# exp#

ivy.exp(x, /, *, out=None)[source]#

Calculate an implementation-dependent approximation to the exponential function, having domain `[-infinity, +infinity]` and codomain `[+0, +infinity]`, for each element `x_i` of the input array `x` (`e` raised to the power of `x_i`, where `e` is the base of the natural logarithm).

Note

For complex floating-point operands, `exp(conj(x))` must equal `conj(exp(x))`.

Note

The exponential function is an entire function in the complex plane and has no branch cuts.

Special cases

For floating-point operands,

• If `x_i` is `NaN`, the result is `NaN`.

• If `x_i` is `+0`, the result is `1`.

• If `x_i` is `-0`, the result is `1`.

• If `x_i` is `+infinity`, the result is `+infinity`.

• If `x_i` is `-infinity`, the result is `+0`.

For complex floating-point operands, let `a = real(x_i)`, `b = imag(x_i)`, and

• If `a` is either `+0` or `-0` and `b` is `+0`, the result is `1 + 0j`.

• If `a` is a finite number and `b` is `+infinity`, the result is `NaN + NaN j`.

• If `a` is a finite number and `b` is `NaN`, the result is `NaN + NaN j`.

• If `a` is `+infinity` and `b` is `+0`, the result is `infinity + 0j`.

• If `a` is `-infinity` and `b` is a finite number, the result is `+0 * cis(b)`.

• If `a` is `+infinity` and `b` is a nonzero finite number, the result is `+infinity * cis(b)`.

• If `a` is `-infinity` and `b` is `+infinity`, the result is `0 + 0j` (signs of real and imaginary components are unspecified).

• If `a` is `+infinity` and `b` is `+infinity`, the result is `infinity + NaN j` (sign of real component is unspecified).

• If `a` is `-infinity` and `b` is `NaN`, the result is `0 + 0j` (signs of real and imaginary components are unspecified).

• If `a` is `+infinity` and `b` is `NaN`, the result is `infinity + NaN j` (sign of real component is unspecified).

• If `a` is `NaN` and `b` is `+0`, the result is `NaN + 0j`.

• If `a` is `NaN` and `b` is not equal to `0`, the result is `NaN + NaN j`.

• If `a` is `NaN` and `b` is `NaN`, the result is `NaN + NaN j`.

where `cis(v)` is `cos(v) + sin(v)*1j`.

Parameters:
• x (`Union`[`Array`, `NativeArray`, `Number`]) – input array. Should have a floating-point data type.

• out (`Optional`[`Array`], default: `None`) – optional output array, for writing the result to. It must have a shape that the inputs broadcast to.

Return type:

`Array`

Returns:

• ret – an array containing the evaluated exponential function result for each element in `x`. The returned array must have a floating-point data type determined by type-promotion.

• This method conforms to the

• This docstring is an extension of the

• `docstring <https (//data-apis.org/array-api/latest/)

• API_specification/generated/array_api.exp.html>`_

• in the standard.

• Both the description and the type hints above assumes an array input for simplicity,

• but this function is nestable, and therefore also accepts `ivy.Container`

• instances in place of any of the arguments.

Examples

With :class:Number:

```>>> x = 3
>>> y = ivy.exp(x)
>>> print(y)
ivy.array(20.08553692)
```

With `ivy.Array` input:

```>>> x = ivy.array([1., 2., 3.])
>>> y = ivy.exp(x)
>>> print(y)
ivy.array([ 2.71828175,  7.38905621, 20.08553696])
```

With nested inputs in `ivy.Array`:

```>>> x = ivy.array([[-5.67], [ivy.nan], [0.567]])
>>> y = ivy.exp(x)
>>> print(y)
ivy.array([[0.00344786],
[       nan],
[1.76297021]])
```

With `ivy.NativeArray` input:

```>>> x = ivy.native_array([0., 4., 2.])
>>> y = ivy.exp(x)
>>> print(y)
ivy.array([ 1.        , 54.59814835,  7.38905621])
```

With `ivy.Container` input:

```>>> x = ivy.Container(a=3.1, b=ivy.array([3.2, 1.]))
>>> y = ivy.exp(x)
>>> print(y)
{
a: ivy.array(22.197948),
b: ivy.array([24.53253174, 2.71828175])
}
```
Array.exp(self, *, out=None)[source]#

ivy.Array instance method variant of ivy.exp. This method simply wraps the function, and so the docstring for ivy.exp also applies to this method with minimal changes.

Parameters:
• self (`Array`) – input array. Should have a floating-point data type.

• out (`Optional`[`Array`], default: `None`) – optional output array, for writing the result to. It must have a shape that the inputs broadcast to.

Return type:

`Array`

Returns:

ret – an array containing the evaluated exponential function result for each element in `self`. The returned array must have a floating-point data type determined by type-promotion.

Examples

```>>> x = ivy.array([1., 2., 3.])
>>> print(x.exp())
ivy.array([ 2.71828198,  7.38905573, 20.08553696])
```
Container.exp(self, *, key_chains=None, to_apply=True, prune_unapplied=False, map_sequences=False, out=None)[source]#

ivy.Container instance method variant of ivy.exp. This method simply wraps the function, and so the docstring for ivy.exp also applies to this method with minimal changes.

Parameters:
• self (`Container`) – input container. Should have a floating-point data type.

• key_chains (`Optional`[`Union`[`List`[`str`], `Dict`[`str`, `str`], `Container`]], default: `None`) – The key-chains to apply or not apply the method to. Default is `None`.

• to_apply (`Union`[`bool`, `Container`], default: `True`) – If True, the method will be applied to key_chains, otherwise key_chains will be skipped. Default is `True`.

• prune_unapplied (`Union`[`bool`, `Container`], default: `False`) – Whether to prune key_chains for which the function was not applied. Default is `False`.

• map_sequences (`Union`[`bool`, `Container`], default: `False`) – Whether to also map method to sequences (lists, tuples). Default is `False`.

• out (`Optional`[`Container`], default: `None`) – optional output container, for writing the result to. It must have a shape that the inputs broadcast to.

Return type:

`Container`

Returns:

ret – a container containing the evaluated result for each element in `self`. The returned array must have a real-valued floating-point data type determined by type-promotion.

Examples

```>>> x = ivy.Container(a=ivy.array([1., 2., 3.]), b=ivy.array([4., 5., 6.]))
>>> y = x.exp()
>>> print(y)
{
a: ivy.array([2.71828198, 7.38905573, 20.08553696]),
b: ivy.array([54.59814835, 148.4131622, 403.428772])
}
```