HardSigmoid on LLVM CPU

Hard Sigmoid Approximation

⏳ PENDING — not yet measured

Operation

Operation	HardSigmoid (`bpd_hardsigmoid`)
Formula	f(x) = max(0, min(1, (x + 3) / 6))
Category	Piecewise linear

Kernel Specification (Prolog/Logtalk)

This is the backend-neutral op_expr fact that specifies the operation. The same term is lowered to LLVM IR, CUDA C, MLIR, and every other backend — one specification, many targets.

op_expr(bpd_hardsigmoid,
    sel(le(var, const(-3.0)), const(0.0),
        sel(ge(var, const(3.0)), const(1.0),
            add(mul(var, const(0.16666667)), const(0.5))))).

Backend

Backend	LLVM CPU (`llvm_cpu`)
Target	cpu
Description	LLVM IR targeting x86-64 CPU. Compiled with llc + clang.

Verification

This (operation, backend) pair has not yet been measured. When the backend emitter and verification infrastructure are ready, this cell will be tested against the PyTorch reference.