From 7a0fcaa8694c018c7f4f7bfd6d6e8ed051b3902c Mon Sep 17 00:00:00 2001 From: Dmitriy Date: Tue, 1 Dec 2020 22:25:57 +0300 Subject: [PATCH] Update math-functions.md MIME-Version: 1.0 Content-Type: text/plain; charset=UTF-8 Content-Transfer-Encoding: 8bit Выполнил описание некоторых математических функций. --- .../sql-reference/functions/math-functions.md | 302 ++++++++++++++++++ 1 file changed, 302 insertions(+) diff --git a/docs/en/sql-reference/functions/math-functions.md b/docs/en/sql-reference/functions/math-functions.md index acb88afd219..8373205e6b9 100644 --- a/docs/en/sql-reference/functions/math-functions.md +++ b/docs/en/sql-reference/functions/math-functions.md @@ -111,4 +111,306 @@ Accepts a numeric argument and returns a UInt64 number close to 2 to the power o Accepts a numeric argument and returns a UInt64 number close to 10 to the power of x. +## cosh(x) {#coshx} + +[Hyperbolic cosine](https://in.mathworks.com/help/matlab/ref/cosh.html). + +**Syntax** + +``` sql +cosh(x) +``` + +**Parameters** + +- `x` — The angle, in radians. Values are from the interval: `-∞ < x < +∞`. [Float64](../../sql-reference/data-types/float.md#float32-float64). + +**Returned value** + +- Values are from the interval: `1 <= cosh(x) < +∞`. + +Type: [Float64](../../sql-reference/data-types/float.md#float32-float64). + +**Example** + +Query: + +``` sql +SELECT cosh(0); +``` + +Result: + +``` text +┌─cosh(0)──┐ +│ 1 │ +└──────────┘ +``` + +## acosh(x) {#acoshx} + +[Inverse hyperbolic cosine](https://www.mathworks.com/help/matlab/ref/acosh.html). + +**Syntax** + +``` sql +acosh(x) +``` + +**Parameters** + +- `x` — The angle, in radians. Values are from the interval: `1 <= x < +∞`. [Float64](../../sql-reference/data-types/float.md#float32-float64). + +**Returned value** + +- Values are from the interval: `0 <= acosh(x) < +∞`. + +Type: [Float64](../../sql-reference/data-types/float.md#float32-float64). + +**Example** + +Query: + +``` sql +SELECT acosh(1); +``` + +Result: + +``` text +┌─acosh(1)─┐ +│ 0 │ +└──────────┘ +``` + +**See Also** + +- [cosh(x)](../../sql-reference/functions/math-functions.md#coshx) + +## sinh(x) {#sinhx} + +[Hyperbolic sine](https://www.mathworks.com/help/matlab/ref/sinh.html). + +**Syntax** + +``` sql +sinh(x) +``` + +**Parameters** + +- `x` — The angle, in radians. Values are from the interval: `-∞ < x < +∞`. [Float64](../../sql-reference/data-types/float.md#float32-float64). + +**Returned value** + +- Values are from the interval: `-∞ < sinh(x) < +∞`. + +Type: [Float64](../../sql-reference/data-types/float.md#float32-float64). + +**Example** + +Query: + +``` sql +SELECT sinh(0); +``` + +Result: + +``` text +┌─sinh(0)──┐ +│ 0 │ +└──────────┘ +``` + +## asinh(x) {#asinhx} + +[Inverse hyperbolic sine](https://www.mathworks.com/help/matlab/ref/asinh.html). + +**Syntax** + +``` sql +asinh(x) +``` + +**Parameters** + +- `x` — The angle, in radians. Values are from the interval: `-∞ < x < +∞`. [Float64](../../sql-reference/data-types/float.md#float32-float64). + +**Returned value** + +- Values are from the interval: `-∞ < asinh(x) < +∞`. + +Type: [Float64](../../sql-reference/data-types/float.md#float32-float64). + +**Example** + +Query: + +``` sql +SELECT asinh(0); +``` + +Result: + +``` text +┌─asinh(0)─┐ +│ 0 │ +└──────────┘ +``` + +**See Also** + +- [sinh(x)](../../sql-reference/functions/math-functions.md#sinhx) + +## atanh(x) {#atanhx} + +[Inverse hyperbolic tangent](https://www.mathworks.com/help/matlab/ref/atanh.html). + +**Syntax** + +``` sql +atanh(x) +``` + +**Parameters** + +- `x` — The angle, in radians. Values are from the interval: `–1 < x < 1`. [Float64](../../sql-reference/data-types/float.md#float32-float64). + +**Returned value** + +- Values are from the interval: `-∞ < atanh(x) < +∞`. + +Type: [Float64](../../sql-reference/data-types/float.md#float32-float64). + +**Example** + +Query: + +``` sql +SELECT atanh(0); +``` + +Result: + +``` text +┌─atanh(0)─┐ +│ 0 │ +└──────────┘ +``` + +## atan2(y, x) {#atan2yx} + +The [function](https://en.wikipedia.org/wiki/Atan2) is defined as the angle in the Euclidean plane, given in radians, between the positive x axis and the ray(`r`) to the point `(x, y) ≠ (0, 0)`. + +**Syntax** + +``` sql +atan2(y, x) +``` + +**Parameters** + +- `y` — y axis coordinate of the point through which the ray passes. [Float64](../../sql-reference/data-types/float.md#float32-float64). +- `x` — x axis coordinate of the point through which the ray passes. [Float64](../../sql-reference/data-types/float.md#float32-float64). + +**Returned value** + +- The angle `θ` such that `−π < θ ≤ π` and, for some `r > 0`, in radians. + +Type: [Float64](../../sql-reference/data-types/float.md#float32-float64). + +**Example** + +Query: + +``` sql +SELECT atan2(1, 1); +``` + +Result: + +``` text +┌────────atan2(1, 1)─┐ +│ 0.7853981633974483 │ +└────────────────────┘ +``` + +## hypot(x, y) {#hypotxy} + +The [function](https://en.wikipedia.org/wiki/Hypot) is defined to calculate the length of the hypotenuse of a right-angle triangle. It was designed to avoid errors arising due to limited-precision calculations performed on computers. The function avoids problems that occur when squaring very large or very small numbers. + +**Syntax** + +``` sql +hypot(x, y) +``` + +**Parameters** + +- `x` — The first cathetus of a right-angle triangle. [Float64](../../sql-reference/data-types/float.md#float32-float64). +- `y` — The second cathetus of a right-angle triangle. [Float64](../../sql-reference/data-types/float.md#float32-float64). + +**Returned value** + +- The length of the hypotenuse of a right-angle triangle. + +Type: [Float64](../../sql-reference/data-types/float.md#float32-float64). + +**Example** + +Query: + +``` sql +SELECT hypot(1, 1); +``` + +Result: + +``` text +┌────────hypot(1, 1)─┐ +│ 1.4142135623730951 │ +└────────────────────┘ +``` + +## log1p(x) {#log1px} + +The [function](https://en.wikipedia.org/wiki/Natural_logarithm#lnp1) calculates `log(1 + x)`, compensating for the roundoff in `1+x`. `log1p(x)` is more accurate than `log(1+x)` for small values of `x`. For small `x`, `log1p(x)` is approximately `x`, whereas `log(1+x)` can be zero. + +**Syntax** + +``` sql +log1p(x) +``` + +**Parameters** + +- `x` — Values are from the interval: `-1 < x < +∞`. [Float64](../../sql-reference/data-types/float.md#float32-float64). + +**Returned value** + +- Values are from the interval: `-∞ < log1p(x) < +∞`. + +Type: [Float64](../../sql-reference/data-types/float.md#float32-float64). + +**Example** + +Query: + +``` sql +SELECT log1p(0); +``` + +Result: + +``` text +┌─log1p(0)─┐ +│ 0 │ +└──────────┘ +``` + +**See Also** + +- [log(x)](../../sql-reference/functions/math-functions.md#logx-lnx) + [Original article](https://clickhouse.tech/docs/en/query_language/functions/math_functions/)