ClickHouse/docs/en/sql-reference/functions/math-functions.md

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/en/sql-reference/functions/math-functions	44	Mathematical

Mathematical Functions

All the functions return a Float64 number. The accuracy of the result is close to the maximum precision possible, but the result might not coincide with the machine representable number nearest to the corresponding real number.

e()

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.

erf(x)

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’.

Example (three sigma rule):

SELECT erf(3 / sqrt(2));

┌─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.

pow(x, y), power(x, y)

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)

Hyperbolic cosine.

Syntax

cosh(x)

Arguments

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

Returned value

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

Type: Float64.

Example

Query:

SELECT cosh(0);

Result:

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

acosh(x)

Inverse hyperbolic cosine.

Syntax

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: Float64.

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 < +∞. Float64.

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

asinh(x)

Arguments

• x — Hyperbolic sine of angle. Values from the interval: -∞ < x < +∞. Float64.

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

• sinh(x)

atanh(x)

Inverse hyperbolic tangent.

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: Float64.

Example

Query:

SELECT atanh(0);

Result:

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

atan2(y, x)

The function 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).

Syntax

atan2(y, x)

Arguments

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

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

Returned value

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

Type: Float64.

Example

Query:

SELECT hypot(1, 1);

Result:

┌────────hypot(1, 1)─┐
│ 1.4142135623730951 │
└────────────────────┘

log1p(x)

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

Syntax

log1p(x)

Arguments

• x — Values from the interval: -1 < x < +∞. Float64.

Returned value

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

Type: Float64.

Example

Query:

SELECT log1p(0);

Result:

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

See Also

• log(x)

sign(x)

Returns 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

Examples

Sign for the zero value:

SELECT sign(0);

Result:

┌─sign(0)─┐
│       0 │
└─────────┘

Sign for the positive value:

SELECT sign(1);

Result:

┌─sign(1)─┐
│       1 │
└─────────┘

Sign for the negative value:

SELECT sign(-1);

Result:

┌─sign(-1)─┐
│       -1 │
└──────────┘

degrees(x)

Converts the input value in radians to degrees.

Syntax

degrees(x)

Arguments

• x — Input in radians. Float64.

Returned value

• Value in degrees.

Type: Float64.

Example

Query:

SELECT degrees(3.141592653589793);

Result:

┌─degrees(3.141592653589793)─┐
│                        180 │
└────────────────────────────┘

radians(x)

Converts the input value in degrees to radians.

Syntax

radians(x)

Arguments

• x — Input in degrees. Float64.

Returned value

• Value in radians.

Type: Float64.

Example

Query:

SELECT radians(180);

Result:

┌──────radians(180)─┐
│ 3.141592653589793 │
└───────────────────┘

factorial(n)

Computes the factorial of an integer value. It works with any native integer type including UInt(8|16|32|64) and Int(8|16|32|64). The return type is UInt64.

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 exception throw.

Syntax

factorial(n)

Example

Query:

SELECT factorial(10);

Result:

┌─factorial(10)─┐
│       3628800 │
└───────────────┘

width_bucket(operand, low, high, count)

Returns the number of the bucket in which operand falls in a histogram having count equal-width buckets spanning the range low to high. Returns 0 if operand < low, and returns count+1 if operand >= high.

operand, low, high can be any native number type. count can only be unsigned native integer and its value cannot be zero.

Syntax

widthBucket(operand, low, high, count)

There is also a case insensitive alias called WIDTH_BUCKET to provide compatibility with other databases.

Example

Query:

SELECT widthBucket(10.15, -8.6, 23, 18);

Result:

┌─widthBucket(10.15, -8.6, 23, 18)─┐
│                               11 │
└──────────────────────────────────┘