Guide#

How ExactRef works and how to use it, one topic per page. If you are new, start with Get started. For a specific task, see Solutions; for every function and argument, the Reference.

Tolerances:

  • How tolerance works: what a tolerance means, in small examples: one rounding, the order of additions, the compute format, and the three verdicts.

  • Reading complicated tolerances: whole tensors, overflow, infinities and NaN, several outputs, complex outputs, kernels that round more than the definition, exact enclosures, flushing subnormals, and the matrix exponential.

Working with ExactRef:

  • Results: everything a result holds and the options of its methods.

  • Data in and out: importing from Python, NumPy and PyTorch, converting between formats, reading exact values, and building arrays.

  • Backward: gradients, and checking them against PyTorch's autograd.

  • Chains and any_of: computations with several steps, and implementations that may compute one of several expressions.

  • Algorithms: specific accumulation orders and fused attention kernels.

Each operation's own rules (shapes, promotion, special values, what its tolerance budgets) are on its reference page, for example add and multiply, sum and gemm. PyTorch equivalents maps PyTorch's calls onto them.

What is promised: