/* Chains of recurrences. Copyright (C) 2003, 2004, 2005 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 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, 59 Temple Place - Suite 330, Boston, MA 02111-1307, 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 "errors.h" #include "ggc.h" #include "tree.h" #include "diagnostic.h" #include "varray.h" #include "tree-chrec.h" #include "tree-pass.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)); 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); /* {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), 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) { gcc_assert (poly0); gcc_assert (poly1); gcc_assert (TREE_CODE (poly0) == POLYNOMIAL_CHREC); gcc_assert (TREE_CODE (poly1) == POLYNOMIAL_CHREC); /* {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. */ return build_polynomial_chrec (CHREC_VARIABLE (poly0), build_polynomial_chrec (CHREC_VARIABLE (poly0), /* "a*c". */ chrec_fold_multiply (type, CHREC_LEFT (poly0), CHREC_LEFT (poly1)), /* "a*d + b*c + b*d". */ chrec_fold_plus (type, chrec_fold_multiply (type, CHREC_LEFT (poly0), CHREC_RIGHT (poly1)), chrec_fold_plus (type, chrec_fold_multiply (type, CHREC_RIGHT (poly0), CHREC_LEFT (poly1)), chrec_fold_multiply (type, CHREC_RIGHT (poly0), CHREC_RIGHT (poly1))))), /* "2*b*d". */ chrec_fold_multiply (type, build_int_cst (NULL_TREE, 2), chrec_fold_multiply (type, CHREC_RIGHT (poly0), CHREC_RIGHT (poly1)))); } /* 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), build_int_cst_type (type, -1))); default: if (tree_contains_chrecs (op0) || tree_contains_chrecs (op1)) return build (code, type, op0, op1); else return fold (build (code, type, op0, op1)); } } } /* Fold the addition of two chrecs. */ tree chrec_fold_plus (tree type, tree op0, tree 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 (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 (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 (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 (type, 0); return fold (build (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) || chrec_contains_symbols (x)) return chrec_dont_know; if (dump_file && (dump_flags & TDF_DETAILS)) fprintf (dump_file, "(chrec_apply \n"); if (evolution_function_is_affine_p (chrec)) { /* "{a, +, b} (x)" -> "a + b*x". */ if (TREE_CODE (CHREC_LEFT (chrec)) == INTEGER_CST && integer_zerop (CHREC_LEFT (chrec))) res = chrec_fold_multiply (type, CHREC_RIGHT (chrec), x); else res = chrec_fold_plus (type, CHREC_LEFT (chrec), chrec_fold_multiply (type, CHREC_RIGHT (chrec), x)); } 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; 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) { if (TREE_CODE (chrec) == POLYNOMIAL_CHREC && CHREC_VARIABLE (chrec) > loop_num) return build (TREE_CODE (chrec), build_int_cst (NULL_TREE, CHREC_VARIABLE (chrec)), reset_evolution_in_loop (loop_num, CHREC_LEFT (chrec), new_evol), reset_evolution_in_loop (loop_num, CHREC_RIGHT (chrec), new_evol)); 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 (operand_equal_p (chrec1, chrec2, 0)) 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. */ bool tree_contains_chrecs (tree expr) { if (expr == NULL_TREE) return false; if (tree_is_chrec (expr)) return true; switch (TREE_CODE_LENGTH (TREE_CODE (expr))) { case 3: if (tree_contains_chrecs (TREE_OPERAND (expr, 2))) return true; case 2: if (tree_contains_chrecs (TREE_OPERAND (expr, 1))) return true; case 1: if (tree_contains_chrecs (TREE_OPERAND (expr, 0))) return true; default: 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; } } /* Convert the initial condition of chrec to type. */ tree chrec_convert (tree type, tree chrec) { tree ct; if (automatically_generated_chrec_p (chrec)) return chrec; ct = chrec_type (chrec); if (ct == type) return chrec; if (TYPE_PRECISION (ct) < TYPE_PRECISION (type)) return count_ev_in_wider_type (type, chrec); switch (TREE_CODE (chrec)) { case POLYNOMIAL_CHREC: return build_polynomial_chrec (CHREC_VARIABLE (chrec), chrec_convert (type, CHREC_LEFT (chrec)), chrec_convert (type, CHREC_RIGHT (chrec))); default: { tree res = fold_convert (type, chrec); /* Don't propagate overflows. */ TREE_OVERFLOW (res) = 0; if (CONSTANT_CLASS_P (res)) TREE_CONSTANT_OVERFLOW (res) = 0; return res; } } } /* Returns the type of the chrec. */ tree chrec_type (tree chrec) { if (automatically_generated_chrec_p (chrec)) return NULL_TREE; return TREE_TYPE (chrec); }