xref: /llvm-project/flang/lib/Evaluate/shape.cpp (revision be68a6adfba29b275272cb36e606bc0cb08518b3) 
1 //===-- lib/Evaluate/shape.cpp --------------------------------------------===//
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 #include "flang/Evaluate/shape.h"
10 #include "flang/Common/idioms.h"
11 #include "flang/Common/template.h"
12 #include "flang/Evaluate/characteristics.h"
13 #include "flang/Evaluate/check-expression.h"
14 #include "flang/Evaluate/fold.h"
15 #include "flang/Evaluate/intrinsics.h"
16 #include "flang/Evaluate/tools.h"
17 #include "flang/Evaluate/type.h"
18 #include "flang/Parser/message.h"
19 #include "flang/Semantics/symbol.h"
20 #include <functional>
21 
22 using namespace std::placeholders; // _1, _2, &c. for std::bind()
23 
24 namespace Fortran::evaluate {
25 
26 bool IsImpliedShape(const Symbol &original) {
27   const Symbol &symbol{ResolveAssociations(original)};
28   const auto *details{symbol.detailsIf<semantics::ObjectEntityDetails>()};
29   return details && symbol.attrs().test(semantics::Attr::PARAMETER) &&
30       details->shape().CanBeImpliedShape();
31 }
32 
33 bool IsExplicitShape(const Symbol &original) {
34   const Symbol &symbol{ResolveAssociations(original)};
35   if (const auto *details{symbol.detailsIf<semantics::ObjectEntityDetails>()}) {
36     const auto &shape{details->shape()};
37     return shape.Rank() == 0 ||
38         shape.IsExplicitShape(); // true when scalar, too
39   } else {
40     return symbol
41         .has<semantics::AssocEntityDetails>(); // exprs have explicit shape
42   }
43 }
44 
45 Shape GetShapeHelper::ConstantShape(const Constant<ExtentType> &arrayConstant) {
46   CHECK(arrayConstant.Rank() == 1);
47   Shape result;
48   std::size_t dimensions{arrayConstant.size()};
49   for (std::size_t j{0}; j < dimensions; ++j) {
50     Scalar<ExtentType> extent{arrayConstant.values().at(j)};
51     result.emplace_back(MaybeExtentExpr{ExtentExpr{std::move(extent)}});
52   }
53   return result;
54 }
55 
56 auto GetShapeHelper::AsShapeResult(ExtentExpr &&arrayExpr) const -> Result {
57   if (context_) {
58     arrayExpr = Fold(*context_, std::move(arrayExpr));
59   }
60   if (const auto *constArray{UnwrapConstantValue<ExtentType>(arrayExpr)}) {
61     return ConstantShape(*constArray);
62   }
63   if (auto *constructor{UnwrapExpr<ArrayConstructor<ExtentType>>(arrayExpr)}) {
64     Shape result;
65     for (auto &value : *constructor) {
66       auto *expr{std::get_if<ExtentExpr>(&value.u)};
67       if (expr && expr->Rank() == 0) {
68         result.emplace_back(std::move(*expr));
69       } else {
70         return std::nullopt;
71       }
72     }
73     return result;
74   } else {
75     return std::nullopt;
76   }
77 }
78 
79 Shape GetShapeHelper::CreateShape(int rank, NamedEntity &base) {
80   Shape shape;
81   for (int dimension{0}; dimension < rank; ++dimension) {
82     shape.emplace_back(GetExtent(base, dimension));
83   }
84   return shape;
85 }
86 
87 std::optional<ExtentExpr> AsExtentArrayExpr(const Shape &shape) {
88   ArrayConstructorValues<ExtentType> values;
89   for (const auto &dim : shape) {
90     if (dim) {
91       values.Push(common::Clone(*dim));
92     } else {
93       return std::nullopt;
94     }
95   }
96   return ExtentExpr{ArrayConstructor<ExtentType>{std::move(values)}};
97 }
98 
99 std::optional<Constant<ExtentType>> AsConstantShape(
100     FoldingContext &context, const Shape &shape) {
101   if (auto shapeArray{AsExtentArrayExpr(shape)}) {
102     auto folded{Fold(context, std::move(*shapeArray))};
103     if (auto *p{UnwrapConstantValue<ExtentType>(folded)}) {
104       return std::move(*p);
105     }
106   }
107   return std::nullopt;
108 }
109 
110 Constant<SubscriptInteger> AsConstantShape(const ConstantSubscripts &shape) {
111   using IntType = Scalar<SubscriptInteger>;
112   std::vector<IntType> result;
113   for (auto dim : shape) {
114     result.emplace_back(dim);
115   }
116   return {std::move(result), ConstantSubscripts{GetRank(shape)}};
117 }
118 
119 ConstantSubscripts AsConstantExtents(const Constant<ExtentType> &shape) {
120   ConstantSubscripts result;
121   for (const auto &extent : shape.values()) {
122     result.push_back(extent.ToInt64());
123   }
124   return result;
125 }
126 
127 std::optional<ConstantSubscripts> AsConstantExtents(
128     FoldingContext &context, const Shape &shape) {
129   if (auto shapeConstant{AsConstantShape(context, shape)}) {
130     return AsConstantExtents(*shapeConstant);
131   } else {
132     return std::nullopt;
133   }
134 }
135 
136 Shape AsShape(const ConstantSubscripts &shape) {
137   Shape result;
138   for (const auto &extent : shape) {
139     result.emplace_back(ExtentExpr{extent});
140   }
141   return result;
142 }
143 
144 std::optional<Shape> AsShape(const std::optional<ConstantSubscripts> &shape) {
145   if (shape) {
146     return AsShape(*shape);
147   } else {
148     return std::nullopt;
149   }
150 }
151 
152 Shape Fold(FoldingContext &context, Shape &&shape) {
153   for (auto &dim : shape) {
154     dim = Fold(context, std::move(dim));
155   }
156   return std::move(shape);
157 }
158 
159 std::optional<Shape> Fold(
160     FoldingContext &context, std::optional<Shape> &&shape) {
161   if (shape) {
162     return Fold(context, std::move(*shape));
163   } else {
164     return std::nullopt;
165   }
166 }
167 
168 static ExtentExpr ComputeTripCount(
169     ExtentExpr &&lower, ExtentExpr &&upper, ExtentExpr &&stride) {
170   ExtentExpr strideCopy{common::Clone(stride)};
171   ExtentExpr span{
172       (std::move(upper) - std::move(lower) + std::move(strideCopy)) /
173       std::move(stride)};
174   return ExtentExpr{
175       Extremum<ExtentType>{Ordering::Greater, std::move(span), ExtentExpr{0}}};
176 }
177 
178 ExtentExpr CountTrips(
179     ExtentExpr &&lower, ExtentExpr &&upper, ExtentExpr &&stride) {
180   return ComputeTripCount(
181       std::move(lower), std::move(upper), std::move(stride));
182 }
183 
184 ExtentExpr CountTrips(const ExtentExpr &lower, const ExtentExpr &upper,
185     const ExtentExpr &stride) {
186   return ComputeTripCount(
187       common::Clone(lower), common::Clone(upper), common::Clone(stride));
188 }
189 
190 MaybeExtentExpr CountTrips(MaybeExtentExpr &&lower, MaybeExtentExpr &&upper,
191     MaybeExtentExpr &&stride) {
192   std::function<ExtentExpr(ExtentExpr &&, ExtentExpr &&, ExtentExpr &&)> bound{
193       std::bind(ComputeTripCount, _1, _2, _3)};
194   return common::MapOptional(
195       std::move(bound), std::move(lower), std::move(upper), std::move(stride));
196 }
197 
198 MaybeExtentExpr GetSize(Shape &&shape) {
199   ExtentExpr extent{1};
200   for (auto &&dim : std::move(shape)) {
201     if (dim) {
202       extent = std::move(extent) * std::move(*dim);
203     } else {
204       return std::nullopt;
205     }
206   }
207   return extent;
208 }
209 
210 ConstantSubscript GetSize(const ConstantSubscripts &shape) {
211   ConstantSubscript size{1};
212   for (auto dim : shape) {
213     CHECK(dim >= 0);
214     size *= dim;
215   }
216   return size;
217 }
218 
219 bool ContainsAnyImpliedDoIndex(const ExtentExpr &expr) {
220   struct MyVisitor : public AnyTraverse<MyVisitor> {
221     using Base = AnyTraverse<MyVisitor>;
222     MyVisitor() : Base{*this} {}
223     using Base::operator();
224     bool operator()(const ImpliedDoIndex &) { return true; }
225   };
226   return MyVisitor{}(expr);
227 }
228 
229 // Determines lower bound on a dimension.  This can be other than 1 only
230 // for a reference to a whole array object or component. (See LBOUND, 16.9.109).
231 // ASSOCIATE construct entities may require traversal of their referents.
232 template <typename RESULT, bool LBOUND_SEMANTICS>
233 class GetLowerBoundHelper
234     : public Traverse<GetLowerBoundHelper<RESULT, LBOUND_SEMANTICS>, RESULT> {
235 public:
236   using Result = RESULT;
237   using Base = Traverse<GetLowerBoundHelper, RESULT>;
238   using Base::operator();
239   explicit GetLowerBoundHelper(int d, FoldingContext *context)
240       : Base{*this}, dimension_{d}, context_{context} {}
241   static Result Default() { return Result{1}; }
242   static Result Combine(Result &&, Result &&) {
243     // Operator results and array references always have lower bounds == 1
244     return Result{1};
245   }
246 
247   Result GetLowerBound(const Symbol &symbol0, NamedEntity &&base) const {
248     const Symbol &symbol{symbol0.GetUltimate()};
249     if (const auto *details{
250             symbol.detailsIf<semantics::ObjectEntityDetails>()}) {
251       int rank{details->shape().Rank()};
252       if (dimension_ < rank) {
253         const semantics::ShapeSpec &shapeSpec{details->shape()[dimension_]};
254         if (shapeSpec.lbound().isExplicit()) {
255           if (const auto &lbound{shapeSpec.lbound().GetExplicit()}) {
256             if constexpr (LBOUND_SEMANTICS) {
257               bool ok{false};
258               auto lbValue{ToInt64(*lbound)};
259               if (dimension_ == rank - 1 && details->IsAssumedSize()) {
260                 // last dimension of assumed-size dummy array: don't worry
261                 // about handling an empty dimension
262                 ok = IsScopeInvariantExpr(*lbound);
263               } else if (lbValue.value_or(0) == 1) {
264                 // Lower bound is 1, regardless of extent
265                 ok = true;
266               } else if (const auto &ubound{shapeSpec.ubound().GetExplicit()}) {
267                 // If we can't prove that the dimension is nonempty,
268                 // we must be conservative.
269                 // TODO: simple symbolic math in expression rewriting to
270                 // cope with cases like A(J:J)
271                 if (context_) {
272                   auto extent{ToInt64(Fold(*context_,
273                       ExtentExpr{*ubound} - ExtentExpr{*lbound} +
274                           ExtentExpr{1}))};
275                   if (extent) {
276                     if (extent <= 0) {
277                       return Result{1};
278                     }
279                     ok = true;
280                   } else {
281                     ok = false;
282                   }
283                 } else {
284                   auto ubValue{ToInt64(*ubound)};
285                   if (lbValue && ubValue) {
286                     if (*lbValue > *ubValue) {
287                       return Result{1};
288                     }
289                     ok = true;
290                   } else {
291                     ok = false;
292                   }
293                 }
294               }
295               return ok ? *lbound : Result{};
296             } else {
297               return *lbound;
298             }
299           } else {
300             return Result{1};
301           }
302         }
303         if (IsDescriptor(symbol)) {
304           return ExtentExpr{DescriptorInquiry{std::move(base),
305               DescriptorInquiry::Field::LowerBound, dimension_}};
306         }
307       }
308     } else if (const auto *assoc{
309                    symbol.detailsIf<semantics::AssocEntityDetails>()}) {
310       if (assoc->rank()) { // SELECT RANK case
311         const Symbol &resolved{ResolveAssociations(symbol)};
312         if (IsDescriptor(resolved) && dimension_ < *assoc->rank()) {
313           return ExtentExpr{DescriptorInquiry{std::move(base),
314               DescriptorInquiry::Field::LowerBound, dimension_}};
315         }
316       } else {
317         return (*this)(assoc->expr());
318       }
319     }
320     if constexpr (LBOUND_SEMANTICS) {
321       return Result{};
322     } else {
323       return Result{1};
324     }
325   }
326 
327   Result operator()(const Symbol &symbol0) const {
328     return GetLowerBound(symbol0, NamedEntity{symbol0});
329   }
330 
331   Result operator()(const Component &component) const {
332     if (component.base().Rank() == 0) {
333       return GetLowerBound(
334           component.GetLastSymbol(), NamedEntity{common::Clone(component)});
335     }
336     return Result{1};
337   }
338 
339 private:
340   int dimension_;
341   FoldingContext *context_{nullptr};
342 };
343 
344 ExtentExpr GetRawLowerBound(const NamedEntity &base, int dimension) {
345   return GetLowerBoundHelper<ExtentExpr, false>{dimension, nullptr}(base);
346 }
347 
348 ExtentExpr GetRawLowerBound(
349     FoldingContext &context, const NamedEntity &base, int dimension) {
350   return Fold(context,
351       GetLowerBoundHelper<ExtentExpr, false>{dimension, &context}(base));
352 }
353 
354 MaybeExtentExpr GetLBOUND(const NamedEntity &base, int dimension) {
355   return GetLowerBoundHelper<MaybeExtentExpr, true>{dimension, nullptr}(base);
356 }
357 
358 MaybeExtentExpr GetLBOUND(
359     FoldingContext &context, const NamedEntity &base, int dimension) {
360   return Fold(context,
361       GetLowerBoundHelper<MaybeExtentExpr, true>{dimension, &context}(base));
362 }
363 
364 Shape GetRawLowerBounds(const NamedEntity &base) {
365   Shape result;
366   int rank{base.Rank()};
367   for (int dim{0}; dim < rank; ++dim) {
368     result.emplace_back(GetRawLowerBound(base, dim));
369   }
370   return result;
371 }
372 
373 Shape GetRawLowerBounds(FoldingContext &context, const NamedEntity &base) {
374   Shape result;
375   int rank{base.Rank()};
376   for (int dim{0}; dim < rank; ++dim) {
377     result.emplace_back(GetRawLowerBound(context, base, dim));
378   }
379   return result;
380 }
381 
382 Shape GetLBOUNDs(const NamedEntity &base) {
383   Shape result;
384   int rank{base.Rank()};
385   for (int dim{0}; dim < rank; ++dim) {
386     result.emplace_back(GetLBOUND(base, dim));
387   }
388   return result;
389 }
390 
391 Shape GetLBOUNDs(FoldingContext &context, const NamedEntity &base) {
392   Shape result;
393   int rank{base.Rank()};
394   for (int dim{0}; dim < rank; ++dim) {
395     result.emplace_back(GetLBOUND(context, base, dim));
396   }
397   return result;
398 }
399 
400 // If the upper and lower bounds are constant, return a constant expression for
401 // the extent.  In particular, if the upper bound is less than the lower bound,
402 // return zero.
403 static MaybeExtentExpr GetNonNegativeExtent(
404     const semantics::ShapeSpec &shapeSpec) {
405   const auto &ubound{shapeSpec.ubound().GetExplicit()};
406   const auto &lbound{shapeSpec.lbound().GetExplicit()};
407   std::optional<ConstantSubscript> uval{ToInt64(ubound)};
408   std::optional<ConstantSubscript> lval{ToInt64(lbound)};
409   if (uval && lval) {
410     if (*uval < *lval) {
411       return ExtentExpr{0};
412     } else {
413       return ExtentExpr{*uval - *lval + 1};
414     }
415   } else if (lbound && ubound && IsScopeInvariantExpr(*lbound) &&
416       IsScopeInvariantExpr(*ubound)) {
417     // Apply effective IDIM (MAX calculation with 0) so thet the
418     // result is never negative
419     if (lval.value_or(0) == 1) {
420       return ExtentExpr{Extremum<SubscriptInteger>{
421           Ordering::Greater, ExtentExpr{0}, common::Clone(*ubound)}};
422     } else {
423       return ExtentExpr{
424           Extremum<SubscriptInteger>{Ordering::Greater, ExtentExpr{0},
425               common::Clone(*ubound) - common::Clone(*lbound) + ExtentExpr{1}}};
426     }
427   } else {
428     return std::nullopt;
429   }
430 }
431 
432 MaybeExtentExpr GetExtent(const NamedEntity &base, int dimension) {
433   CHECK(dimension >= 0);
434   const Symbol &last{base.GetLastSymbol()};
435   const Symbol &symbol{ResolveAssociations(last)};
436   if (const auto *assoc{last.detailsIf<semantics::AssocEntityDetails>()}) {
437     if (assoc->rank()) { // SELECT RANK case
438       if (semantics::IsDescriptor(symbol) && dimension < *assoc->rank()) {
439         return ExtentExpr{DescriptorInquiry{
440             NamedEntity{base}, DescriptorInquiry::Field::Extent, dimension}};
441       }
442     } else if (auto shape{GetShape(assoc->expr())}) {
443       if (dimension < static_cast<int>(shape->size())) {
444         return std::move(shape->at(dimension));
445       }
446     }
447   }
448   if (const auto *details{symbol.detailsIf<semantics::ObjectEntityDetails>()}) {
449     if (IsImpliedShape(symbol) && details->init()) {
450       if (auto shape{GetShape(symbol)}) {
451         if (dimension < static_cast<int>(shape->size())) {
452           return std::move(shape->at(dimension));
453         }
454       }
455     } else {
456       int j{0};
457       for (const auto &shapeSpec : details->shape()) {
458         if (j++ == dimension) {
459           if (auto extent{GetNonNegativeExtent(shapeSpec)}) {
460             return extent;
461           } else if (details->IsAssumedSize() && j == symbol.Rank()) {
462             return std::nullopt;
463           } else if (semantics::IsDescriptor(symbol)) {
464             return ExtentExpr{DescriptorInquiry{NamedEntity{base},
465                 DescriptorInquiry::Field::Extent, dimension}};
466           } else {
467             break;
468           }
469         }
470       }
471     }
472   }
473   return std::nullopt;
474 }
475 
476 MaybeExtentExpr GetExtent(
477     FoldingContext &context, const NamedEntity &base, int dimension) {
478   return Fold(context, GetExtent(base, dimension));
479 }
480 
481 MaybeExtentExpr GetExtent(
482     const Subscript &subscript, const NamedEntity &base, int dimension) {
483   return common::visit(
484       common::visitors{
485           [&](const Triplet &triplet) -> MaybeExtentExpr {
486             MaybeExtentExpr upper{triplet.upper()};
487             if (!upper) {
488               upper = GetUBOUND(base, dimension);
489             }
490             MaybeExtentExpr lower{triplet.lower()};
491             if (!lower) {
492               lower = GetLBOUND(base, dimension);
493             }
494             return CountTrips(std::move(lower), std::move(upper),
495                 MaybeExtentExpr{triplet.stride()});
496           },
497           [&](const IndirectSubscriptIntegerExpr &subs) -> MaybeExtentExpr {
498             if (auto shape{GetShape(subs.value())}) {
499               if (GetRank(*shape) > 0) {
500                 CHECK(GetRank(*shape) == 1); // vector-valued subscript
501                 return std::move(shape->at(0));
502               }
503             }
504             return std::nullopt;
505           },
506       },
507       subscript.u);
508 }
509 
510 MaybeExtentExpr GetExtent(FoldingContext &context, const Subscript &subscript,
511     const NamedEntity &base, int dimension) {
512   return Fold(context, GetExtent(subscript, base, dimension));
513 }
514 
515 MaybeExtentExpr ComputeUpperBound(
516     ExtentExpr &&lower, MaybeExtentExpr &&extent) {
517   if (extent) {
518     if (ToInt64(lower).value_or(0) == 1) {
519       return std::move(*extent);
520     } else {
521       return std::move(*extent) + std::move(lower) - ExtentExpr{1};
522     }
523   } else {
524     return std::nullopt;
525   }
526 }
527 
528 MaybeExtentExpr ComputeUpperBound(
529     FoldingContext &context, ExtentExpr &&lower, MaybeExtentExpr &&extent) {
530   return Fold(context, ComputeUpperBound(std::move(lower), std::move(extent)));
531 }
532 
533 MaybeExtentExpr GetRawUpperBound(const NamedEntity &base, int dimension) {
534   const Symbol &symbol{ResolveAssociations(base.GetLastSymbol())};
535   if (const auto *details{symbol.detailsIf<semantics::ObjectEntityDetails>()}) {
536     int rank{details->shape().Rank()};
537     if (dimension < rank) {
538       const auto &bound{details->shape()[dimension].ubound().GetExplicit()};
539       if (bound && IsScopeInvariantExpr(*bound)) {
540         return *bound;
541       } else if (details->IsAssumedSize() && dimension + 1 == symbol.Rank()) {
542         return std::nullopt;
543       } else {
544         return ComputeUpperBound(
545             GetRawLowerBound(base, dimension), GetExtent(base, dimension));
546       }
547     }
548   } else if (const auto *assoc{
549                  symbol.detailsIf<semantics::AssocEntityDetails>()}) {
550     if (auto shape{GetShape(assoc->expr())}) {
551       if (dimension < static_cast<int>(shape->size())) {
552         return ComputeUpperBound(
553             GetRawLowerBound(base, dimension), std::move(shape->at(dimension)));
554       }
555     }
556   }
557   return std::nullopt;
558 }
559 
560 MaybeExtentExpr GetRawUpperBound(
561     FoldingContext &context, const NamedEntity &base, int dimension) {
562   return Fold(context, GetRawUpperBound(base, dimension));
563 }
564 
565 static MaybeExtentExpr GetExplicitUBOUND(
566     FoldingContext *context, const semantics::ShapeSpec &shapeSpec) {
567   const auto &ubound{shapeSpec.ubound().GetExplicit()};
568   if (ubound && IsScopeInvariantExpr(*ubound)) {
569     if (auto extent{GetNonNegativeExtent(shapeSpec)}) {
570       if (auto cstExtent{ToInt64(
571               context ? Fold(*context, std::move(*extent)) : *extent)}) {
572         if (cstExtent > 0) {
573           return *ubound;
574         } else if (cstExtent == 0) {
575           return ExtentExpr{0};
576         }
577       }
578     }
579   }
580   return std::nullopt;
581 }
582 
583 static MaybeExtentExpr GetUBOUND(
584     FoldingContext *context, const NamedEntity &base, int dimension) {
585   const Symbol &symbol{ResolveAssociations(base.GetLastSymbol())};
586   if (const auto *details{symbol.detailsIf<semantics::ObjectEntityDetails>()}) {
587     int rank{details->shape().Rank()};
588     if (dimension < rank) {
589       const semantics::ShapeSpec &shapeSpec{details->shape()[dimension]};
590       if (auto ubound{GetExplicitUBOUND(context, shapeSpec)}) {
591         return *ubound;
592       } else if (details->IsAssumedSize() && dimension + 1 == symbol.Rank()) {
593         return std::nullopt;
594       } else if (auto lb{GetLBOUND(base, dimension)}) {
595         return ComputeUpperBound(std::move(*lb), GetExtent(base, dimension));
596       }
597     }
598   } else if (const auto *assoc{
599                  symbol.detailsIf<semantics::AssocEntityDetails>()}) {
600     if (auto shape{GetShape(assoc->expr())}) {
601       if (dimension < static_cast<int>(shape->size())) {
602         if (auto lb{GetLBOUND(base, dimension)}) {
603           return ComputeUpperBound(
604               std::move(*lb), std::move(shape->at(dimension)));
605         }
606       }
607     }
608   }
609   return std::nullopt;
610 }
611 
612 MaybeExtentExpr GetUBOUND(const NamedEntity &base, int dimension) {
613   return GetUBOUND(nullptr, base, dimension);
614 }
615 
616 MaybeExtentExpr GetUBOUND(
617     FoldingContext &context, const NamedEntity &base, int dimension) {
618   return Fold(context, GetUBOUND(&context, base, dimension));
619 }
620 
621 static Shape GetUBOUNDs(FoldingContext *context, const NamedEntity &base) {
622   const Symbol &symbol{ResolveAssociations(base.GetLastSymbol())};
623   if (const auto *details{symbol.detailsIf<semantics::ObjectEntityDetails>()}) {
624     Shape result;
625     int dim{0};
626     for (const auto &shapeSpec : details->shape()) {
627       if (auto ubound{GetExplicitUBOUND(context, shapeSpec)}) {
628         result.emplace_back(*ubound);
629       } else if (details->IsAssumedSize() && dim + 1 == base.Rank()) {
630         result.emplace_back(std::nullopt); // UBOUND folding replaces with -1
631       } else if (auto lb{GetLBOUND(base, dim)}) {
632         result.emplace_back(
633             ComputeUpperBound(std::move(*lb), GetExtent(base, dim)));
634       } else {
635         result.emplace_back(); // unknown
636       }
637       ++dim;
638     }
639     CHECK(GetRank(result) == symbol.Rank());
640     return result;
641   } else {
642     return std::move(GetShape(symbol).value());
643   }
644 }
645 
646 Shape GetUBOUNDs(FoldingContext &context, const NamedEntity &base) {
647   return Fold(context, GetUBOUNDs(&context, base));
648 }
649 
650 Shape GetUBOUNDs(const NamedEntity &base) { return GetUBOUNDs(nullptr, base); }
651 
652 auto GetShapeHelper::operator()(const Symbol &symbol) const -> Result {
653   return common::visit(
654       common::visitors{
655           [&](const semantics::ObjectEntityDetails &object) {
656             if (IsImpliedShape(symbol) && object.init()) {
657               return (*this)(object.init());
658             } else if (IsAssumedRank(symbol)) {
659               return Result{};
660             } else {
661               int n{object.shape().Rank()};
662               NamedEntity base{symbol};
663               return Result{CreateShape(n, base)};
664             }
665           },
666           [](const semantics::EntityDetails &) {
667             return ScalarShape(); // no dimensions seen
668           },
669           [&](const semantics::ProcEntityDetails &proc) {
670             if (const Symbol * interface{proc.interface().symbol()}) {
671               return (*this)(*interface);
672             } else {
673               return ScalarShape();
674             }
675           },
676           [&](const semantics::AssocEntityDetails &assoc) {
677             if (assoc.rank()) { // SELECT RANK case
678               int n{assoc.rank().value()};
679               NamedEntity base{symbol};
680               return Result{CreateShape(n, base)};
681             } else {
682               return (*this)(assoc.expr());
683             }
684           },
685           [&](const semantics::SubprogramDetails &subp) -> Result {
686             if (subp.isFunction()) {
687               auto resultShape{(*this)(subp.result())};
688               if (resultShape && !useResultSymbolShape_) {
689                 // Ensure the shape is constant. Otherwise, it may be referring
690                 // to symbols that belong to the subroutine scope and are
691                 // meaningless on the caller side without the related call
692                 // expression.
693                 for (auto &extent : *resultShape) {
694                   if (extent && !IsActuallyConstant(*extent)) {
695                     extent.reset();
696                   }
697                 }
698               }
699               return resultShape;
700             } else {
701               return Result{};
702             }
703           },
704           [&](const semantics::ProcBindingDetails &binding) {
705             return (*this)(binding.symbol());
706           },
707           [](const semantics::TypeParamDetails &) { return ScalarShape(); },
708           [](const auto &) { return Result{}; },
709       },
710       symbol.GetUltimate().details());
711 }
712 
713 auto GetShapeHelper::operator()(const Component &component) const -> Result {
714   const Symbol &symbol{component.GetLastSymbol()};
715   int rank{symbol.Rank()};
716   if (rank == 0) {
717     return (*this)(component.base());
718   } else if (symbol.has<semantics::ObjectEntityDetails>()) {
719     NamedEntity base{Component{component}};
720     return CreateShape(rank, base);
721   } else if (symbol.has<semantics::AssocEntityDetails>()) {
722     NamedEntity base{Component{component}};
723     return Result{CreateShape(rank, base)};
724   } else {
725     return (*this)(symbol);
726   }
727 }
728 
729 auto GetShapeHelper::operator()(const ArrayRef &arrayRef) const -> Result {
730   Shape shape;
731   int dimension{0};
732   const NamedEntity &base{arrayRef.base()};
733   for (const Subscript &ss : arrayRef.subscript()) {
734     if (ss.Rank() > 0) {
735       shape.emplace_back(GetExtent(ss, base, dimension));
736     }
737     ++dimension;
738   }
739   if (shape.empty()) {
740     if (const Component * component{base.UnwrapComponent()}) {
741       return (*this)(component->base());
742     }
743   }
744   return shape;
745 }
746 
747 auto GetShapeHelper::operator()(const CoarrayRef &coarrayRef) const -> Result {
748   NamedEntity base{coarrayRef.GetBase()};
749   if (coarrayRef.subscript().empty()) {
750     return (*this)(base);
751   } else {
752     Shape shape;
753     int dimension{0};
754     for (const Subscript &ss : coarrayRef.subscript()) {
755       if (ss.Rank() > 0) {
756         shape.emplace_back(GetExtent(ss, base, dimension));
757       }
758       ++dimension;
759     }
760     return shape;
761   }
762 }
763 
764 auto GetShapeHelper::operator()(const Substring &substring) const -> Result {
765   return (*this)(substring.parent());
766 }
767 
768 auto GetShapeHelper::operator()(const ProcedureRef &call) const -> Result {
769   if (call.Rank() == 0) {
770     return ScalarShape();
771   } else if (call.IsElemental()) {
772     for (const auto &arg : call.arguments()) {
773       if (arg && arg->Rank() > 0) {
774         return (*this)(*arg);
775       }
776     }
777     return ScalarShape();
778   } else if (const Symbol * symbol{call.proc().GetSymbol()}) {
779     return (*this)(*symbol);
780   } else if (const auto *intrinsic{call.proc().GetSpecificIntrinsic()}) {
781     if (intrinsic->name == "shape" || intrinsic->name == "lbound" ||
782         intrinsic->name == "ubound") {
783       // For LBOUND/UBOUND, these are the array-valued cases (no DIM=)
784       if (!call.arguments().empty() && call.arguments().front()) {
785         return Shape{
786             MaybeExtentExpr{ExtentExpr{call.arguments().front()->Rank()}}};
787       }
788     } else if (intrinsic->name == "all" || intrinsic->name == "any" ||
789         intrinsic->name == "count" || intrinsic->name == "iall" ||
790         intrinsic->name == "iany" || intrinsic->name == "iparity" ||
791         intrinsic->name == "maxval" || intrinsic->name == "minval" ||
792         intrinsic->name == "norm2" || intrinsic->name == "parity" ||
793         intrinsic->name == "product" || intrinsic->name == "sum") {
794       // Reduction with DIM=
795       if (call.arguments().size() >= 2) {
796         auto arrayShape{
797             (*this)(UnwrapExpr<Expr<SomeType>>(call.arguments().at(0)))};
798         const auto *dimArg{UnwrapExpr<Expr<SomeType>>(call.arguments().at(1))};
799         if (arrayShape && dimArg) {
800           if (auto dim{ToInt64(*dimArg)}) {
801             if (*dim >= 1 &&
802                 static_cast<std::size_t>(*dim) <= arrayShape->size()) {
803               arrayShape->erase(arrayShape->begin() + (*dim - 1));
804               return std::move(*arrayShape);
805             }
806           }
807         }
808       }
809     } else if (intrinsic->name == "findloc" || intrinsic->name == "maxloc" ||
810         intrinsic->name == "minloc") {
811       std::size_t dimIndex{intrinsic->name == "findloc" ? 2u : 1u};
812       if (call.arguments().size() > dimIndex) {
813         if (auto arrayShape{
814                 (*this)(UnwrapExpr<Expr<SomeType>>(call.arguments().at(0)))}) {
815           auto rank{static_cast<int>(arrayShape->size())};
816           if (const auto *dimArg{
817                   UnwrapExpr<Expr<SomeType>>(call.arguments()[dimIndex])}) {
818             auto dim{ToInt64(*dimArg)};
819             if (dim && *dim >= 1 && *dim <= rank) {
820               arrayShape->erase(arrayShape->begin() + (*dim - 1));
821               return std::move(*arrayShape);
822             }
823           } else {
824             // xxxLOC(no DIM=) result is vector(1:RANK(ARRAY=))
825             return Shape{ExtentExpr{rank}};
826           }
827         }
828       }
829     } else if (intrinsic->name == "cshift" || intrinsic->name == "eoshift") {
830       if (!call.arguments().empty()) {
831         return (*this)(call.arguments()[0]);
832       }
833     } else if (intrinsic->name == "matmul") {
834       if (call.arguments().size() == 2) {
835         if (auto ashape{(*this)(call.arguments()[0])}) {
836           if (auto bshape{(*this)(call.arguments()[1])}) {
837             if (ashape->size() == 1 && bshape->size() == 2) {
838               bshape->erase(bshape->begin());
839               return std::move(*bshape); // matmul(vector, matrix)
840             } else if (ashape->size() == 2 && bshape->size() == 1) {
841               ashape->pop_back();
842               return std::move(*ashape); // matmul(matrix, vector)
843             } else if (ashape->size() == 2 && bshape->size() == 2) {
844               (*ashape)[1] = std::move((*bshape)[1]);
845               return std::move(*ashape); // matmul(matrix, matrix)
846             }
847           }
848         }
849       }
850     } else if (intrinsic->name == "pack") {
851       if (call.arguments().size() >= 3 && call.arguments().at(2)) {
852         // SHAPE(PACK(,,VECTOR=v)) -> SHAPE(v)
853         return (*this)(call.arguments().at(2));
854       } else if (call.arguments().size() >= 2 && context_) {
855         if (auto maskShape{(*this)(call.arguments().at(1))}) {
856           if (maskShape->size() == 0) {
857             // Scalar MASK= -> [MERGE(SIZE(ARRAY=), 0, mask)]
858             if (auto arrayShape{(*this)(call.arguments().at(0))}) {
859               auto arraySize{GetSize(std::move(*arrayShape))};
860               CHECK(arraySize);
861               ActualArguments toMerge{
862                   ActualArgument{AsGenericExpr(std::move(*arraySize))},
863                   ActualArgument{AsGenericExpr(ExtentExpr{0})},
864                   common::Clone(call.arguments().at(1))};
865               auto specific{context_->intrinsics().Probe(
866                   CallCharacteristics{"merge"}, toMerge, *context_)};
867               CHECK(specific);
868               return Shape{ExtentExpr{FunctionRef<ExtentType>{
869                   ProcedureDesignator{std::move(specific->specificIntrinsic)},
870                   std::move(specific->arguments)}}};
871             }
872           } else {
873             // Non-scalar MASK= -> [COUNT(mask)]
874             ActualArguments toCount{ActualArgument{common::Clone(
875                 DEREF(call.arguments().at(1).value().UnwrapExpr()))}};
876             auto specific{context_->intrinsics().Probe(
877                 CallCharacteristics{"count"}, toCount, *context_)};
878             CHECK(specific);
879             return Shape{ExtentExpr{FunctionRef<ExtentType>{
880                 ProcedureDesignator{std::move(specific->specificIntrinsic)},
881                 std::move(specific->arguments)}}};
882           }
883         }
884       }
885     } else if (intrinsic->name == "reshape") {
886       if (call.arguments().size() >= 2 && call.arguments().at(1)) {
887         // SHAPE(RESHAPE(array,shape)) -> shape
888         if (const auto *shapeExpr{
889                 call.arguments().at(1).value().UnwrapExpr()}) {
890           auto shapeArg{std::get<Expr<SomeInteger>>(shapeExpr->u)};
891           if (auto result{AsShapeResult(
892                   ConvertToType<ExtentType>(std::move(shapeArg)))}) {
893             return result;
894           }
895         }
896       }
897     } else if (intrinsic->name == "spread") {
898       // SHAPE(SPREAD(ARRAY,DIM,NCOPIES)) = SHAPE(ARRAY) with NCOPIES inserted
899       // at position DIM.
900       if (call.arguments().size() == 3) {
901         auto arrayShape{
902             (*this)(UnwrapExpr<Expr<SomeType>>(call.arguments().at(0)))};
903         const auto *dimArg{UnwrapExpr<Expr<SomeType>>(call.arguments().at(1))};
904         const auto *nCopies{
905             UnwrapExpr<Expr<SomeInteger>>(call.arguments().at(2))};
906         if (arrayShape && dimArg && nCopies) {
907           if (auto dim{ToInt64(*dimArg)}) {
908             if (*dim >= 1 &&
909                 static_cast<std::size_t>(*dim) <= arrayShape->size() + 1) {
910               arrayShape->emplace(arrayShape->begin() + *dim - 1,
911                   ConvertToType<ExtentType>(common::Clone(*nCopies)));
912               return std::move(*arrayShape);
913             }
914           }
915         }
916       }
917     } else if (intrinsic->name == "transfer") {
918       if (call.arguments().size() == 3 && call.arguments().at(2)) {
919         // SIZE= is present; shape is vector [SIZE=]
920         if (const auto *size{
921                 UnwrapExpr<Expr<SomeInteger>>(call.arguments().at(2))}) {
922           return Shape{
923               MaybeExtentExpr{ConvertToType<ExtentType>(common::Clone(*size))}};
924         }
925       } else if (context_) {
926         if (auto moldTypeAndShape{characteristics::TypeAndShape::Characterize(
927                 call.arguments().at(1), *context_)}) {
928           if (GetRank(moldTypeAndShape->shape()) == 0) {
929             // SIZE= is absent and MOLD= is scalar: result is scalar
930             return ScalarShape();
931           } else {
932             // SIZE= is absent and MOLD= is array: result is vector whose
933             // length is determined by sizes of types.  See 16.9.193p4 case(ii).
934             // Note that if sourceBytes is not known to be empty, we
935             // can fold only when moldElementBytes is known to not be zero;
936             // the most general case risks a division by zero otherwise.
937             if (auto sourceTypeAndShape{
938                     characteristics::TypeAndShape::Characterize(
939                         call.arguments().at(0), *context_)}) {
940               if (auto sourceBytes{
941                       sourceTypeAndShape->MeasureSizeInBytes(*context_)}) {
942                 *sourceBytes = Fold(*context_, std::move(*sourceBytes));
943                 if (auto sourceBytesConst{ToInt64(*sourceBytes)}) {
944                   if (*sourceBytesConst == 0) {
945                     return Shape{ExtentExpr{0}};
946                   }
947                 }
948                 if (auto moldElementBytes{
949                         moldTypeAndShape->MeasureElementSizeInBytes(
950                             *context_, true)}) {
951                   *moldElementBytes =
952                       Fold(*context_, std::move(*moldElementBytes));
953                   auto moldElementBytesConst{ToInt64(*moldElementBytes)};
954                   if (moldElementBytesConst && *moldElementBytesConst != 0) {
955                     ExtentExpr extent{Fold(*context_,
956                         (std::move(*sourceBytes) +
957                             common::Clone(*moldElementBytes) - ExtentExpr{1}) /
958                             common::Clone(*moldElementBytes))};
959                     return Shape{MaybeExtentExpr{std::move(extent)}};
960                   }
961                 }
962               }
963             }
964           }
965         }
966       }
967     } else if (intrinsic->name == "transpose") {
968       if (call.arguments().size() >= 1) {
969         if (auto shape{(*this)(call.arguments().at(0))}) {
970           if (shape->size() == 2) {
971             std::swap((*shape)[0], (*shape)[1]);
972             return shape;
973           }
974         }
975       }
976     } else if (intrinsic->name == "unpack") {
977       if (call.arguments().size() >= 2) {
978         return (*this)(call.arguments()[1]); // MASK=
979       }
980     } else if (intrinsic->characteristics.value().attrs.test(characteristics::
981                        Procedure::Attr::NullPointer)) { // NULL(MOLD=)
982       return (*this)(call.arguments());
983     } else {
984       // TODO: shapes of other non-elemental intrinsic results
985     }
986   }
987   // The rank is always known even if the extents are not.
988   return Shape(static_cast<std::size_t>(call.Rank()), MaybeExtentExpr{});
989 }
990 
991 // Check conformance of the passed shapes.
992 std::optional<bool> CheckConformance(parser::ContextualMessages &messages,
993     const Shape &left, const Shape &right, CheckConformanceFlags::Flags flags,
994     const char *leftIs, const char *rightIs) {
995   int n{GetRank(left)};
996   if (n == 0 && (flags & CheckConformanceFlags::LeftScalarExpandable)) {
997     return true;
998   }
999   int rn{GetRank(right)};
1000   if (rn == 0 && (flags & CheckConformanceFlags::RightScalarExpandable)) {
1001     return true;
1002   }
1003   if (n != rn) {
1004     messages.Say("Rank of %1$s is %2$d, but %3$s has rank %4$d"_err_en_US,
1005         leftIs, n, rightIs, rn);
1006     return false;
1007   }
1008   for (int j{0}; j < n; ++j) {
1009     if (auto leftDim{ToInt64(left[j])}) {
1010       if (auto rightDim{ToInt64(right[j])}) {
1011         if (*leftDim != *rightDim) {
1012           messages.Say("Dimension %1$d of %2$s has extent %3$jd, "
1013                        "but %4$s has extent %5$jd"_err_en_US,
1014               j + 1, leftIs, *leftDim, rightIs, *rightDim);
1015           return false;
1016         }
1017       } else if (!(flags & CheckConformanceFlags::RightIsDeferredShape)) {
1018         return std::nullopt;
1019       }
1020     } else if (!(flags & CheckConformanceFlags::LeftIsDeferredShape)) {
1021       return std::nullopt;
1022     }
1023   }
1024   return true;
1025 }
1026 
1027 bool IncrementSubscripts(
1028     ConstantSubscripts &indices, const ConstantSubscripts &extents) {
1029   std::size_t rank(indices.size());
1030   CHECK(rank <= extents.size());
1031   for (std::size_t j{0}; j < rank; ++j) {
1032     if (extents[j] < 1) {
1033       return false;
1034     }
1035   }
1036   for (std::size_t j{0}; j < rank; ++j) {
1037     if (indices[j]++ < extents[j]) {
1038       return true;
1039     }
1040     indices[j] = 1;
1041   }
1042   return false;
1043 }
1044 
1045 } // namespace Fortran::evaluate
1046