The document describes Halide, a domain specific language for image processing pipelines that decouples algorithms from schedules. This decoupling allows for easy optimization by specifying schedules that control parallelism, locality, and vectorization without changing the underlying algorithm. The Halide compiler then generates efficient code from the algorithm and schedule. Key features include expressing algorithms with Funcs and scheduling with operations like tile, split, fuse, and parallel. Halide is embedded in C++ and uses metaprogramming to represent programs as abstract syntax trees, enabling just-in-time or ahead-of-time compilation to optimized code.

1. Halide
Domain Specific Language

2. Decoupling Algorithms from Schedules for Easy
Optimization of Image Processing Pipelines
Jonathan Ragan-Kelley, Andrew Adams, Sylvain Paris, Marc Levoy,
Saman Amarasinghe, Frédo Durand
ACM Transactions on Graphics (TOG) - Proceedings of ACM SIGGRAPH 2012

3. Sobel Edge Detection
-1 0 1
-2 0 2
-1 0 1
1 2 1
0 0 0
-1 -2 -1
Gx Gy

5. Making Image processing faster by hardward
● Parallel Programming
● Memory Locality
=> Requires to reorganize computation!

6. Message #1: Performance requires complex tradeoffs

7. Message #2: organization of computation

8. Existing languages make critical optimizations hard
Parallelism : vectorization / multithreading
Locality : fusion / tiling
C - parallelism + tiling + fusion are hard to write or automate
CUDA, OpenCL, shaders - data parallelism is easy, fusion is hard
libraries don’t help:
BLAS, IPP, MKL, OpenCV, MATLAB
optimized kernels compose into ine ffi cient pipelines (no fusion)

9. Halide DSL : decouple algorithm from schedule
Algorithm: what is computed
Schedule: where and when it’s computed
Easy for programmers to build pipelines
simplifies algorithm code
improves modularity
Easy for programmers to specify & explore optimizations
fusion, tiling, parallelism, vectorization
can’t break the algorithm
Easy for the compiler to generate fast code

10. Halide is embedded in C++
● Build Halide functions and expressions using C++
● Evaluate Halide functions immediately
○ just-in-time compile to produce and run a Halide pipeline
● Or statically compile to an object file and header
○ One C++ program creates the Halide pipeline When run, it produces an object file and header
You link this into your actual program

11. Halide Language
● Algorithm
○ Halide::Image
○ Halide::Var
○ Halide::Expr
○ Halide::Buffer
● Scheduling
○ next slide

12. Halide Language

13. Default and Reorder Schedule
Default Reorder

14. Split Schedule
gradient.split(x, x_outer, x_inner, 4);
gradient.split(y, y_outer, y_inner, 4);

15. Evaluating in vectors
gradient.split(x, x_outer, x_inner, 4);
gradient.vectorize(x_inner);

16. Parallel
Var x_outer, y_outer, x_inner, y_inner, tile_index;
gradient.tile(x, y, x_outer, y_outer, x_inner, y_inner, 4, 4);
gradient.fuse(x_outer, y_outer, tile_index);
gradient.parallel(tile_index);

19. Parallelism
distribute across threads and
SIMD parallel vector

20. Locality
compute in tiles interleave
tiles of blurx, blury store blurx
in local cache

22. Input Image
Blur X
Blur Y

23. Halide Compiler

24. Basic Halide program (default schedule)
Image<float> input = load<float>("images/rgb.png");
Var x, y;
Func blur_x;
Func blur_y;
blur_x(x,y) = (input(x,y)+input(x+1,y)+input(x+2,y))/3.0;
blur_y(x,y) = (blur_x(x,y)+blur_x(x,y+1)+blur_x(x,y+2))/3.0;
Image<float> output = blur_y.realize(input.width()-2,input.height()-2);

25. Metaprogramming
● Create C++ objects that describe a Halide program
● Essentially algebraic trees (Abstract Syntax Tree, AST)
● Once the representation is constructed, call .realize() tocompile and execute
● This calls the C++ Halide compiler, creates binary, executes it
● Metaprogramming makes it easy to embed in an existing language and
codebase, avoids the need to parse

26. Syntax: Main types/keywords
Func : pure functions over an integer domain
Var : pure abstract variables for domain of Funcs
Expr: algebraic expressions of Funcs and Var including standard operators and
functions (+,-,&, /, **, sqrt, sin, cos...)
Image: arrays used as inputs and outputs

27. Q & A