: Returns the binary representation of an integer value, that is, a string of 0 and 1 digits.

Return type: `STRING`

CEIL(DOUBLE a), CEIL(DECIMAL(p,s) a), CEILING(DOUBLE a), CEILING(DECIMAL(p,s) a), DCEIL(DOUBLE a), DCEIL(DECIMAL(p,s) a)
Purpose: Returns the smallest integer that is greater than or equal to the argument.

Return type: Same as the input type

CONV(BIGINT n, INT from_base, INT to_base), CONV(STRING s, INT from_base, INT to_base)
Purpose: Returns a string representation of the first argument converted from `from_base` to `to_base`. The first argument can be specified as a number or a string. For example, `conv(100, 2, 10)` and `conv('100', 2, 10)` both return `'4'`.

Return type: `STRING`

Usage notes:

If `to_base` is negative, the first argument is treated as signed, and otherwise, it is treated as unsigned. For example:

• `conv(-17, 10, -2) `returns `'-10001'`,``` -17``` in base 2.
• `conv(-17, 10, 10)` returns `'18446744073709551599'`. `-17` is interpreted as an unsigned, 2^64-17, and then the value is returned in base 10.

The function returns `NULL` when the following invalid arguments are specified:

• Any argument is `NULL`.
• `from_base` or `to_base` is below `-36` or above `36`.
• `from_base` or `to_base` is `-1`, `0`, or `1`.
• The first argument represents a positive number and `from_base` is a negative number.

If the first argument represents a negative number and `from_base` is a negative number, the function returns `0`.

If the first argument represents a number larger than the maximum `bigint`, the function returns:

• The string representation of -1 in `to_base` if `to_base` is negative.
• The string representation of 18446744073709551615' (2^64 - 1) in `to_base` if `to_base` is positive.

If the first argument does not represent a valid number in `from_base`, e.g. 3 in base 2 or '1a23' in base 10, the digits in the first argument are evaluated from left-to-right and used if a valid digit in `from_base`. The invalid digit and the digits to the right are ignored.

For example:
• ` conv(445, 5, 10)` is converted to ```conv(44, 5, 10)``` and returns `'24'`.
• ` conv('1a23', 10, 16)` is converted to ```conv('1', 10 , 16)``` and returns `'1'`.
COS(DOUBLE a)
Purpose: Returns the cosine of the argument.

Return type: `DOUBLE`

COSH(DOUBLE a)
Purpose: Returns the hyperbolic cosine of the argument.

Return type: `DOUBLE`

COT(DOUBLE a)
Purpose: Returns the cotangent of the argument.

Return type: `DOUBLE`

DEGREES(DOUBLE a)
Purpose: Converts argument value from radians to degrees.

Return type: `DOUBLE`

E()
Purpose: Returns the mathematical constant e.

Return type: `DOUBLE`

EXP(DOUBLE a), DEXP(DOUBLE a)
Purpose: Returns the mathematical constant e raised to the power of the argument.

Return type: `DOUBLE`

FACTORIAL(integer_type a)
Purpose: Computes the factorial of an integer value. It works with any integer type.

Usage notes: You can use either the `factorial()` function or the `!` operator. The factorial of 0 is 1. Likewise, the `factorial()` function returns 1 for any negative value. The maximum positive value for the input argument is 20; a value of 21 or greater overflows the range for a `BIGINT` and causes an error.

Return type: `BIGINT`

``````select factorial(5);
+--------------+
| factorial(5) |
+--------------+
| 120          |
+--------------+

select 5!;
+-----+
| 5!  |
+-----+
| 120 |
+-----+
``````
FLOOR(DOUBLE a), FLOOR(DECIMAL(p,s) a), DFLOOR(DOUBLE a), DFLOOR(DECIMAL(p,s) a)
Purpose: Returns the largest integer that is less than or equal to the argument.

Return type: Same as the input type

FMOD(DOUBLE a, DOUBLE b), FMOD(FLOAT a, FLOAT b)
Purpose: Returns the modulus of a floating-point number.

Return type: `FLOAT` or `DOUBLE`, depending on type of arguments

Usage notes:

Because this function operates on `DOUBLE` or `FLOAT` values, it is subject to potential rounding errors for values that cannot be represented precisely. Prefer to use whole numbers, or values that you know can be represented precisely by the `DOUBLE` or `FLOAT` types.

Examples:

The following examples show equivalent operations with the `fmod()` function and the `%` arithmetic operator, for values not subject to any rounding error.

``````select fmod(10,3);
+-------------+
| fmod(10, 3) |
+-------------+
| 1           |
+-------------+

select fmod(5.5,2);
+--------------+
| fmod(5.5, 2) |
+--------------+
| 1.5          |
+--------------+

select 10 % 3;
+--------+
| 10 % 3 |
+--------+
| 1      |
+--------+

select 5.5 % 2;
+---------+
| 5.5 % 2 |
+---------+
| 1.5     |
+---------+
``````

The following examples show operations with the `fmod()` function for values that cannot be represented precisely by the `DOUBLE` or `FLOAT` types, and thus are subject to rounding error. `fmod(9.9,3.0)` returns a value slightly different than the expected 0.9 because of rounding. `fmod(9.9,3.3)` returns a value quite different from the expected value of 0 because of rounding error during intermediate calculations.

``````select fmod(9.9,3.0);
+--------------------+
| fmod(9.9, 3.0)     |
+--------------------+
| 0.8999996185302734 |
+--------------------+

select fmod(9.9,3.3);
+-------------------+
| fmod(9.9, 3.3)    |
+-------------------+
| 3.299999713897705 |
+-------------------+
``````
FNV_HASH(type v)
Purpose: Returns a consistent 64-bit value derived from the input argument, for convenience of implementing hashing logic in an application.

Return type: `BIGINT`

Usage notes:

You might use the return value in an application where you perform load balancing, bucketing, or some other technique to divide processing or storage.

Because the result can be any 64-bit value, to restrict the value to a particular range, you can use an expression that includes the `ABS()` function and the `%` (modulo) operator. For example, to produce a hash value in the range 0-9, you could use the expression `ABS(FNV_HASH(x)) % 10`.

This function implements the same algorithm that Impala uses internally for hashing, on systems where the CRC32 instructions are not available.

This function implements the Fowler–Noll–Vo hash function, in particular the FNV-1a variation. This is not a perfect hash function: some combinations of values could produce the same result value. It is not suitable for cryptographic use.

Similar input values of different types could produce different hash values, for example the same numeric value represented as `SMALLINT` or `BIGINT`, `FLOAT` or `DOUBLE`, or `DECIMAL(5,2)` or `DECIMAL(20,5)`.

Examples:

``````[localhost:21000] > create table h (x int, s string);
[localhost:21000] > insert into h values (0, 'hello'), (1,'world'), (1234567890,'antidisestablishmentarianism');
[localhost:21000] > select x, fnv_hash(x) from h;
+------------+----------------------+
| x          | fnv_hash(x)          |
+------------+----------------------+
| 0          | -2611523532599129963 |
| 1          | 4307505193096137732  |
| 1234567890 | 3614724209955230832  |
+------------+----------------------+
[localhost:21000] > select s, fnv_hash(s) from h;
+------------------------------+---------------------+
| s                            | fnv_hash(s)         |
+------------------------------+---------------------+
| hello                        | 6414202926103426347 |
| world                        | 6535280128821139475 |
| antidisestablishmentarianism | -209330013948433970 |
+------------------------------+---------------------+
[localhost:21000] > select s, abs(fnv_hash(s)) % 10 from h;
+------------------------------+-------------------------+
| s                            | abs(fnv_hash(s)) % 10.0 |
+------------------------------+-------------------------+
| hello                        | 8                       |
| world                        | 6                       |
| antidisestablishmentarianism | 4                       |
+------------------------------+-------------------------+``````

For short argument values, the high-order bits of the result have relatively low entropy:

``````[localhost:21000] > create table b (x boolean);
[localhost:21000] > insert into b values (true), (true), (false), (false);
[localhost:21000] > select x, fnv_hash(x) from b;
+-------+---------------------+
| x     | fnv_hash(x)         |
+-------+---------------------+
| true  | 2062020650953872396 |
| true  | 2062020650953872396 |
| false | 2062021750465500607 |
| false | 2062021750465500607 |
+-------+---------------------+``````

GREATEST(BIGINT a[, BIGINT b ...]), GREATEST(DOUBLE a[, DOUBLE b ...]), GREATEST(DECIMAL(p,s) a[, DECIMAL(p,s) b ...]), GREATEST(STRING a[, STRING b ...]), GREATEST(TIMESTAMP a[, TIMESTAMP b ...])
Purpose: Returns the largest value from a list of expressions.

Return type: same as the initial argument value, except that integer values are promoted to `BIGINT` and floating-point values are promoted to `DOUBLE`; use `CAST()` when inserting into a smaller numeric column

HEX(BIGINT a), HEX(STRING a)
Purpose: Returns the hexadecimal representation of an integer value, or of the characters in a string.

Return type: `STRING`

IS_INF(DOUBLE a)
Purpose: Tests whether a value is equal to the special value inf, signifying infinity.

Return type: `BOOLEAN`

Usage notes:

Infinity and NaN can be specified in text data files as `inf` and `nan` respectively, and Impala interprets them as these special values. They can also be produced by certain arithmetic expressions; for example, `1/0` returns `Infinity` and `pow(-1, 0.5)` returns `NaN`. Or you can cast the literal values, such as ```CAST('nan' AS DOUBLE)``` or `CAST('inf' AS DOUBLE)`.

IS_NAN(DOUBLE a)
Purpose: Tests whether a value is equal to the special value NaN, signifying not a number.

Return type: `BOOLEAN`

Usage notes:

Infinity and NaN can be specified in text data files as `inf` and `nan` respectively, and Impala interprets them as these special values. They can also be produced by certain arithmetic expressions; for example, `1/0` returns `Infinity` and `pow(-1, 0.5)` returns `NaN`. Or you can cast the literal values, such as ```CAST('nan' AS DOUBLE)``` or `CAST('inf' AS DOUBLE)`.

LEAST(BIGINT a[, BIGINT b ...]), LEAST(DOUBLE a[, DOUBLE b ...]), LEAST(DECIMAL(p,s) a[, DECIMAL(p,s) b ...]), LEAST(STRING a[, STRING b ...]), LEAST(TIMESTAMP a[, TIMESTAMP b ...])
Purpose: Returns the smallest value from a list of expressions.

Return type: same as the initial argument value, except that integer values are promoted to `BIGINT` and floating-point values are promoted to `DOUBLE`; use `CAST()` when inserting into a smaller numeric column

LN(DOUBLE a), DLOG1(DOUBLE a)
Purpose: Returns the natural logarithm of the argument.

Return type: `DOUBLE`

LOG(DOUBLE base, DOUBLE a)
Purpose: Returns the logarithm of the second argument to the specified base.

Return type: `DOUBLE`

LOG10(DOUBLE a), DLOG10(DOUBLE a)
Purpose: Returns the logarithm of the argument to the base 10.

Return type: `DOUBLE`

LOG2(DOUBLE a)
Purpose: Returns the logarithm of the argument to the base 2.

Return type: `DOUBLE`

MAX_INT(), MAX_TINYINT(), MAX_SMALLINT(), MAX_BIGINT()
Purpose: Returns the largest value of the associated integral type.

Return type: The same as the integral type being checked.

Usage notes: Use the corresponding `min_` and `max_` functions to check if all values in a column are within the allowed range, before copying data or altering column definitions. If not, switch to the next higher integral type or to a `DECIMAL` with sufficient precision.

MIN_INT(), MIN_TINYINT(), MIN_SMALLINT(), MIN_BIGINT()
Purpose: Returns the smallest value of the associated integral type (a negative number).

Return type: The same as the integral type being checked.

Usage notes: Use the corresponding `min_` and `max_` functions to check if all values in a column are within the allowed range, before copying data or altering column definitions. If not, switch to the next higher integral type or to a `DECIMAL` with sufficient precision.

MOD(numeric_type a, same_type b)
Purpose: Returns the modulus of a number. Equivalent to the `%` arithmetic operator. Works with any size integer type, any size floating-point type, and `DECIMAL` with any precision and scale.

Return type: Same as the input value

Usage notes:

Because this function works with `DECIMAL` values, prefer it over `fmod()` when working with fractional values. It is not subject to the rounding errors that make `fmod()` problematic with floating-point numbers.

Query plans shows the `MOD()` function as the `%` operator.

Examples:

The following examples show how the `mod()` function works for whole numbers and fractional values, and how the `%` operator works the same way. In the case of `mod(9.9,3)`, the type conversion for the second argument results in the first argument being interpreted as `DOUBLE`, so to produce an accurate `DECIMAL` result requires casting the second argument or writing it as a `DECIMAL` literal, 3.0.

``````select mod(10,3);
+-------------+
| mod(10, 3) |
+-------------+
| 1           |
+-------------+

select mod(5.5,2);
+--------------+
| mod(5.5, 2) |
+--------------+
| 1.5          |
+--------------+

select 10 % 3;
+--------+
| 10 % 3 |
+--------+
| 1      |
+--------+

select 5.5 % 2;
+---------+
| 5.5 % 2 |
+---------+
| 1.5     |
+---------+

select mod(9.9,3.3);
+---------------+
| mod(9.9, 3.3) |
+---------------+
| 0.0           |
+---------------+

select mod(9.9,3);
+--------------------+
| mod(9.9, 3)        |
+--------------------+
| 0.8999996185302734 |
+--------------------+

select mod(9.9, cast(3 as decimal(2,1)));
+-----------------------------------+
| mod(9.9, cast(3 as decimal(2,1))) |
+-----------------------------------+
| 0.9                               |
+-----------------------------------+

select mod(9.9,3.0);
+---------------+
| mod(9.9, 3.0) |
+---------------+
| 0.9           |
+---------------+
``````
MURMUR_HASH(type v)
Purpose: Returns a consistent 64-bit value derived from the input argument, for convenience of implementing MurmurHash2 non-cryptographic hash function.

Return type: `BIGINT`

Usage notes:

You might use the return value in an application where you perform load balancing, bucketing, or some other technique to divide processing or storage. This function provides a good performance for all kinds of keys such as number, ascii string and UTF-8. It can be recommended as general-purpose hashing function.

Regarding comparison of murmur_hash with fnv_hash, murmur_hash is based on Murmur2 hash algorithm and fnv_hash function is based on FNV-1a hash algorithm. Murmur2 and FNV-1a can show very good randomness and performance compared with well known other hash algorithms, but Murmur2 slightly show better randomness and performance than FNV-1a.

Similar input values of different types could produce different hash values, for example the same numeric value represented as `SMALLINT` or `BIGINT`, `FLOAT` or `DOUBLE`, or `DECIMAL(5,2)` or `DECIMAL(20,5)`.

Examples:

``````[localhost:21000] > create table h (x int, s string);
[localhost:21000] > insert into h values (0, 'hello'), (1,'world'), (1234567890,'antidisestablishmentarianism');
[localhost:21000] > select x, murmur_hash(x) from h;
+------------+----------------------+
| x          | murmur_hash(x)       |
+------------+----------------------+
| 0          | 6960269033020761575  |
| 1          | -780611581681153783  |
| 1234567890 | -5754914572385924334 |
+------------+----------------------+
[localhost:21000] > select s, murmur_hash(s) from h;
+------------------------------+----------------------+
| s                            | murmur_hash(s)       |
+------------------------------+----------------------+
| hello                        | 2191231550387646743  |
| world                        | 5568329560871645431  |
| antidisestablishmentarianism | -2261804666958489663 |
+------------------------------+----------------------+ ``````

For short argument values, the high-order bits of the result have relatively higher entropy than fnv_hash:

``````[localhost:21000] > create table b (x boolean);
[localhost:21000] > insert into b values (true), (true), (false), (false);
[localhost:21000] > select x, murmur_hash(x) from b;
+-------+----------------------+
| x     | murmur_hash(x)       |
+-------+---------------------++
| true  | -5720937396023583481 |
| true  | -5720937396023583481 |
| false | 6351753276682545529  |
| false | 6351753276682545529  |
+-------+--------------------+-+``````

NEGATIVE(numeric_type a)
Purpose: Returns the argument with the sign reversed; returns a positive value if the argument was already negative.

Return type: Same as the input value

Usage notes: Use `-abs(a)` instead if you need to ensure all return values are negative.

PI()
Purpose: Returns the constant pi.

Return type: `double`

PMOD(BIGINT a, BIGINT b), PMOD(DOUBLE a, DOUBLE b)
Purpose: Returns the positive modulus of a number. Primarily for Hive SQL compatibility.

Return type: `INT` or `DOUBLE`, depending on type of arguments

Examples:

The following examples show how the `fmod()` function sometimes returns a negative value depending on the sign of its arguments, and the `pmod()` function returns the same value as `fmod()`, but sometimes with the sign flipped.

``````select fmod(-5,2);
+-------------+
| fmod(-5, 2) |
+-------------+
| -1          |
+-------------+

select pmod(-5,2);
+-------------+
| pmod(-5, 2) |
+-------------+
| 1           |
+-------------+

select fmod(-5,-2);
+--------------+
| fmod(-5, -2) |
+--------------+
| -1           |
+--------------+

select pmod(-5,-2);
+--------------+
| pmod(-5, -2) |
+--------------+
| -1           |
+--------------+

select fmod(5,-2);
+-------------+
| fmod(5, -2) |
+-------------+
| 1           |
+-------------+

select pmod(5,-2);
+-------------+
| pmod(5, -2) |
+-------------+
| -1          |
+-------------+
``````
POSITIVE(numeric_type a)
Purpose: Returns the original argument unchanged (even if the argument is negative).

Return type: Same as the input value

Usage notes: Use `abs()` instead if you need to ensure all return values are positive.

POW(DOUBLE a, double p), POWER(DOUBLE a, DOUBLE p), DPOW(DOUBLE a, DOUBLE p), FPOW(DOUBLE a, DOUBLE p)
Purpose: Returns the first argument raised to the power of the second argument.

Return type: `DOUBLE`

PRECISION(numeric_expression)
Purpose: Computes the precision (number of decimal digits) needed to represent the type of the argument expression as a `DECIMAL` value.

Usage notes:

Typically used in combination with the `scale()` function, to determine the appropriate `DECIMAL(precision,scale)` type to declare in a `CREATE TABLE` statement or `CAST()` function.

Return type: `INT`

Examples:

The following examples demonstrate how to check the precision and scale of numeric literals or other numeric expressions. Impala represents numeric literals in the smallest appropriate type. 5 is a `TINYINT` value, which ranges from -128 to 127, therefore 3 decimal digits are needed to represent the entire range, and because it is an integer value there are no fractional digits. 1.333 is interpreted as a `DECIMAL` value, with 4 digits total and 3 digits after the decimal point.
``````[localhost:21000] > select precision(5), scale(5);
+--------------+----------+
| precision(5) | scale(5) |
+--------------+----------+
| 3            | 0        |
+--------------+----------+
[localhost:21000] > select precision(1.333), scale(1.333);
+------------------+--------------+
| precision(1.333) | scale(1.333) |
+------------------+--------------+
| 4                | 3            |
+------------------+--------------+
[localhost:21000] > with t1 as
( select cast(12.34 as decimal(20,2)) x union select cast(1 as decimal(8,6)) x )
select precision(x), scale(x) from t1 limit 1;
+--------------+----------+
| precision(x) | scale(x) |
+--------------+----------+
| 24           | 6        |
+--------------+----------+
``````
QUOTIENT(BIGINT numerator, BIGINT denominator), QUOTIENT(DOUBLE numerator, DOUBLE denominator)
Purpose: Returns the first argument divided by the second argument, discarding any fractional part. Avoids promoting integer arguments to `DOUBLE` as happens with the `/` SQL operator. Also includes an overload that accepts `DOUBLE` arguments, discards the fractional part of each argument value before dividing, and again returns `BIGINT`. With integer arguments, this function works the same as the `DIV` operator.

Return type: `BIGINT`

Purpose: Converts argument value from degrees to radians.

Return type: `DOUBLE`

RAND(), RAND(BIGINT seed), RANDOM(), RANDOM(BIGINT seed)
Purpose: Returns a random value between 0 and 1. After `rand()` is called with a seed argument, it produces a consistent random sequence based on the seed value.

Return type: `DOUBLE`

Usage notes: Currently, the random sequence is reset after each query, and multiple calls to `rand()` within the same query return the same value each time. For different number sequences that are different for each query, pass a unique seed value to each call to `rand()`. For example, `select rand(unix_timestamp()) from ...`

Examples:

The following examples show how `rand()` can produce sequences of varying predictability, so that you can reproduce query results involving random values or generate unique sequences of random values for each query. When `rand()` is called with no argument, it generates the same sequence of values each time, regardless of the ordering of the result set. When `rand()` is called with a constant integer, it generates a different sequence of values, but still always the same sequence for the same seed value. If you pass in a seed value that changes, such as the return value of the expression `unix_timestamp(now())`, each query will use a different sequence of random values, potentially more useful in probability calculations although more difficult to reproduce at a later time. Therefore, the final two examples with an unpredictable seed value also include the seed in the result set, to make it possible to reproduce the same random sequence later.

``````select x, rand() from three_rows;
+---+-----------------------+
| x | rand()                |
+---+-----------------------+
| 1 | 0.0004714746030380365 |
| 2 | 0.5895895192351144    |
| 3 | 0.4431900859080209    |
+---+-----------------------+

select x, rand() from three_rows order by x desc;
+---+-----------------------+
| x | rand()                |
+---+-----------------------+
| 3 | 0.0004714746030380365 |
| 2 | 0.5895895192351144    |
| 1 | 0.4431900859080209    |
+---+-----------------------+

select x, rand(1234) from three_rows order by x;
+---+----------------------+
| x | rand(1234)           |
+---+----------------------+
| 1 | 0.7377511392057646   |
| 2 | 0.009428468537250751 |
| 3 | 0.208117277924026    |
+---+----------------------+

select x, rand(1234) from three_rows order by x desc;
+---+----------------------+
| x | rand(1234)           |
+---+----------------------+
| 3 | 0.7377511392057646   |
| 2 | 0.009428468537250751 |
| 1 | 0.208117277924026    |
+---+----------------------+

select x, unix_timestamp(now()), rand(unix_timestamp(now()))
from three_rows order by x;
+---+-----------------------+-----------------------------+
| x | unix_timestamp(now()) | rand(unix_timestamp(now())) |
+---+-----------------------+-----------------------------+
| 1 | 1440777752            | 0.002051228658320023        |
| 2 | 1440777752            | 0.5098743483004506          |
| 3 | 1440777752            | 0.9517714925817081          |
+---+-----------------------+-----------------------------+

select x, unix_timestamp(now()), rand(unix_timestamp(now()))
from three_rows order by x desc;
+---+-----------------------+-----------------------------+
| x | unix_timestamp(now()) | rand(unix_timestamp(now())) |
+---+-----------------------+-----------------------------+
| 3 | 1440777761            | 0.9985985015512437          |
| 2 | 1440777761            | 0.3251255333074953          |
| 1 | 1440777761            | 0.02422675025846192         |
+---+-----------------------+-----------------------------+
``````
ROUND(DOUBLE a), ROUND(DOUBLE a, INT d), ROUND(DECIMAL a, int_type d), DROUND(DOUBLE a), DROUND(DOUBLE a, INT d), DROUND(DECIMAL(p,s) a, int_type d)
Purpose: Rounds a floating-point value. By default (with a single argument), rounds to the nearest integer. Values ending in .5 are rounded up for positive numbers, down for negative numbers (that is, away from zero). The optional second argument specifies how many digits to leave after the decimal point; values greater than zero produce a floating-point return value rounded to the requested number of digits to the right of the decimal point.

Return type: Same as the input type

SCALE(numeric_expression)
Purpose: Computes the scale (number of decimal digits to the right of the decimal point) needed to represent the type of the argument expression as a `DECIMAL` value.

Usage notes:

Typically used in combination with the `precision()` function, to determine the appropriate `DECIMAL(precision,scale)` type to declare in a `CREATE TABLE` statement or `CAST()` function.

Return type: `int`

Examples:

The following examples demonstrate how to check the precision and scale of numeric literals or other numeric expressions. Impala represents numeric literals in the smallest appropriate type. 5 is a `TINYINT` value, which ranges from -128 to 127, therefore 3 decimal digits are needed to represent the entire range, and because it is an integer value there are no fractional digits. 1.333 is interpreted as a `DECIMAL` value, with 4 digits total and 3 digits after the decimal point.
``````[localhost:21000] > select precision(5), scale(5);
+--------------+----------+
| precision(5) | scale(5) |
+--------------+----------+
| 3            | 0        |
+--------------+----------+
[localhost:21000] > select precision(1.333), scale(1.333);
+------------------+--------------+
| precision(1.333) | scale(1.333) |
+------------------+--------------+
| 4                | 3            |
+------------------+--------------+
[localhost:21000] > with t1 as
( select cast(12.34 as decimal(20,2)) x union select cast(1 as decimal(8,6)) x )
select precision(x), scale(x) from t1 limit 1;
+--------------+----------+
| precision(x) | scale(x) |
+--------------+----------+
| 24           | 6        |
+--------------+----------+
``````
SIGN(DOUBLE a)
Purpose: Returns -1, 0, or 1 to indicate the signedness of the argument value.

Return type: `INT`

SIN(DOUBLE a)
Purpose: Returns the sine of the argument.

Return type: `DOUBLE`

SINH(DOUBLE a)
Purpose: Returns the hyperbolic sine of the argument.

Return type: `DOUBLE`

SQRT(DOUBLE a), DSQRT(DOUBLE a)
Purpose: Returns the square root of the argument.

Return type: `DOUBLE`

TAN(DOUBLE a)
Purpose: Returns the tangent of the argument.

Return type: `DOUBLE`

TANH(DOUBLE a)
Purpose: Returns the hyperbolic tangent of the argument.

Return type: `DOUBLE`

TRUNCATE(DOUBLE_or_DECIMAL a[, digits_to_leave]), DTRUNC(DOUBLE_or_DECIMAL a[, digits_to_leave]), TRUNC(DOUBLE_or_DECIMAL a[, digits_to_leave])
Purpose: Removes some or all fractional digits from a numeric value.

Arguments: With a single floating-point argument, removes all fractional digits, leaving an integer value. The optional second argument specifies the number of fractional digits to include in the return value, and only applies when the argument type is `DECIMAL`. A second argument of 0 truncates to a whole integer value. A second argument of negative N sets N digits to 0 on the left side of the decimal

Scale argument: The scale argument applies only when truncating `DECIMAL` values. It is an integer specifying how many significant digits to leave to the right of the decimal point. A scale argument of 0 truncates to a whole integer value. A scale argument of negative N sets N digits to 0 on the left side of the decimal point.

`TRUNCATE()`, `DTRUNC()`, and `TRUNC()` are aliases for the same function.

Return type: Same as the input type

Added in: The `TRUNC()` alias was added in Impala 2.10.0.

Usage notes:

You can also pass a `DOUBLE` argument, or `DECIMAL` argument with optional scale, to the `DTRUNC()` or `TRUNCATE` functions. Using the `TRUNC()` function for numeric values is common with other industry-standard database systems, so you might find such `TRUNC()` calls in code that you are porting to Impala.

The `TRUNC()` function also has a signature that applies to `TIMESTAMP` values.

Examples:

The following examples demonstrate the `TRUNCATE()` and `DTRUNC()` signatures for this function:

``````select truncate(3.45);
+----------------+
| truncate(3.45) |
+----------------+
| 3              |
+----------------+

select truncate(-3.45);
+-----------------+
| truncate(-3.45) |
+-----------------+
| -3              |
+-----------------+

select truncate(3.456,1);
+--------------------+
| truncate(3.456, 1) |
+--------------------+
| 3.4                |
+--------------------+

select dtrunc(3.456,1);
+------------------+
| dtrunc(3.456, 1) |
+------------------+
| 3.4              |
+------------------+

select truncate(3.456,2);
+--------------------+
| truncate(3.456, 2) |
+--------------------+
| 3.45               |
+--------------------+

select truncate(3.456,7);
+--------------------+
| truncate(3.456, 7) |
+--------------------+
| 3.4560000          |
+--------------------+
``````

The following examples demonstrate using `TRUNC()` with `DECIMAL` or `DOUBLE` values, and with an optional scale argument for `DECIMAL` values. (The behavior is the same for the `TRUNCATE()` and `DTRUNC()` aliases also.)

``````
create table t1 (d decimal(20,7));

-- By default, no digits to the right of the decimal point.
insert into t1 values (1.1), (2.22), (3.333), (4.4444), (5.55555);
select trunc(d) from t1 order by d;
+----------+
| trunc(d) |
+----------+
| 1        |
| 2        |
| 3        |
| 4        |
| 5        |
+----------+

-- 1 digit to the right of the decimal point.
select trunc(d,1) from t1 order by d;
+-------------+
| trunc(d, 1) |
+-------------+
| 1.1         |
| 2.2         |
| 3.3         |
| 4.4         |
| 5.5         |
+-------------+

-- 2 digits to the right of the decimal point,
-- including trailing zeroes if needed.
select trunc(d,2) from t1 order by d;
+-------------+
| trunc(d, 2) |
+-------------+
| 1.10        |
| 2.22        |
| 3.33        |
| 4.44        |
| 5.55        |
+-------------+

insert into t1 values (9999.9999), (8888.8888);

-- Negative scale truncates digits to the left
-- of the decimal point.
select trunc(d,-2) from t1 where d > 100 order by d;
+--------------+
| trunc(d, -2) |
+--------------+
| 8800         |
| 9900         |
+--------------+

-- The scale of the result is adjusted to match the
-- scale argument.
select trunc(d,2),
precision(trunc(d,2)) as p,
scale(trunc(d,2)) as s
from t1 order by d;
+-------------+----+---+
| trunc(d, 2) | p  | s |
+-------------+----+---+
| 1.10        | 15 | 2 |
| 2.22        | 15 | 2 |
| 3.33        | 15 | 2 |
| 4.44        | 15 | 2 |
| 5.55        | 15 | 2 |
| 8888.88     | 15 | 2 |
| 9999.99     | 15 | 2 |
+-------------+----+---+
``````
``````
create table dbl (d double);

insert into dbl values
(1.1), (2.22), (3.333), (4.4444), (5.55555),
(8888.8888), (9999.9999);

-- With double values, there is no optional scale argument.
select trunc(d) from dbl order by d;
+----------+
| trunc(d) |
+----------+
| 1        |
| 2        |
| 3        |
| 4        |
| 5        |
| 8888     |
| 9999     |
+----------+
``````
UNHEX(STRING a)
Purpose: Returns a string of characters with ASCII values corresponding to pairs of hexadecimal digits in the argument.

Return type: `STRING`

WIDTH_BUCKET(DECIMAL expr, DECIMAL min_value, DECIMAL max_value, INT num_buckets)
Purpose: Returns the bucket number in which the `expr` value would fall in the histogram where its range between `min_value` and `max_value` is divided into `num_buckets` buckets of identical sizes.
The function returns:
• `NULL` if any argument is `NULL`.
• `0` if `expr` < `min_value`.
• `num_buckets + 1` if `expr` >= `max_val`.
• If none of the above, the bucket number where `expr` falls.
Arguments:The following rules apply to the arguments.
• `min_val` is the minimum value of the histogram range.
• `max_val` is the maximum value of the histogram range.
• `num_buckets` must be greater than `0`.
• `min_value` must be less than `max_value`.

Usage notes:

Each bucket contains values equal to or greater than the base value of that bucket and less than the base value of the next bucket. For example, with `width_bucket(8, 1, 10, 3)`, the bucket ranges are actually the 0th "underflow bucket" with the range (-infinity to 0.999...), (1 to 3.999...), (4, to 6.999...), (7 to 9.999...), and the "overflow bucket" with the range (10 to infinity).

Return type: `BIGINT`

The below function creates `3` buckets between the range of `1` and `20` with the bucket width of 6.333, and returns `2` for the bucket #2 where the value `8` falls in:
``WIDTH_BUCKET(8, 1, 20, 3)``
``````SELECT account, invoice_amount, WIDTH_BUCKET(invoice_amount,50,1000,10)