precise-missing-on-iterative-refine
Status: stub. The full-length analysis is queued for a v1.0.x patch release per ADR 0018, section 5, criterion #6. The companion rule page at docs/rules/precise-missing-on-iterative-refine.md contains the canonical detection logic + GPU reasoning.
TL;DR
GPU compilers for HLSL run aggressive fast-math reordering by default. The optimiser sees x = x - f(x)/fprime(x) and is free to: (a) apply mul-add fusion that changes rounding, (b) reorder the subtraction with respect to constant folds, (c) re-associate x*x*x to x*(x*x) or pow(x, 3), and crucially (d) recognise that across an unbounded number of iterations the algebraic limit collapses certain residuals to zero — at which point the optimiser may fold the entire iteration to the initial guess, on the grounds that x = x - 0 is identity. On AMD RDNA 2/3, NVIDIA Ada Lovelace, and Intel Xe-HPG the resulting codegen is silently a no-op iteration: the initial guess passes through unchanged. The author intended N rounds of quadratic-convergence refinement; the shader runs zero rounds.
What the rule fires on
A loop whose body implements a Newton-Raphson, Halley, or related iterative-refinement step on a floating-point quantity, where the residual update (the term that drives convergence) lacks the precise qualifier. Pattern shapes: for (uint i = 0; i < N; ++i) { x = x - f(x) / fprime(x); } or the equivalent x = (x + a / x) * 0.5; for square root, or x = x * (1.5 - 0.5 * a * x * x); for inverse-square-root refinement, where x is a plain float rather than precise float.
See the What it detects section of the rule page for the full pattern definition.
Why it matters
The full GPU-mechanism analysis lives in the Why it matters on a GPU section of the companion rule page.
Examples
The bad / good code snippets are kept canonical on the rule page; see precise-missing-on-iterative-refine.md -> Examples.
See also
- Rule page -- canonical reference + change log.
- math overview -- broader context.
- ADR 0018 -- v1.0 readiness plan.
This is a v1.0-ship stub. Full analysis pending; track issue link TBD.