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5c9c1e7c | 1 | /* Support routines for range operations on wide ints. |
fbd26352 | 2 | Copyright (C) 2018-2019 Free Software Foundation, Inc. |
5c9c1e7c | 3 | |
4 | This file is part of GCC. | |
5 | ||
6 | GCC is free software; you can redistribute it and/or modify | |
7 | it under the terms of the GNU General Public License as published by | |
8 | the Free Software Foundation; either version 3, or (at your option) | |
9 | any later version. | |
10 | ||
11 | GCC is distributed in the hope that it will be useful, | |
12 | but WITHOUT ANY WARRANTY; without even the implied warranty of | |
13 | MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the | |
14 | GNU General Public License for more details. | |
15 | ||
16 | You should have received a copy of the GNU General Public License | |
17 | along with GCC; see the file COPYING3. If not see | |
18 | <http://www.gnu.org/licenses/>. */ | |
19 | ||
20 | #include "config.h" | |
21 | #include "system.h" | |
22 | #include "coretypes.h" | |
23 | #include "tree.h" | |
dcea420d | 24 | #include "function.h" |
5c9c1e7c | 25 | #include "fold-const.h" |
26 | #include "wide-int-range.h" | |
27 | ||
28 | /* Wrapper around wide_int_binop that adjusts for overflow. | |
29 | ||
30 | Return true if we can compute the result; i.e. if the operation | |
31 | doesn't overflow or if the overflow is undefined. In the latter | |
32 | case (if the operation overflows and overflow is undefined), then | |
33 | adjust the result to be -INF or +INF depending on CODE, VAL1 and | |
34 | VAL2. Return the value in *RES. | |
35 | ||
36 | Return false for division by zero, for which the result is | |
37 | indeterminate. */ | |
38 | ||
39 | static bool | |
40 | wide_int_binop_overflow (wide_int &res, | |
41 | enum tree_code code, | |
42 | const wide_int &w0, const wide_int &w1, | |
43 | signop sign, bool overflow_undefined) | |
44 | { | |
45 | wi::overflow_type overflow; | |
46 | if (!wide_int_binop (res, code, w0, w1, sign, &overflow)) | |
47 | return false; | |
48 | ||
49 | /* If the operation overflowed return -INF or +INF depending on the | |
50 | operation and the combination of signs of the operands. */ | |
51 | if (overflow && overflow_undefined) | |
52 | { | |
53 | switch (code) | |
54 | { | |
55 | case MULT_EXPR: | |
56 | /* For multiplication, the sign of the overflow is given | |
57 | by the comparison of the signs of the operands. */ | |
58 | if (sign == UNSIGNED || w0.sign_mask () == w1.sign_mask ()) | |
59 | res = wi::max_value (w0.get_precision (), sign); | |
60 | else | |
61 | res = wi::min_value (w0.get_precision (), sign); | |
62 | return true; | |
63 | ||
64 | case TRUNC_DIV_EXPR: | |
65 | case FLOOR_DIV_EXPR: | |
66 | case CEIL_DIV_EXPR: | |
67 | case EXACT_DIV_EXPR: | |
68 | case ROUND_DIV_EXPR: | |
69 | /* For division, the only case is -INF / -1 = +INF. */ | |
70 | res = wi::max_value (w0.get_precision (), sign); | |
71 | return true; | |
72 | ||
73 | default: | |
74 | gcc_unreachable (); | |
75 | } | |
76 | } | |
77 | return !overflow; | |
78 | } | |
79 | ||
80 | /* For range [LB, UB] compute two wide_int bit masks. | |
81 | ||
82 | In the MAY_BE_NONZERO bit mask, if some bit is unset, it means that | |
83 | for all numbers in the range the bit is 0, otherwise it might be 0 | |
84 | or 1. | |
85 | ||
86 | In the MUST_BE_NONZERO bit mask, if some bit is set, it means that | |
87 | for all numbers in the range the bit is 1, otherwise it might be 0 | |
88 | or 1. */ | |
89 | ||
90 | void | |
91 | wide_int_range_set_zero_nonzero_bits (signop sign, | |
92 | const wide_int &lb, const wide_int &ub, | |
93 | wide_int &may_be_nonzero, | |
94 | wide_int &must_be_nonzero) | |
95 | { | |
96 | may_be_nonzero = wi::minus_one (lb.get_precision ()); | |
97 | must_be_nonzero = wi::zero (lb.get_precision ()); | |
98 | ||
99 | if (wi::eq_p (lb, ub)) | |
100 | { | |
101 | may_be_nonzero = lb; | |
102 | must_be_nonzero = may_be_nonzero; | |
103 | } | |
104 | else if (wi::ge_p (lb, 0, sign) || wi::lt_p (ub, 0, sign)) | |
105 | { | |
106 | wide_int xor_mask = lb ^ ub; | |
107 | may_be_nonzero = lb | ub; | |
108 | must_be_nonzero = lb & ub; | |
109 | if (xor_mask != 0) | |
110 | { | |
111 | wide_int mask = wi::mask (wi::floor_log2 (xor_mask), false, | |
112 | may_be_nonzero.get_precision ()); | |
113 | may_be_nonzero = may_be_nonzero | mask; | |
114 | must_be_nonzero = wi::bit_and_not (must_be_nonzero, mask); | |
115 | } | |
116 | } | |
117 | } | |
118 | ||
119 | /* Order 2 sets of wide int ranges (w0/w1, w2/w3) and set MIN/MAX | |
120 | accordingly. */ | |
121 | ||
122 | static void | |
9e4ef9ee | 123 | wide_int_range_order_set (wide_int &min, wide_int &max, |
124 | wide_int &w0, wide_int &w1, | |
125 | wide_int &w2, wide_int &w3, | |
126 | signop sign) | |
5c9c1e7c | 127 | { |
128 | /* Order pairs w0,w1 and w2,w3. */ | |
129 | if (wi::gt_p (w0, w1, sign)) | |
130 | std::swap (w0, w1); | |
131 | if (wi::gt_p (w2, w3, sign)) | |
132 | std::swap (w2, w3); | |
133 | ||
134 | /* Choose min and max from the ordered pairs. */ | |
135 | min = wi::min (w0, w2, sign); | |
136 | max = wi::max (w1, w3, sign); | |
137 | } | |
138 | ||
139 | /* Calculate the cross product of two sets of ranges (VR0 and VR1) and | |
140 | store the result in [RES_LB, RES_UB]. | |
141 | ||
142 | CODE is the operation to perform with sign SIGN. | |
143 | ||
144 | OVERFLOW_UNDEFINED is set if overflow is undefined for the operation type. | |
145 | ||
146 | Return TRUE if we were able to calculate the cross product. */ | |
147 | ||
148 | bool | |
149 | wide_int_range_cross_product (wide_int &res_lb, wide_int &res_ub, | |
150 | enum tree_code code, signop sign, | |
151 | const wide_int &vr0_lb, const wide_int &vr0_ub, | |
152 | const wide_int &vr1_lb, const wide_int &vr1_ub, | |
153 | bool overflow_undefined) | |
154 | { | |
155 | wide_int cp1, cp2, cp3, cp4; | |
156 | ||
157 | /* Compute the 4 cross operations, bailing if we get an overflow we | |
158 | can't handle. */ | |
159 | ||
160 | if (!wide_int_binop_overflow (cp1, code, vr0_lb, vr1_lb, sign, | |
161 | overflow_undefined)) | |
162 | return false; | |
163 | ||
164 | if (wi::eq_p (vr0_lb, vr0_ub)) | |
165 | cp3 = cp1; | |
166 | else if (!wide_int_binop_overflow (cp3, code, vr0_ub, vr1_lb, sign, | |
167 | overflow_undefined)) | |
168 | return false; | |
169 | ||
170 | if (wi::eq_p (vr1_lb, vr1_ub)) | |
171 | cp2 = cp1; | |
172 | else if (!wide_int_binop_overflow (cp2, code, vr0_lb, vr1_ub, sign, | |
173 | overflow_undefined)) | |
174 | return false; | |
175 | ||
176 | if (wi::eq_p (vr0_lb, vr0_ub)) | |
177 | cp4 = cp2; | |
178 | else if (!wide_int_binop_overflow (cp4, code, vr0_ub, vr1_ub, sign, | |
179 | overflow_undefined)) | |
180 | return false; | |
181 | ||
9e4ef9ee | 182 | wide_int_range_order_set (res_lb, res_ub, cp1, cp2, cp3, cp4, sign); |
5c9c1e7c | 183 | return true; |
184 | } | |
185 | ||
186 | /* Multiply two ranges when TYPE_OVERFLOW_WRAPS: | |
187 | ||
188 | [RES_LB, RES_UB] = [MIN0, MAX0] * [MIN1, MAX1] | |
189 | ||
190 | This is basically fancy code so we don't drop to varying with an | |
191 | unsigned [-3,-1]*[-3,-1]. | |
192 | ||
193 | Return TRUE if we were able to perform the operation. */ | |
194 | ||
195 | bool | |
196 | wide_int_range_mult_wrapping (wide_int &res_lb, | |
197 | wide_int &res_ub, | |
198 | signop sign, | |
199 | unsigned prec, | |
200 | const wide_int &min0_, | |
201 | const wide_int &max0_, | |
202 | const wide_int &min1_, | |
203 | const wide_int &max1_) | |
204 | { | |
205 | /* This test requires 2*prec bits if both operands are signed and | |
206 | 2*prec + 2 bits if either is not. Therefore, extend the values | |
207 | using the sign of the result to PREC2. From here on out, | |
208 | everthing is just signed math no matter what the input types | |
209 | were. */ | |
210 | widest2_int min0 = widest2_int::from (min0_, sign); | |
211 | widest2_int max0 = widest2_int::from (max0_, sign); | |
212 | widest2_int min1 = widest2_int::from (min1_, sign); | |
213 | widest2_int max1 = widest2_int::from (max1_, sign); | |
214 | widest2_int sizem1 = wi::mask <widest2_int> (prec, false); | |
215 | widest2_int size = sizem1 + 1; | |
216 | ||
217 | /* Canonicalize the intervals. */ | |
218 | if (sign == UNSIGNED) | |
219 | { | |
220 | if (wi::ltu_p (size, min0 + max0)) | |
221 | { | |
222 | min0 -= size; | |
223 | max0 -= size; | |
224 | } | |
225 | ||
226 | if (wi::ltu_p (size, min1 + max1)) | |
227 | { | |
228 | min1 -= size; | |
229 | max1 -= size; | |
230 | } | |
231 | } | |
232 | ||
233 | widest2_int prod0 = min0 * min1; | |
234 | widest2_int prod1 = min0 * max1; | |
235 | widest2_int prod2 = max0 * min1; | |
236 | widest2_int prod3 = max0 * max1; | |
237 | ||
238 | /* Sort the 4 products so that min is in prod0 and max is in | |
239 | prod3. */ | |
240 | /* min0min1 > max0max1 */ | |
241 | if (prod0 > prod3) | |
242 | std::swap (prod0, prod3); | |
243 | ||
244 | /* min0max1 > max0min1 */ | |
245 | if (prod1 > prod2) | |
246 | std::swap (prod1, prod2); | |
247 | ||
248 | if (prod0 > prod1) | |
249 | std::swap (prod0, prod1); | |
250 | ||
251 | if (prod2 > prod3) | |
252 | std::swap (prod2, prod3); | |
253 | ||
254 | /* diff = max - min. */ | |
255 | prod2 = prod3 - prod0; | |
256 | if (wi::geu_p (prod2, sizem1)) | |
257 | /* The range covers all values. */ | |
258 | return false; | |
259 | ||
260 | res_lb = wide_int::from (prod0, prec, sign); | |
261 | res_ub = wide_int::from (prod3, prec, sign); | |
262 | return true; | |
263 | } | |
264 | ||
265 | /* Perform multiplicative operation CODE on two ranges: | |
266 | ||
267 | [RES_LB, RES_UB] = [VR0_LB, VR0_UB] .CODE. [VR1_LB, VR1_LB] | |
268 | ||
269 | Return TRUE if we were able to perform the operation. | |
270 | ||
2e73c0cf | 271 | NOTE: If code is MULT_EXPR and !TYPE_OVERFLOW_UNDEFINED, the resulting |
5c9c1e7c | 272 | range must be canonicalized by the caller because its components |
273 | may be swapped. */ | |
274 | ||
275 | bool | |
276 | wide_int_range_multiplicative_op (wide_int &res_lb, wide_int &res_ub, | |
277 | enum tree_code code, | |
278 | signop sign, | |
279 | unsigned prec, | |
280 | const wide_int &vr0_lb, | |
281 | const wide_int &vr0_ub, | |
282 | const wide_int &vr1_lb, | |
283 | const wide_int &vr1_ub, | |
2e73c0cf | 284 | bool overflow_undefined) |
5c9c1e7c | 285 | { |
286 | /* Multiplications, divisions and shifts are a bit tricky to handle, | |
287 | depending on the mix of signs we have in the two ranges, we | |
288 | need to operate on different values to get the minimum and | |
289 | maximum values for the new range. One approach is to figure | |
290 | out all the variations of range combinations and do the | |
291 | operations. | |
292 | ||
293 | However, this involves several calls to compare_values and it | |
294 | is pretty convoluted. It's simpler to do the 4 operations | |
295 | (MIN0 OP MIN1, MIN0 OP MAX1, MAX0 OP MIN1 and MAX0 OP MAX0 OP | |
296 | MAX1) and then figure the smallest and largest values to form | |
297 | the new range. */ | |
2e73c0cf | 298 | if (code == MULT_EXPR && !overflow_undefined) |
5c9c1e7c | 299 | return wide_int_range_mult_wrapping (res_lb, res_ub, |
300 | sign, prec, | |
301 | vr0_lb, vr0_ub, vr1_lb, vr1_ub); | |
302 | return wide_int_range_cross_product (res_lb, res_ub, | |
303 | code, sign, | |
304 | vr0_lb, vr0_ub, vr1_lb, vr1_ub, | |
305 | overflow_undefined); | |
306 | } | |
307 | ||
308 | /* Perform a left shift operation on two ranges: | |
309 | ||
310 | [RES_LB, RES_UB] = [VR0_LB, VR0_UB] << [VR1_LB, VR1_LB] | |
311 | ||
312 | Return TRUE if we were able to perform the operation. | |
313 | ||
314 | NOTE: The resulting range must be canonicalized by the caller | |
315 | because its contents components may be swapped. */ | |
316 | ||
317 | bool | |
318 | wide_int_range_lshift (wide_int &res_lb, wide_int &res_ub, | |
319 | signop sign, unsigned prec, | |
320 | const wide_int &vr0_lb, const wide_int &vr0_ub, | |
321 | const wide_int &vr1_lb, const wide_int &vr1_ub, | |
2e73c0cf | 322 | bool overflow_undefined) |
5c9c1e7c | 323 | { |
324 | /* Transform left shifts by constants into multiplies. */ | |
325 | if (wi::eq_p (vr1_lb, vr1_ub)) | |
326 | { | |
b7faf40d | 327 | unsigned shift = vr1_ub.to_uhwi (); |
5c9c1e7c | 328 | wide_int tmp = wi::set_bit_in_zero (shift, prec); |
329 | return wide_int_range_multiplicative_op (res_lb, res_ub, | |
330 | MULT_EXPR, sign, prec, | |
331 | vr0_lb, vr0_ub, tmp, tmp, | |
2e73c0cf | 332 | /*overflow_undefined=*/false); |
5c9c1e7c | 333 | } |
334 | ||
335 | int overflow_pos = prec; | |
336 | if (sign == SIGNED) | |
337 | overflow_pos -= 1; | |
338 | int bound_shift = overflow_pos - vr1_ub.to_shwi (); | |
339 | /* If bound_shift == HOST_BITS_PER_WIDE_INT, the llshift can | |
340 | overflow. However, for that to happen, vr1.max needs to be | |
341 | zero, which means vr1 is a singleton range of zero, which | |
342 | means it should be handled by the previous LSHIFT_EXPR | |
343 | if-clause. */ | |
344 | wide_int bound = wi::set_bit_in_zero (bound_shift, prec); | |
345 | wide_int complement = ~(bound - 1); | |
346 | wide_int low_bound, high_bound; | |
347 | bool in_bounds = false; | |
348 | if (sign == UNSIGNED) | |
349 | { | |
350 | low_bound = bound; | |
351 | high_bound = complement; | |
352 | if (wi::ltu_p (vr0_ub, low_bound)) | |
353 | { | |
354 | /* [5, 6] << [1, 2] == [10, 24]. */ | |
355 | /* We're shifting out only zeroes, the value increases | |
356 | monotonically. */ | |
357 | in_bounds = true; | |
358 | } | |
359 | else if (wi::ltu_p (high_bound, vr0_lb)) | |
360 | { | |
361 | /* [0xffffff00, 0xffffffff] << [1, 2] | |
362 | == [0xfffffc00, 0xfffffffe]. */ | |
363 | /* We're shifting out only ones, the value decreases | |
364 | monotonically. */ | |
365 | in_bounds = true; | |
366 | } | |
367 | } | |
368 | else | |
369 | { | |
370 | /* [-1, 1] << [1, 2] == [-4, 4]. */ | |
371 | low_bound = complement; | |
372 | high_bound = bound; | |
373 | if (wi::lts_p (vr0_ub, high_bound) | |
374 | && wi::lts_p (low_bound, vr0_lb)) | |
375 | { | |
376 | /* For non-negative numbers, we're shifting out only | |
377 | zeroes, the value increases monotonically. | |
378 | For negative numbers, we're shifting out only ones, the | |
379 | value decreases monotomically. */ | |
380 | in_bounds = true; | |
381 | } | |
382 | } | |
383 | if (in_bounds) | |
384 | return wide_int_range_multiplicative_op (res_lb, res_ub, | |
385 | LSHIFT_EXPR, sign, prec, | |
386 | vr0_lb, vr0_ub, | |
387 | vr1_lb, vr1_ub, | |
2e73c0cf | 388 | overflow_undefined); |
5c9c1e7c | 389 | return false; |
390 | } | |
391 | ||
392 | /* Return TRUE if a bit operation on two ranges can be easily | |
393 | optimized in terms of a mask. | |
394 | ||
395 | Basically, for BIT_AND_EXPR or BIT_IOR_EXPR see if we can optimize: | |
396 | ||
397 | [LB, UB] op Z | |
398 | into: | |
399 | [LB op Z, UB op Z] | |
400 | ||
401 | It is up to the caller to perform the actual folding above. */ | |
402 | ||
f0c8c617 | 403 | static bool |
5c9c1e7c | 404 | wide_int_range_can_optimize_bit_op (tree_code code, |
405 | const wide_int &lb, const wide_int &ub, | |
406 | const wide_int &mask) | |
407 | ||
408 | { | |
409 | if (code != BIT_AND_EXPR && code != BIT_IOR_EXPR) | |
410 | return false; | |
411 | /* If Z is a constant which (for op | its bitwise not) has n | |
412 | consecutive least significant bits cleared followed by m 1 | |
413 | consecutive bits set immediately above it and either | |
414 | m + n == precision, or (x >> (m + n)) == (y >> (m + n)). | |
415 | ||
416 | The least significant n bits of all the values in the range are | |
417 | cleared or set, the m bits above it are preserved and any bits | |
418 | above these are required to be the same for all values in the | |
419 | range. */ | |
420 | ||
421 | wide_int w = mask; | |
422 | int m = 0, n = 0; | |
423 | if (code == BIT_IOR_EXPR) | |
424 | w = ~w; | |
425 | if (wi::eq_p (w, 0)) | |
426 | n = w.get_precision (); | |
427 | else | |
428 | { | |
429 | n = wi::ctz (w); | |
430 | w = ~(w | wi::mask (n, false, w.get_precision ())); | |
431 | if (wi::eq_p (w, 0)) | |
432 | m = w.get_precision () - n; | |
433 | else | |
434 | m = wi::ctz (w) - n; | |
435 | } | |
436 | wide_int new_mask = wi::mask (m + n, true, w.get_precision ()); | |
437 | if ((new_mask & lb) == (new_mask & ub)) | |
438 | return true; | |
439 | ||
440 | return false; | |
441 | } | |
442 | ||
f0c8c617 | 443 | /* Helper function for wide_int_range_optimize_bit_op. |
444 | ||
445 | Calculates bounds and mask for a pair of ranges. The mask is the | |
446 | singleton range among the ranges, if any. The bounds are the | |
447 | bounds for the remaining range. */ | |
448 | ||
449 | bool | |
450 | wide_int_range_get_mask_and_bounds (wide_int &mask, | |
451 | wide_int &lower_bound, | |
452 | wide_int &upper_bound, | |
453 | const wide_int &vr0_min, | |
454 | const wide_int &vr0_max, | |
455 | const wide_int &vr1_min, | |
456 | const wide_int &vr1_max) | |
457 | { | |
458 | if (wi::eq_p (vr1_min, vr1_max)) | |
459 | { | |
460 | mask = vr1_min; | |
461 | lower_bound = vr0_min; | |
462 | upper_bound = vr0_max; | |
463 | return true; | |
464 | } | |
465 | else if (wi::eq_p (vr0_min, vr0_max)) | |
466 | { | |
467 | mask = vr0_min; | |
468 | lower_bound = vr1_min; | |
469 | upper_bound = vr1_max; | |
470 | return true; | |
471 | } | |
472 | return false; | |
473 | } | |
474 | ||
475 | /* Optimize a bit operation (BIT_AND_EXPR or BIT_IOR_EXPR) if | |
476 | possible. If so, return TRUE and store the result in | |
477 | [RES_LB, RES_UB]. */ | |
478 | ||
479 | bool | |
480 | wide_int_range_optimize_bit_op (wide_int &res_lb, wide_int &res_ub, | |
481 | enum tree_code code, | |
482 | signop sign, | |
483 | const wide_int &vr0_min, | |
484 | const wide_int &vr0_max, | |
485 | const wide_int &vr1_min, | |
486 | const wide_int &vr1_max) | |
487 | { | |
488 | gcc_assert (code == BIT_AND_EXPR || code == BIT_IOR_EXPR); | |
489 | ||
490 | wide_int lower_bound, upper_bound, mask; | |
491 | if (!wide_int_range_get_mask_and_bounds (mask, lower_bound, upper_bound, | |
492 | vr0_min, vr0_max, vr1_min, vr1_max)) | |
493 | return false; | |
494 | if (wide_int_range_can_optimize_bit_op (code, | |
495 | lower_bound, upper_bound, mask)) | |
496 | { | |
497 | wi::overflow_type ovf; | |
498 | wide_int_binop (res_lb, code, lower_bound, mask, sign, &ovf); | |
499 | wide_int_binop (res_ub, code, upper_bound, mask, sign, &ovf); | |
500 | return true; | |
501 | } | |
502 | return false; | |
503 | } | |
504 | ||
5c9c1e7c | 505 | /* Calculate the XOR of two ranges and store the result in [WMIN,WMAX]. |
506 | The two input ranges are described by their MUST_BE_NONZERO and | |
507 | MAY_BE_NONZERO bit masks. | |
508 | ||
509 | Return TRUE if we were able to successfully calculate the new range. */ | |
510 | ||
511 | bool | |
512 | wide_int_range_bit_xor (wide_int &wmin, wide_int &wmax, | |
513 | signop sign, | |
514 | unsigned prec, | |
515 | const wide_int &must_be_nonzero0, | |
516 | const wide_int &may_be_nonzero0, | |
517 | const wide_int &must_be_nonzero1, | |
518 | const wide_int &may_be_nonzero1) | |
519 | { | |
520 | wide_int result_zero_bits = ((must_be_nonzero0 & must_be_nonzero1) | |
521 | | ~(may_be_nonzero0 | may_be_nonzero1)); | |
522 | wide_int result_one_bits | |
523 | = (wi::bit_and_not (must_be_nonzero0, may_be_nonzero1) | |
524 | | wi::bit_and_not (must_be_nonzero1, may_be_nonzero0)); | |
525 | wmax = ~result_zero_bits; | |
526 | wmin = result_one_bits; | |
527 | /* If the range has all positive or all negative values, the result | |
528 | is better than VARYING. */ | |
529 | if (wi::lt_p (wmin, 0, sign) || wi::ge_p (wmax, 0, sign)) | |
530 | return true; | |
531 | wmin = wi::min_value (prec, sign); | |
532 | wmax = wi::max_value (prec, sign); | |
533 | return false; | |
534 | } | |
535 | ||
536 | /* Calculate the IOR of two ranges and store the result in [WMIN,WMAX]. | |
537 | Return TRUE if we were able to successfully calculate the new range. */ | |
538 | ||
539 | bool | |
540 | wide_int_range_bit_ior (wide_int &wmin, wide_int &wmax, | |
541 | signop sign, | |
542 | const wide_int &vr0_min, | |
543 | const wide_int &vr0_max, | |
544 | const wide_int &vr1_min, | |
545 | const wide_int &vr1_max, | |
546 | const wide_int &must_be_nonzero0, | |
547 | const wide_int &may_be_nonzero0, | |
548 | const wide_int &must_be_nonzero1, | |
549 | const wide_int &may_be_nonzero1) | |
550 | { | |
f0c8c617 | 551 | if (wide_int_range_optimize_bit_op (wmin, wmax, BIT_IOR_EXPR, sign, |
552 | vr0_min, vr0_max, | |
553 | vr1_min, vr1_max)) | |
554 | return true; | |
5c9c1e7c | 555 | wmin = must_be_nonzero0 | must_be_nonzero1; |
556 | wmax = may_be_nonzero0 | may_be_nonzero1; | |
557 | /* If the input ranges contain only positive values we can | |
558 | truncate the minimum of the result range to the maximum | |
559 | of the input range minima. */ | |
560 | if (wi::ge_p (vr0_min, 0, sign) | |
561 | && wi::ge_p (vr1_min, 0, sign)) | |
562 | { | |
563 | wmin = wi::max (wmin, vr0_min, sign); | |
564 | wmin = wi::max (wmin, vr1_min, sign); | |
565 | } | |
566 | /* If either input range contains only negative values | |
567 | we can truncate the minimum of the result range to the | |
568 | respective minimum range. */ | |
569 | if (wi::lt_p (vr0_max, 0, sign)) | |
570 | wmin = wi::max (wmin, vr0_min, sign); | |
571 | if (wi::lt_p (vr1_max, 0, sign)) | |
572 | wmin = wi::max (wmin, vr1_min, sign); | |
573 | /* If the limits got swapped around, indicate error so we can adjust | |
574 | the range to VARYING. */ | |
575 | if (wi::gt_p (wmin, wmax,sign)) | |
576 | return false; | |
577 | return true; | |
578 | } | |
579 | ||
580 | /* Calculate the bitwise AND of two ranges and store the result in [WMIN,WMAX]. | |
581 | Return TRUE if we were able to successfully calculate the new range. */ | |
582 | ||
583 | bool | |
584 | wide_int_range_bit_and (wide_int &wmin, wide_int &wmax, | |
585 | signop sign, | |
586 | unsigned prec, | |
587 | const wide_int &vr0_min, | |
588 | const wide_int &vr0_max, | |
589 | const wide_int &vr1_min, | |
590 | const wide_int &vr1_max, | |
591 | const wide_int &must_be_nonzero0, | |
592 | const wide_int &may_be_nonzero0, | |
593 | const wide_int &must_be_nonzero1, | |
594 | const wide_int &may_be_nonzero1) | |
595 | { | |
f0c8c617 | 596 | if (wide_int_range_optimize_bit_op (wmin, wmax, BIT_AND_EXPR, sign, |
597 | vr0_min, vr0_max, | |
598 | vr1_min, vr1_max)) | |
599 | return true; | |
5c9c1e7c | 600 | wmin = must_be_nonzero0 & must_be_nonzero1; |
601 | wmax = may_be_nonzero0 & may_be_nonzero1; | |
602 | /* If both input ranges contain only negative values we can | |
603 | truncate the result range maximum to the minimum of the | |
604 | input range maxima. */ | |
605 | if (wi::lt_p (vr0_max, 0, sign) && wi::lt_p (vr1_max, 0, sign)) | |
606 | { | |
607 | wmax = wi::min (wmax, vr0_max, sign); | |
608 | wmax = wi::min (wmax, vr1_max, sign); | |
609 | } | |
610 | /* If either input range contains only non-negative values | |
611 | we can truncate the result range maximum to the respective | |
612 | maximum of the input range. */ | |
613 | if (wi::ge_p (vr0_min, 0, sign)) | |
614 | wmax = wi::min (wmax, vr0_max, sign); | |
615 | if (wi::ge_p (vr1_min, 0, sign)) | |
616 | wmax = wi::min (wmax, vr1_max, sign); | |
617 | /* PR68217: In case of signed & sign-bit-CST should | |
618 | result in [-INF, 0] instead of [-INF, INF]. */ | |
619 | if (wi::gt_p (wmin, wmax, sign)) | |
620 | { | |
621 | wide_int sign_bit = wi::set_bit_in_zero (prec - 1, prec); | |
622 | if (sign == SIGNED | |
623 | && ((wi::eq_p (vr0_min, vr0_max) | |
624 | && !wi::cmps (vr0_min, sign_bit)) | |
625 | || (wi::eq_p (vr1_min, vr1_max) | |
626 | && !wi::cmps (vr1_min, sign_bit)))) | |
627 | { | |
628 | wmin = wi::min_value (prec, sign); | |
629 | wmax = wi::zero (prec); | |
630 | } | |
631 | } | |
632 | /* If the limits got swapped around, indicate error so we can adjust | |
633 | the range to VARYING. */ | |
634 | if (wi::gt_p (wmin, wmax,sign)) | |
635 | return false; | |
636 | return true; | |
637 | } | |
638 | ||
639 | /* Calculate TRUNC_MOD_EXPR on two ranges and store the result in | |
640 | [WMIN,WMAX]. */ | |
641 | ||
642 | void | |
643 | wide_int_range_trunc_mod (wide_int &wmin, wide_int &wmax, | |
644 | signop sign, | |
645 | unsigned prec, | |
646 | const wide_int &vr0_min, | |
647 | const wide_int &vr0_max, | |
648 | const wide_int &vr1_min, | |
649 | const wide_int &vr1_max) | |
650 | { | |
651 | wide_int tmp; | |
652 | ||
653 | /* ABS (A % B) < ABS (B) and either | |
654 | 0 <= A % B <= A or A <= A % B <= 0. */ | |
655 | wmax = vr1_max - 1; | |
656 | if (sign == SIGNED) | |
657 | { | |
658 | tmp = -1 - vr1_min; | |
659 | wmax = wi::smax (wmax, tmp); | |
660 | } | |
661 | ||
662 | if (sign == UNSIGNED) | |
663 | wmin = wi::zero (prec); | |
664 | else | |
665 | { | |
666 | wmin = -wmax; | |
667 | tmp = vr0_min; | |
668 | if (wi::gts_p (tmp, 0)) | |
669 | tmp = wi::zero (prec); | |
670 | wmin = wi::smax (wmin, tmp); | |
671 | } | |
672 | tmp = vr0_max; | |
673 | if (sign == SIGNED && wi::neg_p (tmp)) | |
674 | tmp = wi::zero (prec); | |
675 | wmax = wi::min (wmax, tmp, sign); | |
676 | } | |
9e4ef9ee | 677 | |
678 | /* Calculate ABS_EXPR on a range and store the result in [MIN, MAX]. */ | |
679 | ||
680 | bool | |
681 | wide_int_range_abs (wide_int &min, wide_int &max, | |
682 | signop sign, unsigned prec, | |
683 | const wide_int &vr0_min, const wide_int &vr0_max, | |
684 | bool overflow_undefined) | |
685 | { | |
686 | /* Pass through VR0 the easy cases. */ | |
687 | if (sign == UNSIGNED || wi::ge_p (vr0_min, 0, sign)) | |
688 | { | |
689 | min = vr0_min; | |
690 | max = vr0_max; | |
691 | return true; | |
692 | } | |
693 | ||
694 | /* -TYPE_MIN_VALUE = TYPE_MIN_VALUE with flag_wrapv so we can't get a | |
695 | useful range. */ | |
696 | wide_int min_value = wi::min_value (prec, sign); | |
697 | wide_int max_value = wi::max_value (prec, sign); | |
698 | if (!overflow_undefined && wi::eq_p (vr0_min, min_value)) | |
699 | return false; | |
700 | ||
701 | /* ABS_EXPR may flip the range around, if the original range | |
702 | included negative values. */ | |
703 | if (wi::eq_p (vr0_min, min_value)) | |
704 | min = max_value; | |
705 | else | |
706 | min = wi::abs (vr0_min); | |
707 | if (wi::eq_p (vr0_max, min_value)) | |
708 | max = max_value; | |
709 | else | |
710 | max = wi::abs (vr0_max); | |
711 | ||
712 | /* If the range contains zero then we know that the minimum value in the | |
713 | range will be zero. */ | |
714 | if (wi::le_p (vr0_min, 0, sign) && wi::ge_p (vr0_max, 0, sign)) | |
715 | { | |
716 | if (wi::gt_p (min, max, sign)) | |
717 | max = min; | |
718 | min = wi::zero (prec); | |
719 | } | |
720 | else | |
721 | { | |
722 | /* If the range was reversed, swap MIN and MAX. */ | |
723 | if (wi::gt_p (min, max, sign)) | |
724 | std::swap (min, max); | |
725 | } | |
726 | ||
727 | /* If the new range has its limits swapped around (MIN > MAX), then | |
e3fdb3c6 | 728 | the operation caused one of them to wrap around. The only thing |
729 | we know is that the result is positive. */ | |
9e4ef9ee | 730 | if (wi::gt_p (min, max, sign)) |
e3fdb3c6 | 731 | { |
732 | min = wi::zero (prec); | |
733 | max = max_value; | |
734 | } | |
9e4ef9ee | 735 | return true; |
736 | } | |
dcea420d | 737 | |
38f851c4 | 738 | /* Calculate ABSU_EXPR on a range and store the result in [MIN, MAX]. */ |
739 | ||
740 | void | |
741 | wide_int_range_absu (wide_int &min, wide_int &max, | |
742 | unsigned prec, const wide_int &vr0_min, | |
743 | const wide_int &vr0_max) | |
744 | { | |
745 | /* Pass through VR0 the easy cases. */ | |
746 | if (wi::ges_p (vr0_min, 0)) | |
747 | { | |
748 | min = vr0_min; | |
749 | max = vr0_max; | |
750 | return; | |
751 | } | |
752 | ||
753 | min = wi::abs (vr0_min); | |
754 | max = wi::abs (vr0_max); | |
755 | ||
756 | /* If the range contains zero then we know that the minimum value in the | |
757 | range will be zero. */ | |
758 | if (wi::ges_p (vr0_max, 0)) | |
759 | { | |
760 | if (wi::gtu_p (min, max)) | |
761 | max = min; | |
762 | min = wi::zero (prec); | |
763 | } | |
764 | else | |
765 | /* Otherwise, swap MIN and MAX. */ | |
766 | std::swap (min, max); | |
767 | } | |
768 | ||
ed81b3ca | 769 | /* Convert range in [VR0_MIN, VR0_MAX] with INNER_SIGN and INNER_PREC, |
770 | to a range in [MIN, MAX] with OUTER_SIGN and OUTER_PREC. | |
771 | ||
772 | Return TRUE if we were able to successfully calculate the new range. | |
773 | ||
774 | Caller is responsible for canonicalizing the resulting range. */ | |
775 | ||
776 | bool | |
777 | wide_int_range_convert (wide_int &min, wide_int &max, | |
778 | signop inner_sign, | |
779 | unsigned inner_prec, | |
780 | signop outer_sign, | |
781 | unsigned outer_prec, | |
782 | const wide_int &vr0_min, | |
783 | const wide_int &vr0_max) | |
784 | { | |
785 | /* If the conversion is not truncating we can convert the min and | |
786 | max values and canonicalize the resulting range. Otherwise we | |
787 | can do the conversion if the size of the range is less than what | |
788 | the precision of the target type can represent. */ | |
789 | if (outer_prec >= inner_prec | |
790 | || wi::rshift (wi::sub (vr0_max, vr0_min), | |
791 | wi::uhwi (outer_prec, inner_prec), | |
792 | inner_sign) == 0) | |
793 | { | |
794 | min = wide_int::from (vr0_min, outer_prec, inner_sign); | |
795 | max = wide_int::from (vr0_max, outer_prec, inner_sign); | |
796 | return (!wi::eq_p (min, wi::min_value (outer_prec, outer_sign)) | |
797 | || !wi::eq_p (max, wi::max_value (outer_prec, outer_sign))); | |
798 | } | |
799 | return false; | |
800 | } | |
801 | ||
dcea420d | 802 | /* Calculate a division operation on two ranges and store the result in |
803 | [WMIN, WMAX] U [EXTRA_MIN, EXTRA_MAX]. | |
804 | ||
805 | If EXTRA_RANGE_P is set upon return, EXTRA_MIN/EXTRA_MAX hold | |
806 | meaningful information, otherwise they should be ignored. | |
807 | ||
808 | Return TRUE if we were able to successfully calculate the new range. */ | |
809 | ||
810 | bool | |
811 | wide_int_range_div (wide_int &wmin, wide_int &wmax, | |
812 | tree_code code, signop sign, unsigned prec, | |
813 | const wide_int ÷nd_min, const wide_int ÷nd_max, | |
814 | const wide_int &divisor_min, const wide_int &divisor_max, | |
815 | bool overflow_undefined, | |
dcea420d | 816 | bool &extra_range_p, |
817 | wide_int &extra_min, wide_int &extra_max) | |
818 | { | |
819 | extra_range_p = false; | |
820 | ||
821 | /* If we know we won't divide by zero, just do the division. */ | |
822 | if (!wide_int_range_includes_zero_p (divisor_min, divisor_max, sign)) | |
eba1b999 | 823 | return wide_int_range_multiplicative_op (wmin, wmax, code, sign, prec, |
824 | dividend_min, dividend_max, | |
825 | divisor_min, divisor_max, | |
2e73c0cf | 826 | overflow_undefined); |
dcea420d | 827 | |
828 | /* If flag_non_call_exceptions, we must not eliminate a division | |
829 | by zero. */ | |
830 | if (cfun->can_throw_non_call_exceptions) | |
831 | return false; | |
832 | ||
833 | /* If we're definitely dividing by zero, there's nothing to do. */ | |
834 | if (wide_int_range_zero_p (divisor_min, divisor_max, prec)) | |
835 | return false; | |
836 | ||
837 | /* Perform the division in 2 parts, [LB, -1] and [1, UB], | |
838 | which will skip any division by zero. | |
839 | ||
840 | First divide by the negative numbers, if any. */ | |
841 | if (wi::neg_p (divisor_min, sign)) | |
842 | { | |
843 | if (!wide_int_range_multiplicative_op (wmin, wmax, | |
844 | code, sign, prec, | |
845 | dividend_min, dividend_max, | |
846 | divisor_min, wi::minus_one (prec), | |
2e73c0cf | 847 | overflow_undefined)) |
dcea420d | 848 | return false; |
849 | extra_range_p = true; | |
850 | } | |
851 | /* Then divide by the non-zero positive numbers, if any. */ | |
852 | if (wi::gt_p (divisor_max, wi::zero (prec), sign)) | |
853 | { | |
854 | if (!wide_int_range_multiplicative_op (extra_range_p ? extra_min : wmin, | |
855 | extra_range_p ? extra_max : wmax, | |
856 | code, sign, prec, | |
857 | dividend_min, dividend_max, | |
858 | wi::one (prec), divisor_max, | |
2e73c0cf | 859 | overflow_undefined)) |
dcea420d | 860 | return false; |
861 | } | |
862 | else | |
863 | extra_range_p = false; | |
864 | return true; | |
865 | } |