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layout.hpp
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/***************************************************************************************************
* Copyright (c) 2023 - 2024 NVIDIA CORPORATION & AFFILIATES. All rights reserved.
* SPDX-License-Identifier: BSD-3-Clause
*
* Redistribution and use in source and binary forms, with or without
* modification, are permitted provided that the following conditions are met:
*
* 1. Redistributions of source code must retain the above copyright notice, this
* list of conditions and the following disclaimer.
*
* 2. Redistributions in binary form must reproduce the above copyright notice,
* this list of conditions and the following disclaimer in the documentation
* and/or other materials provided with the distribution.
*
* 3. Neither the name of the copyright holder nor the names of its
* contributors may be used to endorse or promote products derived from
* this software without specific prior written permission.
*
* THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND CONTRIBUTORS "AS IS"
* AND ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE
* IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE ARE
* DISCLAIMED. IN NO EVENT SHALL THE COPYRIGHT HOLDER OR CONTRIBUTORS BE LIABLE
* FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL
* DAMAGES (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS OR
* SERVICES; LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION) HOWEVER
* CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT LIABILITY,
* OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY OUT OF THE USE
* OF THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF SUCH DAMAGE.
*
**************************************************************************************************/
#pragma once
#include <cute/config.hpp>
#include <cute/underscore.hpp>
#include <cute/int_tuple.hpp>
#include <cute/stride.hpp>
#include <cute/numeric/arithmetic_tuple.hpp>
#include <cute/numeric/integral_ratio.hpp>
#include <cute/numeric/integral_constant.hpp>
namespace cute
{
// Aliases
template <class... Shapes>
using Shape = cute::tuple<Shapes...>;
template <class... Strides>
using Stride = cute::tuple<Strides...>;
template <class... Strides>
using Step = cute::tuple<Strides...>;
template <class... Coords>
using Coord = cute::tuple<Coords...>;
template <class... Layouts>
using Tile = cute::tuple<Layouts...>;
template <class... Ts>
CUTE_HOST_DEVICE constexpr
Shape<Ts...>
make_shape(Ts const&... t) {
return {t...};
}
template <class... Ts>
CUTE_HOST_DEVICE constexpr
Stride<Ts...>
make_stride(Ts const&... t) {
return {t...};
}
template <class... Ts>
CUTE_HOST_DEVICE constexpr
Step<Ts...>
make_step(Ts const&... t) {
return {t...};
}
template <class... Ts>
CUTE_HOST_DEVICE constexpr
Coord<Ts...>
make_coord(Ts const&... t) {
return {t...};
}
template <class... Ts>
CUTE_HOST_DEVICE constexpr
Tile<Ts...>
make_tile(Ts const&... t)
{
return {t...};
}
//
// Layout
//
template <class Shape, class Stride = LayoutLeft::Apply<Shape> >
struct Layout
: private cute::tuple<Shape, Stride> // EBO for static layouts
{
// Expensive in compilation time...
//static_assert(is_congruent<Shape, Stride>::value, "Shape and Stride must be congruent");
// NOTE: This defaults static Shapes/Strides correctly, but not dynamic
CUTE_HOST_DEVICE constexpr
Layout(Shape const& shape = {}, Stride const& stride = {})
: cute::tuple<Shape, Stride>(shape, stride)
{}
//
// Accessors
//
static constexpr int rank = rank_v<Shape>;
CUTE_HOST_DEVICE constexpr
decltype(auto)
layout() {
return *this;
}
CUTE_HOST_DEVICE constexpr
decltype(auto)
layout() const {
return *this;
}
template <int... I>
CUTE_HOST_DEVICE constexpr
decltype(auto)
shape() {
return get<0,I...>(static_cast<cute::tuple<Shape, Stride>&>(*this));
}
template <int... I>
CUTE_HOST_DEVICE constexpr
decltype(auto)
shape() const {
return get<0,I...>(static_cast<cute::tuple<Shape, Stride> const&>(*this));
}
template <int... I>
CUTE_HOST_DEVICE constexpr
decltype(auto)
stride() {
return get<1,I...>(static_cast<cute::tuple<Shape, Stride>&>(*this));
}
template <int... I>
CUTE_HOST_DEVICE constexpr
decltype(auto)
stride() const {
return get<1,I...>(static_cast<cute::tuple<Shape, Stride> const&>(*this));
}
//
// Mappings
//
// Map a logical coordinate to a linear index (Coord has no Underscore slice operators)
// OR
// Slice the layout and return the sublayout (Coord has an Underscore slice op)
template <class Coord>
CUTE_HOST_DEVICE constexpr
auto
operator()(Coord const& coord) const {
if constexpr (has_underscore<Coord>::value) {
return slice(coord, *this);
} else {
return crd2idx(coord, shape(), stride());
}
CUTE_GCC_UNREACHABLE;
}
// Convenience function for multi-dimensional coordinates
template <class Coord0, class Coord1, class... Coords>
CUTE_HOST_DEVICE constexpr
auto
operator()(Coord0 const& c0, Coord1 const& c1, Coords const&... cs) const {
return operator()(make_coord(c0,c1,cs...));
}
//
// Compose
//
template <class OtherLayout>
CUTE_HOST_DEVICE constexpr
auto
compose(OtherLayout const& other) const {
return composition(*this, other);
}
template <class... Layouts>
CUTE_HOST_DEVICE constexpr
auto
compose(Layouts const&... layouts) const {
return composition(*this, make_tile(layouts...));
}
template <class OtherShape>
CUTE_HOST_DEVICE constexpr
auto
with_shape(OtherShape const& shape) const {
return composition(*this, make_layout(shape));
}
template <class... Shapes>
CUTE_HOST_DEVICE constexpr
auto
with_shape(Shapes const&... shapes) const {
return composition(*this, make_layout(make_shape(shapes...)));
}
//
// Tile
//
template <class OtherLayout>
CUTE_HOST_DEVICE constexpr
auto
tile(OtherLayout const& other) const {
return tiled_divide(*this, other);
}
template <class... Layouts>
CUTE_HOST_DEVICE constexpr
auto
tile(Layouts const&... layouts) const {
return tiled_divide(*this, make_tile(layouts...));
}
//
// Utility
//
//
// Index to Coordinate
//
// NOTE: Only valid for compact layouts
// Return the (hierarchical) ND logical coordinate corresponding to the linear index
// @post crd2idx(@a result, shape(), stride()) == idx
// @post congruent(@a result, shape())
template <class IInt,
__CUTE_REQUIRES(is_integral<IInt>::value)>
CUTE_HOST_DEVICE constexpr
auto
get_hier_coord(IInt const& idx) const {
return cute::idx2crd(idx, shape(), stride());
}
// Return the (flat) ND logical coordinate corresponding to the linear index
// @post crd2idx(@a result, shape(), stride()) == idx
// @post rank(@a result) == rank(shape()) && depth(@a result) == 1
template <class IInt,
__CUTE_REQUIRES(is_integral<IInt>::value)>
CUTE_HOST_DEVICE constexpr
auto
get_flat_coord(IInt const& idx) const {
return cute::crd2crd(this->get_hier_coord(idx), shape(), repeat<rank>(Int<1>{}));
}
// Return the generalized column-major 1D logical coordinate corresponding to the linear index
// @post crd2idx(@a result, shape(), stride()) == idx
// @post is_integral<decltype(@a result)>::value
template <class IInt,
__CUTE_REQUIRES(is_integral<IInt>::value)>
CUTE_HOST_DEVICE constexpr
auto
get_1d_coord(IInt const& idx) const {
return cute::crd2idx(this->get_hier_coord(idx), shape());
}
//
// Coordinate to Coordinate
//
#if 0
// Return the (hierarchical) ND logical coordinate corresponding to the linear index
// @post congruent(@a result, shape())
template <class Coord>
CUTE_HOST_DEVICE constexpr
auto
crd_2_hier_coord(Coord const& crd) const {
return cute::crd2crd(crd, shape(), shape());
}
// Return the (flat) ND logical coordinate corresponding to the linear index
// @post rank(@a result) == rank(shape()) && depth(@a result) == 1
template <class Coord>
CUTE_HOST_DEVICE constexpr
auto
crd_2_flat_coord(Coord const& crd) const {
return cute::crd2crd(crd, shape(), product_each(shape()));
}
// Return the generalized column-major 1D logical coordinate corresponding to the linear index
// @post is_integral<decltype(@a result)>::value
template <class Coord>
CUTE_HOST_DEVICE constexpr
auto
crd_2_1d_coord(Coord const& crd) const {
//return cute::crd2crd(crd, shape(), product(shape()));
return cute::crd2idx(crd, shape());
}
#endif
};
// Equality, return a static or dynamic boolean
template <class ShapeA, class StrideA,
class ShapeB, class StrideB>
CUTE_HOST_DEVICE constexpr
auto
operator==(Layout<ShapeA,StrideA> const& layoutA, Layout<ShapeB,StrideB> const& layoutB)
{
return layoutA.shape() == layoutB.shape() && layoutA.stride() == layoutB.stride();
}
template <class Layout>
struct is_layout : false_type {};
template <class Shape, class Stride>
struct is_layout<Layout<Shape,Stride>> : true_type {};
//
// Layout construction
//
template <class Shape, class Stride,
__CUTE_REQUIRES((is_tuple<Shape >::value || is_integral<Shape >::value) &&
(is_tuple<Stride>::value || is_integral<Stride>::value))>
CUTE_HOST_DEVICE constexpr
auto
make_layout(Shape const& shape, Stride const& stride)
{
return Layout<Shape,Stride>(shape, stride);
}
template <class Shape,
__CUTE_REQUIRES(is_tuple<Shape>::value || is_integral<Shape>::value)>
CUTE_HOST_DEVICE constexpr
auto
make_layout(Shape const& shape)
{
return make_layout(shape, compact_col_major(shape));
}
// Construct a layout from multiple layouts by
// concatenating each layout as an independent mode
template <class... Shapes, class... Strides>
CUTE_HOST_DEVICE constexpr
auto
make_layout(Layout<Shapes,Strides> const&... layouts)
{
return make_layout(make_shape (layouts.shape()...),
make_stride(layouts.stride()...));
}
//
// Convenience tags for common layouts
//
template <class Shape>
CUTE_HOST_DEVICE constexpr
auto
make_layout(Shape const& shape, GenColMajor)
{
return make_layout(shape, compact_col_major(shape));
}
template <class Shape>
CUTE_HOST_DEVICE constexpr
auto
make_layout(Shape const& shape, GenRowMajor)
{
return make_layout(shape, compact_row_major(shape));
}
//
// Advanced Layout constructions
//
// Make a compact layout with shape @a shape and strides following the order induced by @a order.
// Dynamic values in @a order are ignored, considered large, and considered ordered from left to right.
// Example:
// make_ordered_layout(Shape<_2,_2,_2,_2>{}, Step<_0,_2,_3,_1>{})
// -> (_2,_2,_2,_2):(_1,_4,_8,_2)
// make_ordered_layout(make_shape(2,3,4,5), make_step(Int<2>{}, 67, 42, Int<50>{}))
// -> (2,3,4,5):(_1,10,30,2)
template <class Shape, class Order>
CUTE_HOST_DEVICE constexpr
auto
make_ordered_layout(Shape const& shape, Order const& order)
{
return make_layout(shape, compact_order(shape, order));
}
// Make a compact layout with the same shape as @a layout
// and strides following the order induced by @a layout.stride().
// Static-0 strides in the input @a layout are preserved in the output.
// Example:
// make_layout_like(Layout<Shape<_2,_2,_2,_2>, Stride<_0,_2,_4,_1>>{})
// -> (_2,_2,_2,_2):(_0,_2,_4,_1)
// make_layout_like(make_layout(make_shape(2,3,4,5), make_stride(Int<0>{},42,Int<1>{},Int<0>{})))
// -> (2,3,4,5):(_0,4,_1,_0)
template <class Shape, class Stride>
CUTE_HOST_DEVICE constexpr
auto
make_layout_like(Layout<Shape,Stride> const& layout)
{
return make_layout(layout.shape(),
compact_order(filter_zeros(layout.stride(), layout.shape()), layout.stride()));
}
// Make a compact layout with the same shape as @a layout
// and strides following the order induced by @a layout.stride(),
// except mode-0 is always stride-1 and generated column-major.
// The 0th mode is commonly used for MMA_Atoms or Copy_Atoms
// so this generates the 0th mode with LayoutLeft regardless of the reference layout.
template <class Shape, class Stride>
CUTE_HOST_DEVICE constexpr
auto
make_fragment_like(Layout<Shape,Stride> const& layout)
{
constexpr int R = Layout<Shape,Stride>::rank;
if constexpr (R > 1 && is_static<Shape>::value) {
return tiled_product(make_layout(shape<0>(layout)),
make_ordered_layout(take<1,R>(layout.shape()), take<1,R>(layout.stride())));
} else {
return make_layout(layout.shape());
}
CUTE_GCC_UNREACHABLE;
}
template <class Shape,
__CUTE_REQUIRES(is_tuple<Shape>::value || is_integral<Shape>::value)>
CUTE_HOST_DEVICE constexpr
auto
make_fragment_like(Shape const& shape)
{
return make_layout(shape);
}
//
// Make an identity layout that maps a coordinate to itself
//
template <class Shape>
CUTE_HOST_DEVICE constexpr
auto
make_identity_layout(Shape const& shape)
{
return make_layout(shape, make_basis_like(shape));
}
//
// Operations to manipulate Layouts like a tuple of pairs
//
// Return the Is...th sublayout.
// For Is... = <I0,I1,...,IN>, equivalent to get<IN>(...get<I1>(get<I0>(layout)))
template <size_t... Is, class Shape, class Stride>
CUTE_HOST_DEVICE constexpr
auto
get(Layout<Shape,Stride> const& layout)
{
return make_layout(get<Is...>(layout.shape()),
get<Is...>(layout.stride()));
}
// Return a new layout with only the modes in the range [B,E)
template <int B, int E, class Shape, class Stride>
CUTE_HOST_DEVICE constexpr
auto
take(Layout<Shape,Stride> const& layout)
{
static_assert(B < E, "take: empty range error");
static_assert(0 <= B && E <= Layout<Shape,Stride>::rank, "take: range out of bounds");
return make_layout(take<B,E>(layout.shape()),
take<B,E>(layout.stride()));
}
// Return a new layout with only the modes Is... = <I0,I1,...,IN>
template <int... Is, class Shape, class Stride>
CUTE_HOST_DEVICE constexpr
auto
select(Layout<Shape,Stride> const& layout)
{
return make_layout(select<Is...>(layout.shape()),
select<Is...>(layout.stride()));
}
// Return a layout with depth at most 1
template <class Shape, class Stride>
CUTE_HOST_DEVICE constexpr
auto
flatten(Layout<Shape,Stride> const& layout)
{
return make_layout(flatten(layout.shape()),
flatten(layout.stride()));
}
// Return a layout whose profile is congruent to TargetProfile
// @pre Input layout is flat, flatten(@a layout) == @a layout
// @pre Input layout can be folded to profile, rank(@a layout) == rank(flatten(@a target_profile))
// @post congruent(@a result, @a target_profile)
template <class Shape, class Stride, class TargetProfile>
CUTE_HOST_DEVICE constexpr
auto
unflatten(Layout<Shape,Stride> const& layout, TargetProfile const& target_profile)
{
return make_layout(unflatten(layout.shape(), target_profile),
unflatten(layout.stride(), target_profile));
}
//
// Utilities
//
// Return the sublayout of mode I...
template <int... Is, class Shape, class Stride>
CUTE_HOST_DEVICE constexpr
decltype(auto)
layout(Layout<Shape,Stride> const& layout)
{
if constexpr (sizeof...(Is) == 0) {
return layout;
} else {
return get<Is...>(layout);
}
CUTE_GCC_UNREACHABLE;
}
// Return the shape of a mode
template <int... Is, class Shape, class Stride>
CUTE_HOST_DEVICE constexpr
decltype(auto)
shape(Layout<Shape,Stride>& layout)
{
return layout.template shape<Is...>();
}
template <int... Is, class Shape, class Stride>
CUTE_HOST_DEVICE constexpr
decltype(auto)
shape(Layout<Shape,Stride> const& layout)
{
return layout.template shape<Is...>();
}
// Return the stride of a mode
template <int... Is, class Shape, class Stride>
CUTE_HOST_DEVICE constexpr
decltype(auto)
stride(Layout<Shape,Stride>& layout)
{
return layout.template stride<Is...>();
}
template <int... Is, class Shape, class Stride>
CUTE_HOST_DEVICE constexpr
decltype(auto)
stride(Layout<Shape,Stride> const& layout)
{
return layout.template stride<Is...>();
}
// Return the number of elements in a mode
template <int... Is, class Shape, class Stride>
CUTE_HOST_DEVICE constexpr
auto
size(Layout<Shape,Stride> const& layout)
{
return size(shape<Is...>(layout));
}
// Return the number of modes
template <int... Is, class Shape, class Stride>
CUTE_HOST_DEVICE constexpr
auto
rank(Layout<Shape,Stride> const& layout)
{
return rank(shape<Is...>(layout));
}
// Return the depth of the layout
template <int... Is, class Shape, class Stride>
CUTE_HOST_DEVICE constexpr
auto
depth(Layout<Shape,Stride> const& layout)
{
return depth(shape<Is...>(layout));
}
// Return the codomain shape of a mode
// @post size(coshape(@a a)) == cosize(@a a)
// @return C Coordinate with smallest elements such that
// @a elem_less(sub_layout(c), C) for all c < size(@a sub_layout)
// where sub_layout = get<Is...>(layout).
template <int... Is, class Shape, class Stride>
CUTE_HOST_DEVICE constexpr
auto
coshape(Layout<Shape,Stride> const& layout)
{
// Protect against negative strides
auto abs_sub_layout = make_layout(shape<Is...>(layout),
transform_leaf(stride<Is...>(layout), abs_fn{}));
auto co_coord = as_arithmetic_tuple(abs_sub_layout(size(abs_sub_layout) - Int<1>{}));
return co_coord + repeat_like(co_coord, Int<1>{});
}
// Return the codomain size of a mode
// @return M smallest integer such that
// @a sub_layout(c) < M for all c < size(@a sub_layout)
// where sub_layout = get<Is...>(layout).
template <int... Is, class Shape, class Stride>
CUTE_HOST_DEVICE constexpr
auto
cosize(Layout<Shape,Stride> const& layout)
{
return size(coshape<Is...>(layout));
}
template <class Layout>
using cosize_t = decltype(cosize(declval<Layout>()));
template <class Layout>
static constexpr int cosize_v = cosize_t<Layout>::value;
// With crd2idx(coord, shape), makes sense to have crd2idx(coord, Layout) as well
template <class Coord, class Shape, class Stride>
CUTE_HOST_DEVICE constexpr
auto
crd2idx(Coord const& c, Layout<Shape,Stride> const& layout)
{
return crd2idx(c, layout.shape(), layout.stride());
}
//
// Slice and Dice a layout
//
template <class Coord, class Shape, class Stride>
CUTE_HOST_DEVICE constexpr
auto
slice(Coord const& c, Layout<Shape,Stride> const& layout)
{
return make_layout(slice(c, layout.shape()),
slice(c, layout.stride()));
}
template <class Coord, class Shape, class Stride>
CUTE_HOST_DEVICE constexpr
auto
slice_and_offset(Coord const& c, Layout<Shape,Stride> const& layout)
{
return cute::make_tuple(slice(c, layout), crd2idx(c, layout));
}
template <class Coord, class Shape, class Stride>
CUTE_HOST_DEVICE constexpr
auto
dice(Coord const& c, Layout<Shape,Stride> const& layout)
{
return make_layout(dice(c, layout.shape()),
dice(c, layout.stride()));
}
// Compute a pointer offset and (potentially modified) layout from a coordinate
// This exists so it can be overloaded for ComposedLayout
template <class Coord, class Shape, class Stride>
CUTE_HOST_DEVICE constexpr
auto
domain_offset(Coord const& coord, Layout<Shape,Stride> const& layout)
{
return cute::make_tuple(layout, layout(coord));
}
//
// Transform the modes of a layout
//
namespace detail {
template <class Tuple, class F, int... I>
CUTE_HOST_DEVICE constexpr
auto
transform_layout(Tuple const& t, F&& f, seq<I...>)
{
return make_layout(f(get<I>(t))...);
}
template <class Tuple0, class Tuple1, class F, int... I, int... I0, int... I1>
CUTE_HOST_DEVICE constexpr
auto
transform_layout(Tuple0 const& t0, Tuple1 const& t1, F&& f, seq<I...>, seq<I0...>, seq<I1...>)
{
return make_layout(f(get<I>(t0),get<I>(t1))..., get<I0>(t0)..., get<I1>(t1)...);
}
} // end namespace detail
template <class Tuple, class F>
CUTE_HOST_DEVICE constexpr
auto
transform_layout(Tuple const& t, F&& f)
{
return detail::transform_layout(t, f, make_seq<decltype(rank(t))::value>{});
}
template <class Tuple0, class Tuple1, class F>
CUTE_HOST_DEVICE constexpr
auto
transform_layout(Tuple0 const& t0, Tuple1 const& t1, F&& f)
{
constexpr int R0 = decltype(rank(t0))::value;
constexpr int R1 = decltype(rank(t1))::value;
constexpr int R = (R0 < R1) ? R0 : R1;
return detail::transform_layout(t0, t1, f, make_seq<R>{}, make_range<R,R0>{}, make_range<R,R1>{});
}
//
// Coalesce and Filter
//
namespace detail {
// Look at each element and the front of the stack (in order of priority)
// front(NewLayout) get<I>(Layout)
// s0:d0 _1:d1 => continue
// _1:d0 s1:d1 => replace_front s1:d1
// s0:s1*d1 s1:d1 => replace_front s0*s1:d1
// s0:d0 s1:d1 => prepend s1:d1
//
// @pre OldShape and OldStride are flat
template <int I, class OldShape, class OldStride, class NewShape, class NewStride>
CUTE_HOST_DEVICE constexpr
auto
bw_coalesce(OldShape const& old_shape, OldStride const& old_stride,
NewShape const& new_shape, NewStride const& new_stride)
{
if constexpr (I == -1) {
// Base case, we're done
if constexpr (is_constant<1, NewShape>::value) {
return Layout<_1,_0>{};
} else {
return Layout<NewShape,NewStride>{new_shape,new_stride};
}
} else if constexpr (is_constant<1, decltype(get<I>(old_shape))>::value) {
// shape<I>(layout) == _1, skip it and continue
return bw_coalesce<I-1>(old_shape, old_stride, new_shape, new_stride);
} else if constexpr (is_constant<1, NewShape>::value) {
// Replace our shape-1 with anything (Can only happen on input new_shape/new_stride)
return bw_coalesce<I-1>(old_shape, old_stride, get<I>(old_shape), get<I>(old_stride));
} else if constexpr (is_constant<true, decltype(get<I>(old_shape) * get<I>(old_stride) == get<0>(new_stride))>::value) {
// Merge modes because the shapes and strides match
return bw_coalesce<I-1>(old_shape, old_stride,
replace_front(new_shape, get<I>(old_shape) * get<0>(new_shape)),
replace_front(new_stride, get<I>(old_stride)));
} else {
// Can't replace or merge, so prepend a new mode
return bw_coalesce<I-1>(old_shape, old_stride,
prepend(new_shape, get<I>(old_shape)),
prepend(new_stride, get<I>(old_stride)));
}
CUTE_GCC_UNREACHABLE;
}
} // end namespace detail
// "Simplify" the layout by combining modes that are possible to combine
// Does not respect the shape of the layout, but does preserve total size
// @post size(@a result) == size(@a layout)
// @post depth(@a result) <= 1
// @post for all i, 0 <= i < size(@a layout), @a layout(i) == @a result(i)
template <class Shape, class Stride>
CUTE_HOST_DEVICE constexpr
auto
coalesce(Layout<Shape,Stride> const& layout)
{
auto flat_shape = flatten(layout.shape());
auto flat_stride = flatten(layout.stride());
constexpr int R = decltype(rank(flat_shape))::value;
return detail::bw_coalesce<R-2>(flat_shape, flat_stride, get<R-1>(flat_shape), get<R-1>(flat_stride));
}
// Apply coalesce at the terminals of trg_profile
template <class Shape, class Stride, class IntTuple>
CUTE_HOST_DEVICE constexpr
auto
coalesce(Layout<Shape,Stride> const& layout, IntTuple const& trg_profile)
{
if constexpr (is_tuple<IntTuple>::value) {
static_assert(tuple_size<IntTuple>::value <= Layout<Shape,Stride>::rank);
return transform_layout(layout, trg_profile, [](auto const& l, auto const& t) { return coalesce(l,t); });
} else {
return coalesce(layout);
}
CUTE_GCC_UNREACHABLE;
}
// Replace the modes in layout that have a 0-stride with a 1-size
template <class Shape, class Stride>
CUTE_HOST_DEVICE constexpr
auto
filter_zeros(Layout<Shape,Stride> const& layout)
{
return make_layout(filter_zeros(layout.stride(), layout.shape()), layout.stride());
}
// Remove all of the 0-strides and 1-sizes
// Return 1-shape if empty
template <class Shape, class Stride>
CUTE_HOST_DEVICE constexpr
auto
filter(Layout<Shape,Stride> const& layout)
{
return coalesce(filter_zeros(layout));
}
// Apply filter at the terminals of trg_profile
template <class Shape, class Stride, class IntTuple>
CUTE_HOST_DEVICE constexpr
auto
filter(Layout<Shape,Stride> const& layout, IntTuple const& trg_profile)
{
if constexpr (is_tuple<IntTuple>::value) {
static_assert(tuple_size<IntTuple>::value <= Layout<Shape,Stride>::rank);
return transform_layout(layout, trg_profile, [](auto const& l, auto const& t) { return filter(l,t); });
} else {
return filter(layout);
}
CUTE_GCC_UNREACHABLE;
}
//
// Append, Prepend, Replace
//
template <int N, class ShapeA, class StrideA, class ShapeX = _1, class StrideX = _0>
CUTE_HOST_DEVICE constexpr
auto
append(Layout<ShapeA,StrideA> const& layout,
Layout<ShapeX,StrideX> const& x = {})
{
return make_layout(append<N>(layout.shape(), x.shape()),
append<N>(layout.stride(), x.stride()));
}
template <class ShapeA, class StrideA, class ShapeX = _1, class StrideX = _0>
CUTE_HOST_DEVICE constexpr
auto
append(Layout<ShapeA,StrideA> const& layout,
Layout<ShapeX,StrideX> const& x = {})
{
return make_layout(append(layout.shape(), x.shape()),
append(layout.stride(), x.stride()));
}
template <int N, class ShapeA, class StrideA, class ShapeX = _1, class StrideX = _0>
CUTE_HOST_DEVICE constexpr
auto
prepend(Layout<ShapeA,StrideA> const& layout,
Layout<ShapeX,StrideX> const& x = {})
{
return make_layout(prepend<N>(layout.shape(), x.shape()),
prepend<N>(layout.stride(), x.stride()));
}
template <class ShapeA, class StrideA, class ShapeX = _1, class StrideX = _0>
CUTE_HOST_DEVICE constexpr
auto
prepend(Layout<ShapeA,StrideA> const& layout,
Layout<ShapeX,StrideX> const& x = {})
{
return make_layout(prepend(layout.shape(), x.shape()),
prepend(layout.stride(), x.stride()));
}
template <int N, class ShapeA, class StrideA, class ShapeX, class StrideX>
CUTE_HOST_DEVICE constexpr
auto
replace(Layout<ShapeA,StrideA> const& layout,
Layout<ShapeX,StrideX> const& x)
{
return make_layout(replace<N>(layout.shape(), x.shape()),
replace<N>(layout.stride(), x.stride()));
}
template <int B, int E, class Shape, class Stride>
CUTE_HOST_DEVICE constexpr
auto
group(Layout<Shape,Stride> const& layout)
{
return make_layout(group<B,E>(layout.shape()),
group<B,E>(layout.stride()));
}
//
// Composition of two layouts: lhs o rhs
// @post compatible(rhs, result)
// @post result(c) = lhs(rhs(c))
// for all c in the domain of rhs
//
namespace detail {
template <class LShape, class LStride,
class RShape, class RStride>
CUTE_HOST_DEVICE constexpr
auto
composition_impl(Layout<LShape,LStride> const& lhs,
RShape const& rhs_shape, RStride const& rhs_stride)
{
if constexpr (is_tuple<RShape>::value) {
// Apply the right-distributivity of Layout composition
return transform_layout(rhs_shape, rhs_stride, [&](auto const& s, auto const& d) { return composition_impl(lhs, s, d); });
} else
if constexpr (is_scaled_basis<RStride>::value) {
// Special case for a ScaledBasis stride
return composition_impl(get<RStride::mode()>(lhs), rhs_shape, rhs_stride.value());
} else
if constexpr (is_integral<RStride>::value) {
// Integral Rstride (and RShape)
// NOTE: Should only flatten once for efficiency
auto flat_shape = flatten(lhs.shape());
[[maybe_unused]] auto flat_stride = flatten(lhs.stride());
[[maybe_unused]] constexpr int R = rank(flat_shape);
if constexpr (is_constant<0, RStride>::value) {
// Special case shortcut for any static stride-0
return Layout<RShape, RStride>{rhs_shape, rhs_stride};
} else
if constexpr (is_integral<decltype(flat_shape)>::value) {
// Special case shortcut for any integral LShape
auto result_stride = rhs_stride * flat_stride;
return Layout<RShape, decltype(result_stride)>{rhs_shape, result_stride};
} else
if constexpr (is_constant<1, RStride>::value) {
// Special case shortcut for any static stride-1
auto result_shape_0 = take<0,R-1>(flat_shape);
// Mod out the rhs_shape from the lhs.shape()
auto const [result_shape_1, rest_shape] = fold(result_shape_0, cute::make_tuple(cute::make_tuple(), rhs_shape),
[] (auto const& init, auto const& si) {
return cute::make_tuple(append(get<0>(init), shape_min(abs(si), get<1>(init))), shape_div(get<1>(init), abs(si)));
});
// Jump into coalesce and append (rest_shape, get<R-1>(lhs.stride())
return detail::bw_coalesce<R-2>(result_shape_1, flat_stride, rest_shape, get<R-1>(flat_stride));
} else
{
// General case
auto result_shape_0 = take<0,R-1>(flat_shape);
auto result_stride_0 = take<0,R-1>(flat_stride);
// Divide out the rhs_stride from the lhs.shape()
auto const [result_shape_1, rest_stride] = fold(result_shape_0, cute::make_tuple(cute::make_tuple(), rhs_stride),
[] (auto const& init, auto const& di) {
return cute::make_tuple(append(get<0>(init), shape_div(di, get<1>(init))), shape_div(get<1>(init), di));
});
// Apply any lhs.shape() changes to the stride
auto result_stride_1 = elem_scale(result_stride_0, shape_div(result_shape_0, result_shape_1));
// Mod out the rhs_shape from the lhs.shape()
auto const [result_shape_2, rest_shape] = fold(result_shape_1, cute::make_tuple(cute::make_tuple(), rhs_shape),
[] (auto const& init, auto const& si) {
return cute::make_tuple(append(get<0>(init), shape_min(abs(si), get<1>(init))), shape_div(get<1>(init), abs(si)));
});
// Jump into coalesce and append (rest_shape, rest_stride * get<R-1>(lhs.stride())
return detail::bw_coalesce<R-2>(result_shape_2, result_stride_1, rest_shape, rest_stride * get<R-1>(flat_stride));
}
}
CUTE_GCC_UNREACHABLE;
}
} // end namespace detail
template <class LShape, class LStride,
class RShape, class RStride>
CUTE_HOST_DEVICE constexpr
auto
composition(Layout<LShape,LStride> const& lhs,
Layout<RShape,RStride> const& rhs)
{
return detail::composition_impl(lhs, rhs.shape(), rhs.stride());
}