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1 //===--------- SCEVAffinator.cpp  - Create Scops from LLVM IR -------------===//
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 // Create a polyhedral description for a SCEV value.
10 //
11 //===----------------------------------------------------------------------===//
12 
13 #include "polly/Support/SCEVAffinator.h"
14 #include "polly/Options.h"
15 #include "polly/ScopInfo.h"
16 #include "polly/Support/GICHelper.h"
17 #include "polly/Support/SCEVValidator.h"
18 #include "isl/aff.h"
19 #include "isl/local_space.h"
20 #include "isl/set.h"
21 #include "isl/val.h"
22 
23 using namespace llvm;
24 using namespace polly;
25 
26 static cl::opt<bool> IgnoreIntegerWrapping(
27     "polly-ignore-integer-wrapping",
28     cl::desc("Do not build run-time checks to proof absence of integer "
29              "wrapping"),
30     cl::Hidden, cl::ZeroOrMore, cl::init(false), cl::cat(PollyCategory));
31 
32 // The maximal number of basic sets we allow during the construction of a
33 // piecewise affine function. More complex ones will result in very high
34 // compile time.
35 static int const MaxDisjunctionsInPwAff = 100;
36 
37 // The maximal number of bits for which a general expression is modeled
38 // precisely.
39 static unsigned const MaxSmallBitWidth = 7;
40 
41 /// Add the number of basic sets in @p Domain to @p User
addNumBasicSets(__isl_take isl_set * Domain,__isl_take isl_aff * Aff,void * User)42 static isl_stat addNumBasicSets(__isl_take isl_set *Domain,
43                                 __isl_take isl_aff *Aff, void *User) {
44   auto *NumBasicSets = static_cast<unsigned *>(User);
45   *NumBasicSets += isl_set_n_basic_set(Domain);
46   isl_set_free(Domain);
47   isl_aff_free(Aff);
48   return isl_stat_ok;
49 }
50 
51 /// Determine if @p PWAC is too complex to continue.
isTooComplex(PWACtx PWAC)52 static bool isTooComplex(PWACtx PWAC) {
53   unsigned NumBasicSets = 0;
54   isl_pw_aff_foreach_piece(PWAC.first.get(), addNumBasicSets, &NumBasicSets);
55   if (NumBasicSets <= MaxDisjunctionsInPwAff)
56     return false;
57   return true;
58 }
59 
60 /// Return the flag describing the possible wrapping of @p Expr.
getNoWrapFlags(const SCEV * Expr)61 static SCEV::NoWrapFlags getNoWrapFlags(const SCEV *Expr) {
62   if (auto *NAry = dyn_cast<SCEVNAryExpr>(Expr))
63     return NAry->getNoWrapFlags();
64   return SCEV::NoWrapMask;
65 }
66 
combine(PWACtx PWAC0,PWACtx PWAC1,__isl_give isl_pw_aff * (Fn)(__isl_take isl_pw_aff *,__isl_take isl_pw_aff *))67 static PWACtx combine(PWACtx PWAC0, PWACtx PWAC1,
68                       __isl_give isl_pw_aff *(Fn)(__isl_take isl_pw_aff *,
69                                                   __isl_take isl_pw_aff *)) {
70   PWAC0.first = isl::manage(Fn(PWAC0.first.release(), PWAC1.first.release()));
71   PWAC0.second = PWAC0.second.unite(PWAC1.second);
72   return PWAC0;
73 }
74 
getWidthExpValOnDomain(unsigned Width,__isl_take isl_set * Dom)75 static __isl_give isl_pw_aff *getWidthExpValOnDomain(unsigned Width,
76                                                      __isl_take isl_set *Dom) {
77   auto *Ctx = isl_set_get_ctx(Dom);
78   auto *WidthVal = isl_val_int_from_ui(Ctx, Width);
79   auto *ExpVal = isl_val_2exp(WidthVal);
80   return isl_pw_aff_val_on_domain(Dom, ExpVal);
81 }
82 
SCEVAffinator(Scop * S,LoopInfo & LI)83 SCEVAffinator::SCEVAffinator(Scop *S, LoopInfo &LI)
84     : S(S), Ctx(S->getIslCtx().get()), SE(*S->getSE()), LI(LI),
85       TD(S->getFunction().getParent()->getDataLayout()) {}
86 
getScope()87 Loop *SCEVAffinator::getScope() { return BB ? LI.getLoopFor(BB) : nullptr; }
88 
interpretAsUnsigned(PWACtx & PWAC,unsigned Width)89 void SCEVAffinator::interpretAsUnsigned(PWACtx &PWAC, unsigned Width) {
90   auto *NonNegDom = isl_pw_aff_nonneg_set(PWAC.first.copy());
91   auto *NonNegPWA =
92       isl_pw_aff_intersect_domain(PWAC.first.copy(), isl_set_copy(NonNegDom));
93   auto *ExpPWA = getWidthExpValOnDomain(Width, isl_set_complement(NonNegDom));
94   PWAC.first = isl::manage(isl_pw_aff_union_add(
95       NonNegPWA, isl_pw_aff_add(PWAC.first.release(), ExpPWA)));
96 }
97 
takeNonNegativeAssumption(PWACtx & PWAC,RecordedAssumptionsTy * RecordedAssumptions)98 void SCEVAffinator::takeNonNegativeAssumption(
99     PWACtx &PWAC, RecordedAssumptionsTy *RecordedAssumptions) {
100   this->RecordedAssumptions = RecordedAssumptions;
101 
102   auto *NegPWA = isl_pw_aff_neg(PWAC.first.copy());
103   auto *NegDom = isl_pw_aff_pos_set(NegPWA);
104   PWAC.second =
105       isl::manage(isl_set_union(PWAC.second.release(), isl_set_copy(NegDom)));
106   auto *Restriction = BB ? NegDom : isl_set_params(NegDom);
107   auto DL = BB ? BB->getTerminator()->getDebugLoc() : DebugLoc();
108   recordAssumption(RecordedAssumptions, UNSIGNED, isl::manage(Restriction), DL,
109                    AS_RESTRICTION, BB);
110 }
111 
getPWACtxFromPWA(isl::pw_aff PWA)112 PWACtx SCEVAffinator::getPWACtxFromPWA(isl::pw_aff PWA) {
113   return std::make_pair(PWA, isl::set::empty(isl::space(Ctx, 0, NumIterators)));
114 }
115 
getPwAff(const SCEV * Expr,BasicBlock * BB,RecordedAssumptionsTy * RecordedAssumptions)116 PWACtx SCEVAffinator::getPwAff(const SCEV *Expr, BasicBlock *BB,
117                                RecordedAssumptionsTy *RecordedAssumptions) {
118   this->BB = BB;
119   this->RecordedAssumptions = RecordedAssumptions;
120 
121   if (BB) {
122     auto *DC = S->getDomainConditions(BB).release();
123     NumIterators = isl_set_n_dim(DC);
124     isl_set_free(DC);
125   } else
126     NumIterators = 0;
127 
128   return visit(Expr);
129 }
130 
checkForWrapping(const SCEV * Expr,PWACtx PWAC) const131 PWACtx SCEVAffinator::checkForWrapping(const SCEV *Expr, PWACtx PWAC) const {
132   // If the SCEV flags do contain NSW (no signed wrap) then PWA already
133   // represents Expr in modulo semantic (it is not allowed to overflow), thus we
134   // are done. Otherwise, we will compute:
135   //   PWA = ((PWA + 2^(n-1)) mod (2 ^ n)) - 2^(n-1)
136   // whereas n is the number of bits of the Expr, hence:
137   //   n = bitwidth(ExprType)
138 
139   if (IgnoreIntegerWrapping || (getNoWrapFlags(Expr) & SCEV::FlagNSW))
140     return PWAC;
141 
142   isl::pw_aff PWAMod = addModuloSemantic(PWAC.first, Expr->getType());
143 
144   isl::set NotEqualSet = PWAC.first.ne_set(PWAMod);
145   PWAC.second = PWAC.second.unite(NotEqualSet).coalesce();
146 
147   const DebugLoc &Loc = BB ? BB->getTerminator()->getDebugLoc() : DebugLoc();
148   if (!BB)
149     NotEqualSet = NotEqualSet.params();
150   NotEqualSet = NotEqualSet.coalesce();
151 
152   if (!NotEqualSet.is_empty())
153     recordAssumption(RecordedAssumptions, WRAPPING, NotEqualSet, Loc,
154                      AS_RESTRICTION, BB);
155 
156   return PWAC;
157 }
158 
addModuloSemantic(isl::pw_aff PWA,Type * ExprType) const159 isl::pw_aff SCEVAffinator::addModuloSemantic(isl::pw_aff PWA,
160                                              Type *ExprType) const {
161   unsigned Width = TD.getTypeSizeInBits(ExprType);
162 
163   auto ModVal = isl::val::int_from_ui(Ctx, Width);
164   ModVal = ModVal.pow2();
165 
166   isl::set Domain = PWA.domain();
167   isl::pw_aff AddPW =
168       isl::manage(getWidthExpValOnDomain(Width - 1, Domain.release()));
169 
170   return PWA.add(AddPW).mod(ModVal).sub(AddPW);
171 }
172 
hasNSWAddRecForLoop(Loop * L) const173 bool SCEVAffinator::hasNSWAddRecForLoop(Loop *L) const {
174   for (const auto &CachedPair : CachedExpressions) {
175     auto *AddRec = dyn_cast<SCEVAddRecExpr>(CachedPair.first.first);
176     if (!AddRec)
177       continue;
178     if (AddRec->getLoop() != L)
179       continue;
180     if (AddRec->getNoWrapFlags() & SCEV::FlagNSW)
181       return true;
182   }
183 
184   return false;
185 }
186 
computeModuloForExpr(const SCEV * Expr)187 bool SCEVAffinator::computeModuloForExpr(const SCEV *Expr) {
188   unsigned Width = TD.getTypeSizeInBits(Expr->getType());
189   // We assume nsw expressions never overflow.
190   if (auto *NAry = dyn_cast<SCEVNAryExpr>(Expr))
191     if (NAry->getNoWrapFlags() & SCEV::FlagNSW)
192       return false;
193   return Width <= MaxSmallBitWidth;
194 }
195 
visit(const SCEV * Expr)196 PWACtx SCEVAffinator::visit(const SCEV *Expr) {
197 
198   auto Key = std::make_pair(Expr, BB);
199   PWACtx PWAC = CachedExpressions[Key];
200   if (PWAC.first)
201     return PWAC;
202 
203   auto ConstantAndLeftOverPair = extractConstantFactor(Expr, SE);
204   auto *Factor = ConstantAndLeftOverPair.first;
205   Expr = ConstantAndLeftOverPair.second;
206 
207   auto *Scope = getScope();
208   S->addParams(getParamsInAffineExpr(&S->getRegion(), Scope, Expr, SE));
209 
210   // In case the scev is a valid parameter, we do not further analyze this
211   // expression, but create a new parameter in the isl_pw_aff. This allows us
212   // to treat subexpressions that we cannot translate into an piecewise affine
213   // expression, as constant parameters of the piecewise affine expression.
214   if (isl_id *Id = S->getIdForParam(Expr).release()) {
215     isl_space *Space = isl_space_set_alloc(Ctx.get(), 1, NumIterators);
216     Space = isl_space_set_dim_id(Space, isl_dim_param, 0, Id);
217 
218     isl_set *Domain = isl_set_universe(isl_space_copy(Space));
219     isl_aff *Affine = isl_aff_zero_on_domain(isl_local_space_from_space(Space));
220     Affine = isl_aff_add_coefficient_si(Affine, isl_dim_param, 0, 1);
221 
222     PWAC = getPWACtxFromPWA(isl::manage(isl_pw_aff_alloc(Domain, Affine)));
223   } else {
224     PWAC = SCEVVisitor<SCEVAffinator, PWACtx>::visit(Expr);
225     if (computeModuloForExpr(Expr))
226       PWAC.first = addModuloSemantic(PWAC.first, Expr->getType());
227     else
228       PWAC = checkForWrapping(Expr, PWAC);
229   }
230 
231   if (!Factor->getType()->isIntegerTy(1)) {
232     PWAC = combine(PWAC, visitConstant(Factor), isl_pw_aff_mul);
233     if (computeModuloForExpr(Key.first))
234       PWAC.first = addModuloSemantic(PWAC.first, Expr->getType());
235   }
236 
237   // For compile time reasons we need to simplify the PWAC before we cache and
238   // return it.
239   PWAC.first = PWAC.first.coalesce();
240   if (!computeModuloForExpr(Key.first))
241     PWAC = checkForWrapping(Key.first, PWAC);
242 
243   CachedExpressions[Key] = PWAC;
244   return PWAC;
245 }
246 
visitConstant(const SCEVConstant * Expr)247 PWACtx SCEVAffinator::visitConstant(const SCEVConstant *Expr) {
248   ConstantInt *Value = Expr->getValue();
249   isl_val *v;
250 
251   // LLVM does not define if an integer value is interpreted as a signed or
252   // unsigned value. Hence, without further information, it is unknown how
253   // this value needs to be converted to GMP. At the moment, we only support
254   // signed operations. So we just interpret it as signed. Later, there are
255   // two options:
256   //
257   // 1. We always interpret any value as signed and convert the values on
258   //    demand.
259   // 2. We pass down the signedness of the calculation and use it to interpret
260   //    this constant correctly.
261   v = isl_valFromAPInt(Ctx.get(), Value->getValue(), /* isSigned */ true);
262 
263   isl_space *Space = isl_space_set_alloc(Ctx.get(), 0, NumIterators);
264   isl_local_space *ls = isl_local_space_from_space(Space);
265   return getPWACtxFromPWA(
266       isl::manage(isl_pw_aff_from_aff(isl_aff_val_on_domain(ls, v))));
267 }
268 
visitPtrToIntExpr(const SCEVPtrToIntExpr * Expr)269 PWACtx SCEVAffinator::visitPtrToIntExpr(const SCEVPtrToIntExpr *Expr) {
270   return visit(Expr->getOperand(0));
271 }
272 
visitTruncateExpr(const SCEVTruncateExpr * Expr)273 PWACtx SCEVAffinator::visitTruncateExpr(const SCEVTruncateExpr *Expr) {
274   // Truncate operations are basically modulo operations, thus we can
275   // model them that way. However, for large types we assume the operand
276   // to fit in the new type size instead of introducing a modulo with a very
277   // large constant.
278 
279   auto *Op = Expr->getOperand();
280   auto OpPWAC = visit(Op);
281 
282   unsigned Width = TD.getTypeSizeInBits(Expr->getType());
283 
284   if (computeModuloForExpr(Expr))
285     return OpPWAC;
286 
287   auto *Dom = OpPWAC.first.domain().release();
288   auto *ExpPWA = getWidthExpValOnDomain(Width - 1, Dom);
289   auto *GreaterDom =
290       isl_pw_aff_ge_set(OpPWAC.first.copy(), isl_pw_aff_copy(ExpPWA));
291   auto *SmallerDom =
292       isl_pw_aff_lt_set(OpPWAC.first.copy(), isl_pw_aff_neg(ExpPWA));
293   auto *OutOfBoundsDom = isl_set_union(SmallerDom, GreaterDom);
294   OpPWAC.second = OpPWAC.second.unite(isl::manage_copy(OutOfBoundsDom));
295 
296   if (!BB) {
297     assert(isl_set_dim(OutOfBoundsDom, isl_dim_set) == 0 &&
298            "Expected a zero dimensional set for non-basic-block domains");
299     OutOfBoundsDom = isl_set_params(OutOfBoundsDom);
300   }
301 
302   recordAssumption(RecordedAssumptions, UNSIGNED, isl::manage(OutOfBoundsDom),
303                    DebugLoc(), AS_RESTRICTION, BB);
304 
305   return OpPWAC;
306 }
307 
visitZeroExtendExpr(const SCEVZeroExtendExpr * Expr)308 PWACtx SCEVAffinator::visitZeroExtendExpr(const SCEVZeroExtendExpr *Expr) {
309   // A zero-extended value can be interpreted as a piecewise defined signed
310   // value. If the value was non-negative it stays the same, otherwise it
311   // is the sum of the original value and 2^n where n is the bit-width of
312   // the original (or operand) type. Examples:
313   //   zext i8 127 to i32 -> { [127] }
314   //   zext i8  -1 to i32 -> { [256 + (-1)] } = { [255] }
315   //   zext i8  %v to i32 -> [v] -> { [v] | v >= 0; [256 + v] | v < 0 }
316   //
317   // However, LLVM/Scalar Evolution uses zero-extend (potentially lead by a
318   // truncate) to represent some forms of modulo computation. The left-hand side
319   // of the condition in the code below would result in the SCEV
320   // "zext i1 <false, +, true>for.body" which is just another description
321   // of the C expression "i & 1 != 0" or, equivalently, "i % 2 != 0".
322   //
323   //   for (i = 0; i < N; i++)
324   //     if (i & 1 != 0 /* == i % 2 */)
325   //       /* do something */
326   //
327   // If we do not make the modulo explicit but only use the mechanism described
328   // above we will get the very restrictive assumption "N < 3", because for all
329   // values of N >= 3 the SCEVAddRecExpr operand of the zero-extend would wrap.
330   // Alternatively, we can make the modulo in the operand explicit in the
331   // resulting piecewise function and thereby avoid the assumption on N. For the
332   // example this would result in the following piecewise affine function:
333   // { [i0] -> [(1)] : 2*floor((-1 + i0)/2) = -1 + i0;
334   //   [i0] -> [(0)] : 2*floor((i0)/2) = i0 }
335   // To this end we can first determine if the (immediate) operand of the
336   // zero-extend can wrap and, in case it might, we will use explicit modulo
337   // semantic to compute the result instead of emitting non-wrapping
338   // assumptions.
339   //
340   // Note that operands with large bit-widths are less likely to be negative
341   // because it would result in a very large access offset or loop bound after
342   // the zero-extend. To this end one can optimistically assume the operand to
343   // be positive and avoid the piecewise definition if the bit-width is bigger
344   // than some threshold (here MaxZextSmallBitWidth).
345   //
346   // We choose to go with a hybrid solution of all modeling techniques described
347   // above. For small bit-widths (up to MaxZextSmallBitWidth) we will model the
348   // wrapping explicitly and use a piecewise defined function. However, if the
349   // bit-width is bigger than MaxZextSmallBitWidth we will employ overflow
350   // assumptions and assume the "former negative" piece will not exist.
351 
352   auto *Op = Expr->getOperand();
353   auto OpPWAC = visit(Op);
354 
355   // If the width is to big we assume the negative part does not occur.
356   if (!computeModuloForExpr(Op)) {
357     takeNonNegativeAssumption(OpPWAC, RecordedAssumptions);
358     return OpPWAC;
359   }
360 
361   // If the width is small build the piece for the non-negative part and
362   // the one for the negative part and unify them.
363   unsigned Width = TD.getTypeSizeInBits(Op->getType());
364   interpretAsUnsigned(OpPWAC, Width);
365   return OpPWAC;
366 }
367 
visitSignExtendExpr(const SCEVSignExtendExpr * Expr)368 PWACtx SCEVAffinator::visitSignExtendExpr(const SCEVSignExtendExpr *Expr) {
369   // As all values are represented as signed, a sign extension is a noop.
370   return visit(Expr->getOperand());
371 }
372 
visitAddExpr(const SCEVAddExpr * Expr)373 PWACtx SCEVAffinator::visitAddExpr(const SCEVAddExpr *Expr) {
374   PWACtx Sum = visit(Expr->getOperand(0));
375 
376   for (int i = 1, e = Expr->getNumOperands(); i < e; ++i) {
377     Sum = combine(Sum, visit(Expr->getOperand(i)), isl_pw_aff_add);
378     if (isTooComplex(Sum))
379       return complexityBailout();
380   }
381 
382   return Sum;
383 }
384 
visitMulExpr(const SCEVMulExpr * Expr)385 PWACtx SCEVAffinator::visitMulExpr(const SCEVMulExpr *Expr) {
386   PWACtx Prod = visit(Expr->getOperand(0));
387 
388   for (int i = 1, e = Expr->getNumOperands(); i < e; ++i) {
389     Prod = combine(Prod, visit(Expr->getOperand(i)), isl_pw_aff_mul);
390     if (isTooComplex(Prod))
391       return complexityBailout();
392   }
393 
394   return Prod;
395 }
396 
visitAddRecExpr(const SCEVAddRecExpr * Expr)397 PWACtx SCEVAffinator::visitAddRecExpr(const SCEVAddRecExpr *Expr) {
398   assert(Expr->isAffine() && "Only affine AddRecurrences allowed");
399 
400   auto Flags = Expr->getNoWrapFlags();
401 
402   // Directly generate isl_pw_aff for Expr if 'start' is zero.
403   if (Expr->getStart()->isZero()) {
404     assert(S->contains(Expr->getLoop()) &&
405            "Scop does not contain the loop referenced in this AddRec");
406 
407     PWACtx Step = visit(Expr->getOperand(1));
408     isl_space *Space = isl_space_set_alloc(Ctx.get(), 0, NumIterators);
409     isl_local_space *LocalSpace = isl_local_space_from_space(Space);
410 
411     unsigned loopDimension = S->getRelativeLoopDepth(Expr->getLoop());
412 
413     isl_aff *LAff = isl_aff_set_coefficient_si(
414         isl_aff_zero_on_domain(LocalSpace), isl_dim_in, loopDimension, 1);
415     isl_pw_aff *LPwAff = isl_pw_aff_from_aff(LAff);
416 
417     Step.first = Step.first.mul(isl::manage(LPwAff));
418     return Step;
419   }
420 
421   // Translate AddRecExpr from '{start, +, inc}' into 'start + {0, +, inc}'
422   // if 'start' is not zero.
423   // TODO: Using the original SCEV no-wrap flags is not always safe, however
424   //       as our code generation is reordering the expression anyway it doesn't
425   //       really matter.
426   const SCEV *ZeroStartExpr =
427       SE.getAddRecExpr(SE.getConstant(Expr->getStart()->getType(), 0),
428                        Expr->getStepRecurrence(SE), Expr->getLoop(), Flags);
429 
430   PWACtx Result = visit(ZeroStartExpr);
431   PWACtx Start = visit(Expr->getStart());
432   Result = combine(Result, Start, isl_pw_aff_add);
433   return Result;
434 }
435 
visitSMaxExpr(const SCEVSMaxExpr * Expr)436 PWACtx SCEVAffinator::visitSMaxExpr(const SCEVSMaxExpr *Expr) {
437   PWACtx Max = visit(Expr->getOperand(0));
438 
439   for (int i = 1, e = Expr->getNumOperands(); i < e; ++i) {
440     Max = combine(Max, visit(Expr->getOperand(i)), isl_pw_aff_max);
441     if (isTooComplex(Max))
442       return complexityBailout();
443   }
444 
445   return Max;
446 }
447 
visitSMinExpr(const SCEVSMinExpr * Expr)448 PWACtx SCEVAffinator::visitSMinExpr(const SCEVSMinExpr *Expr) {
449   PWACtx Min = visit(Expr->getOperand(0));
450 
451   for (int i = 1, e = Expr->getNumOperands(); i < e; ++i) {
452     Min = combine(Min, visit(Expr->getOperand(i)), isl_pw_aff_min);
453     if (isTooComplex(Min))
454       return complexityBailout();
455   }
456 
457   return Min;
458 }
459 
visitUMaxExpr(const SCEVUMaxExpr * Expr)460 PWACtx SCEVAffinator::visitUMaxExpr(const SCEVUMaxExpr *Expr) {
461   llvm_unreachable("SCEVUMaxExpr not yet supported");
462 }
463 
visitUMinExpr(const SCEVUMinExpr * Expr)464 PWACtx SCEVAffinator::visitUMinExpr(const SCEVUMinExpr *Expr) {
465   llvm_unreachable("SCEVUMinExpr not yet supported");
466 }
467 
visitUDivExpr(const SCEVUDivExpr * Expr)468 PWACtx SCEVAffinator::visitUDivExpr(const SCEVUDivExpr *Expr) {
469   // The handling of unsigned division is basically the same as for signed
470   // division, except the interpretation of the operands. As the divisor
471   // has to be constant in both cases we can simply interpret it as an
472   // unsigned value without additional complexity in the representation.
473   // For the dividend we could choose from the different representation
474   // schemes introduced for zero-extend operations but for now we will
475   // simply use an assumption.
476   auto *Dividend = Expr->getLHS();
477   auto *Divisor = Expr->getRHS();
478   assert(isa<SCEVConstant>(Divisor) &&
479          "UDiv is no parameter but has a non-constant RHS.");
480 
481   auto DividendPWAC = visit(Dividend);
482   auto DivisorPWAC = visit(Divisor);
483 
484   if (SE.isKnownNegative(Divisor)) {
485     // Interpret negative divisors unsigned. This is a special case of the
486     // piece-wise defined value described for zero-extends as we already know
487     // the actual value of the constant divisor.
488     unsigned Width = TD.getTypeSizeInBits(Expr->getType());
489     auto *DivisorDom = DivisorPWAC.first.domain().release();
490     auto *WidthExpPWA = getWidthExpValOnDomain(Width, DivisorDom);
491     DivisorPWAC.first = DivisorPWAC.first.add(isl::manage(WidthExpPWA));
492   }
493 
494   // TODO: One can represent the dividend as piece-wise function to be more
495   //       precise but therefor a heuristic is needed.
496 
497   // Assume a non-negative dividend.
498   takeNonNegativeAssumption(DividendPWAC, RecordedAssumptions);
499 
500   DividendPWAC = combine(DividendPWAC, DivisorPWAC, isl_pw_aff_div);
501   DividendPWAC.first = DividendPWAC.first.floor();
502 
503   return DividendPWAC;
504 }
505 
visitSDivInstruction(Instruction * SDiv)506 PWACtx SCEVAffinator::visitSDivInstruction(Instruction *SDiv) {
507   assert(SDiv->getOpcode() == Instruction::SDiv && "Assumed SDiv instruction!");
508 
509   auto *Scope = getScope();
510   auto *Divisor = SDiv->getOperand(1);
511   auto *DivisorSCEV = SE.getSCEVAtScope(Divisor, Scope);
512   auto DivisorPWAC = visit(DivisorSCEV);
513   assert(isa<SCEVConstant>(DivisorSCEV) &&
514          "SDiv is no parameter but has a non-constant RHS.");
515 
516   auto *Dividend = SDiv->getOperand(0);
517   auto *DividendSCEV = SE.getSCEVAtScope(Dividend, Scope);
518   auto DividendPWAC = visit(DividendSCEV);
519   DividendPWAC = combine(DividendPWAC, DivisorPWAC, isl_pw_aff_tdiv_q);
520   return DividendPWAC;
521 }
522 
visitSRemInstruction(Instruction * SRem)523 PWACtx SCEVAffinator::visitSRemInstruction(Instruction *SRem) {
524   assert(SRem->getOpcode() == Instruction::SRem && "Assumed SRem instruction!");
525 
526   auto *Scope = getScope();
527   auto *Divisor = SRem->getOperand(1);
528   auto *DivisorSCEV = SE.getSCEVAtScope(Divisor, Scope);
529   auto DivisorPWAC = visit(DivisorSCEV);
530   assert(isa<ConstantInt>(Divisor) &&
531          "SRem is no parameter but has a non-constant RHS.");
532 
533   auto *Dividend = SRem->getOperand(0);
534   auto *DividendSCEV = SE.getSCEVAtScope(Dividend, Scope);
535   auto DividendPWAC = visit(DividendSCEV);
536   DividendPWAC = combine(DividendPWAC, DivisorPWAC, isl_pw_aff_tdiv_r);
537   return DividendPWAC;
538 }
539 
visitUnknown(const SCEVUnknown * Expr)540 PWACtx SCEVAffinator::visitUnknown(const SCEVUnknown *Expr) {
541   if (Instruction *I = dyn_cast<Instruction>(Expr->getValue())) {
542     switch (I->getOpcode()) {
543     case Instruction::IntToPtr:
544       return visit(SE.getSCEVAtScope(I->getOperand(0), getScope()));
545     case Instruction::SDiv:
546       return visitSDivInstruction(I);
547     case Instruction::SRem:
548       return visitSRemInstruction(I);
549     default:
550       break; // Fall through.
551     }
552   }
553 
554   llvm_unreachable(
555       "Unknowns SCEV was neither parameter nor a valid instruction.");
556 }
557 
complexityBailout()558 PWACtx SCEVAffinator::complexityBailout() {
559   // We hit the complexity limit for affine expressions; invalidate the scop
560   // and return a constant zero.
561   const DebugLoc &Loc = BB ? BB->getTerminator()->getDebugLoc() : DebugLoc();
562   S->invalidate(COMPLEXITY, Loc);
563   return visit(SE.getZero(Type::getInt32Ty(S->getFunction().getContext())));
564 }
565