java coins.driver.Driver -coins:hirOpt=hiroptspec/hiroptspec/...where each of the hiroptspec specifies some optimizing option such as cf for constant folding, cpf for constant propagation, cse for local common subexpression elimination, etc.
ex. java coins.Driver -S -coins:hirOpt=cf/cpfThe order of the optimizations is approximately the same to the order of the optimization specifications by the command line, but in some cases, some optimization may be inserted to make ready to apply another specified optimization, or neglected when the effect of the optimization is covered by another optimization specified. For example, by the command
java coins.Driver -S -coins:hirOpt=cf/cpfconstant folding is done at first and then constant propagation and folding.
java coins.Driver -S -coins:hirOpt=precommon subexpression elimination within basic blocks is automatically inserted. As another example, by a command
java coins.Driver -S -coins:hirOpt=pre/csecse is neglected because pre will cover the effect of cse.
java coins.driver.Driver -coins:hirOpt=fromcIt is not treated by coins.opt.Opt but treated by C-front
java coins.driver.Driver -coins:hirOpt=globalReformIt can cover wide variety of transformations according to the patterns given as a part of the input program.
noSimplify // do no simplification cf // constant folding cpf // constant propagation and folding triggered by the propagation cse // common subexpression elimination within basic blocks dce // dead code elimination fromc // simple optimizations done by C parser gt // global variable temporalization within basic blocksThe optimizers cf and gt do not require data flow analysis, however, cpf, cse, dce require some result of data flow analysis. noSimplify specifies not to do HIR simplification. When this option is not specified, unused labels are removed immediately before transforming HIR to LIR. It removes such labels as else-label generated for if-statement without else part.
java cooins.driver.Driver -S -coins:hirOpt=cf/cpf
int main () { int a, b, c, d, x; a = 1; b = 2; c = a + b; d = a + b; if (a+1 < c-1) x = a - b; else x = a + b; printf("%d\n",x); }is compiled by
java coins.driver.Driver -S -coins:hirOpt=cf/cpf/dce,hir2c=optthen following C program will be generated by converting resulting HIR to C by hir2c.
int main( ) { int a; int b; int c; int d; int x; a = (int )1; b = (int )2; if (((int )2) < ((int )2)) { x = ((a) - (b)); } else { x = ((a) + (b)); } (&(printf))( (const char * )((("%d\n"))),x); }The statement
d = a + b;is eliminated as a dead code and condition expression is changed to an expression that can be evaluated as false at compile time. In the backend part of COINS, code sequence for only else-part is generated for such if-statement as follows:
.global main main: save %sp,-96,%sp .L18: mov 1,%i1 mov 2,%i0 .L20: add %i1,%i0,%o1 .L21: sethi %hi(string.17),%o0 or %o0,%lo(string.17),%o0 call printf nop .L22: ret restore
java -coins:regpromoteis specified, it is not required to specify hirOpt=gt because register promotion for global variables is done in the COINS backend. In many cases, regpromote option will produce more efficient code than hirOpt=gt option.
ex. new ConstFolding(lResults).doSubp(lSubpFlow);The method will return a boolean value indicating whether the program has been changed (optimized) as a result of the call to this optimizer method. For more examples, see the basic optimizer driver class coins.opt.Opt.
java coins.driver.Driver -S -coins:hirOpt=loopexp java coins.driver.Driver -S -coins:hirOpt=loopif java coins.driver.Driver -S -coins:hirOpt=inline java coins.driver.Driver -S -coins:hirOpt=preThe option inlinedepth controls inline expansion as it is mentioned later. The option globalReform is explained in section 5.7.
4 if number of registers N <= 16 8 if N > 16as default, but it can be changed by specifying expansion number as a sub-option in such a way as
hirOpt=loopexp.6Following loops are not expanded:
(1) Outer loop (not an inner-most loop) (2) Loop including subprogram call (3) Loop including volatile variable (4) Non-simple for-loop, that is, a loop having some of following characteristics not a for-loop start condition is null start condition is not a simple arithmetic comparison expression for loop control variable loop control variable is changed in the loop body (not in loop step part) complexity level of the loop body is large, that is, if (((R <= 8)&&(E * N > 200))|| ((R <= 32)&&(E * N > 300))|| ((R > 32)&&(E * N > 600))) is true, where, R: number of general registers of the target machine. E: expansion number N: the number of executable operators and assign-operatorsStatements in the loop body may be changed if reordering does not affect execution results. For example, following loop
for (i = 0; i < 100; i++) { sum1 = sum1 + i; sum2 = sum2 + a[i]; }will be expanded as follows:
_var5 = 1*7; _var7 = 1*8; for (i = 0; i < 100 - _var5; i = i + _var7) { sum1 = sum1 + i + i + 1 + i + 2 + i + 3 + i + 4 + i + 5 + i + 6 + i + 7; sum2 = sum2 + a[i] + a[i+1] + a[i+2] + a[i+3] + a[i+4] + a[i+5] + a[i+6] + a[i+7]; } for (; i < 100; i = i + 1) { sum1 = sum1 + i; sum2 = sum2 + a[i]; }
for (i = 0; i < pn; i++) { lSum = lSum + pa[i]; if (pMode > 0) lSum = lSum + i; else lSum = lSum + i * i; }will be transformed as follows:
if (pMode > 0) { for (i = 0; i < pn; i++) { lSum = lSum + pa[i]; lSum = lSum + i; } }else { for (i = 0; i < pn; i++) { lSum = lSum + pa[i]; lSum = lSum + i * i; } }If hirOpt=loopif/loopexp is specified, then the resultant loops in then-part and else-part will be expanded by the loop expansion optimizer.
(1) Complexity of subprogram body is large Subprograms having more than 100 HIR nodes are not expanded. This complexity threshold can be changed by sub-option; for example, hirOpt=inline.200 will expand subprograms up to 200 HIR nodes. (2) Call is included in conditional expression of if-statement, loop-statement, or included in case-selection expression of switch-statement. (3) Subprogram whose definition is not given in the same compile unit.Subprograms called before giving its definition can be expanded. Recursive subprograms are also expanded up to 2 times. For example,
int fact(int p) { if (p > 0) return p * fact(p - 1); else return 1; }will be expanded as follows:
int fact( int p ) { int _var1, _var3, _var5, _var7, _var9, _var11; if (p > 0) { _var1 = p - 1; if (_var1 > 0) { _var5 = _var1 - 1; if (_var5 > 0) { _var7 = _var5 - 1; if (_var7 > 0) { _var9 = _var7 * fact(_var7 - 1); goto _lab19; }else { _var9 = 1; goto _lab19; } _lab19:; _var11 = _var5 * _var9; goto _lab22; }else { _var11 = 1; goto _lab22; } _lab22:; _var3 = _var1 * _var11; goto _lab12; }else { _var3 = 1; goto _lab12; } _lab12:; return p * _var3; } else { return 1; } }The option inlinedepth changes this limitation. The option
locally available: EGen (downward exposed) After computation, operands are not changed. available: AvailIn locally anticipable: AntLoc (upward exposed) Operands are not set in preceding operations (before use) in a basic block. safe: Either anticipable or available. e-path([b_i ... b_k]) = set of eliminatable computation e included in b_k, i.e. {e | e is locally available in b_i and locally anticipable in b_k } & empty((b_i ... b_k)) & // not computed in intermediate point e is safe at exit of each node on the path [b_i ... b_k),where, b_i, ..., b_k are basic block i, ..., basic block k, respectively. e-path suffix is the maximal suffix of an E-path such that
AntIn * (not AvIn) = true for each node in it.Data flow properties are as follows:
Comp_i : e is locally available in b_i Antloc_i : e is locally anticipable in b_i Transp_i : b_i does not contain definitions of e's operands AvIn_i : e is available at entry of b_i AvOut_i : e is available at exit of b_i AntIn_i : e is anticipable at entry of b_i AntOut_i : e is anticipable at exit of b_i EpsIn_i : entry of b_i is in an e-path suffix EpsOut_i : exit of b_i is in an e-path suffix Redund_i : Occurrence of e in b_i is redundant Insert_i : Insert t_e := e in node b_i Insert_i_j : Insert t_e := e along edge (b_i, b_j) SaIn_i : A Save must be inserted above the entry of b_i SaOut_i : A Save must be inserted above the exit of b_i Save_i : e should be saved in t_e in node b_iwhere, t_e is a temporal variable to hold the value of e.
AvIn_i = PAI_p (AvOut_p) AvOut_i = AvIn_i * Transp_i + Comp_i AntIn_i = AntOut_i * Transp_i + Antloc_i AntOut_i = PAI_s (AntIn_s) EpsIn_i = SIGMA_p (AvOut_p + EpsOut_p) * AntIn_i * (not AvIn_i) EpsOut_i = EpsIn_i * (not Antloc_i) Redund_i = (EpxIn_i + AvIn_i) * Antloc_i Insert_i = (not AvOut_i) * (not EpsOut_i) * PAI_s(EpsIn_s) Insert_i_j = (not AvOut_i) * (not EpsOut_i) * (not Insert_i) * EpsIn_j SaOut_i = SIGMA_s (EpsIn_s + Redund_s + SaIn_s) * AvOut_i SaIn_i = SaOut_i * (not Comp_i) Save_i = SaOut_i * Comp_i * (not Redund_i * Transp_i)where, _s means successor and _p means predecessor.
Save the value of e: computation t_e is inserted before an occurrence of e and the occurrence of e are replaced by t_e (as indicated by Save_i). Insert an evaluation of e: A computation t_e <- e is inserted (as indicated by Insert_i and Insert_i_j). Eliminate a redundant evaluation of e: An occurrence of e is replaced by t_e (as indicated by Redund_i).Before doing partial redundancy elimination, critical edges[3] in control flow graphs are removed by preparatory transformation phase (NormalizeHir). A critical edge is an edge that goes from a basic block having multiple successors to a basic block having multiple predecessors. For example,
switch (i) { case 0: s = 0; case 1: s = s + i; .... }will be changed by the preparatory transformation phase to
switch (i) { case 0: s = 0; goto _lab11; case 1: { _lab11:; s = s + i; } ...... }
java coins.driver.Driver -S -coins:hirOpt=fromc xxx.cMost optimizations done by fromc specification are covered by other HIR and LIR optimizations. The effect of the optimization in C front is to make slim the HIR representation of source program so that succeeding processing will be simplified.
coins.flow: Flow analysis used currently in all HIR optimizations such as loopif/loopexp/inline/cf/cpf/cse/gt/pre. coins.aflow: Old version flow analysis which is used currently in loop parallelizer, coarse grain parallelizing module (-coins:mdf).In building new modules, it is recommended to use coins.flow version because coins.aflow version may take long compile time and huge storage space for large subprograms.
flowRoot: instance of FlowRoot (usually passed from Driver). subpDefinition: instance for SubpDefinition representing the HIR subtree of a subprogram. subpFlow: instance of SubpFlow to represent control/data flow information of specified subprogram.The instance of HirSubpFlowImpl is required to be made only once for each subprogram. All control flow information and data flow information are linked from this instance and if you renew the instance, then all flow information previously computed will be reset.
coins.flow.SubpFlow lSubpFlow = new HirSubpFlowImpl(flowRoot, subpDefinition);and after executing it, the instance can be referred by
flowRoot.fSubpFlowTo do control flow analysis, it is necessary to prepare for it by
flowRoot.flow.controlFlowAnal(lSubpFlow);After executing this statement, methods related to basic blocks such as
cfgIterator(), getEntryBBlock(), getBBlockOfIR(ir.getIndex()), bblockSubtreeIterator(bblock), ...are made available. There are many other methods for control/data flow analysis as they are shown in the interface coins.flow.SubpFlow. After executing controlFlowAnal(lSubpFlow), methods of coins.flow.BBlock interface such as
getPredList(), getSuccList(), getImmediateDominator(), getPostDominatedChildren(), ...are made available. To see the result of control flow analysis, the coding sequence
coins.flow.ShowControlFlow lShow = flowRoot.controlFlow.getShowControlFlow(); lShow.showAll();will print the result of control flow analysis.
flowRoot.flow.controlFlowAnal(lSubpFlow);resets previous control flow analysis information and begins to re-compute. If there is no change in HIR subtree of SubpDefinition instance, then it is not necessary to re-compute it. It is recommended to avoid it by following coding sequence:
if (flowRoot.flow.getFlowAnalStateLevel() < coins.flow.Flow.STATE_CFG_AVAILABLE) flowRoot.flow.controlFlowAnal(lSubpFlow);The method finishHir() and setIndexNumbetToAllNodes() of HIR0 interface will make
getGlowAnalStateLevel() < coins.flow.Flow.STATE_CFG_AVAILABLE)true so as to inform re-computation is required.
x, y, t, u : variable or register representing an operand. (variable may be a compound variable such as array element or structure element.) op : operator. def(x) : shows that value of x is defined (value is set). def(x, y, ...) : shows that values of x, y, ... are defined. use(x) : shows that x is used. p(use(x)) : x is used at program point p. or_all(z) : construct a set by applying or-operation on all components indicated by z. and_all(z) : construct a set by applying and-operation on all components indicated by z.The data flow analyzer will compute following information according to requests:
Def(B) = { p | for some x, p(def(x)) is included in B and after that point there is no p'(def(x)) in B. } Kill(B) = { p | for some x, p(def(x)) is included in B' (where, B' != B) and there exists some defining point of x p'(def(x)) in B. } Reach(B)= { p | there is some path from program point p defining x (that is p(def(x))) to the entry of B such that there is no p'(def(x)) on that path. } Reach(B) = or_all( (Def(B') | (Reach(B') - Kill(B'))) for all predecessors B' of B) Defined(B) = { x | x is defined in B. } Exposed(B) = { x | x is used in B and x is not defined in B before x is used. } Used(B) = {x|x is used in B} EGen(B) = { op(x,y) | expression op(x,y) is computed in B and after that point, neither x nor y are defined in B. } Thus, the result of op(x,y) is available after B. EKill(B) = { op(x,y) | operand x or y is defined in B and the expression op(x,y) is not re-evaluated after that definition in B. } If t = op(x,y) is killed in B, then op(t,u) should also be killed in B. AvailIn(B) = { op(x,y) | op(x,y) is computed in every paths to B and x, y are not defined after the computations on the paths. } Thus, the result of op(x,y) can be used without re-evaluation in B. AvailOut(B) = { op(x,y) | op(x,y) is computed in every paths to the exit of B and x, y are not defined after the computations on the paths. } Thus, op(x,y) can be used without re-evaluation after B. Following relations hold. AvailIn(B) = and_all(AvailOut(B') for all predecessors B' of B) if B is not an entry block; AvailIn(B) = { } if B is an entry block. AvailOut(B) = EGen(B) | (AvailIn(B) - EKill(B)) LiveIn(B) = { x | x is alive at entry to B, that is, on some path from entrance point of B to use point of x, x is not defined. } Thus, x in LiveIn(B) should not be changed until it is used. LiveOut(B) = { x | x is live at exit from B, that is, there is some path from B to B' where x is in Exposed(B'). } Following relations hold. LiveOut(B) = or_all(LiveIn(B') for all successors B' of B LiveIn(B) = Exposed(B) | (LiveOut(B) - Defined(B)) DefIn(B) = { x | x is always defined at entry to B whichever path may be taken. } DefIn(B) = and_all(DefOut(B') for all predecessors B' of B) DefOut(B) = { x | x is always defined at exit from B whichever path may be taken.} DefOut(B) = Defined(B) | DefIn(B) Reach(p(use(x))) = { p'(def(x)) | there are some paths from p to p' on which x is not re-defined. } DefUseList(p(def(x))) = { p'(use(x)) | p(def(x)) is included in p'(use(x)). } UseDefList(p(use(x))) = { p'(def(x)) | p'(def(x)) is included in p(use(x)). }
flowRoot.flow.dataFlwoAnal(subpDefinition);at the first time. This makes coins.flow.SubpFlow methods such as
getDefinedSyms(), getUsedSyms(), ...available. It also makes coins.flow.BBlock methods such as
getDefIn(), getDefOut(), getRech(), getLiveIn(), getLiveOut(), getAvailIn(), getAvailOut(), ....available. available. There are many other methods for accessing data flow information as shown in the interface SubpFlow. Such methods can be called via the SubpFlow instance
flowRoot.fSubpFlowwhich is prepared by calling dataFlwoAnal(subpDefinition);
if (flowRoot.flow.getFlowAnalStateLevel() < coins.flow.Flow.STATE_DATA_FLOW_AVAILABLE) flowRoot.dataFlow = flowRoot.flow.dataFlowAnal(subpDefinition);The methods finishHir() and setIndexNumbetToAllNodes() of HIR0 interface will make getFlowAnalStateLevel() as STATE_DATA_UNAVAILABLE, that is, it will make
getFlowAnalStateLevel() < coins.flow.Flow.STATE_DATA_FLOW_AVAILABLEtrue so as to inform re-computation is required.
AssignStmt Conditional expressions in LoopStmt Subprogram call ReturnStmtwhich are treated as a statement in the data flow analysis. Following methods are available for SetRefRepr.
defSym() returns the set of symbols definitely defined. modSyms() returns the set of symbols that are possibly defined. useSyms() returns the set of symbols definitely used (referred).As for expressions, ExpId interface provides following methods:
getOperandSet() returns the set of variables used as leaf operand. getExpInf().hasCall() returns true if the expression has call.SubpFlow interface provides following methods for corresponding subprogram:
cfgIterator() traverses all reachable basic blocks of the subprogram. bblockSubtreeItrator(BBlock pBBlock) returns iterator that traverse top subtrees of the basic block pBBlock. Traversed top-subtrees are LabeledStmt, AssignStmt, ExpStmt, ReturnStmt, IfStmt, LoopStmt, SwitchStmt Conditional expression in IfStmt and LoopStmt Case-selection expression in SwitchStmt Call subtree (irrespective of contained in ExpStmt or Exp) bblockStmtIterator(BBlock pBBlock) returns iterator to traverse all HIR statements in the basic block pBBlock. bblockNodeIterator(BBlock pBBlock) returns iterator to traverse all HIR nodes in the basic block pBBlock. getSetRefReprOfIR(IR pIr) returns SetRefRepr corresponding to pIr or returns null if pIr has no SetRefRepr instance. getExpId(IR pIr) returns ExpId corresponding to pIr. getExpOfTemp(Var pTemp) returns the expression represented by the temporal variable pTemp. setOfGlobalVariables() returns the set of global variables appeared. setOfAddressTakenVariables() returns the set of address taken variables. getRecordAlias() returns the instance of RecordAlias that is used to access alias information of the subprogram.DefUseList and UseDefList are computed by the information of definitely defined and definitely used relations because if all possibilities are unconditionally included, define/use lists and use/define lists will become very large. Possibly defined symbols and possibly used symbols can be get from defSyms() and useSyms() by using the set of global variables, the set of address-taken variables, and the set of variables aliased to a variable.
int printf(char*, ...); int func(int pa[10], int pn); int ga1[10] = {1, 2, 3, 4, 5, 6, 7, 8, 9, 10}; int main() { int a = 1, b = 2, c, d; int i = 0; int *ptrc, *ptry; int sum; int x[10]; int y[10] = { 1, 2, 3, 4, 5, 6, 7, 8, 9, 10}; int z[10] = {10, 20, 30, 40, 50, 60, 70, 80, 90, 100}; int zz[10] = {1, 2, 3, 4, 5, 6, 7, 8, 9, 10}; ptrc = &c; ptry = y; x[i] = a; *ptrc = x[i] + 1; sum = c + func(z, 10); d = zz[2] + zz[3]; printf(" sum=%d ", sum); for (i = 0; i < 10; i++) { d = d + (zz[2] + zz[3]); d = d + z[i] + z[i]; d = d + zz[i] + zz[i]; sum = ga1[i] + ga1[i]; sum = sum + *ptry; printf(" *ptry=%d d=%d ", *ptry, d); ptry = ptry + 1; sum = sum + z[i] + z[i]; sum = sum + zz[i] + zz[i]; d = d + ga1[i] + ga1[i]; } d = d + ga1[2] + ga1[2]; printf("\n"); d = d + (zz[2] + zz[3]); d = d + ga1[2] + ga1[2]; printf("%d %d %d \n", sum, c, d); return 0; }basic blocks are
BBlock 1: statements from the beginning up to "i=0;" of for-statement BBlock 2: conditional expression "i < 10" BBlock 3: from "d=d+(zz[2]+zz[3]);" to "d=d+ga1[i]+ga1[i];" BBlock 4: "i++" BBlock 5: rest of statements (from "d=d+ga1[2]+ga1[2];" to "return 0;" and setOfAddressTakenVariables() = { c, z, y } Available expressions of basic blocks are BBlock 1 AvailOut= { zz[2], zz[3], &c, zz[2]+zz[3] } BBlock 2 AvailIn = { zz[2], zz[3], &c, zz[2]+zz[3] } AvailOut= { zz[2], zz[3], &c, zz[2]+zz[3], i<10 } BBlock 3 AvailIn = { zz[2], zz[3], &c, zz[2]+zz[3] } AvailOut= { zz[2], zz[3], &c, zz[2]+zz[3], i<10, z[i], zz[i], ga1[i] } BBlock 4 AvailIn = { zz[2], zz[3], &c, zz[2]+zz[3], i<10, z[i], zz[i], ga1[i] } AvailOut= { zz[2], zz[3], &c, zz[2]+zz[3] } BBlock 5 AvailIn = { zz[2], zz[3], &c, zz[2]+zz[3], i<10 } AvailOut= { zz[2], zz[3], &c, zz[2]+zz[3], i<10 }At the statement "ptrc = x[i] + 1;" address taken variables are assumed to be modified.
defSym = { *ptrc } modSyms= { c, *ptrc, z, ptrc, y }At the statement "sum = c + func(z, 10);" global variables are assumed to be modified.
defSym = { sum } modSyms= { z, ga1, sum }Thus, after partial redundancy elimination, z[i]+z[i] is re-computed after subprogram call but z[i]+z[i] is not re-computed (eliminated as common subexpression), and zz[2]+zz[3] is recorded in a temporal variable before entering the for-loop and all later occurrences of zz[2]+zz[3] are replaced by the temporal variable.
SubpFlow lSubpFlow = new HirSubpFlowImpl(flowRoot, subpDefinition); ControlFlow lControlFlow = flowRoot.flow.controlFlowAnal(lSubpFlow); DataFlow lDataFlow = flowRoot.flow.dataFlowAnal(lSubpFlow); RecordAlias lRecordAlias = lSubpFlow.getRecordAlias(); for (Iterator lBBlockIterator = lSubpFlow.cfgIterator(); lBBlockIterator.hasNext(); ) { BBlock lBBlock = (BBlock)lBBlockIterator.next(); ExpVector lAvailableExp = lBBlock.getAvailIn(); for (BBlockSubtreeIterator lSubtreeIterator = lSubpFlow.bblockSubtreeIterator(lBBlock); lSubtreeIterator.hasNext(); ) { HIR lSubtree = (HIR)lSubtreeIterator.next(); SetRefRepr lSetRefRepr = lSubpFlow.getSetRefReprOfIR(lSubtree); Set lModSyms = lSetRefRepr.modSyms(); Set lModSymsAlias = fRecordAlias.aliasSymGroup(lModSyms); // Set of // symbold aliased to some of modified variables. for (ExpVectorIterator lExpIterator = lAvailableExp.expVectorIterator(); lExpIterator.hasNext(); ) { ExpId lExpId = nextExpId(); Set lOperands = lExpId.getOperandSet(); if (! lOperands.retailAll(lModSymsAlias).isEmpty()) { // Treat the expression corresponding to lExpId as unavailable // because some operand may be changed by the subtree lSubtree. } ...... } .... } .... }To see the result of data flow analysis, execute following statement:
flowRoot.dataFlow.showSummary();The amount of printed result may be large for subprograms with hundreds of statements.
package coins.flow; import coins.FlowRoot; import coins.ir.hir.SubpDefinition; import java.util.Iterator; public class MySubpFlow extends HirSubpFlowImpl implements HirSubpFlow { ExpVector fTransparent[]; public MySubpFlow(FlowRoot pFlowRoot, SubpDefinition pSubpDefinition) { super(pFlowRoot, pSubpDefinition); } // MySubpFlow public void computeTransparent() { ExpVector lEKillAll; ExpVector lTemp1 = expVector(); ExpVector lTemp2 = expVector(); FlowAnalSymVector lDefined; int lBBlockNum; fTransparent = new ExpVector[fBBlockCount + 1]; // Get space // to record transparent vectors for all basic blocks. for (Iterator lIterator = cfgIterator(); lIterator.hasNext(); ) { // Repeat for each basic block. BBlock lBBlock = (BBlock)lIterator.next(); if (lBBlock == null) continue; lBBlockNum = lBBlock.getBBlockNumber(); // Get basic block number. fTransparent[lBBlockNum] = expVector(); // Initiate by zero vector. lEKillAll = lBBlock.getEKillAll(); // Get the cumulative set of //expressions killed by some statements in this BBlock. lEKillAll.vectorNot(lTemp1); // lTemp1 is negation of lEKillAll.. // Get the set of defined variables. lDefined = (FlowAnalSymVector)lBBlock.getDefined(); lTemp2 = lDefined.flowAnalSymToExpVector(); // Change the set to vector. lTemp1.vectorSub(lTemp2, fTransparent[lBBlockNum]); // fTransparent[lBBlockNum] = lTemp1 - lTemp2 if (fDbgLevel > 1) // If trace=Flow.2 or more, print the result. ioRoot.dbgFlow.print(2, "Transparent B"+lBBlockNum, fTransparent[lBBlockNum].toStringShort()); } setComputedFlag(DF_TRSNSPARENT); // Set already-computed flag. } // computeTransparent /** * Get the transparent expression for the basic block pBBlock. * Expressions are represented by ExpId corresponding to the expression. * @param pBBlock basic block. * @return expression vector showing transparent expressions. */ public ExpVector getTransparent( BBlock pBBlock ) { if (! isComputed(DF_TRSNSPARENT)) // If already computed, computeTransparent(); // do not re-compute but reuse. return fTransparent[pBBlock.getBBlockNumber()]; } // getTransparent } // MySubpFlowIn this example, it is necessary to add
public static final int DF_TRANSPARENT = 26;as a flag number to SubpFlow.java. To use the subclass for extending the flow analysis capability, write such coding as
SubpFlow lSubpFlow = new MySubpFlow(flowRoot, subpDefinition);instead of
SubpFlow lSubpFlow = new HirSubpFlowImpl(flowRoot, subpDefinition);which is shown in the previous example.
x, y, t, u : variable or register representing an operand. op : operator. def(x) : shows that value of x is definitely defined. mod(x) : shows that value of x is possibly defined. use(x) : shows that x is used. p(def(x)) : value of x is (definitely) modified (i.e. via assign) at program point p. p(mod(x, y, ...)) : value of x, y, ... are modified at program point p (modified means possibly changed). p(use(x)) : x is used at program point p. or_all(z) : construct a set by applying or-operation on all components indicated by z. and_all(z) : construct a set by applying and-operation on all components indicated by z.The data flow analyzer will compute following information according to requests:
PDef(B) = { p | p(mod(x, y, ...)) is included in B and after that point there is no p' s.t. p'(def(x)) nor p" s.t. p"(def(y)), ... in B. } DKill(B) = { p | p(def(x)) is not included in B and p'(def(x)) is included in B. } PReach(B)= { p | there is some path from program point p that modifies some variables x, y, ... (that is, p(mod(x, y, ...))) to the entry of B such that there is no p'(def(x)) or no p''(def(y)) or ... on that path. } PReach(B) = or_all( (PDef(B') | (PReach(B') - DKill(B'))) for all predecessors B' of B) DDefined(B) = { x | x is definitely modified in B. } PDefined(B) = { x | x is posibly modified in B. } PExposed(B) = { x | x is possibly used in B and x is not definitely set in B before x is used. } PUsed(B) = {x|x is possibly used in B} DEGen(B) = { op(x,y) | expression op(x,y) is computed in B and after that point, neither x nor y are possibly set in B. } Thus, the result of op(x,y) is available after B. PEKill(B) = { op(x,y) | operand x or y is possibly modified in B and the expression op(x,y) is not re-evaluated after that definition in B. } If t = op(x,y) is killed in B, then op(t,u) should also be killed in B. DAvailIn(B) = { op(x,y) | op(x,y) is computed in every paths to B and x, y are not modified after the computations on the paths. } Thus, the result of op(x,y) can be used without re-evaluation in B. DAvailOut(B) = { op(x,y) | op(x,y) is computed in every paths to the exit of B and x, y are not modified after the computations on the paths. } Thus, op(x,y) can be used without re-evaluation after B. Following relations hold. DAvailIn(B) = and_all(DAvailOut(B') for all predecessors B' of B) if B is not an entry block; DAvailIn(B) = { } if B is an entry block. DAvailOut(B) = DEGen(B) | (DAvailIn(B) - PEKill(B)) PLiveIn(B) = { x | x is alive at entry to B, that is, on some path from entrance point of B to use point of x, x is not definitely set. } Thus, x in PLiveIn(B) should not be changed until it is used. PLiveOut(B) = { x | x is live at exit from B, that is, there is some path from B to B' where x is in PExposed(B'). } Following relations hold. PLiveOut(B) = or_all(PLiveIn(B') for all successors B' of B PLiveIn(B) = PExposed(B) | (PLiveOut(B) - DDefined(B)) DDefIn(B) = { x | x is always defined at entry to B whichever path may be taken. } DDefIn(B) = and_all(DDefOut(B') for all predecessors B' of B) DDefOut(B) = { x | x is always defined at exit from B whichever path may be taken.} DDefOut(B) = DDefined(B) | DefIn(B)
ex. find("Def", lBBlock);(2) get
ex. get("Def", lBBlock);(3) put
ex. put("Def", lBBlock, lDefVector);(4) getRaw
ex. getRaw("Def", lBBlock)In the following code snippet, the Reach vector for the exit BBlock of the SubpDefinition variable subpDef is going to be stored in the local variable lReach.
// Establishes the map between the analysis names and the analyzer methods // that actually do the analysis. // A key of this map together with the arguments of the associated // analyzer class methods forms a piece of information that supports the // automatic analysis mechanism. // This method will be called only twice during the program life; once // for HIR and once for LIR. FlowResults.putRegClasses(new RegisterFlowAnalClasses()); // Instantiate a FlowResults map. FlowResults lResults = flow.results(); // Instantiate a SubpFlow object, with FlowResults object passed as an // argument to the factory method. SubpFlow lSubpFlow = flow.subpFlow(subpDef, lResults); // Performs control flow analysis. // Control flow analysis does not support the automatic flow analysis // mechanism and must be called explicitly. lSubpFlow.controlFlowAnal(); // Collects some basic information that does not require a complex // algorithm. // Some pieces of information obtained here ARE part of the automatic // analysis picture, but some are not, so I call it explicitly. lSubpFlow.initiateDataFlow(); // Finds the Reach vector for each of the BBlocks that belong to lSubpFlow. // There is no need to call lSubpFlow.getExitBBlock().findDef() or // lSubpFlow.getExitBBlock().findKill() (or lSubpFlow.findReach()) since // they are called automatically (automatic analysis). lReach = lResults.get("Reach", lSubpFlow.getExitBBlock()); // OR lReach = lSubpFlow.getExitBBlock().getReach(); ...
The following command invokes HIR flow analyzer.
java coins.driver.Driver -S -coins:hirAnal,trace=Flow.2The trace option is attached to see the result of the flow analysis.
There are 2 levels of analysis:
Also, there are 2 modes of analysis for both AliasAnalLevel1 and AliasAnalLevel2:
-coins:alias=optThere are fine computation mode and coarse computation mode in the alias analysis. The fine computation mode will consume much time and memory. For large subprograms (more than 1000 HIR nodes), the coarse computation mode is automatically adopted. In the fine computation mode, size of set showing aliased symbols will be small compared to the coarse computation mode.
RecordAlias lRecordAlias = flowRoot.subpFlow.getRecordAlias(); .... if(lRecordAlias.mayAlias(x, y)) { // Assume y may be changed when x is changed. .... } Set lSetOfVariablesAliased = lRecordAlias.aliasSyms(x);where, x, y are variables.
#pragma globalReform patternSym copy #pragma globalReform target main void copy( char *pa, char *pb, int pn, int pi ) { iPattern: { for (pi = 0; pi < pn; pi++) *pb++ = *pa++; } oPattern: { memcpy(pb, pa, pn); } } int main() { char x[100] = {1, 2, 3, 4, 5, 6, 7, 8}, y[100]; int j; char *px = x; char *py = y; for (j = 0; j < 100; j++) *py++ = *px++; printf(" %d %d %d \n", y[0], y[1], y[2]); return 0; }In this example, the in-pattern is
for (pi = 0; pi < pn; pi++) *pb++ = *pa++;and the out-pattern is
memcpy(pb, pa, pn);The description of the global patterns may have some pragmas that start with the keyword "globalReform". The pragma
#pragma globalReform patternSym copyindicates that the subprogram showing the correspondence of above in-pattern and out-pattern is "copy".
#pragma globalReform target mainindicates that above transformation should be applied to the subprogram "main".
for (j = 0; j < 100; j++) *py++ = *px++;fits in with the in-pattern and it is transformed to
memcpy(py, px, 100);where, the parameters pa, pb, pn, pi correspond to expressions px, py, 100, j respectively and the parameters contained in the out-pattern are replaced with these expressions, respectively.
#pragma globalReform patternSym pattern1 pattern2 ...where the keyword "globalReform" indicates that this pragma is specified for the global pattern matching, and the keyword "patternSym" indicates that names of subprograms showing pattern correspondence follows in the same line.
#pragma globalReform target subp1 subp2 ...where the keyword "target" indicates that names of subprograms to be transformed follows in the same line.
void patternSymbol( type1 pParam1, type2 pParam2, ... ) { iPattern: { statement1 statement2 .... } oPattern: { statement4 statement5 .... } }where, patternSymbol is an identifier showing the name of the pattern correspondence. Parameter types (type1, type2, ... ) are usually a type of expression (Exp or subclass of Exp) and the corresponding parameter (formal parameter pParam1, pParam2, ...) fits in with an expression of the type compatible with the parameter type. A parameter qualified as "const" can match only with a constant of the specified type.
#pragma globalReform stmtParam param1in the scope of the parameter in such a way as
void patternSymbol( type1 pParam1, type2 pParam2, ... ) { #pragma globalReform stmtParam param1 param2 ... iPattern: { statement1 statement2 .... } oPattern: { statement1 statement2 .... } }For the parameter representing a statement (statement parameter), give void* as its type in the parameter list. The statement parameter fits in with a statement that is placed at the same position in the input program as the position where the statement parameter is located in the in-pattern. As for other matters, the same rules as above are applied to the statement parameters.
iPattern { p * 10; }If an in-pattern is an expression then corresponding out-pattern should also be an expression, e.g.,
oPattern: { p * 8 + p * 2; }In the global transformation, each one of in-patterns may be considered as a template to be matched with a part of the input program, where a parameter in the in-pattern may be considered as a hole in the template. The template is considered to be fitted in with a part of the input program if both of them have the same form except for the hole where any expression/statement may fall in, that is, in the pattern matching, HIR subtrees having the same form as some in-pattern are searched where each parameter in the in-pattern is treated to be a formal parameter to which an actual parameter of any complexity may correspond as far as the type of the actual parameter is compatible with the type of the formal parameter.
#pragma globalReform patternSym absAdd #pragma globalReform target main #define BSIZE 256 void absAdd( signed char pd[], int pi, int pm, int psum ) { iPattern: { psum = 0; for (pi = 0; pi < pm; pi = pi + 1 ) { if (pd[pi] >= 0) psum = psum + pd[pi]; else psum = psum - pd[pi]; } } oPattern: { psum = absAddChar(pd, pm); } } int main() { signed char buf[BSIZE], v; int i, j; int sum; for (j = 0; j < BSIZE; j++) { buf[j] = 128 - j; } sum = 0; for (i = 0; i < BSIZE; i = i + 1) { if (buf[i] >= 0) sum = sum + buf[i]; else sum = sum - buf[i]; } printf("sum= %d\n", sum); return 0; }the sequence of statements
sum = 0; for (i = 0; i < 256; i = i + 1) { if (buf[i] >= 0) sum = sum + buf[i]; else sum = sum - buf[i]; }can fit in with the in-pattern of the pattern symbol named "absAdd" and it is changed to the statement calling "absAddChar" function that does the same computation by using one of the SIMD instructions.
for (i=0; i< 4; i++) { t[i]=c[3]*m[i][3]+c[2]*m[i][2] +c[1]*m[i][1]+c[0]*m[i][0]; } for(j=0; j< 4; j++) c[j]=t[j];using a temporal variable t and integer variables i and j.
mov eax,c //edi = &c[0] mov ebx,m //ebx = &m[0][0] movq mm0,[eax] //mm0: c[3]: c[2]: c[1]: c[O] // move quad words to mm0 (64bits) movq mm1,[ebx] //mm1: m[0][3]:m[0][2]:m[0][1]:m[0][0] movq mm2,[ebx+8] //mm2: m[1][3]:m[1][2]:m[1][1]:m[1][0] movq mm3,[ebx+16]//mm3: m[2][3]:m[2][2]:m[2][1]:m[2][0] movq mm4,[ebx+24]//mm4: m[3][3]:m[3][2]:m[3][1]:m[3][O] pmaddwd mm1,mm0 //mm1: c[3]*m[0][3]+c[2]*m[0][2]: c[1]*m[0][1]+c[0]*m[0][0] pmaddwd mm2,mm0 //mm2: c[3]*m[1][3]+c[2]*m[1][2]: c[1]*m[1][1]+c[0]*m[1][0] pmaddwd mm3,mm0 //mm3: c[3]*m[2][3]+c[2]*m[2][2]: c[1]*m[2][1]+c[0]*m[2][0] pmaddwd mm4,mm0 //mm4: c[3]*m[3][3]+c[2]*m[3][2]: c[1]*m[3][1]+c[0]*m[3][0] packssdw mm1,mm2 //mm1: c[3]*m[1][3]+c[2]*m[1][2]: c[1]*m[1][1]+c[0]*m[1][0] // : c[3]*m[0][3]+c[2]*m[0][2]: c[1]*m[0][1]+c[0]*m[0][0] // 4 packed words in mm1, mm2 to 4 packed words in mm1 // with saturation operation. movq [temp1],mm1 // short temp1[4]; packssdw mm3,mm4 //mm3: c[3]*m[3][3]+c[2]*m[3][2]: c[1]*m[3][1]+c[0]*m[3][0] // : c[3]*m[2][3]+c[2]*m[2][2]: c[1]*m[2][1]+c[0]*m[2][0] movq[temp2],mm3 // short temp2[4]; emms // empty MMX state so that FPU reg can be used for floating op. ) c[0]=temp1[0]+temp1[1]; // Move the results from temp1 and temp2. c[1]=temp1[2]+temp1[3]; c[2]=temp2[0]+temp2[1]; c[3]=temp2[2]+temp2[3];In the MMX instruction coding, the saturation operation is executed but in the above C language coding, the saturation operation is not yet considered.
#pragma globalReform patternSym linearTrans #pragma globalReform target main int printf(char*, ...); void linearTrans(short pc[4], short pm[4][4], short pt[4], int pi, int pj) { short temp1[4], temp2[4]; iPattern: { for (pi=0;pi< 4;pi++) { pt[pi]=pc[3]*pm[pi][3]+pc[2]*pm[pi][2]+pc[1]*pm[pi][1]+pc[0]*pm[pi][0]; } for(pj=0;pj< 4;pj++) pc[pj]=pt[pj]; } oPattern: { asm ( "#param %I32,%I32,%I32,%I32\n" "#clobber %mm0,%mm1,%mm2,%mm3,%mm4\n" "movq (%1),%mm0\n" "movq (%2),%mm1\n" "movq 8(%2),%mm2\n" "movq 16(%2),%mm3\n" "movq 24(%2),%mm4\n" "pmaddwd %mm0,%mm1\n" "pmaddwd %mm0,%mm2\n" "pmaddwd %mm0,%mm3\n" "pmaddwd %mm0,%mm4\n" "packssdw %mm2,%mm1\n" "movq %mm1,(%3)\n" "packssdw %mm4,%mm3\n" "movq %mm3,(%4)\n" "emms\n", pc, pm, temp1, temp2 ); pc[0]=temp1[0]+temp1[1]; pc[1]=temp1[2]+temp1[3]; pc[2]=temp2[0]+temp2[1]; pc[3]=temp2[2]+temp2[3]; } } // linearTrans int main() { int i; short tt[4][4] = {{1, 0, 0, 0}, {0, 1, 0, 1}, {0, 0, 1, 0}, {0, 0, 0, 1}}; short xyz[4] = {10, 12, 13, 3}; short tmp[4] = {0}; printf("before %d %d %d %d \n", xyz[0], xyz[1], xyz[2], xyz[3]); for (i=0;i< 4;i++) { tmp[i]=xyz[3]*tt[i][3]+xyz[2]*tt[i][2]+xyz[1]*tt[i][1]+xyz[0]*tt[i][0]; } for(i=0;i< 4;i++) xyz[i]=tmp[i]; printf("linTrans %d %d %d %d \n", xyz[0], xyz[1], xyz[2], xyz[3]); return 0; }The function definition linearTrans defines the C coding pattern as the block labeled by iPattern and the corresponding MMX coding sequence as the block labeled by oPattern.
asm("#param descriptor-list\n" "#clobber destroyed registers...\n" "instruction 1\n" ... "instruction n\n", input arguments(any expression)...);where,
for (i=0;i< 4;i++) { tmp[i]=xyz[3]*tt[i][3]+xyz[2]*tt[i][2]+xyz[1]*tt[i][1]+xyz[0]*tt[i][0]; } for(i=0;i< 4;i++) xyz[i]=tmp[i];in the main program matches with this pattern.
with globalReform without globalReform real 8.712s 17.389s user 8.624s 17.331s sys 0.015s 0.031sThis shows the effectiveness of MMX code generation by using globalReform optimization.
#pragma globalReform patternSym recmult #pragma globalReform target fact int recmult( int px ) { iPattern: { if (px <= 1) return 1; else return px * recmult(px - 1); } oPattern: { int lx, i; lx = 1; for (i = 1; i <= px; i++) { lx = lx * i; } return lx; } } int fact( int p ) { if (p <= 1) return 1; else return p * fact(p - 1); }Note that this is not a general transformation of recursion to loop but a transformation of program fragments that matches with the given in-pattern.
#pragma globalReform patternSym extractPower #pragma globalReform nonterminal power #pragma globalReform target main int _bnfOr(int p, ...); double power( double p1 ); double transformPower( double p2 ); void extractPower( double pv1 ) { iPattern: { power(pv1) * pv1; } oPattern: { transformPower(power(pv1) * pv1); } } double power( double pv2) { _bnfOr(2, pv2 * pv2, power(pv2) * pv2 ); } double a = 2.0, b = 3.0, c = 4.0; int main() { double x, y, z; x = a * a * a; y = b * b * b * b; z = a * a * b; printf(" %f %f %f \n", x, y, z); return 0; }The above example extracts power expressions that multiply the same variable several times and call the function transformPower. (This example is made to explain the usage of pattern nonterminals and is not intended to increase execution speed.) The function power is a pattern nonterminal that is similar to BNF nonterminal. In BNF, a power expression of variable v may be defined as
powerExp ::= powerExp "*" var | varbut if the symbol var is a nonterminal representing variables, then it is not possible to restrict its operand to the same variable. If nonterminals may have parameters, then such restriction can be specified.
double power( double pv2) { _bnfOr(2, pv2*pv2, power(pv2)*pv2); }pv2 is a formal parameter of the pattern nonterminal named "power".
_bnfOr(2, pv2*pv2, power(pv2)*pv2 );represents to select either
int _bnfOr(int, ...);The first parameter of _bnfOr is a dummy one attached to make _bnfOr as a C function having indefinite number of parameters. The search of production is done from left to right and the one fitted first is selected. If there is no production fitted, then the nonterminal is treated to be not fitted with the input program.
a * a * ais given as an expression of input program, then
power(pv2) * pv2is selected as the production to be matched because the other production pv2*pv2 does not fit in with a*a*a. In the next step, trial matching of power(pv2) with a*a is performed after tentatively setting pv2 to the variable "a". This trial succeeds by selecting the production pv2*pv2. Thus, the in-pattern fits in with the input expression a*a*a.
b * b * b * bis given as an input expression, at the first trial,
power(pv2) * pv2is selected matching pv2 to b and trying to match power(pv2) with b*b*b peeling off the trailing "*b". This trial matching succeeds and the in-pattern fits in with the expression b*b*b*b, too.
a * a * bis given as an input expression, power(pv2) does not fits in with it, because, at the first trial,
power(pv2) * pv2is selected matching pv2 to b, then in the second trial, power(pv2) fails to match with a*a as the power(pv2) requests the variable b as a multiplicand.
#pragma globalReform patternSym loopUnroll #pragma globalReform nonterminal subsVar expS termS factS iExp #pragma globalReform target main #define BSIZE 999 int expS( int pzz[], int pi); int termS( int pzz[], int pi); int factS( int pzz[], int pi); int subsVar( int pzz[], int pi); int iExp( int px); int printf(char*, ...); void loopUnroll( int pzz[], int pi, int pFrom, int pTo) { iPattern: { for (pi = pFrom; pi < pTo; pi++) { pzz[iExp(pi)] = expS(pzz, pi); } } oPattern: { for (pi = pFrom; pi < pTo-1; pi=pi+2) { pzz[iExp(pi)] = expS(pzz, pi); pzz[iExp(pi+1)] = expS(pzz, pi+1); } if ((pTo-pFrom) % 2 != 0) pzz[pTo-1] = expS(pzz, pTo-1); } } int subsVar( int pzz1[], int pi1) { pzz1[iExp(pi1)]; } int expS( int pzz2[], int pi2) { #pragma globalReform transparentFitting pc (pzz2, pi2) int pc; _bnfOr(1, expS(pzz2,iExp(pi2))+termS(pzz2,iExp(pi2)), expS(pzz2,iExp(pi2))-termS(pzz2,iExp(pi2)), expS(pzz2,iExp(pi2))+pc, expS(pzz2,iExp(pi2))-pc, expS(pzz2,iExp(pi2)) ); } int termS( int pzz3[], int pi3 ) { #pragma globalReform transparentFitting pc2 (pzz3, pi3) int pc2; _bnfOr(1, termS(pzz3,iExp(pi3))*factS(pzz3,iExp(pi3)), termS(pzz3,iExp(pi3))/factS(pzz3,iExp(pi3)), termS(pzz3,iExp(pi3))*pc2, termS(pzz3,iExp(pi3))/pc2, factS(pzz3,iExp(pi3)) ); } int factS( int pzz4[], int pi4 ) { #pragma globalReform transparentFitting pc3 (pzz4, pi4) int pc3; _bnfOr(2, pc3*subsVar(pzz4,iExp(pi4)), pc3/subsVar(pzz4,iExp(pi4)), subsVar(pzz4,iExp(pi4))); } int iExp( int px ) { #pragma globalReform transparentFitting pc4 (px) int pc4; _bnfOr(3, px+pc4, px-pc4, px); } int main() { int zz[BSIZE]; int i, n; n = BSIZE; for (i = 0; i < n; i++) { zz[i] = i; } for (i = 0; i < n; i++) { zz[i] = zz[i]*2; } printf(" %d %d %d %d %d\n", n, zz[0], zz[1], zz[n-2], zz[n-1]); return 0; }The pattern named loopUnroll changes loops such as
for (i = 0; i < n; i++) { zz[i] = zz[i]*2; }to such a form as
for (i = 0; i < n-1; i=i+2) { zz[i] = zz[i]*2; zz[i+1] = zz[i+1]*2; } if ((n-0) % 2 != 0) zz[n-1] = zz[n-1]*2;by unrolling the loops. The factors of the loop body may be any subscripted variable having i+c2 or i-c2 as its subscript, where c1 and c2 may be any integer expression that does not contain i. Pattern nonterminals are used to specify such syntax. The pattern nonterminal
int iExp( int px ) { #pragma globalReform transparentFitting pc4 (px) int pc4; _bnfOr(3, px + pc4, px - pc4, px ); }fits in with one of expressions px+pc4, px-pc4, px where the expression pc4 does not contain the variable px which is conveyed from the upper construct.
int subsVar( int pzz1[], int pi1) { pzz1[iExp(pi1)]; }fits in with any subscripted variable whose subscript is an integer expression satisfying the restriction of iExp(pi1), where pzz1 is an array conveyed from the upper construct, and pi1 is an integer variable conveyed from the upper construct.
expS ::= expS "+" termS | expS "-" termS | expS "+" pc | expS "-" pc | termS termS ::= termS "*" factS | termS "/" factS | termS "*" pc2 | termS "/" pc2 | factS factS ::= pc3 "*" subsVar | pc3 "/" subsVar | subsVarThe pattern nonterminal
int factS( int pzz4[], int pi4 ) { #pragma globalReform transparentFitting pc3 (pzz4, pi4) int pc3; _bnfOr(2, pc3 * subsVar(pzz4, i(pi4)), pc3 / subsVar(pzz4, iExp(pi4)), subsVar(pzz4, iExp(pi4)) ); }fits in with a subscripted variable as described above or a multiplication/division expression whose first operand pc3 does not contain any of pzz4 and pi4. Variables pzz4, pi4 are conveyed from the upper construct.
int termS( int pzz3[], int pi3 ) { #pragma globalReform transparentFitting pc2 (pzz3, pi3) int pc2; _bnfOr(1, termS(pzz3, iExp(pi3)) * factS(pzz3, iExp(pi3)), termS(pzz3, iExp(pi3)) / factS(pzz3, iExp(pi3)), termS(pzz3, iExp(pi3)) * pc2, termS(pzz3, iExp(pi3)) / pc2, factS(pzz3, iExp(pi3)) ); }fits in with any subscripted expression specified by factS(pzz3, iExp(pi3)) when the top operator of the expression is neither '*' nor '/'. If the top operator of the expression is either '*' or '/', then the pattern nonterminal fits in with the expression when its first operand fits in with termS(pzz3, iExp(pi3)) and its second operand is an expression specified by subsVar(pzz3, iExp(pi3)) or pc2. The variables pzz3, pi3 are conveyed from the upper construct.
int expS( int pzz2[], int pi2) { #pragma globalReform transparentFitting pc (pzz2, pi2) int pc; _bnfOr(1, expS(pzz2, iExp(pi2)) + termS(pzz2, iExp(pi2)), expS(pzz2, iExp(pi2)) - termS(pzz2, iExp(pi2)), expS(pzz2, iExp(pi2)) + pc, expS(pzz2, iExp(pi2)) - pc, termS(pzz2, iExp(pi2)) ); }matches with any subscripted variable expression specified by
for (i = 0; i < n; i++) { zz[i] = zz[i]*2; }to such form as
for (i = 0; i < n-1; i=i+2) { zz[i] = zz[i]*2; zz[i+1] = zz[i+1]*2; } if ((n-0) % 2 != 0) zz[n-1] = zz[n-1]*2;COINS has the optimization module that is dedicated to loop unrolling. It is implemented in about 2000 lines of coding and can be applied to wide variety of loops. The above global pattern matching example cannot replace the dedicated loop unrolling module but shows another implementation of loop unrolling transformation in less than 100 lines of coding applicable only for typical coding patterns.