Basic Blocks Mooly Sagiv Schrierber 317 03-640-7606 Wed 10:00-12:00 html://msagiv/courses/wcc01.html...

Basic BlocksMooly Sagiv

Schrierber 31703-640-7606

Wed 10:00-12:00

html://www.math.tau.ac.il/~msagiv/courses/wcc01.html

Chapter 8

Already StudiedSource program (string)

lexical analysis

syntax analysis

semantic analysis

Translate

Tokens

Abstract syntax tree

Tree IR

Abstract syntax tree

Mismatches between IR and Machine Languages

• CJUMP jumps into two labels– But typical machine instructions use one target

BEQ Ri, Rj, L

• Optimizing IR programs is difficult due to side effects in expressions– ESEQ nodes– Call nodes

• Call nodes within expressions prevent passing arguments in registers

Mismatches between IR and Machine Languages

• Call nodes within expressions prevent passing arguments and results in registers

binop

plus call call

Namef1

exp1

Namef2

exp2

Why can’t we be smarter?

• Avoid two-way jumps

• Do not use ESEQ expressions

Three Phase Solution• Rewrite the tree into a list of canonical trees

without SEQ or ESEQ nodes

• Group the list into basic blocks

• Order basic blocks into a set of traces – CJUMP is immediately followed by false label

nfact example

function nfactor (n: int): int=

if n = 0

then 1

else n * nfactor(n-1)

MOVE

TEMP t103

ESEQ

CJUMP

EQ TEMP t128 CONST 0

ESEQ

LABEL l0 ESEQ

MOVE

TEMP t129 CONST 1

l1l0ESEQ

JUMP

NAME l2

ESEQ

LABEL l1 ESEQ

MOVE

TEMP t129 BINOP

TIMES TEMP t128 CALL

nfactor BINOP

MINUS TEMP t128 CONST 1

ESEQ

LABEL l2

TEMP t129

Missing updates for static link

SEQ

CJUMP

EQ

TEMP t128

CONST 0

LABEL l0

SEQ

MOVE

TEMP t129CONST 1

l1l0

SEQ

JUMP

NAME l2

SEQ

LABEL l1

SEQ

SEQ

TEMP t129BINOP

TIMES

TEMP t131

CALL

nfactor

BINOP


MOVE

TEMP t103

TEMP t129

SEQ

LABEL l2

SEQ

TEMP t130

MOVE

TEMP t130

MOVE

TEMP t128

TEMP t131

SEQ

MOVE

LABEL(l3)

CJUMP(EQ, TEMP t128, CONST 0, l0, l1)

LABEL( l0)

MOVE(TEMP t129, CONST 1)

JUMP(NAME l2)

LABEL( l1)

MOVE(TEMP t131, TEMP t128)

MOVE(TEMP t130, CALL(nfactor, BINOP(MINUS, TEMP t128, CONST 1)))

MOVE(TEMP t129, BINOP(TIMES, TEMP t131, TEMP t30))

JUMP(NEME l2)

LABEL( l2)


JUMP(NAME lend)

LABEL(l3)


LABEL( l0)


JUMP(NAME l2)

LABEL( l1)




/* JUMP(NAME l2) */

LABEL( l2)


JUMP(NAME lend)

Outline• The Cannon Interface

• Phase 1: Removal of ESEQ nodes

• Phase 2: Basic Blocks

• Phase 3: Order traces– CJUMP is followed by a false label

/* canon.h */

typedef struct C_stmListList *C_stmListList;

struct C_block {C_stmListList stmLists; Temp_label label;}

struct C_stmListList_ { T_stmList head; C_stmListList tail;}

T_stmList C_linearize(T_stm stm); /* Eliminate ESEQs */

struct C_block C_basicBlocks(T_stmList stmList);

T_stmList C_traceSchedule(struct C_block b);

/* main.c */

static void doProc(FILE *out, F_frame frame, T_stm body)

{ T_stmList stmList;

AS_instrList iList;

stmList = C_linearize(body); /* Removes ESEQs */

stmList = C_traceSchedule(C_basicBlocks(stmList));

iList = F_codegen(frame, stmList); /* 9 */

}

Canonical Trees (Phase 1)• Rewrite the tree

– No SEQ and ESEQ– The parent of each CALL is either EXP or

MOVE(TEMP t, …)

• Apply “meaning preserving” rewriting rules

• Sometimes generates temporaries

ESEQs1 ESEQ

s2 e

ESEQSEQ

s1

e

s2

BINOP

op e2

s e1

ESEQ

ESEQs BINOP

e2op e1

MEM

s e

ESEQ

ESEQ

s

e

MEM

JUMP

s e

ESEQ

SEQ

s

e

JUMP

CJUMP

s e1

ESEQop e2 l1 l1

BINOP

op ESEQ

s e2

e1

ESEQs BINOP

e2op e1

When s and e1 commutes

Which statements commute?• In general very difficult

• Example

• The compiler decides conservatively

MEM

e1

MOVE

MEM

e2

e3

Which statements commute?static bool commute(T_stm x, T_exp y)

{

if (isNop(x)) return TRUE;

if (y->kind == T_NAME || y->kind == T_CONST) return TRUE;

return FALSE;

}

BINOP

op ESEQ

s e2

e1

ESEQ

MOVE

BINOP

e2op TEMP t

When s and e1 may not commute

sTEMP t e1

ESEQ

CJUMP

s e2

e1op ESEQ l1 l1

When s and e1 may not commute

CJUMPs

TEMP top e2 l1 l1

SEQ

MOVE

TEMP t e1

SEQ

MOVE

TEMP t103

ESEQ

CJUMP

EQ TEMP t128 CONST 0

ESEQ

LABEL l0 ESEQ

MOVE

TEMP t129 CONST 1

l1l0ESEQ

JUMP

NAME l2

ESEQ

LABEL l1 ESEQ

MOVE

TEMP t129 BINOP


nfactor BINOP


ESEQ

LABEL l2

TEMP t129

SEQ

CJUMP

EQ TEMP t128

CONST 0

ESEQ

LABEL l0 ESEQ

MOVE

TEMP t129 CONST 1

l1l0ESEQ

JUMP

NAME l2

ESEQ

LABEL l1 ESEQ

MOVE

TEMP t129 BINOP


nfactor BINOP


ESEQ

LABEL l2

TEMP t129

TEMP t103

MOVE

SEQ

CJUMP

EQ TEMP t128

CONST 0

LABEL l0ESEQ

MOVE

TEMP t129 CONST 1

l1l0ESEQ

JUMP

NAME l2

ESEQ

LABEL l1 ESEQ

MOVE

TEMP t129 BINOP


nfactor BINOP


ESEQ

LABEL l2

TEMP t129

TEMP t103

MOVESEQ

SEQ

CJUMP

EQ

TEMP t128

CONST 0

LABEL l0

SEQ

MOVE

TEMP t129CONST 1

l1l0 ESEQ

JUMP

NAME l2

ESEQ

LABEL l1 ESEQ

MOVE

TEMP t129 BINOP


nfactor BINOP


ESEQ

LABEL l2

TEMP t129

SEQ

TEMP t103

MOVE

SEQ

CJUMP

EQ

TEMP t128

CONST 0

LABEL l0

SEQ

MOVE

TEMP t129CONST 1

l1l0

SEQ

JUMP

NAME l2

ESEQ

LABEL l1 ESEQ

MOVE

TEMP t129 BINOP


nfactor BINOP


ESEQ

LABEL l2

TEMP t129

SEQ

TEMP t103

MOVE

SEQ

CJUMP

EQ

TEMP t128

CONST 0

LABEL l0

SEQ

MOVE

TEMP t129CONST 1

l1l0

SEQ

JUMP

NAME l2

SEQ

LABEL l1

ESEQ

MOVE

TEMP t129 BINOP


nfactor BINOP


ESEQ

LABEL l2

TEMP t129

SEQ

TEMP t103

MOVE

SEQ

CJUMP

EQ

TEMP t128

CONST 0

LABEL l0

SEQ

MOVE

TEMP t129CONST 1

l1l0

SEQ

JUMP

NAME l2

SEQ

LABEL l1

SEQ

MOVE

TEMP t129 BINOP


nfactor BINOP


ESEQ

LABEL l2

TEMP t129

SEQ

TEMP t103

MOVE

SEQ

CJUMP

EQ

TEMP t128

CONST 0

LABEL l0

SEQ

MOVE

TEMP t129CONST 1

l1l0

SEQ

JUMP

NAME l2

SEQ

LABEL l1

SEQ

MOVETEMP t129

BINOP

TIMES TEMP t128

CALL

nfactor

BINOP


ESEQ

LABEL l2

TEMP t129

SEQ

TEMP t103

MOVE

ESEQ

TEMP t130MOVE

TEMP t130

SEQ

CJUMP

EQ

TEMP t128

CONST 0

LABEL l0

SEQ

MOVE

TEMP t129CONST 1

l1l0

SEQ

JUMP

NAME l2

SEQ

LABEL l1

SEQ

MOVETEMP t129

BINOP

TIMES

TEMP t131

CALL

nfactor

BINOP


ESEQ

LABEL l2

TEMP t129

SEQ

TEMP t103

MOVE

TEMP t130

MOVE

TEMP t130

ESEQMOVE

TEMP t128

TEMP t131

ESEQ

SEQ

CJUMP

EQ

TEMP t128

CONST 0

LABEL l0

SEQ

MOVE

TEMP t129CONST 1

l1l0

SEQ

JUMP

NAME l2

SEQ

LABEL l1

SEQ

SEQ

TEMP t129

BINOP

TIMES

TEMP t131

CALL

nfactor

BINOP


ESEQ

LABEL l2

TEMP t129

SEQ

TEMP t103

MOVE

TEMP t130

MOVE

TEMP t130

MOVE

TEMP t128

TEMP t131

ESEQ

MOVE

SEQ

CJUMP

EQ

TEMP t128

CONST 0

LABEL l0

SEQ

MOVE

TEMP t129CONST 1

l1l0

SEQ

JUMP

NAME l2

SEQ

LABEL l1

SEQ

SEQ

TEMP t129BINOP

TIMES

TEMP t131

CALL

nfactor

BINOP


ESEQ

LABEL l2

TEMP t129

SEQ

TEMP t103

MOVE

TEMP t130

MOVE

TEMP t130

MOVE

TEMP t128

TEMP t131

SEQ

MOVE

SEQ

CJUMP

EQ

TEMP t128

CONST 0

LABEL l0

SEQ

MOVE

TEMP t129CONST 1

l1l0

SEQ

JUMP

NAME l2

SEQ

LABEL l1

SEQ

SEQ

TEMP t129BINOP

TIMES

TEMP t131

CALL

nfactor

BINOP


MOVE

TEMP t103

TEMP t129

SEQ

LABEL l2

SEQ

TEMP t130

MOVE

TEMP t130

MOVE

TEMP t128

TEMP t131

SEQ

MOVE

A Theoretical Solution• Apply rewriting rules until convergence

• The result need not be unique

• Efficiency and termination of the compiler

A Practical Solution• Apply rewriting rules in “one” pass

• Two mutually recursive routines– do_stm(s) applies rewritings to s– do_exp(e) applies rewritings to e

• reorder(expRefList) – Returns the side effect statements in expRefList

– Replaces expressions by temporaries

• Code distributed in “cannon.c”

Taming Conditional Brunch• Reorder statements so that CJUMP is

followed by a false label

• Two subphases:– Partition the statement list into basic blocks

(straightline programs starting with a label and ending with a branch)

– Reorder basic blocks (Traces)

Phase 2: Basic Blocks• The compiler does not know which branch

will be taken

• Conservatively analyze the control flow of the program

• A basic block– The first statement is a LABEL– The last statement is JUMP or CJUMP– There are no other LABELs, JUMPs, or

CJUMPs

An Algorithm for Basic BlocksC_basicBlocks()

• Applied for each function body• Scan the statement list from left to right• Whenever a LABEL is found

– a new block begins (and the previous block ends)

• Whenever JUMP or CJUMP are found – the current block ends (and the next block begins)

• When a block ends without JUMP or CJUMP– JUMP to the following LABEL

• When a block does not start with a LABEL– Add a LABEL

• At the end of the function body jump to the beginning of the epilogue

LABEL(l3)


LABEL( l0)


JUMP(NAME l2)

LABEL( l1)




LABEL( l2)


JUMP(NAME l2)

JUMP(NAME lend)

Traces

• Reorder basic blocks– Every CJUMP is followed by a false label

– Many of the unconditional jumps are followed by the corresponding labels

• can be eliminated

• A trace – a sequence of basic blocks that are executed sequentially

• A program has many overlapping traces• Find a set of traces that exactly covers the program

– every block appears in exactly one trace

• Minimize the number of traces

An Algorithm for Generating Traces C_traceSchedule()

Put all the blocks of the program into a list Q

while Q is not empty do

Start a new (empty) trace, call it T

Remove the head element b of Q

while b is not marked do

mark b

append b to the end of the current trace T

if there is an unmarked successor c of b

b := c

end of current trace T

LABEL(l3)


LABEL( l0)


JUMP(NAME l2)

LABEL( l1)




JUMP(NAME l2)

LABEL( l2)


JUMP(NAME lend)

T1

T2

Finishing-Up• CJUMP followed by a false label is left alone• JUMP (NAME l) that is followed by a label l is

removed• CJUMP followed by a true label

– replace true and false labels and negate the condition

• If CJUMP(cond, a, b, lt, lf) is not followed by lt or lf

– Replace by: CJUMP(cond, a, b, lt, l'f)LABEL(l'f)JUMP(NAME lf)

• At the end of the process flat basic blocks (trade simplicity for efficiency of the compiler and of the generated code)

LABEL(l3)


LABEL( l0)


JUMP(NAME l2)

LABEL( l1)




JUMP(NAME l2)

LABEL( l2)


JUMP(NAME lend)

T1

T2

LABEL(l3)


LABEL( l0)


JUMP(NAME l2)

LABEL( l1)




JUMP(NAME l2)

LABEL( l2)


JUMP(NAME lend)

LABEL(l3)


LABEL( l0)


JUMP(NAME l2)

LABEL( l1)




/* JUMP(NAME l2) */

LABEL( l2)


JUMP(NAME lend)

Optimal-Traces• Optimizing compilers locate traces for

frequently executed instructions• Minimize the (dynamic) number of jumps

– Improve instruction cache performance

• Improves register allocation • Optimize loops• Sometimes use

– Static heuristics– Profiling information– Dynamic compilation

prologue statements

JUMP (NAME test)

LABEL (test)

CJ(>, i, N, done, body)

LABEL(body)

loop-body statements

JUMP(NAME(test))

LABEL(done)

epilogue statements

prologue statements

JUMP (NAME test)

LABEL (test)

CJ(<=, i, N, body, done)

LABEL(done)

epilogue statements

LABEL(body)


JUMP(NAME test)

prologue statements

JUMP (NAME test)

LABEL (body)


JUMP(NAME TEST)

LABEL(TEST)

CJ(<=, i, N, body, done)

LABEL(done)

epilogue statements

Summary

• Tree like IR saves temporary variables

• But ESEQ nodes may require some temporaries– Late decision

• Rewriting rules is a powerful mechanism

• Estimating “commuting” statements is a challenge

• Traces may effect the performance of the generated code

Basic Blocks Mooly Sagiv Schrierber 317 03-640-7606 Wed 10:00-12:00 html://msagiv/courses/wcc01.html...

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