binary_gemm_kernel.py

import torch

import triton
import triton.language as tl

def pack(x, n_bits=32):
    """
    pack n_bits of x into a single integer
    
    x: bool tensor (*, K, N)
    return: int tensor (*, K // n_bits, N)
    """
    assert x.shape[-2] % n_bits == 0, "K must be divisible by n_bits"

    shift = torch.arange(n_bits, device=x.device)
    shape = x.shape[:-2]
    x = x.view(-1, x.shape[-2]//n_bits, n_bits, x.shape[-1])
    x = x << shift[None, None, :, None]
    x = x.sum(-2)
    x = x.view(*shape, *x.shape[-2:])
    
    # determine dtype
    if n_bits == 8:
        dtype = torch.uint8
    elif n_bits == 16:
        dtype = torch.int16
    elif n_bits == 32:
        dtype = torch.int32
    elif n_bits == 64:
        dtype = torch.int64

    return x.to(dtype)

def unpack(x, n_bits=32):
    """
    unpack n_bits of x into a single integer
    
    x: int tensor (*, K // n_bits, N)
    return: bool tensor (*, K, N)
    """
    shift = torch.arange(n_bits, device=x.device)
    shape = x.shape[:-2]
    x = x.view(-1, x.shape[-2], 1, x.shape[-1])
    x = (x >> shift[None, None, :, None]) & 0x1
    x = x.view(*shape, -1, x.shape[-1])
    return x.bool()

@triton.autotune(
    configs=[
        triton.Config({'BLOCK_SIZE_M': 16, 'BLOCK_SIZE_N': 256, 'BLOCK_SIZE_K': 64, 'GROUP_SIZE_M': 8}, num_stages=3, num_warps=8),
        triton.Config({'BLOCK_SIZE_M': 16, 'BLOCK_SIZE_N': 128, 'BLOCK_SIZE_K': 32, 'GROUP_SIZE_M': 8}, num_stages=4, num_warps=4),
        triton.Config({'BLOCK_SIZE_M': 16, 'BLOCK_SIZE_N': 64, 'BLOCK_SIZE_K': 32, 'GROUP_SIZE_M': 8}, num_stages=4, num_warps=4),
        triton.Config({'BLOCK_SIZE_M': 16, 'BLOCK_SIZE_N': 32, 'BLOCK_SIZE_K': 32, 'GROUP_SIZE_M': 8}, num_stages=4, num_warps=4),
    ],
    key=['M', 'N', 'K'],
)
@triton.jit
def binary_matmul_kernel(
    # Pointers to matrices
    a_ptr, b_ptr, c_ptr,
    # Matrix dimensions
    M, N, K,
    n_bits,
    # The stride variables represent how much to increase the ptr by when moving by 1
    # element in a particular dimension. E.g. `stride_am` is how much to increase `a_ptr`
    # by to get the element one row down (A has M rows).
    stride_am, stride_ak,
    stride_bk, stride_bn,
    stride_cm, stride_cn,
    # Meta-parameters
    BLOCK_SIZE_M: tl.constexpr, BLOCK_SIZE_N: tl.constexpr, BLOCK_SIZE_K: tl.constexpr,
    GROUP_SIZE_M: tl.constexpr,
    ACTIVATION: tl.constexpr,
):
    """Kernel for computing the matmul C = A x B.
    A has shape (M, K), float
    B has shape (K//n_bits, N), int, packed boolean
    C has shape (M, N),
    """
    # -----------------------------------------------------------
    # Map program ids `pid` to the block of C it should compute.
    # This is done in a grouped ordering to promote L2 data reuse.
    # See above `L2 Cache Optimizations` section for details.
    pid = tl.program_id(axis=0)
    num_pid_m = tl.cdiv(M, BLOCK_SIZE_M)
    num_pid_n = tl.cdiv(N, BLOCK_SIZE_N)
    num_pid_in_group = GROUP_SIZE_M * num_pid_n
    group_id = pid // num_pid_in_group
    first_pid_m = group_id * GROUP_SIZE_M
    group_size_m = min(num_pid_m - first_pid_m, GROUP_SIZE_M)
    pid_m = first_pid_m + (pid % group_size_m)
    pid_n = (pid % num_pid_in_group) // group_size_m

    # ----------------------------------------------------------
    # Create pointers for the first blocks of A and B.
    # We will advance this pointer as we move in the K direction
    # and accumulate
    # `a_ptrs` is a block of [BLOCK_SIZE_M, BLOCK_SIZE_K] pointers
    # `b_ptrs` is a block of [BLOCK_SIZE_K, BLOCK_SIZE_N] pointers
    # See above `Pointer Arithmetics` section for details
    offs_am = (pid_m * BLOCK_SIZE_M + tl.arange(0, BLOCK_SIZE_M)) % M
    offs_bn = (pid_n * BLOCK_SIZE_N + tl.arange(0, BLOCK_SIZE_N)) % N
    offs_k = tl.arange(0, BLOCK_SIZE_K)
    a_ptrs = a_ptr + (offs_am[:, None] * stride_am + offs_k[None, :] * stride_ak)
    # b_ptrs = b_ptr + (offs_k[:, None] * stride_bk + offs_bn[None, :] * stride_bn)

    # Adapted from GPTQ-Triton (https://github.com/fpgaminer/GPTQ-triton)
    # b_ptrs is set up such that it repeats elements along the K axis n_bits times
    b_ptrs = b_ptr + ((offs_k[:, None] // n_bits) * stride_bk + offs_bn[None, :] * stride_bn)   # (BLOCK_SIZE_K, BLOCK_SIZE_N)
    # shifter is used to extract each bit of each element in the int matrix
    shifter = (offs_k % n_bits)[:, None]

    # -----------------------------------------------------------
    # Iterate to compute a block of the C matrix.
    # We accumulate into a `[BLOCK_SIZE_M, BLOCK_SIZE_N]` block
    # of fp32 values for higher accuracy.
    # `accumulator` will be converted back to fp16 after the loop.
    accumulator = tl.zeros((BLOCK_SIZE_M, BLOCK_SIZE_N), dtype=tl.float32)
    for k in range(0, tl.cdiv(K, BLOCK_SIZE_K)):
        # Load the next block of A and B, generate a mask by checking the K dimension.
        # If it is out of bounds, set it to 0.
        a = tl.load(a_ptrs, mask=offs_k[None, :] < K - k * BLOCK_SIZE_K, other=0.0)
        # b = tl.load(b_ptrs, mask=offs_k[:, None] < K - k * BLOCK_SIZE_K, other=0)
        b = tl.load(b_ptrs)

        # Convert B from int to a.dtype, for each bit in B, 0 becomes -1.0, 1 becomes 1.0
        # b: (BLOCK_SIZE_K, BLOCK_SIZE_N)
        b = (b >> shifter) & 0x1
        b = b.to(a.dtype) * 2 - 1
        
        # Simply convert to a.dtype
        # b = b.to(a.dtype)
        # We accumulate along the K dimension.
        accumulator += tl.dot(a, b)
        # Advance the ptrs to the next K block.
        a_ptrs += BLOCK_SIZE_K * stride_ak
        # b_ptrs += BLOCK_SIZE_K * stride_bk
        b_ptrs += (BLOCK_SIZE_K // n_bits) * stride_bk
    # You can fuse arbitrary activation functions here
    # while the accumulator is still in FP32!
    # if ACTIVATION == "leaky_relu":
    #     accumulator = leaky_relu(accumulator)
    c = accumulator.to(tl.float16)

    # -----------------------------------------------------------
    # Write back the block of the output matrix C with masks.
    offs_cm = pid_m * BLOCK_SIZE_M + tl.arange(0, BLOCK_SIZE_M)
    offs_cn = pid_n * BLOCK_SIZE_N + tl.arange(0, BLOCK_SIZE_N)
    c_ptrs = c_ptr + stride_cm * offs_cm[:, None] + stride_cn * offs_cn[None, :]
    c_mask = (offs_cm[:, None] < M) & (offs_cn[None, :] < N)
    tl.store(c_ptrs, c, mask=c_mask)

def binary_matmul(a, b, n_bits=32, activation=""):
    """
        a: float tensor (M, K)
        b: int tensor (K, N)
        n_bits: int, number of bits that each element in b represents
    """
    # Check constraints.
    assert a.shape[1] == b.shape[0] * n_bits, "Incompatible dimensions"
    assert a.is_contiguous(), "Matrix A must be contiguous"
    assert b.is_contiguous(), "Matrix B must be contiguous"
    M, K = a.shape
    _, N = b.shape

    # Allocates output.
    c = torch.empty((M, N), device=a.device, dtype=a.dtype)
    # 1D launch kernel where each block gets its own program.
    grid = lambda META: (
        triton.cdiv(M, META['BLOCK_SIZE_M']) * triton.cdiv(N, META['BLOCK_SIZE_N']),
    )

    # print(f"Launching kernel with M = {M}, N = {N}, K = {K}, n_bits = {n_bits}, activation = {activation}")

    binary_matmul_kernel[grid](
        a, b, c,
        M, N, K,
        n_bits,
        a.stride(0), a.stride(1),
        b.stride(0), b.stride(1),
        c.stride(0), c.stride(1),
        ACTIVATION=activation
    )
    return c

@triton.autotune(
    configs=[
        triton.Config({'BLOCK_SIZE_M': 16, 'BLOCK_SIZE_N': 256, 'BLOCK_SIZE_K': 64, 'GROUP_SIZE_M': 8}, num_stages=3, num_warps=4),
        triton.Config({'BLOCK_SIZE_M': 16, 'BLOCK_SIZE_N': 128, 'BLOCK_SIZE_K': 32, 'GROUP_SIZE_M': 8}, num_stages=4, num_warps=2),
        triton.Config({'BLOCK_SIZE_M': 16, 'BLOCK_SIZE_N': 64, 'BLOCK_SIZE_K': 32, 'GROUP_SIZE_M': 8}, num_stages=4, num_warps=2),
        triton.Config({'BLOCK_SIZE_M': 16, 'BLOCK_SIZE_N': 32, 'BLOCK_SIZE_K': 32, 'GROUP_SIZE_M': 8}, num_stages=4, num_warps=2),
    ],
    key=['M', 'N', 'K'],
)
@triton.jit
def binary_bmm_kernel(
    # Pointers to matrices
    a_ptr, b_ptr, c_ptr,
    # Matrix dimensions
    M, N, K,
    n_bits,
    # The stride variables represent how much to increase the ptr by when moving by 1
    # element in a particular dimension. E.g. `stride_am` is how much to increase `a_ptr`
    # by to get the element one row down (A has M rows).
    stride_am, stride_ak,
    stride_bk, stride_bn,
    stride_cm, stride_cn,
    stride_batch_a, stride_batch_b, stride_batch_c,
    # Meta-parameters
    BLOCK_SIZE_M: tl.constexpr, BLOCK_SIZE_N: tl.constexpr, BLOCK_SIZE_K: tl.constexpr,
    GROUP_SIZE_M: tl.constexpr,
    ACTIVATION: tl.constexpr,
):
    """Kernel for computing the matmul C = A x B.
    A has shape (B, M, K), float
    B has shape (B, K//n_bits, N), int, packed boolean
    C has shape (B, M, N),
    """
    # -----------------------------------------------------------
    # Map program ids `pid` to the block of C it should compute.
    # This is done in a grouped ordering to promote L2 data reuse.
    # See above `L2 Cache Optimizations` section for details.
    pid = tl.program_id(axis=0)
    pid_batch = tl.program_id(axis=1)

    num_pid_m = tl.cdiv(M, BLOCK_SIZE_M)
    num_pid_n = tl.cdiv(N, BLOCK_SIZE_N)
    num_pid_in_group = GROUP_SIZE_M * num_pid_n
    group_id = pid // num_pid_in_group
    first_pid_m = group_id * GROUP_SIZE_M
    group_size_m = min(num_pid_m - first_pid_m, GROUP_SIZE_M)
    pid_m = first_pid_m + (pid % group_size_m)
    pid_n = (pid % num_pid_in_group) // group_size_m

    # ----------------------------------------------------------
    # Create pointers for the first blocks of A and B.
    # We will advance this pointer as we move in the K direction
    # and accumulate
    # `a_ptrs` is a block of [BLOCK_SIZE_M, BLOCK_SIZE_K] pointers
    # `b_ptrs` is a block of [BLOCK_SIZE_K, BLOCK_SIZE_N] pointers
    # See above `Pointer Arithmetics` section for details
    offs_am = (pid_m * BLOCK_SIZE_M + tl.arange(0, BLOCK_SIZE_M)) % M
    offs_bn = (pid_n * BLOCK_SIZE_N + tl.arange(0, BLOCK_SIZE_N)) % N
    offs_k = tl.arange(0, BLOCK_SIZE_K)
    a_ptrs = a_ptr + (offs_am[:, None] * stride_am + offs_k[None, :] * stride_ak) + pid_batch * stride_batch_a
    # b_ptrs = b_ptr + (offs_k[:, None] * stride_bk + offs_bn[None, :] * stride_bn)

    # Adapted from GPTQ-Triton (https://github.com/fpgaminer/GPTQ-triton)
    # b_ptrs is set up such that it repeats elements along the K axis n_bits times
    b_ptrs = b_ptr + ((offs_k[:, None] // n_bits) * stride_bk + offs_bn[None, :] * stride_bn) + pid_batch * stride_batch_b
    # (BLOCK_SIZE_K, BLOCK_SIZE_N)
    # shifter is used to extract each bit of each element in the int matrix
    shifter = (offs_k % n_bits)[:, None]

    # -----------------------------------------------------------
    # Iterate to compute a block of the C matrix.
    # We accumulate into a `[BLOCK_SIZE_M, BLOCK_SIZE_N]` block
    # of fp32 values for higher accuracy.
    # `accumulator` will be converted back to fp16 after the loop.
    accumulator = tl.zeros((BLOCK_SIZE_M, BLOCK_SIZE_N), dtype=tl.float32)
    for k in range(0, tl.cdiv(K, BLOCK_SIZE_K)):
        # Load the next block of A and B, generate a mask by checking the K dimension.
        # If it is out of bounds, set it to 0.
        a = tl.load(a_ptrs, mask=offs_k[None, :] < K - k * BLOCK_SIZE_K, other=0.0)
        # b = tl.load(b_ptrs, mask=offs_k[:, None] < K - k * BLOCK_SIZE_K, other=0)
        b = tl.load(b_ptrs)

        # Convert B from int to a.dtype, for each bit in B, 0 becomes -1.0, 1 becomes 1.0
        # b: (BLOCK_SIZE_K, BLOCK_SIZE_N)
        b = (b >> shifter) & 0x1
        # b = b.to(a.dtype) * 2 - 1
        b = (2*b-1).to(a.dtype)


        # Simply convert to a.dtype
        # b = b.to(a.dtype)
        # We accumulate along the K dimension.
        accumulator += tl.dot(a, b)
        # Advance the ptrs to the next K block.
        a_ptrs += BLOCK_SIZE_K * stride_ak
        # b_ptrs += BLOCK_SIZE_K * stride_bk
        b_ptrs += (BLOCK_SIZE_K // n_bits) * stride_bk
    # You can fuse arbitrary activation functions here
    # while the accumulator is still in FP32!
    # if ACTIVATION == "leaky_relu":
    #     accumulator = leaky_relu(accumulator)
    c = accumulator.to(tl.float16)

    # -----------------------------------------------------------
    # Write back the block of the output matrix C with masks.
    offs_cm = pid_m * BLOCK_SIZE_M + tl.arange(0, BLOCK_SIZE_M)
    offs_cn = pid_n * BLOCK_SIZE_N + tl.arange(0, BLOCK_SIZE_N)
    c_ptrs = c_ptr + stride_cm * offs_cm[:, None] + stride_cn * offs_cn[None, :] + pid_batch * stride_batch_c
    c_mask = (offs_cm[:, None] < M) & (offs_cn[None, :] < N)
    tl.store(c_ptrs, c, mask=c_mask)

def binary_bmm(a, b, n_bits=32, activation=""):
    """
        a: float tensor (B, M, K)
        b: int tensor (B, K, N)
        n_bits: int, number of bits that each element in b represents
    """
    assert a.dim() == 3, "Matrix A must be 3D"
    assert b.dim() == 3, "Matrix B must be 3D"
    assert a.shape[2] == b.shape[1] * n_bits, "Incompatible dimensions"
    assert a.shape[0] == b.shape[0], "Incompatible batch dimensions"
    assert a.is_contiguous(), "Matrix A must be contiguous"
    assert b.is_contiguous(), "Matrix B must be contiguous"
    assert a.device == b.device, "A and B must be on the same device"
    B, M, K = a.shape
    _, _, N = b.shape

    # Allocates output.
    c = torch.empty((B, M, N), device=a.device, dtype=a.dtype)
    # 1D launch kernel where each block gets its own program.
    grid = lambda META: (
        triton.cdiv(M, META['BLOCK_SIZE_M']) * triton.cdiv(N, META['BLOCK_SIZE_N']),
        B
    )

    # print(f"Launching kernel with M = {M}, N = {N}, K = {K}, n_bits = {n_bits}, activation = {activation}")

    # wrap this, otherwise triton tries to launch from cuda:0
    with torch.cuda.device(a.device):
        binary_bmm_kernel[grid](
            a, b, c,
            M, N, K,
            n_bits,
            a.stride(1), a.stride(2),
            b.stride(1), b.stride(2),
            c.stride(1), c.stride(2),
            a.stride(0), b.stride(0), c.stride(0),
            ACTIVATION=activation
        )
        return c