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+/* Global, SSA-based optimizations using mathematical identities.
+ Copyright (C) 2005 Free Software Foundation, Inc.
+
+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. */
+
+/* Currently, the only mini-pass in this file tries to CSE reciprocal
+ operations. These are common in sequences such as this one:
+
+ modulus = sqrt(x*x + y*y + z*z);
+ x = x / modulus;
+ y = y / modulus;
+ z = z / modulus;
+
+ that can be optimized to
+
+ modulus = sqrt(x*x + y*y + z*z);
+ rmodulus = 1.0 / modulus;
+ x = x * rmodulus;
+ y = y * rmodulus;
+ z = z * rmodulus;
+
+ We do this for loop invariant divisors, and with this pass whenever
+ we notice that a division has the same divisor multiple times.
+
+ Of course, like in PRE, we don't insert a division if a dominator
+ already has one. However, this cannot be done as an extension of
+ PRE for several reasons.
+
+ First of all, with some experiments it was found out that the
+ transformation is not always useful if there are only two divisions
+ hy the same divisor. This is probably because modern processors
+ can pipeline the divisions; on older, in-order processors it should
+ still be effective to optimize two divisions by the same number.
+ We make this a param, and it shall be called N in the remainder of
+ this comment.
+
+ Second, if trapping math is active, we have less freedom on where
+ to insert divisions: we can only do so in basic blocks that already
+ contain one. (If divisions don't trap, instead, we can insert
+ divisions elsewhere, which will be in blocks that are common dominators
+ of those that have the division).
+
+ We really don't want to compute the reciprocal unless a division will
+ be found. To do this, we won't insert the division in a basic block
+ that has less than N divisions *post-dominating* it.
+
+ The algorithm constructs a subset of the dominator tree, holding the
+ blocks containing the divisions and the common dominators to them,
+ and walk it twice. The first walk is in post-order, and it annotates
+ each block with the number of divisions that post-dominate it: this
+ gives information on where divisions can be inserted profitably.
+ The second walk is in pre-order, and it inserts divisions as explained
+ above, and replaces divisions by multiplications.
+
+ In the best case, the cost of the pass is O(n_statements). In the
+ worst-case, the cost is due to creating the dominator tree subset,
+ with a cost of O(n_basic_blocks ^ 2); however this can only happen
+ for n_statements / n_basic_blocks statements. So, the amortized cost
+ of creating the dominator tree subset is O(n_basic_blocks) and the
+ worst-case cost of the pass is O(n_statements * n_basic_blocks).
+
+ More practically, the cost will be small because there are few
+ divisions, and they tend to be in the same basic block, so insert_bb
+ is called very few times.
+
+ If we did this using domwalk.c, an efficient implementation would have
+ to work on all the variables in a single pass, because we could not
+ work on just a subset of the dominator tree, as we do now, and the
+ cost would also be something like O(n_statements * n_basic_blocks).
+ The data structures would be more complex in order to work on all the
+ variables in a single pass. */
+
+#include "config.h"
+#include "system.h"
+#include "coretypes.h"
+#include "tm.h"
+#include "flags.h"
+#include "tree.h"
+#include "tree-flow.h"
+#include "real.h"
+#include "timevar.h"
+#include "tree-pass.h"
+#include "alloc-pool.h"
+#include "basic-block.h"
+#include "target.h"
+
+
+/* This structure represents one basic block that either computes a
+ division, or is a common dominator for basic block that compute a
+ division. */
+struct occurrence {
+ /* The basic block represented by this structure. */
+ basic_block bb;
+
+ /* If non-NULL, the SSA_NAME holding the definition for a reciprocal
+ inserted in BB. */
+ tree recip_def;
+
+ /* If non-NULL, the MODIFY_EXPR for a reciprocal computation that
+ was inserted in BB. */
+ tree recip_def_stmt;
+
+ /* Pointer to a list of "struct occurrence"s for blocks dominated
+ by BB. */
+ struct occurrence *children;
+
+ /* Pointer to the next "struct occurrence"s in the list of blocks
+ sharing a common dominator. */
+ struct occurrence *next;
+
+ /* The number of divisions that are in BB before compute_merit. The
+ number of divisions that are in BB or post-dominate it after
+ compute_merit. */
+ int num_divisions;
+
+ /* True if the basic block has a division, false if it is a common
+ dominator for basic blocks that do. If it is false and trapping
+ math is active, BB is not a candidate for inserting a reciprocal. */
+ bool bb_has_division;
+};
+
+
+/* The instance of "struct occurrence" representing the highest
+ interesting block in the dominator tree. */
+static struct occurrence *occ_head;
+
+/* Allocation pool for getting instances of "struct occurrence". */
+static alloc_pool occ_pool;
+
+
+
+/* Allocate and return a new struct occurrence for basic block BB, and
+ whose children list is headed by CHILDREN. */
+static struct occurrence *
+occ_new (basic_block bb, struct occurrence *children)
+{
+ struct occurrence *occ;
+
+ occ = bb->aux = pool_alloc (occ_pool);
+ memset (occ, 0, sizeof (struct occurrence));
+
+ occ->bb = bb;
+ occ->children = children;
+ return occ;
+}
+
+
+/* Insert NEW_OCC into our subset of the dominator tree. P_HEAD points to a
+ list of "struct occurrence"s, one per basic block, having IDOM as
+ their common dominator.
+
+ We try to insert NEW_OCC as deep as possible in the tree, and we also
+ insert any other block that is a common dominator for BB and one
+ block already in the tree. */
+
+static void
+insert_bb (struct occurrence *new_occ, basic_block idom,
+ struct occurrence **p_head)
+{
+ struct occurrence *occ, **p_occ;
+
+ for (p_occ = p_head; (occ = *p_occ) != NULL; )
+ {
+ basic_block bb = new_occ->bb, occ_bb = occ->bb;
+ basic_block dom = nearest_common_dominator (CDI_DOMINATORS, occ_bb, bb);
+ if (dom == bb)
+ {
+ /* BB dominates OCC_BB. OCC becomes NEW_OCC's child: remove OCC
+ from its list. */
+ *p_occ = occ->next;
+ occ->next = new_occ->children;
+ new_occ->children = occ;
+
+ /* Try the next block (it may as well be dominated by BB). */
+ }
+
+ else if (dom == occ_bb)
+ {
+ /* OCC_BB dominates BB. Tail recurse to look deeper. */
+ insert_bb (new_occ, dom, &occ->children);
+ return;
+ }
+
+ else if (dom != idom)
+ {
+ gcc_assert (!dom->aux);
+
+ /* There is a dominator between IDOM and BB, add it and make
+ two children out of NEW_OCC and OCC. First, remove OCC from
+ its list. */
+ *p_occ = occ->next;
+ new_occ->next = occ;
+ occ->next = NULL;
+
+ /* None of the previous blocks has DOM as a dominator: if we tail
+ recursed, we would reexamine them uselessly. Just switch BB with
+ DOM, and go on looking for blocks dominated by DOM. */
+ new_occ = occ_new (dom, new_occ);
+ }
+
+ else
+ {
+ /* Nothing special, go on with the next element. */
+ p_occ = &occ->next;
+ }
+ }
+
+ /* No place was found as a child of IDOM. Make BB a sibling of IDOM. */
+ new_occ->next = *p_head;
+ *p_head = new_occ;
+}
+
+/* Register that we found a division in BB. */
+
+static inline void
+register_division_in (basic_block bb)
+{
+ struct occurrence *occ;
+
+ occ = (struct occurrence *) bb->aux;
+ if (!occ)
+ {
+ occ = occ_new (bb, NULL);
+ insert_bb (occ, ENTRY_BLOCK_PTR, &occ_head);
+ }
+
+ occ->bb_has_division = true;
+ occ->num_divisions++;
+}
+
+
+/* Compute the number of divisions that postdominate each block in OCC and
+ its children. */
+
+static void
+compute_merit (struct occurrence *occ)
+{
+ struct occurrence *occ_child;
+ basic_block dom = occ->bb;
+
+ for (occ_child = occ->children; occ_child; occ_child = occ_child->next)
+ {
+ basic_block bb;
+ if (occ_child->children)
+ compute_merit (occ_child);
+
+ if (flag_exceptions)
+ bb = single_noncomplex_succ (dom);
+ else
+ bb = dom;
+
+ if (dominated_by_p (CDI_POST_DOMINATORS, bb, occ_child->bb))
+ occ->num_divisions += occ_child->num_divisions;
+ }
+}
+
+
+/* Return whether USE_STMT is a floating-point division by DEF. */
+static inline bool
+is_division_by (tree use_stmt, tree def)
+{
+ return TREE_CODE (use_stmt) == MODIFY_EXPR
+ && TREE_CODE (TREE_OPERAND (use_stmt, 1)) == RDIV_EXPR
+ && TREE_OPERAND (TREE_OPERAND (use_stmt, 1), 1) == def;
+}
+
+/* Walk the subset of the dominator tree rooted at OCC, setting the
+ RECIP_DEF field to a definition of 1.0 / DEF that can be used in
+ the given basic block. The field may be left NULL, of course,
+ if it is not possible or profitable to do the optimization.
+
+ DEF_BSI is an iterator pointing at the statement defining DEF.
+ If RECIP_DEF is set, a dominator already has a computation that can
+ be used. */
+
+static void
+insert_reciprocals (block_stmt_iterator *def_bsi, struct occurrence *occ,
+ tree def, tree recip_def, int threshold)
+{
+ tree type, new_stmt;
+ block_stmt_iterator bsi;
+ struct occurrence *occ_child;
+
+ if (!recip_def
+ && (occ->bb_has_division || !flag_trapping_math)
+ && occ->num_divisions >= threshold)
+ {
+ /* Make a variable with the replacement and substitute it. */
+ type = TREE_TYPE (def);
+ recip_def = make_rename_temp (type, "reciptmp");
+ new_stmt = build2 (MODIFY_EXPR, void_type_node, recip_def,
+ fold_build2 (RDIV_EXPR, type, build_one_cst (type),
+ def));
+
+
+ if (occ->bb_has_division)
+ {
+ /* Case 1: insert before an existing division. */
+ bsi = bsi_after_labels (occ->bb);
+ while (!bsi_end_p (bsi) && !is_division_by (bsi_stmt (bsi), def))
+ bsi_next (&bsi);
+
+ bsi_insert_before (&bsi, new_stmt, BSI_SAME_STMT);
+ }
+ else if (def_bsi && occ->bb == def_bsi->bb)
+ {
+ /* Case 2: insert right after the definition. Note that this will
+ never happen if the definition statement can throw, because in
+ that case the sole successor of the statement's basic block will
+ dominate all the uses as well. */
+ bsi_insert_after (def_bsi, new_stmt, BSI_NEW_STMT);
+ }
+ else
+ {
+ /* Case 3: insert in a basic block not containing defs/uses. */
+ bsi = bsi_after_labels (occ->bb);
+ bsi_insert_before (&bsi, new_stmt, BSI_SAME_STMT);
+ }
+
+ occ->recip_def_stmt = new_stmt;
+ }
+
+ occ->recip_def = recip_def;
+ for (occ_child = occ->children; occ_child; occ_child = occ_child->next)
+ insert_reciprocals (def_bsi, occ_child, def, recip_def, threshold);
+}
+
+
+/* Replace the division at USE_P with a multiplication by the reciprocal, if
+ possible. */
+
+static inline void
+replace_reciprocal (use_operand_p use_p)
+{
+ tree use_stmt = USE_STMT (use_p);
+ basic_block bb = bb_for_stmt (use_stmt);
+ struct occurrence *occ = (struct occurrence *) bb->aux;
+
+ if (occ->recip_def && use_stmt != occ->recip_def_stmt)
+ {
+ TREE_SET_CODE (TREE_OPERAND (use_stmt, 1), MULT_EXPR);
+ SET_USE (use_p, occ->recip_def);
+ fold_stmt_inplace (use_stmt);
+ update_stmt (use_stmt);
+ }
+}
+
+
+/* Free OCC and return one more "struct occurrence" to be freed. */
+
+static struct occurrence *
+free_bb (struct occurrence *occ)
+{
+ struct occurrence *child, *next;
+
+ /* First get the two pointers hanging off OCC. */
+ next = occ->next;
+ child = occ->children;
+ occ->bb->aux = NULL;
+ pool_free (occ_pool, occ);
+
+ /* Now ensure that we don't recurse unless it is necessary. */
+ if (!child)
+ return next;
+ else
+ {
+ while (next)
+ next = free_bb (next);
+
+ return child;
+ }
+}
+
+
+/* Look for floating-point divisions among DEF's uses, and try to
+ replace them by multiplications with the reciprocal. Add
+ as many statements computing the reciprocal as needed.
+
+ DEF must be a GIMPLE register of a floating-point type. */
+
+static void
+execute_cse_reciprocals_1 (block_stmt_iterator *def_bsi, tree def)
+{
+ use_operand_p use_p;
+ imm_use_iterator use_iter;
+ struct occurrence *occ;
+ int count = 0, threshold;
+
+ gcc_assert (FLOAT_TYPE_P (TREE_TYPE (def)) && is_gimple_reg (def));
+
+ FOR_EACH_IMM_USE_FAST (use_p, use_iter, def)
+ {
+ tree use_stmt = USE_STMT (use_p);
+ if (is_division_by (use_stmt, def))
+ {
+ register_division_in (bb_for_stmt (use_stmt));
+ count++;
+ }
+ }
+
+ /* Do the expensive part only if we can hope to optimize something. */
+ threshold = targetm.min_divisions_for_recip_mul (TYPE_MODE (TREE_TYPE (def)));
+ if (count >= threshold)
+ {
+ tree use_stmt;
+ for (occ = occ_head; occ; occ = occ->next)
+ {
+ compute_merit (occ);
+ insert_reciprocals (def_bsi, occ, def, NULL, threshold);
+ }
+
+ FOR_EACH_IMM_USE_STMT (use_stmt, use_iter, def)
+ {
+ if (is_division_by (use_stmt, def))
+ {
+ FOR_EACH_IMM_USE_ON_STMT (use_p, use_iter)
+ replace_reciprocal (use_p);
+ }
+ }
+ }
+
+ for (occ = occ_head; occ; )
+ occ = free_bb (occ);
+
+ occ_head = NULL;
+}
+
+
+static bool
+gate_cse_reciprocals (void)
+{
+ return optimize && !optimize_size && flag_unsafe_math_optimizations;
+}
+
+
+/* Go through all the floating-point SSA_NAMEs, and call
+ execute_cse_reciprocals_1 on each of them. */
+static unsigned int
+execute_cse_reciprocals (void)
+{
+ basic_block bb;
+ tree arg;
+
+ occ_pool = create_alloc_pool ("dominators for recip",
+ sizeof (struct occurrence),
+ n_basic_blocks / 3 + 1);
+
+ calculate_dominance_info (CDI_DOMINATORS);
+ calculate_dominance_info (CDI_POST_DOMINATORS);
+
+#ifdef ENABLE_CHECKING
+ FOR_EACH_BB (bb)
+ gcc_assert (!bb->aux);
+#endif
+
+ for (arg = DECL_ARGUMENTS (cfun->decl); arg; arg = TREE_CHAIN (arg))
+ if (default_def (arg)
+ && FLOAT_TYPE_P (TREE_TYPE (arg))
+ && is_gimple_reg (arg))
+ execute_cse_reciprocals_1 (NULL, default_def (arg));
+
+ FOR_EACH_BB (bb)
+ {
+ block_stmt_iterator bsi;
+ tree phi, def;
+
+ for (phi = phi_nodes (bb); phi; phi = PHI_CHAIN (phi))
+ {
+ def = PHI_RESULT (phi);
+ if (FLOAT_TYPE_P (TREE_TYPE (def))
+ && is_gimple_reg (def))
+ execute_cse_reciprocals_1 (NULL, def);
+ }
+
+ for (bsi = bsi_after_labels (bb); !bsi_end_p (bsi); bsi_next (&bsi))
+ {
+ tree stmt = bsi_stmt (bsi);
+ if (TREE_CODE (stmt) == MODIFY_EXPR
+ && (def = SINGLE_SSA_TREE_OPERAND (stmt, SSA_OP_DEF)) != NULL
+ && FLOAT_TYPE_P (TREE_TYPE (def))
+ && TREE_CODE (def) == SSA_NAME)
+ execute_cse_reciprocals_1 (&bsi, def);
+ }
+ }
+
+ free_dominance_info (CDI_DOMINATORS);
+ free_dominance_info (CDI_POST_DOMINATORS);
+ free_alloc_pool (occ_pool);
+ return 0;
+}
+
+struct tree_opt_pass pass_cse_reciprocals =
+{
+ "recip", /* name */
+ gate_cse_reciprocals, /* gate */
+ execute_cse_reciprocals, /* execute */
+ NULL, /* sub */
+ NULL, /* next */
+ 0, /* static_pass_number */
+ 0, /* tv_id */
+ PROP_ssa, /* properties_required */
+ 0, /* properties_provided */
+ 0, /* properties_destroyed */
+ 0, /* todo_flags_start */
+ TODO_dump_func | TODO_update_ssa | TODO_verify_ssa
+ | TODO_verify_stmts, /* todo_flags_finish */
+ 0 /* letter */
+};
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