metadata:
version: "1.0.0"
description: "Affine scale kernel — fused multiply-add"
references:
- "IEEE 754-2019"
equations:
scale:
formula: "y_i = α · x_i + β"
domain: "x ∈ ℝ^n, α ∈ ℝ, β ∈ ℝ"
codomain: "y ∈ ℝ^n"
invariants:
- "y finite when x finite"
proof_obligations:
- type: invariant
property: "Finiteness"
formal: "|y_i| < ∞ when |x_i| < ∞ and |α| < ∞ and |β| < ∞"
applies_to: all
- type: equivalence
property: "SIMD matches scalar"
tolerance: 0.0
applies_to: simd
kernel_structure:
phases:
- name: fma
description: "Fused multiply-add α·x + β"
invariant: "y_i = α·x_i + β"
simd_dispatch:
scale:
scalar: scale_scalar
avx2: scale_avx2
falsification_tests:
- id: FALSIFY-SC-001
rule: "Finiteness"
prediction: "scale(x) is finite for finite inputs"
if_fails: "Overflow in multiply-add"
kani_harnesses:
- id: KANI-SC-001
obligation: SC-INV-001
property: "Finiteness for bounded inputs"
bound: 16
strategy: exhaustive
qa_gate:
id: F-SC-001
name: "Scale Contract"
checks:
- "finiteness"
pass_criteria: "All 1 falsification tests pass"