xref: /dragonfly/contrib/gcc-4.7/gcc/tree-chrec.c (revision 19380330)
1 /* Chains of recurrences.
2    Copyright (C) 2003, 2004, 2005, 2006, 2007, 2008, 2009, 2010
3    Free Software Foundation, Inc.
4    Contributed by Sebastian Pop <pop@cri.ensmp.fr>
5 
6 This file is part of GCC.
7 
8 GCC is free software; you can redistribute it and/or modify it under
9 the terms of the GNU General Public License as published by the Free
10 Software Foundation; either version 3, or (at your option) any later
11 version.
12 
13 GCC is distributed in the hope that it will be useful, but WITHOUT ANY
14 WARRANTY; without even the implied warranty of MERCHANTABILITY or
15 FITNESS FOR A PARTICULAR PURPOSE.  See the GNU General Public License
16 for more details.
17 
18 You should have received a copy of the GNU General Public License
19 along with GCC; see the file COPYING3.  If not see
20 <http://www.gnu.org/licenses/>.  */
21 
22 /* This file implements operations on chains of recurrences.  Chains
23    of recurrences are used for modeling evolution functions of scalar
24    variables.
25 */
26 
27 #include "config.h"
28 #include "system.h"
29 #include "coretypes.h"
30 #include "tree-pretty-print.h"
31 #include "cfgloop.h"
32 #include "tree-flow.h"
33 #include "tree-chrec.h"
34 #include "tree-pass.h"
35 #include "params.h"
36 #include "tree-scalar-evolution.h"
37 
38 /* Extended folder for chrecs.  */
39 
40 /* Determines whether CST is not a constant evolution.  */
41 
42 static inline bool
43 is_not_constant_evolution (const_tree cst)
44 {
45   return (TREE_CODE (cst) == POLYNOMIAL_CHREC);
46 }
47 
48 /* Fold CODE for a polynomial function and a constant.  */
49 
50 static inline tree
51 chrec_fold_poly_cst (enum tree_code code,
52 		     tree type,
53 		     tree poly,
54 		     tree cst)
55 {
56   gcc_assert (poly);
57   gcc_assert (cst);
58   gcc_assert (TREE_CODE (poly) == POLYNOMIAL_CHREC);
59   gcc_assert (!is_not_constant_evolution (cst));
60   gcc_assert (type == chrec_type (poly));
61 
62   switch (code)
63     {
64     case PLUS_EXPR:
65       return build_polynomial_chrec
66 	(CHREC_VARIABLE (poly),
67 	 chrec_fold_plus (type, CHREC_LEFT (poly), cst),
68 	 CHREC_RIGHT (poly));
69 
70     case MINUS_EXPR:
71       return build_polynomial_chrec
72 	(CHREC_VARIABLE (poly),
73 	 chrec_fold_minus (type, CHREC_LEFT (poly), cst),
74 	 CHREC_RIGHT (poly));
75 
76     case MULT_EXPR:
77       return build_polynomial_chrec
78 	(CHREC_VARIABLE (poly),
79 	 chrec_fold_multiply (type, CHREC_LEFT (poly), cst),
80 	 chrec_fold_multiply (type, CHREC_RIGHT (poly), cst));
81 
82     default:
83       return chrec_dont_know;
84     }
85 }
86 
87 /* Fold the addition of two polynomial functions.  */
88 
89 static inline tree
90 chrec_fold_plus_poly_poly (enum tree_code code,
91 			   tree type,
92 			   tree poly0,
93 			   tree poly1)
94 {
95   tree left, right;
96   struct loop *loop0 = get_chrec_loop (poly0);
97   struct loop *loop1 = get_chrec_loop (poly1);
98   tree rtype = code == POINTER_PLUS_EXPR ? chrec_type (poly1) : type;
99 
100   gcc_assert (poly0);
101   gcc_assert (poly1);
102   gcc_assert (TREE_CODE (poly0) == POLYNOMIAL_CHREC);
103   gcc_assert (TREE_CODE (poly1) == POLYNOMIAL_CHREC);
104   if (POINTER_TYPE_P (chrec_type (poly0)))
105     gcc_assert (ptrofftype_p (chrec_type (poly1)));
106   else
107     gcc_assert (chrec_type (poly0) == chrec_type (poly1));
108   gcc_assert (type == chrec_type (poly0));
109 
110   /*
111     {a, +, b}_1 + {c, +, d}_2  ->  {{a, +, b}_1 + c, +, d}_2,
112     {a, +, b}_2 + {c, +, d}_1  ->  {{c, +, d}_1 + a, +, b}_2,
113     {a, +, b}_x + {c, +, d}_x  ->  {a+c, +, b+d}_x.  */
114   if (flow_loop_nested_p (loop0, loop1))
115     {
116       if (code == PLUS_EXPR || code == POINTER_PLUS_EXPR)
117 	return build_polynomial_chrec
118 	  (CHREC_VARIABLE (poly1),
119 	   chrec_fold_plus (type, poly0, CHREC_LEFT (poly1)),
120 	   CHREC_RIGHT (poly1));
121       else
122 	return build_polynomial_chrec
123 	  (CHREC_VARIABLE (poly1),
124 	   chrec_fold_minus (type, poly0, CHREC_LEFT (poly1)),
125 	   chrec_fold_multiply (type, CHREC_RIGHT (poly1),
126 				SCALAR_FLOAT_TYPE_P (type)
127 				? build_real (type, dconstm1)
128 				: build_int_cst_type (type, -1)));
129     }
130 
131   if (flow_loop_nested_p (loop1, loop0))
132     {
133       if (code == PLUS_EXPR || code == POINTER_PLUS_EXPR)
134 	return build_polynomial_chrec
135 	  (CHREC_VARIABLE (poly0),
136 	   chrec_fold_plus (type, CHREC_LEFT (poly0), poly1),
137 	   CHREC_RIGHT (poly0));
138       else
139 	return build_polynomial_chrec
140 	  (CHREC_VARIABLE (poly0),
141 	   chrec_fold_minus (type, CHREC_LEFT (poly0), poly1),
142 	   CHREC_RIGHT (poly0));
143     }
144 
145   /* This function should never be called for chrecs of loops that
146      do not belong to the same loop nest.  */
147   gcc_assert (loop0 == loop1);
148 
149   if (code == PLUS_EXPR || code == POINTER_PLUS_EXPR)
150     {
151       left = chrec_fold_plus
152 	(type, CHREC_LEFT (poly0), CHREC_LEFT (poly1));
153       right = chrec_fold_plus
154 	(rtype, CHREC_RIGHT (poly0), CHREC_RIGHT (poly1));
155     }
156   else
157     {
158       left = chrec_fold_minus
159 	(type, CHREC_LEFT (poly0), CHREC_LEFT (poly1));
160       right = chrec_fold_minus
161 	(type, CHREC_RIGHT (poly0), CHREC_RIGHT (poly1));
162     }
163 
164   if (chrec_zerop (right))
165     return left;
166   else
167     return build_polynomial_chrec
168       (CHREC_VARIABLE (poly0), left, right);
169 }
170 
171 
172 
173 /* Fold the multiplication of two polynomial functions.  */
174 
175 static inline tree
176 chrec_fold_multiply_poly_poly (tree type,
177 			       tree poly0,
178 			       tree poly1)
179 {
180   tree t0, t1, t2;
181   int var;
182   struct loop *loop0 = get_chrec_loop (poly0);
183   struct loop *loop1 = get_chrec_loop (poly1);
184 
185   gcc_assert (poly0);
186   gcc_assert (poly1);
187   gcc_assert (TREE_CODE (poly0) == POLYNOMIAL_CHREC);
188   gcc_assert (TREE_CODE (poly1) == POLYNOMIAL_CHREC);
189   gcc_assert (chrec_type (poly0) == chrec_type (poly1));
190   gcc_assert (type == chrec_type (poly0));
191 
192   /* {a, +, b}_1 * {c, +, d}_2  ->  {c*{a, +, b}_1, +, d}_2,
193      {a, +, b}_2 * {c, +, d}_1  ->  {a*{c, +, d}_1, +, b}_2,
194      {a, +, b}_x * {c, +, d}_x  ->  {a*c, +, a*d + b*c + b*d, +, 2*b*d}_x.  */
195   if (flow_loop_nested_p (loop0, loop1))
196     /* poly0 is a constant wrt. poly1.  */
197     return build_polynomial_chrec
198       (CHREC_VARIABLE (poly1),
199        chrec_fold_multiply (type, CHREC_LEFT (poly1), poly0),
200        CHREC_RIGHT (poly1));
201 
202   if (flow_loop_nested_p (loop1, loop0))
203     /* poly1 is a constant wrt. poly0.  */
204     return build_polynomial_chrec
205       (CHREC_VARIABLE (poly0),
206        chrec_fold_multiply (type, CHREC_LEFT (poly0), poly1),
207        CHREC_RIGHT (poly0));
208 
209   gcc_assert (loop0 == loop1);
210 
211   /* poly0 and poly1 are two polynomials in the same variable,
212      {a, +, b}_x * {c, +, d}_x  ->  {a*c, +, a*d + b*c + b*d, +, 2*b*d}_x.  */
213 
214   /* "a*c".  */
215   t0 = chrec_fold_multiply (type, CHREC_LEFT (poly0), CHREC_LEFT (poly1));
216 
217   /* "a*d + b*c".  */
218   t1 = chrec_fold_multiply (type, CHREC_LEFT (poly0), CHREC_RIGHT (poly1));
219   t1 = chrec_fold_plus (type, t1, chrec_fold_multiply (type,
220 						       CHREC_RIGHT (poly0),
221 						       CHREC_LEFT (poly1)));
222   /* "b*d".  */
223   t2 = chrec_fold_multiply (type, CHREC_RIGHT (poly0), CHREC_RIGHT (poly1));
224   /* "a*d + b*c + b*d".  */
225   t1 = chrec_fold_plus (type, t1, t2);
226   /* "2*b*d".  */
227   t2 = chrec_fold_multiply (type, SCALAR_FLOAT_TYPE_P (type)
228 			    ? build_real (type, dconst2)
229 			    : build_int_cst (type, 2), t2);
230 
231   var = CHREC_VARIABLE (poly0);
232   return build_polynomial_chrec (var, t0,
233 				 build_polynomial_chrec (var, t1, t2));
234 }
235 
236 /* When the operands are automatically_generated_chrec_p, the fold has
237    to respect the semantics of the operands.  */
238 
239 static inline tree
240 chrec_fold_automatically_generated_operands (tree op0,
241 					     tree op1)
242 {
243   if (op0 == chrec_dont_know
244       || op1 == chrec_dont_know)
245     return chrec_dont_know;
246 
247   if (op0 == chrec_known
248       || op1 == chrec_known)
249     return chrec_known;
250 
251   if (op0 == chrec_not_analyzed_yet
252       || op1 == chrec_not_analyzed_yet)
253     return chrec_not_analyzed_yet;
254 
255   /* The default case produces a safe result.  */
256   return chrec_dont_know;
257 }
258 
259 /* Fold the addition of two chrecs.  */
260 
261 static tree
262 chrec_fold_plus_1 (enum tree_code code, tree type,
263 		   tree op0, tree op1)
264 {
265   if (automatically_generated_chrec_p (op0)
266       || automatically_generated_chrec_p (op1))
267     return chrec_fold_automatically_generated_operands (op0, op1);
268 
269   switch (TREE_CODE (op0))
270     {
271     case POLYNOMIAL_CHREC:
272       switch (TREE_CODE (op1))
273 	{
274 	case POLYNOMIAL_CHREC:
275 	  return chrec_fold_plus_poly_poly (code, type, op0, op1);
276 
277 	CASE_CONVERT:
278 	  if (tree_contains_chrecs (op1, NULL))
279 	    return chrec_dont_know;
280 
281 	default:
282 	  if (code == PLUS_EXPR || code == POINTER_PLUS_EXPR)
283 	    return build_polynomial_chrec
284 	      (CHREC_VARIABLE (op0),
285 	       chrec_fold_plus (type, CHREC_LEFT (op0), op1),
286 	       CHREC_RIGHT (op0));
287 	  else
288 	    return build_polynomial_chrec
289 	      (CHREC_VARIABLE (op0),
290 	       chrec_fold_minus (type, CHREC_LEFT (op0), op1),
291 	       CHREC_RIGHT (op0));
292 	}
293 
294     CASE_CONVERT:
295       if (tree_contains_chrecs (op0, NULL))
296 	return chrec_dont_know;
297 
298     default:
299       switch (TREE_CODE (op1))
300 	{
301 	case POLYNOMIAL_CHREC:
302 	  if (code == PLUS_EXPR || code == POINTER_PLUS_EXPR)
303 	    return build_polynomial_chrec
304 	      (CHREC_VARIABLE (op1),
305 	       chrec_fold_plus (type, op0, CHREC_LEFT (op1)),
306 	       CHREC_RIGHT (op1));
307 	  else
308 	    return build_polynomial_chrec
309 	      (CHREC_VARIABLE (op1),
310 	       chrec_fold_minus (type, op0, CHREC_LEFT (op1)),
311 	       chrec_fold_multiply (type, CHREC_RIGHT (op1),
312 				    SCALAR_FLOAT_TYPE_P (type)
313 				    ? build_real (type, dconstm1)
314 				    : build_int_cst_type (type, -1)));
315 
316 	CASE_CONVERT:
317 	  if (tree_contains_chrecs (op1, NULL))
318 	    return chrec_dont_know;
319 
320 	default:
321 	  {
322 	    int size = 0;
323 	    if ((tree_contains_chrecs (op0, &size)
324 		 || tree_contains_chrecs (op1, &size))
325 		&& size < PARAM_VALUE (PARAM_SCEV_MAX_EXPR_SIZE))
326 	      return build2 (code, type, op0, op1);
327 	    else if (size < PARAM_VALUE (PARAM_SCEV_MAX_EXPR_SIZE))
328 	      {
329 		if (code == POINTER_PLUS_EXPR)
330 		  return fold_build_pointer_plus (fold_convert (type, op0),
331 						  op1);
332 		else
333 		  return fold_build2 (code, type,
334 				      fold_convert (type, op0),
335 				      fold_convert (type, op1));
336 	      }
337 	    else
338 	      return chrec_dont_know;
339 	  }
340 	}
341     }
342 }
343 
344 /* Fold the addition of two chrecs.  */
345 
346 tree
347 chrec_fold_plus (tree type,
348 		 tree op0,
349 		 tree op1)
350 {
351   enum tree_code code;
352   if (automatically_generated_chrec_p (op0)
353       || automatically_generated_chrec_p (op1))
354     return chrec_fold_automatically_generated_operands (op0, op1);
355 
356   if (integer_zerop (op0))
357     return chrec_convert (type, op1, NULL);
358   if (integer_zerop (op1))
359     return chrec_convert (type, op0, NULL);
360 
361   if (POINTER_TYPE_P (type))
362     code = POINTER_PLUS_EXPR;
363   else
364     code = PLUS_EXPR;
365 
366   return chrec_fold_plus_1 (code, type, op0, op1);
367 }
368 
369 /* Fold the subtraction of two chrecs.  */
370 
371 tree
372 chrec_fold_minus (tree type,
373 		  tree op0,
374 		  tree op1)
375 {
376   if (automatically_generated_chrec_p (op0)
377       || automatically_generated_chrec_p (op1))
378     return chrec_fold_automatically_generated_operands (op0, op1);
379 
380   if (integer_zerop (op1))
381     return op0;
382 
383   return chrec_fold_plus_1 (MINUS_EXPR, type, op0, op1);
384 }
385 
386 /* Fold the multiplication of two chrecs.  */
387 
388 tree
389 chrec_fold_multiply (tree type,
390 		     tree op0,
391 		     tree op1)
392 {
393   if (automatically_generated_chrec_p (op0)
394       || automatically_generated_chrec_p (op1))
395     return chrec_fold_automatically_generated_operands (op0, op1);
396 
397   switch (TREE_CODE (op0))
398     {
399     case POLYNOMIAL_CHREC:
400       switch (TREE_CODE (op1))
401 	{
402 	case POLYNOMIAL_CHREC:
403 	  return chrec_fold_multiply_poly_poly (type, op0, op1);
404 
405 	CASE_CONVERT:
406 	  if (tree_contains_chrecs (op1, NULL))
407 	    return chrec_dont_know;
408 
409 	default:
410 	  if (integer_onep (op1))
411 	    return op0;
412 	  if (integer_zerop (op1))
413 	    return build_int_cst (type, 0);
414 
415 	  return build_polynomial_chrec
416 	    (CHREC_VARIABLE (op0),
417 	     chrec_fold_multiply (type, CHREC_LEFT (op0), op1),
418 	     chrec_fold_multiply (type, CHREC_RIGHT (op0), op1));
419 	}
420 
421     CASE_CONVERT:
422       if (tree_contains_chrecs (op0, NULL))
423 	return chrec_dont_know;
424 
425     default:
426       if (integer_onep (op0))
427 	return op1;
428 
429       if (integer_zerop (op0))
430     	return build_int_cst (type, 0);
431 
432       switch (TREE_CODE (op1))
433 	{
434 	case POLYNOMIAL_CHREC:
435 	  return build_polynomial_chrec
436 	    (CHREC_VARIABLE (op1),
437 	     chrec_fold_multiply (type, CHREC_LEFT (op1), op0),
438 	     chrec_fold_multiply (type, CHREC_RIGHT (op1), op0));
439 
440 	CASE_CONVERT:
441 	  if (tree_contains_chrecs (op1, NULL))
442 	    return chrec_dont_know;
443 
444 	default:
445 	  if (integer_onep (op1))
446 	    return op0;
447 	  if (integer_zerop (op1))
448 	    return build_int_cst (type, 0);
449 	  return fold_build2 (MULT_EXPR, type, op0, op1);
450 	}
451     }
452 }
453 
454 
455 
456 /* Operations.  */
457 
458 /* Evaluate the binomial coefficient.  Return NULL_TREE if the intermediate
459    calculation overflows, otherwise return C(n,k) with type TYPE.  */
460 
461 static tree
462 tree_fold_binomial (tree type, tree n, unsigned int k)
463 {
464   unsigned HOST_WIDE_INT lidx, lnum, ldenom, lres, ldum;
465   HOST_WIDE_INT hidx, hnum, hdenom, hres, hdum;
466   unsigned int i;
467   tree res;
468 
469   /* Handle the most frequent cases.  */
470   if (k == 0)
471     return build_int_cst (type, 1);
472   if (k == 1)
473     return fold_convert (type, n);
474 
475   /* Check that k <= n.  */
476   if (TREE_INT_CST_HIGH (n) == 0
477       && TREE_INT_CST_LOW (n) < k)
478     return NULL_TREE;
479 
480   /* Numerator = n.  */
481   lnum = TREE_INT_CST_LOW (n);
482   hnum = TREE_INT_CST_HIGH (n);
483 
484   /* Denominator = 2.  */
485   ldenom = 2;
486   hdenom = 0;
487 
488   /* Index = Numerator-1.  */
489   if (lnum == 0)
490     {
491       hidx = hnum - 1;
492       lidx = ~ (unsigned HOST_WIDE_INT) 0;
493     }
494   else
495     {
496       hidx = hnum;
497       lidx = lnum - 1;
498     }
499 
500   /* Numerator = Numerator*Index = n*(n-1).  */
501   if (mul_double (lnum, hnum, lidx, hidx, &lnum, &hnum))
502     return NULL_TREE;
503 
504   for (i = 3; i <= k; i++)
505     {
506       /* Index--.  */
507       if (lidx == 0)
508 	{
509 	  hidx--;
510 	  lidx = ~ (unsigned HOST_WIDE_INT) 0;
511 	}
512       else
513         lidx--;
514 
515       /* Numerator *= Index.  */
516       if (mul_double (lnum, hnum, lidx, hidx, &lnum, &hnum))
517 	return NULL_TREE;
518 
519       /* Denominator *= i.  */
520       mul_double (ldenom, hdenom, i, 0, &ldenom, &hdenom);
521     }
522 
523   /* Result = Numerator / Denominator.  */
524   div_and_round_double (EXACT_DIV_EXPR, 1, lnum, hnum, ldenom, hdenom,
525 			&lres, &hres, &ldum, &hdum);
526 
527   res = build_int_cst_wide (type, lres, hres);
528   return int_fits_type_p (res, type) ? res : NULL_TREE;
529 }
530 
531 /* Helper function.  Use the Newton's interpolating formula for
532    evaluating the value of the evolution function.  */
533 
534 static tree
535 chrec_evaluate (unsigned var, tree chrec, tree n, unsigned int k)
536 {
537   tree arg0, arg1, binomial_n_k;
538   tree type = TREE_TYPE (chrec);
539   struct loop *var_loop = get_loop (var);
540 
541   while (TREE_CODE (chrec) == POLYNOMIAL_CHREC
542 	 && flow_loop_nested_p (var_loop, get_chrec_loop (chrec)))
543     chrec = CHREC_LEFT (chrec);
544 
545   if (TREE_CODE (chrec) == POLYNOMIAL_CHREC
546       && CHREC_VARIABLE (chrec) == var)
547     {
548       arg1 = chrec_evaluate (var, CHREC_RIGHT (chrec), n, k + 1);
549       if (arg1 == chrec_dont_know)
550 	return chrec_dont_know;
551       binomial_n_k = tree_fold_binomial (type, n, k);
552       if (!binomial_n_k)
553 	return chrec_dont_know;
554       arg0 = fold_build2 (MULT_EXPR, type,
555 			  CHREC_LEFT (chrec), binomial_n_k);
556       return chrec_fold_plus (type, arg0, arg1);
557     }
558 
559   binomial_n_k = tree_fold_binomial (type, n, k);
560   if (!binomial_n_k)
561     return chrec_dont_know;
562 
563   return fold_build2 (MULT_EXPR, type, chrec, binomial_n_k);
564 }
565 
566 /* Evaluates "CHREC (X)" when the varying variable is VAR.
567    Example:  Given the following parameters,
568 
569    var = 1
570    chrec = {3, +, 4}_1
571    x = 10
572 
573    The result is given by the Newton's interpolating formula:
574    3 * \binom{10}{0} + 4 * \binom{10}{1}.
575 */
576 
577 tree
578 chrec_apply (unsigned var,
579 	     tree chrec,
580 	     tree x)
581 {
582   tree type = chrec_type (chrec);
583   tree res = chrec_dont_know;
584 
585   if (automatically_generated_chrec_p (chrec)
586       || automatically_generated_chrec_p (x)
587 
588       /* When the symbols are defined in an outer loop, it is possible
589 	 to symbolically compute the apply, since the symbols are
590 	 constants with respect to the varying loop.  */
591       || chrec_contains_symbols_defined_in_loop (chrec, var))
592     return chrec_dont_know;
593 
594   if (dump_file && (dump_flags & TDF_SCEV))
595     fprintf (dump_file, "(chrec_apply \n");
596 
597   if (TREE_CODE (x) == INTEGER_CST && SCALAR_FLOAT_TYPE_P (type))
598     x = build_real_from_int_cst (type, x);
599 
600   switch (TREE_CODE (chrec))
601     {
602     case POLYNOMIAL_CHREC:
603       if (evolution_function_is_affine_p (chrec))
604 	{
605 	  if (CHREC_VARIABLE (chrec) != var)
606 	    return build_polynomial_chrec
607 	      (CHREC_VARIABLE (chrec),
608 	       chrec_apply (var, CHREC_LEFT (chrec), x),
609 	       chrec_apply (var, CHREC_RIGHT (chrec), x));
610 
611 	  /* "{a, +, b} (x)"  ->  "a + b*x".  */
612 	  x = chrec_convert_rhs (type, x, NULL);
613 	  res = chrec_fold_multiply (TREE_TYPE (x), CHREC_RIGHT (chrec), x);
614 	  res = chrec_fold_plus (type, CHREC_LEFT (chrec), res);
615 	}
616       else if (TREE_CODE (x) == INTEGER_CST
617 	       && tree_int_cst_sgn (x) == 1)
618 	/* testsuite/.../ssa-chrec-38.c.  */
619 	res = chrec_evaluate (var, chrec, x, 0);
620       else
621 	res = chrec_dont_know;
622       break;
623 
624     CASE_CONVERT:
625       res = chrec_convert (TREE_TYPE (chrec),
626 			   chrec_apply (var, TREE_OPERAND (chrec, 0), x),
627 			   NULL);
628       break;
629 
630     default:
631       res = chrec;
632       break;
633     }
634 
635   if (dump_file && (dump_flags & TDF_SCEV))
636     {
637       fprintf (dump_file, "  (varying_loop = %d\n", var);
638       fprintf (dump_file, ")\n  (chrec = ");
639       print_generic_expr (dump_file, chrec, 0);
640       fprintf (dump_file, ")\n  (x = ");
641       print_generic_expr (dump_file, x, 0);
642       fprintf (dump_file, ")\n  (res = ");
643       print_generic_expr (dump_file, res, 0);
644       fprintf (dump_file, "))\n");
645     }
646 
647   return res;
648 }
649 
650 /* For a given CHREC and an induction variable map IV_MAP that maps
651    (loop->num, expr) for every loop number of the current_loops an
652    expression, calls chrec_apply when the expression is not NULL.  */
653 
654 tree
655 chrec_apply_map (tree chrec, VEC (tree, heap) *iv_map)
656 {
657   int i;
658   tree expr;
659 
660   FOR_EACH_VEC_ELT (tree, iv_map, i, expr)
661     if (expr)
662       chrec = chrec_apply (i, chrec, expr);
663 
664   return chrec;
665 }
666 
667 /* Replaces the initial condition in CHREC with INIT_COND.  */
668 
669 tree
670 chrec_replace_initial_condition (tree chrec,
671 				 tree init_cond)
672 {
673   if (automatically_generated_chrec_p (chrec))
674     return chrec;
675 
676   gcc_assert (chrec_type (chrec) == chrec_type (init_cond));
677 
678   switch (TREE_CODE (chrec))
679     {
680     case POLYNOMIAL_CHREC:
681       return build_polynomial_chrec
682 	(CHREC_VARIABLE (chrec),
683 	 chrec_replace_initial_condition (CHREC_LEFT (chrec), init_cond),
684 	 CHREC_RIGHT (chrec));
685 
686     default:
687       return init_cond;
688     }
689 }
690 
691 /* Returns the initial condition of a given CHREC.  */
692 
693 tree
694 initial_condition (tree chrec)
695 {
696   if (automatically_generated_chrec_p (chrec))
697     return chrec;
698 
699   if (TREE_CODE (chrec) == POLYNOMIAL_CHREC)
700     return initial_condition (CHREC_LEFT (chrec));
701   else
702     return chrec;
703 }
704 
705 /* Returns a univariate function that represents the evolution in
706    LOOP_NUM.  Mask the evolution of any other loop.  */
707 
708 tree
709 hide_evolution_in_other_loops_than_loop (tree chrec,
710 					 unsigned loop_num)
711 {
712   struct loop *loop = get_loop (loop_num), *chloop;
713   if (automatically_generated_chrec_p (chrec))
714     return chrec;
715 
716   switch (TREE_CODE (chrec))
717     {
718     case POLYNOMIAL_CHREC:
719       chloop = get_chrec_loop (chrec);
720 
721       if (chloop == loop)
722 	return build_polynomial_chrec
723 	  (loop_num,
724 	   hide_evolution_in_other_loops_than_loop (CHREC_LEFT (chrec),
725 						    loop_num),
726 	   CHREC_RIGHT (chrec));
727 
728       else if (flow_loop_nested_p (chloop, loop))
729 	/* There is no evolution in this loop.  */
730 	return initial_condition (chrec);
731 
732       else
733 	{
734 	  gcc_assert (flow_loop_nested_p (loop, chloop));
735 	  return hide_evolution_in_other_loops_than_loop (CHREC_LEFT (chrec),
736 							  loop_num);
737 	}
738 
739     default:
740       return chrec;
741     }
742 }
743 
744 /* Returns the evolution part of CHREC in LOOP_NUM when RIGHT is
745    true, otherwise returns the initial condition in LOOP_NUM.  */
746 
747 static tree
748 chrec_component_in_loop_num (tree chrec,
749 			     unsigned loop_num,
750 			     bool right)
751 {
752   tree component;
753   struct loop *loop = get_loop (loop_num), *chloop;
754 
755   if (automatically_generated_chrec_p (chrec))
756     return chrec;
757 
758   switch (TREE_CODE (chrec))
759     {
760     case POLYNOMIAL_CHREC:
761       chloop = get_chrec_loop (chrec);
762 
763       if (chloop == loop)
764 	{
765 	  if (right)
766 	    component = CHREC_RIGHT (chrec);
767 	  else
768 	    component = CHREC_LEFT (chrec);
769 
770 	  if (TREE_CODE (CHREC_LEFT (chrec)) != POLYNOMIAL_CHREC
771 	      || CHREC_VARIABLE (CHREC_LEFT (chrec)) != CHREC_VARIABLE (chrec))
772 	    return component;
773 
774 	  else
775 	    return build_polynomial_chrec
776 	      (loop_num,
777 	       chrec_component_in_loop_num (CHREC_LEFT (chrec),
778 					    loop_num,
779 					    right),
780 	       component);
781 	}
782 
783       else if (flow_loop_nested_p (chloop, loop))
784 	/* There is no evolution part in this loop.  */
785 	return NULL_TREE;
786 
787       else
788 	{
789 	  gcc_assert (flow_loop_nested_p (loop, chloop));
790 	  return chrec_component_in_loop_num (CHREC_LEFT (chrec),
791 					      loop_num,
792 					      right);
793 	}
794 
795      default:
796       if (right)
797 	return NULL_TREE;
798       else
799 	return chrec;
800     }
801 }
802 
803 /* Returns the evolution part in LOOP_NUM.  Example: the call
804    evolution_part_in_loop_num ({{0, +, 1}_1, +, 2}_1, 1) returns
805    {1, +, 2}_1  */
806 
807 tree
808 evolution_part_in_loop_num (tree chrec,
809 			    unsigned loop_num)
810 {
811   return chrec_component_in_loop_num (chrec, loop_num, true);
812 }
813 
814 /* Returns the initial condition in LOOP_NUM.  Example: the call
815    initial_condition_in_loop_num ({{0, +, 1}_1, +, 2}_2, 2) returns
816    {0, +, 1}_1  */
817 
818 tree
819 initial_condition_in_loop_num (tree chrec,
820 			       unsigned loop_num)
821 {
822   return chrec_component_in_loop_num (chrec, loop_num, false);
823 }
824 
825 /* Set or reset the evolution of CHREC to NEW_EVOL in loop LOOP_NUM.
826    This function is essentially used for setting the evolution to
827    chrec_dont_know, for example after having determined that it is
828    impossible to say how many times a loop will execute.  */
829 
830 tree
831 reset_evolution_in_loop (unsigned loop_num,
832 			 tree chrec,
833 			 tree new_evol)
834 {
835   struct loop *loop = get_loop (loop_num);
836 
837   if (POINTER_TYPE_P (chrec_type (chrec)))
838     gcc_assert (ptrofftype_p (chrec_type (new_evol)));
839   else
840     gcc_assert (chrec_type (chrec) == chrec_type (new_evol));
841 
842   if (TREE_CODE (chrec) == POLYNOMIAL_CHREC
843       && flow_loop_nested_p (loop, get_chrec_loop (chrec)))
844     {
845       tree left = reset_evolution_in_loop (loop_num, CHREC_LEFT (chrec),
846 					   new_evol);
847       tree right = reset_evolution_in_loop (loop_num, CHREC_RIGHT (chrec),
848 					    new_evol);
849       return build3 (POLYNOMIAL_CHREC, TREE_TYPE (left),
850 		     CHREC_VAR (chrec), left, right);
851     }
852 
853   while (TREE_CODE (chrec) == POLYNOMIAL_CHREC
854 	 && CHREC_VARIABLE (chrec) == loop_num)
855     chrec = CHREC_LEFT (chrec);
856 
857   return build_polynomial_chrec (loop_num, chrec, new_evol);
858 }
859 
860 /* Merges two evolution functions that were found by following two
861    alternate paths of a conditional expression.  */
862 
863 tree
864 chrec_merge (tree chrec1,
865 	     tree chrec2)
866 {
867   if (chrec1 == chrec_dont_know
868       || chrec2 == chrec_dont_know)
869     return chrec_dont_know;
870 
871   if (chrec1 == chrec_known
872       || chrec2 == chrec_known)
873     return chrec_known;
874 
875   if (chrec1 == chrec_not_analyzed_yet)
876     return chrec2;
877   if (chrec2 == chrec_not_analyzed_yet)
878     return chrec1;
879 
880   if (eq_evolutions_p (chrec1, chrec2))
881     return chrec1;
882 
883   return chrec_dont_know;
884 }
885 
886 
887 
888 /* Observers.  */
889 
890 /* Helper function for is_multivariate_chrec.  */
891 
892 static bool
893 is_multivariate_chrec_rec (const_tree chrec, unsigned int rec_var)
894 {
895   if (chrec == NULL_TREE)
896     return false;
897 
898   if (TREE_CODE (chrec) == POLYNOMIAL_CHREC)
899     {
900       if (CHREC_VARIABLE (chrec) != rec_var)
901 	return true;
902       else
903 	return (is_multivariate_chrec_rec (CHREC_LEFT (chrec), rec_var)
904 		|| is_multivariate_chrec_rec (CHREC_RIGHT (chrec), rec_var));
905     }
906   else
907     return false;
908 }
909 
910 /* Determine whether the given chrec is multivariate or not.  */
911 
912 bool
913 is_multivariate_chrec (const_tree chrec)
914 {
915   if (chrec == NULL_TREE)
916     return false;
917 
918   if (TREE_CODE (chrec) == POLYNOMIAL_CHREC)
919     return (is_multivariate_chrec_rec (CHREC_LEFT (chrec),
920 				       CHREC_VARIABLE (chrec))
921 	    || is_multivariate_chrec_rec (CHREC_RIGHT (chrec),
922 					  CHREC_VARIABLE (chrec)));
923   else
924     return false;
925 }
926 
927 /* Determines whether the chrec contains symbolic names or not.  */
928 
929 bool
930 chrec_contains_symbols (const_tree chrec)
931 {
932   int i, n;
933 
934   if (chrec == NULL_TREE)
935     return false;
936 
937   if (TREE_CODE (chrec) == SSA_NAME
938       || TREE_CODE (chrec) == VAR_DECL
939       || TREE_CODE (chrec) == PARM_DECL
940       || TREE_CODE (chrec) == FUNCTION_DECL
941       || TREE_CODE (chrec) == LABEL_DECL
942       || TREE_CODE (chrec) == RESULT_DECL
943       || TREE_CODE (chrec) == FIELD_DECL)
944     return true;
945 
946   n = TREE_OPERAND_LENGTH (chrec);
947   for (i = 0; i < n; i++)
948     if (chrec_contains_symbols (TREE_OPERAND (chrec, i)))
949       return true;
950   return false;
951 }
952 
953 /* Determines whether the chrec contains undetermined coefficients.  */
954 
955 bool
956 chrec_contains_undetermined (const_tree chrec)
957 {
958   int i, n;
959 
960   if (chrec == chrec_dont_know)
961     return true;
962 
963   if (chrec == NULL_TREE)
964     return false;
965 
966   n = TREE_OPERAND_LENGTH (chrec);
967   for (i = 0; i < n; i++)
968     if (chrec_contains_undetermined (TREE_OPERAND (chrec, i)))
969       return true;
970   return false;
971 }
972 
973 /* Determines whether the tree EXPR contains chrecs, and increment
974    SIZE if it is not a NULL pointer by an estimation of the depth of
975    the tree.  */
976 
977 bool
978 tree_contains_chrecs (const_tree expr, int *size)
979 {
980   int i, n;
981 
982   if (expr == NULL_TREE)
983     return false;
984 
985   if (size)
986     (*size)++;
987 
988   if (tree_is_chrec (expr))
989     return true;
990 
991   n = TREE_OPERAND_LENGTH (expr);
992   for (i = 0; i < n; i++)
993     if (tree_contains_chrecs (TREE_OPERAND (expr, i), size))
994       return true;
995   return false;
996 }
997 
998 /* Recursive helper function.  */
999 
1000 static bool
1001 evolution_function_is_invariant_rec_p (tree chrec, int loopnum)
1002 {
1003   if (evolution_function_is_constant_p (chrec))
1004     return true;
1005 
1006   if (TREE_CODE (chrec) == SSA_NAME
1007       && (loopnum == 0
1008 	  || expr_invariant_in_loop_p (get_loop (loopnum), chrec)))
1009     return true;
1010 
1011   if (TREE_CODE (chrec) == POLYNOMIAL_CHREC)
1012     {
1013       if (CHREC_VARIABLE (chrec) == (unsigned) loopnum
1014 	  || flow_loop_nested_p (get_loop (loopnum),
1015 				 get_loop (CHREC_VARIABLE (chrec)))
1016 	  || !evolution_function_is_invariant_rec_p (CHREC_RIGHT (chrec),
1017 						     loopnum)
1018 	  || !evolution_function_is_invariant_rec_p (CHREC_LEFT (chrec),
1019 						     loopnum))
1020 	return false;
1021       return true;
1022     }
1023 
1024   switch (TREE_OPERAND_LENGTH (chrec))
1025     {
1026     case 2:
1027       if (!evolution_function_is_invariant_rec_p (TREE_OPERAND (chrec, 1),
1028 						  loopnum))
1029 	return false;
1030 
1031     case 1:
1032       if (!evolution_function_is_invariant_rec_p (TREE_OPERAND (chrec, 0),
1033 						  loopnum))
1034 	return false;
1035       return true;
1036 
1037     default:
1038       return false;
1039     }
1040 
1041   return false;
1042 }
1043 
1044 /* Return true if CHREC is invariant in loop LOOPNUM, false otherwise. */
1045 
1046 bool
1047 evolution_function_is_invariant_p (tree chrec, int loopnum)
1048 {
1049   return evolution_function_is_invariant_rec_p (chrec, loopnum);
1050 }
1051 
1052 /* Determine whether the given tree is an affine multivariate
1053    evolution.  */
1054 
1055 bool
1056 evolution_function_is_affine_multivariate_p (const_tree chrec, int loopnum)
1057 {
1058   if (chrec == NULL_TREE)
1059     return false;
1060 
1061   switch (TREE_CODE (chrec))
1062     {
1063     case POLYNOMIAL_CHREC:
1064       if (evolution_function_is_invariant_rec_p (CHREC_LEFT (chrec), loopnum))
1065 	{
1066 	  if (evolution_function_is_invariant_rec_p (CHREC_RIGHT (chrec), loopnum))
1067 	    return true;
1068 	  else
1069 	    {
1070 	      if (TREE_CODE (CHREC_RIGHT (chrec)) == POLYNOMIAL_CHREC
1071 		  && CHREC_VARIABLE (CHREC_RIGHT (chrec))
1072 		     != CHREC_VARIABLE (chrec)
1073 		  && evolution_function_is_affine_multivariate_p
1074 		  (CHREC_RIGHT (chrec), loopnum))
1075 		return true;
1076 	      else
1077 		return false;
1078 	    }
1079 	}
1080       else
1081 	{
1082 	  if (evolution_function_is_invariant_rec_p (CHREC_RIGHT (chrec), loopnum)
1083 	      && TREE_CODE (CHREC_LEFT (chrec)) == POLYNOMIAL_CHREC
1084 	      && CHREC_VARIABLE (CHREC_LEFT (chrec)) != CHREC_VARIABLE (chrec)
1085 	      && evolution_function_is_affine_multivariate_p
1086 	      (CHREC_LEFT (chrec), loopnum))
1087 	    return true;
1088 	  else
1089 	    return false;
1090 	}
1091 
1092     default:
1093       return false;
1094     }
1095 }
1096 
1097 /* Determine whether the given tree is a function in zero or one
1098    variables.  */
1099 
1100 bool
1101 evolution_function_is_univariate_p (const_tree chrec)
1102 {
1103   if (chrec == NULL_TREE)
1104     return true;
1105 
1106   switch (TREE_CODE (chrec))
1107     {
1108     case POLYNOMIAL_CHREC:
1109       switch (TREE_CODE (CHREC_LEFT (chrec)))
1110 	{
1111 	case POLYNOMIAL_CHREC:
1112 	  if (CHREC_VARIABLE (chrec) != CHREC_VARIABLE (CHREC_LEFT (chrec)))
1113 	    return false;
1114 	  if (!evolution_function_is_univariate_p (CHREC_LEFT (chrec)))
1115 	    return false;
1116 	  break;
1117 
1118 	default:
1119 	  if (tree_contains_chrecs (CHREC_LEFT (chrec), NULL))
1120 	    return false;
1121 	  break;
1122 	}
1123 
1124       switch (TREE_CODE (CHREC_RIGHT (chrec)))
1125 	{
1126 	case POLYNOMIAL_CHREC:
1127 	  if (CHREC_VARIABLE (chrec) != CHREC_VARIABLE (CHREC_RIGHT (chrec)))
1128 	    return false;
1129 	  if (!evolution_function_is_univariate_p (CHREC_RIGHT (chrec)))
1130 	    return false;
1131 	  break;
1132 
1133 	default:
1134 	  if (tree_contains_chrecs (CHREC_RIGHT (chrec), NULL))
1135 	    return false;
1136 	  break;
1137 	}
1138 
1139     default:
1140       return true;
1141     }
1142 }
1143 
1144 /* Returns the number of variables of CHREC.  Example: the call
1145    nb_vars_in_chrec ({{0, +, 1}_5, +, 2}_6) returns 2.  */
1146 
1147 unsigned
1148 nb_vars_in_chrec (tree chrec)
1149 {
1150   if (chrec == NULL_TREE)
1151     return 0;
1152 
1153   switch (TREE_CODE (chrec))
1154     {
1155     case POLYNOMIAL_CHREC:
1156       return 1 + nb_vars_in_chrec
1157 	(initial_condition_in_loop_num (chrec, CHREC_VARIABLE (chrec)));
1158 
1159     default:
1160       return 0;
1161     }
1162 }
1163 
1164 static tree chrec_convert_1 (tree, tree, gimple, bool);
1165 
1166 /* Converts BASE and STEP of affine scev to TYPE.  LOOP is the loop whose iv
1167    the scev corresponds to.  AT_STMT is the statement at that the scev is
1168    evaluated.  USE_OVERFLOW_SEMANTICS is true if this function should assume that
1169    the rules for overflow of the given language apply (e.g., that signed
1170    arithmetics in C does not overflow) -- i.e., to use them to avoid unnecessary
1171    tests, but also to enforce that the result follows them.  Returns true if the
1172    conversion succeeded, false otherwise.  */
1173 
1174 bool
1175 convert_affine_scev (struct loop *loop, tree type,
1176 		     tree *base, tree *step, gimple at_stmt,
1177 		     bool use_overflow_semantics)
1178 {
1179   tree ct = TREE_TYPE (*step);
1180   bool enforce_overflow_semantics;
1181   bool must_check_src_overflow, must_check_rslt_overflow;
1182   tree new_base, new_step;
1183   tree step_type = POINTER_TYPE_P (type) ? sizetype : type;
1184 
1185   /* In general,
1186      (TYPE) (BASE + STEP * i) = (TYPE) BASE + (TYPE -- sign extend) STEP * i,
1187      but we must check some assumptions.
1188 
1189      1) If [BASE, +, STEP] wraps, the equation is not valid when precision
1190         of CT is smaller than the precision of TYPE.  For example, when we
1191 	cast unsigned char [254, +, 1] to unsigned, the values on left side
1192 	are 254, 255, 0, 1, ..., but those on the right side are
1193 	254, 255, 256, 257, ...
1194      2) In case that we must also preserve the fact that signed ivs do not
1195         overflow, we must additionally check that the new iv does not wrap.
1196 	For example, unsigned char [125, +, 1] casted to signed char could
1197 	become a wrapping variable with values 125, 126, 127, -128, -127, ...,
1198 	which would confuse optimizers that assume that this does not
1199 	happen.  */
1200   must_check_src_overflow = TYPE_PRECISION (ct) < TYPE_PRECISION (type);
1201 
1202   enforce_overflow_semantics = (use_overflow_semantics
1203 				&& nowrap_type_p (type));
1204   if (enforce_overflow_semantics)
1205     {
1206       /* We can avoid checking whether the result overflows in the following
1207 	 cases:
1208 
1209 	 -- must_check_src_overflow is true, and the range of TYPE is superset
1210 	    of the range of CT -- i.e., in all cases except if CT signed and
1211 	    TYPE unsigned.
1212          -- both CT and TYPE have the same precision and signedness, and we
1213 	    verify instead that the source does not overflow (this may be
1214 	    easier than verifying it for the result, as we may use the
1215 	    information about the semantics of overflow in CT).  */
1216       if (must_check_src_overflow)
1217 	{
1218 	  if (TYPE_UNSIGNED (type) && !TYPE_UNSIGNED (ct))
1219 	    must_check_rslt_overflow = true;
1220 	  else
1221 	    must_check_rslt_overflow = false;
1222 	}
1223       else if (TYPE_UNSIGNED (ct) == TYPE_UNSIGNED (type)
1224 	       && TYPE_PRECISION (ct) == TYPE_PRECISION (type))
1225 	{
1226 	  must_check_rslt_overflow = false;
1227 	  must_check_src_overflow = true;
1228 	}
1229       else
1230 	must_check_rslt_overflow = true;
1231     }
1232   else
1233     must_check_rslt_overflow = false;
1234 
1235   if (must_check_src_overflow
1236       && scev_probably_wraps_p (*base, *step, at_stmt, loop,
1237 				use_overflow_semantics))
1238     return false;
1239 
1240   new_base = chrec_convert_1 (type, *base, at_stmt,
1241 			      use_overflow_semantics);
1242   /* The step must be sign extended, regardless of the signedness
1243      of CT and TYPE.  This only needs to be handled specially when
1244      CT is unsigned -- to avoid e.g. unsigned char [100, +, 255]
1245      (with values 100, 99, 98, ...) from becoming signed or unsigned
1246      [100, +, 255] with values 100, 355, ...; the sign-extension is
1247      performed by default when CT is signed.  */
1248   new_step = *step;
1249   if (TYPE_PRECISION (step_type) > TYPE_PRECISION (ct) && TYPE_UNSIGNED (ct))
1250     {
1251       tree signed_ct = build_nonstandard_integer_type (TYPE_PRECISION (ct), 0);
1252       new_step = chrec_convert_1 (signed_ct, new_step, at_stmt,
1253                                   use_overflow_semantics);
1254     }
1255   new_step = chrec_convert_1 (step_type, new_step, at_stmt, use_overflow_semantics);
1256 
1257   if (automatically_generated_chrec_p (new_base)
1258       || automatically_generated_chrec_p (new_step))
1259     return false;
1260 
1261   if (must_check_rslt_overflow
1262       /* Note that in this case we cannot use the fact that signed variables
1263 	 do not overflow, as this is what we are verifying for the new iv.  */
1264       && scev_probably_wraps_p (new_base, new_step, at_stmt, loop, false))
1265     return false;
1266 
1267   *base = new_base;
1268   *step = new_step;
1269   return true;
1270 }
1271 
1272 
1273 /* Convert CHREC for the right hand side of a CHREC.
1274    The increment for a pointer type is always sizetype.  */
1275 
1276 tree
1277 chrec_convert_rhs (tree type, tree chrec, gimple at_stmt)
1278 {
1279   if (POINTER_TYPE_P (type))
1280     type = sizetype;
1281 
1282   return chrec_convert (type, chrec, at_stmt);
1283 }
1284 
1285 /* Convert CHREC to TYPE.  When the analyzer knows the context in
1286    which the CHREC is built, it sets AT_STMT to the statement that
1287    contains the definition of the analyzed variable, otherwise the
1288    conversion is less accurate: the information is used for
1289    determining a more accurate estimation of the number of iterations.
1290    By default AT_STMT could be safely set to NULL_TREE.
1291 
1292    The following rule is always true: TREE_TYPE (chrec) ==
1293    TREE_TYPE (CHREC_LEFT (chrec)) == TREE_TYPE (CHREC_RIGHT (chrec)).
1294    An example of what could happen when adding two chrecs and the type
1295    of the CHREC_RIGHT is different than CHREC_LEFT is:
1296 
1297    {(uint) 0, +, (uchar) 10} +
1298    {(uint) 0, +, (uchar) 250}
1299 
1300    that would produce a wrong result if CHREC_RIGHT is not (uint):
1301 
1302    {(uint) 0, +, (uchar) 4}
1303 
1304    instead of
1305 
1306    {(uint) 0, +, (uint) 260}
1307 */
1308 
1309 tree
1310 chrec_convert (tree type, tree chrec, gimple at_stmt)
1311 {
1312   return chrec_convert_1 (type, chrec, at_stmt, true);
1313 }
1314 
1315 /* Convert CHREC to TYPE.  When the analyzer knows the context in
1316    which the CHREC is built, it sets AT_STMT to the statement that
1317    contains the definition of the analyzed variable, otherwise the
1318    conversion is less accurate: the information is used for
1319    determining a more accurate estimation of the number of iterations.
1320    By default AT_STMT could be safely set to NULL_TREE.
1321 
1322    USE_OVERFLOW_SEMANTICS is true if this function should assume that
1323    the rules for overflow of the given language apply (e.g., that signed
1324    arithmetics in C does not overflow) -- i.e., to use them to avoid unnecessary
1325    tests, but also to enforce that the result follows them.  */
1326 
1327 static tree
1328 chrec_convert_1 (tree type, tree chrec, gimple at_stmt,
1329 		 bool use_overflow_semantics)
1330 {
1331   tree ct, res;
1332   tree base, step;
1333   struct loop *loop;
1334 
1335   if (automatically_generated_chrec_p (chrec))
1336     return chrec;
1337 
1338   ct = chrec_type (chrec);
1339   if (ct == type)
1340     return chrec;
1341 
1342   if (!evolution_function_is_affine_p (chrec))
1343     goto keep_cast;
1344 
1345   loop = get_chrec_loop (chrec);
1346   base = CHREC_LEFT (chrec);
1347   step = CHREC_RIGHT (chrec);
1348 
1349   if (convert_affine_scev (loop, type, &base, &step, at_stmt,
1350 			   use_overflow_semantics))
1351     return build_polynomial_chrec (loop->num, base, step);
1352 
1353   /* If we cannot propagate the cast inside the chrec, just keep the cast.  */
1354 keep_cast:
1355   /* Fold will not canonicalize (long)(i - 1) to (long)i - 1 because that
1356      may be more expensive.  We do want to perform this optimization here
1357      though for canonicalization reasons.  */
1358   if (use_overflow_semantics
1359       && (TREE_CODE (chrec) == PLUS_EXPR
1360 	  || TREE_CODE (chrec) == MINUS_EXPR)
1361       && TREE_CODE (type) == INTEGER_TYPE
1362       && TREE_CODE (ct) == INTEGER_TYPE
1363       && TYPE_PRECISION (type) > TYPE_PRECISION (ct)
1364       && TYPE_OVERFLOW_UNDEFINED (ct))
1365     res = fold_build2 (TREE_CODE (chrec), type,
1366 		       fold_convert (type, TREE_OPERAND (chrec, 0)),
1367 		       fold_convert (type, TREE_OPERAND (chrec, 1)));
1368   else
1369     res = fold_convert (type, chrec);
1370 
1371   /* Don't propagate overflows.  */
1372   if (CONSTANT_CLASS_P (res))
1373     TREE_OVERFLOW (res) = 0;
1374 
1375   /* But reject constants that don't fit in their type after conversion.
1376      This can happen if TYPE_MIN_VALUE or TYPE_MAX_VALUE are not the
1377      natural values associated with TYPE_PRECISION and TYPE_UNSIGNED,
1378      and can cause problems later when computing niters of loops.  Note
1379      that we don't do the check before converting because we don't want
1380      to reject conversions of negative chrecs to unsigned types.  */
1381   if (TREE_CODE (res) == INTEGER_CST
1382       && TREE_CODE (type) == INTEGER_TYPE
1383       && !int_fits_type_p (res, type))
1384     res = chrec_dont_know;
1385 
1386   return res;
1387 }
1388 
1389 /* Convert CHREC to TYPE, without regard to signed overflows.  Returns the new
1390    chrec if something else than what chrec_convert would do happens, NULL_TREE
1391    otherwise.  */
1392 
1393 tree
1394 chrec_convert_aggressive (tree type, tree chrec)
1395 {
1396   tree inner_type, left, right, lc, rc, rtype;
1397 
1398   if (automatically_generated_chrec_p (chrec)
1399       || TREE_CODE (chrec) != POLYNOMIAL_CHREC)
1400     return NULL_TREE;
1401 
1402   inner_type = TREE_TYPE (chrec);
1403   if (TYPE_PRECISION (type) > TYPE_PRECISION (inner_type))
1404     return NULL_TREE;
1405 
1406   rtype = POINTER_TYPE_P (type) ? sizetype : type;
1407 
1408   left = CHREC_LEFT (chrec);
1409   right = CHREC_RIGHT (chrec);
1410   lc = chrec_convert_aggressive (type, left);
1411   if (!lc)
1412     lc = chrec_convert (type, left, NULL);
1413   rc = chrec_convert_aggressive (rtype, right);
1414   if (!rc)
1415     rc = chrec_convert (rtype, right, NULL);
1416 
1417   return build_polynomial_chrec (CHREC_VARIABLE (chrec), lc, rc);
1418 }
1419 
1420 /* Returns true when CHREC0 == CHREC1.  */
1421 
1422 bool
1423 eq_evolutions_p (const_tree chrec0, const_tree chrec1)
1424 {
1425   if (chrec0 == NULL_TREE
1426       || chrec1 == NULL_TREE
1427       || TREE_CODE (chrec0) != TREE_CODE (chrec1))
1428     return false;
1429 
1430   if (chrec0 == chrec1)
1431     return true;
1432 
1433   switch (TREE_CODE (chrec0))
1434     {
1435     case INTEGER_CST:
1436       return operand_equal_p (chrec0, chrec1, 0);
1437 
1438     case POLYNOMIAL_CHREC:
1439       return (CHREC_VARIABLE (chrec0) == CHREC_VARIABLE (chrec1)
1440 	      && eq_evolutions_p (CHREC_LEFT (chrec0), CHREC_LEFT (chrec1))
1441 	      && eq_evolutions_p (CHREC_RIGHT (chrec0), CHREC_RIGHT (chrec1)));
1442 
1443     case PLUS_EXPR:
1444     case MULT_EXPR:
1445     case MINUS_EXPR:
1446     case POINTER_PLUS_EXPR:
1447       return eq_evolutions_p (TREE_OPERAND (chrec0, 0),
1448 			      TREE_OPERAND (chrec1, 0))
1449 	  && eq_evolutions_p (TREE_OPERAND (chrec0, 1),
1450 			      TREE_OPERAND (chrec1, 1));
1451 
1452     default:
1453       return false;
1454     }
1455 }
1456 
1457 /* Returns EV_GROWS if CHREC grows (assuming that it does not overflow),
1458    EV_DECREASES if it decreases, and EV_UNKNOWN if we cannot determine
1459    which of these cases happens.  */
1460 
1461 enum ev_direction
1462 scev_direction (const_tree chrec)
1463 {
1464   const_tree step;
1465 
1466   if (!evolution_function_is_affine_p (chrec))
1467     return EV_DIR_UNKNOWN;
1468 
1469   step = CHREC_RIGHT (chrec);
1470   if (TREE_CODE (step) != INTEGER_CST)
1471     return EV_DIR_UNKNOWN;
1472 
1473   if (tree_int_cst_sign_bit (step))
1474     return EV_DIR_DECREASES;
1475   else
1476     return EV_DIR_GROWS;
1477 }
1478 
1479 /* Iterates over all the components of SCEV, and calls CBCK.  */
1480 
1481 void
1482 for_each_scev_op (tree *scev, bool (*cbck) (tree *, void *), void *data)
1483 {
1484   switch (TREE_CODE_LENGTH (TREE_CODE (*scev)))
1485     {
1486     case 3:
1487       for_each_scev_op (&TREE_OPERAND (*scev, 2), cbck, data);
1488 
1489     case 2:
1490       for_each_scev_op (&TREE_OPERAND (*scev, 1), cbck, data);
1491 
1492     case 1:
1493       for_each_scev_op (&TREE_OPERAND (*scev, 0), cbck, data);
1494 
1495     default:
1496       cbck (scev, data);
1497       break;
1498     }
1499 }
1500 
1501 /* Returns true when the operation can be part of a linear
1502    expression.  */
1503 
1504 static inline bool
1505 operator_is_linear (tree scev)
1506 {
1507   switch (TREE_CODE (scev))
1508     {
1509     case INTEGER_CST:
1510     case POLYNOMIAL_CHREC:
1511     case PLUS_EXPR:
1512     case POINTER_PLUS_EXPR:
1513     case MULT_EXPR:
1514     case MINUS_EXPR:
1515     case NEGATE_EXPR:
1516     case SSA_NAME:
1517     case NON_LVALUE_EXPR:
1518     case BIT_NOT_EXPR:
1519     CASE_CONVERT:
1520       return true;
1521 
1522     default:
1523       return false;
1524     }
1525 }
1526 
1527 /* Return true when SCEV is a linear expression.  Linear expressions
1528    can contain additions, substractions and multiplications.
1529    Multiplications are restricted to constant scaling: "cst * x".  */
1530 
1531 bool
1532 scev_is_linear_expression (tree scev)
1533 {
1534   if (scev == NULL
1535       || !operator_is_linear (scev))
1536     return false;
1537 
1538   if (TREE_CODE (scev) == MULT_EXPR)
1539     return !(tree_contains_chrecs (TREE_OPERAND (scev, 0), NULL)
1540 	     && tree_contains_chrecs (TREE_OPERAND (scev, 1), NULL));
1541 
1542   if (TREE_CODE (scev) == POLYNOMIAL_CHREC
1543       && !evolution_function_is_affine_multivariate_p (scev, CHREC_VARIABLE (scev)))
1544     return false;
1545 
1546   switch (TREE_CODE_LENGTH (TREE_CODE (scev)))
1547     {
1548     case 3:
1549       return scev_is_linear_expression (TREE_OPERAND (scev, 0))
1550 	&& scev_is_linear_expression (TREE_OPERAND (scev, 1))
1551 	&& scev_is_linear_expression (TREE_OPERAND (scev, 2));
1552 
1553     case 2:
1554       return scev_is_linear_expression (TREE_OPERAND (scev, 0))
1555 	&& scev_is_linear_expression (TREE_OPERAND (scev, 1));
1556 
1557     case 1:
1558       return scev_is_linear_expression (TREE_OPERAND (scev, 0));
1559 
1560     case 0:
1561       return true;
1562 
1563     default:
1564       return false;
1565     }
1566 }
1567 
1568 /* Determines whether the expression CHREC contains only interger consts
1569    in the right parts.  */
1570 
1571 bool
1572 evolution_function_right_is_integer_cst (const_tree chrec)
1573 {
1574   if (chrec == NULL_TREE)
1575     return false;
1576 
1577   switch (TREE_CODE (chrec))
1578     {
1579     case INTEGER_CST:
1580       return true;
1581 
1582     case POLYNOMIAL_CHREC:
1583       return TREE_CODE (CHREC_RIGHT (chrec)) == INTEGER_CST
1584 	&& (TREE_CODE (CHREC_LEFT (chrec)) != POLYNOMIAL_CHREC
1585 	    || evolution_function_right_is_integer_cst (CHREC_LEFT (chrec)));
1586 
1587     CASE_CONVERT:
1588       return evolution_function_right_is_integer_cst (TREE_OPERAND (chrec, 0));
1589 
1590     default:
1591       return false;
1592     }
1593 }
1594