TGEMV¶

Tile Operation Diagram¶

TGEMV tile operation

Introduction¶

General Matrix-Vector multiplication (GEMV) producing an accumulator/output tile.

Math Interpretation¶

Let:

M = 1
K = bMatrix.GetValidRow()
N = bMatrix.GetValidCol()

1. TGEMV (Tile-based GEMV)¶

For 0 <= j < N (output elements in the effective matmul domain):

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

2. TGEMV_ACC (Tile-based GEMV with Accumulation)¶

For 0 <= j < N (accumulates into existing tile):

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

3. TGEMV_BIAS (Tile-based GEMV with Bias)¶

For 0 <= j < N (adds bias term to matrix product):

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

Note: Exact accumulator behavior and datatype promotion are target/implementation-defined.

Assembly Syntax¶

PTO-AS form: see PTO-AS Specification.

Synchronous form:

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

%acc1 = tgemv.acc %acc0, %a, %b : (!pto.tile<...>, !pto.tile<...>, !pto.tile<...>) -> !pto.tile<...>

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

AS Level 1 (SSA)¶

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

AS Level 2 (DPS)¶

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

C++ Intrinsic¶

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

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

template <typename TileRes, typename TileLeft, typename TileRight, typename... WaitEvents>
PTO_INST RecordEvent TGEMV_ACC(TileRes &cOutMatrix, TileRes &cInMatrix, TileLeft &aMatrix, TileRight &bMatrix, WaitEvents&... events);

template <typename TileRes, typename TileLeft, typename TileRight, typename TileBias, typename... WaitEvents>
PTO_INST RecordEvent TGEMV_BIAS(TileRes &cMatrix, TileLeft &aMatrix, TileRight &bMatrix, TileBias &biasData, WaitEvents&... events);

Constraints¶

Common shape and location constraints¶

These constraints apply to TGEMV, TGEMV_ACC, and TGEMV_BIAS unless otherwise noted.

Static shape constraints:
- TileLeft::Rows == TileRes::Rows
- TileLeft::Cols == TileRight::Rows
- TileRight::Cols == TileRes::Cols
Tile locations:
- TileLeft::Loc == Left
- TileRight::Loc == Right
- TileRes::Loc == Acc
Runtime valid-size constraints:
- m must be 1
- k and n (taken from bMatrix.GetValidRow() and bMatrix.GetValidCol()) must be in [1, 4095]

TGEMV / TGEMV_ACC datatype constraints¶

Implementation checks (A2A3):
- Supported (CType, AType, BType) triples:
  - (int32_t, int8_t, int8_t)
  - (float, half, half)
  - (float, float, float)
  - (float, bfloat16_t, bfloat16_t)
Implementation checks (A5):
- Accumulator type must be int32_t or float.
- If int32_t: AType == int8_t and BType == int8_t.
- If float: supports half, bfloat16_t, float, and selected fp8 pairs (target-defined).
- Fractal/layout constraints are enforced:
  - Left: Loc == Left, !isRowMajor, SFractal == RowMajor
  - Right: Loc == Right, isRowMajor, SFractal == ColMajor
  - Acc: Loc == Acc, !isRowMajor, SFractal == RowMajor

TGEMV_BIAS additional constraints¶

Bias tile datatype must exactly match TileRes::DType.
Bias tile must be configured as a single row.
Bias tile location must be TileType::Bias.
Additional A5 note:
- No separate explicit m/k/n runtime assertions are enforced in the underlying A5 matmul implementation beyond the GEMV contract described above.

Examples¶

Auto¶

1. TGEMV¶

#include <pto/pto-inst.hpp>

using namespace pto;

void example_auto() {
  using A = TileLeft<half, 1, 16>;
  using B = TileRight<half, 16, 16>;
  using C = TileAcc<float, 1, 16>;
  A a;
  B b;
  C c;
  TGEMV(c, a, b);
}

2. TGEMV_ACC¶

#include <pto/pto-inst.hpp>

using namespace pto;

void example_auto() {
  using A = TileLeft<half, 1, 16>;
  using B = TileRight<half, 16, 16>;
  using C = TileAcc<float, 1, 16>;
  A a;
  B b;
  C c0, c1;
  TGEMV_ACC(c1, c0, a, b);
}

3. TGEMV_BIAS¶

#include <pto/pto-inst.hpp>

using namespace pto;

void example_auto() {
  using A = TileLeft<half, 1, 16>;
  using B = TileRight<half, 16, 16>;
  using Bias = Tile<TileType::Bias, half, 1, 16>;
  using C = TileAcc<float, 1, 16>;
  A a;
  B b;
  Bias bias;
  C c;
  TGEMV_BIAS(c, a, b, bias);
}

Manual¶

1. TGEMV¶

#include <pto/pto-inst.hpp>

using namespace pto;

void example_manual() {
  using A = TileLeft<half, 1, 16>;
  using B = TileRight<half, 16, 16>;
  using C = TileAcc<float, 1, 16>;
  A a;
  B b;
  C c;
  TASSIGN(a, 0x1000);
  TASSIGN(b, 0x2000);
  TASSIGN(c, 0x3000);
  TGEMV(c, a, b);
}

2. TGEMV_ACC¶

#include <pto/pto-inst.hpp>

using namespace pto;

void example_manual() {
  using A = TileLeft<half, 1, 16>;
  using B = TileRight<half, 16, 16>;
  using C = TileAcc<float, 1, 16>;
  A a;
  B b;
  C c0, c1;
  TASSIGN(a, 0x1000);
  TASSIGN(b, 0x2000);
  TASSIGN(c0, 0x3000);
  TASSIGN(c1, 0x4000);
  TGEMV_ACC(c1, c0, a, b);
}

3. TGEMV_BIAS¶

#include <pto/pto-inst.hpp>

using namespace pto;

void example_manual() {
  using A = TileLeft<half, 1, 16>;
  using B = TileRight<half, 16, 16>;
  using Bias = Tile<TileType::Bias, half, 1, 16>;
  using C = TileAcc<float, 1, 16>;
  A a;
  B b;
  Bias bias;
  C c;
  TASSIGN(a, 0x1000);
  TASSIGN(b, 0x2000);
  TASSIGN(bias, 0x3000);
  TASSIGN(c, 0x4000);
  TGEMV_BIAS(c, a, b, bias);
}

ASM Form Examples¶

Auto Mode¶

# Auto mode: compiler/runtime-managed placement and scheduling.
%c = pto.tgemv %a, %b : (!pto.tile<...>, !pto.tile<...>) -> !pto.tile<...>

Manual Mode¶

# Manual mode: bind resources explicitly before issuing the instruction.
# Optional for tile operands:
# pto.tassign %arg0, @tile(0x1000)
# pto.tassign %arg1, @tile(0x2000)
%c = pto.tgemv %a, %b : (!pto.tile<...>, !pto.tile<...>) -> !pto.tile<...>

PTO Assembly Form¶

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