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| slug | sidebar_position | sidebar_label |
|---|---|---|
| /en/sql-reference/functions/arithmetic-functions | 5 | Arithmetic |
Arithmetic Functions
The result type of all arithmetic functions is the smallest type which can represent all possible results. Size promotion happens for integers up to 32 bit, e.g. UInt8 + UInt16 = UInt32. If one of the inters has 64 or more bits, the result is of the same type as the bigger of the input integers, e.g. UInt16 + UInt128 = UInt128. While this introduces a risk of overflows around the value range boundary, it ensures that calculations are performed quickly using the maximum native integer width of 64 bit.
The result of addition or multiplication of two integers is unsigned unless one of the integers is signed.
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 UInt8, UInt16, UInt32, UInt64, Int8, Int16, Int32, Int64, Float32, or Float64 values.
Overflows are produced the same way as in C++.
plus
Calculates the sum of two values a and b.
Syntax
plus(a, b)
It is possible to add an integer and a date or date with time. The former operation increments the number of days in the date, the latter operation increments the number of seconds in the date with time.
Alias: a + b (operator)
minus
Calculates the difference of two values a and b. The result is always signed.
Similar to plus, it is possible to subtract an integer from a date or date with time.
Syntax
minus(a, b)
Alias: a - b (operator)
multiply
Calculates the product of two values a and b.
Syntax
multiply(a, b)
Alias: a \* b (operator)
divide
Calculates the quotient of two values a and b. The result is always a floating-point value. If you need integer division, you can use the intDiv function.
Division by 0 returns inf, -inf, or nan.
Syntax
divide(a, b)
Alias: a / b (operator)
intDiv
Performs an integer division of two values a by b, i.e. computes the quotient rounded down to the next smallest integer.
The result has the same type as the dividend (the first parameter).
An exception is thrown when dividing by zero, when the quotient does not fit in the range of the dividend, or when dividing a minimal negative number by minus one.
Syntax
intDiv(a, b)
Example
Query:
SELECT
intDiv(toFloat64(1), 0.001) AS res,
toTypeName(res)
┌──res─┬─toTypeName(intDiv(toFloat64(1), 0.001))─┐
│ 1000 │ Int64 │
└──────┴─────────────────────────────────────────┘
SELECT
intDiv(1, 0.001) AS res,
toTypeName(res)
Received exception from server (version 23.2.1):
Code: 153. DB::Exception: Received from localhost:9000. DB::Exception: Cannot perform integer division, because it will produce infinite or too large number: While processing intDiv(1, 0.001) AS res, toTypeName(res). (ILLEGAL_DIVISION)
intDivOrZero
Same as intDiv but returns zero when dividing by zero or when dividing a minimal negative number by minus one.
Syntax
intDivOrZero(a, b)
modulo
Calculates the remainder of the division of two values 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.
Syntax
modulo(a, b)
Alias: a % b (operator)
moduloOrZero
Like modulo but returns zero when the divisor is zero.
Syntax
moduloOrZero(a, b)
positiveModulo(a, b)
Like modulo but always returns a non-negative number.
This function is 4-5 times slower than modulo.
Syntax
positiveModulo(a, b)
Alias:
positive_modulo(a, b)pmod(a, b)
Example
Query:
SELECT positiveModulo(-1, 10)
Result:
┌─positiveModulo(-1, 10)─┐
│ 9 │
└────────────────────────┘
negate
Negates a value a. The result is always signed.
Syntax
negate(a)
Alias: -a
abs
Calculates the absolute value of a. Has no effect if a is of an unsigned type. If a is of a signed type, it returns an unsigned number.
Syntax
abs(a)
gcd
Returns the greatest common divisor of two values a and b.
An exception is thrown when dividing by zero or when dividing a minimal negative number by minus one.
Syntax
gcd(a, b)
lcm(a, b)
Returns the least common multiple of two values a and b.
An exception is thrown when dividing by zero or when dividing a minimal negative number by minus one.
Syntax
lcm(a, b)
max2
Returns the bigger of two values a and b. The returned value is of type Float64.
Syntax
max2(a, b)
Example
Query:
SELECT max2(-1, 2);
Result:
┌─max2(-1, 2)─┐
│ 2 │
└─────────────┘
min2
Returns the smaller of two values a and b. The returned value is of type Float64.
Syntax
min2(a, b)
Example
Query:
SELECT min2(-1, 2);
Result:
┌─min2(-1, 2)─┐
│ -1 │
└─────────────┘
multiplyDecimal
Multiplies two decimals a and b. The result value will be of type Decimal256.
The scale of the result can be explicitly specified by result_scale. If result_scale is not specified, it is assumed to be the maximum scale of the input values.
This function work significantly slower than usual multiply. In case no control over the result precision is needed and/or fast computation is desired, 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 │
└────────────────────────────────────────────────────────────────┘
Differences compared to 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);
Result:
┌─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;
Result:
┌─────────────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
Divides two decimals a and b. The result value will be of type Decimal256.
The scale of the result can be explicitly specified by result_scale. If result_scale is not specified, it is assumed to be the maximum scale of the input values.
This function work significantly slower than usual divide. In case no control over the result precision is needed and/or fast computation is desired, 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 │
└──────────────────────────────────────────────────────────────┘
Differences compared to 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);
Result:
┌─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);
Result:
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 │
└─────┴─────┴────────────────────────────────────────────────────────────┴────────────────────────────────────────────────────────────┘