xref: /netbsd-src/external/gpl3/gcc.old/dist/gcc/tree-chrec.c (revision bdc22b2e01993381dcefeff2bc9b56ca75a4235c)
1 /* Chains of recurrences.
2    Copyright (C) 2003-2015 Free Software Foundation, Inc.
3    Contributed by Sebastian Pop <pop@cri.ensmp.fr>
4 
5 This file is part of GCC.
6 
7 GCC is free software; you can redistribute it and/or modify it under
8 the terms of the GNU General Public License as published by the Free
9 Software Foundation; either version 3, or (at your option) any later
10 version.
11 
12 GCC is distributed in the hope that it will be useful, but WITHOUT ANY
13 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 /* This file implements operations on chains of recurrences.  Chains
22    of recurrences are used for modeling evolution functions of scalar
23    variables.
24 */
25 
26 #include "config.h"
27 #include "system.h"
28 #include "coretypes.h"
29 #include "hash-set.h"
30 #include "machmode.h"
31 #include "vec.h"
32 #include "double-int.h"
33 #include "input.h"
34 #include "alias.h"
35 #include "symtab.h"
36 #include "options.h"
37 #include "wide-int.h"
38 #include "inchash.h"
39 #include "real.h"
40 #include "tree.h"
41 #include "fold-const.h"
42 #include "tree-pretty-print.h"
43 #include "cfgloop.h"
44 #include "predict.h"
45 #include "tm.h"
46 #include "hard-reg-set.h"
47 #include "input.h"
48 #include "function.h"
49 #include "dominance.h"
50 #include "cfg.h"
51 #include "basic-block.h"
52 #include "gimple-expr.h"
53 #include "tree-ssa-loop-ivopts.h"
54 #include "tree-ssa-loop-niter.h"
55 #include "tree-chrec.h"
56 #include "dumpfile.h"
57 #include "params.h"
58 #include "tree-scalar-evolution.h"
59 
60 /* Extended folder for chrecs.  */
61 
62 /* Determines whether CST is not a constant evolution.  */
63 
64 static inline bool
65 is_not_constant_evolution (const_tree cst)
66 {
67   return (TREE_CODE (cst) == POLYNOMIAL_CHREC);
68 }
69 
70 /* Fold CODE for a polynomial function and a constant.  */
71 
72 static inline tree
73 chrec_fold_poly_cst (enum tree_code code,
74 		     tree type,
75 		     tree poly,
76 		     tree cst)
77 {
78   gcc_assert (poly);
79   gcc_assert (cst);
80   gcc_assert (TREE_CODE (poly) == POLYNOMIAL_CHREC);
81   gcc_checking_assert (!is_not_constant_evolution (cst));
82   gcc_checking_assert (useless_type_conversion_p (type, chrec_type (poly)));
83 
84   switch (code)
85     {
86     case PLUS_EXPR:
87       return build_polynomial_chrec
88 	(CHREC_VARIABLE (poly),
89 	 chrec_fold_plus (type, CHREC_LEFT (poly), cst),
90 	 CHREC_RIGHT (poly));
91 
92     case MINUS_EXPR:
93       return build_polynomial_chrec
94 	(CHREC_VARIABLE (poly),
95 	 chrec_fold_minus (type, CHREC_LEFT (poly), cst),
96 	 CHREC_RIGHT (poly));
97 
98     case MULT_EXPR:
99       return build_polynomial_chrec
100 	(CHREC_VARIABLE (poly),
101 	 chrec_fold_multiply (type, CHREC_LEFT (poly), cst),
102 	 chrec_fold_multiply (type, CHREC_RIGHT (poly), cst));
103 
104     default:
105       return chrec_dont_know;
106     }
107 }
108 
109 /* Fold the addition of two polynomial functions.  */
110 
111 static inline tree
112 chrec_fold_plus_poly_poly (enum tree_code code,
113 			   tree type,
114 			   tree poly0,
115 			   tree poly1)
116 {
117   tree left, right;
118   struct loop *loop0 = get_chrec_loop (poly0);
119   struct loop *loop1 = get_chrec_loop (poly1);
120   tree rtype = code == POINTER_PLUS_EXPR ? chrec_type (poly1) : type;
121 
122   gcc_assert (poly0);
123   gcc_assert (poly1);
124   gcc_assert (TREE_CODE (poly0) == POLYNOMIAL_CHREC);
125   gcc_assert (TREE_CODE (poly1) == POLYNOMIAL_CHREC);
126   if (POINTER_TYPE_P (chrec_type (poly0)))
127     gcc_checking_assert (ptrofftype_p (chrec_type (poly1))
128 			 && useless_type_conversion_p (type, chrec_type (poly0)));
129   else
130     gcc_checking_assert (useless_type_conversion_p (type, chrec_type (poly0))
131 			 && useless_type_conversion_p (type, chrec_type (poly1)));
132 
133   /*
134     {a, +, b}_1 + {c, +, d}_2  ->  {{a, +, b}_1 + c, +, d}_2,
135     {a, +, b}_2 + {c, +, d}_1  ->  {{c, +, d}_1 + a, +, b}_2,
136     {a, +, b}_x + {c, +, d}_x  ->  {a+c, +, b+d}_x.  */
137   if (flow_loop_nested_p (loop0, loop1))
138     {
139       if (code == PLUS_EXPR || code == POINTER_PLUS_EXPR)
140 	return build_polynomial_chrec
141 	  (CHREC_VARIABLE (poly1),
142 	   chrec_fold_plus (type, poly0, CHREC_LEFT (poly1)),
143 	   CHREC_RIGHT (poly1));
144       else
145 	return build_polynomial_chrec
146 	  (CHREC_VARIABLE (poly1),
147 	   chrec_fold_minus (type, poly0, CHREC_LEFT (poly1)),
148 	   chrec_fold_multiply (type, CHREC_RIGHT (poly1),
149 				SCALAR_FLOAT_TYPE_P (type)
150 				? build_real (type, dconstm1)
151 				: build_int_cst_type (type, -1)));
152     }
153 
154   if (flow_loop_nested_p (loop1, loop0))
155     {
156       if (code == PLUS_EXPR || code == POINTER_PLUS_EXPR)
157 	return build_polynomial_chrec
158 	  (CHREC_VARIABLE (poly0),
159 	   chrec_fold_plus (type, CHREC_LEFT (poly0), poly1),
160 	   CHREC_RIGHT (poly0));
161       else
162 	return build_polynomial_chrec
163 	  (CHREC_VARIABLE (poly0),
164 	   chrec_fold_minus (type, CHREC_LEFT (poly0), poly1),
165 	   CHREC_RIGHT (poly0));
166     }
167 
168   /* This function should never be called for chrecs of loops that
169      do not belong to the same loop nest.  */
170   if (loop0 != loop1)
171     {
172       /* It still can happen if we are not in loop-closed SSA form.  */
173       gcc_assert (! loops_state_satisfies_p (LOOP_CLOSED_SSA));
174       return chrec_dont_know;
175     }
176 
177   if (code == PLUS_EXPR || code == POINTER_PLUS_EXPR)
178     {
179       left = chrec_fold_plus
180 	(type, CHREC_LEFT (poly0), CHREC_LEFT (poly1));
181       right = chrec_fold_plus
182 	(rtype, CHREC_RIGHT (poly0), CHREC_RIGHT (poly1));
183     }
184   else
185     {
186       left = chrec_fold_minus
187 	(type, CHREC_LEFT (poly0), CHREC_LEFT (poly1));
188       right = chrec_fold_minus
189 	(type, CHREC_RIGHT (poly0), CHREC_RIGHT (poly1));
190     }
191 
192   if (chrec_zerop (right))
193     return left;
194   else
195     return build_polynomial_chrec
196       (CHREC_VARIABLE (poly0), left, right);
197 }
198 
199 
200 
201 /* Fold the multiplication of two polynomial functions.  */
202 
203 static inline tree
204 chrec_fold_multiply_poly_poly (tree type,
205 			       tree poly0,
206 			       tree poly1)
207 {
208   tree t0, t1, t2;
209   int var;
210   struct loop *loop0 = get_chrec_loop (poly0);
211   struct loop *loop1 = get_chrec_loop (poly1);
212 
213   gcc_assert (poly0);
214   gcc_assert (poly1);
215   gcc_assert (TREE_CODE (poly0) == POLYNOMIAL_CHREC);
216   gcc_assert (TREE_CODE (poly1) == POLYNOMIAL_CHREC);
217   gcc_checking_assert (useless_type_conversion_p (type, chrec_type (poly0))
218 		       && useless_type_conversion_p (type, chrec_type (poly1)));
219 
220   /* {a, +, b}_1 * {c, +, d}_2  ->  {c*{a, +, b}_1, +, d}_2,
221      {a, +, b}_2 * {c, +, d}_1  ->  {a*{c, +, d}_1, +, b}_2,
222      {a, +, b}_x * {c, +, d}_x  ->  {a*c, +, a*d + b*c + b*d, +, 2*b*d}_x.  */
223   if (flow_loop_nested_p (loop0, loop1))
224     /* poly0 is a constant wrt. poly1.  */
225     return build_polynomial_chrec
226       (CHREC_VARIABLE (poly1),
227        chrec_fold_multiply (type, CHREC_LEFT (poly1), poly0),
228        CHREC_RIGHT (poly1));
229 
230   if (flow_loop_nested_p (loop1, loop0))
231     /* poly1 is a constant wrt. poly0.  */
232     return build_polynomial_chrec
233       (CHREC_VARIABLE (poly0),
234        chrec_fold_multiply (type, CHREC_LEFT (poly0), poly1),
235        CHREC_RIGHT (poly0));
236 
237   if (loop0 != loop1)
238     {
239       /* It still can happen if we are not in loop-closed SSA form.  */
240       gcc_assert (! loops_state_satisfies_p (LOOP_CLOSED_SSA));
241       return chrec_dont_know;
242     }
243 
244   /* poly0 and poly1 are two polynomials in the same variable,
245      {a, +, b}_x * {c, +, d}_x  ->  {a*c, +, a*d + b*c + b*d, +, 2*b*d}_x.  */
246 
247   /* "a*c".  */
248   t0 = chrec_fold_multiply (type, CHREC_LEFT (poly0), CHREC_LEFT (poly1));
249 
250   /* "a*d + b*c".  */
251   t1 = chrec_fold_multiply (type, CHREC_LEFT (poly0), CHREC_RIGHT (poly1));
252   t1 = chrec_fold_plus (type, t1, chrec_fold_multiply (type,
253 						       CHREC_RIGHT (poly0),
254 						       CHREC_LEFT (poly1)));
255   /* "b*d".  */
256   t2 = chrec_fold_multiply (type, CHREC_RIGHT (poly0), CHREC_RIGHT (poly1));
257   /* "a*d + b*c + b*d".  */
258   t1 = chrec_fold_plus (type, t1, t2);
259   /* "2*b*d".  */
260   t2 = chrec_fold_multiply (type, SCALAR_FLOAT_TYPE_P (type)
261 			    ? build_real (type, dconst2)
262 			    : build_int_cst (type, 2), t2);
263 
264   var = CHREC_VARIABLE (poly0);
265   return build_polynomial_chrec (var, t0,
266 				 build_polynomial_chrec (var, t1, t2));
267 }
268 
269 /* When the operands are automatically_generated_chrec_p, the fold has
270    to respect the semantics of the operands.  */
271 
272 static inline tree
273 chrec_fold_automatically_generated_operands (tree op0,
274 					     tree op1)
275 {
276   if (op0 == chrec_dont_know
277       || op1 == chrec_dont_know)
278     return chrec_dont_know;
279 
280   if (op0 == chrec_known
281       || op1 == chrec_known)
282     return chrec_known;
283 
284   if (op0 == chrec_not_analyzed_yet
285       || op1 == chrec_not_analyzed_yet)
286     return chrec_not_analyzed_yet;
287 
288   /* The default case produces a safe result.  */
289   return chrec_dont_know;
290 }
291 
292 /* Fold the addition of two chrecs.  */
293 
294 static tree
295 chrec_fold_plus_1 (enum tree_code code, tree type,
296 		   tree op0, tree op1)
297 {
298   if (automatically_generated_chrec_p (op0)
299       || automatically_generated_chrec_p (op1))
300     return chrec_fold_automatically_generated_operands (op0, op1);
301 
302   switch (TREE_CODE (op0))
303     {
304     case POLYNOMIAL_CHREC:
305       gcc_checking_assert
306 	(!chrec_contains_symbols_defined_in_loop (op0, CHREC_VARIABLE (op0)));
307       switch (TREE_CODE (op1))
308 	{
309 	case POLYNOMIAL_CHREC:
310 	  gcc_checking_assert
311 	    (!chrec_contains_symbols_defined_in_loop (op1,
312 						      CHREC_VARIABLE (op1)));
313 	  return chrec_fold_plus_poly_poly (code, type, op0, op1);
314 
315 	CASE_CONVERT:
316 	  if (tree_contains_chrecs (op1, NULL))
317 	    return chrec_dont_know;
318 
319 	default:
320 	  if (code == PLUS_EXPR || code == POINTER_PLUS_EXPR)
321 	    return build_polynomial_chrec
322 	      (CHREC_VARIABLE (op0),
323 	       chrec_fold_plus (type, CHREC_LEFT (op0), op1),
324 	       CHREC_RIGHT (op0));
325 	  else
326 	    return build_polynomial_chrec
327 	      (CHREC_VARIABLE (op0),
328 	       chrec_fold_minus (type, CHREC_LEFT (op0), op1),
329 	       CHREC_RIGHT (op0));
330 	}
331 
332     CASE_CONVERT:
333       if (tree_contains_chrecs (op0, NULL))
334 	return chrec_dont_know;
335 
336     default:
337       switch (TREE_CODE (op1))
338 	{
339 	case POLYNOMIAL_CHREC:
340 	  gcc_checking_assert
341 	    (!chrec_contains_symbols_defined_in_loop (op1,
342 						      CHREC_VARIABLE (op1)));
343 	  if (code == PLUS_EXPR || code == POINTER_PLUS_EXPR)
344 	    return build_polynomial_chrec
345 	      (CHREC_VARIABLE (op1),
346 	       chrec_fold_plus (type, op0, CHREC_LEFT (op1)),
347 	       CHREC_RIGHT (op1));
348 	  else
349 	    return build_polynomial_chrec
350 	      (CHREC_VARIABLE (op1),
351 	       chrec_fold_minus (type, op0, CHREC_LEFT (op1)),
352 	       chrec_fold_multiply (type, CHREC_RIGHT (op1),
353 				    SCALAR_FLOAT_TYPE_P (type)
354 				    ? build_real (type, dconstm1)
355 				    : build_int_cst_type (type, -1)));
356 
357 	CASE_CONVERT:
358 	  if (tree_contains_chrecs (op1, NULL))
359 	    return chrec_dont_know;
360 
361 	default:
362 	  {
363 	    int size = 0;
364 	    if ((tree_contains_chrecs (op0, &size)
365 		 || tree_contains_chrecs (op1, &size))
366 		&& size < PARAM_VALUE (PARAM_SCEV_MAX_EXPR_SIZE))
367 	      return build2 (code, type, op0, op1);
368 	    else if (size < PARAM_VALUE (PARAM_SCEV_MAX_EXPR_SIZE))
369 	      {
370 		if (code == POINTER_PLUS_EXPR)
371 		  return fold_build_pointer_plus (fold_convert (type, op0),
372 						  op1);
373 		else
374 		  return fold_build2 (code, type,
375 				      fold_convert (type, op0),
376 				      fold_convert (type, op1));
377 	      }
378 	    else
379 	      return chrec_dont_know;
380 	  }
381 	}
382     }
383 }
384 
385 /* Fold the addition of two chrecs.  */
386 
387 tree
388 chrec_fold_plus (tree type,
389 		 tree op0,
390 		 tree op1)
391 {
392   enum tree_code code;
393   if (automatically_generated_chrec_p (op0)
394       || automatically_generated_chrec_p (op1))
395     return chrec_fold_automatically_generated_operands (op0, op1);
396 
397   if (integer_zerop (op0))
398     return chrec_convert (type, op1, NULL);
399   if (integer_zerop (op1))
400     return chrec_convert (type, op0, NULL);
401 
402   if (POINTER_TYPE_P (type))
403     code = POINTER_PLUS_EXPR;
404   else
405     code = PLUS_EXPR;
406 
407   return chrec_fold_plus_1 (code, type, op0, op1);
408 }
409 
410 /* Fold the subtraction of two chrecs.  */
411 
412 tree
413 chrec_fold_minus (tree type,
414 		  tree op0,
415 		  tree op1)
416 {
417   if (automatically_generated_chrec_p (op0)
418       || automatically_generated_chrec_p (op1))
419     return chrec_fold_automatically_generated_operands (op0, op1);
420 
421   if (integer_zerop (op1))
422     return op0;
423 
424   return chrec_fold_plus_1 (MINUS_EXPR, type, op0, op1);
425 }
426 
427 /* Fold the multiplication of two chrecs.  */
428 
429 tree
430 chrec_fold_multiply (tree type,
431 		     tree op0,
432 		     tree op1)
433 {
434   if (automatically_generated_chrec_p (op0)
435       || automatically_generated_chrec_p (op1))
436     return chrec_fold_automatically_generated_operands (op0, op1);
437 
438   switch (TREE_CODE (op0))
439     {
440     case POLYNOMIAL_CHREC:
441       gcc_checking_assert
442 	(!chrec_contains_symbols_defined_in_loop (op0, CHREC_VARIABLE (op0)));
443       switch (TREE_CODE (op1))
444 	{
445 	case POLYNOMIAL_CHREC:
446 	  gcc_checking_assert
447 	    (!chrec_contains_symbols_defined_in_loop (op1,
448 						      CHREC_VARIABLE (op1)));
449 	  return chrec_fold_multiply_poly_poly (type, op0, op1);
450 
451 	CASE_CONVERT:
452 	  if (tree_contains_chrecs (op1, NULL))
453 	    return chrec_dont_know;
454 
455 	default:
456 	  if (integer_onep (op1))
457 	    return op0;
458 	  if (integer_zerop (op1))
459 	    return build_int_cst (type, 0);
460 
461 	  return build_polynomial_chrec
462 	    (CHREC_VARIABLE (op0),
463 	     chrec_fold_multiply (type, CHREC_LEFT (op0), op1),
464 	     chrec_fold_multiply (type, CHREC_RIGHT (op0), op1));
465 	}
466 
467     CASE_CONVERT:
468       if (tree_contains_chrecs (op0, NULL))
469 	return chrec_dont_know;
470 
471     default:
472       if (integer_onep (op0))
473 	return op1;
474 
475       if (integer_zerop (op0))
476     	return build_int_cst (type, 0);
477 
478       switch (TREE_CODE (op1))
479 	{
480 	case POLYNOMIAL_CHREC:
481 	  gcc_checking_assert
482 	    (!chrec_contains_symbols_defined_in_loop (op1,
483 						      CHREC_VARIABLE (op1)));
484 	  return build_polynomial_chrec
485 	    (CHREC_VARIABLE (op1),
486 	     chrec_fold_multiply (type, CHREC_LEFT (op1), op0),
487 	     chrec_fold_multiply (type, CHREC_RIGHT (op1), op0));
488 
489 	CASE_CONVERT:
490 	  if (tree_contains_chrecs (op1, NULL))
491 	    return chrec_dont_know;
492 
493 	default:
494 	  if (integer_onep (op1))
495 	    return op0;
496 	  if (integer_zerop (op1))
497 	    return build_int_cst (type, 0);
498 	  return fold_build2 (MULT_EXPR, type, op0, op1);
499 	}
500     }
501 }
502 
503 
504 
505 /* Operations.  */
506 
507 /* Evaluate the binomial coefficient.  Return NULL_TREE if the intermediate
508    calculation overflows, otherwise return C(n,k) with type TYPE.  */
509 
510 static tree
511 tree_fold_binomial (tree type, tree n, unsigned int k)
512 {
513   bool overflow;
514   unsigned int i;
515 
516   /* Handle the most frequent cases.  */
517   if (k == 0)
518     return build_int_cst (type, 1);
519   if (k == 1)
520     return fold_convert (type, n);
521 
522   widest_int num = wi::to_widest (n);
523 
524   /* Check that k <= n.  */
525   if (wi::ltu_p (num, k))
526     return NULL_TREE;
527 
528   /* Denominator = 2.  */
529   widest_int denom = 2;
530 
531   /* Index = Numerator-1.  */
532   widest_int idx = num - 1;
533 
534   /* Numerator = Numerator*Index = n*(n-1).  */
535   num = wi::smul (num, idx, &overflow);
536   if (overflow)
537     return NULL_TREE;
538 
539   for (i = 3; i <= k; i++)
540     {
541       /* Index--.  */
542       --idx;
543 
544       /* Numerator *= Index.  */
545       num = wi::smul (num, idx, &overflow);
546       if (overflow)
547 	return NULL_TREE;
548 
549       /* Denominator *= i.  */
550       denom *= i;
551     }
552 
553   /* Result = Numerator / Denominator.  */
554   num = wi::udiv_trunc (num, denom);
555   if (! wi::fits_to_tree_p (num, type))
556     return NULL_TREE;
557   return wide_int_to_tree (type, num);
558 }
559 
560 /* Helper function.  Use the Newton's interpolating formula for
561    evaluating the value of the evolution function.  */
562 
563 static tree
564 chrec_evaluate (unsigned var, tree chrec, tree n, unsigned int k)
565 {
566   tree arg0, arg1, binomial_n_k;
567   tree type = TREE_TYPE (chrec);
568   struct loop *var_loop = get_loop (cfun, var);
569 
570   while (TREE_CODE (chrec) == POLYNOMIAL_CHREC
571 	 && flow_loop_nested_p (var_loop, get_chrec_loop (chrec)))
572     chrec = CHREC_LEFT (chrec);
573 
574   if (TREE_CODE (chrec) == POLYNOMIAL_CHREC
575       && CHREC_VARIABLE (chrec) == var)
576     {
577       arg1 = chrec_evaluate (var, CHREC_RIGHT (chrec), n, k + 1);
578       if (arg1 == chrec_dont_know)
579 	return chrec_dont_know;
580       binomial_n_k = tree_fold_binomial (type, n, k);
581       if (!binomial_n_k)
582 	return chrec_dont_know;
583       arg0 = fold_build2 (MULT_EXPR, type,
584 			  CHREC_LEFT (chrec), binomial_n_k);
585       return chrec_fold_plus (type, arg0, arg1);
586     }
587 
588   binomial_n_k = tree_fold_binomial (type, n, k);
589   if (!binomial_n_k)
590     return chrec_dont_know;
591 
592   return fold_build2 (MULT_EXPR, type, chrec, binomial_n_k);
593 }
594 
595 /* Evaluates "CHREC (X)" when the varying variable is VAR.
596    Example:  Given the following parameters,
597 
598    var = 1
599    chrec = {3, +, 4}_1
600    x = 10
601 
602    The result is given by the Newton's interpolating formula:
603    3 * \binom{10}{0} + 4 * \binom{10}{1}.
604 */
605 
606 tree
607 chrec_apply (unsigned var,
608 	     tree chrec,
609 	     tree x)
610 {
611   tree type = chrec_type (chrec);
612   tree res = chrec_dont_know;
613 
614   if (automatically_generated_chrec_p (chrec)
615       || automatically_generated_chrec_p (x)
616 
617       /* When the symbols are defined in an outer loop, it is possible
618 	 to symbolically compute the apply, since the symbols are
619 	 constants with respect to the varying loop.  */
620       || chrec_contains_symbols_defined_in_loop (chrec, var))
621     return chrec_dont_know;
622 
623   if (dump_file && (dump_flags & TDF_SCEV))
624     fprintf (dump_file, "(chrec_apply \n");
625 
626   if (TREE_CODE (x) == INTEGER_CST && SCALAR_FLOAT_TYPE_P (type))
627     x = build_real_from_int_cst (type, x);
628 
629   switch (TREE_CODE (chrec))
630     {
631     case POLYNOMIAL_CHREC:
632       if (evolution_function_is_affine_p (chrec))
633 	{
634 	  if (CHREC_VARIABLE (chrec) != var)
635 	    return build_polynomial_chrec
636 	      (CHREC_VARIABLE (chrec),
637 	       chrec_apply (var, CHREC_LEFT (chrec), x),
638 	       chrec_apply (var, CHREC_RIGHT (chrec), x));
639 
640 	  /* "{a, +, b} (x)"  ->  "a + b*x".  */
641 	  x = chrec_convert_rhs (type, x, NULL);
642 	  res = chrec_fold_multiply (TREE_TYPE (x), CHREC_RIGHT (chrec), x);
643 	  res = chrec_fold_plus (type, CHREC_LEFT (chrec), res);
644 	}
645       else if (TREE_CODE (x) == INTEGER_CST
646 	       && tree_int_cst_sgn (x) == 1)
647 	/* testsuite/.../ssa-chrec-38.c.  */
648 	res = chrec_evaluate (var, chrec, x, 0);
649       else
650 	res = chrec_dont_know;
651       break;
652 
653     CASE_CONVERT:
654       res = chrec_convert (TREE_TYPE (chrec),
655 			   chrec_apply (var, TREE_OPERAND (chrec, 0), x),
656 			   NULL);
657       break;
658 
659     default:
660       res = chrec;
661       break;
662     }
663 
664   if (dump_file && (dump_flags & TDF_SCEV))
665     {
666       fprintf (dump_file, "  (varying_loop = %d\n", var);
667       fprintf (dump_file, ")\n  (chrec = ");
668       print_generic_expr (dump_file, chrec, 0);
669       fprintf (dump_file, ")\n  (x = ");
670       print_generic_expr (dump_file, x, 0);
671       fprintf (dump_file, ")\n  (res = ");
672       print_generic_expr (dump_file, res, 0);
673       fprintf (dump_file, "))\n");
674     }
675 
676   return res;
677 }
678 
679 /* For a given CHREC and an induction variable map IV_MAP that maps
680    (loop->num, expr) for every loop number of the current_loops an
681    expression, calls chrec_apply when the expression is not NULL.  */
682 
683 tree
684 chrec_apply_map (tree chrec, vec<tree> iv_map)
685 {
686   int i;
687   tree expr;
688 
689   FOR_EACH_VEC_ELT (iv_map, i, expr)
690     if (expr)
691       chrec = chrec_apply (i, chrec, expr);
692 
693   return chrec;
694 }
695 
696 /* Replaces the initial condition in CHREC with INIT_COND.  */
697 
698 tree
699 chrec_replace_initial_condition (tree chrec,
700 				 tree init_cond)
701 {
702   if (automatically_generated_chrec_p (chrec))
703     return chrec;
704 
705   gcc_assert (chrec_type (chrec) == chrec_type (init_cond));
706 
707   switch (TREE_CODE (chrec))
708     {
709     case POLYNOMIAL_CHREC:
710       return build_polynomial_chrec
711 	(CHREC_VARIABLE (chrec),
712 	 chrec_replace_initial_condition (CHREC_LEFT (chrec), init_cond),
713 	 CHREC_RIGHT (chrec));
714 
715     default:
716       return init_cond;
717     }
718 }
719 
720 /* Returns the initial condition of a given CHREC.  */
721 
722 tree
723 initial_condition (tree chrec)
724 {
725   if (automatically_generated_chrec_p (chrec))
726     return chrec;
727 
728   if (TREE_CODE (chrec) == POLYNOMIAL_CHREC)
729     return initial_condition (CHREC_LEFT (chrec));
730   else
731     return chrec;
732 }
733 
734 /* Returns a univariate function that represents the evolution in
735    LOOP_NUM.  Mask the evolution of any other loop.  */
736 
737 tree
738 hide_evolution_in_other_loops_than_loop (tree chrec,
739 					 unsigned loop_num)
740 {
741   struct loop *loop = get_loop (cfun, loop_num), *chloop;
742   if (automatically_generated_chrec_p (chrec))
743     return chrec;
744 
745   switch (TREE_CODE (chrec))
746     {
747     case POLYNOMIAL_CHREC:
748       chloop = get_chrec_loop (chrec);
749 
750       if (chloop == loop)
751 	return build_polynomial_chrec
752 	  (loop_num,
753 	   hide_evolution_in_other_loops_than_loop (CHREC_LEFT (chrec),
754 						    loop_num),
755 	   CHREC_RIGHT (chrec));
756 
757       else if (flow_loop_nested_p (chloop, loop))
758 	/* There is no evolution in this loop.  */
759 	return initial_condition (chrec);
760 
761       else if (flow_loop_nested_p (loop, chloop))
762 	return hide_evolution_in_other_loops_than_loop (CHREC_LEFT (chrec),
763 							loop_num);
764 
765       else
766 	return chrec_dont_know;
767 
768     default:
769       return chrec;
770     }
771 }
772 
773 /* Returns the evolution part of CHREC in LOOP_NUM when RIGHT is
774    true, otherwise returns the initial condition in LOOP_NUM.  */
775 
776 static tree
777 chrec_component_in_loop_num (tree chrec,
778 			     unsigned loop_num,
779 			     bool right)
780 {
781   tree component;
782   struct loop *loop = get_loop (cfun, loop_num), *chloop;
783 
784   if (automatically_generated_chrec_p (chrec))
785     return chrec;
786 
787   switch (TREE_CODE (chrec))
788     {
789     case POLYNOMIAL_CHREC:
790       chloop = get_chrec_loop (chrec);
791 
792       if (chloop == loop)
793 	{
794 	  if (right)
795 	    component = CHREC_RIGHT (chrec);
796 	  else
797 	    component = CHREC_LEFT (chrec);
798 
799 	  if (TREE_CODE (CHREC_LEFT (chrec)) != POLYNOMIAL_CHREC
800 	      || CHREC_VARIABLE (CHREC_LEFT (chrec)) != CHREC_VARIABLE (chrec))
801 	    return component;
802 
803 	  else
804 	    return build_polynomial_chrec
805 	      (loop_num,
806 	       chrec_component_in_loop_num (CHREC_LEFT (chrec),
807 					    loop_num,
808 					    right),
809 	       component);
810 	}
811 
812       else if (flow_loop_nested_p (chloop, loop))
813 	/* There is no evolution part in this loop.  */
814 	return NULL_TREE;
815 
816       else
817 	{
818 	  gcc_assert (flow_loop_nested_p (loop, chloop));
819 	  return chrec_component_in_loop_num (CHREC_LEFT (chrec),
820 					      loop_num,
821 					      right);
822 	}
823 
824      default:
825       if (right)
826 	return NULL_TREE;
827       else
828 	return chrec;
829     }
830 }
831 
832 /* Returns the evolution part in LOOP_NUM.  Example: the call
833    evolution_part_in_loop_num ({{0, +, 1}_1, +, 2}_1, 1) returns
834    {1, +, 2}_1  */
835 
836 tree
837 evolution_part_in_loop_num (tree chrec,
838 			    unsigned loop_num)
839 {
840   return chrec_component_in_loop_num (chrec, loop_num, true);
841 }
842 
843 /* Returns the initial condition in LOOP_NUM.  Example: the call
844    initial_condition_in_loop_num ({{0, +, 1}_1, +, 2}_2, 2) returns
845    {0, +, 1}_1  */
846 
847 tree
848 initial_condition_in_loop_num (tree chrec,
849 			       unsigned loop_num)
850 {
851   return chrec_component_in_loop_num (chrec, loop_num, false);
852 }
853 
854 /* Set or reset the evolution of CHREC to NEW_EVOL in loop LOOP_NUM.
855    This function is essentially used for setting the evolution to
856    chrec_dont_know, for example after having determined that it is
857    impossible to say how many times a loop will execute.  */
858 
859 tree
860 reset_evolution_in_loop (unsigned loop_num,
861 			 tree chrec,
862 			 tree new_evol)
863 {
864   struct loop *loop = get_loop (cfun, loop_num);
865 
866   if (POINTER_TYPE_P (chrec_type (chrec)))
867     gcc_assert (ptrofftype_p (chrec_type (new_evol)));
868   else
869     gcc_assert (chrec_type (chrec) == chrec_type (new_evol));
870 
871   if (TREE_CODE (chrec) == POLYNOMIAL_CHREC
872       && flow_loop_nested_p (loop, get_chrec_loop (chrec)))
873     {
874       tree left = reset_evolution_in_loop (loop_num, CHREC_LEFT (chrec),
875 					   new_evol);
876       tree right = reset_evolution_in_loop (loop_num, CHREC_RIGHT (chrec),
877 					    new_evol);
878       return build3 (POLYNOMIAL_CHREC, TREE_TYPE (left),
879 		     CHREC_VAR (chrec), left, right);
880     }
881 
882   while (TREE_CODE (chrec) == POLYNOMIAL_CHREC
883 	 && CHREC_VARIABLE (chrec) == loop_num)
884     chrec = CHREC_LEFT (chrec);
885 
886   return build_polynomial_chrec (loop_num, chrec, new_evol);
887 }
888 
889 /* Merges two evolution functions that were found by following two
890    alternate paths of a conditional expression.  */
891 
892 tree
893 chrec_merge (tree chrec1,
894 	     tree chrec2)
895 {
896   if (chrec1 == chrec_dont_know
897       || chrec2 == chrec_dont_know)
898     return chrec_dont_know;
899 
900   if (chrec1 == chrec_known
901       || chrec2 == chrec_known)
902     return chrec_known;
903 
904   if (chrec1 == chrec_not_analyzed_yet)
905     return chrec2;
906   if (chrec2 == chrec_not_analyzed_yet)
907     return chrec1;
908 
909   if (eq_evolutions_p (chrec1, chrec2))
910     return chrec1;
911 
912   return chrec_dont_know;
913 }
914 
915 
916 
917 /* Observers.  */
918 
919 /* Helper function for is_multivariate_chrec.  */
920 
921 static bool
922 is_multivariate_chrec_rec (const_tree chrec, unsigned int rec_var)
923 {
924   if (chrec == NULL_TREE)
925     return false;
926 
927   if (TREE_CODE (chrec) == POLYNOMIAL_CHREC)
928     {
929       if (CHREC_VARIABLE (chrec) != rec_var)
930 	return true;
931       else
932 	return (is_multivariate_chrec_rec (CHREC_LEFT (chrec), rec_var)
933 		|| is_multivariate_chrec_rec (CHREC_RIGHT (chrec), rec_var));
934     }
935   else
936     return false;
937 }
938 
939 /* Determine whether the given chrec is multivariate or not.  */
940 
941 bool
942 is_multivariate_chrec (const_tree chrec)
943 {
944   if (chrec == NULL_TREE)
945     return false;
946 
947   if (TREE_CODE (chrec) == POLYNOMIAL_CHREC)
948     return (is_multivariate_chrec_rec (CHREC_LEFT (chrec),
949 				       CHREC_VARIABLE (chrec))
950 	    || is_multivariate_chrec_rec (CHREC_RIGHT (chrec),
951 					  CHREC_VARIABLE (chrec)));
952   else
953     return false;
954 }
955 
956 /* Determines whether the chrec contains symbolic names or not.  */
957 
958 bool
959 chrec_contains_symbols (const_tree chrec)
960 {
961   int i, n;
962 
963   if (chrec == NULL_TREE)
964     return false;
965 
966   if (TREE_CODE (chrec) == SSA_NAME
967       || TREE_CODE (chrec) == VAR_DECL
968       || TREE_CODE (chrec) == PARM_DECL
969       || TREE_CODE (chrec) == FUNCTION_DECL
970       || TREE_CODE (chrec) == LABEL_DECL
971       || TREE_CODE (chrec) == RESULT_DECL
972       || TREE_CODE (chrec) == FIELD_DECL)
973     return true;
974 
975   n = TREE_OPERAND_LENGTH (chrec);
976   for (i = 0; i < n; i++)
977     if (chrec_contains_symbols (TREE_OPERAND (chrec, i)))
978       return true;
979   return false;
980 }
981 
982 /* Determines whether the chrec contains undetermined coefficients.  */
983 
984 bool
985 chrec_contains_undetermined (const_tree chrec)
986 {
987   int i, n;
988 
989   if (chrec == chrec_dont_know)
990     return true;
991 
992   if (chrec == NULL_TREE)
993     return false;
994 
995   n = TREE_OPERAND_LENGTH (chrec);
996   for (i = 0; i < n; i++)
997     if (chrec_contains_undetermined (TREE_OPERAND (chrec, i)))
998       return true;
999   return false;
1000 }
1001 
1002 /* Determines whether the tree EXPR contains chrecs, and increment
1003    SIZE if it is not a NULL pointer by an estimation of the depth of
1004    the tree.  */
1005 
1006 bool
1007 tree_contains_chrecs (const_tree expr, int *size)
1008 {
1009   int i, n;
1010 
1011   if (expr == NULL_TREE)
1012     return false;
1013 
1014   if (size)
1015     (*size)++;
1016 
1017   if (tree_is_chrec (expr))
1018     return true;
1019 
1020   n = TREE_OPERAND_LENGTH (expr);
1021   for (i = 0; i < n; i++)
1022     if (tree_contains_chrecs (TREE_OPERAND (expr, i), size))
1023       return true;
1024   return false;
1025 }
1026 
1027 /* Recursive helper function.  */
1028 
1029 static bool
1030 evolution_function_is_invariant_rec_p (tree chrec, int loopnum)
1031 {
1032   if (evolution_function_is_constant_p (chrec))
1033     return true;
1034 
1035   if (TREE_CODE (chrec) == SSA_NAME
1036       && (loopnum == 0
1037 	  || expr_invariant_in_loop_p (get_loop (cfun, loopnum), chrec)))
1038     return true;
1039 
1040   if (TREE_CODE (chrec) == POLYNOMIAL_CHREC)
1041     {
1042       if (CHREC_VARIABLE (chrec) == (unsigned) loopnum
1043 	  || flow_loop_nested_p (get_loop (cfun, loopnum),
1044 				 get_chrec_loop (chrec))
1045 	  || !evolution_function_is_invariant_rec_p (CHREC_RIGHT (chrec),
1046 						     loopnum)
1047 	  || !evolution_function_is_invariant_rec_p (CHREC_LEFT (chrec),
1048 						     loopnum))
1049 	return false;
1050       return true;
1051     }
1052 
1053   switch (TREE_OPERAND_LENGTH (chrec))
1054     {
1055     case 2:
1056       if (!evolution_function_is_invariant_rec_p (TREE_OPERAND (chrec, 1),
1057 						  loopnum))
1058 	return false;
1059 
1060     case 1:
1061       if (!evolution_function_is_invariant_rec_p (TREE_OPERAND (chrec, 0),
1062 						  loopnum))
1063 	return false;
1064       return true;
1065 
1066     default:
1067       return false;
1068     }
1069 
1070   return false;
1071 }
1072 
1073 /* Return true if CHREC is invariant in loop LOOPNUM, false otherwise. */
1074 
1075 bool
1076 evolution_function_is_invariant_p (tree chrec, int loopnum)
1077 {
1078   return evolution_function_is_invariant_rec_p (chrec, loopnum);
1079 }
1080 
1081 /* Determine whether the given tree is an affine multivariate
1082    evolution.  */
1083 
1084 bool
1085 evolution_function_is_affine_multivariate_p (const_tree chrec, int loopnum)
1086 {
1087   if (chrec == NULL_TREE)
1088     return false;
1089 
1090   switch (TREE_CODE (chrec))
1091     {
1092     case POLYNOMIAL_CHREC:
1093       if (evolution_function_is_invariant_rec_p (CHREC_LEFT (chrec), loopnum))
1094 	{
1095 	  if (evolution_function_is_invariant_rec_p (CHREC_RIGHT (chrec), loopnum))
1096 	    return true;
1097 	  else
1098 	    {
1099 	      if (TREE_CODE (CHREC_RIGHT (chrec)) == POLYNOMIAL_CHREC
1100 		  && CHREC_VARIABLE (CHREC_RIGHT (chrec))
1101 		     != CHREC_VARIABLE (chrec)
1102 		  && evolution_function_is_affine_multivariate_p
1103 		  (CHREC_RIGHT (chrec), loopnum))
1104 		return true;
1105 	      else
1106 		return false;
1107 	    }
1108 	}
1109       else
1110 	{
1111 	  if (evolution_function_is_invariant_rec_p (CHREC_RIGHT (chrec), loopnum)
1112 	      && TREE_CODE (CHREC_LEFT (chrec)) == POLYNOMIAL_CHREC
1113 	      && CHREC_VARIABLE (CHREC_LEFT (chrec)) != CHREC_VARIABLE (chrec)
1114 	      && evolution_function_is_affine_multivariate_p
1115 	      (CHREC_LEFT (chrec), loopnum))
1116 	    return true;
1117 	  else
1118 	    return false;
1119 	}
1120 
1121     default:
1122       return false;
1123     }
1124 }
1125 
1126 /* Determine whether the given tree is a function in zero or one
1127    variables.  */
1128 
1129 bool
1130 evolution_function_is_univariate_p (const_tree chrec)
1131 {
1132   if (chrec == NULL_TREE)
1133     return true;
1134 
1135   switch (TREE_CODE (chrec))
1136     {
1137     case POLYNOMIAL_CHREC:
1138       switch (TREE_CODE (CHREC_LEFT (chrec)))
1139 	{
1140 	case POLYNOMIAL_CHREC:
1141 	  if (CHREC_VARIABLE (chrec) != CHREC_VARIABLE (CHREC_LEFT (chrec)))
1142 	    return false;
1143 	  if (!evolution_function_is_univariate_p (CHREC_LEFT (chrec)))
1144 	    return false;
1145 	  break;
1146 
1147 	default:
1148 	  if (tree_contains_chrecs (CHREC_LEFT (chrec), NULL))
1149 	    return false;
1150 	  break;
1151 	}
1152 
1153       switch (TREE_CODE (CHREC_RIGHT (chrec)))
1154 	{
1155 	case POLYNOMIAL_CHREC:
1156 	  if (CHREC_VARIABLE (chrec) != CHREC_VARIABLE (CHREC_RIGHT (chrec)))
1157 	    return false;
1158 	  if (!evolution_function_is_univariate_p (CHREC_RIGHT (chrec)))
1159 	    return false;
1160 	  break;
1161 
1162 	default:
1163 	  if (tree_contains_chrecs (CHREC_RIGHT (chrec), NULL))
1164 	    return false;
1165 	  break;
1166 	}
1167 
1168     default:
1169       return true;
1170     }
1171 }
1172 
1173 /* Returns the number of variables of CHREC.  Example: the call
1174    nb_vars_in_chrec ({{0, +, 1}_5, +, 2}_6) returns 2.  */
1175 
1176 unsigned
1177 nb_vars_in_chrec (tree chrec)
1178 {
1179   if (chrec == NULL_TREE)
1180     return 0;
1181 
1182   switch (TREE_CODE (chrec))
1183     {
1184     case POLYNOMIAL_CHREC:
1185       return 1 + nb_vars_in_chrec
1186 	(initial_condition_in_loop_num (chrec, CHREC_VARIABLE (chrec)));
1187 
1188     default:
1189       return 0;
1190     }
1191 }
1192 
1193 static tree chrec_convert_1 (tree, tree, gimple, bool);
1194 
1195 /* Converts BASE and STEP of affine scev to TYPE.  LOOP is the loop whose iv
1196    the scev corresponds to.  AT_STMT is the statement at that the scev is
1197    evaluated.  USE_OVERFLOW_SEMANTICS is true if this function should assume that
1198    the rules for overflow of the given language apply (e.g., that signed
1199    arithmetics in C does not overflow) -- i.e., to use them to avoid unnecessary
1200    tests, but also to enforce that the result follows them.  Returns true if the
1201    conversion succeeded, false otherwise.  */
1202 
1203 bool
1204 convert_affine_scev (struct loop *loop, tree type,
1205 		     tree *base, tree *step, gimple at_stmt,
1206 		     bool use_overflow_semantics)
1207 {
1208   tree ct = TREE_TYPE (*step);
1209   bool enforce_overflow_semantics;
1210   bool must_check_src_overflow, must_check_rslt_overflow;
1211   tree new_base, new_step;
1212   tree step_type = POINTER_TYPE_P (type) ? sizetype : type;
1213 
1214   /* In general,
1215      (TYPE) (BASE + STEP * i) = (TYPE) BASE + (TYPE -- sign extend) STEP * i,
1216      but we must check some assumptions.
1217 
1218      1) If [BASE, +, STEP] wraps, the equation is not valid when precision
1219         of CT is smaller than the precision of TYPE.  For example, when we
1220 	cast unsigned char [254, +, 1] to unsigned, the values on left side
1221 	are 254, 255, 0, 1, ..., but those on the right side are
1222 	254, 255, 256, 257, ...
1223      2) In case that we must also preserve the fact that signed ivs do not
1224         overflow, we must additionally check that the new iv does not wrap.
1225 	For example, unsigned char [125, +, 1] casted to signed char could
1226 	become a wrapping variable with values 125, 126, 127, -128, -127, ...,
1227 	which would confuse optimizers that assume that this does not
1228 	happen.  */
1229   must_check_src_overflow = TYPE_PRECISION (ct) < TYPE_PRECISION (type);
1230 
1231   enforce_overflow_semantics = (use_overflow_semantics
1232 				&& nowrap_type_p (type));
1233   if (enforce_overflow_semantics)
1234     {
1235       /* We can avoid checking whether the result overflows in the following
1236 	 cases:
1237 
1238 	 -- must_check_src_overflow is true, and the range of TYPE is superset
1239 	    of the range of CT -- i.e., in all cases except if CT signed and
1240 	    TYPE unsigned.
1241          -- both CT and TYPE have the same precision and signedness, and we
1242 	    verify instead that the source does not overflow (this may be
1243 	    easier than verifying it for the result, as we may use the
1244 	    information about the semantics of overflow in CT).  */
1245       if (must_check_src_overflow)
1246 	{
1247 	  if (TYPE_UNSIGNED (type) && !TYPE_UNSIGNED (ct))
1248 	    must_check_rslt_overflow = true;
1249 	  else
1250 	    must_check_rslt_overflow = false;
1251 	}
1252       else if (TYPE_UNSIGNED (ct) == TYPE_UNSIGNED (type)
1253 	       && TYPE_PRECISION (ct) == TYPE_PRECISION (type))
1254 	{
1255 	  must_check_rslt_overflow = false;
1256 	  must_check_src_overflow = true;
1257 	}
1258       else
1259 	must_check_rslt_overflow = true;
1260     }
1261   else
1262     must_check_rslt_overflow = false;
1263 
1264   if (must_check_src_overflow
1265       && scev_probably_wraps_p (*base, *step, at_stmt, loop,
1266 				use_overflow_semantics))
1267     return false;
1268 
1269   new_base = chrec_convert_1 (type, *base, at_stmt,
1270 			      use_overflow_semantics);
1271   /* The step must be sign extended, regardless of the signedness
1272      of CT and TYPE.  This only needs to be handled specially when
1273      CT is unsigned -- to avoid e.g. unsigned char [100, +, 255]
1274      (with values 100, 99, 98, ...) from becoming signed or unsigned
1275      [100, +, 255] with values 100, 355, ...; the sign-extension is
1276      performed by default when CT is signed.  */
1277   new_step = *step;
1278   if (TYPE_PRECISION (step_type) > TYPE_PRECISION (ct) && TYPE_UNSIGNED (ct))
1279     {
1280       tree signed_ct = build_nonstandard_integer_type (TYPE_PRECISION (ct), 0);
1281       new_step = chrec_convert_1 (signed_ct, new_step, at_stmt,
1282                                   use_overflow_semantics);
1283     }
1284   new_step = chrec_convert_1 (step_type, new_step, at_stmt, use_overflow_semantics);
1285 
1286   if (automatically_generated_chrec_p (new_base)
1287       || automatically_generated_chrec_p (new_step))
1288     return false;
1289 
1290   if (must_check_rslt_overflow
1291       /* Note that in this case we cannot use the fact that signed variables
1292 	 do not overflow, as this is what we are verifying for the new iv.  */
1293       && scev_probably_wraps_p (new_base, new_step, at_stmt, loop, false))
1294     return false;
1295 
1296   *base = new_base;
1297   *step = new_step;
1298   return true;
1299 }
1300 
1301 
1302 /* Convert CHREC for the right hand side of a CHREC.
1303    The increment for a pointer type is always sizetype.  */
1304 
1305 tree
1306 chrec_convert_rhs (tree type, tree chrec, gimple at_stmt)
1307 {
1308   if (POINTER_TYPE_P (type))
1309     type = sizetype;
1310 
1311   return chrec_convert (type, chrec, at_stmt);
1312 }
1313 
1314 /* Convert CHREC to TYPE.  When the analyzer knows the context in
1315    which the CHREC is built, it sets AT_STMT to the statement that
1316    contains the definition of the analyzed variable, otherwise the
1317    conversion is less accurate: the information is used for
1318    determining a more accurate estimation of the number of iterations.
1319    By default AT_STMT could be safely set to NULL_TREE.
1320 
1321    The following rule is always true: TREE_TYPE (chrec) ==
1322    TREE_TYPE (CHREC_LEFT (chrec)) == TREE_TYPE (CHREC_RIGHT (chrec)).
1323    An example of what could happen when adding two chrecs and the type
1324    of the CHREC_RIGHT is different than CHREC_LEFT is:
1325 
1326    {(uint) 0, +, (uchar) 10} +
1327    {(uint) 0, +, (uchar) 250}
1328 
1329    that would produce a wrong result if CHREC_RIGHT is not (uint):
1330 
1331    {(uint) 0, +, (uchar) 4}
1332 
1333    instead of
1334 
1335    {(uint) 0, +, (uint) 260}
1336 */
1337 
1338 tree
1339 chrec_convert (tree type, tree chrec, gimple at_stmt)
1340 {
1341   return chrec_convert_1 (type, chrec, at_stmt, true);
1342 }
1343 
1344 /* Convert CHREC to TYPE.  When the analyzer knows the context in
1345    which the CHREC is built, it sets AT_STMT to the statement that
1346    contains the definition of the analyzed variable, otherwise the
1347    conversion is less accurate: the information is used for
1348    determining a more accurate estimation of the number of iterations.
1349    By default AT_STMT could be safely set to NULL_TREE.
1350 
1351    USE_OVERFLOW_SEMANTICS is true if this function should assume that
1352    the rules for overflow of the given language apply (e.g., that signed
1353    arithmetics in C does not overflow) -- i.e., to use them to avoid unnecessary
1354    tests, but also to enforce that the result follows them.  */
1355 
1356 static tree
1357 chrec_convert_1 (tree type, tree chrec, gimple at_stmt,
1358 		 bool use_overflow_semantics)
1359 {
1360   tree ct, res;
1361   tree base, step;
1362   struct loop *loop;
1363 
1364   if (automatically_generated_chrec_p (chrec))
1365     return chrec;
1366 
1367   ct = chrec_type (chrec);
1368   if (useless_type_conversion_p (type, ct))
1369     return chrec;
1370 
1371   if (!evolution_function_is_affine_p (chrec))
1372     goto keep_cast;
1373 
1374   loop = get_chrec_loop (chrec);
1375   base = CHREC_LEFT (chrec);
1376   step = CHREC_RIGHT (chrec);
1377 
1378   if (convert_affine_scev (loop, type, &base, &step, at_stmt,
1379 			   use_overflow_semantics))
1380     return build_polynomial_chrec (loop->num, base, step);
1381 
1382   /* If we cannot propagate the cast inside the chrec, just keep the cast.  */
1383 keep_cast:
1384   /* Fold will not canonicalize (long)(i - 1) to (long)i - 1 because that
1385      may be more expensive.  We do want to perform this optimization here
1386      though for canonicalization reasons.  */
1387   if (use_overflow_semantics
1388       && (TREE_CODE (chrec) == PLUS_EXPR
1389 	  || TREE_CODE (chrec) == MINUS_EXPR)
1390       && TREE_CODE (type) == INTEGER_TYPE
1391       && TREE_CODE (ct) == INTEGER_TYPE
1392       && TYPE_PRECISION (type) > TYPE_PRECISION (ct)
1393       && TYPE_OVERFLOW_UNDEFINED (ct))
1394     res = fold_build2 (TREE_CODE (chrec), type,
1395 		       fold_convert (type, TREE_OPERAND (chrec, 0)),
1396 		       fold_convert (type, TREE_OPERAND (chrec, 1)));
1397   /* Similar perform the trick that (signed char)((int)x + 2) can be
1398      narrowed to (signed char)((unsigned char)x + 2).  */
1399   else if (use_overflow_semantics
1400 	   && TREE_CODE (chrec) == POLYNOMIAL_CHREC
1401 	   && TREE_CODE (ct) == INTEGER_TYPE
1402 	   && TREE_CODE (type) == INTEGER_TYPE
1403 	   && TYPE_OVERFLOW_UNDEFINED (type)
1404 	   && TYPE_PRECISION (type) < TYPE_PRECISION (ct))
1405     {
1406       tree utype = unsigned_type_for (type);
1407       res = build_polynomial_chrec (CHREC_VARIABLE (chrec),
1408 				    fold_convert (utype,
1409 						  CHREC_LEFT (chrec)),
1410 				    fold_convert (utype,
1411 						  CHREC_RIGHT (chrec)));
1412       res = chrec_convert_1 (type, res, at_stmt, use_overflow_semantics);
1413     }
1414   else
1415     res = fold_convert (type, chrec);
1416 
1417   /* Don't propagate overflows.  */
1418   if (CONSTANT_CLASS_P (res))
1419     TREE_OVERFLOW (res) = 0;
1420 
1421   /* But reject constants that don't fit in their type after conversion.
1422      This can happen if TYPE_MIN_VALUE or TYPE_MAX_VALUE are not the
1423      natural values associated with TYPE_PRECISION and TYPE_UNSIGNED,
1424      and can cause problems later when computing niters of loops.  Note
1425      that we don't do the check before converting because we don't want
1426      to reject conversions of negative chrecs to unsigned types.  */
1427   if (TREE_CODE (res) == INTEGER_CST
1428       && TREE_CODE (type) == INTEGER_TYPE
1429       && !int_fits_type_p (res, type))
1430     res = chrec_dont_know;
1431 
1432   return res;
1433 }
1434 
1435 /* Convert CHREC to TYPE, without regard to signed overflows.  Returns the new
1436    chrec if something else than what chrec_convert would do happens, NULL_TREE
1437    otherwise.  */
1438 
1439 tree
1440 chrec_convert_aggressive (tree type, tree chrec)
1441 {
1442   tree inner_type, left, right, lc, rc, rtype;
1443 
1444   if (automatically_generated_chrec_p (chrec)
1445       || TREE_CODE (chrec) != POLYNOMIAL_CHREC)
1446     return NULL_TREE;
1447 
1448   inner_type = TREE_TYPE (chrec);
1449   if (TYPE_PRECISION (type) > TYPE_PRECISION (inner_type))
1450     return NULL_TREE;
1451 
1452   rtype = POINTER_TYPE_P (type) ? sizetype : type;
1453 
1454   left = CHREC_LEFT (chrec);
1455   right = CHREC_RIGHT (chrec);
1456   lc = chrec_convert_aggressive (type, left);
1457   if (!lc)
1458     lc = chrec_convert (type, left, NULL);
1459   rc = chrec_convert_aggressive (rtype, right);
1460   if (!rc)
1461     rc = chrec_convert (rtype, right, NULL);
1462 
1463   return build_polynomial_chrec (CHREC_VARIABLE (chrec), lc, rc);
1464 }
1465 
1466 /* Returns true when CHREC0 == CHREC1.  */
1467 
1468 bool
1469 eq_evolutions_p (const_tree chrec0, const_tree chrec1)
1470 {
1471   if (chrec0 == NULL_TREE
1472       || chrec1 == NULL_TREE
1473       || TREE_CODE (chrec0) != TREE_CODE (chrec1))
1474     return false;
1475 
1476   if (chrec0 == chrec1)
1477     return true;
1478 
1479   if (! types_compatible_p (TREE_TYPE (chrec0), TREE_TYPE (chrec1)))
1480     return false;
1481 
1482   switch (TREE_CODE (chrec0))
1483     {
1484     case POLYNOMIAL_CHREC:
1485       return (CHREC_VARIABLE (chrec0) == CHREC_VARIABLE (chrec1)
1486 	      && eq_evolutions_p (CHREC_LEFT (chrec0), CHREC_LEFT (chrec1))
1487 	      && eq_evolutions_p (CHREC_RIGHT (chrec0), CHREC_RIGHT (chrec1)));
1488 
1489     case PLUS_EXPR:
1490     case MULT_EXPR:
1491     case MINUS_EXPR:
1492     case POINTER_PLUS_EXPR:
1493       return eq_evolutions_p (TREE_OPERAND (chrec0, 0),
1494 			      TREE_OPERAND (chrec1, 0))
1495 	  && eq_evolutions_p (TREE_OPERAND (chrec0, 1),
1496 			      TREE_OPERAND (chrec1, 1));
1497 
1498     CASE_CONVERT:
1499       return eq_evolutions_p (TREE_OPERAND (chrec0, 0),
1500 			      TREE_OPERAND (chrec1, 0));
1501 
1502     default:
1503       return operand_equal_p (chrec0, chrec1, 0);
1504     }
1505 }
1506 
1507 /* Returns EV_GROWS if CHREC grows (assuming that it does not overflow),
1508    EV_DECREASES if it decreases, and EV_UNKNOWN if we cannot determine
1509    which of these cases happens.  */
1510 
1511 enum ev_direction
1512 scev_direction (const_tree chrec)
1513 {
1514   const_tree step;
1515 
1516   if (!evolution_function_is_affine_p (chrec))
1517     return EV_DIR_UNKNOWN;
1518 
1519   step = CHREC_RIGHT (chrec);
1520   if (TREE_CODE (step) != INTEGER_CST)
1521     return EV_DIR_UNKNOWN;
1522 
1523   if (tree_int_cst_sign_bit (step))
1524     return EV_DIR_DECREASES;
1525   else
1526     return EV_DIR_GROWS;
1527 }
1528 
1529 /* Iterates over all the components of SCEV, and calls CBCK.  */
1530 
1531 void
1532 for_each_scev_op (tree *scev, bool (*cbck) (tree *, void *), void *data)
1533 {
1534   switch (TREE_CODE_LENGTH (TREE_CODE (*scev)))
1535     {
1536     case 3:
1537       for_each_scev_op (&TREE_OPERAND (*scev, 2), cbck, data);
1538 
1539     case 2:
1540       for_each_scev_op (&TREE_OPERAND (*scev, 1), cbck, data);
1541 
1542     case 1:
1543       for_each_scev_op (&TREE_OPERAND (*scev, 0), cbck, data);
1544 
1545     default:
1546       cbck (scev, data);
1547       break;
1548     }
1549 }
1550 
1551 /* Returns true when the operation can be part of a linear
1552    expression.  */
1553 
1554 static inline bool
1555 operator_is_linear (tree scev)
1556 {
1557   switch (TREE_CODE (scev))
1558     {
1559     case INTEGER_CST:
1560     case POLYNOMIAL_CHREC:
1561     case PLUS_EXPR:
1562     case POINTER_PLUS_EXPR:
1563     case MULT_EXPR:
1564     case MINUS_EXPR:
1565     case NEGATE_EXPR:
1566     case SSA_NAME:
1567     case NON_LVALUE_EXPR:
1568     case BIT_NOT_EXPR:
1569     CASE_CONVERT:
1570       return true;
1571 
1572     default:
1573       return false;
1574     }
1575 }
1576 
1577 /* Return true when SCEV is a linear expression.  Linear expressions
1578    can contain additions, substractions and multiplications.
1579    Multiplications are restricted to constant scaling: "cst * x".  */
1580 
1581 bool
1582 scev_is_linear_expression (tree scev)
1583 {
1584   if (scev == NULL
1585       || !operator_is_linear (scev))
1586     return false;
1587 
1588   if (TREE_CODE (scev) == MULT_EXPR)
1589     return !(tree_contains_chrecs (TREE_OPERAND (scev, 0), NULL)
1590 	     && tree_contains_chrecs (TREE_OPERAND (scev, 1), NULL));
1591 
1592   if (TREE_CODE (scev) == POLYNOMIAL_CHREC
1593       && !evolution_function_is_affine_multivariate_p (scev, CHREC_VARIABLE (scev)))
1594     return false;
1595 
1596   switch (TREE_CODE_LENGTH (TREE_CODE (scev)))
1597     {
1598     case 3:
1599       return scev_is_linear_expression (TREE_OPERAND (scev, 0))
1600 	&& scev_is_linear_expression (TREE_OPERAND (scev, 1))
1601 	&& scev_is_linear_expression (TREE_OPERAND (scev, 2));
1602 
1603     case 2:
1604       return scev_is_linear_expression (TREE_OPERAND (scev, 0))
1605 	&& scev_is_linear_expression (TREE_OPERAND (scev, 1));
1606 
1607     case 1:
1608       return scev_is_linear_expression (TREE_OPERAND (scev, 0));
1609 
1610     case 0:
1611       return true;
1612 
1613     default:
1614       return false;
1615     }
1616 }
1617 
1618 /* Determines whether the expression CHREC contains only interger consts
1619    in the right parts.  */
1620 
1621 bool
1622 evolution_function_right_is_integer_cst (const_tree chrec)
1623 {
1624   if (chrec == NULL_TREE)
1625     return false;
1626 
1627   switch (TREE_CODE (chrec))
1628     {
1629     case INTEGER_CST:
1630       return true;
1631 
1632     case POLYNOMIAL_CHREC:
1633       return TREE_CODE (CHREC_RIGHT (chrec)) == INTEGER_CST
1634 	&& (TREE_CODE (CHREC_LEFT (chrec)) != POLYNOMIAL_CHREC
1635 	    || evolution_function_right_is_integer_cst (CHREC_LEFT (chrec)));
1636 
1637     CASE_CONVERT:
1638       return evolution_function_right_is_integer_cst (TREE_OPERAND (chrec, 0));
1639 
1640     default:
1641       return false;
1642     }
1643 }
1644