llvm-project/flang/lib/Evaluate/shape.cpp

//===-- lib/Evaluate/shape.cpp --------------------------------------------===//
//
// Part of the LLVM Project, under the Apache License v2.0 with LLVM Exceptions.
// See https://llvm.org/LICENSE.txt for license information.
// SPDX-License-Identifier: Apache-2.0 WITH LLVM-exception
//
//===----------------------------------------------------------------------===//

#include "flang/Evaluate/shape.h"
#include "flang/Common/idioms.h"
#include "flang/Common/template.h"
#include "flang/Evaluate/characteristics.h"
#include "flang/Evaluate/fold.h"
#include "flang/Evaluate/intrinsics.h"
#include "flang/Evaluate/tools.h"
#include "flang/Evaluate/type.h"
#include "flang/Parser/message.h"
#include "flang/Semantics/symbol.h"
#include <functional>

using namespace std::placeholders; // _1, _2, &c. for std::bind()

namespace Fortran::evaluate {

bool IsImpliedShape(const Symbol &symbol0) {
  const Symbol &symbol{ResolveAssociations(symbol0)};
  if (const auto *details{symbol.detailsIf<semantics::ObjectEntityDetails>()}) {
    if (symbol.attrs().test(semantics::Attr::PARAMETER) && details->init()) {
      return details->shape().IsImpliedShape();
    }
  }
  return false;
}

bool IsExplicitShape(const Symbol &symbol0) {
  const Symbol &symbol{ResolveAssociations(symbol0)};
  if (const auto *details{symbol.detailsIf<semantics::ObjectEntityDetails>()}) {
    const auto &shape{details->shape()};
    return shape.Rank() == 0 || shape.IsExplicitShape(); // even if scalar
  } else {
    return false;
  }
}

Shape AsShape(const Constant<ExtentType> &arrayConstant) {
  CHECK(arrayConstant.Rank() == 1);
  Shape result;
  std::size_t dimensions{arrayConstant.size()};
  for (std::size_t j{0}; j < dimensions; ++j) {
    Scalar<ExtentType> extent{arrayConstant.values().at(j)};
    result.emplace_back(MaybeExtentExpr{ExtentExpr{extent}});
  }
  return result;
}

std::optional<Shape> AsShape(FoldingContext &context, ExtentExpr &&arrayExpr) {
  // Flatten any array expression into an array constructor if possible.
  arrayExpr = Fold(context, std::move(arrayExpr));
  if (const auto *constArray{UnwrapConstantValue<ExtentType>(arrayExpr)}) {
    return AsShape(*constArray);
  }
  if (auto *constructor{UnwrapExpr<ArrayConstructor<ExtentType>>(arrayExpr)}) {
    Shape result;
    for (auto &value : *constructor) {
      if (auto *expr{std::get_if<ExtentExpr>(&value.u)}) {
        if (expr->Rank() == 0) {
          result.emplace_back(std::move(*expr));
          continue;
        }
      }
      return std::nullopt;
    }
    return result;
  }
  return std::nullopt;
}

std::optional<ExtentExpr> AsExtentArrayExpr(const Shape &shape) {
  ArrayConstructorValues<ExtentType> values;
  for (const auto &dim : shape) {
    if (dim) {
      values.Push(common::Clone(*dim));
    } else {
      return std::nullopt;
    }
  }
  return ExtentExpr{ArrayConstructor<ExtentType>{std::move(values)}};
}

std::optional<Constant<ExtentType>> AsConstantShape(
    FoldingContext &context, const Shape &shape) {
  if (auto shapeArray{AsExtentArrayExpr(shape)}) {
    auto folded{Fold(context, std::move(*shapeArray))};
    if (auto *p{UnwrapConstantValue<ExtentType>(folded)}) {
      return std::move(*p);
    }
  }
  return std::nullopt;
}

Constant<SubscriptInteger> AsConstantShape(const ConstantSubscripts &shape) {
  using IntType = Scalar<SubscriptInteger>;
  std::vector<IntType> result;
  for (auto dim : shape) {
    result.emplace_back(dim);
  }
  return {std::move(result), ConstantSubscripts{GetRank(shape)}};
}

ConstantSubscripts AsConstantExtents(const Constant<ExtentType> &shape) {
  ConstantSubscripts result;
  for (const auto &extent : shape.values()) {
    result.push_back(extent.ToInt64());
  }
  return result;
}

std::optional<ConstantSubscripts> AsConstantExtents(
    FoldingContext &context, const Shape &shape) {
  if (auto shapeConstant{AsConstantShape(context, shape)}) {
    return AsConstantExtents(*shapeConstant);
  } else {
    return std::nullopt;
  }
}

static ExtentExpr ComputeTripCount(FoldingContext &context, ExtentExpr &&lower,
    ExtentExpr &&upper, ExtentExpr &&stride) {
  ExtentExpr strideCopy{common::Clone(stride)};
  ExtentExpr span{
      (std::move(upper) - std::move(lower) + std::move(strideCopy)) /
      std::move(stride)};
  ExtentExpr extent{
      Extremum<ExtentType>{Ordering::Greater, std::move(span), ExtentExpr{0}}};
  return Fold(context, std::move(extent));
}

ExtentExpr CountTrips(FoldingContext &context, ExtentExpr &&lower,
    ExtentExpr &&upper, ExtentExpr &&stride) {
  return ComputeTripCount(
      context, std::move(lower), std::move(upper), std::move(stride));
}

ExtentExpr CountTrips(FoldingContext &context, const ExtentExpr &lower,
    const ExtentExpr &upper, const ExtentExpr &stride) {
  return ComputeTripCount(context, common::Clone(lower), common::Clone(upper),
      common::Clone(stride));
}

MaybeExtentExpr CountTrips(FoldingContext &context, MaybeExtentExpr &&lower,
    MaybeExtentExpr &&upper, MaybeExtentExpr &&stride) {
  std::function<ExtentExpr(ExtentExpr &&, ExtentExpr &&, ExtentExpr &&)> bound{
      std::bind(ComputeTripCount, context, _1, _2, _3)};
  return common::MapOptional(
      std::move(bound), std::move(lower), std::move(upper), std::move(stride));
}

MaybeExtentExpr GetSize(Shape &&shape) {
  ExtentExpr extent{1};
  for (auto &&dim : std::move(shape)) {
    if (dim) {
      extent = std::move(extent) * std::move(*dim);
    } else {
      return std::nullopt;
    }
  }
  return extent;
}

bool ContainsAnyImpliedDoIndex(const ExtentExpr &expr) {
  struct MyVisitor : public AnyTraverse<MyVisitor> {
    using Base = AnyTraverse<MyVisitor>;
    MyVisitor() : Base{*this} {}
    using Base::operator();
    bool operator()(const ImpliedDoIndex &) { return true; }
  };
  return MyVisitor{}(expr);
}

// Determines lower bound on a dimension.  This can be other than 1 only
// for a reference to a whole array object or component. (See LBOUND, 16.9.109).
// ASSOCIATE construct entities may require tranversal of their referents.
class GetLowerBoundHelper : public Traverse<GetLowerBoundHelper, ExtentExpr> {
public:
  using Result = ExtentExpr;
  using Base = Traverse<GetLowerBoundHelper, ExtentExpr>;
  using Base::operator();
  GetLowerBoundHelper(FoldingContext &c, int d)
      : Base{*this}, context_{c}, dimension_{d} {}
  static ExtentExpr Default() { return ExtentExpr{1}; }
  static ExtentExpr Combine(Result &&, Result &&) { return Default(); }
  ExtentExpr operator()(const Symbol &);
  ExtentExpr operator()(const Component &);

private:
  FoldingContext &context_;
  int dimension_;
};

auto GetLowerBoundHelper::operator()(const Symbol &symbol0) -> Result {
  const Symbol &symbol{symbol0.GetUltimate()};
  if (const auto *details{symbol.detailsIf<semantics::ObjectEntityDetails>()}) {
    int j{0};
    for (const auto &shapeSpec : details->shape()) {
      if (j++ == dimension_) {
        if (const auto &bound{shapeSpec.lbound().GetExplicit()}) {
          return Fold(context_, common::Clone(*bound));
        } else if (IsDescriptor(symbol)) {
          return ExtentExpr{DescriptorInquiry{NamedEntity{symbol0},
              DescriptorInquiry::Field::LowerBound, dimension_}};
        } else {
          break;
        }
      }
    }
  } else if (const auto *assoc{
                 symbol.detailsIf<semantics::AssocEntityDetails>()}) {
    return (*this)(assoc->expr());
  }
  return Default();
}

auto GetLowerBoundHelper::operator()(const Component &component) -> Result {
  if (component.base().Rank() == 0) {
    const Symbol &symbol{component.GetLastSymbol().GetUltimate()};
    if (const auto *details{
            symbol.detailsIf<semantics::ObjectEntityDetails>()}) {
      int j{0};
      for (const auto &shapeSpec : details->shape()) {
        if (j++ == dimension_) {
          if (const auto &bound{shapeSpec.lbound().GetExplicit()}) {
            return Fold(context_, common::Clone(*bound));
          } else if (IsDescriptor(symbol)) {
            return ExtentExpr{
                DescriptorInquiry{NamedEntity{common::Clone(component)},
                    DescriptorInquiry::Field::LowerBound, dimension_}};
          } else {
            break;
          }
        }
      }
    }
  }
  return Default();
}

ExtentExpr GetLowerBound(
    FoldingContext &context, const NamedEntity &base, int dimension) {
  return GetLowerBoundHelper{context, dimension}(base);
}

Shape GetLowerBounds(FoldingContext &context, const NamedEntity &base) {
  Shape result;
  int rank{base.Rank()};
  for (int dim{0}; dim < rank; ++dim) {
    result.emplace_back(GetLowerBound(context, base, dim));
  }
  return result;
}

MaybeExtentExpr GetExtent(
    FoldingContext &context, const NamedEntity &base, int dimension) {
  CHECK(dimension >= 0);
  const Symbol &symbol{ResolveAssociations(base.GetLastSymbol())};
  if (const auto *details{symbol.detailsIf<semantics::ObjectEntityDetails>()}) {
    if (IsImpliedShape(symbol)) {
      Shape shape{GetShape(context, symbol).value()};
      return std::move(shape.at(dimension));
    }
    int j{0};
    for (const auto &shapeSpec : details->shape()) {
      if (j++ == dimension) {
        if (shapeSpec.ubound().isExplicit()) {
          if (const auto &ubound{shapeSpec.ubound().GetExplicit()}) {
            if (const auto &lbound{shapeSpec.lbound().GetExplicit()}) {
              return Fold(context,
                  common::Clone(ubound.value()) -
                      common::Clone(lbound.value()) + ExtentExpr{1});
            } else {
              return Fold(context, common::Clone(ubound.value()));
            }
          }
        } else if (details->IsAssumedSize() && j == symbol.Rank()) {
          return std::nullopt;
        } else if (semantics::IsDescriptor(symbol)) {
          return ExtentExpr{DescriptorInquiry{
              NamedEntity{base}, DescriptorInquiry::Field::Extent, dimension}};
        }
      }
    }
  } else if (const auto *assoc{
                 symbol.detailsIf<semantics::AssocEntityDetails>()}) {
    if (auto shape{GetShape(context, assoc->expr())}) {
      if (dimension < static_cast<int>(shape->size())) {
        return std::move(shape->at(dimension));
      }
    }
  }
  return std::nullopt;
}

MaybeExtentExpr GetExtent(FoldingContext &context, const Subscript &subscript,
    const NamedEntity &base, int dimension) {
  return std::visit(
      common::visitors{
          [&](const Triplet &triplet) -> MaybeExtentExpr {
            MaybeExtentExpr upper{triplet.upper()};
            if (!upper) {
              upper = GetUpperBound(context, base, dimension);
            }
            MaybeExtentExpr lower{triplet.lower()};
            if (!lower) {
              lower = GetLowerBound(context, base, dimension);
            }
            return CountTrips(context, std::move(lower), std::move(upper),
                MaybeExtentExpr{triplet.stride()});
          },
          [&](const IndirectSubscriptIntegerExpr &subs) -> MaybeExtentExpr {
            if (auto shape{GetShape(context, subs.value())}) {
              if (GetRank(*shape) > 0) {
                CHECK(GetRank(*shape) == 1); // vector-valued subscript
                return std::move(shape->at(0));
              }
            }
            return std::nullopt;
          },
      },
      subscript.u);
}

MaybeExtentExpr ComputeUpperBound(
    FoldingContext &context, ExtentExpr &&lower, MaybeExtentExpr &&extent) {
  if (extent) {
    return Fold(context, std::move(*extent) - std::move(lower) + ExtentExpr{1});
  } else {
    return std::nullopt;
  }
}

MaybeExtentExpr GetUpperBound(
    FoldingContext &context, const NamedEntity &base, int dimension) {
  const Symbol &symbol{ResolveAssociations(base.GetLastSymbol())};
  if (const auto *details{symbol.detailsIf<semantics::ObjectEntityDetails>()}) {
    int j{0};
    for (const auto &shapeSpec : details->shape()) {
      if (j++ == dimension) {
        if (const auto &bound{shapeSpec.ubound().GetExplicit()}) {
          return Fold(context, common::Clone(*bound));
        } else if (details->IsAssumedSize() && dimension + 1 == symbol.Rank()) {
          break;
        } else {
          return ComputeUpperBound(context,
              GetLowerBound(context, base, dimension),
              GetExtent(context, base, dimension));
        }
      }
    }
  } else if (const auto *assoc{
                 symbol.detailsIf<semantics::AssocEntityDetails>()}) {
    if (auto shape{GetShape(context, assoc->expr())}) {
      if (dimension < static_cast<int>(shape->size())) {
        return ComputeUpperBound(context,
            GetLowerBound(context, base, dimension),
            std::move(shape->at(dimension)));
      }
    }
  }
  return std::nullopt;
}

Shape GetUpperBounds(FoldingContext &context, const NamedEntity &base) {
  const Symbol &symbol{ResolveAssociations(base.GetLastSymbol())};
  if (const auto *details{symbol.detailsIf<semantics::ObjectEntityDetails>()}) {
    Shape result;
    int dim{0};
    for (const auto &shapeSpec : details->shape()) {
      if (const auto &bound{shapeSpec.ubound().GetExplicit()}) {
        result.emplace_back(Fold(context, common::Clone(*bound)));
      } else if (details->IsAssumedSize()) {
        CHECK(dim + 1 == base.Rank());
        result.emplace_back(std::nullopt); // UBOUND folding replaces with -1
      } else {
        result.emplace_back(ComputeUpperBound(context,
            GetLowerBound(context, base, dim), GetExtent(context, base, dim)));
      }
      ++dim;
    }
    CHECK(GetRank(result) == symbol.Rank());
    return result;
  } else {
    return std::move(GetShape(context, base).value());
  }
}

auto GetShapeHelper::operator()(const Symbol &symbol) const -> Result {
  return std::visit(
      common::visitors{
          [&](const semantics::ObjectEntityDetails &object) {
            if (IsImpliedShape(symbol)) {
              return (*this)(object.init());
            } else {
              int n{object.shape().Rank()};
              NamedEntity base{symbol};
              return Result{CreateShape(n, base)};
            }
          },
          [](const semantics::EntityDetails &) {
            return Scalar(); // no dimensions seen
          },
          [&](const semantics::ProcEntityDetails &proc) {
            if (const Symbol * interface{proc.interface().symbol()}) {
              return (*this)(*interface);
            } else {
              return Scalar();
            }
          },
          [&](const semantics::AssocEntityDetails &assoc) {
            if (!assoc.rank()) {
              return (*this)(assoc.expr());
            } else {
              int n{assoc.rank().value()};
              NamedEntity base{symbol};
              return Result{CreateShape(n, base)};
            }
          },
          [&](const semantics::SubprogramDetails &subp) {
            if (subp.isFunction()) {
              return (*this)(subp.result());
            } else {
              return Result{};
            }
          },
          [&](const semantics::ProcBindingDetails &binding) {
            return (*this)(binding.symbol());
          },
          [&](const semantics::UseDetails &use) {
            return (*this)(use.symbol());
          },
          [&](const semantics::HostAssocDetails &assoc) {
            return (*this)(assoc.symbol());
          },
          [](const semantics::TypeParamDetails &) { return Scalar(); },
          [](const auto &) { return Result{}; },
      },
      symbol.details());
}

auto GetShapeHelper::operator()(const Component &component) const -> Result {
  const Symbol &symbol{component.GetLastSymbol()};
  int rank{symbol.Rank()};
  if (rank == 0) {
    return (*this)(component.base());
  } else if (symbol.has<semantics::ObjectEntityDetails>()) {
    NamedEntity base{Component{component}};
    return CreateShape(rank, base);
  } else if (symbol.has<semantics::AssocEntityDetails>()) {
    NamedEntity base{Component{component}};
    return Result{CreateShape(rank, base)};
  } else {
    return (*this)(symbol);
  }
}

auto GetShapeHelper::operator()(const ArrayRef &arrayRef) const -> Result {
  Shape shape;
  int dimension{0};
  const NamedEntity &base{arrayRef.base()};
  for (const Subscript &ss : arrayRef.subscript()) {
    if (ss.Rank() > 0) {
      shape.emplace_back(GetExtent(context_, ss, base, dimension));
    }
    ++dimension;
  }
  if (shape.empty()) {
    if (const Component * component{base.UnwrapComponent()}) {
      return (*this)(component->base());
    }
  }
  return shape;
}

auto GetShapeHelper::operator()(const CoarrayRef &coarrayRef) const -> Result {
  NamedEntity base{coarrayRef.GetBase()};
  if (coarrayRef.subscript().empty()) {
    return (*this)(base);
  } else {
    Shape shape;
    int dimension{0};
    for (const Subscript &ss : coarrayRef.subscript()) {
      if (ss.Rank() > 0) {
        shape.emplace_back(GetExtent(context_, ss, base, dimension));
      }
      ++dimension;
    }
    return shape;
  }
}

auto GetShapeHelper::operator()(const Substring &substring) const -> Result {
  return (*this)(substring.parent());
}

auto GetShapeHelper::operator()(const ProcedureRef &call) const -> Result {
  if (call.Rank() == 0) {
    return Scalar();
  } else if (call.IsElemental()) {
    for (const auto &arg : call.arguments()) {
      if (arg && arg->Rank() > 0) {
        return (*this)(*arg);
      }
    }
    return Scalar();
  } else if (const Symbol * symbol{call.proc().GetSymbol()}) {
    return (*this)(*symbol);
  } else if (const auto *intrinsic{call.proc().GetSpecificIntrinsic()}) {
    if (intrinsic->name == "shape" || intrinsic->name == "lbound" ||
        intrinsic->name == "ubound") {
      // These are the array-valued cases for LBOUND and UBOUND (no DIM=).
      const auto *expr{call.arguments().front().value().UnwrapExpr()};
      CHECK(expr);
      return Shape{MaybeExtentExpr{ExtentExpr{expr->Rank()}}};
    } else if (intrinsic->name == "all" || intrinsic->name == "any" ||
        intrinsic->name == "count" || intrinsic->name == "iall" ||
        intrinsic->name == "iany" || intrinsic->name == "iparity" ||
        intrinsic->name == "maxloc" || intrinsic->name == "maxval" ||
        intrinsic->name == "minloc" || intrinsic->name == "minval" ||
        intrinsic->name == "norm2" || intrinsic->name == "parity" ||
        intrinsic->name == "product" || intrinsic->name == "sum") {
      // Reduction with DIM=
      if (call.arguments().size() >= 2) {
        auto arrayShape{
            (*this)(UnwrapExpr<Expr<SomeType>>(call.arguments().at(0)))};
        const auto *dimArg{UnwrapExpr<Expr<SomeType>>(call.arguments().at(1))};
        if (arrayShape && dimArg) {
          if (auto dim{ToInt64(*dimArg)}) {
            if (*dim >= 1 &&
                static_cast<std::size_t>(*dim) <= arrayShape->size()) {
              arrayShape->erase(arrayShape->begin() + (*dim - 1));
              return std::move(*arrayShape);
            }
          }
        }
      }
    } else if (intrinsic->name == "cshift" || intrinsic->name == "eoshift") {
      if (!call.arguments().empty()) {
        return (*this)(call.arguments()[0]);
      }
    } else if (intrinsic->name == "matmul") {
      if (call.arguments().size() == 2) {
        if (auto ashape{(*this)(call.arguments()[0])}) {
          if (auto bshape{(*this)(call.arguments()[1])}) {
            if (ashape->size() == 1 && bshape->size() == 2) {
              bshape->erase(bshape->begin());
              return std::move(*bshape); // matmul(vector, matrix)
            } else if (ashape->size() == 2 && bshape->size() == 1) {
              ashape->pop_back();
              return std::move(*ashape); // matmul(matrix, vector)
            } else if (ashape->size() == 2 && bshape->size() == 2) {
              (*ashape)[1] = std::move((*bshape)[1]);
              return std::move(*ashape); // matmul(matrix, matrix)
            }
          }
        }
      }
    } else if (intrinsic->name == "reshape") {
      if (call.arguments().size() >= 2 && call.arguments().at(1)) {
        // SHAPE(RESHAPE(array,shape)) -> shape
        if (const auto *shapeExpr{
                call.arguments().at(1).value().UnwrapExpr()}) {
          auto shape{std::get<Expr<SomeInteger>>(shapeExpr->u)};
          return AsShape(context_, ConvertToType<ExtentType>(std::move(shape)));
        }
      }
    } else if (intrinsic->name == "pack") {
      if (call.arguments().size() >= 3 && call.arguments().at(2)) {
        // SHAPE(PACK(,,VECTOR=v)) -> SHAPE(v)
        return (*this)(call.arguments().at(2));
      } else if (call.arguments().size() >= 2) {
        if (auto maskShape{(*this)(call.arguments().at(1))}) {
          if (maskShape->size() == 0) {
            // Scalar MASK= -> [MERGE(SIZE(ARRAY=), 0, mask)]
            if (auto arrayShape{(*this)(call.arguments().at(0))}) {
              auto arraySize{GetSize(std::move(*arrayShape))};
              CHECK(arraySize);
              ActualArguments toMerge{
                  ActualArgument{AsGenericExpr(std::move(*arraySize))},
                  ActualArgument{AsGenericExpr(ExtentExpr{0})},
                  common::Clone(call.arguments().at(1))};
              auto specific{context_.intrinsics().Probe(
                  CallCharacteristics{"merge"}, toMerge, context_)};
              CHECK(specific);
              return Shape{ExtentExpr{FunctionRef<ExtentType>{
                  ProcedureDesignator{std::move(specific->specificIntrinsic)},
                  std::move(specific->arguments)}}};
            }
          } else {
            // Non-scalar MASK= -> [COUNT(mask)]
            ActualArguments toCount{ActualArgument{common::Clone(
                DEREF(call.arguments().at(1).value().UnwrapExpr()))}};
            auto specific{context_.intrinsics().Probe(
                CallCharacteristics{"count"}, toCount, context_)};
            CHECK(specific);
            return Shape{ExtentExpr{FunctionRef<ExtentType>{
                ProcedureDesignator{std::move(specific->specificIntrinsic)},
                std::move(specific->arguments)}}};
          }
        }
      }
    } else if (intrinsic->name == "spread") {
      // SHAPE(SPREAD(ARRAY,DIM,NCOPIES)) = SHAPE(ARRAY) with NCOPIES inserted
      // at position DIM.
      if (call.arguments().size() == 3) {
        auto arrayShape{
            (*this)(UnwrapExpr<Expr<SomeType>>(call.arguments().at(0)))};
        const auto *dimArg{UnwrapExpr<Expr<SomeType>>(call.arguments().at(1))};
        const auto *nCopies{
            UnwrapExpr<Expr<SomeInteger>>(call.arguments().at(2))};
        if (arrayShape && dimArg && nCopies) {
          if (auto dim{ToInt64(*dimArg)}) {
            if (*dim >= 1 &&
                static_cast<std::size_t>(*dim) <= arrayShape->size() + 1) {
              arrayShape->emplace(arrayShape->begin() + *dim - 1,
                  ConvertToType<ExtentType>(common::Clone(*nCopies)));
              return std::move(*arrayShape);
            }
          }
        }
      }
    } else if (intrinsic->name == "transfer") {
      if (call.arguments().size() == 3 && call.arguments().at(2)) {
        // SIZE= is present; shape is vector [SIZE=]
        if (const auto *size{
                UnwrapExpr<Expr<SomeInteger>>(call.arguments().at(2))}) {
          return Shape{
              MaybeExtentExpr{ConvertToType<ExtentType>(common::Clone(*size))}};
        }
      } else if (auto moldTypeAndShape{
                     characteristics::TypeAndShape::Characterize(
                         call.arguments().at(1), context_)}) {
        if (GetRank(moldTypeAndShape->shape()) == 0) {
          // SIZE= is absent and MOLD= is scalar: result is scalar
          return Scalar();
        } else {
          // SIZE= is absent and MOLD= is array: result is vector whose
          // length is determined by sizes of types.  See 16.9.193p4 case(ii).
          if (auto sourceTypeAndShape{
                  characteristics::TypeAndShape::Characterize(
                      call.arguments().at(0), context_)}) {
            auto sourceElements{
                GetSize(common::Clone(sourceTypeAndShape->shape()))};
            auto sourceElementBytes{
                sourceTypeAndShape->type().MeasureSizeInBytes(&context_)};
            auto moldElementBytes{
                moldTypeAndShape->type().MeasureSizeInBytes(&context_)};
            if (sourceElements && sourceElementBytes && moldElementBytes) {
              ExtentExpr extent{Fold(context_,
                  ((std::move(*sourceElements) *
                       std::move(*sourceElementBytes)) +
                      common::Clone(*moldElementBytes) - ExtentExpr{1}) /
                      common::Clone(*moldElementBytes))};
              return Shape{MaybeExtentExpr{std::move(extent)}};
            }
          }
        }
      }
    } else if (intrinsic->name == "transpose") {
      if (call.arguments().size() >= 1) {
        if (auto shape{(*this)(call.arguments().at(0))}) {
          if (shape->size() == 2) {
            std::swap((*shape)[0], (*shape)[1]);
            return shape;
          }
        }
      }
    } else if (intrinsic->characteristics.value().attrs.test(characteristics::
                       Procedure::Attr::NullPointer)) { // NULL(MOLD=)
      return (*this)(call.arguments());
    } else {
      // TODO: shapes of other non-elemental intrinsic results
    }
  }
  return std::nullopt;
}

bool CheckConformance(parser::ContextualMessages &messages, const Shape &left,
    const Shape &right, const char *leftIs, const char *rightIs) {
  if (!left.empty() && !right.empty()) {
    int n{GetRank(left)};
    int rn{GetRank(right)};
    if (n != rn) {
      messages.Say("Rank of %1$s is %2$d, but %3$s has rank %4$d"_err_en_US,
          leftIs, n, rightIs, rn);
      return false;
    } else {
      for (int j{0}; j < n; ++j) {
        if (auto leftDim{ToInt64(left[j])}) {
          if (auto rightDim{ToInt64(right[j])}) {
            if (*leftDim != *rightDim) {
              messages.Say("Dimension %1$d of %2$s has extent %3$jd, "
                           "but %4$s has extent %5$jd"_err_en_US,
                  j + 1, leftIs, *leftDim, rightIs, *rightDim);
              return false;
            }
          }
        }
      }
    }
  }
  return true;
}

bool IncrementSubscripts(
    ConstantSubscripts &indices, const ConstantSubscripts &extents) {
  std::size_t rank(indices.size());
  CHECK(rank <= extents.size());
  for (std::size_t j{0}; j < rank; ++j) {
    if (extents[j] < 1) {
      return false;
    }
  }
  for (std::size_t j{0}; j < rank; ++j) {
    if (indices[j]++ < extents[j]) {
      return true;
    }
    indices[j] = 1;
  }
  return false;
}
} // namespace Fortran::evaluate