burn_backend/backend/ops/

tensor.rs

use super::cat::cat_with_slice_assign;
use super::grid_sample::float_grid_sample_2d_ref;
use super::repeat_dim::repeat_with_slice_assign;
use super::sort::{argsort, sort, sort_with_indices};
use crate::ops::GridSampleOptions;
use crate::tensor::{BoolTensor, Device, FloatTensor, IntTensor};
use crate::{Backend, Distribution, TensorData, get_or_init_device_settings};
use crate::{ExecutionError, Scalar, TensorMetadata};
use alloc::vec::Vec;
use burn_std::reader::try_read_sync;
use burn_std::{BoolDType, FloatDType, IndexingUpdateOp, IntDType, PadMode, Shape, Slice};

/// Operations on float tensors.
pub trait FloatTensorOps<B: Backend> {
    /// Creates a new tensor from the data structure.
    ///
    /// # Arguments
    ///
    /// * `data` - The data structure.
    /// * `device` - The device to create the tensor on.
    ///
    /// # Returns
    ///
    /// The tensor with the given data.
    fn float_from_data(data: TensorData, device: &Device<B>) -> FloatTensor<B>;

    /// Creates a new 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 float_random(
        shape: Shape,
        distribution: Distribution,
        device: &Device<B>,
        dtype: FloatDType,
    ) -> FloatTensor<B>;

    /// Creates a new tensor with zeros.
    ///
    /// # Arguments
    ///
    /// * `shape` - The shape of the tensor.
    /// * `device` - The device to create the tensor on.
    /// * `dtype` - The target data type.
    ///
    /// # Returns
    ///
    /// The tensor with the given shape and zeros.
    fn float_zeros(shape: Shape, device: &Device<B>, dtype: FloatDType) -> FloatTensor<B> {
        Self::float_from_data(TensorData::full_dtype(shape, 0., dtype.into()), device)
    }

    /// Creates a new tensor with ones.
    ///
    /// # Arguments
    ///
    /// * `shape` - The shape of the tensor.
    /// * `device` - The device to create the tensor on.
    /// * `dtype` - The target data type.
    ///
    /// # Returns
    ///
    /// The tensor with the given shape and ones.
    fn float_ones(shape: Shape, device: &Device<B>, dtype: FloatDType) -> FloatTensor<B> {
        Self::float_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 float_full(
        shape: Shape,
        fill_value: Scalar,
        device: &Device<B>,
        dtype: FloatDType,
    ) -> FloatTensor<B> {
        Self::float_from_data(
            TensorData::full_dtype(shape, fill_value, dtype.into()),
            device,
        )
    }

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

    /// Moves the tensor to the given device.
    ///
    /// # Arguments
    ///
    /// * `tensor` - The tensor.
    /// * `device` - The device to move the tensor to.
    ///
    /// # Returns
    ///
    /// The tensor on the given device.
    fn float_to_device(tensor: FloatTensor<B>, device: &Device<B>) -> FloatTensor<B>;

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

    /// Creates an empty tensor with the given shape.
    ///
    /// # Arguments
    ///
    /// * `shape` - The shape of the tensor.
    /// * `device` - The device to create the tensor on.
    /// * `dtype` - The target data type.
    ///
    /// # Returns
    ///
    /// The empty tensor with the given shape.
    fn float_empty(shape: Shape, device: &Device<B>, dtype: FloatDType) -> FloatTensor<B>;

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

    /// Adds two tensors together.
    ///
    /// # Arguments
    ///
    /// * `lhs` - The left-hand side tensor.
    /// * `rhs` - The right-hand side tensor.
    ///
    /// # Returns
    ///
    /// The result of adding the two tensors together.
    fn float_add(lhs: FloatTensor<B>, rhs: FloatTensor<B>) -> FloatTensor<B>;

    /// Adds a scalar to a tensor.
    ///
    /// # Arguments
    ///
    /// * `lhs` - The left-hand side tensor.
    /// * `rhs` - The right-hand side scalar.
    ///
    /// # Returns
    ///
    /// The result of adding the scalar to the tensor.
    fn float_add_scalar(lhs: FloatTensor<B>, rhs: Scalar) -> FloatTensor<B>;

    /// Clamps a tensor under a minimum value.
    ///
    /// # Arguments
    ///
    /// * `tensor` - The tensor to clamp.
    /// * `min` - The minimum value.
    ///
    /// # Returns
    ///
    /// The clamped tensor.
    fn float_clamp_min(tensor: FloatTensor<B>, min: Scalar) -> FloatTensor<B> {
        let dtype = get_or_init_device_settings::<B>(&tensor.device()).bool_dtype;
        let mask = Self::float_lower_elem(tensor.clone(), min, dtype);
        B::float_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 float_clamp_max(tensor: FloatTensor<B>, max: Scalar) -> FloatTensor<B> {
        let dtype = get_or_init_device_settings::<B>(&tensor.device()).bool_dtype;
        let mask = Self::float_greater_elem(tensor.clone(), max, dtype);
        B::float_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 float_clamp(tensor: FloatTensor<B>, min: Scalar, max: Scalar) -> FloatTensor<B> {
        // Default implementation
        Self::float_clamp_min(Self::float_clamp_max(tensor, max), min)
    }

    /// Subtracts two tensors.
    ///
    /// # Arguments
    ///
    /// * `lhs` - The left-hand side tensor.
    /// * `rhs` - The right-hand side tensor.
    ///
    /// # Returns
    ///
    /// The result of subtracting the two tensors.
    fn float_sub(lhs: FloatTensor<B>, rhs: FloatTensor<B>) -> FloatTensor<B>;

    /// Subtracts a scalar from a tensor.
    ///
    /// # Arguments
    ///
    /// * `lhs` - The left-hand side tensor.
    /// * `rhs` - The right-hand side scalar.
    ///
    /// # Returns
    ///
    /// The result of subtracting the scalar from the tensor.
    fn float_sub_scalar(lhs: FloatTensor<B>, rhs: Scalar) -> FloatTensor<B>;

    /// Multiplies two tensors together element-wise.
    fn float_mul(lhs: FloatTensor<B>, rhs: FloatTensor<B>) -> FloatTensor<B>;

    /// Multiplies a tensor by a scalar.
    ///
    /// # Arguments
    ///
    /// * `lhs` - The left-hand side tensor.
    /// * `rhs` - The right-hand side scalar.
    ///
    /// # Returns
    ///
    /// The result of multiplying the tensor by the scalar.
    fn float_mul_scalar(lhs: FloatTensor<B>, rhs: Scalar) -> FloatTensor<B>;

    /// Divides two tensors element-wise.
    ///
    /// # Arguments
    ///
    /// * `lhs` - The left-hand side tensor.
    /// * `rhs` - The right-hand side tensor.
    ///
    /// # Returns
    ///
    /// The result of dividing the two tensors.
    fn float_div(lhs: FloatTensor<B>, rhs: FloatTensor<B>) -> FloatTensor<B>;

    /// Divides a tensor by a scalar.
    ///
    /// # Arguments
    ///
    /// * `lhs` - The left-hand side tensor.
    /// * `rhs` - The right-hand side scalar.
    ///
    /// # Returns
    ///
    /// The result of dividing the tensor by the scalar.
    fn float_div_scalar(lhs: FloatTensor<B>, rhs: Scalar) -> FloatTensor<B>;

    /// Computes the remainder of division between two tensors element-wise.
    ///
    /// # Arguments
    ///
    /// * `lhs` - The left-hand side tensor.
    /// * `rhs` - The right-hand side tensor.
    ///
    /// # Returns
    ///
    /// The element-wise remainder when dividing `lhs` by `rhs`.
    fn float_remainder(lhs: FloatTensor<B>, rhs: FloatTensor<B>) -> FloatTensor<B>;

    /// Computes the modulus of a tensor given 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 float_remainder_scalar(lhs: FloatTensor<B>, rhs: Scalar) -> FloatTensor<B>;

    /// Computes the floating-point remainder of dividing `lhs` by `rhs` element-wise.
    ///
    /// Unlike [float_remainder](FloatTensorOps::float_remainder), the result has the same sign
    /// as `lhs`, matching C's `fmod`.
    ///
    /// # Arguments
    ///
    /// * `lhs` - The dividend tensor.
    /// * `rhs` - The divisor tensor.
    ///
    /// # Returns
    ///
    /// The element-wise floating-point remainder.
    fn float_fmod(lhs: FloatTensor<B>, rhs: FloatTensor<B>) -> FloatTensor<B>;

    /// Computes the floating-point remainder of dividing `lhs` by a scalar element-wise.
    ///
    /// The result has the same sign as `lhs`, matching C's `fmod`.
    ///
    /// # Arguments
    ///
    /// * `lhs` - The dividend tensor.
    /// * `rhs` - The divisor scalar.
    ///
    /// # Returns
    ///
    /// The element-wise floating-point remainder.
    fn float_fmod_scalar(lhs: FloatTensor<B>, rhs: Scalar) -> FloatTensor<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 float_matmul(lhs: FloatTensor<B>, rhs: FloatTensor<B>) -> FloatTensor<B>;

    /// Computes the cross product of two tensors along a given dimension.
    ///
    /// # Arguments
    ///
    /// * `lhs` - The left-hand side tensor.
    /// * `rhs` - The right-hand side tensor.
    /// * `dim` - The dimension to compute the cross product along.
    ///
    /// # Returns
    ///
    /// The cross product of the two tensors.
    fn float_cross(lhs: FloatTensor<B>, rhs: FloatTensor<B>, dim: usize) -> FloatTensor<B>;

    /// Negates a tensor element-wise.
    fn float_neg(tensor: FloatTensor<B>) -> FloatTensor<B> {
        Self::float_mul_scalar(tensor, (-1f32).into())
    }

    /// Calculates the reciprocals element-wise
    fn float_recip(tensor: FloatTensor<B>) -> FloatTensor<B>;

    /// Transposes a tensor.
    ///
    /// # Arguments
    ///
    /// * `tensor` - The tensor to transpose.
    ///
    /// # Returns
    ///
    /// The transposed tensor.
    fn float_transpose(tensor: FloatTensor<B>) -> FloatTensor<B> {
        let ndims = tensor.shape().num_dims();
        Self::float_swap_dims(tensor, ndims - 2, ndims - 1)
    }

    /// Swaps two dimensions of a 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 float_swap_dims(tensor: FloatTensor<B>, dim1: usize, dim2: usize) -> FloatTensor<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 float_permute(tensor: FloatTensor<B>, axes: &[usize]) -> FloatTensor<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 float_flip(tensor: FloatTensor<B>, axes: &[usize]) -> FloatTensor<B>;

    /// Reshapes a tensor.
    ///
    /// # Arguments
    ///
    /// * `tensor` - The tensor to reshape.
    /// * `shape` - The new shape of the tensor.
    ///
    /// # Returns
    ///
    /// The tensor with the new shape.
    fn float_reshape(tensor: FloatTensor<B>, shape: Shape) -> FloatTensor<B>;

    /// Gather elements from a tensor.
    ///
    /// # Arguments
    ///
    /// * `dim` - The dimension to gather from.
    /// * `tensor` - The tensor to gather from.
    /// * `indices` - The indices to gather.
    ///
    /// # Returns
    ///
    /// The gathered elements.
    fn float_gather(dim: usize, tensor: FloatTensor<B>, indices: IntTensor<B>) -> FloatTensor<B>;

    /// Scatter elements into a tensor using the specified update operation.
    fn float_scatter(
        dim: usize,
        tensor: FloatTensor<B>,
        indices: IntTensor<B>,
        value: FloatTensor<B>,
        update: IndexingUpdateOp,
    ) -> FloatTensor<B>;

    /// Multi-dimensional scatter: update `data` at locations specified by `indices` with `values`.
    ///
    /// # Arguments
    ///
    /// * `data` - The tensor to scatter into.
    /// * `indices` - An M-dimensional integer tensor whose last dimension indexes into `data`.
    /// * `values` - The values to scatter.
    /// * `reduction` - How to combine with existing values.
    ///
    /// # Returns
    ///
    /// The tensor with scattered values.
    fn float_scatter_nd(
        _data: FloatTensor<B>,
        _indices: IntTensor<B>,
        _values: FloatTensor<B>,
        _reduction: crate::tensor::IndexingUpdateOp,
    ) -> FloatTensor<B> {
        unimplemented!("float_scatter_nd is not implemented for this backend")
    }

    /// Multi-dimensional gather: collect slices from `data` at locations specified by `indices`.
    ///
    /// # Arguments
    ///
    /// * `data` - The tensor to gather from.
    /// * `indices` - An M-dimensional integer tensor whose last dimension indexes into `data`.
    ///
    /// # Returns
    ///
    /// The gathered tensor.
    fn float_gather_nd(_data: FloatTensor<B>, _indices: IntTensor<B>) -> FloatTensor<B> {
        unimplemented!("float_gather_nd is not implemented for this backend")
    }

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

    /// Assign selected elements along a dimension using the specified update operation.
    fn float_select_assign(
        tensor: FloatTensor<B>,
        dim: usize,
        indices: IntTensor<B>,
        value: FloatTensor<B>,
        update: IndexingUpdateOp,
    ) -> FloatTensor<B>;

    /// Select tensor elements corresponding to the given slices.
    ///
    /// # Arguments
    ///
    /// * `tensor` - The tensor to select from.
    /// * `slices` - The slices specifying ranges and steps for each dimension.
    ///
    /// # Returns
    ///
    /// The selected elements in a new tensor.
    ///
    /// # 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 float_slice(tensor: FloatTensor<B>, slices: &[Slice]) -> FloatTensor<B>;

    /// Assign the selected elements corresponding to the given slices to the given value.
    ///
    /// # Arguments
    ///
    /// * `tensor` - The tensor to select from.
    /// * `ranges` - The ranges to select.
    /// * `value` - The value to assign.
    ///
    /// # Returns
    ///
    /// The tensor with the selected elements assigned to the given value.
    ///
    /// # 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 float_slice_assign(
        tensor: FloatTensor<B>,
        slices: &[Slice],
        value: FloatTensor<B>,
    ) -> FloatTensor<B>;

    /// Update the given tensor with the value tensor where the mask is true.
    ///
    /// # Arguments
    ///
    /// * `tensor` - The tensor to select from.
    /// * `mask` - The boolean mask to select with.
    /// * `value` - The value to assign to the selected elements from the value tensor.
    ///
    /// # Returns
    ///
    /// The tensor with the selected elements assigned to the given value.
    fn float_mask_where(
        tensor: FloatTensor<B>,
        mask: BoolTensor<B>,
        value: FloatTensor<B>,
    ) -> FloatTensor<B>;

    /// Update the given tensor with the value where the mask is true.
    ///
    /// # Arguments
    ///
    /// * `tensor` - The tensor to select from.
    /// * `mask` - The boolean mask to select with.
    /// * `value` - The value to assign to the selected elements.
    ///
    /// # Returns
    ///
    /// The tensor with the selected elements assigned to the given value.
    fn float_mask_fill(
        tensor: FloatTensor<B>,
        mask: BoolTensor<B>,
        value: Scalar,
    ) -> FloatTensor<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 float_mask_select(
        tensor: FloatTensor<B>,
        mask: BoolTensor<B>,
    ) -> impl Future<Output = FloatTensor<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_or_init_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::float_reshape(tensor, Shape::new([n]));
            B::float_select(tensor, 0, indices)
        }
    }

    /// Equal comparison of two tensors.
    ///
    /// # Arguments
    ///
    /// * `lhs` - The left-hand side tensor.
    /// * `rhs` - The right-hand side tensor.
    /// * `out_dtype` - The output tensor dtype.
    ///
    /// # Returns
    ///
    /// A boolean tensor with the result of the comparison.
    fn float_equal(lhs: FloatTensor<B>, rhs: FloatTensor<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
    ///
    /// A boolean tensor with the result of the comparison.
    fn float_not_equal(
        lhs: FloatTensor<B>,
        rhs: FloatTensor<B>,
        out_dtype: BoolDType,
    ) -> BoolTensor<B> {
        let equal_tensor = B::float_equal(lhs, rhs, out_dtype);
        B::bool_not(equal_tensor)
    }

    /// Equal comparison of a tensor and a scalar.
    ///
    /// # Arguments
    ///
    /// * `lhs` - The left-hand side tensor.
    /// * `rhs` - The right-hand side scalar.
    /// * `out_dtype` - The output tensor dtype.
    ///
    /// # Returns
    ///
    /// A boolean tensor with the result of the comparison.
    fn float_equal_elem(lhs: FloatTensor<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
    ///
    /// A boolean tensor with the result of the comparison.
    fn float_not_equal_elem(
        lhs: FloatTensor<B>,
        rhs: Scalar,
        out_dtype: BoolDType,
    ) -> BoolTensor<B> {
        let equal_tensor = B::float_equal_elem(lhs, rhs, out_dtype);
        B::bool_not(equal_tensor)
    }

    /// Greater than comparison of two tensors.
    ///
    /// # Arguments
    ///
    /// * `lhs` - The left-hand side tensor.
    /// * `rhs` - The right-hand side tensor.
    /// * `out_dtype` - The output tensor dtype.
    ///
    /// # Returns
    ///
    /// A boolean tensor with the result of the comparison.
    fn float_greater(
        lhs: FloatTensor<B>,
        rhs: FloatTensor<B>,
        out_dtype: BoolDType,
    ) -> BoolTensor<B>;

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

    /// Greater than or equal comparison of two tensors.
    ///
    /// # Arguments
    ///
    /// * `lhs` - The left-hand side tensor.
    /// * `rhs` - The right-hand side tensor.
    /// * `out_dtype` - The output tensor dtype.
    ///
    /// # Returns
    ///
    /// A boolean tensor with the result of the comparison.
    fn float_greater_equal(
        lhs: FloatTensor<B>,
        rhs: FloatTensor<B>,
        out_dtype: BoolDType,
    ) -> BoolTensor<B>;

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

    /// Less than comparison of two tensors.
    ///
    /// # Arguments
    ///
    /// * `lhs` - The left-hand side tensor.
    /// * `rhs` - The right-hand side tensor.
    /// * `out_dtype` - The output tensor dtype.
    ///
    /// # Returns
    ///
    /// A boolean tensor with the result of the comparison.
    fn float_lower(lhs: FloatTensor<B>, rhs: FloatTensor<B>, out_dtype: BoolDType)
    -> BoolTensor<B>;

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

    /// Less than or equal comparison of two tensors.
    ///
    /// # Arguments
    ///
    /// * `lhs` - The left-hand side tensor.
    /// * `rhs` - The right-hand side tensor.
    /// * `out_dtype` - The output tensor dtype.
    ///
    /// # Returns
    ///
    /// A boolean tensor with the result of the comparison.
    fn float_lower_equal(
        lhs: FloatTensor<B>,
        rhs: FloatTensor<B>,
        out_dtype: BoolDType,
    ) -> BoolTensor<B>;

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

    /// Detaches a tensor from the computation graph.
    fn float_detach(tensor: FloatTensor<B>) -> FloatTensor<B> {
        // Should only be overridden by autodiff backends.
        tensor
    }

    /// Sets the `require_grad` flag of a tensor.
    fn float_set_require_grad(tensor: FloatTensor<B>, _require_grad: bool) -> FloatTensor<B> {
        // Should only be overridden by autodiff backends.
        tensor
    }

    /// Returns the `require_grad` flag of a tensor.
    fn float_is_require_grad(_tensor: &FloatTensor<B>) -> bool {
        // Should only be overridden by autodiff backends.
        false
    }

    /// Sum of all elements in a tensor.
    ///
    /// # Arguments
    ///
    /// * `tensor` - The tensor to sum.
    ///
    /// # Returns
    ///
    /// A scalar tensor with the sum of all elements in `tensor`.
    fn float_sum(tensor: FloatTensor<B>) -> FloatTensor<B>;

    /// Sum of all elements in a tensor along a dimension.
    ///
    /// # Arguments
    ///
    /// * `tensor` - The tensor to sum.
    /// * `dim` - The dimension along which to sum.
    ///
    /// # Returns
    ///
    /// A tensor with the sum of all elements in `tensor` along `dim`.
    fn float_sum_dim(tensor: FloatTensor<B>, dim: usize) -> FloatTensor<B>;

    /// Sum the tensor along several dimensions at once, keeping each of them
    /// with length one.
    ///
    /// # Arguments
    ///
    /// * `tensor` - The tensor to sum.
    /// * `dims` - The dimensions along which to sum.
    ///
    /// # Returns
    ///
    /// A tensor with the same rank, and length one along each of `dims`.
    ///
    /// The default reduces one dimension at a time, which writes and reads
    /// back an intermediate per dimension. A backend that can fold the
    /// dimensions into fewer reductions should override this.
    fn float_sum_dims(tensor: FloatTensor<B>, dims: &[usize]) -> FloatTensor<B> {
        dims.iter()
            .fold(tensor, |tensor, &dim| B::float_sum_dim(tensor, dim))
    }

    /// Product of all elements in a tensor.
    ///
    /// # Arguments
    ///
    /// * `tensor` - The tensor to product.
    ///
    /// # Returns
    ///
    /// A scalar tensor with the product of all elements in `tensor`.
    fn float_prod(tensor: FloatTensor<B>) -> FloatTensor<B> {
        // Product of all elements in a tensor
        B::float_exp(B::float_sum(B::float_log(tensor)))
    }

    /// Product of all elements in a tensor along a dimension.
    ///
    /// # Arguments
    ///
    /// * `tensor` - The tensor to product.
    ///
    /// # Returns
    ///
    /// A tensor with the product of all elements in `tensor` along `dim`.
    fn float_prod_dim(tensor: FloatTensor<B>, dim: usize) -> FloatTensor<B> {
        // Product of all elements in a tensor along a dimension
        B::float_exp(B::float_sum_dim(B::float_log(tensor), dim))
    }

    /// Mean of all elements in a tensor.
    ///
    /// # Arguments
    ///
    /// * `tensor` - The tensor to mean.
    ///
    /// # Returns
    ///
    /// A scalar tensor with the mean of all elements in `tensor`.
    fn float_mean(tensor: FloatTensor<B>) -> FloatTensor<B> {
        let num_elems = tensor.shape().num_elements() as f32;
        B::float_div_scalar(B::float_sum(tensor), num_elems.into())
    }

    /// Mean of all elements in a tensor along a dimension.
    ///
    /// # Arguments
    ///
    /// * `tensor` - The tensor to mean.
    /// * `dim` - The dimension along which to mean.
    ///
    /// # Returns
    ///
    /// A tensor with the mean of all elements in `tensor` along `dim`.
    fn float_mean_dim(tensor: FloatTensor<B>, dim: usize) -> FloatTensor<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 float_cumsum(tensor: FloatTensor<B>, dim: usize) -> FloatTensor<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 float_cumprod(tensor: FloatTensor<B>, dim: usize) -> FloatTensor<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 float_cummin(tensor: FloatTensor<B>, dim: usize) -> FloatTensor<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 float_cummax(tensor: FloatTensor<B>, dim: usize) -> FloatTensor<B>;

    /// Converts a tensor to another floating point 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 floating point data type.
    fn float_cast(tensor: FloatTensor<B>, dtype: FloatDType) -> FloatTensor<B>;

    /// Returns a new tensor with exponential values.
    ///
    /// # Arguments
    ///
    /// * `tensor` - The tensor to exponentiate.
    ///
    /// # Returns
    ///
    /// A tensor with the same shape as `tensor` with exponential values.
    fn float_exp(tensor: FloatTensor<B>) -> FloatTensor<B>;

    /// Returns a new tensor with natural logarithm values.
    ///
    /// # Arguments
    ///
    /// * `tensor` - The tensor to take the logarithm of.
    ///
    /// # Returns
    ///
    /// A tensor with the same shape as `tensor` with natural logarithm values.
    fn float_log(tensor: FloatTensor<B>) -> FloatTensor<B>;

    /// Returns a new tensor with logarithm values of (1 + Xi).
    ///
    /// # Arguments
    ///
    /// * `tensor` - The tensor to take the logarithm of.
    ///
    /// # Returns
    ///
    /// A tensor with the same shape as `tensor` with logarithm values of (1 + Xi).
    fn float_log1p(tensor: FloatTensor<B>) -> FloatTensor<B>;

    /// Element-wise power with a FloatTensor.
    ///
    /// # Arguments
    ///
    /// * `lhs` - The left-hand side tensor.
    /// * `rhs` - The right-hand side tensor.
    ///
    /// # Returns
    ///
    /// The elements of `lhs` raised to the power of the elements of `rhs`.
    fn float_powf(lhs: FloatTensor<B>, rhs: FloatTensor<B>) -> FloatTensor<B>;

    /// Element-wise power with an IntTensor.
    ///
    /// # Arguments
    ///
    /// * `lhs` - The left-hand side tensor.
    /// * `rhs` - The right-hand side floatTensor.
    ///
    /// # Returns
    ///
    /// The elements of `lhs` raised to the value of `rhs`. Result is an IntTensor.
    fn float_powi(lhs: FloatTensor<B>, rhs: IntTensor<B>) -> FloatTensor<B> {
        let dtype = lhs.dtype();
        Self::float_powf(lhs, B::int_into_float(rhs, dtype.into()))
    }

    /// Raises a tensor to the power of an int 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::float_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 float_powi_scalar(lhs: FloatTensor<B>, rhs: Scalar) -> FloatTensor<B> {
        match rhs.elem::<i64>() {
            0 => Self::float_ones(lhs.shape(), &lhs.device(), lhs.dtype().into()),
            1 => lhs,
            2 => B::float_mul(lhs.clone(), lhs),
            -1 => Self::float_recip(lhs),
            -2 => Self::float_recip(B::float_mul(lhs.clone(), lhs)),
            _ => Self::float_powi_scalar_impl(lhs, rhs),
        }
    }

    /// Raises a tensor to the power of an int scalar.
    ///
    /// # Backend Implementors Note
    ///
    /// This is the generic implementation of integer exponentiation
    /// called by [`Self::float_powi_scalar`] in the fallback case.
    ///
    /// 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 float_powi_scalar_impl(lhs: FloatTensor<B>, rhs: Scalar) -> FloatTensor<B> {
        // Avoid a recursive loop by deferring directly to float_powf_scalar_impl.
        Self::float_powf_scalar_impl(lhs, rhs)
    }

    /// Returns a new tensor with values raised to the power of float `value`.
    ///
    /// # Backend Implementors Note
    ///
    /// This (`Backend` impl overridable) operation dispatches integer exponentiation
    /// to [`Self::float_powi_scalar`], and the remaining non-integer exponent cases to
    /// the (`Backend` impl overridable) [`Self::float_powf_scalar_impl`]
    /// operation to handle the generic case.
    ///
    /// # Arguments
    ///
    /// * `tensor` - The tensor to exponentiate.
    /// * `value` - The exponent.
    ///
    /// # Returns
    ///
    /// A tensor with the same shape as `tensor` with values raised to the power of `value`.
    fn float_powf_scalar(tensor: FloatTensor<B>, value: Scalar) -> FloatTensor<B> {
        if let Some(exp) = value.try_as_integer() {
            Self::float_powi_scalar(tensor, exp)
        } else {
            Self::float_powf_scalar_impl(tensor, value)
        }
    }

    /// Returns a new tensor with values raised to the power of float `value`.
    ///
    /// # Backend Implementors Note
    ///
    /// This is the generic implementation of integer exponentiation
    /// called by [`Self::float_powf_scalar`] in the fallback case.
    ///
    /// This is the minimal required support a `Backend` must implement
    /// for exponentiation.
    ///
    /// As a general rule, this should not be called directly.
    ///
    /// # Arguments
    ///
    /// * `tensor` - The tensor to exponentiate.
    /// * `value` - The exponent.
    ///
    /// # Returns
    ///
    /// A tensor with the same shape as `tensor` with values raised to the power of `value`.
    fn float_powf_scalar_impl(tensor: FloatTensor<B>, value: Scalar) -> FloatTensor<B>;

    /// Returns a new tensor with square root values.
    ///
    /// # Arguments
    ///
    /// * `tensor` - The tensor to take the square root of.
    ///
    /// # Returns
    ///
    /// A tensor with the same shape as `tensor` with square root values.
    fn float_sqrt(tensor: FloatTensor<B>) -> FloatTensor<B>;

    /// Returns a new tensor with the Euclidean distance values.
    ///
    /// # Arguments
    ///
    /// * `lhs` - The left-hand side tensor.
    /// * `rhs` - The right-hand side tensor.
    ///
    /// # Returns
    ///
    /// A tensor with the same shape as `lhs` and `rhs` with hypotenuse values.
    fn float_hypot(lhs: FloatTensor<B>, rhs: FloatTensor<B>) -> FloatTensor<B> {
        // default implementation for any backend that can't either iterator over elements or doesn't have
        // a native hypot implementation

        // Mirrors glibc's approach: scale by max(|lhs|, |rhs|) to avoid
        // overflow/underflow in the intermediate squaring step.
        //
        // hypot(x, y) = |max| * sqrt(1 + (min/max)^2)
        //
        // Edge cases:
        //   - If max == 0, both inputs are 0, result is 0 (division guarded by clamp)
        //   - If max is inf, result is inf (propagates naturally through sqrt)
        //   - NaN propagates naturally
        let abs_lhs = B::float_abs(lhs);
        let abs_rhs = B::float_abs(rhs);

        let diff = B::float_clamp_min(B::float_sub(abs_rhs.clone(), abs_lhs.clone()), 0.0.into());
        let max = B::float_add(abs_lhs.clone(), diff.clone());
        let min = B::float_sub(abs_rhs, diff);

        // Clamp max to at least epsilon to avoid 0/0; result will be 0 anyway
        // since min <= max, so (min/clamped_max)^2 won't blow up meaningfully.
        let max_safe = B::float_clamp_min(
            max.clone(),
            max.dtype().finfo().unwrap().min_positive.into(),
        );

        let ratio = B::float_div(min, max_safe);
        let ratio_sq = B::float_mul(ratio.clone(), ratio);

        let inner = B::float_add_scalar(ratio_sq, 1.0.into());

        B::float_mul(max, B::float_sqrt(inner))
    }

    /// 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 float_abs(tensor: FloatTensor<B>) -> FloatTensor<B>;

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

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

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

    /// Returns a new tensor with hyperbolic cosine values.
    ///
    /// # Arguments
    ///
    /// * `tensor` - The tensor to take the hyperbolic cosine of.
    ///
    /// # Returns
    ///
    /// A tensor with the same shape as `tensor` with hyperbolic cosine values.
    fn float_cosh(tensor: FloatTensor<B>) -> FloatTensor<B>;

    /// Returns a new tensor with hyperbolic sine values.
    ///
    /// # Arguments
    ///
    /// * `tensor` - The tensor to take the hyperbolic sine of.
    ///
    /// # Returns
    ///
    /// A tensor with the same shape as `tensor` with hyperbolic sine values.
    fn float_sinh(tensor: FloatTensor<B>) -> FloatTensor<B>;

    /// Returns a new tensor with hyperbolic tangent values.
    ///
    /// # Arguments
    ///
    /// * `tensor` - The tensor to take the hyperbolic tangent of.
    ///
    /// # Returns
    ///
    /// A tensor with the same shape as `tensor` with hyperbolic tangent values.
    fn float_tanh(tensor: FloatTensor<B>) -> FloatTensor<B>;

    /// Returns a new tensor with inverse cosine values.
    ///
    /// # Arguments
    ///
    /// * `tensor` - The input tensor.
    ///
    /// # Returns
    ///
    /// A tensor with the same shape as `tensor` with inverse cosine values.
    fn float_acos(tensor: FloatTensor<B>) -> FloatTensor<B>;

    /// Returns a new tensor with inverse hyperbolic cosine values.
    ///
    /// # Arguments
    ///
    /// * `tensor` - The input tensor.
    ///
    /// # Returns
    ///
    /// A tensor with the same shape as `tensor` with inverse hyperbolic cosine values.
    fn float_acosh(tensor: FloatTensor<B>) -> FloatTensor<B>;

    /// Returns a new tensor with inverse sine values.
    ///
    /// # Arguments
    ///
    /// * `tensor` - The input tensor.
    ///
    /// # Returns
    ///
    /// A tensor with the same shape as `tensor` with inverse sine values.
    fn float_asin(tensor: FloatTensor<B>) -> FloatTensor<B>;

    /// Returns a new tensor with inverse hyperbolic sine values.
    ///
    /// # Arguments
    ///
    /// * `tensor` - The input tensor.
    ///
    /// # Returns
    ///
    /// A tensor with the same shape as `tensor` with inverse hyperbolic sine values.
    fn float_asinh(tensor: FloatTensor<B>) -> FloatTensor<B>;

    /// Returns a new tensor with the inverse tangent values.
    ///
    /// # Arguments
    ///
    /// * `tensor` - The input tensor.
    ///
    /// # Returns
    ///
    /// A tensor with the same shape as `tensor` with the inverse tangent values.
    fn float_atan(tensor: FloatTensor<B>) -> FloatTensor<B>;

    /// Returns a new tensor with the inverse hyperbolic tangent values.
    ///
    /// # Arguments
    ///
    /// * `tensor` - The input tensor.
    ///
    /// # Returns
    ///
    /// A tensor with the same shape as `tensor` with the inverse hyperbolic tangent values.
    fn float_atanh(tensor: FloatTensor<B>) -> FloatTensor<B>;

    /// Returns a tensor with the four-quadrant inverse tangent values of `y` and `x`.
    ///
    /// # Arguments
    ///
    /// * `lhs` - The tensor with y coordinates.
    /// * `rhs` - The tensor with x coordinates.
    ///
    /// # Returns
    ///
    /// A tensor with the four-quadrant inverse tangent values.
    fn float_atan2(lhs: FloatTensor<B>, rhs: FloatTensor<B>) -> FloatTensor<B>;

    /// Returns a new tensor with rounded values.
    ///
    /// This function should implement the [round half to even](https://en.wikipedia.org/wiki/Rounding#Rounding_half_to_even)
    /// strategy, with halfway cases rounded to the nearest even integer value.
    ///
    /// # Arguments
    ///
    /// * `tensor` - The tensor to be rounded.
    ///
    /// # Returns
    ///
    /// A tensor with the same shape as `tensor` with rounded values.
    fn float_round(tensor: FloatTensor<B>) -> FloatTensor<B>;

    /// Returns a new tensor with floored values.
    ///
    /// # Arguments
    ///
    /// * `tensor` - The tensor to be floored.
    ///
    /// # Returns
    ///
    /// A tensor with the same shape as `tensor` with floored values.
    fn float_floor(tensor: FloatTensor<B>) -> FloatTensor<B>;

    /// Returns a new tensor with ceiled values.
    ///
    /// # Arguments
    ///
    /// * `tensor` - The tensor to be ceiled.
    ///
    /// # Returns
    ///
    /// A tensor with the same shape as `tensor` with ceiled values.
    fn float_ceil(tensor: FloatTensor<B>) -> FloatTensor<B>;

    /// Returns a new tensor with truncated values.
    ///
    /// # Arguments
    ///
    /// * `tensor` - The tensor to be truncated.
    ///
    /// # Returns
    ///
    /// A tensor with the same shape as `tensor` with truncated values.
    fn float_trunc(tensor: FloatTensor<B>) -> FloatTensor<B>;

    /// Returns a new tensor with the error function values.
    ///
    /// # Arguments
    ///
    /// * `tensor` - The tensor to take the error function of.
    ///
    /// # Returns
    ///
    /// A tensor with the same shape as `tensor` with error function values.
    fn float_erf(tensor: FloatTensor<B>) -> FloatTensor<B>;

    /// Concatenates tensors along a dimension.
    ///
    /// # Arguments
    ///
    /// * `tensors` - The tensors to concatenate.
    /// * `dim` - The dimension along which to concatenate.
    ///
    /// # Returns
    ///
    /// A tensor with the concatenated tensors along `dim`.
    ///
    /// # 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 float_cat(tensors: Vec<FloatTensor<B>>, dim: usize) -> FloatTensor<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::float_empty(shape, device, dtype.into()),
            B::float_slice_assign,
        )
    }

    /// Gets the indices of the maximum elements of a tensor along an axis.
    ///
    /// # Arguments
    ///
    /// * `tensor` - The tensor to get the maximum elements of.
    /// * `dim` - The dimension along which to get the maximum elements.
    /// * `out_dtype` - The output tensor dtype.
    ///
    /// # Returns
    ///
    /// A tensor with the indices of the maximum elements of `tensor` along `dim`.
    fn float_argmax(tensor: FloatTensor<B>, dim: usize, out_dtype: IntDType) -> IntTensor<B>;

    /// Gets the indices of the k maximum elements of a tensor along an axis.
    /// if two elements are equals, it will be ordered by lowest indices
    ///
    /// # Arguments
    ///
    /// * `tensor` - The tensor to get the maximum elements of.
    /// * `dim` - The dimension along which to get the maximum elements.
    /// * `k` - number of maximum elements
    /// * `out_dtype` - The output tensor dtype.
    ///
    /// # Returns
    ///
    /// A tensor with the indices of the maximum elements of `tensor` along `dim`.
    fn float_argtopk(
        tensor: FloatTensor<B>,
        dim: usize,
        k: usize,
        out_dtype: IntDType,
    ) -> IntTensor<B> {
        let device = tensor.device();
        let dtype = get_or_init_device_settings::<B>(&device).int_dtype;
        let k_indices = B::int_arange(0..k as i64, &device, dtype);
        B::int_select(
            Self::float_argsort(tensor, dim, true, out_dtype),
            dim,
            k_indices,
        )
    }

    /// Gets the values of the k maximum elements of a tensor along an axis.
    ///
    /// # Arguments
    ///
    /// * `tensor` - The tensor to get the maximum elements of.
    /// * `dim` - The dimension along which to get the maximum elements.
    /// * `k` - number of maximum elements
    /// * `out_dtype` - The output tensor dtype.
    ///
    /// # Returns
    ///
    /// A tensor with the values of the maximum elements of `tensor` along `dim`.
    fn float_topk(tensor: FloatTensor<B>, dim: usize, k: usize) -> FloatTensor<B> {
        let device = tensor.device();
        let dtype = get_or_init_device_settings::<B>(&device).int_dtype;
        let k_indices = B::int_arange(0..k as i64, &device, dtype);
        Self::float_select(Self::float_sort(tensor, dim, true), dim, k_indices)
    }

    /// Gets the values of the k maximum elements of a tensor along an axis, and their indices.
    ///
    /// # Arguments
    ///
    /// * `tensor` - The tensor to get the maximum elements of.
    /// * `dim` - The dimension along which to get the maximum elements.
    /// * `k` - number of maximum elements
    /// * `out_dtype` - The indices tensor dtype.
    ///
    /// # Returns
    ///
    /// A tuple with the values of the k maximum elements of `tensor` along `dim`, and their
    /// indices.
    ///
    /// The default sorts once and keeps the first `k` of each half. It deliberately does not
    /// compose `float_topk` with `float_argtopk`: those default to a sort each, so that would
    /// sort twice, and it would also require `float_argtopk` from backends that only have
    /// sorting. Backends whose top-k already carries both results should override this and
    /// produce them in a single pass.
    fn float_topk_with_indices(
        tensor: FloatTensor<B>,
        dim: usize,
        k: usize,
        out_dtype: IntDType,
    ) -> (FloatTensor<B>, IntTensor<B>) {
        let device = tensor.device();
        let dtype = get_or_init_device_settings::<B>(&device).int_dtype;
        let k_indices = B::int_arange(0..k as i64, &device, dtype);
        let (values, indices) = Self::float_sort_with_indices(tensor, dim, true, out_dtype);

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

    /// Gets the indices of the minimum elements of a tensor along an axis.
    ///
    /// # Arguments
    ///
    /// * `tensor` - The tensor to get the minimum elements of.
    /// * `dim` - The dimension along which to get the minimum elements.
    /// * `out_dtype` - The output tensor dtype.
    ///
    /// # Returns
    ///
    /// A tensor with the indices of the minimum elements of `tensor` along `dim`.
    fn float_argmin(tensor: FloatTensor<B>, dim: usize, out_dtype: IntDType) -> IntTensor<B>;

    /// Gets the maximum element of a tensor.
    ///
    /// # Arguments
    ///
    /// * `tensor` - The tensor to get the maximum elements of.
    ///
    /// # Returns
    ///
    /// A tensor with the maximum element of `tensor`.
    fn float_max(tensor: FloatTensor<B>) -> FloatTensor<B> {
        let shape = tensor.shape();
        let tensor = B::float_reshape(tensor, Shape::new([shape.num_elements()]));

        B::float_max_dim(tensor, 0)
    }

    /// Gets the maximum elements of a tensor along an axis.
    ///
    /// # Arguments
    ///
    /// * `tensor` - The tensor to get the maximum elements of.
    /// * `dim` - The dimension along which to get the maximum elements.
    ///
    /// # Returns
    ///
    /// A tensor with the maximum elements of `tensor` along `dim`.
    fn float_max_dim(tensor: FloatTensor<B>, dim: usize) -> FloatTensor<B> {
        let dtype = get_or_init_device_settings::<B>(&tensor.device()).int_dtype;
        let index = B::float_argmax(tensor.clone(), dim, dtype);

        B::float_gather(dim, tensor, index)
    }

    /// Gets the maximum elements of a tensor along an axis and their indices.
    ///
    /// # Arguments
    ///
    /// * `tensor` - The tensor to get the maximum elements of.
    /// * `dim` - The dimension along which to get the maximum elements.
    /// * `indices_dtype` - The indices tensor dtype.
    ///
    /// # Returns
    ///
    /// A tuple with the maximum elements of `tensor` along `dim` and their indices.
    fn float_max_dim_with_indices(
        tensor: FloatTensor<B>,
        dim: usize,
        indices_dtype: IntDType,
    ) -> (FloatTensor<B>, IntTensor<B>) {
        let index = B::float_argmax(tensor.clone(), dim, indices_dtype);
        let values = B::float_gather(dim, tensor, index.clone());

        (values, index)
    }

    /// Gets the minimum element of a tensor.
    ///
    /// # Arguments
    ///
    /// * `tensor` - The tensor to get the minimum elements of.
    ///
    /// # Returns
    ///
    /// A tensor with the minimum element of `tensor`.
    fn float_min(tensor: FloatTensor<B>) -> FloatTensor<B> {
        let shape = tensor.shape();
        let tensor = B::float_reshape(tensor, Shape::new([shape.num_elements()]));

        B::float_min_dim(tensor, 0)
    }

    /// Gets the minimum elements of a tensor along an axis.
    ///
    /// # Arguments
    ///
    /// * `tensor` - The tensor to get the minimum elements of.
    /// * `dim` - The dimension along which to get the minimum elements.
    ///
    /// # Returns
    ///
    /// A tensor with the minimum elements of `tensor` along `dim`.
    fn float_min_dim(tensor: FloatTensor<B>, dim: usize) -> FloatTensor<B> {
        let dtype = get_or_init_device_settings::<B>(&tensor.device()).int_dtype;
        let index = B::float_argmin(tensor.clone(), dim, dtype);

        B::float_gather(dim, tensor, index)
    }

    /// Gets the minimum elements of a tensor along an axis and their indices.
    ///
    /// # Arguments
    ///
    /// * `tensor` - The tensor to get the minimum elements of.
    /// * `dim` - The dimension along which to get the minimum elements.
    /// * `indices_dtype` - The indices tensor dtype.
    ///
    /// # Returns
    ///
    /// A tuple with the minimum elements of `tensor` along `dim` and their indices.
    fn float_min_dim_with_indices(
        tensor: FloatTensor<B>,
        dim: usize,
        indices_dtype: IntDType,
    ) -> (FloatTensor<B>, IntTensor<B>) {
        let index = B::float_argmin(tensor.clone(), dim, indices_dtype);
        let values = B::float_gather(dim, tensor, index.clone());

        (values, index)
    }

    /// Gets the maximum absolute element of a tensor.
    ///
    /// # Arguments
    ///
    /// * `tensor` - The tensor to get the maximum elements of.
    ///
    /// # Returns
    ///
    /// A tensor with the maximum element of `tensor`.
    fn float_max_abs(tensor: FloatTensor<B>) -> FloatTensor<B> {
        let shape = tensor.shape();
        let tensor = B::float_reshape(tensor, Shape::new([shape.num_elements()]));

        B::float_max_abs_dim(tensor, 0)
    }

    /// Gets the maximum absolute elements of a tensor along an axis.
    ///
    /// # Arguments
    ///
    /// * `tensor` - The tensor to get the maximum elements of.
    /// * `dim` - The dimension along which to get the maximum elements.
    ///
    /// # Returns
    ///
    /// A tensor with the maximum elements of `tensor` along `dim`.
    fn float_max_abs_dim(tensor: FloatTensor<B>, dim: usize) -> FloatTensor<B> {
        B::float_max_dim(B::float_abs(tensor), dim)
    }

    /// Tests if any element in the float `tensor` evaluates to True.
    ///
    /// # Arguments
    ///
    /// * `tensor` - The tensor to test.
    /// * `out_dtype` - The output tensor dtype.
    ///
    /// # Returns
    ///
    /// A boolean tensor with a single element, True if any element in the tensor is True, False otherwise.
    fn float_any(tensor: FloatTensor<B>, out_dtype: BoolDType) -> BoolTensor<B> {
        let float_dtype = tensor.dtype();
        let bool_tensor = B::float_equal_elem(tensor, 0f32.into(), out_dtype);
        let bool_tensor = B::bool_not(bool_tensor);
        let sum = B::float_sum(B::bool_into_float(bool_tensor, float_dtype.into()));
        B::float_greater_elem(sum, 0f32.into(), out_dtype)
    }

    /// Tests if any element in the float `tensor` evaluates 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 any element along this dim in the
    /// input evaluates to True, False otherwise.
    fn float_any_dim(tensor: FloatTensor<B>, dim: usize, out_dtype: BoolDType) -> BoolTensor<B> {
        let float_dtype = tensor.dtype();
        let bool_tensor = B::float_equal_elem(tensor, 0f32.into(), out_dtype);
        let bool_tensor = B::bool_not(bool_tensor);
        let sum = B::float_sum_dim(B::bool_into_float(bool_tensor, float_dtype.into()), dim);
        B::float_greater_elem(sum, 0f32.into(), out_dtype)
    }

    /// Tests if all elements in the float `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 float_all(tensor: FloatTensor<B>, out_dtype: BoolDType) -> BoolTensor<B> {
        let float_dtype = tensor.dtype();
        let num_elems = tensor.shape().num_elements() as f32;
        let bool_tensor = B::float_equal_elem(tensor, 0f32.into(), out_dtype);
        let bool_tensor = B::bool_not(bool_tensor);
        let sum = B::float_sum(B::bool_into_float(bool_tensor, float_dtype.into()));
        B::float_equal_elem(sum, num_elems.into(), out_dtype)
    }

    /// Tests if all elements in the float `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 float_all_dim(tensor: FloatTensor<B>, dim: usize, out_dtype: BoolDType) -> BoolTensor<B> {
        let float_dtype = tensor.dtype();
        let num_elems = tensor.shape()[dim] as f32;
        let bool_tensor = B::float_equal_elem(tensor, 0f32.into(), out_dtype);
        let bool_tensor = B::bool_not(bool_tensor);
        let sum = B::float_sum_dim(B::bool_into_float(bool_tensor, float_dtype.into()), dim);
        B::float_equal_elem(sum, num_elems.into(), out_dtype)
    }

    /// Returns the signs of the float `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`:
    /// `1` where positive, `-1` where negative, and `0` where zero (either sign) or NaN.
    ///
    /// `sign(NaN) == 0` is part of this contract and every backend override must uphold it too.
    fn float_sign(tensor: FloatTensor<B>) -> FloatTensor<B> {
        let device = tensor.device();
        let bool_dtype = get_or_init_device_settings::<B>(&tensor.device()).bool_dtype;
        let zeros = B::float_zeros(tensor.shape(), &device, tensor.dtype().into());
        let less_than_zero = B::float_lower_elem(tensor.clone(), 0f32.into(), bool_dtype);
        let greater_than_zero = B::float_greater_elem(tensor, 0f32.into(), bool_dtype);

        let mut result = B::float_mask_fill(zeros, less_than_zero, (-1f32).into());
        result = B::float_mask_fill(result, greater_than_zero, 1f32.into());
        result
    }

    /// Broadcasts the float `tensor` to the given `shape`.
    fn float_expand(tensor: FloatTensor<B>, shape: Shape) -> FloatTensor<B>;

    /// Sort the elements of the input `tensor` by value in 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 float_sort(tensor: FloatTensor<B>, dim: usize, descending: bool) -> FloatTensor<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::float_into_data(tensor))
                    .expect(msg)
                    .expect(msg)
            },
            |data, device, _dtype| B::float_from_data(data, device),
        )
    }

    /// Sort the elements of the input `tensor` by value in 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.
    /// * `indices_dtype` - The indices tensor dtype.
    ///
    /// # 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 float_sort_with_indices(
        tensor: FloatTensor<B>,
        dim: usize,
        descending: bool,
        indices_dtype: IntDType,
    ) -> (FloatTensor<B>, IntTensor<B>) {
        let device = tensor.device();
        sort_with_indices::<B, _, _, _>(
            tensor,
            dim,
            descending,
            indices_dtype,
            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::float_into_data(tensor))
                    .expect(msg)
                    .expect(msg)
            },
            |data, device, _dtype| B::float_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.
    /// * `out_dtype` - The output tensor dtype.
    ///
    /// # Returns
    ///
    /// A tensor with the same shape as the input tensor the indices map back to the original input tensor.
    fn float_argsort(
        tensor: FloatTensor<B>,
        dim: usize,
        descending: bool,
        out_dtype: IntDType,
    ) -> IntTensor<B> {
        let device = tensor.device();
        argsort::<B, _, _>(tensor, dim, descending, out_dtype, 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::float_into_data(tensor))
                .expect(msg)
                .expect(msg)
        })
    }

    /// Samples tensor as a two-dimensional spatial grid of (possibly multi-channel) values,
    /// using the given locations in [-1, 1].
    ///
    /// # Arguments
    ///
    /// * `tensor` - The tensor being sampled from, must be contiguous with shape (N, C, H_in, W_in)
    /// * `grid` - A tensor of locations, with shape (N, H_out, W_out, 2). Values are [-1, 1].
    ///   A [x = -1, y = -1] means top-left, and [x = 1, y = 1] means bottom-right
    /// * `options` - Grid sampling options (mode, padding_mode, align_corners)
    ///
    /// # Returns
    ///
    /// A tensor with shape (N, C, H_out, W_out)
    fn float_grid_sample_2d(
        tensor: FloatTensor<B>,
        grid: FloatTensor<B>,
        options: GridSampleOptions,
    ) -> FloatTensor<B> {
        // TODO: default impl should get int default dtype
        float_grid_sample_2d_ref::<B>(tensor, grid, options)
    }

    /// 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 `0` when `shape[dim] < size`, and otherwise
    /// `(shape[dim] - size) / step + 1`.
    ///
    /// # 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 float_unfold(tensor: FloatTensor<B>, dim: usize, size: usize, step: usize)
    -> FloatTensor<B>;

    /// Returns a new tensor with boolean elements indicating whether each element of the input is NaN.
    ///
    /// # Returns
    ///
    /// A boolean tensor where `true` indicates NaN and `false` indicates a non-NaN value.
    fn float_is_nan(tensor: FloatTensor<B>, out_dtype: BoolDType) -> BoolTensor<B> {
        // Check if the input tensor is NaN by comparing it to itself
        // NaN is the only value that is not equal to itself
        B::float_not_equal(tensor.clone(), tensor, out_dtype)
    }

    /// Returns a new tensor with boolean elements indicating whether each element of the input is infinite (either +INF or -INF).
    ///
    /// # Returns
    ///
    /// A boolean tensor where `true` indicates that the value is infinite
    fn float_is_inf(tensor: FloatTensor<B>, out_dtype: BoolDType) -> BoolTensor<B> {
        B::float_equal_elem(B::float_abs(tensor), f64::INFINITY.into(), out_dtype)
    }

    /// Pads a tensor with one `(before, after)` pair per dimension.
    fn float_pad(
        tensor: FloatTensor<B>,
        padding: &[(usize, usize)],
        mode: PadMode,
    ) -> FloatTensor<B> {
        super::pad::float_pad::<B>(tensor, padding, mode)
    }
}