Sketching high-performance implementations of bitstream programs.

1
Sketching high-performance implementations of
bitstream programs.

• Armando Solar-Lezama, Rastislav Bodik
• UC Berkeley

2
Bitstream programs

• bitstream programs a growing domain
• crypto, compression, NSA/BitTwiddle, coding in
  general.
• bitstream algorithms easy 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 specification
  in 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
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 transf. spec
TSL with sketching
?
6
DSL StreamIt

• High-level bitstream algorithms written in
  StreamIt.
• Example drop every third bit.
• filter dropThird
• Work push 2 pop 3
• for (int i0 ilt3 i)
• x peek(i)
• if (ilt2) push(x)
• pop()

7
Naïve Compilation of BitStream Program

• The example filter operates on 3- and 2-bit
  chunks.
• unsuitable for the target machines instructions
• So, how to generate code for the example filter?
• transform the filter to operate on word-size
  chunks!
• Decompose new filters into filters corresponding
  to machine instructions
• Such low-level program can be expressed in
  StreamIt!

8
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

9
Transforming into low-level form (1)

• unroll 4x to make input/output a multiple of W4
  bits.

3
1 0 0 0 1 0
2
10
Transforming into low-level form (2)

• decompose into filters operating on W4 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
11
Transforming into low-level form (3)

• decompose into filters producing W4 bits of
  output.

rrobin 4,4,4
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
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
or
12
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
13
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.

14
TSL Transformation spec language

• TSL specification
• describes how to transform a filter into a
  semantically equivalent one with a different
  structure.
• so that you dont need to transform filters
  manually.
• Example. TSL spec for the transformation you
  just saw
• f Unroll4(dropThird)
• f ColSplit4(f)
• f.f_1 RowSplit4(f.f_1)
• f.f_2 RowSplit4(f.f_2)
• f.f_3 RowSplit4(f.f_3)
• TSL Spec can also be thought of as an
  implementation specification.
• Every statement in the above specification
  provides the system more details about the
  implementation.
• This simple specification can be generated
  automatically
• better TSL specs written by system expert, with
  help of sketches

15
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 filters matrix.
• filter filter1 x filter2
• This can be done hierarchically,
• Detail is only added where necessary.

16
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
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
Half way transformation to specify FAST bit
shifting algorithm
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

• 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_3xF.F_2xF.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

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
17
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(sT(P)) System
  expert provides a sketch of a transformation T.
• The compiler completes the sketch by requiring
  that the completed transformation (sT) produces
  a filter semantically equivalent to P.

18
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(116 by 0 1) x
shift(116 by 0 2) x shift(116
by 0 4)
19
Sketching a transformation

• The PermutFactor function specifies each step as
  a list of constraints
• PermutFactor constrList constrList
• Constraints of 3 types
• Type 1 specific shift amount
• shift( bitList by x)
• Type 2 undetermined shift amount
• shift( bitList by ?)
• Type 3 limited choice of shift amount
• shift( bitList by a b )
• System ignores constraints on discarded bits

20
Sketching a transformation-example

• First we must unroll to get a multiple of the
  word size
• Unroll16(filter)
• We want to use the fast algorithm for compacting
  the bits in each word
• The second word can only pack half the bits at a
  time, since half will go to one word and half to
  another

21
Sketching a transformation-example

• If we first pack all bits within a word, we can
  better exploit the parallelism afforded by the
  fast algorithm.
• We want to sketch this transformation.

22
Sketching a transformation-example

• Sketch of the transformation

• Sketch of the transformation
• PermutFactor(filter)

• Sketch of the transformation
• PermutFactor
• shift(116 by ?),
  shift(1732 by ?), shift(3348 by ?)
• (filter)

• Sketch of the transformation
• PermutFactorshift(12 by 0), shift(1718 by 0),
  shift(3334 by 0)
• shift(116 by ?),
  shift(1732 by ?), shift(3348 by ?)
• (filter)
• After this is done, we can proceed hierarchically

23
Sketching a transformation-example

• We can select a specific part of the algorithm
  and add more detail
• Specification of fast bit packing algorithm
  within each word
• PermutFactor shift(116 by 0 1),
• shift(116 by 0
  2),
• shift(116 by 0
  4)
• ( F_i )

24
Complete TSL spec for FAST

• WSIZE16
• subsequence UnrollWSIZE(subsequence)
• subsequence PermutFactor shift(12 by 0),
  shift(1718 by 0), shift(3334 by 0),
• 
  shift(116 by ?), shift(1732 by ?), shift(3348
  by ?)
• ( subsequence )
• subsequence.subsequence_1DiagSplitWSIZE(subsequ
  ence)
• for(i0 ilt3 i)
• bsequence.subsequence_1.filter(i)
• PermutFactor shift(116 by 0 1),
• shift(116 by 0
  2),
• shift(116 by 0
  4)
• ( subsequence.subsequen
  ce_1.filter(i) )
• Size 13 lines

25
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.

26
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.

27
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
• DESIPPermutFactor
• shift(1231 by -33),
• shift(2232 by 0),
•               shift(33263 by 0),
• shift(34264 by 33)
• ,(DESIP)
• Optimized version took .073 seconds, a speedup
  of 28

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0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 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 0 0 0 0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
0 0 0 0 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 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 0 0
28
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.