deep_gemm/utils/math.py

import torch
from typing import Tuple


def ceil_div(x: int, y: int) -> int:
    return (x + y - 1) // y


def align(x: int, y: int) -> int:
    return ceil_div(x, y) * y


def ceil_to_ue8m0(x: torch.Tensor):
    assert x.view(-1).amax().item() > 0
    return torch.pow(2.0, torch.ceil(torch.log2(x.abs())))


def per_token_cast_to_fp8(x: torch.Tensor, use_ue8m0: bool) -> Tuple[torch.Tensor, torch.Tensor]:
    assert x.dim() == 2 and x.size(1) % 128 == 0
    m, n = x.shape
    x_view = x.view(m, -1, 128)
    x_amax = x_view.abs().float().amax(dim=2).view(m, -1).clamp(1e-4)
    sf = x_amax / 448.0
    sf = ceil_to_ue8m0(sf) if use_ue8m0 else sf
    return (x_view * (1.0 / sf.unsqueeze(2))).to(torch.float8_e4m3fn).view(m, n), sf


def per_channel_cast_to_fp8(x: torch.Tensor, use_ue8m0: bool) -> Tuple[torch.Tensor, torch.Tensor]:
    assert x.dim() == 2 and x.size(0) % 128 == 0
    m, n = x.shape
    x_view = x.view(-1, 128, n)
    x_amax = x_view.abs().float().amax(dim=1).view(-1, n).clamp(1e-4)
    sf = x_amax / 448.0
    sf = ceil_to_ue8m0(sf) if use_ue8m0 else sf
    return (x_view * (1.0 / sf.unsqueeze(1))).to(torch.float8_e4m3fn).view(m, n), sf


def per_block_cast_to_fp8(x: torch.Tensor, use_ue8m0: bool) -> Tuple[torch.Tensor, torch.Tensor]:
    assert x.dim() == 2
    m, n = x.shape
    x_padded = torch.zeros((align(m, 128), align(n, 128)), dtype=x.dtype, device=x.device)
    x_padded[:m, :n] = x
    x_view = x_padded.view(-1, 128, x_padded.size(1) // 128, 128)
    x_amax = x_view.abs().float().amax(dim=(1, 3), keepdim=True).clamp(1e-4)
    sf = x_amax / 448.0
    sf = ceil_to_ue8m0(sf) if use_ue8m0 else sf
    x_scaled = (x_view * (1.0 / sf)).to(torch.float8_e4m3fn)
    return x_scaled.view_as(x_padded)[:m, :n].contiguous(), sf.view(x_view.size(0), x_view.size(2))