torch-ext/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, gran_k: int = 128) -> Tuple[torch.Tensor, torch.Tensor]:
    assert x.dim() == 2
    m, n = x.shape
    padded_n = align(n, gran_k)
    x_padded = torch.empty((m, padded_n), dtype=x.dtype, device=x.device).fill_(0)
    x_padded[:, :n] = x
    x_view = x_padded.view(m, -1, gran_k)
    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, padded_n)[:, :n].contiguous(), sf


def per_channel_cast_to_fp8(x: torch.Tensor, use_ue8m0: bool, gran_k: int = 128) -> Tuple[torch.Tensor, torch.Tensor]:
    assert x.dim() == 2 and x.size(0) % gran_k == 0
    m, n = x.shape
    x_view = x.view(-1, gran_k, 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, gran_k: int = 128) -> Tuple[torch.Tensor, torch.Tensor]:
    assert x.dim() == 2
    m, n = x.shape
    x_padded = torch.zeros((align(m, gran_k), align(n, gran_k)), dtype=x.dtype, device=x.device)
    x_padded[:m, :n] = x
    x_view = x_padded.view(-1, gran_k, x_padded.size(1) // gran_k, gran_k)
    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))


def per_custom_dims_cast_to_fp8(x: torch.Tensor, dims: Tuple, use_ue8m0: bool) -> Tuple[torch.Tensor, torch.Tensor]:
    excluded_dims = tuple([i for i in range(x.dim()) if i not in set(dims)])
    x_amax = x.abs().float().amax(dim=excluded_dims, keepdim=True).clamp(1e-4)
    sf = x_amax / 448.0
    sf = ceil_to_ue8m0(sf) if use_ue8m0 else sf
    x_scaled = (x * (1.0 / sf)).to(torch.float8_e4m3fn)
    return x_scaled, sf.squeeze()


def _quantize_to_fp4_e2m1(x: torch.Tensor) -> torch.Tensor:
    ax = x.abs().clamp_max(6.0)
    # {0, 0.5, 1, 1.5, 2, 3, 4, 6}
    # midpoints: 0.25, 0.75, 1.25, 1.75, 2.5, 3.5, 5.0
    boundaries = torch.tensor([0.25, 0.75, 1.25, 1.75, 2.5, 3.5, 5.0],
                              device=x.device, dtype=ax.dtype)
    idx = torch.bucketize(ax, boundaries) 
    code = idx.to(torch.uint8)
    sign = (x < 0) & (idx != 0)
    code = code | (sign.to(torch.uint8) << 3)
    return code  # uint8, 0..15


def per_token_cast_to_fp4(x: torch.Tensor, use_ue8m0: bool, gran_k: int = 128) -> Tuple[torch.Tensor, torch.Tensor]:
    assert x.dim() == 2
    m, n = x.shape
    assert n % 2 == 0
    padded_n = align(n, gran_k)
    x_padded = torch.zeros((m, padded_n), dtype=x.dtype, device=x.device)
    x_padded[:, :n] = x
    x_view = x_padded.view(m, -1, gran_k)
    x_amax = x_view.abs().float().amax(dim=2).clamp_min(1e-4)
    sf = x_amax / 6.0
    sf = ceil_to_ue8m0(sf) if use_ue8m0 else sf
    x_scaled = x_view * (1.0 / sf.unsqueeze(2))
    codes = _quantize_to_fp4_e2m1(x_scaled).view(m, padded_n)  # uint8, (m, padded_n)
    codes2 = codes.view(m, padded_n // 2, 2)
    packed = (codes2[:, :, 0] & 0x0F) | ((codes2[:, :, 1] & 0x0F) << 4)  # uint8
    return packed[:, :n // 2].contiguous(), sf


def transpose_packed_fp4(a: torch.Tensor) -> torch.Tensor:
    assert a.dtype == torch.uint8
    assert a.dim() == 2
    m, n2 = a.shape
    n = n2 * 2
    assert (m % 2) == 0
    lo = a & 0x0F
    hi = (a >> 4) & 0x0F
    codes = torch.empty((m, n), device=a.device, dtype=torch.uint8)
    codes[:, 0::2], codes[:, 1::2] = lo, hi
    codes_t = codes.transpose(0, 1).contiguous()
    codes2 = codes_t.view(n, m // 2, 2)
    out = (codes2[:, :, 0] & 0x0F) | ((codes2[:, :, 1] & 0x0F) << 4)
    return out.contiguous()