Exhaustive Optimization Phase Order Space Exploration Prasad A. - - PowerPoint PPT Presentation

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Symposium on Code Generation and Optimization - 2006

Exhaustive Optimization Phase Order Space Exploration

Prasad A. Kulkarni David B. Whalley Gary S. Tyson Jack W. Davidson

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Optimization Phase Ordering

• Optimizing compilers apply several
• ptimization phases to improve the

performance of applications.

• Optimization phases interact with each other.
• Determining the best order of applying
• ptimization phases has been a long standing

problem in compilers.

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Exhaustive Phase Order Enumeration... is it Feasible ?

• A obvious approach to address the phase
• rdering problem is to exhaustively evaluate

all combinations of optimization phases.

• Exhaustive enumeration is difficult
• compilers typically contain many different
• ptimization phases
• optimizations may be successful multiple times

for each function / program

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Optimization Space Properties

• Phase ordering problem can be made more

manageable by exploiting certain properties

• f the optimization search space
• optimization phases might not apply any

transformations

• many optimization phases are independent
• Thus, many different orderings of
• ptimization phases produce the same code.

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Re-stating the Phase Ordering Problem

• Rather than considering all attempted phase

sequences, the phase ordering problem can be addressed by enumerating all distinct function instances that can be produced by combination of optimization phases.

• We were able to exhaustively enumerate

109 out of 111 functions, in a few minutes for most.

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Outline

• Experimental framework
• Algorithm for exhaustive enumeration of

the phase order space

• Search space enumeration results
• Optimization phase interaction analysis
• Making conventional compilation faster
• Future work and conclusions

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Experimental Framework

• We used the VPO compilation system
• established compiler framework, started development

in 1988

• comparable performance to gcc –O2
• VPO performs all transformations on a single

representation (RTLs), so it is possible to perform most phases in an arbitrary order.

• Experiments use all the 15 available optimization

phases in VPO.

• Target architecture was the StrongARM SA-100

processor.

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VPO Optimization Phases

register allocation k

• remv. useless jumps

u minimize loop jumps j instruction selection s block reordering i reverse branches r dead assignment elim. h strength reduction q loop unrolling g

• eval. order determin.
• remv. unreachable code

d code abstraction n common subexpr. elim. c loop transformations l branch chaining b Optimization Phase ID Optimization Phase ID

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Disclaimers

• Did not include optimization phases normally

associated with compiler front ends

• no memory hierarchy optimizations
• no inlining or other interprocedural optimizations
• Did not vary how phases are applied.
• Did not include optimizations that require

profile data.

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Benchmarks

• Used one program from each of the six

MiBench categories.

• Total of 111 functions.

searches for given words in phrases stringsearch

• ffice

secure hash algorithm sha security image compression / decompression jpeg consumer fast fourier transform fft telecomm Dijkstra’s shortest path algorithm dijkstra network test processor bit manipulation abilities bitcount auto

Description Program Category

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Outline

• Experimental framework
• Exhaustive enumeration of the phase order

space.

• Search space enumeration results
• Optimization phase interaction analysis
• Making conventional compilation faster
• Future work and conclusions

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Naïve Optimization Phase Order Space Exploration

a b c d a b c d a d a d a d b c b c b c

• All combinations of optimization phase

sequences are attempted.

L2 L1 L0

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Eliminating Consecutively Applied Phases

• A phase just applied in our compiler cannot

be immediately active again.

a b c d b c d a d a d a c b b c L2 L1 L0

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Eliminating Dormant Phases

• Get feedback from the compiler indicating

if any transformations were successfully applied in a phase.

L2 L1 L0 a b c d b c d a d a d c b

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Detecting Identical Function Instances

• Some optimization phases are independent
• example: branch chaining & register allocation
• Different phase sequences can produce the

same code

r[2] = 1; r[2] = 1; r[3] = r[4] + r[2]; r[3] = r[4] + r[2]; ⇒ ⇒instruction selection instruction selection r[3] = r[4] + 1; r[3] = r[4] + 1; r[2] = 1; r[2] = 1; r[3] = r[4] + r[2]; r[3] = r[4] + r[2]; ⇒ ⇒constant propagation constant propagation r[2] = 1; r[2] = 1; r[3] = r[4] + 1; r[3] = r[4] + 1; ⇒ ⇒dead assignment elimination dead assignment elimination r[3] = r[4] + 1; r[3] = r[4] + 1;

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Detecting Equivalent Function Instances

sum = 0; for (i = 0; i < 1000; i++ ) sum += a [ i ]; Source Code

r[10]=0; r[12]=HI[a]; r[12]=r[12]+LO[a]; r[1]=r[12]; r[9]=4000+r[12]; L3 r[8]=M[r[1]]; r[10]=r[10]+r[8]; r[1]=r[1]+4; IC=r[1]?r[9]; PC=IC<0,L3;

Register Allocation before Code Motion

r[11]=0; r[10]=HI[a]; r[10]=r[10]+LO[a]; r[1]=r[10]; r[9]=4000+r[10]; L5 r[8]=M[r[1]]; r[11]=r[11]+r[8]; r[1]=r[1]+4; IC=r[1]?r[9]; PC=IC<0,L5;

Code Motion before Register Allocation

r[32]=0; r[33]=HI[a]; r[33]=r[33]+LO[a]; r[34]=r[33]; r[35]=4000+r[33]; L01 r[36]=M[r[34]]; r[32]=r[32]+r[36]; r[34]=r[34]+4; IC=r[34]?r[35]; PC=IC<0,L01;

After Mapping Registers

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Resulting Search Space

• Merging equivalent function instances

transforms the tree to a DAG.

L2 L1 L0 a b c c d a d a d

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Efficient Detection of Unique Function Instances

• Even after pruning there may be tens or

hundreds of thousands of unique instances.

• Use a CRC (cyclic redundancy check)

checksum on the bytes of the RTLs representing the instructions.

• Used a hash table to check if an equivalent

function instance already exists in the DAG.

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Techniques to Make Searches Faster

• Kept a copy of the program representation of the

unoptimized function instance in memory to avoid repeated disk accesses.

• Also kept the program representation after each

active phase in memory to reduce the number of phases applied for each sequence.

• Reduced search time by at least a factor of 5 to 10.
• Out of 111 functions in our benchmark suite we

were able to completely enumerate all instances for 109 functions.

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Outline

• Experimental framework
• Exhaustive enumeration of the phase order

space.

• Search space enumeration results
• Optimization phase interaction analysis
• Making conventional compilation faster
• Future work and conclusions

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Search Space Statistics

182.9 27.5 12 381,857.7 25,362.6 0.9 16.9 166.7 average .... .... .... .... .... .... .... .... .... 1168 18 20 1,361,960 86,370 3 30 354 dijkstra(d) 153 12 17 515,749 33,620 1 40 465 main(j) 159 41 20 772,864 49,412 2 44 472 LZWRea...(j) 540 57 15 511,093 34,270 2 59 480 read_scan...(j) 2964 95 26 5,119,947 343,162 6 33 541 sha_trans...(h) N/A N/A N/A N/A N/A 5 50 624 main(f) N/A N/A N/A N/A N/A 4 45 680 fft_float(f) 52 37 15 106,793 7,018 1 63 795 start_inp...(j) 591 47 18 999,814 64,571 1 82 971 start_inp...(j) 324 18 16 597,147 39,152 1 72 1,009 start_inp...(j) 2365 53 18 2,990,221 200,397 1 198 1,228 parse_swi...(j) 587 153 20 1,153,279 74,950 2 88 1,371 start_inp...(j) Leaves CF Len Phases Instances Loop Blk Insts Function

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Outline

• Experimental framework
• Exhaustive enumeration of the phase order

space.

• Search space enumeration results
• Optimization phase interaction analysis
• Making conventional compilation faster
• Future work and conclusions

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Weighted Function Instance DAG

5 1 1 1 2 2 1 1 1 [abc] [bc] [c] [ab] [d] [a] a b c b a c c b a d

• Each node is weighted by the number of

paths to a leaf node.

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Enabling Interaction Between Phases

• b enables a along the path a-b-a.

5 1 1 1 2 2 1 1 1 [abc] [bc] [c] [ab] [d] [a] a b c b a c c b a d

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Enabling Probabilities

0.03 0.73 u 1.00 0.2 0.53 0.97 0.23 0.16 0.29 1.00 s 0.01 0.05 0.15 0.02 0.45 r 0.08 0.16 q 0.01 0.87

• 0.03

0.05 0.03 0.01 0.01 0.04 0.01 0.22 0.04 0.42 n 0.06 0.03 0.01 0.02 0.06 0.59 l 0.81 0.11 0.01 k 0.13 0.01 0.03 j 0.61 0.01 0.01 0.61 i 0.46 0.03 0.01 0.02 0.7 0.06 h 0.01 0.18 0.01 g d 0.32 0.05 1.00 0.33 0.38 0.72 0.99 0.12 0.14 0.23 0.02 1.00 c 0.06 0.15 0.01 0.62 b u s r q

• n

l k j i h g d c b St Ph

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Disabling Interaction Between Phases

• b disables a along the path b-c-d.

5 1 1 1 2 2 1 1 1 [abc] [bc] [c] [ab] [d] [a] a b c b a c c b a d

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Disabling Probabilities

1.00 0.20 1.00 0.08 u 1.00 0.11 s 1.00 0.53 0.03 0.01 0.05 r 0.12 1.00 q 0.21 1.00 1.00 1.00 1.00 1.00 1.00

• 0.33

0.02 1.00 0.53 0.31 0.07 0.25 0.09 0.49 0.33 n 0.73 1.00 0.30 0.07 0.71 l 1.00 0.01 0.04 k 0.14 0.49 1.00 0.13 j 0.55 0.14 0.14 1.00 0.06 0.08 i 1.00 0.01 h 0.03 0.02 0.19 1.00 0.35 g 1.00 d 0.15 0.02 1.00 c 0.31 0.05 0.08 0.02 0.15 1.00 b u s r q

• n

l k j i h g d c b Ph

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Disabling Probabilities

1.00 0.20 1.00 0.08 u 1.00 0.11 s 1.00 0.53 0.03 0.01 0.05 r 0.12 1.00 q 0.21 1.00 1.00 1.00 1.00 1.00 1.00

• 0.33

0.02 1.00 0.53 0.31 0.07 0.25 0.09 0.49 0.33 n 0.73 1.00 0.30 0.07 0.71 l 1.00 0.01 0.04 k 0.14 0.49 1.00 0.13 j 0.55 0.14 0.14 1.00 0.06 0.08 i 1.00 0.01 h 0.03 0.02 0.19 1.00 0.35 g 1.00 d 0.15 0.02 1.00 c 0.31 0.05 0.08 0.02 0.15 1.00 b u s r q

• n

l k j i h g d c b Ph

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Outline

• Experimental framework
• Exhaustive enumeration of the phase order

space.

• Search space enumeration results
• Optimization phase interaction analysis
• Making conventional compilation faster
• Future work and conclusions

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Faster Conventional Compiler

• We modified the VPO compiler to use enabling and

disabling probabilities to decrease compilation time.

# p[i] - current probability of phase i being active # e[i][j] - probability of phase j enabling phase i # d[i][j] - probability of phase j disabling phase i For each phase i do p[i] = e[i][st]; While (any p[i] > 0) do Select j as the current phase with highest probability of being active Apply phase j If phase j was active then For each phase i, where i != j do p[i] += ((1-p[i]) * e[i][j]) - (p[i] * d[i][j]) p[j] = 0

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Probabilistic Compilation Results

1.005 1.015 0.297 9.6 47.7 8.9 230.3 average .... .... .... .... .... .... .... .... 1.000 1.010 0.409 9 43 9 231 dijkstra(d) 1.000 1.007 0.375 14 57 12 270 main(j) N/A 1.014 0.325 11 45 12 268 LZWReadByte(j) N/A 1.018 0.342 10 43 13 233 read\_scan...(j) 0.953 0.965 0.605 16 67 17 284 sha\_trans...(h) 1.000 1.007 0.550 18 73 20 284 main(f) 0.974 1.012 0.451 25 99 28 463 fft\_float(f) 1.000 1.004 0.436 12 53 11 231 start\_inp...(j) N/A 1.003 0.420 13 49 14 233 start\_inp...(j) N/A 1.010 0.353 14 55 15 270 start\_inp...(j) 0.972 1.016 0.371 12 53 14 233 parse\_swi...(j) N/A 1.014 0.469 14 55 16 233 start\_inp...(j) Speed Size Time Active Attempted Active Attempted

• Prob. / Old
• Prob. Compilation

Old Compilation Function

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Outline

• Experimental framework
• Exhaustive enumeration of the phase order

space.

• Search space enumeration results
• Optimization phase interaction analysis
• Making conventional compilation faster
• Future work and conclusions

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Future Work

• Study methods to find more equivalent performing

function instances to further reduce the

• ptimization phase order space.
• Evaluate approaches to find the dynamically
• ptimal function instance.
• Improve non-exhaustive searches of the phase
• rder space.
• Study additional methods to improve conventional

compilers.

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Conclusions

• First work to show that the optimization phase
• rder space can often be completely enumerated

(at least for the phases in our compiler).

• First analysis of the entire phase order space to

capture various phase probabilities.

• Used phase interaction information to achieve a

much faster compiler that still generates comparable code.

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Optimization Phase Independence

• a-c and c-a are independent.

5 1 1 1 2 2 1 1 1 [abc] [bc] [c] [ab] [d] [a] a b c b a c c b a d

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Optimization Phase Independence

• b-c and c-b are not independent.

5 1 1 1 2 2 1 1 1 [abc] [bc] [c] [ab] [d] [a] a b c b a c c b a d

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Independence Probabilities

0.97 0.98 0.5 0.95 u 0.94 0.89 0.39 0.61 0.45 0.82 0.96 0.96 0.22 s 0.94 0.99 0.97 0.71 0.98 0.99 0.96 r 0.89 0.98 q 0.39 0.58 0.45 0.30 0.59 0.12

• 0.61

0.58 0.78 0.81 0.88 0.98 0.65 0.82 n 0.45 0.45 0.78 0.87 0.96 0.95 0.96 0.44 0.95 l 0.97 0.82 0.99 0.30 0.81 0.87 0.97 0.79 0.45 0.97 k 0.98 0.97 0.98 j 0.5 0.71 0.96 0.97 0.98 0.84 0.94 i 0.96 0.98 0.59 0.88 0.95 0.79 0.98 0.91 h 0.96 0.98 0.96 0.84 0.98 0.96 0.84 g d 0.22 0.99 0.98 0.12 0.65 0.44 0.45 0.91 0.96 c 0.95 0.96 0.82 0.95 0.97 0.94 0.84 b u s r q

• n

l k j i h g d c b Ph

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Independence Probabilities

0.97 0.98 0.5 0.95 u 0.94 0.89 0.39 0.61 0.45 0.82 0.96 0.96 0.22 s 0.94 0.99 0.97 0.71 0.98 0.99 0.96 r 0.89 0.98 q 0.39 0.58 0.45 0.30 0.59 0.12

• 0.61

0.58 0.78 0.81 0.88 0.98 0.65 0.82 n 0.45 0.45 0.78 0.87 0.96 0.95 0.96 0.44 0.95 l 0.97 0.82 0.99 0.30 0.81 0.87 0.97 0.79 0.45 0.97 k 0.98 0.97 0.98 j 0.5 0.71 0.96 0.97 0.98 0.84 0.94 i 0.96 0.98 0.59 0.88 0.95 0.79 0.98 0.91 h 0.96 0.98 0.96 0.84 0.98 0.96 0.84 g d 0.22 0.99 0.98 0.12 0.65 0.44 0.45 0.91 0.96 c 0.95 0.96 0.82 0.95 0.97 0.94 0.84 b u s r q

• n

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VPO Optimization Phases (cont...)

• Register assignment (assigning pseudo registers to

hardware registers) is implicitly performed before the first phase that requires it.

• Some phases are applied after the sequence
• fixing the entry and exit of the function to manage the

run-time stack

• exploiting predication on the ARM
• performing instruction scheduling