Operations

Each operation returns the exact answer rounded once, with its bounds, as a Result. They are available at the top level, such as er.matmul, and under their category, which this page follows.

Linear algebra: exactref.linalg

• matmul (linalg.products.matmul): the matrix product, with NumPy batching.

• gemm (linalg.products.gemm): beta * C + alpha * (A @ B), as in addmm, addmv, addr and baddbmm.

• matrix_exp and matrix_exp_frechet (linalg.matrix_function): the matrix exponential and its derivative.

Arithmetic: exactref.arithmetic

• add and multiply (arithmetic.basic): elementwise x + alpha * y and x * y, with broadcasting.

Reductions: exactref.reduction

• sum (reduction.arithmetic.sum): the sum over some or all dimensions.

Neural networks: exactref.nn

• scaled_dot_product_attention (nn.attention.scaled_dot_product_attention): attention, as in PyTorch.

Every operation with a derivative has a .backward, documented on its page. Named algorithms for these operations are in Algorithms.