TMATMUL_MX¶

指令示意图¶

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¶

设：

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

概念上，结果对应于有效矩阵乘法域（0 <= i < M，0 <= j < N）上的矩阵乘法，缩放 tile aScaleMatrix / bScaleMatrix 配置实现定义的混合精度行为：

aScaleMatrix / bScaleMatrix 的确切作用（以及任何反量化/量化语义）由目标定义。

汇编语法¶

PTO-AS 形式：参见 PTO-AS 规范。

同步形式（概念性）：

%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<...>)

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 取自 aMatrix.GetValidRow()、aMatrix.GetValidCol()、bMatrix.GetValidCol()。
  • 静态合法性检查通过 CheckMadMxValid<...>()（类型、形状、分形和缩放 tile 合法性）。
• 偏置形式:
  • TileBias::DType 必须是 float 且 TileBias::Loc == TileType::Bias，TileBias::Rows == 1（A5 通过 static_assert 检查）。

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);
}

汇编示例（ASM）¶

自动模式¶

# 自动模式：由编译器/运行时负责资源放置与调度。
%c = pto.tmatmul.mx %a, %a_scale, %b, %b_scale : (!pto.tile<...>, !pto.tile<...>, !pto.tile<...>, !pto.tile<...>)

手动模式¶

# 手动模式：先显式绑定资源，再发射指令。
# 可选（当该指令包含 tile 操作数时）：
# pto.tassign %arg0, @tile(0x1000)
# pto.tassign %arg1, @tile(0x2000)
%c = pto.tmatmul.mx %a, %a_scale, %b, %b_scale : (!pto.tile<...>, !pto.tile<...>, !pto.tile<...>, !pto.tile<...>)

PTO 汇编形式¶

%c = pto.tmatmul.mx %a, %a_scale, %b, %b_scale : (!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<...>)