"""Reference implementation — the CORRECTNESS SPEC for `nvfp4_gemm`.

This is correct but slow. It defines exactly what your kernel must reproduce; its speed has no
bearing on your score, which is an absolute TFLOP/s number. GENERATED by _factory/build.py.
"""
import torch


# E2M1: 1 sign bit, 2 exponent bits, 1 mantissa bit -> these 8 magnitudes, negated for codes 8..15.
_E2M1 = (0.0, 0.5, 1.0, 1.5, 2.0, 3.0, 4.0, 6.0)

BLOCK = 16               # NVFP4 block size: one E4M3 scale per 16 consecutive K elements


def _e2m1_table(device):
    t = torch.tensor(_E2M1, dtype=torch.float32, device=device)
    return torch.cat([t, -t])                      # codes 0..7 positive, 8..15 negative


def nvfp4_gemm(a, w_packed, w_scale, global_scale):
    """Dequantise NVFP4 weights to fp32, then GEMM. The numerical SPECIFICATION, not a performance target."""
    N, Kh = w_packed.shape
    K = Kh * 2

    lo = (w_packed & 0x0F).long()                  # even k
    hi = (w_packed >> 4).long()                    # odd  k
    codes = torch.stack([lo, hi], dim=-1).reshape(N, K)

    w = _e2m1_table(a.device)[codes]                                   # (N, K) fp32 element magnitudes
    w = w * w_scale.float().repeat_interleave(BLOCK, dim=1)            # per-16-element E4M3 block scale
    w = w * global_scale.float()                                       # per-tensor fp32 scale

    return (a.float() @ w.t()).to(torch.float32)