from tinygrad import Tensor, Device, Context, GlobalCounters, dtypes from tinygrad.uop.ops import UOp, KernelInfo, sint, AxisType from tinygrad.engine.realize import ExecItem, get_runner from tinygrad.dtype import AddrSpace from tinygrad.helpers import getenv N = 4096 M = K = N run_count = 5 # --------------------------- # launch/config constants # --------------------------- WARP_SIZE = 32 # Threadblock tile sizes (block-level tile of C that a block computes) BLOCK_N = 128 # columns of C (N-dim) per block BLOCK_M = 128 # rows of C (M-dim) per block BLOCK_K = 8 # K-slice per block iteration # Register tile sizes (per-thread accumulator tile of C) TN = 4 # columns per thread TM = 4 # rows per thread is_kernel5 = getenv("K5", 0) THREADS_PER_BLOCK = 128 if is_kernel5 else 256 assert THREADS_PER_BLOCK % BLOCK_N == 0, "THREADS_PER_BLOCK must be divisible by BLOCK_N" assert THREADS_PER_BLOCK % BLOCK_K == 0, "THREADS_PER_BLOCK must be divisible by BLOCK_K" assert (BLOCK_N * BLOCK_K) % THREADS_PER_BLOCK == 0 assert (BLOCK_M * BLOCK_K) % THREADS_PER_BLOCK == 0 WARPS_PER_BLOCK = THREADS_PER_BLOCK // WARP_SIZE WAVE_TILE_N = 128 if is_kernel5 else 64 WAVE_TILE_M = BLOCK_N * BLOCK_M // WARPS_PER_BLOCK // WAVE_TILE_N assert BLOCK_N % WAVE_TILE_N == 0, "BN must be a multiple of WN" assert BLOCK_M % WAVE_TILE_M == 0, "BM must be a multiple of WM" WAVES_IN_BLOCK_X = BLOCK_N // WAVE_TILE_N WAVES_IN_BLOCK_Y = BLOCK_M // WAVE_TILE_M assert WAVES_IN_BLOCK_X * WAVES_IN_BLOCK_Y == WARPS_PER_BLOCK, "wave grid must match warps/block" LANES_PER_WAVE_X = 8 LANES_PER_WAVE_Y = 4 ITERS_PER_WAVE_N = WAVE_TILE_N // (LANES_PER_WAVE_X * TN) ITERS_PER_WAVE_M = WAVE_TILE_M // (LANES_PER_WAVE_Y * TM) assert WAVE_TILE_N % (LANES_PER_WAVE_X * TN) == 0, "WAVE_TILE_N must be divisible by LANES_PER_WAVE_X*TN" assert WAVE_TILE_M % (LANES_PER_WAVE_Y * TM) == 0, "WAVE_TILE_M must be divisible by LANES_PER_WAVE_Y*TM" def rngs_for_shape(shape:tuple[sint, ...], rng:int, axis_type=AxisType.LOOP): return [UOp.range(s, rng+i, axis_type) for i,s in enumerate(shape)] def copy(dest:UOp, src:UOp, rng:int, set=False, upcast=False): assert dest.shape == src.shape rngs = rngs_for_shape(src.shape, rng, AxisType.UPCAST if upcast else AxisType.LOOP) copy = dest[*rngs].store(src[*rngs]).end(*rngs) return dest.after(copy) if set else copy def hand_spec_kernel3(): # --------------------------- # block indices & placeholders # --------------------------- blockIdx_x = UOp.special(N // BLOCK_N, "gidx0") blockIdx_y = UOp.special(N // BLOCK_M, "gidx1") a = UOp.placeholder((N, N), dtypes.float, slot=1) b = UOp.placeholder((N, N), dtypes.float, slot=2) c = UOp.placeholder((N, N), dtypes.float, slot=0) # index the output with the globals c = c.reshape(M // BLOCK_M, BLOCK_M, N // BLOCK_N, BLOCK_N)[blockIdx_y, :, blockIdx_x, :] # open the main reduction range k_tile_range = UOp.range(N // BLOCK_K, 0, AxisType.REDUCE) a = a.reshape(M // BLOCK_M, BLOCK_M, N // BLOCK_K, BLOCK_K)[blockIdx_y, :, k_tile_range, :] b = b.reshape(N // BLOCK_K, BLOCK_K, N // BLOCK_N, BLOCK_N)[k_tile_range, :, blockIdx_x, :] # globals are no longer used, they are already in the indexes del blockIdx_y, blockIdx_x # --------------------------- # GLOBAL -> LOCAL (As, Bs) # --------------------------- tid = UOp.special(THREADS_PER_BLOCK, "lidx0") # A: read BM x BK tiles (permute on store into locals) BM_As_stride = (BLOCK_M + 4) if is_kernel5 else BLOCK_M As = UOp.placeholder((BLOCK_K, BM_As_stride), dtypes.float, slot=0, addrspace=AddrSpace.LOCAL).shrink_to((BLOCK_K, BLOCK_M)) As_store = copy(As.permute((1,0)).reshape(-1, THREADS_PER_BLOCK)[:, tid], a.reshape(-1, THREADS_PER_BLOCK)[:, tid], rng=100) # B: read BK x BN tiles Bs = UOp.placeholder((BLOCK_K, BLOCK_N), dtypes.float, slot=1, addrspace=AddrSpace.LOCAL) Bs_store = copy(Bs.reshape(-1, THREADS_PER_BLOCK)[:, tid], b.reshape(-1, THREADS_PER_BLOCK)[:, tid], rng=200) # TODO: can we automate barrier? barrier = UOp.barrier(As_store, Bs_store) As, Bs = As.after(barrier), Bs.after(barrier) # open inner k range k = UOp.range(BLOCK_K, 3, AxisType.REDUCE) # --------------------------- # LOCAL -> REG (per-wave tiles) # --------------------------- waveIdx = (tid // WARP_SIZE) % WAVES_IN_BLOCK_X waveIdy = (tid // WARP_SIZE) // WAVES_IN_BLOCK_X assert waveIdy.vmax+1 == WAVES_IN_BLOCK_Y laneIdx = (tid % WARP_SIZE) % LANES_PER_WAVE_X laneIdy = (tid % WARP_SIZE) // LANES_PER_WAVE_X assert laneIdy.vmax+1 == LANES_PER_WAVE_Y A_col = UOp.placeholder((ITERS_PER_WAVE_M, TM), dtypes.float, slot=0, addrspace=AddrSpace.REG) A_col = copy(A_col, As[k, :].reshape(WAVES_IN_BLOCK_Y, ITERS_PER_WAVE_M, LANES_PER_WAVE_Y, TM)[waveIdy, :, laneIdy, :], 300, set=True, upcast=True) B_row = UOp.placeholder((ITERS_PER_WAVE_N, TN), dtypes.float, slot=1, addrspace=AddrSpace.REG) B_row = copy(B_row, Bs[k, :].reshape(WAVES_IN_BLOCK_X, ITERS_PER_WAVE_N, LANES_PER_WAVE_X, TN)[waveIdx, :, laneIdx, :], 400, set=True, upcast=True) # --------------------------- # FMA: c_regs += A_col * B_row # --------------------------- c_regs = UOp.placeholder((ITERS_PER_WAVE_M, TM, ITERS_PER_WAVE_N, TN), dtypes.float, slot=2, addrspace=AddrSpace.REG) i = UOp.range(c_regs.size, 16) c_regs = c_regs.after(c_regs.flatten()[i].store(0.0).end(i)) # TODO: why don't these work as upcast? # why if the ranges merge is it slow?!? (if you change the order on end, they will merge. big slowdown on METAL) iterWaveM, yt, iterWaveN, xt = rngs = rngs_for_shape(c_regs.shape, 500) sink = c_regs[*rngs].store(c_regs.after(k)[*rngs] + A_col[iterWaveM, yt] * B_row[iterWaveN, xt]).end(iterWaveM, iterWaveN, yt, xt) # Close k, sync, and close K tiles sink = sink.end(k).barrier().end(k_tile_range) # --------------------------- # REG -> GLOBAL (epilogue) # --------------------------- c = c.reshape(WAVES_IN_BLOCK_Y, ITERS_PER_WAVE_M, LANES_PER_WAVE_Y, TM, WAVES_IN_BLOCK_X, ITERS_PER_WAVE_N, LANES_PER_WAVE_X, TN) c = c[waveIdy, :, laneIdy, :, waveIdx, :, laneIdx, :] sink = copy(c, c_regs.after(sink), rng=600) return sink.sink(arg=KernelInfo(opts_to_apply=())).simplify() def test_matmul(sink:UOp, N=N): with Context(DEBUG=0): a = Tensor.randn(N, N) b = Tensor.randn(N, N) hc = Tensor.empty(N, N) Tensor.realize(a, b, hc) ei = ExecItem(get_runner(Device.DEFAULT, sink), [t.uop.buffer for t in [hc, a, b]]) GlobalCounters.reset() ets = [] with Context(DEBUG=2): for _ in range(run_count): ets.append(ei.run(wait=True)) print(f"REAL TFLOPS {N * N * N * 2 / min(ets) * 1e-12:.2f}") GlobalCounters.reset() with Context(DEBUG=2): tc = (a @ b).realize() with Context(DEBUG=0): err = (hc - tc).square().mean().item() print(f"mean squared error {err}") if err > 1e-06: raise RuntimeError("matmul is wrong!") if __name__ == "__main__": test_matmul(hand_spec_kernel3(), N=N)