gcc/tree-chrec.c

   1 /* Chains of recurrences.
   2    Copyright (C) 2003-2019 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 "backend.h"
  30 #include "tree.h"
  31 #include "gimple-expr.h"
  32 #include "tree-pretty-print.h"
  33 #include "fold-const.h"
  34 #include "cfgloop.h"
  35 #include "tree-ssa-loop-ivopts.h"
  36 #include "tree-ssa-loop-niter.h"
  37 #include "tree-chrec.h"
  38 #include "dumpfile.h"
  39 #include "params.h"
  40 #include "tree-scalar-evolution.h"
  41
  42 /* Extended folder for chrecs.  */
  43
  44 /* Fold the addition of two polynomial functions.  */
  45
  46 static inline tree
  47 chrec_fold_plus_poly_poly (enum tree_code code,
  48                            tree type,
  49                            tree poly0,
  50                            tree poly1)
  51 {
  52   tree left, right;
  53   struct loop *loop0 = get_chrec_loop (poly0);
  54   struct loop *loop1 = get_chrec_loop (poly1);
  55   tree rtype = code == POINTER_PLUS_EXPR ? chrec_type (poly1) : type;
  56
  57   gcc_assert (poly0);
  58   gcc_assert (poly1);
  59   gcc_assert (TREE_CODE (poly0) == POLYNOMIAL_CHREC);
  60   gcc_assert (TREE_CODE (poly1) == POLYNOMIAL_CHREC);
  61   if (POINTER_TYPE_P (chrec_type (poly0)))
  62     gcc_checking_assert (ptrofftype_p (chrec_type (poly1))
  63                          && useless_type_conversion_p (type, chrec_type (poly0)));
  64   else
  65     gcc_checking_assert (useless_type_conversion_p (type, chrec_type (poly0))
  66                          && useless_type_conversion_p (type, chrec_type (poly1)));
  67
  68   /*
  69     {a, +, b}_1 + {c, +, d}_2  ->  {{a, +, b}_1 + c, +, d}_2,
  70     {a, +, b}_2 + {c, +, d}_1  ->  {{c, +, d}_1 + a, +, b}_2,
  71     {a, +, b}_x + {c, +, d}_x  ->  {a+c, +, b+d}_x.  */
  72   if (flow_loop_nested_p (loop0, loop1))
  73     {
  74       if (code == PLUS_EXPR || code == POINTER_PLUS_EXPR)
  75         return build_polynomial_chrec
  76           (CHREC_VARIABLE (poly1),
  77            chrec_fold_plus (type, poly0, CHREC_LEFT (poly1)),
  78            CHREC_RIGHT (poly1));
  79       else
  80         return build_polynomial_chrec
  81           (CHREC_VARIABLE (poly1),
  82            chrec_fold_minus (type, poly0, CHREC_LEFT (poly1)),
  83            chrec_fold_multiply (type, CHREC_RIGHT (poly1),
  84                                 SCALAR_FLOAT_TYPE_P (type)
  85                                 ? build_real (type, dconstm1)
  86                                 : build_int_cst_type (type, -1)));
  87     }
  88
  89   if (flow_loop_nested_p (loop1, loop0))
  90     {
  91       if (code == PLUS_EXPR || code == POINTER_PLUS_EXPR)
  92         return build_polynomial_chrec
  93           (CHREC_VARIABLE (poly0),
  94            chrec_fold_plus (type, CHREC_LEFT (poly0), poly1),
  95            CHREC_RIGHT (poly0));
  96       else
  97         return build_polynomial_chrec
  98           (CHREC_VARIABLE (poly0),
  99            chrec_fold_minus (type, CHREC_LEFT (poly0), poly1),
 100            CHREC_RIGHT (poly0));
 101     }
 102
 103   /* This function should never be called for chrecs of loops that
 104      do not belong to the same loop nest.  */
 105   if (loop0 != loop1)
 106     {
 107       /* It still can happen if we are not in loop-closed SSA form.  */
 108       gcc_assert (! loops_state_satisfies_p (LOOP_CLOSED_SSA));
 109       return chrec_dont_know;
 110     }
 111
 112   if (code == PLUS_EXPR || code == POINTER_PLUS_EXPR)
 113     {
 114       left = chrec_fold_plus
 115         (type, CHREC_LEFT (poly0), CHREC_LEFT (poly1));
 116       right = chrec_fold_plus
 117         (rtype, CHREC_RIGHT (poly0), CHREC_RIGHT (poly1));
 118     }
 119   else
 120     {
 121       left = chrec_fold_minus
 122         (type, CHREC_LEFT (poly0), CHREC_LEFT (poly1));
 123       right = chrec_fold_minus
 124         (type, CHREC_RIGHT (poly0), CHREC_RIGHT (poly1));
 125     }
 126
 127   if (chrec_zerop (right))
 128     return left;
 129   else
 130     return build_polynomial_chrec
 131       (CHREC_VARIABLE (poly0), left, right);
 132 }
 133
 134 \f
 135
 136 /* Fold the multiplication of two polynomial functions.  */
 137
 138 static inline tree
 139 chrec_fold_multiply_poly_poly (tree type,
 140                                tree poly0,
 141                                tree poly1)
 142 {
 143   tree t0, t1, t2;
 144   int var;
 145   struct loop *loop0 = get_chrec_loop (poly0);
 146   struct loop *loop1 = get_chrec_loop (poly1);
 147
 148   gcc_assert (poly0);
 149   gcc_assert (poly1);
 150   gcc_assert (TREE_CODE (poly0) == POLYNOMIAL_CHREC);
 151   gcc_assert (TREE_CODE (poly1) == POLYNOMIAL_CHREC);
 152   gcc_checking_assert (useless_type_conversion_p (type, chrec_type (poly0))
 153                        && useless_type_conversion_p (type, chrec_type (poly1)));
 154
 155   /* {a, +, b}_1 * {c, +, d}_2  ->  {c*{a, +, b}_1, +, d}_2,
 156      {a, +, b}_2 * {c, +, d}_1  ->  {a*{c, +, d}_1, +, b}_2,
 157      {a, +, b}_x * {c, +, d}_x  ->  {a*c, +, a*d + b*c + b*d, +, 2*b*d}_x.  */
 158   if (flow_loop_nested_p (loop0, loop1))
 159     /* poly0 is a constant wrt. poly1.  */
 160     return build_polynomial_chrec
 161       (CHREC_VARIABLE (poly1),
 162        chrec_fold_multiply (type, CHREC_LEFT (poly1), poly0),
 163        CHREC_RIGHT (poly1));
 164
 165   if (flow_loop_nested_p (loop1, loop0))
 166     /* poly1 is a constant wrt. poly0.  */
 167     return build_polynomial_chrec
 168       (CHREC_VARIABLE (poly0),
 169        chrec_fold_multiply (type, CHREC_LEFT (poly0), poly1),
 170        CHREC_RIGHT (poly0));
 171
 172   if (loop0 != loop1)
 173     {
 174       /* It still can happen if we are not in loop-closed SSA form.  */
 175       gcc_assert (! loops_state_satisfies_p (LOOP_CLOSED_SSA));
 176       return chrec_dont_know;
 177     }
 178
 179   /* poly0 and poly1 are two polynomials in the same variable,
 180      {a, +, b}_x * {c, +, d}_x  ->  {a*c, +, a*d + b*c + b*d, +, 2*b*d}_x.  */
 181
 182   /* "a*c".  */
 183   t0 = chrec_fold_multiply (type, CHREC_LEFT (poly0), CHREC_LEFT (poly1));
 184
 185   /* "a*d + b*c".  */
 186   t1 = chrec_fold_multiply (type, CHREC_LEFT (poly0), CHREC_RIGHT (poly1));
 187   t1 = chrec_fold_plus (type, t1, chrec_fold_multiply (type,
 188                                                        CHREC_RIGHT (poly0),
 189                                                        CHREC_LEFT (poly1)));
 190   /* "b*d".  */
 191   t2 = chrec_fold_multiply (type, CHREC_RIGHT (poly0), CHREC_RIGHT (poly1));
 192   /* "a*d + b*c + b*d".  */
 193   t1 = chrec_fold_plus (type, t1, t2);
 194   /* "2*b*d".  */
 195   t2 = chrec_fold_multiply (type, SCALAR_FLOAT_TYPE_P (type)
 196                             ? build_real (type, dconst2)
 197                             : build_int_cst (type, 2), t2);
 198
 199   var = CHREC_VARIABLE (poly0);
 200   return build_polynomial_chrec (var, t0,
 201                                  build_polynomial_chrec (var, t1, t2));
 202 }
 203
 204 /* When the operands are automatically_generated_chrec_p, the fold has
 205    to respect the semantics of the operands.  */
 206
 207 static inline tree
 208 chrec_fold_automatically_generated_operands (tree op0,
 209                                              tree op1)
 210 {
 211   if (op0 == chrec_dont_know
 212       || op1 == chrec_dont_know)
 213     return chrec_dont_know;
 214
 215   if (op0 == chrec_known
 216       || op1 == chrec_known)
 217     return chrec_known;
 218
 219   if (op0 == chrec_not_analyzed_yet
 220       || op1 == chrec_not_analyzed_yet)
 221     return chrec_not_analyzed_yet;
 222
 223   /* The default case produces a safe result.  */
 224   return chrec_dont_know;
 225 }
 226
 227 /* Fold the addition of two chrecs.  */
 228
 229 static tree
 230 chrec_fold_plus_1 (enum tree_code code, tree type,
 231                    tree op0, tree op1)
 232 {
 233   if (automatically_generated_chrec_p (op0)
 234       || automatically_generated_chrec_p (op1))
 235     return chrec_fold_automatically_generated_operands (op0, op1);
 236
 237   switch (TREE_CODE (op0))
 238     {
 239     case POLYNOMIAL_CHREC:
 240       gcc_checking_assert
 241         (!chrec_contains_symbols_defined_in_loop (op0, CHREC_VARIABLE (op0)));
 242       switch (TREE_CODE (op1))
 243         {
 244         case POLYNOMIAL_CHREC:
 245           gcc_checking_assert
 246             (!chrec_contains_symbols_defined_in_loop (op1,
 247                                                       CHREC_VARIABLE (op1)));
 248           return chrec_fold_plus_poly_poly (code, type, op0, op1);
 249
 250         CASE_CONVERT:
 251           {
 252             /* We can strip sign-conversions to signed by performing the
 253                operation in unsigned.  */
 254             tree optype = TREE_TYPE (TREE_OPERAND (op1, 0));
 255             if (INTEGRAL_TYPE_P (type)
 256                 && INTEGRAL_TYPE_P (optype)
 257                 && tree_nop_conversion_p (type, optype)
 258                 && TYPE_UNSIGNED (optype))
 259               return chrec_convert (type,
 260                                     chrec_fold_plus_1 (code, optype,
 261                                                        chrec_convert (optype,
 262                                                                       op0, NULL),
 263                                                        TREE_OPERAND (op1, 0)),
 264                                     NULL);
 265             if (tree_contains_chrecs (op1, NULL))
 266               return chrec_dont_know;
 267           }
 268           /* FALLTHRU */
 269
 270         default:
 271           if (code == PLUS_EXPR || code == POINTER_PLUS_EXPR)
 272             return build_polynomial_chrec
 273               (CHREC_VARIABLE (op0),
 274                chrec_fold_plus (type, CHREC_LEFT (op0), op1),
 275                CHREC_RIGHT (op0));
 276           else
 277             return build_polynomial_chrec
 278               (CHREC_VARIABLE (op0),
 279                chrec_fold_minus (type, CHREC_LEFT (op0), op1),
 280                CHREC_RIGHT (op0));
 281         }
 282
 283     CASE_CONVERT:
 284       {
 285         /* We can strip sign-conversions to signed by performing the
 286            operation in unsigned.  */
 287         tree optype = TREE_TYPE (TREE_OPERAND (op0, 0));
 288         if (INTEGRAL_TYPE_P (type)
 289             && INTEGRAL_TYPE_P (optype)
 290             && tree_nop_conversion_p (type, optype)
 291             && TYPE_UNSIGNED (optype))
 292           return chrec_convert (type,
 293                                 chrec_fold_plus_1 (code, optype,
 294                                                    TREE_OPERAND (op0, 0),
 295                                                    chrec_convert (optype,
 296                                                                   op1, NULL)),
 297                                 NULL);
 298         if (tree_contains_chrecs (op0, NULL))
 299           return chrec_dont_know;
 300       }
 301       /* FALLTHRU */
 302
 303     default:
 304       switch (TREE_CODE (op1))
 305         {
 306         case POLYNOMIAL_CHREC:
 307           gcc_checking_assert
 308             (!chrec_contains_symbols_defined_in_loop (op1,
 309                                                       CHREC_VARIABLE (op1)));
 310           if (code == PLUS_EXPR || code == POINTER_PLUS_EXPR)
 311             return build_polynomial_chrec
 312               (CHREC_VARIABLE (op1),
 313                chrec_fold_plus (type, op0, CHREC_LEFT (op1)),
 314                CHREC_RIGHT (op1));
 315           else
 316             return build_polynomial_chrec
 317               (CHREC_VARIABLE (op1),
 318                chrec_fold_minus (type, op0, CHREC_LEFT (op1)),
 319                chrec_fold_multiply (type, CHREC_RIGHT (op1),
 320                                     SCALAR_FLOAT_TYPE_P (type)
 321                                     ? build_real (type, dconstm1)
 322                                     : build_int_cst_type (type, -1)));
 323
 324         CASE_CONVERT:
 325           if (tree_contains_chrecs (op1, NULL))
 326             return chrec_dont_know;
 327           /* FALLTHRU */
 328
 329         default:
 330           {
 331             int size = 0;
 332             if ((tree_contains_chrecs (op0, &size)
 333                  || tree_contains_chrecs (op1, &size))
 334                 && size < PARAM_VALUE (PARAM_SCEV_MAX_EXPR_SIZE))
 335               return build2 (code, type, op0, op1);
 336             else if (size < PARAM_VALUE (PARAM_SCEV_MAX_EXPR_SIZE))
 337               {
 338                 if (code == POINTER_PLUS_EXPR)
 339                   return fold_build_pointer_plus (fold_convert (type, op0),
 340                                                   op1);
 341                 else
 342                   return fold_build2 (code, type,
 343                                       fold_convert (type, op0),
 344                                       fold_convert (type, op1));
 345               }
 346             else
 347               return chrec_dont_know;
 348           }
 349         }
 350     }
 351 }
 352
 353 /* Fold the addition of two chrecs.  */
 354
 355 tree
 356 chrec_fold_plus (tree type,
 357                  tree op0,
 358                  tree op1)
 359 {
 360   enum tree_code code;
 361   if (automatically_generated_chrec_p (op0)
 362       || automatically_generated_chrec_p (op1))
 363     return chrec_fold_automatically_generated_operands (op0, op1);
 364
 365   if (integer_zerop (op0))
 366     return chrec_convert (type, op1, NULL);
 367   if (integer_zerop (op1))
 368     return chrec_convert (type, op0, NULL);
 369
 370   if (POINTER_TYPE_P (type))
 371     code = POINTER_PLUS_EXPR;
 372   else
 373     code = PLUS_EXPR;
 374
 375   return chrec_fold_plus_1 (code, type, op0, op1);
 376 }
 377
 378 /* Fold the subtraction of two chrecs.  */
 379
 380 tree
 381 chrec_fold_minus (tree type,
 382                   tree op0,
 383                   tree op1)
 384 {
 385   if (automatically_generated_chrec_p (op0)
 386       || automatically_generated_chrec_p (op1))
 387     return chrec_fold_automatically_generated_operands (op0, op1);
 388
 389   if (integer_zerop (op1))
 390     return op0;
 391
 392   return chrec_fold_plus_1 (MINUS_EXPR, type, op0, op1);
 393 }
 394
 395 /* Fold the multiplication of two chrecs.  */
 396
 397 tree
 398 chrec_fold_multiply (tree type,
 399                      tree op0,
 400                      tree op1)
 401 {
 402   if (automatically_generated_chrec_p (op0)
 403       || automatically_generated_chrec_p (op1))
 404     return chrec_fold_automatically_generated_operands (op0, op1);
 405
 406   switch (TREE_CODE (op0))
 407     {
 408     case POLYNOMIAL_CHREC:
 409       gcc_checking_assert
 410         (!chrec_contains_symbols_defined_in_loop (op0, CHREC_VARIABLE (op0)));
 411       switch (TREE_CODE (op1))
 412         {
 413         case POLYNOMIAL_CHREC:
 414           gcc_checking_assert
 415             (!chrec_contains_symbols_defined_in_loop (op1,
 416                                                       CHREC_VARIABLE (op1)));
 417           return chrec_fold_multiply_poly_poly (type, op0, op1);
 418
 419         CASE_CONVERT:
 420           if (tree_contains_chrecs (op1, NULL))
 421             return chrec_dont_know;
 422           /* FALLTHRU */
 423
 424         default:
 425           if (integer_onep (op1))
 426             return op0;
 427           if (integer_zerop (op1))
 428             return build_int_cst (type, 0);
 429
 430           return build_polynomial_chrec
 431             (CHREC_VARIABLE (op0),
 432              chrec_fold_multiply (type, CHREC_LEFT (op0), op1),
 433              chrec_fold_multiply (type, CHREC_RIGHT (op0), op1));
 434         }
 435
 436     CASE_CONVERT:
 437       if (tree_contains_chrecs (op0, NULL))
 438         return chrec_dont_know;
 439       /* FALLTHRU */
 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           /* FALLTHRU */
 463
 464         default:
 465           if (integer_onep (op1))
 466             return op0;
 467           if (integer_zerop (op1))
 468             return build_int_cst (type, 0);
 469           return fold_build2 (MULT_EXPR, type, op0, op1);
 470         }
 471     }
 472 }
 473
 474 \f
 475
 476 /* Operations.  */
 477
 478 /* Evaluate the binomial coefficient.  Return NULL_TREE if the intermediate
 479    calculation overflows, otherwise return C(n,k) with type TYPE.  */
 480
 481 static tree
 482 tree_fold_binomial (tree type, tree n, unsigned int k)
 483 {
 484   wi::overflow_type overflow;
 485   unsigned int i;
 486
 487   /* Handle the most frequent cases.  */
 488   if (k == 0)
 489     return build_int_cst (type, 1);
 490   if (k == 1)
 491     return fold_convert (type, n);
 492
 493   widest_int num = wi::to_widest (n);
 494
 495   /* Check that k <= n.  */
 496   if (wi::ltu_p (num, k))
 497     return NULL_TREE;
 498
 499   /* Denominator = 2.  */
 500   widest_int denom = 2;
 501
 502   /* Index = Numerator-1.  */
 503   widest_int idx = num - 1;
 504
 505   /* Numerator = Numerator*Index = n*(n-1).  */
 506   num = wi::smul (num, idx, &overflow);
 507   if (overflow)
 508     return NULL_TREE;
 509
 510   for (i = 3; i <= k; i++)
 511     {
 512       /* Index--.  */
 513       --idx;
 514
 515       /* Numerator *= Index.  */
 516       num = wi::smul (num, idx, &overflow);
 517       if (overflow)
 518         return NULL_TREE;
 519
 520       /* Denominator *= i.  */
 521       denom *= i;
 522     }
 523
 524   /* Result = Numerator / Denominator.  */
 525   num = wi::udiv_trunc (num, denom);
 526   if (! wi::fits_to_tree_p (num, type))
 527     return NULL_TREE;
 528   return wide_int_to_tree (type, num);
 529 }
 530
 531 /* Helper function.  Use the Newton's interpolating formula for
 532    evaluating the value of the evolution function.
 533    The result may be in an unsigned type of CHREC.  */
 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   /* The formula associates the expression and thus we have to make
 547      sure to not introduce undefined overflow.  */
 548   tree ctype = type;
 549   if (INTEGRAL_TYPE_P (type)
 550       && ! TYPE_OVERFLOW_WRAPS (type))
 551     ctype = unsigned_type_for (type);
 552
 553   if (TREE_CODE (chrec) == POLYNOMIAL_CHREC
 554       && CHREC_VARIABLE (chrec) == var)
 555     {
 556       arg1 = chrec_evaluate (var, CHREC_RIGHT (chrec), n, k + 1);
 557       if (arg1 == chrec_dont_know)
 558         return chrec_dont_know;
 559       binomial_n_k = tree_fold_binomial (ctype, n, k);
 560       if (!binomial_n_k)
 561         return chrec_dont_know;
 562       tree l = chrec_convert (ctype, CHREC_LEFT (chrec), NULL);
 563       arg0 = fold_build2 (MULT_EXPR, ctype, l, binomial_n_k);
 564       return chrec_fold_plus (ctype, arg0, arg1);
 565     }
 566
 567   binomial_n_k = tree_fold_binomial (ctype, n, k);
 568   if (!binomial_n_k)
 569     return chrec_dont_know;
 570
 571   return fold_build2 (MULT_EXPR, ctype,
 572                       chrec_convert (ctype, chrec, NULL), binomial_n_k);
 573 }
 574
 575 /* Evaluates "CHREC (X)" when the varying variable is VAR.
 576    Example:  Given the following parameters,
 577
 578    var = 1
 579    chrec = {3, +, 4}_1
 580    x = 10
 581
 582    The result is given by the Newton's interpolating formula:
 583    3 * \binom{10}{0} + 4 * \binom{10}{1}.
 584 */
 585
 586 tree
 587 chrec_apply (unsigned var,
 588              tree chrec,
 589              tree x)
 590 {
 591   tree type = chrec_type (chrec);
 592   tree res = chrec_dont_know;
 593
 594   if (automatically_generated_chrec_p (chrec)
 595       || automatically_generated_chrec_p (x)
 596
 597       /* When the symbols are defined in an outer loop, it is possible
 598          to symbolically compute the apply, since the symbols are
 599          constants with respect to the varying loop.  */
 600       || chrec_contains_symbols_defined_in_loop (chrec, var))
 601     return chrec_dont_know;
 602
 603   if (dump_file && (dump_flags & TDF_SCEV))
 604     fprintf (dump_file, "(chrec_apply \n");
 605
 606   if (TREE_CODE (x) == INTEGER_CST && SCALAR_FLOAT_TYPE_P (type))
 607     x = build_real_from_int_cst (type, x);
 608
 609   switch (TREE_CODE (chrec))
 610     {
 611     case POLYNOMIAL_CHREC:
 612       if (evolution_function_is_affine_p (chrec))
 613         {
 614           if (CHREC_VARIABLE (chrec) != var)
 615             return build_polynomial_chrec
 616               (CHREC_VARIABLE (chrec),
 617                chrec_apply (var, CHREC_LEFT (chrec), x),
 618                chrec_apply (var, CHREC_RIGHT (chrec), x));
 619
 620           /* "{a, +, b} (x)"  ->  "a + b*x".  */
 621           x = chrec_convert_rhs (type, x, NULL);
 622           res = chrec_fold_multiply (TREE_TYPE (x), CHREC_RIGHT (chrec), x);
 623           res = chrec_fold_plus (type, CHREC_LEFT (chrec), res);
 624         }
 625       else if (TREE_CODE (x) == INTEGER_CST
 626                && tree_int_cst_sgn (x) == 1)
 627         /* testsuite/.../ssa-chrec-38.c.  */
 628         res = chrec_convert (type, chrec_evaluate (var, chrec, x, 0), NULL);
 629       else
 630         res = chrec_dont_know;
 631       break;
 632
 633     CASE_CONVERT:
 634       res = chrec_convert (TREE_TYPE (chrec),
 635                            chrec_apply (var, TREE_OPERAND (chrec, 0), x),
 636                            NULL);
 637       break;
 638
 639     default:
 640       res = chrec;
 641       break;
 642     }
 643
 644   if (dump_file && (dump_flags & TDF_SCEV))
 645     {
 646       fprintf (dump_file, "  (varying_loop = %d\n", var);
 647       fprintf (dump_file, ")\n  (chrec = ");
 648       print_generic_expr (dump_file, chrec);
 649       fprintf (dump_file, ")\n  (x = ");
 650       print_generic_expr (dump_file, x);
 651       fprintf (dump_file, ")\n  (res = ");
 652       print_generic_expr (dump_file, res);
 653       fprintf (dump_file, "))\n");
 654     }
 655
 656   return res;
 657 }
 658
 659 /* For a given CHREC and an induction variable map IV_MAP that maps
 660    (loop->num, expr) for every loop number of the current_loops an
 661    expression, calls chrec_apply when the expression is not NULL.  */
 662
 663 tree
 664 chrec_apply_map (tree chrec, vec<tree> iv_map)
 665 {
 666   int i;
 667   tree expr;
 668
 669   FOR_EACH_VEC_ELT (iv_map, i, expr)
 670     if (expr)
 671       chrec = chrec_apply (i, chrec, expr);
 672
 673   return chrec;
 674 }
 675
 676 /* Replaces the initial condition in CHREC with INIT_COND.  */
 677
 678 tree
 679 chrec_replace_initial_condition (tree chrec,
 680                                  tree init_cond)
 681 {
 682   if (automatically_generated_chrec_p (chrec))
 683     return chrec;
 684
 685   gcc_assert (chrec_type (chrec) == chrec_type (init_cond));
 686
 687   switch (TREE_CODE (chrec))
 688     {
 689     case POLYNOMIAL_CHREC:
 690       return build_polynomial_chrec
 691         (CHREC_VARIABLE (chrec),
 692          chrec_replace_initial_condition (CHREC_LEFT (chrec), init_cond),
 693          CHREC_RIGHT (chrec));
 694
 695     default:
 696       return init_cond;
 697     }
 698 }
 699
 700 /* Returns the initial condition of a given CHREC.  */
 701
 702 tree
 703 initial_condition (tree chrec)
 704 {
 705   if (automatically_generated_chrec_p (chrec))
 706     return chrec;
 707
 708   if (TREE_CODE (chrec) == POLYNOMIAL_CHREC)
 709     return initial_condition (CHREC_LEFT (chrec));
 710   else
 711     return chrec;
 712 }
 713
 714 /* Returns a univariate function that represents the evolution in
 715    LOOP_NUM.  Mask the evolution of any other loop.  */
 716
 717 tree
 718 hide_evolution_in_other_loops_than_loop (tree chrec,
 719                                          unsigned loop_num)
 720 {
 721   struct loop *loop = get_loop (cfun, loop_num), *chloop;
 722   if (automatically_generated_chrec_p (chrec))
 723     return chrec;
 724
 725   switch (TREE_CODE (chrec))
 726     {
 727     case POLYNOMIAL_CHREC:
 728       chloop = get_chrec_loop (chrec);
 729
 730       if (chloop == loop)
 731         return build_polynomial_chrec
 732           (loop_num,
 733            hide_evolution_in_other_loops_than_loop (CHREC_LEFT (chrec),
 734                                                     loop_num),
 735            CHREC_RIGHT (chrec));
 736
 737       else if (flow_loop_nested_p (chloop, loop))
 738         /* There is no evolution in this loop.  */
 739         return initial_condition (chrec);
 740
 741       else if (flow_loop_nested_p (loop, chloop))
 742         return hide_evolution_in_other_loops_than_loop (CHREC_LEFT (chrec),
 743                                                         loop_num);
 744
 745       else
 746         return chrec_dont_know;
 747
 748     default:
 749       return chrec;
 750     }
 751 }
 752
 753 /* Returns the evolution part of CHREC in LOOP_NUM when RIGHT is
 754    true, otherwise returns the initial condition in LOOP_NUM.  */
 755
 756 static tree
 757 chrec_component_in_loop_num (tree chrec,
 758                              unsigned loop_num,
 759                              bool right)
 760 {
 761   tree component;
 762   struct loop *loop = get_loop (cfun, loop_num), *chloop;
 763
 764   if (automatically_generated_chrec_p (chrec))
 765     return chrec;
 766
 767   switch (TREE_CODE (chrec))
 768     {
 769     case POLYNOMIAL_CHREC:
 770       chloop = get_chrec_loop (chrec);
 771
 772       if (chloop == loop)
 773         {
 774           if (right)
 775             component = CHREC_RIGHT (chrec);
 776           else
 777             component = CHREC_LEFT (chrec);
 778
 779           if (TREE_CODE (CHREC_LEFT (chrec)) != POLYNOMIAL_CHREC
 780               || CHREC_VARIABLE (CHREC_LEFT (chrec)) != CHREC_VARIABLE (chrec))
 781             return component;
 782
 783           else
 784             return build_polynomial_chrec
 785               (loop_num,
 786                chrec_component_in_loop_num (CHREC_LEFT (chrec),
 787                                             loop_num,
 788                                             right),
 789                component);
 790         }
 791
 792       else if (flow_loop_nested_p (chloop, loop))
 793         /* There is no evolution part in this loop.  */
 794         return NULL_TREE;
 795
 796       else
 797         {
 798           gcc_assert (flow_loop_nested_p (loop, chloop));
 799           return chrec_component_in_loop_num (CHREC_LEFT (chrec),
 800                                               loop_num,
 801                                               right);
 802         }
 803
 804      default:
 805       if (right)
 806         return NULL_TREE;
 807       else
 808         return chrec;
 809     }
 810 }
 811
 812 /* Returns the evolution part in LOOP_NUM.  Example: the call
 813    evolution_part_in_loop_num ({{0, +, 1}_1, +, 2}_1, 1) returns
 814    {1, +, 2}_1  */
 815
 816 tree
 817 evolution_part_in_loop_num (tree chrec,
 818                             unsigned loop_num)
 819 {
 820   return chrec_component_in_loop_num (chrec, loop_num, true);
 821 }
 822
 823 /* Returns the initial condition in LOOP_NUM.  Example: the call
 824    initial_condition_in_loop_num ({{0, +, 1}_1, +, 2}_2, 2) returns
 825    {0, +, 1}_1  */
 826
 827 tree
 828 initial_condition_in_loop_num (tree chrec,
 829                                unsigned loop_num)
 830 {
 831   return chrec_component_in_loop_num (chrec, loop_num, false);
 832 }
 833
 834 /* Set or reset the evolution of CHREC to NEW_EVOL in loop LOOP_NUM.
 835    This function is essentially used for setting the evolution to
 836    chrec_dont_know, for example after having determined that it is
 837    impossible to say how many times a loop will execute.  */
 838
 839 tree
 840 reset_evolution_in_loop (unsigned loop_num,
 841                          tree chrec,
 842                          tree new_evol)
 843 {
 844   struct loop *loop = get_loop (cfun, loop_num);
 845
 846   if (POINTER_TYPE_P (chrec_type (chrec)))
 847     gcc_assert (ptrofftype_p (chrec_type (new_evol)));
 848   else
 849     gcc_assert (chrec_type (chrec) == chrec_type (new_evol));
 850
 851   if (TREE_CODE (chrec) == POLYNOMIAL_CHREC
 852       && flow_loop_nested_p (loop, get_chrec_loop (chrec)))
 853     {
 854       tree left = reset_evolution_in_loop (loop_num, CHREC_LEFT (chrec),
 855                                            new_evol);
 856       tree right = reset_evolution_in_loop (loop_num, CHREC_RIGHT (chrec),
 857                                             new_evol);
 858       return build_polynomial_chrec (CHREC_VARIABLE (chrec), left, right);
 859     }
 860
 861   while (TREE_CODE (chrec) == POLYNOMIAL_CHREC
 862          && CHREC_VARIABLE (chrec) == loop_num)
 863     chrec = CHREC_LEFT (chrec);
 864
 865   return build_polynomial_chrec (loop_num, chrec, new_evol);
 866 }
 867
 868 /* Merges two evolution functions that were found by following two
 869    alternate paths of a conditional expression.  */
 870
 871 tree
 872 chrec_merge (tree chrec1,
 873              tree chrec2)
 874 {
 875   if (chrec1 == chrec_dont_know
 876       || chrec2 == chrec_dont_know)
 877     return chrec_dont_know;
 878
 879   if (chrec1 == chrec_known
 880       || chrec2 == chrec_known)
 881     return chrec_known;
 882
 883   if (chrec1 == chrec_not_analyzed_yet)
 884     return chrec2;
 885   if (chrec2 == chrec_not_analyzed_yet)
 886     return chrec1;
 887
 888   if (eq_evolutions_p (chrec1, chrec2))
 889     return chrec1;
 890
 891   return chrec_dont_know;
 892 }
 893
 894 \f
 895
 896 /* Observers.  */
 897
 898 /* Helper function for is_multivariate_chrec.  */
 899
 900 static bool
 901 is_multivariate_chrec_rec (const_tree chrec, unsigned int rec_var)
 902 {
 903   if (chrec == NULL_TREE)
 904     return false;
 905
 906   if (TREE_CODE (chrec) == POLYNOMIAL_CHREC)
 907     {
 908       if (CHREC_VARIABLE (chrec) != rec_var)
 909         return true;
 910       else
 911         return (is_multivariate_chrec_rec (CHREC_LEFT (chrec), rec_var)
 912                 || is_multivariate_chrec_rec (CHREC_RIGHT (chrec), rec_var));
 913     }
 914   else
 915     return false;
 916 }
 917
 918 /* Determine whether the given chrec is multivariate or not.  */
 919
 920 bool
 921 is_multivariate_chrec (const_tree chrec)
 922 {
 923   if (chrec == NULL_TREE)
 924     return false;
 925
 926   if (TREE_CODE (chrec) == POLYNOMIAL_CHREC)
 927     return (is_multivariate_chrec_rec (CHREC_LEFT (chrec),
 928                                        CHREC_VARIABLE (chrec))
 929             || is_multivariate_chrec_rec (CHREC_RIGHT (chrec),
 930                                           CHREC_VARIABLE (chrec)));
 931   else
 932     return false;
 933 }
 934
 935 /* Determines whether the chrec contains symbolic names or not.  */
 936
 937 static bool
 938 chrec_contains_symbols (const_tree chrec, hash_set<const_tree> &visited)
 939 {
 940   int i, n;
 941
 942   if (chrec == NULL_TREE)
 943     return false;
 944
 945   if (TREE_CODE (chrec) == SSA_NAME
 946       || VAR_P (chrec)
 947       || TREE_CODE (chrec) == POLY_INT_CST
 948       || TREE_CODE (chrec) == PARM_DECL
 949       || TREE_CODE (chrec) == FUNCTION_DECL
 950       || TREE_CODE (chrec) == LABEL_DECL
 951       || TREE_CODE (chrec) == RESULT_DECL
 952       || TREE_CODE (chrec) == FIELD_DECL)
 953     return true;
 954
 955   n = TREE_OPERAND_LENGTH (chrec);
 956   for (i = 0; i < n; i++)
 957     if (chrec_contains_symbols (TREE_OPERAND (chrec, i), visited))
 958       return true;
 959   return false;
 960 }
 961
 962 bool
 963 chrec_contains_symbols (const_tree chrec)
 964 {
 965   hash_set<const_tree> visited;
 966   return chrec_contains_symbols (chrec, visited);
 967 }
 968
 969 /* Determines whether the chrec contains undetermined coefficients.  */
 970
 971 static bool
 972 chrec_contains_undetermined (const_tree chrec, hash_set<const_tree> &visited)
 973 {
 974   int i, n;
 975
 976   if (chrec == chrec_dont_know)
 977     return true;
 978
 979   if (chrec == NULL_TREE)
 980     return false;
 981
 982   if (visited.add (chrec))
 983     return false;
 984
 985   n = TREE_OPERAND_LENGTH (chrec);
 986   for (i = 0; i < n; i++)
 987     if (chrec_contains_undetermined (TREE_OPERAND (chrec, i), visited))
 988       return true;
 989   return false;
 990 }
 991
 992 bool
 993 chrec_contains_undetermined (const_tree chrec)
 994 {
 995   hash_set<const_tree> visited;
 996   return chrec_contains_undetermined (chrec, visited);
 997 }
 998
 999 /* Determines whether the tree EXPR contains chrecs, and increment
1000    SIZE if it is not a NULL pointer by an estimation of the depth of
1001    the tree.  */
1002
1003 static bool
1004 tree_contains_chrecs (const_tree expr, int *size, hash_set<const_tree> &visited)
1005 {
1006   int i, n;
1007
1008   if (expr == NULL_TREE)
1009     return false;
1010
1011   if (size)
1012     (*size)++;
1013
1014   if (tree_is_chrec (expr))
1015     return true;
1016
1017   n = TREE_OPERAND_LENGTH (expr);
1018   for (i = 0; i < n; i++)
1019     if (tree_contains_chrecs (TREE_OPERAND (expr, i), size, visited))
1020       return true;
1021   return false;
1022 }
1023
1024 bool
1025 tree_contains_chrecs (const_tree expr, int *size)
1026 {
1027   hash_set<const_tree> visited;
1028   return tree_contains_chrecs (expr, size, visited);
1029 }
1030
1031
1032 /* Recursive helper function.  */
1033
1034 static bool
1035 evolution_function_is_invariant_rec_p (tree chrec, int loopnum)
1036 {
1037   if (evolution_function_is_constant_p (chrec))
1038     return true;
1039
1040   if (TREE_CODE (chrec) == SSA_NAME
1041       && (loopnum == 0
1042           || expr_invariant_in_loop_p (get_loop (cfun, loopnum), chrec)))
1043     return true;
1044
1045   if (TREE_CODE (chrec) == POLYNOMIAL_CHREC)
1046     {
1047       if (CHREC_VARIABLE (chrec) == (unsigned) loopnum
1048           || flow_loop_nested_p (get_loop (cfun, loopnum),
1049                                  get_chrec_loop (chrec))
1050           || !evolution_function_is_invariant_rec_p (CHREC_RIGHT (chrec),
1051                                                      loopnum)
1052           || !evolution_function_is_invariant_rec_p (CHREC_LEFT (chrec),
1053                                                      loopnum))
1054         return false;
1055       return true;
1056     }
1057
1058   switch (TREE_OPERAND_LENGTH (chrec))
1059     {
1060     case 2:
1061       if (!evolution_function_is_invariant_rec_p (TREE_OPERAND (chrec, 1),
1062                                                   loopnum))
1063         return false;
1064       /* FALLTHRU */
1065
1066     case 1:
1067       if (!evolution_function_is_invariant_rec_p (TREE_OPERAND (chrec, 0),
1068                                                   loopnum))
1069         return false;
1070       return true;
1071
1072     default:
1073       return false;
1074     }
1075
1076   return false;
1077 }
1078
1079 /* Return true if CHREC is invariant in loop LOOPNUM, false otherwise. */
1080
1081 bool
1082 evolution_function_is_invariant_p (tree chrec, int loopnum)
1083 {
1084   return evolution_function_is_invariant_rec_p (chrec, loopnum);
1085 }
1086
1087 /* Determine whether the given tree is an affine multivariate
1088    evolution.  */
1089
1090 bool
1091 evolution_function_is_affine_multivariate_p (const_tree chrec, int loopnum)
1092 {
1093   if (chrec == NULL_TREE)
1094     return false;
1095
1096   switch (TREE_CODE (chrec))
1097     {
1098     case POLYNOMIAL_CHREC:
1099       if (evolution_function_is_invariant_rec_p (CHREC_LEFT (chrec), loopnum))
1100         {
1101           if (evolution_function_is_invariant_rec_p (CHREC_RIGHT (chrec), loopnum))
1102             return true;
1103           else
1104             {
1105               if (TREE_CODE (CHREC_RIGHT (chrec)) == POLYNOMIAL_CHREC
1106                   && CHREC_VARIABLE (CHREC_RIGHT (chrec))
1107                      != CHREC_VARIABLE (chrec)
1108                   && evolution_function_is_affine_multivariate_p
1109                   (CHREC_RIGHT (chrec), loopnum))
1110                 return true;
1111               else
1112                 return false;
1113             }
1114         }
1115       else
1116         {
1117           if (evolution_function_is_invariant_rec_p (CHREC_RIGHT (chrec), loopnum)
1118               && TREE_CODE (CHREC_LEFT (chrec)) == POLYNOMIAL_CHREC
1119               && CHREC_VARIABLE (CHREC_LEFT (chrec)) != CHREC_VARIABLE (chrec)
1120               && evolution_function_is_affine_multivariate_p
1121               (CHREC_LEFT (chrec), loopnum))
1122             return true;
1123           else
1124             return false;
1125         }
1126
1127     default:
1128       return false;
1129     }
1130 }
1131
1132 /* Determine whether the given tree is a function in zero or one
1133    variables.  */
1134
1135 bool
1136 evolution_function_is_univariate_p (const_tree chrec)
1137 {
1138   if (chrec == NULL_TREE)
1139     return true;
1140
1141   switch (TREE_CODE (chrec))
1142     {
1143     case POLYNOMIAL_CHREC:
1144       switch (TREE_CODE (CHREC_LEFT (chrec)))
1145         {
1146         case POLYNOMIAL_CHREC:
1147           if (CHREC_VARIABLE (chrec) != CHREC_VARIABLE (CHREC_LEFT (chrec)))
1148             return false;
1149           if (!evolution_function_is_univariate_p (CHREC_LEFT (chrec)))
1150             return false;
1151           break;
1152
1153         default:
1154           if (tree_contains_chrecs (CHREC_LEFT (chrec), NULL))
1155             return false;
1156           break;
1157         }
1158
1159       switch (TREE_CODE (CHREC_RIGHT (chrec)))
1160         {
1161         case POLYNOMIAL_CHREC:
1162           if (CHREC_VARIABLE (chrec) != CHREC_VARIABLE (CHREC_RIGHT (chrec)))
1163             return false;
1164           if (!evolution_function_is_univariate_p (CHREC_RIGHT (chrec)))
1165             return false;
1166           break;
1167
1168         default:
1169           if (tree_contains_chrecs (CHREC_RIGHT (chrec), NULL))
1170             return false;
1171           break;
1172         }
1173       return true;
1174
1175     default:
1176       return true;
1177     }
1178 }
1179
1180 /* Returns the number of variables of CHREC.  Example: the call
1181    nb_vars_in_chrec ({{0, +, 1}_5, +, 2}_6) returns 2.  */
1182
1183 unsigned
1184 nb_vars_in_chrec (tree chrec)
1185 {
1186   if (chrec == NULL_TREE)
1187     return 0;
1188
1189   switch (TREE_CODE (chrec))
1190     {
1191     case POLYNOMIAL_CHREC:
1192       return 1 + nb_vars_in_chrec
1193         (initial_condition_in_loop_num (chrec, CHREC_VARIABLE (chrec)));
1194
1195     default:
1196       return 0;
1197     }
1198 }
1199
1200 /* Converts BASE and STEP of affine scev to TYPE.  LOOP is the loop whose iv
1201    the scev corresponds to.  AT_STMT is the statement at that the scev is
1202    evaluated.  USE_OVERFLOW_SEMANTICS is true if this function should assume
1203    that the rules for overflow of the given language apply (e.g., that signed
1204    arithmetics in C does not overflow) -- i.e., to use them to avoid
1205    unnecessary tests, but also to enforce that the result follows them.
1206    FROM is the source variable converted if it's not NULL.  Returns true if
1207    the conversion succeeded, false otherwise.  */
1208
1209 bool
1210 convert_affine_scev (struct loop *loop, tree type,
1211                      tree *base, tree *step, gimple *at_stmt,
1212                      bool use_overflow_semantics, tree from)
1213 {
1214   tree ct = TREE_TYPE (*step);
1215   bool enforce_overflow_semantics;
1216   bool must_check_src_overflow, must_check_rslt_overflow;
1217   tree new_base, new_step;
1218   tree step_type = POINTER_TYPE_P (type) ? sizetype : type;
1219
1220   /* In general,
1221      (TYPE) (BASE + STEP * i) = (TYPE) BASE + (TYPE -- sign extend) STEP * i,
1222      but we must check some assumptions.
1223
1224      1) If [BASE, +, STEP] wraps, the equation is not valid when precision
1225         of CT is smaller than the precision of TYPE.  For example, when we
1226         cast unsigned char [254, +, 1] to unsigned, the values on left side
1227         are 254, 255, 0, 1, ..., but those on the right side are
1228         254, 255, 256, 257, ...
1229      2) In case that we must also preserve the fact that signed ivs do not
1230         overflow, we must additionally check that the new iv does not wrap.
1231         For example, unsigned char [125, +, 1] casted to signed char could
1232         become a wrapping variable with values 125, 126, 127, -128, -127, ...,
1233         which would confuse optimizers that assume that this does not
1234         happen.  */
1235   must_check_src_overflow = TYPE_PRECISION (ct) < TYPE_PRECISION (type);
1236
1237   enforce_overflow_semantics = (use_overflow_semantics
1238                                 && nowrap_type_p (type));
1239   if (enforce_overflow_semantics)
1240     {
1241       /* We can avoid checking whether the result overflows in the following
1242          cases:
1243
1244          -- must_check_src_overflow is true, and the range of TYPE is superset
1245             of the range of CT -- i.e., in all cases except if CT signed and
1246             TYPE unsigned.
1247          -- both CT and TYPE have the same precision and signedness, and we
1248             verify instead that the source does not overflow (this may be
1249             easier than verifying it for the result, as we may use the
1250             information about the semantics of overflow in CT).  */
1251       if (must_check_src_overflow)
1252         {
1253           if (TYPE_UNSIGNED (type) && !TYPE_UNSIGNED (ct))
1254             must_check_rslt_overflow = true;
1255           else
1256             must_check_rslt_overflow = false;
1257         }
1258       else if (TYPE_UNSIGNED (ct) == TYPE_UNSIGNED (type)
1259                && TYPE_PRECISION (ct) == TYPE_PRECISION (type))
1260         {
1261           must_check_rslt_overflow = false;
1262           must_check_src_overflow = true;
1263         }
1264       else
1265         must_check_rslt_overflow = true;
1266     }
1267   else
1268     must_check_rslt_overflow = false;
1269
1270   if (must_check_src_overflow
1271       && scev_probably_wraps_p (from, *base, *step, at_stmt, loop,
1272                                 use_overflow_semantics))
1273     return false;
1274
1275   new_base = chrec_convert (type, *base, at_stmt, use_overflow_semantics);
1276   /* The step must be sign extended, regardless of the signedness
1277      of CT and TYPE.  This only needs to be handled specially when
1278      CT is unsigned -- to avoid e.g. unsigned char [100, +, 255]
1279      (with values 100, 99, 98, ...) from becoming signed or unsigned
1280      [100, +, 255] with values 100, 355, ...; the sign-extension is
1281      performed by default when CT is signed.  */
1282   new_step = *step;
1283   if (TYPE_PRECISION (step_type) > TYPE_PRECISION (ct) && TYPE_UNSIGNED (ct))
1284     {
1285       tree signed_ct = build_nonstandard_integer_type (TYPE_PRECISION (ct), 0);
1286       new_step = chrec_convert (signed_ct, new_step, at_stmt,
1287                                 use_overflow_semantics);
1288     }
1289   new_step = chrec_convert (step_type, new_step, at_stmt,
1290                             use_overflow_semantics);
1291
1292   if (automatically_generated_chrec_p (new_base)
1293       || automatically_generated_chrec_p (new_step))
1294     return false;
1295
1296   if (must_check_rslt_overflow
1297       /* Note that in this case we cannot use the fact that signed variables
1298          do not overflow, as this is what we are verifying for the new iv.  */
1299       && scev_probably_wraps_p (NULL_TREE, new_base, new_step,
1300                                 at_stmt, loop, false))
1301     return false;
1302
1303   *base = new_base;
1304   *step = new_step;
1305   return true;
1306 }
1307 \f
1308
1309 /* Convert CHREC for the right hand side of a CHREC.
1310    The increment for a pointer type is always sizetype.  */
1311
1312 tree
1313 chrec_convert_rhs (tree type, tree chrec, gimple *at_stmt)
1314 {
1315   if (POINTER_TYPE_P (type))
1316     type = sizetype;
1317
1318   return chrec_convert (type, chrec, at_stmt);
1319 }
1320
1321 /* Convert CHREC to TYPE.  When the analyzer knows the context in
1322    which the CHREC is built, it sets AT_STMT to the statement that
1323    contains the definition of the analyzed variable, otherwise the
1324    conversion is less accurate: the information is used for
1325    determining a more accurate estimation of the number of iterations.
1326    By default AT_STMT could be safely set to NULL_TREE.
1327
1328    USE_OVERFLOW_SEMANTICS is true if this function should assume that
1329    the rules for overflow of the given language apply (e.g., that signed
1330    arithmetics in C does not overflow) -- i.e., to use them to avoid
1331    unnecessary tests, but also to enforce that the result follows them.
1332
1333    FROM is the source variable converted if it's not NULL.  */
1334
1335 static tree
1336 chrec_convert_1 (tree type, tree chrec, gimple *at_stmt,
1337                  bool use_overflow_semantics, tree from)
1338 {
1339   tree ct, res;
1340   tree base, step;
1341   struct loop *loop;
1342
1343   if (automatically_generated_chrec_p (chrec))
1344     return chrec;
1345
1346   ct = chrec_type (chrec);
1347   if (useless_type_conversion_p (type, ct))
1348     return chrec;
1349
1350   if (!evolution_function_is_affine_p (chrec))
1351     goto keep_cast;
1352
1353   loop = get_chrec_loop (chrec);
1354   base = CHREC_LEFT (chrec);
1355   step = CHREC_RIGHT (chrec);
1356
1357   if (convert_affine_scev (loop, type, &base, &step, at_stmt,
1358                            use_overflow_semantics, from))
1359     return build_polynomial_chrec (loop->num, base, step);
1360
1361   /* If we cannot propagate the cast inside the chrec, just keep the cast.  */
1362 keep_cast:
1363   /* Fold will not canonicalize (long)(i - 1) to (long)i - 1 because that
1364      may be more expensive.  We do want to perform this optimization here
1365      though for canonicalization reasons.  */
1366   if (use_overflow_semantics
1367       && (TREE_CODE (chrec) == PLUS_EXPR
1368           || TREE_CODE (chrec) == MINUS_EXPR)
1369       && TREE_CODE (type) == INTEGER_TYPE
1370       && TREE_CODE (ct) == INTEGER_TYPE
1371       && TYPE_PRECISION (type) > TYPE_PRECISION (ct)
1372       && TYPE_OVERFLOW_UNDEFINED (ct))
1373     res = fold_build2 (TREE_CODE (chrec), type,
1374                        fold_convert (type, TREE_OPERAND (chrec, 0)),
1375                        fold_convert (type, TREE_OPERAND (chrec, 1)));
1376   /* Similar perform the trick that (signed char)((int)x + 2) can be
1377      narrowed to (signed char)((unsigned char)x + 2).  */
1378   else if (use_overflow_semantics
1379            && TREE_CODE (chrec) == POLYNOMIAL_CHREC
1380            && TREE_CODE (ct) == INTEGER_TYPE
1381            && TREE_CODE (type) == INTEGER_TYPE
1382            && TYPE_OVERFLOW_UNDEFINED (type)
1383            && TYPE_PRECISION (type) < TYPE_PRECISION (ct))
1384     {
1385       tree utype = unsigned_type_for (type);
1386       res = build_polynomial_chrec (CHREC_VARIABLE (chrec),
1387                                     fold_convert (utype,
1388                                                   CHREC_LEFT (chrec)),
1389                                     fold_convert (utype,
1390                                                   CHREC_RIGHT (chrec)));
1391       res = chrec_convert_1 (type, res, at_stmt, use_overflow_semantics, from);
1392     }
1393   else
1394     res = fold_convert (type, chrec);
1395
1396   /* Don't propagate overflows.  */
1397   if (CONSTANT_CLASS_P (res))
1398     TREE_OVERFLOW (res) = 0;
1399
1400   /* But reject constants that don't fit in their type after conversion.
1401      This can happen if TYPE_MIN_VALUE or TYPE_MAX_VALUE are not the
1402      natural values associated with TYPE_PRECISION and TYPE_UNSIGNED,
1403      and can cause problems later when computing niters of loops.  Note
1404      that we don't do the check before converting because we don't want
1405      to reject conversions of negative chrecs to unsigned types.  */
1406   if (TREE_CODE (res) == INTEGER_CST
1407       && TREE_CODE (type) == INTEGER_TYPE
1408       && !int_fits_type_p (res, type))
1409     res = chrec_dont_know;
1410
1411   return res;
1412 }
1413
1414 /* Convert CHREC to TYPE.  When the analyzer knows the context in
1415    which the CHREC is built, it sets AT_STMT to the statement that
1416    contains the definition of the analyzed variable, otherwise the
1417    conversion is less accurate: the information is used for
1418    determining a more accurate estimation of the number of iterations.
1419    By default AT_STMT could be safely set to NULL_TREE.
1420
1421    The following rule is always true: TREE_TYPE (chrec) ==
1422    TREE_TYPE (CHREC_LEFT (chrec)) == TREE_TYPE (CHREC_RIGHT (chrec)).
1423    An example of what could happen when adding two chrecs and the type
1424    of the CHREC_RIGHT is different than CHREC_LEFT is:
1425
1426    {(uint) 0, +, (uchar) 10} +
1427    {(uint) 0, +, (uchar) 250}
1428
1429    that would produce a wrong result if CHREC_RIGHT is not (uint):
1430
1431    {(uint) 0, +, (uchar) 4}
1432
1433    instead of
1434
1435    {(uint) 0, +, (uint) 260}
1436
1437    USE_OVERFLOW_SEMANTICS is true if this function should assume that
1438    the rules for overflow of the given language apply (e.g., that signed
1439    arithmetics in C does not overflow) -- i.e., to use them to avoid
1440    unnecessary tests, but also to enforce that the result follows them.
1441
1442    FROM is the source variable converted if it's not NULL.  */
1443
1444 tree
1445 chrec_convert (tree type, tree chrec, gimple *at_stmt,
1446                bool use_overflow_semantics, tree from)
1447 {
1448   return chrec_convert_1 (type, chrec, at_stmt, use_overflow_semantics, from);
1449 }
1450
1451 /* Convert CHREC to TYPE, without regard to signed overflows.  Returns the new
1452    chrec if something else than what chrec_convert would do happens, NULL_TREE
1453    otherwise.  This function set TRUE to variable pointed by FOLD_CONVERSIONS
1454    if the result chrec may overflow.  */
1455
1456 tree
1457 chrec_convert_aggressive (tree type, tree chrec, bool *fold_conversions)
1458 {
1459   tree inner_type, left, right, lc, rc, rtype;
1460
1461   gcc_assert (fold_conversions != NULL);
1462
1463   if (automatically_generated_chrec_p (chrec)
1464       || TREE_CODE (chrec) != POLYNOMIAL_CHREC)
1465     return NULL_TREE;
1466
1467   inner_type = TREE_TYPE (chrec);
1468   if (TYPE_PRECISION (type) > TYPE_PRECISION (inner_type))
1469     return NULL_TREE;
1470
1471   if (useless_type_conversion_p (type, inner_type))
1472     return NULL_TREE;
1473
1474   if (!*fold_conversions && evolution_function_is_affine_p (chrec))
1475     {
1476       tree base, step;
1477       struct loop *loop;
1478
1479       loop = get_chrec_loop (chrec);
1480       base = CHREC_LEFT (chrec);
1481       step = CHREC_RIGHT (chrec);
1482       if (convert_affine_scev (loop, type, &base, &step, NULL, true))
1483         return build_polynomial_chrec (loop->num, base, step);
1484     }
1485   rtype = POINTER_TYPE_P (type) ? sizetype : type;
1486
1487   left = CHREC_LEFT (chrec);
1488   right = CHREC_RIGHT (chrec);
1489   lc = chrec_convert_aggressive (type, left, fold_conversions);
1490   if (!lc)
1491     lc = chrec_convert (type, left, NULL);
1492   rc = chrec_convert_aggressive (rtype, right, fold_conversions);
1493   if (!rc)
1494     rc = chrec_convert (rtype, right, NULL);
1495
1496   *fold_conversions = true;
1497
1498   return build_polynomial_chrec (CHREC_VARIABLE (chrec), lc, rc);
1499 }
1500
1501 /* Returns true when CHREC0 == CHREC1.  */
1502
1503 bool
1504 eq_evolutions_p (const_tree chrec0, const_tree chrec1)
1505 {
1506   if (chrec0 == NULL_TREE
1507       || chrec1 == NULL_TREE
1508       || TREE_CODE (chrec0) != TREE_CODE (chrec1))
1509     return false;
1510
1511   if (chrec0 == chrec1)
1512     return true;
1513
1514   if (! types_compatible_p (TREE_TYPE (chrec0), TREE_TYPE (chrec1)))
1515     return false;
1516
1517   switch (TREE_CODE (chrec0))
1518     {
1519     case POLYNOMIAL_CHREC:
1520       return (CHREC_VARIABLE (chrec0) == CHREC_VARIABLE (chrec1)
1521               && eq_evolutions_p (CHREC_LEFT (chrec0), CHREC_LEFT (chrec1))
1522               && eq_evolutions_p (CHREC_RIGHT (chrec0), CHREC_RIGHT (chrec1)));
1523
1524     case PLUS_EXPR:
1525     case MULT_EXPR:
1526     case MINUS_EXPR:
1527     case POINTER_PLUS_EXPR:
1528       return eq_evolutions_p (TREE_OPERAND (chrec0, 0),
1529                               TREE_OPERAND (chrec1, 0))
1530           && eq_evolutions_p (TREE_OPERAND (chrec0, 1),
1531                               TREE_OPERAND (chrec1, 1));
1532
1533     CASE_CONVERT:
1534       return eq_evolutions_p (TREE_OPERAND (chrec0, 0),
1535                               TREE_OPERAND (chrec1, 0));
1536
1537     default:
1538       return operand_equal_p (chrec0, chrec1, 0);
1539     }
1540 }
1541
1542 /* Returns EV_GROWS if CHREC grows (assuming that it does not overflow),
1543    EV_DECREASES if it decreases, and EV_UNKNOWN if we cannot determine
1544    which of these cases happens.  */
1545
1546 enum ev_direction
1547 scev_direction (const_tree chrec)
1548 {
1549   const_tree step;
1550
1551   if (!evolution_function_is_affine_p (chrec))
1552     return EV_DIR_UNKNOWN;
1553
1554   step = CHREC_RIGHT (chrec);
1555   if (TREE_CODE (step) != INTEGER_CST)
1556     return EV_DIR_UNKNOWN;
1557
1558   if (tree_int_cst_sign_bit (step))
1559     return EV_DIR_DECREASES;
1560   else
1561     return EV_DIR_GROWS;
1562 }
1563
1564 /* Iterates over all the components of SCEV, and calls CBCK.  */
1565
1566 void
1567 for_each_scev_op (tree *scev, bool (*cbck) (tree *, void *), void *data)
1568 {
1569   switch (TREE_CODE_LENGTH (TREE_CODE (*scev)))
1570     {
1571     case 3:
1572       for_each_scev_op (&TREE_OPERAND (*scev, 2), cbck, data);
1573       /* FALLTHRU */
1574
1575     case 2:
1576       for_each_scev_op (&TREE_OPERAND (*scev, 1), cbck, data);
1577       /* FALLTHRU */
1578
1579     case 1:
1580       for_each_scev_op (&TREE_OPERAND (*scev, 0), cbck, data);
1581       /* FALLTHRU */
1582
1583     default:
1584       cbck (scev, data);
1585       break;
1586     }
1587 }
1588
1589 /* Returns true when the operation can be part of a linear
1590    expression.  */
1591
1592 static inline bool
1593 operator_is_linear (tree scev)
1594 {
1595   switch (TREE_CODE (scev))
1596     {
1597     case INTEGER_CST:
1598     case POLYNOMIAL_CHREC:
1599     case PLUS_EXPR:
1600     case POINTER_PLUS_EXPR:
1601     case MULT_EXPR:
1602     case MINUS_EXPR:
1603     case NEGATE_EXPR:
1604     case SSA_NAME:
1605     case NON_LVALUE_EXPR:
1606     case BIT_NOT_EXPR:
1607     CASE_CONVERT:
1608       return true;
1609
1610     default:
1611       return false;
1612     }
1613 }
1614
1615 /* Return true when SCEV is a linear expression.  Linear expressions
1616    can contain additions, substractions and multiplications.
1617    Multiplications are restricted to constant scaling: "cst * x".  */
1618
1619 bool
1620 scev_is_linear_expression (tree scev)
1621 {
1622   if (evolution_function_is_constant_p (scev))
1623     return true;
1624
1625   if (scev == NULL
1626       || !operator_is_linear (scev))
1627     return false;
1628
1629   if (TREE_CODE (scev) == MULT_EXPR)
1630     return !(tree_contains_chrecs (TREE_OPERAND (scev, 0), NULL)
1631              && tree_contains_chrecs (TREE_OPERAND (scev, 1), NULL));
1632
1633   if (TREE_CODE (scev) == POLYNOMIAL_CHREC
1634       && !evolution_function_is_affine_multivariate_p (scev, CHREC_VARIABLE (scev)))
1635     return false;
1636
1637   switch (TREE_CODE_LENGTH (TREE_CODE (scev)))
1638     {
1639     case 3:
1640       return scev_is_linear_expression (TREE_OPERAND (scev, 0))
1641         && scev_is_linear_expression (TREE_OPERAND (scev, 1))
1642         && scev_is_linear_expression (TREE_OPERAND (scev, 2));
1643
1644     case 2:
1645       return scev_is_linear_expression (TREE_OPERAND (scev, 0))
1646         && scev_is_linear_expression (TREE_OPERAND (scev, 1));
1647
1648     case 1:
1649       return scev_is_linear_expression (TREE_OPERAND (scev, 0));
1650
1651     case 0:
1652       return true;
1653
1654     default:
1655       return false;
1656     }
1657 }
1658
1659 /* Determines whether the expression CHREC contains only interger consts
1660    in the right parts.  */
1661
1662 bool
1663 evolution_function_right_is_integer_cst (const_tree chrec)
1664 {
1665   if (chrec == NULL_TREE)
1666     return false;
1667
1668   switch (TREE_CODE (chrec))
1669     {
1670     case INTEGER_CST:
1671       return true;
1672
1673     case POLYNOMIAL_CHREC:
1674       return TREE_CODE (CHREC_RIGHT (chrec)) == INTEGER_CST
1675         && (TREE_CODE (CHREC_LEFT (chrec)) != POLYNOMIAL_CHREC
1676             || evolution_function_right_is_integer_cst (CHREC_LEFT (chrec)));
1677
1678     CASE_CONVERT:
1679       return evolution_function_right_is_integer_cst (TREE_OPERAND (chrec, 0));
1680
1681     default:
1682       return false;
1683     }
1684 }