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 /* Scalar evolution detector. Copyright (C) 2003-2021 Free Software Foundation, Inc. Contributed by Sebastian Pop This file is part of GCC. GCC is free software; you can redistribute it and/or modify it under the terms of the GNU General Public License as published by the Free Software Foundation; either version 3, or (at your option) any later version. GCC is distributed in the hope that it will be useful, but WITHOUT ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License for more details. You should have received a copy of the GNU General Public License along with GCC; see the file COPYING3. If not see . */ /* Description: This pass analyzes the evolution of scalar variables in loop structures. The algorithm is based on the SSA representation, and on the loop hierarchy tree. This algorithm is not based on the notion of versions of a variable, as it was the case for the previous implementations of the scalar evolution algorithm, but it assumes that each defined name is unique. The notation used in this file is called "chains of recurrences", and has been proposed by Eugene Zima, Robert Van Engelen, and others for describing induction variables in programs. For example "b -> {0, +, 2}_1" means that the scalar variable "b" is equal to 0 when entering in the loop_1 and has a step 2 in this loop, in other words "for (b = 0; b < N; b+=2);". Note that the coefficients of this chain of recurrence (or chrec [shrek]) can contain the name of other variables, in which case they are called parametric chrecs. For example, "b -> {a, +, 2}_1" means that the initial value of "b" is the value of "a". In most of the cases these parametric chrecs are fully instantiated before their use because symbolic names can hide some difficult cases such as self-references described later (see the Fibonacci example). A short sketch of the algorithm is: Given a scalar variable to be analyzed, follow the SSA edge to its definition: - When the definition is a GIMPLE_ASSIGN: if the right hand side (RHS) of the definition cannot be statically analyzed, the answer of the analyzer is: "don't know". Otherwise, for all the variables that are not yet analyzed in the RHS, try to determine their evolution, and finally try to evaluate the operation of the RHS that gives the evolution function of the analyzed variable. - When the definition is a condition-phi-node: determine the evolution function for all the branches of the phi node, and finally merge these evolutions (see chrec_merge). - When the definition is a loop-phi-node: determine its initial condition, that is the SSA edge defined in an outer loop, and keep it symbolic. Then determine the SSA edges that are defined in the body of the loop. Follow the inner edges until ending on another loop-phi-node of the same analyzed loop. If the reached loop-phi-node is not the starting loop-phi-node, then we keep this definition under a symbolic form. If the reached loop-phi-node is the same as the starting one, then we compute a symbolic stride on the return path. The result is then the symbolic chrec {initial_condition, +, symbolic_stride}_loop. Examples: Example 1: Illustration of the basic algorithm. | a = 3 | loop_1 | b = phi (a, c) | c = b + 1 | if (c > 10) exit_loop | endloop Suppose that we want to know the number of iterations of the loop_1. The exit_loop is controlled by a COND_EXPR (c > 10). We ask the scalar evolution analyzer two questions: what's the scalar evolution (scev) of "c", and what's the scev of "10". For "10" the answer is "10" since it is a scalar constant. For the scalar variable "c", it follows the SSA edge to its definition, "c = b + 1", and then asks again what's the scev of "b". Following the SSA edge, we end on a loop-phi-node "b = phi (a, c)", where the initial condition is "a", and the inner loop edge is "c". The initial condition is kept under a symbolic form (it may be the case that the copy constant propagation has done its work and we end with the constant "3" as one of the edges of the loop-phi-node). The update edge is followed to the end of the loop, and until reaching again the starting loop-phi-node: b -> c -> b. At this point we have drawn a path from "b" to "b" from which we compute the stride in the loop: in this example it is "+1". The resulting scev for "b" is "b -> {a, +, 1}_1". Now that the scev for "b" is known, it is possible to compute the scev for "c", that is "c -> {a + 1, +, 1}_1". In order to determine the number of iterations in the loop_1, we have to instantiate_parameters (loop_1, {a + 1, +, 1}_1), that gives after some more analysis the scev {4, +, 1}_1, or in other words, this is the function "f (x) = x + 4", where x is the iteration count of the loop_1. Now we have to solve the inequality "x + 4 > 10", and take the smallest iteration number for which the loop is exited: x = 7. This loop runs from x = 0 to x = 7, and in total there are 8 iterations. In terms of loop normalization, we have created a variable that is implicitly defined, "x" or just "_1", and all the other analyzed scalars of the loop are defined in function of this variable: a -> 3 b -> {3, +, 1}_1 c -> {4, +, 1}_1 or in terms of a C program: | a = 3 | for (x = 0; x <= 7; x++) | { | b = x + 3 | c = x + 4 | } Example 2a: Illustration of the algorithm on nested loops. | loop_1 | a = phi (1, b) | c = a + 2 | loop_2 10 times | b = phi (c, d) | d = b + 3 | endloop | endloop For analyzing the scalar evolution of "a", the algorithm follows the SSA edge into the loop's body: "a -> b". "b" is an inner loop-phi-node, and its analysis as in Example 1, gives: b -> {c, +, 3}_2 d -> {c + 3, +, 3}_2 Following the SSA edge for the initial condition, we end on "c = a + 2", and then on the starting loop-phi-node "a". From this point, the loop stride is computed: back on "c = a + 2" we get a "+2" in the loop_1, then on the loop-phi-node "b" we compute the overall effect of the inner loop that is "b = c + 30", and we get a "+30" in the loop_1. That means that the overall stride in loop_1 is equal to "+32", and the result is: a -> {1, +, 32}_1 c -> {3, +, 32}_1 Example 2b: Multivariate chains of recurrences. | loop_1 | k = phi (0, k + 1) | loop_2 4 times | j = phi (0, j + 1) | loop_3 4 times | i = phi (0, i + 1) | A[j + k] = ... | endloop | endloop | endloop Analyzing the access function of array A with instantiate_parameters (loop_1, "j + k"), we obtain the instantiation and the analysis of the scalar variables "j" and "k" in loop_1. This leads to the scalar evolution {4, +, 1}_1: the end value of loop_2 for "j" is 4, and the evolution of "k" in loop_1 is {0, +, 1}_1. To obtain the evolution function in loop_3 and instantiate the scalar variables up to loop_1, one has to use: instantiate_scev (block_before_loop (loop_1), loop_3, "j + k"). The result of this call is {{0, +, 1}_1, +, 1}_2. Example 3: Higher degree polynomials. | loop_1 | a = phi (2, b) | c = phi (5, d) | b = a + 1 | d = c + a | endloop a -> {2, +, 1}_1 b -> {3, +, 1}_1 c -> {5, +, a}_1 d -> {5 + a, +, a}_1 instantiate_parameters (loop_1, {5, +, a}_1) -> {5, +, 2, +, 1}_1 instantiate_parameters (loop_1, {5 + a, +, a}_1) -> {7, +, 3, +, 1}_1 Example 4: Lucas, Fibonacci, or mixers in general. | loop_1 | a = phi (1, b) | c = phi (3, d) | b = c | d = c + a | endloop a -> (1, c)_1 c -> {3, +, a}_1 The syntax "(1, c)_1" stands for a PEELED_CHREC that has the following semantics: during the first iteration of the loop_1, the variable contains the value 1, and then it contains the value "c". Note that this syntax is close to the syntax of the loop-phi-node: "a -> (1, c)_1" vs. "a = phi (1, c)". The symbolic chrec representation contains all the semantics of the original code. What is more difficult is to use this information. Example 5: Flip-flops, or exchangers. | loop_1 | a = phi (1, b) | c = phi (3, d) | b = c | d = a | endloop a -> (1, c)_1 c -> (3, a)_1 Based on these symbolic chrecs, it is possible to refine this information into the more precise PERIODIC_CHRECs: a -> |1, 3|_1 c -> |3, 1|_1 This transformation is not yet implemented. Further readings: You can find a more detailed description of the algorithm in: http://icps.u-strasbg.fr/~pop/DEA_03_Pop.pdf http://icps.u-strasbg.fr/~pop/DEA_03_Pop.ps.gz. But note that this is a preliminary report and some of the details of the algorithm have changed. I'm working on a research report that updates the description of the algorithms to reflect the design choices used in this implementation. A set of slides show a high level overview of the algorithm and run an example through the scalar evolution analyzer: http://cri.ensmp.fr/~pop/gcc/mar04/slides.pdf The slides that I have presented at the GCC Summit'04 are available at: http://cri.ensmp.fr/~pop/gcc/20040604/gccsummit-lno-spop.pdf */ #include "config.h" #include "system.h" #include "coretypes.h" #include "backend.h" #include "target.h" #include "rtl.h" #include "optabs-query.h" #include "tree.h" #include "gimple.h" #include "ssa.h" #include "gimple-pretty-print.h" #include "fold-const.h" #include "gimplify.h" #include "gimple-iterator.h" #include "gimplify-me.h" #include "tree-cfg.h" #include "tree-ssa-loop-ivopts.h" #include "tree-ssa-loop-manip.h" #include "tree-ssa-loop-niter.h" #include "tree-ssa-loop.h" #include "tree-ssa.h" #include "cfgloop.h" #include "tree-chrec.h" #include "tree-affine.h" #include "tree-scalar-evolution.h" #include "dumpfile.h" #include "tree-ssa-propagate.h" #include "gimple-fold.h" #include "tree-into-ssa.h" #include "builtins.h" #include "case-cfn-macros.h" static tree analyze_scalar_evolution_1 (class loop *, tree); static tree analyze_scalar_evolution_for_address_of (class loop *loop, tree var); /* The cached information about an SSA name with version NAME_VERSION, claiming that below basic block with index INSTANTIATED_BELOW, the value of the SSA name can be expressed as CHREC. */ struct GTY((for_user)) scev_info_str { unsigned int name_version; int instantiated_below; tree chrec; }; /* Counters for the scev database. */ static unsigned nb_set_scev = 0; static unsigned nb_get_scev = 0; struct scev_info_hasher : ggc_ptr_hash { static hashval_t hash (scev_info_str *i); static bool equal (const scev_info_str *a, const scev_info_str *b); }; static GTY (()) hash_table *scalar_evolution_info; /* Constructs a new SCEV_INFO_STR structure for VAR and INSTANTIATED_BELOW. */ static inline struct scev_info_str * new_scev_info_str (basic_block instantiated_below, tree var) { struct scev_info_str *res; res = ggc_alloc (); res->name_version = SSA_NAME_VERSION (var); res->chrec = chrec_not_analyzed_yet; res->instantiated_below = instantiated_below->index; return res; } /* Computes a hash function for database element ELT. */ hashval_t scev_info_hasher::hash (scev_info_str *elt) { return elt->name_version ^ elt->instantiated_below; } /* Compares database elements E1 and E2. */ bool scev_info_hasher::equal (const scev_info_str *elt1, const scev_info_str *elt2) { return (elt1->name_version == elt2->name_version && elt1->instantiated_below == elt2->instantiated_below); } /* Get the scalar evolution of VAR for INSTANTIATED_BELOW basic block. A first query on VAR returns chrec_not_analyzed_yet. */ static tree * find_var_scev_info (basic_block instantiated_below, tree var) { struct scev_info_str *res; struct scev_info_str tmp; tmp.name_version = SSA_NAME_VERSION (var); tmp.instantiated_below = instantiated_below->index; scev_info_str **slot = scalar_evolution_info->find_slot (&tmp, INSERT); if (!*slot) *slot = new_scev_info_str (instantiated_below, var); res = *slot; return &res->chrec; } /* Hashtable helpers for a temporary hash-table used when analyzing a scalar evolution, instantiating a CHREC or resolving mixers. */ class instantiate_cache_type { public: htab_t map; vec entries; instantiate_cache_type () : map (NULL), entries (vNULL) {} ~instantiate_cache_type (); tree get (unsigned slot) { return entries[slot].chrec; } void set (unsigned slot, tree chrec) { entries[slot].chrec = chrec; } }; instantiate_cache_type::~instantiate_cache_type () { if (map != NULL) { htab_delete (map); entries.release (); } } /* Cache to avoid infinite recursion when instantiating an SSA name. Live during the outermost analyze_scalar_evolution, instantiate_scev or resolve_mixers call. */ static instantiate_cache_type *global_cache; /* Return true when PHI is a loop-phi-node. */ static bool loop_phi_node_p (gimple *phi) { /* The implementation of this function is based on the following property: "all the loop-phi-nodes of a loop are contained in the loop's header basic block". */ return loop_containing_stmt (phi)->header == gimple_bb (phi); } /* Compute the scalar evolution for EVOLUTION_FN after crossing LOOP. In general, in the case of multivariate evolutions we want to get the evolution in different loops. LOOP specifies the level for which to get the evolution. Example: | for (j = 0; j < 100; j++) | { | for (k = 0; k < 100; k++) | { | i = k + j; - Here the value of i is a function of j, k. | } | ... = i - Here the value of i is a function of j. | } | ... = i - Here the value of i is a scalar. Example: | i_0 = ... | loop_1 10 times | i_1 = phi (i_0, i_2) | i_2 = i_1 + 2 | endloop This loop has the same effect as: LOOP_1 has the same effect as: | i_1 = i_0 + 20 The overall effect of the loop, "i_0 + 20" in the previous example, is obtained by passing in the parameters: LOOP = 1, EVOLUTION_FN = {i_0, +, 2}_1. */ tree compute_overall_effect_of_inner_loop (class loop *loop, tree evolution_fn) { bool val = false; if (evolution_fn == chrec_dont_know) return chrec_dont_know; else if (TREE_CODE (evolution_fn) == POLYNOMIAL_CHREC) { class loop *inner_loop = get_chrec_loop (evolution_fn); if (inner_loop == loop || flow_loop_nested_p (loop, inner_loop)) { tree nb_iter = number_of_latch_executions (inner_loop); if (nb_iter == chrec_dont_know) return chrec_dont_know; else { tree res; /* evolution_fn is the evolution function in LOOP. Get its value in the nb_iter-th iteration. */ res = chrec_apply (inner_loop->num, evolution_fn, nb_iter); if (chrec_contains_symbols_defined_in_loop (res, loop->num)) res = instantiate_parameters (loop, res); /* Continue the computation until ending on a parent of LOOP. */ return compute_overall_effect_of_inner_loop (loop, res); } } else return evolution_fn; } /* If the evolution function is an invariant, there is nothing to do. */ else if (no_evolution_in_loop_p (evolution_fn, loop->num, &val) && val) return evolution_fn; else return chrec_dont_know; } /* Associate CHREC to SCALAR. */ static void set_scalar_evolution (basic_block instantiated_below, tree scalar, tree chrec) { tree *scalar_info; if (TREE_CODE (scalar) != SSA_NAME) return; scalar_info = find_var_scev_info (instantiated_below, scalar); if (dump_file) { if (dump_flags & TDF_SCEV) { fprintf (dump_file, "(set_scalar_evolution \n"); fprintf (dump_file, " instantiated_below = %d \n", instantiated_below->index); fprintf (dump_file, " (scalar = "); print_generic_expr (dump_file, scalar); fprintf (dump_file, ")\n (scalar_evolution = "); print_generic_expr (dump_file, chrec); fprintf (dump_file, "))\n"); } if (dump_flags & TDF_STATS) nb_set_scev++; } *scalar_info = chrec; } /* Retrieve the chrec associated to SCALAR instantiated below INSTANTIATED_BELOW block. */ static tree get_scalar_evolution (basic_block instantiated_below, tree scalar) { tree res; if (dump_file) { if (dump_flags & TDF_SCEV) { fprintf (dump_file, "(get_scalar_evolution \n"); fprintf (dump_file, " (scalar = "); print_generic_expr (dump_file, scalar); fprintf (dump_file, ")\n"); } if (dump_flags & TDF_STATS) nb_get_scev++; } if (VECTOR_TYPE_P (TREE_TYPE (scalar)) || TREE_CODE (TREE_TYPE (scalar)) == COMPLEX_TYPE) /* For chrec_dont_know we keep the symbolic form. */ res = scalar; else switch (TREE_CODE (scalar)) { case SSA_NAME: if (SSA_NAME_IS_DEFAULT_DEF (scalar)) res = scalar; else res = *find_var_scev_info (instantiated_below, scalar); break; case REAL_CST: case FIXED_CST: case INTEGER_CST: res = scalar; break; default: res = chrec_not_analyzed_yet; break; } if (dump_file && (dump_flags & TDF_SCEV)) { fprintf (dump_file, " (scalar_evolution = "); print_generic_expr (dump_file, res); fprintf (dump_file, "))\n"); } return res; } /* Helper function for add_to_evolution. Returns the evolution function for an assignment of the form "a = b + c", where "a" and "b" are on the strongly connected component. CHREC_BEFORE is the information that we already have collected up to this point. TO_ADD is the evolution of "c". When CHREC_BEFORE has an evolution part in LOOP_NB, add to this evolution the expression TO_ADD, otherwise construct an evolution part for this loop. */ static tree add_to_evolution_1 (unsigned loop_nb, tree chrec_before, tree to_add, gimple *at_stmt) { tree type, left, right; class loop *loop = get_loop (cfun, loop_nb), *chloop; switch (TREE_CODE (chrec_before)) { case POLYNOMIAL_CHREC: chloop = get_chrec_loop (chrec_before); if (chloop == loop || flow_loop_nested_p (chloop, loop)) { unsigned var; type = chrec_type (chrec_before); /* When there is no evolution part in this loop, build it. */ if (chloop != loop) { var = loop_nb; left = chrec_before; right = SCALAR_FLOAT_TYPE_P (type) ? build_real (type, dconst0) : build_int_cst (type, 0); } else { var = CHREC_VARIABLE (chrec_before); left = CHREC_LEFT (chrec_before); right = CHREC_RIGHT (chrec_before); } to_add = chrec_convert (type, to_add, at_stmt); right = chrec_convert_rhs (type, right, at_stmt); right = chrec_fold_plus (chrec_type (right), right, to_add); return build_polynomial_chrec (var, left, right); } else { gcc_assert (flow_loop_nested_p (loop, chloop)); /* Search the evolution in LOOP_NB. */ left = add_to_evolution_1 (loop_nb, CHREC_LEFT (chrec_before), to_add, at_stmt); right = CHREC_RIGHT (chrec_before); right = chrec_convert_rhs (chrec_type (left), right, at_stmt); return build_polynomial_chrec (CHREC_VARIABLE (chrec_before), left, right); } default: /* These nodes do not depend on a loop. */ if (chrec_before == chrec_dont_know) return chrec_dont_know; left = chrec_before; right = chrec_convert_rhs (chrec_type (left), to_add, at_stmt); return build_polynomial_chrec (loop_nb, left, right); } } /* Add TO_ADD to the evolution part of CHREC_BEFORE in the dimension of LOOP_NB. Description (provided for completeness, for those who read code in a plane, and for my poor 62 bytes brain that would have forgotten all this in the next two or three months): The algorithm of translation of programs from the SSA representation into the chrecs syntax is based on a pattern matching. After having reconstructed the overall tree expression for a loop, there are only two cases that can arise: 1. a = loop-phi (init, a + expr) 2. a = loop-phi (init, expr) where EXPR is either a scalar constant with respect to the analyzed loop (this is a degree 0 polynomial), or an expression containing other loop-phi definitions (these are higher degree polynomials). Examples: 1. | init = ... | loop_1 | a = phi (init, a + 5) | endloop 2. | inita = ... | initb = ... | loop_1 | a = phi (inita, 2 * b + 3) | b = phi (initb, b + 1) | endloop For the first case, the semantics of the SSA representation is: | a (x) = init + \sum_{j = 0}^{x - 1} expr (j) that is, there is a loop index "x" that determines the scalar value of the variable during the loop execution. During the first iteration, the value is that of the initial condition INIT, while during the subsequent iterations, it is the sum of the initial condition with the sum of all the values of EXPR from the initial iteration to the before last considered iteration. For the second case, the semantics of the SSA program is: | a (x) = init, if x = 0; | expr (x - 1), otherwise. The second case corresponds to the PEELED_CHREC, whose syntax is close to the syntax of a loop-phi-node: | phi (init, expr) vs. (init, expr)_x The proof of the translation algorithm for the first case is a proof by structural induction based on the degree of EXPR. Degree 0: When EXPR is a constant with respect to the analyzed loop, or in other words when EXPR is a polynomial of degree 0, the evolution of the variable A in the loop is an affine function with an initial condition INIT, and a step EXPR. In order to show this, we start from the semantics of the SSA representation: f (x) = init + \sum_{j = 0}^{x - 1} expr (j) and since "expr (j)" is a constant with respect to "j", f (x) = init + x * expr Finally, based on the semantics of the pure sum chrecs, by identification we get the corresponding chrecs syntax: f (x) = init * \binom{x}{0} + expr * \binom{x}{1} f (x) -> {init, +, expr}_x Higher degree: Suppose that EXPR is a polynomial of degree N with respect to the analyzed loop_x for which we have already determined that it is written under the chrecs syntax: | expr (x) -> {b_0, +, b_1, +, ..., +, b_{n-1}} (x) We start from the semantics of the SSA program: | f (x) = init + \sum_{j = 0}^{x - 1} expr (j) | | f (x) = init + \sum_{j = 0}^{x - 1} | (b_0 * \binom{j}{0} + ... + b_{n-1} * \binom{j}{n-1}) | | f (x) = init + \sum_{j = 0}^{x - 1} | \sum_{k = 0}^{n - 1} (b_k * \binom{j}{k}) | | f (x) = init + \sum_{k = 0}^{n - 1} | (b_k * \sum_{j = 0}^{x - 1} \binom{j}{k}) | | f (x) = init + \sum_{k = 0}^{n - 1} | (b_k * \binom{x}{k + 1}) | | f (x) = init + b_0 * \binom{x}{1} + ... | + b_{n-1} * \binom{x}{n} | | f (x) = init * \binom{x}{0} + b_0 * \binom{x}{1} + ... | + b_{n-1} * \binom{x}{n} | And finally from the definition of the chrecs syntax, we identify: | f (x) -> {init, +, b_0, +, ..., +, b_{n-1}}_x This shows the mechanism that stands behind the add_to_evolution function. An important point is that the use of symbolic parameters avoids the need of an analysis schedule. Example: | inita = ... | initb = ... | loop_1 | a = phi (inita, a + 2 + b) | b = phi (initb, b + 1) | endloop When analyzing "a", the algorithm keeps "b" symbolically: | a -> {inita, +, 2 + b}_1 Then, after instantiation, the analyzer ends on the evolution: | a -> {inita, +, 2 + initb, +, 1}_1 */ static tree add_to_evolution (unsigned loop_nb, tree chrec_before, enum tree_code code, tree to_add, gimple *at_stmt) { tree type = chrec_type (to_add); tree res = NULL_TREE; if (to_add == NULL_TREE) return chrec_before; /* TO_ADD is either a scalar, or a parameter. TO_ADD is not instantiated at this point. */ if (TREE_CODE (to_add) == POLYNOMIAL_CHREC) /* This should not happen. */ return chrec_dont_know; if (dump_file && (dump_flags & TDF_SCEV)) { fprintf (dump_file, "(add_to_evolution \n"); fprintf (dump_file, " (loop_nb = %d)\n", loop_nb); fprintf (dump_file, " (chrec_before = "); print_generic_expr (dump_file, chrec_before); fprintf (dump_file, ")\n (to_add = "); print_generic_expr (dump_file, to_add); fprintf (dump_file, ")\n"); } if (code == MINUS_EXPR) to_add = chrec_fold_multiply (type, to_add, SCALAR_FLOAT_TYPE_P (type) ? build_real (type, dconstm1) : build_int_cst_type (type, -1)); res = add_to_evolution_1 (loop_nb, chrec_before, to_add, at_stmt); if (dump_file && (dump_flags & TDF_SCEV)) { fprintf (dump_file, " (res = "); print_generic_expr (dump_file, res); fprintf (dump_file, "))\n"); } return res; } /* This section selects the loops that will be good candidates for the scalar evolution analysis. For the moment, greedily select all the loop nests we could analyze. */ /* For a loop with a single exit edge, return the COND_EXPR that guards the exit edge. If the expression is too difficult to analyze, then give up. */ gcond * get_loop_exit_condition (const class loop *loop) { gcond *res = NULL; edge exit_edge = single_exit (loop); if (dump_file && (dump_flags & TDF_SCEV)) fprintf (dump_file, "(get_loop_exit_condition \n "); if (exit_edge) { gimple *stmt; stmt = last_stmt (exit_edge->src); if (gcond *cond_stmt = safe_dyn_cast (stmt)) res = cond_stmt; } if (dump_file && (dump_flags & TDF_SCEV)) { print_gimple_stmt (dump_file, res, 0); fprintf (dump_file, ")\n"); } return res; } /* Depth first search algorithm. */ enum t_bool { t_false, t_true, t_dont_know }; static t_bool follow_ssa_edge_expr (class loop *loop, gimple *, tree, gphi *, tree *, int); /* Follow the ssa edge into the binary expression RHS0 CODE RHS1. Return true if the strongly connected component has been found. */ static t_bool follow_ssa_edge_binary (class loop *loop, gimple *at_stmt, tree type, tree rhs0, enum tree_code code, tree rhs1, gphi *halting_phi, tree *evolution_of_loop, int limit) { t_bool res = t_false; tree evol; switch (code) { case POINTER_PLUS_EXPR: case PLUS_EXPR: if (TREE_CODE (rhs0) == SSA_NAME) { if (TREE_CODE (rhs1) == SSA_NAME) { /* Match an assignment under the form: "a = b + c". */ /* We want only assignments of form "name + name" contribute to LIMIT, as the other cases do not necessarily contribute to the complexity of the expression. */ limit++; evol = *evolution_of_loop; evol = add_to_evolution (loop->num, chrec_convert (type, evol, at_stmt), code, rhs1, at_stmt); res = follow_ssa_edge_expr (loop, at_stmt, rhs0, halting_phi, &evol, limit); if (res == t_true) *evolution_of_loop = evol; else if (res == t_false) { *evolution_of_loop = add_to_evolution (loop->num, chrec_convert (type, *evolution_of_loop, at_stmt), code, rhs0, at_stmt); res = follow_ssa_edge_expr (loop, at_stmt, rhs1, halting_phi, evolution_of_loop, limit); } } else gcc_unreachable (); /* Handled in caller. */ } else if (TREE_CODE (rhs1) == SSA_NAME) { /* Match an assignment under the form: "a = ... + c". */ *evolution_of_loop = add_to_evolution (loop->num, chrec_convert (type, *evolution_of_loop, at_stmt), code, rhs0, at_stmt); res = follow_ssa_edge_expr (loop, at_stmt, rhs1, halting_phi, evolution_of_loop, limit); } else /* Otherwise, match an assignment under the form: "a = ... + ...". */ /* And there is nothing to do. */ res = t_false; break; case MINUS_EXPR: /* This case is under the form "opnd0 = rhs0 - rhs1". */ if (TREE_CODE (rhs0) == SSA_NAME) gcc_unreachable (); /* Handled in caller. */ else /* Otherwise, match an assignment under the form: "a = ... - ...". */ /* And there is nothing to do. */ res = t_false; break; default: res = t_false; } return res; } /* Checks whether the I-th argument of a PHI comes from a backedge. */ static bool backedge_phi_arg_p (gphi *phi, int i) { const_edge e = gimple_phi_arg_edge (phi, i); /* We would in fact like to test EDGE_DFS_BACK here, but we do not care about updating it anywhere, and this should work as well most of the time. */ if (e->flags & EDGE_IRREDUCIBLE_LOOP) return true; return false; } /* Helper function for one branch of the condition-phi-node. Return true if the strongly connected component has been found following this path. */ static inline t_bool follow_ssa_edge_in_condition_phi_branch (int i, class loop *loop, gphi *condition_phi, gphi *halting_phi, tree *evolution_of_branch, tree init_cond, int limit) { tree branch = PHI_ARG_DEF (condition_phi, i); *evolution_of_branch = chrec_dont_know; /* Do not follow back edges (they must belong to an irreducible loop, which we really do not want to worry about). */ if (backedge_phi_arg_p (condition_phi, i)) return t_false; if (TREE_CODE (branch) == SSA_NAME) { *evolution_of_branch = init_cond; return follow_ssa_edge_expr (loop, condition_phi, branch, halting_phi, evolution_of_branch, limit); } /* This case occurs when one of the condition branches sets the variable to a constant: i.e. a phi-node like "a_2 = PHI ;". FIXME: This case have to be refined correctly: in some cases it is possible to say something better than chrec_dont_know, for example using a wrap-around notation. */ return t_false; } /* This function merges the branches of a condition-phi-node in a loop. */ static t_bool follow_ssa_edge_in_condition_phi (class loop *loop, gphi *condition_phi, gphi *halting_phi, tree *evolution_of_loop, int limit) { int i, n; tree init = *evolution_of_loop; tree evolution_of_branch; t_bool res = follow_ssa_edge_in_condition_phi_branch (0, loop, condition_phi, halting_phi, &evolution_of_branch, init, limit); if (res == t_false || res == t_dont_know) return res; *evolution_of_loop = evolution_of_branch; n = gimple_phi_num_args (condition_phi); for (i = 1; i < n; i++) { /* Quickly give up when the evolution of one of the branches is not known. */ if (*evolution_of_loop == chrec_dont_know) return t_true; /* Increase the limit by the PHI argument number to avoid exponential time and memory complexity. */ res = follow_ssa_edge_in_condition_phi_branch (i, loop, condition_phi, halting_phi, &evolution_of_branch, init, limit + i); if (res == t_false || res == t_dont_know) return res; *evolution_of_loop = chrec_merge (*evolution_of_loop, evolution_of_branch); } return t_true; } /* Follow an SSA edge in an inner loop. It computes the overall effect of the loop, and following the symbolic initial conditions, it follows the edges in the parent loop. The inner loop is considered as a single statement. */ static t_bool follow_ssa_edge_inner_loop_phi (class loop *outer_loop, gphi *loop_phi_node, gphi *halting_phi, tree *evolution_of_loop, int limit) { class loop *loop = loop_containing_stmt (loop_phi_node); tree ev = analyze_scalar_evolution (loop, PHI_RESULT (loop_phi_node)); /* Sometimes, the inner loop is too difficult to analyze, and the result of the analysis is a symbolic parameter. */ if (ev == PHI_RESULT (loop_phi_node)) { t_bool res = t_false; int i, n = gimple_phi_num_args (loop_phi_node); for (i = 0; i < n; i++) { tree arg = PHI_ARG_DEF (loop_phi_node, i); basic_block bb; /* Follow the edges that exit the inner loop. */ bb = gimple_phi_arg_edge (loop_phi_node, i)->src; if (!flow_bb_inside_loop_p (loop, bb)) res = follow_ssa_edge_expr (outer_loop, loop_phi_node, arg, halting_phi, evolution_of_loop, limit); if (res == t_true) break; } /* If the path crosses this loop-phi, give up. */ if (res == t_true) *evolution_of_loop = chrec_dont_know; return res; } /* Otherwise, compute the overall effect of the inner loop. */ ev = compute_overall_effect_of_inner_loop (loop, ev); return follow_ssa_edge_expr (outer_loop, loop_phi_node, ev, halting_phi, evolution_of_loop, limit); } /* Follow the ssa edge into the expression EXPR. Return true if the strongly connected component has been found. */ static t_bool follow_ssa_edge_expr (class loop *loop, gimple *at_stmt, tree expr, gphi *halting_phi, tree *evolution_of_loop, int limit) { enum tree_code code; tree type, rhs0, rhs1 = NULL_TREE; /* The EXPR is one of the following cases: - an SSA_NAME, - an INTEGER_CST, - a PLUS_EXPR, - a POINTER_PLUS_EXPR, - a MINUS_EXPR, - an ASSERT_EXPR, - other cases are not yet handled. */ /* For SSA_NAME look at the definition statement, handling PHI nodes and otherwise expand appropriately for the expression handling below. */ tail_recurse: if (TREE_CODE (expr) == SSA_NAME) { gimple *def = SSA_NAME_DEF_STMT (expr); if (gimple_nop_p (def)) return t_false; /* Give up if the path is longer than the MAX that we allow. */ if (limit > param_scev_max_expr_complexity) { *evolution_of_loop = chrec_dont_know; return t_dont_know; } if (gphi *phi = dyn_cast (def)) { if (!loop_phi_node_p (phi)) /* DEF is a condition-phi-node. Follow the branches, and record their evolutions. Finally, merge the collected information and set the approximation to the main variable. */ return follow_ssa_edge_in_condition_phi (loop, phi, halting_phi, evolution_of_loop, limit); /* When the analyzed phi is the halting_phi, the depth-first search is over: we have found a path from the halting_phi to itself in the loop. */ if (phi == halting_phi) return t_true; /* Otherwise, the evolution of the HALTING_PHI depends on the evolution of another loop-phi-node, i.e. the evolution function is a higher degree polynomial. */ class loop *def_loop = loop_containing_stmt (def); if (def_loop == loop) return t_false; /* Inner loop. */ if (flow_loop_nested_p (loop, def_loop)) return follow_ssa_edge_inner_loop_phi (loop, phi, halting_phi, evolution_of_loop, limit + 1); /* Outer loop. */ return t_false; } /* At this level of abstraction, the program is just a set of GIMPLE_ASSIGNs and PHI_NODEs. In principle there is no other def to be handled. */ if (!is_gimple_assign (def)) return t_false; code = gimple_assign_rhs_code (def); switch (get_gimple_rhs_class (code)) { case GIMPLE_BINARY_RHS: rhs0 = gimple_assign_rhs1 (def); rhs1 = gimple_assign_rhs2 (def); break; case GIMPLE_UNARY_RHS: case GIMPLE_SINGLE_RHS: rhs0 = gimple_assign_rhs1 (def); break; default: return t_false; } type = TREE_TYPE (gimple_assign_lhs (def)); at_stmt = def; } else { code = TREE_CODE (expr); type = TREE_TYPE (expr); switch (code) { CASE_CONVERT: rhs0 = TREE_OPERAND (expr, 0); break; case POINTER_PLUS_EXPR: case PLUS_EXPR: case MINUS_EXPR: rhs0 = TREE_OPERAND (expr, 0); rhs1 = TREE_OPERAND (expr, 1); break; default: rhs0 = expr; } } switch (code) { CASE_CONVERT: { /* This assignment is under the form "a_1 = (cast) rhs. */ t_bool res = follow_ssa_edge_expr (loop, at_stmt, rhs0, halting_phi, evolution_of_loop, limit); *evolution_of_loop = chrec_convert (type, *evolution_of_loop, at_stmt); return res; } case INTEGER_CST: /* This assignment is under the form "a_1 = 7". */ return t_false; case ADDR_EXPR: { /* Handle &MEM[ptr + CST] which is equivalent to POINTER_PLUS_EXPR. */ if (TREE_CODE (TREE_OPERAND (rhs0, 0)) != MEM_REF) return t_false; tree mem = TREE_OPERAND (rhs0, 0); rhs0 = TREE_OPERAND (mem, 0); rhs1 = TREE_OPERAND (mem, 1); code = POINTER_PLUS_EXPR; } /* Fallthru. */ case POINTER_PLUS_EXPR: case PLUS_EXPR: case MINUS_EXPR: /* This case is under the form "rhs0 +- rhs1". */ STRIP_USELESS_TYPE_CONVERSION (rhs0); STRIP_USELESS_TYPE_CONVERSION (rhs1); if (TREE_CODE (rhs0) == SSA_NAME && (TREE_CODE (rhs1) != SSA_NAME || code == MINUS_EXPR)) { /* Match an assignment under the form: "a = b +- ...". Use tail-recursion for the simple case. */ *evolution_of_loop = add_to_evolution (loop->num, chrec_convert (type, *evolution_of_loop, at_stmt), code, rhs1, at_stmt); expr = rhs0; goto tail_recurse; } /* Else search for the SCC in both rhs0 and rhs1. */ return follow_ssa_edge_binary (loop, at_stmt, type, rhs0, code, rhs1, halting_phi, evolution_of_loop, limit); case ASSERT_EXPR: /* This assignment is of the form: "a_1 = ASSERT_EXPR " It must be handled as a copy assignment of the form a_1 = a_2. */ expr = ASSERT_EXPR_VAR (rhs0); goto tail_recurse; default: return t_false; } } /* Simplify PEELED_CHREC represented by (init_cond, arg) in LOOP. Handle below case and return the corresponding POLYNOMIAL_CHREC: # i_17 = PHI # _20 = PHI <_5(5), start_4(D)(3)> ... i_13 = i_17 + 1; _5 = start_4(D) + i_13; Though variable _20 appears as a PEELED_CHREC in the form of (start_4, _5)_LOOP, it's a POLYNOMIAL_CHREC like {start_4, 1}_LOOP. See PR41488. */ static tree simplify_peeled_chrec (class loop *loop, tree arg, tree init_cond) { aff_tree aff1, aff2; tree ev, left, right, type, step_val; hash_map *peeled_chrec_map = NULL; ev = instantiate_parameters (loop, analyze_scalar_evolution (loop, arg)); if (ev == NULL_TREE || TREE_CODE (ev) != POLYNOMIAL_CHREC) return chrec_dont_know; left = CHREC_LEFT (ev); right = CHREC_RIGHT (ev); type = TREE_TYPE (left); step_val = chrec_fold_plus (type, init_cond, right); /* Transform (init, {left, right}_LOOP)_LOOP to {init, right}_LOOP if "left" equals to "init + right". */ if (operand_equal_p (left, step_val, 0)) { if (dump_file && (dump_flags & TDF_SCEV)) fprintf (dump_file, "Simplify PEELED_CHREC into POLYNOMIAL_CHREC.\n"); return build_polynomial_chrec (loop->num, init_cond, right); } /* The affine code only deals with pointer and integer types. */ if (!POINTER_TYPE_P (type) && !INTEGRAL_TYPE_P (type)) return chrec_dont_know; /* Try harder to check if they are equal. */ tree_to_aff_combination_expand (left, type, &aff1, &peeled_chrec_map); tree_to_aff_combination_expand (step_val, type, &aff2, &peeled_chrec_map); free_affine_expand_cache (&peeled_chrec_map); aff_combination_scale (&aff2, -1); aff_combination_add (&aff1, &aff2); /* Transform (init, {left, right}_LOOP)_LOOP to {init, right}_LOOP if "left" equals to "init + right". */ if (aff_combination_zero_p (&aff1)) { if (dump_file && (dump_flags & TDF_SCEV)) fprintf (dump_file, "Simplify PEELED_CHREC into POLYNOMIAL_CHREC.\n"); return build_polynomial_chrec (loop->num, init_cond, right); } return chrec_dont_know; } /* Given a LOOP_PHI_NODE, this function determines the evolution function from LOOP_PHI_NODE to LOOP_PHI_NODE in the loop. */ static tree analyze_evolution_in_loop (gphi *loop_phi_node, tree init_cond) { int i, n = gimple_phi_num_args (loop_phi_node); tree evolution_function = chrec_not_analyzed_yet; class loop *loop = loop_containing_stmt (loop_phi_node); basic_block bb; static bool simplify_peeled_chrec_p = true; if (dump_file && (dump_flags & TDF_SCEV)) { fprintf (dump_file, "(analyze_evolution_in_loop \n"); fprintf (dump_file, " (loop_phi_node = "); print_gimple_stmt (dump_file, loop_phi_node, 0); fprintf (dump_file, ")\n"); } for (i = 0; i < n; i++) { tree arg = PHI_ARG_DEF (loop_phi_node, i); tree ev_fn; t_bool res; /* Select the edges that enter the loop body. */ bb = gimple_phi_arg_edge (loop_phi_node, i)->src; if (!flow_bb_inside_loop_p (loop, bb)) continue; if (TREE_CODE (arg) == SSA_NAME) { bool val = false; /* Pass in the initial condition to the follow edge function. */ ev_fn = init_cond; res = follow_ssa_edge_expr (loop, loop_phi_node, arg, loop_phi_node, &ev_fn, 0); /* If ev_fn has no evolution in the inner loop, and the init_cond is not equal to ev_fn, then we have an ambiguity between two possible values, as we cannot know the number of iterations at this point. */ if (TREE_CODE (ev_fn) != POLYNOMIAL_CHREC && no_evolution_in_loop_p (ev_fn, loop->num, &val) && val && !operand_equal_p (init_cond, ev_fn, 0)) ev_fn = chrec_dont_know; } else res = t_false; /* When it is impossible to go back on the same loop_phi_node by following the ssa edges, the evolution is represented by a peeled chrec, i.e. the first iteration, EV_FN has the value INIT_COND, then all the other iterations it has the value of ARG. For the moment, PEELED_CHREC nodes are not built. */ if (res != t_true) { ev_fn = chrec_dont_know; /* Try to recognize POLYNOMIAL_CHREC which appears in the form of PEELED_CHREC, but guard the process with a bool variable to keep the analyzer from infinite recurrence for real PEELED_RECs. */ if (simplify_peeled_chrec_p && TREE_CODE (arg) == SSA_NAME) { simplify_peeled_chrec_p = false; ev_fn = simplify_peeled_chrec (loop, arg, init_cond); simplify_peeled_chrec_p = true; } } /* When there are multiple back edges of the loop (which in fact never happens currently, but nevertheless), merge their evolutions. */ evolution_function = chrec_merge (evolution_function, ev_fn); if (evolution_function == chrec_dont_know) break; } if (dump_file && (dump_flags & TDF_SCEV)) { fprintf (dump_file, " (evolution_function = "); print_generic_expr (dump_file, evolution_function); fprintf (dump_file, "))\n"); } return evolution_function; } /* Looks to see if VAR is a copy of a constant (via straightforward assignments or degenerate phi's). If so, returns the constant; else, returns VAR. */ static tree follow_copies_to_constant (tree var) { tree res = var; while (TREE_CODE (res) == SSA_NAME /* We face not updated SSA form in multiple places and this walk may end up in sibling loops so we have to guard it. */ && !name_registered_for_update_p (res)) { gimple *def = SSA_NAME_DEF_STMT (res); if (gphi *phi = dyn_cast (def)) { if (tree rhs = degenerate_phi_result (phi)) res = rhs; else break; } else if (gimple_assign_single_p (def)) /* Will exit loop if not an SSA_NAME. */ res = gimple_assign_rhs1 (def); else break; } if (CONSTANT_CLASS_P (res)) return res; return var; } /* Given a loop-phi-node, return the initial conditions of the variable on entry of the loop. When the CCP has propagated constants into the loop-phi-node, the initial condition is instantiated, otherwise the initial condition is kept symbolic. This analyzer does not analyze the evolution outside the current loop, and leaves this task to the on-demand tree reconstructor. */ static tree analyze_initial_condition (gphi *loop_phi_node) { int i, n; tree init_cond = chrec_not_analyzed_yet; class loop *loop = loop_containing_stmt (loop_phi_node); if (dump_file && (dump_flags & TDF_SCEV)) { fprintf (dump_file, "(analyze_initial_condition \n"); fprintf (dump_file, " (loop_phi_node = \n"); print_gimple_stmt (dump_file, loop_phi_node, 0); fprintf (dump_file, ")\n"); } n = gimple_phi_num_args (loop_phi_node); for (i = 0; i < n; i++) { tree branch = PHI_ARG_DEF (loop_phi_node, i); basic_block bb = gimple_phi_arg_edge (loop_phi_node, i)->src; /* When the branch is oriented to the loop's body, it does not contribute to the initial condition. */ if (flow_bb_inside_loop_p (loop, bb)) continue; if (init_cond == chrec_not_analyzed_yet) { init_cond = branch; continue; } if (TREE_CODE (branch) == SSA_NAME) { init_cond = chrec_dont_know; break; } init_cond = chrec_merge (init_cond, branch); } /* Ooops -- a loop without an entry??? */ if (init_cond == chrec_not_analyzed_yet) init_cond = chrec_dont_know; /* We may not have fully constant propagated IL. Handle degenerate PHIs here to not miss important early loop unrollings. */ init_cond = follow_copies_to_constant (init_cond); if (dump_file && (dump_flags & TDF_SCEV)) { fprintf (dump_file, " (init_cond = "); print_generic_expr (dump_file, init_cond); fprintf (dump_file, "))\n"); } return init_cond; } /* Analyze the scalar evolution for LOOP_PHI_NODE. */ static tree interpret_loop_phi (class loop *loop, gphi *loop_phi_node) { tree res; class loop *phi_loop = loop_containing_stmt (loop_phi_node); tree init_cond; gcc_assert (phi_loop == loop); /* Otherwise really interpret the loop phi. */ init_cond = analyze_initial_condition (loop_phi_node); res = analyze_evolution_in_loop (loop_phi_node, init_cond); /* Verify we maintained the correct initial condition throughout possible conversions in the SSA chain. */ if (res != chrec_dont_know) { tree new_init = res; if (CONVERT_EXPR_P (res) && TREE_CODE (TREE_OPERAND (res, 0)) == POLYNOMIAL_CHREC) new_init = fold_convert (TREE_TYPE (res), CHREC_LEFT (TREE_OPERAND (res, 0))); else if (TREE_CODE (res) == POLYNOMIAL_CHREC) new_init = CHREC_LEFT (res); STRIP_USELESS_TYPE_CONVERSION (new_init); if (TREE_CODE (new_init) == POLYNOMIAL_CHREC || !operand_equal_p (init_cond, new_init, 0)) return chrec_dont_know; } return res; } /* This function merges the branches of a condition-phi-node, contained in the outermost loop, and whose arguments are already analyzed. */ static tree interpret_condition_phi (class loop *loop, gphi *condition_phi) { int i, n = gimple_phi_num_args (condition_phi); tree res = chrec_not_analyzed_yet; for (i = 0; i < n; i++) { tree branch_chrec; if (backedge_phi_arg_p (condition_phi, i)) { res = chrec_dont_know; break; } branch_chrec = analyze_scalar_evolution (loop, PHI_ARG_DEF (condition_phi, i)); res = chrec_merge (res, branch_chrec); if (res == chrec_dont_know) break; } return res; } /* Interpret the operation RHS1 OP RHS2. If we didn't analyze this node before, follow the definitions until ending either on an analyzed GIMPLE_ASSIGN, or on a loop-phi-node. On the return path, this function propagates evolutions (ala constant copy propagation). OPND1 is not a GIMPLE expression because we could analyze the effect of an inner loop: see interpret_loop_phi. */ static tree interpret_rhs_expr (class loop *loop, gimple *at_stmt, tree type, tree rhs1, enum tree_code code, tree rhs2) { tree res, chrec1, chrec2, ctype; gimple *def; if (get_gimple_rhs_class (code) == GIMPLE_SINGLE_RHS) { if (is_gimple_min_invariant (rhs1)) return chrec_convert (type, rhs1, at_stmt); if (code == SSA_NAME) return chrec_convert (type, analyze_scalar_evolution (loop, rhs1), at_stmt); if (code == ASSERT_EXPR) { rhs1 = ASSERT_EXPR_VAR (rhs1); return chrec_convert (type, analyze_scalar_evolution (loop, rhs1), at_stmt); } } switch (code) { case ADDR_EXPR: if (TREE_CODE (TREE_OPERAND (rhs1, 0)) == MEM_REF || handled_component_p (TREE_OPERAND (rhs1, 0))) { machine_mode mode; poly_int64 bitsize, bitpos; int unsignedp, reversep; int volatilep = 0; tree base, offset; tree chrec3; tree unitpos; base = get_inner_reference (TREE_OPERAND (rhs1, 0), &bitsize, &bitpos, &offset, &mode, &unsignedp, &reversep, &volatilep); if (TREE_CODE (base) == MEM_REF) { rhs2 = TREE_OPERAND (base, 1); rhs1 = TREE_OPERAND (base, 0); chrec1 = analyze_scalar_evolution (loop, rhs1); chrec2 = analyze_scalar_evolution (loop, rhs2); chrec1 = chrec_convert (type, chrec1, at_stmt); chrec2 = chrec_convert (TREE_TYPE (rhs2), chrec2, at_stmt); chrec1 = instantiate_parameters (loop, chrec1); chrec2 = instantiate_parameters (loop, chrec2); res = chrec_fold_plus (type, chrec1, chrec2); } else { chrec1 = analyze_scalar_evolution_for_address_of (loop, base); chrec1 = chrec_convert (type, chrec1, at_stmt); res = chrec1; } if (offset != NULL_TREE) { chrec2 = analyze_scalar_evolution (loop, offset); chrec2 = chrec_convert (TREE_TYPE (offset), chrec2, at_stmt); chrec2 = instantiate_parameters (loop, chrec2); res = chrec_fold_plus (type, res, chrec2); } if (maybe_ne (bitpos, 0)) { unitpos = size_int (exact_div (bitpos, BITS_PER_UNIT)); chrec3 = analyze_scalar_evolution (loop, unitpos); chrec3 = chrec_convert (TREE_TYPE (unitpos), chrec3, at_stmt); chrec3 = instantiate_parameters (loop, chrec3); res = chrec_fold_plus (type, res, chrec3); } } else res = chrec_dont_know; break; case POINTER_PLUS_EXPR: chrec1 = analyze_scalar_evolution (loop, rhs1); chrec2 = analyze_scalar_evolution (loop, rhs2); chrec1 = chrec_convert (type, chrec1, at_stmt); chrec2 = chrec_convert (TREE_TYPE (rhs2), chrec2, at_stmt); chrec1 = instantiate_parameters (loop, chrec1); chrec2 = instantiate_parameters (loop, chrec2); res = chrec_fold_plus (type, chrec1, chrec2); break; case PLUS_EXPR: chrec1 = analyze_scalar_evolution (loop, rhs1); chrec2 = analyze_scalar_evolution (loop, rhs2); ctype = type; /* When the stmt is conditionally executed re-write the CHREC into a form that has well-defined behavior on overflow. */ if (at_stmt && INTEGRAL_TYPE_P (type) && ! TYPE_OVERFLOW_WRAPS (type) && ! dominated_by_p (CDI_DOMINATORS, loop->latch, gimple_bb (at_stmt))) ctype = unsigned_type_for (type); chrec1 = chrec_convert (ctype, chrec1, at_stmt); chrec2 = chrec_convert (ctype, chrec2, at_stmt); chrec1 = instantiate_parameters (loop, chrec1); chrec2 = instantiate_parameters (loop, chrec2); res = chrec_fold_plus (ctype, chrec1, chrec2); if (type != ctype) res = chrec_convert (type, res, at_stmt); break; case MINUS_EXPR: chrec1 = analyze_scalar_evolution (loop, rhs1); chrec2 = analyze_scalar_evolution (loop, rhs2); ctype = type; /* When the stmt is conditionally executed re-write the CHREC into a form that has well-defined behavior on overflow. */ if (at_stmt && INTEGRAL_TYPE_P (type) && ! TYPE_OVERFLOW_WRAPS (type) && ! dominated_by_p (CDI_DOMINATORS, loop->latch, gimple_bb (at_stmt))) ctype = unsigned_type_for (type); chrec1 = chrec_convert (ctype, chrec1, at_stmt); chrec2 = chrec_convert (ctype, chrec2, at_stmt); chrec1 = instantiate_parameters (loop, chrec1); chrec2 = instantiate_parameters (loop, chrec2); res = chrec_fold_minus (ctype, chrec1, chrec2); if (type != ctype) res = chrec_convert (type, res, at_stmt); break; case NEGATE_EXPR: chrec1 = analyze_scalar_evolution (loop, rhs1); ctype = type; /* When the stmt is conditionally executed re-write the CHREC into a form that has well-defined behavior on overflow. */ if (at_stmt && INTEGRAL_TYPE_P (type) && ! TYPE_OVERFLOW_WRAPS (type) && ! dominated_by_p (CDI_DOMINATORS, loop->latch, gimple_bb (at_stmt))) ctype = unsigned_type_for (type); chrec1 = chrec_convert (ctype, chrec1, at_stmt); /* TYPE may be integer, real or complex, so use fold_convert. */ chrec1 = instantiate_parameters (loop, chrec1); res = chrec_fold_multiply (ctype, chrec1, fold_convert (ctype, integer_minus_one_node)); if (type != ctype) res = chrec_convert (type, res, at_stmt); break; case BIT_NOT_EXPR: /* Handle ~X as -1 - X. */ chrec1 = analyze_scalar_evolution (loop, rhs1); chrec1 = chrec_convert (type, chrec1, at_stmt); chrec1 = instantiate_parameters (loop, chrec1); res = chrec_fold_minus (type, fold_convert (type, integer_minus_one_node), chrec1); break; case MULT_EXPR: chrec1 = analyze_scalar_evolution (loop, rhs1); chrec2 = analyze_scalar_evolution (loop, rhs2); ctype = type; /* When the stmt is conditionally executed re-write the CHREC into a form that has well-defined behavior on overflow. */ if (at_stmt && INTEGRAL_TYPE_P (type) && ! TYPE_OVERFLOW_WRAPS (type) && ! dominated_by_p (CDI_DOMINATORS, loop->latch, gimple_bb (at_stmt))) ctype = unsigned_type_for (type); chrec1 = chrec_convert (ctype, chrec1, at_stmt); chrec2 = chrec_convert (ctype, chrec2, at_stmt); chrec1 = instantiate_parameters (loop, chrec1); chrec2 = instantiate_parameters (loop, chrec2); res = chrec_fold_multiply (ctype, chrec1, chrec2); if (type != ctype) res = chrec_convert (type, res, at_stmt); break; case LSHIFT_EXPR: { /* Handle A< 0 && (unsigned) precision < TYPE_PRECISION (TREE_TYPE (rhs1))) { tree utype = build_nonstandard_integer_type (precision, 1); if (TYPE_PRECISION (utype) < TYPE_PRECISION (TREE_TYPE (rhs1))) { chrec1 = analyze_scalar_evolution (loop, rhs1); chrec1 = chrec_convert (utype, chrec1, at_stmt); res = chrec_convert (TREE_TYPE (rhs1), chrec1, at_stmt); } } } break; default: res = chrec_dont_know; break; } return res; } /* Interpret the expression EXPR. */ static tree interpret_expr (class loop *loop, gimple *at_stmt, tree expr) { enum tree_code code; tree type = TREE_TYPE (expr), op0, op1; if (automatically_generated_chrec_p (expr)) return expr; if (TREE_CODE (expr) == POLYNOMIAL_CHREC || TREE_CODE (expr) == CALL_EXPR || get_gimple_rhs_class (TREE_CODE (expr)) == GIMPLE_TERNARY_RHS) return chrec_dont_know; extract_ops_from_tree (expr, &code, &op0, &op1); return interpret_rhs_expr (loop, at_stmt, type, op0, code, op1); } /* Interpret the rhs of the assignment STMT. */ static tree interpret_gimple_assign (class loop *loop, gimple *stmt) { tree type = TREE_TYPE (gimple_assign_lhs (stmt)); enum tree_code code = gimple_assign_rhs_code (stmt); return interpret_rhs_expr (loop, stmt, type, gimple_assign_rhs1 (stmt), code, gimple_assign_rhs2 (stmt)); } /* This section contains all the entry points: - number_of_iterations_in_loop, - analyze_scalar_evolution, - instantiate_parameters. */ /* Helper recursive function. */ static tree analyze_scalar_evolution_1 (class loop *loop, tree var) { gimple *def; basic_block bb; class loop *def_loop; tree res; if (TREE_CODE (var) != SSA_NAME) return interpret_expr (loop, NULL, var); def = SSA_NAME_DEF_STMT (var); bb = gimple_bb (def); def_loop = bb->loop_father; if (!flow_bb_inside_loop_p (loop, bb)) { /* Keep symbolic form, but look through obvious copies for constants. */ res = follow_copies_to_constant (var); goto set_and_end; } if (loop != def_loop) { res = analyze_scalar_evolution_1 (def_loop, var); class loop *loop_to_skip = superloop_at_depth (def_loop, loop_depth (loop) + 1); res = compute_overall_effect_of_inner_loop (loop_to_skip, res); if (chrec_contains_symbols_defined_in_loop (res, loop->num)) res = analyze_scalar_evolution_1 (loop, res); goto set_and_end; } switch (gimple_code (def)) { case GIMPLE_ASSIGN: res = interpret_gimple_assign (loop, def); break; case GIMPLE_PHI: if (loop_phi_node_p (def)) res = interpret_loop_phi (loop, as_a (def)); else res = interpret_condition_phi (loop, as_a (def)); break; default: res = chrec_dont_know; break; } set_and_end: /* Keep the symbolic form. */ if (res == chrec_dont_know) res = var; if (loop == def_loop) set_scalar_evolution (block_before_loop (loop), var, res); return res; } /* Analyzes and returns the scalar evolution of the ssa_name VAR in LOOP. LOOP is the loop in which the variable is used. Example of use: having a pointer VAR to a SSA_NAME node, STMT a pointer to the statement that uses this variable, in order to determine the evolution function of the variable, use the following calls: loop_p loop = loop_containing_stmt (stmt); tree chrec_with_symbols = analyze_scalar_evolution (loop, var); tree chrec_instantiated = instantiate_parameters (loop, chrec_with_symbols); */ tree analyze_scalar_evolution (class loop *loop, tree var) { tree res; /* ??? Fix callers. */ if (! loop) return var; if (dump_file && (dump_flags & TDF_SCEV)) { fprintf (dump_file, "(analyze_scalar_evolution \n"); fprintf (dump_file, " (loop_nb = %d)\n", loop->num); fprintf (dump_file, " (scalar = "); print_generic_expr (dump_file, var); fprintf (dump_file, ")\n"); } res = get_scalar_evolution (block_before_loop (loop), var); if (res == chrec_not_analyzed_yet) { /* We'll recurse into instantiate_scev, avoid tearing down the instantiate cache repeatedly and keep it live from here. */ bool destr = false; if (!global_cache) { global_cache = new instantiate_cache_type; destr = true; } res = analyze_scalar_evolution_1 (loop, var); if (destr) { delete global_cache; global_cache = NULL; } } if (dump_file && (dump_flags & TDF_SCEV)) fprintf (dump_file, ")\n"); return res; } /* Analyzes and returns the scalar evolution of VAR address in LOOP. */ static tree analyze_scalar_evolution_for_address_of (class loop *loop, tree var) { return analyze_scalar_evolution (loop, build_fold_addr_expr (var)); } /* Analyze scalar evolution of use of VERSION in USE_LOOP with respect to WRTO_LOOP (which should be a superloop of USE_LOOP) FOLDED_CASTS is set to true if resolve_mixers used chrec_convert_aggressive (TODO -- not really, we are way too conservative at the moment in order to keep things simple). To illustrate the meaning of USE_LOOP and WRTO_LOOP, consider the following example: for (i = 0; i < 100; i++) -- loop 1 { for (j = 0; j < 100; j++) -- loop 2 { k1 = i; k2 = j; use2 (k1, k2); for (t = 0; t < 100; t++) -- loop 3 use3 (k1, k2); } use1 (k1, k2); } Both k1 and k2 are invariants in loop3, thus analyze_scalar_evolution_in_loop (loop3, loop3, k1) = k1 analyze_scalar_evolution_in_loop (loop3, loop3, k2) = k2 As they are invariant, it does not matter whether we consider their usage in loop 3 or loop 2, hence analyze_scalar_evolution_in_loop (loop2, loop3, k1) = analyze_scalar_evolution_in_loop (loop2, loop2, k1) = i analyze_scalar_evolution_in_loop (loop2, loop3, k2) = analyze_scalar_evolution_in_loop (loop2, loop2, k2) = [0,+,1]_2 Similarly for their evolutions with respect to loop 1. The values of K2 in the use in loop 2 vary independently on loop 1, thus we cannot express the evolution with respect to loop 1: analyze_scalar_evolution_in_loop (loop1, loop3, k1) = analyze_scalar_evolution_in_loop (loop1, loop2, k1) = [0,+,1]_1 analyze_scalar_evolution_in_loop (loop1, loop3, k2) = analyze_scalar_evolution_in_loop (loop1, loop2, k2) = dont_know The value of k2 in the use in loop 1 is known, though: analyze_scalar_evolution_in_loop (loop1, loop1, k1) = [0,+,1]_1 analyze_scalar_evolution_in_loop (loop1, loop1, k2) = 100 */ static tree analyze_scalar_evolution_in_loop (class loop *wrto_loop, class loop *use_loop, tree version, bool *folded_casts) { bool val = false; tree ev = version, tmp; /* We cannot just do tmp = analyze_scalar_evolution (use_loop, version); ev = resolve_mixers (wrto_loop, tmp, folded_casts); as resolve_mixers would query the scalar evolution with respect to wrto_loop. For example, in the situation described in the function comment, suppose that wrto_loop = loop1, use_loop = loop3 and version = k2. Then analyze_scalar_evolution (use_loop, version) = k2 and resolve_mixers (loop1, k2, folded_casts) finds that the value of k2 in loop 1 is 100, which is a wrong result, since we are interested in the value in loop 3. Instead, we need to proceed from use_loop to wrto_loop loop by loop, each time checking that there is no evolution in the inner loop. */ if (folded_casts) *folded_casts = false; while (1) { tmp = analyze_scalar_evolution (use_loop, ev); ev = resolve_mixers (use_loop, tmp, folded_casts); if (use_loop == wrto_loop) return ev; /* If the value of the use changes in the inner loop, we cannot express its value in the outer loop (we might try to return interval chrec, but we do not have a user for it anyway) */ if (!no_evolution_in_loop_p (ev, use_loop->num, &val) || !val) return chrec_dont_know; use_loop = loop_outer (use_loop); } } /* Computes a hash function for database element ELT. */ static inline hashval_t hash_idx_scev_info (const void *elt_) { unsigned idx = ((size_t) elt_) - 2; return scev_info_hasher::hash (&global_cache->entries[idx]); } /* Compares database elements E1 and E2. */ static inline int eq_idx_scev_info (const void *e1, const void *e2) { unsigned idx1 = ((size_t) e1) - 2; return scev_info_hasher::equal (&global_cache->entries[idx1], (const scev_info_str *) e2); } /* Returns from CACHE the slot number of the cached chrec for NAME. */ static unsigned get_instantiated_value_entry (instantiate_cache_type &cache, tree name, edge instantiate_below) { if (!cache.map) { cache.map = htab_create (10, hash_idx_scev_info, eq_idx_scev_info, NULL); cache.entries.create (10); } scev_info_str e; e.name_version = SSA_NAME_VERSION (name); e.instantiated_below = instantiate_below->dest->index; void **slot = htab_find_slot_with_hash (cache.map, &e, scev_info_hasher::hash (&e), INSERT); if (!*slot) { e.chrec = chrec_not_analyzed_yet; *slot = (void *)(size_t)(cache.entries.length () + 2); cache.entries.safe_push (e); } return ((size_t)*slot) - 2; } /* Return the closed_loop_phi node for VAR. If there is none, return NULL_TREE. */ static tree loop_closed_phi_def (tree var) { class loop *loop; edge exit; gphi *phi; gphi_iterator psi; if (var == NULL_TREE || TREE_CODE (var) != SSA_NAME) return NULL_TREE; loop = loop_containing_stmt (SSA_NAME_DEF_STMT (var)); exit = single_exit (loop); if (!exit) return NULL_TREE; for (psi = gsi_start_phis (exit->dest); !gsi_end_p (psi); gsi_next (&psi)) { phi = psi.phi (); if (PHI_ARG_DEF_FROM_EDGE (phi, exit) == var) return PHI_RESULT (phi); } return NULL_TREE; } static tree instantiate_scev_r (edge, class loop *, class loop *, tree, bool *, int); /* Analyze all the parameters of the chrec, between INSTANTIATE_BELOW and EVOLUTION_LOOP, that were left under a symbolic form. CHREC is an SSA_NAME to be instantiated. CACHE is the cache of already instantiated values. Variable pointed by FOLD_CONVERSIONS is set to TRUE when the conversions that may wrap in signed/pointer type are folded, as long as the value of the chrec is preserved. If FOLD_CONVERSIONS is NULL then we don't do such fold. SIZE_EXPR is used for computing the size of the expression to be instantiated, and to stop if it exceeds some limit. */ static tree instantiate_scev_name (edge instantiate_below, class loop *evolution_loop, class loop *inner_loop, tree chrec, bool *fold_conversions, int size_expr) { tree res; class loop *def_loop; basic_block def_bb = gimple_bb (SSA_NAME_DEF_STMT (chrec)); /* A parameter, nothing to do. */ if (!def_bb || !dominated_by_p (CDI_DOMINATORS, def_bb, instantiate_below->dest)) return chrec; /* We cache the value of instantiated variable to avoid exponential time complexity due to reevaluations. We also store the convenient value in the cache in order to prevent infinite recursion -- we do not want to instantiate the SSA_NAME if it is in a mixer structure. This is used for avoiding the instantiation of recursively defined functions, such as: | a_2 -> {0, +, 1, +, a_2}_1 */ unsigned si = get_instantiated_value_entry (*global_cache, chrec, instantiate_below); if (global_cache->get (si) != chrec_not_analyzed_yet) return global_cache->get (si); /* On recursion return chrec_dont_know. */ global_cache->set (si, chrec_dont_know); def_loop = find_common_loop (evolution_loop, def_bb->loop_father); if (! dominated_by_p (CDI_DOMINATORS, def_loop->header, instantiate_below->dest)) { gimple *def = SSA_NAME_DEF_STMT (chrec); if (gassign *ass = dyn_cast (def)) { switch (gimple_assign_rhs_class (ass)) { case GIMPLE_UNARY_RHS: { tree op0 = instantiate_scev_r (instantiate_below, evolution_loop, inner_loop, gimple_assign_rhs1 (ass), fold_conversions, size_expr); if (op0 == chrec_dont_know) return chrec_dont_know; res = fold_build1 (gimple_assign_rhs_code (ass), TREE_TYPE (chrec), op0); break; } case GIMPLE_BINARY_RHS: { tree op0 = instantiate_scev_r (instantiate_below, evolution_loop, inner_loop, gimple_assign_rhs1 (ass), fold_conversions, size_expr); if (op0 == chrec_dont_know) return chrec_dont_know; tree op1 = instantiate_scev_r (instantiate_below, evolution_loop, inner_loop, gimple_assign_rhs2 (ass), fold_conversions, size_expr); if (op1 == chrec_dont_know) return chrec_dont_know; res = fold_build2 (gimple_assign_rhs_code (ass), TREE_TYPE (chrec), op0, op1); break; } default: res = chrec_dont_know; } } else res = chrec_dont_know; global_cache->set (si, res); return res; } /* If the analysis yields a parametric chrec, instantiate the result again. */ res = analyze_scalar_evolution (def_loop, chrec); /* Don't instantiate default definitions. */ if (TREE_CODE (res) == SSA_NAME && SSA_NAME_IS_DEFAULT_DEF (res)) ; /* Don't instantiate loop-closed-ssa phi nodes. */ else if (TREE_CODE (res) == SSA_NAME && loop_depth (loop_containing_stmt (SSA_NAME_DEF_STMT (res))) > loop_depth (def_loop)) { if (res == chrec) res = loop_closed_phi_def (chrec); else res = chrec; /* When there is no loop_closed_phi_def, it means that the variable is not used after the loop: try to still compute the value of the variable when exiting the loop. */ if (res == NULL_TREE) { loop_p loop = loop_containing_stmt (SSA_NAME_DEF_STMT (chrec)); res = analyze_scalar_evolution (loop, chrec); res = compute_overall_effect_of_inner_loop (loop, res); res = instantiate_scev_r (instantiate_below, evolution_loop, inner_loop, res, fold_conversions, size_expr); } else if (dominated_by_p (CDI_DOMINATORS, gimple_bb (SSA_NAME_DEF_STMT (res)), instantiate_below->dest)) res = chrec_dont_know; } else if (res != chrec_dont_know) { if (inner_loop && def_bb->loop_father != inner_loop && !flow_loop_nested_p (def_bb->loop_father, inner_loop)) /* ??? We could try to compute the overall effect of the loop here. */ res = chrec_dont_know; else res = instantiate_scev_r (instantiate_below, evolution_loop, inner_loop, res, fold_conversions, size_expr); } /* Store the correct value to the cache. */ global_cache->set (si, res); return res; } /* Analyze all the parameters of the chrec, between INSTANTIATE_BELOW and EVOLUTION_LOOP, that were left under a symbolic form. CHREC is a polynomial chain of recurrence to be instantiated. CACHE is the cache of already instantiated values. Variable pointed by FOLD_CONVERSIONS is set to TRUE when the conversions that may wrap in signed/pointer type are folded, as long as the value of the chrec is preserved. If FOLD_CONVERSIONS is NULL then we don't do such fold. SIZE_EXPR is used for computing the size of the expression to be instantiated, and to stop if it exceeds some limit. */ static tree instantiate_scev_poly (edge instantiate_below, class loop *evolution_loop, class loop *, tree chrec, bool *fold_conversions, int size_expr) { tree op1; tree op0 = instantiate_scev_r (instantiate_below, evolution_loop, get_chrec_loop (chrec), CHREC_LEFT (chrec), fold_conversions, size_expr); if (op0 == chrec_dont_know) return chrec_dont_know; op1 = instantiate_scev_r (instantiate_below, evolution_loop, get_chrec_loop (chrec), CHREC_RIGHT (chrec), fold_conversions, size_expr); if (op1 == chrec_dont_know) return chrec_dont_know; if (CHREC_LEFT (chrec) != op0 || CHREC_RIGHT (chrec) != op1) { op1 = chrec_convert_rhs (chrec_type (op0), op1, NULL); chrec = build_polynomial_chrec (CHREC_VARIABLE (chrec), op0, op1); } return chrec; } /* Analyze all the parameters of the chrec, between INSTANTIATE_BELOW and EVOLUTION_LOOP, that were left under a symbolic form. "C0 CODE C1" is a binary expression of type TYPE to be instantiated. CACHE is the cache of already instantiated values. Variable pointed by FOLD_CONVERSIONS is set to TRUE when the conversions that may wrap in signed/pointer type are folded, as long as the value of the chrec is preserved. If FOLD_CONVERSIONS is NULL then we don't do such fold. SIZE_EXPR is used for computing the size of the expression to be instantiated, and to stop if it exceeds some limit. */ static tree instantiate_scev_binary (edge instantiate_below, class loop *evolution_loop, class loop *inner_loop, tree chrec, enum tree_code code, tree type, tree c0, tree c1, bool *fold_conversions, int size_expr) { tree op1; tree op0 = instantiate_scev_r (instantiate_below, evolution_loop, inner_loop, c0, fold_conversions, size_expr); if (op0 == chrec_dont_know) return chrec_dont_know; /* While we eventually compute the same op1 if c0 == c1 the process of doing this is expensive so the following short-cut prevents exponential compile-time behavior. */ if (c0 != c1) { op1 = instantiate_scev_r (instantiate_below, evolution_loop, inner_loop, c1, fold_conversions, size_expr); if (op1 == chrec_dont_know) return chrec_dont_know; } else op1 = op0; if (c0 != op0 || c1 != op1) { op0 = chrec_convert (type, op0, NULL); op1 = chrec_convert_rhs (type, op1, NULL); switch (code) { case POINTER_PLUS_EXPR: case PLUS_EXPR: return chrec_fold_plus (type, op0, op1); case MINUS_EXPR: return chrec_fold_minus (type, op0, op1); case MULT_EXPR: return chrec_fold_multiply (type, op0, op1); default: gcc_unreachable (); } } return chrec ? chrec : fold_build2 (code, type, c0, c1); } /* Analyze all the parameters of the chrec, between INSTANTIATE_BELOW and EVOLUTION_LOOP, that were left under a symbolic form. "CHREC" that stands for a convert expression "(TYPE) OP" is to be instantiated. CACHE is the cache of already instantiated values. Variable pointed by FOLD_CONVERSIONS is set to TRUE when the conversions that may wrap in signed/pointer type are folded, as long as the value of the chrec is preserved. If FOLD_CONVERSIONS is NULL then we don't do such fold. SIZE_EXPR is used for computing the size of the expression to be instantiated, and to stop if it exceeds some limit. */ static tree instantiate_scev_convert (edge instantiate_below, class loop *evolution_loop, class loop *inner_loop, tree chrec, tree type, tree op, bool *fold_conversions, int size_expr) { tree op0 = instantiate_scev_r (instantiate_below, evolution_loop, inner_loop, op, fold_conversions, size_expr); if (op0 == chrec_dont_know) return chrec_dont_know; if (fold_conversions) { tree tmp = chrec_convert_aggressive (type, op0, fold_conversions); if (tmp) return tmp; /* If we used chrec_convert_aggressive, we can no longer assume that signed chrecs do not overflow, as chrec_convert does, so avoid calling it in that case. */ if (*fold_conversions) { if (chrec && op0 == op) return chrec; return fold_convert (type, op0); } } return chrec_convert (type, op0, NULL); } /* Analyze all the parameters of the chrec, between INSTANTIATE_BELOW and EVOLUTION_LOOP, that were left under a symbolic form. CHREC is a BIT_NOT_EXPR or a NEGATE_EXPR expression to be instantiated. Handle ~X as -1 - X. Handle -X as -1 * X. CACHE is the cache of already instantiated values. Variable pointed by FOLD_CONVERSIONS is set to TRUE when the conversions that may wrap in signed/pointer type are folded, as long as the value of the chrec is preserved. If FOLD_CONVERSIONS is NULL then we don't do such fold. SIZE_EXPR is used for computing the size of the expression to be instantiated, and to stop if it exceeds some limit. */ static tree instantiate_scev_not (edge instantiate_below, class loop *evolution_loop, class loop *inner_loop, tree chrec, enum tree_code code, tree type, tree op, bool *fold_conversions, int size_expr) { tree op0 = instantiate_scev_r (instantiate_below, evolution_loop, inner_loop, op, fold_conversions, size_expr); if (op0 == chrec_dont_know) return chrec_dont_know; if (op != op0) { op0 = chrec_convert (type, op0, NULL); switch (code) { case BIT_NOT_EXPR: return chrec_fold_minus (type, fold_convert (type, integer_minus_one_node), op0); case NEGATE_EXPR: return chrec_fold_multiply (type, fold_convert (type, integer_minus_one_node), op0); default: gcc_unreachable (); } } return chrec ? chrec : fold_build1 (code, type, op0); } /* Analyze all the parameters of the chrec, between INSTANTIATE_BELOW and EVOLUTION_LOOP, that were left under a symbolic form. CHREC is the scalar evolution to instantiate. CACHE is the cache of already instantiated values. Variable pointed by FOLD_CONVERSIONS is set to TRUE when the conversions that may wrap in signed/pointer type are folded, as long as the value of the chrec is preserved. If FOLD_CONVERSIONS is NULL then we don't do such fold. SIZE_EXPR is used for computing the size of the expression to be instantiated, and to stop if it exceeds some limit. */ static tree instantiate_scev_r (edge instantiate_below, class loop *evolution_loop, class loop *inner_loop, tree chrec, bool *fold_conversions, int size_expr) { /* Give up if the expression is larger than the MAX that we allow. */ if (size_expr++ > param_scev_max_expr_size) return chrec_dont_know; if (chrec == NULL_TREE || automatically_generated_chrec_p (chrec) || is_gimple_min_invariant (chrec)) return chrec; switch (TREE_CODE (chrec)) { case SSA_NAME: return instantiate_scev_name (instantiate_below, evolution_loop, inner_loop, chrec, fold_conversions, size_expr); case POLYNOMIAL_CHREC: return instantiate_scev_poly (instantiate_below, evolution_loop, inner_loop, chrec, fold_conversions, size_expr); case POINTER_PLUS_EXPR: case PLUS_EXPR: case MINUS_EXPR: case MULT_EXPR: return instantiate_scev_binary (instantiate_below, evolution_loop, inner_loop, chrec, TREE_CODE (chrec), chrec_type (chrec), TREE_OPERAND (chrec, 0), TREE_OPERAND (chrec, 1), fold_conversions, size_expr); CASE_CONVERT: return instantiate_scev_convert (instantiate_below, evolution_loop, inner_loop, chrec, TREE_TYPE (chrec), TREE_OPERAND (chrec, 0), fold_conversions, size_expr); case NEGATE_EXPR: case BIT_NOT_EXPR: return instantiate_scev_not (instantiate_below, evolution_loop, inner_loop, chrec, TREE_CODE (chrec), TREE_TYPE (chrec), TREE_OPERAND (chrec, 0), fold_conversions, size_expr); case ADDR_EXPR: if (is_gimple_min_invariant (chrec)) return chrec; /* Fallthru. */ case SCEV_NOT_KNOWN: return chrec_dont_know; case SCEV_KNOWN: return chrec_known; default: if (CONSTANT_CLASS_P (chrec)) return chrec; return chrec_dont_know; } } /* Analyze all the parameters of the chrec that were left under a symbolic form. INSTANTIATE_BELOW is the basic block that stops the recursive instantiation of parameters: a parameter is a variable that is defined in a basic block that dominates INSTANTIATE_BELOW or a function parameter. */ tree instantiate_scev (edge instantiate_below, class loop *evolution_loop, tree chrec) { tree res; if (dump_file && (dump_flags & TDF_SCEV)) { fprintf (dump_file, "(instantiate_scev \n"); fprintf (dump_file, " (instantiate_below = %d -> %d)\n", instantiate_below->src->index, instantiate_below->dest->index); if (evolution_loop) fprintf (dump_file, " (evolution_loop = %d)\n", evolution_loop->num); fprintf (dump_file, " (chrec = "); print_generic_expr (dump_file, chrec); fprintf (dump_file, ")\n"); } bool destr = false; if (!global_cache) { global_cache = new instantiate_cache_type; destr = true; } res = instantiate_scev_r (instantiate_below, evolution_loop, NULL, chrec, NULL, 0); if (destr) { delete global_cache; global_cache = NULL; } if (dump_file && (dump_flags & TDF_SCEV)) { fprintf (dump_file, " (res = "); print_generic_expr (dump_file, res); fprintf (dump_file, "))\n"); } return res; } /* Similar to instantiate_parameters, but does not introduce the evolutions in outer loops for LOOP invariants in CHREC, and does not care about causing overflows, as long as they do not affect value of an expression. */ tree resolve_mixers (class loop *loop, tree chrec, bool *folded_casts) { bool destr = false; bool fold_conversions = false; if (!global_cache) { global_cache = new instantiate_cache_type; destr = true; } tree ret = instantiate_scev_r (loop_preheader_edge (loop), loop, NULL, chrec, &fold_conversions, 0); if (folded_casts && !*folded_casts) *folded_casts = fold_conversions; if (destr) { delete global_cache; global_cache = NULL; } return ret; } /* Entry point for the analysis of the number of iterations pass. This function tries to safely approximate the number of iterations the loop will run. When this property is not decidable at compile time, the result is chrec_dont_know. Otherwise the result is a scalar or a symbolic parameter. When the number of iterations may be equal to zero and the property cannot be determined at compile time, the result is a COND_EXPR that represents in a symbolic form the conditions under which the number of iterations is not zero. Example of analysis: suppose that the loop has an exit condition: "if (b > 49) goto end_loop;" and that in a previous analysis we have determined that the variable 'b' has an evolution function: "EF = {23, +, 5}_2". When we evaluate the function at the point 5, i.e. the value of the variable 'b' after 5 iterations in the loop, we have EF (5) = 48, and EF (6) = 53. In this case the value of 'b' on exit is '53' and the loop body has been executed 6 times. */ tree number_of_latch_executions (class loop *loop) { edge exit; class tree_niter_desc niter_desc; tree may_be_zero; tree res; /* Determine whether the number of iterations in loop has already been computed. */ res = loop->nb_iterations; if (res) return res; may_be_zero = NULL_TREE; if (dump_file && (dump_flags & TDF_SCEV)) fprintf (dump_file, "(number_of_iterations_in_loop = \n"); res = chrec_dont_know; exit = single_exit (loop); if (exit && number_of_iterations_exit (loop, exit, &niter_desc, false)) { may_be_zero = niter_desc.may_be_zero; res = niter_desc.niter; } if (res == chrec_dont_know || !may_be_zero || integer_zerop (may_be_zero)) ; else if (integer_nonzerop (may_be_zero)) res = build_int_cst (TREE_TYPE (res), 0); else if (COMPARISON_CLASS_P (may_be_zero)) res = fold_build3 (COND_EXPR, TREE_TYPE (res), may_be_zero, build_int_cst (TREE_TYPE (res), 0), res); else res = chrec_dont_know; if (dump_file && (dump_flags & TDF_SCEV)) { fprintf (dump_file, " (set_nb_iterations_in_loop = "); print_generic_expr (dump_file, res); fprintf (dump_file, "))\n"); } loop->nb_iterations = res; return res; } /* Counters for the stats. */ struct chrec_stats { unsigned nb_chrecs; unsigned nb_affine; unsigned nb_affine_multivar; unsigned nb_higher_poly; unsigned nb_chrec_dont_know; unsigned nb_undetermined; }; /* Reset the counters. */ static inline void reset_chrecs_counters (struct chrec_stats *stats) { stats->nb_chrecs = 0; stats->nb_affine = 0; stats->nb_affine_multivar = 0; stats->nb_higher_poly = 0; stats->nb_chrec_dont_know = 0; stats->nb_undetermined = 0; } /* Dump the contents of a CHREC_STATS structure. */ static void dump_chrecs_stats (FILE *file, struct chrec_stats *stats) { fprintf (file, "\n(\n"); fprintf (file, "-----------------------------------------\n"); fprintf (file, "%d\taffine univariate chrecs\n", stats->nb_affine); fprintf (file, "%d\taffine multivariate chrecs\n", stats->nb_affine_multivar); fprintf (file, "%d\tdegree greater than 2 polynomials\n", stats->nb_higher_poly); fprintf (file, "%d\tchrec_dont_know chrecs\n", stats->nb_chrec_dont_know); fprintf (file, "-----------------------------------------\n"); fprintf (file, "%d\ttotal chrecs\n", stats->nb_chrecs); fprintf (file, "%d\twith undetermined coefficients\n", stats->nb_undetermined); fprintf (file, "-----------------------------------------\n"); fprintf (file, "%d\tchrecs in the scev database\n", (int) scalar_evolution_info->elements ()); fprintf (file, "%d\tsets in the scev database\n", nb_set_scev); fprintf (file, "%d\tgets in the scev database\n", nb_get_scev); fprintf (file, "-----------------------------------------\n"); fprintf (file, ")\n\n"); } /* Gather statistics about CHREC. */ static void gather_chrec_stats (tree chrec, struct chrec_stats *stats) { if (dump_file && (dump_flags & TDF_STATS)) { fprintf (dump_file, "(classify_chrec "); print_generic_expr (dump_file, chrec); fprintf (dump_file, "\n"); } stats->nb_chrecs++; if (chrec == NULL_TREE) { stats->nb_undetermined++; return; } switch (TREE_CODE (chrec)) { case POLYNOMIAL_CHREC: if (evolution_function_is_affine_p (chrec)) { if (dump_file && (dump_flags & TDF_STATS)) fprintf (dump_file, " affine_univariate\n"); stats->nb_affine++; } else if (evolution_function_is_affine_multivariate_p (chrec, 0)) { if (dump_file && (dump_flags & TDF_STATS)) fprintf (dump_file, " affine_multivariate\n"); stats->nb_affine_multivar++; } else { if (dump_file && (dump_flags & TDF_STATS)) fprintf (dump_file, " higher_degree_polynomial\n"); stats->nb_higher_poly++; } break; default: break; } if (chrec_contains_undetermined (chrec)) { if (dump_file && (dump_flags & TDF_STATS)) fprintf (dump_file, " undetermined\n"); stats->nb_undetermined++; } if (dump_file && (dump_flags & TDF_STATS)) fprintf (dump_file, ")\n"); } /* Classify the chrecs of the whole database. */ void gather_stats_on_scev_database (void) { struct chrec_stats stats; if (!dump_file) return; reset_chrecs_counters (&stats); hash_table::iterator iter; scev_info_str *elt; FOR_EACH_HASH_TABLE_ELEMENT (*scalar_evolution_info, elt, scev_info_str *, iter) gather_chrec_stats (elt->chrec, &stats); dump_chrecs_stats (dump_file, &stats); } /* Initialize the analysis of scalar evolutions for LOOPS. */ void scev_initialize (void) { gcc_assert (! scev_initialized_p ()); scalar_evolution_info = hash_table::create_ggc (100); for (auto loop : loops_list (cfun, 0)) loop->nb_iterations = NULL_TREE; } /* Return true if SCEV is initialized. */ bool scev_initialized_p (void) { return scalar_evolution_info != NULL; } /* Cleans up the information cached by the scalar evolutions analysis in the hash table. */ void scev_reset_htab (void) { if (!scalar_evolution_info) return; scalar_evolution_info->empty (); } /* Cleans up the information cached by the scalar evolutions analysis in the hash table and in the loop->nb_iterations. */ void scev_reset (void) { scev_reset_htab (); for (auto loop : loops_list (cfun, 0)) loop->nb_iterations = NULL_TREE; } /* Return true if the IV calculation in TYPE can overflow based on the knowledge of the upper bound on the number of iterations of LOOP, the BASE and STEP of IV. We do not use information whether TYPE can overflow so it is safe to use this test even for derived IVs not computed every iteration or hypotetical IVs to be inserted into code. */ bool iv_can_overflow_p (class loop *loop, tree type, tree base, tree step) { widest_int nit; wide_int base_min, base_max, step_min, step_max, type_min, type_max; signop sgn = TYPE_SIGN (type); value_range r; if (integer_zerop (step)) return false; if (!INTEGRAL_TYPE_P (TREE_TYPE (base)) || !get_range_query (cfun)->range_of_expr (r, base) || r.kind () != VR_RANGE) return true; base_min = r.lower_bound (); base_max = r.upper_bound (); if (!INTEGRAL_TYPE_P (TREE_TYPE (step)) || !get_range_query (cfun)->range_of_expr (r, step) || r.kind () != VR_RANGE) return true; step_min = r.lower_bound (); step_max = r.upper_bound (); if (!get_max_loop_iterations (loop, &nit)) return true; type_min = wi::min_value (type); type_max = wi::max_value (type); /* Just sanity check that we don't see values out of the range of the type. In this case the arithmetics bellow would overflow. */ gcc_checking_assert (wi::ge_p (base_min, type_min, sgn) && wi::le_p (base_max, type_max, sgn)); /* Account the possible increment in the last ieration. */ wi::overflow_type overflow = wi::OVF_NONE; nit = wi::add (nit, 1, SIGNED, &overflow); if (overflow) return true; /* NIT is typeless and can exceed the precision of the type. In this case overflow is always possible, because we know STEP is non-zero. */ if (wi::min_precision (nit, UNSIGNED) > TYPE_PRECISION (type)) return true; wide_int nit2 = wide_int::from (nit, TYPE_PRECISION (type), UNSIGNED); /* If step can be positive, check that nit*step <= type_max-base. This can be done by unsigned arithmetic and we only need to watch overflow in the multiplication. The right hand side can always be represented in the type. */ if (sgn == UNSIGNED || !wi::neg_p (step_max)) { wi::overflow_type overflow = wi::OVF_NONE; if (wi::gtu_p (wi::mul (step_max, nit2, UNSIGNED, &overflow), type_max - base_max) || overflow) return true; } /* If step can be negative, check that nit*(-step) <= base_min-type_min. */ if (sgn == SIGNED && wi::neg_p (step_min)) { wi::overflow_type overflow, overflow2; overflow = overflow2 = wi::OVF_NONE; if (wi::gtu_p (wi::mul (wi::neg (step_min, &overflow2), nit2, UNSIGNED, &overflow), base_min - type_min) || overflow || overflow2) return true; } return false; } /* Given EV with form of "(type) {inner_base, inner_step}_loop", this function tries to derive condition under which it can be simplified into "{(type)inner_base, (type)inner_step}_loop". The condition is the maximum number that inner iv can iterate. */ static tree derive_simple_iv_with_niters (tree ev, tree *niters) { if (!CONVERT_EXPR_P (ev)) return ev; tree inner_ev = TREE_OPERAND (ev, 0); if (TREE_CODE (inner_ev) != POLYNOMIAL_CHREC) return ev; tree init = CHREC_LEFT (inner_ev); tree step = CHREC_RIGHT (inner_ev); if (TREE_CODE (init) != INTEGER_CST || TREE_CODE (step) != INTEGER_CST || integer_zerop (step)) return ev; tree type = TREE_TYPE (ev); tree inner_type = TREE_TYPE (inner_ev); if (TYPE_PRECISION (inner_type) >= TYPE_PRECISION (type)) return ev; /* Type conversion in "(type) {inner_base, inner_step}_loop" can be folded only if inner iv won't overflow. We compute the maximum number the inner iv can iterate before overflowing and return the simplified affine iv. */ tree delta; init = fold_convert (type, init); step = fold_convert (type, step); ev = build_polynomial_chrec (CHREC_VARIABLE (inner_ev), init, step); if (tree_int_cst_sign_bit (step)) { tree bound = lower_bound_in_type (inner_type, inner_type); delta = fold_build2 (MINUS_EXPR, type, init, fold_convert (type, bound)); step = fold_build1 (NEGATE_EXPR, type, step); } else { tree bound = upper_bound_in_type (inner_type, inner_type); delta = fold_build2 (MINUS_EXPR, type, fold_convert (type, bound), init); } *niters = fold_build2 (FLOOR_DIV_EXPR, type, delta, step); return ev; } /* Checks whether use of OP in USE_LOOP behaves as a simple affine iv with respect to WRTO_LOOP and returns its base and step in IV if possible (see analyze_scalar_evolution_in_loop for more details on USE_LOOP and WRTO_LOOP). If ALLOW_NONCONSTANT_STEP is true, we want step to be invariant in LOOP. Otherwise we require it to be an integer constant. IV->no_overflow is set to true if we are sure the iv cannot overflow (e.g. because it is computed in signed arithmetics). Consequently, adding an induction variable for (i = IV->base; ; i += IV->step) is only safe if IV->no_overflow is false, or TYPE_OVERFLOW_UNDEFINED is false for the type of the induction variable, or you can prove that i does not wrap by some other argument. Otherwise, this might introduce undefined behavior, and i = iv->base; for (; ; i = (type) ((unsigned type) i + (unsigned type) iv->step)) must be used instead. When IV_NITERS is not NULL, this function also checks case in which OP is a conversion of an inner simple iv of below form: (outer_type){inner_base, inner_step}_loop. If type of inner iv has smaller precision than outer_type, it can't be folded into {(outer_type)inner_base, (outer_type)inner_step}_loop because the inner iv could overflow/wrap. In this case, we derive a condition under which the inner iv won't overflow/wrap and do the simplification. The derived condition normally is the maximum number the inner iv can iterate, and will be stored in IV_NITERS. This is useful in loop niter analysis, to derive break conditions when a loop must terminate, when is infinite. */ bool simple_iv_with_niters (class loop *wrto_loop, class loop *use_loop, tree op, affine_iv *iv, tree *iv_niters, bool allow_nonconstant_step) { enum tree_code code; tree type, ev, base, e; wide_int extreme; bool folded_casts; iv->base = NULL_TREE; iv->step = NULL_TREE; iv->no_overflow = false; type = TREE_TYPE (op); if (!POINTER_TYPE_P (type) && !INTEGRAL_TYPE_P (type)) return false; ev = analyze_scalar_evolution_in_loop (wrto_loop, use_loop, op, &folded_casts); if (chrec_contains_undetermined (ev) || chrec_contains_symbols_defined_in_loop (ev, wrto_loop->num)) return false; if (tree_does_not_contain_chrecs (ev)) { iv->base = ev; iv->step = build_int_cst (TREE_TYPE (ev), 0); iv->no_overflow = true; return true; } /* If we can derive valid scalar evolution with assumptions. */ if (iv_niters && TREE_CODE (ev) != POLYNOMIAL_CHREC) ev = derive_simple_iv_with_niters (ev, iv_niters); if (TREE_CODE (ev) != POLYNOMIAL_CHREC) return false; if (CHREC_VARIABLE (ev) != (unsigned) wrto_loop->num) return false; iv->step = CHREC_RIGHT (ev); if ((!allow_nonconstant_step && TREE_CODE (iv->step) != INTEGER_CST) || tree_contains_chrecs (iv->step, NULL)) return false; iv->base = CHREC_LEFT (ev); if (tree_contains_chrecs (iv->base, NULL)) return false; iv->no_overflow = !folded_casts && nowrap_type_p (type); if (!iv->no_overflow && !iv_can_overflow_p (wrto_loop, type, iv->base, iv->step)) iv->no_overflow = true; /* Try to simplify iv base: (signed T) ((unsigned T)base + step) ;; TREE_TYPE (base) == signed T == (signed T)(unsigned T)base + step == base + step If we can prove operation (base + step) doesn't overflow or underflow. Specifically, we try to prove below conditions are satisfied: base <= UPPER_BOUND (type) - step ;;step > 0 base >= LOWER_BOUND (type) - step ;;step < 0 This is done by proving the reverse conditions are false using loop's initial conditions. The is necessary to make loop niter, or iv overflow analysis easier for below example: int foo (int *a, signed char s, signed char l) { signed char i; for (i = s; i < l; i++) a[i] = 0; return 0; } Note variable I is firstly converted to type unsigned char, incremented, then converted back to type signed char. */ if (wrto_loop->num != use_loop->num) return true; if (!CONVERT_EXPR_P (iv->base) || TREE_CODE (iv->step) != INTEGER_CST) return true; type = TREE_TYPE (iv->base); e = TREE_OPERAND (iv->base, 0); if (TREE_CODE (e) != PLUS_EXPR || TREE_CODE (TREE_OPERAND (e, 1)) != INTEGER_CST || !tree_int_cst_equal (iv->step, fold_convert (type, TREE_OPERAND (e, 1)))) return true; e = TREE_OPERAND (e, 0); if (!CONVERT_EXPR_P (e)) return true; base = TREE_OPERAND (e, 0); if (!useless_type_conversion_p (type, TREE_TYPE (base))) return true; if (tree_int_cst_sign_bit (iv->step)) { code = LT_EXPR; extreme = wi::min_value (type); } else { code = GT_EXPR; extreme = wi::max_value (type); } wi::overflow_type overflow = wi::OVF_NONE; extreme = wi::sub (extreme, wi::to_wide (iv->step), TYPE_SIGN (type), &overflow); if (overflow) return true; e = fold_build2 (code, boolean_type_node, base, wide_int_to_tree (type, extreme)); e = simplify_using_initial_conditions (use_loop, e); if (!integer_zerop (e)) return true; if (POINTER_TYPE_P (TREE_TYPE (base))) code = POINTER_PLUS_EXPR; else code = PLUS_EXPR; iv->base = fold_build2 (code, TREE_TYPE (base), base, iv->step); return true; } /* Like simple_iv_with_niters, but return TRUE when OP behaves as a simple affine iv unconditionally. */ bool simple_iv (class loop *wrto_loop, class loop *use_loop, tree op, affine_iv *iv, bool allow_nonconstant_step) { return simple_iv_with_niters (wrto_loop, use_loop, op, iv, NULL, allow_nonconstant_step); } /* Finalize the scalar evolution analysis. */ void scev_finalize (void) { if (!scalar_evolution_info) return; scalar_evolution_info->empty (); scalar_evolution_info = NULL; free_numbers_of_iterations_estimates (cfun); } /* Returns true if the expression EXPR is considered to be too expensive for scev_const_prop. */ static bool expression_expensive_p (tree expr, hash_map &cache, uint64_t &cost) { enum tree_code code; if (is_gimple_val (expr)) return false; code = TREE_CODE (expr); if (code == TRUNC_DIV_EXPR || code == CEIL_DIV_EXPR || code == FLOOR_DIV_EXPR || code == ROUND_DIV_EXPR || code == TRUNC_MOD_EXPR || code == CEIL_MOD_EXPR || code == FLOOR_MOD_EXPR || code == ROUND_MOD_EXPR || code == EXACT_DIV_EXPR) { /* Division by power of two is usually cheap, so we allow it. Forbid anything else. */ if (!integer_pow2p (TREE_OPERAND (expr, 1))) return true; } bool visited_p; uint64_t &local_cost = cache.get_or_insert (expr