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Advanced Features

This chapter covers advanced Tileon features for optimization and specialized operations.

Softmax

Row-wise softmax implementation:

@tileon.jit
def softmax_kernel(x_ptr, output_ptr, row_stride, n_cols, BLOCK_SIZE: tl.constexpr):
    row_idx = tl.program_id(0)
    row_start = row_idx * row_stride
    row_offset = row_start + tl.arange(0, BLOCK_SIZE)
    mask = row_offset < row_start + n_cols
    x = tl.load(x_ptr + row_offset, mask=mask, other=float('-inf'))
    x_max = tl.max(x, axis=0)
    x_exp = tl.exp(x - x_max)
    x_sum = tl.sum(x_exp, axis=0)
    softmax_vals = x_exp / x_sum
    tl.store(output_ptr + row_offset, softmax_vals, mask=mask)

Flash Attention

Efficient attention mechanism for transformer models.

Block-Sparse Attention

Sparse attention with custom block patterns.

Random Number Generation

Philox-based RNG for generating random values in kernels:

import tileon.language.random as tl_random

@tileon.jit
def random_kernel(output_ptr, seed, n_elements, BLOCK_SIZE: tl.constexpr):
    pid = tl.program_id(axis=0)
    offsets = pid * BLOCK_SIZE + tl.arange(0, BLOCK_SIZE)
    mask = offsets < n_elements

    random_vals = tl_random.rand(seed, offsets)

    tl.store(output_ptr + offsets, random_vals, mask=mask)

Matrix Multiplication Optimization

Tips for optimal GEMM:

  1. Choose appropriate block sizes based on hardware
  2. Use tl.dot for efficient tile multiplication
  3. Minimize shared memory bank conflicts
  4. Optimize memory access patterns
BLOCK_M = 128
BLOCK_N = 256
BLOCK_K = 64

Atomic Operations

Atomic operations for parallel reductions:

tl.atomic_add(output_ptr, value, mask)
tl.atomic_max(output_ptr, value, mask)
tl.atomic_min(output_ptr, value, mask)

Debugging

Print and assert:

tl.device_print("value: ", value)
tl.static_assert(BLOCK_SIZE <= 1024)
tl.device_assert(x > 0, "x must be positive")

Performance Tuning

  1. Profile your kernels to identify bottlenecks
  2. Optimize memory access patterns
  3. Use appropriate block sizes
  4. Leverage shared memory when possible
  5. Minimize divergence within warps