TMATMUL_MX

Instruction Diagram

Introduction

Matrix multiplication (GEMM) with additional scale tiles, used to support mixed-precision/quantized matrix multiplication on the target.

This instruction is currently implemented only on Ascend 950PR/Ascend 950DT (see include/pto/npu/a5/TMatmul.hpp).

Mathematical Semantics

Assume:

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

Conceptually, the result corresponds to matrix multiplication over the valid matrix multiplication domain (0 <= i < M, 0 <= j < N), where the scale tiles aScaleMatrix / bScaleMatrix configure 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 (as well as any dequantization/quantization semantics) is defined by the target.

Assembly Syntax

Synchronization form (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<...>)

C++ Built-in APIs

Declared in include/pto/common/pto_instr.hpp:

The public include header is <pto/pto-inst.hpp>, and the internal declaration is located in 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);

Constraints

• Implementation check (Ascend 950PR/Ascend 950DT):
  • m/k/n are taken from aMatrix.GetValidRow(), aMatrix.GetValidCol(), and bMatrix.GetValidCol().
  • Static validity check is performed through CheckMadMxValid<...>() (type, shape, fractal, and scale tile validity).
  • Supported (C, A, B) triplets (C is always float; the scale tile is float8_e8m0_t):
    • FP8: (float, float8_e4m3_t, float8_e4m3_t), (float, float8_e4m3_t, float8_e5m2_t), (float, float8_e5m2_t, float8_e4m3_t), (float, float8_e5m2_t, float8_e5m2_t).
    • FP4: (float, float4_e1m2x2_t, float4_e1m2x2_t), (float, float4_e1m2x2_t, float4_e2m1x2_t), (float, float4_e2m1x2_t, float4_e2m1x2_t), (float, float4_e2m1x2_t, float4_e1m2x2_t).
• Bias form:
  • TileBias::DType must be float and TileBias::Loc == TileType::Bias, TileBias::Rows == 1 (checked via static_assert on Ascend 950PR/Ascend 950DT).

Examples

Automatic

#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);
}

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);
}

ASM Examples

Automatic Mode

# Automatic mode: the compiler/runtime handles resource placement and scheduling.
%c = pto.tmatmul.mx %a, %a_scale, %b, %b_scale : (!pto.tile<...>, !pto.tile<...>, !pto.tile<...>, !pto.tile<...>)

Manual Mode

# Manual mode: explicitly bind resources first, then issue the instruction.
# Optional (when the instruction contains tile operands):
# 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 Assembly Form

%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<...>)