# Math module {#js_math}

The module contains mathematical methods and constants. Call the `require` function to load the module before first using its methods:

```js
let math = require("math");
```

# Constants

## PI
The number π = 3.14159265358979323846264338327950288.

## E
The number e (Euler's number) = 2.71828182845904523536028747135266250.

## EPSILON
The smallest number that satisfies the condition: 1.0 + EPSILON != 1.0.
EPSILON = 2.2204460492503131e-16.

<br>

---

# Methods

## abs()
Return the absolute value of a number.

**Parameters**
- x: A number

**Returns**

The absolute value of `x`. If `x` is negative (including -0), returns `-x`. Otherwise, returns `x`. The result is therefore always a positive number or 0.

**Example**
```js
math.abs(-5); // 5
```

<br>

## acos()
Return the inverse cosine (in radians) of a number.

**Parameters**
- x: A number between -1 and 1, inclusive, representing the angle's cosine value

**Returns**

The inverse cosine (angle in radians between 0 and π, inclusive) of `x`. If `x` is less than -1 or greater than 1, returns `NaN`.

**Example**
```js
math.acos(-1); // 3.141592653589793
```

<br>

## acosh()
Return the inverse hyperbolic cosine of a number.

**Parameters**
- x: A number greater than or equal to 1

**Returns**

The inverse hyperbolic cosine of `x`.

**Example**
```js
math.acosh(1); // 0
```

<br>

## asin()
Return the inverse sine (in radians) of a number.

**Parameters**
- x: A number between -1 and 1, inclusive, representing the angle's sine value

**Returns**

The inverse sine (angle in radians between -𝜋/2 and 𝜋/2, inclusive) of `x`.

**Example**
```js
math.asin(0.5); // 0.5235987755982989
```

<br>

## asinh()
Return the inverse hyperbolic sine of a number.

**Parameters**
- x: A number

**Returns**

The inverse hyperbolic sine of `x`.

**Example**
```js
math.asinh(1); // 0.881373587019543
```

<br>

## atan()
Return the inverse tangent (in radians) of a number.

**Parameters**
- x: A number

**Returns**

The inverse tangent (angle in radians between -𝜋/2 and 𝜋/2, inclusive) of `x`.

**Example**
```js
math.atan(1); // 0.7853981633974483
```

<br>

## atan2()
Return the angle in the plane (in radians) between the positive x-axis and the ray from (0, 0) to the point (x, y), for math.atan2(y, x).

**Parameters**
- y: The y coordinate of the point
- x: The x coordinate of the point

**Returns**

The angle in radians (between -π and π, inclusive) between the positive x-axis and the ray from (0, 0) to the point (x, y).

**Example**
```js
math.atan2(90, 15); // 1.4056476493802699
```

<br>

## atanh()
The method returns the inverse hyperbolic tangent of a number.

**Parameters**
- x: A number between -1 and 1, inclusive

**Returns**

The inverse hyperbolic tangent of `x`.

**Example**
```js
math.atanh(0.5); // 0.5493061443340548
```

<br>

## cbrt()
Return the cube root of a number.

**Parameters**
- x: A number

**Returns**

The cube root of `x`.

**Example**
```js
math.cbrt(2); // 1.2599210498948732
```

<br>

## ceil()
Round up and return the smallest integer greater than or equal to a given number.

**Parameters**
- x: A number

**Returns**

The smallest integer greater than or equal to `x`. It's the same value as `-math.floor(-x)`.

**Example**
```js
math.ceil(-7.004); // -7
math.ceil(7.004);  // 8
```

<br>

## clz32()
Return the number of leading zero bits in the 32-bit binary representation of a number.

**Parameters**
- x: A number

**Returns**

The number of leading zero bits in the 32-bit binary representation of `x`.

**Example**
```js
math.clz32(1);    // 31
math.clz32(1000); // 22
```

<br>

## cos()
Return the cosine of a number in radians.

**Parameters**
- x: A number representing an angle in radians

**Returns**

The cosine of `x`, between -1 and 1, inclusive.

**Example**
```js
math.cos(math.PI); // -1
```

<br>

## exp()
Return e raised to the power of a number.

**Parameters**
- x: A number

**Returns**

A nonnegative number representing `e^x`, where `e` is the base of the natural logarithm.

**Example**
```js
math.exp(0); // 1
math.exp(1); // 2.718281828459045
```

<br>

## floor()
Round down and return the largest integer less than or equal to a given number.

**Parameters**
- x: A number

**Returns**

The largest integer smaller than or equal to `x`. It's the same value as `-math.ceil(-x)`.

**Example**
```js
math.floor(-45.95); // -46
math.floor(-45.05); // -46
math.floor(-0); // -0
math.floor(0); // 0
math.floor(45.05); // 45
math.floor(45.95); // 45
```

<br>

## log()
Return the natural logarithm of x.

**Parameters**
- x: A number

**Returns**

The natural logarithm of `x`, as in `ln(x)` where `e` is the base of the natural logarithm.

**Example**
```js
math.log(1); // 0
math.log(3); // 1.0986122886681098
```

## isEqual()
Return true if the difference between numbers `a` and `b` is less than the specified `tolerance`.

**Parameters**
- a: A number a
- b: A number b
- tolerance: How much difference is allowed between the numbers to be considered equal

**Returns**

True if the difference between numbers `a` and `b` is less than the specified parameter `e`. Otherwise, false.

**Example**
```js
math.isEqual(1.4, 1.6, 0.2);      // false
math.isEqual(3.556, 3.555, 0.01); // true
```

<br>

## max()
Return the largest of two numbers given as input parameters.

**Parameters**
- a: A number a
- b: A number b

**Returns**

The largest of the given numbers.

**Example**
```js
math.max(10, 20);   // 20
math.max(-10, -20); // -10
```

<br>

## min()
Return the smallest of two numbers given as input parameters.

**Parameters**
- a: A number a
- b: A number b

**Returns**

The smallest of the given numbers.

**Example**
```js
math.min(10, 20);   // 10
math.min(-10, -20); // -20
```

<br>

## pow()
Return the value of a base raised to a power.

**Parameters**
- base: The base number
- exponent: The exponent number

**Returns**

A number representing base taken to the power of exponent.

**Example**
```js
math.pow(7, 2);  // 49
math.pow(7, 3);  // 343
math.pow(2, 10); // 1024
```

<br>

## random()
Return a floating-point, pseudo-random number that's greater than or equal to 0 and less than 1, with approximately uniform distribution over that range — which you can then scale to your desired range.

**Returns**

A floating-point, pseudo-random number between 0 (inclusive) and 1 (exclusive).

**Example**
```js
let num = math.random();
```

<br>

## sign()
Return 1 or -1, indicating the sign of the number passed as argument.

**Parameters**
- x: A number

**Returns**

-1 if the number is less than 0, and 1 otherwise.

**Example**
```js
math.sign(3);  // 1
math.sign(0);  // 1
math.sign(-3); // -1
```

<br>

## sin()
Return the sine of a number in radians.

**Parameters**
- x: A number representing an angle in radians

**Returns**

The sine of `x`, between -1 and 1, inclusive.

**Example**
```js
math.sin(math.PI / 2); // 1
```

<br>

## sqrt()
Return the square root of a number.

**Parameters**
- x: A number greater than or equal to 0

**Returns**


The square root of `x`, a nonnegative number. If `x` < 0, script will fail with an error.

**Example**
```js
math.sqrt(25); // 5
```

<br>

## trunc()
Return the integer part of a number by removing any fractional digits.

**Parameters**
- x: A number

**Returns**

The integer part of `x`.

**Example**
```js
math.trunc(-1.123); // -1
math.trunc(0.123);  // 0
math.trunc(13.37);  // 13
math.trunc(42.84);  // 42
```