burn_backend/backend/ops/

int_tensor.rs

use super::cat::cat_with_slice_assign;
use super::repeat_dim::repeat_with_slice_assign;
use super::sort::{argsort, sort, sort_with_indices};
use crate::tensor::{BoolTensor, Device, FloatTensor, IntTensor};
use crate::{Backend, Distribution, TensorData, TensorMetadata};
use crate::{ExecutionError, Scalar, get_device_settings};
use alloc::vec::Vec;
use burn_std::reader::try_read_sync;
use burn_std::{BoolDType, FloatDType, IndexingUpdateOp, IntDType, Shape, Slice};
use core::ops::Range;

/// Int Tensor API for basic and numeric operations, see
#[cfg_attr(doc, doc = crate::doc_tensor!())]
#[cfg_attr(not(doc), doc = "`Tensor`")]
/// for documentation on each function.
pub trait IntTensorOps<B: Backend> {
    /// Creates a new int tensor.
    ///
    /// # Arguments
    ///
    /// * `shape` - The shape of the tensor.
    /// * `device` - The device to create the tensor on.
    /// * `dtype` - The target data type.
    ///
    /// # Returns
    ///
    /// The integer tensor with the given shape.
    fn int_empty(shape: Shape, device: &Device<B>, dtype: IntDType) -> IntTensor<B>;

    /// Converts the tensor to a data structure.
    ///
    /// # Arguments
    ///
    /// * `tensor` - The tensor.
    ///
    /// # Returns
    ///
    /// The data structure with the tensor's data.
    fn int_into_data(
        tensor: IntTensor<B>,
    ) -> impl Future<Output = Result<TensorData, ExecutionError>> + Send;

    /// Creates a tensor from the data structure.
    ///
    /// # Arguments
    ///
    /// * `data` - The data structure.
    /// * `device` - The device to create the tensor on.
    ///
    /// # Returns
    ///
    /// The tensor with the data.
    fn int_from_data(data: TensorData, device: &Device<B>) -> IntTensor<B>;

    /// Moves the tensor to the given device.
    fn int_to_device(tensor: IntTensor<B>, device: &Device<B>) -> IntTensor<B>;

    /// Reshapes the tensor.
    ///
    /// # Arguments
    ///
    /// * `tensor` - The tensor.
    /// * `shape` - The new shape.
    ///
    /// # Returns
    ///
    /// The tensor with the new shape.
    fn int_reshape(tensor: IntTensor<B>, shape: Shape) -> IntTensor<B>;

    /// Gets the element at the given indices.
    ///
    /// # Arguments
    ///
    /// * `tensor` - The tensor.
    /// * `slices` - The slices specifying ranges and steps for each dimension.
    ///
    /// # Returns
    ///
    /// The elements at the given indices.
    ///
    /// # Note
    ///
    /// Empty slices (where start >= end) are handled at the high-level tensor API and will not
    /// be passed to this method. Backend implementations do not need to handle empty slices.
    fn int_slice(tensor: IntTensor<B>, slices: &[Slice]) -> IntTensor<B>;

    /// Sets the values in the tensor for the given ranges.
    ///
    /// # Arguments
    ///
    /// * `tensor` - The tensor.
    /// * `ranges` - The ranges to set the values for.
    ///
    /// # Returns
    ///
    /// The tensor with the values set for the given ranges.
    ///
    /// # Note
    ///
    /// Empty slice assignments (where any slice range produces 0 elements) are handled at the
    /// high-level tensor API and will not be passed to this method. Backend implementations do
    /// not need to handle empty slice assignments.
    fn int_slice_assign(
        tensor: IntTensor<B>,
        slices: &[Slice],
        value: IntTensor<B>,
    ) -> IntTensor<B>;

    /// Converts int tensor to float tensor.
    ///
    /// # Arguments
    ///
    /// * `tensor` - The tensor.
    /// * `out_dtype` - The output tensor dtype.
    ///
    /// # Returns
    ///
    /// The int tensor with the same data as the float tensor.
    fn int_into_float(tensor: IntTensor<B>, out_dtype: FloatDType) -> FloatTensor<B>;

    /// Fills the tensor with values from the value tensor if the mask is true at the given
    /// indices.
    ///
    /// # Arguments
    ///
    /// * `tensor` - The tensor.
    /// * `mask` - The mask.
    /// * `value` - The value tensor.
    ///
    /// # Returns
    ///
    /// The tensor with the values filled.
    fn int_mask_where(
        tensor: IntTensor<B>,
        mask: BoolTensor<B>,
        value: IntTensor<B>,
    ) -> IntTensor<B>;

    /// Fills the tensor with the given value if the mask is true at the given indices.
    ///
    /// # Arguments
    ///
    /// * `tensor` - The tensor.
    /// * `mask` - The mask.
    /// * `value` - The value.
    ///
    /// # Returns
    ///
    /// The tensor with the values filled.
    fn int_mask_fill(tensor: IntTensor<B>, mask: BoolTensor<B>, value: Scalar) -> IntTensor<B>;

    /// Selects the elements of the tensor where the mask is true, returned as a 1D tensor.
    ///
    /// The elements are collected in row-major order. Because the number of selected elements
    /// depends on the mask values, the output shape is data-dependent: computing it may require
    /// synchronizing with the device, which is why this operation is asynchronous.
    ///
    /// # Arguments
    ///
    /// * `tensor` - The tensor to select from.
    /// * `mask` - The boolean mask, with the same shape as the tensor.
    ///
    /// # Returns
    ///
    /// A 1D tensor containing the selected elements.
    fn int_mask_select(
        tensor: IntTensor<B>,
        mask: BoolTensor<B>,
    ) -> impl Future<Output = IntTensor<B>> + 'static + Send {
        async move {
            // Data-dependent output length, so we defer to `bool_argwhere` (the only pre-existing
            // data-dependent op) to collect the flat indices of the true mask values, then select.
            let n = mask.shape().num_elements();
            let int_dtype = get_device_settings::<B>(&mask.device()).int_dtype;
            let mask = B::bool_reshape(mask, Shape::new([n]));
            let indices = B::bool_argwhere(mask, int_dtype).await; // [count, 1]
            let count = indices.shape()[0];
            let indices = B::int_reshape(indices, Shape::new([count])); // squeeze to [count]
            let tensor = B::int_reshape(tensor, Shape::new([n]));
            B::int_select(tensor, 0, indices)
        }
    }

    /// Gather elements from the tensor at the given indices.
    ///
    /// # Arguments
    ///
    /// * `dim` - The dimension to gather from.
    /// * `tensor` - The tensor.
    /// * `indices` - The indices.
    fn int_gather(dim: usize, tensor: IntTensor<B>, indices: IntTensor<B>) -> IntTensor<B>;

    /// Scatter a given value to the tensor at the given indices using sum reduction.
    ///
    /// # Arguments
    ///
    /// * `dim` - The dimension to scatter to.
    /// * `tensor` - The tensor.
    /// * `indices` - The indices.
    /// * `value` - The value.
    ///
    /// # Returns
    ///
    /// The tensor with the values scattered.
    fn int_scatter_add(
        dim: usize,
        tensor: IntTensor<B>,
        indices: IntTensor<B>,
        value: IntTensor<B>,
    ) -> IntTensor<B>;

    /// Scatter elements into a tensor using the specified update operation.
    ///
    /// Backend implementations may override this to support operations beyond add.
    fn int_scatter(
        dim: usize,
        tensor: IntTensor<B>,
        indices: IntTensor<B>,
        value: IntTensor<B>,
        update: IndexingUpdateOp,
    ) -> IntTensor<B> {
        match update {
            IndexingUpdateOp::Add => Self::int_scatter_add(dim, tensor, indices, value),
            other => unimplemented!("int_scatter with {other:?} update is not implemented"),
        }
    }

    /// Multi-dimensional scatter for int tensors.
    fn int_scatter_nd(
        _data: IntTensor<B>,
        _indices: IntTensor<B>,
        _values: IntTensor<B>,
        _reduction: crate::tensor::IndexingUpdateOp,
    ) -> IntTensor<B> {
        unimplemented!("int_scatter_nd is not implemented for this backend")
    }

    /// Multi-dimensional gather for int tensors.
    fn int_gather_nd(_data: IntTensor<B>, _indices: IntTensor<B>) -> IntTensor<B> {
        unimplemented!("int_gather_nd is not implemented for this backend")
    }

    /// Select tensor elements along the given dimension corresponding to the given indices.
    ///
    /// # Arguments
    ///
    /// * `tensor` - The tensor.
    /// * `dim` - The dimension to select from.
    /// * `indices` - The indices.
    ///
    /// # Returns
    ///
    /// The tensor with the selected elements.
    fn int_select(tensor: IntTensor<B>, dim: usize, indices: IntTensor<B>) -> IntTensor<B>;

    /// Assign the selected elements along the given dimension corresponding to the given indices
    /// to the given value using sum reduction.
    ///
    /// # Arguments
    ///
    /// * `tensor` - The tensor.
    /// * `dim` - The dimension to select from.
    /// * `indices` - The indices.
    /// * `value` - The value.
    ///
    /// # Returns
    ///
    /// The tensor with the selected elements assigned to the given value.
    fn int_select_add(
        tensor: IntTensor<B>,
        dim: usize,
        indices: IntTensor<B>,
        value: IntTensor<B>,
    ) -> IntTensor<B>;

    /// Assign selected elements along a dimension using the specified update operation.
    ///
    /// Backend implementations may override this to support operations beyond add.
    fn int_select_assign(
        tensor: IntTensor<B>,
        dim: usize,
        indices: IntTensor<B>,
        value: IntTensor<B>,
        update: IndexingUpdateOp,
    ) -> IntTensor<B> {
        match update {
            IndexingUpdateOp::Add => Self::int_select_add(tensor, dim, indices, value),
            other => unimplemented!("int_select_assign with {other:?} update is not implemented"),
        }
    }

    /// Repeats the tensor along the given dimension the given number of times.
    ///
    /// # Arguments
    ///
    /// * `tensor` - The tensor.
    /// * `dim` - The dimension to repeat.
    /// * `times` - The number of times to repeat.
    ///
    /// # Returns
    ///
    /// The tensor with the given dimension repeated the given number of times.
    fn int_repeat_dim(tensor: IntTensor<B>, dim: usize, times: usize) -> IntTensor<B> {
        let device = tensor.device();
        repeat_with_slice_assign::<B, _, _, _>(
            tensor,
            dim,
            times,
            device,
            |shape, device, dtype| B::int_empty(shape, device, dtype.into()),
            B::int_slice_assign,
        )
    }

    /// Concatenates the given tensors along the given dimension.
    ///
    /// # Arguments
    ///
    /// * `tensors` - The tensors.
    /// * `dim` - The dimension to concatenate along.
    ///
    /// # Returns
    ///
    /// The concatenated tensor.
    ///
    /// # Note
    ///
    /// Empty tensors (where the concatenation dimension has size 0) are filtered out at the
    /// high-level tensor API and will not be passed to this method. Backend implementations do
    /// not need to handle empty tensors.
    fn int_cat(tensors: Vec<IntTensor<B>>, dim: usize) -> IntTensor<B> {
        let first_tensor = tensors.first().expect("Tensors should not be empty");
        let device = first_tensor.device();
        cat_with_slice_assign::<B, _, _, _>(
            tensors,
            dim,
            device,
            |shape, device, dtype| B::int_empty(shape, device, dtype.into()),
            B::int_slice_assign,
        )
    }

    /// Element-wise equality comparison.
    ///
    /// # Arguments
    ///
    /// * `lhs` - The left-hand side tensor.
    /// * `rhs` - The right-hand side tensor.
    /// * `out_dtype` - The output tensor dtype.
    ///
    /// # Returns
    ///
    /// The boolean tensor with the result of the comparison.
    fn int_equal(lhs: IntTensor<B>, rhs: IntTensor<B>, out_dtype: BoolDType) -> BoolTensor<B>;

    /// Element-wise non-equality comparison.
    ///
    /// # Arguments
    ///
    /// * `lhs` - The left-hand side tensor.
    /// * `rhs` - The right-hand side tensor.
    /// * `out_dtype` - The output tensor dtype.
    ///
    /// # Returns
    ///
    /// The boolean tensor with the result of the comparison.
    fn int_not_equal(lhs: IntTensor<B>, rhs: IntTensor<B>, out_dtype: BoolDType) -> BoolTensor<B> {
        let equal_tensor = B::int_equal(lhs, rhs, out_dtype);
        B::bool_not(equal_tensor)
    }

    /// Element-wise equality comparison with a scalar.
    ///
    /// # Arguments
    ///
    /// * `lhs` - The left-hand side tensor.
    /// * `rhs` - The right-hand side scalar.
    /// * `out_dtype` - The output tensor dtype.
    ///
    /// # Returns
    ///
    /// The boolean tensor with the result of the comparison.
    fn int_equal_elem(lhs: IntTensor<B>, rhs: Scalar, out_dtype: BoolDType) -> BoolTensor<B>;

    /// Element-wise non-equality comparison with a scalar.
    ///
    /// # Arguments
    ///
    /// * `lhs` - The left-hand side tensor.
    /// * `rhs` - The right-hand side scalar.
    /// * `out_dtype` - The output tensor dtype.
    ///
    /// # Returns
    ///
    /// The boolean tensor with the result of the comparison.
    fn int_not_equal_elem(lhs: IntTensor<B>, rhs: Scalar, out_dtype: BoolDType) -> BoolTensor<B> {
        let equal_tensor = B::int_equal_elem(lhs, rhs, out_dtype);
        B::bool_not(equal_tensor)
    }

    /// Element-wise greater than comparison.
    ///
    /// # Arguments
    ///
    /// * `lhs` - The left-hand side tensor.
    /// * `rhs` - The right-hand side tensor.
    /// * `out_dtype` - The output tensor dtype.
    ///
    /// # Returns
    ///
    /// The boolean tensor with the result of the comparison.
    fn int_greater(lhs: IntTensor<B>, rhs: IntTensor<B>, out_dtype: BoolDType) -> BoolTensor<B>;

    /// Element-wise greater than comparison with a scalar.
    ///
    /// # Arguments
    ///
    /// * `lhs` - The left-hand side tensor.
    /// * `rhs` - The right-hand side scalar.
    /// * `out_dtype` - The output tensor dtype.
    ///
    /// # Returns
    ///
    /// The boolean tensor with the result of the comparison.
    fn int_greater_elem(lhs: IntTensor<B>, rhs: Scalar, out_dtype: BoolDType) -> BoolTensor<B>;

    /// Element-wise greater than or equal comparison.
    ///
    /// # Arguments
    ///
    /// * `lhs` - The left-hand side tensor.
    /// * `rhs` - The right-hand side tensor.
    /// * `out_dtype` - The output tensor dtype.
    ///
    /// # Returns
    ///
    /// The boolean tensor with the result of the comparison.
    fn int_greater_equal(
        lhs: IntTensor<B>,
        rhs: IntTensor<B>,
        out_dtype: BoolDType,
    ) -> BoolTensor<B>;

    /// Element-wise greater than or equal comparison with a scalar.
    ///
    /// # Arguments
    ///
    /// * `lhs` - The left-hand side tensor.
    /// * `rhs` - The right-hand side scalar.
    /// * `out_dtype` - The output tensor dtype.
    ///
    /// # Returns
    ///
    /// The boolean tensor with the result of the comparison.
    fn int_greater_equal_elem(
        lhs: IntTensor<B>,
        rhs: Scalar,
        out_dtype: BoolDType,
    ) -> BoolTensor<B>;

    /// Element-wise less than comparison.
    ///
    /// # Arguments
    ///
    /// * `lhs` - The left-hand side tensor.
    /// * `rhs` - The right-hand side tensor.
    /// * `out_dtype` - The output tensor dtype.
    ///
    /// # Returns
    ///
    /// The boolean tensor with the result of the comparison.
    fn int_lower(lhs: IntTensor<B>, rhs: IntTensor<B>, out_dtype: BoolDType) -> BoolTensor<B>;

    /// Element-wise less than comparison with a scalar.
    ///
    /// # Arguments
    ///
    /// * `lhs` - The left-hand side tensor.
    /// * `rhs` - The right-hand side scalar.
    /// * `out_dtype` - The output tensor dtype.
    ///
    /// # Returns
    ///
    /// The boolean tensor with the result of the comparison.
    fn int_lower_elem(lhs: IntTensor<B>, rhs: Scalar, out_dtype: BoolDType) -> BoolTensor<B>;

    /// Element-wise less than or equal comparison.
    ///
    /// # Arguments
    ///
    /// * `lhs` - The left-hand side tensor.
    /// * `rhs` - The right-hand side tensor.
    /// * `out_dtype` - The output tensor dtype.
    ///
    /// # Returns
    ///
    /// The boolean tensor with the result of the comparison.
    fn int_lower_equal(lhs: IntTensor<B>, rhs: IntTensor<B>, out_dtype: BoolDType)
    -> BoolTensor<B>;

    /// Element-wise less than or equal comparison with a scalar.
    ///
    /// # Arguments
    ///
    /// * `lhs` - The left-hand side tensor.
    /// * `rhs` - The right-hand side scalar.
    /// * `out_dtype` - The output tensor dtype.
    ///
    /// # Returns
    ///
    /// The boolean tensor with the result of the comparison.
    fn int_lower_equal_elem(lhs: IntTensor<B>, rhs: Scalar, out_dtype: BoolDType) -> BoolTensor<B>;

    // ====  NUMERIC ==== //

    /// Element-wise addition.
    ///
    /// # Arguments
    ///
    /// * `lhs` - The left-hand side tensor.
    /// * `rhs` - The right-hand side tensor.
    ///
    /// # Returns
    ///
    /// The result of the addition.
    fn int_add(lhs: IntTensor<B>, rhs: IntTensor<B>) -> IntTensor<B>;

    /// Element-wise addition with a scalar.
    ///
    /// # Arguments
    ///
    /// * `lhs` - The left-hand side tensor.
    /// * `rhs` - The right-hand side scalar.
    ///
    /// # Returns
    ///
    /// The result of the addition.
    fn int_add_scalar(lhs: IntTensor<B>, rhs: Scalar) -> IntTensor<B>;

    /// Element-wise square with a IntTensor.
    ///
    /// # Arguments
    ///
    /// * `tensor` - The IntTensor.
    ///
    /// # Returns
    ///
    /// The element-wise square of `tensor`.
    fn int_square(tensor: IntTensor<B>) -> IntTensor<B> {
        Self::int_powi_scalar(tensor, Scalar::from(2))
    }

    /// Element-wise power with a IntTensor.
    ///
    /// # Arguments
    ///
    /// * `lhs` - The left-hand side IntTensor.
    /// * `rhs` - The right-hand side IntTensor.
    ///
    /// # Returns
    ///
    /// The elements of `lhs` raised to the power of the elements of `rhs`.
    fn int_powi(lhs: IntTensor<B>, rhs: IntTensor<B>) -> IntTensor<B> {
        let dtype = lhs.dtype();
        let float_dtype = get_device_settings::<B>(&lhs.device()).float_dtype;
        B::float_into_int(
            B::float_powi(B::int_into_float(lhs, float_dtype), rhs),
            dtype.into(),
        )
    }

    /// Element-wise power with a scalar.
    ///
    /// # Backend Implementors Note
    ///
    /// A number of common exponent cases can be implemented with operations
    /// which are much cheaper than generic exponentiation.
    ///
    /// This (`Backend` impl overridable) operation handles generic optimizations
    /// for several common integer exponent cases; and then dispatches to
    /// the (`Backend` impl overridable) [`Self::int_powi_scalar_impl`]
    /// operation to handle the generic case.
    ///
    /// # Arguments
    ///
    /// * `lhs` - The left-hand side tensor.
    /// * `rhs` - The right-hand side scalar.
    ///
    /// # Returns
    ///
    /// The elements of `lhs` raised to the value of `rhs`.
    fn int_powi_scalar(lhs: IntTensor<B>, rhs: Scalar) -> IntTensor<B> {
        let exp = rhs.elem::<i32>();
        match exp {
            0 => Self::int_ones(lhs.shape(), &lhs.device(), lhs.dtype().into()),
            1 => lhs,
            2 => Self::int_mul(lhs.clone(), lhs),
            _ => Self::int_powi_scalar_impl(lhs, rhs),
        }
    }

    /// Element-wise power with a scalar.
    ///
    /// # Backend Implementors Note
    ///
    /// This is the generic implementation of integer exponentiation
    /// called by [`Self::int_powi_scalar`] in the fallback case.
    ///
    /// By default, this performs a relatively expensive conversion to float,
    /// exponentiation in float, and conversion back to int.
    /// This reduces the minimal operation set for `Backend`s,
    /// at the cost of performance.
    ///
    /// This is a good target for specialized optimizations in `Backend` implementations.
    ///
    /// As a general rule, this should not be called directly.
    ///
    /// # Arguments
    ///
    /// * `lhs` - The left-hand side tensor.
    /// * `rhs` - The right-hand side scalar.
    ///
    /// # Returns
    ///
    /// The elements of `lhs` raised to the value of `rhs`.
    fn int_powi_scalar_impl(lhs: IntTensor<B>, rhs: Scalar) -> IntTensor<B> {
        let dtype = lhs.dtype();
        let float_dtype = get_device_settings::<B>(&lhs.device()).float_dtype;
        B::float_into_int(
            B::float_powi_scalar_impl(B::int_into_float(lhs, float_dtype), rhs),
            dtype.into(),
        )
    }

    /// Clamps a tensor under a minimum value.
    ///
    /// # Arguments
    ///
    /// * `tensor` - The tensor to clamp.
    /// * `min` - The minimum value.
    ///
    /// # Returns
    ///
    /// The clamped tensor.
    fn int_clamp_min(tensor: IntTensor<B>, min: Scalar) -> IntTensor<B> {
        let dtype = get_device_settings::<B>(&tensor.device()).bool_dtype;
        let mask = Self::int_lower_elem(tensor.clone(), min, dtype);
        Self::int_mask_fill(tensor, mask, min)
    }

    /// Clamps a tensor over a maximum value.
    ///
    /// # Arguments
    ///
    /// * `tensor` - The tensor to clamp.
    /// * `max` - The maximum value.
    ///
    /// # Returns
    ///
    /// The clamped tensor.
    fn int_clamp_max(tensor: IntTensor<B>, max: Scalar) -> IntTensor<B> {
        let dtype = get_device_settings::<B>(&tensor.device()).bool_dtype;
        let mask = Self::int_greater_elem(tensor.clone(), max, dtype);
        Self::int_mask_fill(tensor, mask, max)
    }

    /// Clamps a tensor between a minimum and maximum value.
    ///
    /// # Arguments
    ///
    /// * `tensor` - The tensor to clamp.
    /// * `min` - The minimum value.
    /// * `max` - The maximum value.
    ///
    /// # Returns
    ///
    /// The clamped tensor.
    fn int_clamp(tensor: IntTensor<B>, min: Scalar, max: Scalar) -> IntTensor<B> {
        Self::int_clamp_min(Self::int_clamp_max(tensor, max), min)
    }

    /// Element-wise subtraction.
    ///
    /// # Arguments
    ///
    /// * `lhs` - The left-hand side tensor.
    /// * `rhs` - The right-hand side tensor.
    ///
    /// # Returns
    ///
    /// The result of the subtraction.
    fn int_sub(lhs: IntTensor<B>, rhs: IntTensor<B>) -> IntTensor<B>;

    /// Element-wise subtraction with a scalar.
    ///
    /// # Arguments
    ///
    /// * `lhs` - The left-hand side tensor.
    /// * `rhs` - The right-hand side scalar.
    ///
    /// # Returns
    ///
    /// The result of the subtraction.
    fn int_sub_scalar(lhs: IntTensor<B>, rhs: Scalar) -> IntTensor<B>;

    /// Element-wise multiplication.
    ///
    /// # Arguments
    ///
    /// * `lhs` - The left-hand side tensor.
    /// * `rhs` - The right-hand side tensor.
    ///
    /// # Returns
    ///
    /// The result of the multiplication.
    fn int_mul(lhs: IntTensor<B>, rhs: IntTensor<B>) -> IntTensor<B>;

    /// Element-wise multiplication with a scalar.
    ///
    /// # Arguments
    ///
    /// * `lhs` - The left-hand side tensor.
    /// * `rhs` - The right-hand side scalar.
    ///
    /// # Returns
    ///
    /// The result of the multiplication.
    fn int_mul_scalar(lhs: IntTensor<B>, rhs: Scalar) -> IntTensor<B>;

    /// Element-wise division.
    ///
    /// # Arguments
    ///
    /// * `lhs` - The left-hand side tensor.
    /// * `rhs` - The right-hand side tensor.
    ///
    /// # Returns
    ///
    /// The result of the division.
    fn int_div(lhs: IntTensor<B>, rhs: IntTensor<B>) -> IntTensor<B>;

    /// Element-wise division with a scalar.
    ///
    /// # Arguments
    ///
    /// * `lhs` - The left-hand side tensor.
    /// * `rhs` - The right-hand side scalar.
    ///
    /// # Returns
    ///
    /// The result of the division.
    fn int_div_scalar(lhs: IntTensor<B>, rhs: Scalar) -> IntTensor<B>;

    /// Element-wise modulus.
    ///
    /// # Arguments
    /// * `lhs` - The left-hand side tensor.
    /// * `rhs` - The right-hand side scalar.
    ///
    /// # Returns
    ///
    /// The result of applying the modulus of the scalar to the tensor.
    fn int_remainder(lhs: IntTensor<B>, rhs: IntTensor<B>) -> IntTensor<B>;

    /// Element-wise modulus with a scalar.
    ///
    /// # Arguments
    /// * `lhs` - The left-hand side tensor.
    /// * `rhs` - The right-hand side scalar.
    ///
    /// # Returns
    ///
    /// The result of applying the modulus of the scalar to the tensor.
    fn int_remainder_scalar(lhs: IntTensor<B>, rhs: Scalar) -> IntTensor<B>;

    /// Multiplies two tensors together using matrix multiplication.
    ///
    /// # Arguments
    ///
    /// * `lhs` - The left-hand side tensor.
    /// * `rhs` - The right-hand side tensor.
    ///
    /// # Returns
    ///
    /// The result of multiplying the two tensors together using matrix multiplication.
    fn int_matmul(lhs: IntTensor<B>, rhs: IntTensor<B>) -> IntTensor<B>;

    /// Element-wise negation.
    ///
    /// # Arguments
    ///
    /// * `tensor` - The tensor to negate.
    ///
    /// # Returns
    ///
    /// The negated tensor.
    fn int_neg(tensor: IntTensor<B>) -> IntTensor<B> {
        Self::int_mul_scalar(tensor, (-1).into())
    }

    /// Creates a tensor of zeros.
    ///
    /// # Arguments
    ///
    /// * `shape` - The shape of the tensor.
    /// * `device` - The device to create the tensor on.
    /// * `dtype` - The target data type.
    ///
    /// # Returns
    ///
    /// The tensor of zeros.
    fn int_zeros(shape: Shape, device: &Device<B>, dtype: IntDType) -> IntTensor<B> {
        Self::int_from_data(TensorData::full_dtype(shape, 0, dtype.into()), device)
    }

    /// Creates a tensor of ones.
    ///
    /// # Arguments
    ///
    /// * `shape` - The shape of the tensor.
    /// * `device` - The device to create the tensor on.
    /// * `dtype` - The target data type.
    ///
    /// # Returns
    ///
    /// The tensor of ones.
    fn int_ones(shape: Shape, device: &Device<B>, dtype: IntDType) -> IntTensor<B> {
        Self::int_from_data(TensorData::full_dtype(shape, 1, dtype.into()), device)
    }

    /// Creates a tensor filled with given value.
    ///
    /// # Arguments
    ///
    /// * `shape` - The shape of the tensor.
    /// * `fill_value` - The value with which to fill the tensor.
    /// * `device` - The device to create the tensor on.
    /// * `dtype` - The target data type.
    ///
    /// # Returns
    ///
    /// The tensor filled with given value
    fn int_full(
        shape: Shape,
        fill_value: Scalar,
        device: &Device<B>,
        dtype: IntDType,
    ) -> IntTensor<B> {
        Self::int_from_data(
            TensorData::full_dtype(shape, fill_value, dtype.into()),
            device,
        )
    }

    /// Sums all elements in the tensor.
    ///
    /// # Arguments
    ///
    /// * `tensor` - The tensor to sum.
    ///
    /// # Returns
    ///
    /// The sum of all elements in the tensor.
    fn int_sum(tensor: IntTensor<B>) -> IntTensor<B>;

    /// Sums all elements in the tensor along a dimension.
    ///
    /// # Arguments
    ///
    /// * `tensor` - The tensor to sum.
    /// * `dim` - The dimension to sum along.
    ///
    /// # Returns
    ///
    /// The sum of all elements in the tensor along the dimension.
    fn int_sum_dim(tensor: IntTensor<B>, dim: usize) -> IntTensor<B>;

    /// Computes the product of all elements in the tensor.
    ///
    /// # Arguments
    ///
    /// * `tensor` - The tensor to compute the product of.
    ///
    /// # Returns
    ///
    /// The product of all elements in the tensor.
    fn int_prod(tensor: IntTensor<B>) -> IntTensor<B>;

    /// Computes the product of all elements in the tensor along a dimension.
    ///
    /// # Arguments
    ///
    /// * `tensor` - The tensor to compute the product of.
    /// * `dim` - The dimension to compute the product along.
    ///
    /// # Returns
    ///
    /// The product of all elements in the tensor along the dimension.
    fn int_prod_dim(tensor: IntTensor<B>, dim: usize) -> IntTensor<B>;

    /// Computes the mean of all elements in the tensor.
    ///
    /// # Arguments
    ///
    /// * `tensor` - The tensor to compute the mean of.
    ///
    /// # Returns
    ///
    /// The mean of all elements in the tensor.
    fn int_mean(tensor: IntTensor<B>) -> IntTensor<B> {
        let num_elems = tensor.shape().num_elements() as i64;
        B::int_div_scalar(B::int_sum(tensor), num_elems.into())
    }

    /// Computes the mean of all elements in the tensor along a dimension.
    ///
    /// # Arguments
    ///
    /// * `tensor` - The tensor to compute the mean of.
    ///
    /// # Returns
    ///
    /// The mean of all elements in the tensor along the dimension.
    fn int_mean_dim(tensor: IntTensor<B>, dim: usize) -> IntTensor<B>;

    /// Computes the cumulative sum of elements along a dimension.
    ///
    /// # Arguments
    ///
    /// * `tensor` - The tensor to compute the cumulative sum of.
    /// * `dim` - The dimension along which to compute the cumulative sum.
    ///
    /// # Returns
    ///
    /// A tensor with the same shape where each element is the cumulative sum
    /// of all elements up to and including that position along the dimension.
    fn int_cumsum(tensor: IntTensor<B>, dim: usize) -> IntTensor<B>;

    /// Computes the cumulative product of elements along a dimension.
    ///
    /// # Arguments
    ///
    /// * `tensor` - The tensor to compute the cumulative product of.
    /// * `dim` - The dimension along which to compute the cumulative product.
    ///
    /// # Returns
    ///
    /// A tensor with the same shape where each element is the cumulative product
    /// of all elements up to and including that position along the dimension.
    fn int_cumprod(tensor: IntTensor<B>, dim: usize) -> IntTensor<B>;

    /// Computes the cumulative minimum of elements along a dimension.
    ///
    /// # Arguments
    ///
    /// * `tensor` - The tensor to compute the cumulative minimum of.
    /// * `dim` - The dimension along which to compute the cumulative minimum.
    ///
    /// # Returns
    ///
    /// A tensor with the same shape where each element is the minimum
    /// of all elements up to and including that position along the dimension.
    fn int_cummin(tensor: IntTensor<B>, dim: usize) -> IntTensor<B>;

    /// Computes the cumulative maximum of elements along a dimension.
    ///
    /// # Arguments
    ///
    /// * `tensor` - The tensor to compute the cumulative maximum of.
    /// * `dim` - The dimension along which to compute the cumulative maximum.
    ///
    /// # Returns
    ///
    /// A tensor with the same shape where each element is the maximum
    /// of all elements up to and including that position along the dimension.
    fn int_cummax(tensor: IntTensor<B>, dim: usize) -> IntTensor<B>;

    /// Gets the indices of the maximum elements along a dimension.
    ///
    /// # Arguments
    ///
    /// * `tensor` - The tensor to get the maximum indices of.
    /// * `dim` - The dimension to get the maximum indices along.
    ///
    /// # Returns
    ///
    /// The indices of the maximum elements along the dimension.
    fn int_argmax(tensor: IntTensor<B>, dim: usize) -> IntTensor<B>;

    /// Gets the indices of the k maximum elements along a dimension.
    /// If two elements share the same value, it will be ordered by the lowest
    /// coordinate
    ///
    /// # Arguments
    ///
    /// * `tensor` - The tensor to get the maximum indices of.
    /// * `dim` - The dimension to get the maximum indices along.
    /// * `k` - number of maximum elements.
    ///
    /// # Returns
    ///
    /// The indices of the maximum elements along the dimension.
    fn int_argtopk(tensor: IntTensor<B>, dim: usize, k: usize) -> IntTensor<B> {
        let device = &tensor.device();
        let dtype = get_device_settings::<B>(device).int_dtype;
        let k_indices = B::int_arange(0..k as i64, device, dtype);
        Self::int_select(Self::int_argsort(tensor, dim, true), dim, k_indices)
    }

    /// Gets the values of the k maximum elements along a dimension.
    /// # Arguments
    ///
    /// * `tensor` - The tensor to get the maximum values of.
    /// * `dim` - The dimension to get the maximum values along.
    /// * `k` - number of maximum elements.
    ///
    /// # Returns
    ///
    /// The values of the maximum elements along the dimension.
    fn int_topk(tensor: IntTensor<B>, dim: usize, k: usize) -> IntTensor<B> {
        let device = &tensor.device();
        let dtype = get_device_settings::<B>(device).int_dtype;
        let k_indices = Self::int_arange(0..k as i64, device, dtype);
        Self::int_select(Self::int_sort(tensor, dim, true), dim, k_indices)
    }

    /// Gets the values of the k maximum elements along a dimension, and their indices.
    ///
    /// # Arguments
    ///
    /// * `tensor` - The tensor to get the maximum values of.
    /// * `dim` - The dimension to get the maximum values along.
    /// * `k` - number of maximum elements.
    ///
    /// # Returns
    ///
    /// A tuple with the values of the k maximum elements along the dimension, and their indices.
    ///
    /// The default sorts once and keeps the first `k` of each half. It deliberately does not
    /// compose `int_topk` with `int_argtopk`: those default to a sort each, so that would sort
    /// twice, and `int_argtopk` has no default at all, so backends that only sort could not
    /// serve this. Backends whose top-k already carries both results should override this and
    /// produce them in a single pass.
    fn int_topk_with_indices(
        tensor: IntTensor<B>,
        dim: usize,
        k: usize,
    ) -> (IntTensor<B>, IntTensor<B>) {
        let device = tensor.device();
        let dtype = get_device_settings::<B>(&device).int_dtype;
        let k_indices = Self::int_arange(0..k as i64, &device, dtype);
        let (values, indices) = Self::int_sort_with_indices(tensor, dim, true);

        (
            Self::int_select(values, dim, k_indices.clone()),
            Self::int_select(indices, dim, k_indices),
        )
    }

    /// Gets the indices of the minimum elements along a dimension.
    ///
    /// # Arguments
    ///
    /// * `tensor` - The tensor to get the minimum indices of.
    /// * `dim` - The dimension to get the minimum indices along.
    ///
    /// # Returns
    ///
    /// The indices of the minimum elements along the dimension.
    fn int_argmin(tensor: IntTensor<B>, dim: usize) -> IntTensor<B>;

    /// Gets the maximum element in the tensor.
    ///
    /// # Arguments
    ///
    /// * `tensor` - The tensor to get the maximum element of.
    ///
    /// # Returns
    ///
    /// The maximum element in the tensor.
    fn int_max(tensor: IntTensor<B>) -> IntTensor<B> {
        let shape = tensor.shape();
        let tensor = B::int_reshape(tensor, Shape::new([shape.num_elements()]));

        B::int_max_dim(tensor, 0)
    }

    /// Gets the maximum element in the tensor along a dimension.
    ///
    /// # Arguments
    ///
    /// * `tensor` - The tensor to get the maximum element of.
    /// * `dim` - The dimension to get the maximum element along.
    ///
    /// # Returns
    ///
    /// The maximum element in the tensor along the dimension.
    fn int_max_dim(tensor: IntTensor<B>, dim: usize) -> IntTensor<B> {
        let index = B::int_argmax(tensor.clone(), dim);
        B::int_gather(dim, tensor, index)
    }

    /// Gets the maximum elements and corresponding indices along a dimension.
    ///
    /// # Arguments
    ///
    /// * `tensor` - The tensor to get the maximum elements and indices of.
    /// * `dim` - The dimension to get the maximum elements and indices along.
    ///
    /// # Returns
    ///
    /// The maximum elements and corresponding indices along the dimension.
    fn int_max_dim_with_indices(tensor: IntTensor<B>, dim: usize) -> (IntTensor<B>, IntTensor<B>) {
        let index = B::int_argmax(tensor.clone(), dim);
        let values = B::int_gather(dim, tensor, index.clone());

        (values, index)
    }

    /// Gets the maximum absolute element in the tensor.
    ///
    /// # Arguments
    ///
    /// * `tensor` - The tensor to get the maximum element of.
    ///
    /// # Returns
    ///
    /// The maximum element in the tensor.
    fn int_max_abs(tensor: IntTensor<B>) -> IntTensor<B> {
        let shape = tensor.shape();
        let tensor = B::int_reshape(tensor, Shape::new([shape.num_elements()]));

        B::int_max_abs_dim(tensor, 0)
    }

    /// Gets the maximum absolute element in the tensor along a dimension.
    ///
    /// # Arguments
    ///
    /// * `tensor` - The tensor to get the maximum element of.
    /// * `dim` - The dimension to get the maximum element along.
    ///
    /// # Returns
    ///
    /// The maximum element in the tensor along the dimension.
    fn int_max_abs_dim(tensor: IntTensor<B>, dim: usize) -> IntTensor<B> {
        B::int_max_dim(B::int_abs(tensor), dim)
    }

    /// Gets the minimum element in the tensor.
    ///
    /// # Arguments
    ///
    /// * `tensor` - The tensor to get the minimum element of.
    ///
    /// # Returns
    ///
    /// The minimum element in the tensor.
    fn int_min(tensor: IntTensor<B>) -> IntTensor<B> {
        let shape = tensor.shape();
        let tensor = B::int_reshape(tensor, Shape::new([shape.num_elements()]));

        B::int_min_dim(tensor, 0)
    }

    /// Gets the minimum elements in the tensor along a dimension.
    ///
    /// # Arguments
    ///
    /// * `tensor` - The tensor to get the minimum element of.
    /// * `dim` - The dimension to get the minimum element along.
    ///
    /// # Returns
    ///
    /// The minimum element in the tensor along the dimension.
    fn int_min_dim(tensor: IntTensor<B>, dim: usize) -> IntTensor<B> {
        let index = B::int_argmin(tensor.clone(), dim);
        B::int_gather(dim, tensor, index)
    }

    /// Gets the minimum elements and corresponding indices along a dimension.
    ///
    /// # Arguments
    ///
    /// * `tensor` - The tensor to get the minimum elements and indices of.
    /// * `dim` - The dimension to get the minimum elements and indices along.
    ///
    /// # Returns
    ///
    /// The minimum elements and corresponding indices along the dimension.
    fn int_min_dim_with_indices(tensor: IntTensor<B>, dim: usize) -> (IntTensor<B>, IntTensor<B>) {
        let indices = B::int_argmin(tensor.clone(), dim);
        let values = B::int_gather(dim, tensor, indices.clone());

        (values, indices)
    }

    /// Returns a new tensor with absolute values.
    ///
    /// # Arguments
    ///
    /// * `tensor` - The tensor to take absolute value of.
    ///
    /// # Returns
    ///
    /// A tensor with the same shape as `tensor` with absolute values.
    fn int_abs(tensor: IntTensor<B>) -> IntTensor<B>;

    /// Transposes an int tensor.
    ///
    /// # Arguments
    ///
    /// * `tensor` - The tensor to transpose.
    ///
    /// # Returns
    ///
    /// The transposed tensor.
    fn int_transpose(tensor: IntTensor<B>) -> IntTensor<B> {
        let ndims = tensor.shape().num_dims();
        Self::int_swap_dims(tensor, ndims - 2, ndims - 1)
    }

    /// Swaps two dimensions of an int tensor.
    ///
    /// # Arguments
    ///
    /// * `tensor` - The tensor to swap the dimensions of.
    /// * `dim1` - The first dimension to swap.
    /// * `dim2` - The second dimension to swap.
    ///
    /// # Returns
    ///
    /// The tensor with the dimensions swapped.
    fn int_swap_dims(tensor: IntTensor<B>, dim1: usize, dim2: usize) -> IntTensor<B>;

    /// Permutes the dimensions of a tensor.
    ///
    /// # Arguments
    ///
    /// * `tensor` - The tensor to permute the dimensions of.
    /// * `axes` - The new order of the dimensions.
    /// # Returns
    ///
    /// The tensor with the dimensions permuted.
    fn int_permute(tensor: IntTensor<B>, axes: &[usize]) -> IntTensor<B>;

    /// Reverse the order of elements in a tensor along the given axes.
    ///
    /// # Arguments
    ///
    /// * `tensor` - The tensor to reverse.
    /// * `axes` - The axes to reverse.
    ///
    /// The tensor with the elements reversed.
    fn int_flip(tensor: IntTensor<B>, axes: &[usize]) -> IntTensor<B>;

    /// Creates a new int tensor with random values.
    ///
    ///  # Arguments
    ///  * `shape` - The shape of the tensor.
    ///  * `distribution` - The distribution to sample from.
    ///  * `device` - The device to create the tensor on.
    /// * `dtype` - The target data type.
    ///
    ///  # Returns
    ///
    ///  The tensor with the given shape and random values.
    fn int_random(
        shape: Shape,
        distribution: Distribution,
        device: &Device<B>,
        dtype: IntDType,
    ) -> IntTensor<B>;

    /// Creates a new tensor with values from the given range with the given step size.
    ///
    /// # Arguments
    ///
    /// * `range` - The range of values.
    /// * `step` - The step size.
    /// * `device` - The device to create the tensor on.
    /// * `dtype` - The target data type.
    ///
    /// # Returns
    ///
    /// The tensor with the given values.
    fn int_arange_step(
        range: Range<i64>,
        step: usize,
        device: &Device<B>,
        dtype: IntDType,
    ) -> IntTensor<B> {
        let value = range.step_by(step).collect::<Vec<_>>();
        let shape = Shape::new([value.len()]);
        let data = TensorData::new(value, shape).convert_dtype(dtype.into());
        B::int_from_data(data, device)
    }

    /// Creates a new tensor with values from the given range.
    ///
    /// # Arguments
    ///
    /// * `range` - The range of values.
    /// * `device` - The device to create the tensor on.
    ///
    /// # Returns
    ///
    /// The tensor with the given values.
    ///
    /// # Remarks
    ///
    /// Uses `arange_step` with a step size of 1 under the hood.
    fn int_arange(range: Range<i64>, device: &Device<B>, dtype: IntDType) -> IntTensor<B> {
        Self::int_arange_step(range, 1, device, dtype)
    }

    /// Tests if any element in the int `tensor` evaluates to True.
    ///
    /// # Arguments
    ///
    /// * `tensor` - The tensor to test.
    ///
    /// # Returns
    ///
    /// A boolean tensor with a single element, True if any element in the tensor is True, False otherwise.
    fn int_any(tensor: IntTensor<B>, out_dtype: BoolDType) -> BoolTensor<B> {
        let int_dtype = tensor.dtype();
        let bool_tensor = B::int_equal_elem(tensor, 0.into(), out_dtype);
        let bool_tensor = B::bool_not(bool_tensor);
        let sum = B::int_sum(B::bool_into_int(bool_tensor, int_dtype.into()));
        B::int_greater_elem(sum, 0.into(), out_dtype)
    }

    /// Tests if any element in the int `tensor` evaluates to True along a given dimension `dim`.
    ///
    /// # Arguments
    ///
    /// * `tensor` - The tensor to test.
    /// * `dim` - The axis along which to test.
    ///
    /// # Returns
    ///
    /// A boolean tensor `Tensor<B, D, Bool>` with the same size as input `tensor`, except in the `dim` axis
    /// where the size is 1. The elem in the `dim` axis is True if any element along this dim in the input
    /// evaluates to True, False otherwise.
    fn int_any_dim(tensor: IntTensor<B>, dim: usize, out_dtype: BoolDType) -> BoolTensor<B> {
        let int_dtype = tensor.dtype();
        let bool_tensor = B::int_equal_elem(tensor, 0.into(), out_dtype);
        let bool_tensor = B::bool_not(bool_tensor);
        let sum = B::int_sum_dim(B::bool_into_int(bool_tensor, int_dtype.into()), dim);
        B::int_greater_elem(sum, 0.into(), out_dtype)
    }

    /// Tests if all elements in the int `tensor` evaluate to True.
    ///
    /// # Arguments
    ///
    /// * `tensor` - The tensor to test.
    /// * `out_dtype` - The output tensor dtype.
    ///
    /// # Returns
    ///
    /// A boolean tensor `Tensor<B, 1, Bool>` with a single element, True if all elements in the input tensor
    /// evaluate to True, False otherwise.
    fn int_all(tensor: IntTensor<B>, out_dtype: BoolDType) -> BoolTensor<B> {
        let int_dtype = tensor.dtype();
        let num_elems = tensor.shape().num_elements() as i64;
        let bool_tensor = B::int_equal_elem(tensor, 0.into(), out_dtype);
        let bool_tensor = B::bool_not(bool_tensor);
        let sum = B::int_sum(B::bool_into_int(bool_tensor, int_dtype.into()));
        B::int_equal_elem(sum, num_elems.into(), out_dtype)
    }

    /// Tests if all elements in the int `tensor` evaluate to True along a given dimension `dim`.
    ///
    /// # Arguments
    ///
    /// * `tensor` - The tensor to test.
    /// * `dim` - The axis along which to test.
    /// * `out_dtype` - The output tensor dtype.
    ///
    /// # Returns
    ///
    /// A boolean tensor `Tensor<B, D, Bool>` with the same size as input `tensor`, except in the `dim` axis
    /// where the size is 1. The elem in the `dim` axis is True if all elements along this dim in the input
    /// evaluates to True, False otherwise.
    fn int_all_dim(tensor: IntTensor<B>, dim: usize, out_dtype: BoolDType) -> BoolTensor<B> {
        let int_dtype = tensor.dtype();
        let num_elems = tensor.shape()[dim] as i64;
        let bool_tensor = B::int_equal_elem(tensor, 0.into(), out_dtype);
        let bool_tensor = B::bool_not(bool_tensor);
        let sum = B::int_sum_dim(B::bool_into_int(bool_tensor, int_dtype.into()), dim);
        B::int_equal_elem(sum, num_elems.into(), out_dtype)
    }

    /// Returns the signs of the int `tensor`.
    ///
    /// # Arguments
    ///
    /// * `tensor` - The tensor to extract the signs from.
    ///
    /// # Returns
    ///
    /// A tensor with the same shape as `tensor` containing the signs of the elements of `tensor`.
    fn int_sign(tensor: IntTensor<B>) -> IntTensor<B> {
        let dtype = tensor.dtype();
        let device = &tensor.device();
        let bool_dtype = get_device_settings::<B>(&tensor.device()).bool_dtype;
        let zeros = B::int_zeros(tensor.shape(), device, dtype.into());
        let less_than_zero = B::int_lower_elem(tensor.clone(), 0.into(), bool_dtype);
        let greater_than_zero = B::int_greater_elem(tensor, 0.into(), bool_dtype);

        let mut result = B::int_mask_fill(zeros, less_than_zero, (-1).into());
        result = B::int_mask_fill(result, greater_than_zero, 1.into());
        result
    }

    /// Broadcasts the int `tensor` to the given `shape`.
    fn int_expand(tensor: IntTensor<B>, shape: Shape) -> IntTensor<B>;

    /// Sort the elements of the input `tensor` by value along a given dimension.
    ///
    /// This sort is unstable (i.e., may reorder equal elements).
    ///
    /// # Arguments
    ///
    /// * `tensor` - The input tensor.
    /// * `dim` - The axis along which to sort.
    /// * `descending` - The sorting order.
    ///
    /// # Returns
    ///
    /// A tensor with the same shape as the input tensor, where the elements are sorted by value.
    fn int_sort(tensor: IntTensor<B>, dim: usize, descending: bool) -> IntTensor<B> {
        let device = tensor.device();
        sort::<B, _, _, _>(
            tensor,
            dim,
            descending,
            device,
            |tensor| {
                let msg = "Failed to synchronously read tensor data. This operation is not supported until this backend has a GPU sorting implementation.";
                try_read_sync(B::int_into_data(tensor))
                    .expect(msg)
                    .expect(msg)
            },
            |data, device, _dtype| B::int_from_data(data, device),
        )
    }

    /// Sort the elements of the input `tensor` by value along a given dimension.
    ///
    /// This sort is unstable (i.e., may reorder equal elements).
    ///
    /// # Arguments
    ///
    /// * `tensor` - The input tensor.
    /// * `dim` - The axis along which to sort.
    ///
    /// # Returns
    ///
    /// A tensor with the same shape as the input tensor and corresponding indices, where
    /// the elements are sorted by value and the indices map back to the original input tensor.
    fn int_sort_with_indices(
        tensor: IntTensor<B>,
        dim: usize,
        descending: bool,
    ) -> (IntTensor<B>, IntTensor<B>) {
        let dtype = tensor.dtype();
        let device = tensor.device();
        sort_with_indices::<B, _, _, _>(
            tensor,
            dim,
            descending,
            dtype.into(),
            device,
            |tensor| {
                let msg = "Failed to synchronously read tensor data. This operation is not supported until this backend has a GPU sorting implementation.";
                try_read_sync(B::int_into_data(tensor))
                    .expect(msg)
                    .expect(msg)
            },
            |data, device, _dtype| B::int_from_data(data, device),
        )
    }

    /// Returns the indices that sort the elements of the input `tensor` by value
    /// along a given dimension.
    ///
    /// This sort is unstable (i.e., may reorder equal elements).
    ///
    /// # Arguments
    ///
    /// * `tensor` - The input tensor.
    /// * `dim` - The axis along which to sort.
    /// * `descending` - The sorting order.
    ///
    /// # Returns
    ///
    /// A tensor with the same shape as the input tensor the indices map back to the original input tensor.
    fn int_argsort(tensor: IntTensor<B>, dim: usize, descending: bool) -> IntTensor<B> {
        let dtype = tensor.dtype();
        let device = tensor.device();
        argsort::<B, _, _>(tensor, dim, descending, dtype.into(), device, |tensor| {
            let msg = "Failed to synchronously read tensor data. This operation is not supported until this backend has a GPU sorting implementation.";
            try_read_sync(B::int_into_data(tensor))
                .expect(msg)
                .expect(msg)
        })
    }

    /// Bitwise AND operation for Int Tensors
    fn bitwise_and(lhs: IntTensor<B>, rhs: IntTensor<B>) -> IntTensor<B>;

    /// Bitwise AND operation for Int Tensors with a scalar
    fn bitwise_and_scalar(lhs: IntTensor<B>, rhs: Scalar) -> IntTensor<B>;

    /// Bitwise OR operation for Int Tensors
    fn bitwise_or(lhs: IntTensor<B>, rhs: IntTensor<B>) -> IntTensor<B>;

    /// Bitwise OR operation for Int Tensors with a scalar
    fn bitwise_or_scalar(lhs: IntTensor<B>, rhs: Scalar) -> IntTensor<B>;

    /// Bitwise XOR operation for Int Tensors
    fn bitwise_xor(lhs: IntTensor<B>, rhs: IntTensor<B>) -> IntTensor<B>;

    /// Bitwise XOR operation for Int Tensors with a scalar
    fn bitwise_xor_scalar(lhs: IntTensor<B>, rhs: Scalar) -> IntTensor<B>;

    /// Bitwise NOT operation for Int Tensors
    fn bitwise_not(tensor: IntTensor<B>) -> IntTensor<B>;

    /// Bitwise left shift operation for Int Tensors
    fn bitwise_left_shift(lhs: IntTensor<B>, rhs: IntTensor<B>) -> IntTensor<B>;

    /// Bitwise left shift operation for Int Tensors with a scalar
    fn bitwise_left_shift_scalar(lhs: IntTensor<B>, rhs: Scalar) -> IntTensor<B>;

    /// Bitwise right shift operation for Int Tensors
    fn bitwise_right_shift(lhs: IntTensor<B>, rhs: IntTensor<B>) -> IntTensor<B>;

    /// Bitwise right shift operation for Int Tensors with a scalar
    fn bitwise_right_shift_scalar(lhs: IntTensor<B>, rhs: Scalar) -> IntTensor<B>;

    /// Converts a tensor to another integer data type.
    ///
    /// # Arguments
    ///
    /// * `tensor` - The tensor to convert.
    /// * `dtype` - The target data type.
    ///
    /// # Returns
    ///
    /// A tensor with the same values as `tensor` but in the target integer data type.
    fn int_cast(tensor: IntTensor<B>, dtype: IntDType) -> IntTensor<B>;

    /// Unfold windows along a dimension.
    ///
    /// Returns a view of the tensor with all complete windows of size `size` in dimension `dim`;
    /// where windows are advanced by `step` at each index.
    ///
    /// The number of windows is `max(0, (shape[dim] - size).ceil_div(step))`.
    ///
    /// # Arguments
    ///
    /// * `tensor` - The input tensor to unfold; of shape ``[pre=..., dim shape, post=...]``
    /// * `dim` - the selected dim.
    /// * `size` - the size of each unfolded window.
    /// * `step` - the step between each window.
    ///
    /// # Returns
    ///
    /// A tensor view with shape ``[pre=..., windows, size, post=...]``.
    fn int_unfold(tensor: IntTensor<B>, dim: usize, size: usize, step: usize) -> IntTensor<B>;
}