# 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:

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                                   │└───────────────┴────────────────────────┴─────────────────────────────────┴──────────────────────────────────────────┘

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 type is always Float64. Integer division is provided by 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 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

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)

## isFinite​

Returns 1 if the Float32 or Float64 argument not infinite and not a NaN, otherwise this function returns 0.

Syntax

isFinite(x)

## isInfinite​

Returns 1 if the Float32 or Float64 argument is infinite, otherwise this function returns 0. Note that 0 is returned for a NaN.

Syntax

isInfinite(x)

## ifNotFinite​

Checks whether a floating point value is finite.

Syntax

ifNotFinite(x,y)

Arguments

• x — Value to check for infinity. Float*.
• y — Fallback value. Float*.

Returned value

• x if x is finite.
• y if x is not finite.

Example

Query:

SELECT 1/0 as infimum, ifNotFinite(infimum,42)

Result:

┌─infimum─┬─ifNotFinite(divide(1, 0), 42)─┐│     inf │                            42 │└─────────┴───────────────────────────────┘

You can get similar result by using the ternary operator: isFinite(x) ? x : y.

## isNaN​

Returns 1 if the Float32 and Float64 argument is NaN, otherwise this function 0.

Syntax

isNaN(x)

## 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.

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

• a — First value. Decimal.
• b — Second value. Decimal.
• result_scale — Scale of result. Int/UInt.

Returned value

• The result of multiplication with given scale. 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 │└───────────────────────────────────────────────────────────┘┌───────a─┬──────b─┬─multiplyDecimal(toDecimal64(-12.647, 3), toDecimal32(2.1239, 4))─┐│ -12.647 │ 2.1239 │                                                         -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

• a — First value: Decimal.
• b — Second value: Decimal.
• result_scale — Scale of result: Int/UInt.

Returned value

• The result of division with given scale. 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 │└─────┴─────┴────────────────────────────────────────────────────────────┴────────────────────────────────────────────────────────────┘

## byteSwap​

Reverses the bytes of an integer, i.e. changes its endianness.

Syntax

byteSwap(a)

Example

byteSwap(3351772109)

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:

┌─toIPv4(byteSwap(toUInt32(toIPv4('205.251.199.199'))))─┐│ 199.199.251.205                                       │└───────────────────────────────────────────────────────┘