dootdoot mathx Contract

mathx owns every transcendental used by the audio path. The implementation contract is mathx-v1; changing any table, coefficient, range-reduction rule, or saturation threshold is sample-affecting and therefore part of VOICE_V1.

API

The runtime API is deliberately small:

• sin(x) and cos(x) for oscillator phase, vibrato, and ring-modulation.
• exp(x) for envelopes and filter coefficient calculations that need exponentials.
• tanh(x) implemented through exp(x) for the semantic squash.

All functions operate in f64 and return f64. Integer conversion is kept out of this module; audio conversion uses the project-wide round-half-to-even rule in the WAV/buffer layer.

Tables And Polynomials

The pinned v1 shape is:

• Sine/cosine range reduction uses a 4096-interval full-turn table (2^12) plus a degree-7 local correction polynomial.
• Exponential range reduction uses a 1024-interval table (2^10) across one ln(2) span plus a degree-5 residual polynomial.
• Hyperbolic tangent is computed from the owned exponential and saturates at |x| >= 20.

These sizes are intentionally small enough to keep cache behavior predictable and large enough that the correction polynomials can stay low-degree. T-07 through T-10 will fill in the coefficients and pinned output fixtures against this contract.

Determinism Rationale

No libm transcendentals are allowed in the audio path. Platform sin, cos, exp, and tanh implementations can differ by small amounts, and those differences can move final samples after scaling and round-half-to-even conversion. mathx instead uses fixed tables, fixed polynomial evaluation order, f64 arithmetic, and no fast-math assumptions.