Mercurial > hg > CbC > CbC_gcc
annotate gcc/tree-chrec.c @ 22:0eb6cac880f0
add cbc example of quicksort.
| author | kent <kent@cr.ie.u-ryukyu.ac.jp> |
|---|---|
| date | Tue, 13 Oct 2009 17:15:58 +0900 |
| parents | 58ad6c70ea60 |
| children | 77e2b8dfacca |
| rev | line source |
|---|---|
| 0 | 1 /* Chains of recurrences. |
| 2 Copyright (C) 2003, 2004, 2005, 2006, 2007, 2008, 2009 | |
| 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 "tm.h" | |
| 31 #include "ggc.h" | |
| 32 #include "tree.h" | |
| 33 #include "real.h" | |
| 34 #include "diagnostic.h" | |
| 35 #include "cfgloop.h" | |
| 36 #include "tree-flow.h" | |
| 37 #include "tree-chrec.h" | |
| 38 #include "tree-pass.h" | |
| 39 #include "params.h" | |
| 40 #include "tree-scalar-evolution.h" | |
| 41 | |
| 42 | |
| 43 | |
| 44 /* Extended folder for chrecs. */ | |
| 45 | |
| 46 /* Determines whether CST is not a constant evolution. */ | |
| 47 | |
| 48 static inline bool | |
| 49 is_not_constant_evolution (const_tree cst) | |
| 50 { | |
| 51 return (TREE_CODE (cst) == POLYNOMIAL_CHREC); | |
| 52 } | |
| 53 | |
| 54 /* Fold CODE for a polynomial function and a constant. */ | |
| 55 | |
| 56 static inline tree | |
| 57 chrec_fold_poly_cst (enum tree_code code, | |
| 58 tree type, | |
| 59 tree poly, | |
| 60 tree cst) | |
| 61 { | |
| 62 gcc_assert (poly); | |
| 63 gcc_assert (cst); | |
| 64 gcc_assert (TREE_CODE (poly) == POLYNOMIAL_CHREC); | |
| 65 gcc_assert (!is_not_constant_evolution (cst)); | |
| 66 gcc_assert (type == chrec_type (poly)); | |
| 67 | |
| 68 switch (code) | |
| 69 { | |
| 70 case PLUS_EXPR: | |
| 71 return build_polynomial_chrec | |
| 72 (CHREC_VARIABLE (poly), | |
| 73 chrec_fold_plus (type, CHREC_LEFT (poly), cst), | |
| 74 CHREC_RIGHT (poly)); | |
| 75 | |
| 76 case MINUS_EXPR: | |
| 77 return build_polynomial_chrec | |
| 78 (CHREC_VARIABLE (poly), | |
| 79 chrec_fold_minus (type, CHREC_LEFT (poly), cst), | |
| 80 CHREC_RIGHT (poly)); | |
| 81 | |
| 82 case MULT_EXPR: | |
| 83 return build_polynomial_chrec | |
| 84 (CHREC_VARIABLE (poly), | |
| 85 chrec_fold_multiply (type, CHREC_LEFT (poly), cst), | |
| 86 chrec_fold_multiply (type, CHREC_RIGHT (poly), cst)); | |
| 87 | |
| 88 default: | |
| 89 return chrec_dont_know; | |
| 90 } | |
| 91 } | |
| 92 | |
| 93 /* Fold the addition of two polynomial functions. */ | |
| 94 | |
| 95 static inline tree | |
| 96 chrec_fold_plus_poly_poly (enum tree_code code, | |
| 97 tree type, | |
| 98 tree poly0, | |
| 99 tree poly1) | |
| 100 { | |
| 101 tree left, right; | |
| 102 struct loop *loop0 = get_chrec_loop (poly0); | |
| 103 struct loop *loop1 = get_chrec_loop (poly1); | |
| 104 tree rtype = code == POINTER_PLUS_EXPR ? sizetype : type; | |
| 105 | |
| 106 gcc_assert (poly0); | |
| 107 gcc_assert (poly1); | |
| 108 gcc_assert (TREE_CODE (poly0) == POLYNOMIAL_CHREC); | |
| 109 gcc_assert (TREE_CODE (poly1) == POLYNOMIAL_CHREC); | |
| 110 if (POINTER_TYPE_P (chrec_type (poly0))) | |
| 111 gcc_assert (chrec_type (poly1) == sizetype); | |
| 112 else | |
| 113 gcc_assert (chrec_type (poly0) == chrec_type (poly1)); | |
| 114 gcc_assert (type == chrec_type (poly0)); | |
| 115 | |
| 116 /* | |
| 117 {a, +, b}_1 + {c, +, d}_2 -> {{a, +, b}_1 + c, +, d}_2, | |
| 118 {a, +, b}_2 + {c, +, d}_1 -> {{c, +, d}_1 + a, +, b}_2, | |
| 119 {a, +, b}_x + {c, +, d}_x -> {a+c, +, b+d}_x. */ | |
| 120 if (flow_loop_nested_p (loop0, loop1)) | |
| 121 { | |
| 122 if (code == PLUS_EXPR || code == POINTER_PLUS_EXPR) | |
| 123 return build_polynomial_chrec | |
| 124 (CHREC_VARIABLE (poly1), | |
| 125 chrec_fold_plus (type, poly0, CHREC_LEFT (poly1)), | |
| 126 CHREC_RIGHT (poly1)); | |
| 127 else | |
| 128 return build_polynomial_chrec | |
| 129 (CHREC_VARIABLE (poly1), | |
| 130 chrec_fold_minus (type, poly0, CHREC_LEFT (poly1)), | |
| 131 chrec_fold_multiply (type, CHREC_RIGHT (poly1), | |
| 132 SCALAR_FLOAT_TYPE_P (type) | |
| 133 ? build_real (type, dconstm1) | |
| 134 : build_int_cst_type (type, -1))); | |
| 135 } | |
| 136 | |
| 137 if (flow_loop_nested_p (loop1, loop0)) | |
| 138 { | |
| 139 if (code == PLUS_EXPR || code == POINTER_PLUS_EXPR) | |
| 140 return build_polynomial_chrec | |
| 141 (CHREC_VARIABLE (poly0), | |
| 142 chrec_fold_plus (type, CHREC_LEFT (poly0), poly1), | |
| 143 CHREC_RIGHT (poly0)); | |
| 144 else | |
| 145 return build_polynomial_chrec | |
| 146 (CHREC_VARIABLE (poly0), | |
| 147 chrec_fold_minus (type, CHREC_LEFT (poly0), poly1), | |
| 148 CHREC_RIGHT (poly0)); | |
| 149 } | |
| 150 | |
| 151 /* This function should never be called for chrecs of loops that | |
| 152 do not belong to the same loop nest. */ | |
| 153 gcc_assert (loop0 == loop1); | |
| 154 | |
| 155 if (code == PLUS_EXPR || code == POINTER_PLUS_EXPR) | |
| 156 { | |
| 157 left = chrec_fold_plus | |
| 158 (type, CHREC_LEFT (poly0), CHREC_LEFT (poly1)); | |
| 159 right = chrec_fold_plus | |
| 160 (rtype, CHREC_RIGHT (poly0), CHREC_RIGHT (poly1)); | |
| 161 } | |
| 162 else | |
| 163 { | |
| 164 left = chrec_fold_minus | |
| 165 (type, CHREC_LEFT (poly0), CHREC_LEFT (poly1)); | |
| 166 right = chrec_fold_minus | |
| 167 (type, CHREC_RIGHT (poly0), CHREC_RIGHT (poly1)); | |
| 168 } | |
| 169 | |
| 170 if (chrec_zerop (right)) | |
| 171 return left; | |
| 172 else | |
| 173 return build_polynomial_chrec | |
| 174 (CHREC_VARIABLE (poly0), left, right); | |
| 175 } | |
| 176 | |
| 177 | |
| 178 | |
| 179 /* Fold the multiplication of two polynomial functions. */ | |
| 180 | |
| 181 static inline tree | |
| 182 chrec_fold_multiply_poly_poly (tree type, | |
| 183 tree poly0, | |
| 184 tree poly1) | |
| 185 { | |
| 186 tree t0, t1, t2; | |
| 187 int var; | |
| 188 struct loop *loop0 = get_chrec_loop (poly0); | |
| 189 struct loop *loop1 = get_chrec_loop (poly1); | |
| 190 | |
| 191 gcc_assert (poly0); | |
| 192 gcc_assert (poly1); | |
| 193 gcc_assert (TREE_CODE (poly0) == POLYNOMIAL_CHREC); | |
| 194 gcc_assert (TREE_CODE (poly1) == POLYNOMIAL_CHREC); | |
| 195 gcc_assert (chrec_type (poly0) == chrec_type (poly1)); | |
| 196 gcc_assert (type == chrec_type (poly0)); | |
| 197 | |
| 198 /* {a, +, b}_1 * {c, +, d}_2 -> {c*{a, +, b}_1, +, d}_2, | |
| 199 {a, +, b}_2 * {c, +, d}_1 -> {a*{c, +, d}_1, +, b}_2, | |
| 200 {a, +, b}_x * {c, +, d}_x -> {a*c, +, a*d + b*c + b*d, +, 2*b*d}_x. */ | |
| 201 if (flow_loop_nested_p (loop0, loop1)) | |
| 202 /* poly0 is a constant wrt. poly1. */ | |
| 203 return build_polynomial_chrec | |
| 204 (CHREC_VARIABLE (poly1), | |
| 205 chrec_fold_multiply (type, CHREC_LEFT (poly1), poly0), | |
| 206 CHREC_RIGHT (poly1)); | |
| 207 | |
| 208 if (flow_loop_nested_p (loop1, loop0)) | |
| 209 /* poly1 is a constant wrt. poly0. */ | |
| 210 return build_polynomial_chrec | |
| 211 (CHREC_VARIABLE (poly0), | |
| 212 chrec_fold_multiply (type, CHREC_LEFT (poly0), poly1), | |
| 213 CHREC_RIGHT (poly0)); | |
| 214 | |
| 215 gcc_assert (loop0 == loop1); | |
| 216 | |
| 217 /* poly0 and poly1 are two polynomials in the same variable, | |
| 218 {a, +, b}_x * {c, +, d}_x -> {a*c, +, a*d + b*c + b*d, +, 2*b*d}_x. */ | |
| 219 | |
| 220 /* "a*c". */ | |
| 221 t0 = chrec_fold_multiply (type, CHREC_LEFT (poly0), CHREC_LEFT (poly1)); | |
| 222 | |
|
19
58ad6c70ea60
update gcc from 4.4.0 to 4.4.1.
kent@firefly.cr.ie.u-ryukyu.ac.jp
parents:
0
diff
changeset
|
223 /* "a*d + b*c". */ |
| 0 | 224 t1 = chrec_fold_multiply (type, CHREC_LEFT (poly0), CHREC_RIGHT (poly1)); |
| 225 t1 = chrec_fold_plus (type, t1, chrec_fold_multiply (type, | |
| 226 CHREC_RIGHT (poly0), | |
| 227 CHREC_LEFT (poly1))); | |
|
19
58ad6c70ea60
update gcc from 4.4.0 to 4.4.1.
kent@firefly.cr.ie.u-ryukyu.ac.jp
parents:
0
diff
changeset
|
228 /* "b*d". */ |
|
58ad6c70ea60
update gcc from 4.4.0 to 4.4.1.
kent@firefly.cr.ie.u-ryukyu.ac.jp
parents:
0
diff
changeset
|
229 t2 = chrec_fold_multiply (type, CHREC_RIGHT (poly0), CHREC_RIGHT (poly1)); |
|
58ad6c70ea60
update gcc from 4.4.0 to 4.4.1.
kent@firefly.cr.ie.u-ryukyu.ac.jp
parents:
0
diff
changeset
|
230 /* "a*d + b*c + b*d". */ |
|
58ad6c70ea60
update gcc from 4.4.0 to 4.4.1.
kent@firefly.cr.ie.u-ryukyu.ac.jp
parents:
0
diff
changeset
|
231 t1 = chrec_fold_plus (type, t1, t2); |
| 0 | 232 /* "2*b*d". */ |
| 233 t2 = chrec_fold_multiply (type, SCALAR_FLOAT_TYPE_P (type) | |
| 234 ? build_real (type, dconst2) | |
| 235 : build_int_cst (type, 2), t2); | |
| 236 | |
| 237 var = CHREC_VARIABLE (poly0); | |
| 238 return build_polynomial_chrec (var, t0, | |
| 239 build_polynomial_chrec (var, t1, t2)); | |
| 240 } | |
| 241 | |
| 242 /* When the operands are automatically_generated_chrec_p, the fold has | |
| 243 to respect the semantics of the operands. */ | |
| 244 | |
| 245 static inline tree | |
| 246 chrec_fold_automatically_generated_operands (tree op0, | |
| 247 tree op1) | |
| 248 { | |
| 249 if (op0 == chrec_dont_know | |
| 250 || op1 == chrec_dont_know) | |
| 251 return chrec_dont_know; | |
| 252 | |
| 253 if (op0 == chrec_known | |
| 254 || op1 == chrec_known) | |
| 255 return chrec_known; | |
| 256 | |
| 257 if (op0 == chrec_not_analyzed_yet | |
| 258 || op1 == chrec_not_analyzed_yet) | |
| 259 return chrec_not_analyzed_yet; | |
| 260 | |
| 261 /* The default case produces a safe result. */ | |
| 262 return chrec_dont_know; | |
| 263 } | |
| 264 | |
| 265 /* Fold the addition of two chrecs. */ | |
| 266 | |
| 267 static tree | |
| 268 chrec_fold_plus_1 (enum tree_code code, tree type, | |
| 269 tree op0, tree op1) | |
| 270 { | |
| 271 tree op1_type = code == POINTER_PLUS_EXPR ? sizetype : type; | |
| 272 | |
| 273 if (automatically_generated_chrec_p (op0) | |
| 274 || automatically_generated_chrec_p (op1)) | |
| 275 return chrec_fold_automatically_generated_operands (op0, op1); | |
| 276 | |
| 277 switch (TREE_CODE (op0)) | |
| 278 { | |
| 279 case POLYNOMIAL_CHREC: | |
| 280 switch (TREE_CODE (op1)) | |
| 281 { | |
| 282 case POLYNOMIAL_CHREC: | |
| 283 return chrec_fold_plus_poly_poly (code, type, op0, op1); | |
| 284 | |
| 285 default: | |
| 286 if (code == PLUS_EXPR || code == POINTER_PLUS_EXPR) | |
| 287 return build_polynomial_chrec | |
| 288 (CHREC_VARIABLE (op0), | |
| 289 chrec_fold_plus (type, CHREC_LEFT (op0), op1), | |
| 290 CHREC_RIGHT (op0)); | |
| 291 else | |
| 292 return build_polynomial_chrec | |
| 293 (CHREC_VARIABLE (op0), | |
| 294 chrec_fold_minus (type, CHREC_LEFT (op0), op1), | |
| 295 CHREC_RIGHT (op0)); | |
| 296 } | |
| 297 | |
| 298 default: | |
| 299 switch (TREE_CODE (op1)) | |
| 300 { | |
| 301 case POLYNOMIAL_CHREC: | |
| 302 if (code == PLUS_EXPR || code == POINTER_PLUS_EXPR) | |
| 303 return build_polynomial_chrec | |
| 304 (CHREC_VARIABLE (op1), | |
| 305 chrec_fold_plus (type, op0, CHREC_LEFT (op1)), | |
| 306 CHREC_RIGHT (op1)); | |
| 307 else | |
| 308 return build_polynomial_chrec | |
| 309 (CHREC_VARIABLE (op1), | |
| 310 chrec_fold_minus (type, op0, CHREC_LEFT (op1)), | |
| 311 chrec_fold_multiply (type, CHREC_RIGHT (op1), | |
| 312 SCALAR_FLOAT_TYPE_P (type) | |
| 313 ? build_real (type, dconstm1) | |
| 314 : build_int_cst_type (type, -1))); | |
| 315 | |
| 316 default: | |
| 317 { | |
| 318 int size = 0; | |
| 319 if ((tree_contains_chrecs (op0, &size) | |
| 320 || tree_contains_chrecs (op1, &size)) | |
| 321 && size < PARAM_VALUE (PARAM_SCEV_MAX_EXPR_SIZE)) | |
| 322 return build2 (code, type, op0, op1); | |
| 323 else if (size < PARAM_VALUE (PARAM_SCEV_MAX_EXPR_SIZE)) | |
| 324 return fold_build2 (code, type, | |
| 325 fold_convert (type, op0), | |
| 326 fold_convert (op1_type, op1)); | |
| 327 else | |
| 328 return chrec_dont_know; | |
| 329 } | |
| 330 } | |
| 331 } | |
| 332 } | |
| 333 | |
| 334 /* Fold the addition of two chrecs. */ | |
| 335 | |
| 336 tree | |
| 337 chrec_fold_plus (tree type, | |
| 338 tree op0, | |
| 339 tree op1) | |
| 340 { | |
| 341 enum tree_code code; | |
| 342 if (automatically_generated_chrec_p (op0) | |
| 343 || automatically_generated_chrec_p (op1)) | |
| 344 return chrec_fold_automatically_generated_operands (op0, op1); | |
| 345 | |
| 346 if (integer_zerop (op0)) | |
| 347 return chrec_convert (type, op1, NULL); | |
| 348 if (integer_zerop (op1)) | |
| 349 return chrec_convert (type, op0, NULL); | |
| 350 | |
| 351 if (POINTER_TYPE_P (type)) | |
| 352 code = POINTER_PLUS_EXPR; | |
| 353 else | |
| 354 code = PLUS_EXPR; | |
| 355 | |
| 356 return chrec_fold_plus_1 (code, type, op0, op1); | |
| 357 } | |
| 358 | |
| 359 /* Fold the subtraction of two chrecs. */ | |
| 360 | |
| 361 tree | |
| 362 chrec_fold_minus (tree type, | |
| 363 tree op0, | |
| 364 tree op1) | |
| 365 { | |
| 366 if (automatically_generated_chrec_p (op0) | |
| 367 || automatically_generated_chrec_p (op1)) | |
| 368 return chrec_fold_automatically_generated_operands (op0, op1); | |
| 369 | |
| 370 if (integer_zerop (op1)) | |
| 371 return op0; | |
| 372 | |
| 373 return chrec_fold_plus_1 (MINUS_EXPR, type, op0, op1); | |
| 374 } | |
| 375 | |
| 376 /* Fold the multiplication of two chrecs. */ | |
| 377 | |
| 378 tree | |
| 379 chrec_fold_multiply (tree type, | |
| 380 tree op0, | |
| 381 tree op1) | |
| 382 { | |
| 383 if (automatically_generated_chrec_p (op0) | |
| 384 || automatically_generated_chrec_p (op1)) | |
| 385 return chrec_fold_automatically_generated_operands (op0, op1); | |
| 386 | |
| 387 switch (TREE_CODE (op0)) | |
| 388 { | |
| 389 case POLYNOMIAL_CHREC: | |
| 390 switch (TREE_CODE (op1)) | |
| 391 { | |
| 392 case POLYNOMIAL_CHREC: | |
| 393 return chrec_fold_multiply_poly_poly (type, op0, op1); | |
| 394 | |
| 395 default: | |
| 396 if (integer_onep (op1)) | |
| 397 return op0; | |
| 398 if (integer_zerop (op1)) | |
| 399 return build_int_cst (type, 0); | |
| 400 | |
| 401 return build_polynomial_chrec | |
| 402 (CHREC_VARIABLE (op0), | |
| 403 chrec_fold_multiply (type, CHREC_LEFT (op0), op1), | |
| 404 chrec_fold_multiply (type, CHREC_RIGHT (op0), op1)); | |
| 405 } | |
| 406 | |
| 407 default: | |
| 408 if (integer_onep (op0)) | |
| 409 return op1; | |
| 410 | |
| 411 if (integer_zerop (op0)) | |
| 412 return build_int_cst (type, 0); | |
| 413 | |
| 414 switch (TREE_CODE (op1)) | |
| 415 { | |
| 416 case POLYNOMIAL_CHREC: | |
| 417 return build_polynomial_chrec | |
| 418 (CHREC_VARIABLE (op1), | |
| 419 chrec_fold_multiply (type, CHREC_LEFT (op1), op0), | |
| 420 chrec_fold_multiply (type, CHREC_RIGHT (op1), op0)); | |
| 421 | |
| 422 default: | |
| 423 if (integer_onep (op1)) | |
| 424 return op0; | |
| 425 if (integer_zerop (op1)) | |
| 426 return build_int_cst (type, 0); | |
| 427 return fold_build2 (MULT_EXPR, type, op0, op1); | |
| 428 } | |
| 429 } | |
| 430 } | |
| 431 | |
| 432 | |
| 433 | |
| 434 /* Operations. */ | |
| 435 | |
| 436 /* Evaluate the binomial coefficient. Return NULL_TREE if the intermediate | |
| 437 calculation overflows, otherwise return C(n,k) with type TYPE. */ | |
| 438 | |
| 439 static tree | |
| 440 tree_fold_binomial (tree type, tree n, unsigned int k) | |
| 441 { | |
| 442 unsigned HOST_WIDE_INT lidx, lnum, ldenom, lres, ldum; | |
| 443 HOST_WIDE_INT hidx, hnum, hdenom, hres, hdum; | |
| 444 unsigned int i; | |
| 445 tree res; | |
| 446 | |
| 447 /* Handle the most frequent cases. */ | |
| 448 if (k == 0) | |
| 449 return build_int_cst (type, 1); | |
| 450 if (k == 1) | |
| 451 return fold_convert (type, n); | |
| 452 | |
| 453 /* Check that k <= n. */ | |
| 454 if (TREE_INT_CST_HIGH (n) == 0 | |
| 455 && TREE_INT_CST_LOW (n) < k) | |
| 456 return NULL_TREE; | |
| 457 | |
| 458 /* Numerator = n. */ | |
| 459 lnum = TREE_INT_CST_LOW (n); | |
| 460 hnum = TREE_INT_CST_HIGH (n); | |
| 461 | |
| 462 /* Denominator = 2. */ | |
| 463 ldenom = 2; | |
| 464 hdenom = 0; | |
| 465 | |
| 466 /* Index = Numerator-1. */ | |
| 467 if (lnum == 0) | |
| 468 { | |
| 469 hidx = hnum - 1; | |
| 470 lidx = ~ (unsigned HOST_WIDE_INT) 0; | |
| 471 } | |
| 472 else | |
| 473 { | |
| 474 hidx = hnum; | |
| 475 lidx = lnum - 1; | |
| 476 } | |
| 477 | |
| 478 /* Numerator = Numerator*Index = n*(n-1). */ | |
| 479 if (mul_double (lnum, hnum, lidx, hidx, &lnum, &hnum)) | |
| 480 return NULL_TREE; | |
| 481 | |
| 482 for (i = 3; i <= k; i++) | |
| 483 { | |
| 484 /* Index--. */ | |
| 485 if (lidx == 0) | |
| 486 { | |
| 487 hidx--; | |
| 488 lidx = ~ (unsigned HOST_WIDE_INT) 0; | |
| 489 } | |
| 490 else | |
| 491 lidx--; | |
| 492 | |
| 493 /* Numerator *= Index. */ | |
| 494 if (mul_double (lnum, hnum, lidx, hidx, &lnum, &hnum)) | |
| 495 return NULL_TREE; | |
| 496 | |
| 497 /* Denominator *= i. */ | |
| 498 mul_double (ldenom, hdenom, i, 0, &ldenom, &hdenom); | |
| 499 } | |
| 500 | |
| 501 /* Result = Numerator / Denominator. */ | |
| 502 div_and_round_double (EXACT_DIV_EXPR, 1, lnum, hnum, ldenom, hdenom, | |
| 503 &lres, &hres, &ldum, &hdum); | |
| 504 | |
| 505 res = build_int_cst_wide (type, lres, hres); | |
| 506 return int_fits_type_p (res, type) ? res : NULL_TREE; | |
| 507 } | |
| 508 | |
| 509 /* Helper function. Use the Newton's interpolating formula for | |
| 510 evaluating the value of the evolution function. */ | |
| 511 | |
| 512 static tree | |
| 513 chrec_evaluate (unsigned var, tree chrec, tree n, unsigned int k) | |
| 514 { | |
| 515 tree arg0, arg1, binomial_n_k; | |
| 516 tree type = TREE_TYPE (chrec); | |
| 517 struct loop *var_loop = get_loop (var); | |
| 518 | |
| 519 while (TREE_CODE (chrec) == POLYNOMIAL_CHREC | |
| 520 && flow_loop_nested_p (var_loop, get_chrec_loop (chrec))) | |
| 521 chrec = CHREC_LEFT (chrec); | |
| 522 | |
| 523 if (TREE_CODE (chrec) == POLYNOMIAL_CHREC | |
| 524 && CHREC_VARIABLE (chrec) == var) | |
| 525 { | |
| 526 arg1 = chrec_evaluate (var, CHREC_RIGHT (chrec), n, k + 1); | |
| 527 if (arg1 == chrec_dont_know) | |
| 528 return chrec_dont_know; | |
| 529 binomial_n_k = tree_fold_binomial (type, n, k); | |
| 530 if (!binomial_n_k) | |
| 531 return chrec_dont_know; | |
| 532 arg0 = fold_build2 (MULT_EXPR, type, | |
| 533 CHREC_LEFT (chrec), binomial_n_k); | |
| 534 return chrec_fold_plus (type, arg0, arg1); | |
| 535 } | |
| 536 | |
| 537 binomial_n_k = tree_fold_binomial (type, n, k); | |
| 538 if (!binomial_n_k) | |
| 539 return chrec_dont_know; | |
| 540 | |
| 541 return fold_build2 (MULT_EXPR, type, chrec, binomial_n_k); | |
| 542 } | |
| 543 | |
| 544 /* Evaluates "CHREC (X)" when the varying variable is VAR. | |
| 545 Example: Given the following parameters, | |
| 546 | |
| 547 var = 1 | |
| 548 chrec = {3, +, 4}_1 | |
| 549 x = 10 | |
| 550 | |
| 551 The result is given by the Newton's interpolating formula: | |
| 552 3 * \binom{10}{0} + 4 * \binom{10}{1}. | |
| 553 */ | |
| 554 | |
| 555 tree | |
| 556 chrec_apply (unsigned var, | |
| 557 tree chrec, | |
| 558 tree x) | |
| 559 { | |
| 560 tree type = chrec_type (chrec); | |
| 561 tree res = chrec_dont_know; | |
| 562 | |
| 563 if (automatically_generated_chrec_p (chrec) | |
| 564 || automatically_generated_chrec_p (x) | |
| 565 | |
| 566 /* When the symbols are defined in an outer loop, it is possible | |
| 567 to symbolically compute the apply, since the symbols are | |
| 568 constants with respect to the varying loop. */ | |
| 569 || chrec_contains_symbols_defined_in_loop (chrec, var)) | |
| 570 return chrec_dont_know; | |
| 571 | |
| 572 if (dump_file && (dump_flags & TDF_DETAILS)) | |
| 573 fprintf (dump_file, "(chrec_apply \n"); | |
| 574 | |
| 575 if (TREE_CODE (x) == INTEGER_CST && SCALAR_FLOAT_TYPE_P (type)) | |
| 576 x = build_real_from_int_cst (type, x); | |
| 577 | |
| 578 if (evolution_function_is_affine_p (chrec)) | |
| 579 { | |
| 580 /* "{a, +, b} (x)" -> "a + b*x". */ | |
| 581 x = chrec_convert_rhs (type, x, NULL); | |
| 582 res = chrec_fold_multiply (TREE_TYPE (x), CHREC_RIGHT (chrec), x); | |
| 583 res = chrec_fold_plus (type, CHREC_LEFT (chrec), res); | |
| 584 } | |
| 585 | |
| 586 else if (TREE_CODE (chrec) != POLYNOMIAL_CHREC) | |
| 587 res = chrec; | |
| 588 | |
| 589 else if (TREE_CODE (x) == INTEGER_CST | |
| 590 && tree_int_cst_sgn (x) == 1) | |
| 591 /* testsuite/.../ssa-chrec-38.c. */ | |
| 592 res = chrec_evaluate (var, chrec, x, 0); | |
| 593 else | |
| 594 res = chrec_dont_know; | |
| 595 | |
| 596 if (dump_file && (dump_flags & TDF_DETAILS)) | |
| 597 { | |
| 598 fprintf (dump_file, " (varying_loop = %d\n", var); | |
| 599 fprintf (dump_file, ")\n (chrec = "); | |
| 600 print_generic_expr (dump_file, chrec, 0); | |
| 601 fprintf (dump_file, ")\n (x = "); | |
| 602 print_generic_expr (dump_file, x, 0); | |
| 603 fprintf (dump_file, ")\n (res = "); | |
| 604 print_generic_expr (dump_file, res, 0); | |
| 605 fprintf (dump_file, "))\n"); | |
| 606 } | |
| 607 | |
| 608 return res; | |
| 609 } | |
| 610 | |
| 611 /* Replaces the initial condition in CHREC with INIT_COND. */ | |
| 612 | |
| 613 tree | |
| 614 chrec_replace_initial_condition (tree chrec, | |
| 615 tree init_cond) | |
| 616 { | |
| 617 if (automatically_generated_chrec_p (chrec)) | |
| 618 return chrec; | |
| 619 | |
| 620 gcc_assert (chrec_type (chrec) == chrec_type (init_cond)); | |
| 621 | |
| 622 switch (TREE_CODE (chrec)) | |
| 623 { | |
| 624 case POLYNOMIAL_CHREC: | |
| 625 return build_polynomial_chrec | |
| 626 (CHREC_VARIABLE (chrec), | |
| 627 chrec_replace_initial_condition (CHREC_LEFT (chrec), init_cond), | |
| 628 CHREC_RIGHT (chrec)); | |
| 629 | |
| 630 default: | |
| 631 return init_cond; | |
| 632 } | |
| 633 } | |
| 634 | |
| 635 /* Returns the initial condition of a given CHREC. */ | |
| 636 | |
| 637 tree | |
| 638 initial_condition (tree chrec) | |
| 639 { | |
| 640 if (automatically_generated_chrec_p (chrec)) | |
| 641 return chrec; | |
| 642 | |
| 643 if (TREE_CODE (chrec) == POLYNOMIAL_CHREC) | |
| 644 return initial_condition (CHREC_LEFT (chrec)); | |
| 645 else | |
| 646 return chrec; | |
| 647 } | |
| 648 | |
| 649 /* Returns a univariate function that represents the evolution in | |
| 650 LOOP_NUM. Mask the evolution of any other loop. */ | |
| 651 | |
| 652 tree | |
| 653 hide_evolution_in_other_loops_than_loop (tree chrec, | |
| 654 unsigned loop_num) | |
| 655 { | |
| 656 struct loop *loop = get_loop (loop_num), *chloop; | |
| 657 if (automatically_generated_chrec_p (chrec)) | |
| 658 return chrec; | |
| 659 | |
| 660 switch (TREE_CODE (chrec)) | |
| 661 { | |
| 662 case POLYNOMIAL_CHREC: | |
| 663 chloop = get_chrec_loop (chrec); | |
| 664 | |
| 665 if (chloop == loop) | |
| 666 return build_polynomial_chrec | |
| 667 (loop_num, | |
| 668 hide_evolution_in_other_loops_than_loop (CHREC_LEFT (chrec), | |
| 669 loop_num), | |
| 670 CHREC_RIGHT (chrec)); | |
| 671 | |
| 672 else if (flow_loop_nested_p (chloop, loop)) | |
| 673 /* There is no evolution in this loop. */ | |
| 674 return initial_condition (chrec); | |
| 675 | |
| 676 else | |
| 677 { | |
| 678 gcc_assert (flow_loop_nested_p (loop, chloop)); | |
| 679 return hide_evolution_in_other_loops_than_loop (CHREC_LEFT (chrec), | |
| 680 loop_num); | |
| 681 } | |
| 682 | |
| 683 default: | |
| 684 return chrec; | |
| 685 } | |
| 686 } | |
| 687 | |
| 688 /* Returns the evolution part of CHREC in LOOP_NUM when RIGHT is | |
| 689 true, otherwise returns the initial condition in LOOP_NUM. */ | |
| 690 | |
| 691 static tree | |
| 692 chrec_component_in_loop_num (tree chrec, | |
| 693 unsigned loop_num, | |
| 694 bool right) | |
| 695 { | |
| 696 tree component; | |
| 697 struct loop *loop = get_loop (loop_num), *chloop; | |
| 698 | |
| 699 if (automatically_generated_chrec_p (chrec)) | |
| 700 return chrec; | |
| 701 | |
| 702 switch (TREE_CODE (chrec)) | |
| 703 { | |
| 704 case POLYNOMIAL_CHREC: | |
| 705 chloop = get_chrec_loop (chrec); | |
| 706 | |
| 707 if (chloop == loop) | |
| 708 { | |
| 709 if (right) | |
| 710 component = CHREC_RIGHT (chrec); | |
| 711 else | |
| 712 component = CHREC_LEFT (chrec); | |
| 713 | |
| 714 if (TREE_CODE (CHREC_LEFT (chrec)) != POLYNOMIAL_CHREC | |
| 715 || CHREC_VARIABLE (CHREC_LEFT (chrec)) != CHREC_VARIABLE (chrec)) | |
| 716 return component; | |
| 717 | |
| 718 else | |
| 719 return build_polynomial_chrec | |
| 720 (loop_num, | |
| 721 chrec_component_in_loop_num (CHREC_LEFT (chrec), | |
| 722 loop_num, | |
| 723 right), | |
| 724 component); | |
| 725 } | |
| 726 | |
| 727 else if (flow_loop_nested_p (chloop, loop)) | |
| 728 /* There is no evolution part in this loop. */ | |
| 729 return NULL_TREE; | |
| 730 | |
| 731 else | |
| 732 { | |
| 733 gcc_assert (flow_loop_nested_p (loop, chloop)); | |
| 734 return chrec_component_in_loop_num (CHREC_LEFT (chrec), | |
| 735 loop_num, | |
| 736 right); | |
| 737 } | |
| 738 | |
| 739 default: | |
| 740 if (right) | |
| 741 return NULL_TREE; | |
| 742 else | |
| 743 return chrec; | |
| 744 } | |
| 745 } | |
| 746 | |
| 747 /* Returns the evolution part in LOOP_NUM. Example: the call | |
| 748 evolution_part_in_loop_num ({{0, +, 1}_1, +, 2}_1, 1) returns | |
| 749 {1, +, 2}_1 */ | |
| 750 | |
| 751 tree | |
| 752 evolution_part_in_loop_num (tree chrec, | |
| 753 unsigned loop_num) | |
| 754 { | |
| 755 return chrec_component_in_loop_num (chrec, loop_num, true); | |
| 756 } | |
| 757 | |
| 758 /* Returns the initial condition in LOOP_NUM. Example: the call | |
| 759 initial_condition_in_loop_num ({{0, +, 1}_1, +, 2}_2, 2) returns | |
| 760 {0, +, 1}_1 */ | |
| 761 | |
| 762 tree | |
| 763 initial_condition_in_loop_num (tree chrec, | |
| 764 unsigned loop_num) | |
| 765 { | |
| 766 return chrec_component_in_loop_num (chrec, loop_num, false); | |
| 767 } | |
| 768 | |
| 769 /* Set or reset the evolution of CHREC to NEW_EVOL in loop LOOP_NUM. | |
| 770 This function is essentially used for setting the evolution to | |
| 771 chrec_dont_know, for example after having determined that it is | |
| 772 impossible to say how many times a loop will execute. */ | |
| 773 | |
| 774 tree | |
| 775 reset_evolution_in_loop (unsigned loop_num, | |
| 776 tree chrec, | |
| 777 tree new_evol) | |
| 778 { | |
| 779 struct loop *loop = get_loop (loop_num); | |
| 780 | |
| 781 if (POINTER_TYPE_P (chrec_type (chrec))) | |
| 782 gcc_assert (sizetype == chrec_type (new_evol)); | |
| 783 else | |
| 784 gcc_assert (chrec_type (chrec) == chrec_type (new_evol)); | |
| 785 | |
| 786 if (TREE_CODE (chrec) == POLYNOMIAL_CHREC | |
| 787 && flow_loop_nested_p (loop, get_chrec_loop (chrec))) | |
| 788 { | |
| 789 tree left = reset_evolution_in_loop (loop_num, CHREC_LEFT (chrec), | |
| 790 new_evol); | |
| 791 tree right = reset_evolution_in_loop (loop_num, CHREC_RIGHT (chrec), | |
| 792 new_evol); | |
| 793 return build3 (POLYNOMIAL_CHREC, TREE_TYPE (left), | |
| 794 build_int_cst (NULL_TREE, CHREC_VARIABLE (chrec)), | |
| 795 left, right); | |
| 796 } | |
| 797 | |
| 798 while (TREE_CODE (chrec) == POLYNOMIAL_CHREC | |
| 799 && CHREC_VARIABLE (chrec) == loop_num) | |
| 800 chrec = CHREC_LEFT (chrec); | |
| 801 | |
| 802 return build_polynomial_chrec (loop_num, chrec, new_evol); | |
| 803 } | |
| 804 | |
| 805 /* Merges two evolution functions that were found by following two | |
| 806 alternate paths of a conditional expression. */ | |
| 807 | |
| 808 tree | |
| 809 chrec_merge (tree chrec1, | |
| 810 tree chrec2) | |
| 811 { | |
| 812 if (chrec1 == chrec_dont_know | |
| 813 || chrec2 == chrec_dont_know) | |
| 814 return chrec_dont_know; | |
| 815 | |
| 816 if (chrec1 == chrec_known | |
| 817 || chrec2 == chrec_known) | |
| 818 return chrec_known; | |
| 819 | |
| 820 if (chrec1 == chrec_not_analyzed_yet) | |
| 821 return chrec2; | |
| 822 if (chrec2 == chrec_not_analyzed_yet) | |
| 823 return chrec1; | |
| 824 | |
| 825 if (eq_evolutions_p (chrec1, chrec2)) | |
| 826 return chrec1; | |
| 827 | |
| 828 return chrec_dont_know; | |
| 829 } | |
| 830 | |
| 831 | |
| 832 | |
| 833 /* Observers. */ | |
| 834 | |
| 835 /* Helper function for is_multivariate_chrec. */ | |
| 836 | |
| 837 static bool | |
| 838 is_multivariate_chrec_rec (const_tree chrec, unsigned int rec_var) | |
| 839 { | |
| 840 if (chrec == NULL_TREE) | |
| 841 return false; | |
| 842 | |
| 843 if (TREE_CODE (chrec) == POLYNOMIAL_CHREC) | |
| 844 { | |
| 845 if (CHREC_VARIABLE (chrec) != rec_var) | |
| 846 return true; | |
| 847 else | |
| 848 return (is_multivariate_chrec_rec (CHREC_LEFT (chrec), rec_var) | |
| 849 || is_multivariate_chrec_rec (CHREC_RIGHT (chrec), rec_var)); | |
| 850 } | |
| 851 else | |
| 852 return false; | |
| 853 } | |
| 854 | |
| 855 /* Determine whether the given chrec is multivariate or not. */ | |
| 856 | |
| 857 bool | |
| 858 is_multivariate_chrec (const_tree chrec) | |
| 859 { | |
| 860 if (chrec == NULL_TREE) | |
| 861 return false; | |
| 862 | |
| 863 if (TREE_CODE (chrec) == POLYNOMIAL_CHREC) | |
| 864 return (is_multivariate_chrec_rec (CHREC_LEFT (chrec), | |
| 865 CHREC_VARIABLE (chrec)) | |
| 866 || is_multivariate_chrec_rec (CHREC_RIGHT (chrec), | |
| 867 CHREC_VARIABLE (chrec))); | |
| 868 else | |
| 869 return false; | |
| 870 } | |
| 871 | |
| 872 /* Determines whether the chrec contains symbolic names or not. */ | |
| 873 | |
| 874 bool | |
| 875 chrec_contains_symbols (const_tree chrec) | |
| 876 { | |
| 877 int i, n; | |
| 878 | |
| 879 if (chrec == NULL_TREE) | |
| 880 return false; | |
| 881 | |
| 882 if (TREE_CODE (chrec) == SSA_NAME | |
| 883 || TREE_CODE (chrec) == VAR_DECL | |
| 884 || TREE_CODE (chrec) == PARM_DECL | |
| 885 || TREE_CODE (chrec) == FUNCTION_DECL | |
| 886 || TREE_CODE (chrec) == LABEL_DECL | |
| 887 || TREE_CODE (chrec) == RESULT_DECL | |
| 888 || TREE_CODE (chrec) == FIELD_DECL) | |
| 889 return true; | |
| 890 | |
| 891 n = TREE_OPERAND_LENGTH (chrec); | |
| 892 for (i = 0; i < n; i++) | |
| 893 if (chrec_contains_symbols (TREE_OPERAND (chrec, i))) | |
| 894 return true; | |
| 895 return false; | |
| 896 } | |
| 897 | |
| 898 /* Determines whether the chrec contains undetermined coefficients. */ | |
| 899 | |
| 900 bool | |
| 901 chrec_contains_undetermined (const_tree chrec) | |
| 902 { | |
| 903 int i, n; | |
| 904 | |
| 905 if (chrec == chrec_dont_know) | |
| 906 return true; | |
| 907 | |
| 908 if (chrec == NULL_TREE) | |
| 909 return false; | |
| 910 | |
| 911 n = TREE_OPERAND_LENGTH (chrec); | |
| 912 for (i = 0; i < n; i++) | |
| 913 if (chrec_contains_undetermined (TREE_OPERAND (chrec, i))) | |
| 914 return true; | |
| 915 return false; | |
| 916 } | |
| 917 | |
| 918 /* Determines whether the tree EXPR contains chrecs, and increment | |
| 919 SIZE if it is not a NULL pointer by an estimation of the depth of | |
| 920 the tree. */ | |
| 921 | |
| 922 bool | |
| 923 tree_contains_chrecs (const_tree expr, int *size) | |
| 924 { | |
| 925 int i, n; | |
| 926 | |
| 927 if (expr == NULL_TREE) | |
| 928 return false; | |
| 929 | |
| 930 if (size) | |
| 931 (*size)++; | |
| 932 | |
| 933 if (tree_is_chrec (expr)) | |
| 934 return true; | |
| 935 | |
| 936 n = TREE_OPERAND_LENGTH (expr); | |
| 937 for (i = 0; i < n; i++) | |
| 938 if (tree_contains_chrecs (TREE_OPERAND (expr, i), size)) | |
| 939 return true; | |
| 940 return false; | |
| 941 } | |
| 942 | |
| 943 /* Recursive helper function. */ | |
| 944 | |
| 945 static bool | |
| 946 evolution_function_is_invariant_rec_p (tree chrec, int loopnum) | |
| 947 { | |
| 948 if (evolution_function_is_constant_p (chrec)) | |
| 949 return true; | |
| 950 | |
| 951 if (TREE_CODE (chrec) == SSA_NAME | |
| 952 && (loopnum == 0 | |
| 953 || expr_invariant_in_loop_p (get_loop (loopnum), chrec))) | |
| 954 return true; | |
| 955 | |
| 956 if (TREE_CODE (chrec) == POLYNOMIAL_CHREC) | |
| 957 { | |
| 958 if (CHREC_VARIABLE (chrec) == (unsigned) loopnum | |
| 959 || !evolution_function_is_invariant_rec_p (CHREC_RIGHT (chrec), | |
| 960 loopnum) | |
| 961 || !evolution_function_is_invariant_rec_p (CHREC_LEFT (chrec), | |
| 962 loopnum)) | |
| 963 return false; | |
| 964 return true; | |
| 965 } | |
| 966 | |
| 967 switch (TREE_OPERAND_LENGTH (chrec)) | |
| 968 { | |
| 969 case 2: | |
| 970 if (!evolution_function_is_invariant_rec_p (TREE_OPERAND (chrec, 1), | |
| 971 loopnum)) | |
| 972 return false; | |
| 973 | |
| 974 case 1: | |
| 975 if (!evolution_function_is_invariant_rec_p (TREE_OPERAND (chrec, 0), | |
| 976 loopnum)) | |
| 977 return false; | |
| 978 return true; | |
| 979 | |
| 980 default: | |
| 981 return false; | |
| 982 } | |
| 983 | |
| 984 return false; | |
| 985 } | |
| 986 | |
| 987 /* Return true if CHREC is invariant in loop LOOPNUM, false otherwise. */ | |
| 988 | |
| 989 bool | |
| 990 evolution_function_is_invariant_p (tree chrec, int loopnum) | |
| 991 { | |
| 992 return evolution_function_is_invariant_rec_p (chrec, loopnum); | |
| 993 } | |
| 994 | |
| 995 /* Determine whether the given tree is an affine multivariate | |
| 996 evolution. */ | |
| 997 | |
| 998 bool | |
| 999 evolution_function_is_affine_multivariate_p (const_tree chrec, int loopnum) | |
| 1000 { | |
| 1001 if (chrec == NULL_TREE) | |
| 1002 return false; | |
| 1003 | |
| 1004 switch (TREE_CODE (chrec)) | |
| 1005 { | |
| 1006 case POLYNOMIAL_CHREC: | |
| 1007 if (evolution_function_is_invariant_rec_p (CHREC_LEFT (chrec), loopnum)) | |
| 1008 { | |
| 1009 if (evolution_function_is_invariant_rec_p (CHREC_RIGHT (chrec), loopnum)) | |
| 1010 return true; | |
| 1011 else | |
| 1012 { | |
| 1013 if (TREE_CODE (CHREC_RIGHT (chrec)) == POLYNOMIAL_CHREC | |
| 1014 && CHREC_VARIABLE (CHREC_RIGHT (chrec)) | |
| 1015 != CHREC_VARIABLE (chrec) | |
| 1016 && evolution_function_is_affine_multivariate_p | |
| 1017 (CHREC_RIGHT (chrec), loopnum)) | |
| 1018 return true; | |
| 1019 else | |
| 1020 return false; | |
| 1021 } | |
| 1022 } | |
| 1023 else | |
| 1024 { | |
| 1025 if (evolution_function_is_invariant_rec_p (CHREC_RIGHT (chrec), loopnum) | |
| 1026 && TREE_CODE (CHREC_LEFT (chrec)) == POLYNOMIAL_CHREC | |
| 1027 && CHREC_VARIABLE (CHREC_LEFT (chrec)) != CHREC_VARIABLE (chrec) | |
| 1028 && evolution_function_is_affine_multivariate_p | |
| 1029 (CHREC_LEFT (chrec), loopnum)) | |
| 1030 return true; | |
| 1031 else | |
| 1032 return false; | |
| 1033 } | |
| 1034 | |
| 1035 default: | |
| 1036 return false; | |
| 1037 } | |
| 1038 } | |
| 1039 | |
| 1040 /* Determine whether the given tree is a function in zero or one | |
| 1041 variables. */ | |
| 1042 | |
| 1043 bool | |
| 1044 evolution_function_is_univariate_p (const_tree chrec) | |
| 1045 { | |
| 1046 if (chrec == NULL_TREE) | |
| 1047 return true; | |
| 1048 | |
| 1049 switch (TREE_CODE (chrec)) | |
| 1050 { | |
| 1051 case POLYNOMIAL_CHREC: | |
| 1052 switch (TREE_CODE (CHREC_LEFT (chrec))) | |
| 1053 { | |
| 1054 case POLYNOMIAL_CHREC: | |
| 1055 if (CHREC_VARIABLE (chrec) != CHREC_VARIABLE (CHREC_LEFT (chrec))) | |
| 1056 return false; | |
| 1057 if (!evolution_function_is_univariate_p (CHREC_LEFT (chrec))) | |
| 1058 return false; | |
| 1059 break; | |
| 1060 | |
| 1061 default: | |
| 1062 break; | |
| 1063 } | |
| 1064 | |
| 1065 switch (TREE_CODE (CHREC_RIGHT (chrec))) | |
| 1066 { | |
| 1067 case POLYNOMIAL_CHREC: | |
| 1068 if (CHREC_VARIABLE (chrec) != CHREC_VARIABLE (CHREC_RIGHT (chrec))) | |
| 1069 return false; | |
| 1070 if (!evolution_function_is_univariate_p (CHREC_RIGHT (chrec))) | |
| 1071 return false; | |
| 1072 break; | |
| 1073 | |
| 1074 default: | |
| 1075 break; | |
| 1076 } | |
| 1077 | |
| 1078 default: | |
| 1079 return true; | |
| 1080 } | |
| 1081 } | |
| 1082 | |
| 1083 /* Returns the number of variables of CHREC. Example: the call | |
| 1084 nb_vars_in_chrec ({{0, +, 1}_5, +, 2}_6) returns 2. */ | |
| 1085 | |
| 1086 unsigned | |
| 1087 nb_vars_in_chrec (tree chrec) | |
| 1088 { | |
| 1089 if (chrec == NULL_TREE) | |
| 1090 return 0; | |
| 1091 | |
| 1092 switch (TREE_CODE (chrec)) | |
| 1093 { | |
| 1094 case POLYNOMIAL_CHREC: | |
| 1095 return 1 + nb_vars_in_chrec | |
| 1096 (initial_condition_in_loop_num (chrec, CHREC_VARIABLE (chrec))); | |
| 1097 | |
| 1098 default: | |
| 1099 return 0; | |
| 1100 } | |
| 1101 } | |
| 1102 | |
| 1103 /* Returns true if TYPE is a type in that we cannot directly perform | |
| 1104 arithmetics, even though it is a scalar type. */ | |
| 1105 | |
| 1106 static bool | |
| 1107 avoid_arithmetics_in_type_p (const_tree type) | |
| 1108 { | |
| 1109 /* Ada frontend uses subtypes -- an arithmetic cannot be directly performed | |
| 1110 in the subtype, but a base type must be used, and the result then can | |
| 1111 be casted to the subtype. */ | |
| 1112 if (TREE_CODE (type) == INTEGER_TYPE && TREE_TYPE (type) != NULL_TREE) | |
| 1113 return true; | |
| 1114 | |
| 1115 return false; | |
| 1116 } | |
| 1117 | |
| 1118 static tree chrec_convert_1 (tree, tree, gimple, bool); | |
| 1119 | |
| 1120 /* Converts BASE and STEP of affine scev to TYPE. LOOP is the loop whose iv | |
| 1121 the scev corresponds to. AT_STMT is the statement at that the scev is | |
| 1122 evaluated. USE_OVERFLOW_SEMANTICS is true if this function should assume that | |
| 1123 the rules for overflow of the given language apply (e.g., that signed | |
| 1124 arithmetics in C does not overflow) -- i.e., to use them to avoid unnecessary | |
| 1125 tests, but also to enforce that the result follows them. Returns true if the | |
| 1126 conversion succeeded, false otherwise. */ | |
| 1127 | |
| 1128 bool | |
| 1129 convert_affine_scev (struct loop *loop, tree type, | |
| 1130 tree *base, tree *step, gimple at_stmt, | |
| 1131 bool use_overflow_semantics) | |
| 1132 { | |
| 1133 tree ct = TREE_TYPE (*step); | |
| 1134 bool enforce_overflow_semantics; | |
| 1135 bool must_check_src_overflow, must_check_rslt_overflow; | |
| 1136 tree new_base, new_step; | |
| 1137 tree step_type = POINTER_TYPE_P (type) ? sizetype : type; | |
| 1138 | |
| 1139 /* If we cannot perform arithmetic in TYPE, avoid creating an scev. */ | |
| 1140 if (avoid_arithmetics_in_type_p (type)) | |
| 1141 return false; | |
| 1142 | |
| 1143 /* In general, | |
| 1144 (TYPE) (BASE + STEP * i) = (TYPE) BASE + (TYPE -- sign extend) STEP * i, | |
| 1145 but we must check some assumptions. | |
| 1146 | |
| 1147 1) If [BASE, +, STEP] wraps, the equation is not valid when precision | |
| 1148 of CT is smaller than the precision of TYPE. For example, when we | |
| 1149 cast unsigned char [254, +, 1] to unsigned, the values on left side | |
| 1150 are 254, 255, 0, 1, ..., but those on the right side are | |
| 1151 254, 255, 256, 257, ... | |
| 1152 2) In case that we must also preserve the fact that signed ivs do not | |
| 1153 overflow, we must additionally check that the new iv does not wrap. | |
| 1154 For example, unsigned char [125, +, 1] casted to signed char could | |
| 1155 become a wrapping variable with values 125, 126, 127, -128, -127, ..., | |
| 1156 which would confuse optimizers that assume that this does not | |
| 1157 happen. */ | |
| 1158 must_check_src_overflow = TYPE_PRECISION (ct) < TYPE_PRECISION (type); | |
| 1159 | |
| 1160 enforce_overflow_semantics = (use_overflow_semantics | |
| 1161 && nowrap_type_p (type)); | |
| 1162 if (enforce_overflow_semantics) | |
| 1163 { | |
| 1164 /* We can avoid checking whether the result overflows in the following | |
| 1165 cases: | |
| 1166 | |
| 1167 -- must_check_src_overflow is true, and the range of TYPE is superset | |
| 1168 of the range of CT -- i.e., in all cases except if CT signed and | |
| 1169 TYPE unsigned. | |
| 1170 -- both CT and TYPE have the same precision and signedness, and we | |
| 1171 verify instead that the source does not overflow (this may be | |
| 1172 easier than verifying it for the result, as we may use the | |
| 1173 information about the semantics of overflow in CT). */ | |
| 1174 if (must_check_src_overflow) | |
| 1175 { | |
| 1176 if (TYPE_UNSIGNED (type) && !TYPE_UNSIGNED (ct)) | |
| 1177 must_check_rslt_overflow = true; | |
| 1178 else | |
| 1179 must_check_rslt_overflow = false; | |
| 1180 } | |
| 1181 else if (TYPE_UNSIGNED (ct) == TYPE_UNSIGNED (type) | |
| 1182 && TYPE_PRECISION (ct) == TYPE_PRECISION (type)) | |
| 1183 { | |
| 1184 must_check_rslt_overflow = false; | |
| 1185 must_check_src_overflow = true; | |
| 1186 } | |
| 1187 else | |
| 1188 must_check_rslt_overflow = true; | |
| 1189 } | |
| 1190 else | |
| 1191 must_check_rslt_overflow = false; | |
| 1192 | |
| 1193 if (must_check_src_overflow | |
| 1194 && scev_probably_wraps_p (*base, *step, at_stmt, loop, | |
| 1195 use_overflow_semantics)) | |
| 1196 return false; | |
| 1197 | |
| 1198 new_base = chrec_convert_1 (type, *base, at_stmt, | |
| 1199 use_overflow_semantics); | |
| 1200 /* The step must be sign extended, regardless of the signedness | |
| 1201 of CT and TYPE. This only needs to be handled specially when | |
| 1202 CT is unsigned -- to avoid e.g. unsigned char [100, +, 255] | |
| 1203 (with values 100, 99, 98, ...) from becoming signed or unsigned | |
| 1204 [100, +, 255] with values 100, 355, ...; the sign-extension is | |
| 1205 performed by default when CT is signed. */ | |
| 1206 new_step = *step; | |
| 1207 if (TYPE_PRECISION (step_type) > TYPE_PRECISION (ct) && TYPE_UNSIGNED (ct)) | |
| 1208 new_step = chrec_convert_1 (signed_type_for (ct), new_step, at_stmt, | |
| 1209 use_overflow_semantics); | |
| 1210 new_step = chrec_convert_1 (step_type, new_step, at_stmt, use_overflow_semantics); | |
| 1211 | |
| 1212 if (automatically_generated_chrec_p (new_base) | |
| 1213 || automatically_generated_chrec_p (new_step)) | |
| 1214 return false; | |
| 1215 | |
| 1216 if (must_check_rslt_overflow | |
| 1217 /* Note that in this case we cannot use the fact that signed variables | |
| 1218 do not overflow, as this is what we are verifying for the new iv. */ | |
| 1219 && scev_probably_wraps_p (new_base, new_step, at_stmt, loop, false)) | |
| 1220 return false; | |
| 1221 | |
| 1222 *base = new_base; | |
| 1223 *step = new_step; | |
| 1224 return true; | |
| 1225 } | |
| 1226 | |
| 1227 | |
| 1228 /* Convert CHREC for the right hand side of a CREC. | |
| 1229 The increment for a pointer type is always sizetype. */ | |
| 1230 tree | |
| 1231 chrec_convert_rhs (tree type, tree chrec, gimple at_stmt) | |
| 1232 { | |
| 1233 if (POINTER_TYPE_P (type)) | |
| 1234 type = sizetype; | |
| 1235 return chrec_convert (type, chrec, at_stmt); | |
| 1236 } | |
| 1237 | |
| 1238 /* Convert CHREC to TYPE. When the analyzer knows the context in | |
| 1239 which the CHREC is built, it sets AT_STMT to the statement that | |
| 1240 contains the definition of the analyzed variable, otherwise the | |
| 1241 conversion is less accurate: the information is used for | |
| 1242 determining a more accurate estimation of the number of iterations. | |
| 1243 By default AT_STMT could be safely set to NULL_TREE. | |
| 1244 | |
| 1245 The following rule is always true: TREE_TYPE (chrec) == | |
| 1246 TREE_TYPE (CHREC_LEFT (chrec)) == TREE_TYPE (CHREC_RIGHT (chrec)). | |
| 1247 An example of what could happen when adding two chrecs and the type | |
| 1248 of the CHREC_RIGHT is different than CHREC_LEFT is: | |
| 1249 | |
| 1250 {(uint) 0, +, (uchar) 10} + | |
| 1251 {(uint) 0, +, (uchar) 250} | |
| 1252 | |
| 1253 that would produce a wrong result if CHREC_RIGHT is not (uint): | |
| 1254 | |
| 1255 {(uint) 0, +, (uchar) 4} | |
| 1256 | |
| 1257 instead of | |
| 1258 | |
| 1259 {(uint) 0, +, (uint) 260} | |
| 1260 */ | |
| 1261 | |
| 1262 tree | |
| 1263 chrec_convert (tree type, tree chrec, gimple at_stmt) | |
| 1264 { | |
| 1265 return chrec_convert_1 (type, chrec, at_stmt, true); | |
| 1266 } | |
| 1267 | |
| 1268 /* Convert CHREC to TYPE. When the analyzer knows the context in | |
| 1269 which the CHREC is built, it sets AT_STMT to the statement that | |
| 1270 contains the definition of the analyzed variable, otherwise the | |
| 1271 conversion is less accurate: the information is used for | |
| 1272 determining a more accurate estimation of the number of iterations. | |
| 1273 By default AT_STMT could be safely set to NULL_TREE. | |
| 1274 | |
| 1275 USE_OVERFLOW_SEMANTICS is true if this function should assume that | |
| 1276 the rules for overflow of the given language apply (e.g., that signed | |
| 1277 arithmetics in C does not overflow) -- i.e., to use them to avoid unnecessary | |
| 1278 tests, but also to enforce that the result follows them. */ | |
| 1279 | |
| 1280 static tree | |
| 1281 chrec_convert_1 (tree type, tree chrec, gimple at_stmt, | |
| 1282 bool use_overflow_semantics) | |
| 1283 { | |
| 1284 tree ct, res; | |
| 1285 tree base, step; | |
| 1286 struct loop *loop; | |
| 1287 | |
| 1288 if (automatically_generated_chrec_p (chrec)) | |
| 1289 return chrec; | |
| 1290 | |
| 1291 ct = chrec_type (chrec); | |
| 1292 if (ct == type) | |
| 1293 return chrec; | |
| 1294 | |
| 1295 if (!evolution_function_is_affine_p (chrec)) | |
| 1296 goto keep_cast; | |
| 1297 | |
| 1298 loop = get_chrec_loop (chrec); | |
| 1299 base = CHREC_LEFT (chrec); | |
| 1300 step = CHREC_RIGHT (chrec); | |
| 1301 | |
| 1302 if (convert_affine_scev (loop, type, &base, &step, at_stmt, | |
| 1303 use_overflow_semantics)) | |
| 1304 return build_polynomial_chrec (loop->num, base, step); | |
| 1305 | |
| 1306 /* If we cannot propagate the cast inside the chrec, just keep the cast. */ | |
| 1307 keep_cast: | |
| 1308 res = fold_convert (type, chrec); | |
| 1309 | |
| 1310 /* Don't propagate overflows. */ | |
| 1311 if (CONSTANT_CLASS_P (res)) | |
| 1312 TREE_OVERFLOW (res) = 0; | |
| 1313 | |
| 1314 /* But reject constants that don't fit in their type after conversion. | |
| 1315 This can happen if TYPE_MIN_VALUE or TYPE_MAX_VALUE are not the | |
| 1316 natural values associated with TYPE_PRECISION and TYPE_UNSIGNED, | |
| 1317 and can cause problems later when computing niters of loops. Note | |
| 1318 that we don't do the check before converting because we don't want | |
| 1319 to reject conversions of negative chrecs to unsigned types. */ | |
| 1320 if (TREE_CODE (res) == INTEGER_CST | |
| 1321 && TREE_CODE (type) == INTEGER_TYPE | |
| 1322 && !int_fits_type_p (res, type)) | |
| 1323 res = chrec_dont_know; | |
| 1324 | |
| 1325 return res; | |
| 1326 } | |
| 1327 | |
| 1328 /* Convert CHREC to TYPE, without regard to signed overflows. Returns the new | |
| 1329 chrec if something else than what chrec_convert would do happens, NULL_TREE | |
| 1330 otherwise. */ | |
| 1331 | |
| 1332 tree | |
| 1333 chrec_convert_aggressive (tree type, tree chrec) | |
| 1334 { | |
| 1335 tree inner_type, left, right, lc, rc, rtype; | |
| 1336 | |
| 1337 if (automatically_generated_chrec_p (chrec) | |
| 1338 || TREE_CODE (chrec) != POLYNOMIAL_CHREC) | |
| 1339 return NULL_TREE; | |
| 1340 | |
| 1341 inner_type = TREE_TYPE (chrec); | |
| 1342 if (TYPE_PRECISION (type) > TYPE_PRECISION (inner_type)) | |
| 1343 return NULL_TREE; | |
| 1344 | |
| 1345 /* If we cannot perform arithmetic in TYPE, avoid creating an scev. */ | |
| 1346 if (avoid_arithmetics_in_type_p (type)) | |
| 1347 return NULL_TREE; | |
| 1348 | |
| 1349 rtype = POINTER_TYPE_P (type) ? sizetype : type; | |
| 1350 | |
| 1351 left = CHREC_LEFT (chrec); | |
| 1352 right = CHREC_RIGHT (chrec); | |
| 1353 lc = chrec_convert_aggressive (type, left); | |
| 1354 if (!lc) | |
| 1355 lc = chrec_convert (type, left, NULL); | |
| 1356 rc = chrec_convert_aggressive (rtype, right); | |
| 1357 if (!rc) | |
| 1358 rc = chrec_convert (rtype, right, NULL); | |
| 1359 | |
| 1360 return build_polynomial_chrec (CHREC_VARIABLE (chrec), lc, rc); | |
| 1361 } | |
| 1362 | |
| 1363 /* Returns true when CHREC0 == CHREC1. */ | |
| 1364 | |
| 1365 bool | |
| 1366 eq_evolutions_p (const_tree chrec0, const_tree chrec1) | |
| 1367 { | |
| 1368 if (chrec0 == NULL_TREE | |
| 1369 || chrec1 == NULL_TREE | |
| 1370 || TREE_CODE (chrec0) != TREE_CODE (chrec1)) | |
| 1371 return false; | |
| 1372 | |
| 1373 if (chrec0 == chrec1) | |
| 1374 return true; | |
| 1375 | |
| 1376 switch (TREE_CODE (chrec0)) | |
| 1377 { | |
| 1378 case INTEGER_CST: | |
| 1379 return operand_equal_p (chrec0, chrec1, 0); | |
| 1380 | |
| 1381 case POLYNOMIAL_CHREC: | |
| 1382 return (CHREC_VARIABLE (chrec0) == CHREC_VARIABLE (chrec1) | |
| 1383 && eq_evolutions_p (CHREC_LEFT (chrec0), CHREC_LEFT (chrec1)) | |
| 1384 && eq_evolutions_p (CHREC_RIGHT (chrec0), CHREC_RIGHT (chrec1))); | |
| 1385 default: | |
| 1386 return false; | |
| 1387 } | |
| 1388 } | |
| 1389 | |
| 1390 /* Returns EV_GROWS if CHREC grows (assuming that it does not overflow), | |
| 1391 EV_DECREASES if it decreases, and EV_UNKNOWN if we cannot determine | |
| 1392 which of these cases happens. */ | |
| 1393 | |
| 1394 enum ev_direction | |
| 1395 scev_direction (const_tree chrec) | |
| 1396 { | |
| 1397 const_tree step; | |
| 1398 | |
| 1399 if (!evolution_function_is_affine_p (chrec)) | |
| 1400 return EV_DIR_UNKNOWN; | |
| 1401 | |
| 1402 step = CHREC_RIGHT (chrec); | |
| 1403 if (TREE_CODE (step) != INTEGER_CST) | |
| 1404 return EV_DIR_UNKNOWN; | |
| 1405 | |
| 1406 if (tree_int_cst_sign_bit (step)) | |
| 1407 return EV_DIR_DECREASES; | |
| 1408 else | |
| 1409 return EV_DIR_GROWS; | |
| 1410 } | |
| 1411 | |
| 1412 /* Iterates over all the components of SCEV, and calls CBCK. */ | |
| 1413 | |
| 1414 void | |
| 1415 for_each_scev_op (tree *scev, bool (*cbck) (tree *, void *), void *data) | |
| 1416 { | |
| 1417 switch (TREE_CODE_LENGTH (TREE_CODE (*scev))) | |
| 1418 { | |
| 1419 case 3: | |
| 1420 for_each_scev_op (&TREE_OPERAND (*scev, 2), cbck, data); | |
| 1421 | |
| 1422 case 2: | |
| 1423 for_each_scev_op (&TREE_OPERAND (*scev, 1), cbck, data); | |
| 1424 | |
| 1425 case 1: | |
| 1426 for_each_scev_op (&TREE_OPERAND (*scev, 0), cbck, data); | |
| 1427 | |
| 1428 default: | |
| 1429 cbck (scev, data); | |
| 1430 break; | |
| 1431 } | |
| 1432 } | |
| 1433 | |
| 1434 /* Returns true when the operation can be part of a linear | |
| 1435 expression. */ | |
| 1436 | |
| 1437 static inline bool | |
| 1438 operator_is_linear (tree scev) | |
| 1439 { | |
| 1440 switch (TREE_CODE (scev)) | |
| 1441 { | |
| 1442 case INTEGER_CST: | |
| 1443 case POLYNOMIAL_CHREC: | |
| 1444 case PLUS_EXPR: | |
| 1445 case POINTER_PLUS_EXPR: | |
| 1446 case MULT_EXPR: | |
| 1447 case MINUS_EXPR: | |
| 1448 case NEGATE_EXPR: | |
| 1449 case SSA_NAME: | |
| 1450 case NON_LVALUE_EXPR: | |
| 1451 CASE_CONVERT: | |
| 1452 return true; | |
| 1453 | |
| 1454 default: | |
| 1455 return false; | |
| 1456 } | |
| 1457 } | |
| 1458 | |
| 1459 /* Return true when SCEV is a linear expression. Linear expressions | |
| 1460 can contain additions, substractions and multiplications. | |
| 1461 Multiplications are restricted to constant scaling: "cst * x". */ | |
| 1462 | |
| 1463 bool | |
| 1464 scev_is_linear_expression (tree scev) | |
| 1465 { | |
| 1466 if (scev == NULL | |
| 1467 || !operator_is_linear (scev)) | |
| 1468 return false; | |
| 1469 | |
| 1470 if (TREE_CODE (scev) == MULT_EXPR) | |
| 1471 return !(tree_contains_chrecs (TREE_OPERAND (scev, 0), NULL) | |
| 1472 && tree_contains_chrecs (TREE_OPERAND (scev, 1), NULL)); | |
| 1473 | |
| 1474 switch (TREE_CODE_LENGTH (TREE_CODE (scev))) | |
| 1475 { | |
| 1476 case 3: | |
| 1477 return scev_is_linear_expression (TREE_OPERAND (scev, 0)) | |
| 1478 && scev_is_linear_expression (TREE_OPERAND (scev, 1)) | |
| 1479 && scev_is_linear_expression (TREE_OPERAND (scev, 2)); | |
| 1480 | |
| 1481 case 2: | |
| 1482 return scev_is_linear_expression (TREE_OPERAND (scev, 0)) | |
| 1483 && scev_is_linear_expression (TREE_OPERAND (scev, 1)); | |
| 1484 | |
| 1485 case 1: | |
| 1486 return scev_is_linear_expression (TREE_OPERAND (scev, 0)); | |
| 1487 | |
| 1488 case 0: | |
| 1489 return true; | |
| 1490 | |
| 1491 default: | |
| 1492 return false; | |
| 1493 } | |
| 1494 } |