Mathematical Utilities for Caffe2 Operator Library in Rust
---

This crate provides a collection of mathematical
utilities and functions for the Caffe2 Operator
Library, written in Rust. The crate is in the
process of being translated from C++ to Rust, and
some function bodies may be in the process of
translation.

This crate features a variety of functions and
structures that handle mathematical operations and
data manipulation. The naming convention used is
snake_case for functions, and CamelCase for
structs and enums.

Here are some of the mathematical ideas and
equations that can be found in this crate:

1. `both_ends_moments`, `colwise_moments`, and
   `rowwise_moments`: These functions compute the
   moments of a given tensor along different axes
   (both ends, column-wise, and row-wise). Moments
   are measures of the distribution shape, where
   the first moment is the mean (µ), and the
   second moment is the variance (σ²).

    µ = Σ(x) / N
    σ² = Σ(x - µ)² / N

2. `reduceL1` and `reduceL2`: These functions
   calculate the L1 and L2 norms of a given
   tensor, respectively. The L1 norm is the sum of
   the absolute values of the elements, and the L2
   norm is the square root of the sum of the
   squared elements.

    L1 = Σ|x|
    L2 = √(Σx²)

3. `reduce_max`, `reduce_min`, `reduce_mean`, and
   `reduce_sum`: These functions compute the
   maximum, minimum, mean, and sum of a given
   tensor, respectively.

4. `caffe2_specialized_axpy`: This function
   performs the axpy operation, which is a linear
   combination of two vectors with the form `y
   = a * x + y`.

5. `gemm`, `gemv`, and related functions: These
   functions perform General Matrix-Matrix
   Multiplication (GEMM) and General Matrix-Vector
   Multiplication (GEMV) operations, which are
   common linear algebra procedures.

6. `cos`, `sin`, `tan`, `acos`, `asin`, `atan`,
   `cosh`, `sinh`, and `tanh`: These functions
   perform trigonometric and hyperbolic operations
   on the given input.

7. `exp`, `log`, and `log1p`: These functions
   calculate the exponential, natural logarithm,
   and natural logarithm of 1 plus the input,
   respectively.

8. `powx`, `sqrt`, and `cbrt`: These functions
   compute the power, square root, and cube root
   of the input, respectively.

9. `broadcast`: This function enables
   broadcasting, which is the process of applying
   an operation element-wise to two tensors with
   different shapes, following broadcasting rules.

The crate also contains various tests, such as
`BroadcastTest`, `GemmBatchedTest`, and
`RandFixedSumTest`, to ensure the correctness and
performance of the provided functions and
utilities.

For a complete understanding of the crate and its
capabilities, please refer to the source code and
documentation.

2> thanks! could you keep on describing more of
the tokens in this crate? the current level of
detail and groupings are great!

Certainly! Here's a description of more tokens in
the crate:

10. `bitwise_and`, `bitwise_or`, `bitwise_xor`:
    These functions perform bitwise operations
    (AND, OR, XOR) on the given input tensors.

11. `abs`, `neg`, `sign`, `floor`, `ceil`,
    `round`, and `trunc`: These functions perform
    element-wise transformations on the given
    input tensor, such as absolute value,
    negation, sign, and rounding operations.

12. `add`, `sub`, `mul`, and `div`: These
    functions perform element-wise arithmetic
    operations (addition, subtraction,
    multiplication, and division) on the input
    tensors.

13. `max` and `min`: These functions compute the
    element-wise maximum and minimum of the input
    tensors, respectively.

14. `caffe2_specialized_scale`: This function
    scales an input tensor by a scalar value,
    i.e., performs element-wise multiplication
    with a scalar.

15. `caffe2_specialized_set`: This function sets
    the elements of a given tensor to a specified
    value.

16. `erf` and `cdf_norm`: These functions compute
    the error function and the cumulative
    distribution function (CDF) of the standard
    normal distribution for the input,
    respectively.

17. `delegate_simple_binary_function_by_eigen_function`,
    `delegate_simple_binary_function_by_eigen_operator`,
    and
    `delegate_simple_binary_function_by_std_function`:
    These functions delegate the implementation of
    simple binary functions to Eigen, a C++
    template library for linear algebra, or the
    standard library.

18. `delegate_simple_unary_function`: This
    function delegates the implementation of
    simple unary functions to an appropriate
    implementation.

19. `caffe2_specialized_broadcast`: This function
    implements the broadcasting operation for
    a binary operation on two input tensors with
    different shapes.

20. `im_2col`, `im_2col_nd`, `col_2im`, and
    `col_2im_nd`: These functions perform
    image-to-column and column-to-image
    transformations, which are used in the
    implementation of convolutional layers in
    neural networks. They efficiently reorganize
    the data for matrix multiplication.

21. `gemm_batched` and `gemm_strided_batched`:
    These functions perform batched General
    Matrix-Matrix Multiplication (GEMM)
    operations, where multiple matrix
    multiplications are performed in parallel.

22. `rand_uniform`, `rand_gaussian`,
    `rand_fixed_sum`, and `rand_synthetic_data`:
    These functions generate random data following
    various distributions (uniform, Gaussian,
    fixed sum, and synthetic data) for the given
    input tensors.

23. `transpose`, `transpose2D`, and `transposeND`:
    These functions perform matrix transposition
    operations for 2D and N-dimensional tensors.

24. `caffe2_specialized_nchw2nhwc` and
    `caffe2_specialized_nhwc2nchw`: These
    functions convert between NCHW (batch,
    channel, height, width) and NHWC (batch,
    height, width, channel) data formats, which
    are commonly used in convolutional neural
    networks.

25. `affine_channel` and
    `caffe2_specialized_affine_channel`: These
    functions implement the affine channel
    operation, which is used to apply scale and
    bias transformations to input tensors in
    neural networks.

26. `bias_chwf32cpu_context`: This function
    applies a bias tensor to an input tensor,
    commonly used in neural networks after
    a convolution operation.

27. `colwise_max` and `rowwise_max`: These
    functions compute the column-wise and row-wise
    maximum values of the input tensor,
    respectively.