Compensated arithmetic

Owner import path¶

jaxstro.numerics.compensated

Purpose¶

Neumaier-style compensated scalar, array, vector, and dot-product reductions.

Public records and callables¶

neumaier_add, compensated_sum, compensated_sum_array, compensated_vector_sum, and compensated_dot.

Shape and dtype expectations¶

Inputs are floating arrays. Array and vector helpers use a leading reduction axis; dot products require matching one-dimensional shapes.

JAX transforms and AD classification¶

Fixed-order reductions compose with JIT and AD. Compensation improves rounding behavior but does not make floating arithmetic exact or order-independent.

Failure behavior¶

Shape and dtype errors propagate. Non-finite inputs remain non-finite; no values are silently replaced.

Contract and evidence links¶

See Linear algebra helpers and the numerical tests linked from Validation and provenance tooling.

Canonical import example¶

from jaxstro.numerics.compensated import compensated_sum_array