Load-Reuse Analysis design and evaluation

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Load-Reuse Analysisdesign and evaluation

• Rastislav Bodík Rajiv Gupta Mary
  Lou Soffa

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Partial Redundancy Elimination (PRE)

• Partially redundant computed on some incoming
  paths

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a..
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(No Transcript)
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Register promotion PRE of loads
store a1, x
load a2
store a3
load a4

• Three steps
• ? load-reuse analysis find loads that can
  reuse prior loads/stores
• ? alias analysis which stores may kill
  reuse?
• ? transformation remove redundancy PRE
  PLDI 98

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Load-reuse analysis

• Design goal
• completeness find all reuse
• To approach completeness, the analysis is
• uniform analyze scalar, array,
  and pointer loads
• path-sensitive different source of
  reuse on each path

• Evaluation goal
• how complete?
• compare with ideal analysis
• Detecting all reuse is undecidable
• no ideal algorithm exists
• instead, use simulation

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Experimental framework
program
input
load-reuse analysis
simulator
1.
2.
data-flow solution
profile
estimator
3.
reuse level
weighted solution
transformation
PLDI 98
comparison
4.
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1. Load-reuse analysis

• Its a data-flow analysis
• on a reuse-aware representation
• Value Name Graph (VNG) POPL98
• Whats new?
• Sparse version of the VNG
• up to 30-times smaller than non-sparse
• Analyzing indirect loads/stores
• also, model killing stores

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Naming the value
y bc
a c-1
x ab1
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bc
ab1
x
names for the value in x
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GEN
1
1
1
x
bc
ab1
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Naming the value across loads
f
offset 0
next
4
p
1
.. p-gtf
.. p-gtnext-gtf
GEN
(p4)
1
r ...
(p4)
1
p p-gtnext
p
1
p
(p4)
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kill if r p4 or r (p4)
KILL ?
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Sparse representation
for I 1, N .. AI AI-1
a1 AI
load a1
a2 AI-1
load a2
I I1
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Ø
Ø
1
1
GEN
load a1
1
1
1
1
load a2
1
1
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2. The simulator algorithm
for I 1, N .. AI AI-1
Ø
memory access history
load a1
AI
103
102
101
100
history length 1 to 4
load a2
AI-1
102
101
100
99
Simulator detects all PRE-exploitable reuse (up
to given history length), but also some noise
e.g. due to hash table accesses
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Ideal amount of load reuse
of all dynamic loads
go m88ksim gcc compress li ijpeg vortex tomcatv sw
im su2cor hydro
history length
1
4
65 of executed loads has reuse exploitable by
PRE intra-procedural reuse, history1
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3. How frequent is the reuse?
load x
Edge profile cheap and available - cannot
reconstruct frequencies of reuse paths
50
100
10
65
35
load x
40
75
5
40
35
30
900
855
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kill x
75
20
55
load x
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• Path profile
• precise
• - more expensive
• ? Use edge profile, but
• bound its inherent error
• compute lower upper bound on reuse

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Hierarchy of estimators
Estimator data-flow solution edge profile ?
weighted data-flow solution
PRE
CMP1
smaller error (but more complex)
CMPc
CMPr
CMPf
Hierarchy a practical approach ? A simple
estimator not precise enough? Use next better
one !
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The algorithms
1. The bounds generators points generating
reuse stealers points with no reuse upper bound
all reuse consumed lower bound all reuse stolen
load x
50
100
10
65
35
load x
75
40
5
40
35
30
900
855
25
kill x
75
20
55
load x
150
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• 2. Separating uncertainty
• using the CMP region
• defined for PRE PLDI 98
• CMP code-motion preventing
• all error is contained in the CMP region!

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Improving precision
one region
connected regions
control flow reachability
network flow reachability
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Estimators precision
PRE
CMP1
CMPc
smaller error
CMPr
CMPf
INT
FP
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4. Analysis how close to ideal ?
100 reuse seen by simulator
p
ideal alias info
p
calls
array pointer stores calls
all stores calls
reuse killed by
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Related Work

• Load-Reuse Analysis
• makes value numbering path-sensitive
• Steffen, Knoop, Rüthing Value Flow Graph ESOP
  90
• we show how analyze indirect loads, via symbolic
  evaluation
• Simulation-based analysis evaluation
• Diwan, McKinley, Moss PLDI98
• Type-based alias analysis how powerful it needs
  to be?
• Estimators
• Ramalingam Frequency Analysis PLDI96
• returns a single estimate, not its bounds

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Summary

• Load-reuse analysis
• reuse across indirect memory references
• sparse representation
• Estimators three principles
• confidence bound the edge-profile error
• separation of uncertainty inside/outside the CMP
  region
• hierarchy increasing precision and complexity
• Evaluation
• about 65 loads are amenable to PRE
• our analysis can find about 80 of those

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Combine three removal methods
PLDI 98
control speculation
S
code motion
restructuring
M
R
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Example


10


50
ab
ab
ab
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Relative removal power
Loads removed, dynamic count, normalized
INT
FP
Global CSE path-insensitive