Last active
November 11, 2021 02:52
-
-
Save AranKomat/be50d1bcee38411681f7218d2b81dede to your computer and use it in GitHub Desktop.
Log-linear version of cumsum and cumprod
This file contains bidirectional Unicode text that may be interpreted or compiled differently than what appears below. To review, open the file in an editor that reveals hidden Unicode characters.
Learn more about bidirectional Unicode characters
from functools import partial | |
import torch | |
def _const(example, val): | |
return torch.tensor(val, dtype=example.dtype) | |
def pad(x, axis, side): | |
shape = list(x.size()) | |
if axis == -1: | |
axis = len(shape) - 1 | |
length = shape[axis] | |
x = x.unsqueeze(axis+1) | |
if side == 'right': | |
x = torch.cat([x, torch.zeros_like(x)], axis+1) | |
else: | |
x = torch.cat([torch.zeros_like(x), x], axis+1) | |
shape[axis] = 2*length | |
return x.reshape(shape) | |
def slice_in_dim(operand, start_index, limit_index, stride: int = 1, axis: int = 0): | |
"""Convenience wrapper around slice applying to only one dimension.""" | |
# translate `None` | |
len_axis = operand.shape[axis] | |
start_index_int = int(start_index) if start_index is not None else 0 | |
limit_index_int = int(limit_index) if limit_index is not None else len_axis | |
# translate negative indices | |
if start_index_int < 0: | |
start_index_int = start_index_int + len_axis | |
if limit_index_int < 0: | |
limit_index_int = limit_index_int + len_axis | |
axis = int(axis) | |
return operand.transpose(axis, -1)[..., start_index_int:limit_index_int:stride].transpose(axis, -1) | |
def _prescan_power_of_two(x, axis, op, unit): | |
n = x.shape[axis] | |
assert n != 0 and n & (n - 1) == 0, "n must be a power of 2" | |
# Upsweep | |
xs = [] | |
for d in range(0, n.bit_length() - 1): | |
x1 = slice_in_dim(x, 0, None, stride=2, axis=axis) | |
xs.append(x1) | |
x2 = slice_in_dim(x, 1, None, stride=2, axis=axis) | |
x = op(x1, x2) | |
total = x | |
# Downsweep | |
x = torch.full_like(total, unit) | |
for w in reversed(xs): | |
x1 = pad(x, axis=axis, side='right') | |
x2 = pad(x, axis=axis, side='left') | |
w = pad(w, axis=axis, side='left') | |
x = x1 + op(x2, w) | |
return x, total | |
def _parallel_prefix_scan(x, axis, op, unit): | |
n = x.shape[axis] | |
if n == 0: | |
return x | |
# Pads to the next largest power of two | |
nbits = n.bit_length() | |
if n == (1 << (nbits - 1)): | |
nbits -= 1 | |
shape = list(x.size()) | |
shape[axis] = (1 << nbits) - n | |
padding = x.new_zeros(shape).fill_(unit) | |
x = torch.cat([x, padding], axis) | |
x, total = _prescan_power_of_two(x, axis, op, unit) | |
return torch.cat([slice_in_dim(x, 1, n, axis=axis), total], axis) | |
def cumsum(x, dim=-1): | |
def add(y, z): return y + z | |
return _parallel_prefix_scan(x, axis=dim, op=add, unit=0) | |
def cumprod(x, dim=-1): | |
def mult(y, z): return y * z | |
return _parallel_prefix_scan(x, axis=dim, op=mult, unit=1) | |
import os | |
os.environ['CUDA_VISIBLE_DEVICES']='0' | |
a = torch.empty(512, 8000, dtype=torch.float32).to('cuda') | |
cumsum(a, dim=-1) |
Sign up for free
to join this conversation on GitHub.
Already have an account?
Sign in to comment