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/* Global, SSA-based optimizations using mathematical identities.
Copyright (C) 2005-2021 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 3, or (at your option) any
later version.
GCC is distributed in the hope that it will be useful, but WITHOUT
ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or
FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License
for more details.
You should have received a copy of the GNU General Public License
along with GCC; see the file COPYING3. If not see
<http://www.gnu.org/licenses/>. */
/* 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
by 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 "backend.h"
#include "target.h"
#include "rtl.h"
#include "tree.h"
#include "gimple.h"
#include "predict.h"
#include "alloc-pool.h"
#include "tree-pass.h"
#include "ssa.h"
#include "optabs-tree.h"
#include "gimple-pretty-print.h"
#include "alias.h"
#include "fold-const.h"
#include "gimple-fold.h"
#include "gimple-iterator.h"
#include "gimplify.h"
#include "gimplify-me.h"
#include "stor-layout.h"
#include "tree-cfg.h"
#include "tree-dfa.h"
#include "tree-ssa.h"
#include "builtins.h"
#include "internal-fn.h"
#include "case-cfn-macros.h"
#include "optabs-libfuncs.h"
#include "tree-eh.h"
#include "targhooks.h"
#include "domwalk.h"
#include "tree-ssa-math-opts.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 = basic_block();
/* If non-NULL, the SSA_NAME holding the definition for a reciprocal
inserted in BB. */
tree recip_def = tree();
/* If non-NULL, the SSA_NAME holding the definition for a squared
reciprocal inserted in BB. */
tree square_recip_def = tree();
/* If non-NULL, the GIMPLE_ASSIGN for a reciprocal computation that
was inserted in BB. */
gimple *recip_def_stmt = nullptr;
/* Pointer to a list of "struct occurrence"s for blocks dominated
by BB. */
struct occurrence *children = nullptr;
/* Pointer to the next "struct occurrence"s in the list of blocks
sharing a common dominator. */
struct occurrence *next = nullptr;
/* 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 = 0;
/* 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 = false;
/* Construct a struct occurrence for basic block BB, and whose
children list is headed by CHILDREN. */
occurrence (basic_block bb, struct occurrence *children)
: bb (bb), children (children)
{
bb->aux = this;
}
/* Destroy a struct occurrence and remove it from its basic block. */
~occurrence ()
{
bb->aux = nullptr;
}
/* Allocate memory for a struct occurrence from OCC_POOL. */
static void* operator new (size_t);
/* Return memory for a struct occurrence to OCC_POOL. */
static void operator delete (void*, size_t);
};
static struct
{
/* Number of 1.0/X ops inserted. */
int rdivs_inserted;
/* Number of 1.0/FUNC ops inserted. */
int rfuncs_inserted;
} reciprocal_stats;
static struct
{
/* Number of cexpi calls inserted. */
int inserted;
/* Number of conversions removed. */
int conv_removed;
} sincos_stats;
static struct
{
/* Number of widening multiplication ops inserted. */
int widen_mults_inserted;
/* Number of integer multiply-and-accumulate ops inserted. */
int maccs_inserted;
/* Number of fp fused multiply-add ops inserted. */
int fmas_inserted;
/* Number of divmod calls inserted. */
int divmod_calls_inserted;
} widen_mul_stats;
/* 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 object_allocator<occurrence> *occ_pool;
void* occurrence::operator new (size_t n)
{
gcc_assert (n == sizeof(occurrence));
return occ_pool->allocate_raw ();
}
void occurrence::operator delete (void *occ, size_t n)
{
gcc_assert (n == sizeof(occurrence));
occ_pool->remove_raw (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 = new occurrence (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.
IMPORTANCE is a measure of how much weighting to give
that division. Use IMPORTANCE = 2 to register a single
division. If the division is going to be found multiple
times use 1 (as it is with squares). */
static inline void
register_division_in (basic_block bb, int importance)
{
struct occurrence *occ;
occ = (struct occurrence *) bb->aux;
if (!occ)
{
occ = new occurrence (bb, NULL);
insert_bb (occ, ENTRY_BLOCK_PTR_FOR_FN (cfun), &occ_head);
}
occ->bb_has_division = true;
occ->num_divisions += importance;
}
/* 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 (gimple *use_stmt, tree def)
{
return is_gimple_assign (use_stmt)
&& gimple_assign_rhs_code (use_stmt) == RDIV_EXPR
&& gimple_assign_rhs2 (use_stmt) == def
/* Do not recognize x / x as valid division, as we are getting
confused later by replacing all immediate uses x in such
a stmt. */
&& gimple_assign_rhs1 (use_stmt) != def
&& !stmt_can_throw_internal (cfun, use_stmt);
}
/* Return TRUE if USE_STMT is a multiplication of DEF by A. */
static inline bool
is_mult_by (gimple *use_stmt, tree def, tree a)
{
if (gimple_code (use_stmt) == GIMPLE_ASSIGN
&& gimple_assign_rhs_code (use_stmt) == MULT_EXPR)
{
tree op0 = gimple_assign_rhs1 (use_stmt);
tree op1 = gimple_assign_rhs2 (use_stmt);
return (op0 == def && op1 == a)
|| (op0 == a && op1 == def);
}
return 0;
}
/* Return whether USE_STMT is DEF * DEF. */
static inline bool
is_square_of (gimple *use_stmt, tree def)
{
return is_mult_by (use_stmt, def, def);
}
/* Return whether USE_STMT is a floating-point division by
DEF * DEF. */
static inline bool
is_division_by_square (gimple *use_stmt, tree def)
{
if (gimple_code (use_stmt) == GIMPLE_ASSIGN
&& gimple_assign_rhs_code (use_stmt) == RDIV_EXPR
&& gimple_assign_rhs1 (use_stmt) != gimple_assign_rhs2 (use_stmt)
&& !stmt_can_throw_internal (cfun, use_stmt))
{
tree denominator = gimple_assign_rhs2 (use_stmt);
if (TREE_CODE (denominator) == SSA_NAME)
return is_square_of (SSA_NAME_DEF_STMT (denominator), def);
}
return 0;
}
/* 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.
If should_insert_square_recip is set, then this also inserts
the square of the reciprocal immediately after the definition
of the reciprocal. */
static void
insert_reciprocals (gimple_stmt_iterator *def_gsi, struct occurrence *occ,
tree def, tree recip_def, tree square_recip_def,
int should_insert_square_recip, int threshold)
{
tree type;
gassign *new_stmt, *new_square_stmt;
gimple_stmt_iterator gsi;
struct occurrence *occ_child;
if (!recip_def
&& (occ->bb_has_division || !flag_trapping_math)
/* Divide by two as all divisions are counted twice in
the costing loop. */
&& occ->num_divisions / 2 >= threshold)
{
/* Make a variable with the replacement and substitute it. */
type = TREE_TYPE (def);
recip_def = create_tmp_reg (type, "reciptmp");
new_stmt = gimple_build_assign (recip_def, RDIV_EXPR,
build_one_cst (type), def);
if (should_insert_square_recip)
{
square_recip_def = create_tmp_reg (type, "powmult_reciptmp");
new_square_stmt = gimple_build_assign (square_recip_def, MULT_EXPR,
recip_def, recip_def);
}
if (occ->bb_has_division)
{
/* Case 1: insert before an existing division. */
gsi = gsi_after_labels (occ->bb);
while (!gsi_end_p (gsi)
&& (!is_division_by (gsi_stmt (gsi), def))
&& (!is_division_by_square (gsi_stmt (gsi), def)))
gsi_next (&gsi);
gsi_insert_before (&gsi, new_stmt, GSI_SAME_STMT);
if (should_insert_square_recip)
gsi_insert_before (&gsi, new_square_stmt, GSI_SAME_STMT);
}
else if (def_gsi && occ->bb == gsi_bb (*def_gsi))
{
/* 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. */
gsi_insert_after (def_gsi, new_stmt, GSI_NEW_STMT);
if (should_insert_square_recip)
gsi_insert_after (def_gsi, new_square_stmt, GSI_NEW_STMT);
}
else
{
/* Case 3: insert in a basic block not containing defs/uses. */
gsi = gsi_after_labels (occ->bb);
gsi_insert_before (&gsi, new_stmt, GSI_SAME_STMT);
if (should_insert_square_recip)
gsi_insert_before (&gsi, new_square_stmt, GSI_SAME_STMT);
}
reciprocal_stats.rdivs_inserted++;
occ->recip_def_stmt = new_stmt;
}
occ->recip_def = recip_def;
occ->square_recip_def = square_recip_def;
for (occ_child = occ->children; occ_child; occ_child = occ_child->next)
insert_reciprocals (def_gsi, occ_child, def, recip_def,
square_recip_def, should_insert_square_recip,
threshold);
}
/* Replace occurrences of expr / (x * x) with expr * ((1 / x) * (1 / x)).
Take as argument the use for (x * x). */
static inline void
replace_reciprocal_squares (use_operand_p use_p)
{
gimple *use_stmt = USE_STMT (use_p);
basic_block bb = gimple_bb (use_stmt);
struct occurrence *occ = (struct occurrence *) bb->aux;
if (optimize_bb_for_speed_p (bb) && occ->square_recip_def
&& occ->recip_def)
{
gimple_stmt_iterator gsi = gsi_for_stmt (use_stmt);
gimple_assign_set_rhs_code (use_stmt, MULT_EXPR);
gimple_assign_set_rhs2 (use_stmt, occ->square_recip_def);
SET_USE (use_p, occ->square_recip_def);
fold_stmt_inplace (&gsi);
update_stmt (use_stmt);
}
}
/* Replace the division at USE_P with a multiplication by the reciprocal, if
possible. */
static inline void
replace_reciprocal (use_operand_p use_p)
{
gimple *use_stmt = USE_STMT (use_p);
basic_block bb = gimple_bb (use_stmt);
struct occurrence *occ = (struct occurrence *) bb->aux;
if (optimize_bb_for_speed_p (bb)
&& occ->recip_def && use_stmt != occ->recip_def_stmt)
{
gimple_stmt_iterator gsi = gsi_for_stmt (use_stmt);
gimple_assign_set_rhs_code (use_stmt, MULT_EXPR);
SET_USE (use_p, occ->recip_def);
fold_stmt_inplace (&gsi);
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;
delete 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;
}
}
/* Transform sequences like
t = sqrt (a)
x = 1.0 / t;
r1 = x * x;
r2 = a * x;
into:
t = sqrt (a)
r1 = 1.0 / a;
r2 = t;
x = r1 * r2;
depending on the uses of x, r1, r2. This removes one multiplication and
allows the sqrt and division operations to execute in parallel.
DEF_GSI is the gsi of the initial division by sqrt that defines
DEF (x in the example above). */
static void
optimize_recip_sqrt (gimple_stmt_iterator *def_gsi, tree def)
{
gimple *use_stmt;
imm_use_iterator use_iter;
gimple *stmt = gsi_stmt (*def_gsi);
tree x = def;
tree orig_sqrt_ssa_name = gimple_assign_rhs2 (stmt);
tree div_rhs1 = gimple_assign_rhs1 (stmt);
if (TREE_CODE (orig_sqrt_ssa_name) != SSA_NAME
|| TREE_CODE (div_rhs1) != REAL_CST
|| !real_equal (&TREE_REAL_CST (div_rhs1), &dconst1))
return;
gcall *sqrt_stmt
= dyn_cast <gcall *> (SSA_NAME_DEF_STMT (orig_sqrt_ssa_name));
if (!sqrt_stmt || !gimple_call_lhs (sqrt_stmt))
return;
switch (gimple_call_combined_fn (sqrt_stmt))
{
CASE_CFN_SQRT:
CASE_CFN_SQRT_FN:
break;
default:
return;
}
tree a = gimple_call_arg (sqrt_stmt, 0);
/* We have 'a' and 'x'. Now analyze the uses of 'x'. */
/* Statements that use x in x * x. */
auto_vec<gimple *> sqr_stmts;
/* Statements that use x in a * x. */
auto_vec<gimple *> mult_stmts;
bool has_other_use = false;
bool mult_on_main_path = false;
FOR_EACH_IMM_USE_STMT (use_stmt, use_iter, x)
{
if (is_gimple_debug (use_stmt))
continue;
if (is_square_of (use_stmt, x))
{
sqr_stmts.safe_push (use_stmt);
if (gimple_bb (use_stmt) == gimple_bb (stmt))
mult_on_main_path = true;
}
else if (is_mult_by (use_stmt, x, a))
{
mult_stmts.safe_push (use_stmt);
if (gimple_bb (use_stmt) == gimple_bb (stmt))
mult_on_main_path = true;
}
else
has_other_use = true;
}
/* In the x * x and a * x cases we just rewire stmt operands or
remove multiplications. In the has_other_use case we introduce
a multiplication so make sure we don't introduce a multiplication
on a path where there was none. */
if (has_other_use && !mult_on_main_path)
return;
if (sqr_stmts.is_empty () && mult_stmts.is_empty ())
return;
/* If x = 1.0 / sqrt (a) has uses other than those optimized here we want
to be able to compose it from the sqr and mult cases. */
if (has_other_use && (sqr_stmts.is_empty () || mult_stmts.is_empty ()))
return;
if (dump_file)
{
fprintf (dump_file, "Optimizing reciprocal sqrt multiplications of\n");
print_gimple_stmt (dump_file, sqrt_stmt, 0, TDF_NONE);
print_gimple_stmt (dump_file, stmt, 0, TDF_NONE);
fprintf (dump_file, "\n");
}
bool delete_div = !has_other_use;
tree sqr_ssa_name = NULL_TREE;
if (!sqr_stmts.is_empty ())
{
/* r1 = x * x. Transform the original
x = 1.0 / t
into
tmp1 = 1.0 / a
r1 = tmp1. */
sqr_ssa_name
= make_temp_ssa_name (TREE_TYPE (a), NULL, "recip_sqrt_sqr");
if (dump_file)
{
fprintf (dump_file, "Replacing original division\n");
print_gimple_stmt (dump_file, stmt, 0, TDF_NONE);
fprintf (dump_file, "with new division\n");
}
stmt
= gimple_build_assign (sqr_ssa_name, gimple_assign_rhs_code (stmt),
gimple_assign_rhs1 (stmt), a);
gsi_insert_before (def_gsi, stmt, GSI_SAME_STMT);
gsi_remove (def_gsi, true);
*def_gsi = gsi_for_stmt (stmt);
fold_stmt_inplace (def_gsi);
update_stmt (stmt);
if (dump_file)
print_gimple_stmt (dump_file, stmt, 0, TDF_NONE);
delete_div = false;
gimple *sqr_stmt;
unsigned int i;
FOR_EACH_VEC_ELT (sqr_stmts, i, sqr_stmt)
{
gimple_stmt_iterator gsi2 = gsi_for_stmt (sqr_stmt);
gimple_assign_set_rhs_from_tree (&gsi2, sqr_ssa_name);
update_stmt (sqr_stmt);
}
}
if (!mult_stmts.is_empty ())
{
/* r2 = a * x. Transform this into:
r2 = t (The original sqrt (a)). */
unsigned int i;
gimple *mult_stmt = NULL;
FOR_EACH_VEC_ELT (mult_stmts, i, mult_stmt)
{
gimple_stmt_iterator gsi2 = gsi_for_stmt (mult_stmt);
if (dump_file)
{
fprintf (dump_file, "Replacing squaring multiplication\n");
print_gimple_stmt (dump_file, mult_stmt, 0, TDF_NONE);
fprintf (dump_file, "with assignment\n");
}
gimple_assign_set_rhs_from_tree (&gsi2, orig_sqrt_ssa_name);
fold_stmt_inplace (&gsi2);
update_stmt (mult_stmt);
if (dump_file)
print_gimple_stmt (dump_file, mult_stmt, 0, TDF_NONE);
}
}
if (has_other_use)
{
/* Using the two temporaries tmp1, tmp2 from above
the original x is now:
x = tmp1 * tmp2. */
gcc_assert (orig_sqrt_ssa_name);
gcc_assert (sqr_ssa_name);
gimple *new_stmt
= gimple_build_assign (x, MULT_EXPR,
orig_sqrt_ssa_name, sqr_ssa_name);
gsi_insert_after (def_gsi, new_stmt, GSI_NEW_STMT);
update_stmt (stmt);
}
else if (delete_div)
{
/* Remove the original division. */
gimple_stmt_iterator gsi2 = gsi_for_stmt (stmt);
gsi_remove (&gsi2, true);
release_defs (stmt);
}
else
release_ssa_name (x);
}
/* 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 (gimple_stmt_iterator *def_gsi, tree def)
{
use_operand_p use_p, square_use_p;
imm_use_iterator use_iter, square_use_iter;
tree square_def;
struct occurrence *occ;
int count = 0;
int threshold;
int square_recip_count = 0;
int sqrt_recip_count = 0;
gcc_assert (FLOAT_TYPE_P (TREE_TYPE (def)) && TREE_CODE (def) == SSA_NAME);
threshold = targetm.min_divisions_for_recip_mul (TYPE_MODE (TREE_TYPE (def)));
/* If DEF is a square (x * x), count the number of divisions by x.
If there are more divisions by x than by (DEF * DEF), prefer to optimize
the reciprocal of x instead of DEF. This improves cases like:
def = x * x
t0 = a / def
t1 = b / def
t2 = c / x
Reciprocal optimization of x results in 1 division rather than 2 or 3. */
gimple *def_stmt = SSA_NAME_DEF_STMT (def);
if (is_gimple_assign (def_stmt)
&& gimple_assign_rhs_code (def_stmt) == MULT_EXPR
&& TREE_CODE (gimple_assign_rhs1 (def_stmt)) == SSA_NAME
&& gimple_assign_rhs1 (def_stmt) == gimple_assign_rhs2 (def_stmt))
{
tree op0 = gimple_assign_rhs1 (def_stmt);
FOR_EACH_IMM_USE_FAST (use_p, use_iter, op0)
{
gimple *use_stmt = USE_STMT (use_p);
if (is_division_by (use_stmt, op0))
sqrt_recip_count++;
}
}
FOR_EACH_IMM_USE_FAST (use_p, use_iter, def)
{
gimple *use_stmt = USE_STMT (use_p);
if (is_division_by (use_stmt, def))
{
register_division_in (gimple_bb (use_stmt), 2);
count++;
}
if (is_square_of (use_stmt, def))
{
square_def = gimple_assign_lhs (use_stmt);
FOR_EACH_IMM_USE_FAST (square_use_p, square_use_iter, square_def)
{
gimple *square_use_stmt = USE_STMT (square_use_p);
if (is_division_by (square_use_stmt, square_def))
{
/* This is executed twice for each division by a square. */
register_division_in (gimple_bb (square_use_stmt), 1);
square_recip_count++;
}
}
}
}
/* Square reciprocals were counted twice above. */
square_recip_count /= 2;
/* If it is more profitable to optimize 1 / x, don't optimize 1 / (x * x). */
if (sqrt_recip_count > square_recip_count)
goto out;
/* Do the expensive part only if we can hope to optimize something. */
if (count + square_recip_count >= threshold && count >= 1)
{
gimple *use_stmt;
for (occ = occ_head; occ; occ = occ->next)
{
compute_merit (occ);
insert_reciprocals (def_gsi, occ, def, NULL, NULL,
square_recip_count, 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);
}
else if (square_recip_count > 0 && is_square_of (use_stmt, def))
{
FOR_EACH_IMM_USE_ON_STMT (use_p, use_iter)
{
/* Find all uses of the square that are divisions and
* replace them by multiplications with the inverse. */
imm_use_iterator square_iterator;
gimple *powmult_use_stmt = USE_STMT (use_p);
tree powmult_def_name = gimple_assign_lhs (powmult_use_stmt);
FOR_EACH_IMM_USE_STMT (powmult_use_stmt,
square_iterator, powmult_def_name)
FOR_EACH_IMM_USE_ON_STMT (square_use_p, square_iterator)
{
gimple *powmult_use_stmt = USE_STMT (square_use_p);
if (is_division_by (powmult_use_stmt, powmult_def_name))
replace_reciprocal_squares (square_use_p);
}
}
}
}
}
out:
for (occ = occ_head; occ; )
occ = free_bb (occ);
occ_head = NULL;
}
/* Return an internal function that implements the reciprocal of CALL,
or IFN_LAST if there is no such function that the target supports. */
internal_fn
internal_fn_reciprocal (gcall *call)
{
internal_fn ifn;
switch (gimple_call_combined_fn (call))
{
CASE_CFN_SQRT:
CASE_CFN_SQRT_FN:
ifn = IFN_RSQRT;
break;
default:
return IFN_LAST;
}
tree_pair types = direct_internal_fn_types (ifn, call);
if (!direct_internal_fn_supported_p (ifn, types, OPTIMIZE_FOR_SPEED))
return IFN_LAST;
return ifn;
}
/* Go through all the floating-point SSA_NAMEs, and call
execute_cse_reciprocals_1 on each of them. */
namespace {
const pass_data pass_data_cse_reciprocals =
{
GIMPLE_PASS, /* type */
"recip", /* name */
OPTGROUP_NONE, /* optinfo_flags */
TV_TREE_RECIP, /* tv_id */
PROP_ssa, /* properties_required */
0, /* properties_provided */
0, /* properties_destroyed */
0, /* todo_flags_start */
TODO_update_ssa, /* todo_flags_finish */
};
class pass_cse_reciprocals : public gimple_opt_pass
{
public:
pass_cse_reciprocals (gcc::context *ctxt)
: gimple_opt_pass (pass_data_cse_reciprocals, ctxt)
{}
/* opt_pass methods: */
virtual bool gate (function *) { return optimize && flag_reciprocal_math; }
virtual unsigned int execute (function *);
}; // class pass_cse_reciprocals
unsigned int
pass_cse_reciprocals::execute (function *fun)
{
basic_block bb;
tree arg;
occ_pool = new object_allocator<occurrence> ("dominators for recip");
memset (&reciprocal_stats, 0, sizeof (reciprocal_stats));
calculate_dominance_info (CDI_DOMINATORS);
calculate_dominance_info (CDI_POST_DOMINATORS);
if (flag_checking)
FOR_EACH_BB_FN (bb, fun)
gcc_assert (!bb->aux);
for (arg = DECL_ARGUMENTS (fun->decl); arg; arg = DECL_CHAIN (arg))
if (FLOAT_TYPE_P (TREE_TYPE (arg))
&& is_gimple_reg (arg))
{
tree name = ssa_default_def (fun, arg);
if (name)
execute_cse_reciprocals_1 (NULL, name);
}
FOR_EACH_BB_FN (bb, fun)
{
tree def;
for (gphi_iterator gsi = gsi_start_phis (bb); !gsi_end_p (gsi);
gsi_next (&gsi))
{
gphi *phi = gsi.phi ();
def = PHI_RESULT (phi);
if (! virtual_operand_p (def)
&& FLOAT_TYPE_P (TREE_TYPE (def)))
execute_cse_reciprocals_1 (NULL, def);
}
for (gimple_stmt_iterator gsi = gsi_after_labels (bb); !gsi_end_p (gsi);
gsi_next (&gsi))
{
gimple *stmt = gsi_stmt (gsi);
if (gimple_has_lhs (stmt)
&& (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 (&gsi, def);
stmt = gsi_stmt (gsi);
if (flag_unsafe_math_optimizations
&& is_gimple_assign (stmt)
&& gimple_assign_lhs (stmt) == def
&& !stmt_can_throw_internal (cfun, stmt)
&& gimple_assign_rhs_code (stmt) == RDIV_EXPR)
optimize_recip_sqrt (&gsi, def);
}
}
if (optimize_bb_for_size_p (bb))
continue;
/* Scan for a/func(b) and convert it to reciprocal a*rfunc(b). */
for (gimple_stmt_iterator gsi = gsi_after_labels (bb); !gsi_end_p (gsi);
gsi_next (&gsi))
{
gimple *stmt = gsi_stmt (gsi);
if (is_gimple_assign (stmt)
&& gimple_assign_rhs_code (stmt) == RDIV_EXPR)
{
tree arg1 = gimple_assign_rhs2 (stmt);
gimple *stmt1;
if (TREE_CODE (arg1) != SSA_NAME)
continue;
stmt1 = SSA_NAME_DEF_STMT (arg1);
if (is_gimple_call (stmt1)
&& gimple_call_lhs (stmt1))
{
bool fail;
imm_use_iterator ui;
use_operand_p use_p;
tree fndecl = NULL_TREE;
gcall *call = as_a <gcall *> (stmt1);
internal_fn ifn = internal_fn_reciprocal (call);
if (ifn == IFN_LAST)
{
fndecl = gimple_call_fndecl (call);
if (!fndecl
|| !fndecl_built_in_p (fndecl, BUILT_IN_MD))
continue;
fndecl = targetm.builtin_reciprocal (fndecl);
if (!fndecl)
continue;
}
/* Check that all uses of the SSA name are divisions,
otherwise replacing the defining statement will do
the wrong thing. */
fail = false;
FOR_EACH_IMM_USE_FAST (use_p, ui, arg1)
{
gimple *stmt2 = USE_STMT (use_p);
if (is_gimple_debug (stmt2))
continue;
if (!is_gimple_assign (stmt2)
|| gimple_assign_rhs_code (stmt2) != RDIV_EXPR
|| gimple_assign_rhs1 (stmt2) == arg1
|| gimple_assign_rhs2 (stmt2) != arg1)
{
fail = true;
break;
}
}
if (fail)
continue;
gimple_replace_ssa_lhs (call, arg1);
if (gimple_call_internal_p (call) != (ifn != IFN_LAST))
{
auto_vec<tree, 4> args;
for (unsigned int i = 0;
i < gimple_call_num_args (call); i++)
args.safe_push (gimple_call_arg (call, i));
gcall *stmt2;
if (ifn == IFN_LAST)
stmt2 = gimple_build_call_vec (fndecl, args);
else
stmt2 = gimple_build_call_internal_vec (ifn, args);
gimple_call_set_lhs (stmt2, arg1);
gimple_move_vops (stmt2, call);
gimple_call_set_nothrow (stmt2,
gimple_call_nothrow_p (call));
gimple_stmt_iterator gsi2 = gsi_for_stmt (call);
gsi_replace (&gsi2, stmt2, true);
}
else
{
if (ifn == IFN_LAST)
gimple_call_set_fndecl (call, fndecl);
else
gimple_call_set_internal_fn (call, ifn);
update_stmt (call);
}
reciprocal_stats.rfuncs_inserted++;
FOR_EACH_IMM_USE_STMT (stmt, ui, arg1)
{
gimple_stmt_iterator gsi = gsi_for_stmt (stmt);
gimple_assign_set_rhs_code (stmt, MULT_EXPR);
fold_stmt_inplace (&gsi);
update_stmt (stmt);
}
}
}
}
}
statistics_counter_event (fun, "reciprocal divs inserted",
reciprocal_stats.rdivs_inserted);
statistics_counter_event (fun, "reciprocal functions inserted",
reciprocal_stats.rfuncs_inserted);
free_dominance_info (CDI_DOMINATORS);
free_dominance_info (CDI_POST_DOMINATORS);
delete occ_pool;
return 0;
}
} // anon namespace
gimple_opt_pass *
make_pass_cse_reciprocals (gcc::context *ctxt)
{
return new pass_cse_reciprocals (ctxt);
}
/* If NAME is the result of a type conversion, look for other
equivalent dominating or dominated conversions, and replace all
uses with the earliest dominating name, removing the redundant
conversions. Return the prevailing name. */
static tree
execute_cse_conv_1 (tree name)
{
if (SSA_NAME_IS_DEFAULT_DEF (name)
|| SSA_NAME_OCCURS_IN_ABNORMAL_PHI (name))
return name;
gimple *def_stmt = SSA_NAME_DEF_STMT (name);
if (!gimple_assign_cast_p (def_stmt))
return name;
tree src = gimple_assign_rhs1 (def_stmt);
if (TREE_CODE (src) != SSA_NAME)
return name;
imm_use_iterator use_iter;
gimple *use_stmt;
/* Find the earliest dominating def. */
FOR_EACH_IMM_USE_STMT (use_stmt, use_iter, src)
{
if (use_stmt == def_stmt
|| !gimple_assign_cast_p (use_stmt))
continue;
tree lhs = gimple_assign_lhs (use_stmt);
if (SSA_NAME_OCCURS_IN_ABNORMAL_PHI (lhs)
|| (gimple_assign_rhs1 (use_stmt)
!= gimple_assign_rhs1 (def_stmt))
|| !types_compatible_p (TREE_TYPE (name), TREE_TYPE (lhs)))
continue;
bool use_dominates;
if (gimple_bb (def_stmt) == gimple_bb (use_stmt))
{
gimple_stmt_iterator gsi = gsi_for_stmt (use_stmt);
while (!gsi_end_p (gsi) && gsi_stmt (gsi) != def_stmt)
gsi_next (&gsi);
use_dominates = !gsi_end_p (gsi);
}
else if (dominated_by_p (CDI_DOMINATORS, gimple_bb (use_stmt),
gimple_bb (def_stmt)))
use_dominates = false;
else if (dominated_by_p (CDI_DOMINATORS, gimple_bb (def_stmt),
gimple_bb (use_stmt)))
use_dominates = true;
else
continue;
if (use_dominates)
{
std::swap (name, lhs);
std::swap (def_stmt, use_stmt);
}
}
/* Now go through all uses of SRC again, replacing the equivalent
dominated conversions. We may replace defs that were not
dominated by the then-prevailing defs when we first visited
them. */
FOR_EACH_IMM_USE_STMT (use_stmt, use_iter, src)
{
if (use_stmt == def_stmt
|| !gimple_assign_cast_p (use_stmt))
continue;
tree lhs = gimple_assign_lhs (use_stmt);
if (SSA_NAME_OCCURS_IN_ABNORMAL_PHI (lhs)
|| (gimple_assign_rhs1 (use_stmt)
!= gimple_assign_rhs1 (def_stmt))
|| !types_compatible_p (TREE_TYPE (name), TREE_TYPE (lhs)))
continue;
if (gimple_bb (def_stmt) == gimple_bb (use_stmt)
|| dominated_by_p (CDI_DOMINATORS, gimple_bb (use_stmt),
gimple_bb (def_stmt)))
{
sincos_stats.conv_removed++;
gimple_stmt_iterator gsi = gsi_for_stmt (use_stmt);
replace_uses_by (lhs, name);
gsi_remove (&gsi, true);
}
}
return name;
}
/* Records an occurrence at statement USE_STMT in the vector of trees
STMTS if it is dominated by *TOP_BB or dominates it or this basic block
is not yet initialized. Returns true if the occurrence was pushed on
the vector. Adjusts *TOP_BB to be the basic block dominating all
statements in the vector. */
static bool
maybe_record_sincos (vec<gimple *> *stmts,
basic_block *top_bb, gimple *use_stmt)
{
basic_block use_bb = gimple_bb (use_stmt);
if (*top_bb
&& (*top_bb == use_bb
|| dominated_by_p (CDI_DOMINATORS, use_bb, *top_bb)))
stmts->safe_push (use_stmt);
else if (!*top_bb
|| dominated_by_p (CDI_DOMINATORS, *top_bb, use_bb))
{
stmts->safe_push (use_stmt);
*top_bb = use_bb;
}
else
return false;
return true;
}
/* Look for sin, cos and cexpi calls with the same argument NAME and
create a single call to cexpi CSEing the result in this case.
We first walk over all immediate uses of the argument collecting
statements that we can CSE in a vector and in a second pass replace
the statement rhs with a REALPART or IMAGPART expression on the
result of the cexpi call we insert before the use statement that
dominates all other candidates. */
static bool
execute_cse_sincos_1 (tree name)
{
gimple_stmt_iterator gsi;
imm_use_iterator use_iter;
tree fndecl, res, type = NULL_TREE;
gimple *def_stmt, *use_stmt, *stmt;
int seen_cos = 0, seen_sin = 0, seen_cexpi = 0;
auto_vec<gimple *> stmts;
basic_block top_bb = NULL;
int i;
bool cfg_changed = false;
name = execute_cse_conv_1 (name);
FOR_EACH_IMM_USE_STMT (use_stmt, use_iter, name)
{
if (gimple_code (use_stmt) != GIMPLE_CALL
|| !gimple_call_lhs (use_stmt))
continue;
switch (gimple_call_combined_fn (use_stmt))
{
CASE_CFN_COS:
seen_cos |= maybe_record_sincos (&stmts, &top_bb, use_stmt) ? 1 : 0;
break;
CASE_CFN_SIN:
seen_sin |= maybe_record_sincos (&stmts, &top_bb, use_stmt) ? 1 : 0;
break;
CASE_CFN_CEXPI:
seen_cexpi |= maybe_record_sincos (&stmts, &top_bb, use_stmt) ? 1 : 0;
break;
default:;
continue;
}
tree t = mathfn_built_in_type (gimple_call_combined_fn (use_stmt));
if (!type)
{
type = t;
t = TREE_TYPE (name);
}
/* This checks that NAME has the right type in the first round,
and, in subsequent rounds, that the built_in type is the same
type, or a compatible type. */
if (type != t && !types_compatible_p (type, t))
return false;
}
if (seen_cos + seen_sin + seen_cexpi <= 1)
return false;
/* Simply insert cexpi at the beginning of top_bb but not earlier than
the name def statement. */
fndecl = mathfn_built_in (type, BUILT_IN_CEXPI);
if (!fndecl)
return false;
stmt = gimple_build_call (fndecl, 1, name);
res = make_temp_ssa_name (TREE_TYPE (TREE_TYPE (fndecl)), stmt, "sincostmp");
gimple_call_set_lhs (stmt, res);
def_stmt = SSA_NAME_DEF_STMT (name);
if (!SSA_NAME_IS_DEFAULT_DEF (name)
&& gimple_code (def_stmt) != GIMPLE_PHI
&& gimple_bb (def_stmt) == top_bb)
{
gsi = gsi_for_stmt (def_stmt);
gsi_insert_after (&gsi, stmt, GSI_SAME_STMT);
}
else
{
gsi = gsi_after_labels (top_bb);
gsi_insert_before (&gsi, stmt, GSI_SAME_STMT);
}
sincos_stats.inserted++;
/* And adjust the recorded old call sites. */
for (i = 0; stmts.iterate (i, &use_stmt); ++i)
{
tree rhs = NULL;
switch (gimple_call_combined_fn (use_stmt))
{
CASE_CFN_COS:
rhs = fold_build1 (REALPART_EXPR, type, res);
break;
CASE_CFN_SIN:
rhs = fold_build1 (IMAGPART_EXPR, type, res);
break;
CASE_CFN_CEXPI:
rhs = res;
break;
default:;
gcc_unreachable ();
}
/* Replace call with a copy. */
stmt = gimple_build_assign (gimple_call_lhs (use_stmt), rhs);
gsi = gsi_for_stmt (use_stmt);
gsi_replace (&gsi, stmt, true);
if (gimple_purge_dead_eh_edges (gimple_bb (stmt)))
cfg_changed = true;
}
return cfg_changed;
}
/* To evaluate powi(x,n), the floating point value x raised to the
constant integer exponent n, we use a hybrid algorithm that
combines the "window method" with look-up tables. For an
introduction to exponentiation algorithms and "addition chains",
see section 4.6.3, "Evaluation of Powers" of Donald E. Knuth,
"Seminumerical Algorithms", Vol. 2, "The Art of Computer Programming",
3rd Edition, 1998, and Daniel M. Gordon, "A Survey of Fast Exponentiation
Methods", Journal of Algorithms, Vol. 27, pp. 129-146, 1998. */
/* Provide a default value for POWI_MAX_MULTS, the maximum number of
multiplications to inline before calling the system library's pow
function. powi(x,n) requires at worst 2*bits(n)-2 multiplications,
so this default never requires calling pow, powf or powl. */
#ifndef POWI_MAX_MULTS
#define POWI_MAX_MULTS (2*HOST_BITS_PER_WIDE_INT-2)
#endif
/* The size of the "optimal power tree" lookup table. All
exponents less than this value are simply looked up in the
powi_table below. This threshold is also used to size the
cache of pseudo registers that hold intermediate results. */
#define POWI_TABLE_SIZE 256
/* The size, in bits of the window, used in the "window method"
exponentiation algorithm. This is equivalent to a radix of
(1<<POWI_WINDOW_SIZE) in the corresponding "m-ary method". */
#define POWI_WINDOW_SIZE 3
/* The following table is an efficient representation of an
"optimal power tree". For each value, i, the corresponding
value, j, in the table states than an optimal evaluation
sequence for calculating pow(x,i) can be found by evaluating
pow(x,j)*pow(x,i-j). An optimal power tree for the first
100 integers is given in Knuth's "Seminumerical algorithms". */
static const unsigned char powi_table[POWI_TABLE_SIZE] =
{
0, 1, 1, 2, 2, 3, 3, 4, /* 0 - 7 */
4, 6, 5, 6, 6, 10, 7, 9, /* 8 - 15 */
8, 16, 9, 16, 10, 12, 11, 13, /* 16 - 23 */
12, 17, 13, 18, 14, 24, 15, 26, /* 24 - 31 */
16, 17, 17, 19, 18, 33, 19, 26, /* 32 - 39 */
20, 25, 21, 40, 22, 27, 23, 44, /* 40 - 47 */
24, 32, 25, 34, 26, 29, 27, 44, /* 48 - 55 */
28, 31, 29, 34, 30, 60, 31, 36, /* 56 - 63 */
32, 64, 33, 34, 34, 46, 35, 37, /* 64 - 71 */
36, 65, 37, 50, 38, 48, 39, 69, /* 72 - 79 */
40, 49, 41, 43, 42, 51, 43, 58, /* 80 - 87 */
44, 64, 45, 47, 46, 59, 47, 76, /* 88 - 95 */
48, 65, 49, 66, 50, 67, 51, 66, /* 96 - 103 */
52, 70, 53, 74, 54, 104, 55, 74, /* 104 - 111 */
56, 64, 57, 69, 58, 78, 59, 68, /* 112 - 119 */
60, 61, 61, 80, 62, 75, 63, 68, /* 120 - 127 */
64, 65, 65, 128, 66, 129, 67, 90, /* 128 - 135 */
68, 73, 69, 131, 70, 94, 71, 88, /* 136 - 143 */
72, 128, 73, 98, 74, 132, 75, 121, /* 144 - 151 */
76, 102, 77, 124, 78, 132, 79, 106, /* 152 - 159 */
80, 97, 81, 160, 82, 99, 83, 134, /* 160 - 167 */
84, 86, 85, 95, 86, 160, 87, 100, /* 168 - 175 */
88, 113, 89, 98, 90, 107, 91, 122, /* 176 - 183 */
92, 111, 93, 102, 94, 126, 95, 150, /* 184 - 191 */
96, 128, 97, 130, 98, 133, 99, 195, /* 192 - 199 */
100, 128, 101, 123, 102, 164, 103, 138, /* 200 - 207 */
104, 145, 105, 146, 106, 109, 107, 149, /* 208 - 215 */
108, 200, 109, 146, 110, 170, 111, 157, /* 216 - 223 */
112, 128, 113, 130, 114, 182, 115, 132, /* 224 - 231 */
116, 200, 117, 132, 118, 158, 119, 206, /* 232 - 239 */
120, 240, 121, 162, 122, 147, 123, 152, /* 240 - 247 */
124, 166, 125, 214, 126, 138, 127, 153, /* 248 - 255 */
};
/* Return the number of multiplications required to calculate
powi(x,n) where n is less than POWI_TABLE_SIZE. This is a
subroutine of powi_cost. CACHE is an array indicating
which exponents have already been calculated. */
static int
powi_lookup_cost (unsigned HOST_WIDE_INT n, bool *cache)
{
/* If we've already calculated this exponent, then this evaluation
doesn't require any additional multiplications. */
if (cache[n])
return 0;
cache[n] = true;
return powi_lookup_cost (n - powi_table[n], cache)
+ powi_lookup_cost (powi_table[n], cache) + 1;
}
/* Return the number of multiplications required to calculate
powi(x,n) for an arbitrary x, given the exponent N. This
function needs to be kept in sync with powi_as_mults below. */
static int
powi_cost (HOST_WIDE_INT n)
{
bool cache[POWI_TABLE_SIZE];
unsigned HOST_WIDE_INT digit;
unsigned HOST_WIDE_INT val;
int result;
if (n == 0)
return 0;
/* Ignore the reciprocal when calculating the cost. */
val = (n < 0) ? -n : n;
/* Initialize the exponent cache. */
memset (cache, 0, POWI_TABLE_SIZE * sizeof (bool));
cache[1] = true;
result = 0;
while (val >= POWI_TABLE_SIZE)
{
if (val & 1)
{
digit = val & ((1 << POWI_WINDOW_SIZE) - 1);
result += powi_lookup_cost (digit, cache)
+ POWI_WINDOW_SIZE + 1;
val >>= POWI_WINDOW_SIZE;
}
else
{
val >>= 1;
result++;
}
}
return result + powi_lookup_cost (val, cache);
}
/* Recursive subroutine of powi_as_mults. This function takes the
array, CACHE, of already calculated exponents and an exponent N and
returns a tree that corresponds to CACHE[1]**N, with type TYPE. */
static tree
powi_as_mults_1 (gimple_stmt_iterator *gsi, location_t loc, tree type,
HOST_WIDE_INT n, tree *cache)
{
tree op0, op1, ssa_target;
unsigned HOST_WIDE_INT digit;
gassign *mult_stmt;
if (n < POWI_TABLE_SIZE && cache[n])
return cache[n];
ssa_target = make_temp_ssa_name (type, NULL, "powmult");
if (n < POWI_TABLE_SIZE)
{
cache[n] = ssa_target;
op0 = powi_as_mults_1 (gsi, loc, type, n - powi_table[n], cache);
op1 = powi_as_mults_1 (gsi, loc, type, powi_table[n], cache);
}
else if (n & 1)
{
digit = n & ((1 << POWI_WINDOW_SIZE) - 1);
op0 = powi_as_mults_1 (gsi, loc, type, n - digit, cache);
op1 = powi_as_mults_1 (gsi, loc, type, digit, cache);
}
else
{
op0 = powi_as_mults_1 (gsi, loc, type, n >> 1, cache);
op1 = op0;
}
mult_stmt = gimple_build_assign (ssa_target, MULT_EXPR, op0, op1);
gimple_set_location (mult_stmt, loc);
gsi_insert_before (gsi, mult_stmt, GSI_SAME_STMT);
return ssa_target;
}
/* Convert ARG0**N to a tree of multiplications of ARG0 with itself.
This function needs to be kept in sync with powi_cost above. */
tree
powi_as_mults (gimple_stmt_iterator *gsi, location_t loc,
tree arg0, HOST_WIDE_INT n)
{
tree cache[POWI_TABLE_SIZE], result, type = TREE_TYPE (arg0);
gassign *div_stmt;
tree target;
if (n == 0)
return build_one_cst (type);
memset (cache, 0, sizeof (cache));
cache[1] = arg0;
result = powi_as_mults_1 (gsi, loc, type, (n < 0) ? -n : n, cache);
if (n >= 0)
return result;
/* If the original exponent was negative, reciprocate the result. */
target = make_temp_ssa_name (type, NULL, "powmult");
div_stmt = gimple_build_assign (target, RDIV_EXPR,
build_real (type, dconst1), result);
gimple_set_location (div_stmt, loc);
gsi_insert_before (gsi, div_stmt, GSI_SAME_STMT);
return target;
}
/* ARG0 and N are the two arguments to a powi builtin in GSI with
location info LOC. If the arguments are appropriate, create an
equivalent sequence of statements prior to GSI using an optimal
number of multiplications, and return an expession holding the
result. */
static tree
gimple_expand_builtin_powi (gimple_stmt_iterator *gsi, location_t loc,
tree arg0, HOST_WIDE_INT n)
{
/* Avoid largest negative number. */
if (n != -n
&& ((n >= -1 && n <= 2)
|| (optimize_function_for_speed_p (cfun)
&& powi_cost (n) <= POWI_MAX_MULTS)))
return powi_as_mults (gsi, loc, arg0, n);
return NULL_TREE;
}
/* Build a gimple call statement that calls FN with argument ARG.
Set the lhs of the call statement to a fresh SSA name. Insert the
statement prior to GSI's current position, and return the fresh
SSA name. */
static tree
build_and_insert_call (gimple_stmt_iterator *gsi, location_t loc,
tree fn, tree arg)
{
gcall *call_stmt;
tree ssa_target;
call_stmt = gimple_build_call (fn, 1, arg);
ssa_target = make_temp_ssa_name (TREE_TYPE (arg), NULL, "powroot");
gimple_set_lhs (call_stmt, ssa_target);
gimple_set_location (call_stmt, loc);
gsi_insert_before (gsi, call_stmt, GSI_SAME_STMT);
return ssa_target;
}
/* Build a gimple binary operation with the given CODE and arguments
ARG0, ARG1, assigning the result to a new SSA name for variable
TARGET. Insert the statement prior to GSI's current position, and
return the fresh SSA name.*/
static tree
build_and_insert_binop (gimple_stmt_iterator *gsi, location_t loc,
const char *name, enum tree_code code,
tree arg0, tree arg1)
{
tree result = make_temp_ssa_name (TREE_TYPE (arg0), NULL, name);
gassign *stmt = gimple_build_assign (result, code, arg0, arg1);
gimple_set_location (stmt, loc);
gsi_insert_before (gsi, stmt, GSI_SAME_STMT);
return result;
}
/* Build a gimple reference operation with the given CODE and argument
ARG, assigning the result to a new SSA name of TYPE with NAME.
Insert the statement prior to GSI's current position, and return
the fresh SSA name. */
static inline tree
build_and_insert_ref (gimple_stmt_iterator *gsi, location_t loc, tree type,
const char *name, enum tree_code code, tree arg0)
{
tree result = make_temp_ssa_name (type, NULL, name);
gimple *stmt = gimple_build_assign (result, build1 (code, type, arg0));
gimple_set_location (stmt, loc);
gsi_insert_before (gsi, stmt, GSI_SAME_STMT);
return result;
}
/* Build a gimple assignment to cast VAL to TYPE. Insert the statement
prior to GSI's current position, and return the fresh SSA name. */
static tree
build_and_insert_cast (gimple_stmt_iterator *gsi, location_t loc,
tree type, tree val)
{
tree result = make_ssa_name (type);
gassign *stmt = gimple_build_assign (result, NOP_EXPR, val);
gimple_set_location (stmt, loc);
gsi_insert_before (gsi, stmt, GSI_SAME_STMT);
return result;
}
struct pow_synth_sqrt_info
{
bool *factors;
unsigned int deepest;
unsigned int num_mults;
};
/* Return true iff the real value C can be represented as a
sum of powers of 0.5 up to N. That is:
C == SUM<i from 1..N> (a[i]*(0.5**i)) where a[i] is either 0 or 1.
Record in INFO the various parameters of the synthesis algorithm such
as the factors a[i], the maximum 0.5 power and the number of
multiplications that will be required. */
bool
representable_as_half_series_p (REAL_VALUE_TYPE c, unsigned n,
struct pow_synth_sqrt_info *info)
{
REAL_VALUE_TYPE factor = dconsthalf;
REAL_VALUE_TYPE remainder = c;
info->deepest = 0;
info->num_mults = 0;
memset (info->factors, 0, n * sizeof (bool));
for (unsigned i = 0; i < n; i++)
{
REAL_VALUE_TYPE res;
/* If something inexact happened bail out now. */
if (real_arithmetic (&res, MINUS_EXPR, &remainder, &factor))
return false;
/* We have hit zero. The number is representable as a sum
of powers of 0.5. */
if (real_equal (&res, &dconst0))
{
info->factors[i] = true;
info->deepest = i + 1;
return true;
}
else if (!REAL_VALUE_NEGATIVE (res))
{
remainder = res;
info->factors[i] = true;
info->num_mults++;
}
else
info->factors[i] = false;
real_arithmetic (&factor, MULT_EXPR, &factor, &dconsthalf);
}
return false;
}
/* Return the tree corresponding to FN being applied
to ARG N times at GSI and LOC.
Look up previous results from CACHE if need be.
cache[0] should contain just plain ARG i.e. FN applied to ARG 0 times. */
static tree
get_fn_chain (tree arg, unsigned int n, gimple_stmt_iterator *gsi,
tree fn, location_t loc, tree *cache)
{
tree res = cache[n];
if (!res)
{
tree prev = get_fn_chain (arg, n - 1, gsi, fn, loc, cache);
res = build_and_insert_call (gsi, loc, fn, prev);
cache[n] = res;
}
return res;
}
/* Print to STREAM the repeated application of function FNAME to ARG
N times. So, for FNAME = "foo", ARG = "x", N = 2 it would print:
"foo (foo (x))". */
static void
print_nested_fn (FILE* stream, const char *fname, const char* arg,
unsigned int n)
{
if (n == 0)
fprintf (stream, "%s", arg);
else
{
fprintf (stream, "%s (", fname);
print_nested_fn (stream, fname, arg, n - 1);
fprintf (stream, ")");
}
}
/* Print to STREAM the fractional sequence of sqrt chains
applied to ARG, described by INFO. Used for the dump file. */
static void
dump_fractional_sqrt_sequence (FILE *stream, const char *arg,
struct pow_synth_sqrt_info *info)
{
for (unsigned int i = 0; i < info->deepest; i++)
{
bool is_set = info->factors[i];
if (is_set)
{
print_nested_fn (stream, "sqrt", arg, i + 1);
if (i != info->deepest - 1)
fprintf (stream, " * ");
}
}
}
/* Print to STREAM a representation of raising ARG to an integer
power N. Used for the dump file. */
static void
dump_integer_part (FILE *stream, const char* arg, HOST_WIDE_INT n)
{
if (n > 1)
fprintf (stream, "powi (%s, " HOST_WIDE_INT_PRINT_DEC ")", arg, n);
else if (n == 1)
fprintf (stream, "%s", arg);
}
/* Attempt to synthesize a POW[F] (ARG0, ARG1) call using chains of
square roots. Place at GSI and LOC. Limit the maximum depth
of the sqrt chains to MAX_DEPTH. Return the tree holding the
result of the expanded sequence or NULL_TREE if the expansion failed.
This routine assumes that ARG1 is a real number with a fractional part
(the integer exponent case will have been handled earlier in
gimple_expand_builtin_pow).
For ARG1 > 0.0:
* For ARG1 composed of a whole part WHOLE_PART and a fractional part
FRAC_PART i.e. WHOLE_PART == floor (ARG1) and
FRAC_PART == ARG1 - WHOLE_PART:
Produce POWI (ARG0, WHOLE_PART) * POW (ARG0, FRAC_PART) where
POW (ARG0, FRAC_PART) is expanded as a product of square root chains
if it can be expressed as such, that is if FRAC_PART satisfies:
FRAC_PART == <SUM from i = 1 until MAX_DEPTH> (a[i] * (0.5**i))
where integer a[i] is either 0 or 1.
Example:
POW (x, 3.625) == POWI (x, 3) * POW (x, 0.625)
--> POWI (x, 3) * SQRT (x) * SQRT (SQRT (SQRT (x)))
For ARG1 < 0.0 there are two approaches:
* (A) Expand to 1.0 / POW (ARG0, -ARG1) where POW (ARG0, -ARG1)
is calculated as above.
Example:
POW (x, -5.625) == 1.0 / POW (x, 5.625)
--> 1.0 / (POWI (x, 5) * SQRT (x) * SQRT (SQRT (SQRT (x))))
* (B) : WHOLE_PART := - ceil (abs (ARG1))
FRAC_PART := ARG1 - WHOLE_PART
and expand to POW (x, FRAC_PART) / POWI (x, WHOLE_PART).
Example:
POW (x, -5.875) == POW (x, 0.125) / POWI (X, 6)
--> SQRT (SQRT (SQRT (x))) / (POWI (x, 6))
For ARG1 < 0.0 we choose between (A) and (B) depending on
how many multiplications we'd have to do.
So, for the example in (B): POW (x, -5.875), if we were to
follow algorithm (A) we would produce:
1.0 / POWI (X, 5) * SQRT (X) * SQRT (SQRT (X)) * SQRT (SQRT (SQRT (X)))
which contains more multiplications than approach (B).
Hopefully, this approach will eliminate potentially expensive POW library
calls when unsafe floating point math is enabled and allow the compiler to
further optimise the multiplies, square roots and divides produced by this
function. */
static tree
expand_pow_as_sqrts (gimple_stmt_iterator *gsi, location_t loc,
tree arg0, tree arg1, HOST_WIDE_INT max_depth)
{
tree type = TREE_TYPE (arg0);
machine_mode mode = TYPE_MODE (type);
tree sqrtfn = mathfn_built_in (type, BUILT_IN_SQRT);
bool one_over = true;
if (!sqrtfn)
return NULL_TREE;
if (TREE_CODE (arg1) != REAL_CST)
return NULL_TREE;
REAL_VALUE_TYPE exp_init = TREE_REAL_CST (arg1);
gcc_assert (max_depth > 0);
tree *cache = XALLOCAVEC (tree, max_depth + 1);
struct pow_synth_sqrt_info synth_info;
synth_info.factors = XALLOCAVEC (bool, max_depth + 1);
synth_info.deepest = 0;
synth_info.num_mults = 0;
bool neg_exp = REAL_VALUE_NEGATIVE (exp_init);
REAL_VALUE_TYPE exp = real_value_abs (&exp_init);
/* The whole and fractional parts of exp. */
REAL_VALUE_TYPE whole_part;
REAL_VALUE_TYPE frac_part;
real_floor (&whole_part, mode, &exp);
real_arithmetic (&frac_part, MINUS_EXPR, &exp, &whole_part);
REAL_VALUE_TYPE ceil_whole = dconst0;
REAL_VALUE_TYPE ceil_fract = dconst0;
if (neg_exp)
{
real_ceil (&ceil_whole, mode, &exp);
real_arithmetic (&ceil_fract, MINUS_EXPR, &ceil_whole, &exp);
}
if (!representable_as_half_series_p (frac_part, max_depth, &synth_info))
return NULL_TREE;
/* Check whether it's more profitable to not use 1.0 / ... */
if (neg_exp)
{
struct pow_synth_sqrt_info alt_synth_info;
alt_synth_info.factors = XALLOCAVEC (bool, max_depth + 1);
alt_synth_info.deepest = 0;
alt_synth_info.num_mults = 0;
if (representable_as_half_series_p (ceil_fract, max_depth,
&alt_synth_info)
&& alt_synth_info.deepest <= synth_info.deepest
&& alt_synth_info.num_mults < synth_info.num_mults)
{
whole_part = ceil_whole;
frac_part = ceil_fract;
synth_info.deepest = alt_synth_info.deepest;
synth_info.num_mults = alt_synth_info.num_mults;
memcpy (synth_info.factors, alt_synth_info.factors,
(max_depth + 1) * sizeof (bool));
one_over = false;
}
}
HOST_WIDE_INT n = real_to_integer (&whole_part);
REAL_VALUE_TYPE cint;
real_from_integer (&cint, VOIDmode, n, SIGNED);
if (!real_identical (&whole_part, &cint))
return NULL_TREE;
if (powi_cost (n) + synth_info.num_mults > POWI_MAX_MULTS)
return NULL_TREE;
memset (cache, 0, (max_depth + 1) * sizeof (tree));
tree integer_res = n == 0 ? build_real (type, dconst1) : arg0;
/* Calculate the integer part of the exponent. */
if (n > 1)
{
integer_res = gimple_expand_builtin_powi (gsi, loc, arg0, n);
if (!integer_res)
return NULL_TREE;
}
if (dump_file)
{
char string[64];
real_to_decimal (string, &exp_init, sizeof (string), 0, 1);
fprintf (dump_file, "synthesizing pow (x, %s) as:\n", string);
if (neg_exp)
{
if (one_over)
{
fprintf (dump_file, "1.0 / (");
dump_integer_part (dump_file, "x", n);
if (n > 0)
fprintf (dump_file, " * ");
dump_fractional_sqrt_sequence (dump_file, "x", &synth_info);
fprintf (dump_file, ")");
}
else
{
dump_fractional_sqrt_sequence (dump_file, "x", &synth_info);
fprintf (dump_file, " / (");
dump_integer_part (dump_file, "x", n);
fprintf (dump_file, ")");
}
}
else
{
dump_fractional_sqrt_sequence (dump_file, "x", &synth_info);
if (n > 0)
fprintf (dump_file, " * ");
dump_integer_part (dump_file, "x", n);
}
fprintf (dump_file, "\ndeepest sqrt chain: %d\n", synth_info.deepest);
}
tree fract_res = NULL_TREE;
cache[0] = arg0;
/* Calculate the fractional part of the exponent. */
for (unsigned i = 0; i < synth_info.deepest; i++)
{
if (synth_info.factors[i])
{
tree sqrt_chain = get_fn_chain (arg0, i + 1, gsi, sqrtfn, loc, cache);
if (!fract_res)
fract_res = sqrt_chain;
else
fract_res = build_and_insert_binop (gsi, loc, "powroot", MULT_EXPR,
fract_res, sqrt_chain);
}
}
tree res = NULL_TREE;
if (neg_exp)
{
if (one_over)
{
if (n > 0)
res = build_and_insert_binop (gsi, loc, "powroot", MULT_EXPR,
fract_res, integer_res);
else
res = fract_res;
res = build_and_insert_binop (gsi, loc, "powrootrecip", RDIV_EXPR,
build_real (type, dconst1), res);
}
else
{
res = build_and_insert_binop (gsi, loc, "powroot", RDIV_EXPR,
fract_res, integer_res);
}
}
else
res = build_and_insert_binop (gsi, loc, "powroot", MULT_EXPR,
fract_res, integer_res);
return res;
}
/* ARG0 and ARG1 are the two arguments to a pow builtin call in GSI
with location info LOC. If possible, create an equivalent and
less expensive sequence of statements prior to GSI, and return an
expession holding the result. */
static tree
gimple_expand_builtin_pow (gimple_stmt_iterator *gsi, location_t loc,
tree arg0, tree arg1)
{
REAL_VALUE_TYPE c, cint, dconst1_3, dconst1_4, dconst1_6;
REAL_VALUE_TYPE c2, dconst3;
HOST_WIDE_INT n;
tree type, sqrtfn, cbrtfn, sqrt_arg0, result, cbrt_x, powi_cbrt_x;
machine_mode mode;
bool speed_p = optimize_bb_for_speed_p (gsi_bb (*gsi));
bool hw_sqrt_exists, c_is_int, c2_is_int;
dconst1_4 = dconst1;
SET_REAL_EXP (&dconst1_4, REAL_EXP (&dconst1_4) - 2);
/* If the exponent isn't a constant, there's nothing of interest
to be done. */
if (TREE_CODE (arg1) != REAL_CST)
return NULL_TREE;
/* Don't perform the operation if flag_signaling_nans is on
and the operand is a signaling NaN. */
if (HONOR_SNANS (TYPE_MODE (TREE_TYPE (arg1)))
&& ((TREE_CODE (arg0) == REAL_CST
&& REAL_VALUE_ISSIGNALING_NAN (TREE_REAL_CST (arg0)))
|| REAL_VALUE_ISSIGNALING_NAN (TREE_REAL_CST (arg1))))
return NULL_TREE;
/* If the exponent is equivalent to an integer, expand to an optimal
multiplication sequence when profitable. */
c = TREE_REAL_CST (arg1);
n = real_to_integer (&c);
real_from_integer (&cint, VOIDmode, n, SIGNED);
c_is_int = real_identical (&c, &cint);
if (c_is_int
&& ((n >= -1 && n <= 2)
|| (flag_unsafe_math_optimizations
&& speed_p
&& powi_cost (n) <= POWI_MAX_MULTS)))
return gimple_expand_builtin_powi (gsi, loc, arg0, n);
/* Attempt various optimizations using sqrt and cbrt. */
type = TREE_TYPE (arg0);
mode = TYPE_MODE (type);
sqrtfn = mathfn_built_in (type, BUILT_IN_SQRT);
/* Optimize pow(x,0.5) = sqrt(x). This replacement is always safe
unless signed zeros must be maintained. pow(-0,0.5) = +0, while
sqrt(-0) = -0. */
if (sqrtfn
&& real_equal (&c, &dconsthalf)
&& !HONOR_SIGNED_ZEROS (mode))
return build_and_insert_call (gsi, loc, sqrtfn, arg0);
hw_sqrt_exists = optab_handler (sqrt_optab, mode) != CODE_FOR_nothing;
/* Optimize pow(x,1./3.) = cbrt(x). This requires unsafe math
optimizations since 1./3. is not exactly representable. If x
is negative and finite, the correct value of pow(x,1./3.) is
a NaN with the "invalid" exception raised, because the value
of 1./3. actually has an even denominator. The correct value
of cbrt(x) is a negative real value. */
cbrtfn = mathfn_built_in (type, BUILT_IN_CBRT);
dconst1_3 = real_value_truncate (mode, dconst_third ());
if (flag_unsafe_math_optimizations
&& cbrtfn
&& (!HONOR_NANS (mode) || tree_expr_nonnegative_p (arg0))
&& real_equal (&c, &dconst1_3))
return build_and_insert_call (gsi, loc, cbrtfn, arg0);
/* Optimize pow(x,1./6.) = cbrt(sqrt(x)). Don't do this optimization
if we don't have a hardware sqrt insn. */
dconst1_6 = dconst1_3;
SET_REAL_EXP (&dconst1_6, REAL_EXP (&dconst1_6) - 1);
if (flag_unsafe_math_optimizations
&& sqrtfn
&& cbrtfn
&& (!HONOR_NANS (mode) || tree_expr_nonnegative_p (arg0))
&& speed_p
&& hw_sqrt_exists
&& real_equal (&c, &dconst1_6))
{
/* sqrt(x) */
sqrt_arg0 = build_and_insert_call (gsi, loc, sqrtfn, arg0);
/* cbrt(sqrt(x)) */
return build_and_insert_call (gsi, loc, cbrtfn, sqrt_arg0);
}
/* Attempt to expand the POW as a product of square root chains.
Expand the 0.25 case even when otpimising for size. */
if (flag_unsafe_math_optimizations
&& sqrtfn
&& hw_sqrt_exists
&& (speed_p || real_equal (&c, &dconst1_4))
&& !HONOR_SIGNED_ZEROS (mode))
{
unsigned int max_depth = speed_p
? param_max_pow_sqrt_depth
: 2;
tree expand_with_sqrts
= expand_pow_as_sqrts (gsi, loc, arg0, arg1, max_depth);
if (expand_with_sqrts)
return expand_with_sqrts;
}
real_arithmetic (&c2, MULT_EXPR, &c, &dconst2);
n = real_to_integer (&c2);
real_from_integer (&cint, VOIDmode, n, SIGNED);
c2_is_int = real_identical (&c2, &cint);
/* Optimize pow(x,c), where 3c = n for some nonzero integer n, into
powi(x, n/3) * powi(cbrt(x), n%3), n > 0;
1.0 / (powi(x, abs(n)/3) * powi(cbrt(x), abs(n)%3)), n < 0.
Do not calculate the first factor when n/3 = 0. As cbrt(x) is
different from pow(x, 1./3.) due to rounding and behavior with
negative x, we need to constrain this transformation to unsafe
math and positive x or finite math. */
real_from_integer (&dconst3, VOIDmode, 3, SIGNED);
real_arithmetic (&c2, MULT_EXPR, &c, &dconst3);
real_round (&c2, mode, &c2);
n = real_to_integer (&c2);
real_from_integer (&cint, VOIDmode, n, SIGNED);
real_arithmetic (&c2, RDIV_EXPR, &cint, &dconst3);
real_convert (&c2, mode, &c2);
if (flag_unsafe_math_optimizations
&& cbrtfn
&& (!HONOR_NANS (mode) || tree_expr_nonnegative_p (arg0))
&& real_identical (&c2, &c)
&& !c2_is_int
&& optimize_function_for_speed_p (cfun)
&& powi_cost (n / 3) <= POWI_MAX_MULTS)
{
tree powi_x_ndiv3 = NULL_TREE;
/* Attempt to fold powi(arg0, abs(n/3)) into multiplies. If not
possible or profitable, give up. Skip the degenerate case when
abs(n) < 3, where the result is always 1. */
if (absu_hwi (n) >= 3)
{
powi_x_ndiv3 = gimple_expand_builtin_powi (gsi, loc, arg0,
abs_hwi (n / 3));
if (!powi_x_ndiv3)
return NULL_TREE;
}
/* Calculate powi(cbrt(x), n%3). Don't use gimple_expand_builtin_powi
as that creates an unnecessary variable. Instead, just produce
either cbrt(x) or cbrt(x) * cbrt(x). */
cbrt_x = build_and_insert_call (gsi, loc, cbrtfn, arg0);
if (absu_hwi (n) % 3 == 1)
powi_cbrt_x = cbrt_x;
else
powi_cbrt_x = build_and_insert_binop (gsi, loc, "powroot", MULT_EXPR,
cbrt_x, cbrt_x);
/* Multiply the two subexpressions, unless powi(x,abs(n)/3) = 1. */
if (absu_hwi (n) < 3)
result = powi_cbrt_x;
else
result = build_and_insert_binop (gsi, loc, "powroot", MULT_EXPR,
powi_x_ndiv3, powi_cbrt_x);
/* If n is negative, reciprocate the result. */
if (n < 0)
result = build_and_insert_binop (gsi, loc, "powroot", RDIV_EXPR,
build_real (type, dconst1), result);
return result;
}
/* No optimizations succeeded. */
return NULL_TREE;
}
/* ARG is the argument to a cabs builtin call in GSI with location info
LOC. Create a sequence of statements prior to GSI that calculates
sqrt(R*R + I*I), where R and I are the real and imaginary components
of ARG, respectively. Return an expression holding the result. */
static tree
gimple_expand_builtin_cabs (gimple_stmt_iterator *gsi, location_t loc, tree arg)
{
tree real_part, imag_part, addend1, addend2, sum, result;
tree type = TREE_TYPE (TREE_TYPE (arg));
tree sqrtfn = mathfn_built_in (type, BUILT_IN_SQRT);
machine_mode mode = TYPE_MODE (type);
if (!flag_unsafe_math_optimizations
|| !optimize_bb_for_speed_p (gimple_bb (gsi_stmt (*gsi)))
|| !sqrtfn
|| optab_handler (sqrt_optab, mode) == CODE_FOR_nothing)
return NULL_TREE;
real_part = build_and_insert_ref (gsi, loc, type, "cabs",
REALPART_EXPR, arg);
addend1 = build_and_insert_binop (gsi, loc, "cabs", MULT_EXPR,
real_part, real_part);
imag_part = build_and_insert_ref (gsi, loc, type, "cabs",
IMAGPART_EXPR, arg);
addend2 = build_and_insert_binop (gsi, loc, "cabs", MULT_EXPR,
imag_part, imag_part);
sum = build_and_insert_binop (gsi, loc, "cabs", PLUS_EXPR, addend1, addend2);
result = build_and_insert_call (gsi, loc, sqrtfn, sum);
return result;
}
/* Go through all calls to sin, cos and cexpi and call execute_cse_sincos_1
on the SSA_NAME argument of each of them. Also expand powi(x,n) into
an optimal number of multiplies, when n is a constant. */
namespace {
const pass_data pass_data_cse_sincos =
{
GIMPLE_PASS, /* type */
"sincos", /* name */
OPTGROUP_NONE, /* optinfo_flags */
TV_TREE_SINCOS, /* tv_id */
PROP_ssa, /* properties_required */
PROP_gimple_opt_math, /* properties_provided */
0, /* properties_destroyed */
0, /* todo_flags_start */
TODO_update_ssa, /* todo_flags_finish */
};
class pass_cse_sincos : public gimple_opt_pass
{
public:
pass_cse_sincos (gcc::context *ctxt)
: gimple_opt_pass (pass_data_cse_sincos, ctxt)
{}
/* opt_pass methods: */
virtual bool gate (function *)
{
/* We no longer require either sincos or cexp, since powi expansion
piggybacks on this pass. */
return optimize;
}
virtual unsigned int execute (function *);
}; // class pass_cse_sincos
unsigned int
pass_cse_sincos::execute (function *fun)
{
basic_block bb;
bool cfg_changed = false;
calculate_dominance_info (CDI_DOMINATORS);
memset (&sincos_stats, 0, sizeof (sincos_stats));
FOR_EACH_BB_FN (bb, fun)
{
gimple_stmt_iterator gsi;
bool cleanup_eh = false;
for (gsi = gsi_after_labels (bb); !gsi_end_p (gsi); gsi_next (&gsi))
{
gimple *stmt = gsi_stmt (gsi);
/* Only the last stmt in a bb could throw, no need to call
gimple_purge_dead_eh_edges if we change something in the middle
of a basic block. */
cleanup_eh = false;
if (is_gimple_call (stmt)
&& gimple_call_lhs (stmt))
{
tree arg, arg0, arg1, result;
HOST_WIDE_INT n;
location_t loc;
switch (gimple_call_combined_fn (stmt))
{
CASE_CFN_COS:
CASE_CFN_SIN:
CASE_CFN_CEXPI:
arg = gimple_call_arg (stmt, 0);
/* Make sure we have either sincos or cexp. */
if (!targetm.libc_has_function (function_c99_math_complex,
TREE_TYPE (arg))
&& !targetm.libc_has_function (function_sincos,
TREE_TYPE (arg)))
break;
if (TREE_CODE (arg) == SSA_NAME)
cfg_changed |= execute_cse_sincos_1 (arg);
break;
CASE_CFN_POW:
arg0 = gimple_call_arg (stmt, 0);
arg1 = gimple_call_arg (stmt, 1);
loc = gimple_location (stmt);
result = gimple_expand_builtin_pow (&gsi, loc, arg0, arg1);
if (result)
{
tree lhs = gimple_get_lhs (stmt);
gassign *new_stmt = gimple_build_assign (lhs, result);
gimple_set_location (new_stmt, loc);
unlink_stmt_vdef (stmt);
gsi_replace (&gsi, new_stmt, true);
cleanup_eh = true;
if (gimple_vdef (stmt))
release_ssa_name (gimple_vdef (stmt));
}
break;
CASE_CFN_POWI:
arg0 = gimple_call_arg (stmt, 0);
arg1 = gimple_call_arg (stmt, 1);
loc = gimple_location (stmt);
if (real_minus_onep (arg0))
{
tree t0, t1, cond, one, minus_one;
gassign *stmt;
t0 = TREE_TYPE (arg0);
t1 = TREE_TYPE (arg1);
one = build_real (t0, dconst1);
minus_one = build_real (t0, dconstm1);
cond = make_temp_ssa_name (t1, NULL, "powi_cond");
stmt = gimple_build_assign (cond, BIT_AND_EXPR,
arg1, build_int_cst (t1, 1));
gimple_set_location (stmt, loc);
gsi_insert_before (&gsi, stmt, GSI_SAME_STMT);
result = make_temp_ssa_name (t0, NULL, "powi");
stmt = gimple_build_assign (result, COND_EXPR, cond,
minus_one, one);
gimple_set_location (stmt, loc);
gsi_insert_before (&gsi, stmt, GSI_SAME_STMT);
}
else
{
if (!tree_fits_shwi_p (arg1))
break;
n = tree_to_shwi (arg1);
result = gimple_expand_builtin_powi (&gsi, loc, arg0, n);
}
if (result)
{
tree lhs = gimple_get_lhs (stmt);
gassign *new_stmt = gimple_build_assign (lhs, result);
gimple_set_location (new_stmt, loc);
unlink_stmt_vdef (stmt);
gsi_replace (&gsi, new_stmt, true);
cleanup_eh = true;
if (gimple_vdef (stmt))
release_ssa_name (gimple_vdef (stmt));
}
break;
CASE_CFN_CABS:
arg0 = gimple_call_arg (stmt, 0);
loc = gimple_location (stmt);
result = gimple_expand_builtin_cabs (&gsi, loc, arg0);
if (result)
{
tree lhs = gimple_get_lhs (stmt);
gassign *new_stmt = gimple_build_assign (lhs, result);
gimple_set_location (new_stmt, loc);
unlink_stmt_vdef (stmt);
gsi_replace (&gsi, new_stmt, true);
cleanup_eh = true;
if (gimple_vdef (stmt))
release_ssa_name (gimple_vdef (stmt));
}
break;
default:;
}
}
}
if (cleanup_eh)
cfg_changed |= gimple_purge_dead_eh_edges (bb);
}
statistics_counter_event (fun, "sincos statements inserted",
sincos_stats.inserted);
statistics_counter_event (fun, "conv statements removed",
sincos_stats.conv_removed);
return cfg_changed ? TODO_cleanup_cfg : 0;
}
} // anon namespace
gimple_opt_pass *
make_pass_cse_sincos (gcc::context *ctxt)
{
return new pass_cse_sincos (ctxt);
}
/* Return true if stmt is a type conversion operation that can be stripped
when used in a widening multiply operation. */
static bool
widening_mult_conversion_strippable_p (tree result_type, gimple *stmt)
{
enum tree_code rhs_code = gimple_assign_rhs_code (stmt);
if (TREE_CODE (result_type) == INTEGER_TYPE)
{
tree op_type;
tree inner_op_type;
if (!CONVERT_EXPR_CODE_P (rhs_code))
return false;
op_type = TREE_TYPE (gimple_assign_lhs (stmt));
/* If the type of OP has the same precision as the result, then
we can strip this conversion. The multiply operation will be
selected to create the correct extension as a by-product. */
if (TYPE_PRECISION (result_type) == TYPE_PRECISION (op_type))
return true;
/* We can also strip a conversion if it preserves the signed-ness of
the operation and doesn't narrow the range. */
inner_op_type = TREE_TYPE (gimple_assign_rhs1 (stmt));
/* If the inner-most type is unsigned, then we can strip any
intermediate widening operation. If it's signed, then the
intermediate widening operation must also be signed. */
if ((TYPE_UNSIGNED (inner_op_type)
|| TYPE_UNSIGNED (op_type) == TYPE_UNSIGNED (inner_op_type))
&& TYPE_PRECISION (op_type) > TYPE_PRECISION (inner_op_type))
return true;
return false;
}
return rhs_code == FIXED_CONVERT_EXPR;
}
/* Return true if RHS is a suitable operand for a widening multiplication,
assuming a target type of TYPE.
There are two cases:
- RHS makes some value at least twice as wide. Store that value
in *NEW_RHS_OUT if so, and store its type in *TYPE_OUT.
- RHS is an integer constant. Store that value in *NEW_RHS_OUT if so,
but leave *TYPE_OUT untouched. */
static bool
is_widening_mult_rhs_p (tree type, tree rhs, tree *type_out,
tree *new_rhs_out)
{
gimple *stmt;
tree type1, rhs1;
if (TREE_CODE (rhs) == SSA_NAME)
{
stmt = SSA_NAME_DEF_STMT (rhs);
if (is_gimple_assign (stmt))
{
if (! widening_mult_conversion_strippable_p (type, stmt))
rhs1 = rhs;
else
{
rhs1 = gimple_assign_rhs1 (stmt);
if (TREE_CODE (rhs1) == INTEGER_CST)
{
*new_rhs_out = rhs1;
*type_out = NULL;
return true;
}
}
}
else
rhs1 = rhs;
type1 = TREE_TYPE (rhs1);
if (TREE_CODE (type1) != TREE_CODE (type)
|| TYPE_PRECISION (type1) * 2 > TYPE_PRECISION (type))
return false;
*new_rhs_out = rhs1;
*type_out = type1;
return true;
}
if (TREE_CODE (rhs) == INTEGER_CST)
{
*new_rhs_out = rhs;
*type_out = NULL;
return true;
}
return false;
}
/* Return true if STMT performs a widening multiplication, assuming the
output type is TYPE. If so, store the unwidened types of the operands
in *TYPE1_OUT and *TYPE2_OUT respectively. Also fill *RHS1_OUT and
*RHS2_OUT such that converting those operands to types *TYPE1_OUT
and *TYPE2_OUT would give the operands of the multiplication. */
static bool
is_widening_mult_p (gimple *stmt,
tree *type1_out, tree *rhs1_out,
tree *type2_out, tree *rhs2_out)
{
tree type = TREE_TYPE (gimple_assign_lhs (stmt));
if (TREE_CODE (type) == INTEGER_TYPE)
{
if (TYPE_OVERFLOW_TRAPS (type))
return false;
}
else if (TREE_CODE (type) != FIXED_POINT_TYPE)
return false;
if (!is_widening_mult_rhs_p (type, gimple_assign_rhs1 (stmt), type1_out,
rhs1_out))
return false;
if (!is_widening_mult_rhs_p (type, gimple_assign_rhs2 (stmt), type2_out,
rhs2_out))
return false;
if (*type1_out == NULL)
{
if (*type2_out == NULL || !int_fits_type_p (*rhs1_out, *type2_out))
return false;
*type1_out = *type2_out;
}
if (*type2_out == NULL)
{
if (!int_fits_type_p (*rhs2_out, *type1_out))
return false;
*type2_out = *type1_out;
}
/* Ensure that the larger of the two operands comes first. */
if (TYPE_PRECISION (*type1_out) < TYPE_PRECISION (*type2_out))
{
std::swap (*type1_out, *type2_out);
std::swap (*rhs1_out, *rhs2_out);
}
return true;
}
/* Check to see if the CALL statement is an invocation of copysign
with 1. being the first argument. */
static bool
is_copysign_call_with_1 (gimple *call)
{
gcall *c = dyn_cast <gcall *> (call);
if (! c)
return false;
enum combined_fn code = gimple_call_combined_fn (c);
if (code == CFN_LAST)
return false;
if (builtin_fn_p (code))
{
switch (as_builtin_fn (code))
{
CASE_FLT_FN (BUILT_IN_COPYSIGN):
CASE_FLT_FN_FLOATN_NX (BUILT_IN_COPYSIGN):
return real_onep (gimple_call_arg (c, 0));
default:
return false;
}
}
if (internal_fn_p (code))
{
switch (as_internal_fn (code))
{
case IFN_COPYSIGN:
return real_onep (gimple_call_arg (c, 0));
default:
return false;
}
}
return false;
}
/* Try to expand the pattern x * copysign (1, y) into xorsign (x, y).
This only happens when the xorsign optab is defined, if the
pattern is not a xorsign pattern or if expansion fails FALSE is
returned, otherwise TRUE is returned. */
static bool
convert_expand_mult_copysign (gimple *stmt, gimple_stmt_iterator *gsi)
{
tree treeop0, treeop1, lhs, type;
location_t loc = gimple_location (stmt);
lhs = gimple_assign_lhs (stmt);
treeop0 = gimple_assign_rhs1 (stmt);
treeop1 = gimple_assign_rhs2 (stmt);
type = TREE_TYPE (lhs);
machine_mode mode = TYPE_MODE (type);
if (HONOR_SNANS (type))
return false;
if (TREE_CODE (treeop0) == SSA_NAME && TREE_CODE (treeop1) == SSA_NAME)
{
gimple *call0 = SSA_NAME_DEF_STMT (treeop0);
if (!has_single_use (treeop0) || !is_copysign_call_with_1 (call0))
{
call0 = SSA_NAME_DEF_STMT (treeop1);
if (!has_single_use (treeop1) || !is_copysign_call_with_1 (call0))
return false;
treeop1 = treeop0;
}
if (optab_handler (xorsign_optab, mode) == CODE_FOR_nothing)
return false;
gcall *c = as_a<gcall*> (call0);
treeop0 = gimple_call_arg (c, 1);
gcall *call_stmt
= gimple_build_call_internal (IFN_XORSIGN, 2, treeop1, treeop0);
gimple_set_lhs (call_stmt, lhs);
gimple_set_location (call_stmt, loc);
gsi_replace (gsi, call_stmt, true);
return true;
}
return false;
}
/* Process a single gimple statement STMT, which has a MULT_EXPR as
its rhs, and try to convert it into a WIDEN_MULT_EXPR. The return
value is true iff we converted the statement. */
static bool
convert_mult_to_widen (gimple *stmt, gimple_stmt_iterator *gsi)
{
tree lhs, rhs1, rhs2, type, type1, type2;
enum insn_code handler;
scalar_int_mode to_mode, from_mode, actual_mode;
optab op;
int actual_precision;
location_t loc = gimple_location (stmt);
bool from_unsigned1, from_unsigned2;
lhs = gimple_assign_lhs (stmt);
type = TREE_TYPE (lhs);
if (TREE_CODE (type) != INTEGER_TYPE)
return false;
if (!is_widening_mult_p (stmt, &type1, &rhs1, &type2, &rhs2))
return false;
to_mode = SCALAR_INT_TYPE_MODE (type);
from_mode = SCALAR_INT_TYPE_MODE (type1);
if (to_mode == from_mode)
return false;
from_unsigned1 = TYPE_UNSIGNED (type1);
from_unsigned2 = TYPE_UNSIGNED (type2);
if (from_unsigned1 && from_unsigned2)
op = umul_widen_optab;
else if (!from_unsigned1 && !from_unsigned2)
op = smul_widen_optab;
else
op = usmul_widen_optab;
handler = find_widening_optab_handler_and_mode (op, to_mode, from_mode,
&actual_mode);
if (handler == CODE_FOR_nothing)
{
if (op != smul_widen_optab)
{
/* We can use a signed multiply with unsigned types as long as
there is a wider mode to use, or it is the smaller of the two
types that is unsigned. Note that type1 >= type2, always. */
if ((TYPE_UNSIGNED (type1)
&& TYPE_PRECISION (type1) == GET_MODE_PRECISION (from_mode))
|| (TYPE_UNSIGNED (type2)
&& TYPE_PRECISION (type2) == GET_MODE_PRECISION (from_mode)))
{
if (!GET_MODE_WIDER_MODE (from_mode).exists (&from_mode)
|| GET_MODE_SIZE (to_mode) <= GET_MODE_SIZE (from_mode))
return false;
}
op = smul_widen_optab;
handler = find_widening_optab_handler_and_mode (op, to_mode,
from_mode,
&actual_mode);
if (handler == CODE_FOR_nothing)
return false;
from_unsigned1 = from_unsigned2 = false;
}
else
return false;
}
/* Ensure that the inputs to the handler are in the correct precison
for the opcode. This will be the full mode size. */
actual_precision = GET_MODE_PRECISION (actual_mode);
if (2 * actual_precision > TYPE_PRECISION (type))
return false;
if (actual_precision != TYPE_PRECISION (type1)
|| from_unsigned1 != TYPE_UNSIGNED (type1))
rhs1 = build_and_insert_cast (gsi, loc,
build_nonstandard_integer_type
(actual_precision, from_unsigned1), rhs1);
if (actual_precision != TYPE_PRECISION (type2)
|| from_unsigned2 != TYPE_UNSIGNED (type2))
rhs2 = build_and_insert_cast (gsi, loc,
build_nonstandard_integer_type
(actual_precision, from_unsigned2), rhs2);
/* Handle constants. */
if (TREE_CODE (rhs1) == INTEGER_CST)
rhs1 = fold_convert (type1, rhs1);
if (TREE_CODE (rhs2) == INTEGER_CST)
rhs2 = fold_convert (type2, rhs2);
gimple_assign_set_rhs1 (stmt, rhs1);
gimple_assign_set_rhs2 (stmt, rhs2);
gimple_assign_set_rhs_code (stmt, WIDEN_MULT_EXPR);
update_stmt (stmt);
widen_mul_stats.widen_mults_inserted++;
return true;
}
/* Process a single gimple statement STMT, which is found at the
iterator GSI and has a either a PLUS_EXPR or a MINUS_EXPR as its
rhs (given by CODE), and try to convert it into a
WIDEN_MULT_PLUS_EXPR or a WIDEN_MULT_MINUS_EXPR. The return value
is true iff we converted the statement. */
static bool
convert_plusminus_to_widen (gimple_stmt_iterator *gsi, gimple *stmt,
enum tree_code code)
{
gimple *rhs1_stmt = NULL, *rhs2_stmt = NULL;
gimple *conv1_stmt = NULL, *conv2_stmt = NULL, *conv_stmt;
tree type, type1, type2, optype;
tree lhs, rhs1, rhs2, mult_rhs1, mult_rhs2, add_rhs;
enum tree_code rhs1_code = ERROR_MARK, rhs2_code = ERROR_MARK;
optab this_optab;
enum tree_code wmult_code;
enum insn_code handler;
scalar_mode to_mode, from_mode, actual_mode;
location_t loc = gimple_location (stmt);
int actual_precision;
bool from_unsigned1, from_unsigned2;
lhs = gimple_assign_lhs (stmt);
type = TREE_TYPE (lhs);
if (TREE_CODE (type) != INTEGER_TYPE
&& TREE_CODE (type) != FIXED_POINT_TYPE)
return false;
if (code == MINUS_EXPR)
wmult_code = WIDEN_MULT_MINUS_EXPR;
else
wmult_code = WIDEN_MULT_PLUS_EXPR;
rhs1 = gimple_assign_rhs1 (stmt);
rhs2 = gimple_assign_rhs2 (stmt);
if (TREE_CODE (rhs1) == SSA_NAME)
{
rhs1_stmt = SSA_NAME_DEF_STMT (rhs1);
if (is_gimple_assign (rhs1_stmt))
rhs1_code = gimple_assign_rhs_code (rhs1_stmt);
}
if (TREE_CODE (rhs2) == SSA_NAME)
{
rhs2_stmt = SSA_NAME_DEF_STMT (rhs2);
if (is_gimple_assign (rhs2_stmt))
rhs2_code = gimple_assign_rhs_code (rhs2_stmt);
}
/* Allow for one conversion statement between the multiply
and addition/subtraction statement. If there are more than
one conversions then we assume they would invalidate this
transformation. If that's not the case then they should have
been folded before now. */
if (CONVERT_EXPR_CODE_P (rhs1_code))
{
conv1_stmt = rhs1_stmt;
rhs1 = gimple_assign_rhs1 (rhs1_stmt);
if (TREE_CODE (rhs1) == SSA_NAME)
{
rhs1_stmt = SSA_NAME_DEF_STMT (rhs1);
if (is_gimple_assign (rhs1_stmt))
rhs1_code = gimple_assign_rhs_code (rhs1_stmt);
}
else
return false;
}
if (CONVERT_EXPR_CODE_P (rhs2_code))
{
conv2_stmt = rhs2_stmt;
rhs2 = gimple_assign_rhs1 (rhs2_stmt);
if (TREE_CODE (rhs2) == SSA_NAME)
{
rhs2_stmt = SSA_NAME_DEF_STMT (rhs2);
if (is_gimple_assign (rhs2_stmt))
rhs2_code = gimple_assign_rhs_code (rhs2_stmt);
}
else
return false;