"""Utility functions used for tests and benchmarks"""
import random
from typing import List
import numpy
import torch
from .marlin_utils_test import marlin_weights
from .quant_utils import quantize_weights
# This is PyTorch implementation of main part of reorder_meta()
# function, from tools/util/include/cutlass/util/host_reorder.h file
# of CUTLASS source tree. Furthermore, CUTLASS template for sparse
# GEMM decides upon layout of this matrix, and at the moment for the
# sparse GEMM executed on tensor cores, this is layout described by
# ColumnMajorInterleaved<2> data structure, in
# include/cutlass/layout/matrix.h of CUTLASS source tree. The
# reordering of meta matrix into meta_reordered matrix calculated
# according to these segments of CUTLASS code is re-implemented here.
# Note that this calculation produces offsets for scattering metadata
# matrix elements into reordered metadata matrix elements (or,
# equivalently, for gathering reordered metadata matrix element back
# into metadata matrix elements).
def _calculate_meta_reordering_scatter_offsets(m, meta_ncols, meta_dtype,
device):
dst_rows = torch.arange(0, m, device=device)[:, None].repeat(1, meta_ncols)
dst_cols = torch.arange(0, meta_ncols, device=device).repeat(m, 1)
# Reorder the rows, then swizzle the 2x2 blocks.
group_x = 64
group_y = 32 if meta_dtype.itemsize == 2 else 16
dst_rows = (dst_rows // group_x * group_x + (dst_rows % 2) * 2 +
(dst_rows % 8) // 4 + ((dst_rows % group_y) % 4) // 2 * 32 +
((dst_rows % group_x) // 8) * 4)
topright = ((dst_rows % 2 == 0) & (dst_cols % 2 == 1)).to(torch.int8)
bottomleft = ((dst_rows % 2 == 1) & (dst_cols % 2 == 0)).to(torch.int8)
dst_rows += topright - bottomleft
dst_cols -= topright - bottomleft
# Assumed that meta tensor is to be stored in CUTLASS
# InterleavedColumnMajor layout, and reverse engineered
# corresponding code to store values into this tensor.
interleave = 2
cols_maj = dst_cols // interleave
cols_min = dst_cols % interleave
return (cols_maj * m * interleave + dst_rows * interleave +
cols_min).view(-1)
# This function converts dense matrix into sparse semi-structured
# representation, producing "compressed" matrix, in the layout used by
# CUTLASS backend, and corresponding metadata matrix.
def sparse_semi_structured_from_dense_cutlass(dense):
if dense.dim() != 2:
raise RuntimeError(
f"Expected 2-dimensional dense tensor, got {dense.dim()}-dimensional tensor" # noqa: E501
)
m, k = dense.shape
device = dense.device
meta_dtype = torch.int8
if dense.dtype == torch.int8:
meta_dtype = torch.int32
elif dense.dtype in [torch.half, torch.bfloat16, torch.float, torch.int32]:
meta_dtype = torch.int16
else:
raise RuntimeError(f"Invalid datatype {dense.dtype} of dense matrix")
quadbits_per_meta_elem = meta_dtype.itemsize * 8 // 4
if quadbits_per_meta_elem not in (4, 8):
raise RuntimeError(
"Invalid number of elements per meta element calculated")
if meta_dtype == torch.int32:
if m % 16 != 0:
raise RuntimeError(
f"Number of rows of dense matrix {m} must be divisible by 16")
else:
if m % 32 != 0:
raise RuntimeError(
f"Number of rows of dense matrix {m} must be divisible by 32")
if k % (4 * quadbits_per_meta_elem) != 0:
raise RuntimeError(
f"Number of columns of dense matrix {k} must be divisible by {4 * quadbits_per_meta_elem}" # noqa: E501
)
if dense.dtype != torch.float:
ksparse = 4
dense_4 = dense.view(-1, k // ksparse, ksparse)
m0, m1, m2, m3 = (dense_4 != 0).unbind(-1)
else:
ksparse = 2
dense_2 = dense.view(-1, k // ksparse, ksparse)
m0, m2 = m1, m3 = (dense_2 != 0).unbind(-1)
meta_ncols = k // (ksparse * quadbits_per_meta_elem)
# Encoding quadruples of True/False values as follows:
# [True, True, False, False] -> 0b0100
# [True, False, True, False] -> 0b1000
# [False, True, True, False] -> 0b1001
# [True, False, False, True ] -> 0b1100
# [False, True, False, True ] -> 0b1101
# [False, False, True, True ] -> 0b1110
# Thus, lower two bits in the encoding are index of the True value
# at the lowest index in the quadruple, and the higher two bits in
# the encoding are index of the other True value in the quadruple.
# In case there are less than two True values, than False value or
# values at some index or indices are considered True for the
# encoding. In case there are more than two True values, then the
# excess True value(s) at some indices are considered False for
# the encoding. The exact encodings used for these cases are as
# follows:
# [False, False, False, False] -> 0b1110
# [False, False, False, True ] -> 0b1110
# [False, False, True, False] -> 0b1110
# [False, True, False, False] -> 0b1001
# [False, True, True, True ] -> 0b1101
# [True, False, False, False] -> 0b1000
# [True, False, True, True ] -> 0b1100
# [True, True, False, True ] -> 0b0100
# [True, True, True, False] -> 0b0100
# [True, True, True, True ] -> 0b0100
# These particular encodings are chosen, with the help of Espresso
# logic minimizer software, for the purpose of minimization of
# corresponding Boolean functions, that translate non-zero flags
# into encoding bits. Note also possible choices for the first
# and last of these encodings were limited only to (0b0100,
# 0b1110), in order to produce valid encodings for 1:2 sparsity
# case.
expr0 = m0 & m1
expr1 = ~m0 & m1
expr2 = ~m0 & ~m1
bit0 = expr1
bit1 = expr2
bit2 = expr0 | expr2 | m3
bit3 = expr1 | ~m1
idxs0 = bit0 | (bit1.to(torch.int64) << 1)
idxs1 = bit2 | (bit3.to(torch.int64) << 1)
if dense.dtype != torch.float:
sparse0 = dense_4.gather(
-1, idxs0.unsqueeze(-1)) # type: ignore[possibly-undefined]
sparse1 = dense_4.gather(-1, idxs1.unsqueeze(-1))
sparse = torch.stack((sparse0, sparse1), dim=-1).view(m, k // 2)
else:
sparse = dense_2.gather(-1,
idxs0.unsqueeze(-1) // 2).view(
m,
k // 2) # type: ignore[possibly-undefined]
meta_4 = idxs0 | (idxs1 << 2)
meta_n = meta_4.view(
(-1, meta_ncols, quadbits_per_meta_elem)).to(meta_dtype)
if quadbits_per_meta_elem == 4:
meta = (meta_n[:, :, 0]
| (meta_n[:, :, 1] << 4)
| (meta_n[:, :, 2] << 8)
| (meta_n[:, :, 3] << 12))
elif quadbits_per_meta_elem == 8:
meta = (meta_n[:, :, 0]
| (meta_n[:, :, 1] << 4)
| (meta_n[:, :, 2] << 8)
| (meta_n[:, :, 3] << 12)
| (meta_n[:, :, 4] << 16)
| (meta_n[:, :, 5] << 20)
| (meta_n[:, :, 6] << 24)
| (meta_n[:, :, 7] << 28))
# Reorder meta tensor elements.
meta_reordered = meta.new_empty(
(m * meta_ncols, )) # type: ignore[possibly-undefined]
meta_offsets = _calculate_meta_reordering_scatter_offsets(
m, meta_ncols, meta_dtype, device)
meta_reordered.scatter_(0, meta_offsets, meta.view(-1))
return (sparse, meta_reordered.view(m, meta_ncols))
# This function performs reverse of the function above - it
# reconstructs dense matrix from a pair of "compressed" matrix, given
# in the layout used by CUTLASS backend, and accompanying metadata
# matrix.
def sparse_semi_structured_to_dense_cutlass(sparse, meta_reordered):
if sparse.dim() != 2:
raise RuntimeError(
f"Expected 2-dimensional sparse tensor, got {sparse.dim()}-dimensional tensor" # noqa: E501
)
m, k = sparse.shape
device = sparse.device
if meta_reordered.dim() != 2:
raise RuntimeError(
f"Expected 2-dimensional meta tensor, got {meta_reordered.dim()}-dimensional tensor" # noqa: E501
)
if meta_reordered.device != device:
raise RuntimeError(
f"Expected meta matrix to be on {device} device, got matrix on {meta_reordered.device} device" # noqa: E501
)
meta_dtype = meta_reordered.dtype
if meta_dtype not in (torch.int16, torch.int32):
raise RuntimeError(f"Invalid datatype {meta_dtype} of meta matrix")
quadbits_per_meta_elem = meta_dtype.itemsize * 8 // 4
ksparse = 4 if sparse.dtype != torch.float else 2
meta_nrows, meta_ncols = meta_reordered.shape
if meta_nrows != m:
raise RuntimeError(
f"Number of rows of meta matrix {meta_nrows} must be equal to number of columns of spase matrix {m}" # noqa: E501
)
if meta_ncols * ksparse * quadbits_per_meta_elem != 2 * k:
raise RuntimeError(
f"Number of columns of sparse matrix {k} different from the {meta_ncols * ksparse * quadbits_per_meta_elem // 2}, " # noqa: E501
"expected according to the number of columns of meta matrix")
# Undo meta tensor elements reordering.
meta_offsets = _calculate_meta_reordering_scatter_offsets(
m, meta_ncols, meta_dtype, device)
meta = torch.gather(meta_reordered.view(-1), 0,
meta_offsets).view(m, meta_ncols)
# Unpack sparse tensor back to original dense tensor, using
# information provided by meta tensor. Note that torch.float
# datatype is handled pretty much the same as
# torch.half/torch.bfloat16, as metadata for a pair of torch.float
# value is encoded as if underlying 8 bytes contain four
# torch.half/torch.bfloat16 values, where either first two or last
# two are zeros.
meta_2 = torch.empty(
(m, meta_ncols, 2 * quadbits_per_meta_elem),
dtype=meta_dtype,
device=device,
)
if quadbits_per_meta_elem == 4:
meta_2[:, :, 0] = meta & 0b11
meta_2[:, :, 1] = (meta >> 2) & 0b11
meta_2[:, :, 2] = (meta >> 4) & 0b11
meta_2[:, :, 3] = (meta >> 6) & 0b11
meta_2[:, :, 4] = (meta >> 8) & 0b11
meta_2[:, :, 5] = (meta >> 10) & 0b11
meta_2[:, :, 6] = (meta >> 12) & 0b11
meta_2[:, :, 7] = (meta >> 14) & 0b11
elif quadbits_per_meta_elem == 8:
meta_2[:, :, 0] = meta & 0b11
meta_2[:, :, 1] = (meta >> 2) & 0b11
meta_2[:, :, 2] = (meta >> 4) & 0b11
meta_2[:, :, 3] = (meta >> 6) & 0b11
meta_2[:, :, 4] = (meta >> 8) & 0b11
meta_2[:, :, 5] = (meta >> 10) & 0b11
meta_2[:, :, 6] = (meta >> 12) & 0b11
meta_2[:, :, 7] = (meta >> 14) & 0b11
meta_2[:, :, 8] = (meta >> 16) & 0b11
meta_2[:, :, 9] = (meta >> 18) & 0b11
meta_2[:, :, 10] = (meta >> 20) & 0b11
meta_2[:, :, 11] = (meta >> 22) & 0b11
meta_2[:, :, 12] = (meta >> 24) & 0b11
meta_2[:, :, 13] = (meta >> 26) & 0b11
meta_2[:, :, 14] = (meta >> 28) & 0b11
meta_2[:, :, 15] = (meta >> 30) & 0b11
dense_offsets = meta_2.view(-1) + (
torch.arange(0, 2 * m * k // ksparse, device=device) * 4).view(
-1, 1).repeat(1, 2).view(-1)
dense = torch.zeros((m * 2 * k, ), dtype=sparse.dtype, device=device)
if sparse.dtype != torch.float:
# dense.scatter_(0, dense_offsets, sparse.view(-1))
dense.scatter_(0, dense_offsets, sparse.reshape(-1))
else:
dense.view(torch.half).scatter_(0, dense_offsets,
sparse.view(torch.half).view(-1))
return dense.view(m, 2 * k)
def mask_creator(tensor):
"""
Class for creating N:M sparsity masks.
Masks will be created using the N:M ratio, where for every block of
M weights, N will be pruned based on ranked weight value. Each mask
will correspond to the given tensor.
:param N: The number of weights in a group to keep
:param M: The size of a weight group
"""
N = 2
M = 4
mask = None
# for i, tensor in enumerate(tensors):
if tensor.numel() % M != 0:
raise ValueError(
f"Tensor of size {tensor.shape} can't be evenly divided into "
f"{M} groups")
num_groups = tensor.numel() // M
# N:M sparsity for linear layers
tensor_temp = tensor.detach().abs().reshape(num_groups, M)
index = torch.argsort(tensor_temp, dim=1)[:, :int(M - N)]
w_b = torch.ones(tensor_temp.shape, device=tensor_temp.device)
mask = w_b.scatter_(dim=1, index=index, value=0).reshape(tensor.shape)
return mask
def inject_24(w, size_k, size_n):
assert w.shape == (size_k, size_n)
mask = mask_creator(w.t()).t().cuda().bool()
return (mask * w).contiguous(), mask.contiguous()
def check_24(w, num_rows_to_sample=50, _verbose=False):
BLOCK_SIZE = 4
MAX_NON_ZEROS = 2
w = w.t().contiguous()
print("check_24: w.shape = {}".format(w.shape))
num_rows, num_cols = w.shape
sampled_row_idxs = random.choices(range(num_rows), k=num_rows_to_sample)
if _verbose:
print(f"Sampled row idxs = {sampled_row_idxs}")
total_segments = 0
non_24_segments = 0
for i in sampled_row_idxs:
for j in range(0, num_cols - BLOCK_SIZE, BLOCK_SIZE):
total_segments += 1
block = w[i, j:j + BLOCK_SIZE]
num_nonzero = torch.count_nonzero(block)
if num_nonzero > MAX_NON_ZEROS:
print("i = {} j = {} block = {}".format(i, j, block))
non_24_segments += 1
print(f"{non_24_segments} / {total_segments} do not have 2:4 structure.")
def compress_quantized_24_weight(q_24, size_k, size_n, num_bits):
assert q_24.shape == (size_k, size_n)
# Remove zp to normalize over 0
max_q_val = (1 << num_bits) - 1
zp = (max_q_val + 1) // 2
q_24_no_zp = q_24 - zp
# Compress
q_24_no_zp = q_24_no_zp.t().contiguous()
q_24_no_zp_comp, meta = sparse_semi_structured_from_dense_cutlass(
q_24_no_zp)
q_24_no_zp_comp = q_24_no_zp_comp.t().contiguous()
# Restore zp
q_24_comp = q_24_no_zp_comp + zp
# Resize meta to its actual shape (without moving any data)
meta = meta.resize_(meta.shape[1] // 2, meta.shape[0] * 2)
return q_24_comp, meta
def get_scale_perms_24():
scale_perm: List[int] = []
for i in range(8):
scale_perm.extend([i * 8 + j for j in [0, 4, 1, 5, 2, 6, 3, 7]])
scale_perm_single: List[int] = []
for i in range(8):
scale_perm_single.extend([8 * i + j for j in [0, 1, 2, 3, 4, 5, 6, 7]])
return scale_perm, scale_perm_single
def get_weight_perm_24(num_bits: int):
perm_list: List[int] = []
for i in range(32):
perm1: List[int] = []
col = i // 4
col_o = col // 2
for block in [0, 1]:
for row in [
2 * (i % 4),
2 * (i % 4) + 1,
2 * (i % 4 + 4),
2 * (i % 4 + 4) + 1,
]:
perm1.append(16 * row + col_o * 256 + 8 * (col % 2) +
4 * block)
for j in range(4):
perm_list.extend([p + 1 * j for p in perm1])
perm = numpy.array(perm_list)
if num_bits == 4:
interleave = numpy.array([0, 2, 4, 6, 1, 3, 5, 7])
elif num_bits == 8:
interleave = numpy.array([0, 2, 1, 3])
else:
raise ValueError("num_bits must be 4 or 8, got {}".format(num_bits))
perm = perm.reshape((-1, len(interleave)))[:, interleave].ravel()
perm = torch.from_numpy(perm)
return perm
def marlin_permute_scales_24(s: torch.Tensor, size_k: int, size_n: int,
group_size: int) -> torch.Tensor:
scale_perm, scale_perm_single = get_scale_perms_24()
if group_size < size_k and group_size != -1:
s = s.reshape((-1, len(scale_perm)))[:, scale_perm]
else:
s = s.reshape((-1, len(scale_perm_single)))[:, scale_perm_single]
s = s.reshape((-1, size_n)).contiguous()
return s
def marlin_24_quantize(
w: torch.Tensor,
num_bits: int,
group_size: int,
):
size_k, size_n = w.shape
# Normalize group_size
if group_size == -1:
group_size = size_k
assert group_size <= size_k
# Inject 2:4 sparsity
w_24, mask_24 = inject_24(w, size_k, size_n)
# Quantize
w_24_ref, q_w_24, s, g_idx, rand_perm = quantize_weights(w_24,
num_bits,
group_size,
act_order=False)
# Compress quantized weight
q_w_24_comp, meta = compress_quantized_24_weight(q_w_24, size_k, size_n,
num_bits)
size_k_comp = size_k // 2
# Reformat to marlin
weight_perm = get_weight_perm_24(num_bits)
marlin_24_q_w_comp = marlin_weights(q_w_24_comp, size_k_comp, size_n,
num_bits, weight_perm)
marlin_24_s = marlin_permute_scales_24(s, size_k, size_n, group_size)
# Create result
res_list = [w_24_ref, marlin_24_q_w_comp, meta, marlin_24_s]
for i in range(len(res_list)):
res_list[i] = res_list[i].to(w.device)
return res_list