TMATMUL_MX

指令示意图

TMATMUL_MX tile operation

简介

带额外缩放 Tile 的矩阵乘法 (GEMM)，用于支持目标上的混合精度/量化矩阵乘法。

数学语义

Let:

  • M = aMatrix.GetValidRow()
  • K = aMatrix.GetValidCol()
  • N = bMatrix.GetValidCol()

Conceptually, the result corresponds to a matrix multiply over the effective matmul domain (0 <= i < M, 0 <= j < N), with the scaling tiles aScaleMatrix / bScaleMatrix configuring implementation-defined mixed-precision behavior:

\[ \mathrm{C}_{i,j} = \sum_{k=0}^{K-1} \mathrm{A}_{i,k} \cdot \mathrm{B}_{k,j} \]

The exact role of aScaleMatrix / bScaleMatrix (and any dequant/quant semantics) is target-defined.

汇编语法

PTO-AS 形式：参见 PTO-AS Specification.

Synchronous forms (conceptual):

%c = tmatmul.mx %a, %a_scale, %b, %b_scale : (!pto.tile<...>, !pto.tile<...>, !pto.tile<...>, !pto.tile<...>) -> !pto.tile<...>
%c_out = tmatmul.mx.acc %c_in, %a, %a_scale, %b, %b_scale : (!pto.tile<...>, !pto.tile<...>, !pto.tile<...>, !pto.tile<...>, !pto.tile<...>) -> !pto.tile<...>
%c = tmatmul.mx.bias %a, %a_scale, %b, %b_scale, %bias : (!pto.tile<...>, !pto.tile<...>, !pto.tile<...>, !pto.tile<...>, !pto.tile<...>) -> !pto.tile<...>

AS Level 1 (SSA)

%c = pto.tmatmul.mx %a, %a_scale, %b, %b_scale : (!pto.tile<...>, !pto.tile<...>, !pto.tile<...>, !pto.tile<...>)
-> !pto.tile<...>
%c_out = pto.tmatmul.mx.acc %c_in, %a, %a_scale, %b, %b_scale : (!pto.tile<...>, !pto.tile<...>,
!pto.tile<...>, !pto.tile<...>, !pto.tile<...>)  -> !pto.tile<...>
%c = pto.tmatmul.mx.bias %a, %a_scale, %b, %b_scale, %bias : (!pto.tile<...>, !pto.tile<...>,
!pto.tile<...>, !pto.tile<...>, !pto.tile<...>)  -> !pto.tile<...>

AS Level 2 (DPS)

pto.tmatmul.mx ins(%a, %a_scale, %b, %b_scale : !pto.tile_buf<...>, !pto.tile_buf<...>, !pto.tile_buf<...>, !pto.tile_buf<...>)
outs(%c :  !pto.tile_buf<...>)
pto.tmatmul.mx.acc ins(%c_in, %a, %a_scale, %b, %b_scale : !pto.tile_buf<...>, !pto.tile_buf<...>, !pto.tile_buf<...>,
!pto.tile_buf<...>, !pto.tile_buf<...>) outs(%c_out : !pto.tile_buf<...>)
pto.tmatmul.mx.bias ins(%a, %a_scale, %b, %b_scale, %bias : !pto.tile_buf<...>, !pto.tile_buf<...>, !pto.tile_buf<...>,
!pto.tile_buf<...>, !pto.tile_buf<...>) outs(%c : !pto.tile_buf<...>)

AS Level 1（SSA）

%c = pto.tmatmul.mx %a, %a_scale, %b, %b_scale : (!pto.tile<...>, !pto.tile<...>, !pto.tile<...>, !pto.tile<...>)
-> !pto.tile<...>
%c_out = pto.tmatmul.mx.acc %c_in, %a, %a_scale, %b, %b_scale : (!pto.tile<...>, !pto.tile<...>,
!pto.tile<...>, !pto.tile<...>, !pto.tile<...>)  -> !pto.tile<...>
%c = pto.tmatmul.mx.bias %a, %a_scale, %b, %b_scale, %bias : (!pto.tile<...>, !pto.tile<...>,
!pto.tile<...>, !pto.tile<...>, !pto.tile<...>)  -> !pto.tile<...>

AS Level 2（DPS）

pto.tmatmul.mx ins(%a, %a_scale, %b, %b_scale : !pto.tile_buf<...>, !pto.tile_buf<...>, !pto.tile_buf<...>, !pto.tile_buf<...>)
outs(%c :  !pto.tile_buf<...>)
pto.tmatmul.mx.acc ins(%c_in, %a, %a_scale, %b, %b_scale : !pto.tile_buf<...>, !pto.tile_buf<...>, !pto.tile_buf<...>,
!pto.tile_buf<...>, !pto.tile_buf<...>) outs(%c_out : !pto.tile_buf<...>)
pto.tmatmul.mx.bias ins(%a, %a_scale, %b, %b_scale, %bias : !pto.tile_buf<...>, !pto.tile_buf<...>, !pto.tile_buf<...>,
!pto.tile_buf<...>, !pto.tile_buf<...>) outs(%c : !pto.tile_buf<...>)

C++ 内建接口

声明于 include/pto/common/pto_instr.hpp:

template <typename TileRes, typename TileLeft, typename TileLeftScale, typename TileRight, typename TileRightScale,
          typename... WaitEvents>
PTO_INST RecordEvent TMATMUL_MX(TileRes &cMatrix, TileLeft &aMatrix, TileLeftScale &aScaleMatrix, TileRight &bMatrix, TileRightScale &bScaleMatrix, WaitEvents &... events);

template <AccPhase Phase, typename TileRes, typename TileLeft, typename TileLeftScale, typename TileRight,
          typename TileRightScale, typename... WaitEvents>
PTO_INST RecordEvent TMATMUL_MX(TileRes &cMatrix, TileLeft &aMatrix, TileLeftScale &aScaleMatrix, TileRight &bMatrix, TileRightScale &bScaleMatrix, WaitEvents &... events);

template <typename TileRes, typename TileLeft, typename TileLeftScale, typename TileRight, typename TileRightScale,
          typename... WaitEvents>
PTO_INST RecordEvent TMATMUL_MX(TileRes &cOutMatrix, TileRes &cInMatrix, TileLeft &aMatrix, TileLeftScale &aScaleMatrix, TileRight &bMatrix, TileRightScale &bScaleMatrix, WaitEvents &... events);

template <AccPhase Phase, typename TileRes, typename TileLeft, typename TileLeftScale, typename TileRight,
          typename TileRightScale, typename... WaitEvents>
PTO_INST RecordEvent TMATMUL_MX(TileRes &cOutMatrix, TileRes &cInMatrix, TileLeft &aMatrix, TileLeftScale &aScaleMatrix, TileRight &bMatrix, TileRightScale &bScaleMatrix, WaitEvents &... events);

template <typename TileRes, typename TileLeft, typename TileLeftScale, typename TileRight, typename TileRightScale,
          typename TileBias, typename... WaitEvents>
PTO_INST RecordEvent TMATMUL_MX(TileRes &cMatrix, TileLeft &aMatrix, TileLeftScale &aScaleMatrix, TileRight &bMatrix, TileRightScale &bScaleMatrix, TileBias &biasData, WaitEvents &... events);

template <AccPhase Phase, typename TileRes, typename TileLeft, typename TileLeftScale, typename TileRight,
          typename TileRightScale, typename TileBias, typename... WaitEvents>
PTO_INST RecordEvent TMATMUL_MX(TileRes &cMatrix, TileLeft &aMatrix, TileLeftScale &aScaleMatrix, TileRight &bMatrix, TileRightScale &bScaleMatrix, TileBias &biasData, WaitEvents &... events);

约束

  • 实现检查 (A5):
    • m/k/n are taken from aMatrix.GetValidRow(), aMatrix.GetValidCol(), bMatrix.GetValidCol().
    • Static legality checks are enforced via CheckMadMxValid<...>() (types, shapes, fractals, and scaling tile legality).
  • Bias form:
    • TileBias::DType must be float and TileBias::Loc == TileType::Bias with TileBias::Rows == 1 (A5 checks via static_assert).

示例

自动（Auto）

#include <pto/pto-inst.hpp>

using namespace pto;

void example_auto() {
  using A = TileLeft<float8_e5m2_t, 16, 64>;
  using B = TileRight<float8_e5m2_t, 64, 32>;
  using ScaleA = TileLeftScale<float8_e8m0_t, 16, 2>;
  using ScaleB = TileRightScale<float8_e8m0_t, 2, 32>;
  using Bias = Tile<TileType::Bias, float, 1, 32>;
  using C = TileAcc<float, 16, 32>;
  A a;
  B b;
  ScaleA scaleA;
  ScaleB scaleB;
  Bias bias;
  C c;
  TMATMUL_MX(c, a, scaleA, b, scaleB, bias);
}

手动（Manual）

#include <pto/pto-inst.hpp>

using namespace pto;

void example_manual() {
  using A = TileLeft<float8_e5m2_t, 16, 64>;
  using B = TileRight<float8_e5m2_t, 64, 32>;
  using ScaleA = TileLeftScale<float8_e8m0_t, 16, 2>;
  using ScaleB = TileRightScale<float8_e8m0_t, 2, 32>;
  using Bias = Tile<TileType::Bias, float, 1, 32>;
  using C = TileAcc<float, 16, 32>;
  A a;
  B b;
  ScaleA scaleA;
  ScaleB scaleB;
  Bias bias;
  C c;
  TASSIGN(a, 0x1000);
  TASSIGN(b, 0x2000);
  TASSIGN(scaleA, GetScaleAddr(a.data()));
  TASSIGN(scaleB, GetScaleAddr(b.data()));
  TASSIGN(bias, 0x3000);
  TASSIGN(c, 0x4000);
  TMATMUL_MX(c, a, scaleA, b, scaleB, bias);
}