TMATMUL

Instruction Diagram

Introduction

Matrix multiplication (GEMM), which generates an accumulator/output tile.

Mathematical Semantics

Assume:

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

For 0 <= i < M and 0 <= j < N (output elements in the valid matrix multiplication domain):

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

The exact accumulator behavior and data type promotion are defined by the target/implementation.

Assembly Syntax

Synchronous form:

%acc = tmatmul %a, %b : (!pto.tile<...>, !pto.tile<...>) -> !pto.tile<...>

AS Level 1 (SSA)

%c = pto.tmatmul %a, %b : (!pto.tile<...>, !pto.tile<...>) -> !pto.tile<...>

AS Level 2 (DPS)

pto.tmatmul ins(%a, %b : !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 TileRight, typename... WaitEvents>
PTO_INST RecordEvent TMATMUL(TileRes &cMatrix, TileLeft &aMatrix, TileRight &bMatrix, WaitEvents &... events);

template <AccPhase Phase, typename TileRes, typename TileLeft, typename TileRight, typename... WaitEvents>
PTO_INST RecordEvent TMATMUL(TileRes &cMatrix, TileLeft &aMatrix, TileRight &bMatrix, WaitEvents &... events);

Constraints

Implementation check (Atlas A2/A3 training products/Atlas A2/A3 inference products):
- Supported (CType, AType, BType) triples:
- (int32_t, int8_t, int8_t)
- (float, half, half)
- (float, float, float)
- (float, bfloat16_t, bfloat16_t)
- Static shape constraints: TileLeft::Rows == TileRes::Rows, TileLeft::Cols == TileRight::Rows, TileRight::Cols == TileRes::Cols.
- Tile positions: TileLeft::Loc == Left, TileRight::Loc == Right, TileRes::Loc == Acc.
- Runtime: m/k/n (obtained from aMatrix.GetValidRow(), aMatrix.GetValidCol(), bMatrix.GetValidCol()) must be within the range [1, 4095].
Implementation check (Ascend 950PR/Ascend 950DT):
- The accumulator type must be int32_t or float.
- If it is int32_t: AType == int8_t and BType == int8_t.
- If it is float: supports half/bfloat16_t/float, selected fp8 pairs, and hifloat8_t/hifloat8_t (target-defined).
- Static shape constraints: TileLeft::Rows == TileRes::Rows, TileLeft::Cols == TileRight::Rows, TileRight::Cols == TileRes::Cols.
- Enforce fractal/layout constraints:
- Left: Loc == Left, !isRowMajor, SFractal == RowMajor
- Right: Loc == Right, isRowMajor, SFractal == ColMajor
- Acc: Loc == Acc, !isRowMajor, SFractal == RowMajor
- Runtime: m/k/n (obtained from aMatrix.GetValidRow(), aMatrix.GetValidCol(), bMatrix.GetValidCol()) must be within the range [1, 4095].

Examples

Automatic

#include <pto/pto-inst.hpp>

using namespace pto;

void example_auto() {
  using A = TileLeft<half, 16, 16>;
  using B = TileRight<half, 16, 16>;
  using C = TileAcc<float, 16, 16>;
  A a;
  B b;
  C c;
  TMATMUL(c, a, b);
}

Manual

#include <pto/pto-inst.hpp>

using namespace pto;

void example_manual() {
  using A = TileLeft<half, 16, 16>;
  using B = TileRight<half, 16, 16>;
  using C = TileAcc<float, 16, 16>;
  A a;
  B b;
  C c;
  TASSIGN(a, 0x1000);
  TASSIGN(b, 0x2000);
  TASSIGN(c, 0x3000);
  TMATMUL(c, a, b);
}

ASM Examples

Automatic Mode

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

PTO Assembly Form

%acc = tmatmul %a, %b : (!pto.tile<...>, !pto.tile<...>) -> !pto.tile<...>
# AS Level 2 (DPS)
pto.tmatmul ins(%a, %b : !pto.tile_buf<...>, !pto.tile_buf<...>) outs(%c : !pto.tile_buf<...>)