xref: /llvm-project/flang/lib/Evaluate/shape.cpp (revision 9bbec0ad42a8e8c8f564a36adb1e819a0921a7f9) 
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) const {
80   Shape shape;
81   for (int dimension{0}; dimension < rank; ++dimension) {
82     shape.emplace_back(GetExtent(base, dimension, invariantOnly_));
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(
240       int d, FoldingContext *context, bool invariantOnly)
241       : Base{*this}, dimension_{d}, context_{context},
242         invariantOnly_{invariantOnly} {}
243   static Result Default() { return Result{1}; }
244   static Result Combine(Result &&, Result &&) {
245     // Operator results and array references always have lower bounds == 1
246     return Result{1};
247   }
248 
249   Result GetLowerBound(const Symbol &symbol0, NamedEntity &&base) const {
250     const Symbol &symbol{symbol0.GetUltimate()};
251     if (const auto *object{
252             symbol.detailsIf<semantics::ObjectEntityDetails>()}) {
253       int rank{object->shape().Rank()};
254       if (dimension_ < rank) {
255         const semantics::ShapeSpec &shapeSpec{object->shape()[dimension_]};
256         if (shapeSpec.lbound().isExplicit()) {
257           if (const auto &lbound{shapeSpec.lbound().GetExplicit()}) {
258             if constexpr (LBOUND_SEMANTICS) {
259               bool ok{false};
260               auto lbValue{ToInt64(*lbound)};
261               if (dimension_ == rank - 1 && object->IsAssumedSize()) {
262                 // last dimension of assumed-size dummy array: don't worry
263                 // about handling an empty dimension
264                 ok = !invariantOnly_ || IsScopeInvariantExpr(*lbound);
265               } else if (lbValue.value_or(0) == 1) {
266                 // Lower bound is 1, regardless of extent
267                 ok = true;
268               } else if (const auto &ubound{shapeSpec.ubound().GetExplicit()}) {
269                 // If we can't prove that the dimension is nonempty,
270                 // we must be conservative.
271                 // TODO: simple symbolic math in expression rewriting to
272                 // cope with cases like A(J:J)
273                 if (context_) {
274                   auto extent{ToInt64(Fold(*context_,
275                       ExtentExpr{*ubound} - ExtentExpr{*lbound} +
276                           ExtentExpr{1}))};
277                   if (extent) {
278                     if (extent <= 0) {
279                       return Result{1};
280                     }
281                     ok = true;
282                   } else {
283                     ok = false;
284                   }
285                 } else {
286                   auto ubValue{ToInt64(*ubound)};
287                   if (lbValue && ubValue) {
288                     if (*lbValue > *ubValue) {
289                       return Result{1};
290                     }
291                     ok = true;
292                   } else {
293                     ok = false;
294                   }
295                 }
296               }
297               return ok ? *lbound : Result{};
298             } else {
299               return *lbound;
300             }
301           } else {
302             return Result{1};
303           }
304         }
305         if (IsDescriptor(symbol)) {
306           return ExtentExpr{DescriptorInquiry{std::move(base),
307               DescriptorInquiry::Field::LowerBound, dimension_}};
308         }
309       }
310     } else if (const auto *assoc{
311                    symbol.detailsIf<semantics::AssocEntityDetails>()}) {
312       if (assoc->IsAssumedSize()) { // RANK(*)
313         return Result{1};
314       } else if (assoc->IsAssumedRank()) { // RANK DEFAULT
315       } else if (assoc->rank()) { // RANK(n)
316         const Symbol &resolved{ResolveAssociations(symbol)};
317         if (IsDescriptor(resolved) && dimension_ < *assoc->rank()) {
318           return ExtentExpr{DescriptorInquiry{std::move(base),
319               DescriptorInquiry::Field::LowerBound, dimension_}};
320         }
321       } else {
322         Result exprLowerBound{((*this)(assoc->expr()))};
323         if (IsActuallyConstant(exprLowerBound)) {
324           return std::move(exprLowerBound);
325         } else {
326           // If the lower bound of the associated entity is not resolved to a
327           // constant expression at the time of the association, it is unsafe
328           // to re-evaluate it later in the associate construct. Statements
329           // in between may have modified its operands value.
330           return ExtentExpr{DescriptorInquiry{std::move(base),
331               DescriptorInquiry::Field::LowerBound, dimension_}};
332         }
333       }
334     }
335     if constexpr (LBOUND_SEMANTICS) {
336       return Result{};
337     } else {
338       return Result{1};
339     }
340   }
341 
342   Result operator()(const Symbol &symbol) const {
343     return GetLowerBound(symbol, NamedEntity{symbol});
344   }
345 
346   Result operator()(const Component &component) const {
347     if (component.base().Rank() == 0) {
348       return GetLowerBound(
349           component.GetLastSymbol(), NamedEntity{common::Clone(component)});
350     }
351     return Result{1};
352   }
353 
354   template <typename T> Result operator()(const Expr<T> &expr) const {
355     if (const Symbol * whole{UnwrapWholeSymbolOrComponentDataRef(expr)}) {
356       return (*this)(*whole);
357     } else if constexpr (common::HasMember<Constant<T>, decltype(expr.u)>) {
358       if (const auto *con{std::get_if<Constant<T>>(&expr.u)}) {
359         ConstantSubscripts lb{con->lbounds()};
360         if (dimension_ < GetRank(lb)) {
361           return Result{lb[dimension_]};
362         }
363       } else { // operation
364         return Result{1};
365       }
366     } else {
367       return (*this)(expr.u);
368     }
369     if constexpr (LBOUND_SEMANTICS) {
370       return Result{};
371     } else {
372       return Result{1};
373     }
374   }
375 
376 private:
377   int dimension_; // zero-based
378   FoldingContext *context_{nullptr};
379   bool invariantOnly_{false};
380 };
381 
382 ExtentExpr GetRawLowerBound(
383     const NamedEntity &base, int dimension, bool invariantOnly) {
384   return GetLowerBoundHelper<ExtentExpr, false>{
385       dimension, nullptr, invariantOnly}(base);
386 }
387 
388 ExtentExpr GetRawLowerBound(FoldingContext &context, const NamedEntity &base,
389     int dimension, bool invariantOnly) {
390   return Fold(context,
391       GetLowerBoundHelper<ExtentExpr, false>{
392           dimension, &context, invariantOnly}(base));
393 }
394 
395 MaybeExtentExpr GetLBOUND(
396     const NamedEntity &base, int dimension, bool invariantOnly) {
397   return GetLowerBoundHelper<MaybeExtentExpr, true>{
398       dimension, nullptr, invariantOnly}(base);
399 }
400 
401 MaybeExtentExpr GetLBOUND(FoldingContext &context, const NamedEntity &base,
402     int dimension, bool invariantOnly) {
403   return Fold(context,
404       GetLowerBoundHelper<MaybeExtentExpr, true>{
405           dimension, &context, invariantOnly}(base));
406 }
407 
408 Shape GetRawLowerBounds(const NamedEntity &base, bool invariantOnly) {
409   Shape result;
410   int rank{base.Rank()};
411   for (int dim{0}; dim < rank; ++dim) {
412     result.emplace_back(GetRawLowerBound(base, dim, invariantOnly));
413   }
414   return result;
415 }
416 
417 Shape GetRawLowerBounds(
418     FoldingContext &context, const NamedEntity &base, bool invariantOnly) {
419   Shape result;
420   int rank{base.Rank()};
421   for (int dim{0}; dim < rank; ++dim) {
422     result.emplace_back(GetRawLowerBound(context, base, dim, invariantOnly));
423   }
424   return result;
425 }
426 
427 Shape GetLBOUNDs(const NamedEntity &base, bool invariantOnly) {
428   Shape result;
429   int rank{base.Rank()};
430   for (int dim{0}; dim < rank; ++dim) {
431     result.emplace_back(GetLBOUND(base, dim, invariantOnly));
432   }
433   return result;
434 }
435 
436 Shape GetLBOUNDs(
437     FoldingContext &context, const NamedEntity &base, bool invariantOnly) {
438   Shape result;
439   int rank{base.Rank()};
440   for (int dim{0}; dim < rank; ++dim) {
441     result.emplace_back(GetLBOUND(context, base, dim, invariantOnly));
442   }
443   return result;
444 }
445 
446 // If the upper and lower bounds are constant, return a constant expression for
447 // the extent.  In particular, if the upper bound is less than the lower bound,
448 // return zero.
449 static MaybeExtentExpr GetNonNegativeExtent(
450     const semantics::ShapeSpec &shapeSpec, bool invariantOnly) {
451   const auto &ubound{shapeSpec.ubound().GetExplicit()};
452   const auto &lbound{shapeSpec.lbound().GetExplicit()};
453   std::optional<ConstantSubscript> uval{ToInt64(ubound)};
454   std::optional<ConstantSubscript> lval{ToInt64(lbound)};
455   if (uval && lval) {
456     if (*uval < *lval) {
457       return ExtentExpr{0};
458     } else {
459       return ExtentExpr{*uval - *lval + 1};
460     }
461   } else if (lbound && ubound &&
462       (!invariantOnly ||
463           (IsScopeInvariantExpr(*lbound) && IsScopeInvariantExpr(*ubound)))) {
464     // Apply effective IDIM (MAX calculation with 0) so thet the
465     // result is never negative
466     if (lval.value_or(0) == 1) {
467       return ExtentExpr{Extremum<SubscriptInteger>{
468           Ordering::Greater, ExtentExpr{0}, common::Clone(*ubound)}};
469     } else {
470       return ExtentExpr{
471           Extremum<SubscriptInteger>{Ordering::Greater, ExtentExpr{0},
472               common::Clone(*ubound) - common::Clone(*lbound) + ExtentExpr{1}}};
473     }
474   } else {
475     return std::nullopt;
476   }
477 }
478 
479 static MaybeExtentExpr GetAssociatedExtent(
480     const Symbol &symbol, int dimension) {
481   if (const auto *assoc{symbol.detailsIf<semantics::AssocEntityDetails>()};
482       assoc && !assoc->rank()) { // not SELECT RANK case
483     if (auto shape{GetShape(assoc->expr())};
484         shape && dimension < static_cast<int>(shape->size())) {
485       if (auto &extent{shape->at(dimension)};
486           // Don't return a non-constant extent, as the variables that
487           // determine the shape of the selector's expression may change
488           // during execution of the construct.
489           extent && IsActuallyConstant(*extent)) {
490         return std::move(extent);
491       }
492     }
493   }
494   return ExtentExpr{DescriptorInquiry{
495       NamedEntity{symbol}, DescriptorInquiry::Field::Extent, dimension}};
496 }
497 
498 MaybeExtentExpr GetExtent(
499     const NamedEntity &base, int dimension, bool invariantOnly) {
500   CHECK(dimension >= 0);
501   const Symbol &last{base.GetLastSymbol()};
502   const Symbol &symbol{ResolveAssociations(last)};
503   if (const auto *assoc{last.detailsIf<semantics::AssocEntityDetails>()}) {
504     if (assoc->IsAssumedSize() || assoc->IsAssumedRank()) { // RANK(*)/DEFAULT
505       return std::nullopt;
506     } else if (assoc->rank()) { // RANK(n)
507       if (semantics::IsDescriptor(symbol) && dimension < *assoc->rank()) {
508         return ExtentExpr{DescriptorInquiry{
509             NamedEntity{base}, DescriptorInquiry::Field::Extent, dimension}};
510       } else {
511         return std::nullopt;
512       }
513     } else {
514       return GetAssociatedExtent(last, dimension);
515     }
516   }
517   if (const auto *details{symbol.detailsIf<semantics::ObjectEntityDetails>()}) {
518     if (IsImpliedShape(symbol) && details->init()) {
519       if (auto shape{GetShape(symbol, invariantOnly)}) {
520         if (dimension < static_cast<int>(shape->size())) {
521           return std::move(shape->at(dimension));
522         }
523       }
524     } else {
525       int j{0};
526       for (const auto &shapeSpec : details->shape()) {
527         if (j++ == dimension) {
528           if (auto extent{GetNonNegativeExtent(shapeSpec, invariantOnly)}) {
529             return extent;
530           } else if (details->IsAssumedSize() && j == symbol.Rank()) {
531             break;
532           } else if (semantics::IsDescriptor(symbol)) {
533             return ExtentExpr{DescriptorInquiry{NamedEntity{base},
534                 DescriptorInquiry::Field::Extent, dimension}};
535           } else {
536             break;
537           }
538         }
539       }
540     }
541   }
542   return std::nullopt;
543 }
544 
545 MaybeExtentExpr GetExtent(FoldingContext &context, const NamedEntity &base,
546     int dimension, bool invariantOnly) {
547   return Fold(context, GetExtent(base, dimension, invariantOnly));
548 }
549 
550 MaybeExtentExpr GetExtent(const Subscript &subscript, const NamedEntity &base,
551     int dimension, bool invariantOnly) {
552   return common::visit(
553       common::visitors{
554           [&](const Triplet &triplet) -> MaybeExtentExpr {
555             MaybeExtentExpr upper{triplet.upper()};
556             if (!upper) {
557               upper = GetUBOUND(base, dimension, invariantOnly);
558             }
559             MaybeExtentExpr lower{triplet.lower()};
560             if (!lower) {
561               lower = GetLBOUND(base, dimension, invariantOnly);
562             }
563             return CountTrips(std::move(lower), std::move(upper),
564                 MaybeExtentExpr{triplet.stride()});
565           },
566           [&](const IndirectSubscriptIntegerExpr &subs) -> MaybeExtentExpr {
567             if (auto shape{GetShape(subs.value())}) {
568               if (GetRank(*shape) > 0) {
569                 CHECK(GetRank(*shape) == 1); // vector-valued subscript
570                 return std::move(shape->at(0));
571               }
572             }
573             return std::nullopt;
574           },
575       },
576       subscript.u);
577 }
578 
579 MaybeExtentExpr GetExtent(FoldingContext &context, const Subscript &subscript,
580     const NamedEntity &base, int dimension, bool invariantOnly) {
581   return Fold(context, GetExtent(subscript, base, dimension, invariantOnly));
582 }
583 
584 MaybeExtentExpr ComputeUpperBound(
585     ExtentExpr &&lower, MaybeExtentExpr &&extent) {
586   if (extent) {
587     if (ToInt64(lower).value_or(0) == 1) {
588       return std::move(*extent);
589     } else {
590       return std::move(*extent) + std::move(lower) - ExtentExpr{1};
591     }
592   } else {
593     return std::nullopt;
594   }
595 }
596 
597 MaybeExtentExpr ComputeUpperBound(
598     FoldingContext &context, ExtentExpr &&lower, MaybeExtentExpr &&extent) {
599   return Fold(context, ComputeUpperBound(std::move(lower), std::move(extent)));
600 }
601 
602 MaybeExtentExpr GetRawUpperBound(
603     const NamedEntity &base, int dimension, bool invariantOnly) {
604   const Symbol &symbol{ResolveAssociations(base.GetLastSymbol())};
605   if (const auto *details{symbol.detailsIf<semantics::ObjectEntityDetails>()}) {
606     int rank{details->shape().Rank()};
607     if (dimension < rank) {
608       const auto &bound{details->shape()[dimension].ubound().GetExplicit()};
609       if (bound && (!invariantOnly || IsScopeInvariantExpr(*bound))) {
610         return *bound;
611       } else if (details->IsAssumedSize() && dimension + 1 == symbol.Rank()) {
612         return std::nullopt;
613       } else {
614         return ComputeUpperBound(
615             GetRawLowerBound(base, dimension), GetExtent(base, dimension));
616       }
617     }
618   } else if (const auto *assoc{
619                  symbol.detailsIf<semantics::AssocEntityDetails>()}) {
620     if (assoc->IsAssumedSize() || assoc->IsAssumedRank()) {
621       return std::nullopt;
622     } else if (assoc->rank() && dimension >= *assoc->rank()) {
623       return std::nullopt;
624     } else if (auto extent{GetAssociatedExtent(symbol, dimension)}) {
625       return ComputeUpperBound(
626           GetRawLowerBound(base, dimension), std::move(extent));
627     }
628   }
629   return std::nullopt;
630 }
631 
632 MaybeExtentExpr GetRawUpperBound(FoldingContext &context,
633     const NamedEntity &base, int dimension, bool invariantOnly) {
634   return Fold(context, GetRawUpperBound(base, dimension, invariantOnly));
635 }
636 
637 static MaybeExtentExpr GetExplicitUBOUND(FoldingContext *context,
638     const semantics::ShapeSpec &shapeSpec, bool invariantOnly) {
639   const auto &ubound{shapeSpec.ubound().GetExplicit()};
640   if (ubound && (!invariantOnly || IsScopeInvariantExpr(*ubound))) {
641     if (auto extent{GetNonNegativeExtent(shapeSpec, invariantOnly)}) {
642       if (auto cstExtent{ToInt64(
643               context ? Fold(*context, std::move(*extent)) : *extent)}) {
644         if (cstExtent > 0) {
645           return *ubound;
646         } else if (cstExtent == 0) {
647           return ExtentExpr{0};
648         }
649       }
650     }
651   }
652   return std::nullopt;
653 }
654 
655 static MaybeExtentExpr GetUBOUND(FoldingContext *context,
656     const NamedEntity &base, int dimension, bool invariantOnly) {
657   const Symbol &symbol{ResolveAssociations(base.GetLastSymbol())};
658   if (const auto *details{symbol.detailsIf<semantics::ObjectEntityDetails>()}) {
659     int rank{details->shape().Rank()};
660     if (dimension < rank) {
661       const semantics::ShapeSpec &shapeSpec{details->shape()[dimension]};
662       if (auto ubound{GetExplicitUBOUND(context, shapeSpec, invariantOnly)}) {
663         return *ubound;
664       } else if (details->IsAssumedSize() && dimension + 1 == symbol.Rank()) {
665         return std::nullopt; // UBOUND() folding replaces with -1
666       } else if (auto lb{GetLBOUND(base, dimension, invariantOnly)}) {
667         return ComputeUpperBound(
668             std::move(*lb), GetExtent(base, dimension, invariantOnly));
669       }
670     }
671   } else if (const auto *assoc{
672                  symbol.detailsIf<semantics::AssocEntityDetails>()}) {
673     if (assoc->IsAssumedSize() || assoc->IsAssumedRank()) {
674       return std::nullopt;
675     } else if (assoc->rank()) { // RANK (n)
676       const Symbol &resolved{ResolveAssociations(symbol)};
677       if (IsDescriptor(resolved) && dimension < *assoc->rank()) {
678         ExtentExpr lb{DescriptorInquiry{NamedEntity{base},
679             DescriptorInquiry::Field::LowerBound, dimension}};
680         ExtentExpr extent{DescriptorInquiry{
681             std::move(base), DescriptorInquiry::Field::Extent, dimension}};
682         return ComputeUpperBound(std::move(lb), std::move(extent));
683       }
684     } else if (auto extent{GetAssociatedExtent(symbol, dimension)}) {
685       if (auto lb{GetLBOUND(base, dimension, invariantOnly)}) {
686         return ComputeUpperBound(std::move(*lb), std::move(extent));
687       }
688     }
689   }
690   return std::nullopt;
691 }
692 
693 MaybeExtentExpr GetUBOUND(
694     const NamedEntity &base, int dimension, bool invariantOnly) {
695   return GetUBOUND(nullptr, base, dimension, invariantOnly);
696 }
697 
698 MaybeExtentExpr GetUBOUND(FoldingContext &context, const NamedEntity &base,
699     int dimension, bool invariantOnly) {
700   return Fold(context, GetUBOUND(&context, base, dimension, invariantOnly));
701 }
702 
703 static Shape GetUBOUNDs(
704     FoldingContext *context, const NamedEntity &base, bool invariantOnly) {
705   Shape result;
706   int rank{base.Rank()};
707   for (int dim{0}; dim < rank; ++dim) {
708     result.emplace_back(GetUBOUND(context, base, dim, invariantOnly));
709   }
710   return result;
711 }
712 
713 Shape GetUBOUNDs(
714     FoldingContext &context, const NamedEntity &base, bool invariantOnly) {
715   return Fold(context, GetUBOUNDs(&context, base, invariantOnly));
716 }
717 
718 Shape GetUBOUNDs(const NamedEntity &base, bool invariantOnly) {
719   return GetUBOUNDs(nullptr, base, invariantOnly);
720 }
721 
722 auto GetShapeHelper::operator()(const Symbol &symbol) const -> Result {
723   return common::visit(
724       common::visitors{
725           [&](const semantics::ObjectEntityDetails &object) {
726             if (IsImpliedShape(symbol) && object.init()) {
727               return (*this)(object.init());
728             } else if (IsAssumedRank(symbol)) {
729               return Result{};
730             } else {
731               int n{object.shape().Rank()};
732               NamedEntity base{symbol};
733               return Result{CreateShape(n, base)};
734             }
735           },
736           [](const semantics::EntityDetails &) {
737             return ScalarShape(); // no dimensions seen
738           },
739           [&](const semantics::ProcEntityDetails &proc) {
740             if (const Symbol * interface{proc.procInterface()}) {
741               return (*this)(*interface);
742             } else {
743               return ScalarShape();
744             }
745           },
746           [&](const semantics::AssocEntityDetails &assoc) {
747             NamedEntity base{symbol};
748             if (assoc.rank()) { // SELECT RANK case
749               int n{assoc.rank().value()};
750               return Result{CreateShape(n, base)};
751             } else {
752               auto exprShape{((*this)(assoc.expr()))};
753               if (exprShape) {
754                 int rank{static_cast<int>(exprShape->size())};
755                 for (int dimension{0}; dimension < rank; ++dimension) {
756                   auto &extent{(*exprShape)[dimension]};
757                   if (extent && !IsActuallyConstant(*extent)) {
758                     extent = GetExtent(base, dimension);
759                   }
760                 }
761               }
762               return exprShape;
763             }
764           },
765           [&](const semantics::SubprogramDetails &subp) -> Result {
766             if (subp.isFunction()) {
767               auto resultShape{(*this)(subp.result())};
768               if (resultShape && !useResultSymbolShape_) {
769                 // Ensure the shape is constant. Otherwise, it may be referring
770                 // to symbols that belong to the function's scope and are
771                 // meaningless on the caller side without the related call
772                 // expression.
773                 for (auto &extent : *resultShape) {
774                   if (extent && !IsActuallyConstant(*extent)) {
775                     extent.reset();
776                   }
777                 }
778               }
779               return resultShape;
780             } else {
781               return Result{};
782             }
783           },
784           [&](const semantics::ProcBindingDetails &binding) {
785             return (*this)(binding.symbol());
786           },
787           [](const semantics::TypeParamDetails &) { return ScalarShape(); },
788           [](const auto &) { return Result{}; },
789       },
790       symbol.GetUltimate().details());
791 }
792 
793 auto GetShapeHelper::operator()(const Component &component) const -> Result {
794   const Symbol &symbol{component.GetLastSymbol()};
795   int rank{symbol.Rank()};
796   if (rank == 0) {
797     return (*this)(component.base());
798   } else if (symbol.has<semantics::ObjectEntityDetails>()) {
799     NamedEntity base{Component{component}};
800     return CreateShape(rank, base);
801   } else {
802     return (*this)(symbol);
803   }
804 }
805 
806 auto GetShapeHelper::operator()(const ArrayRef &arrayRef) const -> Result {
807   Shape shape;
808   int dimension{0};
809   const NamedEntity &base{arrayRef.base()};
810   for (const Subscript &ss : arrayRef.subscript()) {
811     if (ss.Rank() > 0) {
812       shape.emplace_back(GetExtent(ss, base, dimension));
813     }
814     ++dimension;
815   }
816   if (shape.empty()) {
817     if (const Component * component{base.UnwrapComponent()}) {
818       return (*this)(component->base());
819     }
820   }
821   return shape;
822 }
823 
824 auto GetShapeHelper::operator()(const CoarrayRef &coarrayRef) const -> Result {
825   NamedEntity base{coarrayRef.GetBase()};
826   if (coarrayRef.subscript().empty()) {
827     return (*this)(base);
828   } else {
829     Shape shape;
830     int dimension{0};
831     for (const Subscript &ss : coarrayRef.subscript()) {
832       if (ss.Rank() > 0) {
833         shape.emplace_back(GetExtent(ss, base, dimension));
834       }
835       ++dimension;
836     }
837     return shape;
838   }
839 }
840 
841 auto GetShapeHelper::operator()(const Substring &substring) const -> Result {
842   return (*this)(substring.parent());
843 }
844 
845 auto GetShapeHelper::operator()(const ProcedureRef &call) const -> Result {
846   if (call.Rank() == 0) {
847     return ScalarShape();
848   } else if (call.IsElemental()) {
849     // Use the shape of an actual array argument associated with a
850     // non-OPTIONAL dummy object argument.
851     if (context_) {
852       if (auto chars{characteristics::Procedure::FromActuals(
853               call.proc(), call.arguments(), *context_)}) {
854         std::size_t j{0};
855         std::size_t anyArrayArgRank{0};
856         for (const auto &arg : call.arguments()) {
857           if (arg && arg->Rank() > 0 && j < chars->dummyArguments.size()) {
858             anyArrayArgRank = arg->Rank();
859             if (!chars->dummyArguments[j].IsOptional()) {
860               return (*this)(*arg);
861             }
862           }
863           ++j;
864         }
865         if (anyArrayArgRank) {
866           // All dummy array arguments of the procedure are OPTIONAL.
867           // We cannot take the shape from just any array argument,
868           // because all of them might be OPTIONAL dummy arguments
869           // of the caller. Return unknown shape ranked according
870           // to the last actual array argument.
871           return Shape(anyArrayArgRank, MaybeExtentExpr{});
872         }
873       }
874     }
875     return ScalarShape();
876   } else if (const Symbol * symbol{call.proc().GetSymbol()}) {
877     auto restorer{common::ScopedSet(useResultSymbolShape_, false)};
878     return (*this)(*symbol);
879   } else if (const auto *intrinsic{call.proc().GetSpecificIntrinsic()}) {
880     if (intrinsic->name == "shape" || intrinsic->name == "lbound" ||
881         intrinsic->name == "ubound") {
882       // For LBOUND/UBOUND, these are the array-valued cases (no DIM=)
883       if (!call.arguments().empty() && call.arguments().front()) {
884         return Shape{
885             MaybeExtentExpr{ExtentExpr{call.arguments().front()->Rank()}}};
886       }
887     } else if (intrinsic->name == "all" || intrinsic->name == "any" ||
888         intrinsic->name == "count" || intrinsic->name == "iall" ||
889         intrinsic->name == "iany" || intrinsic->name == "iparity" ||
890         intrinsic->name == "maxval" || intrinsic->name == "minval" ||
891         intrinsic->name == "norm2" || intrinsic->name == "parity" ||
892         intrinsic->name == "product" || intrinsic->name == "sum") {
893       // Reduction with DIM=
894       if (call.arguments().size() >= 2) {
895         auto arrayShape{
896             (*this)(UnwrapExpr<Expr<SomeType>>(call.arguments().at(0)))};
897         const auto *dimArg{UnwrapExpr<Expr<SomeType>>(call.arguments().at(1))};
898         if (arrayShape && dimArg) {
899           if (auto dim{ToInt64(*dimArg)}) {
900             if (*dim >= 1 &&
901                 static_cast<std::size_t>(*dim) <= arrayShape->size()) {
902               arrayShape->erase(arrayShape->begin() + (*dim - 1));
903               return std::move(*arrayShape);
904             }
905           }
906         }
907       }
908     } else if (intrinsic->name == "findloc" || intrinsic->name == "maxloc" ||
909         intrinsic->name == "minloc") {
910       std::size_t dimIndex{intrinsic->name == "findloc" ? 2u : 1u};
911       if (call.arguments().size() > dimIndex) {
912         if (auto arrayShape{
913                 (*this)(UnwrapExpr<Expr<SomeType>>(call.arguments().at(0)))}) {
914           auto rank{static_cast<int>(arrayShape->size())};
915           if (const auto *dimArg{
916                   UnwrapExpr<Expr<SomeType>>(call.arguments()[dimIndex])}) {
917             auto dim{ToInt64(*dimArg)};
918             if (dim && *dim >= 1 && *dim <= rank) {
919               arrayShape->erase(arrayShape->begin() + (*dim - 1));
920               return std::move(*arrayShape);
921             }
922           } else {
923             // xxxLOC(no DIM=) result is vector(1:RANK(ARRAY=))
924             return Shape{ExtentExpr{rank}};
925           }
926         }
927       }
928     } else if (intrinsic->name == "cshift" || intrinsic->name == "eoshift") {
929       if (!call.arguments().empty()) {
930         return (*this)(call.arguments()[0]);
931       }
932     } else if (intrinsic->name == "matmul") {
933       if (call.arguments().size() == 2) {
934         if (auto ashape{(*this)(call.arguments()[0])}) {
935           if (auto bshape{(*this)(call.arguments()[1])}) {
936             if (ashape->size() == 1 && bshape->size() == 2) {
937               bshape->erase(bshape->begin());
938               return std::move(*bshape); // matmul(vector, matrix)
939             } else if (ashape->size() == 2 && bshape->size() == 1) {
940               ashape->pop_back();
941               return std::move(*ashape); // matmul(matrix, vector)
942             } else if (ashape->size() == 2 && bshape->size() == 2) {
943               (*ashape)[1] = std::move((*bshape)[1]);
944               return std::move(*ashape); // matmul(matrix, matrix)
945             }
946           }
947         }
948       }
949     } else if (intrinsic->name == "pack") {
950       if (call.arguments().size() >= 3 && call.arguments().at(2)) {
951         // SHAPE(PACK(,,VECTOR=v)) -> SHAPE(v)
952         return (*this)(call.arguments().at(2));
953       } else if (call.arguments().size() >= 2 && context_) {
954         if (auto maskShape{(*this)(call.arguments().at(1))}) {
955           if (maskShape->size() == 0) {
956             // Scalar MASK= -> [MERGE(SIZE(ARRAY=), 0, mask)]
957             if (auto arrayShape{(*this)(call.arguments().at(0))}) {
958               if (auto arraySize{GetSize(std::move(*arrayShape))}) {
959                 ActualArguments toMerge{
960                     ActualArgument{AsGenericExpr(std::move(*arraySize))},
961                     ActualArgument{AsGenericExpr(ExtentExpr{0})},
962                     common::Clone(call.arguments().at(1))};
963                 auto specific{context_->intrinsics().Probe(
964                     CallCharacteristics{"merge"}, toMerge, *context_)};
965                 CHECK(specific);
966                 return Shape{ExtentExpr{FunctionRef<ExtentType>{
967                     ProcedureDesignator{std::move(specific->specificIntrinsic)},
968                     std::move(specific->arguments)}}};
969               }
970             }
971           } else {
972             // Non-scalar MASK= -> [COUNT(mask)]
973             ActualArguments toCount{ActualArgument{common::Clone(
974                 DEREF(call.arguments().at(1).value().UnwrapExpr()))}};
975             auto specific{context_->intrinsics().Probe(
976                 CallCharacteristics{"count"}, toCount, *context_)};
977             CHECK(specific);
978             return Shape{ExtentExpr{FunctionRef<ExtentType>{
979                 ProcedureDesignator{std::move(specific->specificIntrinsic)},
980                 std::move(specific->arguments)}}};
981           }
982         }
983       }
984     } else if (intrinsic->name == "reshape") {
985       if (call.arguments().size() >= 2 && call.arguments().at(1)) {
986         // SHAPE(RESHAPE(array,shape)) -> shape
987         if (const auto *shapeExpr{
988                 call.arguments().at(1).value().UnwrapExpr()}) {
989           auto shapeArg{std::get<Expr<SomeInteger>>(shapeExpr->u)};
990           if (auto result{AsShapeResult(
991                   ConvertToType<ExtentType>(std::move(shapeArg)))}) {
992             return result;
993           }
994         }
995       }
996     } else if (intrinsic->name == "spread") {
997       // SHAPE(SPREAD(ARRAY,DIM,NCOPIES)) = SHAPE(ARRAY) with NCOPIES inserted
998       // at position DIM.
999       if (call.arguments().size() == 3) {
1000         auto arrayShape{
1001             (*this)(UnwrapExpr<Expr<SomeType>>(call.arguments().at(0)))};
1002         const auto *dimArg{UnwrapExpr<Expr<SomeType>>(call.arguments().at(1))};
1003         const auto *nCopies{
1004             UnwrapExpr<Expr<SomeInteger>>(call.arguments().at(2))};
1005         if (arrayShape && dimArg && nCopies) {
1006           if (auto dim{ToInt64(*dimArg)}) {
1007             if (*dim >= 1 &&
1008                 static_cast<std::size_t>(*dim) <= arrayShape->size() + 1) {
1009               arrayShape->emplace(arrayShape->begin() + *dim - 1,
1010                   ConvertToType<ExtentType>(common::Clone(*nCopies)));
1011               return std::move(*arrayShape);
1012             }
1013           }
1014         }
1015       }
1016     } else if (intrinsic->name == "transfer") {
1017       if (call.arguments().size() == 3 && call.arguments().at(2)) {
1018         // SIZE= is present; shape is vector [SIZE=]
1019         if (const auto *size{
1020                 UnwrapExpr<Expr<SomeInteger>>(call.arguments().at(2))}) {
1021           return Shape{
1022               MaybeExtentExpr{ConvertToType<ExtentType>(common::Clone(*size))}};
1023         }
1024       } else if (context_) {
1025         if (auto moldTypeAndShape{characteristics::TypeAndShape::Characterize(
1026                 call.arguments().at(1), *context_)}) {
1027           if (GetRank(moldTypeAndShape->shape()) == 0) {
1028             // SIZE= is absent and MOLD= is scalar: result is scalar
1029             return ScalarShape();
1030           } else {
1031             // SIZE= is absent and MOLD= is array: result is vector whose
1032             // length is determined by sizes of types.  See 16.9.193p4 case(ii).
1033             // Note that if sourceBytes is not known to be empty, we
1034             // can fold only when moldElementBytes is known to not be zero;
1035             // the most general case risks a division by zero otherwise.
1036             if (auto sourceTypeAndShape{
1037                     characteristics::TypeAndShape::Characterize(
1038                         call.arguments().at(0), *context_)}) {
1039               if (auto sourceBytes{
1040                       sourceTypeAndShape->MeasureSizeInBytes(*context_)}) {
1041                 *sourceBytes = Fold(*context_, std::move(*sourceBytes));
1042                 if (auto sourceBytesConst{ToInt64(*sourceBytes)}) {
1043                   if (*sourceBytesConst == 0) {
1044                     return Shape{ExtentExpr{0}};
1045                   }
1046                 }
1047                 if (auto moldElementBytes{
1048                         moldTypeAndShape->MeasureElementSizeInBytes(
1049                             *context_, true)}) {
1050                   *moldElementBytes =
1051                       Fold(*context_, std::move(*moldElementBytes));
1052                   auto moldElementBytesConst{ToInt64(*moldElementBytes)};
1053                   if (moldElementBytesConst && *moldElementBytesConst != 0) {
1054                     ExtentExpr extent{Fold(*context_,
1055                         (std::move(*sourceBytes) +
1056                             common::Clone(*moldElementBytes) - ExtentExpr{1}) /
1057                             common::Clone(*moldElementBytes))};
1058                     return Shape{MaybeExtentExpr{std::move(extent)}};
1059                   }
1060                 }
1061               }
1062             }
1063           }
1064         }
1065       }
1066     } else if (intrinsic->name == "transpose") {
1067       if (call.arguments().size() >= 1) {
1068         if (auto shape{(*this)(call.arguments().at(0))}) {
1069           if (shape->size() == 2) {
1070             std::swap((*shape)[0], (*shape)[1]);
1071             return shape;
1072           }
1073         }
1074       }
1075     } else if (intrinsic->name == "unpack") {
1076       if (call.arguments().size() >= 2) {
1077         return (*this)(call.arguments()[1]); // MASK=
1078       }
1079     } else if (intrinsic->characteristics.value().attrs.test(characteristics::
1080                        Procedure::Attr::NullPointer)) { // NULL(MOLD=)
1081       return (*this)(call.arguments());
1082     } else {
1083       // TODO: shapes of other non-elemental intrinsic results
1084     }
1085   }
1086   // The rank is always known even if the extents are not.
1087   return Shape(static_cast<std::size_t>(call.Rank()), MaybeExtentExpr{});
1088 }
1089 
1090 void GetShapeHelper::AccumulateExtent(
1091     ExtentExpr &result, ExtentExpr &&n) const {
1092   result = std::move(result) + std::move(n);
1093   if (context_) {
1094     // Fold during expression creation to avoid creating an expression so
1095     // large we can't evaluate it without overflowing the stack.
1096     result = Fold(*context_, std::move(result));
1097   }
1098 }
1099 
1100 // Check conformance of the passed shapes.
1101 std::optional<bool> CheckConformance(parser::ContextualMessages &messages,
1102     const Shape &left, const Shape &right, CheckConformanceFlags::Flags flags,
1103     const char *leftIs, const char *rightIs) {
1104   int n{GetRank(left)};
1105   if (n == 0 && (flags & CheckConformanceFlags::LeftScalarExpandable)) {
1106     return true;
1107   }
1108   int rn{GetRank(right)};
1109   if (rn == 0 && (flags & CheckConformanceFlags::RightScalarExpandable)) {
1110     return true;
1111   }
1112   if (n != rn) {
1113     messages.Say("Rank of %1$s is %2$d, but %3$s has rank %4$d"_err_en_US,
1114         leftIs, n, rightIs, rn);
1115     return false;
1116   }
1117   for (int j{0}; j < n; ++j) {
1118     if (auto leftDim{ToInt64(left[j])}) {
1119       if (auto rightDim{ToInt64(right[j])}) {
1120         if (*leftDim != *rightDim) {
1121           messages.Say("Dimension %1$d of %2$s has extent %3$jd, "
1122                        "but %4$s has extent %5$jd"_err_en_US,
1123               j + 1, leftIs, *leftDim, rightIs, *rightDim);
1124           return false;
1125         }
1126       } else if (!(flags & CheckConformanceFlags::RightIsDeferredShape)) {
1127         return std::nullopt;
1128       }
1129     } else if (!(flags & CheckConformanceFlags::LeftIsDeferredShape)) {
1130       return std::nullopt;
1131     }
1132   }
1133   return true;
1134 }
1135 
1136 bool IncrementSubscripts(
1137     ConstantSubscripts &indices, const ConstantSubscripts &extents) {
1138   std::size_t rank(indices.size());
1139   CHECK(rank <= extents.size());
1140   for (std::size_t j{0}; j < rank; ++j) {
1141     if (extents[j] < 1) {
1142       return false;
1143     }
1144   }
1145   for (std::size_t j{0}; j < rank; ++j) {
1146     if (indices[j]++ < extents[j]) {
1147       return true;
1148     }
1149     indices[j] = 1;
1150   }
1151   return false;
1152 }
1153 
1154 } // namespace Fortran::evaluate
1155