Elementary Function Precision

Summary

Precision targets for elementary functions are tiered by scalar type, not by target device: f64 targets a relative error below 1e-14, f32 targets a relative error below 1e-6, both measured over the primary domain [-2π, 2π].

Scope

Applies to every elementary function the scalar type provides — trigonometric functions, exponential, logarithm, and similar — over the domain [-2π, 2π]. Behavior outside that domain is explicitly out of scope for any precision guarantee.

Decision

Two fixed precision tiers exist, keyed only to which concrete floating-point type is in use, with no per-device variation: every target using f64 gets the same precision target as every other target using f64, regardless of whether that target is a desktop machine or a microcontroller, and likewise for f32.

No separate, reduced-precision fast path is provided for smaller or more constrained devices. That option was considered and rejected: there is no concrete evidence of demand for it, and building it would compete directly with higher-priority work (Krylov solver development) for the same engineering time.

Constraints

• Outside the primary domain [-2π, 2π], elementary function behavior is documented as degraded and untested — not bounded by any stated precision guarantee. Callers operating outside this domain get no promise about the result’s accuracy.
• Precision targets are a function of scalar type alone; no code path may vary an elementary function’s precision based on which target device it is compiled for.
• A reduced-precision fast path must not be added without a concrete, evidenced use case — the absence of demand today is a real constraint on scope, not an oversight to be filled in speculatively.

Status

Implemented. Elementary function implementations are verified against a high-precision reference over [-2π, 2π], meeting the stated per-type targets. No fast-path variant exists.