Mathematical functions

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acos

acos(x)

• x — The value for which to find arc cosine of. (U)Int* or Float* or Decimal*

SELECT acos(0.5);

1.0471975511965979

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acosh

acosh(x)

• x — Hyperbolic cosine of angle. Values from the interval: 1 ≤ x < +∞. (U)Int* or Float* or Decimal*

SELECT acosh(1)

0

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asin

asin(x)

• x — Argument for which to calculate arcsine of. (U)Int* or Float* or Decimal

SELECT asin(1.0) = pi() / 2, sin(asin(1)), asin(sin(1))

1 1 1

SELECT toTypeName(asin(1.0::Float32))

Float64

SELECT asin(1.1), asin(-2), asin(inf), asin(nan)

nan nan nan nan

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asinh

asinh(x)

• x — Hyperbolic sine of angle. Values from the interval: -∞ < x < +∞. (U)Int* or Float* or Decimal*

SELECT asinh(0)

0

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atan

atan(x)

• x — The value for which to find arc tangent of. (U)Int* or Float* or Decimal*

SELECT atan(1);

0.7853981633974483

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atan2

atan2(y, x)

• y — y-coordinate of the point through which the ray passes. (U)Int* or Float* or Decimal*
• x — x-coordinate of the point through which the ray passes. (U)Int* or Float* or Decimal*

SELECT atan2(1, 1)

0.7853981633974483

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atanh

atanh(x)

• x — Hyperbolic tangent of angle. Values from the interval: -1 < x < 1. (U)Int*, Float* or Decimal*. (U)Int* or Float* or Decimal*

SELECT atanh(0)

0

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cbrt

cbrt(x)

• x — The value for which to find the cubic root of. (U)Int* or Float* or Decimal*

SELECT cbrt(8);

2

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cos

cos(x)

• x — The angle in radians. (U)Int* or Float* or Decimal*

SELECT cos(0);

1

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cosh

cosh(x)

• x — The angle, in radians. Values from the interval: -∞ < x < +∞. (U)Int* or Float* or Decimal*

SELECT cosh(0)

1

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degrees

degrees(x)

• x — Input in radians. (U)Int* or Float* or Decimal*

SELECT degrees(3.141592653589793)

180

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e

e()

• None.

SELECT e();

2.718281828459045

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erf

erf(x)

• x — The value for which to compute the error function value. (U)Int* or Float* or Decimal*

SELECT erf(3 / sqrt(2))

┌─erf(divide(3, sqrt(2)))─┐
│      0.9973002039367398 │
└─────────────────────────┘

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erfc

erfc(x)

• x — The value for which to find the error function value. (U)Int* or Float* or Decimal*

SELECT erfc(0);

1

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exp

exp(x)

• x — The exponent. (U)Int* or Float* or Decimal*

SELECT round(exp(-1), 4)

┌─round(exp(-1), 4)─┐
│            0.3679 │
└───────────────────┘

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exp10

exp10(x)

• x — The exponent. (U)Int* or Float* or Decimal*

SELECT exp10(2);

100

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exp2

exp2(x)

• x — The exponent. (U)Int* or Float* or Decimal*

SELECT exp2(3);

8

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factorial

factorial(n)

• n — Integer value for which to calculate the factorial. Maximum value is 20. (U)Int8/16/32/64

factorial(10)

3628800

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hypot

hypot(x, y)

• x — The first cathetus of a right-angle triangle. (U)Int* or Float* or Decimal*
• y — The second cathetus of a right-angle triangle. (U)Int* or Float* or Decimal*

SELECT hypot(1, 1)

1.4142135623730951

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intExp10

intExp10(x)

• x — The exponent. Int* or UInt* or Float*

SELECT intExp10(2);

100

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intExp2

intExp2(x)

• x — The exponent. Int* or UInt* or Float*

SELECT intExp2(3);

8

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isPrime

isPrime(n)

• n — Unsigned integer to test for primality. UInt8 or UInt16 or UInt32 or UInt64

SELECT isPrime(17)

1

SELECT isPrime(18)

0

SELECT isPrime(18446744073709551557)

1

SELECT isPrime(18446744073709551615)

0

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isProbablePrime

isProbablePrime(n[, rounds])

• n — Unsigned integer to test for primality. UInt8 or UInt16 or UInt32 or UInt64 or UInt128 or UInt256
• rounds — Optional positive integer constant in [1, 256]. Number of Miller-Rabin rounds for UInt128/UInt256 (ignored for narrower types). Default 25. UInt8 or UInt16 or UInt32 or UInt64

SELECT isProbablePrime(17)

1

SELECT isProbablePrime(18)

0

SELECT isProbablePrime(18446744073709551557)

1

SELECT isProbablePrime(toUInt128('170141183460469231731687303715884105727'))

1

SELECT isProbablePrime(toUInt256('57896044618658097711785492504343953926634992332820282019728792003956564819949'))

1

SELECT isProbablePrime(toUInt256('57896044618658097711785492504343953926634992332820282019728792003956564819949'), 5)

1

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lgamma

lgamma(x)

• x — The number for which to compute the logarithm of the gamma function. (U)Int* or Float* or Decimal*

SELECT lgamma(5);

3.1780538303479458

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log

log(x)

• x — The number for which to compute the natural logarithm of. (U)Int* or Float* or Decimal*

SELECT log(10);

2.302585092994046

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log10

log10(x)

• x — Number for which to compute the decimal logarithm of. (U)Int* or Float* or Decimal*

SELECT log10(100);

2

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log1p

log1p(x)

• x — Values from the interval: -1 < x < +∞. (U)Int* or Float* or Decimal*

SELECT log1p(0)

0

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log2

log2(x)

• x — The number for which to compute the binary logarithm of. (U)Int* or Float* or Decimal*

SELECT log2(8);

3

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pi

pi()

• None.

SELECT pi();

3.141592653589793

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pow

pow(x, y)

• x — The base. (U)Int8/16/32/64 or Float* or Decimal*
• y — The exponent. (U)Int8/16/32/64 or Float* or Decimal*

SELECT pow(2, 3);

8

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proportionsZTest

proportionsZTest(successes_x, successes_y, trials_x, trials_y, conf_level, pool_type)

• successes_x — Number of successes in population x. UInt64
• successes_y — Number of successes in population y. UInt64
• trials_x — Number of trials in population x. UInt64
• trials_y — Number of trials in population y. UInt64
• conf_level — Confidence level for the test. Float64
• pool_type — Selection of pooling method for standard error estimation. Can be either ‘unpooled’ or ‘pooled’. String

SELECT proportionsZTest(10, 11, 100, 101, 0.95, 'unpooled');

┌─proportionsZTest(10, 11, 100, 101, 0.95, 'unpooled')───────────────────────────────┐
│ (-0.20656724435948853,0.8363478437079654,-0.09345975390115283,0.07563797172293502) │
└────────────────────────────────────────────────────────────────────────────────────┘

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radians

radians(x)

• x — Input in degrees. (U)Int* or Float* or Decimal*

SELECT radians(180)

3.141592653589793

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sigmoid

sigmoid(x)

• x — The input value. (U)Int* or Float*

SELECT sigmoid(0)

0.5

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sign

sign(x)

• x — Values from -∞ to +∞. (U)Int* or Decimal* or Float*

SELECT sign(0)

0

SELECT sign(1)

1

SELECT sign(-1)

-1

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sin

sin(x)

• x — The number whose sine will be returned. (U)Int* or Float* or Decimal*

SELECT sin(1.23)

0.9424888019316975

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sinh

sinh(x)

• x — The angle, in radians. Values from the interval: -∞ < x < +∞. (U)Int* or Float* or Decimal*

SELECT sinh(0)

0

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sqrt

sqrt(x)

• x — The number for which to find the square root of. (U)Int* or Float* or Decimal*

SELECT sqrt(16);

4

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tan

tan(x)

• x — The angle in radians. (U)Int* or Float* or Decimal*

SELECT tan(0);

0

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tanh

tanh(x)

• x — The angle in radians. Values from the interval: -∞ < x < +∞. (U)Int* or Float* or Decimal*

SELECT tanh(0)

0

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tgamma

tgamma(x)

• x — The number for which to compute the gamma function of. (U)Int* or Float* or Decimal*

SELECT tgamma(5);

24

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widthBucket

widthBucket(operand, low, high, count)

• operand — The value for which to determine the bucket. (U)Int8/16/32/64
• low — The lower bound of the histogram range. (U)Int8/16/32/64
• high — The upper bound of the histogram range. (U)Int8/16/32/64
• count — The number of equal-width buckets. Cannot be zero. UInt8/16/32/64

widthBucket(10.15, -8.6, 23, 18)

11