xref: /llvm-project/mlir/lib/Interfaces/Utils/InferIntRangeCommon.cpp (revision 4a88b9043fc400e9c7a8a7ca3cfd7a67be3a6a7f) 
1 //===- InferIntRangeCommon.cpp - Inference for common ops ------------===//
2 //
3 // Part of the LLVM Project, under the Apache License v2.0 with LLVM Exceptions.
4 // See https://llvm.org/LICENSE.txt for license information.
5 // SPDX-License-Identifier: Apache-2.0 WITH LLVM-exception
6 //
7 //===----------------------------------------------------------------------===//
8 //
9 // This file contains implementations of range inference for operations that are
10 // common to both the `arith` and `index` dialects to facilitate reuse.
11 //
12 //===----------------------------------------------------------------------===//
13 
14 #include "mlir/Interfaces/Utils/InferIntRangeCommon.h"
15 
16 #include "mlir/Interfaces/InferIntRangeInterface.h"
17 
18 #include "llvm/ADT/ArrayRef.h"
19 #include "llvm/ADT/STLExtras.h"
20 
21 #include "llvm/Support/Debug.h"
22 
23 #include <iterator>
24 #include <optional>
25 
26 using namespace mlir;
27 
28 #define DEBUG_TYPE "int-range-analysis"
29 
30 //===----------------------------------------------------------------------===//
31 // General utilities
32 //===----------------------------------------------------------------------===//
33 
34 /// Function that evaluates the result of doing something on arithmetic
35 /// constants and returns std::nullopt on overflow.
36 using ConstArithFn =
37     function_ref<std::optional<APInt>(const APInt &, const APInt &)>;
38 using ConstArithStdFn =
39     std::function<std::optional<APInt>(const APInt &, const APInt &)>;
40 
41 /// Compute op(minLeft, minRight) and op(maxLeft, maxRight) if possible,
42 /// If either computation overflows, make the result unbounded.
43 static ConstantIntRanges computeBoundsBy(ConstArithFn op, const APInt &minLeft,
44                                          const APInt &minRight,
45                                          const APInt &maxLeft,
46                                          const APInt &maxRight, bool isSigned) {
47   std::optional<APInt> maybeMin = op(minLeft, minRight);
48   std::optional<APInt> maybeMax = op(maxLeft, maxRight);
49   if (maybeMin && maybeMax)
50     return ConstantIntRanges::range(*maybeMin, *maybeMax, isSigned);
51   return ConstantIntRanges::maxRange(minLeft.getBitWidth());
52 }
53 
54 /// Compute the minimum and maximum of `(op(l, r) for l in lhs for r in rhs)`,
55 /// ignoring unbounded values. Returns the maximal range if `op` overflows.
56 static ConstantIntRanges minMaxBy(ConstArithFn op, ArrayRef<APInt> lhs,
57                                   ArrayRef<APInt> rhs, bool isSigned) {
58   unsigned width = lhs[0].getBitWidth();
59   APInt min =
60       isSigned ? APInt::getSignedMaxValue(width) : APInt::getMaxValue(width);
61   APInt max =
62       isSigned ? APInt::getSignedMinValue(width) : APInt::getZero(width);
63   for (const APInt &left : lhs) {
64     for (const APInt &right : rhs) {
65       std::optional<APInt> maybeThisResult = op(left, right);
66       if (!maybeThisResult)
67         return ConstantIntRanges::maxRange(width);
68       APInt result = std::move(*maybeThisResult);
69       min = (isSigned ? result.slt(min) : result.ult(min)) ? result : min;
70       max = (isSigned ? result.sgt(max) : result.ugt(max)) ? result : max;
71     }
72   }
73   return ConstantIntRanges::range(min, max, isSigned);
74 }
75 
76 //===----------------------------------------------------------------------===//
77 // Ext, trunc, index op handling
78 //===----------------------------------------------------------------------===//
79 
80 ConstantIntRanges
81 mlir::intrange::inferIndexOp(const InferRangeFn &inferFn,
82                              ArrayRef<ConstantIntRanges> argRanges,
83                              intrange::CmpMode mode) {
84   ConstantIntRanges sixtyFour = inferFn(argRanges);
85   SmallVector<ConstantIntRanges, 2> truncated;
86   llvm::transform(argRanges, std::back_inserter(truncated),
87                   [](const ConstantIntRanges &range) {
88                     return truncRange(range, /*destWidth=*/indexMinWidth);
89                   });
90   ConstantIntRanges thirtyTwo = inferFn(truncated);
91   ConstantIntRanges thirtyTwoAsSixtyFour =
92       extRange(thirtyTwo, /*destWidth=*/indexMaxWidth);
93   ConstantIntRanges sixtyFourAsThirtyTwo =
94       truncRange(sixtyFour, /*destWidth=*/indexMinWidth);
95 
96   LLVM_DEBUG(llvm::dbgs() << "Index handling: 64-bit result = " << sixtyFour
97                           << " 32-bit = " << thirtyTwo << "\n");
98   bool truncEqual = false;
99   switch (mode) {
100   case intrange::CmpMode::Both:
101     truncEqual = (thirtyTwo == sixtyFourAsThirtyTwo);
102     break;
103   case intrange::CmpMode::Signed:
104     truncEqual = (thirtyTwo.smin() == sixtyFourAsThirtyTwo.smin() &&
105                   thirtyTwo.smax() == sixtyFourAsThirtyTwo.smax());
106     break;
107   case intrange::CmpMode::Unsigned:
108     truncEqual = (thirtyTwo.umin() == sixtyFourAsThirtyTwo.umin() &&
109                   thirtyTwo.umax() == sixtyFourAsThirtyTwo.umax());
110     break;
111   }
112   if (truncEqual)
113     // Returing the 64-bit result preserves more information.
114     return sixtyFour;
115   ConstantIntRanges merged = sixtyFour.rangeUnion(thirtyTwoAsSixtyFour);
116   return merged;
117 }
118 
119 ConstantIntRanges mlir::intrange::extRange(const ConstantIntRanges &range,
120                                            unsigned int destWidth) {
121   APInt umin = range.umin().zext(destWidth);
122   APInt umax = range.umax().zext(destWidth);
123   APInt smin = range.smin().sext(destWidth);
124   APInt smax = range.smax().sext(destWidth);
125   return {umin, umax, smin, smax};
126 }
127 
128 ConstantIntRanges mlir::intrange::extUIRange(const ConstantIntRanges &range,
129                                              unsigned destWidth) {
130   APInt umin = range.umin().zext(destWidth);
131   APInt umax = range.umax().zext(destWidth);
132   return ConstantIntRanges::fromUnsigned(umin, umax);
133 }
134 
135 ConstantIntRanges mlir::intrange::extSIRange(const ConstantIntRanges &range,
136                                              unsigned destWidth) {
137   APInt smin = range.smin().sext(destWidth);
138   APInt smax = range.smax().sext(destWidth);
139   return ConstantIntRanges::fromSigned(smin, smax);
140 }
141 
142 ConstantIntRanges mlir::intrange::truncRange(const ConstantIntRanges &range,
143                                              unsigned int destWidth) {
144   // If you truncate the first four bytes in [0xaaaabbbb, 0xccccbbbb],
145   // the range of the resulting value is not contiguous ind includes 0.
146   // Ex. If you truncate [256, 258] from i16 to i8, you validly get [0, 2],
147   // but you can't truncate [255, 257] similarly.
148   bool hasUnsignedRollover =
149       range.umin().lshr(destWidth) != range.umax().lshr(destWidth);
150   APInt umin = hasUnsignedRollover ? APInt::getZero(destWidth)
151                                    : range.umin().trunc(destWidth);
152   APInt umax = hasUnsignedRollover ? APInt::getMaxValue(destWidth)
153                                    : range.umax().trunc(destWidth);
154 
155   // Signed post-truncation rollover will not occur when either:
156   // - The high parts of the min and max, plus the sign bit, are the same
157   // - The high halves + sign bit of the min and max are either all 1s or all 0s
158   //  and you won't create a [positive, negative] range by truncating.
159   // For example, you can truncate the ranges [256, 258]_i16 to [0, 2]_i8
160   // but not [255, 257]_i16 to a range of i8s. You can also truncate
161   // [-256, -256]_i16 to [-2, 0]_i8, but not [-257, -255]_i16.
162   // You can also truncate [-130, 0]_i16 to i8 because -130_i16 (0xff7e)
163   // will truncate to 0x7e, which is greater than 0
164   APInt sminHighPart = range.smin().ashr(destWidth - 1);
165   APInt smaxHighPart = range.smax().ashr(destWidth - 1);
166   bool hasSignedOverflow =
167       (sminHighPart != smaxHighPart) &&
168       !(sminHighPart.isAllOnes() &&
169         (smaxHighPart.isAllOnes() || smaxHighPart.isZero())) &&
170       !(sminHighPart.isZero() && smaxHighPart.isZero());
171   APInt smin = hasSignedOverflow ? APInt::getSignedMinValue(destWidth)
172                                  : range.smin().trunc(destWidth);
173   APInt smax = hasSignedOverflow ? APInt::getSignedMaxValue(destWidth)
174                                  : range.smax().trunc(destWidth);
175   return {umin, umax, smin, smax};
176 }
177 
178 //===----------------------------------------------------------------------===//
179 // Addition
180 //===----------------------------------------------------------------------===//
181 
182 ConstantIntRanges
183 mlir::intrange::inferAdd(ArrayRef<ConstantIntRanges> argRanges,
184                          OverflowFlags ovfFlags) {
185   const ConstantIntRanges &lhs = argRanges[0], &rhs = argRanges[1];
186 
187   ConstArithStdFn uadd = [=](const APInt &a,
188                              const APInt &b) -> std::optional<APInt> {
189     bool overflowed = false;
190     APInt result = any(ovfFlags & OverflowFlags::Nuw)
191                        ? a.uadd_sat(b)
192                        : a.uadd_ov(b, overflowed);
193     return overflowed ? std::optional<APInt>() : result;
194   };
195   ConstArithStdFn sadd = [=](const APInt &a,
196                              const APInt &b) -> std::optional<APInt> {
197     bool overflowed = false;
198     APInt result = any(ovfFlags & OverflowFlags::Nsw)
199                        ? a.sadd_sat(b)
200                        : a.sadd_ov(b, overflowed);
201     return overflowed ? std::optional<APInt>() : result;
202   };
203 
204   ConstantIntRanges urange = computeBoundsBy(
205       uadd, lhs.umin(), rhs.umin(), lhs.umax(), rhs.umax(), /*isSigned=*/false);
206   ConstantIntRanges srange = computeBoundsBy(
207       sadd, lhs.smin(), rhs.smin(), lhs.smax(), rhs.smax(), /*isSigned=*/true);
208   return urange.intersection(srange);
209 }
210 
211 //===----------------------------------------------------------------------===//
212 // Subtraction
213 //===----------------------------------------------------------------------===//
214 
215 ConstantIntRanges
216 mlir::intrange::inferSub(ArrayRef<ConstantIntRanges> argRanges,
217                          OverflowFlags ovfFlags) {
218   const ConstantIntRanges &lhs = argRanges[0], &rhs = argRanges[1];
219 
220   ConstArithStdFn usub = [=](const APInt &a,
221                              const APInt &b) -> std::optional<APInt> {
222     bool overflowed = false;
223     APInt result = any(ovfFlags & OverflowFlags::Nuw)
224                        ? a.usub_sat(b)
225                        : a.usub_ov(b, overflowed);
226     return overflowed ? std::optional<APInt>() : result;
227   };
228   ConstArithStdFn ssub = [=](const APInt &a,
229                              const APInt &b) -> std::optional<APInt> {
230     bool overflowed = false;
231     APInt result = any(ovfFlags & OverflowFlags::Nsw)
232                        ? a.ssub_sat(b)
233                        : a.ssub_ov(b, overflowed);
234     return overflowed ? std::optional<APInt>() : result;
235   };
236   ConstantIntRanges urange = computeBoundsBy(
237       usub, lhs.umin(), rhs.umax(), lhs.umax(), rhs.umin(), /*isSigned=*/false);
238   ConstantIntRanges srange = computeBoundsBy(
239       ssub, lhs.smin(), rhs.smax(), lhs.smax(), rhs.smin(), /*isSigned=*/true);
240   return urange.intersection(srange);
241 }
242 
243 //===----------------------------------------------------------------------===//
244 // Multiplication
245 //===----------------------------------------------------------------------===//
246 
247 ConstantIntRanges
248 mlir::intrange::inferMul(ArrayRef<ConstantIntRanges> argRanges,
249                          OverflowFlags ovfFlags) {
250   const ConstantIntRanges &lhs = argRanges[0], &rhs = argRanges[1];
251 
252   ConstArithStdFn umul = [=](const APInt &a,
253                              const APInt &b) -> std::optional<APInt> {
254     bool overflowed = false;
255     APInt result = any(ovfFlags & OverflowFlags::Nuw)
256                        ? a.umul_sat(b)
257                        : a.umul_ov(b, overflowed);
258     return overflowed ? std::optional<APInt>() : result;
259   };
260   ConstArithStdFn smul = [=](const APInt &a,
261                              const APInt &b) -> std::optional<APInt> {
262     bool overflowed = false;
263     APInt result = any(ovfFlags & OverflowFlags::Nsw)
264                        ? a.smul_sat(b)
265                        : a.smul_ov(b, overflowed);
266     return overflowed ? std::optional<APInt>() : result;
267   };
268 
269   ConstantIntRanges urange =
270       minMaxBy(umul, {lhs.umin(), lhs.umax()}, {rhs.umin(), rhs.umax()},
271                /*isSigned=*/false);
272   ConstantIntRanges srange =
273       minMaxBy(smul, {lhs.smin(), lhs.smax()}, {rhs.smin(), rhs.smax()},
274                /*isSigned=*/true);
275   return urange.intersection(srange);
276 }
277 
278 //===----------------------------------------------------------------------===//
279 // DivU, CeilDivU (Unsigned division)
280 //===----------------------------------------------------------------------===//
281 
282 /// Fix up division results (ex. for ceiling and floor), returning an APInt
283 /// if there has been no overflow
284 using DivisionFixupFn = function_ref<std::optional<APInt>(
285     const APInt &lhs, const APInt &rhs, const APInt &result)>;
286 
287 static ConstantIntRanges inferDivURange(const ConstantIntRanges &lhs,
288                                         const ConstantIntRanges &rhs,
289                                         DivisionFixupFn fixup) {
290   const APInt &lhsMin = lhs.umin(), &lhsMax = lhs.umax(), &rhsMin = rhs.umin(),
291               &rhsMax = rhs.umax();
292 
293   if (!rhsMin.isZero()) {
294     auto udiv = [&fixup](const APInt &a,
295                          const APInt &b) -> std::optional<APInt> {
296       return fixup(a, b, a.udiv(b));
297     };
298     return minMaxBy(udiv, {lhsMin, lhsMax}, {rhsMin, rhsMax},
299                     /*isSigned=*/false);
300   }
301 
302   APInt umin = APInt::getZero(rhsMin.getBitWidth());
303   if (lhsMin.uge(rhsMax) && !rhsMax.isZero())
304     umin = lhsMin.udiv(rhsMax);
305 
306   // X u/ Y u<= X.
307   APInt umax = lhsMax;
308   return ConstantIntRanges::fromUnsigned(umin, umax);
309 }
310 
311 ConstantIntRanges
312 mlir::intrange::inferDivU(ArrayRef<ConstantIntRanges> argRanges) {
313   return inferDivURange(argRanges[0], argRanges[1],
314                         [](const APInt &lhs, const APInt &rhs,
315                            const APInt &result) { return result; });
316 }
317 
318 ConstantIntRanges
319 mlir::intrange::inferCeilDivU(ArrayRef<ConstantIntRanges> argRanges) {
320   const ConstantIntRanges &lhs = argRanges[0], &rhs = argRanges[1];
321 
322   auto ceilDivUIFix = [](const APInt &lhs, const APInt &rhs,
323                          const APInt &result) -> std::optional<APInt> {
324     if (!lhs.urem(rhs).isZero()) {
325       bool overflowed = false;
326       APInt corrected =
327           result.uadd_ov(APInt(result.getBitWidth(), 1), overflowed);
328       return overflowed ? std::optional<APInt>() : corrected;
329     }
330     return result;
331   };
332   return inferDivURange(lhs, rhs, ceilDivUIFix);
333 }
334 
335 //===----------------------------------------------------------------------===//
336 // DivS, CeilDivS, FloorDivS (Signed division)
337 //===----------------------------------------------------------------------===//
338 
339 static ConstantIntRanges inferDivSRange(const ConstantIntRanges &lhs,
340                                         const ConstantIntRanges &rhs,
341                                         DivisionFixupFn fixup) {
342   const APInt &lhsMin = lhs.smin(), &lhsMax = lhs.smax(), &rhsMin = rhs.smin(),
343               &rhsMax = rhs.smax();
344   bool canDivide = rhsMin.isStrictlyPositive() || rhsMax.isNegative();
345 
346   if (canDivide) {
347     auto sdiv = [&fixup](const APInt &a,
348                          const APInt &b) -> std::optional<APInt> {
349       bool overflowed = false;
350       APInt result = a.sdiv_ov(b, overflowed);
351       return overflowed ? std::optional<APInt>() : fixup(a, b, result);
352     };
353     return minMaxBy(sdiv, {lhsMin, lhsMax}, {rhsMin, rhsMax},
354                     /*isSigned=*/true);
355   }
356   return ConstantIntRanges::maxRange(rhsMin.getBitWidth());
357 }
358 
359 ConstantIntRanges
360 mlir::intrange::inferDivS(ArrayRef<ConstantIntRanges> argRanges) {
361   return inferDivSRange(argRanges[0], argRanges[1],
362                         [](const APInt &lhs, const APInt &rhs,
363                            const APInt &result) { return result; });
364 }
365 
366 ConstantIntRanges
367 mlir::intrange::inferCeilDivS(ArrayRef<ConstantIntRanges> argRanges) {
368   const ConstantIntRanges &lhs = argRanges[0], &rhs = argRanges[1];
369 
370   auto ceilDivSIFix = [](const APInt &lhs, const APInt &rhs,
371                          const APInt &result) -> std::optional<APInt> {
372     if (!lhs.srem(rhs).isZero() && lhs.isNonNegative() == rhs.isNonNegative()) {
373       bool overflowed = false;
374       APInt corrected =
375           result.sadd_ov(APInt(result.getBitWidth(), 1), overflowed);
376       return overflowed ? std::optional<APInt>() : corrected;
377     }
378     return result;
379   };
380   return inferDivSRange(lhs, rhs, ceilDivSIFix);
381 }
382 
383 ConstantIntRanges
384 mlir::intrange::inferFloorDivS(ArrayRef<ConstantIntRanges> argRanges) {
385   const ConstantIntRanges &lhs = argRanges[0], &rhs = argRanges[1];
386 
387   auto floorDivSIFix = [](const APInt &lhs, const APInt &rhs,
388                           const APInt &result) -> std::optional<APInt> {
389     if (!lhs.srem(rhs).isZero() && lhs.isNonNegative() != rhs.isNonNegative()) {
390       bool overflowed = false;
391       APInt corrected =
392           result.ssub_ov(APInt(result.getBitWidth(), 1), overflowed);
393       return overflowed ? std::optional<APInt>() : corrected;
394     }
395     return result;
396   };
397   return inferDivSRange(lhs, rhs, floorDivSIFix);
398 }
399 
400 //===----------------------------------------------------------------------===//
401 // Signed remainder (RemS)
402 //===----------------------------------------------------------------------===//
403 
404 ConstantIntRanges
405 mlir::intrange::inferRemS(ArrayRef<ConstantIntRanges> argRanges) {
406   const ConstantIntRanges &lhs = argRanges[0], &rhs = argRanges[1];
407   const APInt &lhsMin = lhs.smin(), &lhsMax = lhs.smax(), &rhsMin = rhs.smin(),
408               &rhsMax = rhs.smax();
409 
410   unsigned width = rhsMax.getBitWidth();
411   APInt smin = APInt::getSignedMinValue(width);
412   APInt smax = APInt::getSignedMaxValue(width);
413   // No bounds if zero could be a divisor.
414   bool canBound = (rhsMin.isStrictlyPositive() || rhsMax.isNegative());
415   if (canBound) {
416     APInt maxDivisor = rhsMin.isStrictlyPositive() ? rhsMax : rhsMin.abs();
417     bool canNegativeDividend = lhsMin.isNegative();
418     bool canPositiveDividend = lhsMax.isStrictlyPositive();
419     APInt zero = APInt::getZero(maxDivisor.getBitWidth());
420     APInt maxPositiveResult = maxDivisor - 1;
421     APInt minNegativeResult = -maxPositiveResult;
422     smin = canNegativeDividend ? minNegativeResult : zero;
423     smax = canPositiveDividend ? maxPositiveResult : zero;
424     // Special case: sweeping out a contiguous range in N/[modulus].
425     if (rhsMin == rhsMax) {
426       if ((lhsMax - lhsMin).ult(maxDivisor)) {
427         APInt minRem = lhsMin.srem(maxDivisor);
428         APInt maxRem = lhsMax.srem(maxDivisor);
429         if (minRem.sle(maxRem)) {
430           smin = minRem;
431           smax = maxRem;
432         }
433       }
434     }
435   }
436   return ConstantIntRanges::fromSigned(smin, smax);
437 }
438 
439 //===----------------------------------------------------------------------===//
440 // Unsigned remainder (RemU)
441 //===----------------------------------------------------------------------===//
442 
443 ConstantIntRanges
444 mlir::intrange::inferRemU(ArrayRef<ConstantIntRanges> argRanges) {
445   const ConstantIntRanges &lhs = argRanges[0], &rhs = argRanges[1];
446   const APInt &rhsMin = rhs.umin(), &rhsMax = rhs.umax();
447 
448   unsigned width = rhsMin.getBitWidth();
449   APInt umin = APInt::getZero(width);
450   // Remainder can't be larger than either of its arguments.
451   APInt umax = llvm::APIntOps::umin((rhsMax - 1), lhs.umax());
452 
453   if (!rhsMin.isZero()) {
454     // Special case: sweeping out a contiguous range in N/[modulus]
455     if (rhsMin == rhsMax) {
456       const APInt &lhsMin = lhs.umin(), &lhsMax = lhs.umax();
457       if ((lhsMax - lhsMin).ult(rhsMax)) {
458         APInt minRem = lhsMin.urem(rhsMax);
459         APInt maxRem = lhsMax.urem(rhsMax);
460         if (minRem.ule(maxRem)) {
461           umin = minRem;
462           umax = maxRem;
463         }
464       }
465     }
466   }
467   return ConstantIntRanges::fromUnsigned(umin, umax);
468 }
469 
470 //===----------------------------------------------------------------------===//
471 // Max and min (MaxS, MaxU, MinS, MinU)
472 //===----------------------------------------------------------------------===//
473 
474 ConstantIntRanges
475 mlir::intrange::inferMaxS(ArrayRef<ConstantIntRanges> argRanges) {
476   const ConstantIntRanges &lhs = argRanges[0], &rhs = argRanges[1];
477 
478   const APInt &smin = lhs.smin().sgt(rhs.smin()) ? lhs.smin() : rhs.smin();
479   const APInt &smax = lhs.smax().sgt(rhs.smax()) ? lhs.smax() : rhs.smax();
480   return ConstantIntRanges::fromSigned(smin, smax);
481 }
482 
483 ConstantIntRanges
484 mlir::intrange::inferMaxU(ArrayRef<ConstantIntRanges> argRanges) {
485   const ConstantIntRanges &lhs = argRanges[0], &rhs = argRanges[1];
486 
487   const APInt &umin = lhs.umin().ugt(rhs.umin()) ? lhs.umin() : rhs.umin();
488   const APInt &umax = lhs.umax().ugt(rhs.umax()) ? lhs.umax() : rhs.umax();
489   return ConstantIntRanges::fromUnsigned(umin, umax);
490 }
491 
492 ConstantIntRanges
493 mlir::intrange::inferMinS(ArrayRef<ConstantIntRanges> argRanges) {
494   const ConstantIntRanges &lhs = argRanges[0], &rhs = argRanges[1];
495 
496   const APInt &smin = lhs.smin().slt(rhs.smin()) ? lhs.smin() : rhs.smin();
497   const APInt &smax = lhs.smax().slt(rhs.smax()) ? lhs.smax() : rhs.smax();
498   return ConstantIntRanges::fromSigned(smin, smax);
499 }
500 
501 ConstantIntRanges
502 mlir::intrange::inferMinU(ArrayRef<ConstantIntRanges> argRanges) {
503   const ConstantIntRanges &lhs = argRanges[0], &rhs = argRanges[1];
504 
505   const APInt &umin = lhs.umin().ult(rhs.umin()) ? lhs.umin() : rhs.umin();
506   const APInt &umax = lhs.umax().ult(rhs.umax()) ? lhs.umax() : rhs.umax();
507   return ConstantIntRanges::fromUnsigned(umin, umax);
508 }
509 
510 //===----------------------------------------------------------------------===//
511 // Bitwise operators (And, Or, Xor)
512 //===----------------------------------------------------------------------===//
513 
514 /// "Widen" bounds - if 0bvvvvv??? <= a <= 0bvvvvv???,
515 /// relax the bounds to 0bvvvvv000 <= a <= 0bvvvvv111, where vvvvv are the bits
516 /// that both bonuds have in common. This gives us a consertive approximation
517 /// for what values can be passed to bitwise operations.
518 static std::tuple<APInt, APInt>
519 widenBitwiseBounds(const ConstantIntRanges &bound) {
520   APInt leftVal = bound.umin(), rightVal = bound.umax();
521   unsigned bitwidth = leftVal.getBitWidth();
522   unsigned differingBits = bitwidth - (leftVal ^ rightVal).countl_zero();
523   leftVal.clearLowBits(differingBits);
524   rightVal.setLowBits(differingBits);
525   return std::make_tuple(std::move(leftVal), std::move(rightVal));
526 }
527 
528 ConstantIntRanges
529 mlir::intrange::inferAnd(ArrayRef<ConstantIntRanges> argRanges) {
530   auto [lhsZeros, lhsOnes] = widenBitwiseBounds(argRanges[0]);
531   auto [rhsZeros, rhsOnes] = widenBitwiseBounds(argRanges[1]);
532   auto andi = [](const APInt &a, const APInt &b) -> std::optional<APInt> {
533     return a & b;
534   };
535   return minMaxBy(andi, {lhsZeros, lhsOnes}, {rhsZeros, rhsOnes},
536                   /*isSigned=*/false);
537 }
538 
539 ConstantIntRanges
540 mlir::intrange::inferOr(ArrayRef<ConstantIntRanges> argRanges) {
541   auto [lhsZeros, lhsOnes] = widenBitwiseBounds(argRanges[0]);
542   auto [rhsZeros, rhsOnes] = widenBitwiseBounds(argRanges[1]);
543   auto ori = [](const APInt &a, const APInt &b) -> std::optional<APInt> {
544     return a | b;
545   };
546   return minMaxBy(ori, {lhsZeros, lhsOnes}, {rhsZeros, rhsOnes},
547                   /*isSigned=*/false);
548 }
549 
550 ConstantIntRanges
551 mlir::intrange::inferXor(ArrayRef<ConstantIntRanges> argRanges) {
552   auto [lhsZeros, lhsOnes] = widenBitwiseBounds(argRanges[0]);
553   auto [rhsZeros, rhsOnes] = widenBitwiseBounds(argRanges[1]);
554   auto xori = [](const APInt &a, const APInt &b) -> std::optional<APInt> {
555     return a ^ b;
556   };
557   return minMaxBy(xori, {lhsZeros, lhsOnes}, {rhsZeros, rhsOnes},
558                   /*isSigned=*/false);
559 }
560 
561 //===----------------------------------------------------------------------===//
562 // Shifts (Shl, ShrS, ShrU)
563 //===----------------------------------------------------------------------===//
564 
565 ConstantIntRanges
566 mlir::intrange::inferShl(ArrayRef<ConstantIntRanges> argRanges,
567                          OverflowFlags ovfFlags) {
568   const ConstantIntRanges &lhs = argRanges[0], &rhs = argRanges[1];
569   const APInt &rhsUMin = rhs.umin(), &rhsUMax = rhs.umax();
570 
571   // The signed/unsigned overflow behavior of shl by `rhs` matches a mul with
572   // 2^rhs.
573   ConstArithStdFn ushl = [=](const APInt &l,
574                              const APInt &r) -> std::optional<APInt> {
575     bool overflowed = false;
576     APInt result = any(ovfFlags & OverflowFlags::Nuw)
577                        ? l.ushl_sat(r)
578                        : l.ushl_ov(r, overflowed);
579     return overflowed ? std::optional<APInt>() : result;
580   };
581   ConstArithStdFn sshl = [=](const APInt &l,
582                              const APInt &r) -> std::optional<APInt> {
583     bool overflowed = false;
584     APInt result = any(ovfFlags & OverflowFlags::Nsw)
585                        ? l.sshl_sat(r)
586                        : l.sshl_ov(r, overflowed);
587     return overflowed ? std::optional<APInt>() : result;
588   };
589 
590   ConstantIntRanges urange =
591       minMaxBy(ushl, {lhs.umin(), lhs.umax()}, {rhsUMin, rhsUMax},
592                /*isSigned=*/false);
593   ConstantIntRanges srange =
594       minMaxBy(sshl, {lhs.smin(), lhs.smax()}, {rhsUMin, rhsUMax},
595                /*isSigned=*/true);
596   return urange.intersection(srange);
597 }
598 
599 ConstantIntRanges
600 mlir::intrange::inferShrS(ArrayRef<ConstantIntRanges> argRanges) {
601   const ConstantIntRanges &lhs = argRanges[0], &rhs = argRanges[1];
602 
603   auto ashr = [](const APInt &l, const APInt &r) -> std::optional<APInt> {
604     return r.uge(r.getBitWidth()) ? std::optional<APInt>() : l.ashr(r);
605   };
606 
607   return minMaxBy(ashr, {lhs.smin(), lhs.smax()}, {rhs.umin(), rhs.umax()},
608                   /*isSigned=*/true);
609 }
610 
611 ConstantIntRanges
612 mlir::intrange::inferShrU(ArrayRef<ConstantIntRanges> argRanges) {
613   const ConstantIntRanges &lhs = argRanges[0], &rhs = argRanges[1];
614 
615   auto lshr = [](const APInt &l, const APInt &r) -> std::optional<APInt> {
616     return r.uge(r.getBitWidth()) ? std::optional<APInt>() : l.lshr(r);
617   };
618   return minMaxBy(lshr, {lhs.umin(), lhs.umax()}, {rhs.umin(), rhs.umax()},
619                   /*isSigned=*/false);
620 }
621 
622 //===----------------------------------------------------------------------===//
623 // Comparisons (Cmp)
624 //===----------------------------------------------------------------------===//
625 
626 static intrange::CmpPredicate invertPredicate(intrange::CmpPredicate pred) {
627   switch (pred) {
628   case intrange::CmpPredicate::eq:
629     return intrange::CmpPredicate::ne;
630   case intrange::CmpPredicate::ne:
631     return intrange::CmpPredicate::eq;
632   case intrange::CmpPredicate::slt:
633     return intrange::CmpPredicate::sge;
634   case intrange::CmpPredicate::sle:
635     return intrange::CmpPredicate::sgt;
636   case intrange::CmpPredicate::sgt:
637     return intrange::CmpPredicate::sle;
638   case intrange::CmpPredicate::sge:
639     return intrange::CmpPredicate::slt;
640   case intrange::CmpPredicate::ult:
641     return intrange::CmpPredicate::uge;
642   case intrange::CmpPredicate::ule:
643     return intrange::CmpPredicate::ugt;
644   case intrange::CmpPredicate::ugt:
645     return intrange::CmpPredicate::ule;
646   case intrange::CmpPredicate::uge:
647     return intrange::CmpPredicate::ult;
648   }
649   llvm_unreachable("unknown cmp predicate value");
650 }
651 
652 static bool isStaticallyTrue(intrange::CmpPredicate pred,
653                              const ConstantIntRanges &lhs,
654                              const ConstantIntRanges &rhs) {
655   switch (pred) {
656   case intrange::CmpPredicate::sle:
657     return lhs.smax().sle(rhs.smin());
658   case intrange::CmpPredicate::slt:
659     return lhs.smax().slt(rhs.smin());
660   case intrange::CmpPredicate::ule:
661     return lhs.umax().ule(rhs.umin());
662   case intrange::CmpPredicate::ult:
663     return lhs.umax().ult(rhs.umin());
664   case intrange::CmpPredicate::sge:
665     return lhs.smin().sge(rhs.smax());
666   case intrange::CmpPredicate::sgt:
667     return lhs.smin().sgt(rhs.smax());
668   case intrange::CmpPredicate::uge:
669     return lhs.umin().uge(rhs.umax());
670   case intrange::CmpPredicate::ugt:
671     return lhs.umin().ugt(rhs.umax());
672   case intrange::CmpPredicate::eq: {
673     std::optional<APInt> lhsConst = lhs.getConstantValue();
674     std::optional<APInt> rhsConst = rhs.getConstantValue();
675     return lhsConst && rhsConst && lhsConst == rhsConst;
676   }
677   case intrange::CmpPredicate::ne: {
678     // While equality requires that there is an interpration of the preceeding
679     // computations that produces equal constants, whether that be signed or
680     // unsigned, statically determining inequality requires that neither
681     // interpretation produce potentially overlapping ranges.
682     bool sne = isStaticallyTrue(intrange::CmpPredicate::slt, lhs, rhs) ||
683                isStaticallyTrue(intrange::CmpPredicate::sgt, lhs, rhs);
684     bool une = isStaticallyTrue(intrange::CmpPredicate::ult, lhs, rhs) ||
685                isStaticallyTrue(intrange::CmpPredicate::ugt, lhs, rhs);
686     return sne && une;
687   }
688   }
689   return false;
690 }
691 
692 std::optional<bool> mlir::intrange::evaluatePred(CmpPredicate pred,
693                                                  const ConstantIntRanges &lhs,
694                                                  const ConstantIntRanges &rhs) {
695   if (isStaticallyTrue(pred, lhs, rhs))
696     return true;
697   if (isStaticallyTrue(invertPredicate(pred), lhs, rhs))
698     return false;
699   return std::nullopt;
700 }
701