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### PaCoProbability-Based Path Confidence Prediction

Kshitiz Malik, Mayank Agarwal, Vikram Dhar,

Matthew Frank

Implicitly Parallel Architectures Group

University of Illinois at Urbana-Champaign

Summary

- Path Confidence: likelihood of correct path
- Pipeline Gating, SMT Fetch
- Conventional: use count of low-conf branches
- Inaccurate
- PaCo: Directly estimates goodpath probability
- Highly accurate, modest hardware
- Improves performance on gating, SMT Fetch

HPCA-14

February 18, 2008

Branch Confidence Prediction

- Branch Confidence: Single Branches
- Low Conf / High Conf
- Applications: Checkpointing, Multipath etc

HPCA-14

February 18, 2008

Path Confidence Prediction

- Path Confidence: likelihood of being on correct path
- Contributions from Multiple Branches
- Conventionally: Count of (unexecuted) low-confidence branches.

HPCA-14

February 18, 2008

Path Confidence: Applications

- Path Confidence: Multiple Branches
- Count of low-confidence branches.
- Applications: Pipeline Gating, SMT Prioritization

Gate-Count = 5

(Fetch gated when conf >= 5)

Gated

HPCA-14

February 18, 2008

Path Confidence: Applications

- Path Confidence: Multiple Branches
- Count of low-confidence branches.
- Applications: Pipeline Gating, SMT Prioritization

HPCA-14

February 18, 2008

Issues with Conventional Approach

- Path Confidence: Multiple Branches
- Count of low-confidence branches.
- Applications: Pipeline Gating, SMT Prioritization
- Problem: implicit assumption that
- High-conf branches never mispredict
- All low-conf branches have same misprediction probability

HPCA-14

February 18, 2008

Path Confidence using PaCo

- Directly estimates goodpath probability
- Highly Accurate: RMS error 3.8%
- Modest Hardware: 60 bytes of counters
- Excellent Performance in applications
- Gating: BadpathInstrs. Performance Conv↓ 7%↓ 0.1%

PaCo ↓ 32%↓ 0.01%

- SMT Fetch Prioritization: ↑ perfupto 23% (5.5% av.)

HPCA-14

February 18, 2008

Branch Confidence Prediction

- Classify branches as low conf. or high conf.
- JRS predictor:
- Count consecutive correct predictions
- Below threshold: Low Confidence
- Table of Miss-Distance Counters (MDCs)

MDC Value

<

Threshold?

+

MDC Table

MDC

Value

5

Mispredict?

1

Branch

PC

0

+

On Branch Execution

Global

Hist

HPCA-14

February 18, 2008

4 bits

Conventional Path Confidence Prediction

- Count of low-confidence branches = measure of path confidence
- Threshold-and-Count Approach
- Inaccurate
- Coarseness
- No relation to goodpath probability

MDC

Table

Threshold Function

Sum

Low Conf / High Conf

(1 bit)

Miss Distance Counter Value

(4 bits)

Path Confidence

Branch

HPCA-14

February 18, 2008

Low Conf / High Conf

(1 bit)

CoarsenessMiss Distance Counter Value

(4 bits)

a

JRS Threshold = 3

- All low-conf branches are equal
- Eg: SMT prior.
- gcc:
- a pending
- 0.57 gpathprob
- vortex:
- 2 bpend.
- Prob = 0.88*0.88 = .78
- yet, fetch from gcc!

b

High Conf

Low Conf

HPCA-14

February 18, 2008

Low Conf / High Conf

(1 bit)

CoarsenessMiss Distance Counter Value

(4 bits)

- All low-conf branches are equal
- High-conf branches don’t mispredict
- twolf, vortex, mdc=3
- Don’t affect conf.

HPCA-14

February 18, 2008

Sum ≠ Probability

Sum

Low Conf / High Conf

(1 bit)

Path Confidence

- Gating at count=5
- Too aggressive for gzip, not useful for route
- SMT Fetch:
- gzip and route, conf = 5. Equal bandwith?

Goodpath Likelihood when 5 low-confidence branches are pending

HPCA-14

February 18, 2008

Sum ≠ Probability

Goodpath Likelihood when 5 low-confidence branches are pending

HPCA-14

February 18, 2008

Sum ≠ Probability

Sum

Low Conf / High Conf

(1 bit)

Path Confidence

- Hard to choose optimal gate-count
- Different gate-counts for different benchmarks
- Different gate-counts for different phases
- Hard to compare path confidence of diff. apps
- SMT Fetch Prioritization sub-optimal

HPCA-14

February 18, 2008

Design

- Calculate Goodpath Probability directly

- Finding ‘correct prediction probability’ for a branch
- MDC table good differentiator of misprediction rates
- Find misprediction rate for each MDC value
- No thresholding!
- Other, more h/w intensive approaches possible

HPCA-14

February 18, 2008

Threshold-and-count vs. PaCo

MDC

Table

Threshold Function

Sum

Low Conf / High Conf

(1 bit)

Miss Distance Counter Value

(4 bits)

Path Confidence

Branch

Mispredict Rate

Calculator

(MRT)

Product

Mispredict

Probability

Path Confidence

Mispred Rate Table

0

PaCo

1

2

.

.

.

Misprediction

Rate

13

14

15

HPCA-Practice Talk

February 13, 2008

MDC Value

Hardware Complexity

- Remove floating point: scale to integer values

- Hardware Complexity
- Floating point MUL and DIV required
- Use logarithms, remove mul/div

HPCA-14

February 18, 2008

PaCo Hardware

5

Branch

PC

Feedback from Backend

60 bytes of counters, 10-bit shift register

Global

Hist

Mispredict Rate Calculator

Path Confidence Predictor

Encoded

Probability

Correct Preds

MDC 0

Mispreds

MDC 0

MDC 1

Correct Preds

MDC 1

Log

Circuit

Mispreds

.

.

.

.

.

.

.

.

.

.

.

Path Confidence

6 bits

+

+

10 bits

Correct Preds

MDC 15

MDC 15

Mispreds

12 bits

Evaluation: Prediction Accuracy

- RMS Error = 0.038.
- Example:
- Predicted 60% goodpath likelihood
- Should be within (60 ± 3.8) = 56.2% - 63.8%

HPCA-14

February 18, 2008

Accuracy: Reliability Diagram

RMS Error

Applications: Pipeline Gating

0.1% perf loss

32% redn. in badpath instructions

HPCA-14

February 18, 2008

Conclusions

- Threshold-and-Count predictors are inaccurate
- PaCo: Directly produces goodpath probability
- Uses modest h/w by using logarithms
- Highly accurate: low RMS error (3.8%)
- PaCo does very well in Pipeline Gating and SMT Fetch Prioritization

HPCA-14

February 18, 2008

Backup1: Comparison with WPUP

- WPUP: Perfect Fetch gating improves average performance by 2.3% (excl. mcf and parser)
- Badpath Instructions
- Good: prefetching (useful: small ROBs, wide machines)
- Bad: BTB/Cache pollution (prob: smaller BTBs/caches)
- Prefetching much less useful with 512 ROB

Table

Threshold Function

Sum

Low Conf / High Conf

(1 bit)

Miss Distance Counter Value

(4 bits)

Path Confidence

Branch

HPCA-Practice Talk

February 13, 2008

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