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Mathematical functions

acos​

Introduced in: v1.1

Returns the arc cosine of the argument.

Syntax

acos(x)

Arguments

Returned value

Returns the arc cosine of x Float*

Examples

Usage example

SELECT acos(0.5);

1.0471975511965979

acosh​

Introduced in: v20.12

Returns the inverse hyperbolic cosine.

Syntax

acosh(x)

Arguments

  • x — Hyperbolic cosine of angle. Values from the interval: 1 ≤ x < +∞. (U)Int* or Float* or Decimal*

Returned value

Returns the angle, in radians. Values from the interval: 0 ≤ acosh(x) < +∞. Float64

Examples

Usage example

SELECT acosh(1)

0

asin​

Introduced in: v1.1

Calculates the arcsine of the provided argument. For arguments in the range [-1, 1] it returns the value in the range of [-pi() / 2, pi() / 2].

Syntax

asin(x)

Arguments

Returned value

Returns the arcsine value of the provided argument x Float64

Examples

inverse

SELECT asin(1.0) = pi() / 2, sin(asin(1)), asin(sin(1))

1 1 1

float32

SELECT toTypeName(asin(1.0::Float32))

Float64

nan

SELECT asin(1.1), asin(-2), asin(inf), asin(nan)

nan nan nan nan

asinh​

Introduced in: v20.12

Returns the inverse hyperbolic sine.

Syntax

asinh(x)

Arguments

  • x — Hyperbolic sine of angle. Values from the interval: -∞ < x < +∞. (U)Int* or Float* or Decimal*

Returned value

Returns the angle, in radians. Values from the interval: -∞ < asinh(x) < +∞. Float64

Examples

Basic usage

SELECT asinh(0)

0

atan​

Introduced in: v1.1

Returns the arc tangent of the argument.

Syntax

atan(x)

Arguments

Returned value

Returns the arc tangent of x. Float*

Examples

Usage example

SELECT atan(1);

0.7853981633974483

atan2​

Introduced in: v20.12

Returns the atan2 as the angle in the Euclidean plane, given in radians, between the positive x axis and the ray to the point (x, y) ≠ (0, 0).

Syntax

atan2(y, x)

Arguments

Returned value

Returns the angle θ such that -π < θ ≤ π, in radians Float64

Examples

Usage example

SELECT atan2(1, 1)

0.7853981633974483

atanh​

Introduced in: v20.12

Returns the inverse hyperbolic tangent.

Syntax

atanh(x)

Arguments

  • x — Hyperbolic tangent of angle. Values from the interval: -1 < x < 1. (U)Int*, Float* or Decimal*. (U)Int* or Float* or Decimal*

Returned value

Returns the angle, in radians. Values from the interval: -∞ < atanh(x) < +∞ Float64

Examples

Usage example

SELECT atanh(0)

0

cbrt​

Introduced in: v1.1

Returns the cubic root of the argument.

Syntax

cbrt(x)

Arguments

Returned value

Returns the cubic root of x. Float*

Examples

Usage example

SELECT cbrt(8);

2

cos​

Introduced in: v1.1

Returns the cosine of the argument.

Syntax

cos(x)

Arguments

Returned value

Returns the cosine of x. Float*

Examples

Usage example

SELECT cos(0);

1

cosh​

Introduced in: v20.12

Returns the hyperbolic cosine of the argument.

Syntax

cosh(x)

Arguments

Returned value

Returns values from the interval: 1 ≤ cosh(x) < +∞ Float64

Examples

Basic usage

SELECT cosh(0)

1

degrees​

Introduced in: v22.2

Converts radians to degrees.

Syntax

degrees(x)

Arguments

Returned value

Returns the value of x in degrees. Float64

Examples

Basic usage

SELECT degrees(3.141592653589793)

180

e​

Introduced in: v1.1

Returns Euler's constant (e).

Syntax

e()

Arguments

  • None. Returned value

Returns Euler's constant Float64

Examples

Usage example

SELECT e();

2.718281828459045

erf​

Introduced in: v1.1

If x is non-negative, then erf(x/(σ√2)) is the probability that a random variable having a normal distribution with standard deviation σ takes the value that is separated from the expected value by more than x.

Syntax

erf(x)

Arguments

Returned value

Returns the error function value Float*

Examples

Three sigma rule

SELECT erf(3 / sqrt(2))

┌─erf(divide(3, sqrt(2)))─┐
│      0.9973002039367398 │
└─────────────────────────┘

erfc​

Introduced in: v1.1

Returns a number close to 1-erf(x) without loss of precision for large x values.

Syntax

erfc(x)

Arguments

Returned value

Returns the complementary error function value Float*

Examples

Usage example

SELECT erfc(0);

1

exp​

Introduced in: v1.1

Returns e raised to the power of x, where x is the given argument to the function.

Syntax

exp(x)

Arguments

Returned value

Returns e^x Float*

Examples

Basic usage

SELECT round(exp(-1), 4)

┌─round(exp(-1), 4)─┐
│            0.3679 │
└───────────────────┘

exp10​

Introduced in: v1.1

Returns 10 to the power of the given argument.

Syntax

exp10(x)

Arguments

Returned value

Returns 10^x Float*

Examples

Usage example

SELECT exp10(2);

100

exp2​

Introduced in: v1.1

Returns 2 to the power of the given argument.

Syntax

exp2(x)

Arguments

Returned value

Returns 2^x Float*

Examples

Usage example

SELECT exp2(3);

8

factorial​

Introduced in: v22.11

Computes the factorial of an integer value. 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 will cause an exception.

Syntax

factorial(n)

Arguments

  • n — Integer value for which to calculate the factorial. Maximum value is 20. (U)Int8/16/32/64

Returned value

Returns the factorial of the input as UInt64. Returns 1 for input 0 or any negative value. UInt64

Examples

Usage example

factorial(10)

3628800

hypot​

Introduced in: v20.12

Returns the length of the hypotenuse of a right-angle triangle. Hypot avoids problems that occur when squaring very large or very small numbers.

Syntax

hypot(x, y)

Arguments

Returned value

Returns the length of the hypotenuse of a right-angle triangle. Float64

Examples

Basic usage

SELECT hypot(1, 1)

1.4142135623730951

intExp10​

Introduced in: v1.1

Like exp10 but returns a UInt64 number.

Syntax

intExp10(x)

Arguments

Returned value

Returns 10^x. UInt64

Examples

Usage example

SELECT intExp10(2);

100

intExp2​

Introduced in: v1.1

Like exp2 but returns a UInt64 number.

Syntax

intExp2(x)

Arguments

Returned value

Returns 2^x. UInt64

Examples

Usage example

SELECT intExp2(3);

8

lgamma​

Introduced in: v1.1

Returns the logarithm of the gamma function.

Syntax

lgamma(x)

Arguments

  • x — The number for which to compute the logarithm of the gamma function. (U)Int* or Float* or Decimal*

Returned value

Returns the logarithm of the gamma function of x. Float*

Examples

Usage example

SELECT lgamma(5);

3.1780538303479458

log​

Introduced in: v1.1

Returns the natural logarithm of the argument.

Syntax

log(x)

Arguments

Returned value

Returns the natural logarithm of x. Float*

Examples

Usage example

SELECT log(10);

2.302585092994046

log10​

Introduced in: v1.1

Returns the decimal logarithm of the argument.

Syntax

log10(x)

Arguments

Returned value

Returns the decimal logarithm of x. Float*

Examples

Usage example

SELECT log10(100);

2

log1p​

Introduced in: v20.12

Calculates log(1+x). The calculation log1p(x) is more accurate than log(1+x) for small values of x.

Syntax

log1p(x)

Arguments

Returned value

Returns values from the interval: -∞ < log1p(x) < +∞ Float64

Examples

Usage example

SELECT log1p(0)

0

log2​

Introduced in: v1.1

Returns the binary logarithm of the argument.

Syntax

log2(x)

Arguments

Returned value

Returns the binary logarithm of x. Float*

Examples

Usage example

SELECT log2(8);

3

pi​

Introduced in: v1.1

Returns pi (π).

Syntax

pi()

Arguments

  • None. Returned value

Returns pi Float64

Examples

Usage example

SELECT pi();

3.141592653589793

pow​

Introduced in: v1.1

Returns x raised to the power of y.

Syntax

pow(x, y)

Arguments

Returned value

Returns x^y Float64

Examples

Usage example

SELECT pow(2, 3);

8

radians​

Introduced in: v22.2

Converts degrees to radians.

Syntax

radians(x)

Arguments

Returned value

Returns value in radians Float64

Examples

Usage example

SELECT radians(180)

3.141592653589793

sign​

Introduced in: v21.2

Returns the sign of a real number.

Syntax

sign(x)

Arguments

Returned value

Returns -1 for x < 0, 0 for x = 0, 1 for x > 0. Int8

Examples

Sign for zero

SELECT sign(0)

0

Sign for positive

SELECT sign(1)

1

Sign for negative

SELECT sign(-1)

-1

sin​

Introduced in: v

Returns the sine of the argument.

Syntax

sin(x)

Arguments

Returned value

Returns the sine of x.

Examples

simple

SELECT sin(1.23)

0.9424888019316975

sinh​

Introduced in: v20.12

Returns the hyperbolic sine.

Syntax

sinh(x)

Arguments

Returned value

Returns values from the interval: -∞ < sinh(x) < +∞ Float64

Examples

Usage example

SELECT sinh(0)

0

sqrt​

Introduced in: v1.1

Returns the square root of the argument.

Syntax

sqrt(x)

Arguments

Returned value

Returns the square root of x Float*

Examples

Usage example

SELECT sqrt(16);

4

tan​

Introduced in: v1.1

Returns the tangent of the argument.

Syntax

tan(x)

Arguments

Returned value

Returns the tangent of x. Float*

Examples

Usage example

SELECT tan(0);

0

tanh​

Introduced in: v20.1

Returns the hyperbolic tangent.

Syntax

tanh(x)

Arguments

Returned value

Returns values from the interval: -1 < tanh(x) < 1 Float*

Examples

Usage example

SELECT tanh(0)

0

tgamma​

Introduced in: v1.1

Returns the gamma function.

Syntax

tgamma(x)

Arguments

Returned value

Returns the gamma function value Float*

Examples

Usage example

SELECT tgamma(5);

24

widthBucket​

Introduced in: v23.3

Returns the number of the bucket in which parameter operand falls in a histogram having count equal-width buckets spanning the range low to high. Returns 0 if operand is less than low, and returns count+1 if operand is greater than or equal to high. There is also a case insensitive alias called WIDTH_BUCKET to provide compatibility with other databases.

Syntax

widthBucket(operand, low, high, count)

Arguments

Returned value

Returns the bucket number as an integer. Returns 0 if operand < low, returns count+1 if operand >= high. UInt8/16/32/64

Examples

Usage example

widthBucket(10.15, -8.6, 23, 18)

11