thevar1able/ClickHouse
1
0
Fork 0
mirror of https://github.com/ClickHouse/ClickHouse.git synced 2024-11-28 02:21:59 +00:00
Code Issues Packages Projects Releases Wiki Activity
f6b975dfcd
ClickHouse/docs/en/sql-reference/functions/math-functions.md
Blargian 029e2ea226 Standardize references to data type docs
2024-05-24 05:54:16 +02:00

993 lines
18 KiB
Markdown
Raw Blame History

This file contains ambiguous Unicode characters

This file contains Unicode characters that might be confused with other characters. If you think that this is intentional, you can safely ignore this warning. Use the Escape button to reveal them.

---
slug: /en/sql-reference/functions/math-functions
sidebar_position: 125
sidebar_label: Mathematical
---
# Mathematical Functions
## e
Returns e ([Euler's constant](https://en.wikipedia.org/wiki/Euler%27s_constant)).
**Syntax**
```sql
e()
```
**Returned value**
Type: [Float64](../data-types/float.md).
## pi
Returns π ([Pi](https://en.wikipedia.org/wiki/Pi)).
**Syntax**
```sql
pi()
```
**Returned value**
Type: [Float64](../data-types/float.md).
## exp
Returns e to the power of the given argument.
**Syntax**
```sql
exp(x)
```
**Arguments**
- `x` - [(U)Int*](../data-types/int-uint.md), [Float*](../data-types/float.md) or [Decimal*](../data-types/decimal.md).
**Returned value**
Type: [Float*](../data-types/float.md).
## log
Returns the natural logarithm of the argument.
**Syntax**
```sql
log(x)
```
Alias: `ln(x)`
**Arguments**
- `x` - [(U)Int*](../data-types/int-uint.md), [Float*](../data-types/float.md) or [Decimal*](../data-types/decimal.md).
**Returned value**
Type: [Float*](../data-types/float.md).
## exp2
Returns 2 to the power of the given argument
**Syntax**
```sql
exp2(x)
```
**Arguments**
- `x` - [(U)Int*](../data-types/int-uint.md), [Float*](../data-types/float.md) or [Decimal*](../data-types/decimal.md).
**Returned value**
Type: [Float*](../data-types/float.md).
## intExp2
Like `exp` but returns a UInt64.
**Syntax**
```sql
intExp2(x)
```
## log2
Returns the binary logarithm of the argument.
**Syntax**
```sql
log2(x)
```
**Arguments**
- `x` - [(U)Int*](../data-types/int-uint.md), [Float*](../data-types/float.md) or [Decimal*](../data-types/decimal.md).
**Returned value**
Type: [Float*](../data-types/float.md).
## exp10
Returns 10 to the power of the given argument.
**Syntax**
```sql
exp10(x)
```
**Arguments**
- `x` - [(U)Int*](../data-types/int-uint.md), [Float*](../data-types/float.md) or [Decimal*](../data-types/decimal.md).
**Returned value**
Type: [Float*](../data-types/float.md).
## intExp10
Like `exp10` but returns a UInt64.
**Syntax**
```sql
intExp10(x)
```
## log10
Returns the decimal logarithm of the argument.
**Syntax**
```sql
log10(x)
```
**Arguments**
- `x` - [(U)Int*](../data-types/int-uint.md), [Float*](../data-types/float.md) or [Decimal*](../data-types/decimal.md).
**Returned value**
Type: [Float*](../data-types/float.md).
## sqrt
Returns the square root of the argument.
```sql
sqrt(x)
```
**Arguments**
- `x` - [(U)Int*](../data-types/int-uint.md), [Float*](../data-types/float.md) or [Decimal*](../data-types/decimal.md).
**Returned value**
Type: [Float*](../data-types/float.md).
## cbrt
Returns the cubic root of the argument.
```sql
cbrt(x)
```
**Arguments**
- `x` - [(U)Int*](../data-types/int-uint.md), [Float*](../data-types/float.md) or [Decimal*](../data-types/decimal.md).
**Returned value**
Type: [Float*](../data-types/float.md).
## erf
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**
```sql
erf(x)
```
**Arguments**
- `x` - [(U)Int*](../data-types/int-uint.md), [Float*](../data-types/float.md) or [Decimal*](../data-types/decimal.md).
**Returned value**
Type: [Float*](../data-types/float.md).
**Example**
(three sigma rule)
``` sql
SELECT erf(3 / sqrt(2));
```
```result
┌─erf(divide(3, sqrt(2)))─┐
│ 0.9973002039367398 │
└─────────────────────────┘
```
## erfc
Returns a number close to `1 - erf(x)` without loss of precision for large ‘x’ values.
**Syntax**
```sql
erfc(x)
```
**Arguments**
- `x` - [(U)Int*](../data-types/int-uint.md), [Float*](../data-types/float.md) or [Decimal*](../data-types/decimal.md).
**Returned value**
Type: [Float*](../data-types/float.md).
## lgamma
Returns the logarithm of the gamma function.
**Syntax**
```sql
lgamma(x)
```
**Arguments**
- `x` - [(U)Int*](../data-types/int-uint.md), [Float*](../data-types/float.md) or [Decimal*](../data-types/decimal.md).
**Returned value**
Type: [Float*](../data-types/float.md).
## tgamma
Returns the gamma function.
**Syntax**
```sql
gamma(x)
```
**Arguments**
- `x` - [(U)Int*](../data-types/int-uint.md), [Float*](../data-types/float.md) or [Decimal*](../data-types/decimal.md).
**Returned value**
Type: [Float*](../data-types/float.md).
## sin
Returns the sine of the argument
**Syntax**
```sql
sin(x)
```
**Arguments**
- `x` - [(U)Int*](../data-types/int-uint.md), [Float*](../data-types/float.md) or [Decimal*](../data-types/decimal.md).
**Returned value**
Type: [Float*](../data-types/float.md).
**Example**
Query:
```sql
SELECT sin(1.23);
```
```response
0.9424888019316975
```
## cos
Returns the cosine of the argument.
**Syntax**
```sql
cos(x)
```
**Arguments**
- `x` - [(U)Int*](../data-types/int-uint.md), [Float*](../data-types/float.md) or [Decimal*](../data-types/decimal.md).
**Returned value**
Type: [Float*](../data-types/float.md).
## tan
Returns the tangent of the argument.
**Syntax**
```sql
tan(x)
```
**Arguments**
- `x` - [(U)Int*](../data-types/int-uint.md), [Float*](../data-types/float.md) or [Decimal*](../data-types/decimal.md).
**Returned value**
Type: [Float*](../data-types/float.md).
## asin
Returns the arc sine of the argument.
**Syntax**
```sql
asin(x)
```
**Arguments**
- `x` - [(U)Int*](../data-types/int-uint.md), [Float*](../data-types/float.md) or [Decimal*](../data-types/decimal.md).
**Returned value**
Type: [Float*](../data-types/float.md).
## acos
Returns the arc cosine of the argument.
**Syntax**
```sql
acos(x)
```
**Arguments**
- `x` - [(U)Int*](../data-types/int-uint.md), [Float*](../data-types/float.md) or [Decimal*](../data-types/decimal.md).
**Returned value**
Type: [Float*](../data-types/float.md).
## atan
Returns the arc tangent of the argument.
**Syntax**
```sql
atan(x)
```
**Arguments**
- `x` - [(U)Int*](../data-types/int-uint.md), [Float*](../data-types/float.md) or [Decimal*](../data-types/decimal.md).
**Returned value**
Type: [Float*](../data-types/float.md).
## pow
Returns `x` to the power of `y`.
**Syntax**
```sql
pow(x, y)
```
Alias: `power(x, y)`
**Arguments**
- `x` - [(U)Int8/16/32/64](../data-types/int-uint.md) or [Float*](../data-types/float.md)
- `y` - [(U)Int8/16/32/64](../data-types/int-uint.md) or [Float*](../data-types/float.md)
**Returned value**
Type: [Float64](../data-types/float.md).
## cosh
Returns the [hyperbolic cosine](https://in.mathworks.com/help/matlab/ref/cosh.html) of the argument.
**Syntax**
``` sql
cosh(x)
```
**Arguments**
- `x` — The angle, in radians. Values from the interval: `-∞ < x < +∞`. [(U)Int*](../data-types/int-uint.md), [Float*](../data-types/float.md) or [Decimal*](../data-types/decimal.md).
**Returned value**
- Values from the interval: `1 <= cosh(x) < +∞`.
Type: [Float64](../data-types/float.md#float32-float64).
**Example**
``` sql
SELECT cosh(0);
```
Result:
```result
┌─cosh(0)──┐
│ 1 │
└──────────┘
```
## acosh
Returns the [inverse hyperbolic cosine](https://www.mathworks.com/help/matlab/ref/acosh.html).
**Syntax**
``` sql
acosh(x)
```
**Arguments**
- `x` — Hyperbolic cosine of angle. Values from the interval: `1 <= x < +∞`. [(U)Int*](../data-types/int-uint.md), [Float*](../data-types/float.md) or [Decimal*](../data-types/decimal.md).
**Returned value**
- The angle, in radians. Values from the interval: `0 <= acosh(x) < +∞`.
Type: [Float64](../data-types/float.md#float32-float64).
**Example**
``` sql
SELECT acosh(1);
```
Result:
```result
┌─acosh(1)─┐
│ 0 │
└──────────┘
```
## sinh
Returns the [hyperbolic sine](https://www.mathworks.com/help/matlab/ref/sinh.html).
**Syntax**
``` sql
sinh(x)
```
**Arguments**
- `x` — The angle, in radians. Values from the interval: `-∞ < x < +∞`. [(U)Int*](../data-types/int-uint.md), [Float*](../data-types/float.md) or [Decimal*](../data-types/decimal.md).
**Returned value**
- Values from the interval: `-∞ < sinh(x) < +∞`.
Type: [Float64](../data-types/float.md#float32-float64).
**Example**
``` sql
SELECT sinh(0);
```
Result:
```result
┌─sinh(0)──┐
│ 0 │
└──────────┘
```
## asinh
Returns the [inverse hyperbolic sine](https://www.mathworks.com/help/matlab/ref/asinh.html).
**Syntax**
``` sql
asinh(x)
```
**Arguments**
- `x` — Hyperbolic sine of angle. Values from the interval: `-∞ < x < +∞`. [(U)Int*](../data-types/int-uint.md), [Float*](../data-types/float.md) or [Decimal*](../data-types/decimal.md).
**Returned value**
- The angle, in radians. Values from the interval: `-∞ < asinh(x) < +∞`.
Type: [Float64](../data-types/float.md#float32-float64).
**Example**
``` sql
SELECT asinh(0);
```
Result:
```result
┌─asinh(0)─┐
│ 0 │
└──────────┘
```
## tanh
Returns the [hyperbolic tangent](https://www.mathworks.com/help/matlab/ref/tanh.html).
**Syntax**
``` sql
tanh(x)
```
**Arguments**
- `x` — The angle, in radians. Values from the interval: `-∞ < x < +∞`. [(U)Int*](../data-types/int-uint.md), [Float*](../data-types/float.md) or [Decimal*](../data-types/decimal.md).
**Returned value**
- Values from the interval: `-1 < tanh(x) < 1`.
Type: [Float*](../data-types/float.md#float32-float64).
**Example**
``` sql
SELECT tanh(0);
```
Result:
```result
0
```
## atanh
Returns the [inverse hyperbolic tangent](https://www.mathworks.com/help/matlab/ref/atanh.html).
**Syntax**
``` sql
atanh(x)
```
**Arguments**
- `x` — Hyperbolic tangent of angle. Values from the interval: `–1 < x < 1`. [(U)Int*](../data-types/int-uint.md), [Float*](../data-types/float.md) or [Decimal*](../data-types/decimal.md).
**Returned value**
- The angle, in radians. Values from the interval: `-∞ < atanh(x) < +∞`.
Type: [Float64](../data-types/float.md#float32-float64).
**Example**
``` sql
SELECT atanh(0);
```
Result:
```result
┌─atanh(0)─┐
│ 0 │
└──────────┘
```
## atan2
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)`.
**Syntax**
``` sql
atan2(y, x)
```
**Arguments**
- `y` — y-coordinate of the point through which the ray passes. [(U)Int*](../data-types/int-uint.md), [Float*](../data-types/float.md).
- `x` — x-coordinate of the point through which the ray passes. [(U)Int*](../data-types/int-uint.md), [Float*](../data-types/float.md).
**Returned value**
- The angle `θ` such that `−π < θ ≤ π`, in radians.
Type: [Float64](../data-types/float.md#float32-float64).
**Example**
``` sql
SELECT atan2(1, 1);
```
Result:
```result
┌────────atan2(1, 1)─┐
│ 0.7853981633974483 │
└────────────────────┘
```
## hypot
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.
**Syntax**
``` sql
hypot(x, y)
```
**Arguments**
- `x` — The first cathetus of a right-angle triangle. [(U)Int*](../data-types/int-uint.md), [Float*](../data-types/float.md).
- `y` — The second cathetus of a right-angle triangle. [(U)Int*](../data-types/int-uint.md), [Float*](../data-types/float.md).
**Returned value**
- The length of the hypotenuse of a right-angle triangle.
Type: [Float64](../data-types/float.md#float32-float64).
**Example**
``` sql
SELECT hypot(1, 1);
```
Result:
```result
┌────────hypot(1, 1)─┐
│ 1.4142135623730951 │
└────────────────────┘
```
## log1p
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.
**Syntax**
``` sql
log1p(x)
```
**Arguments**
- `x` — Values from the interval: `-1 < x < +∞`. [(U)Int*](../data-types/int-uint.md), [Float*](../data-types/float.md) or [Decimal*](../data-types/decimal.md).
**Returned value**
- Values from the interval: `-∞ < log1p(x) < +∞`.
Type: [Float64](../data-types/float.md#float32-float64).
**Example**
``` sql
SELECT log1p(0);
```
Result:
```result
┌─log1p(0)─┐
│ 0 │
└──────────┘
```
## sign
Returns the sign of a real number.
**Syntax**
``` sql
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`
Type: [Int8](../data-types/int-uint.md).
**Examples**
Sign for the zero value:
``` sql
SELECT sign(0);
```
Result:
```result
┌─sign(0)─┐
│ 0 │
└─────────┘
```
Sign for the positive value:
``` sql
SELECT sign(1);
```
Result:
```result
┌─sign(1)─┐
│ 1 │
└─────────┘
```
Sign for the negative value:
``` sql
SELECT sign(-1);
```
Result:
```result
┌─sign(-1)─┐
│ -1 │
└──────────┘
```
## sigmoid
Returns the [sigmoid function](https://en.wikipedia.org/wiki/Sigmoid_function).
**Syntax**
```sql
sigmoid(x)
```
**Parameters**
- `x` — input value. Values from the interval: `-∞ < x < +∞`. [(U)Int*](../data-types/int-uint.md), [Float*](../data-types/float.md) or [Decimal*](../data-types/decimal.md).
**Returned value**
- Corresponding value along the sigmoid curve between 0 and 1. [Float64](../data-types/float.md).
**Example**
Query:
``` sql
SELECT round(sigmoid(x), 5) FROM (SELECT arrayJoin([-1, 0, 1]) AS x);
```
Result:
```result
0.26894
0.5
0.73106
```
## degrees
Converts radians to degrees.
**Syntax**
``` sql
degrees(x)
```
**Arguments**
- `x` — Input in radians. [(U)Int*](../data-types/int-uint.md), [Float*](../data-types/float.md) or [Decimal*](../data-types/decimal.md).
**Returned value**
- Value in degrees. [Float64](../data-types/float.md#float32-float64).
**Example**
``` sql
SELECT degrees(3.141592653589793);
```
Result:
```result
┌─degrees(3.141592653589793)─┐
│ 180 │
└────────────────────────────┘
```
## radians
Converts degrees to radians.
**Syntax**
``` sql
radians(x)
```
**Arguments**
- `x` — Input in degrees. [(U)Int*](../data-types/int-uint.md), [Float*](../data-types/float.md) or [Decimal*](../data-types/decimal.md).
**Returned value**
- Value in radians.
Type: [Float64](../data-types/float.md#float32-float64).
**Example**
``` sql
SELECT radians(180);
```
Result:
```result
┌──────radians(180)─┐
│ 3.141592653589793 │
└───────────────────┘
```
## factorial
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.
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**
``` sql
factorial(n)
```
**Example**
``` sql
SELECT factorial(10);
```
Result:
```result
┌─factorial(10)─┐
│ 3628800 │
└───────────────┘
```
## width_bucket
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**
```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 │
└──────────────────────────────────┘
```
## proportionsZTest
Returns test statistics for the two proportion Z-test - a statistical test for comparing the proportions from two populations `x` and `y`.
**Syntax**
```sql
proportionsZTest(successes_x, successes_y, trials_x, trials_y, conf_level, pool_type)
```
**Arguments**
- `successes_x`: Number of successes in population `x`. [UInt64](../data-types/int-uint.md).
- `successes_y`: Number of successes in population `y`. [UInt64](../data-types/int-uint.md).
- `trials_x`: Number of trials in population `x`. [UInt64](../data-types/int-uint.md).
- `trials_y`: Number of trials in population `y`. [UInt64](../data-types/int-uint.md).
- `conf_level`: Confidence level for the test. [Float64](../data-types/float.md).
- `pool_type`: Selection of pooling (way in which the standard error is estimated). Can be either `unpooled` or `pooled`. [String](../data-types/string.md).
:::note
For argument `pool_type`: In the pooled version, the two proportions are averaged, and only one proportion is used to estimate the standard error. In the unpooled version, the two proportions are used separately.
:::
**Returned value**
- `z_stat`: Z statistic. [Float64](../data-types/float.md).
- `p_val`: P value. [Float64](../data-types/float.md).
- `ci_low`: The lower confidence interval. [Float64](../data-types/float.md).
- `ci_high`: The upper confidence interval. [Float64](../data-types/float.md).
**Example**
Query:
```sql
SELECT proportionsZTest(10, 11, 100, 101, 0.95, 'unpooled');
```
Result:
```response
┌─proportionsZTest(10, 11, 100, 101, 0.95, 'unpooled')───────────────────────────────┐
│ (-0.20656724435948853,0.8363478437079654,-0.09345975390115283,0.07563797172293502) │
└────────────────────────────────────────────────────────────────────────────────────┘
```
Reference in New Issue View Git Blame Copy Permalink