| /* Chains of recurrences. |
| Copyright (C) 2003, 2004, 2005 Free Software Foundation, Inc. |
| Contributed by Sebastian Pop <s.pop@laposte.net> |
| |
| 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" |
| #include "params.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) |
| { |
| /* APPLE LOCAL begin 4233898 */ |
| tree t0, t1, t2; |
| int var; |
| /* APPLE LOCAL end 4233898 */ |
| |
| 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. */ |
| |
| /* APPLE LOCAL begin 4233898 */ |
| /* "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, build_int_cst_type (type, 2), t2); |
| |
| var = CHREC_VARIABLE (poly0); |
| return build_polynomial_chrec (var, t0, |
| build_polynomial_chrec (var, t1, t2)); |
| /* APPLE LOCAL end 4233898 */ |
| } |
| |
| /* 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: |
| { |
| 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, op0, op1)); |
| else |
| return chrec_dont_know; |
| } |
| } |
| } |
| } |
| |
| /* 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 (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) |
| || 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 build2 |
| (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, 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; |
| } |
| } |
| |
| /* 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 CHREC to TYPE. The following is 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 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; |
| |
| /* 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; |
| } |
| } |
| } |
| |
| /* Returns the type of the chrec. */ |
| |
| tree |
| chrec_type (tree chrec) |
| { |
| if (automatically_generated_chrec_p (chrec)) |
| return NULL_TREE; |
| |
| return TREE_TYPE (chrec); |
| } |