Register Usage

• Keep as many values in registers as possible• Register assignment• Register allocation• Popular techniques– Local vs. global– Graph coloring– Bin packing

Local Register Assignment

• Given – Control-flow graph of basic blocks– List of 3-addr statements per BB– Set of “live” scalar values per stmt– Sets of scalar values used, defined per stmt

• Design a local register assignment/allocation algorithm

Graph Coloring

• Assign a color to each node in graph• Two nodes connected by an edge must have

different colors• Classic problem in graph theory• NP complete– But good heuristics exist for register allocation

Live Ranges

def y

def xuse y

def xdef y

use xdef x

use x

use xuse y

Graph Coloring Register Assign• Each value is allocated a (symbolic) register• “Variables” interfere iff live ranges overlap• Two interfering values cannot share register• How can we tell if two values interfere?

s1 s2

s3 s4

Interference Graph

• Values and interference– Nodes are the values– Edge between two nodes iff they interfere

s1 s2

s3 s4

Graph Coloring Example

Graph Coloring Example

• 3 Colors

Heuristics for Register Coloring

• Coloring a graph with N colors• For each node, m – If degree(m) < N • Node can always be colored, because• After coloring adjacent nodes, at least one color left for

current node

– If degree(m) >= N• Still may be colorable with N colors

Heuristics for Register Coloring

• Remove nodes that have degree < N– Push the removed nodes onto a stack

• When all the nodes have degree >= N – Find a node to spill (no color for that node)– Remove that node

• When graph empty, start to color– Pop a node from stack back– Color node different from adjacent (colored) nodes

Another Coloring Example

s1 s2

s3 s4

s0

N = 3

Another Coloring Example

s1 s2

s3 s4

s0

N = 3

s4

Another Coloring Example

s1 s2

s3 s4

s0

N = 3

s4

Another Coloring Example

s1 s2

s3 s4

s0

N = 3

s4s3

Another Coloring Example

s1 s2

s3 s4

s0

N = 3

s4s3s2

Another Coloring Example

s1 s2

s3 s4

s0

N = 3

s4s3s2

Another Coloring Example

s1 s2

s3 s4

s0

N = 3

s4s3s2

Another Coloring Example

s1

s3 s4

s0

N = 3

s4s3

s2

Another Coloring Example

s1

s3 s4

s0

N = 3

s4

s2

Another Coloring Example

s1

s3 s4

s0

N = 3

s2

Another Coloring Example

s1

s3 s4

s0

N = 3

s2

Which value to pick?

• One with interference degree >= N• One with minimal spill cost (cost of placing

value in memory rather than in register)• What is spill cost? – Cost of extra load and store instructions

One Way to Compute Spill Cost

• Goal: give priority to values used in loops• So assume loops execute 10 times• Spill cost = defCost + useCost• defCost = sum over all definitions of cost of a

store times 10nestingDepthOfLoop

• useCost = sum over all uses of cost of a load times 10nestingDepthOfLoop

• Choose the value with the lowest spill cost