WO2000038058A2 - Method and system for identifying locations to move portions of the computer program - Google Patents
Method and system for identifying locations to move portions of the computer program Download PDFInfo
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- WO2000038058A2 WO2000038058A2 PCT/US1999/030805 US9930805W WO0038058A2 WO 2000038058 A2 WO2000038058 A2 WO 2000038058A2 US 9930805 W US9930805 W US 9930805W WO 0038058 A2 WO0038058 A2 WO 0038058A2
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- G—PHYSICS
- G06—COMPUTING; CALCULATING OR COUNTING
- G06F—ELECTRIC DIGITAL DATA PROCESSING
- G06F8/00—Arrangements for software engineering
- G06F8/40—Transformation of program code
- G06F8/41—Compilation
- G06F8/43—Checking; Contextual analysis
- G06F8/433—Dependency analysis; Data or control flow analysis
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- G—PHYSICS
- G06—COMPUTING; CALCULATING OR COUNTING
- G06F—ELECTRIC DIGITAL DATA PROCESSING
- G06F8/00—Arrangements for software engineering
- G06F8/40—Transformation of program code
- G06F8/41—Compilation
- G06F8/44—Encoding
- G06F8/443—Optimisation
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- G—PHYSICS
- G06—COMPUTING; CALCULATING OR COUNTING
- G06F—ELECTRIC DIGITAL DATA PROCESSING
- G06F8/00—Arrangements for software engineering
- G06F8/40—Transformation of program code
- G06F8/41—Compilation
- G06F8/44—Encoding
- G06F8/445—Exploiting fine grain parallelism, i.e. parallelism at instruction level
Definitions
- the present invention relates generally to compilation of computer programs and, more particularly, to the optimization of computer programs.
- Computer programs can be very complex and consume enormous amounts of computational resources when executed.
- a computer program that models the weather over the entire earth may model the weather to an accuracy of a square mile of the surface of the earth and at elevations that are multiples of 1000 feet.
- a complex computation may need to be performed for each square mile of the surface of the earth at various elevations.
- the complex computation may need to be repeated multiple times to simulate the changing weather conditions.
- Such complex computer programs in practice, can only be executed on the fastest supercomputers. Even when executing such complex computer programs on a supercomputer, they may take too long to execute to be practical.
- even less complex computer programs may consume enough computational resources so that a user of the computer program becomes frustrated with the speed of execution. For example, a user may replace a spreadsheet program that is slow at performing a recalculation with another spreadsheet program that can perform the recalculation much faster.
- Embodiments of the present invention provide a method system for optimizing a computer program.
- the system identifies depths of blocks of a computer program and identifies the availability of expressions of the computer program.
- the system modifies the computer program when he identified availability of the expression and the identified depth of a block indicate that the expression can be moved to the block.
- the depth of the block may represent the number of dominator blocks of that block.
- the availability of the expression may represent the depth of a block to which the expression may be moved. In one embodiment, when the identified availability of the expression is less than the identified depth of the block, the expression can be moved to the block.
- Another aspect of the present invention determines the availability of expressions of a computer program.
- the system for determining such availability visits blocks of the computer program during a forward traversal of a control flow graph representing that computer program. For each expression of each block visited, the system sets the availability of the expression based on the reaching definition when the operation of the expression is a load from memory. The system also sets the availability of an expression to the latest availability of its operands when the operation is not store from memory.
- the setting of the availability of the expression based on the reaching definition may include the setting of the availability of the expression to the availability of the reaching definition when the reaching definition is a store of the result of expression with the same value as the value of the expression.
- Another aspect of the present invention identifies a direct dominator of a block of the computer program.
- the system identifies the closest dominator of the block such that the block is contained in the inner most region containing that dominator. That identified closest dominator is the direct dominator of the block. In one embodiment, the system identifies the direct dominator by first selecting the closest dominator of the block. The system then selects the least common region that contains the region that contains the block and the region that contains the selected dominator of the block. The system then loops searching for the least common region that is the same as an inner most region of a currently selected dominator.
- Figure 1 illustrates differences between the depth and avail values.
- Figure 2 illustrates a portion of a control flow graph that can benefit by code movement when both paths of a conditional branch have the same assignment statement.
- Figure 3 A illustrates a portion of a control full graph that can benefit by code movement when both paths of a conditional branch have the same assignment statement and re-join later.
- Figure 3B illustrates a code portion of control flow graph that cannot benefit from the b code movement of Figure 3 A.
- Figure 4 illustrates a portion of a control flow graph representing code that can benefit from code movement.
- Figure 5 illustrates a portion of a control flow graph representing code that can benefit from knowing that a variable is invariant within a loop.
- Figure 6 is a flow diagram of an example implementation a label_graph routine.
- Figure 7 is a flow diagram of an example implementation of the label_expr routine.
- Figure 8 is a flow diagram of the value_flow_edge routine.
- Figure 9 is a flow diagram of the move_value routine.
- Figure 10 is a flow diagram of the move_inputs routine.
- Figure 1 1 is a flow diagram of the substitute_def ⁇ nition routine.
- Figure 12 illustrates the nesting of regions.
- Figure 13 is a flow diagram of an example implementation of the find_direct_dominator routine.
- Figure 14 is a flow diagram of an example implementation of the find_direct_ post_dominator routine.
- Figure 15 is a flow diagram of an example implementation of the least_common_region routine.
- Figure 16 is a flow diagram of an example implementation of the least_common_direct_dominator routine.
- Figure 17 is a flow diagram of an example implementation of the walk ree routine.
- Figure 18 is a flow diagram of an example implementation of the walk in routine.
- Figure 19 is a flow diagram of an example implementation of the walk_out routine.
- Figure 20 is an example implementation of the visit_ops routine.
- Figure 21 is a flow diagram of an example implementation of the propagate_speculation routine.
- Figure 22 is a flow diagram of an example implementation of the spec_reg routine.
- Figure 23 is a flow diagram of an example implementation of the artempt_to_move routine.
- Figure 24 is flow diagram of an example implementation of the use_value routine.
- Figure 25 is a flow diagram of an example implementation of the movable routine.
- Embodiments of the present invention provide techniques for identifying an earlier location in a path of execution of a computer program to which an expression of the computer program can be moved.
- the code mover (“CM") system of the present invention attempts to identify the earliest location within the computer program to which each expression can be moved without re-writing the expression, which is referred to as the "depth" of the expression.
- the CM system also attempts to identify the earliest location within the computer program to which each expression can be moved with re-writing the expression, which is referred to as the "avail” or “availability” of the expression.
- the depth and avail of the expressions can be used by various compilation processes.
- the CM system also identifies a depth of each block of the computer program.
- the depth of a block indicates the depth of the immediate dominator block in a dominator tree for the computer program.
- Figure 1 illustrates differences between the depth and avail values.
- Figure 2 illustrates a portion of a control flow graph that can benefit by code movement when both paths of a conditional branch have the same assignment statement.
- the graph on the left represents the blocks of the portion before code movement, and the graph on the right represents the blocks of the portion after code movement.
- Figure 3 A illustrates a portion of a control full graph that can benefit by code movement when both paths of a conditional branch have the same assignment statement and re-join later.
- the graph on the left represents the blocks of the portion before code movement, and the graph on the right represents the blocks of the portion after code movement.
- This portion may correspond to an "if- then-else" statement.
- the removal and replacement is shown in the graph on the right.
- Figure 3B illustrates a code portion of control flow graph that cannot benefit from the b code movement of Figure 3 A.
- Figure 4 illustrates a portion of a control flow graph representing code that can benefit from code movement.
- the graph on the left represents the blocks of the portion before code at movement, and the graph on the right represents the blocks of the portion after code movement.
- Block 402 represents a loop
- block 401 represents the pre-header of the loop.
- the calculation of the value "a+b" used in the loop can be moved to the pre-header.
- the graph on the right illustrates the placing of the calculation in the pre-header. Thus, the calculation needs all it to be performed once each time the loop is performed.
- Figure 5 illustrates a portion of a control flow graph representing code that can benefit from knowing that a variable is invariant within a loop.
- the grass on the left represents the blocks of a portion before coat movement, and the graph on the right represents the blocks after code movement.
- Block 502 represents the loop
- block 501 represents the pre-header of the loop.
- the loop represents a "for" loop that is executed 100 times with the index "i” being incremented from 1 to 100.
- each of the 100 executions of the loop can be performed in parallel, because the values of the variables from one execution to the next are no longer dependent.
- the graph on the right illustrates this parallel execution of the loop.
- the CM system inputs a control flow graph and annotates each expression with its depth and avail and each block with its depth. Alternatively, these values can be calculated dynamically as they are needed by a compilation process.
- the input control flow graph includes basic blocks ("blocks") and edges between the blocks.
- the control flow graph includes a single "preheader" for each loop that, when the loop is irreducible, may have multiple successors in the loop. Such a preheader dominates all nodes in the loop. If a block is a head of a back edge, it is the "top" of a loop and is a successor of the preheader of the loop.
- Each block has a list of expressions.
- the expressions have pointers to operand expressions earlier in the block.
- the control flow graph may have a special memory operation called a "merge node" (also known as a "phi function") at the beginning of blocks.
- a merge node for a variable indicates that the predecessor blocks of the block containing the merge node are reached by different "dominating definitions" of the variable.
- a domination definition of a path of execution is the definition for a load that is closest to the load on that path of execution.
- a merge node is a definition of the variable.
- the flow control graph of Figure 3 A may have a merge operation stored at the beginning of block 304.
- This merge operation identifies that blocks 302 and 303 have definitions of each expression that is a memory reference (other than a merge operation) has a pointer to the unique memory references that- dominates it and there are no references between those memory references that define the memory. That unique memory reference is the "reaching definition" for the memory reference.
- Each expression of the input control flow graph also has a "global value number" ("vn"). If two expressions have the same value number, then they result in the same value. If a memory reference is a load whose reaching definition is a store, then the load has the same value number as that expression being stored. For example, in the following expression
- a dominating block (“dominator") dominates a dominated block when the blocks are distinct and all paths from the start block of the control flow graph to the dominated block contain the dominating block.
- a dominating block is an immediate dominating block of a dominated block when no other block, that is also dominated by the dominating block, dominates that dominated block.
- the immediate dominator of a block "b" is "dom(b)."
- a post-dominating block post-dominator post-dominates a post- 5 dominated block when the blocks are distinct and all paths from the post-dominated block to the end block of the control flow graph contain the post-dominating block.
- a post-dominating block is an immediate post-dominating block of a post- dominated block when no other block, that is also post-dominated by the post- dominating block, post-dominates that post-dominated block.
- the immediate post- l o dominator of a block "b" is "pdom("b") .
- the depth of a block is the number of dominator blocks of that block.
- the depth of a block may be considered as the level of the block within a "dominator tree.”
- a dominator tree is a representation of the blocks of a flow control graph in which each block has an edge to its immediate dominating block.
- each block only has one immediate dominator, the blocks and the edges form a tree data structure.
- the CM system annotates the expressions of a control flow graph with depth and avail, and annotates the blocks with depth.
- the depth of an expression indicates the depth of highest block in the dominator tree to which the expression 0 can be moved.
- the avail value of an expression indicates the depth of the highest block in the dominator tree to which the expression can be moved with re-writing. If the depth of an expression is less than or equal to the depth of a block (on its path of execution), then that expression can be moved to that block. If the avail of an expression is less than or equal to the depth of a block (on its path of execution), 5 then the expression can be moved to that block with rewriting.
- FIG. 6 is a flow diagram of an example implementation a label_graph routine.
- This routine is passed a control flow graph representing a computer program and calculates depth and avail for each expression in the control flow graph.
- the routine loops selecting each block in a forward traversal of the control flow graph.
- the routine selects each expression within each block and invokes a routine to calculate depth and avail for the selected expression.
- a forward traversal of a flow control graph selects each block that is a tail of a forward edge before selecting the block that is the head of that forward edge.
- step 601 the routine selects the next block during the forward traversal starting with the first block.
- step 602 if all blocks have already been selected, then routine completes, else the routine continues at step 603.
- step 603 the routine selects the next expression of the selected block.
- step 604 if all the expressions of the selected block have already been selected, then the routine loops to step 601 to select the next block, else the routine continues that step 605.
- step 605 the routine invokes the label_expr routine to generate depth and avail for the selected expression. The routine then loops to step 603 to select the next expression of the selected block.
- FIG 7 is a flow diagram of an example implementation of the label_expr routine.
- This routine calculates its depth and avail for a passed expression.
- the routine initializes the depth and avail for the passed expression to zero.
- the routine sets the depth and avail to the maximum of the depth and avail of the operands of the passed expression.
- the depth and avail of an expression can be no less than the maximum depth and avail of its arguments.
- the routine selects the next operand of the passed expression.
- step 703 if all operands have already been selected, then the routine continues to step 705, else the routine continues at step 704.
- step 704 the routine sets the depth of the passed expression to the maximum of the current depth of the passed expression and the depth of the selected operand and sets the avail of the passed expression to the maximum of the current avail of the passed expression and the avail of the selected operand.
- the routine then loops to step 702 to select the next operand.
- step 705 the routine determines whether the passed expression is a load from memory or either a store to memory or a merge. If the passed expression is a load from memory, then the routine continues at step 706. If the passed expression is a store to memory or a merge, then the routine continues at step 711. Otherwise, the routine returns.
- steps 706-710 the routine sets the depth and avail for a load expression based on its reaching definition.
- the avail of the load expression can be set to the avail of the reaching definition.
- the routine selects the reaching definition of the passed expression.
- the routine invokes the value_flow_edge routine to determine whether the avail value of the load can be set to the avail of the reaching definition with re-writing can be located. If the avail value can be set to that of the reaching definition, then the routine continues at step 708, else the routine continues at step 709. In step 708, the routine sets the avail of the passed expression to the avail of the selected reaching definition.
- step 709 the routine sets the avail of the passed expression to the maximum of the current avail of the passed expression and of the depth of the block that contains the selected reaching definition. That is, the load expression cannot be located before its reaching definition even with re- writing.
- step 710 the routine sets the depth of the passed expression to the maximum of the current depth of the passed expression and of the depth of the block that contains the selected reaching definition and then returns. That is, the load expression cannot be located before its reaching definition without re-writing.
- steps 711-715 the routine sets the depth for a store and a merge and sets the avail for a scalar merge. The depth of a store or a merge is the depth of the block that contains the store merge.
- step 711 the routine set the depth of the passed expression to the depth of the block that contains the passed expression.
- step 712 if passed expression is a merge of a scalar, then the routine continues at step 713, else the routine returns.
- steps 713-715 the routine sets the avail of the passed expression to the minimum of its current avail and the minimum of the avail of the reaching definitions whose value number is equal to the value number of the passed expression and that is contained block that already has a depth and avail.
- step 713 the routine selects the next reaching definition whose value number equals the value number of the passed expression and that is contained in a block that already had had its depth and avail calculated.
- step 714 if all such reaching definitions have already been selected, then the routine returns, else the routine continues that step 715.
- step 715 the routine sets the avail of the passed expression equal to the minimum of the current avail of the passed expression and the avail of the selected reaching definitions. The routine then loops to step 713.
- Figure 8 is a flow diagram of the value_flow_edge routine.
- This routine is passed an expression along with the reaching definition for that expression.
- the routine returns as its value an indication of whether the expression can be located with re-writing in the same block as the reaching definition can be located.
- the reaching definition is a merge of a scalar loaded by the passed expression, then the expression can be so located along with its reaching definition and the routine returns a true indication.
- the reaching definition is a store and the expression that generates the stored value has the same value number of the passed expression, then the expression can be so located along with its reaching definition.
- the routine returns a true indication, else the routine returns a false indication.
- the move_value routine uses the depth and avail of an expression and the depth of the blocks to move an expression to a dominating block.
- Figure 9 is a flow diagram of the move_value routine. This routine is passed the expression and the block that dominates that expression. If the depth of the expression is greater than the depth of the passed dominating block, then the routine first moves the operands of the expression to the passed dominating block. The routine then stores the result of the expression in the dominating block and replaces the expression with a load of the stored result. In step 901, if the depth of the passed expression is greater than the depth of the passed block, then the routine continues that step 902, else the routine continues at step 903. In step 902, the routine invokes the move_inputs routine passing the passed expression and the passed block.
- step 903 the routine creates a new variable in which to store the result passed expression.
- step 904 the routine replaces the reference to the passed expression in its previous block with a load of the created variable.
- step 905 the routine moves the passed expression and its operands to the end of the passed block.
- step 906 the routine creates an operation that stores the value of the passed expression into the new variable and inserts that operation after the passed expression in the passed block. The routine then returns an indication of the created store operation.
- Figure 10 is a flow diagram of the move_inputs routine.
- This routine is passed an expression and its dominating block. The routine rewrites the inputs of the passed expression as needed to allow the expression to be moved to the dominating block.
- step 1001 if the passed expression is a memory reference, then the routine continues at step 1002, else the routine continues at step 1005. If the passed expression is a memory reference (e.g., a load), then in step 1002, the routines selects the reaching definition of the passed expression.
- the routine invokes the value_flow_edge routines passing the passed expression and the selected reaching definition. If the result of the invoked routine is true, then the routine continues at step 1004, else the routine continues at step 1005.
- step 1004 the routine invokes the substitute_definition routine passing the passed expression, the selected reaching definition, and the passed block and then returns.
- the substitute definition routine moves the definition of the expression to a reaching definition.
- steps 1005-1008 the routine loops selecting each operand of the passed expression and rewriting it to the passed dominating block. The depth of the operand is greater than the depth of the passed dominating block.
- step 1005 the routine selects the next operand of the passed expression.
- step 1006 if all the operands have already been selected, then the routine returns, else the routine continues at step 1007.
- step 1007 if the depth of the selected operand is greater than the depth of the passed block, then the routine continues that step 1008, else the routine loops to step 1005 to select the next operand.
- step 1008 the routine invokes the move_value routine passing the selected operand and the passed block. The routine then loops to step 1005 to select the next operand.
- Figure 11 is a flow diagram of the substitute_definition routine.
- This routine is passed expression, its reaching definition, and the block to which the expression is to be moved.
- the routine identifies a substitute reaching definition for the passed reaching definition.
- steps 1101-1102 if the passed reaching definition is a merge, the routine selects the first reaching definition in a chain of reaching definitions whose depth is less than or equal to the passed block or is not a merge.
- the routine first selects the passed reaching definition.
- step 1 101 if the selected reaching definition is a merge and the depth of the selected reaching definition is greater than the depth of the passed block, then the routine continues at step 1102, else the routine continues at step 1104.
- step 1102 the routine selects a reaching definition of the currently selected reaching definition such that the block that contains the reaching definition precedes the block of the currently selected reaching definition and the avail of the reaching definition is less than or equal to the avail of the currently selected reaching definition.
- the routine then loops to step 1 101.
- step 1104 if the reaching definition has a depth less than or equal to the depth of the passed block, then the routine continues that step 1105, else the routine continues that step 1106.
- step 1 105 the routine sets the selected reaching definition to be the reaching definition of the passed expression and then returns.
- steps 1106- 1108 the routine sets the selected reaching definition to be a store of the result of an expression whose value number is the same as that of the passed expression and moves the inputs to the expression to the passed block.
- step 1106 the routine sets the selected reaching definition to a store of an expression such that the value number of the expression is the same as the value number of the passed expression.
- step 1107 the routine invokes the move_inputs routine passing the expression of the selected reaching definition and the passed block.
- step 1108 the routine replaces the passed expression with a load of the variable for the newly created expression that stores the value into the variable. The routine then returns.
- the avail and depth values can be used to optimize a computer program in several ways, such as common sub-expression elimination, invariant code motion, and partial redundancy elimination.
- Common sub-expression elimination refers to the replacing of multiple evaluations of an expression by a single evaluation of that expression and modifying those multiple evaluations to access the result of the single evaluation. The following illustrates a portion of a program that can benefit from common sub-expression elimination:
- walk_tree routine makes one pass through the program and performs various optimizations based on the depth and avail of the expressions and the depth of the blocks.
- the routine is described using various terms that are defined in the following.
- a nested region is a set of blocks such that is two regions overlap, then one completely encompasses the other.
- Each block has a pointer ("region(block)") to the smallest (innermost) containing region.
- Each region has a pointer ("outer(region)”) to the smallest containing region.
- the region that contains the start block contains all blocks in the program.
- Each region also has a depth value (“depth(region)”) that indicates the number of regions that contain that region (i.e., the nesting level).
- a direct dominating block (“direct dominator”) of a block is the most immediate dominator of that block such that that block is contained in the innermost region containing the direct dominating block.
- the direct dominator of a block is designated as "dom*(block)."
- a direct post-dominating block (“direct post-dominator”) of a block is the most immediate post-dominator of that block such that that block is contained in the innermost region containing the direct post-dominating block.
- the direct post- dominator of a block is designated as "pdom*(block)."
- Each region has a dominating block ("region_dom(region)”) that directly dominates all blocks in the region and no other block that is directly dominated by this block directly dominates all the blocks in the region.
- Region A is the outermost region and contains all the blocks in the program.
- the depth of region A is 0, and it has no outer region.
- Region A contains regions AA and AB, which are both at depths of 1.
- Region AA contains regions AAA, AAB, and AAC which are each a depths of 2.
- Region AA is the least common region of any combination of regions AAA, AAB, and AAC.
- Region AB contains region ABA at depth 2, which contains region ABAA at depth 3, which contains region ABAAA depth 4.
- the least common region of regions AAC and ABAAA is region A.
- Nested regions include loops, parallel regions, and critical section.
- Parallel region are single-entry and single-exit regions that are identified by either the program or the compiler as being concurrently executable.
- Critical section are single-entry and single exit regions that are associated with exclusive access to a shared resource.
- the direct depth (“ddepth”) of a block as the depth of a block in a direct dominator tree.
- the children of a block is the set of all blocks such that the block is the direct dominator of each child block and the child block is not the direct post- dominator of the block.
- the children of a block is represented by the following equation:
- the next equivalent block of a block is a block that is directly dominated by the block and that is a direct post-dominator of the block.
- the next equivalent block of a block is represented by the following equation:
- the first block of a block is a block that is directly dominates the block and that is directly post-dominated by the block or if there is not such block, the block itself.
- the first block of a block is represented by the following equation:
- Current[] is an array indexed by value number. Each entry points to an expression or a block or contains null.
- Blocks are numbered ("num(block)") such that if a block precedes another block in a forward traversal of the control flow graph (i.e., visited first), then that block has a lower block number than the other block.
- Every expression has a speculation level ("spec(e)”) that corresponds to the number of a block and represents a limit on how early the expression may be speculated.
- spec(e) a speculation level
- Each expression is identified as “safe” or “unsafe” with respect to speculation. For example, integer division by an unknown denominator, stores, and function calls with side effects to memory are unsafe.
- load_safe Each load from memory is marked as “load_safe” or “load_unsafe.”
- loadjmsafe A load that is “loadjmsafe” may be speculated, but no use of that load may be speculated. For example, accesses to static variables and static allocated scalar variables are "load-safe,” whereas accesses via pointers to subscripted arrays are
- the root of a block is the least common direct dominator of the set of successor blocks that do not directly post-dominate the block. This set is represented by the following equation:
- a sink region marks the end of a subgraph that is dominated by a target.
- the definition of a sink is represented by the following equation:
- the reference of a block (“ref(block)") is the set of value number of all expressions that appear in the block.
- the computed set of a block (“comp(block)”) is a safe approximation of the set of value numbers of expressions that need to be evaluated after control reaches the block and before control reach the post-dominator of the block or exits the region of the block.
- the computed set has three types of references: (1) those directly in the block, (2) those that need to occur between the block and its direct post-dominator, and (3) those that occur in or after the direct post-dominator.
- the computed set of a block is represented by the following equation:
- the needed set of a block (“needed(block)") is a subset of the computed set of the block that are needed after the block and before the direct post- dominator of the block.
- the needed set of a block is represented by the following equation:
- the post-computed set of block (“pcomp(block)”) is the set of value numbers of expressions computed in the direct post-dominator of the block if that block is a direct dominator equivalent to the block.
- the post-computed set of a block is represented by the following equation:
- the edge computed set of a block and an expression (“ecomp(b,x)”) filters the information from a successor to present values from being propagated from a sink or from outside a nesting region.
- the above sets can be computed in a single backwards traversal of the control flow graph.
- FIG. 13 is a flow diagram of an example implementation of the fmd_direct_dominator routine.
- This routine finds the direct dominator for the passed block.
- the routine sets the variable d equal to the dominator of the passed block.
- the routine sets the variable 1 equal to the least common region of the region of the passed block and the region of the dominator block of the passed block.
- the routine continues at step 1306, else the routine continues at step 1304.
- routine sets the variable d to the value of its dominator.
- the routine sets the variable 1 to the least command region of it and the region of the variable d.
- the routine then loops to step 1303.
- the routine sets the direct dominator of the passed block to the block identified by variable d and returns.
- Figure 14 is a flow diagram of an example implementation of the find_direct_ post_dominator routine.
- This routine finds the direct post-dominator for the passed block.
- the routine sets the variable p equal to the post- dominator of the passed block.
- the routine sets the variable 1 equal to the least common region of the region of the passed block and region of the post- dominator block of the passed block.
- the routine continues at step 1406, else the routine continues at step 1404.
- routine sets the variable p to the value of its post-dominator.
- the routine sets the variable 1 to the least common region of it and the region of the variable p.
- the routine then loops to step 1403.
- the routine sets the direct post-dominator of the passed block to the block identified variable p and returns.
- Figure 15 is a flow diagram of an example implementation of the least_common_region routine.
- This routine is passed two regions and determines the least common enclosing region.
- steps 1501-1502 the routine selects the innermost, outer region of the first region whose depth is not greater than the depth of the second region.
- step 1501 if the depth of the first region is greater than the depth of the second region, then the routine continues at step 1502, else the routine continues at step 1503.
- the routine sets the first region to its outer region and loops to step 1501.
- steps 1503-1504 the routine selects the innermost, outer region of the second whose depth is not greater than the depth of the first region.
- step 1502 if the depth of the second region is greater than the depth of the first region, then the routine continues at step 1504, else the routine continues at step 1505.
- step 1504 the routine sets the second region equal to its outer region and loops to step 1503.
- steps 1505-1506 the routine loops until the least common region is identified.
- step 1505 if the first region equals the second region, then the routine returns, else the routine continues at step 1506.
- step 1506 the routine sets the first region to its outer region and the second region its outer region and loops to step 1505.
- Figure 16 is a flow diagram of an example implementation of the least_common_direct_dominator routine. This routine is passed two blocks and finds the least common direct dominator of the passed blocks.
- steps 1601-1602 the routine selects the direct dominator of the first block whose direct depth is not greater than the direct depth of the second block.
- step 1601 if the direct depth of the first block one is greater than the direct depth of the second block, then the routine continues at step 1602, else the routine continues it step 1603.
- step 1602 routine selects as the first block the direct dominator of the first block and loops to step 1601.
- steps 1603-1604 the routine selects the direct dominator of the second block whose direct depth is not greater than the direct depth of the first block.
- step 1603 if the direct depth of the second block is greater then the direct depth of the first block, the routine continues at step 1604, else the routine continues at step 1605.
- step 1604 the routine selects as the second block the direct dominator of the second block and loops to step 1603.
- steps 1605-1606 the routine finds the least common direct dominator of the first and second blocks.
- step 1605 if the first block equals the second block, then the routine returns that block as the least common direct dominator, else the routine continues at step 1606.
- step 1606 the routine selects as the first block its direct dominator and selects as the second block its direct dominator and loops to step 1605.
- FIG 17 is a flow diagram of an example implementation of the walk_tree routine.
- This routine walks the direct dominator tree and walks equivalent direct post-dominators before children.
- This routine is passed a block.
- the routine invokes the routine walk_in routine.
- the routine selects the passed block.
- the routine selects the next child of the currently selected block.
- the routine continues at step 1706, else the routine continues at step 1705.
- step 1705 the routine recursively invokes the walk_tree routine and loops to step 1703 to select the next child of the selected block.
- step 1706 the routine selects the next equivalent block of the selected block.
- step 1707 if all the equivalent blocks have already been selected, then the routine continues at step 1708, else the routine loops to step 1703 to select the next child of the selected block.
- step 1708 the routine invokes the walk_out routine passing the passed block. The routine then completes.
- FIG. 18 is a flow diagram of an example implementation of the walk_in routine.
- This routine is passed a block. This routine notes the available values and attempts to move code or eliminate common sub expressions.
- the routine invokes the visit_ops routine passing the passed block.
- the routine invokes the visit_ops routine passing the passed block.
- step 1802 if there is no next equivalent block of the passed block, then the routine continues at step 1804, else the routine continues at step .1803.
- the routine invokes the walk_in routine passing the next equivalent block of the passed block.
- step 1804 if the passed block is a target, then the routine continues at step 1805, else the routine returns.
- steps 1805-1808 the routine loops processing the needed values of the selected block.
- step 1806 if all such values have already- been selected, then the routine returns, else the routine continues at step 1807.
- step 1807 if the current of the selected value is null, then the routine continues at step 1808, else the routine loops to step 1805 to select the next value.
- step 1808 the routine sets current of the value equal to the passed block and loops to step 1805 to select the next value.
- Figure 19 is a flow diagram of an example implementation of the walk_out routine.
- This routine is passed a block and clears the available values for the passed block.
- step 1901 if there are no next equivalent blocks of the passed block, then the routine continues in step 1903, else the routine continues at step 1902.
- step 1902 the routine recursively invokes the walk_out routine passing the next equivalent block of the passed block.
- step 1903 if the passed block is a target, then the routine continues at step 1904, else the routine continues at step 1908.
- steps 1904-1907 the routine loops selecting the needed values of the passed block.
- step 1904 the routine selects the next needed value of the passed block.
- step 1905 if all such needed values and have already been selected, then the routine continues at step 1908, else the routine continues at step 1906.
- step 1906 if the current of the selected needed value is equal to the passed block, then the routine continues at step 1907, else the routine loops to step 1904 to select the next needed value.
- step 1907 the routine sets the current for the selected needed value to null and loops to step 1904 to select the next needed value.
- steps 1908- 1911 the routine loops processing each of the operations in the passed block.
- step 1908 the routine selects the next operation in the passed block.
- step 1909 if all such operations have already been selected, then the routine returns, else the routine continues to step 1910.
- step 1910 if the current for the value number of the expression is equal to the expression, then the routine sets the current of the value number of the expression equal to null in step 1911. The routine then loops to step 1908 to select the next operation.
- Figure 20 is an example implementation of the visit_ops routine.
- This routine attempts to find a better placement for the expressions in the passed block. If the routine does not move an expression, then it records that the expression may be a candidate for a common sub-expression elimination.
- the routine selects the next expression in the passed block.
- the routine if all such expressions have already been selected, then the routine returns, else the routine continues at step 2003.
- the routine invokes the propagate_speculation routine passing the selected expression.
- step 2004, if the selected expression is movable then the routine continues at step 2005, else the routine loops to step 2001 to select the next expression.
- the routine invokes the attempt_to_move routine passing the selected expression and then loops to step 2001 to select the next expression.
- Figure 21 is a flow diagram of an example implementation of the propagate_speculation routine.
- This routine determines the limits of speculation for the passed expression based on the limits of its inputs. If the passed expression is a merge or a load, then the routine considers the limits of the reaching definitions since the move_value routine attempts to move those reaching definitions. In step 2101, if the expression is unsafe and not a store or merge, then the routine continues at step 2102, else the routine continues at step 2103. In step 2102, the routine sets the spec of the expression to num(first(block(e))) and then returns. In step 2103, the routine sets the spec of the passed expression to zero. In step 2104, if the passed expression is a merge, then the routine continues at step 2107.
- step 2105 the routine selects the reaching definition of the passed expression.
- step 2106 the routine sets the spec of the passed expression to the maximum of the current spec of the passed expression and the spec of the selected reaching definition.
- steps 2107-2110 the routine loops processing all reaching definitions of the merge.
- step 2107 the routine selects the next reaching definition of the passed expression.
- step 2108 if all such reaching definitions have already been selected, then the routine continues at step 211 1, else the routine continues at step 2109.
- step 2109 if the avail of the selected reaching definition is less than or equal to the avail of the passed expression, then the routine continues at step 2110, else the routine loops to step 2107 to select the next reaching definition.
- step 2110 the routine sets the spec of the passed expression to the maximum of the current value of the spec of the passed expression and the spec of the reaching definition. The routine then loops to step 2107 to select the next reaching definition.
- steps 21 11-2114 the routine loops processing each operand of the passed expression.
- step 2111 the routine selects of the next operand of the passed expression.
- step 2112 if all such operands have already been selected, then the routine returns.
- step 2113 if the selected operand is a load which is load unsafe, then the routine continues it step 21 15, else the routine continues at step 2114.
- step 2114 the routine sets the spec of the passed expression equal to the maximum of the current spec of the passed expression and the spec of the selected operand and loops to step 2111 to select the next operand.
- step 2115 the routine sets the spec of the passed expression equal to num(first(block(e))) and returns.
- Figure 22 is a flow diagram of an example implementation of the spec_reg routine.
- This routine determines the outermost point with the lowest frequency where the passed expression can be speculated.
- the routine sets the variable last equal to null.
- the routine sets the variable next equal to region_dom(region(block(e)) and initializes the variable last_freq to the frequency of the block containing the proposed expression.
- step 2203 if the variable next is not equal to null and the number of next is greater than the spec of the passed expression and the passed expression is available at next, then the routine returns the variable last, else the routine continues at step 2204.
- step 2204 if the frequency of next is less than the variable last_freq, then the routine continues at step 2205, else the routine loops to step 2203.
- step 2205 the routine sets the variable last equal to the variable next, sets the variable last_freq to the frequency of the block last, and loops to step 2203.
- Figure 23 is a flow diagram of an example implementation of the attempt_to_move routine.
- This routine is passed an expression and attempts to move the expression speculatively to a point where it is needed or to eliminate its common sub expression with another expression.
- the routine sets the variable c equal to the current of the value number of the passed expression and sets the variable s equal to the spec_reg of the passed expression.
- the routine sets the variable cd equal to the block of the passed expression in step 2305. If the variable c is an expression, then the routine sets the variable cd to the block of the variable c in step 2303. Otherwise, the routine sets the variable cd equal to the variable c in step 2304.
- step 2306 if the variable s equals null, then the routine sets the variable sb equal to the block of the passed expression in step 2308, else the routine sets the variable sb to the variable s in step 2307.
- step 2309 the routine sets the variable lb equal to the least_common_direct_dominator of variable cd and variable sb.
- step 2310 if the variable c is an expression and is available at variable lb, then the routine continues at step 2311. Otherwise, if the passed expression is not available at lb or the block of the passed expression e is equal to variable lb then the routine continues at step 2314. Otherwise, the routine continues at step 2315.
- step 2311 if the block of the variable c is equal to the variable lb, then the routine continues at step 2313, else the routine continues at step 2312.
- step 2312 the routine moves the value of variable c to variable lb and sets the current of the value number of the passed expression to the variable c.
- step 2313 the routine invokes the use_value routine passing the passed expression and the variable c and then returns.
- step 2314 the routine sets the current of the value number of the passed expression equal to do the passed expression and then returns.
- step 2315 the routine moves the value of the passed expression to variable lb and sets the current value of the passed expression equal to the passed expression.
- step 2316 if the variable c is an expression, then. the routine continues at step 2317, else the routine returns.
- step 2317 the routine invoke the use_value routine passing the variable c and the passed expression and then returns.
- Figure 24 is flow diagram of an example implementation of the use_value routine.
- the routine stores the passed variable c into a simple variable.
- the routine replaces the passed expression with a load of simple variable.
- the routine marks the store as a reaching definition of the load.
- the routine sets the spec for the new store to the spec of the variable c and then returns.
- Figure 25 is a flow diagram of an example implementation of the movable routine. This routine returns a value of true if the passed expression is movable. In step 2501, if the passed expression is a store or a merge, or a load of the simple variable, then the routine returns false, else the routine returns true.
- the traversal order of the direct dominator tree is illustrated by the following:
- walk ree(Bl) walk_in(Bl) walk_in(B3) /* current[vn(a+b)] is set walk_tree(B2) walk_in(B2) /* the common sub-expression is eliminated walk_out(B2) walk_out(Bl) walk_out(B2)
- block B1 and block B2 are in an inner loop (and hence inner region) compared to block B3.
- the processing is similar to that of the above example, but block B0 is the least common direct dominator of blocks B2 and B3.
- the expression "a+b" is placed outside of the loop as shown by the following:
- block B6 is the post-dominator block B I . Since block BI dominates both successor blocks B2 and B3, block BI is a target and block B6 is a sink. The needed set of both blocks B 1 and B2 contains the value number of expression el . However, a copy of el is placed only in block BI since it dominates its successors.
Abstract
Description
Claims
Priority Applications (2)
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AU27146/00A AU2714600A (en) | 1998-12-23 | 1999-12-22 | Method and system for identifying locations to move portions of the computer program |
EP99968955.7A EP1141825B1 (en) | 1998-12-23 | 1999-12-22 | Method and system for identifying locations to move portions of the computer program |
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US09/221,031 US6415433B1 (en) | 1998-12-23 | 1998-12-23 | Method and system for identifying locations to move portions of the computer program |
US09/221,031 | 1998-12-23 |
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US9250879B2 (en) * | 2012-07-02 | 2016-02-02 | International Business Machines Corporation | Strength reduction compiler optimizations |
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Also Published As
Publication number | Publication date |
---|---|
EP1141825B1 (en) | 2013-04-17 |
WO2000038058A3 (en) | 2000-11-02 |
EP1141825A2 (en) | 2001-10-10 |
AU2714600A (en) | 2000-07-12 |
US6415433B1 (en) | 2002-07-02 |
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