--- slug: /en/sql-reference/functions/arithmetic-functions sidebar_position: 5 sidebar_label: Arithmetic --- # Arithmetic Functions Arithmetic functions work for any two operands of type `UInt8`, `UInt16`, `UInt32`, `UInt64`, `Int8`, `Int16`, `Int32`, `Int64`, `Float32`, or `Float64`. Before performing the operation, both operands are casted to the result type. The result type is determined as follows (unless specified differently in the function documentation below): - If both operands are up to 32 bits wide, the size of the result type will be the size of the next bigger type following the bigger of the two operands (integer size promotion). For example, `UInt8 + UInt16 = UInt32` or `Float32 * Float32 = Float64`. - If one of the operands has 64 or more bits, the size of the result type will be the same size as the bigger of the two operands. For example, `UInt32 + UInt128 = UInt128` or `Float32 * Float64 = Float64`. - If one of the operands is signed, the result type will also be signed, otherwise it will be signed. For example, `UInt32 * Int32 = Int64`. These rules make sure that the result type will be the smallest type which can represent all possible results. 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. This behavior also guarantees compatibility with many other databases which provide 64 bit integers (BIGINT) as the biggest integer type. Example: ``` sql SELECT toTypeName(0), toTypeName(0 + 0), toTypeName(0 + 0 + 0), toTypeName(0 + 0 + 0 + 0) ``` ``` text ┌─toTypeName(0)─┬─toTypeName(plus(0, 0))─┬─toTypeName(plus(plus(0, 0), 0))─┬─toTypeName(plus(plus(plus(0, 0), 0), 0))─┐ │ UInt8 │ UInt16 │ UInt32 │ UInt64 │ └───────────────┴────────────────────────┴─────────────────────────────────┴──────────────────────────────────────────┘ ``` Overflows are produced the same way as in C++. ## plus Calculates the sum of two values `a` and `b`. **Syntax** ```sql 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** ```sql minus(a, b) ``` Alias: `a - b` (operator) ## multiply Calculates the product of two values `a` and `b`. **Syntax** ```sql multiply(a, b) ``` Alias: `a * b` (operator) ## divide Calculates the quotient of two values `a` and `b`. The result type is always [Float64](../../sql-reference/data-types/float.md). Integer division is provided by the `intDiv` function. Division by 0 returns `inf`, `-inf`, or `nan`. **Syntax** ```sql 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 width 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** ```sql intDiv(a, b) ``` **Example** Query: ```sql SELECT intDiv(toFloat64(1), 0.001) AS res, toTypeName(res) ``` ```response ┌──res─┬─toTypeName(intDiv(toFloat64(1), 0.001))─┐ │ 1000 │ Int64 │ └──────┴─────────────────────────────────────────┘ ``` ```sql SELECT intDiv(1, 0.001) AS res, toTypeName(res) ``` ```response 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** ```sql 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 type is [Float64](../../sql-reference/data-types/float.md). 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** ```sql modulo(a, b) ``` Alias: `a % b` (operator) ## moduloOrZero Like [modulo](#modulo) but returns zero when the divisor is zero. **Syntax** ```sql moduloOrZero(a, b) ``` ## positiveModulo(a, b) Like [modulo](#modulo) but always returns a non-negative number. This function is 4-5 times slower than `modulo`. **Syntax** ```sql positiveModulo(a, b) ``` Alias: - `positive_modulo(a, b)` - `pmod(a, b)` **Example** Query: ```sql SELECT positiveModulo(-1, 10) ``` Result: ```result ┌─positiveModulo(-1, 10)─┐ │ 9 │ └────────────────────────┘ ``` ## negate Negates a value `a`. The result is always signed. **Syntax** ```sql 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** ```sql 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** ```sql 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** ```sql lcm(a, b) ``` ## max2 Returns the bigger of two values `a` and `b`. The returned value is of type [Float64](../../sql-reference/data-types/float.md). **Syntax** ```sql max2(a, b) ``` **Example** Query: ```sql SELECT max2(-1, 2); ``` Result: ```result ┌─max2(-1, 2)─┐ │ 2 │ └─────────────┘ ``` ## min2 Returns the smaller of two values `a` and `b`. The returned value is of type [Float64](../../sql-reference/data-types/float.md). **Syntax** ```sql min2(a, b) ``` **Example** Query: ```sql SELECT min2(-1, 2); ``` Result: ```result ┌─min2(-1, 2)─┐ │ -1 │ └─────────────┘ ``` ## multiplyDecimal Multiplies two decimals `a` and `b`. The result value will be of type [Decimal256](../../sql-reference/data-types/decimal.md). 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** ```sql multiplyDecimal(a, b[, result_scale]) ``` **Arguments** - `a` — First value: [Decimal](../../sql-reference/data-types/decimal.md). - `b` — Second value: [Decimal](../../sql-reference/data-types/decimal.md). - `result_scale` — Scale of result: [Int/UInt](../../sql-reference/data-types/int-uint.md). **Returned value** - The result of multiplication with given scale. [Decimal256](../../sql-reference/data-types/decimal.md). **Example** ```result ┌─multiplyDecimal(toDecimal256(-12, 0), toDecimal32(-2.1, 1), 1)─┐ │ 25.2 │ └────────────────────────────────────────────────────────────────┘ ``` **Differences compared to regular multiplication:** ```sql 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: ```result ┌─multiply(toDecimal64(-12.647, 3), toDecimal32(2.1239, 4))─┐ │ -26.8609633 │ └───────────────────────────────────────────────────────────┘ ┌───────a─┬──────b─┬─multiplyDecimal(toDecimal64(-12.647, 3), toDecimal32(2.1239, 4))─┐ │ -12.647 │ 2.1239 │ -26.8609 │ └─────────┴────────┴──────────────────────────────────────────────────────────────────┘ ``` ```sql 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: ```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](../../sql-reference/data-types/decimal.md). 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** ```sql divideDecimal(a, b[, result_scale]) ``` **Arguments** - `a` — First value: [Decimal](../../sql-reference/data-types/decimal.md). - `b` — Second value: [Decimal](../../sql-reference/data-types/decimal.md). - `result_scale` — Scale of result: [Int/UInt](../../sql-reference/data-types/int-uint.md). **Returned value** - The result of division with given scale. [Decimal256](../../sql-reference/data-types/decimal.md). **Example** ```result ┌─divideDecimal(toDecimal256(-12, 0), toDecimal32(2.1, 1), 10)─┐ │ -5.7142857142 │ └──────────────────────────────────────────────────────────────┘ ``` **Differences compared to regular division:** ```sql 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: ```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 │ └─────┴─────┴────────────────────────────────────────────────────────────┴────────────────────────────────────────────────────────────┘ ``` ```sql 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: ```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 │ └─────┴─────┴────────────────────────────────────────────────────────────┴────────────────────────────────────────────────────────────┘ ``` ## byteSwap Reverses the bytes of an integer, i.e. changes its [endianness](https://en.wikipedia.org/wiki/Endianness). **Syntax** ```sql byteSwap(a) ``` **Example** ```sql byteSwap(3351772109) ``` Result: ```result ┌─byteSwap(3351772109)─┐ │ 3455829959 │ └──────────────────────┘ ``` The above example can be worked out in the following manner: 1. Convert the base-10 integer to its equivalent hexadecimal format in big-endian format, i.e. 3351772109 -> C7 C7 FB CD (4 bytes) 2. Reverse the bytes, i.e. C7 C7 FB CD -> CD FB C7 C7 3. Convert the result back to an integer assuming big-endian, i.e. CD FB C7 C7 -> 3455829959 One use case of this function is reversing IPv4s: ```result ┌─toIPv4(byteSwap(toUInt32(toIPv4('205.251.199.199'))))─┐ │ 199.199.251.205 │ └───────────────────────────────────────────────────────┘ ```