TTRI

Tile Operation Diagram

TTRI tile operation

Introduction

Generate a (lower/upper) triangular mask tile with ones and zeros. The triangular orientation is controlled by the compile-time template parameter isUpperOrLower (0 = lower, 1 = upper).

Math Interpretation

Let R = dst.GetValidRow() and C = dst.GetValidCol(). Let d = diagonal.

Lower-triangular (isUpperOrLower=0) conceptually produces:

\[ \mathrm{dst}_{i,j} = \begin{cases}1 & j \le i + d \\\\ 0 & \text{otherwise}\end{cases} \]

Upper-triangular (isUpperOrLower=1) conceptually produces:

\[ \mathrm{dst}_{i,j} = \begin{cases}0 & j < i + d \\\\ 1 & \text{otherwise}\end{cases} \]

C++ Intrinsic

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

template <typename TileData, int isUpperOrLower, typename... WaitEvents>
PTO_INST RecordEvent TTRI(TileData &dst, int diagonal, WaitEvents &... events);

Constraints

  • isUpperOrLower must be 0 (lower) or 1 (upper).
  • Implementation checks (A2A3):
    • Destination tile must be row-major (isRowMajor), enforced by static_assert.
    • Supported element types: int32_t, int, int16_t, uint32_t, uint16_t, half, float16_t, float, float32_t.
  • Implementation checks (A5):
    • Supported element types: int32_t, int16_t, int8_t, uint32_t, uint16_t, uint8_t, half, float16_t, float32_t, bfloat16_t.
    • Lower (upperOrLower == 0) and upper (upperOrLower == 1) are distinguished by if constexpr branches.
  • Valid region is obtained via dst.GetValidRow() / dst.GetValidCol().

Assembly Syntax

AS Level 1 (SSA)

%dst = pto.ttri %diag : i32 -> !pto.tile<...>

AS Level 2 (DPS)

pto.ttri ins(%diag : i32) outs(%dst : !pto.tile_buf<...>)

Examples

#include <pto/pto-inst.hpp>

using namespace pto;

void example_lower() {
  using TileT = Tile<TileType::Vec, float, 16, 16>;
  TileT dst;
  TASSIGN(dst, 0x1000);
  TTRI<0>(dst, /*diagonal=*/0);   // lower triangular
}

void example_upper() {
  using TileT = Tile<TileType::Vec, float, 16, 16>;
  TileT dst;
  TASSIGN(dst, 0x1000);
  TTRI<1>(dst, /*diagonal=*/-1);  // upper triangular
}

ASM Form Examples

Auto Mode

# Auto mode: compiler/runtime-managed placement and scheduling.
%dst = pto.ttri {isUpperOrLower = 0} : i32 -> !pto.tile<...>

Manual Mode

# Manual mode: resources must be bound explicitly before issuing the instruction.
# pto.tassign %arg0, @tile(0x1000)
%dst = pto.ttri %diag : i32 -> !pto.tile<...>

PTO Assembly Form

%dst = pto.ttri %diag : i32 -> !pto.tile<...>
# AS Level 2 (DPS)
pto.ttri ins(%diag : i32) outs(%dst : !pto.tile_buf<...>)