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fix: route every transcendental through libm, and combine sigmas with hypot

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Follow-on from #41, which added `libm` for `erfc`. Surveying what else
the dependency offers: its unique surface over `std` is `erf`/`erfc`,
`lgamma`/`tgamma` and Bessel functions, and only the first was ever
needed. But the survey found something better than another special
function.

`std`'s `exp` and `ln` delegate to the *system* math library. IEEE 754
specifies the basic operations and `sqrt` exactly and says nothing about
transcendentals, so those differ per platform. Measured here over 200k
inputs:

    exp: 19425/200000 differ from libm (worst 1 ulp)
    log:  9932/200000 differ

Inference is an iterative fixed point, so a one-ULP difference can change
an iteration count and move the answer by more than one ULP. Routing
every transcendental through `libm` makes a fit reproducible across
platforms — a stronger guarantee than `tests/determinism.rs`, which only
covers thread counts.

It costs nothing. `Batch::iteration` measured -2.7% [-5.7%, -0.3%] with
the whole set swapped, and not one golden moved.

Also switches the two places that combined sigmas as
`sqrt(a^2 + b^2)` to `hypot`. Squaring overflows to infinity above
~1.3e154 and flushes to zero below ~1.5e-154 — measured, the naive form
returns `inf` where `hypot` returns 1.41e160 — and `Gaussian`'s
constructors are public, so a caller can reach both ends.

Deliberately not done: rewriting the KL divergence's `ln` of a ratio via
`ln_1p`. The cancellation is real as the ratio approaches one, but
measured absolute error is at most ~1e-11 in a quantity of order 0.4
nats, so it changes nothing.

The invariant is recorded in `CLAUDE.md` and on `erfc`'s own docs, since
nothing enforces it mechanically.

Co-Authored-By: Claude Opus 5 (1M context) <noreply@anthropic.com>
Claude-Session: https://claude.ai/code/session_011hcFjNDmHXZF8URGLku5zZ
This commit is contained in:
logaritmisk
2026-09-07 22:33:30 +02:00
co-authored by Claude Opus 5
parent 3dd659307a
commit 17d072b2ae
5 changed files with 45 additions and 18 deletions
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src/factor/margin.rs
+4 -1
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@@ -74,7 +74,10 @@ impl Factor for MarginFactor {
/// far from what the model expected is exactly the observation a log-evidence
/// figure exists to notice.
fn cavity_log_evidence(cavity: Gaussian, m_obs: f64, sigma: f64) -> f64 {
let combined_sigma = (cavity.sigma().powi(2) + sigma.powi(2)).sqrt();
// `hypot`, not `sqrt(a^2 + b^2)`: squaring overflows to infinity above a
// sigma of ~1.3e154 and flushes to zero below ~1.5e-154, and `Gaussian`'s
// constructors are public so a caller can reach both.
let combined_sigma = cavity.sigma().hypot(sigma);
let value = ln_pdf(m_obs, cavity.mu(), combined_sigma);
// A degenerate cavity (infinite sigma) is the only way to reach a