1 /* Global, SSA-based optimizations using mathematical identities.
2    Copyright (C) 2005, 2006, 2007, 2008, 2009, 2010, 2011, 2012
3    Free Software Foundation, Inc.
4 
5 This file is part of GCC.
6 
7 GCC is free software; you can redistribute it and/or modify it
8 under the terms of the GNU General Public License as published by the
9 Free Software Foundation; either version 3, or (at your option) any
10 later version.
11 
12 GCC is distributed in the hope that it will be useful, but WITHOUT
13 ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or
14 FITNESS FOR A PARTICULAR PURPOSE.  See the GNU General Public License
15 for more details.
16 
17 You should have received a copy of the GNU General Public License
18 along with GCC; see the file COPYING3.  If not see
19 <http://www.gnu.org/licenses/>.  */
20 
21 /* Currently, the only mini-pass in this file tries to CSE reciprocal
22    operations.  These are common in sequences such as this one:
23 
24 	modulus = sqrt(x*x + y*y + z*z);
25 	x = x / modulus;
26 	y = y / modulus;
27 	z = z / modulus;
28 
29    that can be optimized to
30 
31 	modulus = sqrt(x*x + y*y + z*z);
32         rmodulus = 1.0 / modulus;
33 	x = x * rmodulus;
34 	y = y * rmodulus;
35 	z = z * rmodulus;
36 
37    We do this for loop invariant divisors, and with this pass whenever
38    we notice that a division has the same divisor multiple times.
39 
40    Of course, like in PRE, we don't insert a division if a dominator
41    already has one.  However, this cannot be done as an extension of
42    PRE for several reasons.
43 
44    First of all, with some experiments it was found out that the
45    transformation is not always useful if there are only two divisions
46    hy the same divisor.  This is probably because modern processors
47    can pipeline the divisions; on older, in-order processors it should
48    still be effective to optimize two divisions by the same number.
49    We make this a param, and it shall be called N in the remainder of
50    this comment.
51 
52    Second, if trapping math is active, we have less freedom on where
53    to insert divisions: we can only do so in basic blocks that already
54    contain one.  (If divisions don't trap, instead, we can insert
55    divisions elsewhere, which will be in blocks that are common dominators
56    of those that have the division).
57 
58    We really don't want to compute the reciprocal unless a division will
59    be found.  To do this, we won't insert the division in a basic block
60    that has less than N divisions *post-dominating* it.
61 
62    The algorithm constructs a subset of the dominator tree, holding the
63    blocks containing the divisions and the common dominators to them,
64    and walk it twice.  The first walk is in post-order, and it annotates
65    each block with the number of divisions that post-dominate it: this
66    gives information on where divisions can be inserted profitably.
67    The second walk is in pre-order, and it inserts divisions as explained
68    above, and replaces divisions by multiplications.
69 
70    In the best case, the cost of the pass is O(n_statements).  In the
71    worst-case, the cost is due to creating the dominator tree subset,
72    with a cost of O(n_basic_blocks ^ 2); however this can only happen
73    for n_statements / n_basic_blocks statements.  So, the amortized cost
74    of creating the dominator tree subset is O(n_basic_blocks) and the
75    worst-case cost of the pass is O(n_statements * n_basic_blocks).
76 
77    More practically, the cost will be small because there are few
78    divisions, and they tend to be in the same basic block, so insert_bb
79    is called very few times.
80 
81    If we did this using domwalk.c, an efficient implementation would have
82    to work on all the variables in a single pass, because we could not
83    work on just a subset of the dominator tree, as we do now, and the
84    cost would also be something like O(n_statements * n_basic_blocks).
85    The data structures would be more complex in order to work on all the
86    variables in a single pass.  */
87 
88 #include "config.h"
89 #include "system.h"
90 #include "coretypes.h"
91 #include "tm.h"
92 #include "flags.h"
93 #include "tree.h"
94 #include "tree-flow.h"
95 #include "timevar.h"
96 #include "tree-pass.h"
97 #include "alloc-pool.h"
98 #include "basic-block.h"
99 #include "target.h"
100 #include "gimple-pretty-print.h"
101 
102 /* FIXME: RTL headers have to be included here for optabs.  */
103 #include "rtl.h"		/* Because optabs.h wants enum rtx_code.  */
104 #include "expr.h"		/* Because optabs.h wants sepops.  */
105 #include "optabs.h"
106 
107 /* This structure represents one basic block that either computes a
108    division, or is a common dominator for basic block that compute a
109    division.  */
110 struct occurrence {
111   /* The basic block represented by this structure.  */
112   basic_block bb;
113 
114   /* If non-NULL, the SSA_NAME holding the definition for a reciprocal
115      inserted in BB.  */
116   tree recip_def;
117 
118   /* If non-NULL, the GIMPLE_ASSIGN for a reciprocal computation that
119      was inserted in BB.  */
120   gimple recip_def_stmt;
121 
122   /* Pointer to a list of "struct occurrence"s for blocks dominated
123      by BB.  */
124   struct occurrence *children;
125 
126   /* Pointer to the next "struct occurrence"s in the list of blocks
127      sharing a common dominator.  */
128   struct occurrence *next;
129 
130   /* The number of divisions that are in BB before compute_merit.  The
131      number of divisions that are in BB or post-dominate it after
132      compute_merit.  */
133   int num_divisions;
134 
135   /* True if the basic block has a division, false if it is a common
136      dominator for basic blocks that do.  If it is false and trapping
137      math is active, BB is not a candidate for inserting a reciprocal.  */
138   bool bb_has_division;
139 };
140 
141 static struct
142 {
143   /* Number of 1.0/X ops inserted.  */
144   int rdivs_inserted;
145 
146   /* Number of 1.0/FUNC ops inserted.  */
147   int rfuncs_inserted;
148 } reciprocal_stats;
149 
150 static struct
151 {
152   /* Number of cexpi calls inserted.  */
153   int inserted;
154 } sincos_stats;
155 
156 static struct
157 {
158   /* Number of hand-written 32-bit bswaps found.  */
159   int found_32bit;
160 
161   /* Number of hand-written 64-bit bswaps found.  */
162   int found_64bit;
163 } bswap_stats;
164 
165 static struct
166 {
167   /* Number of widening multiplication ops inserted.  */
168   int widen_mults_inserted;
169 
170   /* Number of integer multiply-and-accumulate ops inserted.  */
171   int maccs_inserted;
172 
173   /* Number of fp fused multiply-add ops inserted.  */
174   int fmas_inserted;
175 } widen_mul_stats;
176 
177 /* The instance of "struct occurrence" representing the highest
178    interesting block in the dominator tree.  */
179 static struct occurrence *occ_head;
180 
181 /* Allocation pool for getting instances of "struct occurrence".  */
182 static alloc_pool occ_pool;
183 
184 
185 
186 /* Allocate and return a new struct occurrence for basic block BB, and
187    whose children list is headed by CHILDREN.  */
188 static struct occurrence *
189 occ_new (basic_block bb, struct occurrence *children)
190 {
191   struct occurrence *occ;
192 
193   bb->aux = occ = (struct occurrence *) pool_alloc (occ_pool);
194   memset (occ, 0, sizeof (struct occurrence));
195 
196   occ->bb = bb;
197   occ->children = children;
198   return occ;
199 }
200 
201 
202 /* Insert NEW_OCC into our subset of the dominator tree.  P_HEAD points to a
203    list of "struct occurrence"s, one per basic block, having IDOM as
204    their common dominator.
205 
206    We try to insert NEW_OCC as deep as possible in the tree, and we also
207    insert any other block that is a common dominator for BB and one
208    block already in the tree.  */
209 
210 static void
211 insert_bb (struct occurrence *new_occ, basic_block idom,
212 	   struct occurrence **p_head)
213 {
214   struct occurrence *occ, **p_occ;
215 
216   for (p_occ = p_head; (occ = *p_occ) != NULL; )
217     {
218       basic_block bb = new_occ->bb, occ_bb = occ->bb;
219       basic_block dom = nearest_common_dominator (CDI_DOMINATORS, occ_bb, bb);
220       if (dom == bb)
221 	{
222 	  /* BB dominates OCC_BB.  OCC becomes NEW_OCC's child: remove OCC
223 	     from its list.  */
224 	  *p_occ = occ->next;
225 	  occ->next = new_occ->children;
226 	  new_occ->children = occ;
227 
228 	  /* Try the next block (it may as well be dominated by BB).  */
229 	}
230 
231       else if (dom == occ_bb)
232 	{
233 	  /* OCC_BB dominates BB.  Tail recurse to look deeper.  */
234 	  insert_bb (new_occ, dom, &occ->children);
235 	  return;
236 	}
237 
238       else if (dom != idom)
239 	{
240 	  gcc_assert (!dom->aux);
241 
242 	  /* There is a dominator between IDOM and BB, add it and make
243 	     two children out of NEW_OCC and OCC.  First, remove OCC from
244 	     its list.	*/
245 	  *p_occ = occ->next;
246 	  new_occ->next = occ;
247 	  occ->next = NULL;
248 
249 	  /* None of the previous blocks has DOM as a dominator: if we tail
250 	     recursed, we would reexamine them uselessly. Just switch BB with
251 	     DOM, and go on looking for blocks dominated by DOM.  */
252           new_occ = occ_new (dom, new_occ);
253 	}
254 
255       else
256 	{
257 	  /* Nothing special, go on with the next element.  */
258 	  p_occ = &occ->next;
259 	}
260     }
261 
262   /* No place was found as a child of IDOM.  Make BB a sibling of IDOM.  */
263   new_occ->next = *p_head;
264   *p_head = new_occ;
265 }
266 
267 /* Register that we found a division in BB.  */
268 
269 static inline void
270 register_division_in (basic_block bb)
271 {
272   struct occurrence *occ;
273 
274   occ = (struct occurrence *) bb->aux;
275   if (!occ)
276     {
277       occ = occ_new (bb, NULL);
278       insert_bb (occ, ENTRY_BLOCK_PTR, &occ_head);
279     }
280 
281   occ->bb_has_division = true;
282   occ->num_divisions++;
283 }
284 
285 
286 /* Compute the number of divisions that postdominate each block in OCC and
287    its children.  */
288 
289 static void
290 compute_merit (struct occurrence *occ)
291 {
292   struct occurrence *occ_child;
293   basic_block dom = occ->bb;
294 
295   for (occ_child = occ->children; occ_child; occ_child = occ_child->next)
296     {
297       basic_block bb;
298       if (occ_child->children)
299         compute_merit (occ_child);
300 
301       if (flag_exceptions)
302 	bb = single_noncomplex_succ (dom);
303       else
304 	bb = dom;
305 
306       if (dominated_by_p (CDI_POST_DOMINATORS, bb, occ_child->bb))
307         occ->num_divisions += occ_child->num_divisions;
308     }
309 }
310 
311 
312 /* Return whether USE_STMT is a floating-point division by DEF.  */
313 static inline bool
314 is_division_by (gimple use_stmt, tree def)
315 {
316   return is_gimple_assign (use_stmt)
317 	 && gimple_assign_rhs_code (use_stmt) == RDIV_EXPR
318 	 && gimple_assign_rhs2 (use_stmt) == def
319 	 /* Do not recognize x / x as valid division, as we are getting
320 	    confused later by replacing all immediate uses x in such
321 	    a stmt.  */
322 	 && gimple_assign_rhs1 (use_stmt) != def;
323 }
324 
325 /* Walk the subset of the dominator tree rooted at OCC, setting the
326    RECIP_DEF field to a definition of 1.0 / DEF that can be used in
327    the given basic block.  The field may be left NULL, of course,
328    if it is not possible or profitable to do the optimization.
329 
330    DEF_BSI is an iterator pointing at the statement defining DEF.
331    If RECIP_DEF is set, a dominator already has a computation that can
332    be used.  */
333 
334 static void
335 insert_reciprocals (gimple_stmt_iterator *def_gsi, struct occurrence *occ,
336 		    tree def, tree recip_def, int threshold)
337 {
338   tree type;
339   gimple new_stmt;
340   gimple_stmt_iterator gsi;
341   struct occurrence *occ_child;
342 
343   if (!recip_def
344       && (occ->bb_has_division || !flag_trapping_math)
345       && occ->num_divisions >= threshold)
346     {
347       /* Make a variable with the replacement and substitute it.  */
348       type = TREE_TYPE (def);
349       recip_def = make_rename_temp (type, "reciptmp");
350       new_stmt = gimple_build_assign_with_ops (RDIV_EXPR, recip_def,
351 					       build_one_cst (type), def);
352 
353       if (occ->bb_has_division)
354         {
355           /* Case 1: insert before an existing division.  */
356           gsi = gsi_after_labels (occ->bb);
357           while (!gsi_end_p (gsi) && !is_division_by (gsi_stmt (gsi), def))
358 	    gsi_next (&gsi);
359 
360           gsi_insert_before (&gsi, new_stmt, GSI_SAME_STMT);
361         }
362       else if (def_gsi && occ->bb == def_gsi->bb)
363         {
364           /* Case 2: insert right after the definition.  Note that this will
365 	     never happen if the definition statement can throw, because in
366 	     that case the sole successor of the statement's basic block will
367 	     dominate all the uses as well.  */
368           gsi_insert_after (def_gsi, new_stmt, GSI_NEW_STMT);
369         }
370       else
371         {
372           /* Case 3: insert in a basic block not containing defs/uses.  */
373           gsi = gsi_after_labels (occ->bb);
374           gsi_insert_before (&gsi, new_stmt, GSI_SAME_STMT);
375         }
376 
377       reciprocal_stats.rdivs_inserted++;
378 
379       occ->recip_def_stmt = new_stmt;
380     }
381 
382   occ->recip_def = recip_def;
383   for (occ_child = occ->children; occ_child; occ_child = occ_child->next)
384     insert_reciprocals (def_gsi, occ_child, def, recip_def, threshold);
385 }
386 
387 
388 /* Replace the division at USE_P with a multiplication by the reciprocal, if
389    possible.  */
390 
391 static inline void
392 replace_reciprocal (use_operand_p use_p)
393 {
394   gimple use_stmt = USE_STMT (use_p);
395   basic_block bb = gimple_bb (use_stmt);
396   struct occurrence *occ = (struct occurrence *) bb->aux;
397 
398   if (optimize_bb_for_speed_p (bb)
399       && occ->recip_def && use_stmt != occ->recip_def_stmt)
400     {
401       gimple_stmt_iterator gsi = gsi_for_stmt (use_stmt);
402       gimple_assign_set_rhs_code (use_stmt, MULT_EXPR);
403       SET_USE (use_p, occ->recip_def);
404       fold_stmt_inplace (&gsi);
405       update_stmt (use_stmt);
406     }
407 }
408 
409 
410 /* Free OCC and return one more "struct occurrence" to be freed.  */
411 
412 static struct occurrence *
413 free_bb (struct occurrence *occ)
414 {
415   struct occurrence *child, *next;
416 
417   /* First get the two pointers hanging off OCC.  */
418   next = occ->next;
419   child = occ->children;
420   occ->bb->aux = NULL;
421   pool_free (occ_pool, occ);
422 
423   /* Now ensure that we don't recurse unless it is necessary.  */
424   if (!child)
425     return next;
426   else
427     {
428       while (next)
429 	next = free_bb (next);
430 
431       return child;
432     }
433 }
434 
435 
436 /* Look for floating-point divisions among DEF's uses, and try to
437    replace them by multiplications with the reciprocal.  Add
438    as many statements computing the reciprocal as needed.
439 
440    DEF must be a GIMPLE register of a floating-point type.  */
441 
442 static void
443 execute_cse_reciprocals_1 (gimple_stmt_iterator *def_gsi, tree def)
444 {
445   use_operand_p use_p;
446   imm_use_iterator use_iter;
447   struct occurrence *occ;
448   int count = 0, threshold;
449 
450   gcc_assert (FLOAT_TYPE_P (TREE_TYPE (def)) && is_gimple_reg (def));
451 
452   FOR_EACH_IMM_USE_FAST (use_p, use_iter, def)
453     {
454       gimple use_stmt = USE_STMT (use_p);
455       if (is_division_by (use_stmt, def))
456 	{
457 	  register_division_in (gimple_bb (use_stmt));
458 	  count++;
459 	}
460     }
461 
462   /* Do the expensive part only if we can hope to optimize something.  */
463   threshold = targetm.min_divisions_for_recip_mul (TYPE_MODE (TREE_TYPE (def)));
464   if (count >= threshold)
465     {
466       gimple use_stmt;
467       for (occ = occ_head; occ; occ = occ->next)
468 	{
469 	  compute_merit (occ);
470 	  insert_reciprocals (def_gsi, occ, def, NULL, threshold);
471 	}
472 
473       FOR_EACH_IMM_USE_STMT (use_stmt, use_iter, def)
474 	{
475 	  if (is_division_by (use_stmt, def))
476 	    {
477 	      FOR_EACH_IMM_USE_ON_STMT (use_p, use_iter)
478 		replace_reciprocal (use_p);
479 	    }
480 	}
481     }
482 
483   for (occ = occ_head; occ; )
484     occ = free_bb (occ);
485 
486   occ_head = NULL;
487 }
488 
489 static bool
490 gate_cse_reciprocals (void)
491 {
492   return optimize && flag_reciprocal_math;
493 }
494 
495 /* Go through all the floating-point SSA_NAMEs, and call
496    execute_cse_reciprocals_1 on each of them.  */
497 static unsigned int
498 execute_cse_reciprocals (void)
499 {
500   basic_block bb;
501   tree arg;
502 
503   occ_pool = create_alloc_pool ("dominators for recip",
504 				sizeof (struct occurrence),
505 				n_basic_blocks / 3 + 1);
506 
507   memset (&reciprocal_stats, 0, sizeof (reciprocal_stats));
508   calculate_dominance_info (CDI_DOMINATORS);
509   calculate_dominance_info (CDI_POST_DOMINATORS);
510 
511 #ifdef ENABLE_CHECKING
512   FOR_EACH_BB (bb)
513     gcc_assert (!bb->aux);
514 #endif
515 
516   for (arg = DECL_ARGUMENTS (cfun->decl); arg; arg = DECL_CHAIN (arg))
517     if (gimple_default_def (cfun, arg)
518 	&& FLOAT_TYPE_P (TREE_TYPE (arg))
519 	&& is_gimple_reg (arg))
520       execute_cse_reciprocals_1 (NULL, gimple_default_def (cfun, arg));
521 
522   FOR_EACH_BB (bb)
523     {
524       gimple_stmt_iterator gsi;
525       gimple phi;
526       tree def;
527 
528       for (gsi = gsi_start_phis (bb); !gsi_end_p (gsi); gsi_next (&gsi))
529 	{
530 	  phi = gsi_stmt (gsi);
531 	  def = PHI_RESULT (phi);
532 	  if (FLOAT_TYPE_P (TREE_TYPE (def))
533 	      && is_gimple_reg (def))
534 	    execute_cse_reciprocals_1 (NULL, def);
535 	}
536 
537       for (gsi = gsi_after_labels (bb); !gsi_end_p (gsi); gsi_next (&gsi))
538         {
539 	  gimple stmt = gsi_stmt (gsi);
540 
541 	  if (gimple_has_lhs (stmt)
542 	      && (def = SINGLE_SSA_TREE_OPERAND (stmt, SSA_OP_DEF)) != NULL
543 	      && FLOAT_TYPE_P (TREE_TYPE (def))
544 	      && TREE_CODE (def) == SSA_NAME)
545 	    execute_cse_reciprocals_1 (&gsi, def);
546 	}
547 
548       if (optimize_bb_for_size_p (bb))
549         continue;
550 
551       /* Scan for a/func(b) and convert it to reciprocal a*rfunc(b).  */
552       for (gsi = gsi_after_labels (bb); !gsi_end_p (gsi); gsi_next (&gsi))
553         {
554 	  gimple stmt = gsi_stmt (gsi);
555 	  tree fndecl;
556 
557 	  if (is_gimple_assign (stmt)
558 	      && gimple_assign_rhs_code (stmt) == RDIV_EXPR)
559 	    {
560 	      tree arg1 = gimple_assign_rhs2 (stmt);
561 	      gimple stmt1;
562 
563 	      if (TREE_CODE (arg1) != SSA_NAME)
564 		continue;
565 
566 	      stmt1 = SSA_NAME_DEF_STMT (arg1);
567 
568 	      if (is_gimple_call (stmt1)
569 		  && gimple_call_lhs (stmt1)
570 		  && (fndecl = gimple_call_fndecl (stmt1))
571 		  && (DECL_BUILT_IN_CLASS (fndecl) == BUILT_IN_NORMAL
572 		      || DECL_BUILT_IN_CLASS (fndecl) == BUILT_IN_MD))
573 		{
574 		  enum built_in_function code;
575 		  bool md_code, fail;
576 		  imm_use_iterator ui;
577 		  use_operand_p use_p;
578 
579 		  code = DECL_FUNCTION_CODE (fndecl);
580 		  md_code = DECL_BUILT_IN_CLASS (fndecl) == BUILT_IN_MD;
581 
582 		  fndecl = targetm.builtin_reciprocal (code, md_code, false);
583 		  if (!fndecl)
584 		    continue;
585 
586 		  /* Check that all uses of the SSA name are divisions,
587 		     otherwise replacing the defining statement will do
588 		     the wrong thing.  */
589 		  fail = false;
590 		  FOR_EACH_IMM_USE_FAST (use_p, ui, arg1)
591 		    {
592 		      gimple stmt2 = USE_STMT (use_p);
593 		      if (is_gimple_debug (stmt2))
594 			continue;
595 		      if (!is_gimple_assign (stmt2)
596 			  || gimple_assign_rhs_code (stmt2) != RDIV_EXPR
597 			  || gimple_assign_rhs1 (stmt2) == arg1
598 			  || gimple_assign_rhs2 (stmt2) != arg1)
599 			{
600 			  fail = true;
601 			  break;
602 			}
603 		    }
604 		  if (fail)
605 		    continue;
606 
607 		  gimple_replace_lhs (stmt1, arg1);
608 		  gimple_call_set_fndecl (stmt1, fndecl);
609 		  update_stmt (stmt1);
610 		  reciprocal_stats.rfuncs_inserted++;
611 
612 		  FOR_EACH_IMM_USE_STMT (stmt, ui, arg1)
613 		    {
614 		      gimple_stmt_iterator gsi = gsi_for_stmt (stmt);
615 		      gimple_assign_set_rhs_code (stmt, MULT_EXPR);
616 		      fold_stmt_inplace (&gsi);
617 		      update_stmt (stmt);
618 		    }
619 		}
620 	    }
621 	}
622     }
623 
624   statistics_counter_event (cfun, "reciprocal divs inserted",
625 			    reciprocal_stats.rdivs_inserted);
626   statistics_counter_event (cfun, "reciprocal functions inserted",
627 			    reciprocal_stats.rfuncs_inserted);
628 
629   free_dominance_info (CDI_DOMINATORS);
630   free_dominance_info (CDI_POST_DOMINATORS);
631   free_alloc_pool (occ_pool);
632   return 0;
633 }
634 
635 struct gimple_opt_pass pass_cse_reciprocals =
636 {
637  {
638   GIMPLE_PASS,
639   "recip",				/* name */
640   gate_cse_reciprocals,			/* gate */
641   execute_cse_reciprocals,		/* execute */
642   NULL,					/* sub */
643   NULL,					/* next */
644   0,					/* static_pass_number */
645   TV_NONE,				/* tv_id */
646   PROP_ssa,				/* properties_required */
647   0,					/* properties_provided */
648   0,					/* properties_destroyed */
649   0,					/* todo_flags_start */
650   TODO_update_ssa | TODO_verify_ssa
651     | TODO_verify_stmts                /* todo_flags_finish */
652  }
653 };
654 
655 /* Records an occurrence at statement USE_STMT in the vector of trees
656    STMTS if it is dominated by *TOP_BB or dominates it or this basic block
657    is not yet initialized.  Returns true if the occurrence was pushed on
658    the vector.  Adjusts *TOP_BB to be the basic block dominating all
659    statements in the vector.  */
660 
661 static bool
662 maybe_record_sincos (VEC(gimple, heap) **stmts,
663 		     basic_block *top_bb, gimple use_stmt)
664 {
665   basic_block use_bb = gimple_bb (use_stmt);
666   if (*top_bb
667       && (*top_bb == use_bb
668 	  || dominated_by_p (CDI_DOMINATORS, use_bb, *top_bb)))
669     VEC_safe_push (gimple, heap, *stmts, use_stmt);
670   else if (!*top_bb
671 	   || dominated_by_p (CDI_DOMINATORS, *top_bb, use_bb))
672     {
673       VEC_safe_push (gimple, heap, *stmts, use_stmt);
674       *top_bb = use_bb;
675     }
676   else
677     return false;
678 
679   return true;
680 }
681 
682 /* Look for sin, cos and cexpi calls with the same argument NAME and
683    create a single call to cexpi CSEing the result in this case.
684    We first walk over all immediate uses of the argument collecting
685    statements that we can CSE in a vector and in a second pass replace
686    the statement rhs with a REALPART or IMAGPART expression on the
687    result of the cexpi call we insert before the use statement that
688    dominates all other candidates.  */
689 
690 static bool
691 execute_cse_sincos_1 (tree name)
692 {
693   gimple_stmt_iterator gsi;
694   imm_use_iterator use_iter;
695   tree fndecl, res, type;
696   gimple def_stmt, use_stmt, stmt;
697   int seen_cos = 0, seen_sin = 0, seen_cexpi = 0;
698   VEC(gimple, heap) *stmts = NULL;
699   basic_block top_bb = NULL;
700   int i;
701   bool cfg_changed = false;
702 
703   type = TREE_TYPE (name);
704   FOR_EACH_IMM_USE_STMT (use_stmt, use_iter, name)
705     {
706       if (gimple_code (use_stmt) != GIMPLE_CALL
707 	  || !gimple_call_lhs (use_stmt)
708 	  || !(fndecl = gimple_call_fndecl (use_stmt))
709 	  || DECL_BUILT_IN_CLASS (fndecl) != BUILT_IN_NORMAL)
710 	continue;
711 
712       switch (DECL_FUNCTION_CODE (fndecl))
713 	{
714 	CASE_FLT_FN (BUILT_IN_COS):
715 	  seen_cos |= maybe_record_sincos (&stmts, &top_bb, use_stmt) ? 1 : 0;
716 	  break;
717 
718 	CASE_FLT_FN (BUILT_IN_SIN):
719 	  seen_sin |= maybe_record_sincos (&stmts, &top_bb, use_stmt) ? 1 : 0;
720 	  break;
721 
722 	CASE_FLT_FN (BUILT_IN_CEXPI):
723 	  seen_cexpi |= maybe_record_sincos (&stmts, &top_bb, use_stmt) ? 1 : 0;
724 	  break;
725 
726 	default:;
727 	}
728     }
729 
730   if (seen_cos + seen_sin + seen_cexpi <= 1)
731     {
732       VEC_free(gimple, heap, stmts);
733       return false;
734     }
735 
736   /* Simply insert cexpi at the beginning of top_bb but not earlier than
737      the name def statement.  */
738   fndecl = mathfn_built_in (type, BUILT_IN_CEXPI);
739   if (!fndecl)
740     return false;
741   res = create_tmp_reg (TREE_TYPE (TREE_TYPE (fndecl)), "sincostmp");
742   stmt = gimple_build_call (fndecl, 1, name);
743   res = make_ssa_name (res, stmt);
744   gimple_call_set_lhs (stmt, res);
745 
746   def_stmt = SSA_NAME_DEF_STMT (name);
747   if (!SSA_NAME_IS_DEFAULT_DEF (name)
748       && gimple_code (def_stmt) != GIMPLE_PHI
749       && gimple_bb (def_stmt) == top_bb)
750     {
751       gsi = gsi_for_stmt (def_stmt);
752       gsi_insert_after (&gsi, stmt, GSI_SAME_STMT);
753     }
754   else
755     {
756       gsi = gsi_after_labels (top_bb);
757       gsi_insert_before (&gsi, stmt, GSI_SAME_STMT);
758     }
759   update_stmt (stmt);
760   sincos_stats.inserted++;
761 
762   /* And adjust the recorded old call sites.  */
763   for (i = 0; VEC_iterate(gimple, stmts, i, use_stmt); ++i)
764     {
765       tree rhs = NULL;
766       fndecl = gimple_call_fndecl (use_stmt);
767 
768       switch (DECL_FUNCTION_CODE (fndecl))
769 	{
770 	CASE_FLT_FN (BUILT_IN_COS):
771 	  rhs = fold_build1 (REALPART_EXPR, type, res);
772 	  break;
773 
774 	CASE_FLT_FN (BUILT_IN_SIN):
775 	  rhs = fold_build1 (IMAGPART_EXPR, type, res);
776 	  break;
777 
778 	CASE_FLT_FN (BUILT_IN_CEXPI):
779 	  rhs = res;
780 	  break;
781 
782 	default:;
783 	  gcc_unreachable ();
784 	}
785 
786 	/* Replace call with a copy.  */
787 	stmt = gimple_build_assign (gimple_call_lhs (use_stmt), rhs);
788 
789 	gsi = gsi_for_stmt (use_stmt);
790 	gsi_replace (&gsi, stmt, true);
791 	if (gimple_purge_dead_eh_edges (gimple_bb (stmt)))
792 	  cfg_changed = true;
793     }
794 
795   VEC_free(gimple, heap, stmts);
796 
797   return cfg_changed;
798 }
799 
800 /* To evaluate powi(x,n), the floating point value x raised to the
801    constant integer exponent n, we use a hybrid algorithm that
802    combines the "window method" with look-up tables.  For an
803    introduction to exponentiation algorithms and "addition chains",
804    see section 4.6.3, "Evaluation of Powers" of Donald E. Knuth,
805    "Seminumerical Algorithms", Vol. 2, "The Art of Computer Programming",
806    3rd Edition, 1998, and Daniel M. Gordon, "A Survey of Fast Exponentiation
807    Methods", Journal of Algorithms, Vol. 27, pp. 129-146, 1998.  */
808 
809 /* Provide a default value for POWI_MAX_MULTS, the maximum number of
810    multiplications to inline before calling the system library's pow
811    function.  powi(x,n) requires at worst 2*bits(n)-2 multiplications,
812    so this default never requires calling pow, powf or powl.  */
813 
814 #ifndef POWI_MAX_MULTS
815 #define POWI_MAX_MULTS  (2*HOST_BITS_PER_WIDE_INT-2)
816 #endif
817 
818 /* The size of the "optimal power tree" lookup table.  All
819    exponents less than this value are simply looked up in the
820    powi_table below.  This threshold is also used to size the
821    cache of pseudo registers that hold intermediate results.  */
822 #define POWI_TABLE_SIZE 256
823 
824 /* The size, in bits of the window, used in the "window method"
825    exponentiation algorithm.  This is equivalent to a radix of
826    (1<<POWI_WINDOW_SIZE) in the corresponding "m-ary method".  */
827 #define POWI_WINDOW_SIZE 3
828 
829 /* The following table is an efficient representation of an
830    "optimal power tree".  For each value, i, the corresponding
831    value, j, in the table states than an optimal evaluation
832    sequence for calculating pow(x,i) can be found by evaluating
833    pow(x,j)*pow(x,i-j).  An optimal power tree for the first
834    100 integers is given in Knuth's "Seminumerical algorithms".  */
835 
836 static const unsigned char powi_table[POWI_TABLE_SIZE] =
837   {
838       0,   1,   1,   2,   2,   3,   3,   4,  /*   0 -   7 */
839       4,   6,   5,   6,   6,  10,   7,   9,  /*   8 -  15 */
840       8,  16,   9,  16,  10,  12,  11,  13,  /*  16 -  23 */
841      12,  17,  13,  18,  14,  24,  15,  26,  /*  24 -  31 */
842      16,  17,  17,  19,  18,  33,  19,  26,  /*  32 -  39 */
843      20,  25,  21,  40,  22,  27,  23,  44,  /*  40 -  47 */
844      24,  32,  25,  34,  26,  29,  27,  44,  /*  48 -  55 */
845      28,  31,  29,  34,  30,  60,  31,  36,  /*  56 -  63 */
846      32,  64,  33,  34,  34,  46,  35,  37,  /*  64 -  71 */
847      36,  65,  37,  50,  38,  48,  39,  69,  /*  72 -  79 */
848      40,  49,  41,  43,  42,  51,  43,  58,  /*  80 -  87 */
849      44,  64,  45,  47,  46,  59,  47,  76,  /*  88 -  95 */
850      48,  65,  49,  66,  50,  67,  51,  66,  /*  96 - 103 */
851      52,  70,  53,  74,  54, 104,  55,  74,  /* 104 - 111 */
852      56,  64,  57,  69,  58,  78,  59,  68,  /* 112 - 119 */
853      60,  61,  61,  80,  62,  75,  63,  68,  /* 120 - 127 */
854      64,  65,  65, 128,  66, 129,  67,  90,  /* 128 - 135 */
855      68,  73,  69, 131,  70,  94,  71,  88,  /* 136 - 143 */
856      72, 128,  73,  98,  74, 132,  75, 121,  /* 144 - 151 */
857      76, 102,  77, 124,  78, 132,  79, 106,  /* 152 - 159 */
858      80,  97,  81, 160,  82,  99,  83, 134,  /* 160 - 167 */
859      84,  86,  85,  95,  86, 160,  87, 100,  /* 168 - 175 */
860      88, 113,  89,  98,  90, 107,  91, 122,  /* 176 - 183 */
861      92, 111,  93, 102,  94, 126,  95, 150,  /* 184 - 191 */
862      96, 128,  97, 130,  98, 133,  99, 195,  /* 192 - 199 */
863     100, 128, 101, 123, 102, 164, 103, 138,  /* 200 - 207 */
864     104, 145, 105, 146, 106, 109, 107, 149,  /* 208 - 215 */
865     108, 200, 109, 146, 110, 170, 111, 157,  /* 216 - 223 */
866     112, 128, 113, 130, 114, 182, 115, 132,  /* 224 - 231 */
867     116, 200, 117, 132, 118, 158, 119, 206,  /* 232 - 239 */
868     120, 240, 121, 162, 122, 147, 123, 152,  /* 240 - 247 */
869     124, 166, 125, 214, 126, 138, 127, 153,  /* 248 - 255 */
870   };
871 
872 
873 /* Return the number of multiplications required to calculate
874    powi(x,n) where n is less than POWI_TABLE_SIZE.  This is a
875    subroutine of powi_cost.  CACHE is an array indicating
876    which exponents have already been calculated.  */
877 
878 static int
879 powi_lookup_cost (unsigned HOST_WIDE_INT n, bool *cache)
880 {
881   /* If we've already calculated this exponent, then this evaluation
882      doesn't require any additional multiplications.  */
883   if (cache[n])
884     return 0;
885 
886   cache[n] = true;
887   return powi_lookup_cost (n - powi_table[n], cache)
888 	 + powi_lookup_cost (powi_table[n], cache) + 1;
889 }
890 
891 /* Return the number of multiplications required to calculate
892    powi(x,n) for an arbitrary x, given the exponent N.  This
893    function needs to be kept in sync with powi_as_mults below.  */
894 
895 static int
896 powi_cost (HOST_WIDE_INT n)
897 {
898   bool cache[POWI_TABLE_SIZE];
899   unsigned HOST_WIDE_INT digit;
900   unsigned HOST_WIDE_INT val;
901   int result;
902 
903   if (n == 0)
904     return 0;
905 
906   /* Ignore the reciprocal when calculating the cost.  */
907   val = (n < 0) ? -n : n;
908 
909   /* Initialize the exponent cache.  */
910   memset (cache, 0, POWI_TABLE_SIZE * sizeof (bool));
911   cache[1] = true;
912 
913   result = 0;
914 
915   while (val >= POWI_TABLE_SIZE)
916     {
917       if (val & 1)
918 	{
919 	  digit = val & ((1 << POWI_WINDOW_SIZE) - 1);
920 	  result += powi_lookup_cost (digit, cache)
921 		    + POWI_WINDOW_SIZE + 1;
922 	  val >>= POWI_WINDOW_SIZE;
923 	}
924       else
925 	{
926 	  val >>= 1;
927 	  result++;
928 	}
929     }
930 
931   return result + powi_lookup_cost (val, cache);
932 }
933 
934 /* Recursive subroutine of powi_as_mults.  This function takes the
935    array, CACHE, of already calculated exponents and an exponent N and
936    returns a tree that corresponds to CACHE[1]**N, with type TYPE.  */
937 
938 static tree
939 powi_as_mults_1 (gimple_stmt_iterator *gsi, location_t loc, tree type,
940 		 HOST_WIDE_INT n, tree *cache, tree target)
941 {
942   tree op0, op1, ssa_target;
943   unsigned HOST_WIDE_INT digit;
944   gimple mult_stmt;
945 
946   if (n < POWI_TABLE_SIZE && cache[n])
947     return cache[n];
948 
949   ssa_target = make_ssa_name (target, NULL);
950 
951   if (n < POWI_TABLE_SIZE)
952     {
953       cache[n] = ssa_target;
954       op0 = powi_as_mults_1 (gsi, loc, type, n - powi_table[n], cache, target);
955       op1 = powi_as_mults_1 (gsi, loc, type, powi_table[n], cache, target);
956     }
957   else if (n & 1)
958     {
959       digit = n & ((1 << POWI_WINDOW_SIZE) - 1);
960       op0 = powi_as_mults_1 (gsi, loc, type, n - digit, cache, target);
961       op1 = powi_as_mults_1 (gsi, loc, type, digit, cache, target);
962     }
963   else
964     {
965       op0 = powi_as_mults_1 (gsi, loc, type, n >> 1, cache, target);
966       op1 = op0;
967     }
968 
969   mult_stmt = gimple_build_assign_with_ops (MULT_EXPR, ssa_target, op0, op1);
970   gimple_set_location (mult_stmt, loc);
971   gsi_insert_before (gsi, mult_stmt, GSI_SAME_STMT);
972 
973   return ssa_target;
974 }
975 
976 /* Convert ARG0**N to a tree of multiplications of ARG0 with itself.
977    This function needs to be kept in sync with powi_cost above.  */
978 
979 static tree
980 powi_as_mults (gimple_stmt_iterator *gsi, location_t loc,
981 	       tree arg0, HOST_WIDE_INT n)
982 {
983   tree cache[POWI_TABLE_SIZE], result, type = TREE_TYPE (arg0), target;
984   gimple div_stmt;
985 
986   if (n == 0)
987     return build_real (type, dconst1);
988 
989   memset (cache, 0,  sizeof (cache));
990   cache[1] = arg0;
991 
992   target = create_tmp_reg (type, "powmult");
993   add_referenced_var (target);
994 
995   result = powi_as_mults_1 (gsi, loc, type, (n < 0) ? -n : n, cache, target);
996 
997   if (n >= 0)
998     return result;
999 
1000   /* If the original exponent was negative, reciprocate the result.  */
1001   target = make_ssa_name (target, NULL);
1002   div_stmt = gimple_build_assign_with_ops (RDIV_EXPR, target,
1003 					   build_real (type, dconst1),
1004 					   result);
1005   gimple_set_location (div_stmt, loc);
1006   gsi_insert_before (gsi, div_stmt, GSI_SAME_STMT);
1007 
1008   return target;
1009 }
1010 
1011 /* ARG0 and N are the two arguments to a powi builtin in GSI with
1012    location info LOC.  If the arguments are appropriate, create an
1013    equivalent sequence of statements prior to GSI using an optimal
1014    number of multiplications, and return an expession holding the
1015    result.  */
1016 
1017 static tree
1018 gimple_expand_builtin_powi (gimple_stmt_iterator *gsi, location_t loc,
1019 			    tree arg0, HOST_WIDE_INT n)
1020 {
1021   /* Avoid largest negative number.  */
1022   if (n != -n
1023       && ((n >= -1 && n <= 2)
1024 	  || (optimize_function_for_speed_p (cfun)
1025 	      && powi_cost (n) <= POWI_MAX_MULTS)))
1026     return powi_as_mults (gsi, loc, arg0, n);
1027 
1028   return NULL_TREE;
1029 }
1030 
1031 /* Build a gimple call statement that calls FN with argument ARG.
1032    Set the lhs of the call statement to a fresh SSA name for
1033    variable VAR.  If VAR is NULL, first allocate it.  Insert the
1034    statement prior to GSI's current position, and return the fresh
1035    SSA name.  */
1036 
1037 static tree
1038 build_and_insert_call (gimple_stmt_iterator *gsi, location_t loc,
1039 		       tree *var, tree fn, tree arg)
1040 {
1041   gimple call_stmt;
1042   tree ssa_target;
1043 
1044   if (!*var)
1045     {
1046       *var = create_tmp_reg (TREE_TYPE (arg), "powroot");
1047       add_referenced_var (*var);
1048     }
1049 
1050   call_stmt = gimple_build_call (fn, 1, arg);
1051   ssa_target = make_ssa_name (*var, NULL);
1052   gimple_set_lhs (call_stmt, ssa_target);
1053   gimple_set_location (call_stmt, loc);
1054   gsi_insert_before (gsi, call_stmt, GSI_SAME_STMT);
1055 
1056   return ssa_target;
1057 }
1058 
1059 /* Build a gimple binary operation with the given CODE and arguments
1060    ARG0, ARG1, assigning the result to a new SSA name for variable
1061    TARGET.  Insert the statement prior to GSI's current position, and
1062    return the fresh SSA name.*/
1063 
1064 static tree
1065 build_and_insert_binop (gimple_stmt_iterator *gsi, location_t loc,
1066 			tree target, enum tree_code code, tree arg0, tree arg1)
1067 {
1068   tree result = make_ssa_name (target, NULL);
1069   gimple stmt = gimple_build_assign_with_ops (code, result, arg0, arg1);
1070   gimple_set_location (stmt, loc);
1071   gsi_insert_before (gsi, stmt, GSI_SAME_STMT);
1072   return result;
1073 }
1074 
1075 /* Build a gimple reference operation with the given CODE and argument
1076    ARG, assigning the result to a new SSA name for variable TARGET.
1077    Insert the statement prior to GSI's current position, and return
1078    the fresh SSA name.  */
1079 
1080 static inline tree
1081 build_and_insert_ref (gimple_stmt_iterator *gsi, location_t loc, tree type,
1082 		      tree target, enum tree_code code, tree arg0)
1083 {
1084   tree result = make_ssa_name (target, NULL);
1085   gimple stmt = gimple_build_assign (result, build1 (code, type, arg0));
1086   gimple_set_location (stmt, loc);
1087   gsi_insert_before (gsi, stmt, GSI_SAME_STMT);
1088   return result;
1089 }
1090 
1091 /* Build a gimple assignment to cast VAL to TARGET.  Insert the statement
1092    prior to GSI's current position, and return the fresh SSA name.  */
1093 
1094 static tree
1095 build_and_insert_cast (gimple_stmt_iterator *gsi, location_t loc,
1096 		       tree target, tree val)
1097 {
1098   return build_and_insert_binop (gsi, loc, target, CONVERT_EXPR, val, NULL);
1099 }
1100 
1101 /* ARG0 and ARG1 are the two arguments to a pow builtin call in GSI
1102    with location info LOC.  If possible, create an equivalent and
1103    less expensive sequence of statements prior to GSI, and return an
1104    expession holding the result.  */
1105 
1106 static tree
1107 gimple_expand_builtin_pow (gimple_stmt_iterator *gsi, location_t loc,
1108 			   tree arg0, tree arg1)
1109 {
1110   REAL_VALUE_TYPE c, cint, dconst1_4, dconst3_4, dconst1_3, dconst1_6;
1111   REAL_VALUE_TYPE c2, dconst3;
1112   HOST_WIDE_INT n;
1113   tree type, sqrtfn, cbrtfn, sqrt_arg0, sqrt_sqrt, result, cbrt_x, powi_cbrt_x;
1114   tree target = NULL_TREE;
1115   enum machine_mode mode;
1116   bool hw_sqrt_exists, c_is_int, c2_is_int;
1117 
1118   /* If the exponent isn't a constant, there's nothing of interest
1119      to be done.  */
1120   if (TREE_CODE (arg1) != REAL_CST)
1121     return NULL_TREE;
1122 
1123   /* If the exponent is equivalent to an integer, expand to an optimal
1124      multiplication sequence when profitable.  */
1125   c = TREE_REAL_CST (arg1);
1126   n = real_to_integer (&c);
1127   real_from_integer (&cint, VOIDmode, n, n < 0 ? -1 : 0, 0);
1128   c_is_int = real_identical (&c, &cint);
1129 
1130   if (c_is_int
1131       && ((n >= -1 && n <= 2)
1132 	  || (flag_unsafe_math_optimizations
1133 	      && optimize_insn_for_speed_p ()
1134 	      && powi_cost (n) <= POWI_MAX_MULTS)))
1135     return gimple_expand_builtin_powi (gsi, loc, arg0, n);
1136 
1137   /* Attempt various optimizations using sqrt and cbrt.  */
1138   type = TREE_TYPE (arg0);
1139   mode = TYPE_MODE (type);
1140   sqrtfn = mathfn_built_in (type, BUILT_IN_SQRT);
1141 
1142   /* Optimize pow(x,0.5) = sqrt(x).  This replacement is always safe
1143      unless signed zeros must be maintained.  pow(-0,0.5) = +0, while
1144      sqrt(-0) = -0.  */
1145   if (sqrtfn
1146       && REAL_VALUES_EQUAL (c, dconsthalf)
1147       && !HONOR_SIGNED_ZEROS (mode))
1148     return build_and_insert_call (gsi, loc, &target, sqrtfn, arg0);
1149 
1150   /* Optimize pow(x,0.25) = sqrt(sqrt(x)).  Assume on most machines that
1151      a builtin sqrt instruction is smaller than a call to pow with 0.25,
1152      so do this optimization even if -Os.  Don't do this optimization
1153      if we don't have a hardware sqrt insn.  */
1154   dconst1_4 = dconst1;
1155   SET_REAL_EXP (&dconst1_4, REAL_EXP (&dconst1_4) - 2);
1156   hw_sqrt_exists = optab_handler (sqrt_optab, mode) != CODE_FOR_nothing;
1157 
1158   if (flag_unsafe_math_optimizations
1159       && sqrtfn
1160       && REAL_VALUES_EQUAL (c, dconst1_4)
1161       && hw_sqrt_exists)
1162     {
1163       /* sqrt(x)  */
1164       sqrt_arg0 = build_and_insert_call (gsi, loc, &target, sqrtfn, arg0);
1165 
1166       /* sqrt(sqrt(x))  */
1167       return build_and_insert_call (gsi, loc, &target, sqrtfn, sqrt_arg0);
1168     }
1169 
1170   /* Optimize pow(x,0.75) = sqrt(x) * sqrt(sqrt(x)) unless we are
1171      optimizing for space.  Don't do this optimization if we don't have
1172      a hardware sqrt insn.  */
1173   real_from_integer (&dconst3_4, VOIDmode, 3, 0, 0);
1174   SET_REAL_EXP (&dconst3_4, REAL_EXP (&dconst3_4) - 2);
1175 
1176   if (flag_unsafe_math_optimizations
1177       && sqrtfn
1178       && optimize_function_for_speed_p (cfun)
1179       && REAL_VALUES_EQUAL (c, dconst3_4)
1180       && hw_sqrt_exists)
1181     {
1182       /* sqrt(x)  */
1183       sqrt_arg0 = build_and_insert_call (gsi, loc, &target, sqrtfn, arg0);
1184 
1185       /* sqrt(sqrt(x))  */
1186       sqrt_sqrt = build_and_insert_call (gsi, loc, &target, sqrtfn, sqrt_arg0);
1187 
1188       /* sqrt(x) * sqrt(sqrt(x))  */
1189       return build_and_insert_binop (gsi, loc, target, MULT_EXPR,
1190 				     sqrt_arg0, sqrt_sqrt);
1191     }
1192 
1193   /* Optimize pow(x,1./3.) = cbrt(x).  This requires unsafe math
1194      optimizations since 1./3. is not exactly representable.  If x
1195      is negative and finite, the correct value of pow(x,1./3.) is
1196      a NaN with the "invalid" exception raised, because the value
1197      of 1./3. actually has an even denominator.  The correct value
1198      of cbrt(x) is a negative real value.  */
1199   cbrtfn = mathfn_built_in (type, BUILT_IN_CBRT);
1200   dconst1_3 = real_value_truncate (mode, dconst_third ());
1201 
1202   if (flag_unsafe_math_optimizations
1203       && cbrtfn
1204       && (gimple_val_nonnegative_real_p (arg0) || !HONOR_NANS (mode))
1205       && REAL_VALUES_EQUAL (c, dconst1_3))
1206     return build_and_insert_call (gsi, loc, &target, cbrtfn, arg0);
1207 
1208   /* Optimize pow(x,1./6.) = cbrt(sqrt(x)).  Don't do this optimization
1209      if we don't have a hardware sqrt insn.  */
1210   dconst1_6 = dconst1_3;
1211   SET_REAL_EXP (&dconst1_6, REAL_EXP (&dconst1_6) - 1);
1212 
1213   if (flag_unsafe_math_optimizations
1214       && sqrtfn
1215       && cbrtfn
1216       && (gimple_val_nonnegative_real_p (arg0) || !HONOR_NANS (mode))
1217       && optimize_function_for_speed_p (cfun)
1218       && hw_sqrt_exists
1219       && REAL_VALUES_EQUAL (c, dconst1_6))
1220     {
1221       /* sqrt(x)  */
1222       sqrt_arg0 = build_and_insert_call (gsi, loc, &target, sqrtfn, arg0);
1223 
1224       /* cbrt(sqrt(x))  */
1225       return build_and_insert_call (gsi, loc, &target, cbrtfn, sqrt_arg0);
1226     }
1227 
1228   /* Optimize pow(x,c), where n = 2c for some nonzero integer n
1229      and c not an integer, into
1230 
1231        sqrt(x) * powi(x, n/2),                n > 0;
1232        1.0 / (sqrt(x) * powi(x, abs(n/2))),   n < 0.
1233 
1234      Do not calculate the powi factor when n/2 = 0.  */
1235   real_arithmetic (&c2, MULT_EXPR, &c, &dconst2);
1236   n = real_to_integer (&c2);
1237   real_from_integer (&cint, VOIDmode, n, n < 0 ? -1 : 0, 0);
1238   c2_is_int = real_identical (&c2, &cint);
1239 
1240   if (flag_unsafe_math_optimizations
1241       && sqrtfn
1242       && c2_is_int
1243       && !c_is_int
1244       && optimize_function_for_speed_p (cfun))
1245     {
1246       tree powi_x_ndiv2 = NULL_TREE;
1247 
1248       /* Attempt to fold powi(arg0, abs(n/2)) into multiplies.  If not
1249          possible or profitable, give up.  Skip the degenerate case when
1250          n is 1 or -1, where the result is always 1.  */
1251       if (absu_hwi (n) != 1)
1252 	{
1253 	  powi_x_ndiv2 = gimple_expand_builtin_powi (gsi, loc, arg0,
1254 						     abs_hwi (n / 2));
1255 	  if (!powi_x_ndiv2)
1256 	    return NULL_TREE;
1257 	}
1258 
1259       /* Calculate sqrt(x).  When n is not 1 or -1, multiply it by the
1260 	 result of the optimal multiply sequence just calculated.  */
1261       sqrt_arg0 = build_and_insert_call (gsi, loc, &target, sqrtfn, arg0);
1262 
1263       if (absu_hwi (n) == 1)
1264 	result = sqrt_arg0;
1265       else
1266 	result = build_and_insert_binop (gsi, loc, target, MULT_EXPR,
1267 					 sqrt_arg0, powi_x_ndiv2);
1268 
1269       /* If n is negative, reciprocate the result.  */
1270       if (n < 0)
1271 	result = build_and_insert_binop (gsi, loc, target, RDIV_EXPR,
1272 					 build_real (type, dconst1), result);
1273       return result;
1274     }
1275 
1276   /* Optimize pow(x,c), where 3c = n for some nonzero integer n, into
1277 
1278      powi(x, n/3) * powi(cbrt(x), n%3),                    n > 0;
1279      1.0 / (powi(x, abs(n)/3) * powi(cbrt(x), abs(n)%3)),  n < 0.
1280 
1281      Do not calculate the first factor when n/3 = 0.  As cbrt(x) is
1282      different from pow(x, 1./3.) due to rounding and behavior with
1283      negative x, we need to constrain this transformation to unsafe
1284      math and positive x or finite math.  */
1285   real_from_integer (&dconst3, VOIDmode, 3, 0, 0);
1286   real_arithmetic (&c2, MULT_EXPR, &c, &dconst3);
1287   real_round (&c2, mode, &c2);
1288   n = real_to_integer (&c2);
1289   real_from_integer (&cint, VOIDmode, n, n < 0 ? -1 : 0, 0);
1290   real_arithmetic (&c2, RDIV_EXPR, &cint, &dconst3);
1291   real_convert (&c2, mode, &c2);
1292 
1293   if (flag_unsafe_math_optimizations
1294       && cbrtfn
1295       && (gimple_val_nonnegative_real_p (arg0) || !HONOR_NANS (mode))
1296       && real_identical (&c2, &c)
1297       && !c2_is_int
1298       && optimize_function_for_speed_p (cfun)
1299       && powi_cost (n / 3) <= POWI_MAX_MULTS)
1300     {
1301       tree powi_x_ndiv3 = NULL_TREE;
1302 
1303       /* Attempt to fold powi(arg0, abs(n/3)) into multiplies.  If not
1304          possible or profitable, give up.  Skip the degenerate case when
1305          abs(n) < 3, where the result is always 1.  */
1306       if (absu_hwi (n) >= 3)
1307 	{
1308 	  powi_x_ndiv3 = gimple_expand_builtin_powi (gsi, loc, arg0,
1309 						     abs_hwi (n / 3));
1310 	  if (!powi_x_ndiv3)
1311 	    return NULL_TREE;
1312 	}
1313 
1314       /* Calculate powi(cbrt(x), n%3).  Don't use gimple_expand_builtin_powi
1315          as that creates an unnecessary variable.  Instead, just produce
1316          either cbrt(x) or cbrt(x) * cbrt(x).  */
1317       cbrt_x = build_and_insert_call (gsi, loc, &target, cbrtfn, arg0);
1318 
1319       if (absu_hwi (n) % 3 == 1)
1320 	powi_cbrt_x = cbrt_x;
1321       else
1322 	powi_cbrt_x = build_and_insert_binop (gsi, loc, target, MULT_EXPR,
1323 					      cbrt_x, cbrt_x);
1324 
1325       /* Multiply the two subexpressions, unless powi(x,abs(n)/3) = 1.  */
1326       if (absu_hwi (n) < 3)
1327 	result = powi_cbrt_x;
1328       else
1329 	result = build_and_insert_binop (gsi, loc, target, MULT_EXPR,
1330 					 powi_x_ndiv3, powi_cbrt_x);
1331 
1332       /* If n is negative, reciprocate the result.  */
1333       if (n < 0)
1334 	result = build_and_insert_binop (gsi, loc, target, RDIV_EXPR,
1335 					 build_real (type, dconst1), result);
1336 
1337       return result;
1338     }
1339 
1340   /* No optimizations succeeded.  */
1341   return NULL_TREE;
1342 }
1343 
1344 /* ARG is the argument to a cabs builtin call in GSI with location info
1345    LOC.  Create a sequence of statements prior to GSI that calculates
1346    sqrt(R*R + I*I), where R and I are the real and imaginary components
1347    of ARG, respectively.  Return an expression holding the result.  */
1348 
1349 static tree
1350 gimple_expand_builtin_cabs (gimple_stmt_iterator *gsi, location_t loc, tree arg)
1351 {
1352   tree target, real_part, imag_part, addend1, addend2, sum, result;
1353   tree type = TREE_TYPE (TREE_TYPE (arg));
1354   tree sqrtfn = mathfn_built_in (type, BUILT_IN_SQRT);
1355   enum machine_mode mode = TYPE_MODE (type);
1356 
1357   if (!flag_unsafe_math_optimizations
1358       || !optimize_bb_for_speed_p (gimple_bb (gsi_stmt (*gsi)))
1359       || !sqrtfn
1360       || optab_handler (sqrt_optab, mode) == CODE_FOR_nothing)
1361     return NULL_TREE;
1362 
1363   target = create_tmp_reg (type, "cabs");
1364   add_referenced_var (target);
1365 
1366   real_part = build_and_insert_ref (gsi, loc, type, target,
1367 				    REALPART_EXPR, arg);
1368   addend1 = build_and_insert_binop (gsi, loc, target, MULT_EXPR,
1369 				    real_part, real_part);
1370   imag_part = build_and_insert_ref (gsi, loc, type, target,
1371 				    IMAGPART_EXPR, arg);
1372   addend2 = build_and_insert_binop (gsi, loc, target, MULT_EXPR,
1373 				    imag_part, imag_part);
1374   sum = build_and_insert_binop (gsi, loc, target, PLUS_EXPR, addend1, addend2);
1375   result = build_and_insert_call (gsi, loc, &target, sqrtfn, sum);
1376 
1377   return result;
1378 }
1379 
1380 /* Go through all calls to sin, cos and cexpi and call execute_cse_sincos_1
1381    on the SSA_NAME argument of each of them.  Also expand powi(x,n) into
1382    an optimal number of multiplies, when n is a constant.  */
1383 
1384 static unsigned int
1385 execute_cse_sincos (void)
1386 {
1387   basic_block bb;
1388   bool cfg_changed = false;
1389 
1390   calculate_dominance_info (CDI_DOMINATORS);
1391   memset (&sincos_stats, 0, sizeof (sincos_stats));
1392 
1393   FOR_EACH_BB (bb)
1394     {
1395       gimple_stmt_iterator gsi;
1396       bool cleanup_eh = false;
1397 
1398       for (gsi = gsi_after_labels (bb); !gsi_end_p (gsi); gsi_next (&gsi))
1399         {
1400 	  gimple stmt = gsi_stmt (gsi);
1401 	  tree fndecl;
1402 
1403 	  /* Only the last stmt in a bb could throw, no need to call
1404 	     gimple_purge_dead_eh_edges if we change something in the middle
1405 	     of a basic block.  */
1406 	  cleanup_eh = false;
1407 
1408 	  if (is_gimple_call (stmt)
1409 	      && gimple_call_lhs (stmt)
1410 	      && (fndecl = gimple_call_fndecl (stmt))
1411 	      && DECL_BUILT_IN_CLASS (fndecl) == BUILT_IN_NORMAL)
1412 	    {
1413 	      tree arg, arg0, arg1, result;
1414 	      HOST_WIDE_INT n;
1415 	      location_t loc;
1416 
1417 	      switch (DECL_FUNCTION_CODE (fndecl))
1418 		{
1419 		CASE_FLT_FN (BUILT_IN_COS):
1420 		CASE_FLT_FN (BUILT_IN_SIN):
1421 		CASE_FLT_FN (BUILT_IN_CEXPI):
1422 		  /* Make sure we have either sincos or cexp.  */
1423 		  if (!TARGET_HAS_SINCOS && !TARGET_C99_FUNCTIONS)
1424 		    break;
1425 
1426 		  arg = gimple_call_arg (stmt, 0);
1427 		  if (TREE_CODE (arg) == SSA_NAME)
1428 		    cfg_changed |= execute_cse_sincos_1 (arg);
1429 		  break;
1430 
1431 		CASE_FLT_FN (BUILT_IN_POW):
1432 		  arg0 = gimple_call_arg (stmt, 0);
1433 		  arg1 = gimple_call_arg (stmt, 1);
1434 
1435 		  loc = gimple_location (stmt);
1436 		  result = gimple_expand_builtin_pow (&gsi, loc, arg0, arg1);
1437 
1438 		  if (result)
1439 		    {
1440 		      tree lhs = gimple_get_lhs (stmt);
1441 		      gimple new_stmt = gimple_build_assign (lhs, result);
1442 		      gimple_set_location (new_stmt, loc);
1443 		      unlink_stmt_vdef (stmt);
1444 		      gsi_replace (&gsi, new_stmt, true);
1445 		      cleanup_eh = true;
1446 		    }
1447 		  break;
1448 
1449 		CASE_FLT_FN (BUILT_IN_POWI):
1450 		  arg0 = gimple_call_arg (stmt, 0);
1451 		  arg1 = gimple_call_arg (stmt, 1);
1452 		  if (!host_integerp (arg1, 0))
1453 		    break;
1454 
1455 		  n = TREE_INT_CST_LOW (arg1);
1456 		  loc = gimple_location (stmt);
1457 		  result = gimple_expand_builtin_powi (&gsi, loc, arg0, n);
1458 
1459 		  if (result)
1460 		    {
1461 		      tree lhs = gimple_get_lhs (stmt);
1462 		      gimple new_stmt = gimple_build_assign (lhs, result);
1463 		      gimple_set_location (new_stmt, loc);
1464 		      unlink_stmt_vdef (stmt);
1465 		      gsi_replace (&gsi, new_stmt, true);
1466 		      cleanup_eh = true;
1467 		    }
1468 		  break;
1469 
1470 		CASE_FLT_FN (BUILT_IN_CABS):
1471 		  arg0 = gimple_call_arg (stmt, 0);
1472 		  loc = gimple_location (stmt);
1473 		  result = gimple_expand_builtin_cabs (&gsi, loc, arg0);
1474 
1475 		  if (result)
1476 		    {
1477 		      tree lhs = gimple_get_lhs (stmt);
1478 		      gimple new_stmt = gimple_build_assign (lhs, result);
1479 		      gimple_set_location (new_stmt, loc);
1480 		      unlink_stmt_vdef (stmt);
1481 		      gsi_replace (&gsi, new_stmt, true);
1482 		      cleanup_eh = true;
1483 		    }
1484 		  break;
1485 
1486 		default:;
1487 		}
1488 	    }
1489 	}
1490       if (cleanup_eh)
1491 	cfg_changed |= gimple_purge_dead_eh_edges (bb);
1492     }
1493 
1494   statistics_counter_event (cfun, "sincos statements inserted",
1495 			    sincos_stats.inserted);
1496 
1497   free_dominance_info (CDI_DOMINATORS);
1498   return cfg_changed ? TODO_cleanup_cfg : 0;
1499 }
1500 
1501 static bool
1502 gate_cse_sincos (void)
1503 {
1504   /* We no longer require either sincos or cexp, since powi expansion
1505      piggybacks on this pass.  */
1506   return optimize;
1507 }
1508 
1509 struct gimple_opt_pass pass_cse_sincos =
1510 {
1511  {
1512   GIMPLE_PASS,
1513   "sincos",				/* name */
1514   gate_cse_sincos,			/* gate */
1515   execute_cse_sincos,			/* execute */
1516   NULL,					/* sub */
1517   NULL,					/* next */
1518   0,					/* static_pass_number */
1519   TV_NONE,				/* tv_id */
1520   PROP_ssa,				/* properties_required */
1521   0,					/* properties_provided */
1522   0,					/* properties_destroyed */
1523   0,					/* todo_flags_start */
1524   TODO_update_ssa | TODO_verify_ssa
1525     | TODO_verify_stmts                 /* todo_flags_finish */
1526  }
1527 };
1528 
1529 /* A symbolic number is used to detect byte permutation and selection
1530    patterns.  Therefore the field N contains an artificial number
1531    consisting of byte size markers:
1532 
1533    0    - byte has the value 0
1534    1..size - byte contains the content of the byte
1535    number indexed with that value minus one  */
1536 
1537 struct symbolic_number {
1538   unsigned HOST_WIDEST_INT n;
1539   int size;
1540 };
1541 
1542 /* Perform a SHIFT or ROTATE operation by COUNT bits on symbolic
1543    number N.  Return false if the requested operation is not permitted
1544    on a symbolic number.  */
1545 
1546 static inline bool
1547 do_shift_rotate (enum tree_code code,
1548 		 struct symbolic_number *n,
1549 		 int count)
1550 {
1551   if (count % 8 != 0)
1552     return false;
1553 
1554   /* Zero out the extra bits of N in order to avoid them being shifted
1555      into the significant bits.  */
1556   if (n->size < (int)sizeof (HOST_WIDEST_INT))
1557     n->n &= ((unsigned HOST_WIDEST_INT)1 << (n->size * BITS_PER_UNIT)) - 1;
1558 
1559   switch (code)
1560     {
1561     case LSHIFT_EXPR:
1562       n->n <<= count;
1563       break;
1564     case RSHIFT_EXPR:
1565       n->n >>= count;
1566       break;
1567     case LROTATE_EXPR:
1568       n->n = (n->n << count) | (n->n >> ((n->size * BITS_PER_UNIT) - count));
1569       break;
1570     case RROTATE_EXPR:
1571       n->n = (n->n >> count) | (n->n << ((n->size * BITS_PER_UNIT) - count));
1572       break;
1573     default:
1574       return false;
1575     }
1576   /* Zero unused bits for size.  */
1577   if (n->size < (int)sizeof (HOST_WIDEST_INT))
1578     n->n &= ((unsigned HOST_WIDEST_INT)1 << (n->size * BITS_PER_UNIT)) - 1;
1579   return true;
1580 }
1581 
1582 /* Perform sanity checking for the symbolic number N and the gimple
1583    statement STMT.  */
1584 
1585 static inline bool
1586 verify_symbolic_number_p (struct symbolic_number *n, gimple stmt)
1587 {
1588   tree lhs_type;
1589 
1590   lhs_type = gimple_expr_type (stmt);
1591 
1592   if (TREE_CODE (lhs_type) != INTEGER_TYPE)
1593     return false;
1594 
1595   if (TYPE_PRECISION (lhs_type) != n->size * BITS_PER_UNIT)
1596     return false;
1597 
1598   return true;
1599 }
1600 
1601 /* find_bswap_1 invokes itself recursively with N and tries to perform
1602    the operation given by the rhs of STMT on the result.  If the
1603    operation could successfully be executed the function returns the
1604    tree expression of the source operand and NULL otherwise.  */
1605 
1606 static tree
1607 find_bswap_1 (gimple stmt, struct symbolic_number *n, int limit)
1608 {
1609   enum tree_code code;
1610   tree rhs1, rhs2 = NULL;
1611   gimple rhs1_stmt, rhs2_stmt;
1612   tree source_expr1;
1613   enum gimple_rhs_class rhs_class;
1614 
1615   if (!limit || !is_gimple_assign (stmt))
1616     return NULL_TREE;
1617 
1618   rhs1 = gimple_assign_rhs1 (stmt);
1619 
1620   if (TREE_CODE (rhs1) != SSA_NAME)
1621     return NULL_TREE;
1622 
1623   code = gimple_assign_rhs_code (stmt);
1624   rhs_class = gimple_assign_rhs_class (stmt);
1625   rhs1_stmt = SSA_NAME_DEF_STMT (rhs1);
1626 
1627   if (rhs_class == GIMPLE_BINARY_RHS)
1628     rhs2 = gimple_assign_rhs2 (stmt);
1629 
1630   /* Handle unary rhs and binary rhs with integer constants as second
1631      operand.  */
1632 
1633   if (rhs_class == GIMPLE_UNARY_RHS
1634       || (rhs_class == GIMPLE_BINARY_RHS
1635 	  && TREE_CODE (rhs2) == INTEGER_CST))
1636     {
1637       if (code != BIT_AND_EXPR
1638 	  && code != LSHIFT_EXPR
1639 	  && code != RSHIFT_EXPR
1640 	  && code != LROTATE_EXPR
1641 	  && code != RROTATE_EXPR
1642 	  && code != NOP_EXPR
1643 	  && code != CONVERT_EXPR)
1644 	return NULL_TREE;
1645 
1646       source_expr1 = find_bswap_1 (rhs1_stmt, n, limit - 1);
1647 
1648       /* If find_bswap_1 returned NULL STMT is a leaf node and we have
1649 	 to initialize the symbolic number.  */
1650       if (!source_expr1)
1651 	{
1652 	  /* Set up the symbolic number N by setting each byte to a
1653 	     value between 1 and the byte size of rhs1.  The highest
1654 	     order byte is set to n->size and the lowest order
1655 	     byte to 1.  */
1656 	  n->size = TYPE_PRECISION (TREE_TYPE (rhs1));
1657 	  if (n->size % BITS_PER_UNIT != 0)
1658 	    return NULL_TREE;
1659 	  n->size /= BITS_PER_UNIT;
1660 	  n->n = (sizeof (HOST_WIDEST_INT) < 8 ? 0 :
1661 		  (unsigned HOST_WIDEST_INT)0x08070605 << 32 | 0x04030201);
1662 
1663 	  if (n->size < (int)sizeof (HOST_WIDEST_INT))
1664 	    n->n &= ((unsigned HOST_WIDEST_INT)1 <<
1665 		     (n->size * BITS_PER_UNIT)) - 1;
1666 
1667 	  source_expr1 = rhs1;
1668 	}
1669 
1670       switch (code)
1671 	{
1672 	case BIT_AND_EXPR:
1673 	  {
1674 	    int i;
1675 	    unsigned HOST_WIDEST_INT val = widest_int_cst_value (rhs2);
1676 	    unsigned HOST_WIDEST_INT tmp = val;
1677 
1678 	    /* Only constants masking full bytes are allowed.  */
1679 	    for (i = 0; i < n->size; i++, tmp >>= BITS_PER_UNIT)
1680 	      if ((tmp & 0xff) != 0 && (tmp & 0xff) != 0xff)
1681 		return NULL_TREE;
1682 
1683 	    n->n &= val;
1684 	  }
1685 	  break;
1686 	case LSHIFT_EXPR:
1687 	case RSHIFT_EXPR:
1688 	case LROTATE_EXPR:
1689 	case RROTATE_EXPR:
1690 	  if (!do_shift_rotate (code, n, (int)TREE_INT_CST_LOW (rhs2)))
1691 	    return NULL_TREE;
1692 	  break;
1693 	CASE_CONVERT:
1694 	  {
1695 	    int type_size;
1696 
1697 	    type_size = TYPE_PRECISION (gimple_expr_type (stmt));
1698 	    if (type_size % BITS_PER_UNIT != 0)
1699 	      return NULL_TREE;
1700 
1701 	    if (type_size / BITS_PER_UNIT < (int)(sizeof (HOST_WIDEST_INT)))
1702 	      {
1703 		/* If STMT casts to a smaller type mask out the bits not
1704 		   belonging to the target type.  */
1705 		n->n &= ((unsigned HOST_WIDEST_INT)1 << type_size) - 1;
1706 	      }
1707 	    n->size = type_size / BITS_PER_UNIT;
1708 	  }
1709 	  break;
1710 	default:
1711 	  return NULL_TREE;
1712 	};
1713       return verify_symbolic_number_p (n, stmt) ? source_expr1 : NULL;
1714     }
1715 
1716   /* Handle binary rhs.  */
1717 
1718   if (rhs_class == GIMPLE_BINARY_RHS)
1719     {
1720       struct symbolic_number n1, n2;
1721       tree source_expr2;
1722 
1723       if (code != BIT_IOR_EXPR)
1724 	return NULL_TREE;
1725 
1726       if (TREE_CODE (rhs2) != SSA_NAME)
1727 	return NULL_TREE;
1728 
1729       rhs2_stmt = SSA_NAME_DEF_STMT (rhs2);
1730 
1731       switch (code)
1732 	{
1733 	case BIT_IOR_EXPR:
1734 	  source_expr1 = find_bswap_1 (rhs1_stmt, &n1, limit - 1);
1735 
1736 	  if (!source_expr1)
1737 	    return NULL_TREE;
1738 
1739 	  source_expr2 = find_bswap_1 (rhs2_stmt, &n2, limit - 1);
1740 
1741 	  if (source_expr1 != source_expr2
1742 	      || n1.size != n2.size)
1743 	    return NULL_TREE;
1744 
1745 	  n->size = n1.size;
1746 	  n->n = n1.n | n2.n;
1747 
1748 	  if (!verify_symbolic_number_p (n, stmt))
1749 	    return NULL_TREE;
1750 
1751 	  break;
1752 	default:
1753 	  return NULL_TREE;
1754 	}
1755       return source_expr1;
1756     }
1757   return NULL_TREE;
1758 }
1759 
1760 /* Check if STMT completes a bswap implementation consisting of ORs,
1761    SHIFTs and ANDs.  Return the source tree expression on which the
1762    byte swap is performed and NULL if no bswap was found.  */
1763 
1764 static tree
1765 find_bswap (gimple stmt)
1766 {
1767 /* The number which the find_bswap result should match in order to
1768    have a full byte swap.  The number is shifted to the left according
1769    to the size of the symbolic number before using it.  */
1770   unsigned HOST_WIDEST_INT cmp =
1771     sizeof (HOST_WIDEST_INT) < 8 ? 0 :
1772     (unsigned HOST_WIDEST_INT)0x01020304 << 32 | 0x05060708;
1773 
1774   struct symbolic_number n;
1775   tree source_expr;
1776   int limit;
1777 
1778   /* The last parameter determines the depth search limit.  It usually
1779      correlates directly to the number of bytes to be touched.  We
1780      increase that number by three  here in order to also
1781      cover signed -> unsigned converions of the src operand as can be seen
1782      in libgcc, and for initial shift/and operation of the src operand.  */
1783   limit = TREE_INT_CST_LOW (TYPE_SIZE_UNIT (gimple_expr_type (stmt)));
1784   limit += 1 + (int) ceil_log2 ((unsigned HOST_WIDE_INT) limit);
1785   source_expr =  find_bswap_1 (stmt, &n, limit);
1786 
1787   if (!source_expr)
1788     return NULL_TREE;
1789 
1790   /* Zero out the extra bits of N and CMP.  */
1791   if (n.size < (int)sizeof (HOST_WIDEST_INT))
1792     {
1793       unsigned HOST_WIDEST_INT mask =
1794 	((unsigned HOST_WIDEST_INT)1 << (n.size * BITS_PER_UNIT)) - 1;
1795 
1796       n.n &= mask;
1797       cmp >>= (sizeof (HOST_WIDEST_INT) - n.size) * BITS_PER_UNIT;
1798     }
1799 
1800   /* A complete byte swap should make the symbolic number to start
1801      with the largest digit in the highest order byte.  */
1802   if (cmp != n.n)
1803     return NULL_TREE;
1804 
1805   return source_expr;
1806 }
1807 
1808 /* Find manual byte swap implementations and turn them into a bswap
1809    builtin invokation.  */
1810 
1811 static unsigned int
1812 execute_optimize_bswap (void)
1813 {
1814   basic_block bb;
1815   bool bswap32_p, bswap64_p;
1816   bool changed = false;
1817   tree bswap32_type = NULL_TREE, bswap64_type = NULL_TREE;
1818 
1819   if (BITS_PER_UNIT != 8)
1820     return 0;
1821 
1822   if (sizeof (HOST_WIDEST_INT) < 8)
1823     return 0;
1824 
1825   bswap32_p = (builtin_decl_explicit_p (BUILT_IN_BSWAP32)
1826 	       && optab_handler (bswap_optab, SImode) != CODE_FOR_nothing);
1827   bswap64_p = (builtin_decl_explicit_p (BUILT_IN_BSWAP64)
1828 	       && (optab_handler (bswap_optab, DImode) != CODE_FOR_nothing
1829 		   || (bswap32_p && word_mode == SImode)));
1830 
1831   if (!bswap32_p && !bswap64_p)
1832     return 0;
1833 
1834   /* Determine the argument type of the builtins.  The code later on
1835      assumes that the return and argument type are the same.  */
1836   if (bswap32_p)
1837     {
1838       tree fndecl = builtin_decl_explicit (BUILT_IN_BSWAP32);
1839       bswap32_type = TREE_VALUE (TYPE_ARG_TYPES (TREE_TYPE (fndecl)));
1840     }
1841 
1842   if (bswap64_p)
1843     {
1844       tree fndecl = builtin_decl_explicit (BUILT_IN_BSWAP64);
1845       bswap64_type = TREE_VALUE (TYPE_ARG_TYPES (TREE_TYPE (fndecl)));
1846     }
1847 
1848   memset (&bswap_stats, 0, sizeof (bswap_stats));
1849 
1850   FOR_EACH_BB (bb)
1851     {
1852       gimple_stmt_iterator gsi;
1853 
1854       /* We do a reverse scan for bswap patterns to make sure we get the
1855 	 widest match. As bswap pattern matching doesn't handle
1856 	 previously inserted smaller bswap replacements as sub-
1857 	 patterns, the wider variant wouldn't be detected.  */
1858       for (gsi = gsi_last_bb (bb); !gsi_end_p (gsi); gsi_prev (&gsi))
1859         {
1860 	  gimple stmt = gsi_stmt (gsi);
1861 	  tree bswap_src, bswap_type;
1862 	  tree bswap_tmp;
1863 	  tree fndecl = NULL_TREE;
1864 	  int type_size;
1865 	  gimple call;
1866 
1867 	  if (!is_gimple_assign (stmt)
1868 	      || gimple_assign_rhs_code (stmt) != BIT_IOR_EXPR)
1869 	    continue;
1870 
1871 	  type_size = TYPE_PRECISION (gimple_expr_type (stmt));
1872 
1873 	  switch (type_size)
1874 	    {
1875 	    case 32:
1876 	      if (bswap32_p)
1877 		{
1878 		  fndecl = builtin_decl_explicit (BUILT_IN_BSWAP32);
1879 		  bswap_type = bswap32_type;
1880 		}
1881 	      break;
1882 	    case 64:
1883 	      if (bswap64_p)
1884 		{
1885 		  fndecl = builtin_decl_explicit (BUILT_IN_BSWAP64);
1886 		  bswap_type = bswap64_type;
1887 		}
1888 	      break;
1889 	    default:
1890 	      continue;
1891 	    }
1892 
1893 	  if (!fndecl)
1894 	    continue;
1895 
1896 	  bswap_src = find_bswap (stmt);
1897 
1898 	  if (!bswap_src)
1899 	    continue;
1900 
1901 	  changed = true;
1902 	  if (type_size == 32)
1903 	    bswap_stats.found_32bit++;
1904 	  else
1905 	    bswap_stats.found_64bit++;
1906 
1907 	  bswap_tmp = bswap_src;
1908 
1909 	  /* Convert the src expression if necessary.  */
1910 	  if (!useless_type_conversion_p (TREE_TYPE (bswap_tmp), bswap_type))
1911 	    {
1912 	      gimple convert_stmt;
1913 
1914 	      bswap_tmp = create_tmp_var (bswap_type, "bswapsrc");
1915 	      add_referenced_var (bswap_tmp);
1916 	      bswap_tmp = make_ssa_name (bswap_tmp, NULL);
1917 
1918 	      convert_stmt = gimple_build_assign_with_ops (
1919 			       CONVERT_EXPR, bswap_tmp, bswap_src, NULL);
1920 	      gsi_insert_before (&gsi, convert_stmt, GSI_SAME_STMT);
1921 	    }
1922 
1923 	  call = gimple_build_call (fndecl, 1, bswap_tmp);
1924 
1925 	  bswap_tmp = gimple_assign_lhs (stmt);
1926 
1927 	  /* Convert the result if necessary.  */
1928 	  if (!useless_type_conversion_p (TREE_TYPE (bswap_tmp), bswap_type))
1929 	    {
1930 	      gimple convert_stmt;
1931 
1932 	      bswap_tmp = create_tmp_var (bswap_type, "bswapdst");
1933 	      add_referenced_var (bswap_tmp);
1934 	      bswap_tmp = make_ssa_name (bswap_tmp, NULL);
1935 	      convert_stmt = gimple_build_assign_with_ops (
1936 		               CONVERT_EXPR, gimple_assign_lhs (stmt), bswap_tmp, NULL);
1937 	      gsi_insert_after (&gsi, convert_stmt, GSI_SAME_STMT);
1938 	    }
1939 
1940 	  gimple_call_set_lhs (call, bswap_tmp);
1941 
1942 	  if (dump_file)
1943 	    {
1944 	      fprintf (dump_file, "%d bit bswap implementation found at: ",
1945 		       (int)type_size);
1946 	      print_gimple_stmt (dump_file, stmt, 0, 0);
1947 	    }
1948 
1949 	  gsi_insert_after (&gsi, call, GSI_SAME_STMT);
1950 	  gsi_remove (&gsi, true);
1951 	}
1952     }
1953 
1954   statistics_counter_event (cfun, "32-bit bswap implementations found",
1955 			    bswap_stats.found_32bit);
1956   statistics_counter_event (cfun, "64-bit bswap implementations found",
1957 			    bswap_stats.found_64bit);
1958 
1959   return (changed ? TODO_update_ssa | TODO_verify_ssa
1960 	  | TODO_verify_stmts : 0);
1961 }
1962 
1963 static bool
1964 gate_optimize_bswap (void)
1965 {
1966   return flag_expensive_optimizations && optimize;
1967 }
1968 
1969 struct gimple_opt_pass pass_optimize_bswap =
1970 {
1971  {
1972   GIMPLE_PASS,
1973   "bswap",				/* name */
1974   gate_optimize_bswap,                  /* gate */
1975   execute_optimize_bswap,		/* execute */
1976   NULL,					/* sub */
1977   NULL,					/* next */
1978   0,					/* static_pass_number */
1979   TV_NONE,				/* tv_id */
1980   PROP_ssa,				/* properties_required */
1981   0,					/* properties_provided */
1982   0,					/* properties_destroyed */
1983   0,					/* todo_flags_start */
1984   0                                     /* todo_flags_finish */
1985  }
1986 };
1987 
1988 /* Return true if RHS is a suitable operand for a widening multiplication,
1989    assuming a target type of TYPE.
1990    There are two cases:
1991 
1992      - RHS makes some value at least twice as wide.  Store that value
1993        in *NEW_RHS_OUT if so, and store its type in *TYPE_OUT.
1994 
1995      - RHS is an integer constant.  Store that value in *NEW_RHS_OUT if so,
1996        but leave *TYPE_OUT untouched.  */
1997 
1998 static bool
1999 is_widening_mult_rhs_p (tree type, tree rhs, tree *type_out,
2000 			tree *new_rhs_out)
2001 {
2002   gimple stmt;
2003   tree type1, rhs1;
2004   enum tree_code rhs_code;
2005 
2006   if (TREE_CODE (rhs) == SSA_NAME)
2007     {
2008       stmt = SSA_NAME_DEF_STMT (rhs);
2009       if (is_gimple_assign (stmt))
2010 	{
2011 	  rhs_code = gimple_assign_rhs_code (stmt);
2012 	  if (TREE_CODE (type) == INTEGER_TYPE
2013 	      ? !CONVERT_EXPR_CODE_P (rhs_code)
2014 	      : rhs_code != FIXED_CONVERT_EXPR)
2015 	    rhs1 = rhs;
2016 	  else
2017 	    {
2018 	      rhs1 = gimple_assign_rhs1 (stmt);
2019 
2020 	      if (TREE_CODE (rhs1) == INTEGER_CST)
2021 		{
2022 		  *new_rhs_out = rhs1;
2023 		  *type_out = NULL;
2024 		  return true;
2025 		}
2026 	    }
2027 	}
2028       else
2029 	rhs1 = rhs;
2030 
2031       type1 = TREE_TYPE (rhs1);
2032 
2033       if (TREE_CODE (type1) != TREE_CODE (type)
2034 	  || TYPE_PRECISION (type1) * 2 > TYPE_PRECISION (type))
2035 	return false;
2036 
2037       *new_rhs_out = rhs1;
2038       *type_out = type1;
2039       return true;
2040     }
2041 
2042   if (TREE_CODE (rhs) == INTEGER_CST)
2043     {
2044       *new_rhs_out = rhs;
2045       *type_out = NULL;
2046       return true;
2047     }
2048 
2049   return false;
2050 }
2051 
2052 /* Return true if STMT performs a widening multiplication, assuming the
2053    output type is TYPE.  If so, store the unwidened types of the operands
2054    in *TYPE1_OUT and *TYPE2_OUT respectively.  Also fill *RHS1_OUT and
2055    *RHS2_OUT such that converting those operands to types *TYPE1_OUT
2056    and *TYPE2_OUT would give the operands of the multiplication.  */
2057 
2058 static bool
2059 is_widening_mult_p (gimple stmt,
2060 		    tree *type1_out, tree *rhs1_out,
2061 		    tree *type2_out, tree *rhs2_out)
2062 {
2063   tree type = TREE_TYPE (gimple_assign_lhs (stmt));
2064 
2065   if (TREE_CODE (type) != INTEGER_TYPE
2066       && TREE_CODE (type) != FIXED_POINT_TYPE)
2067     return false;
2068 
2069   if (!is_widening_mult_rhs_p (type, gimple_assign_rhs1 (stmt), type1_out,
2070 			       rhs1_out))
2071     return false;
2072 
2073   if (!is_widening_mult_rhs_p (type, gimple_assign_rhs2 (stmt), type2_out,
2074 			       rhs2_out))
2075     return false;
2076 
2077   if (*type1_out == NULL)
2078     {
2079       if (*type2_out == NULL || !int_fits_type_p (*rhs1_out, *type2_out))
2080 	return false;
2081       *type1_out = *type2_out;
2082     }
2083 
2084   if (*type2_out == NULL)
2085     {
2086       if (!int_fits_type_p (*rhs2_out, *type1_out))
2087 	return false;
2088       *type2_out = *type1_out;
2089     }
2090 
2091   /* Ensure that the larger of the two operands comes first. */
2092   if (TYPE_PRECISION (*type1_out) < TYPE_PRECISION (*type2_out))
2093     {
2094       tree tmp;
2095       tmp = *type1_out;
2096       *type1_out = *type2_out;
2097       *type2_out = tmp;
2098       tmp = *rhs1_out;
2099       *rhs1_out = *rhs2_out;
2100       *rhs2_out = tmp;
2101     }
2102 
2103   return true;
2104 }
2105 
2106 /* Process a single gimple statement STMT, which has a MULT_EXPR as
2107    its rhs, and try to convert it into a WIDEN_MULT_EXPR.  The return
2108    value is true iff we converted the statement.  */
2109 
2110 static bool
2111 convert_mult_to_widen (gimple stmt, gimple_stmt_iterator *gsi)
2112 {
2113   tree lhs, rhs1, rhs2, type, type1, type2, tmp = NULL;
2114   enum insn_code handler;
2115   enum machine_mode to_mode, from_mode, actual_mode;
2116   optab op;
2117   int actual_precision;
2118   location_t loc = gimple_location (stmt);
2119   bool from_unsigned1, from_unsigned2;
2120 
2121   lhs = gimple_assign_lhs (stmt);
2122   type = TREE_TYPE (lhs);
2123   if (TREE_CODE (type) != INTEGER_TYPE)
2124     return false;
2125 
2126   if (!is_widening_mult_p (stmt, &type1, &rhs1, &type2, &rhs2))
2127     return false;
2128 
2129   to_mode = TYPE_MODE (type);
2130   from_mode = TYPE_MODE (type1);
2131   from_unsigned1 = TYPE_UNSIGNED (type1);
2132   from_unsigned2 = TYPE_UNSIGNED (type2);
2133 
2134   if (from_unsigned1 && from_unsigned2)
2135     op = umul_widen_optab;
2136   else if (!from_unsigned1 && !from_unsigned2)
2137     op = smul_widen_optab;
2138   else
2139     op = usmul_widen_optab;
2140 
2141   handler = find_widening_optab_handler_and_mode (op, to_mode, from_mode,
2142 						  0, &actual_mode);
2143 
2144   if (handler == CODE_FOR_nothing)
2145     {
2146       if (op != smul_widen_optab)
2147 	{
2148 	  /* We can use a signed multiply with unsigned types as long as
2149 	     there is a wider mode to use, or it is the smaller of the two
2150 	     types that is unsigned.  Note that type1 >= type2, always.  */
2151 	  if ((TYPE_UNSIGNED (type1)
2152 	       && TYPE_PRECISION (type1) == GET_MODE_PRECISION (from_mode))
2153 	      || (TYPE_UNSIGNED (type2)
2154 		  && TYPE_PRECISION (type2) == GET_MODE_PRECISION (from_mode)))
2155 	    {
2156 	      from_mode = GET_MODE_WIDER_MODE (from_mode);
2157 	      if (GET_MODE_SIZE (to_mode) <= GET_MODE_SIZE (from_mode))
2158 		return false;
2159 	    }
2160 
2161 	  op = smul_widen_optab;
2162 	  handler = find_widening_optab_handler_and_mode (op, to_mode,
2163 							  from_mode, 0,
2164 							  &actual_mode);
2165 
2166 	  if (handler == CODE_FOR_nothing)
2167 	    return false;
2168 
2169 	  from_unsigned1 = from_unsigned2 = false;
2170 	}
2171       else
2172 	return false;
2173     }
2174 
2175   /* Ensure that the inputs to the handler are in the correct precison
2176      for the opcode.  This will be the full mode size.  */
2177   actual_precision = GET_MODE_PRECISION (actual_mode);
2178   if (actual_precision != TYPE_PRECISION (type1)
2179       || from_unsigned1 != TYPE_UNSIGNED (type1))
2180     {
2181       tmp = create_tmp_var (build_nonstandard_integer_type
2182 				(actual_precision, from_unsigned1),
2183 			    NULL);
2184       rhs1 = build_and_insert_cast (gsi, loc, tmp, rhs1);
2185     }
2186   if (actual_precision != TYPE_PRECISION (type2)
2187       || from_unsigned2 != TYPE_UNSIGNED (type2))
2188     {
2189       /* Reuse the same type info, if possible.  */
2190       if (!tmp || from_unsigned1 != from_unsigned2)
2191 	tmp = create_tmp_var (build_nonstandard_integer_type
2192 				(actual_precision, from_unsigned2),
2193 			      NULL);
2194       rhs2 = build_and_insert_cast (gsi, loc, tmp, rhs2);
2195     }
2196 
2197   /* Handle constants.  */
2198   if (TREE_CODE (rhs1) == INTEGER_CST)
2199     rhs1 = fold_convert (type1, rhs1);
2200   if (TREE_CODE (rhs2) == INTEGER_CST)
2201     rhs2 = fold_convert (type2, rhs2);
2202 
2203   gimple_assign_set_rhs1 (stmt, rhs1);
2204   gimple_assign_set_rhs2 (stmt, rhs2);
2205   gimple_assign_set_rhs_code (stmt, WIDEN_MULT_EXPR);
2206   update_stmt (stmt);
2207   widen_mul_stats.widen_mults_inserted++;
2208   return true;
2209 }
2210 
2211 /* Process a single gimple statement STMT, which is found at the
2212    iterator GSI and has a either a PLUS_EXPR or a MINUS_EXPR as its
2213    rhs (given by CODE), and try to convert it into a
2214    WIDEN_MULT_PLUS_EXPR or a WIDEN_MULT_MINUS_EXPR.  The return value
2215    is true iff we converted the statement.  */
2216 
2217 static bool
2218 convert_plusminus_to_widen (gimple_stmt_iterator *gsi, gimple stmt,
2219 			    enum tree_code code)
2220 {
2221   gimple rhs1_stmt = NULL, rhs2_stmt = NULL;
2222   gimple conv1_stmt = NULL, conv2_stmt = NULL, conv_stmt;
2223   tree type, type1, type2, optype, tmp = NULL;
2224   tree lhs, rhs1, rhs2, mult_rhs1, mult_rhs2, add_rhs;
2225   enum tree_code rhs1_code = ERROR_MARK, rhs2_code = ERROR_MARK;
2226   optab this_optab;
2227   enum tree_code wmult_code;
2228   enum insn_code handler;
2229   enum machine_mode to_mode, from_mode, actual_mode;
2230   location_t loc = gimple_location (stmt);
2231   int actual_precision;
2232   bool from_unsigned1, from_unsigned2;
2233 
2234   lhs = gimple_assign_lhs (stmt);
2235   type = TREE_TYPE (lhs);
2236   if (TREE_CODE (type) != INTEGER_TYPE
2237       && TREE_CODE (type) != FIXED_POINT_TYPE)
2238     return false;
2239 
2240   if (code == MINUS_EXPR)
2241     wmult_code = WIDEN_MULT_MINUS_EXPR;
2242   else
2243     wmult_code = WIDEN_MULT_PLUS_EXPR;
2244 
2245   rhs1 = gimple_assign_rhs1 (stmt);
2246   rhs2 = gimple_assign_rhs2 (stmt);
2247 
2248   if (TREE_CODE (rhs1) == SSA_NAME)
2249     {
2250       rhs1_stmt = SSA_NAME_DEF_STMT (rhs1);
2251       if (is_gimple_assign (rhs1_stmt))
2252 	rhs1_code = gimple_assign_rhs_code (rhs1_stmt);
2253     }
2254 
2255   if (TREE_CODE (rhs2) == SSA_NAME)
2256     {
2257       rhs2_stmt = SSA_NAME_DEF_STMT (rhs2);
2258       if (is_gimple_assign (rhs2_stmt))
2259 	rhs2_code = gimple_assign_rhs_code (rhs2_stmt);
2260     }
2261 
2262   /* Allow for one conversion statement between the multiply
2263      and addition/subtraction statement.  If there are more than
2264      one conversions then we assume they would invalidate this
2265      transformation.  If that's not the case then they should have
2266      been folded before now.  */
2267   if (CONVERT_EXPR_CODE_P (rhs1_code))
2268     {
2269       conv1_stmt = rhs1_stmt;
2270       rhs1 = gimple_assign_rhs1 (rhs1_stmt);
2271       if (TREE_CODE (rhs1) == SSA_NAME)
2272 	{
2273 	  rhs1_stmt = SSA_NAME_DEF_STMT (rhs1);
2274 	  if (is_gimple_assign (rhs1_stmt))
2275 	    rhs1_code = gimple_assign_rhs_code (rhs1_stmt);
2276 	}
2277       else
2278 	return false;
2279     }
2280   if (CONVERT_EXPR_CODE_P (rhs2_code))
2281     {
2282       conv2_stmt = rhs2_stmt;
2283       rhs2 = gimple_assign_rhs1 (rhs2_stmt);
2284       if (TREE_CODE (rhs2) == SSA_NAME)
2285 	{
2286 	  rhs2_stmt = SSA_NAME_DEF_STMT (rhs2);
2287 	  if (is_gimple_assign (rhs2_stmt))
2288 	    rhs2_code = gimple_assign_rhs_code (rhs2_stmt);
2289 	}
2290       else
2291 	return false;
2292     }
2293 
2294   /* If code is WIDEN_MULT_EXPR then it would seem unnecessary to call
2295      is_widening_mult_p, but we still need the rhs returns.
2296 
2297      It might also appear that it would be sufficient to use the existing
2298      operands of the widening multiply, but that would limit the choice of
2299      multiply-and-accumulate instructions.  */
2300   if (code == PLUS_EXPR
2301       && (rhs1_code == MULT_EXPR || rhs1_code == WIDEN_MULT_EXPR))
2302     {
2303       if (!is_widening_mult_p (rhs1_stmt, &type1, &mult_rhs1,
2304 			       &type2, &mult_rhs2))
2305 	return false;
2306       add_rhs = rhs2;
2307       conv_stmt = conv1_stmt;
2308     }
2309   else if (rhs2_code == MULT_EXPR || rhs2_code == WIDEN_MULT_EXPR)
2310     {
2311       if (!is_widening_mult_p (rhs2_stmt, &type1, &mult_rhs1,
2312 			       &type2, &mult_rhs2))
2313 	return false;
2314       add_rhs = rhs1;
2315       conv_stmt = conv2_stmt;
2316     }
2317   else
2318     return false;
2319 
2320   to_mode = TYPE_MODE (type);
2321   from_mode = TYPE_MODE (type1);
2322   from_unsigned1 = TYPE_UNSIGNED (type1);
2323   from_unsigned2 = TYPE_UNSIGNED (type2);
2324   optype = type1;
2325 
2326   /* There's no such thing as a mixed sign madd yet, so use a wider mode.  */
2327   if (from_unsigned1 != from_unsigned2)
2328     {
2329       if (!INTEGRAL_TYPE_P (type))
2330 	return false;
2331       /* We can use a signed multiply with unsigned types as long as
2332 	 there is a wider mode to use, or it is the smaller of the two
2333 	 types that is unsigned.  Note that type1 >= type2, always.  */
2334       if ((from_unsigned1
2335 	   && TYPE_PRECISION (type1) == GET_MODE_PRECISION (from_mode))
2336 	  || (from_unsigned2
2337 	      && TYPE_PRECISION (type2) == GET_MODE_PRECISION (from_mode)))
2338 	{
2339 	  from_mode = GET_MODE_WIDER_MODE (from_mode);
2340 	  if (GET_MODE_SIZE (from_mode) >= GET_MODE_SIZE (to_mode))
2341 	    return false;
2342 	}
2343 
2344       from_unsigned1 = from_unsigned2 = false;
2345       optype = build_nonstandard_integer_type (GET_MODE_PRECISION (from_mode),
2346 					       false);
2347     }
2348 
2349   /* If there was a conversion between the multiply and addition
2350      then we need to make sure it fits a multiply-and-accumulate.
2351      The should be a single mode change which does not change the
2352      value.  */
2353   if (conv_stmt)
2354     {
2355       /* We use the original, unmodified data types for this.  */
2356       tree from_type = TREE_TYPE (gimple_assign_rhs1 (conv_stmt));
2357       tree to_type = TREE_TYPE (gimple_assign_lhs (conv_stmt));
2358       int data_size = TYPE_PRECISION (type1) + TYPE_PRECISION (type2);
2359       bool is_unsigned = TYPE_UNSIGNED (type1) && TYPE_UNSIGNED (type2);
2360 
2361       if (TYPE_PRECISION (from_type) > TYPE_PRECISION (to_type))
2362 	{
2363 	  /* Conversion is a truncate.  */
2364 	  if (TYPE_PRECISION (to_type) < data_size)
2365 	    return false;
2366 	}
2367       else if (TYPE_PRECISION (from_type) < TYPE_PRECISION (to_type))
2368 	{
2369 	  /* Conversion is an extend.  Check it's the right sort.  */
2370 	  if (TYPE_UNSIGNED (from_type) != is_unsigned
2371 	      && !(is_unsigned && TYPE_PRECISION (from_type) > data_size))
2372 	    return false;
2373 	}
2374       /* else convert is a no-op for our purposes.  */
2375     }
2376 
2377   /* Verify that the machine can perform a widening multiply
2378      accumulate in this mode/signedness combination, otherwise
2379      this transformation is likely to pessimize code.  */
2380   this_optab = optab_for_tree_code (wmult_code, optype, optab_default);
2381   handler = find_widening_optab_handler_and_mode (this_optab, to_mode,
2382 						  from_mode, 0, &actual_mode);
2383 
2384   if (handler == CODE_FOR_nothing)
2385     return false;
2386 
2387   /* Ensure that the inputs to the handler are in the correct precison
2388      for the opcode.  This will be the full mode size.  */
2389   actual_precision = GET_MODE_PRECISION (actual_mode);
2390   if (actual_precision != TYPE_PRECISION (type1)
2391       || from_unsigned1 != TYPE_UNSIGNED (type1))
2392     {
2393       tmp = create_tmp_var (build_nonstandard_integer_type
2394 				(actual_precision, from_unsigned1),
2395 			    NULL);
2396       mult_rhs1 = build_and_insert_cast (gsi, loc, tmp, mult_rhs1);
2397     }
2398   if (actual_precision != TYPE_PRECISION (type2)
2399       || from_unsigned2 != TYPE_UNSIGNED (type2))
2400     {
2401       if (!tmp || from_unsigned1 != from_unsigned2)
2402 	tmp = create_tmp_var (build_nonstandard_integer_type
2403 				(actual_precision, from_unsigned2),
2404 			      NULL);
2405       mult_rhs2 = build_and_insert_cast (gsi, loc, tmp, mult_rhs2);
2406     }
2407 
2408   if (!useless_type_conversion_p (type, TREE_TYPE (add_rhs)))
2409     add_rhs = build_and_insert_cast (gsi, loc, create_tmp_var (type, NULL),
2410 				     add_rhs);
2411 
2412   /* Handle constants.  */
2413   if (TREE_CODE (mult_rhs1) == INTEGER_CST)
2414     mult_rhs1 = fold_convert (type1, mult_rhs1);
2415   if (TREE_CODE (mult_rhs2) == INTEGER_CST)
2416     mult_rhs2 = fold_convert (type2, mult_rhs2);
2417 
2418   gimple_assign_set_rhs_with_ops_1 (gsi, wmult_code, mult_rhs1, mult_rhs2,
2419 				    add_rhs);
2420   update_stmt (gsi_stmt (*gsi));
2421   widen_mul_stats.maccs_inserted++;
2422   return true;
2423 }
2424 
2425 /* Combine the multiplication at MUL_STMT with operands MULOP1 and MULOP2
2426    with uses in additions and subtractions to form fused multiply-add
2427    operations.  Returns true if successful and MUL_STMT should be removed.  */
2428 
2429 static bool
2430 convert_mult_to_fma (gimple mul_stmt, tree op1, tree op2)
2431 {
2432   tree mul_result = gimple_get_lhs (mul_stmt);
2433   tree type = TREE_TYPE (mul_result);
2434   gimple use_stmt, neguse_stmt, fma_stmt;
2435   use_operand_p use_p;
2436   imm_use_iterator imm_iter;
2437 
2438   if (FLOAT_TYPE_P (type)
2439       && flag_fp_contract_mode == FP_CONTRACT_OFF)
2440     return false;
2441 
2442   /* We don't want to do bitfield reduction ops.  */
2443   if (INTEGRAL_TYPE_P (type)
2444       && (TYPE_PRECISION (type)
2445 	  != GET_MODE_PRECISION (TYPE_MODE (type))))
2446     return false;
2447 
2448   /* If the target doesn't support it, don't generate it.  We assume that
2449      if fma isn't available then fms, fnma or fnms are not either.  */
2450   if (optab_handler (fma_optab, TYPE_MODE (type)) == CODE_FOR_nothing)
2451     return false;
2452 
2453   /* If the multiplication has zero uses, it is kept around probably because
2454      of -fnon-call-exceptions.  Don't optimize it away in that case,
2455      it is DCE job.  */
2456   if (has_zero_uses (mul_result))
2457     return false;
2458 
2459   /* Make sure that the multiplication statement becomes dead after
2460      the transformation, thus that all uses are transformed to FMAs.
2461      This means we assume that an FMA operation has the same cost
2462      as an addition.  */
2463   FOR_EACH_IMM_USE_FAST (use_p, imm_iter, mul_result)
2464     {
2465       enum tree_code use_code;
2466       tree result = mul_result;
2467       bool negate_p = false;
2468 
2469       use_stmt = USE_STMT (use_p);
2470 
2471       if (is_gimple_debug (use_stmt))
2472 	continue;
2473 
2474       /* For now restrict this operations to single basic blocks.  In theory
2475 	 we would want to support sinking the multiplication in
2476 	 m = a*b;
2477 	 if ()
2478 	   ma = m + c;
2479 	 else
2480 	   d = m;
2481 	 to form a fma in the then block and sink the multiplication to the
2482 	 else block.  */
2483       if (gimple_bb (use_stmt) != gimple_bb (mul_stmt))
2484 	return false;
2485 
2486       if (!is_gimple_assign (use_stmt))
2487 	return false;
2488 
2489       use_code = gimple_assign_rhs_code (use_stmt);
2490 
2491       /* A negate on the multiplication leads to FNMA.  */
2492       if (use_code == NEGATE_EXPR)
2493 	{
2494 	  ssa_op_iter iter;
2495 	  use_operand_p usep;
2496 
2497 	  result = gimple_assign_lhs (use_stmt);
2498 
2499 	  /* Make sure the negate statement becomes dead with this
2500 	     single transformation.  */
2501 	  if (!single_imm_use (gimple_assign_lhs (use_stmt),
2502 			       &use_p, &neguse_stmt))
2503 	    return false;
2504 
2505 	  /* Make sure the multiplication isn't also used on that stmt.  */
2506 	  FOR_EACH_PHI_OR_STMT_USE (usep, neguse_stmt, iter, SSA_OP_USE)
2507 	    if (USE_FROM_PTR (usep) == mul_result)
2508 	      return false;
2509 
2510 	  /* Re-validate.  */
2511 	  use_stmt = neguse_stmt;
2512 	  if (gimple_bb (use_stmt) != gimple_bb (mul_stmt))
2513 	    return false;
2514 	  if (!is_gimple_assign (use_stmt))
2515 	    return false;
2516 
2517 	  use_code = gimple_assign_rhs_code (use_stmt);
2518 	  negate_p = true;
2519 	}
2520 
2521       switch (use_code)
2522 	{
2523 	case MINUS_EXPR:
2524 	  if (gimple_assign_rhs2 (use_stmt) == result)
2525 	    negate_p = !negate_p;
2526 	  break;
2527 	case PLUS_EXPR:
2528 	  break;
2529 	default:
2530 	  /* FMA can only be formed from PLUS and MINUS.  */
2531 	  return false;
2532 	}
2533 
2534       /* We can't handle a * b + a * b.  */
2535       if (gimple_assign_rhs1 (use_stmt) == gimple_assign_rhs2 (use_stmt))
2536 	return false;
2537 
2538       /* While it is possible to validate whether or not the exact form
2539 	 that we've recognized is available in the backend, the assumption
2540 	 is that the transformation is never a loss.  For instance, suppose
2541 	 the target only has the plain FMA pattern available.  Consider
2542 	 a*b-c -> fma(a,b,-c): we've exchanged MUL+SUB for FMA+NEG, which
2543 	 is still two operations.  Consider -(a*b)-c -> fma(-a,b,-c): we
2544 	 still have 3 operations, but in the FMA form the two NEGs are
2545 	 independant and could be run in parallel.  */
2546     }
2547 
2548   FOR_EACH_IMM_USE_STMT (use_stmt, imm_iter, mul_result)
2549     {
2550       gimple_stmt_iterator gsi = gsi_for_stmt (use_stmt);
2551       enum tree_code use_code;
2552       tree addop, mulop1 = op1, result = mul_result;
2553       bool negate_p = false;
2554 
2555       if (is_gimple_debug (use_stmt))
2556 	continue;
2557 
2558       use_code = gimple_assign_rhs_code (use_stmt);
2559       if (use_code == NEGATE_EXPR)
2560 	{
2561 	  result = gimple_assign_lhs (use_stmt);
2562 	  single_imm_use (gimple_assign_lhs (use_stmt), &use_p, &neguse_stmt);
2563 	  gsi_remove (&gsi, true);
2564 	  release_defs (use_stmt);
2565 
2566 	  use_stmt = neguse_stmt;
2567 	  gsi = gsi_for_stmt (use_stmt);
2568 	  use_code = gimple_assign_rhs_code (use_stmt);
2569 	  negate_p = true;
2570 	}
2571 
2572       if (gimple_assign_rhs1 (use_stmt) == result)
2573 	{
2574 	  addop = gimple_assign_rhs2 (use_stmt);
2575 	  /* a * b - c -> a * b + (-c)  */
2576 	  if (gimple_assign_rhs_code (use_stmt) == MINUS_EXPR)
2577 	    addop = force_gimple_operand_gsi (&gsi,
2578 					      build1 (NEGATE_EXPR,
2579 						      type, addop),
2580 					      true, NULL_TREE, true,
2581 					      GSI_SAME_STMT);
2582 	}
2583       else
2584 	{
2585 	  addop = gimple_assign_rhs1 (use_stmt);
2586 	  /* a - b * c -> (-b) * c + a */
2587 	  if (gimple_assign_rhs_code (use_stmt) == MINUS_EXPR)
2588 	    negate_p = !negate_p;
2589 	}
2590 
2591       if (negate_p)
2592 	mulop1 = force_gimple_operand_gsi (&gsi,
2593 					   build1 (NEGATE_EXPR,
2594 						   type, mulop1),
2595 					   true, NULL_TREE, true,
2596 					   GSI_SAME_STMT);
2597 
2598       fma_stmt = gimple_build_assign_with_ops3 (FMA_EXPR,
2599 						gimple_assign_lhs (use_stmt),
2600 						mulop1, op2,
2601 						addop);
2602       gsi_replace (&gsi, fma_stmt, true);
2603       widen_mul_stats.fmas_inserted++;
2604     }
2605 
2606   return true;
2607 }
2608 
2609 /* Find integer multiplications where the operands are extended from
2610    smaller types, and replace the MULT_EXPR with a WIDEN_MULT_EXPR
2611    where appropriate.  */
2612 
2613 static unsigned int
2614 execute_optimize_widening_mul (void)
2615 {
2616   basic_block bb;
2617   bool cfg_changed = false;
2618 
2619   memset (&widen_mul_stats, 0, sizeof (widen_mul_stats));
2620 
2621   FOR_EACH_BB (bb)
2622     {
2623       gimple_stmt_iterator gsi;
2624 
2625       for (gsi = gsi_after_labels (bb); !gsi_end_p (gsi);)
2626         {
2627 	  gimple stmt = gsi_stmt (gsi);
2628 	  enum tree_code code;
2629 
2630 	  if (is_gimple_assign (stmt))
2631 	    {
2632 	      code = gimple_assign_rhs_code (stmt);
2633 	      switch (code)
2634 		{
2635 		case MULT_EXPR:
2636 		  if (!convert_mult_to_widen (stmt, &gsi)
2637 		      && convert_mult_to_fma (stmt,
2638 					      gimple_assign_rhs1 (stmt),
2639 					      gimple_assign_rhs2 (stmt)))
2640 		    {
2641 		      gsi_remove (&gsi, true);
2642 		      release_defs (stmt);
2643 		      continue;
2644 		    }
2645 		  break;
2646 
2647 		case PLUS_EXPR:
2648 		case MINUS_EXPR:
2649 		  convert_plusminus_to_widen (&gsi, stmt, code);
2650 		  break;
2651 
2652 		default:;
2653 		}
2654 	    }
2655 	  else if (is_gimple_call (stmt)
2656 		   && gimple_call_lhs (stmt))
2657 	    {
2658 	      tree fndecl = gimple_call_fndecl (stmt);
2659 	      if (fndecl
2660 		  && DECL_BUILT_IN_CLASS (fndecl) == BUILT_IN_NORMAL)
2661 		{
2662 		  switch (DECL_FUNCTION_CODE (fndecl))
2663 		    {
2664 		      case BUILT_IN_POWF:
2665 		      case BUILT_IN_POW:
2666 		      case BUILT_IN_POWL:
2667 			if (TREE_CODE (gimple_call_arg (stmt, 1)) == REAL_CST
2668 			    && REAL_VALUES_EQUAL
2669 			         (TREE_REAL_CST (gimple_call_arg (stmt, 1)),
2670 				  dconst2)
2671 			    && convert_mult_to_fma (stmt,
2672 						    gimple_call_arg (stmt, 0),
2673 						    gimple_call_arg (stmt, 0)))
2674 			  {
2675 			    unlink_stmt_vdef (stmt);
2676 			    gsi_remove (&gsi, true);
2677 			    release_defs (stmt);
2678 			    if (gimple_purge_dead_eh_edges (bb))
2679 			      cfg_changed = true;
2680 			    continue;
2681 			  }
2682 			  break;
2683 
2684 		      default:;
2685 		    }
2686 		}
2687 	    }
2688 	  gsi_next (&gsi);
2689 	}
2690     }
2691 
2692   statistics_counter_event (cfun, "widening multiplications inserted",
2693 			    widen_mul_stats.widen_mults_inserted);
2694   statistics_counter_event (cfun, "widening maccs inserted",
2695 			    widen_mul_stats.maccs_inserted);
2696   statistics_counter_event (cfun, "fused multiply-adds inserted",
2697 			    widen_mul_stats.fmas_inserted);
2698 
2699   return cfg_changed ? TODO_cleanup_cfg : 0;
2700 }
2701 
2702 static bool
2703 gate_optimize_widening_mul (void)
2704 {
2705   return flag_expensive_optimizations && optimize;
2706 }
2707 
2708 struct gimple_opt_pass pass_optimize_widening_mul =
2709 {
2710  {
2711   GIMPLE_PASS,
2712   "widening_mul",			/* name */
2713   gate_optimize_widening_mul,		/* gate */
2714   execute_optimize_widening_mul,	/* execute */
2715   NULL,					/* sub */
2716   NULL,					/* next */
2717   0,					/* static_pass_number */
2718   TV_NONE,				/* tv_id */
2719   PROP_ssa,				/* properties_required */
2720   0,					/* properties_provided */
2721   0,					/* properties_destroyed */
2722   0,					/* todo_flags_start */
2723   TODO_verify_ssa
2724   | TODO_verify_stmts
2725   | TODO_update_ssa                     /* todo_flags_finish */
2726  }
2727 };
2728