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# Copyright (c) 2025 NVIDIA CORPORATION.
# Licensed under the MIT license.
# Adapted from https://github.com/NVlabs/VILA/tree/main under the Apache 2.0 license.
# LICENSE is in incl_licenses directory.
import torch
import triton
import triton.language as tl
from triton.language.extra.cuda import libdevice
try:
from .common import FP8_MAX_VALUE, SCALE_MIN_THRES, convert_fp8_to_embit, convert_str_to_fp8
from .division import _stochastic_rounding
except:
from common import SCALE_MIN_THRES, FP8_MAX_VALUE, convert_str_to_fp8, convert_fp8_to_embit
from division import _stochastic_rounding
import os
import time
"""Linear Layer Forward + Backward"""
"""Input uses per-tensor quantization"""
"""Output is full-precision/BF16 (for FlashAttention) or 1 * 16 quantization (for the rest)"""
"""The input can be 2D or 3D, but the calculation is performed in 2D"""
def get_configs_io_block():
configs = []
for nstages in [3]:
for block_m in [128, 256]:
for block_n in [128, 256]:
for block_k in [128, 256]:
for nwarps in [8]:
configs.append(
triton.Config(
{"BLOCK_M": block_m, "BLOCK_N": block_n, "BLOCK_K": block_k},
num_stages=nstages,
num_warps=nwarps,
)
)
return configs
@triton.autotune(
configs=get_configs_io_block(),
key=["N"],
)
@triton.jit
def _fp8matmul_kernel(
A,
B,
C,
noise_ptr, # noise for stochastic
M,
N,
K, #
stride_am,
stride_ak, #
stride_bk,
stride_bn, #
stride_cm,
stride_cn, ##
Scale_A,
Scale_B,
Scale_C,
stride_scm,
stride_scn,
output_quantize: tl.constexpr,
QB: tl.constexpr, # default to use 1 * 16 quantization
BIAS,
fp8_max,
e_bit,
m_bit,
SCALE_MIN_THRES: tl.constexpr,
STOCHASTIC: tl.constexpr,
BLOCK_M: tl.constexpr,
BLOCK_N: tl.constexpr,
BLOCK_K: tl.constexpr,
GROUP_M: tl.constexpr,
):
# matrix multiplication
pid = tl.program_id(0)
grid_m = tl.cdiv(M, BLOCK_M)
grid_n = tl.cdiv(N, BLOCK_N)
# re-order program ID for better L2 performance
width = GROUP_M * grid_n
group_id = pid // width
group_size = min(grid_m - group_id * GROUP_M, GROUP_M)
pid_m = group_id * GROUP_M + (pid % group_size)
pid_n = (pid % width) // (group_size)
# do matrix multiplication
rm = pid_m * BLOCK_M + tl.arange(0, BLOCK_M)
rn = pid_n * BLOCK_N + tl.arange(0, BLOCK_N)
ram = tl.max_contiguous(tl.multiple_of(rm % M, BLOCK_M), BLOCK_M)
rbn = tl.max_contiguous(tl.multiple_of(rn % N, BLOCK_N), BLOCK_N)
rk = tl.arange(0, BLOCK_K)
# pointers
A = A + (ram[:, None] * stride_am + rk[None, :] * stride_ak)
B = B + (rk[:, None] * stride_bk + rbn[None, :] * stride_bn)
acc = tl.zeros((BLOCK_M, BLOCK_N), dtype=tl.float32)
for k in range(0, tl.cdiv(K, BLOCK_K)):
# a = tl.load(A)
# b = tl.load(B)
k_remaining = K - k * BLOCK_K
_0 = tl.zeros((1, 1), dtype=C.dtype.element_ty)
a = tl.load(A, mask=rk[None, :] < k_remaining, other=_0)
b = tl.load(B, mask=rk[:, None] < k_remaining, other=_0)
acc = tl.dot(a, b, acc)
A += BLOCK_K * stride_ak
B += BLOCK_K * stride_bk
scale_a = tl.load(Scale_A)
scale_b = tl.load(Scale_B)
scale_ab = scale_a.to(tl.float32) * scale_b.to(tl.float32)
# fp8 dequantize
acc = acc * scale_ab
if BIAS:
bias = tl.load(BIAS + rbn)
acc = acc + bias
# rematerialize rm and rn to save registers
rm = pid_m * BLOCK_M + tl.arange(0, BLOCK_M)
rn = pid_n * BLOCK_N + tl.arange(0, BLOCK_N)
C = C + (rm[:, None] * stride_cm + rn[None, :] * stride_cn)
mask = (rm < M)[:, None] & (rn < N)[None, :]
if output_quantize:
acc = tl.reshape(acc, (BLOCK_M, BLOCK_N // QB, QB))
abs_acc = tl.abs(acc)
acc_max = tl.max(abs_acc, axis=2) + SCALE_MIN_THRES
# tl.device_print("acc_max", acc_max)
acc_scale = acc_max / fp8_max
# tl.device_print("acc_scale", acc_scale)
acc_scale = tl.reshape(acc_scale, (BLOCK_M, BLOCK_N // QB, 1))
acc = tl.div_rn(acc, acc_scale)
acc = tl.reshape(acc, (BLOCK_M, BLOCK_N))
if STOCHASTIC:
noise_block_ptr = noise_ptr + (rm[:, None] * stride_cm + rn[None, :] * stride_cn)
noise = tl.load(noise_block_ptr, boundary_check=(0, 1))
acc = _stochastic_rounding(acc, noise, e_bit, m_bit)
acc_scale = tl.reshape(acc_scale, (BLOCK_M, BLOCK_N // QB))
acc = acc.to(C.dtype.element_ty)
rsm = pid_m * BLOCK_M + tl.arange(0, BLOCK_M)
rsn = pid_n * BLOCK_N // QB + tl.arange(0, BLOCK_N // QB)
Scale_C = Scale_C + (rsm[:, None] * stride_scm + rsn[None, :] * stride_scn)
tl.store(C, acc, mask=mask, boundary_check=(0, 1))
tl.store(Scale_C, acc_scale)
else:
# handles write-back with reduction-splitting
acc = acc.to(C.dtype.element_ty)
tl.store(C, acc, mask=mask)
def fp8matmul(a, b, output_quantize, scale_a, scale_b, QB, bias=None, stochastic=False):
# Deal with batched input
if len(a.shape) == 3:
BS, batched = a.shape[0], True
a = a.reshape(-1, a.shape[2])
else:
batched = False
# Check constraints.
assert a.shape[1] == b.shape[0], "Incompatible dimensions"
assert a.is_contiguous(), "Matrix A must be contiguous"
M, K = a.shape
K, N = b.shape
fp8MaxValue = FP8_MAX_VALUE[a.dtype] # E4M3 and E5M2 have different max value
e_bit, m_bit = convert_fp8_to_embit[a.dtype]
# Allocates output.
if output_quantize:
c = torch.empty((M, N), device=a.device, dtype=a.dtype)
# c = torch.empty((M, N), device=a.device, dtype=torch.float32)
scale_c = torch.empty((M, N // QB), device=a.device, dtype=torch.float32)
else:
c = torch.empty((M, N), device=a.device, dtype=torch.bfloat16)
scale_c = torch.empty(
(1, 1), device=a.device, dtype=torch.bfloat16
) # This line is useless, equivalent to scale_c = None
if stochastic:
noise = torch.empty_like(c, dtype=torch.float32).uniform_(-0.5, 0.5)
else:
noise = None
# 1D launch kernel where each block gets its own program.
grid = lambda META: (triton.cdiv(M, META["BLOCK_M"]) * triton.cdiv(N, META["BLOCK_N"]),)
_fp8matmul_kernel[grid](
a,
b,
c,
noise, #
M,
N,
K, #
a.stride(0),
a.stride(1), #
b.stride(0),
b.stride(1), #
c.stride(0),
c.stride(1), #
scale_a,
scale_b,
scale_c,
scale_c.stride(0),
scale_c.stride(1),
output_quantize=output_quantize,
QB=QB,
BIAS=bias,
fp8_max=fp8MaxValue,
e_bit=e_bit,
m_bit=m_bit,
SCALE_MIN_THRES=SCALE_MIN_THRES,
STOCHASTIC=stochastic,
# BLOCK_M=128,
# BLOCK_N=256,
# BLOCK_K=128,
GROUP_M=8,
# num_stages=3,
# num_warps=8,
)
# Reshape output to batch
if batched:
c = c.reshape(BS, -1, N)
if output_quantize:
scale_c = scale_c.reshape(BS, -1, N // QB)
return c, scale_c
else:
if output_quantize:
scale_c = scale_c.reshape(M, N // QB)
return c, scale_c
return c
def fp8_linear_forward(x, s, w, s_w, output_quantize, QB, bias=None):
w_t = w.t()
return fp8matmul(x, w_t, output_quantize, s, s_w, QB, bias)
# def fp8_linear_forward(x, s, w, s_w, output_quantize, QB):
# print("you are using the wrong linear function. ")
# w_t = w.t()
# if output_quantize:
# return fp8matmul(x, w_t, True, s, s_w, QB)
# else:
# y = fp8matmul(x, w_t, False, s, s_w, QB)
# return y
def fp8_linear_backward(
x_t, s, g, s_g, g_t, w_t, s_w, QB, bias=None, stochastic=False, dgrad_quantize=True
): # dgrad_quantize=True for backward before flashattention
batched = False
if len(g.shape) == 3: # others must be of 2D!
batched = True
BS = g.shape[0]
g = g.reshape(-1, g.shape[-1])
w_t_t = w_t.t()
x_t_t = x_t.t()
if dgrad_quantize:
y, s_y = fp8matmul(g, w_t_t, True, s_g, s_w, QB, stochastic=stochastic)
else:
y = fp8matmul(g, w_t_t, False, s_g, s_w, QB)
w_g = fp8matmul(g_t, x_t_t, False, s_g, s, QB)
if batched:
y = y.reshape(BS, -1, y.shape[-1])
if dgrad_quantize:
if s_y.numel() > 1:
s_y = s_y.reshape(BS, -1, s_y.shape[-1])
if dgrad_quantize:
return y, s_y, w_g
else:
return y, w_g
if __name__ == "__main__":
# Input = torch.load("/home/hxi/lustre_hxi/workdir/FP8_OLMo/debug_linear.pt")
# mul_x_t, mul_s, out_g, out_gs, out_g_t, weight2_t, weight2_s, qgroup_size = Input
# fc2_g, fc2_gs, weight2_grad = fp8_linear_backward(mul_x_t, mul_s, out_g, out_gs, out_g_t, weight2_t, weight2_s, qgroup_size, stochastic=True)
# # fc2_x = fp8_linear_forward(flash_x, flash_s, weight2, weight2_s, False, 16)
# import IPython
# IPython.embed()
def validity_check(M, N, K):
a = torch.randn((M, K), device="cuda", dtype=torch.float32)
b = torch.randn((N, K), device="cuda", dtype=torch.bfloat16)
scale_a, scale_b = torch.randn((1), device="cuda", dtype=torch.bfloat16), torch.randn(
(1), device="cuda", dtype=torch.bfloat16
)
a = a.to(torch.float8_e4m3fn)
b = b.T
b = b.to(torch.float8_e4m3fn)
output_fp8_y, output_fp8_s = fp8matmul(a, b, True, scale_a, scale_b, 16)
a_32, b_32 = a.to(torch.float32), b.to(torch.float32)
output_torch = torch.matmul(a_32, b_32) * scale_a * scale_b
import IPython
IPython.embed()
def time_check(M, N, K):
a = torch.randn((M, K), device="cuda", dtype=torch.float32)
b = torch.randn((N, K), device="cuda", dtype=torch.bfloat16)
scale_a, scale_b = torch.randn((1), device="cuda", dtype=torch.bfloat16), torch.randn(
(1), device="cuda", dtype=torch.bfloat16
)
a = a.to(torch.float8_e4m3fn)
b = b.T
b = b.to(torch.float8_e4m3fn)
for _ in range(10):
torch.cuda.synchronize()
start = time.time()
output_fp8_y = fp8matmul(a, b, False, scale_a, scale_b, 16)
torch.cuda.synchronize()
end = time.time()
print(end - start)
# import IPython
# IPython.embed()
configs = []
for fp8_inputs in [True]:
configs.append(
triton.testing.Benchmark(
x_names=["M", "N", "K"], # Argument names to use as an x-axis for the plot
x_vals=[512 * i for i in range(2, 17)], # Different possible values for `x_name`
line_arg="provider", # Argument name whose value corresponds to a different line in the plot
# Possible values for `line_arg`
# Don't compare to cublas for fp8 cases as torch.matmul doesn't support fp8 at the moment.
line_vals=["triton"] if fp8_inputs else ["cublas", "triton"], # Label name for the lines
line_names=["Triton"] if fp8_inputs else ["cuBLAS", "Triton"], # Line styles
styles=[("green", "-"), ("blue", "-")],
ylabel="TFLOPS", # Label name for the y-axis
plot_name="matmul-performance-"
+ (
"fp16" if not fp8_inputs else "fp8"
), # Name for the plot, used also as a file name for saving the plot.
args={"fp8_inputs": fp8_inputs},
)
)
@triton.testing.perf_report(configs)
def benchmark(M, N, K, provider, fp8_inputs):
a = torch.randn((M, K), device="cuda", dtype=torch.bfloat16)
b = torch.randn((N, K), device="cuda", dtype=torch.bfloat16)
if fp8_inputs:
a = a.to(torch.float8_e4m3fn)
b = b.T
b = b.to(torch.float8_e4m3fn)
scale_a, scale_b = torch.randn((1), device="cuda", dtype=torch.bfloat16), torch.randn(
(1), device="cuda", dtype=torch.bfloat16
)
quantiles = [0.5, 0.2, 0.8]
if provider == "cublas":
import IPython
IPython.embed()
ms, min_ms, max_ms = triton.testing.do_bench(lambda: torch.matmul(a, b), quantiles=quantiles)
if provider == "triton":
ms, min_ms, max_ms = triton.testing.do_bench(
lambda: fp8matmul(a, b, False, scale_a, scale_b, 16), quantiles=quantiles
)
perf = lambda ms: 2 * M * N * K * 1e-12 / (ms * 1e-3)
return perf(ms), perf(max_ms), perf(min_ms)
torch.set_printoptions(sci_mode=False, linewidth=200, precision=6)
# time_check(4096, 11008, 5380)
# validity_check(2048, 1024, 4096)
benchmark.run(show_plots=True, print_data=True)
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