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| slug | sidebar_position | sidebar_label |
|---|---|---|
| /en/sql-reference/functions/arithmetic-functions | 34 | Arithmetic |
Arithmetic Functions
For all arithmetic functions, the result type is calculated as the smallest number type that the result fits in, if there is such a type. The minimum is taken simultaneously based on the number of bits, whether it is signed, and whether it floats. If there are not enough bits, the highest bit type is taken.
Example:
SELECT toTypeName(0), toTypeName(0 + 0), toTypeName(0 + 0 + 0), toTypeName(0 + 0 + 0 + 0)
┌─toTypeName(0)─┬─toTypeName(plus(0, 0))─┬─toTypeName(plus(plus(0, 0), 0))─┬─toTypeName(plus(plus(plus(0, 0), 0), 0))─┐
│ UInt8 │ UInt16 │ UInt32 │ UInt64 │
└───────────────┴────────────────────────┴─────────────────────────────────┴──────────────────────────────────────────┘
Arithmetic functions work for any pair of types from UInt8, UInt16, UInt32, UInt64, Int8, Int16, Int32, Int64, Float32, or Float64.
Overflow is produced the same way as in C++.
plus(a, b), a + b operator
Calculates the sum of the numbers. You can also add integer numbers with a date or date and time. In the case of a date, adding an integer means adding the corresponding number of days. For a date with time, it means adding the corresponding number of seconds.
minus(a, b), a - b operator
Calculates the difference. The result is always signed.
You can also calculate integer numbers from a date or date with time. The idea is the same – see above for ‘plus’.
multiply(a, b), a * b operator
Calculates the product of the numbers.
divide(a, b), a / b operator
Calculates the quotient of the numbers. The result type is always a floating-point type. It is not integer division. For integer division, use the ‘intDiv’ function. When dividing by zero you get ‘inf’, ‘-inf’, or ‘nan’.
intDiv(a, b)
Calculates the quotient of the numbers. Divides into integers, rounding down (by the absolute value). An exception is thrown when dividing by zero or when dividing a minimal negative number by minus one.
intDivOrZero(a, b)
Differs from ‘intDiv’ in that it returns zero when dividing by zero or when dividing a minimal negative number by minus one.
modulo(a, b), a % b operator
Calculates the remainder when dividing a by b.
The result type is an integer if both inputs are integers. If one of the inputs is a floating-point number, the result is a floating-point number.
The remainder is computed like in C++. Truncated division is used for negative numbers.
An exception is thrown when dividing by zero or when dividing a minimal negative number by minus one.
moduloOrZero(a, b)
Differs from modulo in that it returns zero when the divisor is zero.
positive_modulo(a, b)
Calculates the remainder when dividing a by b. Similar to function modulo except that positive_modulo always return non-negative number.
Notice that positive_modulo is 4-5 times slower than modulo. You should not use positive_modulo unless you want to get positive result and don't care about performance too much.
negate(a), -a operator
Calculates a number with the reverse sign. The result is always signed.
abs(a)
Calculates the absolute value of the number (a). That is, if a < 0, it returns -a. For unsigned types it does not do anything. For signed integer types, it returns an unsigned number.
gcd(a, b)
Returns the greatest common divisor of the numbers. An exception is thrown when dividing by zero or when dividing a minimal negative number by minus one.
lcm(a, b)
Returns the least common multiple of the numbers. An exception is thrown when dividing by zero or when dividing a minimal negative number by minus one.
max2
Compares two values and returns the maximum. The returned value is converted to Float64.
Syntax
max2(value1, value2)
Arguments
Returned value
- The maximum of two values.
Type: Float.
Example
Query:
SELECT max2(-1, 2);
Result:
┌─max2(-1, 2)─┐
│ 2 │
└─────────────┘
min2
Compares two values and returns the minimum. The returned value is converted to Float64.
Syntax
max2(value1, value2)
Arguments
Returned value
- The minimum of two values.
Type: Float.
Example
Query:
SELECT min2(-1, 2);
Result:
┌─min2(-1, 2)─┐
│ -1 │
└─────────────┘
multiplyDecimal(a, b[, result_scale])
Performs multiplication on two decimals. Result value will be of type Decimal256.
Result scale can be explicitly specified by result_scale argument (const Integer in range [0, 76]). If not specified, the result scale is the max scale of given arguments.
:::note
These functions work significantly slower than usual multiply.
In case you don't really need controlled precision and/or need fast computation, consider using multiply
:::
Syntax
multiplyDecimal(a, b[, result_scale])
Arguments
Returned value
- The result of multiplication with given scale.
Type: Decimal256.
Example
┌─multiplyDecimal(toDecimal256(-12, 0), toDecimal32(-2.1, 1), 1)─┐
│ 25.2 │
└────────────────────────────────────────────────────────────────┘
Difference from regular multiplication:
SELECT toDecimal64(-12.647, 3) * toDecimal32(2.1239, 4);
SELECT toDecimal64(-12.647, 3) as a, toDecimal32(2.1239, 4) as b, multiplyDecimal(a, b);
┌─multiply(toDecimal64(-12.647, 3), toDecimal32(2.1239, 4))─┐
│ -26.8609633 │
└───────────────────────────────────────────────────────────┘
┌─multiplyDecimal(toDecimal64(-12.647, 3), toDecimal32(2.1239, 4))─┐
│ -26.8609 │
└──────────────────────────────────────────────────────────────────┘
SELECT
toDecimal64(-12.647987876, 9) AS a,
toDecimal64(123.967645643, 9) AS b,
multiplyDecimal(a, b);
SELECT
toDecimal64(-12.647987876, 9) AS a,
toDecimal64(123.967645643, 9) AS b,
a * b;
┌─────────────a─┬─────────────b─┬─multiplyDecimal(toDecimal64(-12.647987876, 9), toDecimal64(123.967645643, 9))─┐
│ -12.647987876 │ 123.967645643 │ -1567.941279108 │
└───────────────┴───────────────┴───────────────────────────────────────────────────────────────────────────────┘
Received exception from server (version 22.11.1):
Code: 407. DB::Exception: Received from localhost:9000. DB::Exception: Decimal math overflow: While processing toDecimal64(-12.647987876, 9) AS a, toDecimal64(123.967645643, 9) AS b, a * b. (DECIMAL_OVERFLOW)
divideDecimal(a, b[, result_scale])
Performs division on two decimals. Result value will be of type Decimal256.
Result scale can be explicitly specified by result_scale argument (const Integer in range [0, 76]). If not specified, the result scale is the max scale of given arguments.
:::note
These function work significantly slower than usual divide.
In case you don't really need controlled precision and/or need fast computation, consider using divide.
:::
Syntax
divideDecimal(a, b[, result_scale])
Arguments
Returned value
- The result of division with given scale.
Type: Decimal256.
Example
┌─divideDecimal(toDecimal256(-12, 0), toDecimal32(2.1, 1), 10)─┐
│ -5.7142857142 │
└──────────────────────────────────────────────────────────────┘
Difference from regular division:
SELECT toDecimal64(-12, 1) / toDecimal32(2.1, 1);
SELECT toDecimal64(-12, 1) as a, toDecimal32(2.1, 1) as b, divideDecimal(a, b, 1), divideDecimal(a, b, 5);
┌─divide(toDecimal64(-12, 1), toDecimal32(2.1, 1))─┐
│ -5.7 │
└──────────────────────────────────────────────────┘
┌───a─┬───b─┬─divideDecimal(toDecimal64(-12, 1), toDecimal32(2.1, 1), 1)─┬─divideDecimal(toDecimal64(-12, 1), toDecimal32(2.1, 1), 5)─┐
│ -12 │ 2.1 │ -5.7 │ -5.71428 │
└─────┴─────┴────────────────────────────────────────────────────────────┴────────────────────────────────────────────────────────────┘
SELECT toDecimal64(-12, 0) / toDecimal32(2.1, 1);
SELECT toDecimal64(-12, 0) as a, toDecimal32(2.1, 1) as b, divideDecimal(a, b, 1), divideDecimal(a, b, 5);
DB::Exception: Decimal result's scale is less than argument's one: While processing toDecimal64(-12, 0) / toDecimal32(2.1, 1). (ARGUMENT_OUT_OF_BOUND)
┌───a─┬───b─┬─divideDecimal(toDecimal64(-12, 0), toDecimal32(2.1, 1), 1)─┬─divideDecimal(toDecimal64(-12, 0), toDecimal32(2.1, 1), 5)─┐
│ -12 │ 2.1 │ -5.7 │ -5.71428 │
└─────┴─────┴────────────────────────────────────────────────────────────┴────────────────────────────────────────────────────────────┘