18 KiB
| slug | sidebar_position | sidebar_label |
|---|---|---|
| /en/sql-reference/functions/math-functions | 125 | Mathematical |
Mathematical Functions
e
Returns e (Euler's constant).
Syntax
e()
Returned value
Type: Float64.
pi
Returns π (Pi).
Syntax
pi()
Returned value
Type: Float64.
exp
Returns e to the power of the given argument.
Syntax
exp(x)
Arguments
Returned value
Type: Float*.
log
Returns the natural logarithm of the argument.
Syntax
log(x)
Alias: ln(x)
Arguments
Returned value
Type: Float*.
exp2
Returns 2 to the power of the given argument
Syntax
exp2(x)
Arguments
Returned value
Type: Float*.
intExp2
Like exp but returns a UInt64.
Syntax
intExp2(x)
log2
Returns the binary logarithm of the argument.
Syntax
log2(x)
Arguments
Returned value
Type: Float*.
exp10
Returns 10 to the power of the given argument.
Syntax
exp10(x)
Arguments
Returned value
Type: Float*.
intExp10
Like exp10 but returns a UInt64.
Syntax
intExp10(x)
log10
Returns the decimal logarithm of the argument.
Syntax
log10(x)
Arguments
Returned value
Type: Float*.
sqrt
Returns the square root of the argument.
sqrt(x)
Arguments
Returned value
Type: Float*.
cbrt
Returns the cubic root of the argument.
cbrt(x)
Arguments
Returned value
Type: Float*.
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
erf(x)
Arguments
Returned value
Type: Float*.
Example
(three sigma rule)
SELECT erf(3 / sqrt(2));
┌─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
erfc(x)
Arguments
Returned value
Type: Float*.
lgamma
Returns the logarithm of the gamma function.
Syntax
lgamma(x)
Arguments
Returned value
Type: Float*.
tgamma
Returns the gamma function.
Syntax
gamma(x)
Arguments
Returned value
Type: Float*.
sin
Returns the sine of the argument
Syntax
sin(x)
Arguments
Returned value
Type: Float*.
Example
Query:
SELECT sin(1.23);
0.9424888019316975
cos
Returns the cosine of the argument.
Syntax
cos(x)
Arguments
Returned value
Type: Float*.
tan
Returns the tangent of the argument.
Syntax
tan(x)
Arguments
Returned value
Type: Float*.
asin
Returns the arc sine of the argument.
Syntax
asin(x)
Arguments
Returned value
Type: Float*.
acos
Returns the arc cosine of the argument.
Syntax
acos(x)
Arguments
Returned value
Type: Float*.
atan
Returns the arc tangent of the argument.
Syntax
atan(x)
Arguments
Returned value
Type: Float*.
pow
Returns x to the power of y.
Syntax
pow(x, y)
Alias: power(x, y)
Arguments
x- (U)Int8/16/32/64 or Float*y- (U)Int8/16/32/64 or Float*
Returned value
Type: Float64.
cosh
Returns the hyperbolic cosine of the argument.
Syntax
cosh(x)
Arguments
Returned value
- Values from the interval:
1 <= cosh(x) < +∞.
Type: Float64.
Example
SELECT cosh(0);
Result:
┌─cosh(0)──┐
│ 1 │
└──────────┘
acosh
Returns the inverse hyperbolic cosine.
Syntax
acosh(x)
Arguments
Returned value
- The angle, in radians. Values from the interval:
0 <= acosh(x) < +∞.
Type: Float64.
Example
SELECT acosh(1);
Result:
┌─acosh(1)─┐
│ 0 │
└──────────┘
sinh
Returns the hyperbolic sine.
Syntax
sinh(x)
Arguments
Returned value
- Values from the interval:
-∞ < sinh(x) < +∞.
Type: Float64.
Example
SELECT sinh(0);
Result:
┌─sinh(0)──┐
│ 0 │
└──────────┘
asinh
Returns the inverse hyperbolic sine.
Syntax
asinh(x)
Arguments
Returned value
- The angle, in radians. Values from the interval:
-∞ < asinh(x) < +∞.
Type: Float64.
Example
SELECT asinh(0);
Result:
┌─asinh(0)─┐
│ 0 │
└──────────┘
tanh
Returns the hyperbolic tangent.
Syntax
tanh(x)
Arguments
Returned value
- Values from the interval:
-1 < tanh(x) < 1.
Type: Float*.
Example
SELECT tanh(0);
Result:
0
atanh
Returns the inverse hyperbolic tangent.
Syntax
atanh(x)
Arguments
Returned value
- The angle, in radians. Values from the interval:
-∞ < atanh(x) < +∞.
Type: Float64.
Example
SELECT atanh(0);
Result:
┌─atanh(0)─┐
│ 0 │
└──────────┘
atan2
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
y— y-coordinate of the point through which the ray passes. (U)Int*, Float*.x— x-coordinate of the point through which the ray passes. (U)Int*, Float*.
Returned value
- The angle
θsuch that−π < θ ≤ π, in radians.
Type: Float64.
Example
SELECT atan2(1, 1);
Result:
┌────────atan2(1, 1)─┐
│ 0.7853981633974483 │
└────────────────────┘
hypot
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
x— The first cathetus of a right-angle triangle. (U)Int*, Float*.y— The second cathetus of a right-angle triangle. (U)Int*, Float*.
Returned value
- The length of the hypotenuse of a right-angle triangle.
Type: Float64.
Example
SELECT hypot(1, 1);
Result:
┌────────hypot(1, 1)─┐
│ 1.4142135623730951 │
└────────────────────┘
log1p
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
- Values from the interval:
-∞ < log1p(x) < +∞.
Type: Float64.
Example
SELECT log1p(0);
Result:
┌─log1p(0)─┐
│ 0 │
└──────────┘
sign
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
Type: Int8.
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 │
└──────────┘
sigmoid
Returns the sigmoid function.
Syntax
sigmoid(x)
Parameters
Returned value
- Corresponding value along the sigmoid curve between 0 and 1. Float64.
Example
Query:
SELECT round(sigmoid(x), 5) FROM (SELECT arrayJoin([-1, 0, 1]) AS x);
Result:
0.26894
0.5
0.73106
degrees
Converts radians to degrees.
Syntax
degrees(x)
Arguments
Returned value
- Value in degrees.
Type: Float64.
Example
SELECT degrees(3.141592653589793);
Result:
┌─degrees(3.141592653589793)─┐
│ 180 │
└────────────────────────────┘
radians
Converts degrees to radians.
Syntax
radians(x)
Arguments
Returned value
- Value in radians.
Type: Float64.
Example
SELECT radians(180);
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
factorial(n)
Example
SELECT factorial(10);
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
widthBucket(operand, low, high, count)
Alias: WIDTH_BUCKET
Example
SELECT widthBucket(10.15, -8.6, 23, 18);
Result:
┌─widthBucket(10.15, -8.6, 23, 18)─┐
│ 11 │
└──────────────────────────────────┘