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Diffstat (limited to 'gcc-4.2.1-5666.3/gcc/tree-chrec.c')
| -rw-r--r-- | gcc-4.2.1-5666.3/gcc/tree-chrec.c | 1397 |
1 files changed, 1397 insertions, 0 deletions
diff --git a/gcc-4.2.1-5666.3/gcc/tree-chrec.c b/gcc-4.2.1-5666.3/gcc/tree-chrec.c new file mode 100644 index 000000000..a74a49c39 --- /dev/null +++ b/gcc-4.2.1-5666.3/gcc/tree-chrec.c @@ -0,0 +1,1397 @@ +/* Chains of recurrences. + Copyright (C) 2003, 2004, 2005, 2006 Free Software Foundation, Inc. + Contributed by Sebastian Pop <pop@cri.ensmp.fr> + +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 2, 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 COPYING. If not, write to the Free +Software Foundation, 51 Franklin Street, Fifth Floor, Boston, MA +02110-1301, USA. */ + +/* This file implements operations on chains of recurrences. Chains + of recurrences are used for modeling evolution functions of scalar + variables. +*/ + +#include "config.h" +#include "system.h" +#include "coretypes.h" +#include "tm.h" +#include "ggc.h" +#include "tree.h" +#include "real.h" +#include "diagnostic.h" +#include "cfgloop.h" +#include "tree-flow.h" +#include "tree-chrec.h" +#include "tree-pass.h" +#include "params.h" +#include "tree-scalar-evolution.h" + + + +/* Extended folder for chrecs. */ + +/* Determines whether CST is not a constant evolution. */ + +static inline bool +is_not_constant_evolution (tree cst) +{ + return (TREE_CODE (cst) == POLYNOMIAL_CHREC); +} + +/* Fold CODE for a polynomial function and a constant. */ + +static inline tree +chrec_fold_poly_cst (enum tree_code code, + tree type, + tree poly, + tree cst) +{ + gcc_assert (poly); + gcc_assert (cst); + gcc_assert (TREE_CODE (poly) == POLYNOMIAL_CHREC); + gcc_assert (!is_not_constant_evolution (cst)); + gcc_assert (type == chrec_type (poly)); + + switch (code) + { + case PLUS_EXPR: + return build_polynomial_chrec + (CHREC_VARIABLE (poly), + chrec_fold_plus (type, CHREC_LEFT (poly), cst), + CHREC_RIGHT (poly)); + + case MINUS_EXPR: + return build_polynomial_chrec + (CHREC_VARIABLE (poly), + chrec_fold_minus (type, CHREC_LEFT (poly), cst), + CHREC_RIGHT (poly)); + + case MULT_EXPR: + return build_polynomial_chrec + (CHREC_VARIABLE (poly), + chrec_fold_multiply (type, CHREC_LEFT (poly), cst), + chrec_fold_multiply (type, CHREC_RIGHT (poly), cst)); + + default: + return chrec_dont_know; + } +} + +/* Fold the addition of two polynomial functions. */ + +static inline tree +chrec_fold_plus_poly_poly (enum tree_code code, + tree type, + tree poly0, + tree poly1) +{ + tree left, right; + + gcc_assert (poly0); + gcc_assert (poly1); + gcc_assert (TREE_CODE (poly0) == POLYNOMIAL_CHREC); + gcc_assert (TREE_CODE (poly1) == POLYNOMIAL_CHREC); + gcc_assert (chrec_type (poly0) == chrec_type (poly1)); + gcc_assert (type == chrec_type (poly0)); + + /* + {a, +, b}_1 + {c, +, d}_2 -> {{a, +, b}_1 + c, +, d}_2, + {a, +, b}_2 + {c, +, d}_1 -> {{c, +, d}_1 + a, +, b}_2, + {a, +, b}_x + {c, +, d}_x -> {a+c, +, b+d}_x. */ + if (CHREC_VARIABLE (poly0) < CHREC_VARIABLE (poly1)) + { + if (code == PLUS_EXPR) + return build_polynomial_chrec + (CHREC_VARIABLE (poly1), + chrec_fold_plus (type, poly0, CHREC_LEFT (poly1)), + CHREC_RIGHT (poly1)); + else + return build_polynomial_chrec + (CHREC_VARIABLE (poly1), + chrec_fold_minus (type, poly0, CHREC_LEFT (poly1)), + chrec_fold_multiply (type, CHREC_RIGHT (poly1), + SCALAR_FLOAT_TYPE_P (type) + ? build_real (type, dconstm1) + : build_int_cst_type (type, -1))); + } + + if (CHREC_VARIABLE (poly0) > CHREC_VARIABLE (poly1)) + { + if (code == PLUS_EXPR) + return build_polynomial_chrec + (CHREC_VARIABLE (poly0), + chrec_fold_plus (type, CHREC_LEFT (poly0), poly1), + CHREC_RIGHT (poly0)); + else + return build_polynomial_chrec + (CHREC_VARIABLE (poly0), + chrec_fold_minus (type, CHREC_LEFT (poly0), poly1), + CHREC_RIGHT (poly0)); + } + + if (code == PLUS_EXPR) + { + left = chrec_fold_plus + (type, CHREC_LEFT (poly0), CHREC_LEFT (poly1)); + right = chrec_fold_plus + (type, CHREC_RIGHT (poly0), CHREC_RIGHT (poly1)); + } + else + { + left = chrec_fold_minus + (type, CHREC_LEFT (poly0), CHREC_LEFT (poly1)); + right = chrec_fold_minus + (type, CHREC_RIGHT (poly0), CHREC_RIGHT (poly1)); + } + + if (chrec_zerop (right)) + return left; + else + return build_polynomial_chrec + (CHREC_VARIABLE (poly0), left, right); +} + + + +/* Fold the multiplication of two polynomial functions. */ + +static inline tree +chrec_fold_multiply_poly_poly (tree type, + tree poly0, + tree poly1) +{ + tree t0, t1, t2; + int var; + + gcc_assert (poly0); + gcc_assert (poly1); + gcc_assert (TREE_CODE (poly0) == POLYNOMIAL_CHREC); + gcc_assert (TREE_CODE (poly1) == POLYNOMIAL_CHREC); + gcc_assert (chrec_type (poly0) == chrec_type (poly1)); + gcc_assert (type == chrec_type (poly0)); + + /* {a, +, b}_1 * {c, +, d}_2 -> {c*{a, +, b}_1, +, d}_2, + {a, +, b}_2 * {c, +, d}_1 -> {a*{c, +, d}_1, +, b}_2, + {a, +, b}_x * {c, +, d}_x -> {a*c, +, a*d + b*c + b*d, +, 2*b*d}_x. */ + if (CHREC_VARIABLE (poly0) < CHREC_VARIABLE (poly1)) + /* poly0 is a constant wrt. poly1. */ + return build_polynomial_chrec + (CHREC_VARIABLE (poly1), + chrec_fold_multiply (type, CHREC_LEFT (poly1), poly0), + CHREC_RIGHT (poly1)); + + if (CHREC_VARIABLE (poly1) < CHREC_VARIABLE (poly0)) + /* poly1 is a constant wrt. poly0. */ + return build_polynomial_chrec + (CHREC_VARIABLE (poly0), + chrec_fold_multiply (type, CHREC_LEFT (poly0), poly1), + CHREC_RIGHT (poly0)); + + /* poly0 and poly1 are two polynomials in the same variable, + {a, +, b}_x * {c, +, d}_x -> {a*c, +, a*d + b*c + b*d, +, 2*b*d}_x. */ + + /* "a*c". */ + t0 = chrec_fold_multiply (type, CHREC_LEFT (poly0), CHREC_LEFT (poly1)); + + /* "a*d + b*c + b*d". */ + t1 = chrec_fold_multiply (type, CHREC_LEFT (poly0), CHREC_RIGHT (poly1)); + t1 = chrec_fold_plus (type, t1, chrec_fold_multiply (type, + CHREC_RIGHT (poly0), + CHREC_LEFT (poly1))); + t1 = chrec_fold_plus (type, t1, chrec_fold_multiply (type, + CHREC_RIGHT (poly0), + CHREC_RIGHT (poly1))); + /* "2*b*d". */ + t2 = chrec_fold_multiply (type, CHREC_RIGHT (poly0), CHREC_RIGHT (poly1)); + t2 = chrec_fold_multiply (type, SCALAR_FLOAT_TYPE_P (type) + ? build_real (type, dconst2) + : build_int_cst (type, 2), t2); + + var = CHREC_VARIABLE (poly0); + return build_polynomial_chrec (var, t0, + build_polynomial_chrec (var, t1, t2)); +} + +/* When the operands are automatically_generated_chrec_p, the fold has + to respect the semantics of the operands. */ + +static inline tree +chrec_fold_automatically_generated_operands (tree op0, + tree op1) +{ + if (op0 == chrec_dont_know + || op1 == chrec_dont_know) + return chrec_dont_know; + + if (op0 == chrec_known + || op1 == chrec_known) + return chrec_known; + + if (op0 == chrec_not_analyzed_yet + || op1 == chrec_not_analyzed_yet) + return chrec_not_analyzed_yet; + + /* The default case produces a safe result. */ + return chrec_dont_know; +} + +/* Fold the addition of two chrecs. */ + +static tree +chrec_fold_plus_1 (enum tree_code code, tree type, + tree op0, tree op1) +{ + if (automatically_generated_chrec_p (op0) + || automatically_generated_chrec_p (op1)) + return chrec_fold_automatically_generated_operands (op0, op1); + + switch (TREE_CODE (op0)) + { + case POLYNOMIAL_CHREC: + switch (TREE_CODE (op1)) + { + case POLYNOMIAL_CHREC: + return chrec_fold_plus_poly_poly (code, type, op0, op1); + + default: + if (code == PLUS_EXPR) + return build_polynomial_chrec + (CHREC_VARIABLE (op0), + chrec_fold_plus (type, CHREC_LEFT (op0), op1), + CHREC_RIGHT (op0)); + else + return build_polynomial_chrec + (CHREC_VARIABLE (op0), + chrec_fold_minus (type, CHREC_LEFT (op0), op1), + CHREC_RIGHT (op0)); + } + + default: + switch (TREE_CODE (op1)) + { + case POLYNOMIAL_CHREC: + if (code == PLUS_EXPR) + return build_polynomial_chrec + (CHREC_VARIABLE (op1), + chrec_fold_plus (type, op0, CHREC_LEFT (op1)), + CHREC_RIGHT (op1)); + else + return build_polynomial_chrec + (CHREC_VARIABLE (op1), + chrec_fold_minus (type, op0, CHREC_LEFT (op1)), + chrec_fold_multiply (type, CHREC_RIGHT (op1), + SCALAR_FLOAT_TYPE_P (type) + ? build_real (type, dconstm1) + : build_int_cst_type (type, -1))); + + default: + { + int size = 0; + if ((tree_contains_chrecs (op0, &size) + || tree_contains_chrecs (op1, &size)) + && size < PARAM_VALUE (PARAM_SCEV_MAX_EXPR_SIZE)) + return build2 (code, type, op0, op1); + else if (size < PARAM_VALUE (PARAM_SCEV_MAX_EXPR_SIZE)) + return fold_build2 (code, type, + fold_convert (type, op0), + fold_convert (type, op1)); + else + return chrec_dont_know; + } + } + } +} + +/* Fold the addition of two chrecs. */ + +tree +chrec_fold_plus (tree type, + tree op0, + tree op1) +{ + if (automatically_generated_chrec_p (op0) + || automatically_generated_chrec_p (op1)) + return chrec_fold_automatically_generated_operands (op0, op1); + + if (integer_zerop (op0)) + return op1; + if (integer_zerop (op1)) + return op0; + + return chrec_fold_plus_1 (PLUS_EXPR, type, op0, op1); +} + +/* Fold the subtraction of two chrecs. */ + +tree +chrec_fold_minus (tree type, + tree op0, + tree op1) +{ + if (automatically_generated_chrec_p (op0) + || automatically_generated_chrec_p (op1)) + return chrec_fold_automatically_generated_operands (op0, op1); + + if (integer_zerop (op1)) + return op0; + + return chrec_fold_plus_1 (MINUS_EXPR, type, op0, op1); +} + +/* Fold the multiplication of two chrecs. */ + +tree +chrec_fold_multiply (tree type, + tree op0, + tree op1) +{ + if (automatically_generated_chrec_p (op0) + || automatically_generated_chrec_p (op1)) + return chrec_fold_automatically_generated_operands (op0, op1); + + switch (TREE_CODE (op0)) + { + case POLYNOMIAL_CHREC: + switch (TREE_CODE (op1)) + { + case POLYNOMIAL_CHREC: + return chrec_fold_multiply_poly_poly (type, op0, op1); + + default: + if (integer_onep (op1)) + return op0; + if (integer_zerop (op1)) + return build_int_cst (type, 0); + + return build_polynomial_chrec + (CHREC_VARIABLE (op0), + chrec_fold_multiply (type, CHREC_LEFT (op0), op1), + chrec_fold_multiply (type, CHREC_RIGHT (op0), op1)); + } + + default: + if (integer_onep (op0)) + return op1; + + if (integer_zerop (op0)) + return build_int_cst (type, 0); + + switch (TREE_CODE (op1)) + { + case POLYNOMIAL_CHREC: + return build_polynomial_chrec + (CHREC_VARIABLE (op1), + chrec_fold_multiply (type, CHREC_LEFT (op1), op0), + chrec_fold_multiply (type, CHREC_RIGHT (op1), op0)); + + default: + if (integer_onep (op1)) + return op0; + if (integer_zerop (op1)) + return build_int_cst (type, 0); + return fold_build2 (MULT_EXPR, type, op0, op1); + } + } +} + + + +/* Operations. */ + +/* Evaluate the binomial coefficient. Return NULL_TREE if the intermediate + calculation overflows, otherwise return C(n,k) with type TYPE. */ + +static tree +tree_fold_binomial (tree type, tree n, unsigned int k) +{ + unsigned HOST_WIDE_INT lidx, lnum, ldenom, lres, ldum; + HOST_WIDE_INT hidx, hnum, hdenom, hres, hdum; + unsigned int i; + tree res; + + /* Handle the most frequent cases. */ + if (k == 0) + return build_int_cst (type, 1); + if (k == 1) + return fold_convert (type, n); + + /* Check that k <= n. */ + if (TREE_INT_CST_HIGH (n) == 0 + && TREE_INT_CST_LOW (n) < k) + return NULL_TREE; + + /* Numerator = n. */ + lnum = TREE_INT_CST_LOW (n); + hnum = TREE_INT_CST_HIGH (n); + + /* Denominator = 2. */ + ldenom = 2; + hdenom = 0; + + /* Index = Numerator-1. */ + if (lnum == 0) + { + hidx = hnum - 1; + lidx = ~ (unsigned HOST_WIDE_INT) 0; + } + else + { + hidx = hnum; + lidx = lnum - 1; + } + + /* Numerator = Numerator*Index = n*(n-1). */ + if (mul_double (lnum, hnum, lidx, hidx, &lnum, &hnum)) + return NULL_TREE; + + for (i = 3; i <= k; i++) + { + /* Index--. */ + if (lidx == 0) + { + hidx--; + lidx = ~ (unsigned HOST_WIDE_INT) 0; + } + else + lidx--; + + /* Numerator *= Index. */ + if (mul_double (lnum, hnum, lidx, hidx, &lnum, &hnum)) + return NULL_TREE; + + /* Denominator *= i. */ + mul_double (ldenom, hdenom, i, 0, &ldenom, &hdenom); + } + + /* Result = Numerator / Denominator. */ + div_and_round_double (EXACT_DIV_EXPR, 1, lnum, hnum, ldenom, hdenom, + &lres, &hres, &ldum, &hdum); + + res = build_int_cst_wide (type, lres, hres); + return int_fits_type_p (res, type) ? res : NULL_TREE; +} + +/* Helper function. Use the Newton's interpolating formula for + evaluating the value of the evolution function. */ + +static tree +chrec_evaluate (unsigned var, tree chrec, tree n, unsigned int k) +{ + tree arg0, arg1, binomial_n_k; + tree type = TREE_TYPE (chrec); + + while (TREE_CODE (chrec) == POLYNOMIAL_CHREC + && CHREC_VARIABLE (chrec) > var) + chrec = CHREC_LEFT (chrec); + + if (TREE_CODE (chrec) == POLYNOMIAL_CHREC + && CHREC_VARIABLE (chrec) == var) + { + arg0 = chrec_evaluate (var, CHREC_RIGHT (chrec), n, k + 1); + if (arg0 == chrec_dont_know) + return chrec_dont_know; + binomial_n_k = tree_fold_binomial (type, n, k); + if (!binomial_n_k) + return chrec_dont_know; + arg1 = fold_build2 (MULT_EXPR, type, + CHREC_LEFT (chrec), binomial_n_k); + return chrec_fold_plus (type, arg0, arg1); + } + + binomial_n_k = tree_fold_binomial (type, n, k); + if (!binomial_n_k) + return chrec_dont_know; + + return fold_build2 (MULT_EXPR, type, chrec, binomial_n_k); +} + +/* Evaluates "CHREC (X)" when the varying variable is VAR. + Example: Given the following parameters, + + var = 1 + chrec = {3, +, 4}_1 + x = 10 + + The result is given by the Newton's interpolating formula: + 3 * \binom{10}{0} + 4 * \binom{10}{1}. +*/ + +tree +chrec_apply (unsigned var, + tree chrec, + tree x) +{ + tree type = chrec_type (chrec); + tree res = chrec_dont_know; + + if (automatically_generated_chrec_p (chrec) + || automatically_generated_chrec_p (x) + + /* When the symbols are defined in an outer loop, it is possible + to symbolically compute the apply, since the symbols are + constants with respect to the varying loop. */ + || chrec_contains_symbols_defined_in_loop (chrec, var)) + return chrec_dont_know; + + if (dump_file && (dump_flags & TDF_DETAILS)) + fprintf (dump_file, "(chrec_apply \n"); + + if (TREE_CODE (x) == INTEGER_CST && SCALAR_FLOAT_TYPE_P (type)) + x = build_real_from_int_cst (type, x); + + if (evolution_function_is_affine_p (chrec)) + { + /* "{a, +, b} (x)" -> "a + b*x". */ + x = chrec_convert (type, x, NULL_TREE); + res = chrec_fold_multiply (type, CHREC_RIGHT (chrec), x); + if (!integer_zerop (CHREC_LEFT (chrec))) + res = chrec_fold_plus (type, CHREC_LEFT (chrec), res); + } + + else if (TREE_CODE (chrec) != POLYNOMIAL_CHREC) + res = chrec; + + else if (TREE_CODE (x) == INTEGER_CST + && tree_int_cst_sgn (x) == 1) + /* testsuite/.../ssa-chrec-38.c. */ + res = chrec_evaluate (var, chrec, x, 0); + else + res = chrec_dont_know; + + if (dump_file && (dump_flags & TDF_DETAILS)) + { + fprintf (dump_file, " (varying_loop = %d\n", var); + fprintf (dump_file, ")\n (chrec = "); + print_generic_expr (dump_file, chrec, 0); + fprintf (dump_file, ")\n (x = "); + print_generic_expr (dump_file, x, 0); + fprintf (dump_file, ")\n (res = "); + print_generic_expr (dump_file, res, 0); + fprintf (dump_file, "))\n"); + } + + return res; +} + +/* Replaces the initial condition in CHREC with INIT_COND. */ + +tree +chrec_replace_initial_condition (tree chrec, + tree init_cond) +{ + if (automatically_generated_chrec_p (chrec)) + return chrec; + + gcc_assert (chrec_type (chrec) == chrec_type (init_cond)); + + switch (TREE_CODE (chrec)) + { + case POLYNOMIAL_CHREC: + return build_polynomial_chrec + (CHREC_VARIABLE (chrec), + chrec_replace_initial_condition (CHREC_LEFT (chrec), init_cond), + CHREC_RIGHT (chrec)); + + default: + return init_cond; + } +} + +/* Returns the initial condition of a given CHREC. */ + +tree +initial_condition (tree chrec) +{ + if (automatically_generated_chrec_p (chrec)) + return chrec; + + if (TREE_CODE (chrec) == POLYNOMIAL_CHREC) + return initial_condition (CHREC_LEFT (chrec)); + else + return chrec; +} + +/* Returns a univariate function that represents the evolution in + LOOP_NUM. Mask the evolution of any other loop. */ + +tree +hide_evolution_in_other_loops_than_loop (tree chrec, + unsigned loop_num) +{ + if (automatically_generated_chrec_p (chrec)) + return chrec; + + switch (TREE_CODE (chrec)) + { + case POLYNOMIAL_CHREC: + if (CHREC_VARIABLE (chrec) == loop_num) + return build_polynomial_chrec + (loop_num, + hide_evolution_in_other_loops_than_loop (CHREC_LEFT (chrec), + loop_num), + CHREC_RIGHT (chrec)); + + else if (CHREC_VARIABLE (chrec) < loop_num) + /* There is no evolution in this loop. */ + return initial_condition (chrec); + + else + return hide_evolution_in_other_loops_than_loop (CHREC_LEFT (chrec), + loop_num); + + default: + return chrec; + } +} + +/* Returns the evolution part of CHREC in LOOP_NUM when RIGHT is + true, otherwise returns the initial condition in LOOP_NUM. */ + +static tree +chrec_component_in_loop_num (tree chrec, + unsigned loop_num, + bool right) +{ + tree component; + + if (automatically_generated_chrec_p (chrec)) + return chrec; + + switch (TREE_CODE (chrec)) + { + case POLYNOMIAL_CHREC: + if (CHREC_VARIABLE (chrec) == loop_num) + { + if (right) + component = CHREC_RIGHT (chrec); + else + component = CHREC_LEFT (chrec); + + if (TREE_CODE (CHREC_LEFT (chrec)) != POLYNOMIAL_CHREC + || CHREC_VARIABLE (CHREC_LEFT (chrec)) != CHREC_VARIABLE (chrec)) + return component; + + else + return build_polynomial_chrec + (loop_num, + chrec_component_in_loop_num (CHREC_LEFT (chrec), + loop_num, + right), + component); + } + + else if (CHREC_VARIABLE (chrec) < loop_num) + /* There is no evolution part in this loop. */ + return NULL_TREE; + + else + return chrec_component_in_loop_num (CHREC_LEFT (chrec), + loop_num, + right); + + default: + if (right) + return NULL_TREE; + else + return chrec; + } +} + +/* Returns the evolution part in LOOP_NUM. Example: the call + evolution_part_in_loop_num ({{0, +, 1}_1, +, 2}_1, 1) returns + {1, +, 2}_1 */ + +tree +evolution_part_in_loop_num (tree chrec, + unsigned loop_num) +{ + return chrec_component_in_loop_num (chrec, loop_num, true); +} + +/* Returns the initial condition in LOOP_NUM. Example: the call + initial_condition_in_loop_num ({{0, +, 1}_1, +, 2}_2, 2) returns + {0, +, 1}_1 */ + +tree +initial_condition_in_loop_num (tree chrec, + unsigned loop_num) +{ + return chrec_component_in_loop_num (chrec, loop_num, false); +} + +/* Set or reset the evolution of CHREC to NEW_EVOL in loop LOOP_NUM. + This function is essentially used for setting the evolution to + chrec_dont_know, for example after having determined that it is + impossible to say how many times a loop will execute. */ + +tree +reset_evolution_in_loop (unsigned loop_num, + tree chrec, + tree new_evol) +{ + gcc_assert (chrec_type (chrec) == chrec_type (new_evol)); + + if (TREE_CODE (chrec) == POLYNOMIAL_CHREC + && CHREC_VARIABLE (chrec) > loop_num) + { + tree left = reset_evolution_in_loop (loop_num, CHREC_LEFT (chrec), + new_evol); + tree right = reset_evolution_in_loop (loop_num, CHREC_RIGHT (chrec), + new_evol); + return build3 (POLYNOMIAL_CHREC, TREE_TYPE (left), + build_int_cst (NULL_TREE, CHREC_VARIABLE (chrec)), + left, right); + } + + while (TREE_CODE (chrec) == POLYNOMIAL_CHREC + && CHREC_VARIABLE (chrec) == loop_num) + chrec = CHREC_LEFT (chrec); + + return build_polynomial_chrec (loop_num, chrec, new_evol); +} + +/* Merges two evolution functions that were found by following two + alternate paths of a conditional expression. */ + +tree +chrec_merge (tree chrec1, + tree chrec2) +{ + if (chrec1 == chrec_dont_know + || chrec2 == chrec_dont_know) + return chrec_dont_know; + + if (chrec1 == chrec_known + || chrec2 == chrec_known) + return chrec_known; + + if (chrec1 == chrec_not_analyzed_yet) + return chrec2; + if (chrec2 == chrec_not_analyzed_yet) + return chrec1; + + if (eq_evolutions_p (chrec1, chrec2)) + return chrec1; + + return chrec_dont_know; +} + + + +/* Observers. */ + +/* Helper function for is_multivariate_chrec. */ + +static bool +is_multivariate_chrec_rec (tree chrec, unsigned int rec_var) +{ + if (chrec == NULL_TREE) + return false; + + if (TREE_CODE (chrec) == POLYNOMIAL_CHREC) + { + if (CHREC_VARIABLE (chrec) != rec_var) + return true; + else + return (is_multivariate_chrec_rec (CHREC_LEFT (chrec), rec_var) + || is_multivariate_chrec_rec (CHREC_RIGHT (chrec), rec_var)); + } + else + return false; +} + +/* Determine whether the given chrec is multivariate or not. */ + +bool +is_multivariate_chrec (tree chrec) +{ + if (chrec == NULL_TREE) + return false; + + if (TREE_CODE (chrec) == POLYNOMIAL_CHREC) + return (is_multivariate_chrec_rec (CHREC_LEFT (chrec), + CHREC_VARIABLE (chrec)) + || is_multivariate_chrec_rec (CHREC_RIGHT (chrec), + CHREC_VARIABLE (chrec))); + else + return false; +} + +/* Determines whether the chrec contains symbolic names or not. */ + +bool +chrec_contains_symbols (tree chrec) +{ + if (chrec == NULL_TREE) + return false; + + if (TREE_CODE (chrec) == SSA_NAME + || TREE_CODE (chrec) == VAR_DECL + || TREE_CODE (chrec) == PARM_DECL + || TREE_CODE (chrec) == FUNCTION_DECL + || TREE_CODE (chrec) == LABEL_DECL + || TREE_CODE (chrec) == RESULT_DECL + || TREE_CODE (chrec) == FIELD_DECL) + return true; + + switch (TREE_CODE_LENGTH (TREE_CODE (chrec))) + { + case 3: + if (chrec_contains_symbols (TREE_OPERAND (chrec, 2))) + return true; + + case 2: + if (chrec_contains_symbols (TREE_OPERAND (chrec, 1))) + return true; + + case 1: + if (chrec_contains_symbols (TREE_OPERAND (chrec, 0))) + return true; + + default: + return false; + } +} + +/* Determines whether the chrec contains undetermined coefficients. */ + +bool +chrec_contains_undetermined (tree chrec) +{ + if (chrec == chrec_dont_know + || chrec == chrec_not_analyzed_yet + || chrec == NULL_TREE) + return true; + + switch (TREE_CODE_LENGTH (TREE_CODE (chrec))) + { + case 3: + if (chrec_contains_undetermined (TREE_OPERAND (chrec, 2))) + return true; + + case 2: + if (chrec_contains_undetermined (TREE_OPERAND (chrec, 1))) + return true; + + case 1: + if (chrec_contains_undetermined (TREE_OPERAND (chrec, 0))) + return true; + + default: + return false; + } +} + +/* Determines whether the tree EXPR contains chrecs, and increment + SIZE if it is not a NULL pointer by an estimation of the depth of + the tree. */ + +bool +tree_contains_chrecs (tree expr, int *size) +{ + if (expr == NULL_TREE) + return false; + + if (size) + (*size)++; + + if (tree_is_chrec (expr)) + return true; + + switch (TREE_CODE_LENGTH (TREE_CODE (expr))) + { + case 3: + if (tree_contains_chrecs (TREE_OPERAND (expr, 2), size)) + return true; + + case 2: + if (tree_contains_chrecs (TREE_OPERAND (expr, 1), size)) + return true; + + case 1: + if (tree_contains_chrecs (TREE_OPERAND (expr, 0), size)) + return true; + + default: + return false; + } +} + +/* Recursive helper function. */ + +static bool +evolution_function_is_invariant_rec_p (tree chrec, int loopnum) +{ + if (evolution_function_is_constant_p (chrec)) + return true; + + if (TREE_CODE (chrec) == SSA_NAME + && expr_invariant_in_loop_p (current_loops->parray[loopnum], + chrec)) + return true; + + if (TREE_CODE (chrec) == POLYNOMIAL_CHREC) + { + if (CHREC_VARIABLE (chrec) == (unsigned) loopnum + || !evolution_function_is_invariant_rec_p (CHREC_RIGHT (chrec), + loopnum) + || !evolution_function_is_invariant_rec_p (CHREC_LEFT (chrec), + loopnum)) + return false; + return true; + } + + switch (TREE_CODE_LENGTH (TREE_CODE (chrec))) + { + case 2: + if (!evolution_function_is_invariant_rec_p (TREE_OPERAND (chrec, 1), + loopnum)) + return false; + + case 1: + if (!evolution_function_is_invariant_rec_p (TREE_OPERAND (chrec, 0), + loopnum)) + return false; + return true; + + default: + return false; + } + + return false; +} + +/* Return true if CHREC is invariant in loop LOOPNUM, false otherwise. */ + +bool +evolution_function_is_invariant_p (tree chrec, int loopnum) +{ + if (evolution_function_is_constant_p (chrec)) + return true; + + if (current_loops != NULL) + return evolution_function_is_invariant_rec_p (chrec, loopnum); + + return false; +} + +/* Determine whether the given tree is an affine multivariate + evolution. */ + +bool +evolution_function_is_affine_multivariate_p (tree chrec) +{ + if (chrec == NULL_TREE) + return false; + + switch (TREE_CODE (chrec)) + { + case POLYNOMIAL_CHREC: + if (evolution_function_is_constant_p (CHREC_LEFT (chrec))) + { + if (evolution_function_is_constant_p (CHREC_RIGHT (chrec))) + return true; + else + { + if (TREE_CODE (CHREC_RIGHT (chrec)) == POLYNOMIAL_CHREC + && CHREC_VARIABLE (CHREC_RIGHT (chrec)) + != CHREC_VARIABLE (chrec) + && evolution_function_is_affine_multivariate_p + (CHREC_RIGHT (chrec))) + return true; + else + return false; + } + } + else + { + if (evolution_function_is_constant_p (CHREC_RIGHT (chrec)) + && TREE_CODE (CHREC_LEFT (chrec)) == POLYNOMIAL_CHREC + && CHREC_VARIABLE (CHREC_LEFT (chrec)) != CHREC_VARIABLE (chrec) + && evolution_function_is_affine_multivariate_p + (CHREC_LEFT (chrec))) + return true; + else + return false; + } + + default: + return false; + } +} + +/* Determine whether the given tree is a function in zero or one + variables. */ + +bool +evolution_function_is_univariate_p (tree chrec) +{ + if (chrec == NULL_TREE) + return true; + + switch (TREE_CODE (chrec)) + { + case POLYNOMIAL_CHREC: + switch (TREE_CODE (CHREC_LEFT (chrec))) + { + case POLYNOMIAL_CHREC: + if (CHREC_VARIABLE (chrec) != CHREC_VARIABLE (CHREC_LEFT (chrec))) + return false; + if (!evolution_function_is_univariate_p (CHREC_LEFT (chrec))) + return false; + break; + + default: + break; + } + + switch (TREE_CODE (CHREC_RIGHT (chrec))) + { + case POLYNOMIAL_CHREC: + if (CHREC_VARIABLE (chrec) != CHREC_VARIABLE (CHREC_RIGHT (chrec))) + return false; + if (!evolution_function_is_univariate_p (CHREC_RIGHT (chrec))) + return false; + break; + + default: + break; + } + + default: + return true; + } +} + +/* Returns the number of variables of CHREC. Example: the call + nb_vars_in_chrec ({{0, +, 1}_5, +, 2}_6) returns 2. */ + +unsigned +nb_vars_in_chrec (tree chrec) +{ + if (chrec == NULL_TREE) + return 0; + + switch (TREE_CODE (chrec)) + { + case POLYNOMIAL_CHREC: + return 1 + nb_vars_in_chrec + (initial_condition_in_loop_num (chrec, CHREC_VARIABLE (chrec))); + + default: + return 0; + } +} + +/* Returns true if TYPE is a type in that we cannot directly perform + arithmetics, even though it is a scalar type. */ + +static bool +avoid_arithmetics_in_type_p (tree type) +{ + /* Ada frontend uses subtypes -- an arithmetic cannot be directly performed + in the subtype, but a base type must be used, and the result then can + be casted to the subtype. */ + if (TREE_CODE (type) == INTEGER_TYPE && TREE_TYPE (type) != NULL_TREE) + return true; + + return false; +} + +static tree chrec_convert_1 (tree, tree, tree, bool); + +/* Converts BASE and STEP of affine scev to TYPE. LOOP is the loop whose iv + the scev corresponds to. AT_STMT is the statement at that the scev is + evaluated. USE_OVERFLOW_SEMANTICS is true if this function should assume that + the rules for overflow of the given language apply (e.g., that signed + arithmetics in C does not overflow) -- i.e., to use them to avoid unnecessary + tests, but also to enforce that the result follows them. Returns true if the + conversion succeeded, false otherwise. */ + +bool +convert_affine_scev (struct loop *loop, tree type, + tree *base, tree *step, tree at_stmt, + bool use_overflow_semantics) +{ + tree ct = TREE_TYPE (*step); + bool enforce_overflow_semantics; + bool must_check_src_overflow, must_check_rslt_overflow; + tree new_base, new_step; + + /* If we cannot perform arithmetic in TYPE, avoid creating an scev. */ + if (avoid_arithmetics_in_type_p (type)) + return false; + + /* In general, + (TYPE) (BASE + STEP * i) = (TYPE) BASE + (TYPE -- sign extend) STEP * i, + but we must check some assumptions. + + 1) If [BASE, +, STEP] wraps, the equation is not valid when precision + of CT is smaller than the precision of TYPE. For example, when we + cast unsigned char [254, +, 1] to unsigned, the values on left side + are 254, 255, 0, 1, ..., but those on the right side are + 254, 255, 256, 257, ... + 2) In case that we must also preserve the fact that signed ivs do not + overflow, we must additionally check that the new iv does not wrap. + For example, unsigned char [125, +, 1] casted to signed char could + become a wrapping variable with values 125, 126, 127, -128, -127, ..., + which would confuse optimizers that assume that this does not + happen. */ + must_check_src_overflow = TYPE_PRECISION (ct) < TYPE_PRECISION (type); + + enforce_overflow_semantics = (use_overflow_semantics + && nowrap_type_p (type)); + if (enforce_overflow_semantics) + { + /* We can avoid checking whether the result overflows in the following + cases: + + -- must_check_src_overflow is true, and the range of TYPE is superset + of the range of CT -- i.e., in all cases except if CT signed and + TYPE unsigned. + -- both CT and TYPE have the same precision and signedness, and we + verify instead that the source does not overflow (this may be + easier than verifying it for the result, as we may use the + information about the semantics of overflow in CT). */ + if (must_check_src_overflow) + { + if (TYPE_UNSIGNED (type) && !TYPE_UNSIGNED (ct)) + must_check_rslt_overflow = true; + else + must_check_rslt_overflow = false; + } + else if (TYPE_UNSIGNED (ct) == TYPE_UNSIGNED (type) + && TYPE_PRECISION (ct) == TYPE_PRECISION (type)) + { + must_check_rslt_overflow = false; + must_check_src_overflow = true; + } + else + must_check_rslt_overflow = true; + } + else + must_check_rslt_overflow = false; + + if (must_check_src_overflow + && scev_probably_wraps_p (*base, *step, at_stmt, loop, + use_overflow_semantics)) + return false; + + new_base = chrec_convert_1 (type, *base, at_stmt, + use_overflow_semantics); + /* The step must be sign extended, regardless of the signedness + of CT and TYPE. This only needs to be handled specially when + CT is unsigned -- to avoid e.g. unsigned char [100, +, 255] + (with values 100, 99, 98, ...) from becoming signed or unsigned + [100, +, 255] with values 100, 355, ...; the sign-extension is + performed by default when CT is signed. */ + new_step = *step; + if (TYPE_PRECISION (type) > TYPE_PRECISION (ct) && TYPE_UNSIGNED (ct)) + new_step = chrec_convert_1 (signed_type_for (ct), new_step, at_stmt, + use_overflow_semantics); + new_step = chrec_convert_1 (type, new_step, at_stmt, use_overflow_semantics); + + if (automatically_generated_chrec_p (new_base) + || automatically_generated_chrec_p (new_step)) + return false; + + if (must_check_rslt_overflow + /* Note that in this case we cannot use the fact that signed variables + do not overflow, as this is what we are verifying for the new iv. */ + && scev_probably_wraps_p (new_base, new_step, at_stmt, loop, false)) + return false; + + *base = new_base; + *step = new_step; + return true; +} + + +/* Convert CHREC to TYPE. When the analyzer knows the context in + which the CHREC is built, it sets AT_STMT to the statement that + contains the definition of the analyzed variable, otherwise the + conversion is less accurate: the information is used for + determining a more accurate estimation of the number of iterations. + By default AT_STMT could be safely set to NULL_TREE. + + The following rule is always true: TREE_TYPE (chrec) == + TREE_TYPE (CHREC_LEFT (chrec)) == TREE_TYPE (CHREC_RIGHT (chrec)). + An example of what could happen when adding two chrecs and the type + of the CHREC_RIGHT is different than CHREC_LEFT is: + + {(uint) 0, +, (uchar) 10} + + {(uint) 0, +, (uchar) 250} + + that would produce a wrong result if CHREC_RIGHT is not (uint): + + {(uint) 0, +, (uchar) 4} + + instead of + + {(uint) 0, +, (uint) 260} +*/ + +tree +chrec_convert (tree type, tree chrec, tree at_stmt) +{ + return chrec_convert_1 (type, chrec, at_stmt, true); +} + +/* Convert CHREC to TYPE. When the analyzer knows the context in + which the CHREC is built, it sets AT_STMT to the statement that + contains the definition of the analyzed variable, otherwise the + conversion is less accurate: the information is used for + determining a more accurate estimation of the number of iterations. + By default AT_STMT could be safely set to NULL_TREE. + + USE_OVERFLOW_SEMANTICS is true if this function should assume that + the rules for overflow of the given language apply (e.g., that signed + arithmetics in C does not overflow) -- i.e., to use them to avoid unnecessary + tests, but also to enforce that the result follows them. */ + +static tree +chrec_convert_1 (tree type, tree chrec, tree at_stmt, + bool use_overflow_semantics) +{ + tree ct, res; + tree base, step; + struct loop *loop; + + if (automatically_generated_chrec_p (chrec)) + return chrec; + + ct = chrec_type (chrec); + if (ct == type) + return chrec; + + if (!evolution_function_is_affine_p (chrec)) + goto keep_cast; + + loop = current_loops->parray[CHREC_VARIABLE (chrec)]; + base = CHREC_LEFT (chrec); + step = CHREC_RIGHT (chrec); + + if (convert_affine_scev (loop, type, &base, &step, at_stmt, + use_overflow_semantics)) + return build_polynomial_chrec (loop->num, base, step); + + /* If we cannot propagate the cast inside the chrec, just keep the cast. */ +keep_cast: + res = fold_convert (type, chrec); + + /* Don't propagate overflows. */ + if (CONSTANT_CLASS_P (res)) + { + TREE_CONSTANT_OVERFLOW (res) = 0; + TREE_OVERFLOW (res) = 0; + } + + /* But reject constants that don't fit in their type after conversion. + This can happen if TYPE_MIN_VALUE or TYPE_MAX_VALUE are not the + natural values associated with TYPE_PRECISION and TYPE_UNSIGNED, + and can cause problems later when computing niters of loops. Note + that we don't do the check before converting because we don't want + to reject conversions of negative chrecs to unsigned types. */ + if (TREE_CODE (res) == INTEGER_CST + && TREE_CODE (type) == INTEGER_TYPE + && !int_fits_type_p (res, type)) + res = chrec_dont_know; + + return res; +} + +/* Convert CHREC to TYPE, without regard to signed overflows. Returns the new + chrec if something else than what chrec_convert would do happens, NULL_TREE + otherwise. */ + +tree +chrec_convert_aggressive (tree type, tree chrec) +{ + tree inner_type, left, right, lc, rc; + + if (automatically_generated_chrec_p (chrec) + || TREE_CODE (chrec) != POLYNOMIAL_CHREC) + return NULL_TREE; + + inner_type = TREE_TYPE (chrec); + if (TYPE_PRECISION (type) > TYPE_PRECISION (inner_type)) + return NULL_TREE; + + /* If we cannot perform arithmetic in TYPE, avoid creating an scev. */ + if (avoid_arithmetics_in_type_p (type)) + return NULL_TREE; + + left = CHREC_LEFT (chrec); + right = CHREC_RIGHT (chrec); + lc = chrec_convert_aggressive (type, left); + if (!lc) + lc = chrec_convert (type, left, NULL_TREE); + rc = chrec_convert_aggressive (type, right); + if (!rc) + rc = chrec_convert (type, right, NULL_TREE); + + return build_polynomial_chrec (CHREC_VARIABLE (chrec), lc, rc); +} + +/* Returns true when CHREC0 == CHREC1. */ + +bool +eq_evolutions_p (tree chrec0, + tree chrec1) +{ + if (chrec0 == NULL_TREE + || chrec1 == NULL_TREE + || TREE_CODE (chrec0) != TREE_CODE (chrec1)) + return false; + + if (chrec0 == chrec1) + return true; + + switch (TREE_CODE (chrec0)) + { + case INTEGER_CST: + return operand_equal_p (chrec0, chrec1, 0); + + case POLYNOMIAL_CHREC: + return (CHREC_VARIABLE (chrec0) == CHREC_VARIABLE (chrec1) + && eq_evolutions_p (CHREC_LEFT (chrec0), CHREC_LEFT (chrec1)) + && eq_evolutions_p (CHREC_RIGHT (chrec0), CHREC_RIGHT (chrec1))); + default: + return false; + } +} + +/* Returns EV_GROWS if CHREC grows (assuming that it does not overflow), + EV_DECREASES if it decreases, and EV_UNKNOWN if we cannot determine + which of these cases happens. */ + +enum ev_direction +scev_direction (tree chrec) +{ + tree step; + + if (!evolution_function_is_affine_p (chrec)) + return EV_DIR_UNKNOWN; + + step = CHREC_RIGHT (chrec); + if (TREE_CODE (step) != INTEGER_CST) + return EV_DIR_UNKNOWN; + + if (tree_int_cst_sign_bit (step)) + return EV_DIR_DECREASES; + else + return EV_DIR_GROWS; +} |