inv-sqrt-to-rsqrt
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/inv-sqrt-to-rsqrt.md contains the canonical detection logic + GPU reasoning.
TL;DR
On AMD RDNA/RDNA 2/RDNA 3, NVIDIA Turing/Ada Lovelace, and Intel Xe-HPG, sqrt is a transcendental instruction (v_sqrt_f32 on RDNA, SQRT on Xe-HPG) executing at one-quarter peak VALU throughput. A reciprocal (rcp, v_rcp_f32) is also a special-function-unit instruction, again at quarter rate. The expression 1.0 / sqrt(x) therefore chains two quarter-rate instructions — sqrt, then rcp — for an effective cost of roughly 8 full-rate cycles per wave on most architectures.
What the rule fires on
The expression 1.0 / sqrt(x) — or 1.0f / sqrt(x), rcp(sqrt(x)), or a division by sqrt of any sub-expression — where the numerator is the literal constant 1. The rule matches the structural pattern of a reciprocal of a square root, regardless of whether x is a scalar, vector component, or a compound expression such as dot(v, v). It does not fire when the numerator is not a constant 1, or when the division is by something other than sqrt(...).
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 inv-sqrt-to-rsqrt.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.