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714 lines
11 KiB
Markdown
714 lines
11 KiB
Markdown
---
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slug: /en/sql-reference/functions/math-functions
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sidebar_position: 125
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sidebar_label: Mathematical
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---
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# Mathematical Functions
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All the functions return a Float64 number. Results are generally as close to the actual result as possible, but in some cases less precise than the machine-representable number.
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## e
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Returns e.
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**Syntax**
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```sql
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e()
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```
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## pi
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Returns π.
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**Syntax**
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```sql
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pi()
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```
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## exp
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Returns e to the power of the given argument.
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**Syntax**
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```sql
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exp(x)
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```
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## log
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Returns the natural logarithm of the argument.
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**Syntax**
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```sql
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log(x)
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```
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Alias: `ln(x)`
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## exp2
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Returns 2 to the power of the given argumetn
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**Syntax**
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```sql
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exp2(x)
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```
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## intExp2
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Like `exp` but returns a UInt64.
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**Syntax**
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```sql
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intExp2(x)
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```
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## log2
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Returns the binary logarithm of the argument.
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**Syntax**
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```sql
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log2(x)
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```
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## exp10
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Returns 10 to the power of the given argumetn
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**Syntax**
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```sql
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exp10(x)
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```
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## intExp10
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Like `exp10` but returns a UInt64.
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**Syntax**
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```sql
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intExp10(x)
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```
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## log10
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Returns the decimal logarithm of the argument.
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**Syntax**
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```sql
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log10(x)
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```
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## sqrt
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Returns the square root of the argument.
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```sql
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sqrt(x)
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```
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## cbrt
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Returns the cubic root of the argument.
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```sql
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cbrt(x)
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```
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## erf
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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`.
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**Syntax**
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```sql
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erf(x)
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```
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**Example**
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(three sigma rule)
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``` sql
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SELECT erf(3 / sqrt(2));
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```
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```result
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┌─erf(divide(3, sqrt(2)))─┐
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│ 0.9973002039367398 │
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└─────────────────────────┘
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```
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## erfc
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Returns a number close to `1 - erf(x)` without loss of precision for large ‘x’ values.
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**Syntax**
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```sql
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erfc(x)
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```
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## lgamma
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Returns the logarithm of the gamma function.
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**Syntax**
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```sql
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lgamma(x)
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```
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## tgamma
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Returns the gamma function.
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**Syntax**
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```sql
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gamma(x)
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```
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## sin
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Returns the sine of the argument
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**Syntax**
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```sql
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sin(x)
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```
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## cos
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Returns the cosine of the argument.
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**Syntax**
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```sql
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cos(x)
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```
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## tan
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Returns the tangent of the argument.
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**Syntax**
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```sql
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tan(x)
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```
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## asin
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Returns the arc sine of the argument.
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**Syntax**
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```sql
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asin(x)
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```
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## acos
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Returns the arc cosine of the argument.
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**Syntax**
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```sql
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acos(x)
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```
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## atan
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Returns the arc tangent of the argument.
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**Syntax**
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```sql
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atan(x)
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```
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## pow
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Returns `x` to the power of `y`.
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**Syntax**
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```sql
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pow(x, y)
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```
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Alias: `power(x, y)`
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## cosh
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Returns the [hyperbolic cosine](https://in.mathworks.com/help/matlab/ref/cosh.html) of the argument.
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**Syntax**
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``` sql
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cosh(x)
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```
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**Arguments**
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- `x` — The angle, in radians. Values from the interval: `-∞ < x < +∞`. [Float64](../../sql-reference/data-types/float.md#float32-float64).
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**Returned value**
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- Values from the interval: `1 <= cosh(x) < +∞`.
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Type: [Float64](../../sql-reference/data-types/float.md#float32-float64).
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**Example**
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``` sql
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SELECT cosh(0);
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```
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Result:
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```result
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┌─cosh(0)──┐
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│ 1 │
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└──────────┘
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```
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## acosh
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Returns the [inverse hyperbolic cosine](https://www.mathworks.com/help/matlab/ref/acosh.html).
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**Syntax**
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``` sql
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acosh(x)
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```
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**Arguments**
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- `x` — Hyperbolic cosine of angle. Values from the interval: `1 <= x < +∞`. [Float64](../../sql-reference/data-types/float.md#float32-float64).
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**Returned value**
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- The angle, in radians. Values from the interval: `0 <= acosh(x) < +∞`.
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Type: [Float64](../../sql-reference/data-types/float.md#float32-float64).
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**Example**
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``` sql
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SELECT acosh(1);
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```
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Result:
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```result
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┌─acosh(1)─┐
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│ 0 │
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└──────────┘
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```
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## sinh
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Returns the [hyperbolic sine](https://www.mathworks.com/help/matlab/ref/sinh.html).
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**Syntax**
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``` sql
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sinh(x)
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```
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**Arguments**
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- `x` — The angle, in radians. Values from the interval: `-∞ < x < +∞`. [Float64](../../sql-reference/data-types/float.md#float32-float64).
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**Returned value**
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- Values from the interval: `-∞ < sinh(x) < +∞`.
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Type: [Float64](../../sql-reference/data-types/float.md#float32-float64).
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**Example**
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``` sql
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SELECT sinh(0);
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```
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Result:
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```result
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┌─sinh(0)──┐
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│ 0 │
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└──────────┘
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```
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## asinh
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Returns the [inverse hyperbolic sine](https://www.mathworks.com/help/matlab/ref/asinh.html).
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**Syntax**
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``` sql
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asinh(x)
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```
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**Arguments**
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- `x` — Hyperbolic sine of angle. Values from the interval: `-∞ < x < +∞`. [Float64](../../sql-reference/data-types/float.md#float32-float64).
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**Returned value**
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- The angle, in radians. Values from the interval: `-∞ < asinh(x) < +∞`.
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Type: [Float64](../../sql-reference/data-types/float.md#float32-float64).
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**Example**
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``` sql
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SELECT asinh(0);
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```
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Result:
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```result
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┌─asinh(0)─┐
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│ 0 │
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└──────────┘
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```
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## atanh
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Returns the [inverse hyperbolic tangent](https://www.mathworks.com/help/matlab/ref/atanh.html).
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**Syntax**
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``` sql
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atanh(x)
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```
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**Arguments**
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- `x` — Hyperbolic tangent of angle. Values from the interval: `–1 < x < 1`. [Float64](../../sql-reference/data-types/float.md#float32-float64).
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**Returned value**
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- The angle, in radians. Values from the interval: `-∞ < atanh(x) < +∞`.
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Type: [Float64](../../sql-reference/data-types/float.md#float32-float64).
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**Example**
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``` sql
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SELECT atanh(0);
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```
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Result:
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```result
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┌─atanh(0)─┐
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│ 0 │
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└──────────┘
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```
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## atan2
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Returns the [atan2](https://en.wikipedia.org/wiki/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)`.
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**Syntax**
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``` sql
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atan2(y, x)
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```
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**Arguments**
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- `y` — y-coordinate of the point through which the ray passes. [Float64](../../sql-reference/data-types/float.md#float32-float64).
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- `x` — x-coordinate of the point through which the ray passes. [Float64](../../sql-reference/data-types/float.md#float32-float64).
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**Returned value**
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- The angle `θ` such that `−π < θ ≤ π`, in radians.
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Type: [Float64](../../sql-reference/data-types/float.md#float32-float64).
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**Example**
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``` sql
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SELECT atan2(1, 1);
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```
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Result:
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```result
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┌────────atan2(1, 1)─┐
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│ 0.7853981633974483 │
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└────────────────────┘
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```
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## hypot
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Returns the length of the hypotenuse of a right-angle triangle. [Hypot](https://en.wikipedia.org/wiki/Hypot) avoids problems that occur when squaring very large or very small numbers.
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**Syntax**
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``` sql
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hypot(x, y)
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```
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**Arguments**
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- `x` — The first cathetus of a right-angle triangle. [Float64](../../sql-reference/data-types/float.md#float32-float64).
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- `y` — The second cathetus of a right-angle triangle. [Float64](../../sql-reference/data-types/float.md#float32-float64).
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**Returned value**
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- The length of the hypotenuse of a right-angle triangle.
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Type: [Float64](../../sql-reference/data-types/float.md#float32-float64).
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**Example**
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``` sql
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SELECT hypot(1, 1);
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```
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Result:
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```result
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┌────────hypot(1, 1)─┐
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│ 1.4142135623730951 │
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└────────────────────┘
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```
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## log1p
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Calculates `log(1+x)`. The [calculation](https://en.wikipedia.org/wiki/Natural_logarithm#lnp1) `log1p(x)` is more accurate than `log(1+x)` for small values of x.
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**Syntax**
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``` sql
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log1p(x)
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```
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**Arguments**
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- `x` — Values from the interval: `-1 < x < +∞`. [Float64](../../sql-reference/data-types/float.md#float32-float64).
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**Returned value**
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- Values from the interval: `-∞ < log1p(x) < +∞`.
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Type: [Float64](../../sql-reference/data-types/float.md#float32-float64).
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**Example**
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``` sql
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SELECT log1p(0);
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```
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Result:
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```result
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┌─log1p(0)─┐
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│ 0 │
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└──────────┘
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```
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## sign
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Returns the sign of a real number.
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**Syntax**
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``` sql
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sign(x)
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```
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**Arguments**
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- `x` — Values from `-∞` to `+∞`. Support all numeric types in ClickHouse.
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**Returned value**
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- -1 for `x < 0`
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- 0 for `x = 0`
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- 1 for `x > 0`
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**Examples**
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Sign for the zero value:
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``` sql
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SELECT sign(0);
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```
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Result:
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```result
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┌─sign(0)─┐
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│ 0 │
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└─────────┘
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```
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Sign for the positive value:
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``` sql
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SELECT sign(1);
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```
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Result:
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```result
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┌─sign(1)─┐
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│ 1 │
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└─────────┘
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```
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Sign for the negative value:
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``` sql
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SELECT sign(-1);
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```
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Result:
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```result
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┌─sign(-1)─┐
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│ -1 │
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└──────────┘
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```
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## degrees
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Converts radians to degrees.
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**Syntax**
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``` sql
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degrees(x)
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```
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**Arguments**
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- `x` — Input in radians. [Float64](../../sql-reference/data-types/float.md#float32-float64).
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**Returned value**
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- Value in degrees.
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Type: [Float64](../../sql-reference/data-types/float.md#float32-float64).
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**Example**
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``` sql
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SELECT degrees(3.141592653589793);
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```
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Result:
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```result
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┌─degrees(3.141592653589793)─┐
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│ 180 │
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└────────────────────────────┘
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```
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## radians
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Converts degrees to radians.
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**Syntax**
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``` sql
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radians(x)
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```
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**Arguments**
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- `x` — Input in degrees. [Float64](../../sql-reference/data-types/float.md#float32-float64).
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**Returned value**
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- Value in radians.
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Type: [Float64](../../sql-reference/data-types/float.md#float32-float64).
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**Example**
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``` sql
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SELECT radians(180);
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```
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Result:
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```result
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┌──────radians(180)─┐
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│ 3.141592653589793 │
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└───────────────────┘
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```
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## factorial
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Computes the factorial of an integer value. Works with any native integer type including UInt(8|16|32|64) and Int(8|16|32|64). The return type is UInt64.
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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.
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**Syntax**
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``` sql
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factorial(n)
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```
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**Example**
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``` sql
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SELECT factorial(10);
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```
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Result:
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```result
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┌─factorial(10)─┐
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│ 3628800 │
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└───────────────┘
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```
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## width_bucket
|
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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`.
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`operand`, `low`, `high` can be any native number type. `count` can only be unsigned native integer and its value cannot be zero.
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**Syntax**
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```sql
|
||
widthBucket(operand, low, high, count)
|
||
```
|
||
Alias: `WIDTH_BUCKET`
|
||
|
||
**Example**
|
||
|
||
``` sql
|
||
SELECT widthBucket(10.15, -8.6, 23, 18);
|
||
```
|
||
|
||
Result:
|
||
|
||
```result
|
||
┌─widthBucket(10.15, -8.6, 23, 18)─┐
|
||
│ 11 │
|
||
└──────────────────────────────────┘
|
||
```
|