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
θ
such 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 │
└──────────┘
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 │
└──────────────────────────────────┘