GELU on LLVM CPU

Gaussian Error Linear Unit

⏳ PENDING — not yet measured

Operation

Operation	GELU (`bpd_gelu`)
Formula	f(x) = 0.5x · (1 + erf(x/√2))
Category	Transcendental (erf)

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_gelu,
    mul(mul(var, const(0.5)),
        add(const(1.0),
            call(erf, mul(var, const(0.7071067811865476)))))).

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.