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def calc_mantissa(abs_x, exponent, normal_mask, MANTISSA_BITS, EXPONENT_BIAS, generator=None):
mantissa_scaled = torch.where(
normal_mask,
(abs_x / (2.0 ** (exponent - EXPONENT_BIAS)) - 1.0) * (2**MANTISSA_BITS),
(abs_x / (2.0 ** (-EXPONENT_BIAS + 1 - MANTISSA_BITS)))
)
mantissa_scaled += torch.rand(mantissa_scaled.size(), dtype=mantissa_scaled.dtype, layout=mantissa_scaled.layout, device=mantissa_scaled.device, generator=generator)
return mantissa_scaled.floor() / (2**MANTISSA_BITS)
#Not 100% sure about this
def manual_stochastic_round_to_float8(x, dtype, generator=None):
if dtype == torch.float8_e4m3fn:
EXPONENT_BITS, MANTISSA_BITS, EXPONENT_BIAS = 4, 3, 7
elif dtype == torch.float8_e5m2:
EXPONENT_BITS, MANTISSA_BITS, EXPONENT_BIAS = 5, 2, 15
else:
raise ValueError("Unsupported dtype")
x = x.half()
sign = torch.sign(x)
abs_x = x.abs()
sign = torch.where(abs_x == 0, 0, sign)
# Combine exponent calculation and clamping
exponent = torch.clamp(
torch.floor(torch.log2(abs_x)) + EXPONENT_BIAS,
0, 2**EXPONENT_BITS - 1
)
# Combine mantissa calculation and rounding
normal_mask = ~(exponent == 0)
abs_x[:] = calc_mantissa(abs_x, exponent, normal_mask, MANTISSA_BITS, EXPONENT_BIAS, generator=generator)
sign *= torch.where(
normal_mask,
(2.0 ** (exponent - EXPONENT_BIAS)) * (1.0 + abs_x),
(2.0 ** (-EXPONENT_BIAS + 1)) * abs_x
)
inf = torch.finfo(dtype)
torch.clamp(sign, min=inf.min, max=inf.max, out=sign)
return sign
def stochastic_rounding(value, dtype, seed=0):
if dtype == torch.float32:
return value.to(dtype=torch.float32)
if dtype == torch.float16:
return value.to(dtype=torch.float16)
if dtype == torch.bfloat16:
return value.to(dtype=torch.bfloat16)
if dtype == torch.float8_e4m3fn or dtype == torch.float8_e5m2:
generator = torch.Generator(device=value.device)
generator.manual_seed(seed)
output = torch.empty_like(value, dtype=dtype)
num_slices = max(1, (value.numel() / (4096 * 4096)))
slice_size = max(1, round(value.shape[0] / num_slices))
for i in range(0, value.shape[0], slice_size):
output[i:i+slice_size].copy_(manual_stochastic_round_to_float8(value[i:i+slice_size], dtype, generator=generator))
return output
return value.to(dtype=dtype)
# TODO: improve this?
def stochastic_float_to_fp4_e2m1(x, generator):
orig_shape = x.shape
sign = torch.signbit(x).to(torch.uint8)
exp = torch.floor(torch.log2(x.abs()) + 1.0).clamp(0, 3)
x += (torch.rand(x.size(), dtype=x.dtype, layout=x.layout, device=x.device, generator=generator) - 0.5) * (2 ** (exp - 2.0)) * 1.25
x = x.abs()
exp = torch.floor(torch.log2(x) + 1.1925).clamp(0, 3)
mantissa = torch.where(
exp > 0,
(x / (2.0 ** (exp - 1)) - 1.0) * 2.0,
(x * 2.0),
out=x
).round().to(torch.uint8)
del x
exp = exp.to(torch.uint8)
fp4 = (sign << 3) | (exp << 1) | mantissa
del sign, exp, mantissa
fp4_flat = fp4.view(-1)
packed = (fp4_flat[0::2] << 4) | fp4_flat[1::2]
return packed.reshape(list(orig_shape)[:-1] + [-1])
def to_blocked(input_matrix, flatten: bool = True) -> torch.Tensor:
"""
Rearrange a large matrix by breaking it into blocks and applying the rearrangement pattern.
See:
https://docs.nvidia.com/cuda/cublas/index.html#d-block-scaling-factors-layout
Args:
input_matrix: Input tensor of shape (H, W)
Returns:
Rearranged tensor of shape (32*ceil_div(H,128), 16*ceil_div(W,4))
"""
def ceil_div(a, b):
return (a + b - 1) // b
rows, cols = input_matrix.shape
n_row_blocks = ceil_div(rows, 128)
n_col_blocks = ceil_div(cols, 4)
# Calculate the padded shape
padded_rows = n_row_blocks * 128
padded_cols = n_col_blocks * 4
padded = input_matrix
if (rows, cols) != (padded_rows, padded_cols):
padded = torch.zeros(
(padded_rows, padded_cols),
device=input_matrix.device,
dtype=input_matrix.dtype,
)
padded[:rows, :cols] = input_matrix
# Rearrange the blocks
blocks = padded.view(n_row_blocks, 128, n_col_blocks, 4).permute(0, 2, 1, 3)
rearranged = blocks.reshape(-1, 4, 32, 4).transpose(1, 2).reshape(-1, 32, 16)
if flatten:
return rearranged.flatten()
return rearranged.reshape(padded_rows, padded_cols)
def stochastic_round_quantize_nvfp4_block(x, per_tensor_scale, generator):
F4_E2M1_MAX = 6.0
F8_E4M3_MAX = 448.0
orig_shape = x.shape
block_size = 16
x = x.reshape(orig_shape[0], -1, block_size)
scaled_block_scales_fp8 = torch.clamp(((torch.amax(torch.abs(x), dim=-1)) / F4_E2M1_MAX) / per_tensor_scale.to(x.dtype), max=F8_E4M3_MAX).to(torch.float8_e4m3fn)
x = x / (per_tensor_scale.to(x.dtype) * scaled_block_scales_fp8.to(x.dtype)).unsqueeze(-1)
x = x.view(orig_shape).nan_to_num()
data_lp = stochastic_float_to_fp4_e2m1(x, generator=generator)
return data_lp, scaled_block_scales_fp8
def stochastic_round_quantize_nvfp4(x, per_tensor_scale, pad_16x, seed=0):
def roundup(x: int, multiple: int) -> int:
"""Round up x to the nearest multiple."""
return ((x + multiple - 1) // multiple) * multiple
generator = torch.Generator(device=x.device)
generator.manual_seed(seed)
# Handle padding
if pad_16x:
rows, cols = x.shape
padded_rows = roundup(rows, 16)
padded_cols = roundup(cols, 16)
if padded_rows != rows or padded_cols != cols:
x = torch.nn.functional.pad(x, (0, padded_cols - cols, 0, padded_rows - rows))
x, blocked_scaled = stochastic_round_quantize_nvfp4_block(x, per_tensor_scale, generator)
return x, to_blocked(blocked_scaled, flatten=False)
def stochastic_round_quantize_nvfp4_by_block(x, per_tensor_scale, pad_16x, seed=0, block_size=4096 * 4096):
def roundup(x: int, multiple: int) -> int:
"""Round up x to the nearest multiple."""
return ((x + multiple - 1) // multiple) * multiple
orig_shape = x.shape
# Handle padding
if pad_16x:
rows, cols = x.shape
padded_rows = roundup(rows, 16)
padded_cols = roundup(cols, 16)
if padded_rows != rows or padded_cols != cols:
x = torch.nn.functional.pad(x, (0, padded_cols - cols, 0, padded_rows - rows))
# Note: We update orig_shape because the output tensor logic below assumes x.shape matches
# what we want to produce. If we pad here, we want the padded output.
orig_shape = x.shape
orig_shape = list(orig_shape)
output_fp4 = torch.empty(orig_shape[:-1] + [orig_shape[-1] // 2], dtype=torch.uint8, device=x.device)
output_block = torch.empty(orig_shape[:-1] + [orig_shape[-1] // 16], dtype=torch.float8_e4m3fn, device=x.device)
generator = torch.Generator(device=x.device)
generator.manual_seed(seed)
num_slices = max(1, (x.numel() / block_size))
slice_size = max(1, (round(x.shape[0] / num_slices)))
for i in range(0, x.shape[0], slice_size):
fp4, block = stochastic_round_quantize_nvfp4_block(x[i: i + slice_size], per_tensor_scale, generator=generator)
output_fp4[i:i + slice_size].copy_(fp4)
output_block[i:i + slice_size].copy_(block)
return output_fp4, to_blocked(output_block, flatten=False)
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