@c Copyright (c) 2004, 2005 Free Software Foundation, Inc. @c Free Software Foundation, Inc. @c This is part of the GCC manual. @c For copying conditions, see the file gcc.texi. @c --------------------------------------------------------------------- @c Tree SSA @c --------------------------------------------------------------------- @node Tree SSA @chapter Analysis and Optimization of GIMPLE Trees @cindex Tree SSA @cindex Optimization infrastructure for GIMPLE GCC uses three main intermediate languages to represent the program during compilation: GENERIC, GIMPLE and RTL@. GENERIC is a language-independent representation generated by each front end. It is used to serve as an interface between the parser and optimizer. GENERIC is a common representation that is able to represent programs written in all the languages supported by GCC@. GIMPLE and RTL are used to optimize the program. GIMPLE is used for target and language independent optimizations (e.g., inlining, constant propagation, tail call elimination, redundancy elimination, etc). Much like GENERIC, GIMPLE is a language independent, tree based representation. However, it differs from GENERIC in that the GIMPLE grammar is more restrictive: expressions contain no more than 3 operands (except function calls), it has no control flow structures and expressions with side-effects are only allowed on the right hand side of assignments. See the chapter describing GENERIC and GIMPLE for more details. This chapter describes the data structures and functions used in the GIMPLE optimizers (also known as ``tree optimizers'' or ``middle end''). In particular, it focuses on all the macros, data structures, functions and programming constructs needed to implement optimization passes for GIMPLE@. @menu * GENERIC:: A high-level language-independent representation. * GIMPLE:: A lower-level factored tree representation. * Annotations:: Attributes for statements and variables. * Statement Operands:: Variables referenced by GIMPLE statements. * SSA:: Static Single Assignment representation. * Alias analysis:: Representing aliased loads and stores. @end menu @node GENERIC @section GENERIC @cindex GENERIC The purpose of GENERIC is simply to provide a language-independent way of representing an entire function in trees. To this end, it was necessary to add a few new tree codes to the back end, but most everything was already there. If you can express it with the codes in @code{gcc/tree.def}, it's GENERIC@. Early on, there was a great deal of debate about how to think about statements in a tree IL@. In GENERIC, a statement is defined as any expression whose value, if any, is ignored. A statement will always have @code{TREE_SIDE_EFFECTS} set (or it will be discarded), but a non-statement expression may also have side effects. A @code{CALL_EXPR}, for instance. It would be possible for some local optimizations to work on the GENERIC form of a function; indeed, the adapted tree inliner works fine on GENERIC, but the current compiler performs inlining after lowering to GIMPLE (a restricted form described in the next section). Indeed, currently the frontends perform this lowering before handing off to @code{tree_rest_of_compilation}, but this seems inelegant. If necessary, a front end can use some language-dependent tree codes in its GENERIC representation, so long as it provides a hook for converting them to GIMPLE and doesn't expect them to work with any (hypothetical) optimizers that run before the conversion to GIMPLE@. The intermediate representation used while parsing C and C++ looks very little like GENERIC, but the C and C++ gimplifier hooks are perfectly happy to take it as input and spit out GIMPLE@. @node GIMPLE @section GIMPLE @cindex GIMPLE GIMPLE is a simplified subset of GENERIC for use in optimization. The particular subset chosen (and the name) was heavily influenced by the SIMPLE IL used by the McCAT compiler project at McGill University, though we have made some different choices. For one thing, SIMPLE doesn't support @code{goto}; a production compiler can't afford that kind of restriction. GIMPLE retains much of the structure of the parse trees: lexical scopes are represented as containers, rather than markers. However, expressions are broken down into a 3-address form, using temporary variables to hold intermediate values. Also, control structures are lowered to gotos. In GIMPLE no container node is ever used for its value; if a @code{COND_EXPR} or @code{BIND_EXPR} has a value, it is stored into a temporary within the controlled blocks, and that temporary is used in place of the container. The compiler pass which lowers GENERIC to GIMPLE is referred to as the @samp{gimplifier}. The gimplifier works recursively, replacing complex statements with sequences of simple statements. @c Currently, the only way to @c tell whether or not an expression is in GIMPLE form is by recursively @c examining it; in the future there will probably be a flag to help avoid @c redundant work. FIXME FIXME @menu * Interfaces:: * Temporaries:: * GIMPLE Expressions:: * Statements:: * GIMPLE Example:: * Rough GIMPLE Grammar:: @end menu @node Interfaces @subsection Interfaces @cindex gimplification The tree representation of a function is stored in @code{DECL_SAVED_TREE}. It is lowered to GIMPLE by a call to @code{gimplify_function_tree}. If a front end wants to include language-specific tree codes in the tree representation which it provides to the back end, it must provide a definition of @code{LANG_HOOKS_GIMPLIFY_EXPR} which knows how to convert the front end trees to GIMPLE@. Usually such a hook will involve much of the same code for expanding front end trees to RTL@. This function can return fully lowered GIMPLE, or it can return GENERIC trees and let the main gimplifier lower them the rest of the way; this is often simpler. GIMPLE that is not fully lowered is known as ``high GIMPLE'' and consists of the IL before the pass @code{pass_lower_cf}. High GIMPLE still contains lexical scopes and nested expressions, while low GIMPLE exposes all of the implicit jumps for control expressions like @code{COND_EXPR}. The C and C++ front ends currently convert directly from front end trees to GIMPLE, and hand that off to the back end rather than first converting to GENERIC@. Their gimplifier hooks know about all the @code{_STMT} nodes and how to convert them to GENERIC forms. There was some work done on a genericization pass which would run first, but the existence of @code{STMT_EXPR} meant that in order to convert all of the C statements into GENERIC equivalents would involve walking the entire tree anyway, so it was simpler to lower all the way. This might change in the future if someone writes an optimization pass which would work better with higher-level trees, but currently the optimizers all expect GIMPLE@. A front end which wants to use the tree optimizers (and already has some sort of whole-function tree representation) only needs to provide a definition of @code{LANG_HOOKS_GIMPLIFY_EXPR}, call @code{gimplify_function_tree} to lower to GIMPLE, and then hand off to @code{tree_rest_of_compilation} to compile and output the function. You can tell the compiler to dump a C-like representation of the GIMPLE form with the flag @option{-fdump-tree-gimple}. @node Temporaries @subsection Temporaries @cindex Temporaries When gimplification encounters a subexpression which is too complex, it creates a new temporary variable to hold the value of the subexpression, and adds a new statement to initialize it before the current statement. These special temporaries are known as @samp{expression temporaries}, and are allocated using @code{get_formal_tmp_var}. The compiler tries to always evaluate identical expressions into the same temporary, to simplify elimination of redundant calculations. We can only use expression temporaries when we know that it will not be reevaluated before its value is used, and that it will not be otherwise modified@footnote{These restrictions are derived from those in Morgan 4.8.}. Other temporaries can be allocated using @code{get_initialized_tmp_var} or @code{create_tmp_var}. Currently, an expression like @code{a = b + 5} is not reduced any further. We tried converting it to something like @smallexample T1 = b + 5; a = T1; @end smallexample but this bloated the representation for minimal benefit. However, a variable which must live in memory cannot appear in an expression; its value is explicitly loaded into a temporary first. Similarly, storing the value of an expression to a memory variable goes through a temporary. @node GIMPLE Expressions @subsection Expressions @cindex GIMPLE Expressions In general, expressions in GIMPLE consist of an operation and the appropriate number of simple operands; these operands must either be a GIMPLE rvalue (@code{is_gimple_val}), i.e.@: a constant or a register variable. More complex operands are factored out into temporaries, so that @smallexample a = b + c + d @end smallexample becomes @smallexample T1 = b + c; a = T1 + d; @end smallexample The same rule holds for arguments to a @code{CALL_EXPR}. The target of an assignment is usually a variable, but can also be an @code{INDIRECT_REF} or a compound lvalue as described below. @menu * Compound Expressions:: * Compound Lvalues:: * Conditional Expressions:: * Logical Operators:: @end menu @node Compound Expressions @subsubsection Compound Expressions @cindex Compound Expressions The left-hand side of a C comma expression is simply moved into a separate statement. @node Compound Lvalues @subsubsection Compound Lvalues @cindex Compound Lvalues Currently compound lvalues involving array and structure field references are not broken down; an expression like @code{a.b[2] = 42} is not reduced any further (though complex array subscripts are). This restriction is a workaround for limitations in later optimizers; if we were to convert this to @smallexample T1 = &a.b; T1[2] = 42; @end smallexample alias analysis would not remember that the reference to @code{T1[2]} came by way of @code{a.b}, so it would think that the assignment could alias another member of @code{a}; this broke @code{struct-alias-1.c}. Future optimizer improvements may make this limitation unnecessary. @node Conditional Expressions @subsubsection Conditional Expressions @cindex Conditional Expressions A C @code{?:} expression is converted into an @code{if} statement with each branch assigning to the same temporary. So, @smallexample a = b ? c : d; @end smallexample becomes @smallexample if (b) T1 = c; else T1 = d; a = T1; @end smallexample Tree level if-conversion pass re-introduces @code{?:} expression, if appropriate. It is used to vectorize loops with conditions using vector conditional operations. Note that in GIMPLE, @code{if} statements are also represented using @code{COND_EXPR}, as described below. @node Logical Operators @subsubsection Logical Operators @cindex Logical Operators Except when they appear in the condition operand of a @code{COND_EXPR}, logical `and' and `or' operators are simplified as follows: @code{a = b && c} becomes @smallexample T1 = (bool)b; if (T1) T1 = (bool)c; a = T1; @end smallexample Note that @code{T1} in this example cannot be an expression temporary, because it has two different assignments. @node Statements @subsection Statements @cindex Statements Most statements will be assignment statements, represented by @code{MODIFY_EXPR}. A @code{CALL_EXPR} whose value is ignored can also be a statement. No other C expressions can appear at statement level; a reference to a volatile object is converted into a @code{MODIFY_EXPR}. In GIMPLE form, type of @code{MODIFY_EXPR} is not meaningful. Instead, use type of LHS or RHS@. There are also several varieties of complex statements. @menu * Blocks:: * Statement Sequences:: * Empty Statements:: * Loops:: * Selection Statements:: * Jumps:: * Cleanups:: * GIMPLE Exception Handling:: @end menu @node Blocks @subsubsection Blocks @cindex Blocks Block scopes and the variables they declare in GENERIC and GIMPLE are expressed using the @code{BIND_EXPR} code, which in previous versions of GCC was primarily used for the C statement-expression extension. Variables in a block are collected into @code{BIND_EXPR_VARS} in declaration order. Any runtime initialization is moved out of @code{DECL_INITIAL} and into a statement in the controlled block. When gimplifying from C or C++, this initialization replaces the @code{DECL_STMT}. Variable-length arrays (VLAs) complicate this process, as their size often refers to variables initialized earlier in the block. To handle this, we currently split the block at that point, and move the VLA into a new, inner @code{BIND_EXPR}. This strategy may change in the future. @code{DECL_SAVED_TREE} for a GIMPLE function will always be a @code{BIND_EXPR} which contains declarations for the temporary variables used in the function. A C++ program will usually contain more @code{BIND_EXPR}s than there are syntactic blocks in the source code, since several C++ constructs have implicit scopes associated with them. On the other hand, although the C++ front end uses pseudo-scopes to handle cleanups for objects with destructors, these don't translate into the GIMPLE form; multiple declarations at the same level use the same @code{BIND_EXPR}. @node Statement Sequences @subsubsection Statement Sequences @cindex Statement Sequences Multiple statements at the same nesting level are collected into a @code{STATEMENT_LIST}. Statement lists are modified and traversed using the interface in @samp{tree-iterator.h}. @node Empty Statements @subsubsection Empty Statements @cindex Empty Statements Whenever possible, statements with no effect are discarded. But if they are nested within another construct which cannot be discarded for some reason, they are instead replaced with an empty statement, generated by @code{build_empty_stmt}. Initially, all empty statements were shared, after the pattern of the Java front end, but this caused a lot of trouble in practice. An empty statement is represented as @code{(void)0}. @node Loops @subsubsection Loops @cindex Loops At one time loops were expressed in GIMPLE using @code{LOOP_EXPR}, but now they are lowered to explicit gotos. @node Selection Statements @subsubsection Selection Statements @cindex Selection Statements A simple selection statement, such as the C @code{if} statement, is expressed in GIMPLE using a void @code{COND_EXPR}. If only one branch is used, the other is filled with an empty statement. Normally, the condition expression is reduced to a simple comparison. If it is a shortcut (@code{&&} or @code{||}) expression, however, we try to break up the @code{if} into multiple @code{if}s so that the implied shortcut is taken directly, much like the transformation done by @code{do_jump} in the RTL expander. A @code{SWITCH_EXPR} in GIMPLE contains the condition and a @code{TREE_VEC} of @code{CASE_LABEL_EXPR}s describing the case values and corresponding @code{LABEL_DECL}s to jump to. The body of the @code{switch} is moved after the @code{SWITCH_EXPR}. @node Jumps @subsubsection Jumps @cindex Jumps Other jumps are expressed by either @code{GOTO_EXPR} or @code{RETURN_EXPR}. The operand of a @code{GOTO_EXPR} must be either a label or a variable containing the address to jump to. The operand of a @code{RETURN_EXPR} is either @code{NULL_TREE} or a @code{MODIFY_EXPR} which sets the return value. It would be nice to move the @code{MODIFY_EXPR} into a separate statement, but the special return semantics in @code{expand_return} make that difficult. It may still happen in the future, perhaps by moving most of that logic into @code{expand_assignment}. @node Cleanups @subsubsection Cleanups @cindex Cleanups Destructors for local C++ objects and similar dynamic cleanups are represented in GIMPLE by a @code{TRY_FINALLY_EXPR}. @code{TRY_FINALLY_EXPR} has two operands, both of which are a sequence of statements to execute. The first sequence is executed. When it completes the second sequence is executed. The first sequence may complete in the following ways: @enumerate @item Execute the last statement in the sequence and fall off the end. @item Execute a goto statement (@code{GOTO_EXPR}) to an ordinary label outside the sequence. @item Execute a return statement (@code{RETURN_EXPR}). @item Throw an exception. This is currently not explicitly represented in GIMPLE. @end enumerate The second sequence is not executed if the first sequence completes by calling @code{setjmp} or @code{exit} or any other function that does not return. The second sequence is also not executed if the first sequence completes via a non-local goto or a computed goto (in general the compiler does not know whether such a goto statement exits the first sequence or not, so we assume that it doesn't). After the second sequence is executed, if it completes normally by falling off the end, execution continues wherever the first sequence would have continued, by falling off the end, or doing a goto, etc. @code{TRY_FINALLY_EXPR} complicates the flow graph, since the cleanup needs to appear on every edge out of the controlled block; this reduces the freedom to move code across these edges. Therefore, the EH lowering pass which runs before most of the optimization passes eliminates these expressions by explicitly adding the cleanup to each edge. Rethrowing the exception is represented using @code{RESX_EXPR}. @node GIMPLE Exception Handling @subsubsection Exception Handling @cindex GIMPLE Exception Handling Other exception handling constructs are represented using @code{TRY_CATCH_EXPR}. @code{TRY_CATCH_EXPR} has two operands. The first operand is a sequence of statements to execute. If executing these statements does not throw an exception, then the second operand is ignored. Otherwise, if an exception is thrown, then the second operand of the @code{TRY_CATCH_EXPR} is checked. The second operand may have the following forms: @enumerate @item A sequence of statements to execute. When an exception occurs, these statements are executed, and then the exception is rethrown. @item A sequence of @code{CATCH_EXPR} expressions. Each @code{CATCH_EXPR} has a list of applicable exception types and handler code. If the thrown exception matches one of the caught types, the associated handler code is executed. If the handler code falls off the bottom, execution continues after the original @code{TRY_CATCH_EXPR}. @item An @code{EH_FILTER_EXPR} expression. This has a list of permitted exception types, and code to handle a match failure. If the thrown exception does not match one of the allowed types, the associated match failure code is executed. If the thrown exception does match, it continues unwinding the stack looking for the next handler. @end enumerate Currently throwing an exception is not directly represented in GIMPLE, since it is implemented by calling a function. At some point in the future we will want to add some way to express that the call will throw an exception of a known type. Just before running the optimizers, the compiler lowers the high-level EH constructs above into a set of @samp{goto}s, magic labels, and EH regions. Continuing to unwind at the end of a cleanup is represented with a @code{RESX_EXPR}. @node GIMPLE Example @subsection GIMPLE Example @cindex GIMPLE Example @smallexample struct A @{ A(); ~A(); @}; int i; int g(); void f() @{ A a; int j = (--i, i ? 0 : 1); for (int x = 42; x > 0; --x) @{ i += g()*4 + 32; @} @} @end smallexample becomes @smallexample void f() @{ int i.0; int T.1; int iftmp.2; int T.3; int T.4; int T.5; int T.6; @{ struct A a; int j; __comp_ctor (&a); try @{ i.0 = i; T.1 = i.0 - 1; i = T.1; i.0 = i; if (i.0 == 0) iftmp.2 = 1; else iftmp.2 = 0; j = iftmp.2; @{ int x; x = 42; goto test; loop:; T.3 = g (); T.4 = T.3 * 4; i.0 = i; T.5 = T.4 + i.0; T.6 = T.5 + 32; i = T.6; x = x - 1; test:; if (x > 0) goto loop; else goto break_; break_:; @} @} finally @{ __comp_dtor (&a); @} @} @} @end smallexample @node Rough GIMPLE Grammar @subsection Rough GIMPLE Grammar @cindex Rough GIMPLE Grammar @smallexample function : FUNCTION_DECL DECL_SAVED_TREE -> compound-stmt compound-stmt: STATEMENT_LIST members -> stmt stmt : block | if-stmt | switch-stmt | goto-stmt | return-stmt | resx-stmt | label-stmt | try-stmt | modify-stmt | call-stmt block : BIND_EXPR BIND_EXPR_VARS -> chain of DECLs BIND_EXPR_BLOCK -> BLOCK BIND_EXPR_BODY -> compound-stmt if-stmt : COND_EXPR op0 -> condition op1 -> compound-stmt op2 -> compound-stmt switch-stmt : SWITCH_EXPR op0 -> val op1 -> NULL op2 -> TREE_VEC of CASE_LABEL_EXPRs The CASE_LABEL_EXPRs are sorted by CASE_LOW, and default is last. goto-stmt : GOTO_EXPR op0 -> LABEL_DECL | val return-stmt : RETURN_EXPR op0 -> return-value return-value : NULL | RESULT_DECL | MODIFY_EXPR op0 -> RESULT_DECL op1 -> lhs resx-stmt : RESX_EXPR label-stmt : LABEL_EXPR op0 -> LABEL_DECL try-stmt : TRY_CATCH_EXPR op0 -> compound-stmt op1 -> handler | TRY_FINALLY_EXPR op0 -> compound-stmt op1 -> compound-stmt handler : catch-seq | EH_FILTER_EXPR | compound-stmt catch-seq : STATEMENT_LIST members -> CATCH_EXPR modify-stmt : MODIFY_EXPR op0 -> lhs op1 -> rhs call-stmt : CALL_EXPR op0 -> val | OBJ_TYPE_REF op1 -> call-arg-list call-arg-list: TREE_LIST members -> lhs | CONST addr-expr-arg: ID | compref addressable : addr-expr-arg | indirectref with-size-arg: addressable | call-stmt indirectref : INDIRECT_REF op0 -> val lhs : addressable | bitfieldref | WITH_SIZE_EXPR op0 -> with-size-arg op1 -> val min-lval : ID | indirectref bitfieldref : BIT_FIELD_REF op0 -> inner-compref op1 -> CONST op2 -> var compref : inner-compref | TARGET_MEM_REF op0 -> ID op1 -> val op2 -> val op3 -> CONST op4 -> CONST | REALPART_EXPR op0 -> inner-compref | IMAGPART_EXPR op0 -> inner-compref inner-compref: min-lval | COMPONENT_REF op0 -> inner-compref op1 -> FIELD_DECL op2 -> val | ARRAY_REF op0 -> inner-compref op1 -> val op2 -> val op3 -> val | ARRAY_RANGE_REF op0 -> inner-compref op1 -> val op2 -> val op3 -> val | VIEW_CONVERT_EXPR op0 -> inner-compref condition : val | RELOP op0 -> val op1 -> val val : ID | CONST rhs : lhs | CONST | call-stmt | ADDR_EXPR op0 -> addr-expr-arg | UNOP op0 -> val | BINOP op0 -> val op1 -> val | RELOP op0 -> val op1 -> val | COND_EXPR op0 -> condition op1 -> val op2 -> val @end smallexample @node Annotations @section Annotations @cindex annotations The optimizers need to associate attributes with statements and variables during the optimization process. For instance, we need to know what basic block a statement belongs to or whether a variable has aliases. All these attributes are stored in data structures called annotations which are then linked to the field @code{ann} in @code{struct tree_common}. Presently, we define annotations for statements (@code{stmt_ann_t}), variables (@code{var_ann_t}) and SSA names (@code{ssa_name_ann_t}). Annotations are defined and documented in @file{tree-flow.h}. @node Statement Operands @section Statement Operands @cindex operands @cindex virtual operands @cindex real operands @findex update_stmt Almost every GIMPLE statement will contain a reference to a variable or memory location. Since statements come in different shapes and sizes, their operands are going to be located at various spots inside the statement's tree. To facilitate access to the statement's operands, they are organized into lists associated inside each statement's annotation. Each element in an operand list is a pointer to a @code{VAR_DECL}, @code{PARM_DECL} or @code{SSA_NAME} tree node. This provides a very convenient way of examining and replacing operands. Data flow analysis and optimization is done on all tree nodes representing variables. Any node for which @code{SSA_VAR_P} returns nonzero is considered when scanning statement operands. However, not all @code{SSA_VAR_P} variables are processed in the same way. For the purposes of optimization, we need to distinguish between references to local scalar variables and references to globals, statics, structures, arrays, aliased variables, etc. The reason is simple, the compiler can gather complete data flow information for a local scalar. On the other hand, a global variable may be modified by a function call, it may not be possible to keep track of all the elements of an array or the fields of a structure, etc. The operand scanner gathers two kinds of operands: @dfn{real} and @dfn{virtual}. An operand for which @code{is_gimple_reg} returns true is considered real, otherwise it is a virtual operand. We also distinguish between uses and definitions. An operand is used if its value is loaded by the statement (e.g., the operand at the RHS of an assignment). If the statement assigns a new value to the operand, the operand is considered a definition (e.g., the operand at the LHS of an assignment). Virtual and real operands also have very different data flow properties. Real operands are unambiguous references to the full object that they represent. For instance, given @smallexample @{ int a, b; a = b @} @end smallexample Since @code{a} and @code{b} are non-aliased locals, the statement @code{a = b} will have one real definition and one real use because variable @code{b} is completely modified with the contents of variable @code{a}. Real definition are also known as @dfn{killing definitions}. Similarly, the use of @code{a} reads all its bits. In contrast, virtual operands are used with variables that can have a partial or ambiguous reference. This includes structures, arrays, globals, and aliased variables. In these cases, we have two types of definitions. For globals, structures, and arrays, we can determine from a statement whether a variable of these types has a killing definition. If the variable does, then the statement is marked as having a @dfn{must definition} of that variable. However, if a statement is only defining a part of the variable (i.e.@: a field in a structure), or if we know that a statement might define the variable but we cannot say for sure, then we mark that statement as having a @dfn{may definition}. For instance, given @smallexample @{ int a, b, *p; if (...) p = &a; else p = &b; *p = 5; return *p; @} @end smallexample The assignment @code{*p = 5} may be a definition of @code{a} or @code{b}. If we cannot determine statically where @code{p} is pointing to at the time of the store operation, we create virtual definitions to mark that statement as a potential definition site for @code{a} and @code{b}. Memory loads are similarly marked with virtual use operands. Virtual operands are shown in tree dumps right before the statement that contains them. To request a tree dump with virtual operands, use the @option{-vops} option to @option{-fdump-tree}: @smallexample @{ int a, b, *p; if (...) p = &a; else p = &b; # a = V_MAY_DEF # b = V_MAY_DEF *p = 5; # VUSE # VUSE return *p; @} @end smallexample Notice that @code{V_MAY_DEF} operands have two copies of the referenced variable. This indicates that this is not a killing definition of that variable. In this case we refer to it as a @dfn{may definition} or @dfn{aliased store}. The presence of the second copy of the variable in the @code{V_MAY_DEF} operand will become important when the function is converted into SSA form. This will be used to link all the non-killing definitions to prevent optimizations from making incorrect assumptions about them. Operands are updated as soon as the statement is finished via a call to @code{update_stmt}. If statement elements are changed via @code{SET_USE} or @code{SET_DEF}, then no further action is required (ie, those macros take care of updating the statement). If changes are made by manipulating the statement's tree directly, then a call must be made to @code{update_stmt} when complete. Calling one of the @code{bsi_insert} routines or @code{bsi_replace} performs an implicit call to @code{update_stmt}. @subsection Operand Iterators And Access Routines @cindex Operand Iterators @cindex Operand Access Routines Operands are collected by @file{tree-ssa-operands.c}. They are stored inside each statement's annotation and can be accessed through either the operand iterators or an access routine. The following access routines are available for examining operands: @enumerate @item @code{SINGLE_SSA_@{USE,DEF,TREE@}_OPERAND}: These accessors will return NULL unless there is exactly one operand matching the specified flags. If there is exactly one operand, the operand is returned as either a @code{tree}, @code{def_operand_p}, or @code{use_operand_p}. @smallexample tree t = SINGLE_SSA_TREE_OPERAND (stmt, flags); use_operand_p u = SINGLE_SSA_USE_OPERAND (stmt, SSA_ALL_VIRTUAL_USES); def_operand_p d = SINGLE_SSA_DEF_OPERAND (stmt, SSA_OP_ALL_DEFS); @end smallexample @item @code{ZERO_SSA_OPERANDS}: This macro returns true if there are no operands matching the specified flags. @smallexample if (ZERO_SSA_OPERANDS (stmt, SSA_OP_ALL_VIRTUALS)) return; @end smallexample @item @code{NUM_SSA_OPERANDS}: This macro Returns the number of operands matching 'flags'. This actually executes a loop to perform the count, so only use this if it is really needed. @smallexample int count = NUM_SSA_OPERANDS (stmt, flags) @end smallexample @end enumerate If you wish to iterate over some or all operands, use the @code{FOR_EACH_SSA_@{USE,DEF,TREE@}_OPERAND} iterator. For example, to print all the operands for a statement: @smallexample void print_ops (tree stmt) @{ ssa_op_iter; tree var; FOR_EACH_SSA_TREE_OPERAND (var, stmt, iter, SSA_OP_ALL_OPERANDS) print_generic_expr (stderr, var, TDF_SLIM); @} @end smallexample How to choose the appropriate iterator: @enumerate @item Determine whether you are need to see the operand pointers, or just the trees, and choose the appropriate macro: @smallexample Need Macro: ---- ------- use_operand_p FOR_EACH_SSA_USE_OPERAND def_operand_p FOR_EACH_SSA_DEF_OPERAND tree FOR_EACH_SSA_TREE_OPERAND @end smallexample @item You need to declare a variable of the type you are interested in, and an ssa_op_iter structure which serves as the loop controlling variable. @item Determine which operands you wish to use, and specify the flags of those you are interested in. They are documented in @file{tree-ssa-operands.h}: @smallexample #define SSA_OP_USE 0x01 /* @r{Real USE operands.} */ #define SSA_OP_DEF 0x02 /* @r{Real DEF operands.} */ #define SSA_OP_VUSE 0x04 /* @r{VUSE operands.} */ #define SSA_OP_VMAYUSE 0x08 /* @r{USE portion of V_MAY_DEFS.} */ #define SSA_OP_VMAYDEF 0x10 /* @r{DEF portion of V_MAY_DEFS.} */ #define SSA_OP_VMUSTDEF 0x20 /* @r{V_MUST_DEF definitions.} */ /* @r{These are commonly grouped operand flags.} */ #define SSA_OP_VIRTUAL_USES (SSA_OP_VUSE | SSA_OP_VMAYUSE) #define SSA_OP_VIRTUAL_DEFS (SSA_OP_VMAYDEF | SSA_OP_VMUSTDEF) #define SSA_OP_ALL_USES (SSA_OP_VIRTUAL_USES | SSA_OP_USE) #define SSA_OP_ALL_DEFS (SSA_OP_VIRTUAL_DEFS | SSA_OP_DEF) #define SSA_OP_ALL_OPERANDS (SSA_OP_ALL_USES | SSA_OP_ALL_DEFS) @end smallexample @end enumerate So if you want to look at the use pointers for all the @code{USE} and @code{VUSE} operands, you would do something like: @smallexample use_operand_p use_p; ssa_op_iter iter; FOR_EACH_SSA_USE_OPERAND (use_p, stmt, iter, (SSA_OP_USE | SSA_OP_VUSE)) @{ process_use_ptr (use_p); @} @end smallexample The @code{TREE} macro is basically the same as the @code{USE} and @code{DEF} macros, only with the use or def dereferenced via @code{USE_FROM_PTR (use_p)} and @code{DEF_FROM_PTR (def_p)}. Since we aren't using operand pointers, use and defs flags can be mixed. @smallexample tree var; ssa_op_iter iter; FOR_EACH_SSA_TREE_OPERAND (var, stmt, iter, SSA_OP_VUSE | SSA_OP_VMUSTDEF) @{ print_generic_expr (stderr, var, TDF_SLIM); @} @end smallexample @code{V_MAY_DEF}s are broken into two flags, one for the @code{DEF} portion (@code{SSA_OP_VMAYDEF}) and one for the USE portion (@code{SSA_OP_VMAYUSE}). If all you want to look at are the @code{V_MAY_DEF}s together, there is a fourth iterator macro for this, which returns both a def_operand_p and a use_operand_p for each @code{V_MAY_DEF} in the statement. Note that you don't need any flags for this one. @smallexample use_operand_p use_p; def_operand_p def_p; ssa_op_iter iter; FOR_EACH_SSA_MAYDEF_OPERAND (def_p, use_p, stmt, iter) @{ my_code; @} @end smallexample @code{V_MUST_DEF}s are broken into two flags, one for the @code{DEF} portion (@code{SSA_OP_VMUSTDEF}) and one for the kill portion (@code{SSA_OP_VMUSTKILL}). If all you want to look at are the @code{V_MUST_DEF}s together, there is a fourth iterator macro for this, which returns both a def_operand_p and a use_operand_p for each @code{V_MUST_DEF} in the statement. Note that you don't need any flags for this one. @smallexample use_operand_p kill_p; def_operand_p def_p; ssa_op_iter iter; FOR_EACH_SSA_MUSTDEF_OPERAND (def_p, kill_p, stmt, iter) @{ my_code; @} @end smallexample There are many examples in the code as well, as well as the documentation in @file{tree-ssa-operands.h}. There are also a couple of variants on the stmt iterators regarding PHI nodes. @code{FOR_EACH_PHI_ARG} Works exactly like @code{FOR_EACH_SSA_USE_OPERAND}, except it works over @code{PHI} arguments instead of statement operands. @smallexample /* Look at every virtual PHI use. */ FOR_EACH_PHI_ARG (use_p, phi_stmt, iter, SSA_OP_VIRTUAL_USES) @{ my_code; @} /* Look at every real PHI use. */ FOR_EACH_PHI_ARG (use_p, phi_stmt, iter, SSA_OP_USES) my_code; /* Look at every every PHI use. */ FOR_EACH_PHI_ARG (use_p, phi_stmt, iter, SSA_OP_ALL_USES) my_code; @end smallexample @code{FOR_EACH_PHI_OR_STMT_@{USE,DEF@}} works exactly like @code{FOR_EACH_SSA_@{USE,DEF@}_OPERAND}, except it will function on either a statement or a @code{PHI} node. These should be used when it is appropriate but they are not quite as efficient as the individual @code{FOR_EACH_PHI} and @code{FOR_EACH_SSA} routines. @smallexample FOR_EACH_PHI_OR_STMT_USE (use_operand_p, stmt, iter, flags) @{ my_code; @} FOR_EACH_PHI_OR_STMT_DEF (def_operand_p, phi, iter, flags) @{ my_code; @} @end smallexample @subsection Immediate Uses @cindex Immediate Uses Immediate use information is now always available. Using the immediate use iterators, you may examine every use of any @code{SSA_NAME}. For instance, to change each use of @code{ssa_var} to @code{ssa_var2}: @smallexample use_operand_p imm_use_p; imm_use_iterator iterator; tree ssa_var FOR_EACH_IMM_USE_SAFE (imm_use_p, iterator, ssa_var) SET_USE (imm_use_p, ssa_var_2); @end smallexample There are 2 iterators which can be used. @code{FOR_EACH_IMM_USE_FAST} is used when the immediate uses are not changed, ie. you are looking at the uses, but not setting them. If they do get changed, then care must be taken that things are not changed under the iterators, so use the @code{FOR_EACH_IMM_USE_SAFE} iterator. It attempts to preserve the sanity of the use list by moving an iterator element through the use list, preventing insertions and deletions in the list from resulting in invalid pointers. This is a little slower since it adds a placeholder element and moves it through the list. This element must be also be removed if the loop is terminated early. A macro (@code{BREAK_FROM SAFE_IMM_USE}) is provided for this: @smallexample FOR_EACH_IMM_USE_SAFE (use_p, iter, var) @{ if (var == last_var) BREAK_FROM_SAFE_IMM_USE (iter); else SET_USE (use_p, var2); @} @end smallexample There are checks in @code{verify_ssa} which verify that the immediate use list is up to date, as well as checking that an optimization didn't break from the loop without using this macro. It is safe to simply 'break'; from a @code{FOR_EACH_IMM_USE_FAST} traverse. Some useful functions and macros: @enumerate @item @code{has_zero_uses (ssa_var)} : Returns true if there are no uses of @code{ssa_var}. @item @code{has_single_use (ssa_var)} : Returns true if there is only a single use of @code{ssa_var}. @item @code{single_imm_use (ssa_var, use_operand_p *ptr, tree *stmt)} : Returns true if there is only a single use of @code{ssa_var}, and also returns the use pointer and statement it occurs in in the second and third parameters. @item @code{num_imm_uses (ssa_var)} : Returns the number of immediate uses of @code{ssa_var}. It is better not to use this if possible since it simply utilizes a loop to count the uses. @item @code{PHI_ARG_INDEX_FROM_USE (use_p)} : Given a use within a @code{PHI} node, return the index number for the use. An assert is triggered if the use isn't located in a @code{PHI} node. @item @code{USE_STMT (use_p)} : Return the statement a use occurs in. @end enumerate Note that uses are not put into an immediate use list until their statement is actually inserted into the instruction stream via a @code{bsi_*} routine. It is also still possible to utilize lazy updating of statements, but this should be used only when absolutely required. Both alias analysis and the dominator optimizations currently do this. When lazy updating is being used, the immediate use information is out of date and cannot be used reliably. Lazy updating is achieved by simply marking statements modified via calls to @code{mark_stmt_modified} instead of @code{update_stmt}. When lazy updating is no longer required, all the modified statements must have @code{update_stmt} called in order to bring them up to date. This must be done before the optimization is finished, or @code{verify_ssa} will trigger an abort. This is done with a simple loop over the instruction stream: @smallexample block_stmt_iterator bsi; basic_block bb; FOR_EACH_BB (bb) @{ for (bsi = bsi_start (bb); !bsi_end_p (bsi); bsi_next (&bsi)) update_stmt_if_modified (bsi_stmt (bsi)); @} @end smallexample @node SSA @section Static Single Assignment @cindex SSA @cindex static single assignment Most of the tree optimizers rely on the data flow information provided by the Static Single Assignment (SSA) form. We implement the SSA form as described in @cite{R. Cytron, J. Ferrante, B. Rosen, M. Wegman, and K. Zadeck. Efficiently Computing Static Single Assignment Form and the Control Dependence Graph. ACM Transactions on Programming Languages and Systems, 13(4):451-490, October 1991}. The SSA form is based on the premise that program variables are assigned in exactly one location in the program. Multiple assignments to the same variable create new versions of that variable. Naturally, actual programs are seldom in SSA form initially because variables tend to be assigned multiple times. The compiler modifies the program representation so that every time a variable is assigned in the code, a new version of the variable is created. Different versions of the same variable are distinguished by subscripting the variable name with its version number. Variables used in the right-hand side of expressions are renamed so that their version number matches that of the most recent assignment. We represent variable versions using @code{SSA_NAME} nodes. The renaming process in @file{tree-ssa.c} wraps every real and virtual operand with an @code{SSA_NAME} node which contains the version number and the statement that created the @code{SSA_NAME}. Only definitions and virtual definitions may create new @code{SSA_NAME} nodes. Sometimes, flow of control makes it impossible to determine what is the most recent version of a variable. In these cases, the compiler inserts an artificial definition for that variable called @dfn{PHI function} or @dfn{PHI node}. This new definition merges all the incoming versions of the variable to create a new name for it. For instance, @smallexample if (...) a_1 = 5; else if (...) a_2 = 2; else a_3 = 13; # a_4 = PHI return a_4; @end smallexample Since it is not possible to determine which of the three branches will be taken at runtime, we don't know which of @code{a_1}, @code{a_2} or @code{a_3} to use at the return statement. So, the SSA renamer creates a new version @code{a_4} which is assigned the result of ``merging'' @code{a_1}, @code{a_2} and @code{a_3}. Hence, PHI nodes mean ``one of these operands. I don't know which''. The following macros can be used to examine PHI nodes @defmac PHI_RESULT (@var{phi}) Returns the @code{SSA_NAME} created by PHI node @var{phi} (i.e., @var{phi}'s LHS)@. @end defmac @defmac PHI_NUM_ARGS (@var{phi}) Returns the number of arguments in @var{phi}. This number is exactly the number of incoming edges to the basic block holding @var{phi}@. @end defmac @defmac PHI_ARG_ELT (@var{phi}, @var{i}) Returns a tuple representing the @var{i}th argument of @var{phi}@. Each element of this tuple contains an @code{SSA_NAME} @var{var} and the incoming edge through which @var{var} flows. @end defmac @defmac PHI_ARG_EDGE (@var{phi}, @var{i}) Returns the incoming edge for the @var{i}th argument of @var{phi}. @end defmac @defmac PHI_ARG_DEF (@var{phi}, @var{i}) Returns the @code{SSA_NAME} for the @var{i}th argument of @var{phi}. @end defmac @subsection Preserving the SSA form @findex update_ssa @cindex preserving SSA form Some optimization passes make changes to the function that invalidate the SSA property. This can happen when a pass has added new symbols or changed the program so that variables that were previously aliased aren't anymore. Whenever something like this happens, the affected symbols must be renamed into SSA form again. Transformations that emit new code or replicate existing statements will also need to update the SSA form@. Since GCC implements two different SSA forms for register and virtual variables, keeping the SSA form up to date depends on whether you are updating register or virtual names. In both cases, the general idea behind incremental SSA updates is similar: when new SSA names are created, they typically are meant to replace other existing names in the program@. For instance, given the following code: @smallexample 1 L0: 2 x_1 = PHI (0, x_5) 3 if (x_1 < 10) 4 if (x_1 > 7) 5 y_2 = 0 6 else 7 y_3 = x_1 + x_7 8 endif 9 x_5 = x_1 + 1 10 goto L0; 11 endif @end smallexample Suppose that we insert new names @code{x_10} and @code{x_11} (lines @code{4} and @code{8})@. @smallexample 1 L0: 2 x_1 = PHI (0, x_5) 3 if (x_1 < 10) 4 x_10 = ... 5 if (x_1 > 7) 6 y_2 = 0 7 else 8 x_11 = ... 9 y_3 = x_1 + x_7 10 endif 11 x_5 = x_1 + 1 12 goto L0; 13 endif @end smallexample We want to replace all the uses of @code{x_1} with the new definitions of @code{x_10} and @code{x_11}. Note that the only uses that should be replaced are those at lines @code{5}, @code{9} and @code{11}. Also, the use of @code{x_7} at line @code{9} should @emph{not} be replaced (this is why we cannot just mark symbol @code{x} for renaming)@. Additionally, we may need to insert a PHI node at line @code{11} because that is a merge point for @code{x_10} and @code{x_11}. So the use of @code{x_1} at line @code{11} will be replaced with the new PHI node. The insertion of PHI nodes is optional. They are not strictly necessary to preserve the SSA form, and depending on what the caller inserted, they may not even be useful for the optimizers@. Updating the SSA form is a two step process. First, the pass has to identify which names need to be updated and/or which symbols need to be renamed into SSA form for the first time. When new names are introduced to replace existing names in the program, the mapping between the old and the new names are registered by calling @code{register_new_name_mapping} (note that if your pass creates new code by duplicating basic blocks, the call to @code{tree_duplicate_bb} will set up the necessary mappings automatically). On the other hand, if your pass exposes a new symbol that should be put in SSA form for the first time, the new symbol should be registered with @code{mark_sym_for_renaming}. After the replacement mappings have been registered and new symbols marked for renaming, a call to @code{update_ssa} makes the registered changes. This can be done with an explicit call or by creating @code{TODO} flags in the @code{tree_opt_pass} structure for your pass. There are several @code{TODO} flags that control the behavior of @code{update_ssa}: @itemize @bullet @item @code{TODO_update_ssa}. Update the SSA form inserting PHI nodes for newly exposed symbols and virtual names marked for updating. When updating real names, only insert PHI nodes for a real name @code{O_j} in blocks reached by all the new and old definitions for @code{O_j}. If the iterated dominance frontier for @code{O_j} is not pruned, we may end up inserting PHI nodes in blocks that have one or more edges with no incoming definition for @code{O_j}. This would lead to uninitialized warnings for @code{O_j}'s symbol@. @item @code{TODO_update_ssa_no_phi}. Update the SSA form without inserting any new PHI nodes at all. This is used by passes that have either inserted all the PHI nodes themselves or passes that need only to patch use-def and def-def chains for virtuals (e.g., DCE)@. @item @code{TODO_update_ssa_full_phi}. Insert PHI nodes everywhere they are needed. No pruning of the IDF is done. This is used by passes that need the PHI nodes for @code{O_j} even if it means that some arguments will come from the default definition of @code{O_j}'s symbol (e.g., @code{pass_linear_transform})@. WARNING: If you need to use this flag, chances are that your pass may be doing something wrong. Inserting PHI nodes for an old name where not all edges carry a new replacement may lead to silent codegen errors or spurious uninitialized warnings@. @item @code{TODO_update_ssa_only_virtuals}. Passes that update the SSA form on their own may want to delegate the updating of virtual names to the generic updater. Since FUD chains are easier to maintain, this simplifies the work they need to do. NOTE: If this flag is used, any OLD->NEW mappings for real names are explicitly destroyed and only the symbols marked for renaming are processed@. @end itemize @subsection Examining @code{SSA_NAME} nodes @cindex examining SSA_NAMEs The following macros can be used to examine @code{SSA_NAME} nodes @defmac SSA_NAME_DEF_STMT (@var{var}) Returns the statement @var{s} that creates the @code{SSA_NAME} @var{var}. If @var{s} is an empty statement (i.e., @code{IS_EMPTY_STMT (@var{s})} returns @code{true}), it means that the first reference to this variable is a USE or a VUSE@. @end defmac @defmac SSA_NAME_VERSION (@var{var}) Returns the version number of the @code{SSA_NAME} object @var{var}. @end defmac @subsection Walking use-def chains @deftypefn {Tree SSA function} void walk_use_def_chains (@var{var}, @var{fn}, @var{data}) Walks use-def chains starting at the @code{SSA_NAME} node @var{var}. Calls function @var{fn} at each reaching definition found. Function @var{FN} takes three arguments: @var{var}, its defining statement (@var{def_stmt}) and a generic pointer to whatever state information that @var{fn} may want to maintain (@var{data}). Function @var{fn} is able to stop the walk by returning @code{true}, otherwise in order to continue the walk, @var{fn} should return @code{false}. Note, that if @var{def_stmt} is a @code{PHI} node, the semantics are slightly different. For each argument @var{arg} of the PHI node, this function will: @enumerate @item Walk the use-def chains for @var{arg}. @item Call @code{FN (@var{arg}, @var{phi}, @var{data})}. @end enumerate Note how the first argument to @var{fn} is no longer the original variable @var{var}, but the PHI argument currently being examined. If @var{fn} wants to get at @var{var}, it should call @code{PHI_RESULT} (@var{phi}). @end deftypefn @subsection Walking the dominator tree @deftypefn {Tree SSA function} void walk_dominator_tree (@var{walk_data}, @var{bb}) This function walks the dominator tree for the current CFG calling a set of callback functions defined in @var{struct dom_walk_data} in @file{domwalk.h}. The call back functions you need to define give you hooks to execute custom code at various points during traversal: @enumerate @item Once to initialize any local data needed while processing @var{bb} and its children. This local data is pushed into an internal stack which is automatically pushed and popped as the walker traverses the dominator tree. @item Once before traversing all the statements in the @var{bb}. @item Once for every statement inside @var{bb}. @item Once after traversing all the statements and before recursing into @var{bb}'s dominator children. @item It then recurses into all the dominator children of @var{bb}. @item After recursing into all the dominator children of @var{bb} it can, optionally, traverse every statement in @var{bb} again (i.e., repeating steps 2 and 3). @item Once after walking the statements in @var{bb} and @var{bb}'s dominator children. At this stage, the block local data stack is popped. @end enumerate @end deftypefn @node Alias analysis @section Alias analysis @cindex alias @cindex flow-sensitive alias analysis @cindex flow-insensitive alias analysis Alias analysis proceeds in 4 main phases: @enumerate @item Structural alias analysis. This phase walks the types for structure variables, and determines which of the fields can overlap using offset and size of each field. For each field, a ``subvariable'' called a ``Structure field tag'' (SFT)@ is created, which represents that field as a separate variable. All accesses that could possibly overlap with a given field will have virtual operands for the SFT of that field. @smallexample struct foo @{ int a; int b; @} struct foo temp; int bar (void) @{ int tmp1, tmp2, tmp3; SFT.0_2 = V_MUST_DEF temp.a = 5; SFT.1_4 = V_MUST_DEF temp.b = 6; VUSE tmp1_5 = temp.b; VUSE tmp2_6 = temp.a; tmp3_7 = tmp1_5 + tmp2_6; return tmp3_7; @} @end smallexample If you copy the symbol tag for a variable for some reason, you probably also want to copy the subvariables for that variable. @item Points-to and escape analysis. This phase walks the use-def chains in the SSA web looking for three things: @itemize @bullet @item Assignments of the form @code{P_i = &VAR} @item Assignments of the form P_i = malloc() @item Pointers and ADDR_EXPR that escape the current function. @end itemize The concept of `escaping' is the same one used in the Java world. When a pointer or an ADDR_EXPR escapes, it means that it has been exposed outside of the current function. So, assignment to global variables, function arguments and returning a pointer are all escape sites. This is where we are currently limited. Since not everything is renamed into SSA, we lose track of escape properties when a pointer is stashed inside a field in a structure, for instance. In those cases, we are assuming that the pointer does escape. We use escape analysis to determine whether a variable is call-clobbered. Simply put, if an ADDR_EXPR escapes, then the variable is call-clobbered. If a pointer P_i escapes, then all the variables pointed-to by P_i (and its memory tag) also escape. @item Compute flow-sensitive aliases We have two classes of memory tags. Memory tags associated with the pointed-to data type of the pointers in the program. These tags are called ``symbol memory tag'' (SMT)@. The other class are those associated with SSA_NAMEs, called ``name memory tag'' (NMT)@. The basic idea is that when adding operands for an INDIRECT_REF *P_i, we will first check whether P_i has a name tag, if it does we use it, because that will have more precise aliasing information. Otherwise, we use the standard symbol tag. In this phase, we go through all the pointers we found in points-to analysis and create alias sets for the name memory tags associated with each pointer P_i. If P_i escapes, we mark call-clobbered the variables it points to and its tag. @item Compute flow-insensitive aliases This pass will compare the alias set of every symbol memory tag and every addressable variable found in the program. Given a symbol memory tag SMT and an addressable variable V@. If the alias sets of SMT and V conflict (as computed by may_alias_p), then V is marked as an alias tag and added to the alias set of SMT@. @end enumerate For instance, consider the following function: @smallexample foo (int i) @{ int *p, *q, a, b; if (i > 10) p = &a; else q = &b; *p = 3; *q = 5; a = b + 2; return *p; @} @end smallexample After aliasing analysis has finished, the symbol memory tag for pointer @code{p} will have two aliases, namely variables @code{a} and @code{b}. Every time pointer @code{p} is dereferenced, we want to mark the operation as a potential reference to @code{a} and @code{b}. @smallexample foo (int i) @{ int *p, a, b; if (i_2 > 10) p_4 = &a; else p_6 = &b; # p_1 = PHI ; # a_7 = V_MAY_DEF ; # b_8 = V_MAY_DEF ; *p_1 = 3; # a_9 = V_MAY_DEF # VUSE a_9 = b_8 + 2; # VUSE ; # VUSE ; return *p_1; @} @end smallexample In certain cases, the list of may aliases for a pointer may grow too large. This may cause an explosion in the number of virtual operands inserted in the code. Resulting in increased memory consumption and compilation time. When the number of virtual operands needed to represent aliased loads and stores grows too large (configurable with @option{--param max-aliased-vops}), alias sets are grouped to avoid severe compile-time slow downs and memory consumption. The alias grouping heuristic proceeds as follows: @enumerate @item Sort the list of pointers in decreasing number of contributed virtual operands. @item Take the first pointer from the list and reverse the role of the memory tag and its aliases. Usually, whenever an aliased variable Vi is found to alias with a memory tag T, we add Vi to the may-aliases set for T@. Meaning that after alias analysis, we will have: @smallexample may-aliases(T) = @{ V1, V2, V3, ..., Vn @} @end smallexample This means that every statement that references T, will get @code{n} virtual operands for each of the Vi tags. But, when alias grouping is enabled, we make T an alias tag and add it to the alias set of all the Vi variables: @smallexample may-aliases(V1) = @{ T @} may-aliases(V2) = @{ T @} ... may-aliases(Vn) = @{ T @} @end smallexample This has two effects: (a) statements referencing T will only get a single virtual operand, and, (b) all the variables Vi will now appear to alias each other. So, we lose alias precision to improve compile time. But, in theory, a program with such a high level of aliasing should not be very optimizable in the first place. @item Since variables may be in the alias set of more than one memory tag, the grouping done in step (2) needs to be extended to all the memory tags that have a non-empty intersection with the may-aliases set of tag T@. For instance, if we originally had these may-aliases sets: @smallexample may-aliases(T) = @{ V1, V2, V3 @} may-aliases(R) = @{ V2, V4 @} @end smallexample In step (2) we would have reverted the aliases for T as: @smallexample may-aliases(V1) = @{ T @} may-aliases(V2) = @{ T @} may-aliases(V3) = @{ T @} @end smallexample But note that now V2 is no longer aliased with R@. We could add R to may-aliases(V2), but we are in the process of grouping aliases to reduce virtual operands so what we do is add V4 to the grouping to obtain: @smallexample may-aliases(V1) = @{ T @} may-aliases(V2) = @{ T @} may-aliases(V3) = @{ T @} may-aliases(V4) = @{ T @} @end smallexample @item If the total number of virtual operands due to aliasing is still above the threshold set by max-alias-vops, go back to (2). @end enumerate