gcc/tree-chrec.c

   1 /* Chains of recurrences.
   2    Copyright (C) 2003-2014 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 "tree.h"
  30 #include "tree-pretty-print.h"
  31 #include "cfgloop.h"
  32 #include "basic-block.h"
  33 #include "gimple-expr.h"
  34 #include "tree-ssa-loop-ivopts.h"
  35 #include "tree-ssa-loop-niter.h"
  36 #include "tree-chrec.h"
  37 #include "dumpfile.h"
  38 #include "params.h"
  39 #include "tree-scalar-evolution.h"
  40
  41 /* Extended folder for chrecs.  */
  42
  43 /* Determines whether CST is not a constant evolution.  */
  44
  45 static inline bool
  46 is_not_constant_evolution (const_tree cst)
  47 {
  48   return (TREE_CODE (cst) == POLYNOMIAL_CHREC);
  49 }
  50
  51 /* Fold CODE for a polynomial function and a constant.  */
  52
  53 static inline tree
  54 chrec_fold_poly_cst (enum tree_code code,
  55                      tree type,
  56                      tree poly,
  57                      tree cst)
  58 {
  59   gcc_assert (poly);
  60   gcc_assert (cst);
  61   gcc_assert (TREE_CODE (poly) == POLYNOMIAL_CHREC);
  62   gcc_assert (!is_not_constant_evolution (cst));
  63   gcc_assert (type == chrec_type (poly));
  64
  65   switch (code)
  66     {
  67     case PLUS_EXPR:
  68       return build_polynomial_chrec
  69         (CHREC_VARIABLE (poly),
  70          chrec_fold_plus (type, CHREC_LEFT (poly), cst),
  71          CHREC_RIGHT (poly));
  72
  73     case MINUS_EXPR:
  74       return build_polynomial_chrec
  75         (CHREC_VARIABLE (poly),
  76          chrec_fold_minus (type, CHREC_LEFT (poly), cst),
  77          CHREC_RIGHT (poly));
  78
  79     case MULT_EXPR:
  80       return build_polynomial_chrec
  81         (CHREC_VARIABLE (poly),
  82          chrec_fold_multiply (type, CHREC_LEFT (poly), cst),
  83          chrec_fold_multiply (type, CHREC_RIGHT (poly), cst));
  84
  85     default:
  86       return chrec_dont_know;
  87     }
  88 }
  89
  90 /* Fold the addition of two polynomial functions.  */
  91
  92 static inline tree
  93 chrec_fold_plus_poly_poly (enum tree_code code,
  94                            tree type,
  95                            tree poly0,
  96                            tree poly1)
  97 {
  98   tree left, right;
  99   struct loop *loop0 = get_chrec_loop (poly0);
 100   struct loop *loop1 = get_chrec_loop (poly1);
 101   tree rtype = code == POINTER_PLUS_EXPR ? chrec_type (poly1) : type;
 102
 103   gcc_assert (poly0);
 104   gcc_assert (poly1);
 105   gcc_assert (TREE_CODE (poly0) == POLYNOMIAL_CHREC);
 106   gcc_assert (TREE_CODE (poly1) == POLYNOMIAL_CHREC);
 107   if (POINTER_TYPE_P (chrec_type (poly0)))
 108     gcc_assert (ptrofftype_p (chrec_type (poly1)));
 109   else
 110     gcc_assert (chrec_type (poly0) == chrec_type (poly1));
 111   gcc_assert (type == chrec_type (poly0));
 112
 113   /*
 114     {a, +, b}_1 + {c, +, d}_2  ->  {{a, +, b}_1 + c, +, d}_2,
 115     {a, +, b}_2 + {c, +, d}_1  ->  {{c, +, d}_1 + a, +, b}_2,
 116     {a, +, b}_x + {c, +, d}_x  ->  {a+c, +, b+d}_x.  */
 117   if (flow_loop_nested_p (loop0, loop1))
 118     {
 119       if (code == PLUS_EXPR || code == POINTER_PLUS_EXPR)
 120         return build_polynomial_chrec
 121           (CHREC_VARIABLE (poly1),
 122            chrec_fold_plus (type, poly0, CHREC_LEFT (poly1)),
 123            CHREC_RIGHT (poly1));
 124       else
 125         return build_polynomial_chrec
 126           (CHREC_VARIABLE (poly1),
 127            chrec_fold_minus (type, poly0, CHREC_LEFT (poly1)),
 128            chrec_fold_multiply (type, CHREC_RIGHT (poly1),
 129                                 SCALAR_FLOAT_TYPE_P (type)
 130                                 ? build_real (type, dconstm1)
 131                                 : build_int_cst_type (type, -1)));
 132     }
 133
 134   if (flow_loop_nested_p (loop1, loop0))
 135     {
 136       if (code == PLUS_EXPR || code == POINTER_PLUS_EXPR)
 137         return build_polynomial_chrec
 138           (CHREC_VARIABLE (poly0),
 139            chrec_fold_plus (type, CHREC_LEFT (poly0), poly1),
 140            CHREC_RIGHT (poly0));
 141       else
 142         return build_polynomial_chrec
 143           (CHREC_VARIABLE (poly0),
 144            chrec_fold_minus (type, CHREC_LEFT (poly0), poly1),
 145            CHREC_RIGHT (poly0));
 146     }
 147
 148   /* This function should never be called for chrecs of loops that
 149      do not belong to the same loop nest.  */
 150   gcc_assert (loop0 == loop1);
 151
 152   if (code == PLUS_EXPR || code == POINTER_PLUS_EXPR)
 153     {
 154       left = chrec_fold_plus
 155         (type, CHREC_LEFT (poly0), CHREC_LEFT (poly1));
 156       right = chrec_fold_plus
 157         (rtype, CHREC_RIGHT (poly0), CHREC_RIGHT (poly1));
 158     }
 159   else
 160     {
 161       left = chrec_fold_minus
 162         (type, CHREC_LEFT (poly0), CHREC_LEFT (poly1));
 163       right = chrec_fold_minus
 164         (type, CHREC_RIGHT (poly0), CHREC_RIGHT (poly1));
 165     }
 166
 167   if (chrec_zerop (right))
 168     return left;
 169   else
 170     return build_polynomial_chrec
 171       (CHREC_VARIABLE (poly0), left, right);
 172 }
 173
 174 \f
 175
 176 /* Fold the multiplication of two polynomial functions.  */
 177
 178 static inline tree
 179 chrec_fold_multiply_poly_poly (tree type,
 180                                tree poly0,
 181                                tree poly1)
 182 {
 183   tree t0, t1, t2;
 184   int var;
 185   struct loop *loop0 = get_chrec_loop (poly0);
 186   struct loop *loop1 = get_chrec_loop (poly1);
 187
 188   gcc_assert (poly0);
 189   gcc_assert (poly1);
 190   gcc_assert (TREE_CODE (poly0) == POLYNOMIAL_CHREC);
 191   gcc_assert (TREE_CODE (poly1) == POLYNOMIAL_CHREC);
 192   gcc_assert (chrec_type (poly0) == chrec_type (poly1));
 193   gcc_assert (type == chrec_type (poly0));
 194
 195   /* {a, +, b}_1 * {c, +, d}_2  ->  {c*{a, +, b}_1, +, d}_2,
 196      {a, +, b}_2 * {c, +, d}_1  ->  {a*{c, +, d}_1, +, b}_2,
 197      {a, +, b}_x * {c, +, d}_x  ->  {a*c, +, a*d + b*c + b*d, +, 2*b*d}_x.  */
 198   if (flow_loop_nested_p (loop0, loop1))
 199     /* poly0 is a constant wrt. poly1.  */
 200     return build_polynomial_chrec
 201       (CHREC_VARIABLE (poly1),
 202        chrec_fold_multiply (type, CHREC_LEFT (poly1), poly0),
 203        CHREC_RIGHT (poly1));
 204
 205   if (flow_loop_nested_p (loop1, loop0))
 206     /* poly1 is a constant wrt. poly0.  */
 207     return build_polynomial_chrec
 208       (CHREC_VARIABLE (poly0),
 209        chrec_fold_multiply (type, CHREC_LEFT (poly0), poly1),
 210        CHREC_RIGHT (poly0));
 211
 212   gcc_assert (loop0 == loop1);
 213
 214   /* poly0 and poly1 are two polynomials in the same variable,
 215      {a, +, b}_x * {c, +, d}_x  ->  {a*c, +, a*d + b*c + b*d, +, 2*b*d}_x.  */
 216
 217   /* "a*c".  */
 218   t0 = chrec_fold_multiply (type, CHREC_LEFT (poly0), CHREC_LEFT (poly1));
 219
 220   /* "a*d + b*c".  */
 221   t1 = chrec_fold_multiply (type, CHREC_LEFT (poly0), CHREC_RIGHT (poly1));
 222   t1 = chrec_fold_plus (type, t1, chrec_fold_multiply (type,
 223                                                        CHREC_RIGHT (poly0),
 224                                                        CHREC_LEFT (poly1)));
 225   /* "b*d".  */
 226   t2 = chrec_fold_multiply (type, CHREC_RIGHT (poly0), CHREC_RIGHT (poly1));
 227   /* "a*d + b*c + b*d".  */
 228   t1 = chrec_fold_plus (type, t1, t2);
 229   /* "2*b*d".  */
 230   t2 = chrec_fold_multiply (type, SCALAR_FLOAT_TYPE_P (type)
 231                             ? build_real (type, dconst2)
 232                             : build_int_cst (type, 2), t2);
 233
 234   var = CHREC_VARIABLE (poly0);
 235   return build_polynomial_chrec (var, t0,
 236                                  build_polynomial_chrec (var, t1, t2));
 237 }
 238
 239 /* When the operands are automatically_generated_chrec_p, the fold has
 240    to respect the semantics of the operands.  */
 241
 242 static inline tree
 243 chrec_fold_automatically_generated_operands (tree op0,
 244                                              tree op1)
 245 {
 246   if (op0 == chrec_dont_know
 247       || op1 == chrec_dont_know)
 248     return chrec_dont_know;
 249
 250   if (op0 == chrec_known
 251       || op1 == chrec_known)
 252     return chrec_known;
 253
 254   if (op0 == chrec_not_analyzed_yet
 255       || op1 == chrec_not_analyzed_yet)
 256     return chrec_not_analyzed_yet;
 257
 258   /* The default case produces a safe result.  */
 259   return chrec_dont_know;
 260 }
 261
 262 /* Fold the addition of two chrecs.  */
 263
 264 static tree
 265 chrec_fold_plus_1 (enum tree_code code, tree type,
 266                    tree op0, tree op1)
 267 {
 268   if (automatically_generated_chrec_p (op0)
 269       || automatically_generated_chrec_p (op1))
 270     return chrec_fold_automatically_generated_operands (op0, op1);
 271
 272   switch (TREE_CODE (op0))
 273     {
 274     case POLYNOMIAL_CHREC:
 275       gcc_checking_assert
 276         (!chrec_contains_symbols_defined_in_loop (op0, CHREC_VARIABLE (op0)));
 277       switch (TREE_CODE (op1))
 278         {
 279         case POLYNOMIAL_CHREC:
 280           gcc_checking_assert
 281             (!chrec_contains_symbols_defined_in_loop (op1,
 282                                                       CHREC_VARIABLE (op1)));
 283           return chrec_fold_plus_poly_poly (code, type, op0, op1);
 284
 285         CASE_CONVERT:
 286           if (tree_contains_chrecs (op1, NULL))
 287             return chrec_dont_know;
 288
 289         default:
 290           if (code == PLUS_EXPR || code == POINTER_PLUS_EXPR)
 291             return build_polynomial_chrec
 292               (CHREC_VARIABLE (op0),
 293                chrec_fold_plus (type, CHREC_LEFT (op0), op1),
 294                CHREC_RIGHT (op0));
 295           else
 296             return build_polynomial_chrec
 297               (CHREC_VARIABLE (op0),
 298                chrec_fold_minus (type, CHREC_LEFT (op0), op1),
 299                CHREC_RIGHT (op0));
 300         }
 301
 302     CASE_CONVERT:
 303       if (tree_contains_chrecs (op0, NULL))
 304         return chrec_dont_know;
 305
 306     default:
 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           if (code == PLUS_EXPR || code == POINTER_PLUS_EXPR)
 314             return build_polynomial_chrec
 315               (CHREC_VARIABLE (op1),
 316                chrec_fold_plus (type, op0, CHREC_LEFT (op1)),
 317                CHREC_RIGHT (op1));
 318           else
 319             return build_polynomial_chrec
 320               (CHREC_VARIABLE (op1),
 321                chrec_fold_minus (type, op0, CHREC_LEFT (op1)),
 322                chrec_fold_multiply (type, CHREC_RIGHT (op1),
 323                                     SCALAR_FLOAT_TYPE_P (type)
 324                                     ? build_real (type, dconstm1)
 325                                     : build_int_cst_type (type, -1)));
 326
 327         CASE_CONVERT:
 328           if (tree_contains_chrecs (op1, NULL))
 329             return chrec_dont_know;
 330
 331         default:
 332           {
 333             int size = 0;
 334             if ((tree_contains_chrecs (op0, &size)
 335                  || tree_contains_chrecs (op1, &size))
 336                 && size < PARAM_VALUE (PARAM_SCEV_MAX_EXPR_SIZE))
 337               return build2 (code, type, op0, op1);
 338             else if (size < PARAM_VALUE (PARAM_SCEV_MAX_EXPR_SIZE))
 339               {
 340                 if (code == POINTER_PLUS_EXPR)
 341                   return fold_build_pointer_plus (fold_convert (type, op0),
 342                                                   op1);
 343                 else
 344                   return fold_build2 (code, type,
 345                                       fold_convert (type, op0),
 346                                       fold_convert (type, op1));
 347               }
 348             else
 349               return chrec_dont_know;
 350           }
 351         }
 352     }
 353 }
 354
 355 /* Fold the addition of two chrecs.  */
 356
 357 tree
 358 chrec_fold_plus (tree type,
 359                  tree op0,
 360                  tree op1)
 361 {
 362   enum tree_code code;
 363   if (automatically_generated_chrec_p (op0)
 364       || automatically_generated_chrec_p (op1))
 365     return chrec_fold_automatically_generated_operands (op0, op1);
 366
 367   if (integer_zerop (op0))
 368     return chrec_convert (type, op1, NULL);
 369   if (integer_zerop (op1))
 370     return chrec_convert (type, op0, NULL);
 371
 372   if (POINTER_TYPE_P (type))
 373     code = POINTER_PLUS_EXPR;
 374   else
 375     code = PLUS_EXPR;
 376
 377   return chrec_fold_plus_1 (code, type, op0, op1);
 378 }
 379
 380 /* Fold the subtraction of two chrecs.  */
 381
 382 tree
 383 chrec_fold_minus (tree type,
 384                   tree op0,
 385                   tree op1)
 386 {
 387   if (automatically_generated_chrec_p (op0)
 388       || automatically_generated_chrec_p (op1))
 389     return chrec_fold_automatically_generated_operands (op0, op1);
 390
 391   if (integer_zerop (op1))
 392     return op0;
 393
 394   return chrec_fold_plus_1 (MINUS_EXPR, type, op0, op1);
 395 }
 396
 397 /* Fold the multiplication of two chrecs.  */
 398
 399 tree
 400 chrec_fold_multiply (tree type,
 401                      tree op0,
 402                      tree op1)
 403 {
 404   if (automatically_generated_chrec_p (op0)
 405       || automatically_generated_chrec_p (op1))
 406     return chrec_fold_automatically_generated_operands (op0, op1);
 407
 408   switch (TREE_CODE (op0))
 409     {
 410     case POLYNOMIAL_CHREC:
 411       gcc_checking_assert
 412         (!chrec_contains_symbols_defined_in_loop (op0, CHREC_VARIABLE (op0)));
 413       switch (TREE_CODE (op1))
 414         {
 415         case POLYNOMIAL_CHREC:
 416           gcc_checking_assert
 417             (!chrec_contains_symbols_defined_in_loop (op1,
 418                                                       CHREC_VARIABLE (op1)));
 419           return chrec_fold_multiply_poly_poly (type, op0, op1);
 420
 421         CASE_CONVERT:
 422           if (tree_contains_chrecs (op1, NULL))
 423             return chrec_dont_know;
 424
 425         default:
 426           if (integer_onep (op1))
 427             return op0;
 428           if (integer_zerop (op1))
 429             return build_int_cst (type, 0);
 430
 431           return build_polynomial_chrec
 432             (CHREC_VARIABLE (op0),
 433              chrec_fold_multiply (type, CHREC_LEFT (op0), op1),
 434              chrec_fold_multiply (type, CHREC_RIGHT (op0), op1));
 435         }
 436
 437     CASE_CONVERT:
 438       if (tree_contains_chrecs (op0, NULL))
 439         return chrec_dont_know;
 440
 441     default:
 442       if (integer_onep (op0))
 443         return op1;
 444
 445       if (integer_zerop (op0))
 446         return build_int_cst (type, 0);
 447
 448       switch (TREE_CODE (op1))
 449         {
 450         case POLYNOMIAL_CHREC:
 451           gcc_checking_assert
 452             (!chrec_contains_symbols_defined_in_loop (op1,
 453                                                       CHREC_VARIABLE (op1)));
 454           return build_polynomial_chrec
 455             (CHREC_VARIABLE (op1),
 456              chrec_fold_multiply (type, CHREC_LEFT (op1), op0),
 457              chrec_fold_multiply (type, CHREC_RIGHT (op1), op0));
 458
 459         CASE_CONVERT:
 460           if (tree_contains_chrecs (op1, NULL))
 461             return chrec_dont_know;
 462
 463         default:
 464           if (integer_onep (op1))
 465             return op0;
 466           if (integer_zerop (op1))
 467             return build_int_cst (type, 0);
 468           return fold_build2 (MULT_EXPR, type, op0, op1);
 469         }
 470     }
 471 }
 472
 473 \f
 474
 475 /* Operations.  */
 476
 477 /* Evaluate the binomial coefficient.  Return NULL_TREE if the intermediate
 478    calculation overflows, otherwise return C(n,k) with type TYPE.  */
 479
 480 static tree
 481 tree_fold_binomial (tree type, tree n, unsigned int k)
 482 {
 483   double_int num, denom, idx, di_res;
 484   bool overflow;
 485   unsigned int i;
 486   tree res;
 487
 488   /* Handle the most frequent cases.  */
 489   if (k == 0)
 490     return build_int_cst (type, 1);
 491   if (k == 1)
 492     return fold_convert (type, n);
 493
 494   /* Numerator = n.  */
 495   num = TREE_INT_CST (n);
 496
 497   /* Check that k <= n.  */
 498   if (num.ult (double_int::from_uhwi (k)))
 499     return NULL_TREE;
 500
 501   /* Denominator = 2.  */
 502   denom = double_int::from_uhwi (2);
 503
 504   /* Index = Numerator-1.  */
 505   idx = num - double_int_one;
 506
 507   /* Numerator = Numerator*Index = n*(n-1).  */
 508   num = num.mul_with_sign (idx, false, &overflow);
 509   if (overflow)
 510     return NULL_TREE;
 511
 512   for (i = 3; i <= k; i++)
 513     {
 514       /* Index--.  */
 515       --idx;
 516
 517       /* Numerator *= Index.  */
 518       num = num.mul_with_sign (idx, false, &overflow);
 519       if (overflow)
 520         return NULL_TREE;
 521
 522       /* Denominator *= i.  */
 523       denom *= double_int::from_uhwi (i);
 524     }
 525
 526   /* Result = Numerator / Denominator.  */
 527   di_res = num.div (denom, true, EXACT_DIV_EXPR);
 528   res = build_int_cst_wide (type, di_res.low, di_res.high);
 529   return int_fits_type_p (res, type) ? res : NULL_TREE;
 530 }
 531
 532 /* Helper function.  Use the Newton's interpolating formula for
 533    evaluating the value of the evolution function.  */
 534
 535 static tree
 536 chrec_evaluate (unsigned var, tree chrec, tree n, unsigned int k)
 537 {
 538   tree arg0, arg1, binomial_n_k;
 539   tree type = TREE_TYPE (chrec);
 540   struct loop *var_loop = get_loop (cfun, var);
 541
 542   while (TREE_CODE (chrec) == POLYNOMIAL_CHREC
 543          && flow_loop_nested_p (var_loop, get_chrec_loop (chrec)))
 544     chrec = CHREC_LEFT (chrec);
 545
 546   if (TREE_CODE (chrec) == POLYNOMIAL_CHREC
 547       && CHREC_VARIABLE (chrec) == var)
 548     {
 549       arg1 = chrec_evaluate (var, CHREC_RIGHT (chrec), n, k + 1);
 550       if (arg1 == chrec_dont_know)
 551         return chrec_dont_know;
 552       binomial_n_k = tree_fold_binomial (type, n, k);
 553       if (!binomial_n_k)
 554         return chrec_dont_know;
 555       arg0 = fold_build2 (MULT_EXPR, type,
 556                           CHREC_LEFT (chrec), binomial_n_k);
 557       return chrec_fold_plus (type, arg0, arg1);
 558     }
 559
 560   binomial_n_k = tree_fold_binomial (type, n, k);
 561   if (!binomial_n_k)
 562     return chrec_dont_know;
 563
 564   return fold_build2 (MULT_EXPR, type, chrec, binomial_n_k);
 565 }
 566
 567 /* Evaluates "CHREC (X)" when the varying variable is VAR.
 568    Example:  Given the following parameters,
 569
 570    var = 1
 571    chrec = {3, +, 4}_1
 572    x = 10
 573
 574    The result is given by the Newton's interpolating formula:
 575    3 * \binom{10}{0} + 4 * \binom{10}{1}.
 576 */
 577
 578 tree
 579 chrec_apply (unsigned var,
 580              tree chrec,
 581              tree x)
 582 {
 583   tree type = chrec_type (chrec);
 584   tree res = chrec_dont_know;
 585
 586   if (automatically_generated_chrec_p (chrec)
 587       || automatically_generated_chrec_p (x)
 588
 589       /* When the symbols are defined in an outer loop, it is possible
 590          to symbolically compute the apply, since the symbols are
 591          constants with respect to the varying loop.  */
 592       || chrec_contains_symbols_defined_in_loop (chrec, var))
 593     return chrec_dont_know;
 594
 595   if (dump_file && (dump_flags & TDF_SCEV))
 596     fprintf (dump_file, "(chrec_apply \n");
 597
 598   if (TREE_CODE (x) == INTEGER_CST && SCALAR_FLOAT_TYPE_P (type))
 599     x = build_real_from_int_cst (type, x);
 600
 601   switch (TREE_CODE (chrec))
 602     {
 603     case POLYNOMIAL_CHREC:
 604       if (evolution_function_is_affine_p (chrec))
 605         {
 606           if (CHREC_VARIABLE (chrec) != var)
 607             return build_polynomial_chrec
 608               (CHREC_VARIABLE (chrec),
 609                chrec_apply (var, CHREC_LEFT (chrec), x),
 610                chrec_apply (var, CHREC_RIGHT (chrec), x));
 611
 612           /* "{a, +, b} (x)"  ->  "a + b*x".  */
 613           x = chrec_convert_rhs (type, x, NULL);
 614           res = chrec_fold_multiply (TREE_TYPE (x), CHREC_RIGHT (chrec), x);
 615           res = chrec_fold_plus (type, CHREC_LEFT (chrec), res);
 616         }
 617       else if (TREE_CODE (x) == INTEGER_CST
 618                && tree_int_cst_sgn (x) == 1)
 619         /* testsuite/.../ssa-chrec-38.c.  */
 620         res = chrec_evaluate (var, chrec, x, 0);
 621       else
 622         res = chrec_dont_know;
 623       break;
 624
 625     CASE_CONVERT:
 626       res = chrec_convert (TREE_TYPE (chrec),
 627                            chrec_apply (var, TREE_OPERAND (chrec, 0), x),
 628                            NULL);
 629       break;
 630
 631     default:
 632       res = chrec;
 633       break;
 634     }
 635
 636   if (dump_file && (dump_flags & TDF_SCEV))
 637     {
 638       fprintf (dump_file, "  (varying_loop = %d\n", var);
 639       fprintf (dump_file, ")\n  (chrec = ");
 640       print_generic_expr (dump_file, chrec, 0);
 641       fprintf (dump_file, ")\n  (x = ");
 642       print_generic_expr (dump_file, x, 0);
 643       fprintf (dump_file, ")\n  (res = ");
 644       print_generic_expr (dump_file, res, 0);
 645       fprintf (dump_file, "))\n");
 646     }
 647
 648   return res;
 649 }
 650
 651 /* For a given CHREC and an induction variable map IV_MAP that maps
 652    (loop->num, expr) for every loop number of the current_loops an
 653    expression, calls chrec_apply when the expression is not NULL.  */
 654
 655 tree
 656 chrec_apply_map (tree chrec, vec<tree> iv_map)
 657 {
 658   int i;
 659   tree expr;
 660
 661   FOR_EACH_VEC_ELT (iv_map, i, expr)
 662     if (expr)
 663       chrec = chrec_apply (i, chrec, expr);
 664
 665   return chrec;
 666 }
 667
 668 /* Replaces the initial condition in CHREC with INIT_COND.  */
 669
 670 tree
 671 chrec_replace_initial_condition (tree chrec,
 672                                  tree init_cond)
 673 {
 674   if (automatically_generated_chrec_p (chrec))
 675     return chrec;
 676
 677   gcc_assert (chrec_type (chrec) == chrec_type (init_cond));
 678
 679   switch (TREE_CODE (chrec))
 680     {
 681     case POLYNOMIAL_CHREC:
 682       return build_polynomial_chrec
 683         (CHREC_VARIABLE (chrec),
 684          chrec_replace_initial_condition (CHREC_LEFT (chrec), init_cond),
 685          CHREC_RIGHT (chrec));
 686
 687     default:
 688       return init_cond;
 689     }
 690 }
 691
 692 /* Returns the initial condition of a given CHREC.  */
 693
 694 tree
 695 initial_condition (tree chrec)
 696 {
 697   if (automatically_generated_chrec_p (chrec))
 698     return chrec;
 699
 700   if (TREE_CODE (chrec) == POLYNOMIAL_CHREC)
 701     return initial_condition (CHREC_LEFT (chrec));
 702   else
 703     return chrec;
 704 }
 705
 706 /* Returns a univariate function that represents the evolution in
 707    LOOP_NUM.  Mask the evolution of any other loop.  */
 708
 709 tree
 710 hide_evolution_in_other_loops_than_loop (tree chrec,
 711                                          unsigned loop_num)
 712 {
 713   struct loop *loop = get_loop (cfun, loop_num), *chloop;
 714   if (automatically_generated_chrec_p (chrec))
 715     return chrec;
 716
 717   switch (TREE_CODE (chrec))
 718     {
 719     case POLYNOMIAL_CHREC:
 720       chloop = get_chrec_loop (chrec);
 721
 722       if (chloop == loop)
 723         return build_polynomial_chrec
 724           (loop_num,
 725            hide_evolution_in_other_loops_than_loop (CHREC_LEFT (chrec),
 726                                                     loop_num),
 727            CHREC_RIGHT (chrec));
 728
 729       else if (flow_loop_nested_p (chloop, loop))
 730         /* There is no evolution in this loop.  */
 731         return initial_condition (chrec);
 732
 733       else
 734         {
 735           gcc_assert (flow_loop_nested_p (loop, chloop));
 736           return hide_evolution_in_other_loops_than_loop (CHREC_LEFT (chrec),
 737                                                           loop_num);
 738         }
 739
 740     default:
 741       return chrec;
 742     }
 743 }
 744
 745 /* Returns the evolution part of CHREC in LOOP_NUM when RIGHT is
 746    true, otherwise returns the initial condition in LOOP_NUM.  */
 747
 748 static tree
 749 chrec_component_in_loop_num (tree chrec,
 750                              unsigned loop_num,
 751                              bool right)
 752 {
 753   tree component;
 754   struct loop *loop = get_loop (cfun, loop_num), *chloop;
 755
 756   if (automatically_generated_chrec_p (chrec))
 757     return chrec;
 758
 759   switch (TREE_CODE (chrec))
 760     {
 761     case POLYNOMIAL_CHREC:
 762       chloop = get_chrec_loop (chrec);
 763
 764       if (chloop == loop)
 765         {
 766           if (right)
 767             component = CHREC_RIGHT (chrec);
 768           else
 769             component = CHREC_LEFT (chrec);
 770
 771           if (TREE_CODE (CHREC_LEFT (chrec)) != POLYNOMIAL_CHREC
 772               || CHREC_VARIABLE (CHREC_LEFT (chrec)) != CHREC_VARIABLE (chrec))
 773             return component;
 774
 775           else
 776             return build_polynomial_chrec
 777               (loop_num,
 778                chrec_component_in_loop_num (CHREC_LEFT (chrec),
 779                                             loop_num,
 780                                             right),
 781                component);
 782         }
 783
 784       else if (flow_loop_nested_p (chloop, loop))
 785         /* There is no evolution part in this loop.  */
 786         return NULL_TREE;
 787
 788       else
 789         {
 790           gcc_assert (flow_loop_nested_p (loop, chloop));
 791           return chrec_component_in_loop_num (CHREC_LEFT (chrec),
 792                                               loop_num,
 793                                               right);
 794         }
 795
 796      default:
 797       if (right)
 798         return NULL_TREE;
 799       else
 800         return chrec;
 801     }
 802 }
 803
 804 /* Returns the evolution part in LOOP_NUM.  Example: the call
 805    evolution_part_in_loop_num ({{0, +, 1}_1, +, 2}_1, 1) returns
 806    {1, +, 2}_1  */
 807
 808 tree
 809 evolution_part_in_loop_num (tree chrec,
 810                             unsigned loop_num)
 811 {
 812   return chrec_component_in_loop_num (chrec, loop_num, true);
 813 }
 814
 815 /* Returns the initial condition in LOOP_NUM.  Example: the call
 816    initial_condition_in_loop_num ({{0, +, 1}_1, +, 2}_2, 2) returns
 817    {0, +, 1}_1  */
 818
 819 tree
 820 initial_condition_in_loop_num (tree chrec,
 821                                unsigned loop_num)
 822 {
 823   return chrec_component_in_loop_num (chrec, loop_num, false);
 824 }
 825
 826 /* Set or reset the evolution of CHREC to NEW_EVOL in loop LOOP_NUM.
 827    This function is essentially used for setting the evolution to
 828    chrec_dont_know, for example after having determined that it is
 829    impossible to say how many times a loop will execute.  */
 830
 831 tree
 832 reset_evolution_in_loop (unsigned loop_num,
 833                          tree chrec,
 834                          tree new_evol)
 835 {
 836   struct loop *loop = get_loop (cfun, loop_num);
 837
 838   if (POINTER_TYPE_P (chrec_type (chrec)))
 839     gcc_assert (ptrofftype_p (chrec_type (new_evol)));
 840   else
 841     gcc_assert (chrec_type (chrec) == chrec_type (new_evol));
 842
 843   if (TREE_CODE (chrec) == POLYNOMIAL_CHREC
 844       && flow_loop_nested_p (loop, get_chrec_loop (chrec)))
 845     {
 846       tree left = reset_evolution_in_loop (loop_num, CHREC_LEFT (chrec),
 847                                            new_evol);
 848       tree right = reset_evolution_in_loop (loop_num, CHREC_RIGHT (chrec),
 849                                             new_evol);
 850       return build3 (POLYNOMIAL_CHREC, TREE_TYPE (left),
 851                      CHREC_VAR (chrec), left, right);
 852     }
 853
 854   while (TREE_CODE (chrec) == POLYNOMIAL_CHREC
 855          && CHREC_VARIABLE (chrec) == loop_num)
 856     chrec = CHREC_LEFT (chrec);
 857
 858   return build_polynomial_chrec (loop_num, chrec, new_evol);
 859 }
 860
 861 /* Merges two evolution functions that were found by following two
 862    alternate paths of a conditional expression.  */
 863
 864 tree
 865 chrec_merge (tree chrec1,
 866              tree chrec2)
 867 {
 868   if (chrec1 == chrec_dont_know
 869       || chrec2 == chrec_dont_know)
 870     return chrec_dont_know;
 871
 872   if (chrec1 == chrec_known
 873       || chrec2 == chrec_known)
 874     return chrec_known;
 875
 876   if (chrec1 == chrec_not_analyzed_yet)
 877     return chrec2;
 878   if (chrec2 == chrec_not_analyzed_yet)
 879     return chrec1;
 880
 881   if (eq_evolutions_p (chrec1, chrec2))
 882     return chrec1;
 883
 884   return chrec_dont_know;
 885 }
 886
 887 \f
 888
 889 /* Observers.  */
 890
 891 /* Helper function for is_multivariate_chrec.  */
 892
 893 static bool
 894 is_multivariate_chrec_rec (const_tree chrec, unsigned int rec_var)
 895 {
 896   if (chrec == NULL_TREE)
 897     return false;
 898
 899   if (TREE_CODE (chrec) == POLYNOMIAL_CHREC)
 900     {
 901       if (CHREC_VARIABLE (chrec) != rec_var)
 902         return true;
 903       else
 904         return (is_multivariate_chrec_rec (CHREC_LEFT (chrec), rec_var)
 905                 || is_multivariate_chrec_rec (CHREC_RIGHT (chrec), rec_var));
 906     }
 907   else
 908     return false;
 909 }
 910
 911 /* Determine whether the given chrec is multivariate or not.  */
 912
 913 bool
 914 is_multivariate_chrec (const_tree chrec)
 915 {
 916   if (chrec == NULL_TREE)
 917     return false;
 918
 919   if (TREE_CODE (chrec) == POLYNOMIAL_CHREC)
 920     return (is_multivariate_chrec_rec (CHREC_LEFT (chrec),
 921                                        CHREC_VARIABLE (chrec))
 922             || is_multivariate_chrec_rec (CHREC_RIGHT (chrec),
 923                                           CHREC_VARIABLE (chrec)));
 924   else
 925     return false;
 926 }
 927
 928 /* Determines whether the chrec contains symbolic names or not.  */
 929
 930 bool
 931 chrec_contains_symbols (const_tree chrec)
 932 {
 933   int i, n;
 934
 935   if (chrec == NULL_TREE)
 936     return false;
 937
 938   if (TREE_CODE (chrec) == SSA_NAME
 939       || TREE_CODE (chrec) == VAR_DECL
 940       || TREE_CODE (chrec) == PARM_DECL
 941       || TREE_CODE (chrec) == FUNCTION_DECL
 942       || TREE_CODE (chrec) == LABEL_DECL
 943       || TREE_CODE (chrec) == RESULT_DECL
 944       || TREE_CODE (chrec) == FIELD_DECL)
 945     return true;
 946
 947   n = TREE_OPERAND_LENGTH (chrec);
 948   for (i = 0; i < n; i++)
 949     if (chrec_contains_symbols (TREE_OPERAND (chrec, i)))
 950       return true;
 951   return false;
 952 }
 953
 954 /* Determines whether the chrec contains undetermined coefficients.  */
 955
 956 bool
 957 chrec_contains_undetermined (const_tree chrec)
 958 {
 959   int i, n;
 960
 961   if (chrec == chrec_dont_know)
 962     return true;
 963
 964   if (chrec == NULL_TREE)
 965     return false;
 966
 967   n = TREE_OPERAND_LENGTH (chrec);
 968   for (i = 0; i < n; i++)
 969     if (chrec_contains_undetermined (TREE_OPERAND (chrec, i)))
 970       return true;
 971   return false;
 972 }
 973
 974 /* Determines whether the tree EXPR contains chrecs, and increment
 975    SIZE if it is not a NULL pointer by an estimation of the depth of
 976    the tree.  */
 977
 978 bool
 979 tree_contains_chrecs (const_tree expr, int *size)
 980 {
 981   int i, n;
 982
 983   if (expr == NULL_TREE)
 984     return false;
 985
 986   if (size)
 987     (*size)++;
 988
 989   if (tree_is_chrec (expr))
 990     return true;
 991
 992   n = TREE_OPERAND_LENGTH (expr);
 993   for (i = 0; i < n; i++)
 994     if (tree_contains_chrecs (TREE_OPERAND (expr, i), size))
 995       return true;
 996   return false;
 997 }
 998
 999 /* Recursive helper function.  */
1000
1001 static bool
1002 evolution_function_is_invariant_rec_p (tree chrec, int loopnum)
1003 {
1004   if (evolution_function_is_constant_p (chrec))
1005     return true;
1006
1007   if (TREE_CODE (chrec) == SSA_NAME
1008       && (loopnum == 0
1009           || expr_invariant_in_loop_p (get_loop (cfun, loopnum), chrec)))
1010     return true;
1011
1012   if (TREE_CODE (chrec) == POLYNOMIAL_CHREC)
1013     {
1014       if (CHREC_VARIABLE (chrec) == (unsigned) loopnum
1015           || flow_loop_nested_p (get_loop (cfun, loopnum),
1016                                  get_chrec_loop (chrec))
1017           || !evolution_function_is_invariant_rec_p (CHREC_RIGHT (chrec),
1018                                                      loopnum)
1019           || !evolution_function_is_invariant_rec_p (CHREC_LEFT (chrec),
1020                                                      loopnum))
1021         return false;
1022       return true;
1023     }
1024
1025   switch (TREE_OPERAND_LENGTH (chrec))
1026     {
1027     case 2:
1028       if (!evolution_function_is_invariant_rec_p (TREE_OPERAND (chrec, 1),
1029                                                   loopnum))
1030         return false;
1031
1032     case 1:
1033       if (!evolution_function_is_invariant_rec_p (TREE_OPERAND (chrec, 0),
1034                                                   loopnum))
1035         return false;
1036       return true;
1037
1038     default:
1039       return false;
1040     }
1041
1042   return false;
1043 }
1044
1045 /* Return true if CHREC is invariant in loop LOOPNUM, false otherwise. */
1046
1047 bool
1048 evolution_function_is_invariant_p (tree chrec, int loopnum)
1049 {
1050   return evolution_function_is_invariant_rec_p (chrec, loopnum);
1051 }
1052
1053 /* Determine whether the given tree is an affine multivariate
1054    evolution.  */
1055
1056 bool
1057 evolution_function_is_affine_multivariate_p (const_tree chrec, int loopnum)
1058 {
1059   if (chrec == NULL_TREE)
1060     return false;
1061
1062   switch (TREE_CODE (chrec))
1063     {
1064     case POLYNOMIAL_CHREC:
1065       if (evolution_function_is_invariant_rec_p (CHREC_LEFT (chrec), loopnum))
1066         {
1067           if (evolution_function_is_invariant_rec_p (CHREC_RIGHT (chrec), loopnum))
1068             return true;
1069           else
1070             {
1071               if (TREE_CODE (CHREC_RIGHT (chrec)) == POLYNOMIAL_CHREC
1072                   && CHREC_VARIABLE (CHREC_RIGHT (chrec))
1073                      != CHREC_VARIABLE (chrec)
1074                   && evolution_function_is_affine_multivariate_p
1075                   (CHREC_RIGHT (chrec), loopnum))
1076                 return true;
1077               else
1078                 return false;
1079             }
1080         }
1081       else
1082         {
1083           if (evolution_function_is_invariant_rec_p (CHREC_RIGHT (chrec), loopnum)
1084               && TREE_CODE (CHREC_LEFT (chrec)) == POLYNOMIAL_CHREC
1085               && CHREC_VARIABLE (CHREC_LEFT (chrec)) != CHREC_VARIABLE (chrec)
1086               && evolution_function_is_affine_multivariate_p
1087               (CHREC_LEFT (chrec), loopnum))
1088             return true;
1089           else
1090             return false;
1091         }
1092
1093     default:
1094       return false;
1095     }
1096 }
1097
1098 /* Determine whether the given tree is a function in zero or one
1099    variables.  */
1100
1101 bool
1102 evolution_function_is_univariate_p (const_tree chrec)
1103 {
1104   if (chrec == NULL_TREE)
1105     return true;
1106
1107   switch (TREE_CODE (chrec))
1108     {
1109     case POLYNOMIAL_CHREC:
1110       switch (TREE_CODE (CHREC_LEFT (chrec)))
1111         {
1112         case POLYNOMIAL_CHREC:
1113           if (CHREC_VARIABLE (chrec) != CHREC_VARIABLE (CHREC_LEFT (chrec)))
1114             return false;
1115           if (!evolution_function_is_univariate_p (CHREC_LEFT (chrec)))
1116             return false;
1117           break;
1118
1119         default:
1120           if (tree_contains_chrecs (CHREC_LEFT (chrec), NULL))
1121             return false;
1122           break;
1123         }
1124
1125       switch (TREE_CODE (CHREC_RIGHT (chrec)))
1126         {
1127         case POLYNOMIAL_CHREC:
1128           if (CHREC_VARIABLE (chrec) != CHREC_VARIABLE (CHREC_RIGHT (chrec)))
1129             return false;
1130           if (!evolution_function_is_univariate_p (CHREC_RIGHT (chrec)))
1131             return false;
1132           break;
1133
1134         default:
1135           if (tree_contains_chrecs (CHREC_RIGHT (chrec), NULL))
1136             return false;
1137           break;
1138         }
1139
1140     default:
1141       return true;
1142     }
1143 }
1144
1145 /* Returns the number of variables of CHREC.  Example: the call
1146    nb_vars_in_chrec ({{0, +, 1}_5, +, 2}_6) returns 2.  */
1147
1148 unsigned
1149 nb_vars_in_chrec (tree chrec)
1150 {
1151   if (chrec == NULL_TREE)
1152     return 0;
1153
1154   switch (TREE_CODE (chrec))
1155     {
1156     case POLYNOMIAL_CHREC:
1157       return 1 + nb_vars_in_chrec
1158         (initial_condition_in_loop_num (chrec, CHREC_VARIABLE (chrec)));
1159
1160     default:
1161       return 0;
1162     }
1163 }
1164
1165 static tree chrec_convert_1 (tree, tree, gimple, bool);
1166
1167 /* Converts BASE and STEP of affine scev to TYPE.  LOOP is the loop whose iv
1168    the scev corresponds to.  AT_STMT is the statement at that the scev is
1169    evaluated.  USE_OVERFLOW_SEMANTICS is true if this function should assume that
1170    the rules for overflow of the given language apply (e.g., that signed
1171    arithmetics in C does not overflow) -- i.e., to use them to avoid unnecessary
1172    tests, but also to enforce that the result follows them.  Returns true if the
1173    conversion succeeded, false otherwise.  */
1174
1175 bool
1176 convert_affine_scev (struct loop *loop, tree type,
1177                      tree *base, tree *step, gimple at_stmt,
1178                      bool use_overflow_semantics)
1179 {
1180   tree ct = TREE_TYPE (*step);
1181   bool enforce_overflow_semantics;
1182   bool must_check_src_overflow, must_check_rslt_overflow;
1183   tree new_base, new_step;
1184   tree step_type = POINTER_TYPE_P (type) ? sizetype : type;
1185
1186   /* In general,
1187      (TYPE) (BASE + STEP * i) = (TYPE) BASE + (TYPE -- sign extend) STEP * i,
1188      but we must check some assumptions.
1189
1190      1) If [BASE, +, STEP] wraps, the equation is not valid when precision
1191         of CT is smaller than the precision of TYPE.  For example, when we
1192         cast unsigned char [254, +, 1] to unsigned, the values on left side
1193         are 254, 255, 0, 1, ..., but those on the right side are
1194         254, 255, 256, 257, ...
1195      2) In case that we must also preserve the fact that signed ivs do not
1196         overflow, we must additionally check that the new iv does not wrap.
1197         For example, unsigned char [125, +, 1] casted to signed char could
1198         become a wrapping variable with values 125, 126, 127, -128, -127, ...,
1199         which would confuse optimizers that assume that this does not
1200         happen.  */
1201   must_check_src_overflow = TYPE_PRECISION (ct) < TYPE_PRECISION (type);
1202
1203   enforce_overflow_semantics = (use_overflow_semantics
1204                                 && nowrap_type_p (type));
1205   if (enforce_overflow_semantics)
1206     {
1207       /* We can avoid checking whether the result overflows in the following
1208          cases:
1209
1210          -- must_check_src_overflow is true, and the range of TYPE is superset
1211             of the range of CT -- i.e., in all cases except if CT signed and
1212             TYPE unsigned.
1213          -- both CT and TYPE have the same precision and signedness, and we
1214             verify instead that the source does not overflow (this may be
1215             easier than verifying it for the result, as we may use the
1216             information about the semantics of overflow in CT).  */
1217       if (must_check_src_overflow)
1218         {
1219           if (TYPE_UNSIGNED (type) && !TYPE_UNSIGNED (ct))
1220             must_check_rslt_overflow = true;
1221           else
1222             must_check_rslt_overflow = false;
1223         }
1224       else if (TYPE_UNSIGNED (ct) == TYPE_UNSIGNED (type)
1225                && TYPE_PRECISION (ct) == TYPE_PRECISION (type))
1226         {
1227           must_check_rslt_overflow = false;
1228           must_check_src_overflow = true;
1229         }
1230       else
1231         must_check_rslt_overflow = true;
1232     }
1233   else
1234     must_check_rslt_overflow = false;
1235
1236   if (must_check_src_overflow
1237       && scev_probably_wraps_p (*base, *step, at_stmt, loop,
1238                                 use_overflow_semantics))
1239     return false;
1240
1241   new_base = chrec_convert_1 (type, *base, at_stmt,
1242                               use_overflow_semantics);
1243   /* The step must be sign extended, regardless of the signedness
1244      of CT and TYPE.  This only needs to be handled specially when
1245      CT is unsigned -- to avoid e.g. unsigned char [100, +, 255]
1246      (with values 100, 99, 98, ...) from becoming signed or unsigned
1247      [100, +, 255] with values 100, 355, ...; the sign-extension is
1248      performed by default when CT is signed.  */
1249   new_step = *step;
1250   if (TYPE_PRECISION (step_type) > TYPE_PRECISION (ct) && TYPE_UNSIGNED (ct))
1251     {
1252       tree signed_ct = build_nonstandard_integer_type (TYPE_PRECISION (ct), 0);
1253       new_step = chrec_convert_1 (signed_ct, new_step, at_stmt,
1254                                   use_overflow_semantics);
1255     }
1256   new_step = chrec_convert_1 (step_type, new_step, at_stmt, use_overflow_semantics);
1257
1258   if (automatically_generated_chrec_p (new_base)
1259       || automatically_generated_chrec_p (new_step))
1260     return false;
1261
1262   if (must_check_rslt_overflow
1263       /* Note that in this case we cannot use the fact that signed variables
1264          do not overflow, as this is what we are verifying for the new iv.  */
1265       && scev_probably_wraps_p (new_base, new_step, at_stmt, loop, false))
1266     return false;
1267
1268   *base = new_base;
1269   *step = new_step;
1270   return true;
1271 }
1272 \f
1273
1274 /* Convert CHREC for the right hand side of a CHREC.
1275    The increment for a pointer type is always sizetype.  */
1276
1277 tree
1278 chrec_convert_rhs (tree type, tree chrec, gimple at_stmt)
1279 {
1280   if (POINTER_TYPE_P (type))
1281     type = sizetype;
1282
1283   return chrec_convert (type, chrec, at_stmt);
1284 }
1285
1286 /* Convert CHREC to TYPE.  When the analyzer knows the context in
1287    which the CHREC is built, it sets AT_STMT to the statement that
1288    contains the definition of the analyzed variable, otherwise the
1289    conversion is less accurate: the information is used for
1290    determining a more accurate estimation of the number of iterations.
1291    By default AT_STMT could be safely set to NULL_TREE.
1292
1293    The following rule is always true: TREE_TYPE (chrec) ==
1294    TREE_TYPE (CHREC_LEFT (chrec)) == TREE_TYPE (CHREC_RIGHT (chrec)).
1295    An example of what could happen when adding two chrecs and the type
1296    of the CHREC_RIGHT is different than CHREC_LEFT is:
1297
1298    {(uint) 0, +, (uchar) 10} +
1299    {(uint) 0, +, (uchar) 250}
1300
1301    that would produce a wrong result if CHREC_RIGHT is not (uint):
1302
1303    {(uint) 0, +, (uchar) 4}
1304
1305    instead of
1306
1307    {(uint) 0, +, (uint) 260}
1308 */
1309
1310 tree
1311 chrec_convert (tree type, tree chrec, gimple at_stmt)
1312 {
1313   return chrec_convert_1 (type, chrec, at_stmt, true);
1314 }
1315
1316 /* Convert CHREC to TYPE.  When the analyzer knows the context in
1317    which the CHREC is built, it sets AT_STMT to the statement that
1318    contains the definition of the analyzed variable, otherwise the
1319    conversion is less accurate: the information is used for
1320    determining a more accurate estimation of the number of iterations.
1321    By default AT_STMT could be safely set to NULL_TREE.
1322
1323    USE_OVERFLOW_SEMANTICS is true if this function should assume that
1324    the rules for overflow of the given language apply (e.g., that signed
1325    arithmetics in C does not overflow) -- i.e., to use them to avoid unnecessary
1326    tests, but also to enforce that the result follows them.  */
1327
1328 static tree
1329 chrec_convert_1 (tree type, tree chrec, gimple at_stmt,
1330                  bool use_overflow_semantics)
1331 {
1332   tree ct, res;
1333   tree base, step;
1334   struct loop *loop;
1335
1336   if (automatically_generated_chrec_p (chrec))
1337     return chrec;
1338
1339   ct = chrec_type (chrec);
1340   if (ct == type)
1341     return chrec;
1342
1343   if (!evolution_function_is_affine_p (chrec))
1344     goto keep_cast;
1345
1346   loop = get_chrec_loop (chrec);
1347   base = CHREC_LEFT (chrec);
1348   step = CHREC_RIGHT (chrec);
1349
1350   if (convert_affine_scev (loop, type, &base, &step, at_stmt,
1351                            use_overflow_semantics))
1352     return build_polynomial_chrec (loop->num, base, step);
1353
1354   /* If we cannot propagate the cast inside the chrec, just keep the cast.  */
1355 keep_cast:
1356   /* Fold will not canonicalize (long)(i - 1) to (long)i - 1 because that
1357      may be more expensive.  We do want to perform this optimization here
1358      though for canonicalization reasons.  */
1359   if (use_overflow_semantics
1360       && (TREE_CODE (chrec) == PLUS_EXPR
1361           || TREE_CODE (chrec) == MINUS_EXPR)
1362       && TREE_CODE (type) == INTEGER_TYPE
1363       && TREE_CODE (ct) == INTEGER_TYPE
1364       && TYPE_PRECISION (type) > TYPE_PRECISION (ct)
1365       && TYPE_OVERFLOW_UNDEFINED (ct))
1366     res = fold_build2 (TREE_CODE (chrec), type,
1367                        fold_convert (type, TREE_OPERAND (chrec, 0)),
1368                        fold_convert (type, TREE_OPERAND (chrec, 1)));
1369   /* Similar perform the trick that (signed char)((int)x + 2) can be
1370      narrowed to (signed char)((unsigned char)x + 2).  */
1371   else if (use_overflow_semantics
1372            && TREE_CODE (chrec) == POLYNOMIAL_CHREC
1373            && TREE_CODE (ct) == INTEGER_TYPE
1374            && TREE_CODE (type) == INTEGER_TYPE
1375            && TYPE_OVERFLOW_UNDEFINED (type)
1376            && TYPE_PRECISION (type) < TYPE_PRECISION (ct))
1377     {
1378       tree utype = unsigned_type_for (type);
1379       res = build_polynomial_chrec (CHREC_VARIABLE (chrec),
1380                                     fold_convert (utype,
1381                                                   CHREC_LEFT (chrec)),
1382                                     fold_convert (utype,
1383                                                   CHREC_RIGHT (chrec)));
1384       res = chrec_convert_1 (type, res, at_stmt, use_overflow_semantics);
1385     }
1386   else
1387     res = fold_convert (type, chrec);
1388
1389   /* Don't propagate overflows.  */
1390   if (CONSTANT_CLASS_P (res))
1391     TREE_OVERFLOW (res) = 0;
1392
1393   /* But reject constants that don't fit in their type after conversion.
1394      This can happen if TYPE_MIN_VALUE or TYPE_MAX_VALUE are not the
1395      natural values associated with TYPE_PRECISION and TYPE_UNSIGNED,
1396      and can cause problems later when computing niters of loops.  Note
1397      that we don't do the check before converting because we don't want
1398      to reject conversions of negative chrecs to unsigned types.  */
1399   if (TREE_CODE (res) == INTEGER_CST
1400       && TREE_CODE (type) == INTEGER_TYPE
1401       && !int_fits_type_p (res, type))
1402     res = chrec_dont_know;
1403
1404   return res;
1405 }
1406
1407 /* Convert CHREC to TYPE, without regard to signed overflows.  Returns the new
1408    chrec if something else than what chrec_convert would do happens, NULL_TREE
1409    otherwise.  */
1410
1411 tree
1412 chrec_convert_aggressive (tree type, tree chrec)
1413 {
1414   tree inner_type, left, right, lc, rc, rtype;
1415
1416   if (automatically_generated_chrec_p (chrec)
1417       || TREE_CODE (chrec) != POLYNOMIAL_CHREC)
1418     return NULL_TREE;
1419
1420   inner_type = TREE_TYPE (chrec);
1421   if (TYPE_PRECISION (type) > TYPE_PRECISION (inner_type))
1422     return NULL_TREE;
1423
1424   rtype = POINTER_TYPE_P (type) ? sizetype : type;
1425
1426   left = CHREC_LEFT (chrec);
1427   right = CHREC_RIGHT (chrec);
1428   lc = chrec_convert_aggressive (type, left);
1429   if (!lc)
1430     lc = chrec_convert (type, left, NULL);
1431   rc = chrec_convert_aggressive (rtype, right);
1432   if (!rc)
1433     rc = chrec_convert (rtype, right, NULL);
1434
1435   return build_polynomial_chrec (CHREC_VARIABLE (chrec), lc, rc);
1436 }
1437
1438 /* Returns true when CHREC0 == CHREC1.  */
1439
1440 bool
1441 eq_evolutions_p (const_tree chrec0, const_tree chrec1)
1442 {
1443   if (chrec0 == NULL_TREE
1444       || chrec1 == NULL_TREE
1445       || TREE_CODE (chrec0) != TREE_CODE (chrec1))
1446     return false;
1447
1448   if (chrec0 == chrec1)
1449     return true;
1450
1451   switch (TREE_CODE (chrec0))
1452     {
1453     case INTEGER_CST:
1454       return operand_equal_p (chrec0, chrec1, 0);
1455
1456     case POLYNOMIAL_CHREC:
1457       return (CHREC_VARIABLE (chrec0) == CHREC_VARIABLE (chrec1)
1458               && eq_evolutions_p (CHREC_LEFT (chrec0), CHREC_LEFT (chrec1))
1459               && eq_evolutions_p (CHREC_RIGHT (chrec0), CHREC_RIGHT (chrec1)));
1460
1461     case PLUS_EXPR:
1462     case MULT_EXPR:
1463     case MINUS_EXPR:
1464     case POINTER_PLUS_EXPR:
1465       return eq_evolutions_p (TREE_OPERAND (chrec0, 0),
1466                               TREE_OPERAND (chrec1, 0))
1467           && eq_evolutions_p (TREE_OPERAND (chrec0, 1),
1468                               TREE_OPERAND (chrec1, 1));
1469
1470     default:
1471       return false;
1472     }
1473 }
1474
1475 /* Returns EV_GROWS if CHREC grows (assuming that it does not overflow),
1476    EV_DECREASES if it decreases, and EV_UNKNOWN if we cannot determine
1477    which of these cases happens.  */
1478
1479 enum ev_direction
1480 scev_direction (const_tree chrec)
1481 {
1482   const_tree step;
1483
1484   if (!evolution_function_is_affine_p (chrec))
1485     return EV_DIR_UNKNOWN;
1486
1487   step = CHREC_RIGHT (chrec);
1488   if (TREE_CODE (step) != INTEGER_CST)
1489     return EV_DIR_UNKNOWN;
1490
1491   if (tree_int_cst_sign_bit (step))
1492     return EV_DIR_DECREASES;
1493   else
1494     return EV_DIR_GROWS;
1495 }
1496
1497 /* Iterates over all the components of SCEV, and calls CBCK.  */
1498
1499 void
1500 for_each_scev_op (tree *scev, bool (*cbck) (tree *, void *), void *data)
1501 {
1502   switch (TREE_CODE_LENGTH (TREE_CODE (*scev)))
1503     {
1504     case 3:
1505       for_each_scev_op (&TREE_OPERAND (*scev, 2), cbck, data);
1506
1507     case 2:
1508       for_each_scev_op (&TREE_OPERAND (*scev, 1), cbck, data);
1509
1510     case 1:
1511       for_each_scev_op (&TREE_OPERAND (*scev, 0), cbck, data);
1512
1513     default:
1514       cbck (scev, data);
1515       break;
1516     }
1517 }
1518
1519 /* Returns true when the operation can be part of a linear
1520    expression.  */
1521
1522 static inline bool
1523 operator_is_linear (tree scev)
1524 {
1525   switch (TREE_CODE (scev))
1526     {
1527     case INTEGER_CST:
1528     case POLYNOMIAL_CHREC:
1529     case PLUS_EXPR:
1530     case POINTER_PLUS_EXPR:
1531     case MULT_EXPR:
1532     case MINUS_EXPR:
1533     case NEGATE_EXPR:
1534     case SSA_NAME:
1535     case NON_LVALUE_EXPR:
1536     case BIT_NOT_EXPR:
1537     CASE_CONVERT:
1538       return true;
1539
1540     default:
1541       return false;
1542     }
1543 }
1544
1545 /* Return true when SCEV is a linear expression.  Linear expressions
1546    can contain additions, substractions and multiplications.
1547    Multiplications are restricted to constant scaling: "cst * x".  */
1548
1549 bool
1550 scev_is_linear_expression (tree scev)
1551 {
1552   if (scev == NULL
1553       || !operator_is_linear (scev))
1554     return false;
1555
1556   if (TREE_CODE (scev) == MULT_EXPR)
1557     return !(tree_contains_chrecs (TREE_OPERAND (scev, 0), NULL)
1558              && tree_contains_chrecs (TREE_OPERAND (scev, 1), NULL));
1559
1560   if (TREE_CODE (scev) == POLYNOMIAL_CHREC
1561       && !evolution_function_is_affine_multivariate_p (scev, CHREC_VARIABLE (scev)))
1562     return false;
1563
1564   switch (TREE_CODE_LENGTH (TREE_CODE (scev)))
1565     {
1566     case 3:
1567       return scev_is_linear_expression (TREE_OPERAND (scev, 0))
1568         && scev_is_linear_expression (TREE_OPERAND (scev, 1))
1569         && scev_is_linear_expression (TREE_OPERAND (scev, 2));
1570
1571     case 2:
1572       return scev_is_linear_expression (TREE_OPERAND (scev, 0))
1573         && scev_is_linear_expression (TREE_OPERAND (scev, 1));
1574
1575     case 1:
1576       return scev_is_linear_expression (TREE_OPERAND (scev, 0));
1577
1578     case 0:
1579       return true;
1580
1581     default:
1582       return false;
1583     }
1584 }
1585
1586 /* Determines whether the expression CHREC contains only interger consts
1587    in the right parts.  */
1588
1589 bool
1590 evolution_function_right_is_integer_cst (const_tree chrec)
1591 {
1592   if (chrec == NULL_TREE)
1593     return false;
1594
1595   switch (TREE_CODE (chrec))
1596     {
1597     case INTEGER_CST:
1598       return true;
1599
1600     case POLYNOMIAL_CHREC:
1601       return TREE_CODE (CHREC_RIGHT (chrec)) == INTEGER_CST
1602         && (TREE_CODE (CHREC_LEFT (chrec)) != POLYNOMIAL_CHREC
1603             || evolution_function_right_is_integer_cst (CHREC_LEFT (chrec)));
1604
1605     CASE_CONVERT:
1606       return evolution_function_right_is_integer_cst (TREE_OPERAND (chrec, 0));
1607
1608     default:
1609       return false;
1610     }
1611 }