remainder#

ivy.remainder(x1, x2, /, *, modulus=True, out=None)[source]#

Return the remainder of division for each element `x1_i` of the input array `x1` and the respective element `x2_i` of the input array `x2`.

Note

This function is equivalent to the Python modulus operator `x1_i % x2_i`. For input arrays which promote to an integer data type, the result of division by zero is unspecified and thus implementation-defined. In general, similar to Python’s `%` operator, this function is not recommended for floating-point operands as semantics do not follow IEEE 754. That this function is specified to accept floating-point operands is primarily for reasons of backward compatibility.

Special Cases

For floating-point operands,

• If either `x1_i` or `x2_i` is `NaN`, the result is `NaN`.

• If `x1_i` is either `+infinity` or `-infinity` and `x2_i` is either `+infinity` or `-infinity`, the result is `NaN`.

• If `x1_i` is either `+0` or `-0` and `x2_i` is either `+0` or `-0`, the result is `NaN`.

• If `x1_i` is `+0` and `x2_i` is greater than `0`, the result is `+0`.

• If `x1_i` is `-0` and `x2_i` is greater than `0`, the result is `+0`.

• If `x1_i` is `+0` and `x2_i` is less than `0`, the result is `-0`.

• If `x1_i` is `-0` and `x2_i` is less than `0`, the result is `-0`.

• If `x1_i` is greater than `0` and `x2_i` is `+0`, the result is `NaN`.

• If `x1_i` is greater than `0` and `x2_i` is `-0`, the result is `NaN`.

• If `x1_i` is less than `0` and `x2_i` is `+0`, the result is `NaN`.

• If `x1_i` is less than `0` and `x2_i` is `-0`, the result is `NaN`.

• If `x1_i` is `+infinity` and `x2_i` is a positive (i.e., greater than `0`) finite number, the result is `NaN`.

• If `x1_i` is `+infinity` and `x2_i` is a negative (i.e., less than `0`) finite number, the result is `NaN`.

• If `x1_i` is `-infinity` and `x2_i` is a positive (i.e., greater than `0`) finite number, the result is `NaN`.

• If `x1_i` is `-infinity` and `x2_i` is a negative (i.e., less than `0`) finite number, the result is `NaN`.

• If `x1_i` is a positive (i.e., greater than `0`) finite number and `x2_i` is `+infinity`, the result is `x1_i`. (note: this result matches Python behavior.)

• If `x1_i` is a positive (i.e., greater than `0`) finite number and `x2_i` is `-infinity`, the result is `x2_i`. (note: this result matches Python behavior.)

• If `x1_i` is a negative (i.e., less than `0`) finite number and `x2_i` is `+infinity`, the result is `x2_i`. (note: this results matches Python behavior.)

• If `x1_i` is a negative (i.e., less than `0`) finite number and `x2_i` is `-infinity`, the result is `x1_i`. (note: this result matches Python behavior.)

• In the remaining cases, the result must match that of the Python `%` operator.

Parameters:
• x1 (`Union`[`float`, `Array`, `NativeArray`]) – dividend input array. Should have a numeric data type.

• x2 (`Union`[`float`, `Array`, `NativeArray`]) – divisor input array. Must be compatible with `x1` (see ref:Broadcasting). Should have a numeric data type.

• modulus (`bool`, default: `True`) – whether to compute the modulus instead of the remainder. Default is `True`.

• 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 element-wise results. Each element-wise result must have the same sign as the respective element `x2_i`. The returned array must have a data type determined by Type Promotion Rules.

This function conforms to the Array API Standard. This docstring is an extension of the docstring 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 `ivy.Array` inputs:

```>>> x1 = ivy.array([2., 5., 15.])
>>> x2 = ivy.array([3., 2., 4.])
>>> y = ivy.remainder(x1, x2)
>>> print(y)
ivy.array([2., 1., 3.])
```

With mixed `ivy.Array` and `ivy.NativeArray` inputs:

```>>> x1 = ivy.array([23., 1., 6.])
>>> x2 = ivy.native_array([11., 2., 4.])
>>> y = ivy.remainder(x1, x2)
>>> print(y)
ivy.array([1., 1., 2.])
```

With `ivy.Container` inputs:

```>>> x1 = ivy.Container(a=ivy.array([2., 3., 5.]), b=ivy.array([2., 2., 4.]))
>>> x2 = ivy.Container(a=ivy.array([1., 3., 4.]), b=ivy.array([1., 3., 3.]))
>>> y = ivy.remainder(x1, x2)
>>> print(y)
{
a: ivy.array([0., 0., 1.]),
b: ivy.array([0., 2., 1.])
}
```
Array.remainder(self, x2, /, *, modulus=True, out=None)[source]#

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

Parameters:
• self (`Array`) – dividend input array. Should have a real-valued data type.

• x2 (`Union`[`Array`, `NativeArray`]) – divisor input array. Must be compatible with `self` (see broadcasting). Should have a real-valued data type.

• modulus (`bool`, default: `True`) – whether to compute the modulus instead of the remainder. Default is `True`.

• 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 element-wise results. Each element-wise result must have the same sign as the respective element `x2_i`. The returned array must have a data type determined by type-promotion.

Examples

With `ivy.Array` inputs:

```>>> x1 = ivy.array([2., 5., 15.])
>>> x2 = ivy.array([3., 2., 4.])
>>> y = x1.remainder(x2)
>>> print(y)
ivy.array([2., 1., 3.])
```

With mixed `ivy.Array` and `ivy.NativeArray` inputs:

```>>> x1 = ivy.array([11., 4., 18.])
>>> x2 = ivy.native_array([2., 5., 8.])
>>> y = x1.remainder(x2)
>>> print(y)
ivy.array([1., 4., 2.])
```
Container.remainder(self, x2, /, *, modulus=True, key_chains=None, to_apply=True, prune_unapplied=False, map_sequences=False, out=None)[source]#

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

Parameters:
• self (`Container`) – input array or container. Should have a real-valued data type.

• x2 (`Union`[`Container`, `Array`, `NativeArray`]) – input array or container. Must be compatible with `self` (see broadcasting). Should have a real-valued data type.

• modulus (`Union`[`bool`, `Container`], default: `True`) – whether to compute the modulus instead of the remainder. Default is `True`.

• 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 element-wise results. The returned container must have the same sign as the respective element `x2_i`.

Examples

With `ivy.Container` inputs:

```>>> x1 = ivy.Container(a=ivy.array([2., 3., 5.]), b=ivy.array([2., 2., 4.]))
>>> x2 = ivy.Container(a=ivy.array([1., 3., 4.]), b=ivy.array([1., 3., 3.]))
>>> y = x1.remainder(x2)
>>> print(y)
{
a: ivy.array([0., 0., 1.]),
b: ivy.array([0., 2., 1.])
}
```

With mixed `ivy.Container` and ivy.Array inputs:

```>>> x1 = ivy.Container(a=ivy.array([2., 3., 5.]), b=ivy.array([2., 2., 4.]))
>>> x2 = ivy.array([1., 2., 3.])
>>> y = x1.remainder(x2)
>>> print(y)
{
a: ivy.array([0., 1., 2.]),
b: ivy.array([0., 0., 1.])
}
```

With mixed `ivy.Container` and ivy.NativeArray inputs:

```>>> x1 = ivy.Container(a=ivy.array([2., 3., 5.]), b=ivy.array([2., 2., 4.]))
>>> x2 = ivy.native_array([1., 2., 3.])
>>> y = x1.remainder(x2)
>>> print(y)
{
a: ivy.array([0., 1., 2.]),
b: ivy.array([0., 0., 1.])
}
```