flash-attention/csrc/cutlass/python/pycute/int_tuple.py

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"""
Functions for manipulating IntTuples
"""

from functools import reduce
from itertools import chain
from typing import Union
from .typing import Integer


def is_int(x):
  return isinstance(x, Integer)


def is_tuple(x):
  return isinstance(x, tuple)


def flatten(t):
  if is_tuple(t):
    if len(t) == 0:
      return ()
    else:
      return tuple(i for a in t for i in flatten(a))
  else:
    return (t,)


def signum(a):
  return bool(a > 0) - bool(a < 0)


def product(a):
  if is_tuple(a):
    return reduce(lambda val,elem : val*product(elem), a, 1)
  else:
    return a


def inner_product(a, b):
  if is_tuple(a):                      # tuple tuple
    assert len(a) == len(b)
    return sum(inner_product(x,y) for x,y in zip(a,b))
  else:                                # "int" "int"
    assert not is_tuple(b)
    return a * b


def tuple_max(a):
  if is_tuple(a):
    return max(tuple_max(x) for x in a)
  else:
    return a


def elem_scale(a, b):
  if is_tuple(a):
    if is_tuple(b):                     # tuple tuple
      assert len(a) == len(b)
      return tuple(elem_scale(x,y) for x,y in zip(a,b))
    else:                               # tuple "int"
      assert False           # Error
  else:
    if is_tuple(b):                     # "int" tuple
      return elem_scale(a, product(b))
    else:                               # "int" "int"
      return a * b


# Inclusive prefix ceil div with output congruent to input a
def shape_div(a, b):
  if is_tuple(a):
    if is_tuple(b):                    # tuple tuple
      assert len(a) == len(b)
      return tuple(shape_div(x,y) for x,y in zip(a,b))
    else:                              # tuple "int"
      #r = [shape_div(a[0],b)] + [shape_div(a[i],b := shape_div(b, product(a[i-1]))) for i in range(1,len(a))]
      r = []
      for v in a:
        r.append(shape_div(v,b))
        b = shape_div(b,product(v))
      return tuple(r)
  else:
    if is_tuple(b):                    # "int" tuple
      return shape_div(a, product(b))
    else:                              # "int" "int"
      assert a % b == 0 or b % a == 0
      #return -(-a // b)      # Python exclusive impl: "//" is always floor div
      if a % b == 0:
        return a // b
      else:
        return signum(a*b)


# Exclusive prefix product with output congruent to input a
def prefix_product(a, init=1):
  if is_tuple(a):
    if is_tuple(init):                 # tuple tuple
      assert len(a) == len(init)
      return tuple(prefix_product(x,i) for x,i in zip(a,init))
    else:                              # tuple "int"
      #r = [prefix_product(a[0],init)] + [prefix_product(a[i],init := init * product(a[i-1])) for i in range(1,len(a))]
      r = []
      for v in a:
        r.append(prefix_product(v,init))
        init = init * product(v)
      return tuple(r)
  else:
    if is_tuple(init):                 # "int" tuple
      assert False           # Error
    else:                              # "int" "int"
      return init


def idx2crd(idx, shape, stride=None):
  if stride is None:
    stride = prefix_product(shape)

  if is_tuple(idx):
    if is_tuple(shape):                # tuple tuple tuple
      assert len(idx) == len(shape) and len(idx) == len(stride)
      return tuple(idx2crd(i, s, d) for i, s, d in zip(idx,shape,stride))
    else:                              # tuple "int" "int"
      assert False           # Error
  else:
    if is_tuple(shape):                # "int" tuple tuple
      assert len(shape) == len(stride)
      return tuple(idx2crd(idx, s, d) for s,d in zip(shape,stride))
    else:                              # "int" "int" "int"
      return (idx // stride) % shape


def crd2idx(crd, shape, stride=None):
  if stride is None:
    stride = prefix_product(shape)

  if is_tuple(crd):
    if is_tuple(shape):                # tuple tuple tuple
      assert len(crd) == len(shape) and len(crd) == len(stride)
      return sum(crd2idx(c, s, d) for c, s, d in zip(crd, shape, stride))
    else:                              # tuple "int" "int"
      assert False, f"crd={crd}, shape={shape}"           # Error
  else:
    if crd is None:
      crd = 0

    if is_tuple(shape):                # "int" tuple tuple
      assert len(shape) == len(stride)
      result = 0
      for i in range(len(shape)-1):
        result += crd2idx(crd % product(shape[i]), shape[i], stride[i])
        crd = crd // product(shape[i])
      return result + crd2idx(crd, shape[-1], stride[-1])
    else:                              # "int" "int" "int"
      return crd * stride


# Transform crd into the dst_shape's iteration space
def crd2crd(crd, dst_shape, src_shape=None):
  if is_tuple(crd):
    if is_tuple(dst_shape):            # tuple tuple
      assert len(crd) == len(dst_shape)
      return tuple(crd2crd(x, y) for x, y in zip(crd,dst_shape))
    else:                              # tuple "int"
      # Ambiguous unless we have src_shape
      assert src_shape is not None
      return crd2idx(crd, src_shape)
  else:
    if is_tuple(dst_shape):            # "int" tuple
      return idx2crd(crd, dst_shape)
    else:                              # "int" "int"
      assert crd < dst_shape
      return crd


# Filter trg according to crd: keep only elements of trg that are paired with None
def slice_(crd: Union[None, tuple, int],
           trg: Union[tuple, int]):
  if is_tuple(crd):
    if is_tuple(trg):                  # tuple tuple
      assert len(crd) == len(trg)
      # match C++ behavior of `filter_tuple` using `tuple_cat(...)`
      return tuple(chain(*filter(lambda x: x != (), [slice_(c, s) for c, s in zip(crd, trg)])))
    else:
      assert False                     # tuple "int" : Error
  elif crd is None:
    # match C++ behavior `return cute::tuple<B>{b};`
    return (trg,)
  else:
    return ()


# Determine if None appears at any of an int_tuples' terminals
def has_none(a: Union[None, tuple, int]):
  if is_tuple(a):
    return any(has_none(v) for v in a)
  else:
    return a is None