gcc/tree-chrec.c

   1 /* Chains of recurrences.
   2    Copyright (C) 2003, 2004, 2005, 2006, 2007, 2008, 2009, 2010
   3    Free Software Foundation, Inc.
   4    Contributed by Sebastian Pop <pop@cri.ensmp.fr>
   5
   6 This file is part of GCC.
   7
   8 GCC is free software; you can redistribute it and/or modify it under
   9 the terms of the GNU General Public License as published by the Free
  10 Software Foundation; either version 3, or (at your option) any later
  11 version.
  12
  13 GCC is distributed in the hope that it will be useful, but WITHOUT ANY
  14 WARRANTY; without even the implied warranty of MERCHANTABILITY or
  15 FITNESS FOR A PARTICULAR PURPOSE.  See the GNU General Public License
  16 for more details.
  17
  18 You should have received a copy of the GNU General Public License
  19 along with GCC; see the file COPYING3.  If not see
  20 <http://www.gnu.org/licenses/>.  */
  21
  22 /* This file implements operations on chains of recurrences.  Chains
  23    of recurrences are used for modeling evolution functions of scalar
  24    variables.
  25 */
  26
  27 #include "config.h"
  28 #include "system.h"
  29 #include "coretypes.h"
  30 #include "tree-pretty-print.h"
  31 #include "cfgloop.h"
  32 #include "tree-flow.h"
  33 #include "tree-chrec.h"
  34 #include "tree-pass.h"
  35 #include "params.h"
  36 #include "tree-scalar-evolution.h"
  37
  38 /* Extended folder for chrecs.  */
  39
  40 /* Determines whether CST is not a constant evolution.  */
  41
  42 static inline bool
  43 is_not_constant_evolution (const_tree cst)
  44 {
  45   return (TREE_CODE (cst) == POLYNOMIAL_CHREC);
  46 }
  47
  48 /* Fold CODE for a polynomial function and a constant.  */
  49
  50 static inline tree
  51 chrec_fold_poly_cst (enum tree_code code,
  52                      tree type,
  53                      tree poly,
  54                      tree cst)
  55 {
  56   gcc_assert (poly);
  57   gcc_assert (cst);
  58   gcc_assert (TREE_CODE (poly) == POLYNOMIAL_CHREC);
  59   gcc_assert (!is_not_constant_evolution (cst));
  60   gcc_assert (type == chrec_type (poly));
  61
  62   switch (code)
  63     {
  64     case PLUS_EXPR:
  65       return build_polynomial_chrec
  66         (CHREC_VARIABLE (poly),
  67          chrec_fold_plus (type, CHREC_LEFT (poly), cst),
  68          CHREC_RIGHT (poly));
  69
  70     case MINUS_EXPR:
  71       return build_polynomial_chrec
  72         (CHREC_VARIABLE (poly),
  73          chrec_fold_minus (type, CHREC_LEFT (poly), cst),
  74          CHREC_RIGHT (poly));
  75
  76     case MULT_EXPR:
  77       return build_polynomial_chrec
  78         (CHREC_VARIABLE (poly),
  79          chrec_fold_multiply (type, CHREC_LEFT (poly), cst),
  80          chrec_fold_multiply (type, CHREC_RIGHT (poly), cst));
  81
  82     default:
  83       return chrec_dont_know;
  84     }
  85 }
  86
  87 /* Fold the addition of two polynomial functions.  */
  88
  89 static inline tree
  90 chrec_fold_plus_poly_poly (enum tree_code code,
  91                            tree type,
  92                            tree poly0,
  93                            tree poly1)
  94 {
  95   tree left, right;
  96   struct loop *loop0 = get_chrec_loop (poly0);
  97   struct loop *loop1 = get_chrec_loop (poly1);
  98   tree rtype = code == POINTER_PLUS_EXPR ? sizetype : type;
  99
 100   gcc_assert (poly0);
 101   gcc_assert (poly1);
 102   gcc_assert (TREE_CODE (poly0) == POLYNOMIAL_CHREC);
 103   gcc_assert (TREE_CODE (poly1) == POLYNOMIAL_CHREC);
 104   if (POINTER_TYPE_P (chrec_type (poly0)))
 105     gcc_assert (chrec_type (poly1) == sizetype);
 106   else
 107     gcc_assert (chrec_type (poly0) == chrec_type (poly1));
 108   gcc_assert (type == chrec_type (poly0));
 109
 110   /*
 111     {a, +, b}_1 + {c, +, d}_2  ->  {{a, +, b}_1 + c, +, d}_2,
 112     {a, +, b}_2 + {c, +, d}_1  ->  {{c, +, d}_1 + a, +, b}_2,
 113     {a, +, b}_x + {c, +, d}_x  ->  {a+c, +, b+d}_x.  */
 114   if (flow_loop_nested_p (loop0, loop1))
 115     {
 116       if (code == PLUS_EXPR || code == POINTER_PLUS_EXPR)
 117         return build_polynomial_chrec
 118           (CHREC_VARIABLE (poly1),
 119            chrec_fold_plus (type, poly0, CHREC_LEFT (poly1)),
 120            CHREC_RIGHT (poly1));
 121       else
 122         return build_polynomial_chrec
 123           (CHREC_VARIABLE (poly1),
 124            chrec_fold_minus (type, poly0, CHREC_LEFT (poly1)),
 125            chrec_fold_multiply (type, CHREC_RIGHT (poly1),
 126                                 SCALAR_FLOAT_TYPE_P (type)
 127                                 ? build_real (type, dconstm1)
 128                                 : build_int_cst_type (type, -1)));
 129     }
 130
 131   if (flow_loop_nested_p (loop1, loop0))
 132     {
 133       if (code == PLUS_EXPR || code == POINTER_PLUS_EXPR)
 134         return build_polynomial_chrec
 135           (CHREC_VARIABLE (poly0),
 136            chrec_fold_plus (type, CHREC_LEFT (poly0), poly1),
 137            CHREC_RIGHT (poly0));
 138       else
 139         return build_polynomial_chrec
 140           (CHREC_VARIABLE (poly0),
 141            chrec_fold_minus (type, CHREC_LEFT (poly0), poly1),
 142            CHREC_RIGHT (poly0));
 143     }
 144
 145   /* This function should never be called for chrecs of loops that
 146      do not belong to the same loop nest.  */
 147   gcc_assert (loop0 == loop1);
 148
 149   if (code == PLUS_EXPR || code == POINTER_PLUS_EXPR)
 150     {
 151       left = chrec_fold_plus
 152         (type, CHREC_LEFT (poly0), CHREC_LEFT (poly1));
 153       right = chrec_fold_plus
 154         (rtype, CHREC_RIGHT (poly0), CHREC_RIGHT (poly1));
 155     }
 156   else
 157     {
 158       left = chrec_fold_minus
 159         (type, CHREC_LEFT (poly0), CHREC_LEFT (poly1));
 160       right = chrec_fold_minus
 161         (type, CHREC_RIGHT (poly0), CHREC_RIGHT (poly1));
 162     }
 163
 164   if (chrec_zerop (right))
 165     return left;
 166   else
 167     return build_polynomial_chrec
 168       (CHREC_VARIABLE (poly0), left, right);
 169 }
 170
 171 \f
 172
 173 /* Fold the multiplication of two polynomial functions.  */
 174
 175 static inline tree
 176 chrec_fold_multiply_poly_poly (tree type,
 177                                tree poly0,
 178                                tree poly1)
 179 {
 180   tree t0, t1, t2;
 181   int var;
 182   struct loop *loop0 = get_chrec_loop (poly0);
 183   struct loop *loop1 = get_chrec_loop (poly1);
 184
 185   gcc_assert (poly0);
 186   gcc_assert (poly1);
 187   gcc_assert (TREE_CODE (poly0) == POLYNOMIAL_CHREC);
 188   gcc_assert (TREE_CODE (poly1) == POLYNOMIAL_CHREC);
 189   gcc_assert (chrec_type (poly0) == chrec_type (poly1));
 190   gcc_assert (type == chrec_type (poly0));
 191
 192   /* {a, +, b}_1 * {c, +, d}_2  ->  {c*{a, +, b}_1, +, d}_2,
 193      {a, +, b}_2 * {c, +, d}_1  ->  {a*{c, +, d}_1, +, b}_2,
 194      {a, +, b}_x * {c, +, d}_x  ->  {a*c, +, a*d + b*c + b*d, +, 2*b*d}_x.  */
 195   if (flow_loop_nested_p (loop0, loop1))
 196     /* poly0 is a constant wrt. poly1.  */
 197     return build_polynomial_chrec
 198       (CHREC_VARIABLE (poly1),
 199        chrec_fold_multiply (type, CHREC_LEFT (poly1), poly0),
 200        CHREC_RIGHT (poly1));
 201
 202   if (flow_loop_nested_p (loop1, loop0))
 203     /* poly1 is a constant wrt. poly0.  */
 204     return build_polynomial_chrec
 205       (CHREC_VARIABLE (poly0),
 206        chrec_fold_multiply (type, CHREC_LEFT (poly0), poly1),
 207        CHREC_RIGHT (poly0));
 208
 209   gcc_assert (loop0 == loop1);
 210
 211   /* poly0 and poly1 are two polynomials in the same variable,
 212      {a, +, b}_x * {c, +, d}_x  ->  {a*c, +, a*d + b*c + b*d, +, 2*b*d}_x.  */
 213
 214   /* "a*c".  */
 215   t0 = chrec_fold_multiply (type, CHREC_LEFT (poly0), CHREC_LEFT (poly1));
 216
 217   /* "a*d + b*c".  */
 218   t1 = chrec_fold_multiply (type, CHREC_LEFT (poly0), CHREC_RIGHT (poly1));
 219   t1 = chrec_fold_plus (type, t1, chrec_fold_multiply (type,
 220                                                        CHREC_RIGHT (poly0),
 221                                                        CHREC_LEFT (poly1)));
 222   /* "b*d".  */
 223   t2 = chrec_fold_multiply (type, CHREC_RIGHT (poly0), CHREC_RIGHT (poly1));
 224   /* "a*d + b*c + b*d".  */
 225   t1 = chrec_fold_plus (type, t1, t2);
 226   /* "2*b*d".  */
 227   t2 = chrec_fold_multiply (type, SCALAR_FLOAT_TYPE_P (type)
 228                             ? build_real (type, dconst2)
 229                             : build_int_cst (type, 2), t2);
 230
 231   var = CHREC_VARIABLE (poly0);
 232   return build_polynomial_chrec (var, t0,
 233                                  build_polynomial_chrec (var, t1, t2));
 234 }
 235
 236 /* When the operands are automatically_generated_chrec_p, the fold has
 237    to respect the semantics of the operands.  */
 238
 239 static inline tree
 240 chrec_fold_automatically_generated_operands (tree op0,
 241                                              tree op1)
 242 {
 243   if (op0 == chrec_dont_know
 244       || op1 == chrec_dont_know)
 245     return chrec_dont_know;
 246
 247   if (op0 == chrec_known
 248       || op1 == chrec_known)
 249     return chrec_known;
 250
 251   if (op0 == chrec_not_analyzed_yet
 252       || op1 == chrec_not_analyzed_yet)
 253     return chrec_not_analyzed_yet;
 254
 255   /* The default case produces a safe result.  */
 256   return chrec_dont_know;
 257 }
 258
 259 /* Fold the addition of two chrecs.  */
 260
 261 static tree
 262 chrec_fold_plus_1 (enum tree_code code, tree type,
 263                    tree op0, tree op1)
 264 {
 265   tree op1_type = code == POINTER_PLUS_EXPR ? sizetype : type;
 266
 267   if (automatically_generated_chrec_p (op0)
 268       || automatically_generated_chrec_p (op1))
 269     return chrec_fold_automatically_generated_operands (op0, op1);
 270
 271   switch (TREE_CODE (op0))
 272     {
 273     case POLYNOMIAL_CHREC:
 274       switch (TREE_CODE (op1))
 275         {
 276         case POLYNOMIAL_CHREC:
 277           return chrec_fold_plus_poly_poly (code, type, op0, op1);
 278
 279         CASE_CONVERT:
 280           if (tree_contains_chrecs (op1, NULL))
 281             return chrec_dont_know;
 282
 283         default:
 284           if (code == PLUS_EXPR || code == POINTER_PLUS_EXPR)
 285             return build_polynomial_chrec
 286               (CHREC_VARIABLE (op0),
 287                chrec_fold_plus (type, CHREC_LEFT (op0), op1),
 288                CHREC_RIGHT (op0));
 289           else
 290             return build_polynomial_chrec
 291               (CHREC_VARIABLE (op0),
 292                chrec_fold_minus (type, CHREC_LEFT (op0), op1),
 293                CHREC_RIGHT (op0));
 294         }
 295
 296     CASE_CONVERT:
 297       if (tree_contains_chrecs (op0, NULL))
 298         return chrec_dont_know;
 299
 300     default:
 301       switch (TREE_CODE (op1))
 302         {
 303         case POLYNOMIAL_CHREC:
 304           if (code == PLUS_EXPR || code == POINTER_PLUS_EXPR)
 305             return build_polynomial_chrec
 306               (CHREC_VARIABLE (op1),
 307                chrec_fold_plus (type, op0, CHREC_LEFT (op1)),
 308                CHREC_RIGHT (op1));
 309           else
 310             return build_polynomial_chrec
 311               (CHREC_VARIABLE (op1),
 312                chrec_fold_minus (type, op0, CHREC_LEFT (op1)),
 313                chrec_fold_multiply (type, CHREC_RIGHT (op1),
 314                                     SCALAR_FLOAT_TYPE_P (type)
 315                                     ? build_real (type, dconstm1)
 316                                     : build_int_cst_type (type, -1)));
 317
 318         CASE_CONVERT:
 319           if (tree_contains_chrecs (op1, NULL))
 320             return chrec_dont_know;
 321
 322         default:
 323           {
 324             int size = 0;
 325             if ((tree_contains_chrecs (op0, &size)
 326                  || tree_contains_chrecs (op1, &size))
 327                 && size < PARAM_VALUE (PARAM_SCEV_MAX_EXPR_SIZE))
 328               return build2 (code, type, op0, op1);
 329             else if (size < PARAM_VALUE (PARAM_SCEV_MAX_EXPR_SIZE))
 330               return fold_build2 (code, type,
 331                                   fold_convert (type, op0),
 332                                   fold_convert (op1_type, op1));
 333             else
 334               return chrec_dont_know;
 335           }
 336         }
 337     }
 338 }
 339
 340 /* Fold the addition of two chrecs.  */
 341
 342 tree
 343 chrec_fold_plus (tree type,
 344                  tree op0,
 345                  tree op1)
 346 {
 347   enum tree_code code;
 348   if (automatically_generated_chrec_p (op0)
 349       || automatically_generated_chrec_p (op1))
 350     return chrec_fold_automatically_generated_operands (op0, op1);
 351
 352   if (integer_zerop (op0))
 353     return chrec_convert (type, op1, NULL);
 354   if (integer_zerop (op1))
 355     return chrec_convert (type, op0, NULL);
 356
 357   if (POINTER_TYPE_P (type))
 358     code = POINTER_PLUS_EXPR;
 359   else
 360     code = PLUS_EXPR;
 361
 362   return chrec_fold_plus_1 (code, type, op0, op1);
 363 }
 364
 365 /* Fold the subtraction of two chrecs.  */
 366
 367 tree
 368 chrec_fold_minus (tree type,
 369                   tree op0,
 370                   tree op1)
 371 {
 372   if (automatically_generated_chrec_p (op0)
 373       || automatically_generated_chrec_p (op1))
 374     return chrec_fold_automatically_generated_operands (op0, op1);
 375
 376   if (integer_zerop (op1))
 377     return op0;
 378
 379   return chrec_fold_plus_1 (MINUS_EXPR, type, op0, op1);
 380 }
 381
 382 /* Fold the multiplication of two chrecs.  */
 383
 384 tree
 385 chrec_fold_multiply (tree type,
 386                      tree op0,
 387                      tree op1)
 388 {
 389   if (automatically_generated_chrec_p (op0)
 390       || automatically_generated_chrec_p (op1))
 391     return chrec_fold_automatically_generated_operands (op0, op1);
 392
 393   switch (TREE_CODE (op0))
 394     {
 395     case POLYNOMIAL_CHREC:
 396       switch (TREE_CODE (op1))
 397         {
 398         case POLYNOMIAL_CHREC:
 399           return chrec_fold_multiply_poly_poly (type, op0, op1);
 400
 401         CASE_CONVERT:
 402           if (tree_contains_chrecs (op1, NULL))
 403             return chrec_dont_know;
 404
 405         default:
 406           if (integer_onep (op1))
 407             return op0;
 408           if (integer_zerop (op1))
 409             return build_int_cst (type, 0);
 410
 411           return build_polynomial_chrec
 412             (CHREC_VARIABLE (op0),
 413              chrec_fold_multiply (type, CHREC_LEFT (op0), op1),
 414              chrec_fold_multiply (type, CHREC_RIGHT (op0), op1));
 415         }
 416
 417     CASE_CONVERT:
 418       if (tree_contains_chrecs (op0, NULL))
 419         return chrec_dont_know;
 420
 421     default:
 422       if (integer_onep (op0))
 423         return op1;
 424
 425       if (integer_zerop (op0))
 426         return build_int_cst (type, 0);
 427
 428       switch (TREE_CODE (op1))
 429         {
 430         case POLYNOMIAL_CHREC:
 431           return build_polynomial_chrec
 432             (CHREC_VARIABLE (op1),
 433              chrec_fold_multiply (type, CHREC_LEFT (op1), op0),
 434              chrec_fold_multiply (type, CHREC_RIGHT (op1), op0));
 435
 436         CASE_CONVERT:
 437           if (tree_contains_chrecs (op1, NULL))
 438             return chrec_dont_know;
 439
 440         default:
 441           if (integer_onep (op1))
 442             return op0;
 443           if (integer_zerop (op1))
 444             return build_int_cst (type, 0);
 445           return fold_build2 (MULT_EXPR, type, op0, op1);
 446         }
 447     }
 448 }
 449
 450 \f
 451
 452 /* Operations.  */
 453
 454 /* Evaluate the binomial coefficient.  Return NULL_TREE if the intermediate
 455    calculation overflows, otherwise return C(n,k) with type TYPE.  */
 456
 457 static tree
 458 tree_fold_binomial (tree type, tree n, unsigned int k)
 459 {
 460   unsigned HOST_WIDE_INT lidx, lnum, ldenom, lres, ldum;
 461   HOST_WIDE_INT hidx, hnum, hdenom, hres, hdum;
 462   unsigned int i;
 463   tree res;
 464
 465   /* Handle the most frequent cases.  */
 466   if (k == 0)
 467     return build_int_cst (type, 1);
 468   if (k == 1)
 469     return fold_convert (type, n);
 470
 471   /* Check that k <= n.  */
 472   if (TREE_INT_CST_HIGH (n) == 0
 473       && TREE_INT_CST_LOW (n) < k)
 474     return NULL_TREE;
 475
 476   /* Numerator = n.  */
 477   lnum = TREE_INT_CST_LOW (n);
 478   hnum = TREE_INT_CST_HIGH (n);
 479
 480   /* Denominator = 2.  */
 481   ldenom = 2;
 482   hdenom = 0;
 483
 484   /* Index = Numerator-1.  */
 485   if (lnum == 0)
 486     {
 487       hidx = hnum - 1;
 488       lidx = ~ (unsigned HOST_WIDE_INT) 0;
 489     }
 490   else
 491     {
 492       hidx = hnum;
 493       lidx = lnum - 1;
 494     }
 495
 496   /* Numerator = Numerator*Index = n*(n-1).  */
 497   if (mul_double (lnum, hnum, lidx, hidx, &lnum, &hnum))
 498     return NULL_TREE;
 499
 500   for (i = 3; i <= k; i++)
 501     {
 502       /* Index--.  */
 503       if (lidx == 0)
 504         {
 505           hidx--;
 506           lidx = ~ (unsigned HOST_WIDE_INT) 0;
 507         }
 508       else
 509         lidx--;
 510
 511       /* Numerator *= Index.  */
 512       if (mul_double (lnum, hnum, lidx, hidx, &lnum, &hnum))
 513         return NULL_TREE;
 514
 515       /* Denominator *= i.  */
 516       mul_double (ldenom, hdenom, i, 0, &ldenom, &hdenom);
 517     }
 518
 519   /* Result = Numerator / Denominator.  */
 520   div_and_round_double (EXACT_DIV_EXPR, 1, lnum, hnum, ldenom, hdenom,
 521                         &lres, &hres, &ldum, &hdum);
 522
 523   res = build_int_cst_wide (type, lres, hres);
 524   return int_fits_type_p (res, type) ? res : NULL_TREE;
 525 }
 526
 527 /* Helper function.  Use the Newton's interpolating formula for
 528    evaluating the value of the evolution function.  */
 529
 530 static tree
 531 chrec_evaluate (unsigned var, tree chrec, tree n, unsigned int k)
 532 {
 533   tree arg0, arg1, binomial_n_k;
 534   tree type = TREE_TYPE (chrec);
 535   struct loop *var_loop = get_loop (var);
 536
 537   while (TREE_CODE (chrec) == POLYNOMIAL_CHREC
 538          && flow_loop_nested_p (var_loop, get_chrec_loop (chrec)))
 539     chrec = CHREC_LEFT (chrec);
 540
 541   if (TREE_CODE (chrec) == POLYNOMIAL_CHREC
 542       && CHREC_VARIABLE (chrec) == var)
 543     {
 544       arg1 = chrec_evaluate (var, CHREC_RIGHT (chrec), n, k + 1);
 545       if (arg1 == chrec_dont_know)
 546         return chrec_dont_know;
 547       binomial_n_k = tree_fold_binomial (type, n, k);
 548       if (!binomial_n_k)
 549         return chrec_dont_know;
 550       arg0 = fold_build2 (MULT_EXPR, type,
 551                           CHREC_LEFT (chrec), binomial_n_k);
 552       return chrec_fold_plus (type, arg0, arg1);
 553     }
 554
 555   binomial_n_k = tree_fold_binomial (type, n, k);
 556   if (!binomial_n_k)
 557     return chrec_dont_know;
 558
 559   return fold_build2 (MULT_EXPR, type, chrec, binomial_n_k);
 560 }
 561
 562 /* Evaluates "CHREC (X)" when the varying variable is VAR.
 563    Example:  Given the following parameters,
 564
 565    var = 1
 566    chrec = {3, +, 4}_1
 567    x = 10
 568
 569    The result is given by the Newton's interpolating formula:
 570    3 * \binom{10}{0} + 4 * \binom{10}{1}.
 571 */
 572
 573 tree
 574 chrec_apply (unsigned var,
 575              tree chrec,
 576              tree x)
 577 {
 578   tree type = chrec_type (chrec);
 579   tree res = chrec_dont_know;
 580
 581   if (automatically_generated_chrec_p (chrec)
 582       || automatically_generated_chrec_p (x)
 583
 584       /* When the symbols are defined in an outer loop, it is possible
 585          to symbolically compute the apply, since the symbols are
 586          constants with respect to the varying loop.  */
 587       || chrec_contains_symbols_defined_in_loop (chrec, var))
 588     return chrec_dont_know;
 589
 590   if (dump_file && (dump_flags & TDF_DETAILS))
 591     fprintf (dump_file, "(chrec_apply \n");
 592
 593   if (TREE_CODE (x) == INTEGER_CST && SCALAR_FLOAT_TYPE_P (type))
 594     x = build_real_from_int_cst (type, x);
 595
 596   switch (TREE_CODE (chrec))
 597     {
 598     case POLYNOMIAL_CHREC:
 599       if (evolution_function_is_affine_p (chrec))
 600         {
 601           if (CHREC_VARIABLE (chrec) != var)
 602             return build_polynomial_chrec
 603               (CHREC_VARIABLE (chrec),
 604                chrec_apply (var, CHREC_LEFT (chrec), x),
 605                chrec_apply (var, CHREC_RIGHT (chrec), x));
 606
 607           /* "{a, +, b} (x)"  ->  "a + b*x".  */
 608           x = chrec_convert_rhs (type, x, NULL);
 609           res = chrec_fold_multiply (TREE_TYPE (x), CHREC_RIGHT (chrec), x);
 610           res = chrec_fold_plus (type, CHREC_LEFT (chrec), res);
 611         }
 612       else if (TREE_CODE (x) == INTEGER_CST
 613                && tree_int_cst_sgn (x) == 1)
 614         /* testsuite/.../ssa-chrec-38.c.  */
 615         res = chrec_evaluate (var, chrec, x, 0);
 616       else
 617         res = chrec_dont_know;
 618       break;
 619
 620     CASE_CONVERT:
 621       res = chrec_convert (TREE_TYPE (chrec),
 622                            chrec_apply (var, TREE_OPERAND (chrec, 0), x),
 623                            NULL);
 624       break;
 625
 626     default:
 627       res = chrec;
 628       break;
 629     }
 630
 631   if (dump_file && (dump_flags & TDF_DETAILS))
 632     {
 633       fprintf (dump_file, "  (varying_loop = %d\n", var);
 634       fprintf (dump_file, ")\n  (chrec = ");
 635       print_generic_expr (dump_file, chrec, 0);
 636       fprintf (dump_file, ")\n  (x = ");
 637       print_generic_expr (dump_file, x, 0);
 638       fprintf (dump_file, ")\n  (res = ");
 639       print_generic_expr (dump_file, res, 0);
 640       fprintf (dump_file, "))\n");
 641     }
 642
 643   return res;
 644 }
 645
 646 /* For a given CHREC and an induction variable map IV_MAP that maps
 647    (loop->num, expr) for every loop number of the current_loops an
 648    expression, calls chrec_apply when the expression is not NULL.  */
 649
 650 tree
 651 chrec_apply_map (tree chrec, VEC (tree, heap) *iv_map)
 652 {
 653   int i;
 654   tree expr;
 655
 656   FOR_EACH_VEC_ELT (tree, iv_map, i, expr)
 657     if (expr)
 658       chrec = chrec_apply (i, chrec, expr);
 659
 660   return chrec;
 661 }
 662
 663 /* Replaces the initial condition in CHREC with INIT_COND.  */
 664
 665 tree
 666 chrec_replace_initial_condition (tree chrec,
 667                                  tree init_cond)
 668 {
 669   if (automatically_generated_chrec_p (chrec))
 670     return chrec;
 671
 672   gcc_assert (chrec_type (chrec) == chrec_type (init_cond));
 673
 674   switch (TREE_CODE (chrec))
 675     {
 676     case POLYNOMIAL_CHREC:
 677       return build_polynomial_chrec
 678         (CHREC_VARIABLE (chrec),
 679          chrec_replace_initial_condition (CHREC_LEFT (chrec), init_cond),
 680          CHREC_RIGHT (chrec));
 681
 682     default:
 683       return init_cond;
 684     }
 685 }
 686
 687 /* Returns the initial condition of a given CHREC.  */
 688
 689 tree
 690 initial_condition (tree chrec)
 691 {
 692   if (automatically_generated_chrec_p (chrec))
 693     return chrec;
 694
 695   if (TREE_CODE (chrec) == POLYNOMIAL_CHREC)
 696     return initial_condition (CHREC_LEFT (chrec));
 697   else
 698     return chrec;
 699 }
 700
 701 /* Returns a univariate function that represents the evolution in
 702    LOOP_NUM.  Mask the evolution of any other loop.  */
 703
 704 tree
 705 hide_evolution_in_other_loops_than_loop (tree chrec,
 706                                          unsigned loop_num)
 707 {
 708   struct loop *loop = get_loop (loop_num), *chloop;
 709   if (automatically_generated_chrec_p (chrec))
 710     return chrec;
 711
 712   switch (TREE_CODE (chrec))
 713     {
 714     case POLYNOMIAL_CHREC:
 715       chloop = get_chrec_loop (chrec);
 716
 717       if (chloop == loop)
 718         return build_polynomial_chrec
 719           (loop_num,
 720            hide_evolution_in_other_loops_than_loop (CHREC_LEFT (chrec),
 721                                                     loop_num),
 722            CHREC_RIGHT (chrec));
 723
 724       else if (flow_loop_nested_p (chloop, loop))
 725         /* There is no evolution in this loop.  */
 726         return initial_condition (chrec);
 727
 728       else
 729         {
 730           gcc_assert (flow_loop_nested_p (loop, chloop));
 731           return hide_evolution_in_other_loops_than_loop (CHREC_LEFT (chrec),
 732                                                           loop_num);
 733         }
 734
 735     default:
 736       return chrec;
 737     }
 738 }
 739
 740 /* Returns the evolution part of CHREC in LOOP_NUM when RIGHT is
 741    true, otherwise returns the initial condition in LOOP_NUM.  */
 742
 743 static tree
 744 chrec_component_in_loop_num (tree chrec,
 745                              unsigned loop_num,
 746                              bool right)
 747 {
 748   tree component;
 749   struct loop *loop = get_loop (loop_num), *chloop;
 750
 751   if (automatically_generated_chrec_p (chrec))
 752     return chrec;
 753
 754   switch (TREE_CODE (chrec))
 755     {
 756     case POLYNOMIAL_CHREC:
 757       chloop = get_chrec_loop (chrec);
 758
 759       if (chloop == loop)
 760         {
 761           if (right)
 762             component = CHREC_RIGHT (chrec);
 763           else
 764             component = CHREC_LEFT (chrec);
 765
 766           if (TREE_CODE (CHREC_LEFT (chrec)) != POLYNOMIAL_CHREC
 767               || CHREC_VARIABLE (CHREC_LEFT (chrec)) != CHREC_VARIABLE (chrec))
 768             return component;
 769
 770           else
 771             return build_polynomial_chrec
 772               (loop_num,
 773                chrec_component_in_loop_num (CHREC_LEFT (chrec),
 774                                             loop_num,
 775                                             right),
 776                component);
 777         }
 778
 779       else if (flow_loop_nested_p (chloop, loop))
 780         /* There is no evolution part in this loop.  */
 781         return NULL_TREE;
 782
 783       else
 784         {
 785           gcc_assert (flow_loop_nested_p (loop, chloop));
 786           return chrec_component_in_loop_num (CHREC_LEFT (chrec),
 787                                               loop_num,
 788                                               right);
 789         }
 790
 791      default:
 792       if (right)
 793         return NULL_TREE;
 794       else
 795         return chrec;
 796     }
 797 }
 798
 799 /* Returns the evolution part in LOOP_NUM.  Example: the call
 800    evolution_part_in_loop_num ({{0, +, 1}_1, +, 2}_1, 1) returns
 801    {1, +, 2}_1  */
 802
 803 tree
 804 evolution_part_in_loop_num (tree chrec,
 805                             unsigned loop_num)
 806 {
 807   return chrec_component_in_loop_num (chrec, loop_num, true);
 808 }
 809
 810 /* Returns the initial condition in LOOP_NUM.  Example: the call
 811    initial_condition_in_loop_num ({{0, +, 1}_1, +, 2}_2, 2) returns
 812    {0, +, 1}_1  */
 813
 814 tree
 815 initial_condition_in_loop_num (tree chrec,
 816                                unsigned loop_num)
 817 {
 818   return chrec_component_in_loop_num (chrec, loop_num, false);
 819 }
 820
 821 /* Set or reset the evolution of CHREC to NEW_EVOL in loop LOOP_NUM.
 822    This function is essentially used for setting the evolution to
 823    chrec_dont_know, for example after having determined that it is
 824    impossible to say how many times a loop will execute.  */
 825
 826 tree
 827 reset_evolution_in_loop (unsigned loop_num,
 828                          tree chrec,
 829                          tree new_evol)
 830 {
 831   struct loop *loop = get_loop (loop_num);
 832
 833   if (POINTER_TYPE_P (chrec_type (chrec)))
 834     gcc_assert (sizetype == chrec_type (new_evol));
 835   else
 836     gcc_assert (chrec_type (chrec) == chrec_type (new_evol));
 837
 838   if (TREE_CODE (chrec) == POLYNOMIAL_CHREC
 839       && flow_loop_nested_p (loop, get_chrec_loop (chrec)))
 840     {
 841       tree left = reset_evolution_in_loop (loop_num, CHREC_LEFT (chrec),
 842                                            new_evol);
 843       tree right = reset_evolution_in_loop (loop_num, CHREC_RIGHT (chrec),
 844                                             new_evol);
 845       return build3 (POLYNOMIAL_CHREC, TREE_TYPE (left),
 846                      CHREC_VAR (chrec), left, right);
 847     }
 848
 849   while (TREE_CODE (chrec) == POLYNOMIAL_CHREC
 850          && CHREC_VARIABLE (chrec) == loop_num)
 851     chrec = CHREC_LEFT (chrec);
 852
 853   return build_polynomial_chrec (loop_num, chrec, new_evol);
 854 }
 855
 856 /* Merges two evolution functions that were found by following two
 857    alternate paths of a conditional expression.  */
 858
 859 tree
 860 chrec_merge (tree chrec1,
 861              tree chrec2)
 862 {
 863   if (chrec1 == chrec_dont_know
 864       || chrec2 == chrec_dont_know)
 865     return chrec_dont_know;
 866
 867   if (chrec1 == chrec_known
 868       || chrec2 == chrec_known)
 869     return chrec_known;
 870
 871   if (chrec1 == chrec_not_analyzed_yet)
 872     return chrec2;
 873   if (chrec2 == chrec_not_analyzed_yet)
 874     return chrec1;
 875
 876   if (eq_evolutions_p (chrec1, chrec2))
 877     return chrec1;
 878
 879   return chrec_dont_know;
 880 }
 881
 882 \f
 883
 884 /* Observers.  */
 885
 886 /* Helper function for is_multivariate_chrec.  */
 887
 888 static bool
 889 is_multivariate_chrec_rec (const_tree chrec, unsigned int rec_var)
 890 {
 891   if (chrec == NULL_TREE)
 892     return false;
 893
 894   if (TREE_CODE (chrec) == POLYNOMIAL_CHREC)
 895     {
 896       if (CHREC_VARIABLE (chrec) != rec_var)
 897         return true;
 898       else
 899         return (is_multivariate_chrec_rec (CHREC_LEFT (chrec), rec_var)
 900                 || is_multivariate_chrec_rec (CHREC_RIGHT (chrec), rec_var));
 901     }
 902   else
 903     return false;
 904 }
 905
 906 /* Determine whether the given chrec is multivariate or not.  */
 907
 908 bool
 909 is_multivariate_chrec (const_tree chrec)
 910 {
 911   if (chrec == NULL_TREE)
 912     return false;
 913
 914   if (TREE_CODE (chrec) == POLYNOMIAL_CHREC)
 915     return (is_multivariate_chrec_rec (CHREC_LEFT (chrec),
 916                                        CHREC_VARIABLE (chrec))
 917             || is_multivariate_chrec_rec (CHREC_RIGHT (chrec),
 918                                           CHREC_VARIABLE (chrec)));
 919   else
 920     return false;
 921 }
 922
 923 /* Determines whether the chrec contains symbolic names or not.  */
 924
 925 bool
 926 chrec_contains_symbols (const_tree chrec)
 927 {
 928   int i, n;
 929
 930   if (chrec == NULL_TREE)
 931     return false;
 932
 933   if (TREE_CODE (chrec) == SSA_NAME
 934       || TREE_CODE (chrec) == VAR_DECL
 935       || TREE_CODE (chrec) == PARM_DECL
 936       || TREE_CODE (chrec) == FUNCTION_DECL
 937       || TREE_CODE (chrec) == LABEL_DECL
 938       || TREE_CODE (chrec) == RESULT_DECL
 939       || TREE_CODE (chrec) == FIELD_DECL)
 940     return true;
 941
 942   n = TREE_OPERAND_LENGTH (chrec);
 943   for (i = 0; i < n; i++)
 944     if (chrec_contains_symbols (TREE_OPERAND (chrec, i)))
 945       return true;
 946   return false;
 947 }
 948
 949 /* Determines whether the chrec contains undetermined coefficients.  */
 950
 951 bool
 952 chrec_contains_undetermined (const_tree chrec)
 953 {
 954   int i, n;
 955
 956   if (chrec == chrec_dont_know)
 957     return true;
 958
 959   if (chrec == NULL_TREE)
 960     return false;
 961
 962   n = TREE_OPERAND_LENGTH (chrec);
 963   for (i = 0; i < n; i++)
 964     if (chrec_contains_undetermined (TREE_OPERAND (chrec, i)))
 965       return true;
 966   return false;
 967 }
 968
 969 /* Determines whether the tree EXPR contains chrecs, and increment
 970    SIZE if it is not a NULL pointer by an estimation of the depth of
 971    the tree.  */
 972
 973 bool
 974 tree_contains_chrecs (const_tree expr, int *size)
 975 {
 976   int i, n;
 977
 978   if (expr == NULL_TREE)
 979     return false;
 980
 981   if (size)
 982     (*size)++;
 983
 984   if (tree_is_chrec (expr))
 985     return true;
 986
 987   n = TREE_OPERAND_LENGTH (expr);
 988   for (i = 0; i < n; i++)
 989     if (tree_contains_chrecs (TREE_OPERAND (expr, i), size))
 990       return true;
 991   return false;
 992 }
 993
 994 /* Recursive helper function.  */
 995
 996 static bool
 997 evolution_function_is_invariant_rec_p (tree chrec, int loopnum)
 998 {
 999   if (evolution_function_is_constant_p (chrec))
1000     return true;
1001
1002   if (TREE_CODE (chrec) == SSA_NAME
1003       && (loopnum == 0
1004           || expr_invariant_in_loop_p (get_loop (loopnum), chrec)))
1005     return true;
1006
1007   if (TREE_CODE (chrec) == POLYNOMIAL_CHREC)
1008     {
1009       if (CHREC_VARIABLE (chrec) == (unsigned) loopnum
1010           || !evolution_function_is_invariant_rec_p (CHREC_RIGHT (chrec),
1011                                                      loopnum)
1012           || !evolution_function_is_invariant_rec_p (CHREC_LEFT (chrec),
1013                                                      loopnum))
1014         return false;
1015       return true;
1016     }
1017
1018   switch (TREE_OPERAND_LENGTH (chrec))
1019     {
1020     case 2:
1021       if (!evolution_function_is_invariant_rec_p (TREE_OPERAND (chrec, 1),
1022                                                   loopnum))
1023         return false;
1024
1025     case 1:
1026       if (!evolution_function_is_invariant_rec_p (TREE_OPERAND (chrec, 0),
1027                                                   loopnum))
1028         return false;
1029       return true;
1030
1031     default:
1032       return false;
1033     }
1034
1035   return false;
1036 }
1037
1038 /* Return true if CHREC is invariant in loop LOOPNUM, false otherwise. */
1039
1040 bool
1041 evolution_function_is_invariant_p (tree chrec, int loopnum)
1042 {
1043   return evolution_function_is_invariant_rec_p (chrec, loopnum);
1044 }
1045
1046 /* Determine whether the given tree is an affine multivariate
1047    evolution.  */
1048
1049 bool
1050 evolution_function_is_affine_multivariate_p (const_tree chrec, int loopnum)
1051 {
1052   if (chrec == NULL_TREE)
1053     return false;
1054
1055   switch (TREE_CODE (chrec))
1056     {
1057     case POLYNOMIAL_CHREC:
1058       if (evolution_function_is_invariant_rec_p (CHREC_LEFT (chrec), loopnum))
1059         {
1060           if (evolution_function_is_invariant_rec_p (CHREC_RIGHT (chrec), loopnum))
1061             return true;
1062           else
1063             {
1064               if (TREE_CODE (CHREC_RIGHT (chrec)) == POLYNOMIAL_CHREC
1065                   && CHREC_VARIABLE (CHREC_RIGHT (chrec))
1066                      != CHREC_VARIABLE (chrec)
1067                   && evolution_function_is_affine_multivariate_p
1068                   (CHREC_RIGHT (chrec), loopnum))
1069                 return true;
1070               else
1071                 return false;
1072             }
1073         }
1074       else
1075         {
1076           if (evolution_function_is_invariant_rec_p (CHREC_RIGHT (chrec), loopnum)
1077               && TREE_CODE (CHREC_LEFT (chrec)) == POLYNOMIAL_CHREC
1078               && CHREC_VARIABLE (CHREC_LEFT (chrec)) != CHREC_VARIABLE (chrec)
1079               && evolution_function_is_affine_multivariate_p
1080               (CHREC_LEFT (chrec), loopnum))
1081             return true;
1082           else
1083             return false;
1084         }
1085
1086     default:
1087       return false;
1088     }
1089 }
1090
1091 /* Determine whether the given tree is a function in zero or one
1092    variables.  */
1093
1094 bool
1095 evolution_function_is_univariate_p (const_tree chrec)
1096 {
1097   if (chrec == NULL_TREE)
1098     return true;
1099
1100   switch (TREE_CODE (chrec))
1101     {
1102     case POLYNOMIAL_CHREC:
1103       switch (TREE_CODE (CHREC_LEFT (chrec)))
1104         {
1105         case POLYNOMIAL_CHREC:
1106           if (CHREC_VARIABLE (chrec) != CHREC_VARIABLE (CHREC_LEFT (chrec)))
1107             return false;
1108           if (!evolution_function_is_univariate_p (CHREC_LEFT (chrec)))
1109             return false;
1110           break;
1111
1112         default:
1113           break;
1114         }
1115
1116       switch (TREE_CODE (CHREC_RIGHT (chrec)))
1117         {
1118         case POLYNOMIAL_CHREC:
1119           if (CHREC_VARIABLE (chrec) != CHREC_VARIABLE (CHREC_RIGHT (chrec)))
1120             return false;
1121           if (!evolution_function_is_univariate_p (CHREC_RIGHT (chrec)))
1122             return false;
1123           break;
1124
1125         default:
1126           break;
1127         }
1128
1129     default:
1130       return true;
1131     }
1132 }
1133
1134 /* Returns the number of variables of CHREC.  Example: the call
1135    nb_vars_in_chrec ({{0, +, 1}_5, +, 2}_6) returns 2.  */
1136
1137 unsigned
1138 nb_vars_in_chrec (tree chrec)
1139 {
1140   if (chrec == NULL_TREE)
1141     return 0;
1142
1143   switch (TREE_CODE (chrec))
1144     {
1145     case POLYNOMIAL_CHREC:
1146       return 1 + nb_vars_in_chrec
1147         (initial_condition_in_loop_num (chrec, CHREC_VARIABLE (chrec)));
1148
1149     default:
1150       return 0;
1151     }
1152 }
1153
1154 static tree chrec_convert_1 (tree, tree, gimple, bool);
1155
1156 /* Converts BASE and STEP of affine scev to TYPE.  LOOP is the loop whose iv
1157    the scev corresponds to.  AT_STMT is the statement at that the scev is
1158    evaluated.  USE_OVERFLOW_SEMANTICS is true if this function should assume that
1159    the rules for overflow of the given language apply (e.g., that signed
1160    arithmetics in C does not overflow) -- i.e., to use them to avoid unnecessary
1161    tests, but also to enforce that the result follows them.  Returns true if the
1162    conversion succeeded, false otherwise.  */
1163
1164 bool
1165 convert_affine_scev (struct loop *loop, tree type,
1166                      tree *base, tree *step, gimple at_stmt,
1167                      bool use_overflow_semantics)
1168 {
1169   tree ct = TREE_TYPE (*step);
1170   bool enforce_overflow_semantics;
1171   bool must_check_src_overflow, must_check_rslt_overflow;
1172   tree new_base, new_step;
1173   tree step_type = POINTER_TYPE_P (type) ? sizetype : type;
1174
1175   /* In general,
1176      (TYPE) (BASE + STEP * i) = (TYPE) BASE + (TYPE -- sign extend) STEP * i,
1177      but we must check some assumptions.
1178
1179      1) If [BASE, +, STEP] wraps, the equation is not valid when precision
1180         of CT is smaller than the precision of TYPE.  For example, when we
1181         cast unsigned char [254, +, 1] to unsigned, the values on left side
1182         are 254, 255, 0, 1, ..., but those on the right side are
1183         254, 255, 256, 257, ...
1184      2) In case that we must also preserve the fact that signed ivs do not
1185         overflow, we must additionally check that the new iv does not wrap.
1186         For example, unsigned char [125, +, 1] casted to signed char could
1187         become a wrapping variable with values 125, 126, 127, -128, -127, ...,
1188         which would confuse optimizers that assume that this does not
1189         happen.  */
1190   must_check_src_overflow = TYPE_PRECISION (ct) < TYPE_PRECISION (type);
1191
1192   enforce_overflow_semantics = (use_overflow_semantics
1193                                 && nowrap_type_p (type));
1194   if (enforce_overflow_semantics)
1195     {
1196       /* We can avoid checking whether the result overflows in the following
1197          cases:
1198
1199          -- must_check_src_overflow is true, and the range of TYPE is superset
1200             of the range of CT -- i.e., in all cases except if CT signed and
1201             TYPE unsigned.
1202          -- both CT and TYPE have the same precision and signedness, and we
1203             verify instead that the source does not overflow (this may be
1204             easier than verifying it for the result, as we may use the
1205             information about the semantics of overflow in CT).  */
1206       if (must_check_src_overflow)
1207         {
1208           if (TYPE_UNSIGNED (type) && !TYPE_UNSIGNED (ct))
1209             must_check_rslt_overflow = true;
1210           else
1211             must_check_rslt_overflow = false;
1212         }
1213       else if (TYPE_UNSIGNED (ct) == TYPE_UNSIGNED (type)
1214                && TYPE_PRECISION (ct) == TYPE_PRECISION (type))
1215         {
1216           must_check_rslt_overflow = false;
1217           must_check_src_overflow = true;
1218         }
1219       else
1220         must_check_rslt_overflow = true;
1221     }
1222   else
1223     must_check_rslt_overflow = false;
1224
1225   if (must_check_src_overflow
1226       && scev_probably_wraps_p (*base, *step, at_stmt, loop,
1227                                 use_overflow_semantics))
1228     return false;
1229
1230   new_base = chrec_convert_1 (type, *base, at_stmt,
1231                               use_overflow_semantics);
1232   /* The step must be sign extended, regardless of the signedness
1233      of CT and TYPE.  This only needs to be handled specially when
1234      CT is unsigned -- to avoid e.g. unsigned char [100, +, 255]
1235      (with values 100, 99, 98, ...) from becoming signed or unsigned
1236      [100, +, 255] with values 100, 355, ...; the sign-extension is
1237      performed by default when CT is signed.  */
1238   new_step = *step;
1239   if (TYPE_PRECISION (step_type) > TYPE_PRECISION (ct) && TYPE_UNSIGNED (ct))
1240     {
1241       tree signed_ct = build_nonstandard_integer_type (TYPE_PRECISION (ct), 0);
1242       new_step = chrec_convert_1 (signed_ct, new_step, at_stmt,
1243                                   use_overflow_semantics);
1244     }
1245   new_step = chrec_convert_1 (step_type, new_step, at_stmt, use_overflow_semantics);
1246
1247   if (automatically_generated_chrec_p (new_base)
1248       || automatically_generated_chrec_p (new_step))
1249     return false;
1250
1251   if (must_check_rslt_overflow
1252       /* Note that in this case we cannot use the fact that signed variables
1253          do not overflow, as this is what we are verifying for the new iv.  */
1254       && scev_probably_wraps_p (new_base, new_step, at_stmt, loop, false))
1255     return false;
1256
1257   *base = new_base;
1258   *step = new_step;
1259   return true;
1260 }
1261 \f
1262
1263 /* Convert CHREC for the right hand side of a CHREC.
1264    The increment for a pointer type is always sizetype.  */
1265
1266 tree
1267 chrec_convert_rhs (tree type, tree chrec, gimple at_stmt)
1268 {
1269   if (POINTER_TYPE_P (type))
1270     type = sizetype;
1271
1272   return chrec_convert (type, chrec, at_stmt);
1273 }
1274
1275 /* Convert CHREC to TYPE.  When the analyzer knows the context in
1276    which the CHREC is built, it sets AT_STMT to the statement that
1277    contains the definition of the analyzed variable, otherwise the
1278    conversion is less accurate: the information is used for
1279    determining a more accurate estimation of the number of iterations.
1280    By default AT_STMT could be safely set to NULL_TREE.
1281
1282    The following rule is always true: TREE_TYPE (chrec) ==
1283    TREE_TYPE (CHREC_LEFT (chrec)) == TREE_TYPE (CHREC_RIGHT (chrec)).
1284    An example of what could happen when adding two chrecs and the type
1285    of the CHREC_RIGHT is different than CHREC_LEFT is:
1286
1287    {(uint) 0, +, (uchar) 10} +
1288    {(uint) 0, +, (uchar) 250}
1289
1290    that would produce a wrong result if CHREC_RIGHT is not (uint):
1291
1292    {(uint) 0, +, (uchar) 4}
1293
1294    instead of
1295
1296    {(uint) 0, +, (uint) 260}
1297 */
1298
1299 tree
1300 chrec_convert (tree type, tree chrec, gimple at_stmt)
1301 {
1302   return chrec_convert_1 (type, chrec, at_stmt, true);
1303 }
1304
1305 /* Convert CHREC to TYPE.  When the analyzer knows the context in
1306    which the CHREC is built, it sets AT_STMT to the statement that
1307    contains the definition of the analyzed variable, otherwise the
1308    conversion is less accurate: the information is used for
1309    determining a more accurate estimation of the number of iterations.
1310    By default AT_STMT could be safely set to NULL_TREE.
1311
1312    USE_OVERFLOW_SEMANTICS is true if this function should assume that
1313    the rules for overflow of the given language apply (e.g., that signed
1314    arithmetics in C does not overflow) -- i.e., to use them to avoid unnecessary
1315    tests, but also to enforce that the result follows them.  */
1316
1317 static tree
1318 chrec_convert_1 (tree type, tree chrec, gimple at_stmt,
1319                  bool use_overflow_semantics)
1320 {
1321   tree ct, res;
1322   tree base, step;
1323   struct loop *loop;
1324
1325   if (automatically_generated_chrec_p (chrec))
1326     return chrec;
1327
1328   ct = chrec_type (chrec);
1329   if (ct == type)
1330     return chrec;
1331
1332   if (!evolution_function_is_affine_p (chrec))
1333     goto keep_cast;
1334
1335   loop = get_chrec_loop (chrec);
1336   base = CHREC_LEFT (chrec);
1337   step = CHREC_RIGHT (chrec);
1338
1339   if (convert_affine_scev (loop, type, &base, &step, at_stmt,
1340                            use_overflow_semantics))
1341     return build_polynomial_chrec (loop->num, base, step);
1342
1343   /* If we cannot propagate the cast inside the chrec, just keep the cast.  */
1344 keep_cast:
1345   /* Fold will not canonicalize (long)(i - 1) to (long)i - 1 because that
1346      may be more expensive.  We do want to perform this optimization here
1347      though for canonicalization reasons.  */
1348   if (use_overflow_semantics
1349       && (TREE_CODE (chrec) == PLUS_EXPR
1350           || TREE_CODE (chrec) == MINUS_EXPR)
1351       && TREE_CODE (type) == INTEGER_TYPE
1352       && TREE_CODE (ct) == INTEGER_TYPE
1353       && TYPE_PRECISION (type) > TYPE_PRECISION (ct)
1354       && TYPE_OVERFLOW_UNDEFINED (ct))
1355     res = fold_build2 (TREE_CODE (chrec), type,
1356                        fold_convert (type, TREE_OPERAND (chrec, 0)),
1357                        fold_convert (type, TREE_OPERAND (chrec, 1)));
1358   else
1359     res = fold_convert (type, chrec);
1360
1361   /* Don't propagate overflows.  */
1362   if (CONSTANT_CLASS_P (res))
1363     TREE_OVERFLOW (res) = 0;
1364
1365   /* But reject constants that don't fit in their type after conversion.
1366      This can happen if TYPE_MIN_VALUE or TYPE_MAX_VALUE are not the
1367      natural values associated with TYPE_PRECISION and TYPE_UNSIGNED,
1368      and can cause problems later when computing niters of loops.  Note
1369      that we don't do the check before converting because we don't want
1370      to reject conversions of negative chrecs to unsigned types.  */
1371   if (TREE_CODE (res) == INTEGER_CST
1372       && TREE_CODE (type) == INTEGER_TYPE
1373       && !int_fits_type_p (res, type))
1374     res = chrec_dont_know;
1375
1376   return res;
1377 }
1378
1379 /* Convert CHREC to TYPE, without regard to signed overflows.  Returns the new
1380    chrec if something else than what chrec_convert would do happens, NULL_TREE
1381    otherwise.  */
1382
1383 tree
1384 chrec_convert_aggressive (tree type, tree chrec)
1385 {
1386   tree inner_type, left, right, lc, rc, rtype;
1387
1388   if (automatically_generated_chrec_p (chrec)
1389       || TREE_CODE (chrec) != POLYNOMIAL_CHREC)
1390     return NULL_TREE;
1391
1392   inner_type = TREE_TYPE (chrec);
1393   if (TYPE_PRECISION (type) > TYPE_PRECISION (inner_type))
1394     return NULL_TREE;
1395
1396   rtype = POINTER_TYPE_P (type) ? sizetype : type;
1397
1398   left = CHREC_LEFT (chrec);
1399   right = CHREC_RIGHT (chrec);
1400   lc = chrec_convert_aggressive (type, left);
1401   if (!lc)
1402     lc = chrec_convert (type, left, NULL);
1403   rc = chrec_convert_aggressive (rtype, right);
1404   if (!rc)
1405     rc = chrec_convert (rtype, right, NULL);
1406
1407   return build_polynomial_chrec (CHREC_VARIABLE (chrec), lc, rc);
1408 }
1409
1410 /* Returns true when CHREC0 == CHREC1.  */
1411
1412 bool
1413 eq_evolutions_p (const_tree chrec0, const_tree chrec1)
1414 {
1415   if (chrec0 == NULL_TREE
1416       || chrec1 == NULL_TREE
1417       || TREE_CODE (chrec0) != TREE_CODE (chrec1))
1418     return false;
1419
1420   if (chrec0 == chrec1)
1421     return true;
1422
1423   switch (TREE_CODE (chrec0))
1424     {
1425     case INTEGER_CST:
1426       return operand_equal_p (chrec0, chrec1, 0);
1427
1428     case POLYNOMIAL_CHREC:
1429       return (CHREC_VARIABLE (chrec0) == CHREC_VARIABLE (chrec1)
1430               && eq_evolutions_p (CHREC_LEFT (chrec0), CHREC_LEFT (chrec1))
1431               && eq_evolutions_p (CHREC_RIGHT (chrec0), CHREC_RIGHT (chrec1)));
1432
1433     case PLUS_EXPR:
1434     case MULT_EXPR:
1435     case MINUS_EXPR:
1436     case POINTER_PLUS_EXPR:
1437       return eq_evolutions_p (TREE_OPERAND (chrec0, 0),
1438                               TREE_OPERAND (chrec1, 0))
1439           && eq_evolutions_p (TREE_OPERAND (chrec0, 1),
1440                               TREE_OPERAND (chrec1, 1));
1441
1442     default:
1443       return false;
1444     }
1445 }
1446
1447 /* Returns EV_GROWS if CHREC grows (assuming that it does not overflow),
1448    EV_DECREASES if it decreases, and EV_UNKNOWN if we cannot determine
1449    which of these cases happens.  */
1450
1451 enum ev_direction
1452 scev_direction (const_tree chrec)
1453 {
1454   const_tree step;
1455
1456   if (!evolution_function_is_affine_p (chrec))
1457     return EV_DIR_UNKNOWN;
1458
1459   step = CHREC_RIGHT (chrec);
1460   if (TREE_CODE (step) != INTEGER_CST)
1461     return EV_DIR_UNKNOWN;
1462
1463   if (tree_int_cst_sign_bit (step))
1464     return EV_DIR_DECREASES;
1465   else
1466     return EV_DIR_GROWS;
1467 }
1468
1469 /* Iterates over all the components of SCEV, and calls CBCK.  */
1470
1471 void
1472 for_each_scev_op (tree *scev, bool (*cbck) (tree *, void *), void *data)
1473 {
1474   switch (TREE_CODE_LENGTH (TREE_CODE (*scev)))
1475     {
1476     case 3:
1477       for_each_scev_op (&TREE_OPERAND (*scev, 2), cbck, data);
1478
1479     case 2:
1480       for_each_scev_op (&TREE_OPERAND (*scev, 1), cbck, data);
1481
1482     case 1:
1483       for_each_scev_op (&TREE_OPERAND (*scev, 0), cbck, data);
1484
1485     default:
1486       cbck (scev, data);
1487       break;
1488     }
1489 }
1490
1491 /* Returns true when the operation can be part of a linear
1492    expression.  */
1493
1494 static inline bool
1495 operator_is_linear (tree scev)
1496 {
1497   switch (TREE_CODE (scev))
1498     {
1499     case INTEGER_CST:
1500     case POLYNOMIAL_CHREC:
1501     case PLUS_EXPR:
1502     case POINTER_PLUS_EXPR:
1503     case MULT_EXPR:
1504     case MINUS_EXPR:
1505     case NEGATE_EXPR:
1506     case SSA_NAME:
1507     case NON_LVALUE_EXPR:
1508     case BIT_NOT_EXPR:
1509     CASE_CONVERT:
1510       return true;
1511
1512     default:
1513       return false;
1514     }
1515 }
1516
1517 /* Return true when SCEV is a linear expression.  Linear expressions
1518    can contain additions, substractions and multiplications.
1519    Multiplications are restricted to constant scaling: "cst * x".  */
1520
1521 bool
1522 scev_is_linear_expression (tree scev)
1523 {
1524   if (scev == NULL
1525       || !operator_is_linear (scev))
1526     return false;
1527
1528   if (TREE_CODE (scev) == MULT_EXPR)
1529     return !(tree_contains_chrecs (TREE_OPERAND (scev, 0), NULL)
1530              && tree_contains_chrecs (TREE_OPERAND (scev, 1), NULL));
1531
1532   if (TREE_CODE (scev) == POLYNOMIAL_CHREC
1533       && !evolution_function_is_affine_multivariate_p (scev, CHREC_VARIABLE (scev)))
1534     return false;
1535
1536   switch (TREE_CODE_LENGTH (TREE_CODE (scev)))
1537     {
1538     case 3:
1539       return scev_is_linear_expression (TREE_OPERAND (scev, 0))
1540         && scev_is_linear_expression (TREE_OPERAND (scev, 1))
1541         && scev_is_linear_expression (TREE_OPERAND (scev, 2));
1542
1543     case 2:
1544       return scev_is_linear_expression (TREE_OPERAND (scev, 0))
1545         && scev_is_linear_expression (TREE_OPERAND (scev, 1));
1546
1547     case 1:
1548       return scev_is_linear_expression (TREE_OPERAND (scev, 0));
1549
1550     case 0:
1551       return true;
1552
1553     default:
1554       return false;
1555     }
1556 }
1557
1558 /* Determines whether the expression CHREC contains only interger consts
1559    in the right parts.  */
1560
1561 bool
1562 evolution_function_right_is_integer_cst (const_tree chrec)
1563 {
1564   if (chrec == NULL_TREE)
1565     return false;
1566
1567   switch (TREE_CODE (chrec))
1568     {
1569     case INTEGER_CST:
1570       return true;
1571
1572     case POLYNOMIAL_CHREC:
1573       return TREE_CODE (CHREC_RIGHT (chrec)) == INTEGER_CST
1574         && (TREE_CODE (CHREC_LEFT (chrec)) != POLYNOMIAL_CHREC
1575             || evolution_function_right_is_integer_cst (CHREC_LEFT (chrec)));
1576
1577     CASE_CONVERT:
1578       return evolution_function_right_is_integer_cst (TREE_OPERAND (chrec, 0));
1579
1580     default:
1581       return false;
1582     }
1583 }