9.9 KiB
slug | sidebar_position | sidebar_label |
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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)
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)
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
sinh(x)
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)
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
atanh(x)
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
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 │
└───────────────────┘