1 | /* Chains of recurrences. |
---|---|

2 | Copyright (C) 2003-2017 Free Software Foundation, Inc. |

3 | Contributed by Sebastian Pop <pop@cri.ensmp.fr> |

4 | |

5 | This file is part of GCC. |

6 | |

7 | GCC is free software; you can redistribute it and/or modify it under |

8 | the terms of the GNU General Public License as published by the Free |

9 | Software Foundation; either version 3, or (at your option) any later |

10 | version. |

11 | |

12 | GCC is distributed in the hope that it will be useful, but WITHOUT ANY |

13 | WARRANTY; without even the implied warranty of MERCHANTABILITY or |

14 | FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License |

15 | for more details. |

16 | |

17 | You should have received a copy of the GNU General Public License |

18 | along with GCC; see the file COPYING3. If not see |

19 | <http://www.gnu.org/licenses/>. */ |

20 | |

21 | /* This file implements operations on chains of recurrences. Chains |

22 | of recurrences are used for modeling evolution functions of scalar |

23 | variables. |

24 | */ |

25 | |

26 | #include "config.h" |

27 | #include "system.h" |

28 | #include "coretypes.h" |

29 | #include "backend.h" |

30 | #include "tree.h" |

31 | #include "gimple-expr.h" |

32 | #include "tree-pretty-print.h" |

33 | #include "fold-const.h" |

34 | #include "cfgloop.h" |

35 | #include "tree-ssa-loop-ivopts.h" |

36 | #include "tree-ssa-loop-niter.h" |

37 | #include "tree-chrec.h" |

38 | #include "dumpfile.h" |

39 | #include "params.h" |

40 | #include "tree-scalar-evolution.h" |

41 | |

42 | /* Extended folder for chrecs. */ |

43 | |

44 | /* Determines whether CST is not a constant evolution. */ |

45 | |

46 | static inline bool |

47 | is_not_constant_evolution (const_tree cst) |

48 | { |

49 | return (TREE_CODE (cst) == POLYNOMIAL_CHREC); |

50 | } |

51 | |

52 | /* Fold CODE for a polynomial function and a constant. */ |

53 | |

54 | static inline tree |

55 | chrec_fold_poly_cst (enum tree_code code, |

56 | tree type, |

57 | tree poly, |

58 | tree cst) |

59 | { |

60 | gcc_assert (poly); |

61 | gcc_assert (cst); |

62 | gcc_assert (TREE_CODE (poly) == POLYNOMIAL_CHREC); |

63 | gcc_checking_assert (!is_not_constant_evolution (cst)); |

64 | gcc_checking_assert (useless_type_conversion_p (type, chrec_type (poly))); |

65 | |

66 | switch (code) |

67 | { |

68 | case PLUS_EXPR: |

69 | return build_polynomial_chrec |

70 | (CHREC_VARIABLE (poly), |

71 | chrec_fold_plus (type, CHREC_LEFT (poly), cst), |

72 | CHREC_RIGHT (poly)); |

73 | |

74 | case MINUS_EXPR: |

75 | return build_polynomial_chrec |

76 | (CHREC_VARIABLE (poly), |

77 | chrec_fold_minus (type, CHREC_LEFT (poly), cst), |

78 | CHREC_RIGHT (poly)); |

79 | |

80 | case MULT_EXPR: |

81 | return build_polynomial_chrec |

82 | (CHREC_VARIABLE (poly), |

83 | chrec_fold_multiply (type, CHREC_LEFT (poly), cst), |

84 | chrec_fold_multiply (type, CHREC_RIGHT (poly), cst)); |

85 | |

86 | default: |

87 | return chrec_dont_know; |

88 | } |

89 | } |

90 | |

91 | /* Fold the addition of two polynomial functions. */ |

92 | |

93 | static inline tree |

94 | chrec_fold_plus_poly_poly (enum tree_code code, |

95 | tree type, |

96 | tree poly0, |

97 | tree poly1) |

98 | { |

99 | tree left, right; |

100 | struct loop *loop0 = get_chrec_loop (poly0); |

101 | struct loop *loop1 = get_chrec_loop (poly1); |

102 | tree rtype = code == POINTER_PLUS_EXPR ? chrec_type (poly1) : type; |

103 | |

104 | gcc_assert (poly0); |

105 | gcc_assert (poly1); |

106 | gcc_assert (TREE_CODE (poly0) == POLYNOMIAL_CHREC); |

107 | gcc_assert (TREE_CODE (poly1) == POLYNOMIAL_CHREC); |

108 | if (POINTER_TYPE_P (chrec_type (poly0))) |

109 | gcc_checking_assert (ptrofftype_p (chrec_type (poly1)) |

110 | && useless_type_conversion_p (type, chrec_type (poly0))); |

111 | else |

112 | gcc_checking_assert (useless_type_conversion_p (type, chrec_type (poly0)) |

113 | && useless_type_conversion_p (type, chrec_type (poly1))); |

114 | |

115 | /* |

116 | {a, +, b}_1 + {c, +, d}_2 -> {{a, +, b}_1 + c, +, d}_2, |

117 | {a, +, b}_2 + {c, +, d}_1 -> {{c, +, d}_1 + a, +, b}_2, |

118 | {a, +, b}_x + {c, +, d}_x -> {a+c, +, b+d}_x. */ |

119 | if (flow_loop_nested_p (loop0, loop1)) |

120 | { |

121 | if (code == PLUS_EXPR || code == POINTER_PLUS_EXPR) |

122 | return build_polynomial_chrec |

123 | (CHREC_VARIABLE (poly1), |

124 | chrec_fold_plus (type, poly0, CHREC_LEFT (poly1)), |

125 | CHREC_RIGHT (poly1)); |

126 | else |

127 | return build_polynomial_chrec |

128 | (CHREC_VARIABLE (poly1), |

129 | chrec_fold_minus (type, poly0, CHREC_LEFT (poly1)), |

130 | chrec_fold_multiply (type, CHREC_RIGHT (poly1), |

131 | SCALAR_FLOAT_TYPE_P (type) |

132 | ? build_real (type, dconstm1) |

133 | : build_int_cst_type (type, -1))); |

134 | } |

135 | |

136 | if (flow_loop_nested_p (loop1, loop0)) |

137 | { |

138 | if (code == PLUS_EXPR || code == POINTER_PLUS_EXPR) |

139 | return build_polynomial_chrec |

140 | (CHREC_VARIABLE (poly0), |

141 | chrec_fold_plus (type, CHREC_LEFT (poly0), poly1), |

142 | CHREC_RIGHT (poly0)); |

143 | else |

144 | return build_polynomial_chrec |

145 | (CHREC_VARIABLE (poly0), |

146 | chrec_fold_minus (type, CHREC_LEFT (poly0), poly1), |

147 | CHREC_RIGHT (poly0)); |

148 | } |

149 | |

150 | /* This function should never be called for chrecs of loops that |

151 | do not belong to the same loop nest. */ |

152 | if (loop0 != loop1) |

153 | { |

154 | /* It still can happen if we are not in loop-closed SSA form. */ |

155 | gcc_assert (! loops_state_satisfies_p (LOOP_CLOSED_SSA)); |

156 | return chrec_dont_know; |

157 | } |

158 | |

159 | if (code == PLUS_EXPR || code == POINTER_PLUS_EXPR) |

160 | { |

161 | left = chrec_fold_plus |

162 | (type, CHREC_LEFT (poly0), CHREC_LEFT (poly1)); |

163 | right = chrec_fold_plus |

164 | (rtype, CHREC_RIGHT (poly0), CHREC_RIGHT (poly1)); |

165 | } |

166 | else |

167 | { |

168 | left = chrec_fold_minus |

169 | (type, CHREC_LEFT (poly0), CHREC_LEFT (poly1)); |

170 | right = chrec_fold_minus |

171 | (type, CHREC_RIGHT (poly0), CHREC_RIGHT (poly1)); |

172 | } |

173 | |

174 | if (chrec_zerop (right)) |

175 | return left; |

176 | else |

177 | return build_polynomial_chrec |

178 | (CHREC_VARIABLE (poly0), left, right); |

179 | } |

180 | |

181 | |

182 | |

183 | /* Fold the multiplication of two polynomial functions. */ |

184 | |

185 | static inline tree |

186 | chrec_fold_multiply_poly_poly (tree type, |

187 | tree poly0, |

188 | tree poly1) |

189 | { |

190 | tree t0, t1, t2; |

191 | int var; |

192 | struct loop *loop0 = get_chrec_loop (poly0); |

193 | struct loop *loop1 = get_chrec_loop (poly1); |

194 | |

195 | gcc_assert (poly0); |

196 | gcc_assert (poly1); |

197 | gcc_assert (TREE_CODE (poly0) == POLYNOMIAL_CHREC); |

198 | gcc_assert (TREE_CODE (poly1) == POLYNOMIAL_CHREC); |

199 | gcc_checking_assert (useless_type_conversion_p (type, chrec_type (poly0)) |

200 | && useless_type_conversion_p (type, chrec_type (poly1))); |

201 | |

202 | /* {a, +, b}_1 * {c, +, d}_2 -> {c*{a, +, b}_1, +, d}_2, |

203 | {a, +, b}_2 * {c, +, d}_1 -> {a*{c, +, d}_1, +, b}_2, |

204 | {a, +, b}_x * {c, +, d}_x -> {a*c, +, a*d + b*c + b*d, +, 2*b*d}_x. */ |

205 | if (flow_loop_nested_p (loop0, loop1)) |

206 | /* poly0 is a constant wrt. poly1. */ |

207 | return build_polynomial_chrec |

208 | (CHREC_VARIABLE (poly1), |

209 | chrec_fold_multiply (type, CHREC_LEFT (poly1), poly0), |

210 | CHREC_RIGHT (poly1)); |

211 | |

212 | if (flow_loop_nested_p (loop1, loop0)) |

213 | /* poly1 is a constant wrt. poly0. */ |

214 | return build_polynomial_chrec |

215 | (CHREC_VARIABLE (poly0), |

216 | chrec_fold_multiply (type, CHREC_LEFT (poly0), poly1), |

217 | CHREC_RIGHT (poly0)); |

218 | |

219 | if (loop0 != loop1) |

220 | { |

221 | /* It still can happen if we are not in loop-closed SSA form. */ |

222 | gcc_assert (! loops_state_satisfies_p (LOOP_CLOSED_SSA)); |

223 | return chrec_dont_know; |

224 | } |

225 | |

226 | /* poly0 and poly1 are two polynomials in the same variable, |

227 | {a, +, b}_x * {c, +, d}_x -> {a*c, +, a*d + b*c + b*d, +, 2*b*d}_x. */ |

228 | |

229 | /* "a*c". */ |

230 | t0 = chrec_fold_multiply (type, CHREC_LEFT (poly0), CHREC_LEFT (poly1)); |

231 | |

232 | /* "a*d + b*c". */ |

233 | t1 = chrec_fold_multiply (type, CHREC_LEFT (poly0), CHREC_RIGHT (poly1)); |

234 | t1 = chrec_fold_plus (type, t1, chrec_fold_multiply (type, |

235 | CHREC_RIGHT (poly0), |

236 | CHREC_LEFT (poly1))); |

237 | /* "b*d". */ |

238 | t2 = chrec_fold_multiply (type, CHREC_RIGHT (poly0), CHREC_RIGHT (poly1)); |

239 | /* "a*d + b*c + b*d". */ |

240 | t1 = chrec_fold_plus (type, t1, t2); |

241 | /* "2*b*d". */ |

242 | t2 = chrec_fold_multiply (type, SCALAR_FLOAT_TYPE_P (type) |

243 | ? build_real (type, dconst2) |

244 | : build_int_cst (type, 2), t2); |

245 | |

246 | var = CHREC_VARIABLE (poly0); |

247 | return build_polynomial_chrec (var, t0, |

248 | build_polynomial_chrec (var, t1, t2)); |

249 | } |

250 | |

251 | /* When the operands are automatically_generated_chrec_p, the fold has |

252 | to respect the semantics of the operands. */ |

253 | |

254 | static inline tree |

255 | chrec_fold_automatically_generated_operands (tree op0, |

256 | tree op1) |

257 | { |

258 | if (op0 == chrec_dont_know |

259 | || op1 == chrec_dont_know) |

260 | return chrec_dont_know; |

261 | |

262 | if (op0 == chrec_known |

263 | || op1 == chrec_known) |

264 | return chrec_known; |

265 | |

266 | if (op0 == chrec_not_analyzed_yet |

267 | || op1 == chrec_not_analyzed_yet) |

268 | return chrec_not_analyzed_yet; |

269 | |

270 | /* The default case produces a safe result. */ |

271 | return chrec_dont_know; |

272 | } |

273 | |

274 | /* Fold the addition of two chrecs. */ |

275 | |

276 | static tree |

277 | chrec_fold_plus_1 (enum tree_code code, tree type, |

278 | tree op0, tree op1) |

279 | { |

280 | if (automatically_generated_chrec_p (op0) |

281 | || automatically_generated_chrec_p (op1)) |

282 | return chrec_fold_automatically_generated_operands (op0, op1); |

283 | |

284 | switch (TREE_CODE (op0)) |

285 | { |

286 | case POLYNOMIAL_CHREC: |

287 | gcc_checking_assert |

288 | (!chrec_contains_symbols_defined_in_loop (op0, CHREC_VARIABLE (op0))); |

289 | switch (TREE_CODE (op1)) |

290 | { |

291 | case POLYNOMIAL_CHREC: |

292 | gcc_checking_assert |

293 | (!chrec_contains_symbols_defined_in_loop (op1, |

294 | CHREC_VARIABLE (op1))); |

295 | return chrec_fold_plus_poly_poly (code, type, op0, op1); |

296 | |

297 | CASE_CONVERT: |

298 | if (tree_contains_chrecs (op1, NULL)) |

299 | return chrec_dont_know; |

300 | /* FALLTHRU */ |

301 | |

302 | default: |

303 | if (code == PLUS_EXPR || code == POINTER_PLUS_EXPR) |

304 | return build_polynomial_chrec |

305 | (CHREC_VARIABLE (op0), |

306 | chrec_fold_plus (type, CHREC_LEFT (op0), op1), |

307 | CHREC_RIGHT (op0)); |

308 | else |

309 | return build_polynomial_chrec |

310 | (CHREC_VARIABLE (op0), |

311 | chrec_fold_minus (type, CHREC_LEFT (op0), op1), |

312 | CHREC_RIGHT (op0)); |

313 | } |

314 | |

315 | CASE_CONVERT: |

316 | if (tree_contains_chrecs (op0, NULL)) |

317 | return chrec_dont_know; |

318 | /* FALLTHRU */ |

319 | |

320 | default: |

321 | switch (TREE_CODE (op1)) |

322 | { |

323 | case POLYNOMIAL_CHREC: |

324 | gcc_checking_assert |

325 | (!chrec_contains_symbols_defined_in_loop (op1, |

326 | CHREC_VARIABLE (op1))); |

327 | if (code == PLUS_EXPR || code == POINTER_PLUS_EXPR) |

328 | return build_polynomial_chrec |

329 | (CHREC_VARIABLE (op1), |

330 | chrec_fold_plus (type, op0, CHREC_LEFT (op1)), |

331 | CHREC_RIGHT (op1)); |

332 | else |

333 | return build_polynomial_chrec |

334 | (CHREC_VARIABLE (op1), |

335 | chrec_fold_minus (type, op0, CHREC_LEFT (op1)), |

336 | chrec_fold_multiply (type, CHREC_RIGHT (op1), |

337 | SCALAR_FLOAT_TYPE_P (type) |

338 | ? build_real (type, dconstm1) |

339 | : build_int_cst_type (type, -1))); |

340 | |

341 | CASE_CONVERT: |

342 | if (tree_contains_chrecs (op1, NULL)) |

343 | return chrec_dont_know; |

344 | /* FALLTHRU */ |

345 | |

346 | default: |

347 | { |

348 | int size = 0; |

349 | if ((tree_contains_chrecs (op0, &size) |

350 | || tree_contains_chrecs (op1, &size)) |

351 | && size < PARAM_VALUE (PARAM_SCEV_MAX_EXPR_SIZE)) |

352 | return build2 (code, type, op0, op1); |

353 | else if (size < PARAM_VALUE (PARAM_SCEV_MAX_EXPR_SIZE)) |

354 | { |

355 | if (code == POINTER_PLUS_EXPR) |

356 | return fold_build_pointer_plus (fold_convert (type, op0), |

357 | op1); |

358 | else |

359 | return fold_build2 (code, type, |

360 | fold_convert (type, op0), |

361 | fold_convert (type, op1)); |

362 | } |

363 | else |

364 | return chrec_dont_know; |

365 | } |

366 | } |

367 | } |

368 | } |

369 | |

370 | /* Fold the addition of two chrecs. */ |

371 | |

372 | tree |

373 | chrec_fold_plus (tree type, |

374 | tree op0, |

375 | tree op1) |

376 | { |

377 | enum tree_code code; |

378 | if (automatically_generated_chrec_p (op0) |

379 | || automatically_generated_chrec_p (op1)) |

380 | return chrec_fold_automatically_generated_operands (op0, op1); |

381 | |

382 | if (integer_zerop (op0)) |

383 | return chrec_convert (type, op1, NULL); |

384 | if (integer_zerop (op1)) |

385 | return chrec_convert (type, op0, NULL); |

386 | |

387 | if (POINTER_TYPE_P (type)) |

388 | code = POINTER_PLUS_EXPR; |

389 | else |

390 | code = PLUS_EXPR; |

391 | |

392 | return chrec_fold_plus_1 (code, type, op0, op1); |

393 | } |

394 | |

395 | /* Fold the subtraction of two chrecs. */ |

396 | |

397 | tree |

398 | chrec_fold_minus (tree type, |

399 | tree op0, |

400 | tree op1) |

401 | { |

402 | if (automatically_generated_chrec_p (op0) |

403 | || automatically_generated_chrec_p (op1)) |

404 | return chrec_fold_automatically_generated_operands (op0, op1); |

405 | |

406 | if (integer_zerop (op1)) |

407 | return op0; |

408 | |

409 | return chrec_fold_plus_1 (MINUS_EXPR, type, op0, op1); |

410 | } |

411 | |

412 | /* Fold the multiplication of two chrecs. */ |

413 | |

414 | tree |

415 | chrec_fold_multiply (tree type, |

416 | tree op0, |

417 | tree op1) |

418 | { |

419 | if (automatically_generated_chrec_p (op0) |

420 | || automatically_generated_chrec_p (op1)) |

421 | return chrec_fold_automatically_generated_operands (op0, op1); |

422 | |

423 | switch (TREE_CODE (op0)) |

424 | { |

425 | case POLYNOMIAL_CHREC: |

426 | gcc_checking_assert |

427 | (!chrec_contains_symbols_defined_in_loop (op0, CHREC_VARIABLE (op0))); |

428 | switch (TREE_CODE (op1)) |

429 | { |

430 | case POLYNOMIAL_CHREC: |

431 | gcc_checking_assert |

432 | (!chrec_contains_symbols_defined_in_loop (op1, |

433 | CHREC_VARIABLE (op1))); |

434 | return chrec_fold_multiply_poly_poly (type, op0, op1); |

435 | |

436 | CASE_CONVERT: |

437 | if (tree_contains_chrecs (op1, NULL)) |

438 | return chrec_dont_know; |

439 | /* FALLTHRU */ |

440 | |

441 | default: |

442 | if (integer_onep (op1)) |

443 | return op0; |

444 | if (integer_zerop (op1)) |

445 | return build_int_cst (type, 0); |

446 | |

447 | return build_polynomial_chrec |

448 | (CHREC_VARIABLE (op0), |

449 | chrec_fold_multiply (type, CHREC_LEFT (op0), op1), |

450 | chrec_fold_multiply (type, CHREC_RIGHT (op0), op1)); |

451 | } |

452 | |

453 | CASE_CONVERT: |

454 | if (tree_contains_chrecs (op0, NULL)) |

455 | return chrec_dont_know; |

456 | /* FALLTHRU */ |

457 | |

458 | default: |

459 | if (integer_onep (op0)) |

460 | return op1; |

461 | |

462 | if (integer_zerop (op0)) |

463 | return build_int_cst (type, 0); |

464 | |

465 | switch (TREE_CODE (op1)) |

466 | { |

467 | case POLYNOMIAL_CHREC: |

468 | gcc_checking_assert |

469 | (!chrec_contains_symbols_defined_in_loop (op1, |

470 | CHREC_VARIABLE (op1))); |

471 | return build_polynomial_chrec |

472 | (CHREC_VARIABLE (op1), |

473 | chrec_fold_multiply (type, CHREC_LEFT (op1), op0), |

474 | chrec_fold_multiply (type, CHREC_RIGHT (op1), op0)); |

475 | |

476 | CASE_CONVERT: |

477 | if (tree_contains_chrecs (op1, NULL)) |

478 | return chrec_dont_know; |

479 | /* FALLTHRU */ |

480 | |

481 | default: |

482 | if (integer_onep (op1)) |

483 | return op0; |

484 | if (integer_zerop (op1)) |

485 | return build_int_cst (type, 0); |

486 | return fold_build2 (MULT_EXPR, type, op0, op1); |

487 | } |

488 | } |

489 | } |

490 | |

491 | |

492 | |

493 | /* Operations. */ |

494 | |

495 | /* Evaluate the binomial coefficient. Return NULL_TREE if the intermediate |

496 | calculation overflows, otherwise return C(n,k) with type TYPE. */ |

497 | |

498 | static tree |

499 | tree_fold_binomial (tree type, tree n, unsigned int k) |

500 | { |

501 | bool overflow; |

502 | unsigned int i; |

503 | |

504 | /* Handle the most frequent cases. */ |

505 | if (k == 0) |

506 | return build_int_cst (type, 1); |

507 | if (k == 1) |

508 | return fold_convert (type, n); |

509 | |

510 | widest_int num = wi::to_widest (n); |

511 | |

512 | /* Check that k <= n. */ |

513 | if (wi::ltu_p (num, k)) |

514 | return NULL_TREE; |

515 | |

516 | /* Denominator = 2. */ |

517 | widest_int denom = 2; |

518 | |

519 | /* Index = Numerator-1. */ |

520 | widest_int idx = num - 1; |

521 | |

522 | /* Numerator = Numerator*Index = n*(n-1). */ |

523 | num = wi::smul (num, idx, &overflow); |

524 | if (overflow) |

525 | return NULL_TREE; |

526 | |

527 | for (i = 3; i <= k; i++) |

528 | { |

529 | /* Index--. */ |

530 | --idx; |

531 | |

532 | /* Numerator *= Index. */ |

533 | num = wi::smul (num, idx, &overflow); |

534 | if (overflow) |

535 | return NULL_TREE; |

536 | |

537 | /* Denominator *= i. */ |

538 | denom *= i; |

539 | } |

540 | |

541 | /* Result = Numerator / Denominator. */ |

542 | num = wi::udiv_trunc (num, denom); |

543 | if (! wi::fits_to_tree_p (num, type)) |

544 | return NULL_TREE; |

545 | return wide_int_to_tree (type, num); |

546 | } |

547 | |

548 | /* Helper function. Use the Newton's interpolating formula for |

549 | evaluating the value of the evolution function. |

550 | The result may be in an unsigned type of CHREC. */ |

551 | |

552 | static tree |

553 | chrec_evaluate (unsigned var, tree chrec, tree n, unsigned int k) |

554 | { |

555 | tree arg0, arg1, binomial_n_k; |

556 | tree type = TREE_TYPE (chrec); |

557 | struct loop *var_loop = get_loop (cfun, var); |

558 | |

559 | while (TREE_CODE (chrec) == POLYNOMIAL_CHREC |

560 | && flow_loop_nested_p (var_loop, get_chrec_loop (chrec))) |

561 | chrec = CHREC_LEFT (chrec); |

562 | |

563 | /* The formula associates the expression and thus we have to make |

564 | sure to not introduce undefined overflow. */ |

565 | tree ctype = type; |

566 | if (INTEGRAL_TYPE_P (type) |

567 | && ! TYPE_OVERFLOW_WRAPS (type)) |

568 | ctype = unsigned_type_for (type); |

569 | |

570 | if (TREE_CODE (chrec) == POLYNOMIAL_CHREC |

571 | && CHREC_VARIABLE (chrec) == var) |

572 | { |

573 | arg1 = chrec_evaluate (var, CHREC_RIGHT (chrec), n, k + 1); |

574 | if (arg1 == chrec_dont_know) |

575 | return chrec_dont_know; |

576 | binomial_n_k = tree_fold_binomial (ctype, n, k); |

577 | if (!binomial_n_k) |

578 | return chrec_dont_know; |

579 | tree l = chrec_convert (ctype, CHREC_LEFT (chrec), NULL); |

580 | arg0 = fold_build2 (MULT_EXPR, ctype, l, binomial_n_k); |

581 | return chrec_fold_plus (ctype, arg0, arg1); |

582 | } |

583 | |

584 | binomial_n_k = tree_fold_binomial (ctype, n, k); |

585 | if (!binomial_n_k) |

586 | return chrec_dont_know; |

587 | |

588 | return fold_build2 (MULT_EXPR, ctype, |

589 | chrec_convert (ctype, chrec, NULL), binomial_n_k); |

590 | } |

591 | |

592 | /* Evaluates "CHREC (X)" when the varying variable is VAR. |

593 | Example: Given the following parameters, |

594 | |

595 | var = 1 |

596 | chrec = {3, +, 4}_1 |

597 | x = 10 |

598 | |

599 | The result is given by the Newton's interpolating formula: |

600 | 3 * \binom{10}{0} + 4 * \binom{10}{1}. |

601 | */ |

602 | |

603 | tree |

604 | chrec_apply (unsigned var, |

605 | tree chrec, |

606 | tree x) |

607 | { |

608 | tree type = chrec_type (chrec); |

609 | tree res = chrec_dont_know; |

610 | |

611 | if (automatically_generated_chrec_p (chrec) |

612 | || automatically_generated_chrec_p (x) |

613 | |

614 | /* When the symbols are defined in an outer loop, it is possible |

615 | to symbolically compute the apply, since the symbols are |

616 | constants with respect to the varying loop. */ |

617 | || chrec_contains_symbols_defined_in_loop (chrec, var)) |

618 | return chrec_dont_know; |

619 | |

620 | if (dump_file && (dump_flags & TDF_SCEV)) |

621 | fprintf (dump_file, "(chrec_apply \n"); |

622 | |

623 | if (TREE_CODE (x) == INTEGER_CST && SCALAR_FLOAT_TYPE_P (type)) |

624 | x = build_real_from_int_cst (type, x); |

625 | |

626 | switch (TREE_CODE (chrec)) |

627 | { |

628 | case POLYNOMIAL_CHREC: |

629 | if (evolution_function_is_affine_p (chrec)) |

630 | { |

631 | if (CHREC_VARIABLE (chrec) != var) |

632 | return build_polynomial_chrec |

633 | (CHREC_VARIABLE (chrec), |

634 | chrec_apply (var, CHREC_LEFT (chrec), x), |

635 | chrec_apply (var, CHREC_RIGHT (chrec), x)); |

636 | |

637 | /* "{a, +, b} (x)" -> "a + b*x". */ |

638 | x = chrec_convert_rhs (type, x, NULL); |

639 | res = chrec_fold_multiply (TREE_TYPE (x), CHREC_RIGHT (chrec), x); |

640 | res = chrec_fold_plus (type, CHREC_LEFT (chrec), res); |

641 | } |

642 | else if (TREE_CODE (x) == INTEGER_CST |

643 | && tree_int_cst_sgn (x) == 1) |

644 | /* testsuite/.../ssa-chrec-38.c. */ |

645 | res = chrec_convert (type, chrec_evaluate (var, chrec, x, 0), NULL); |

646 | else |

647 | res = chrec_dont_know; |

648 | break; |

649 | |

650 | CASE_CONVERT: |

651 | res = chrec_convert (TREE_TYPE (chrec), |

652 | chrec_apply (var, TREE_OPERAND (chrec, 0), x), |

653 | NULL); |

654 | break; |

655 | |

656 | default: |

657 | res = chrec; |

658 | break; |

659 | } |

660 | |

661 | if (dump_file && (dump_flags & TDF_SCEV)) |

662 | { |

663 | fprintf (dump_file, " (varying_loop = %d\n", var); |

664 | fprintf (dump_file, ")\n (chrec = "); |

665 | print_generic_expr (dump_file, chrec); |

666 | fprintf (dump_file, ")\n (x = "); |

667 | print_generic_expr (dump_file, x); |

668 | fprintf (dump_file, ")\n (res = "); |

669 | print_generic_expr (dump_file, res); |

670 | fprintf (dump_file, "))\n"); |

671 | } |

672 | |

673 | return res; |

674 | } |

675 | |

676 | /* For a given CHREC and an induction variable map IV_MAP that maps |

677 | (loop->num, expr) for every loop number of the current_loops an |

678 | expression, calls chrec_apply when the expression is not NULL. */ |

679 | |

680 | tree |

681 | chrec_apply_map (tree chrec, vec<tree> iv_map) |

682 | { |

683 | int i; |

684 | tree expr; |

685 | |

686 | FOR_EACH_VEC_ELT (iv_map, i, expr) |

687 | if (expr) |

688 | chrec = chrec_apply (i, chrec, expr); |

689 | |

690 | return chrec; |

691 | } |

692 | |

693 | /* Replaces the initial condition in CHREC with INIT_COND. */ |

694 | |

695 | tree |

696 | chrec_replace_initial_condition (tree chrec, |

697 | tree init_cond) |

698 | { |

699 | if (automatically_generated_chrec_p (chrec)) |

700 | return chrec; |

701 | |

702 | gcc_assert (chrec_type (chrec) == chrec_type (init_cond)); |

703 | |

704 | switch (TREE_CODE (chrec)) |

705 | { |

706 | case POLYNOMIAL_CHREC: |

707 | return build_polynomial_chrec |

708 | (CHREC_VARIABLE (chrec), |

709 | chrec_replace_initial_condition (CHREC_LEFT (chrec), init_cond), |

710 | CHREC_RIGHT (chrec)); |

711 | |

712 | default: |

713 | return init_cond; |

714 | } |

715 | } |

716 | |

717 | /* Returns the initial condition of a given CHREC. */ |

718 | |

719 | tree |

720 | initial_condition (tree chrec) |

721 | { |

722 | if (automatically_generated_chrec_p (chrec)) |

723 | return chrec; |

724 | |

725 | if (TREE_CODE (chrec) == POLYNOMIAL_CHREC) |

726 | return initial_condition (CHREC_LEFT (chrec)); |

727 | else |

728 | return chrec; |

729 | } |

730 | |

731 | /* Returns a univariate function that represents the evolution in |

732 | LOOP_NUM. Mask the evolution of any other loop. */ |

733 | |

734 | tree |

735 | hide_evolution_in_other_loops_than_loop (tree chrec, |

736 | unsigned loop_num) |

737 | { |

738 | struct loop *loop = get_loop (cfun, loop_num), *chloop; |

739 | if (automatically_generated_chrec_p (chrec)) |

740 | return chrec; |

741 | |

742 | switch (TREE_CODE (chrec)) |

743 | { |

744 | case POLYNOMIAL_CHREC: |

745 | chloop = get_chrec_loop (chrec); |

746 | |

747 | if (chloop == loop) |

748 | return build_polynomial_chrec |

749 | (loop_num, |

750 | hide_evolution_in_other_loops_than_loop (CHREC_LEFT (chrec), |

751 | loop_num), |

752 | CHREC_RIGHT (chrec)); |

753 | |

754 | else if (flow_loop_nested_p (chloop, loop)) |

755 | /* There is no evolution in this loop. */ |

756 | return initial_condition (chrec); |

757 | |

758 | else if (flow_loop_nested_p (loop, chloop)) |

759 | return hide_evolution_in_other_loops_than_loop (CHREC_LEFT (chrec), |

760 | loop_num); |

761 | |

762 | else |

763 | return chrec_dont_know; |

764 | |

765 | default: |

766 | return chrec; |

767 | } |

768 | } |

769 | |

770 | /* Returns the evolution part of CHREC in LOOP_NUM when RIGHT is |

771 | true, otherwise returns the initial condition in LOOP_NUM. */ |

772 | |

773 | static tree |

774 | chrec_component_in_loop_num (tree chrec, |

775 | unsigned loop_num, |

776 | bool right) |

777 | { |

778 | tree component; |

779 | struct loop *loop = get_loop (cfun, loop_num), *chloop; |

780 | |

781 | if (automatically_generated_chrec_p (chrec)) |

782 | return chrec; |

783 | |

784 | switch (TREE_CODE (chrec)) |

785 | { |

786 | case POLYNOMIAL_CHREC: |

787 | chloop = get_chrec_loop (chrec); |

788 | |

789 | if (chloop == loop) |

790 | { |

791 | if (right) |

792 | component = CHREC_RIGHT (chrec); |

793 | else |

794 | component = CHREC_LEFT (chrec); |

795 | |

796 | if (TREE_CODE (CHREC_LEFT (chrec)) != POLYNOMIAL_CHREC |

797 | || CHREC_VARIABLE (CHREC_LEFT (chrec)) != CHREC_VARIABLE (chrec)) |

798 | return component; |

799 | |

800 | else |

801 | return build_polynomial_chrec |

802 | (loop_num, |

803 | chrec_component_in_loop_num (CHREC_LEFT (chrec), |

804 | loop_num, |

805 | right), |

806 | component); |

807 | } |

808 | |

809 | else if (flow_loop_nested_p (chloop, loop)) |

810 | /* There is no evolution part in this loop. */ |

811 | return NULL_TREE; |

812 | |

813 | else |

814 | { |

815 | gcc_assert (flow_loop_nested_p (loop, chloop)); |

816 | return chrec_component_in_loop_num (CHREC_LEFT (chrec), |

817 | loop_num, |

818 | right); |

819 | } |

820 | |

821 | default: |

822 | if (right) |

823 | return NULL_TREE; |

824 | else |

825 | return chrec; |

826 | } |

827 | } |

828 | |

829 | /* Returns the evolution part in LOOP_NUM. Example: the call |

830 | evolution_part_in_loop_num ({{0, +, 1}_1, +, 2}_1, 1) returns |

831 | {1, +, 2}_1 */ |

832 | |

833 | tree |

834 | evolution_part_in_loop_num (tree chrec, |

835 | unsigned loop_num) |

836 | { |

837 | return chrec_component_in_loop_num (chrec, loop_num, true); |

838 | } |

839 | |

840 | /* Returns the initial condition in LOOP_NUM. Example: the call |

841 | initial_condition_in_loop_num ({{0, +, 1}_1, +, 2}_2, 2) returns |

842 | {0, +, 1}_1 */ |

843 | |

844 | tree |

845 | initial_condition_in_loop_num (tree chrec, |

846 | unsigned loop_num) |

847 | { |

848 | return chrec_component_in_loop_num (chrec, loop_num, false); |

849 | } |

850 | |

851 | /* Set or reset the evolution of CHREC to NEW_EVOL in loop LOOP_NUM. |

852 | This function is essentially used for setting the evolution to |

853 | chrec_dont_know, for example after having determined that it is |

854 | impossible to say how many times a loop will execute. */ |

855 | |

856 | tree |

857 | reset_evolution_in_loop (unsigned loop_num, |

858 | tree chrec, |

859 | tree new_evol) |

860 | { |

861 | struct loop *loop = get_loop (cfun, loop_num); |

862 | |

863 | if (POINTER_TYPE_P (chrec_type (chrec))) |

864 | gcc_assert (ptrofftype_p (chrec_type (new_evol))); |

865 | else |

866 | gcc_assert (chrec_type (chrec) == chrec_type (new_evol)); |

867 | |

868 | if (TREE_CODE (chrec) == POLYNOMIAL_CHREC |

869 | && flow_loop_nested_p (loop, get_chrec_loop (chrec))) |

870 | { |

871 | tree left = reset_evolution_in_loop (loop_num, CHREC_LEFT (chrec), |

872 | new_evol); |

873 | tree right = reset_evolution_in_loop (loop_num, CHREC_RIGHT (chrec), |

874 | new_evol); |

875 | return build_polynomial_chrec (CHREC_VARIABLE (chrec), left, right); |

876 | } |

877 | |

878 | while (TREE_CODE (chrec) == POLYNOMIAL_CHREC |

879 | && CHREC_VARIABLE (chrec) == loop_num) |

880 | chrec = CHREC_LEFT (chrec); |

881 | |

882 | return build_polynomial_chrec (loop_num, chrec, new_evol); |

883 | } |

884 | |

885 | /* Merges two evolution functions that were found by following two |

886 | alternate paths of a conditional expression. */ |

887 | |

888 | tree |

889 | chrec_merge (tree chrec1, |

890 | tree chrec2) |

891 | { |

892 | if (chrec1 == chrec_dont_know |

893 | || chrec2 == chrec_dont_know) |

894 | return chrec_dont_know; |

895 | |

896 | if (chrec1 == chrec_known |

897 | || chrec2 == chrec_known) |

898 | return chrec_known; |

899 | |

900 | if (chrec1 == chrec_not_analyzed_yet) |

901 | return chrec2; |

902 | if (chrec2 == chrec_not_analyzed_yet) |

903 | return chrec1; |

904 | |

905 | if (eq_evolutions_p (chrec1, chrec2)) |

906 | return chrec1; |

907 | |

908 | return chrec_dont_know; |

909 | } |

910 | |

911 | |

912 | |

913 | /* Observers. */ |

914 | |

915 | /* Helper function for is_multivariate_chrec. */ |

916 | |

917 | static bool |

918 | is_multivariate_chrec_rec (const_tree chrec, unsigned int rec_var) |

919 | { |

920 | if (chrec == NULL_TREE) |

921 | return false; |

922 | |

923 | if (TREE_CODE (chrec) == POLYNOMIAL_CHREC) |

924 | { |

925 | if (CHREC_VARIABLE (chrec) != rec_var) |

926 | return true; |

927 | else |

928 | return (is_multivariate_chrec_rec (CHREC_LEFT (chrec), rec_var) |

929 | || is_multivariate_chrec_rec (CHREC_RIGHT (chrec), rec_var)); |

930 | } |

931 | else |

932 | return false; |

933 | } |

934 | |

935 | /* Determine whether the given chrec is multivariate or not. */ |

936 | |

937 | bool |

938 | is_multivariate_chrec (const_tree chrec) |

939 | { |

940 | if (chrec == NULL_TREE) |

941 | return false; |

942 | |

943 | if (TREE_CODE (chrec) == POLYNOMIAL_CHREC) |

944 | return (is_multivariate_chrec_rec (CHREC_LEFT (chrec), |

945 | CHREC_VARIABLE (chrec)) |

946 | || is_multivariate_chrec_rec (CHREC_RIGHT (chrec), |

947 | CHREC_VARIABLE (chrec))); |

948 | else |

949 | return false; |

950 | } |

951 | |

952 | /* Determines whether the chrec contains symbolic names or not. */ |

953 | |

954 | bool |

955 | chrec_contains_symbols (const_tree chrec) |

956 | { |

957 | int i, n; |

958 | |

959 | if (chrec == NULL_TREE) |

960 | return false; |

961 | |

962 | if (TREE_CODE (chrec) == SSA_NAME |

963 | || VAR_P (chrec) |

964 | || TREE_CODE (chrec) == PARM_DECL |

965 | || TREE_CODE (chrec) == FUNCTION_DECL |

966 | || TREE_CODE (chrec) == LABEL_DECL |

967 | || TREE_CODE (chrec) == RESULT_DECL |

968 | || TREE_CODE (chrec) == FIELD_DECL) |

969 | return true; |

970 | |

971 | n = TREE_OPERAND_LENGTH (chrec); |

972 | for (i = 0; i < n; i++) |

973 | if (chrec_contains_symbols (TREE_OPERAND (chrec, i))) |

974 | return true; |

975 | return false; |

976 | } |

977 | |

978 | /* Determines whether the chrec contains undetermined coefficients. */ |

979 | |

980 | bool |

981 | chrec_contains_undetermined (const_tree chrec) |

982 | { |

983 | int i, n; |

984 | |

985 | if (chrec == chrec_dont_know) |

986 | return true; |

987 | |

988 | if (chrec == NULL_TREE) |

989 | return false; |

990 | |

991 | n = TREE_OPERAND_LENGTH (chrec); |

992 | for (i = 0; i < n; i++) |

993 | if (chrec_contains_undetermined (TREE_OPERAND (chrec, i))) |

994 | return true; |

995 | return false; |

996 | } |

997 | |

998 | /* Determines whether the tree EXPR contains chrecs, and increment |

999 | SIZE if it is not a NULL pointer by an estimation of the depth of |

1000 | the tree. */ |

1001 | |

1002 | bool |

1003 | tree_contains_chrecs (const_tree expr, int *size) |

1004 | { |

1005 | int i, n; |

1006 | |

1007 | if (expr == NULL_TREE) |

1008 | return false; |

1009 | |

1010 | if (size) |

1011 | (*size)++; |

1012 | |

1013 | if (tree_is_chrec (expr)) |

1014 | return true; |

1015 | |

1016 | n = TREE_OPERAND_LENGTH (expr); |

1017 | for (i = 0; i < n; i++) |

1018 | if (tree_contains_chrecs (TREE_OPERAND (expr, i), size)) |

1019 | return true; |

1020 | return false; |

1021 | } |

1022 | |

1023 | /* Recursive helper function. */ |

1024 | |

1025 | static bool |

1026 | evolution_function_is_invariant_rec_p (tree chrec, int loopnum) |

1027 | { |

1028 | if (evolution_function_is_constant_p (chrec)) |

1029 | return true; |

1030 | |

1031 | if (TREE_CODE (chrec) == SSA_NAME |

1032 | && (loopnum == 0 |

1033 | || expr_invariant_in_loop_p (get_loop (cfun, loopnum), chrec))) |

1034 | return true; |

1035 | |

1036 | if (TREE_CODE (chrec) == POLYNOMIAL_CHREC) |

1037 | { |

1038 | if (CHREC_VARIABLE (chrec) == (unsigned) loopnum |

1039 | || flow_loop_nested_p (get_loop (cfun, loopnum), |

1040 | get_chrec_loop (chrec)) |

1041 | || !evolution_function_is_invariant_rec_p (CHREC_RIGHT (chrec), |

1042 | loopnum) |

1043 | || !evolution_function_is_invariant_rec_p (CHREC_LEFT (chrec), |

1044 | loopnum)) |

1045 | return false; |

1046 | return true; |

1047 | } |

1048 | |

1049 | switch (TREE_OPERAND_LENGTH (chrec)) |

1050 | { |

1051 | case 2: |

1052 | if (!evolution_function_is_invariant_rec_p (TREE_OPERAND (chrec, 1), |

1053 | loopnum)) |

1054 | return false; |

1055 | /* FALLTHRU */ |

1056 | |

1057 | case 1: |

1058 | if (!evolution_function_is_invariant_rec_p (TREE_OPERAND (chrec, 0), |

1059 | loopnum)) |

1060 | return false; |

1061 | return true; |

1062 | |

1063 | default: |

1064 | return false; |

1065 | } |

1066 | |

1067 | return false; |

1068 | } |

1069 | |

1070 | /* Return true if CHREC is invariant in loop LOOPNUM, false otherwise. */ |

1071 | |

1072 | bool |

1073 | evolution_function_is_invariant_p (tree chrec, int loopnum) |

1074 | { |

1075 | return evolution_function_is_invariant_rec_p (chrec, loopnum); |

1076 | } |

1077 | |

1078 | /* Determine whether the given tree is an affine multivariate |

1079 | evolution. */ |

1080 | |

1081 | bool |

1082 | evolution_function_is_affine_multivariate_p (const_tree chrec, int loopnum) |

1083 | { |

1084 | if (chrec == NULL_TREE) |

1085 | return false; |

1086 | |

1087 | switch (TREE_CODE (chrec)) |

1088 | { |

1089 | case POLYNOMIAL_CHREC: |

1090 | if (evolution_function_is_invariant_rec_p (CHREC_LEFT (chrec), loopnum)) |

1091 | { |

1092 | if (evolution_function_is_invariant_rec_p (CHREC_RIGHT (chrec), loopnum)) |

1093 | return true; |

1094 | else |

1095 | { |

1096 | if (TREE_CODE (CHREC_RIGHT (chrec)) == POLYNOMIAL_CHREC |

1097 | && CHREC_VARIABLE (CHREC_RIGHT (chrec)) |

1098 | != CHREC_VARIABLE (chrec) |

1099 | && evolution_function_is_affine_multivariate_p |

1100 | (CHREC_RIGHT (chrec), loopnum)) |

1101 | return true; |

1102 | else |

1103 | return false; |

1104 | } |

1105 | } |

1106 | else |

1107 | { |

1108 | if (evolution_function_is_invariant_rec_p (CHREC_RIGHT (chrec), loopnum) |

1109 | && TREE_CODE (CHREC_LEFT (chrec)) == POLYNOMIAL_CHREC |

1110 | && CHREC_VARIABLE (CHREC_LEFT (chrec)) != CHREC_VARIABLE (chrec) |

1111 | && evolution_function_is_affine_multivariate_p |

1112 | (CHREC_LEFT (chrec), loopnum)) |

1113 | return true; |

1114 | else |

1115 | return false; |

1116 | } |

1117 | |

1118 | default: |

1119 | return false; |

1120 | } |

1121 | } |

1122 | |

1123 | /* Determine whether the given tree is a function in zero or one |

1124 | variables. */ |

1125 | |

1126 | bool |

1127 | evolution_function_is_univariate_p (const_tree chrec) |

1128 | { |

1129 | if (chrec == NULL_TREE) |

1130 | return true; |

1131 | |

1132 | switch (TREE_CODE (chrec)) |

1133 | { |

1134 | case POLYNOMIAL_CHREC: |

1135 | switch (TREE_CODE (CHREC_LEFT (chrec))) |

1136 | { |

1137 | case POLYNOMIAL_CHREC: |

1138 | if (CHREC_VARIABLE (chrec) != CHREC_VARIABLE (CHREC_LEFT (chrec))) |

1139 | return false; |

1140 | if (!evolution_function_is_univariate_p (CHREC_LEFT (chrec))) |

1141 | return false; |

1142 | break; |

1143 | |

1144 | default: |

1145 | if (tree_contains_chrecs (CHREC_LEFT (chrec), NULL)) |

1146 | return false; |

1147 | break; |

1148 | } |

1149 | |

1150 | switch (TREE_CODE (CHREC_RIGHT (chrec))) |

1151 | { |

1152 | case POLYNOMIAL_CHREC: |

1153 | if (CHREC_VARIABLE (chrec) != CHREC_VARIABLE (CHREC_RIGHT (chrec))) |

1154 | return false; |

1155 | if (!evolution_function_is_univariate_p (CHREC_RIGHT (chrec))) |

1156 | return false; |

1157 | break; |

1158 | |

1159 | default: |

1160 | if (tree_contains_chrecs (CHREC_RIGHT (chrec), NULL)) |

1161 | return false; |

1162 | break; |

1163 | } |

1164 | return true; |

1165 | |

1166 | default: |

1167 | return true; |

1168 | } |

1169 | } |

1170 | |

1171 | /* Returns the number of variables of CHREC. Example: the call |

1172 | nb_vars_in_chrec ({{0, +, 1}_5, +, 2}_6) returns 2. */ |

1173 | |

1174 | unsigned |

1175 | nb_vars_in_chrec (tree chrec) |

1176 | { |

1177 | if (chrec == NULL_TREE) |

1178 | return 0; |

1179 | |

1180 | switch (TREE_CODE (chrec)) |

1181 | { |

1182 | case POLYNOMIAL_CHREC: |

1183 | return 1 + nb_vars_in_chrec |

1184 | (initial_condition_in_loop_num (chrec, CHREC_VARIABLE (chrec))); |

1185 | |

1186 | default: |

1187 | return 0; |

1188 | } |

1189 | } |

1190 | |

1191 | /* Converts BASE and STEP of affine scev to TYPE. LOOP is the loop whose iv |

1192 | the scev corresponds to. AT_STMT is the statement at that the scev is |

1193 | evaluated. USE_OVERFLOW_SEMANTICS is true if this function should assume |

1194 | that the rules for overflow of the given language apply (e.g., that signed |

1195 | arithmetics in C does not overflow) -- i.e., to use them to avoid |

1196 | unnecessary tests, but also to enforce that the result follows them. |

1197 | FROM is the source variable converted if it's not NULL. Returns true if |

1198 | the conversion succeeded, false otherwise. */ |

1199 | |

1200 | bool |

1201 | convert_affine_scev (struct loop *loop, tree type, |

1202 | tree *base, tree *step, gimple *at_stmt, |

1203 | bool use_overflow_semantics, tree from) |

1204 | { |

1205 | tree ct = TREE_TYPE (*step); |

1206 | bool enforce_overflow_semantics; |

1207 | bool must_check_src_overflow, must_check_rslt_overflow; |

1208 | tree new_base, new_step; |

1209 | tree step_type = POINTER_TYPE_P (type) ? sizetype : type; |

1210 | |

1211 | /* In general, |

1212 | (TYPE) (BASE + STEP * i) = (TYPE) BASE + (TYPE -- sign extend) STEP * i, |

1213 | but we must check some assumptions. |

1214 | |

1215 | 1) If [BASE, +, STEP] wraps, the equation is not valid when precision |

1216 | of CT is smaller than the precision of TYPE. For example, when we |

1217 | cast unsigned char [254, +, 1] to unsigned, the values on left side |

1218 | are 254, 255, 0, 1, ..., but those on the right side are |

1219 | 254, 255, 256, 257, ... |

1220 | 2) In case that we must also preserve the fact that signed ivs do not |

1221 | overflow, we must additionally check that the new iv does not wrap. |

1222 | For example, unsigned char [125, +, 1] casted to signed char could |

1223 | become a wrapping variable with values 125, 126, 127, -128, -127, ..., |

1224 | which would confuse optimizers that assume that this does not |

1225 | happen. */ |

1226 | must_check_src_overflow = TYPE_PRECISION (ct) < TYPE_PRECISION (type); |

1227 | |

1228 | enforce_overflow_semantics = (use_overflow_semantics |

1229 | && nowrap_type_p (type)); |

1230 | if (enforce_overflow_semantics) |

1231 | { |

1232 | /* We can avoid checking whether the result overflows in the following |

1233 | cases: |

1234 | |

1235 | -- must_check_src_overflow is true, and the range of TYPE is superset |

1236 | of the range of CT -- i.e., in all cases except if CT signed and |

1237 | TYPE unsigned. |

1238 | -- both CT and TYPE have the same precision and signedness, and we |

1239 | verify instead that the source does not overflow (this may be |

1240 | easier than verifying it for the result, as we may use the |

1241 | information about the semantics of overflow in CT). */ |

1242 | if (must_check_src_overflow) |

1243 | { |

1244 | if (TYPE_UNSIGNED (type) && !TYPE_UNSIGNED (ct)) |

1245 | must_check_rslt_overflow = true; |

1246 | else |

1247 | must_check_rslt_overflow = false; |

1248 | } |

1249 | else if (TYPE_UNSIGNED (ct) == TYPE_UNSIGNED (type) |

1250 | && TYPE_PRECISION (ct) == TYPE_PRECISION (type)) |

1251 | { |

1252 | must_check_rslt_overflow = false; |

1253 | must_check_src_overflow = true; |

1254 | } |

1255 | else |

1256 | must_check_rslt_overflow = true; |

1257 | } |

1258 | else |

1259 | must_check_rslt_overflow = false; |

1260 | |

1261 | if (must_check_src_overflow |

1262 | && scev_probably_wraps_p (from, *base, *step, at_stmt, loop, |

1263 | use_overflow_semantics)) |

1264 | return false; |

1265 | |

1266 | new_base = chrec_convert (type, *base, at_stmt, use_overflow_semantics); |

1267 | /* The step must be sign extended, regardless of the signedness |

1268 | of CT and TYPE. This only needs to be handled specially when |

1269 | CT is unsigned -- to avoid e.g. unsigned char [100, +, 255] |

1270 | (with values 100, 99, 98, ...) from becoming signed or unsigned |

1271 | [100, +, 255] with values 100, 355, ...; the sign-extension is |

1272 | performed by default when CT is signed. */ |

1273 | new_step = *step; |

1274 | if (TYPE_PRECISION (step_type) > TYPE_PRECISION (ct) && TYPE_UNSIGNED (ct)) |

1275 | { |

1276 | tree signed_ct = build_nonstandard_integer_type (TYPE_PRECISION (ct), 0); |

1277 | new_step = chrec_convert (signed_ct, new_step, at_stmt, |

1278 | use_overflow_semantics); |

1279 | } |

1280 | new_step = chrec_convert (step_type, new_step, at_stmt, |

1281 | use_overflow_semantics); |

1282 | |

1283 | if (automatically_generated_chrec_p (new_base) |

1284 | || automatically_generated_chrec_p (new_step)) |

1285 | return false; |

1286 | |

1287 | if (must_check_rslt_overflow |

1288 | /* Note that in this case we cannot use the fact that signed variables |

1289 | do not overflow, as this is what we are verifying for the new iv. */ |

1290 | && scev_probably_wraps_p (NULL_TREE, new_base, new_step, |

1291 | at_stmt, loop, false)) |

1292 | return false; |

1293 | |

1294 | *base = new_base; |

1295 | *step = new_step; |

1296 | return true; |

1297 | } |

1298 | |

1299 | |

1300 | /* Convert CHREC for the right hand side of a CHREC. |

1301 | The increment for a pointer type is always sizetype. */ |

1302 | |

1303 | tree |

1304 | chrec_convert_rhs (tree type, tree chrec, gimple *at_stmt) |

1305 | { |

1306 | if (POINTER_TYPE_P (type)) |

1307 | type = sizetype; |

1308 | |

1309 | return chrec_convert (type, chrec, at_stmt); |

1310 | } |

1311 | |

1312 | /* Convert CHREC to TYPE. When the analyzer knows the context in |

1313 | which the CHREC is built, it sets AT_STMT to the statement that |

1314 | contains the definition of the analyzed variable, otherwise the |

1315 | conversion is less accurate: the information is used for |

1316 | determining a more accurate estimation of the number of iterations. |

1317 | By default AT_STMT could be safely set to NULL_TREE. |

1318 | |

1319 | USE_OVERFLOW_SEMANTICS is true if this function should assume that |

1320 | the rules for overflow of the given language apply (e.g., that signed |

1321 | arithmetics in C does not overflow) -- i.e., to use them to avoid |

1322 | unnecessary tests, but also to enforce that the result follows them. |

1323 | |

1324 | FROM is the source variable converted if it's not NULL. */ |

1325 | |

1326 | static tree |

1327 | chrec_convert_1 (tree type, tree chrec, gimple *at_stmt, |

1328 | bool use_overflow_semantics, tree from) |

1329 | { |

1330 | tree ct, res; |

1331 | tree base, step; |

1332 | struct loop *loop; |

1333 | |

1334 | if (automatically_generated_chrec_p (chrec)) |

1335 | return chrec; |

1336 | |

1337 | ct = chrec_type (chrec); |

1338 | if (useless_type_conversion_p (type, ct)) |

1339 | return chrec; |

1340 | |

1341 | if (!evolution_function_is_affine_p (chrec)) |

1342 | goto keep_cast; |

1343 | |

1344 | loop = get_chrec_loop (chrec); |

1345 | base = CHREC_LEFT (chrec); |

1346 | step = CHREC_RIGHT (chrec); |

1347 | |

1348 | if (convert_affine_scev (loop, type, &base, &step, at_stmt, |

1349 | use_overflow_semantics, from)) |

1350 | return build_polynomial_chrec (loop->num, base, step); |

1351 | |

1352 | /* If we cannot propagate the cast inside the chrec, just keep the cast. */ |

1353 | keep_cast: |

1354 | /* Fold will not canonicalize (long)(i - 1) to (long)i - 1 because that |

1355 | may be more expensive. We do want to perform this optimization here |

1356 | though for canonicalization reasons. */ |

1357 | if (use_overflow_semantics |

1358 | && (TREE_CODE (chrec) == PLUS_EXPR |

1359 | || TREE_CODE (chrec) == MINUS_EXPR) |

1360 | && TREE_CODE (type) == INTEGER_TYPE |

1361 | && TREE_CODE (ct) == INTEGER_TYPE |

1362 | && TYPE_PRECISION (type) > TYPE_PRECISION (ct) |

1363 | && TYPE_OVERFLOW_UNDEFINED (ct)) |

1364 | res = fold_build2 (TREE_CODE (chrec), type, |

1365 | fold_convert (type, TREE_OPERAND (chrec, 0)), |

1366 | fold_convert (type, TREE_OPERAND (chrec, 1))); |

1367 | /* Similar perform the trick that (signed char)((int)x + 2) can be |

1368 | narrowed to (signed char)((unsigned char)x + 2). */ |

1369 | else if (use_overflow_semantics |

1370 | && TREE_CODE (chrec) == POLYNOMIAL_CHREC |

1371 | && TREE_CODE (ct) == INTEGER_TYPE |

1372 | && TREE_CODE (type) == INTEGER_TYPE |

1373 | && TYPE_OVERFLOW_UNDEFINED (type) |

1374 | && TYPE_PRECISION (type) < TYPE_PRECISION (ct)) |

1375 | { |

1376 | tree utype = unsigned_type_for (type); |

1377 | res = build_polynomial_chrec (CHREC_VARIABLE (chrec), |

1378 | fold_convert (utype, |

1379 | CHREC_LEFT (chrec)), |

1380 | fold_convert (utype, |

1381 | CHREC_RIGHT (chrec))); |

1382 | res = chrec_convert_1 (type, res, at_stmt, use_overflow_semantics, from); |

1383 | } |

1384 | else |

1385 | res = fold_convert (type, chrec); |

1386 | |

1387 | /* Don't propagate overflows. */ |

1388 | if (CONSTANT_CLASS_P (res)) |

1389 | TREE_OVERFLOW (res) = 0; |

1390 | |

1391 | /* But reject constants that don't fit in their type after conversion. |

1392 | This can happen if TYPE_MIN_VALUE or TYPE_MAX_VALUE are not the |

1393 | natural values associated with TYPE_PRECISION and TYPE_UNSIGNED, |

1394 | and can cause problems later when computing niters of loops. Note |

1395 | that we don't do the check before converting because we don't want |

1396 | to reject conversions of negative chrecs to unsigned types. */ |

1397 | if (TREE_CODE (res) == INTEGER_CST |

1398 | && TREE_CODE (type) == INTEGER_TYPE |

1399 | && !int_fits_type_p (res, type)) |

1400 | res = chrec_dont_know; |

1401 | |

1402 | return res; |

1403 | } |

1404 | |

1405 | /* Convert CHREC to TYPE. When the analyzer knows the context in |

1406 | which the CHREC is built, it sets AT_STMT to the statement that |

1407 | contains the definition of the analyzed variable, otherwise the |

1408 | conversion is less accurate: the information is used for |

1409 | determining a more accurate estimation of the number of iterations. |

1410 | By default AT_STMT could be safely set to NULL_TREE. |

1411 | |

1412 | The following rule is always true: TREE_TYPE (chrec) == |

1413 | TREE_TYPE (CHREC_LEFT (chrec)) == TREE_TYPE (CHREC_RIGHT (chrec)). |

1414 | An example of what could happen when adding two chrecs and the type |

1415 | of the CHREC_RIGHT is different than CHREC_LEFT is: |

1416 | |

1417 | {(uint) 0, +, (uchar) 10} + |

1418 | {(uint) 0, +, (uchar) 250} |

1419 | |

1420 | that would produce a wrong result if CHREC_RIGHT is not (uint): |

1421 | |

1422 | {(uint) 0, +, (uchar) 4} |

1423 | |

1424 | instead of |

1425 | |

1426 | {(uint) 0, +, (uint) 260} |

1427 | |

1428 | USE_OVERFLOW_SEMANTICS is true if this function should assume that |

1429 | the rules for overflow of the given language apply (e.g., that signed |

1430 | arithmetics in C does not overflow) -- i.e., to use them to avoid |

1431 | unnecessary tests, but also to enforce that the result follows them. |

1432 | |

1433 | FROM is the source variable converted if it's not NULL. */ |

1434 | |

1435 | tree |

1436 | chrec_convert (tree type, tree chrec, gimple *at_stmt, |

1437 | bool use_overflow_semantics, tree from) |

1438 | { |

1439 | return chrec_convert_1 (type, chrec, at_stmt, use_overflow_semantics, from); |

1440 | } |

1441 | |

1442 | /* Convert CHREC to TYPE, without regard to signed overflows. Returns the new |

1443 | chrec if something else than what chrec_convert would do happens, NULL_TREE |

1444 | otherwise. This function set TRUE to variable pointed by FOLD_CONVERSIONS |

1445 | if the result chrec may overflow. */ |

1446 | |

1447 | tree |

1448 | chrec_convert_aggressive (tree type, tree chrec, bool *fold_conversions) |

1449 | { |

1450 | tree inner_type, left, right, lc, rc, rtype; |

1451 | |

1452 | gcc_assert (fold_conversions != NULL); |

1453 | |

1454 | if (automatically_generated_chrec_p (chrec) |

1455 | || TREE_CODE (chrec) != POLYNOMIAL_CHREC) |

1456 | return NULL_TREE; |

1457 | |

1458 | inner_type = TREE_TYPE (chrec); |

1459 | if (TYPE_PRECISION (type) > TYPE_PRECISION (inner_type)) |

1460 | return NULL_TREE; |

1461 | |

1462 | if (useless_type_conversion_p (type, inner_type)) |

1463 | return NULL_TREE; |

1464 | |

1465 | if (!*fold_conversions && evolution_function_is_affine_p (chrec)) |

1466 | { |

1467 | tree base, step; |

1468 | struct loop *loop; |

1469 | |

1470 | loop = get_chrec_loop (chrec); |

1471 | base = CHREC_LEFT (chrec); |

1472 | step = CHREC_RIGHT (chrec); |

1473 | if (convert_affine_scev (loop, type, &base, &step, NULL, true)) |

1474 | return build_polynomial_chrec (loop->num, base, step); |

1475 | } |

1476 | rtype = POINTER_TYPE_P (type) ? sizetype : type; |

1477 | |

1478 | left = CHREC_LEFT (chrec); |

1479 | right = CHREC_RIGHT (chrec); |

1480 | lc = chrec_convert_aggressive (type, left, fold_conversions); |

1481 | if (!lc) |

1482 | lc = chrec_convert (type, left, NULL); |

1483 | rc = chrec_convert_aggressive (rtype, right, fold_conversions); |

1484 | if (!rc) |

1485 | rc = chrec_convert (rtype, right, NULL); |

1486 | |

1487 | *fold_conversions = true; |

1488 | |

1489 | return build_polynomial_chrec (CHREC_VARIABLE (chrec), lc, rc); |

1490 | } |

1491 | |

1492 | /* Returns true when CHREC0 == CHREC1. */ |

1493 | |

1494 | bool |

1495 | eq_evolutions_p (const_tree chrec0, const_tree chrec1) |

1496 | { |

1497 | if (chrec0 == NULL_TREE |

1498 | || chrec1 == NULL_TREE |

1499 | || TREE_CODE (chrec0) != TREE_CODE (chrec1)) |

1500 | return false; |

1501 | |

1502 | if (chrec0 == chrec1) |

1503 | return true; |

1504 | |

1505 | if (! types_compatible_p (TREE_TYPE (chrec0), TREE_TYPE (chrec1))) |

1506 | return false; |

1507 | |

1508 | switch (TREE_CODE (chrec0)) |

1509 | { |

1510 | case POLYNOMIAL_CHREC: |

1511 | return (CHREC_VARIABLE (chrec0) == CHREC_VARIABLE (chrec1) |

1512 | && eq_evolutions_p (CHREC_LEFT (chrec0), CHREC_LEFT (chrec1)) |

1513 | && eq_evolutions_p (CHREC_RIGHT (chrec0), CHREC_RIGHT (chrec1))); |

1514 | |

1515 | case PLUS_EXPR: |

1516 | case MULT_EXPR: |

1517 | case MINUS_EXPR: |

1518 | case POINTER_PLUS_EXPR: |

1519 | return eq_evolutions_p (TREE_OPERAND (chrec0, 0), |

1520 | TREE_OPERAND (chrec1, 0)) |

1521 | && eq_evolutions_p (TREE_OPERAND (chrec0, 1), |

1522 | TREE_OPERAND (chrec1, 1)); |

1523 | |

1524 | CASE_CONVERT: |

1525 | return eq_evolutions_p (TREE_OPERAND (chrec0, 0), |

1526 | TREE_OPERAND (chrec1, 0)); |

1527 | |

1528 | default: |

1529 | return operand_equal_p (chrec0, chrec1, 0); |

1530 | } |

1531 | } |

1532 | |

1533 | /* Returns EV_GROWS if CHREC grows (assuming that it does not overflow), |

1534 | EV_DECREASES if it decreases, and EV_UNKNOWN if we cannot determine |

1535 | which of these cases happens. */ |

1536 | |

1537 | enum ev_direction |

1538 | scev_direction (const_tree chrec) |

1539 | { |

1540 | const_tree step; |

1541 | |

1542 | if (!evolution_function_is_affine_p (chrec)) |

1543 | return EV_DIR_UNKNOWN; |

1544 | |

1545 | step = CHREC_RIGHT (chrec); |

1546 | if (TREE_CODE (step) != INTEGER_CST) |

1547 | return EV_DIR_UNKNOWN; |

1548 | |

1549 | if (tree_int_cst_sign_bit (step)) |

1550 | return EV_DIR_DECREASES; |

1551 | else |

1552 | return EV_DIR_GROWS; |

1553 | } |

1554 | |

1555 | /* Iterates over all the components of SCEV, and calls CBCK. */ |

1556 | |

1557 | void |

1558 | for_each_scev_op (tree *scev, bool (*cbck) (tree *, void *), void *data) |

1559 | { |

1560 | switch (TREE_CODE_LENGTH (TREE_CODE (*scev))) |

1561 | { |

1562 | case 3: |

1563 | for_each_scev_op (&TREE_OPERAND (*scev, 2), cbck, data); |

1564 | /* FALLTHRU */ |

1565 | |

1566 | case 2: |

1567 | for_each_scev_op (&TREE_OPERAND (*scev, 1), cbck, data); |

1568 | /* FALLTHRU */ |

1569 | |

1570 | case 1: |

1571 | for_each_scev_op (&TREE_OPERAND (*scev, 0), cbck, data); |

1572 | /* FALLTHRU */ |

1573 | |

1574 | default: |

1575 | cbck (scev, data); |

1576 | break; |

1577 | } |

1578 | } |

1579 | |

1580 | /* Returns true when the operation can be part of a linear |

1581 | expression. */ |

1582 | |

1583 | static inline bool |

1584 | operator_is_linear (tree scev) |

1585 | { |

1586 | switch (TREE_CODE (scev)) |

1587 | { |

1588 | case INTEGER_CST: |

1589 | case POLYNOMIAL_CHREC: |

1590 | case PLUS_EXPR: |

1591 | case POINTER_PLUS_EXPR: |

1592 | case MULT_EXPR: |

1593 | case MINUS_EXPR: |

1594 | case NEGATE_EXPR: |

1595 | case SSA_NAME: |

1596 | case NON_LVALUE_EXPR: |

1597 | case BIT_NOT_EXPR: |

1598 | CASE_CONVERT: |

1599 | return true; |

1600 | |

1601 | default: |

1602 | return false; |

1603 | } |

1604 | } |

1605 | |

1606 | /* Return true when SCEV is a linear expression. Linear expressions |

1607 | can contain additions, substractions and multiplications. |

1608 | Multiplications are restricted to constant scaling: "cst * x". */ |

1609 | |

1610 | bool |

1611 | scev_is_linear_expression (tree scev) |

1612 | { |

1613 | if (evolution_function_is_constant_p (scev)) |

1614 | return true; |

1615 | |

1616 | if (scev == NULL |

1617 | || !operator_is_linear (scev)) |

1618 | return false; |

1619 | |

1620 | if (TREE_CODE (scev) == MULT_EXPR) |

1621 | return !(tree_contains_chrecs (TREE_OPERAND (scev, 0), NULL) |

1622 | && tree_contains_chrecs (TREE_OPERAND (scev, 1), NULL)); |

1623 | |

1624 | if (TREE_CODE (scev) == POLYNOMIAL_CHREC |

1625 | && !evolution_function_is_affine_multivariate_p (scev, CHREC_VARIABLE (scev))) |

1626 | return false; |

1627 | |

1628 | switch (TREE_CODE_LENGTH (TREE_CODE (scev))) |

1629 | { |

1630 | case 3: |

1631 | return scev_is_linear_expression (TREE_OPERAND (scev, 0)) |

1632 | && scev_is_linear_expression (TREE_OPERAND (scev, 1)) |

1633 | && scev_is_linear_expression (TREE_OPERAND (scev, 2)); |

1634 | |

1635 | case 2: |

1636 | return scev_is_linear_expression (TREE_OPERAND (scev, 0)) |

1637 | && scev_is_linear_expression (TREE_OPERAND (scev, 1)); |

1638 | |

1639 | case 1: |

1640 | return scev_is_linear_expression (TREE_OPERAND (scev, 0)); |

1641 | |

1642 | case 0: |

1643 | return true; |

1644 | |

1645 | default: |

1646 | return false; |

1647 | } |

1648 | } |

1649 | |

1650 | /* Determines whether the expression CHREC contains only interger consts |

1651 | in the right parts. */ |

1652 | |

1653 | bool |

1654 | evolution_function_right_is_integer_cst (const_tree chrec) |

1655 | { |

1656 | if (chrec == NULL_TREE) |

1657 | return false; |

1658 | |

1659 | switch (TREE_CODE (chrec)) |

1660 | { |

1661 | case INTEGER_CST: |

1662 | return true; |

1663 | |

1664 | case POLYNOMIAL_CHREC: |

1665 | return TREE_CODE (CHREC_RIGHT (chrec)) == INTEGER_CST |

1666 | && (TREE_CODE (CHREC_LEFT (chrec)) != POLYNOMIAL_CHREC |

1667 | || evolution_function_right_is_integer_cst (CHREC_LEFT (chrec))); |

1668 | |

1669 | CASE_CONVERT: |

1670 | return evolution_function_right_is_integer_cst (TREE_OPERAND (chrec, 0)); |

1671 | |

1672 | default: |

1673 | return false; |

1674 | } |

1675 | } |

1676 |