gcc/tree-chrec.c

   1 /* Chains of recurrences.
   2    Copyright (C) 2003-2018 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 bool
 938 chrec_contains_symbols (const_tree chrec)
 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)))
 958       return true;
 959   return false;
 960 }
 961
 962 /* Determines whether the chrec contains undetermined coefficients.  */
 963
 964 bool
 965 chrec_contains_undetermined (const_tree chrec)
 966 {
 967   int i, n;
 968
 969   if (chrec == chrec_dont_know)
 970     return true;
 971
 972   if (chrec == NULL_TREE)
 973     return false;
 974
 975   n = TREE_OPERAND_LENGTH (chrec);
 976   for (i = 0; i < n; i++)
 977     if (chrec_contains_undetermined (TREE_OPERAND (chrec, i)))
 978       return true;
 979   return false;
 980 }
 981
 982 /* Determines whether the tree EXPR contains chrecs, and increment
 983    SIZE if it is not a NULL pointer by an estimation of the depth of
 984    the tree.  */
 985
 986 bool
 987 tree_contains_chrecs (const_tree expr, int *size)
 988 {
 989   int i, n;
 990
 991   if (expr == NULL_TREE)
 992     return false;
 993
 994   if (size)
 995     (*size)++;
 996
 997   if (tree_is_chrec (expr))
 998     return true;
 999
1000   n = TREE_OPERAND_LENGTH (expr);
1001   for (i = 0; i < n; i++)
1002     if (tree_contains_chrecs (TREE_OPERAND (expr, i), size))
1003       return true;
1004   return false;
1005 }
1006
1007 /* Recursive helper function.  */
1008
1009 static bool
1010 evolution_function_is_invariant_rec_p (tree chrec, int loopnum)
1011 {
1012   if (evolution_function_is_constant_p (chrec))
1013     return true;
1014
1015   if (TREE_CODE (chrec) == SSA_NAME
1016       && (loopnum == 0
1017           || expr_invariant_in_loop_p (get_loop (cfun, loopnum), chrec)))
1018     return true;
1019
1020   if (TREE_CODE (chrec) == POLYNOMIAL_CHREC)
1021     {
1022       if (CHREC_VARIABLE (chrec) == (unsigned) loopnum
1023           || flow_loop_nested_p (get_loop (cfun, loopnum),
1024                                  get_chrec_loop (chrec))
1025           || !evolution_function_is_invariant_rec_p (CHREC_RIGHT (chrec),
1026                                                      loopnum)
1027           || !evolution_function_is_invariant_rec_p (CHREC_LEFT (chrec),
1028                                                      loopnum))
1029         return false;
1030       return true;
1031     }
1032
1033   switch (TREE_OPERAND_LENGTH (chrec))
1034     {
1035     case 2:
1036       if (!evolution_function_is_invariant_rec_p (TREE_OPERAND (chrec, 1),
1037                                                   loopnum))
1038         return false;
1039       /* FALLTHRU */
1040
1041     case 1:
1042       if (!evolution_function_is_invariant_rec_p (TREE_OPERAND (chrec, 0),
1043                                                   loopnum))
1044         return false;
1045       return true;
1046
1047     default:
1048       return false;
1049     }
1050
1051   return false;
1052 }
1053
1054 /* Return true if CHREC is invariant in loop LOOPNUM, false otherwise. */
1055
1056 bool
1057 evolution_function_is_invariant_p (tree chrec, int loopnum)
1058 {
1059   return evolution_function_is_invariant_rec_p (chrec, loopnum);
1060 }
1061
1062 /* Determine whether the given tree is an affine multivariate
1063    evolution.  */
1064
1065 bool
1066 evolution_function_is_affine_multivariate_p (const_tree chrec, int loopnum)
1067 {
1068   if (chrec == NULL_TREE)
1069     return false;
1070
1071   switch (TREE_CODE (chrec))
1072     {
1073     case POLYNOMIAL_CHREC:
1074       if (evolution_function_is_invariant_rec_p (CHREC_LEFT (chrec), loopnum))
1075         {
1076           if (evolution_function_is_invariant_rec_p (CHREC_RIGHT (chrec), loopnum))
1077             return true;
1078           else
1079             {
1080               if (TREE_CODE (CHREC_RIGHT (chrec)) == POLYNOMIAL_CHREC
1081                   && CHREC_VARIABLE (CHREC_RIGHT (chrec))
1082                      != CHREC_VARIABLE (chrec)
1083                   && evolution_function_is_affine_multivariate_p
1084                   (CHREC_RIGHT (chrec), loopnum))
1085                 return true;
1086               else
1087                 return false;
1088             }
1089         }
1090       else
1091         {
1092           if (evolution_function_is_invariant_rec_p (CHREC_RIGHT (chrec), loopnum)
1093               && TREE_CODE (CHREC_LEFT (chrec)) == POLYNOMIAL_CHREC
1094               && CHREC_VARIABLE (CHREC_LEFT (chrec)) != CHREC_VARIABLE (chrec)
1095               && evolution_function_is_affine_multivariate_p
1096               (CHREC_LEFT (chrec), loopnum))
1097             return true;
1098           else
1099             return false;
1100         }
1101
1102     default:
1103       return false;
1104     }
1105 }
1106
1107 /* Determine whether the given tree is a function in zero or one
1108    variables.  */
1109
1110 bool
1111 evolution_function_is_univariate_p (const_tree chrec)
1112 {
1113   if (chrec == NULL_TREE)
1114     return true;
1115
1116   switch (TREE_CODE (chrec))
1117     {
1118     case POLYNOMIAL_CHREC:
1119       switch (TREE_CODE (CHREC_LEFT (chrec)))
1120         {
1121         case POLYNOMIAL_CHREC:
1122           if (CHREC_VARIABLE (chrec) != CHREC_VARIABLE (CHREC_LEFT (chrec)))
1123             return false;
1124           if (!evolution_function_is_univariate_p (CHREC_LEFT (chrec)))
1125             return false;
1126           break;
1127
1128         default:
1129           if (tree_contains_chrecs (CHREC_LEFT (chrec), NULL))
1130             return false;
1131           break;
1132         }
1133
1134       switch (TREE_CODE (CHREC_RIGHT (chrec)))
1135         {
1136         case POLYNOMIAL_CHREC:
1137           if (CHREC_VARIABLE (chrec) != CHREC_VARIABLE (CHREC_RIGHT (chrec)))
1138             return false;
1139           if (!evolution_function_is_univariate_p (CHREC_RIGHT (chrec)))
1140             return false;
1141           break;
1142
1143         default:
1144           if (tree_contains_chrecs (CHREC_RIGHT (chrec), NULL))
1145             return false;
1146           break;
1147         }
1148       return true;
1149
1150     default:
1151       return true;
1152     }
1153 }
1154
1155 /* Returns the number of variables of CHREC.  Example: the call
1156    nb_vars_in_chrec ({{0, +, 1}_5, +, 2}_6) returns 2.  */
1157
1158 unsigned
1159 nb_vars_in_chrec (tree chrec)
1160 {
1161   if (chrec == NULL_TREE)
1162     return 0;
1163
1164   switch (TREE_CODE (chrec))
1165     {
1166     case POLYNOMIAL_CHREC:
1167       return 1 + nb_vars_in_chrec
1168         (initial_condition_in_loop_num (chrec, CHREC_VARIABLE (chrec)));
1169
1170     default:
1171       return 0;
1172     }
1173 }
1174
1175 /* Converts BASE and STEP of affine scev to TYPE.  LOOP is the loop whose iv
1176    the scev corresponds to.  AT_STMT is the statement at that the scev is
1177    evaluated.  USE_OVERFLOW_SEMANTICS is true if this function should assume
1178    that the rules for overflow of the given language apply (e.g., that signed
1179    arithmetics in C does not overflow) -- i.e., to use them to avoid
1180    unnecessary tests, but also to enforce that the result follows them.
1181    FROM is the source variable converted if it's not NULL.  Returns true if
1182    the conversion succeeded, false otherwise.  */
1183
1184 bool
1185 convert_affine_scev (struct loop *loop, tree type,
1186                      tree *base, tree *step, gimple *at_stmt,
1187                      bool use_overflow_semantics, tree from)
1188 {
1189   tree ct = TREE_TYPE (*step);
1190   bool enforce_overflow_semantics;
1191   bool must_check_src_overflow, must_check_rslt_overflow;
1192   tree new_base, new_step;
1193   tree step_type = POINTER_TYPE_P (type) ? sizetype : type;
1194
1195   /* In general,
1196      (TYPE) (BASE + STEP * i) = (TYPE) BASE + (TYPE -- sign extend) STEP * i,
1197      but we must check some assumptions.
1198
1199      1) If [BASE, +, STEP] wraps, the equation is not valid when precision
1200         of CT is smaller than the precision of TYPE.  For example, when we
1201         cast unsigned char [254, +, 1] to unsigned, the values on left side
1202         are 254, 255, 0, 1, ..., but those on the right side are
1203         254, 255, 256, 257, ...
1204      2) In case that we must also preserve the fact that signed ivs do not
1205         overflow, we must additionally check that the new iv does not wrap.
1206         For example, unsigned char [125, +, 1] casted to signed char could
1207         become a wrapping variable with values 125, 126, 127, -128, -127, ...,
1208         which would confuse optimizers that assume that this does not
1209         happen.  */
1210   must_check_src_overflow = TYPE_PRECISION (ct) < TYPE_PRECISION (type);
1211
1212   enforce_overflow_semantics = (use_overflow_semantics
1213                                 && nowrap_type_p (type));
1214   if (enforce_overflow_semantics)
1215     {
1216       /* We can avoid checking whether the result overflows in the following
1217          cases:
1218
1219          -- must_check_src_overflow is true, and the range of TYPE is superset
1220             of the range of CT -- i.e., in all cases except if CT signed and
1221             TYPE unsigned.
1222          -- both CT and TYPE have the same precision and signedness, and we
1223             verify instead that the source does not overflow (this may be
1224             easier than verifying it for the result, as we may use the
1225             information about the semantics of overflow in CT).  */
1226       if (must_check_src_overflow)
1227         {
1228           if (TYPE_UNSIGNED (type) && !TYPE_UNSIGNED (ct))
1229             must_check_rslt_overflow = true;
1230           else
1231             must_check_rslt_overflow = false;
1232         }
1233       else if (TYPE_UNSIGNED (ct) == TYPE_UNSIGNED (type)
1234                && TYPE_PRECISION (ct) == TYPE_PRECISION (type))
1235         {
1236           must_check_rslt_overflow = false;
1237           must_check_src_overflow = true;
1238         }
1239       else
1240         must_check_rslt_overflow = true;
1241     }
1242   else
1243     must_check_rslt_overflow = false;
1244
1245   if (must_check_src_overflow
1246       && scev_probably_wraps_p (from, *base, *step, at_stmt, loop,
1247                                 use_overflow_semantics))
1248     return false;
1249
1250   new_base = chrec_convert (type, *base, at_stmt, use_overflow_semantics);
1251   /* The step must be sign extended, regardless of the signedness
1252      of CT and TYPE.  This only needs to be handled specially when
1253      CT is unsigned -- to avoid e.g. unsigned char [100, +, 255]
1254      (with values 100, 99, 98, ...) from becoming signed or unsigned
1255      [100, +, 255] with values 100, 355, ...; the sign-extension is
1256      performed by default when CT is signed.  */
1257   new_step = *step;
1258   if (TYPE_PRECISION (step_type) > TYPE_PRECISION (ct) && TYPE_UNSIGNED (ct))
1259     {
1260       tree signed_ct = build_nonstandard_integer_type (TYPE_PRECISION (ct), 0);
1261       new_step = chrec_convert (signed_ct, new_step, at_stmt,
1262                                 use_overflow_semantics);
1263     }
1264   new_step = chrec_convert (step_type, new_step, at_stmt,
1265                             use_overflow_semantics);
1266
1267   if (automatically_generated_chrec_p (new_base)
1268       || automatically_generated_chrec_p (new_step))
1269     return false;
1270
1271   if (must_check_rslt_overflow
1272       /* Note that in this case we cannot use the fact that signed variables
1273          do not overflow, as this is what we are verifying for the new iv.  */
1274       && scev_probably_wraps_p (NULL_TREE, new_base, new_step,
1275                                 at_stmt, loop, false))
1276     return false;
1277
1278   *base = new_base;
1279   *step = new_step;
1280   return true;
1281 }
1282 \f
1283
1284 /* Convert CHREC for the right hand side of a CHREC.
1285    The increment for a pointer type is always sizetype.  */
1286
1287 tree
1288 chrec_convert_rhs (tree type, tree chrec, gimple *at_stmt)
1289 {
1290   if (POINTER_TYPE_P (type))
1291     type = sizetype;
1292
1293   return chrec_convert (type, chrec, at_stmt);
1294 }
1295
1296 /* Convert CHREC to TYPE.  When the analyzer knows the context in
1297    which the CHREC is built, it sets AT_STMT to the statement that
1298    contains the definition of the analyzed variable, otherwise the
1299    conversion is less accurate: the information is used for
1300    determining a more accurate estimation of the number of iterations.
1301    By default AT_STMT could be safely set to NULL_TREE.
1302
1303    USE_OVERFLOW_SEMANTICS is true if this function should assume that
1304    the rules for overflow of the given language apply (e.g., that signed
1305    arithmetics in C does not overflow) -- i.e., to use them to avoid
1306    unnecessary tests, but also to enforce that the result follows them.
1307
1308    FROM is the source variable converted if it's not NULL.  */
1309
1310 static tree
1311 chrec_convert_1 (tree type, tree chrec, gimple *at_stmt,
1312                  bool use_overflow_semantics, tree from)
1313 {
1314   tree ct, res;
1315   tree base, step;
1316   struct loop *loop;
1317
1318   if (automatically_generated_chrec_p (chrec))
1319     return chrec;
1320
1321   ct = chrec_type (chrec);
1322   if (useless_type_conversion_p (type, ct))
1323     return chrec;
1324
1325   if (!evolution_function_is_affine_p (chrec))
1326     goto keep_cast;
1327
1328   loop = get_chrec_loop (chrec);
1329   base = CHREC_LEFT (chrec);
1330   step = CHREC_RIGHT (chrec);
1331
1332   if (convert_affine_scev (loop, type, &base, &step, at_stmt,
1333                            use_overflow_semantics, from))
1334     return build_polynomial_chrec (loop->num, base, step);
1335
1336   /* If we cannot propagate the cast inside the chrec, just keep the cast.  */
1337 keep_cast:
1338   /* Fold will not canonicalize (long)(i - 1) to (long)i - 1 because that
1339      may be more expensive.  We do want to perform this optimization here
1340      though for canonicalization reasons.  */
1341   if (use_overflow_semantics
1342       && (TREE_CODE (chrec) == PLUS_EXPR
1343           || TREE_CODE (chrec) == MINUS_EXPR)
1344       && TREE_CODE (type) == INTEGER_TYPE
1345       && TREE_CODE (ct) == INTEGER_TYPE
1346       && TYPE_PRECISION (type) > TYPE_PRECISION (ct)
1347       && TYPE_OVERFLOW_UNDEFINED (ct))
1348     res = fold_build2 (TREE_CODE (chrec), type,
1349                        fold_convert (type, TREE_OPERAND (chrec, 0)),
1350                        fold_convert (type, TREE_OPERAND (chrec, 1)));
1351   /* Similar perform the trick that (signed char)((int)x + 2) can be
1352      narrowed to (signed char)((unsigned char)x + 2).  */
1353   else if (use_overflow_semantics
1354            && TREE_CODE (chrec) == POLYNOMIAL_CHREC
1355            && TREE_CODE (ct) == INTEGER_TYPE
1356            && TREE_CODE (type) == INTEGER_TYPE
1357            && TYPE_OVERFLOW_UNDEFINED (type)
1358            && TYPE_PRECISION (type) < TYPE_PRECISION (ct))
1359     {
1360       tree utype = unsigned_type_for (type);
1361       res = build_polynomial_chrec (CHREC_VARIABLE (chrec),
1362                                     fold_convert (utype,
1363                                                   CHREC_LEFT (chrec)),
1364                                     fold_convert (utype,
1365                                                   CHREC_RIGHT (chrec)));
1366       res = chrec_convert_1 (type, res, at_stmt, use_overflow_semantics, from);
1367     }
1368   else
1369     res = fold_convert (type, chrec);
1370
1371   /* Don't propagate overflows.  */
1372   if (CONSTANT_CLASS_P (res))
1373     TREE_OVERFLOW (res) = 0;
1374
1375   /* But reject constants that don't fit in their type after conversion.
1376      This can happen if TYPE_MIN_VALUE or TYPE_MAX_VALUE are not the
1377      natural values associated with TYPE_PRECISION and TYPE_UNSIGNED,
1378      and can cause problems later when computing niters of loops.  Note
1379      that we don't do the check before converting because we don't want
1380      to reject conversions of negative chrecs to unsigned types.  */
1381   if (TREE_CODE (res) == INTEGER_CST
1382       && TREE_CODE (type) == INTEGER_TYPE
1383       && !int_fits_type_p (res, type))
1384     res = chrec_dont_know;
1385
1386   return res;
1387 }
1388
1389 /* Convert CHREC to TYPE.  When the analyzer knows the context in
1390    which the CHREC is built, it sets AT_STMT to the statement that
1391    contains the definition of the analyzed variable, otherwise the
1392    conversion is less accurate: the information is used for
1393    determining a more accurate estimation of the number of iterations.
1394    By default AT_STMT could be safely set to NULL_TREE.
1395
1396    The following rule is always true: TREE_TYPE (chrec) ==
1397    TREE_TYPE (CHREC_LEFT (chrec)) == TREE_TYPE (CHREC_RIGHT (chrec)).
1398    An example of what could happen when adding two chrecs and the type
1399    of the CHREC_RIGHT is different than CHREC_LEFT is:
1400
1401    {(uint) 0, +, (uchar) 10} +
1402    {(uint) 0, +, (uchar) 250}
1403
1404    that would produce a wrong result if CHREC_RIGHT is not (uint):
1405
1406    {(uint) 0, +, (uchar) 4}
1407
1408    instead of
1409
1410    {(uint) 0, +, (uint) 260}
1411
1412    USE_OVERFLOW_SEMANTICS is true if this function should assume that
1413    the rules for overflow of the given language apply (e.g., that signed
1414    arithmetics in C does not overflow) -- i.e., to use them to avoid
1415    unnecessary tests, but also to enforce that the result follows them.
1416
1417    FROM is the source variable converted if it's not NULL.  */
1418
1419 tree
1420 chrec_convert (tree type, tree chrec, gimple *at_stmt,
1421                bool use_overflow_semantics, tree from)
1422 {
1423   return chrec_convert_1 (type, chrec, at_stmt, use_overflow_semantics, from);
1424 }
1425
1426 /* Convert CHREC to TYPE, without regard to signed overflows.  Returns the new
1427    chrec if something else than what chrec_convert would do happens, NULL_TREE
1428    otherwise.  This function set TRUE to variable pointed by FOLD_CONVERSIONS
1429    if the result chrec may overflow.  */
1430
1431 tree
1432 chrec_convert_aggressive (tree type, tree chrec, bool *fold_conversions)
1433 {
1434   tree inner_type, left, right, lc, rc, rtype;
1435
1436   gcc_assert (fold_conversions != NULL);
1437
1438   if (automatically_generated_chrec_p (chrec)
1439       || TREE_CODE (chrec) != POLYNOMIAL_CHREC)
1440     return NULL_TREE;
1441
1442   inner_type = TREE_TYPE (chrec);
1443   if (TYPE_PRECISION (type) > TYPE_PRECISION (inner_type))
1444     return NULL_TREE;
1445
1446   if (useless_type_conversion_p (type, inner_type))
1447     return NULL_TREE;
1448
1449   if (!*fold_conversions && evolution_function_is_affine_p (chrec))
1450     {
1451       tree base, step;
1452       struct loop *loop;
1453
1454       loop = get_chrec_loop (chrec);
1455       base = CHREC_LEFT (chrec);
1456       step = CHREC_RIGHT (chrec);
1457       if (convert_affine_scev (loop, type, &base, &step, NULL, true))
1458         return build_polynomial_chrec (loop->num, base, step);
1459     }
1460   rtype = POINTER_TYPE_P (type) ? sizetype : type;
1461
1462   left = CHREC_LEFT (chrec);
1463   right = CHREC_RIGHT (chrec);
1464   lc = chrec_convert_aggressive (type, left, fold_conversions);
1465   if (!lc)
1466     lc = chrec_convert (type, left, NULL);
1467   rc = chrec_convert_aggressive (rtype, right, fold_conversions);
1468   if (!rc)
1469     rc = chrec_convert (rtype, right, NULL);
1470
1471   *fold_conversions = true;
1472
1473   return build_polynomial_chrec (CHREC_VARIABLE (chrec), lc, rc);
1474 }
1475
1476 /* Returns true when CHREC0 == CHREC1.  */
1477
1478 bool
1479 eq_evolutions_p (const_tree chrec0, const_tree chrec1)
1480 {
1481   if (chrec0 == NULL_TREE
1482       || chrec1 == NULL_TREE
1483       || TREE_CODE (chrec0) != TREE_CODE (chrec1))
1484     return false;
1485
1486   if (chrec0 == chrec1)
1487     return true;
1488
1489   if (! types_compatible_p (TREE_TYPE (chrec0), TREE_TYPE (chrec1)))
1490     return false;
1491
1492   switch (TREE_CODE (chrec0))
1493     {
1494     case POLYNOMIAL_CHREC:
1495       return (CHREC_VARIABLE (chrec0) == CHREC_VARIABLE (chrec1)
1496               && eq_evolutions_p (CHREC_LEFT (chrec0), CHREC_LEFT (chrec1))
1497               && eq_evolutions_p (CHREC_RIGHT (chrec0), CHREC_RIGHT (chrec1)));
1498
1499     case PLUS_EXPR:
1500     case MULT_EXPR:
1501     case MINUS_EXPR:
1502     case POINTER_PLUS_EXPR:
1503       return eq_evolutions_p (TREE_OPERAND (chrec0, 0),
1504                               TREE_OPERAND (chrec1, 0))
1505           && eq_evolutions_p (TREE_OPERAND (chrec0, 1),
1506                               TREE_OPERAND (chrec1, 1));
1507
1508     CASE_CONVERT:
1509       return eq_evolutions_p (TREE_OPERAND (chrec0, 0),
1510                               TREE_OPERAND (chrec1, 0));
1511
1512     default:
1513       return operand_equal_p (chrec0, chrec1, 0);
1514     }
1515 }
1516
1517 /* Returns EV_GROWS if CHREC grows (assuming that it does not overflow),
1518    EV_DECREASES if it decreases, and EV_UNKNOWN if we cannot determine
1519    which of these cases happens.  */
1520
1521 enum ev_direction
1522 scev_direction (const_tree chrec)
1523 {
1524   const_tree step;
1525
1526   if (!evolution_function_is_affine_p (chrec))
1527     return EV_DIR_UNKNOWN;
1528
1529   step = CHREC_RIGHT (chrec);
1530   if (TREE_CODE (step) != INTEGER_CST)
1531     return EV_DIR_UNKNOWN;
1532
1533   if (tree_int_cst_sign_bit (step))
1534     return EV_DIR_DECREASES;
1535   else
1536     return EV_DIR_GROWS;
1537 }
1538
1539 /* Iterates over all the components of SCEV, and calls CBCK.  */
1540
1541 void
1542 for_each_scev_op (tree *scev, bool (*cbck) (tree *, void *), void *data)
1543 {
1544   switch (TREE_CODE_LENGTH (TREE_CODE (*scev)))
1545     {
1546     case 3:
1547       for_each_scev_op (&TREE_OPERAND (*scev, 2), cbck, data);
1548       /* FALLTHRU */
1549
1550     case 2:
1551       for_each_scev_op (&TREE_OPERAND (*scev, 1), cbck, data);
1552       /* FALLTHRU */
1553
1554     case 1:
1555       for_each_scev_op (&TREE_OPERAND (*scev, 0), cbck, data);
1556       /* FALLTHRU */
1557
1558     default:
1559       cbck (scev, data);
1560       break;
1561     }
1562 }
1563
1564 /* Returns true when the operation can be part of a linear
1565    expression.  */
1566
1567 static inline bool
1568 operator_is_linear (tree scev)
1569 {
1570   switch (TREE_CODE (scev))
1571     {
1572     case INTEGER_CST:
1573     case POLYNOMIAL_CHREC:
1574     case PLUS_EXPR:
1575     case POINTER_PLUS_EXPR:
1576     case MULT_EXPR:
1577     case MINUS_EXPR:
1578     case NEGATE_EXPR:
1579     case SSA_NAME:
1580     case NON_LVALUE_EXPR:
1581     case BIT_NOT_EXPR:
1582     CASE_CONVERT:
1583       return true;
1584
1585     default:
1586       return false;
1587     }
1588 }
1589
1590 /* Return true when SCEV is a linear expression.  Linear expressions
1591    can contain additions, substractions and multiplications.
1592    Multiplications are restricted to constant scaling: "cst * x".  */
1593
1594 bool
1595 scev_is_linear_expression (tree scev)
1596 {
1597   if (evolution_function_is_constant_p (scev))
1598     return true;
1599
1600   if (scev == NULL
1601       || !operator_is_linear (scev))
1602     return false;
1603
1604   if (TREE_CODE (scev) == MULT_EXPR)
1605     return !(tree_contains_chrecs (TREE_OPERAND (scev, 0), NULL)
1606              && tree_contains_chrecs (TREE_OPERAND (scev, 1), NULL));
1607
1608   if (TREE_CODE (scev) == POLYNOMIAL_CHREC
1609       && !evolution_function_is_affine_multivariate_p (scev, CHREC_VARIABLE (scev)))
1610     return false;
1611
1612   switch (TREE_CODE_LENGTH (TREE_CODE (scev)))
1613     {
1614     case 3:
1615       return scev_is_linear_expression (TREE_OPERAND (scev, 0))
1616         && scev_is_linear_expression (TREE_OPERAND (scev, 1))
1617         && scev_is_linear_expression (TREE_OPERAND (scev, 2));
1618
1619     case 2:
1620       return scev_is_linear_expression (TREE_OPERAND (scev, 0))
1621         && scev_is_linear_expression (TREE_OPERAND (scev, 1));
1622
1623     case 1:
1624       return scev_is_linear_expression (TREE_OPERAND (scev, 0));
1625
1626     case 0:
1627       return true;
1628
1629     default:
1630       return false;
1631     }
1632 }
1633
1634 /* Determines whether the expression CHREC contains only interger consts
1635    in the right parts.  */
1636
1637 bool
1638 evolution_function_right_is_integer_cst (const_tree chrec)
1639 {
1640   if (chrec == NULL_TREE)
1641     return false;
1642
1643   switch (TREE_CODE (chrec))
1644     {
1645     case INTEGER_CST:
1646       return true;
1647
1648     case POLYNOMIAL_CHREC:
1649       return TREE_CODE (CHREC_RIGHT (chrec)) == INTEGER_CST
1650         && (TREE_CODE (CHREC_LEFT (chrec)) != POLYNOMIAL_CHREC
1651             || evolution_function_right_is_integer_cst (CHREC_LEFT (chrec)));
1652
1653     CASE_CONVERT:
1654       return evolution_function_right_is_integer_cst (TREE_OPERAND (chrec, 0));
1655
1656     default:
1657       return false;
1658     }
1659 }