---
metadata:
  - name: generator
    content: Diplodoc Platform v5.50.6
alternate:
  - https://ytsaurus.tech/docs/en/yql/udf/list/math.md
  - https://ytsaurus.tech/docs/ru/yql/udf/list/math.md
---
> **Documentation Index:** Fetch the complete configuration index at https://ytsaurus.tech/docs/en/llms.txt

# Math

A set of wrappers around the functions from the libm library and the Yandex utilities.

## Constants {#constants}

#### List of functions

* `Math::Pi() -> Double`
* `Math::E() -> Double`
* `Math::Eps() -> Double`

#### Examples

```yql
SELECT Math::Pi();  -- 3.141592654
SELECT Math::E();   -- 2.718281828
SELECT Math::Eps(); -- 2.220446049250313e-16
```

## (Double) -> Bool {#double-bool}

#### List of functions

* `Math::IsInf(Double{Flags:AutoMap}) -> Bool`
* `Math::IsNaN(Double{Flags:AutoMap}) -> Bool`
* `Math::IsFinite(Double{Flags:AutoMap}) -> Bool`

#### Examples

```yql
SELECT Math::IsNaN(0.0/0.0);    -- true
SELECT Math::IsFinite(1.0/0.0); -- false
```

## (Double) -> Double {#double-double}

#### List of functions

* `Math::Abs(Double{Flags:AutoMap}) -> Double`
* `Math::Acos(Double{Flags:AutoMap}) -> Double`
* `Math::Asin(Double{Flags:AutoMap}) -> Double`
* `Math::Asinh(Double{Flags:AutoMap}) -> Double`
* `Math::Atan(Double{Flags:AutoMap}) -> Double`
* `Math::Cbrt(Double{Flags:AutoMap}) -> Double`
* `Math::Ceil(Double{Flags:AutoMap}) -> Double`
* `Math::Cos(Double{Flags:AutoMap}) -> Double`
* `Math::Cosh(Double{Flags:AutoMap}) -> Double`
* `Math::Erf(Double{Flags:AutoMap}) -> Double`
* `Math::ErfInv(Double{Flags:AutoMap}) -> Double`
* `Math::ErfcInv(Double{Flags:AutoMap}) -> Double`
* `Math::Exp(Double{Flags:AutoMap}) -> Double`
* `Math::Exp2(Double{Flags:AutoMap}) -> Double`
* `Math::Fabs(Double{Flags:AutoMap}) -> Double`
* `Math::Floor(Double{Flags:AutoMap}) -> Double`
* `Math::Lgamma(Double{Flags:AutoMap}) -> Double`
* `Math::Rint(Double{Flags:AutoMap}) -> Double`
* `Math::Sigmoid(Double{Flags:AutoMap}) -> Double`
* `Math::Sin(Double{Flags:AutoMap}) -> Double`
* `Math::Sinh(Double{Flags:AutoMap}) -> Double`
* `Math::Sqrt(Double{Flags:AutoMap}) -> Double`
* `Math::Tan(Double{Flags:AutoMap}) -> Double`
* `Math::Tanh(Double{Flags:AutoMap}) -> Double`
* `Math::Tgamma(Double{Flags:AutoMap}) -> Double`
* `Math::Trunc(Double{Flags:AutoMap}) -> Double`
* `Math::Log(Double{Flags:AutoMap}) -> Double`
* `Math::Log2(Double{Flags:AutoMap}) -> Double`
* `Math::Log10(Double{Flags:AutoMap}) -> Double`

#### Examples

```yql
SELECT Math::Sqrt(256);     -- 16
SELECT Math::Trunc(1.2345); -- 1
```

## (Double, Double) -> Double {#doubledouble-double}

#### List of functions

* `Math::Atan2(Double{Flags:AutoMap}, Double{Flags:AutoMap}) -> Double`
* `Math::Fmod(Double{Flags:AutoMap}, Double{Flags:AutoMap}) -> Double`
* `Math::Hypot(Double{Flags:AutoMap}, Double{Flags:AutoMap}) -> Double`
* `Math::Pow(Double{Flags:AutoMap}, Double{Flags:AutoMap}) -> Double`
* `Math::Remainder(Double{Flags:AutoMap}, Double{Flags:AutoMap}) -> Double`

#### Examples

```yql
SELECT Math::Atan2(1, 0);       -- 1.570796327
SELECT Math::Remainder(2.1, 2); -- 0.1
```

## (Double, Int32) -> Double {#doubleint32-double}

#### List of functions

* `Math::Ldexp(Double{Flags:AutoMap}, Int32{Flags:AutoMap}) -> Double`
* `Math::Round(Double{Flags:AutoMap}, [Int32?]) -> Double` — the second argument specifies the power of 10 that the number is rounded to (a negative value for decimal places, and a positive for tens, thousands, millions, etc.). 0 by default

#### Examples

```yql
SELECT Math::Pow(2, 10);        -- 1024
SELECT Math::Round(1.2345, -2); -- 1.23
```

## (Double, Double, \[Double?\]) -> Bool {#doubledouble-bool}

#### List of functions

* `Math::FuzzyEquals(Double{Flags:AutoMap}, Double{Flags:AutoMap}, [Double?]) -> Bool` — compares two Doubles with a tolerance specified by the third argument. 1.0e-13 by default. The tolerance is measured in relative units based on the argument whose absolute value is less.

{% note alert %}

If any compared value equals `0.0`, the function returns `false`.

{% endnote %}

#### Examples

```yql
SELECT Math::FuzzyEquals(1.01, 1.0, 0.05); -- true
```

## Functions for computing remainders

#### List of functions

* `Math::Mod(Int64{Flags:AutoMap}, Int64) -> Int64?`
* `Math::Rem(Int64{Flags:AutoMap}, Int64) -> Int64?`

These functions behave similarly to the built-in % operator in the case of non-negative arguments. The differences are noticeable in the case of negative arguments:

* Math::Mod preserves the sign of the second argument (the denominator).
* Math::Rem preserves the sign of the first argument (the numerator).

Functions return null if the divisor is zero.

#### Examples

```yql
SELECT Math::Mod(-1, 7);        -- 6
SELECT Math::Rem(-1, 7);        -- -1
```

## Functions for rounding to integer in a given mode

#### List of functions

* `Math::RoundDownward() -> Tagged<Uint32, MathRoundingMode>` — Rounding toward negative infinity.
* `Math::RoundToNearest() -> Tagged<Uint32, MathRoundingMode>` — Rounding toward the nearest representable value.
* `Math::RoundTowardZero() -> Tagged<Uint32, MathRoundingMode>` — Rounding toward zero.
* `Math::RoundUpward() -> Tagged<Uint32, MathRoundingMode>` — Rounding toward positive infinity.
* `Math::NearbyInt(AutoMap<Double>, Tagged<Uint32, MathRoundingMode>) -> Optional<Int64>` — Rounding to the nearest integer.

The `Math::NearbyInt` function rounds the first argument to an integer according to the mode specified by the second argument.

If the result is beyond a 64-bit integer, it returns NULL.

#### Examples

```yql
SELECT Math::NearbyInt(1.5, Math::RoundDownward()); -- 1
SELECT Math::NearbyInt(1.5, Math::RoundToNearest()); -- 2
SELECT Math::NearbyInt(2.5, Math::RoundToNearest()); -- 2
SELECT Math::NearbyInt(1.5, Math::RoundTowardZero()); -- 1
SELECT Math::NearbyInt(1.5, Math::RoundUpward()); -- 2
SELECT Math::NearbyInt(-1.5, Math::RoundDownward()); -- -2
SELECT Math::NearbyInt(-1.5, Math::RoundToNearest()); -- -2
SELECT Math::NearbyInt(-2.5, Math::RoundToNearest()); -- -2
SELECT Math::NearbyInt(-1.5, Math::RoundTowardZero()); -- -1
SELECT Math::NearbyInt(-1.5, Math::RoundUpward()); -- -1
```