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Branch Prediction Techniques

15-740

Computer Architecture

Vahe Poladian & Stefan Niculescu

October 14, 2002

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Papers surveyed

A Comparative Analysis of Schemes for Correlated Branch Prediction by Cliff Young, Nicolas Gloy, and Michael D. Smith.

Improving Branch Predictors by Correlating on Data Values by Timothy Heil, Zak Smith, and James E Smith.

A Language for Describing Predictors and its Application to Automatic Synthesis by Joel Emer and Nikolas Gloy.

A Comparative Analysis of Schemes for Correlated

Branch Prediction

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Framework

b5,1 b3,1 b4,0 b5,1

Execution Stream

Divider Substreams Predictors

Branch execution = (b,d), b is PC, d is 0 or 1

All prediction schemes described by this model

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Differences among prediction schemes

Path History vs Pattern History

Path: (b1,d1), … , (bn,dn), pattern: (d1, … , dn)

Aliasing extent

Multiple streams using the same predictor

Extent of cross-procedure correlation

Adaptivity

Static vs dynamic

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Path History vs. Pattern History

Path potentially more accurate

Compared to baseline 2 bit per branch predictor, path only slightly improves over pattern

Path requires significant storage

Result holds both in static and dynamic predictors

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Can be constructive, destructive, harmless

Completely removing aliasing slightly improves accuracy over GAs and Gshare with 4096 2-bit counters Should we spend effort on techniques reducing aliasing?

Unliased path history slightly better vs. unaliased pattern history With aliasing constraint, this distinction might be

insignificant, so designers should be careful

Further, under equal table space constraint, path history might even be worse

Aliasing vs Non-Aliasing

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Often mispredictions of the branches just after procedure entry or just after procedure return

Static predictor with cross-procedure correlation support performs significantly better than one without

Strong bias per stream increased

This result somewhat meaningless, as hardware predictors do not suffer from this problem

Cross-procedure Correlation

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Static vs Dynamic

Number of distinct streams for which static predictor better is higher, but

Number of branches executed in dynamic streams for which dynamic is better, is significantly higher

Is it possible to combine static and dynamic predictors?How?

Assign low bias streams to dynamic

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Summary - lessons learnt

Path history performs slightly better than pattern history

Removing the effects of aliasing decreases misprediction, but increases predictor size

Exploiting cross-procedure correlation improves the prediction accuracy

Percentage of adaptive streams small, but dynamic branches executed are significant

Use hybrid schemes to improve accuracy

Learning Predictors Using

Genetic Programming

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Genetic Algorithms

Optimization technique based on simulating natural selection process

High probability that the global optimum is among the results

Principles:

The stronger individuals survive

The offsprings of stronger parents tend to combine the strengths of the parents

Mutations may appear as result of the evolution process

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An Abstract Example

Distribution of Individuals in Generation 0

Distribution of Individuals in Generation N

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Prediction using GAs

Find Branch Predictors that yield low misprediction rates

Find Indirect Jump predictors with low misprediction rates

Find other good predictors (not addressed in the paper, but potential for a research project)

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Prediction using GAs

Algorithm Find efficient encoding of predictors

Start with a set of random predictors (“generation 0”) - 400

Given generation I (20-30 overall):Rank predictors according to fitness function

Choose best to make generation i+1: Copy

Crossover

Mutation

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Primitive predictor

d

wIndex

Update

Result

Primitive Predictor – P[w,d](Index;Update)

• Basic memory unit

• Depth - number of entries

• Width - number of bits per entry

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Algebraic notation – BP expressions

Onebit[d](PC;T) = P[1;d](PC;T);

Counter[n,d](I;T)=

= P[n,d](I; if T then P+1 else P-1);

Twobit[d](PC;T)=

= MSB(Counter[2,d](PC;T));

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Predictor Tree – an example

MSB

PC

P

SELF 1

SSUB

2

Update

Index

SELF 1

SADD

2

IF

T

Two Bit predictor

Question: how to do crossover and mutation?

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Constraints

Validity of expressions

E.g. of NOT valid BP: in crossover, terminal T may become the index of another predictor

If not valid, try to modify the individual to a valid BP expression (e.g. T=1)

Encapsulation

Size of storage limited to 512Kbits

When bigger, reduce size by randomly decreasing the side of a predictor node by one

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Fitness function

Intuitively, the higher the accuracy, the better a predictor is:

fitness(P) = accuracy(P) To compute fitness:To compute fitness:

Parse expression Parse expression

Create subroutines to simulate predictorCreate subroutines to simulate predictor

Run a simulator over benchmarks (SPECint92, Run a simulator over benchmarks (SPECint92, SPECInt95, IBS compiled for DEC Alpha) to SPECInt95, IBS compiled for DEC Alpha) to compute accuracy of the predictorcompute accuracy of the predictor

Not efficient ... Why? Suggestions?Not efficient ... Why? Suggestions?

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Results – branch prediction

The 6 best predictors kept – 30 generations

Predictor SPEC IBS Predictor SPEC IBS

Onebit[1,512K] 17.7 10.0 GP1 9.7 5.7

Twobit[2,256K] 13.1 6.7 GP2 9.5 5.0

GShare[18] 6.7 2.7 GP3 9.7 5.7

GAg[18] 7.9 4.0 GP4 7.2 3.0

PAg[18,8K] 7.9 4.5 GP5 7.0 2.9

PAp[9,18,8K] 11.2 5.5 GP6 7.1 2.9

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Results – Indirect jumps

Best handcrafted predictors: 47% miss

Best learnt predictor: 15% miss

Very complicated structure

Simple learnt predictor with 33.4% miss

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Summary

A powerful algebraic notation for encoding multiple types of predictors

Genetic Algorithms can be successfully applied to obtain very good predictors

Best learnt branch predictors comparable with GShare

Best learnt indirect jump predictors outperform the already existing ones

In general the best learnt predictors are too complex to implement

However, subexpressions of these predictors might be useful for creating simpler, more accurate predictors.

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References:

Genetic Algorithms: A Tutorial* by Wendy Williams

Automatic Generation of Branch Predictors via Genetic Programming by Ziv Bar-Yossef and Kris Hildrum

* Note: we reused some slides with author’s consent

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Where are we right now?

Improving Branch Predictors by Correlating on Data Values

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The Problem

Despite improvements in prediction techniques, such as

Adding global path info

Refining prediction techniques

Reducing branch table interference

… Branch misprediction still a big problem

Goals of work

Understand why

Remedy the problem

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Mispredicted Branches

Loops that iterate too many times

Last branch almost always mispredicted, since history (global or local) not long enough

Large switch statement close to a branch

Gets the predictors confused

Common in applications such as a compiler

Insight: PC: CondJmpEq Ra, Rb, Target

Use the data value

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Using Data Values Directly

Global History

BranchPredictorBranch PC

Data Value History

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Using Data Values Directly

Challenges:

Large number of data values (typically two values involved)

Out-of-order execution delays the update of values needed

Global History

BranchPredictorBranch PC

Data Value History

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Intricacies – Too Many Values

Store differences of source registers

Store value patterns, not values

Handle only exceptional casesA special predictor, called REP, which is the

primary predictor, if value pattern already in it

If pattern not yet in REP, i.e. a non-exceptional case, let Backup (gselect) handle

If Backup mispredicts, then insert value to REP

REP provides data correlation and reduces interference for Backup

Replacement policy of REP critical

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Intricacies – Guessing values

Value not available when predicting

Using committed data not accurate

Employing data prediction expensive

Idea: use last-known good value + a dynamic counter indicating outstanding instances (fetched but not committed) of that same branch

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Branch Difference Predictor

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Optimal Configuration Design

Design space of BCD very large – how to come up with a good (optimal) one?

Use the results of extensive experiments to determine various configuration parameters

No claim of optimality, but pretty good

Optimal configuration:

REP: indexed by GBH + PC, 6 KB table, 2048 x 3 byte entries. 10 bits for “pattern” tag, 8 for branch prediction, 6 for replacement policy

VHT: 2 separate tables: the data cache, and the branch count table, indexed by PC

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Comparative Results

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The Role of the REP

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Conclusions / Discussion

Adding data value information useful to branch prediction

Rare event predictor useful way to handle large number of data values and reduce interference in the traditional predictor

Can be used with other kinds of predictors

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Stop

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AMY, pattern “11” => (Y,0)

BMY, pattern “11” => (Y,1)

Using pattern history greatly improves accuracy over per-branch static predictor

Using Path history – little improvement over pattern history

Pattern-History vs Path-History

B: If A==2

A: If A==0M: If … Y: If A>0

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Algebraic notation – BP expressions

Onebit[d](PC;T) = P[1;d](PC;T);

Counter[n,d](I;T)=

= P[n,d](I; if T then P+1 else P-1);

Twobit[d](PC;T) =MSB(Counter[2,d](PC;T));

Hist[w,d](I;V) = P[w,d](I;P||V);

Gshare[m](PC;T) =

= Twobit[2m](PC ⊕ Hist[m,1](0;T); T);

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Tree Representation

Three types of nodes:Predictors

Primitive predictor + width + height

Has two descendants:• Left: index expression• Right: update expression

Functions … not an exhaustive list XOR, CAT, MASKHI/MASKLO, IF, SATUR,MSB

Terminals … not an exhaustive list PC, Result of the branch (T), SELF(value P)

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Results – Indirect jumps

Existing jump predictors’ performance:

Description BP Expression Misprediction rate

4 traces, 35M jumps

Use target of previous jump

P[12,1](1;target) 63%

Table of previous jumps, indexed by PC

P[12,4096](PC;target) 47%

Target of previous jumps, indexed by PC

and SP

P[12,4096](PC[9..0]||SP[4..0];target)

54%

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Crossover

Randomly choose a node in each of the Randomly choose a node in each of the parents and interchange the corresponding parents and interchange the corresponding subtreessubtrees

What bad things could happen?What bad things could happen?

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Mutation

Applied to children generated by crossoverApplied to children generated by crossover

Node Mutation:Node Mutation:

Replace functions with functionsReplace functions with functions

Replace terminal with another terminalReplace terminal with another terminal

Modify width/height of predictorModify width/height of predictor

Tree Mutation:Tree Mutation:

Randomly pick a node NRandomly pick a node N

Replace Subtree(N) with random subtree of Replace Subtree(N) with random subtree of same height same height

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Using Data Values

Global HistoryBranch

Predictor

Data Value Predictor

Branch PC

Data Value History

Chooser

Branch Execution

What are some of the problems with this approach?

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Using Data Values: Problems

Uses either branch history or data values, but not both

Latency of prediction too high

The data value predictor requires one or two serial table accesses

Plus execution of the branch instruction

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Experimentation - initial

Use interference-free tables, fully populated REC, for each PC, global history, value, and count combination

Values artificially “aged “ by throwing away n most recent values, thus making branch counts (n+1)

Compare with gselect

Run with 5 of the less predictable apps of SPECint95: compress, gcc, go, jpeg, li.

Vary the amount of difference values stored, from 1 to 3

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Results - initial

BDP outperforms gselect

Best gain when using a single branch difference – adding second and third give little improvement

The older the branch difference, the worse the prediction, but degradation slow

Effect on individual branches – varies, but on average, BDP does better, with very few exceptions