Mathematical Functions

Returns a Float64 number that is close to the number e.

pi()

Returns a Float64 number that is close to the number π.

exp(x)

Accepts a numeric argument and returns a Float64 number close to the exponent of the argument.

log(x), ln(x)

Accepts a numeric argument and returns a Float64 number close to the natural logarithm of the argument.

exp2(x)

Accepts a numeric argument and returns a Float64 number close to 2 to the power of x.

log2(x)

Accepts a numeric argument and returns a Float64 number close to the binary logarithm of the argument.

exp10(x)

Accepts a numeric argument and returns a Float64 number close to 10 to the power of x.

log10(x)

Accepts a numeric argument and returns a Float64 number close to the decimal logarithm of the argument.

sqrt(x)

Accepts a numeric argument and returns a Float64 number close to the square root of the argument.

cbrt(x)

Accepts a numeric argument and returns a Float64 number close to the cubic root of the argument.

If ‘x’ is non-negative, then 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’.

Example (three sigma rule):

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

erfc(x)

Accepts a numeric argument and returns a Float64 number close to 1 - erf(x), but without loss of precision for large ‘x’ values.

lgamma(x)

The logarithm of the gamma function.

tgamma(x)

Gamma function.

sin(x)

The sine.

cos(x)

The cosine.

tan(x)

The tangent.

asin(x)

The arc sine.

acos(x)

The arc cosine.

atan(x)

The arc tangent.

Takes two numeric arguments x and y. Returns a Float64 number close to x to the power of y.

intExp2

Accepts a numeric argument and returns a UInt64 number close to 2 to the power of x.

intExp10

Accepts a numeric argument and returns a UInt64 number close to 10 to the power of x.

cosh(x)

.

Syntax

Arguments

• x — The angle, in radians. Values from the interval: -∞ < x < +∞. Float64.

Returned value

• Values from the interval: 1 <= cosh(x) < +∞.

Type: .

Example

Query:

SELECT cosh(0);

Result:

┌─cosh(0)──┐
│        1 │
└──────────┘

acosh(x)

.

acosh(x)

Arguments

• x — Hyperbolic cosine of angle. Values from the interval: 1 <= x < +∞. Float64.

Returned value

• The angle, in radians. Values from the interval: 0 <= acosh(x) < +∞.

Type: .

Example

Query:

SELECT acosh(1);

Result:

┌─acosh(1)─┐
│        0 │
└──────────┘

See Also

• cosh(x)

sinh(x)

Hyperbolic sine.

Syntax

sinh(x)

Arguments

• x — The angle, in radians. Values from the interval: -∞ < x < +∞. .

Returned value

• Values from the interval: -∞ < sinh(x) < +∞.

Type: Float64.

Example

Query:

SELECT sinh(0);

Result:

┌─sinh(0)──┐
│        0 │
└──────────┘

asinh(x)

Inverse hyperbolic sine.

Syntax

Arguments

• x — Hyperbolic sine of angle. Values from the interval: . .

Returned value

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

Type: Float64.

Example

Query:

SELECT asinh(0);

Result:

┌─asinh(0)─┐
│        0 │
└──────────┘

See Also

atanh(x)

.

Syntax

atanh(x)

Arguments

• x — Hyperbolic tangent of angle. Values from the interval: –1 < x < 1. Float64.

Returned value

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

Type: .

Example

Query:

SELECT atanh(0);

Result:

┌─atanh(0)─┐
│        0 │
└──────────┘

atan2(y, x)

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

Arguments

• y — y-coordinate of the point through which the ray passes. Float64.
• x — x-coordinate of the point through which the ray passes. .

Returned value

• The angle θ such that −π < θ ≤ π, in radians.

Type: Float64.

Example

Query:

SELECT atan2(1, 1);

Result:

┌────────atan2(1, 1)─┐
│ 0.7853981633974483 │
└────────────────────┘

hypot(x, y)

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

Syntax

hypot(x, y)

Arguments

• x — The first cathetus of a right-angle triangle. .
• y — The second cathetus of a right-angle triangle. Float64.

Returned value

• The length of the hypotenuse of a right-angle triangle.

Type: .

Example

Query:

SELECT hypot(1, 1);

Result:

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

Syntax

log1p(x)

Arguments

• x — Values from the interval: -1 < x < +∞. .

Returned value

• Values from the interval: -∞ < log1p(x) < +∞.

Type: Float64.

Example

Query:

SELECT log1p(0);

Result:

┌─log1p(0)─┐
│        0 │
└──────────┘

See Also

sign(x)

The sign function can extract the sign of a real number.

Syntax

sign(x)

Arguments

• x — Values from -∞ to +∞. Support all numeric types in ClickHouse.

Returned value

• -1 for x < 0
• 0 for x = 0
• 1 for x > 0

Example

Query:

SELECT sign(0);

Result:

┌─sign(0)─┐
│       0 │
└─────────┘

Query:

SELECT sign(1);

Result:

┌─sign(1)─┐
│       1 │
└─────────┘

Query:

SELECT sign(-1);

┌─sign(-1)─┐