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mma_atom.hpp
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/***************************************************************************************************
* Copyright (c) 2023 - 2025 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/arch/mma.hpp>
#include <cute/atom/mma_traits.hpp>
#include <cute/tensor_impl.hpp>
#include <cute/util/type_traits.hpp>
#if defined(CUTLASS_ENABLE_SYCL)
#include <cute/atom/mma_traits_xe.hpp>
#endif
namespace cute {
template <class... Args>
struct MMA_Atom;
template <class MMAOperation>
struct MMA_Atom<MMAOperation> : MMA_Atom<MMA_Traits<MMAOperation>>
{};
template <class MMAOperation, class... Args>
struct MMA_Atom<MMA_Traits<MMAOperation, Args...>>
: MMA_Traits<MMAOperation, Args...>
{
using MMA_Op = MMAOperation;
using Traits = MMA_Traits<MMAOperation, Args...>;
// Element value types from the MMA_Traits
using ValTypeD = typename Traits::ValTypeD;
using ValTypeA = typename Traits::ValTypeA;
using ValTypeB = typename Traits::ValTypeB;
using ValTypeC = typename Traits::ValTypeC;
// Thr-Val layouts from the MMA_Traits
using Shape_MNK = typename Traits::Shape_MNK;
using ThrID = typename Traits::ThrID;
using LayoutC_TV = typename Traits::CLayout;
using LayoutA_TV = typename Traits::ALayout;
using LayoutB_TV = typename Traits::BLayout;
// Fragment value types from the MMA_Traits (optional, defaults to Val type)
using FrgTypeD = typename detail::FrgTypeC_or_Default<Traits>::type;
using FrgTypeA = typename detail::FrgTypeA_or_Default<Traits>::type;
using FrgTypeB = typename detail::FrgTypeB_or_Default<Traits>::type;
using FrgTypeC = typename detail::FrgTypeC_or_Default<Traits>::type;
// Additional Trait parameters/transformations
template <class... TraitsArgs>
CUTE_HOST_DEVICE
auto
with(TraitsArgs&&... args) const {
auto traits = Traits::with(static_cast<TraitsArgs&&>(args)...);
return MMA_Atom<decltype(traits)>{traits};
}
//
// Tensor call interfaces
//
// Cast, check, and call fma
template <class TD, class DLayout,
class TA, class ALayout,
class TB, class BLayout,
class TC, class CLayout>
CUTE_HOST_DEVICE constexpr
void
call(Tensor<TD, DLayout> & D,
Tensor<TA, ALayout> const& A,
Tensor<TB, BLayout> const& B,
Tensor<TC, CLayout> const& C) const
{
static_assert(DLayout::rank == 1, "Expected rank-1 D tensor");
static_assert(ALayout::rank == 1, "Expected rank-1 A tensor");
static_assert(BLayout::rank == 1, "Expected rank-1 B tensor");
static_assert(CLayout::rank == 1, "Expected rank-1 C tensor");
return mma_unpack(static_cast<Traits const&>(*this), D, A, B, C);
}
// Three arguments reproduces C
template <class TA, class ALayout,
class TB, class BLayout,
class TC, class CLayout>
CUTE_HOST_DEVICE constexpr
void
call(Tensor<TA, ALayout> const& A,
Tensor<TB, BLayout> const& B,
Tensor<TC, CLayout> & C) const
{
return call(C, A, B, C);
}
//
// make_fragment_A|B|C
// These functions are awkward as they expect already-partitioned tensors
// resulting from a previous call to partition_A|B|C
// The reasoning is that we can inspect the layout of the partitioned data
// and attempt to match it in generated fragment to promote vectorization
// when copying from partition to fragment.
//
template <class CTensor>
CUTE_HOST_DEVICE static constexpr
auto
make_fragment_C(CTensor&& ctensor)
{
// Check that this tensor is likely already partitioned
CUTE_STATIC_ASSERT_V(rank(ctensor) >= Int<3>{}); // VMN
CUTE_STATIC_ASSERT_V(size<0>(ctensor) == size<1>(LayoutC_TV{}));
// C is a bit special because we are after accumulators here
// The input/output type doesn't have to match the accumulator type
//static_assert(std::is_same<ValTypeC, typename remove_cvref_t<CTensor>::value_type>::value, "Expecting ValTypeC type");
// We'll never base the accumulator layout on the input tensor layout, so just return a FrgTypeC tensor
return make_tensor<FrgTypeC>(shape(ctensor));
}
template <class ATensor>
CUTE_HOST_DEVICE static constexpr
auto
make_fragment_A(ATensor&& atensor)
{
// Check that this tensor is likely already partitioned
CUTE_STATIC_ASSERT_V(rank(atensor) >= Int<3>{}); // VMK
CUTE_STATIC_ASSERT_V(size<0>(atensor) == size<1>(LayoutA_TV{}));
if constexpr (has_dereference<FrgTypeA>::value) {
// If the intended FrgTypeA is a view (of the current tensor), forward the whole
static_assert(is_same<ValTypeA, typename remove_cvref_t<ATensor>::value_type>::value
|| (sizeof_bits_v<typename remove_cvref_t<ATensor>::value_type> == 8 &&
(sizeof_bits_v<ValTypeA> == 8 || sizeof_bits_v<ValTypeA> == 6 || sizeof_bits_v<ValTypeA> == 4))
|| (sizeof_bits_v<typename remove_cvref_t<ATensor>::value_type> == 4 &&
(sizeof_bits_v<ValTypeA> == 4 || sizeof_bits_v<ValTypeA> == 3 || sizeof_bits_v<ValTypeA> == 2))
, "Expecting ValTypeA type");
return make_tensor<FrgTypeA>(static_cast<ATensor&&>(atensor));
} else {
// Else, the intended FrgTypeA is a value type, construct a new tensor with a fragment layout
return make_fragment_like<FrgTypeA>(atensor);
}
CUTE_GCC_UNREACHABLE;
}
template <class BTensor>
CUTE_HOST_DEVICE static constexpr
auto
make_fragment_B(BTensor&& btensor)
{
// Check that this tensor is likely already partitioned
CUTE_STATIC_ASSERT_V(rank(btensor) >= Int<3>{}); // VNK
CUTE_STATIC_ASSERT_V(size<0>(btensor) == size<1>(LayoutB_TV{}));
if constexpr (has_dereference<FrgTypeB>::value) {
// If the intended FrgTypeB is a view (of the current tensor), forward the whole
static_assert(is_same<ValTypeB, typename remove_cvref_t<BTensor>::value_type>::value
|| (sizeof_bits_v<typename remove_cvref_t<BTensor>::value_type> == 8 &&
(sizeof_bits_v<ValTypeB> == 8 || sizeof_bits_v<ValTypeB> == 6 || sizeof_bits_v<ValTypeB> == 4))
, "Expecting ValTypeB type");
return make_tensor<FrgTypeB>(static_cast<BTensor&&>(btensor));
} else {
// Else, the intended FrgTypeB is a value type, construct a new tensor with a fragment layout
return make_fragment_like<FrgTypeB>(btensor);
}
CUTE_GCC_UNREACHABLE;
}
};
//
// A tiling of mma atoms
//
template <class TiledMMA, class ThrCoord>
struct ThrMMA;
// @tparam MMA_Atom The MMA_Atom to use in the TiledMMA
// @tparam AtomLayoutMNK The MNK-tiling of the Atom to be performed.
// @tparam PermuationsMNK Permutations to apply to each MNK-mode before tiling for the Atom.
template <class MMA_Atom,
class AtomLayoutMNK,
class PermutationMNK = Tile<Underscore,Underscore,Underscore>>
struct TiledMMA : MMA_Atom
{
using Atom = MMA_Atom;
using AtomShape_MNK = typename MMA_Atom::Shape_MNK;
using AtomThrID = typename MMA_Atom::ThrID;
using AtomLayoutC_TV = typename MMA_Atom::LayoutC_TV;
using AtomLayoutA_TV = typename MMA_Atom::LayoutA_TV;
using AtomLayoutB_TV = typename MMA_Atom::LayoutB_TV;
static_assert( rank_v<AtomLayoutMNK> == 3, "TiledMMA requires rank-3 AtomLayoutMNK");
static_assert( rank_v<PermutationMNK> == 3, "TiledMMA requires rank-3 PermutationMNK");
static_assert( is_tuple<PermutationMNK>::value, "TiledMMA requires independent permutations of MNK.");
static_assert(is_static<PermutationMNK>::value, "TiledMMA requires static permutations of MNK.");
using ThrLayoutVMNK = decltype(tiled_product(AtomThrID{}, AtomLayoutMNK{}));
ThrLayoutVMNK thr_layout_vmnk_;
CUTE_HOST_DEVICE constexpr
TiledMMA(MMA_Atom const& mma_atom = {}, AtomLayoutMNK const& thr_layout_mnk = {})
: MMA_Atom(mma_atom),
thr_layout_vmnk_(tiled_product(AtomThrID{}, thr_layout_mnk)) {}
CUTE_HOST_DEVICE constexpr auto
get_thr_layout_vmnk() const {
return thr_layout_vmnk_;
}
// Tile a tensor or a layout from shape
// (M,N,...)
// to shape
// ((ThrV,(ThrM,ThrN)),(FrgV,(RestM,RestN,...)))
// where
// ThrV: The threads local to an MMA. layout<0>(ThrLayoutVMNK): ThrV -> thread_idx
// ThrM: The threads tiled in M. layout<1>(ThrLayoutVMNK): ThrM -> thread_idx
// ThrN: The threads tiled in N. layout<2>(ThrLayoutVMNK): ThrN -> thread_idx
// FrgV: The values local to an MMA.
// RestM: The values tiled in M.
// RestN: The values tiled in N.
template <class CTensor>
CUTE_HOST_DEVICE constexpr
auto
thrfrg_C(CTensor&& ctensor) const
{
CUTE_STATIC_ASSERT_V(rank(ctensor) >= Int<2>{});
// Reorder the tensor for the TiledAtom
auto t_tile = make_tile(permutation_mnk<0>(),
permutation_mnk<1>());
auto t_tensor = logical_divide(ctensor, t_tile); // (PermM,PermN)
// Tile the tensor for the Atom
auto c_tile = make_tile(make_layout(size<0>(AtomShape_MNK{})),
make_layout(size<1>(AtomShape_MNK{})));
auto c_tensor = zipped_divide(t_tensor, c_tile); // ((AtomM,AtomN),(RestM,RestN))
// Transform the Atom mode from (M,K) to (Thr,Val)
auto tv_tensor = c_tensor.compose(AtomLayoutC_TV{},_); // ((ThrV,FrgV),(RestM,RestN))
// Tile the tensor for the C-threads
auto thr_tile = make_tile(_,
make_tile(make_layout(size<1>(thr_layout_vmnk_)),
make_layout(size<2>(thr_layout_vmnk_))));
auto thr_tensor = zipped_divide(tv_tensor, thr_tile); // ((ThrV,(ThrM,ThrN)),(FrgV,(RestM,RestN)))
return thr_tensor;
}
// Tile a tensor or a layout from shape
// (M,K,...)
// to shape
// ((ThrV,(ThrM,ThrK)),(FrgV,(RestM,RestK,...)))
// where
// ThrV: The threads local to an MMA. layout<0>(ThrLayoutVMNK): ThrV -> thread_idx
// ThrM: The threads tiled in M. layout<1>(ThrLayoutVMNK): ThrM -> thread_idx
// ThrK: The threads tiled in K. layout<3>(ThrLayoutVMNK): ThrK -> thread_idx
// FrgV: The values local to an MMA.
// RestM: The values tiled in M.
// RestK: The values tiled in K.
template <class ATensor>
CUTE_HOST_DEVICE constexpr
auto
thrfrg_A(ATensor&& atensor) const
{
CUTE_STATIC_ASSERT_V(rank(atensor) >= Int<2>{});
// Reorder the tensor for the TiledAtom
auto t_tile = make_tile(permutation_mnk<0>(),
permutation_mnk<2>());
auto t_tensor = logical_divide(atensor, t_tile); // (PermM,PermK)
// Tile the tensor for the Atom
auto a_tile = make_tile(make_layout(size<0>(AtomShape_MNK{})),
make_layout(size<2>(AtomShape_MNK{})));
auto a_tensor = zipped_divide(t_tensor, a_tile); // ((AtomM,AtomK),(RestM,RestK))
// Transform the Atom mode from (M,K) to (Thr,Val)
auto tv_tensor = a_tensor.compose(AtomLayoutA_TV{},_); // ((ThrV,FrgV),(RestM,RestK))
// Tile the tensor for the Thread
auto thr_tile = make_tile(_,
make_tile(make_layout(size<1>(thr_layout_vmnk_)),
make_layout(size<3>(thr_layout_vmnk_))));
auto thr_tensor = zipped_divide(tv_tensor, thr_tile); // ((ThrV,(ThrM,ThrK)),(FrgV,(RestM,RestK)))
return thr_tensor;
}
// Tile a tensor or a layout from shape
// (N,K,...)
// to shape
// ((ThrV,(ThrN,ThrK)),(FrgV,(RestN,RestK,...)))
// where
// ThrV: The threads local to an MMA. layout<0>(ThrLayoutVMNK): ThrV -> thread_idx
// ThrN: The threads tiled in N. layout<2>(ThrLayoutVMNK): ThrN -> thread_idx
// ThrK: The threads tiled in K. layout<3>(ThrLayoutVMNK): ThrK -> thread_idx
// FrgV: The values local to an MMA.
// RestN: The values tiled in N.
// RestK: The values tiled in K.
template <class BTensor>
CUTE_HOST_DEVICE constexpr
auto
thrfrg_B(BTensor&& btensor) const
{
CUTE_STATIC_ASSERT_V(rank(btensor) >= Int<2>{});
// Reorder the tensor for the TiledAtom
auto t_tile = make_tile(permutation_mnk<1>(),
permutation_mnk<2>());
auto t_tensor = logical_divide(btensor, t_tile); // (PermN,PermK)
// Tile the tensor for the Atom
auto b_tile = make_tile(make_layout(size<1>(AtomShape_MNK{})),
make_layout(size<2>(AtomShape_MNK{})));
auto b_tensor = zipped_divide(t_tensor, b_tile); // ((AtomN,AtomK),(RestN,RestK))
// Transform the Atom mode from (M,K) to (Thr,Val)
auto tv_tensor = b_tensor.compose(AtomLayoutB_TV{},_); // ((ThrV,FrgV),(RestN,RestK))
// Tile the tensor for the Thread
auto thr_tile = make_tile(_,
make_tile(make_layout(size<2>(thr_layout_vmnk_)),
make_layout(size<3>(thr_layout_vmnk_))));
auto thr_tensor = zipped_divide(tv_tensor, thr_tile); // ((ThrV,(ThrN,ThrK)),(FrgV,(RestN,RestK)))
return thr_tensor;
}
template <class ThrIdx,
__CUTE_REQUIRES(is_integral<ThrIdx>::value)>
CUTE_HOST_DEVICE constexpr
auto
get_slice(ThrIdx const& thr_idx) const
{
auto thr_vmnk = thr_layout_vmnk_.get_flat_coord(thr_idx);
return ThrMMA<TiledMMA, decltype(thr_vmnk)>{*this, thr_vmnk};
}
template <class ThrIdx,
__CUTE_REQUIRES(is_integral<ThrIdx>::value)>
CUTE_HOST_DEVICE constexpr
auto
get_thread_slice(ThrIdx const& thr_idx) const
{
return get_slice(thr_idx);
}
//
// Utility for printing and visualization
//
// The permutation applied to the MNK-mode data
template <int I>
CUTE_HOST_DEVICE constexpr
auto
permutation_mnk() const {
static_assert(0 <= I && I < 3);
auto perm = get<I>(PermutationMNK{});
return conditional_return(is_underscore<decltype(perm)>{}, size<I>(AtomShape_MNK{}) * size<I+1>(get_thr_layout_vmnk()), perm);
}
// The size of the MNK-mode
template <int I>
CUTE_HOST_DEVICE constexpr
auto
tile_size_mnk() const {
static_assert(0 <= I && I < 3);
return size(permutation_mnk<I>());
}
CUTE_HOST_DEVICE constexpr
auto
get_layoutC_MN() const
{
// (M,N) -> (M,N)
auto ref_C = make_layout(make_shape(tile_size_mnk<0>(), tile_size_mnk<1>()));
// (cthrid,val) -> (M,N)
auto layoutC_TV = thrfrg_C(ref_C);
// (M,N) -> (cthrid,frg)
auto layoutC_MN = right_inverse(layoutC_TV).with_shape(shape(ref_C));
// cthrid = (v,m,n) -> thr_idx
auto thrID_C = thr_layout_vmnk_(_,_,_,Int<0>{});
return cute::make_tuple(layoutC_MN, thrID_C);
}
CUTE_HOST_DEVICE constexpr
auto
get_layoutC_TV() const
{
// (M,N) -> (M,N)
auto ref_C = make_layout(make_shape(tile_size_mnk<0>(), tile_size_mnk<1>()));
// (cthrid,val) -> (M,N)
auto layoutC_TV = thrfrg_C(ref_C);
// thr_idx -> (ThrV,ThrM,ThrN,ThrK)
auto thridx_2_thrid = right_inverse(thr_layout_vmnk_);
// (thr_idx,val) -> (M,N)
return layoutC_TV.compose(thridx_2_thrid, _);
}
CUTE_HOST_DEVICE constexpr
auto
get_layoutA_MK() const
{
// (M,K) -> (M,K)
auto ref_A = make_layout(make_shape(tile_size_mnk<0>(), tile_size_mnk<2>()));
// (athrid,val) -> (M,K)
auto layoutA_TV = thrfrg_A(ref_A);
// (M,K) -> (athrid,frg)
auto layoutA_MK = right_inverse(layoutA_TV).with_shape(shape(ref_A));
// athrid = (v,m,k) -> thr_idx
auto thrID_A = thr_layout_vmnk_(_,_,Int<0>{},_);
return cute::make_tuple(layoutA_MK, thrID_A);
}
CUTE_HOST_DEVICE constexpr
auto
get_layoutA_TV() const
{
// (M,K) -> (M,K)
auto ref_A = make_layout(make_shape(tile_size_mnk<0>(), tile_size_mnk<2>()));
// (athrid,val) -> (M,K)
auto layoutA_TV = thrfrg_A(ref_A);
// (ThrV,(ThrM,ThrK)) -> (ThrV,(ThrM,ThrN,ThrK))
auto atile = make_tile(_,
make_tile(make_layout(make_shape (size<1>(thr_layout_vmnk_), size<2>(thr_layout_vmnk_)),
make_stride( Int<1>{} , Int<0>{} )),
_));
// thr_idx -> (ThrV,ThrM,ThrN,ThrK)
auto thridx_2_thrid = right_inverse(thr_layout_vmnk_);
// (thr_idx,val) -> (M,K)
return thrfrg_A(ref_A).compose(atile, _).compose(thridx_2_thrid, _);
}
CUTE_HOST_DEVICE constexpr
auto
get_layoutB_NK() const
{
// (N,K) -> (N,K)
auto ref_B = make_layout(make_shape(tile_size_mnk<1>(), tile_size_mnk<2>()));
// (bthrid,val) -> (N,K)
auto layoutB_TV = thrfrg_B(ref_B);
// (N,K) -> (bthrid,frg)
auto layoutB_NK = right_inverse(layoutB_TV).with_shape(shape(ref_B));
// bthrid = (v,n,k) -> thr_idx
auto thrID_B = thr_layout_vmnk_(_,Int<0>{},_,_);
return cute::make_tuple(layoutB_NK, thrID_B);
}
CUTE_HOST_DEVICE constexpr
auto
get_layoutB_TV() const
{
// (N,K) -> (N,K)
auto ref_B = make_layout(make_shape(tile_size_mnk<1>(), tile_size_mnk<2>()));
// (bthrid,val) -> (N,K)
auto layoutB_TV = thrfrg_B(ref_B);
// (ThrV,(ThrN,ThrK)) -> (ThrV,(ThrM,ThrN,ThrK))
auto btile = make_tile(_,
make_tile(make_layout(make_shape (size<1>(thr_layout_vmnk_), size<2>(thr_layout_vmnk_)),
make_stride( Int<0>{} , Int<1>{} )),
_));
// thr_idx -> (ThrV,ThrM,ThrN,ThrK)
auto thridx_2_thrid = right_inverse(thr_layout_vmnk_);
// (thr_idx,val) -> (N,K)
return thrfrg_B(ref_B).compose(btile, _).compose(thridx_2_thrid, _);
}
};
template <class TiledMMA, class ThrVMNK>
struct ThrMMA : TiledMMA
{
ThrVMNK thr_vmnk_;
template <class CTensor>
CUTE_HOST_DEVICE constexpr
auto
partition_C(CTensor&& ctensor) const
{
auto thr_tensor = make_tensor(static_cast<CTensor&&>(ctensor).data(), this->thrfrg_C(ctensor.layout()));
auto thr_vmn = make_coord(get<0>(thr_vmnk_), make_coord(get<1>(thr_vmnk_), get<2>(thr_vmnk_)));
return thr_tensor(thr_vmn, make_coord(_, repeat<rank<1,1>(thr_tensor)>(_)));
}
template <class ATensor>
CUTE_HOST_DEVICE constexpr
auto
partition_A(ATensor&& atensor) const
{
auto thr_tensor = make_tensor(static_cast<ATensor&&>(atensor).data(), this->thrfrg_A(atensor.layout()));
auto thr_vmk = make_coord(get<0>(thr_vmnk_), make_coord(get<1>(thr_vmnk_), get<3>(thr_vmnk_)));
return thr_tensor(thr_vmk, make_coord(_, repeat<rank<1,1>(thr_tensor)>(_)));
}
template <class BTensor>
CUTE_HOST_DEVICE constexpr
auto
partition_B(BTensor&& btensor) const
{
auto thr_tensor = make_tensor(static_cast<BTensor&&>(btensor).data(), this->thrfrg_B(btensor.layout()));
auto thr_vnk = make_coord(get<0>(thr_vmnk_), make_coord(get<2>(thr_vmnk_), get<3>(thr_vmnk_)));
return thr_tensor(thr_vnk, make_coord(_, repeat<rank<1,1>(thr_tensor)>(_)));
}
template <class CTensor>
CUTE_HOST_DEVICE constexpr
auto
partition_fragment_C(CTensor&& ctensor) const
{
return TiledMMA::make_fragment_C(partition_C(ctensor));
}
template <class ATensor>
CUTE_HOST_DEVICE constexpr
auto
partition_fragment_A(ATensor&& atensor) const
{
return TiledMMA::make_fragment_A(partition_A(atensor));
}
template <class BTensor>
CUTE_HOST_DEVICE constexpr
auto
partition_fragment_B(BTensor&& btensor) const
{
return TiledMMA::make_fragment_B(partition_B(btensor));
}
};
//
// These tile the MMA_Atom as a whole
//
template <class MMA_Op,
class MMAThrLayout = Layout<Shape<_1,_1,_1>>,
class Permutations = Tile<Underscore,Underscore,Underscore>>
CUTE_HOST_DEVICE constexpr
auto
make_tiled_mma(MMA_Atom<MMA_Op> const& mma_atom,
MMAThrLayout const& thr_layout = {},
Permutations const& permutations = {})
{
auto thr_layout_mnk = append<3>(thr_layout, Layout<_1,_0>{});
auto permutation_mnk = append<3>(permutations, _);
return TiledMMA<MMA_Atom<MMA_Op>,
decltype(thr_layout_mnk),
decltype(permutation_mnk)>{mma_atom, thr_layout_mnk};
}
template <class MMA_Op,
class MMAThrLayout = Layout<Shape<_1,_1,_1>>,
class Permutations = Tile<Underscore,Underscore,Underscore>>
CUTE_HOST_DEVICE constexpr
auto
make_tiled_mma(MMA_Op const&,
MMAThrLayout const& thr_layout = {},
Permutations const& permutations = {})
{
// Attempt to wrap in an MMA_Atom<> and forward
return make_tiled_mma(MMA_Atom<MMA_Op>{}, thr_layout, permutations);
}
// This helper fn adopts the approach described in
// media/docs/cute/0t_mma_atom.md#tiledmmas to construct a scatter
// permutation which ensures hardware operates on contiguous
// chunks of the TiledMMA. The docs describe how the Layout
// implies a repetition of the atom across additional hardware.
// Permutations, in the simplest form, imply additional iterations
// to cover a larger tile (i.e. CTALayout) than the hardware can handle
// at once.
//
// Consider an example for PVC hardware:
// using TiledMma =
// TiledMMA<MMA_Atom<XE_8x16x16_F32BF16BF16F32_TT>,
// Layout<Shape<_8, _4, _1>, Stride<_4, _1, _0>>,
// Tile<_256, _256, _32>>;
//
// This MMA_Atom is performed by a whole warp and operates on an 8x16x16 chunk.
// The second arg (Layout) defines a repetition of the atom across *additional warps*,
// i.e. iterating across more hardware. The third arg (Tile) defines a repetition of this
// MMA across *additional values*. For this example, in the M dimension, the atom produces
// 8 values of C, the hardware repetition (8) scales this up to 64 values in M, and the
// requested permutation (256) scales this up to 256 values (implying 4 iterations in the
// M direction).
//
// By cute convention, the repetition of the atom across hardware is the inner
// iteration, while the repetition across values is the outer. We can use a more complex
// permutation to *swap* the 'hardware' and 'iteration' in the layout, so that each 'unit'
// of hardware (warp, in this case) processes contiguous blocks of A, B and C.
// This has the advantage that we can use larger block load operations to load data without
// relying on local memory.
//
// For the given example:
// using TiledMma =
// TiledMMA<MMA_Atom<XE_8x16x16_F32BF16BF16F32_TT>,
// Layout<Shape<_8, _4, _1>, Stride<_4, _1, _0>>, // 8x4 n-major layout of warps
// Tile<Layout<Shape<_8, _8, _4>, Stride<_1, _32, _8>>, // Permutation on M
// Layout<Shape<_16, _4, _4>, Stride<_1, _64, _16>>, // Permutation on N
// _32>>; // K unpermuted
//
// Consider only the M permutation (each mode's permutation is independent and in this
// example the M & N permutations are similar). This permutation maintains blocks of 8
// contiguous values from the canonical tiling (mode 0 is 8:1).
// It scatters 8 of these blocks of 8 to a spacing of 32 values (mode 1 is 8:32), leaving
// a 'gap' of 24. These gaps of 24 are filled by repeating the preceding pattern 4 times,
// at a spacing of 8 values (mode 2 is 4:8).
// In this manner, the tiling has been permuted so that the values handled by each thread are
// closer together.
template <typename MMA_Atom, typename CTALayout, typename WarpLayout>
struct TiledMMAHelper{
private:
using AtomShape = typename MMA_Atom::Shape_MNK;
// Represents the canonical MMA block which would be handled by these subgroups without permutation.
// product_each(shape(...)) converts the layout into a tiler by taking only the shapes
// e.g. (8,8):(1,8) -> 64
static constexpr auto CanonicalBlockShape =
product_each(shape(blocked_product(Layout<AtomShape>{}, WarpLayout{})));
// Construct the default tiled MMA, to extract the iteration count per dim below
static constexpr auto CanonicalTiling = logical_divide(CTALayout{}, CanonicalBlockShape);
static constexpr auto permutation =
transform(AtomShape{}, WarpLayout{}.shape(), CanonicalTiling.shape(),
[](auto atom_size, auto sg_count, auto canonical_tiling) {
constexpr auto iters = get<1>(canonical_tiling);
// atom, tile_over_hardware, tile_over_iteration
auto tiler_shape = make_shape(atom_size, sg_count, iters);
return coalesce(make_ordered_layout(tiler_shape, Step<_0, _2, _1>{}));
});
public:
using Permutation = decltype(permutation);
using TiledMMA = cute::TiledMMA<MMA_Atom, WarpLayout, Permutation>;
};
//
// partition_fragment_C -- static context
//
template <class... Args, class Shape_MN>
CUTE_HOST_DEVICE constexpr
auto
partition_shape_C(TiledMMA<Args...> const& mma, Shape_MN const& shape_MN)
{
auto dummy = make_layout(shape(shape_MN));
auto dummy_tv = mma.thrfrg_C(dummy);
// Slice+rearrange like partition_C
auto dummy_v = dummy_tv(Int<0>{}, make_coord(_, repeat<rank(dummy)>(_)));
return shape(dummy_v);
}
template <class... Args, class Shape_MN>
CUTE_HOST_DEVICE constexpr
auto
partition_fragment_C(TiledMMA<Args...> const& mma, Shape_MN const& shapeMN)
{
return make_tensor<typename TiledMMA<Args...>::FrgTypeC>(partition_shape_C(mma, shapeMN));
}
// partition_fragment_A and partition_fragment_B often depend on the
// layout of A and B and/or the thread_idx that is requesting the partition.
// For these reasons, they should not be used in a static context.
// See TiledMMA::get_slice(thr_idx).partition_fragment_A(tensorA) instead.
template <class... Args, class Shape_MK>
CUTE_HOST_DEVICE constexpr
auto
partition_shape_A(TiledMMA<Args...> const& mma, Shape_MK const& shape_MK)
{
auto dummy = make_layout(shape(shape_MK));
auto dummy_tv = mma.thrfrg_A(dummy);
// Slice+rearrange like partition_A
auto dummy_v = dummy_tv(Int<0>{}, make_coord(_, repeat<rank(dummy)>(_)));
return shape(dummy_v);
}
template <class... Args, class Shape_NK>
CUTE_HOST_DEVICE constexpr
auto
partition_shape_B(TiledMMA<Args...> const& mma, Shape_NK const& shape_NK)
{
auto dummy = make_layout(shape(shape_NK));
auto dummy_tv = mma.thrfrg_B(dummy);
// Slice+rearrange like partition_B
auto dummy_v = dummy_tv(Int<0>{}, make_coord(_, repeat<rank(dummy)>(_)));
return shape(dummy_v);
}
//
// Size
//
template <int I, class... Args>
CUTE_HOST_DEVICE constexpr
auto
tile_size(TiledMMA<Args...> const& mma)
{
return mma.template tile_size_mnk<I>();
}
template <class... Args>
CUTE_HOST_DEVICE constexpr
auto
tile_shape(TiledMMA<Args...> const& mma)
{
return make_shape(tile_size<0>(mma), tile_size<1>(mma), tile_size<2>(mma));
}
// Deprecate?
template <int... I, class... Args>
CUTE_HOST_DEVICE constexpr
auto
size(TiledMMA<Args...> const& mma)
{
return size<I...>(mma.get_thr_layout_vmnk());
}
// Alias
template <int... I, class... Args>
CUTE_HOST_DEVICE constexpr
auto
thr_size(TiledMMA<Args...> const& mma)
{
return size<I...>(mma.get_thr_layout_vmnk());
}
//
// Display utilities
//
template <class... Args>
CUTE_HOST_DEVICE
void
print(MMA_Atom<MMA_Traits<Args...>> const&)
{
using Atom = MMA_Atom<MMA_Traits<Args...>>;
print("MMA_Atom\n");
print(" ThrID: "); print(typename Atom::ThrID{}); print("\n");
print(" Shape_MNK: "); print(typename Atom::Shape_MNK{}); print("\n");
print(" LayoutA_TV: "); print(typename Atom::LayoutA_TV{}); print("\n");
print(" LayoutB_TV: "); print(typename Atom::LayoutB_TV{}); print("\n");
print(" LayoutC_TV: "); print(typename Atom::LayoutC_TV{}); print("\n");
}
template <class Atom, class TiledThr, class TiledPerm>
CUTE_HOST_DEVICE
void
print(TiledMMA<Atom, TiledThr, TiledPerm> const& mma)
{
print("TiledMMA\n");
print(" ThrLayoutVMNK: "); print(mma.get_thr_layout_vmnk()); print("\n");
print(" PermutationMNK: "); print(TiledPerm{}); print("\n");
print(static_cast<Atom const&>(mma));
}
template <class TiledMMA, class ThrVMNK>
CUTE_HOST_DEVICE
void
print(ThrMMA<TiledMMA, ThrVMNK> const& thr_mma)
{
print("ThrMMA\n");
print(" Thr VMNK: "); print(thr_mma.thr_vmnk_); print("\n");
print(static_cast<TiledMMA>(thr_mma));
}
// MMA Atom to LaTeX TikZ
template <class... Args, class TikzColorFn = TikzColor_TV>
CUTE_HOST_DEVICE
void
print_latex(MMA_Atom<Args...> const& mma_atom,
TikzColorFn color = {}) // lambda(thr_idx,val_idx) -> tikz color string
{
print_latex(make_tiled_mma(mma_atom));
}
// TiledMMA to LaTeX TikZ
template <class... Args, class TikzColorFn = TikzColor_TV>
CUTE_HOST_DEVICE
void
print_latex(TiledMMA<Args...> const& mma,
TikzColorFn color = {}) // lambda(thr_idx,val_idx) -> tikz color string
{
auto layout_and_thrid_C = mma.get_layoutC_MN();
auto layoutC_MN = get<0>(layout_and_thrid_C);
auto thrID_C = get<1>(layout_and_thrid_C);
auto layout_and_thrid_A = mma.get_layoutA_MK();
auto layoutA_MK = get<0>(layout_and_thrid_A);
auto thrID_A = get<1>(layout_and_thrid_A);
auto layout_and_thrid_B = mma.get_layoutB_NK();
auto layoutB_NK = get<0>(layout_and_thrid_B);
auto thrID_B = get<1>(layout_and_thrid_B);
print_latex_mma(layoutC_MN, thrID_C,
layoutA_MK, thrID_A,
layoutB_NK, thrID_B);
}
// MNK MMA Layout to LaTeX TikZ
template <class LayoutC, class ThrIDC,
class LayoutA, class ThrIDA,
class LayoutB, class ThrIDB,
class TikzColorFn = TikzColor_TV>
CUTE_HOST_DEVICE
void
print_latex_mma(LayoutC const& C, ThrIDC const& TC, // (m,n) -> (tid,vid) and tid -> thr_idx
LayoutA const& A, ThrIDA const& TA, // (m,k) -> (tid,vid) and tid -> thr_idx
LayoutB const& B, ThrIDB const& TB, // (n,k) -> (tid,vid) and tid -> thr_idx
TikzColorFn color = {}) // lambda(thr_idx,val_idx) -> tikz color string
{
CUTE_STATIC_ASSERT_V(rank(C) == Int<2>{});
CUTE_STATIC_ASSERT_V(rank(A) == Int<2>{});
CUTE_STATIC_ASSERT_V(rank(B) == Int<2>{});
assert(size<0>(A) == size<0>(C));
assert(size<0>(B) == size<1>(C));
assert(size<1>(A) == size<1>(B));
// Commented prints
printf("%% LayoutC: "); print(C); printf("\n");
printf("%% ThrIDC : "); print(TC); printf("\n");
printf("%% LayoutA: "); print(A); printf("\n");
printf("%% ThrIDA : "); print(TA); printf("\n");
printf("%% LayoutB: "); print(B); printf("\n");
printf("%% ThrIDB : "); print(TB); printf("\n\n");
// Header
printf("\\documentclass[convert]{standalone}\n"
"\\usepackage{tikz}\n\n"
"\\begin{document}\n"
"\\begin{tikzpicture}[x={(0cm,-1cm)},y={(1cm,0cm)},every node/.style={minimum size=1cm, outer sep=0pt}]\n\n");
// C starting at 0,0
for (int m = 0; m < size<0>(C); ++m) {
for (int n = 0; n < size<1>(C); ++n) {
int thrid = C(m,n) % size(TC);
int val_idx = C(m,n) / size(TC);
int thr_idx = TC(thrid);
printf("\\node[fill=%s] at (%d,%d) {\\shortstack{T%d \\\\ V%d}};\n",
color(thr_idx, val_idx),
m, n,
thr_idx, val_idx);
}
}
// Grid
printf("\\draw[color=black,thick,shift={(-0.5,-0.5)}] (%d,%d) grid (%d,%d);\n\n",
0, 0, int(size<0>(C)), int(size<1>(C)));
// A starting at 0,-size<1>(A)-1
for (int m = 0; m < size<0>(A); ++m) {
for (int k = 0; k < size<1>(A); ++k) {
int thrid = A(m,k) % size(TA);
int val_idx = A(m,k) / size(TA);
int thr_idx = TA(thrid);
printf("\\node[fill=%s] at (%d,%d) {\\shortstack{T%d \\\\ V%d}};\n",
color(thr_idx, val_idx),
m, k-1-size<1>(A),
thr_idx, val_idx);
}
}
// Grid
printf("\\draw[color=black,thick,shift={(-0.5,-0.5)}] (%d,%d) grid (%d,%d);\n\n",
0, int(-size<1>(A)-1), int(size<0>(A)), -1);
// A labels
for (int m = 0, k = -1; m < size<0>(A); ++m) {
printf("\\node at (%d,%d) {\\Large{\\texttt{%d}}};\n", m, k-1-size<1>(A), m);
}
for (int m = -1, k = 0; k < size<1>(A); ++k) {
printf("\\node at (%d,%d) {\\Large{\\texttt{%d}}};\n", m, k-1-size<1>(A), k);
}
// B starting at -size<1>(B)-1,0
for (int n = 0; n < size<0>(B); ++n) {
for (int k = 0; k < size<1>(B); ++k) {
int thrid = B(n,k) % size(TB);
int val_idx = B(n,k) / size(TB);
int thr_idx = TB(thrid);
printf("\\node[fill=%s] at (%d,%d) {\\shortstack{T%d \\\\ V%d}};\n",
color(thr_idx, val_idx),
k-1-size<1>(B), n,
thr_idx, val_idx);
}
}
// Grid
printf("\\draw[color=black,thick,shift={(-0.5,-0.5)}] (%d,%d) grid (%d,%d);\n\n",
int(-size<1>(B)-1), 0, -1, int(size<0>(B)));
// B labels
for (int n = 0, k = -1; n < size<0>(B); ++n) {
printf("\\node at (%d,%d) {\\Large{\\texttt{%d}}};\n", k-1-size<1>(B), n, n);
}
for (int n = -1, k = 0; k < size<1>(B); ++k) {
printf("\\node at (%d,%d) {\\Large{\\texttt{%d}}};\n", k-1-size<1>(B), n, k);
}
// Footer
printf("\\end{tikzpicture}\n"
"\\end{document}\n");
}
// MNK MMA Layout to console printer
template <class LayoutC, class ThrIDC,
class LayoutA, class ThrIDA,
class LayoutB, class ThrIDB>
CUTE_HOST_DEVICE
void
print_layout_mma(LayoutC const& C, ThrIDC const& TC, // (m,n) -> (tid,vid) and tid -> thr_idx
LayoutA const& A, ThrIDA const& TA, // (m,k) -> (tid,vid) and tid -> thr_idx
LayoutB const& B, ThrIDB const& TB) // (n,k) -> (tid,vid) and tid -> thr_idx
{
CUTE_STATIC_ASSERT_V(rank(C) == Int<2>{});
CUTE_STATIC_ASSERT_V(rank(A) == Int<2>{});
CUTE_STATIC_ASSERT_V(rank(B) == Int<2>{});
assert(size<0>(A) == size<0>(C));
assert(size<0>(B) == size<1>(C));
assert(size<1>(A) == size<1>(B));
int a_width = size<1>(A) * 6 + 4;
// Print out B (white-shifted) k-by-n
for (int k = 0; k < size<1>(B); ++k) {
// Header
printf("%*s", a_width, "");
for (int n = 0; n < size<0>(B); ++n) printf("+-----");
printf("+\n");
// Values
printf("%*s", a_width, "");
for (int n = 0; n < size<0>(B); ++n) printf("|T%02dV%1d", int(TB(B(n,k) % size(TB))), int(B(n,k) / size(TB)));
printf("|\n");
}
// Footer
printf("%*s", a_width, "");
for (int n = 0; n < size<0>(B); ++n) printf("+-----");
printf("+\n\n");
// Print out A m-by-k and C m-by-n
for (int m = 0; m < size<0>(A); ++m) {
// Header
for (int k = 0; k < size<1>(A); ++k) printf("+-----");
printf("+ ");
for (int n = 0; n < size<1>(C); ++n) printf("+-----");
printf("+\n");
// Values
for (int k = 0; k < size<1>(A); ++k) printf("|T%02dV%1d", int(TA(A(m,k) % size(TA))), int(A(m,k) / size(TA)));
printf("| ");
for (int n = 0; n < size<1>(C); ++n) printf("|T%02dV%1d", int(TC(C(m,n) % size(TC))), int(C(m,n) / size(TC)));