8 Instruction Selection

Transcription

1 8 Instrution Seletion The IR ode instrutions were designed to do exatly one operation: load/store, add, subtrat, jump, et. The mahine instrutions of a real CPU often perform several of these primitive operations. Example: The MIPS mahine instrution lw $v0, 3($a) orresponds to the following IR tree: MOVE $v0 PLUS BINOP $a 3 00/03 T.Grust Compiler Constrution: 8. Instrution Seletion

2 Finding the appropriate mahine instrutions to implement a given IR tree is alled instrution seletion. The instrution seletion phase is supplied with a mahine desription, a set of IR tree patterns desribing the mahine instrutions of the target CPU. Instrution seletion then amounts to tiling the IR tree with a (minimal) set of tree patterns. In this hapter we will use a hypothetial target CPU, the Jouette 3 arhiteture. N.B. In the following, we abbreviate the IR tree BINOP e e as e e 3 Frenh: toy. 00/03 T.Grust Compiler Constrution: 8. Instrution Seletion 3

3 Mahine desription for Jouette: 33 Instrution Effet IR Tree Pattern r i r i add r i r j r k * mul r i r j r k - sub r i r j r k / div r i r j /r k addi subi r i r j r i r j - 33 In the Jouette CPU, register r 0 always ontains the value 0 (MIPS: $zero). 00/03 T.Grust Compiler Constrution: 8. Instrution Seletion 4

4 Mahine desription for Jouette (ontinued): 34 Instrution Effet IR Tree Pattern load r i M[r j ] store M[r j ] r i MOVE movem M[r j ] M[r i ] MOVE MOVE MOVE MOVE 34 M[x] denotes the memory word at address x. 00/03 T.Grust Compiler Constrution: 8. Instrution Seletion 5

5 Instrution seletion means tiling the IR tree. The tiles are the tree patterns available in the mahine desription. The fundamental goal is to over the tree with non-overlapping tiles. Example: The Tiger assignment statement a[i] := x is translated into the following IR tree 35 (variables a and x are frame-resident, i lives in register r i ): fp MOVE * frame(a) r i W 35 frame(v) denotes the offset of variable v s slot in the frame, f. aess, Chapter 6. fp frame(x) 00/03 T.Grust Compiler Constrution: 8. Instrution Seletion 6

6 This tree has several valid tilings: fp frame(a) r i * MOVE W fp Jouette mahine instrutions load r, frame(a)(fp) addi r, r 0, W 3 mul r, r i, r 4 add r, r, r 5 load r, frame(x)(fp) 6 store 0(r ), r frame(x) 00/03 T.Grust Compiler Constrution: 8. Instrution Seletion 7

7 fp frame(a) r i * MOVE W fp frame(x) Jouette mahine instrutions load r, frame(a)(fp) addi r, r 0, W 3 mul r, r i, r 4 add r, r, r 5 addi r, fp, frame(x) 6 movem r, r 00/03 T.Grust Compiler Constrution: 8. Instrution Seletion 8

8 Can we always find a tiling suh that the given IR tree an be overed? Yes, if the mahine instrution set is reasonable, we an at least produe a tiling suh that eah tile overs one IR tree node only. Example: naive tiling for the previous IR tree: Jouette mahine instrutions addi r, r 0, frame(a) add r, fp, r 3 load r, 0(r ) 4 addi r, r 0, W 5 mul r, r i, r 6 add r, r, r 7 addi r, r 0, frame(x) 8 load r, 0(r ) 9 store 0(r ), r It is expeted that the exeution ost ( # of instrutions) of the naive tiling is higher than for the two previous tilings. 00/03 T.Grust Compiler Constrution: 8. Instrution Seletion 9

9 8. Algorithms for Instrution Seletion A number of reasonable algorithms exist to solve the IR tree tiling problem. We will first disuss an algorithm that produes an optimal tiling: In an optimal tiling, no two adjaent tiles an be ombined into a single tile of lower ost. For simpliity, we an just set the ost of eah instrution to unit. For a modern CPU, nearby instrutions interat in many ways suh that a good ost funtion will atually be quite ompliated to design. Example: for the Intel Pentium 4, instrution lateny is influened by the following CPU features: branh predition, speulative exeution non-bloking memory aess pipelining multiple ahe levels, temporal/spatial loality of data aess 00/03 T.Grust Compiler Constrution: 8. Instrution Seletion 30

10 8.. Maximal Munh The simple algorithm Maximal Munh always finds an optimal tiling: Start at the root of the IR tree. Find the largest (maximum number of overed IR tree nodes) tile t that fits. 3 Reord the mahine instrution orresponding to t. 4 t overs the root and (perhaps) several other nodes below the root. Tile t leaves several subtrees unovered. 5 Invoke Maximal Munh reursively on all subtrees. 6 Emit the mahine instrutions reorded in step 3 in order of a postorder traversal of the tiled IR tree. Why does the algorithm order the mahine instrutions in a postorder fashion? 00/03 T.Grust Compiler Constrution: 8. Instrution Seletion 3

11 Step of Maximal Munh involves tree pattern mathing. In a C implementation, one will typially find ode fragments like C implementation of Maximal Munh void maximal_munh (T_stm s) {... 3 swith (s->kind) { 4 ase T_MOVE: { 5 T_exp dst = s->u.move.dst; 6 T_exp sr = s->u.move.sr; 7 8 if (dst->kind == T_) { 9 if (dst->u.->kind == T_BINOP && 0 dst->u.->u.binop.op == T_PLUS && dst->u.->u.binop.right->kind == T_) { T_exp e = dst->u.->u.binop.left; 3 T_exp e = sr; 4 5 /* deteted: MOVE ( (BINOP (PLUS, e, ())), e) */ 6 7 maximal_munh (e); 8 maximal_munh (e); 9 emit ("store"); 0 } } else /03 T.Grust Compiler Constrution: 8. Instrution Seletion 3

12 8.. Dynami Programming Maximal Munh makes a loal deision when it selets and plaes the next tile. A more ambitious approah, based on dynami programming tehniques, takes a global view and an produe an optimum tiling: In an optimum tiling, the sum of the overall tile osts is minimum. The basi idea of dynami programming is that an optimum solution of a problem p is based on optimum solutions of the subproblems of p. If p = instrution seletion for an IR tree, then the solutions to subproblems of p are tilings for the tree s subtrees. Tiling based on dynami programming thus proeeds bottom-up. 00/03 T.Grust Compiler Constrution: 8. Instrution Seletion 33

13 The ost of plaing a tile t is #leaves(t) i= where denotes the ost for the tile itself (remember: we assume = for simpliity) and i is the ost of the ith tiled subtree attahed to t. i Note: We have, for example, #leaves ( ) = and #leaves =. Instrution seletion by dynami programming: Of all the tiles that math at a node n starting from the leaves of the IR tree the one with minimum ost is hosen and the (minimum) ost of node n is remembered. 00/03 T.Grust Compiler Constrution: 8. Instrution Seletion 34

14 Example: Selet the optimum Jouette instrutions to implement the IR tree Start at the leaves (the two nodes). For both leaves, the only mathing tile is an addi instrution with total ost 0 i =. i= 00/03 T.Grust Compiler Constrution: 8. Instrution Seletion 35

15 Proeed up the IR tree. At the node, several tiles math: Tile Instrution Tile Cost Leaves Cost i i Total Cost add 3 addi addi 00/03 T.Grust Compiler Constrution: 8. Instrution Seletion 36

16 3 Proeed up the IR tree. Again, at the node, several tiles math: Tile Instrution Tile Cost Leaves Cost i i Total Cost load 3 load 3 load load 00/03 T.Grust Compiler Constrution: 8. Instrution Seletion 37

17 4 When the tiling proess has overed the IR tree root with tile t, swith to ode emission: emit(t): foreah tile t i attahted to tile t do emit(t i ); write instrution for tile t; 5 The final Jouette assembly program is addi r, r 0, load r, (r ) Jouette mahine instrutions 00/03 T.Grust Compiler Constrution: 8. Instrution Seletion 38