Sketching high-performance implementations of bitstream programs.

1. Sketching high-performance implementations of bitstream programs. Armando Solar-Lezama, Rastislav Bodik UC Berkeley

2. SLOW O(n) Bitstream programs • bitstream programs: a growing domain • crypto, compression, NSA/BitTwiddle, coding in general. • bitstream algorithmseasy to state • e.g., “Drop every third bit in the bit stream.” • but bitstream programs hard to implement • because efficient bit manipulations are hard to code • Can only work with word-size arrays of bits • Exponentially many ways of accomplishing the same task FAST O(log n)

3. Current development process • A collaborative experience: • domain expert writes a high-level algorithm, in C/Fortran, • system expert tunes its performance, often drastically turning the algorithm into ugly low-level code. • Now, if the original algorithm needs to be modified: • introduce changes into optimized code (error-prone), or • rewrite the algorithm and repeat tuning (time-consuming).

4. Our development process • A (better) collaborative experience: • domain expert writes a clean algorithm, in a clean DSL, • system expert optimizes the implementation by writing a (reusable) transformation specificationin a TSL. • If the original algorithm is modified, then • simply reapply the transformation specification. • The transformation spec: think of it as … • sequence of program edits, or • high level description of the desired implementation, or • an optimizer tailored to the algorithm

5. functionality sketch full implementation +  ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? Challenges, and our solution (overview) • How to make the transformation reusable? • Transformation should apply after the algorithm changes. • How to simplify transformation development? • Should be much easier than editing the program by hand. • Should not allow you to introduce bugs Our solution: a transformation sketch • system expert sketches the transformation, • details filled in automatically. DSL: StreamIt TSL with sketching TSL: transf. spec ?

6. 3 x y z 2  1 0 0 0 1 0 x y x = consumes a 3-bit chunk of input; produces a 2-bit of output. DSL: StreamIt • High-level bitstream algorithms written in StreamIt. • Example: “drop every third bit”. filter dropThird { Work push 2 pop 3 { for (int i=0; i<3; ++i) { x = peek(i); if (i<2) push(x); pop(); } } }

7. The development strategy • We offer several methods for “lowering” filters into low-level form (i.e., for implementing them with target code): • Manual-transformation: M(P) For any filter P, the system expert could manually write a TSL spec to make P low level. • Auto-transformation: N(P) For any filter P, the system knows how to produce a naïve lowering TSL spec N. • N is thus a simple code generator for P

8. 12 1 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 1 0 8 Transforming into low-level form (1) • unroll 4x to make input/output a multiple of W=4 bits. 3 1 0 0 0 1 0 2

9. rrobin 4,4,4 4 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 1 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 1 0 1 0 0 0 0 1 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 8 or Transforming into low-level form (2) • decompose into filters operating on W=4 bits of input. 12 1 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 1 0 8

10. rrobin 4,4,4 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 1 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 1 0 duplicate 1 0 0 0 0 1 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 cat or Transforming into low-level form (3) • decompose into filters producing W=4 bits of output. rrobin 4,4,4 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 1 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 1 0 1 0 0 0 0 1 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 or

11. in duplicate 0 1 0 0 0 0 1 0 0 0 0 1 0 0 0 0 t2 = in SHIFTL 1 1 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 t1 = in AND 1100 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 t3 = t2 AND 0010 or out = t1 OR t3 Implementing a basic filter (4) • decompose word-size filter into available instructions. 1 0 0 0 0 1 0 0 0 0 0 1 0 0 0 0

12. The development strategy • We offer several methods for “lowering” filters into low-level form (i.e., for implementing them with target code): • Manual-transformation: M(P) For any filter P, the filter system expert could manually bring it to low level form. • Auto-transformation: N(P) For any filter P, the system knows how to produce a naïve lowering TSL spec N. • N is thus a simple code generator for P • Half-way transformation. N(T(P)) System expert provides a spec T that transforms P so that N generates better code. • If written well, T brings P closer to low-level code (gives it a good structure) so that N can do a perfect job generating the code.

13. Half way transformations • The expert guides lowering by imparting structure to the filter • If the system expert has an algorithm in mind to implement a particular filter, the expert can decompose the filter into a sequence of filters, each one implementing one step of the algorithm. • So, specifying an efficient bit manipulation often boils down to specifying a decomposition of the filter’s matrix. • filter = filter1 x filter2 • This can be done hierarchically, • Detail is only added where necessary.

14. Half way transformations-example 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 F.F_1 Half way transformation to specify FAST bit shifting algorithm 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 • System Expert provides high level decomposition • System Takes care of Lowering F.F_1, F.F_2 and F.F_3 • Correctness is guaranteed as long as F = [F.F_3]x[F.F_2]x[F.F_1] • Fully Specifying F.F._1, F.F_2 and F.F_3 is still too difficult. We would like to be able to sketch them F.F_1 F F.F_2 F.F_3 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 F.F_2 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 F.F_3

15. The development strategy • We offer several methods for “lowering” filters into low-level form (i.e., for implementing them with target code): • Manual-transformation: M(P) For any filter P, the filter system expert could manually bring it to low level form. • Auto-transformation: N(P) For any filter P, the system knows how to produce a naïve lowering TSL spec N. • N is thus a simple code generator for P • Half-way transformation. N(T(P)) System expert provides a spec T that transforms P so that N generates better code. • If written well, T brings P closer to low-level code (gives it a good structure) so that N can do a perfect job generating the code. • Half-specified transformation. N(s[T](P)) System expert provides a sketch of a transformation T. • The compiler completes the sketch by requiring that the completed transformation (s[T]) produces a filter semantically equivalent to P.

16. functionality sketch full implementation ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? Sketching a transformation • A transformation sketch: • Specifies the number of stages in the decomposition • Gives constraints on terms of the decomposition • System derives a decomposition satisfying the constraints and semantically equivalent to original filter • Example. A fragment of TSL for FAST compaction: • filter = [shift(1:16 by 0 || 1)] x [shift(1:16 by 0 || 2)] x • [shift(1:16 by 0 || 4)]

17. Complete TSL spec for FAST WSIZE=16; subsequence = Unroll[WSIZE](subsequence); subsequence = PermutFactor[ [shift(1:2 by 0), shift(17:18 by 0), shift(33:34 by 0)], [shift(1:16 by ?), shift(17:32 by ?), shift(33:48 by ?)] ] ( subsequence ); subsequence.subsequence_1=DiagSplit[WSIZE](subsequence); for(i=0; i<3; ++i) { bsequence.subsequence_1.filter(i) = PermutFactor[ [shift(1:16 by 0 || 1)], [shift(1:16 by 0 || 2)], [shift(1:16 by 0 || 4)] ]( subsequence.subsequence_1.filter(i) ); } Size: 13 lines

18. Reusability of the TSL specs • A TSL spec is reusable under a given change to the program if the changed program can still be profitably transformed with the TSL spec. • Experiment: • Start with the program P = “drop every third bit”, • Write the FAST spec for it, • Modify P to “drop the second bit in each three bits.” • no change in the original TSL spec needed. • Modify P to “drop every fourth bit”. • Only minor change in the TSL spec needed.

19. Performance Gain: bit compaction • On a pentium III processor running at 1.5 GHz, the unoptimized code took 0.068 seconds to process .127 Mb of data 100 times. • On the same machine, optimized version took 0.041 seconds, a performance gain of 39%.

20. Performance Gain: Permutation from DES • On the same machine the unoptimized code took .102 seconds to process the same amount of data. • After a simple TSL specification DESIP=PermutFactor[ [ shift(1:2:31 by -33), shift(2:2:32 by 0),               shift(33:2:63 by 0), shift(34:2:64 by 33) ],[]](DESIP); • Optimized version took .073 seconds, a speedup of 28% 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 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21. Conclusions • Our system allows the separation of the algorithm specification from performance tuning through the use of TSL • System expert only needs to specify high level transformations, system can take care of the details • Sketching the transformations makes them reusable and easier to write.