1	//===-- lib/Evaluate/fold-implementation.h --------------------------------===//
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	#ifndef FORTRAN_EVALUATE_FOLD_IMPLEMENTATION_H_
10	#define FORTRAN_EVALUATE_FOLD_IMPLEMENTATION_H_
11
12	#include "character.h"
13	#include "host.h"
14	#include "int-power.h"
15	#include "flang/Common/indirection.h"
16	#include "flang/Common/template.h"
17	#include "flang/Common/unwrap.h"
18	#include "flang/Evaluate/characteristics.h"
19	#include "flang/Evaluate/common.h"
20	#include "flang/Evaluate/constant.h"
21	#include "flang/Evaluate/expression.h"
22	#include "flang/Evaluate/fold.h"
23	#include "flang/Evaluate/formatting.h"
24	#include "flang/Evaluate/intrinsics-library.h"
25	#include "flang/Evaluate/intrinsics.h"
26	#include "flang/Evaluate/shape.h"
27	#include "flang/Evaluate/tools.h"
28	#include "flang/Evaluate/traverse.h"
29	#include "flang/Evaluate/type.h"
30	#include "flang/Parser/message.h"
31	#include "flang/Semantics/scope.h"
32	#include "flang/Semantics/symbol.h"
33	#include "flang/Semantics/tools.h"
34	#include <algorithm>
35	#include <cmath>
36	#include <complex>
37	#include <cstdio>
38	#include <optional>
39	#include <type_traits>
40	#include <variant>
41
42	// Some environments, viz. glibc 2.17 and *BSD, allow the macro HUGE
43	// to leak out of <math.h>.
44	#undef HUGE
45
46	namespace Fortran::evaluate {
47
48	// Don't use Kahan extended precision summation any more when folding
49	// transformational intrinsic functions other than SUM, since it is
50	// not used in the runtime implementations of those functions and we
51	// want results to match.
52	static constexpr bool useKahanSummation{false};
53
54	// Utilities
55	template <typename T> class Folder {
56	public:
57	explicit Folder(FoldingContext &c, bool forOptionalArgument = false)
58	: context_{c}, forOptionalArgument_{forOptionalArgument} {}
59	std::optional<Constant<T>> GetNamedConstant(const Symbol &);
60	std::optional<Constant<T>> ApplySubscripts(const Constant<T> &array,
61	const std::vector<Constant<SubscriptInteger>> &subscripts);
62	std::optional<Constant<T>> ApplyComponent(Constant<SomeDerived> &&,
63	const Symbol &component,
64	const std::vector<Constant<SubscriptInteger>> * = nullptr);
65	std::optional<Constant<T>> GetConstantComponent(
66	Component &, const std::vector<Constant<SubscriptInteger>> * = nullptr);
67	std::optional<Constant<T>> Folding(ArrayRef &);
68	std::optional<Constant<T>> Folding(DataRef &);
69	Expr<T> Folding(Designator<T> &&);
70	Constant<T> *Folding(std::optional<ActualArgument> &);
71
72	Expr<T> CSHIFT(FunctionRef<T> &&);
73	Expr<T> EOSHIFT(FunctionRef<T> &&);
74	Expr<T> MERGE(FunctionRef<T> &&);
75	Expr<T> PACK(FunctionRef<T> &&);
76	Expr<T> RESHAPE(FunctionRef<T> &&);
77	Expr<T> SPREAD(FunctionRef<T> &&);
78	Expr<T> TRANSPOSE(FunctionRef<T> &&);
79	Expr<T> UNPACK(FunctionRef<T> &&);
80
81	Expr<T> TRANSFER(FunctionRef<T> &&);
82
83	private:
84	FoldingContext &context_;
85	bool forOptionalArgument_{false};
86	};
87
88	std::optional<Constant<SubscriptInteger>> GetConstantSubscript(
89	FoldingContext &, Subscript &, const NamedEntity &, int dim);
90
91	// Helper to use host runtime on scalars for folding.
92	template <typename TR, typename... TA>
93	std::optional<std::function<Scalar<TR>(FoldingContext &, Scalar<TA>...)>>
94	GetHostRuntimeWrapper(const std::string &name) {
95	std::vector<DynamicType> argTypes{TA{}.GetType()...};
96	if (auto hostWrapper{GetHostRuntimeWrapper(name, TR{}.GetType(), argTypes)}) {
97	return [hostWrapper](
98	FoldingContext &context, Scalar<TA>... args) -> Scalar<TR> {
99	std::vector<Expr<SomeType>> genericArgs{
100	AsGenericExpr(Constant<TA>{args})...};
101	return GetScalarConstantValue<TR>(
102	(*hostWrapper)(context, std::move(genericArgs)))
103	.value();
104	};
105	}
106	return std::nullopt;
107	}
108
109	// FoldOperation() rewrites expression tree nodes.
110	// If there is any possibility that the rewritten node will
111	// not have the same representation type, the result of
112	// FoldOperation() will be packaged in an Expr<> of the same
113	// specific type.
114
115	// no-op base case
116	template <typename A>
117	common::IfNoLvalue<Expr<ResultType<A>>, A> FoldOperation(
118	FoldingContext &, A &&x) {
119	static_assert(!std::is_same_v<A, Expr<ResultType<A>>>,
120	"call Fold() instead for Expr<>");
121	return Expr<ResultType<A>>{std::move(x)};
122	}
123
124	Component FoldOperation(FoldingContext &, Component &&);
125	NamedEntity FoldOperation(FoldingContext &, NamedEntity &&);
126	Triplet FoldOperation(FoldingContext &, Triplet &&);
127	Subscript FoldOperation(FoldingContext &, Subscript &&);
128	ArrayRef FoldOperation(FoldingContext &, ArrayRef &&);
129	CoarrayRef FoldOperation(FoldingContext &, CoarrayRef &&);
130	DataRef FoldOperation(FoldingContext &, DataRef &&);
131	Substring FoldOperation(FoldingContext &, Substring &&);
132	ComplexPart FoldOperation(FoldingContext &, ComplexPart &&);
133	template <typename T>
134	Expr<T> FoldOperation(FoldingContext &, FunctionRef<T> &&);
135	template <typename T>
136	Expr<T> FoldOperation(FoldingContext &context, Designator<T> &&designator) {
137	return Folder<T>{context}.Folding(std::move(designator));
138	}
139	Expr<TypeParamInquiry::Result> FoldOperation(
140	FoldingContext &, TypeParamInquiry &&);
141	Expr<ImpliedDoIndex::Result> FoldOperation(
142	FoldingContext &context, ImpliedDoIndex &&);
143	template <typename T>
144	Expr<T> FoldOperation(FoldingContext &, ArrayConstructor<T> &&);
145	Expr<SomeDerived> FoldOperation(FoldingContext &, StructureConstructor &&);
146
147	template <typename T>
148	std::optional<Constant<T>> Folder<T>::GetNamedConstant(const Symbol &symbol0) {
149	const Symbol &symbol{ResolveAssociations(symbol0)};
150	if (IsNamedConstant(symbol)) {
151	if (const auto *object{
152	symbol.detailsIf<semantics::ObjectEntityDetails>()}) {
153	if (const auto *constant{UnwrapConstantValue<T>(object->init())}) {
154	return *constant;
155	}
156	}
157	}
158	return std::nullopt;
159	}
160
161	template <typename T>
162	std::optional<Constant<T>> Folder<T>::Folding(ArrayRef &aRef) {
163	std::vector<Constant<SubscriptInteger>> subscripts;
164	int dim{0};
165	for (Subscript &ss : aRef.subscript()) {
166	if (auto constant{GetConstantSubscript(context_, ss, aRef.base(), dim++)}) {
167	subscripts.emplace_back(std::move(*constant));
168	} else {
169	return std::nullopt;
170	}
171	}
172	if (Component * component{aRef.base().UnwrapComponent()}) {
173	return GetConstantComponent(*component, &subscripts);
174	} else if (std::optional<Constant<T>> array{
175	GetNamedConstant(aRef.base().GetLastSymbol())}) {
176	return ApplySubscripts(*array, subscripts);
177	} else {
178	return std::nullopt;
179	}
180	}
181
182	template <typename T>
183	std::optional<Constant<T>> Folder<T>::Folding(DataRef &ref) {
184	return common::visit(
185	common::visitors{
186	[this](SymbolRef &sym) { return GetNamedConstant(*sym); },
187	[this](Component &comp) {
188	comp = FoldOperation(context_, std::move(comp));
189	return GetConstantComponent(comp);
190	},
191	[this](ArrayRef &aRef) {
192	aRef = FoldOperation(context_, std::move(aRef));
193	return Folding(aRef);
194	},
195	[](CoarrayRef &) { return std::optional<Constant<T>>{}; },
196	},
197	ref.u);
198	}
199
200	// TODO: This would be more natural as a member function of Constant<T>.
201	template <typename T>
202	std::optional<Constant<T>> Folder<T>::ApplySubscripts(const Constant<T> &array,
203	const std::vector<Constant<SubscriptInteger>> &subscripts) {
204	const auto &shape{array.shape()};
205	const auto &lbounds{array.lbounds()};
206	int rank{GetRank(shape)};
207	CHECK(rank == static_cast<int>(subscripts.size()));
208	std::size_t elements{1};
209	ConstantSubscripts resultShape;
210	ConstantSubscripts ssLB;
211	for (const auto &ss : subscripts) {
212	if (ss.Rank() == 1) {
213	resultShape.push_back(static_cast<ConstantSubscript>(ss.size()));
214	elements *= ss.size();
215	ssLB.push_back(ss.lbounds().front());
216	} else if (ss.Rank() > 1) {
217	return std::nullopt; // error recovery
218	}
219	}
220	ConstantSubscripts ssAt(rank, 0), at(rank, 0), tmp(1, 0);
221	std::vector<Scalar<T>> values;
222	while (elements-- > 0) {
223	bool increment{true};
224	int k{0};
225	for (int j{0}; j < rank; ++j) {
226	if (subscripts[j].Rank() == 0) {
227	at[j] = subscripts[j].GetScalarValue().value().ToInt64();
228	} else {
229	CHECK(k < GetRank(resultShape));
230	tmp[0] = ssLB.at(k) + ssAt.at(k);
231	at[j] = subscripts[j].At(tmp).ToInt64();
232	if (increment) {
233	if (++ssAt[k] == resultShape[k]) {
234	ssAt[k] = 0;
235	} else {
236	increment = false;
237	}
238	}
239	++k;
240	}
241	if (at[j] < lbounds[j] || at[j] >= lbounds[j] + shape[j]) {
242	context_.messages().Say(
243	"Subscript value (%jd) is out of range on dimension %d in reference to a constant array value"_err_en_US,
244	at[j], j + 1);
245	return std::nullopt;
246	}
247	}
248	values.emplace_back(array.At(at));
249	CHECK(!increment || elements == 0);
250	CHECK(k == GetRank(resultShape));
251	}
252	if constexpr (T::category == TypeCategory::Character) {
253	return Constant<T>{array.LEN(), std::move(values), std::move(resultShape)};
254	} else if constexpr (std::is_same_v<T, SomeDerived>) {
255	return Constant<T>{array.result().derivedTypeSpec(), std::move(values),
256	std::move(resultShape)};
257	} else {
258	return Constant<T>{std::move(values), std::move(resultShape)};
259	}
260	}
261
262	template <typename T>
263	std::optional<Constant<T>> Folder<T>::ApplyComponent(
264	Constant<SomeDerived> &&structures, const Symbol &component,
265	const std::vector<Constant<SubscriptInteger>> *subscripts) {
266	if (auto scalar{structures.GetScalarValue()}) {
267	if (std::optional<Expr<SomeType>> expr{scalar->Find(component)}) {
268	if (const Constant<T> *value{UnwrapConstantValue<T>(*expr)}) {
269	if (subscripts) {
270	return ApplySubscripts(*value, *subscripts);
271	} else {
272	return *value;
273	}
274	}
275	}
276	} else {
277	// A(:)%scalar_component & A(:)%array_component(subscripts)
278	std::unique_ptr<ArrayConstructor<T>> array;
279	if (structures.empty()) {
280	return std::nullopt;
281	}
282	ConstantSubscripts at{structures.lbounds()};
283	do {
284	StructureConstructor scalar{structures.At(at)};
285	if (std::optional<Expr<SomeType>> expr{scalar.Find(component)}) {
286	if (const Constant<T> *value{UnwrapConstantValue<T>(expr.value())}) {
287	if (!array.get()) {
288	// This technique ensures that character length or derived type
289	// information is propagated to the array constructor.
290	auto *typedExpr{UnwrapExpr<Expr<T>>(expr.value())};
291	CHECK(typedExpr);
292	array = std::make_unique<ArrayConstructor<T>>(*typedExpr);
293	if constexpr (T::category == TypeCategory::Character) {
294	array->set_LEN(Expr<SubscriptInteger>{value->LEN()});
295	}
296	}
297	if (subscripts) {
298	if (auto element{ApplySubscripts(*value, *subscripts)}) {
299	CHECK(element->Rank() == 0);
300	array->Push(Expr<T>{std::move(*element)});
301	} else {
302	return std::nullopt;
303	}
304	} else {
305	CHECK(value->Rank() == 0);
306	array->Push(Expr<T>{*value});
307	}
308	} else {
309	return std::nullopt;
310	}
311	}
312	} while (structures.IncrementSubscripts(at));
313	// Fold the ArrayConstructor<> into a Constant<>.
314	CHECK(array);
315	Expr<T> result{Fold(context_, Expr<T>{std::move(*array)})};
316	if (auto *constant{UnwrapConstantValue<T>(result)}) {
317	return constant->Reshape(common::Clone(structures.shape()));
318	}
319	}
320	return std::nullopt;
321	}
322
323	template <typename T>
324	std::optional<Constant<T>> Folder<T>::GetConstantComponent(Component &component,
325	const std::vector<Constant<SubscriptInteger>> *subscripts) {
326	if (std::optional<Constant<SomeDerived>> structures{common::visit(
327	common::visitors{
328	[&](const Symbol &symbol) {
329	return Folder<SomeDerived>{context_}.GetNamedConstant(symbol);
330	},
331	[&](ArrayRef &aRef) {
332	return Folder<SomeDerived>{context_}.Folding(aRef);
333	},
334	[&](Component &base) {
335	return Folder<SomeDerived>{context_}.GetConstantComponent(base);
336	},
337	[&](CoarrayRef &) {
338	return std::optional<Constant<SomeDerived>>{};
339	},
340	},
341	component.base().u)}) {
342	return ApplyComponent(
343	std::move(*structures), component.GetLastSymbol(), subscripts);
344	} else {
345	return std::nullopt;
346	}
347	}
348
349	template <typename T> Expr<T> Folder<T>::Folding(Designator<T> &&designator) {
350	if constexpr (T::category == TypeCategory::Character) {
351	if (auto *substring{common::Unwrap<Substring>(designator.u)}) {
352	if (std::optional<Expr<SomeCharacter>> folded{
353	substring->Fold(context_)}) {
354	if (const auto *specific{std::get_if<Expr<T>>(&folded->u)}) {
355	return std::move(*specific);
356	}
357	}
358	// We used to fold zero-length substrings into zero-length
359	// constants here, but that led to problems in variable
360	// definition contexts.
361	}
362	} else if constexpr (T::category == TypeCategory::Real) {
363	if (auto *zPart{std::get_if<ComplexPart>(&designator.u)}) {
364	*zPart = FoldOperation(context_, std::move(*zPart));
365	using ComplexT = Type<TypeCategory::Complex, T::kind>;
366	if (auto zConst{Folder<ComplexT>{context_}.Folding(zPart->complex())}) {
367	return Fold(context_,
368	Expr<T>{ComplexComponent<T::kind>{
369	zPart->part() == ComplexPart::Part::IM,
370	Expr<ComplexT>{std::move(*zConst)}}});
371	} else {
372	return Expr<T>{Designator<T>{std::move(*zPart)}};
373	}
374	}
375	}
376	return common::visit(
377	common::visitors{
378	[&](SymbolRef &&symbol) {
379	if (auto constant{GetNamedConstant(*symbol)}) {
380	return Expr<T>{std::move(*constant)};
381	}
382	return Expr<T>{std::move(designator)};
383	},
384	[&](ArrayRef &&aRef) {
385	aRef = FoldOperation(context_, std::move(aRef));
386	if (auto c{Folding(aRef)}) {
387	return Expr<T>{std::move(*c)};
388	} else {
389	return Expr<T>{Designator<T>{std::move(aRef)}};
390	}
391	},
392	[&](Component &&component) {
393	component = FoldOperation(context_, std::move(component));
394	if (auto c{GetConstantComponent(component)}) {
395	return Expr<T>{std::move(*c)};
396	} else {
397	return Expr<T>{Designator<T>{std::move(component)}};
398	}
399	},
400	[&](auto &&x) {
401	return Expr<T>{
402	Designator<T>{FoldOperation(context_, std::move(x))}};
403	},
404	},
405	std::move(designator.u));
406	}
407
408	// Apply type conversion and re-folding if necessary.
409	// This is where BOZ arguments are converted.
410	template <typename T>
411	Constant<T> *Folder<T>::Folding(std::optional<ActualArgument> &arg) {
412	if (auto *expr{UnwrapExpr<Expr<SomeType>>(arg)}) {
413	*expr = Fold(context_, std::move(*expr));
414	if constexpr (T::category != TypeCategory::Derived) {
415	if (!UnwrapExpr<Expr<T>>(*expr)) {
416	if (const Symbol *
417	var{forOptionalArgument_
418	? UnwrapWholeSymbolOrComponentDataRef(*expr)
419	: nullptr};
420	var && (IsOptional(*var) || IsAllocatableOrObjectPointer(var))) {
421	// can't safely convert item that may not be present
422	} else if (auto converted{
423	ConvertToType(T::GetType(), std::move(*expr))}) {
424	*expr = Fold(context_, std::move(*converted));
425	}
426	}
427	}
428	return UnwrapConstantValue<T>(*expr);
429	}
430	return nullptr;
431	}
432
433	template <typename... A, std::size_t... I>
434	std::optional<std::tuple<const Constant<A> *...>> GetConstantArgumentsHelper(
435	FoldingContext &context, ActualArguments &arguments,
436	bool hasOptionalArgument, std::index_sequence<I...>) {
437	static_assert(sizeof...(A) > 0);
438	std::tuple<const Constant<A> *...> args{
439	Folder<A>{context, hasOptionalArgument}.Folding(arguments.at(I))...};
440	if ((... && (std::get<I>(args)))) {
441	return args;
442	} else {
443	return std::nullopt;
444	}
445	}
446
447	template <typename... A>
448	std::optional<std::tuple<const Constant<A> *...>> GetConstantArguments(
449	FoldingContext &context, ActualArguments &args, bool hasOptionalArgument) {
450	return GetConstantArgumentsHelper<A...>(
451	context, args, hasOptionalArgument, std::index_sequence_for<A...>{});
452	}
453
454	template <typename... A, std::size_t... I>
455	std::optional<std::tuple<Scalar<A>...>> GetScalarConstantArgumentsHelper(
456	FoldingContext &context, ActualArguments &args, bool hasOptionalArgument,
457	std::index_sequence<I...>) {
458	if (auto constArgs{
459	GetConstantArguments<A...>(context, args, hasOptionalArgument)}) {
460	return std::tuple<Scalar<A>...>{
461	std::get<I>(*constArgs)->GetScalarValue().value()...};
462	} else {
463	return std::nullopt;
464	}
465	}
466
467	template <typename... A>
468	std::optional<std::tuple<Scalar<A>...>> GetScalarConstantArguments(
469	FoldingContext &context, ActualArguments &args, bool hasOptionalArgument) {
470	return GetScalarConstantArgumentsHelper<A...>(
471	context, args, hasOptionalArgument, std::index_sequence_for<A...>{});
472	}
473
474	// helpers to fold intrinsic function references
475	// Define callable types used in a common utility that
476	// takes care of array and cast/conversion aspects for elemental intrinsics
477
478	template <typename TR, typename... TArgs>
479	using ScalarFunc = std::function<Scalar<TR>(const Scalar<TArgs> &...)>;
480	template <typename TR, typename... TArgs>
481	using ScalarFuncWithContext =
482	std::function<Scalar<TR>(FoldingContext &, const Scalar<TArgs> &...)>;
483
484	template <template <typename, typename...> typename WrapperType, typename TR,
485	typename... TA, std::size_t... I>
486	Expr<TR> FoldElementalIntrinsicHelper(FoldingContext &context,
487	FunctionRef<TR> &&funcRef, WrapperType<TR, TA...> func,
488	bool hasOptionalArgument, std::index_sequence<I...>) {
489	if (std::optional<std::tuple<const Constant<TA> *...>> args{
490	GetConstantArguments<TA...>(
491	context, funcRef.arguments(), hasOptionalArgument)}) {
492	// Compute the shape of the result based on shapes of arguments
493	ConstantSubscripts shape;
494	int rank{0};
495	const ConstantSubscripts *shapes[]{&std::get<I>(*args)->shape()...};
496	const int ranks[]{std::get<I>(*args)->Rank()...};
497	for (unsigned int i{0}; i < sizeof...(TA); ++i) {
498	if (ranks[i] > 0) {
499	if (rank == 0) {
500	rank = ranks[i];
501	shape = *shapes[i];
502	} else {
503	if (shape != *shapes[i]) {
504	// TODO: Rank compatibility was already checked but it seems to be
505	// the first place where the actual shapes are checked to be the
506	// same. Shouldn't this be checked elsewhere so that this is also
507	// checked for non constexpr call to elemental intrinsics function?
508	context.messages().Say(
509	"Arguments in elemental intrinsic function are not conformable"_err_en_US);
510	return Expr<TR>{std::move(funcRef)};
511	}
512	}
513	}
514	}
515	CHECK(rank == GetRank(shape));
516	// Compute all the scalar values of the results
517	std::vector<Scalar<TR>> results;
518	std::optional<uint64_t> n{TotalElementCount(shape)};
519	if (!n) {
520	context.messages().Say(
521	"Too many elements in elemental intrinsic function result"_err_en_US);
522	return Expr<TR>{std::move(funcRef)};
523	}
524	if (*n > 0) {
525	ConstantBounds bounds{shape};
526	ConstantSubscripts resultIndex(rank, 1);
527	ConstantSubscripts argIndex[]{std::get<I>(*args)->lbounds()...};
528	do {
529	if constexpr (std::is_same_v<WrapperType<TR, TA...>,
530	ScalarFuncWithContext<TR, TA...>>) {
531	results.emplace_back(
532	func(context, std::get<I>(*args)->At(argIndex[I])...));
533	} else if constexpr (std::is_same_v<WrapperType<TR, TA...>,
534	ScalarFunc<TR, TA...>>) {
535	results.emplace_back(func(std::get<I>(*args)->At(argIndex[I])...));
536	}
537	(std::get<I>(*args)->IncrementSubscripts(argIndex[I]), ...);
538	} while (bounds.IncrementSubscripts(resultIndex));
539	}
540	// Build and return constant result
541	if constexpr (TR::category == TypeCategory::Character) {
542	auto len{static_cast<ConstantSubscript>(
543	results.empty() ? 0 : results[0].length())};
544	return Expr<TR>{Constant<TR>{len, std::move(results), std::move(shape)}};
545	} else if constexpr (TR::category == TypeCategory::Derived) {
546	if (!results.empty()) {
547	return Expr<TR>{rank == 0
548	? Constant<TR>{results.front()}
549	: Constant<TR>{results.front().derivedTypeSpec(),
550	std::move(results), std::move(shape)}};
551	}
552	} else {
553	return Expr<TR>{Constant<TR>{std::move(results), std::move(shape)}};
554	}
555	}
556	return Expr<TR>{std::move(funcRef)};
557	}
558
559	template <typename TR, typename... TA>
560	Expr<TR> FoldElementalIntrinsic(FoldingContext &context,
561	FunctionRef<TR> &&funcRef, ScalarFunc<TR, TA...> func,
562	bool hasOptionalArgument = false) {
563	return FoldElementalIntrinsicHelper<ScalarFunc, TR, TA...>(context,
564	std::move(funcRef), func, hasOptionalArgument,
565	std::index_sequence_for<TA...>{});
566	}
567	template <typename TR, typename... TA>
568	Expr<TR> FoldElementalIntrinsic(FoldingContext &context,
569	FunctionRef<TR> &&funcRef, ScalarFuncWithContext<TR, TA...> func,
570	bool hasOptionalArgument = false) {
571	return FoldElementalIntrinsicHelper<ScalarFuncWithContext, TR, TA...>(context,
572	std::move(funcRef), func, hasOptionalArgument,
573	std::index_sequence_for<TA...>{});
574	}
575
576	std::optional<std::int64_t> GetInt64ArgOr(
577	const std::optional<ActualArgument> &, std::int64_t defaultValue);
578
579	template <typename A, typename B>
580	std::optional<std::vector<A>> GetIntegerVector(const B &x) {
581	static_assert(std::is_integral_v<A>);
582	if (const auto *someInteger{UnwrapExpr<Expr<SomeInteger>>(x)}) {
583	return common::visit(
584	[](const auto &typedExpr) -> std::optional<std::vector<A>> {
585	using T = ResultType<decltype(typedExpr)>;
586	if (const auto *constant{UnwrapConstantValue<T>(typedExpr)}) {
587	if (constant->Rank() == 1) {
588	std::vector<A> result;
589	for (const auto &value : constant->values()) {
590	result.push_back(static_cast<A>(value.ToInt64()));
591	}
592	return result;
593	}
594	}
595	return std::nullopt;
596	},
597	someInteger->u);
598	}
599	return std::nullopt;
600	}
601
602	// Transform an intrinsic function reference that contains user errors
603	// into an intrinsic with the same characteristic but the "invalid" name.
604	// This to prevent generating warnings over and over if the expression
605	// gets re-folded.
606	template <typename T> Expr<T> MakeInvalidIntrinsic(FunctionRef<T> &&funcRef) {
607	SpecificIntrinsic invalid{std::get<SpecificIntrinsic>(funcRef.proc().u)};
608	invalid.name = IntrinsicProcTable::InvalidName;
609	return Expr<T>{FunctionRef<T>{ProcedureDesignator{std::move(invalid)},
610	ActualArguments{std::move(funcRef.arguments())}}};
611	}
612
613	template <typename T> Expr<T> Folder<T>::CSHIFT(FunctionRef<T> &&funcRef) {
614	auto args{funcRef.arguments()};
615	CHECK(args.size() == 3);
616	const auto *array{UnwrapConstantValue<T>(args[0])};
617	const auto *shiftExpr{UnwrapExpr<Expr<SomeInteger>>(args[1])};
618	auto dim{GetInt64ArgOr(args[2], 1)};
619	if (!array || !shiftExpr || !dim) {
620	return Expr<T>{std::move(funcRef)};
621	}
622	auto convertedShift{Fold(context_,
623	ConvertToType<SubscriptInteger>(Expr<SomeInteger>{*shiftExpr}))};
624	const auto *shift{UnwrapConstantValue<SubscriptInteger>(convertedShift)};
625	if (!shift) {
626	return Expr<T>{std::move(funcRef)};
627	}
628	// Arguments are constant
629	if (*dim < 1 || *dim > array->Rank()) {
630	context_.messages().Say("Invalid 'dim=' argument (%jd) in CSHIFT"_err_en_US,
631	static_cast<std::intmax_t>(*dim));
632	} else if (shift->Rank() > 0 && shift->Rank() != array->Rank() - 1) {
633	// message already emitted from intrinsic look-up
634	} else {
635	int rank{array->Rank()};
636	int zbDim{static_cast<int>(*dim) - 1};
637	bool ok{true};
638	if (shift->Rank() > 0) {
639	int k{0};
640	for (int j{0}; j < rank; ++j) {
641	if (j != zbDim) {
642	if (array->shape()[j] != shift->shape()[k]) {
643	context_.messages().Say(
644	"Invalid 'shift=' argument in CSHIFT: extent on dimension %d is %jd but must be %jd"_err_en_US,
645	k + 1, static_cast<std::intmax_t>(shift->shape()[k]),
646	static_cast<std::intmax_t>(array->shape()[j]));
647	ok = false;
648	}
649	++k;
650	}
651	}
652	}
653	if (ok) {
654	std::vector<Scalar<T>> resultElements;
655	ConstantSubscripts arrayLB{array->lbounds()};
656	ConstantSubscripts arrayAt{arrayLB};
657	ConstantSubscript &dimIndex{arrayAt[zbDim]};
658	ConstantSubscript dimLB{dimIndex}; // initial value
659	ConstantSubscript dimExtent{array->shape()[zbDim]};
660	ConstantSubscripts shiftLB{shift->lbounds()};
661	for (auto n{GetSize(array->shape())}; n > 0; --n) {
662	ConstantSubscript origDimIndex{dimIndex};
663	ConstantSubscripts shiftAt;
664	if (shift->Rank() > 0) {
665	int k{0};
666	for (int j{0}; j < rank; ++j) {
667	if (j != zbDim) {
668	shiftAt.emplace_back(shiftLB[k++] + arrayAt[j] - arrayLB[j]);
669	}
670	}
671	}
672	ConstantSubscript shiftCount{shift->At(shiftAt).ToInt64()};
673	dimIndex = dimLB + ((dimIndex - dimLB + shiftCount) % dimExtent);
674	if (dimIndex < dimLB) {
675	dimIndex += dimExtent;
676	} else if (dimIndex >= dimLB + dimExtent) {
677	dimIndex -= dimExtent;
678	}
679	resultElements.push_back(array->At(arrayAt));
680	dimIndex = origDimIndex;
681	array->IncrementSubscripts(arrayAt);
682	}
683	return Expr<T>{PackageConstant<T>(
684	std::move(resultElements), *array, array->shape())};
685	}
686	}
687	// Invalid, prevent re-folding
688	return MakeInvalidIntrinsic(std::move(funcRef));
689	}
690
691	template <typename T> Expr<T> Folder<T>::EOSHIFT(FunctionRef<T> &&funcRef) {
692	auto args{funcRef.arguments()};
693	CHECK(args.size() == 4);
694	const auto *array{UnwrapConstantValue<T>(args[0])};
695	const auto *shiftExpr{UnwrapExpr<Expr<SomeInteger>>(args[1])};
696	auto dim{GetInt64ArgOr(args[3], 1)};
697	if (!array || !shiftExpr || !dim) {
698	return Expr<T>{std::move(funcRef)};
699	}
700	// Apply type conversions to the shift= and boundary= arguments.
701	auto convertedShift{Fold(context_,
702	ConvertToType<SubscriptInteger>(Expr<SomeInteger>{*shiftExpr}))};
703	const auto *shift{UnwrapConstantValue<SubscriptInteger>(convertedShift)};
704	if (!shift) {
705	return Expr<T>{std::move(funcRef)};
706	}
707	const Constant<T> *boundary{nullptr};
708	std::optional<Expr<SomeType>> convertedBoundary;
709	if (const auto *boundaryExpr{UnwrapExpr<Expr<SomeType>>(args[2])}) {
710	convertedBoundary = Fold(context_,
711	ConvertToType(array->GetType(), Expr<SomeType>{*boundaryExpr}));
712	boundary = UnwrapExpr<Constant<T>>(convertedBoundary);
713	if (!boundary) {
714	return Expr<T>{std::move(funcRef)};
715	}
716	}
717	// Arguments are constant
718	if (*dim < 1 || *dim > array->Rank()) {
719	context_.messages().Say(
720	"Invalid 'dim=' argument (%jd) in EOSHIFT"_err_en_US,
721	static_cast<std::intmax_t>(*dim));
722	} else if (shift->Rank() > 0 && shift->Rank() != array->Rank() - 1) {
723	// message already emitted from intrinsic look-up
724	} else if (boundary && boundary->Rank() > 0 &&
725	boundary->Rank() != array->Rank() - 1) {
726	// ditto
727	} else {
728	int rank{array->Rank()};
729	int zbDim{static_cast<int>(*dim) - 1};
730	bool ok{true};
731	if (shift->Rank() > 0) {
732	int k{0};
733	for (int j{0}; j < rank; ++j) {
734	if (j != zbDim) {
735	if (array->shape()[j] != shift->shape()[k]) {
736	context_.messages().Say(
737	"Invalid 'shift=' argument in EOSHIFT: extent on dimension %d is %jd but must be %jd"_err_en_US,
738	k + 1, static_cast<std::intmax_t>(shift->shape()[k]),
739	static_cast<std::intmax_t>(array->shape()[j]));
740	ok = false;
741	}
742	++k;
743	}
744	}
745	}
746	if (boundary && boundary->Rank() > 0) {
747	int k{0};
748	for (int j{0}; j < rank; ++j) {
749	if (j != zbDim) {
750	if (array->shape()[j] != boundary->shape()[k]) {
751	context_.messages().Say(
752	"Invalid 'boundary=' argument in EOSHIFT: extent on dimension %d is %jd but must be %jd"_err_en_US,
753	k + 1, static_cast<std::intmax_t>(boundary->shape()[k]),
754	static_cast<std::intmax_t>(array->shape()[j]));
755	ok = false;
756	}
757	++k;
758	}
759	}
760	}
761	if (ok) {
762	std::vector<Scalar<T>> resultElements;
763	ConstantSubscripts arrayLB{array->lbounds()};
764	ConstantSubscripts arrayAt{arrayLB};
765	ConstantSubscript &dimIndex{arrayAt[zbDim]};
766	ConstantSubscript dimLB{dimIndex}; // initial value
767	ConstantSubscript dimExtent{array->shape()[zbDim]};
768	ConstantSubscripts shiftLB{shift->lbounds()};
769	ConstantSubscripts boundaryLB;
770	if (boundary) {
771	boundaryLB = boundary->lbounds();
772	}
773	for (auto n{GetSize(array->shape())}; n > 0; --n) {
774	ConstantSubscript origDimIndex{dimIndex};
775	ConstantSubscripts shiftAt;
776	if (shift->Rank() > 0) {
777	int k{0};
778	for (int j{0}; j < rank; ++j) {
779	if (j != zbDim) {
780	shiftAt.emplace_back(shiftLB[k++] + arrayAt[j] - arrayLB[j]);
781	}
782	}
783	}
784	ConstantSubscript shiftCount{shift->At(shiftAt).ToInt64()};
785	dimIndex += shiftCount;
786	if (dimIndex >= dimLB && dimIndex < dimLB + dimExtent) {
787	resultElements.push_back(array->At(arrayAt));
788	} else if (boundary) {
789	ConstantSubscripts boundaryAt;
790	if (boundary->Rank() > 0) {
791	for (int j{0}; j < rank; ++j) {
792	int k{0};
793	if (j != zbDim) {
794	boundaryAt.emplace_back(
795	boundaryLB[k++] + arrayAt[j] - arrayLB[j]);
796	}
797	}
798	}
799	resultElements.push_back(boundary->At(boundaryAt));
800	} else if constexpr (T::category == TypeCategory::Integer ||
801	T::category == TypeCategory::Unsigned ||
802	T::category == TypeCategory::Real ||
803	T::category == TypeCategory::Complex ||
804	T::category == TypeCategory::Logical) {
805	resultElements.emplace_back();
806	} else if constexpr (T::category == TypeCategory::Character) {
807	auto len{static_cast<std::size_t>(array->LEN())};
808	typename Scalar<T>::value_type space{' '};
809	resultElements.emplace_back(len, space);
810	} else {
811	DIE("no derived type boundary");
812	}
813	dimIndex = origDimIndex;
814	array->IncrementSubscripts(arrayAt);
815	}
816	return Expr<T>{PackageConstant<T>(
817	std::move(resultElements), *array, array->shape())};
818	}
819	}
820	// Invalid, prevent re-folding
821	return MakeInvalidIntrinsic(std::move(funcRef));
822	}
823
824	template <typename T> Expr<T> Folder<T>::MERGE(FunctionRef<T> &&funcRef) {
825	return FoldElementalIntrinsic<T, T, T, LogicalResult>(context_,
826	std::move(funcRef),
827	ScalarFunc<T, T, T, LogicalResult>(
828	[](const Scalar<T> &ifTrue, const Scalar<T> &ifFalse,
829	const Scalar<LogicalResult> &predicate) -> Scalar<T> {
830	return predicate.IsTrue() ? ifTrue : ifFalse;
831	}));
832	}
833
834	template <typename T> Expr<T> Folder<T>::PACK(FunctionRef<T> &&funcRef) {
835	auto args{funcRef.arguments()};
836	CHECK(args.size() == 3);
837	const auto *array{UnwrapConstantValue<T>(args[0])};
838	const auto *vector{UnwrapConstantValue<T>(args[2])};
839	auto convertedMask{Fold(context_,
840	ConvertToType<LogicalResult>(
841	Expr<SomeLogical>{DEREF(UnwrapExpr<Expr<SomeLogical>>(args[1]))}))};
842	const auto *mask{UnwrapConstantValue<LogicalResult>(convertedMask)};
843	if (!array || !mask || (args[2] && !vector)) {
844	return Expr<T>{std::move(funcRef)};
845	}
846	// Arguments are constant.
847	ConstantSubscript arrayElements{GetSize(array->shape())};
848	ConstantSubscript truths{0};
849	ConstantSubscripts maskAt{mask->lbounds()};
850	if (mask->Rank() == 0) {
851	if (mask->At(maskAt).IsTrue()) {
852	truths = arrayElements;
853	}
854	} else if (array->shape() != mask->shape()) {
855	// Error already emitted from intrinsic processing
856	return MakeInvalidIntrinsic(std::move(funcRef));
857	} else {
858	for (ConstantSubscript j{0}; j < arrayElements;
859	++j, mask->IncrementSubscripts(maskAt)) {
860	if (mask->At(maskAt).IsTrue()) {
861	++truths;
862	}
863	}
864	}
865	std::vector<Scalar<T>> resultElements;
866	ConstantSubscripts arrayAt{array->lbounds()};
867	ConstantSubscript resultSize{truths};
868	if (vector) {
869	resultSize = vector->shape().at(0);
870	if (resultSize < truths) {
871	context_.messages().Say(
872	"Invalid 'vector=' argument in PACK: the 'mask=' argument has %jd true elements, but the vector has only %jd elements"_err_en_US,
873	static_cast<std::intmax_t>(truths),
874	static_cast<std::intmax_t>(resultSize));
875	return MakeInvalidIntrinsic(std::move(funcRef));
876	}
877	}
878	for (ConstantSubscript j{0}; j < truths;) {
879	if (mask->At(maskAt).IsTrue()) {
880	resultElements.push_back(array->At(arrayAt));
881	++j;
882	}
883	array->IncrementSubscripts(arrayAt);
884	mask->IncrementSubscripts(maskAt);
885	}
886	if (vector) {
887	ConstantSubscripts vectorAt{vector->lbounds()};
888	vectorAt.at(0) += truths;
889	for (ConstantSubscript j{truths}; j < resultSize; ++j) {
890	resultElements.push_back(vector->At(vectorAt));
891	++vectorAt[0];
892	}
893	}
894	return Expr<T>{PackageConstant<T>(std::move(resultElements), *array,
895	ConstantSubscripts{static_cast<ConstantSubscript>(resultSize)})};
896	}
897
898	template <typename T> Expr<T> Folder<T>::RESHAPE(FunctionRef<T> &&funcRef) {
899	auto args{funcRef.arguments()};
900	CHECK(args.size() == 4);
901	const auto *source{UnwrapConstantValue<T>(args[0])};
902	const auto *pad{UnwrapConstantValue<T>(args[2])};
903	std::optional<std::vector<ConstantSubscript>> shape{
904	GetIntegerVector<ConstantSubscript>(args[1])};
905	std::optional<std::vector<int>> order{GetIntegerVector<int>(args[3])};
906	std::optional<uint64_t> optResultElement;
907	std::optional<std::vector<int>> dimOrder;
908	bool ok{true};
909	if (shape) {
910	if (shape->size() > common::maxRank) {
911	context_.messages().Say(
912	"Size of 'shape=' argument (%zd) must not be greater than %d"_err_en_US,
913	shape->size(), common::maxRank);
914	ok = false;
915	} else if (HasNegativeExtent(*shape)) {
916	context_.messages().Say(
917	"'shape=' argument (%s) must not have a negative extent"_err_en_US,
918	DEREF(args[1]->UnwrapExpr()).AsFortran());
919	ok = false;
920	} else {
921	optResultElement = TotalElementCount(*shape);
922	if (!optResultElement) {
923	context_.messages().Say(
924	"'shape=' argument (%s) specifies an array with too many elements"_err_en_US,
925	DEREF(args[1]->UnwrapExpr()).AsFortran());
926	ok = false;
927	}
928	}
929	if (order) {
930	dimOrder = ValidateDimensionOrder(GetRank(*shape), *order);
931	if (!dimOrder) {
932	context_.messages().Say(
933	"Invalid 'order=' argument (%s) in RESHAPE"_err_en_US,
934	DEREF(args[3]->UnwrapExpr()).AsFortran());
935	ok = false;
936	}
937	}
938	}
939	if (!ok) {
940	// convert into an invalid intrinsic procedure call below
941	} else if (!source || !shape || (args[2] && !pad) || (args[3] && !order)) {
942	return Expr<T>{std::move(funcRef)}; // Non-constant arguments
943	} else {
944	uint64_t resultElements{*optResultElement};
945	std::vector<int> *dimOrderPtr{dimOrder ? &dimOrder.value() : nullptr};
946	if (resultElements > source->size() && (!pad || pad->empty())) {
947	context_.messages().Say(
948	"Too few elements in 'source=' argument and 'pad=' "
949	"argument is not present or has null size"_err_en_US);
950	ok = false;
951	} else {
952	Constant<T> result{!source->empty() || !pad
953	? source->Reshape(std::move(shape.value()))
954	: pad->Reshape(std::move(shape.value()))};
955	ConstantSubscripts subscripts{result.lbounds()};
956	auto copied{result.CopyFrom(*source,
957	std::min(a: static_cast<uint64_t>(source->size()), b: resultElements),
958	subscripts, dimOrderPtr)};
959	if (copied < resultElements) {
960	CHECK(pad);
961	copied += result.CopyFrom(
962	*pad, resultElements - copied, subscripts, dimOrderPtr);
963	}
964	CHECK(copied == resultElements);
965	return Expr<T>{std::move(result)};
966	}
967	}
968	// Invalid, prevent re-folding
969	return MakeInvalidIntrinsic(std::move(funcRef));
970	}
971
972	template <typename T> Expr<T> Folder<T>::SPREAD(FunctionRef<T> &&funcRef) {
973	auto args{funcRef.arguments()};
974	CHECK(args.size() == 3);
975	const Constant<T> *source{UnwrapConstantValue<T>(args[0])};
976	auto dim{ToInt64(args[1])};
977	auto ncopies{ToInt64(args[2])};
978	if (!source || !dim) {
979	return Expr<T>{std::move(funcRef)};
980	}
981	int sourceRank{source->Rank()};
982	if (sourceRank >= common::maxRank) {
983	context_.messages().Say(
984	"SOURCE= argument to SPREAD has rank %d but must have rank less than %d"_err_en_US,
985	sourceRank, common::maxRank);
986	} else if (*dim < 1 || *dim > sourceRank + 1) {
987	context_.messages().Say(
988	"DIM=%d argument to SPREAD must be between 1 and %d"_err_en_US, *dim,
989	sourceRank + 1);
990	} else if (!ncopies) {
991	return Expr<T>{std::move(funcRef)};
992	} else {
993	if (*ncopies < 0) {
994	ncopies = 0;
995	}
996	// TODO: Consider moving this implementation (after the user error
997	// checks), along with other transformational intrinsics, into
998	// constant.h (or a new header) so that the transformationals
999	// are available for all Constant<>s without needing to be packaged
1000	// as references to intrinsic functions for folding.
1001	ConstantSubscripts shape{source->shape()};
1002	shape.insert(shape.begin() + *dim - 1, *ncopies);
1003	Constant<T> spread{source->Reshape(std::move(shape))};
1004	std::optional<uint64_t> n{TotalElementCount(spread.shape())};
1005	if (!n) {
1006	context_.messages().Say("Too many elements in SPREAD result"_err_en_US);
1007	} else {
1008	std::vector<int> dimOrder;
1009	for (int j{0}; j < sourceRank; ++j) {
1010	dimOrder.push_back(j < *dim - 1 ? j : j + 1);
1011	}
1012	dimOrder.push_back(*dim - 1);
1013	ConstantSubscripts at{spread.lbounds()}; // all 1
1014	spread.CopyFrom(*source, *n, at, &dimOrder);
1015	return Expr<T>{std::move(spread)};
1016	}
1017	}
1018	// Invalid, prevent re-folding
1019	return MakeInvalidIntrinsic(std::move(funcRef));
1020	}
1021
1022	template <typename T> Expr<T> Folder<T>::TRANSPOSE(FunctionRef<T> &&funcRef) {
1023	auto args{funcRef.arguments()};
1024	CHECK(args.size() == 1);
1025	const auto *matrix{UnwrapConstantValue<T>(args[0])};
1026	if (!matrix) {
1027	return Expr<T>{std::move(funcRef)};
1028	}
1029	// Argument is constant. Traverse its elements in transposed order.
1030	std::vector<Scalar<T>> resultElements;
1031	ConstantSubscripts at(2);
1032	for (ConstantSubscript j{0}; j < matrix->shape()[0]; ++j) {
1033	at[0] = matrix->lbounds()[0] + j;
1034	for (ConstantSubscript k{0}; k < matrix->shape()[1]; ++k) {
1035	at[1] = matrix->lbounds()[1] + k;
1036	resultElements.push_back(matrix->At(at));
1037	}
1038	}
1039	at = matrix->shape();
1040	std::swap(at[0], at[1]);
1041	return Expr<T>{PackageConstant<T>(std::move(resultElements), *matrix, at)};
1042	}
1043
1044	template <typename T> Expr<T> Folder<T>::UNPACK(FunctionRef<T> &&funcRef) {
1045	auto args{funcRef.arguments()};
1046	CHECK(args.size() == 3);
1047	const auto *vector{UnwrapConstantValue<T>(args[0])};
1048	auto convertedMask{Fold(context_,
1049	ConvertToType<LogicalResult>(
1050	Expr<SomeLogical>{DEREF(UnwrapExpr<Expr<SomeLogical>>(args[1]))}))};
1051	const auto *mask{UnwrapConstantValue<LogicalResult>(convertedMask)};
1052	const auto *field{UnwrapConstantValue<T>(args[2])};
1053	if (!vector || !mask || !field) {
1054	return Expr<T>{std::move(funcRef)};
1055	}
1056	// Arguments are constant.
1057	if (field->Rank() > 0 && field->shape() != mask->shape()) {
1058	// Error already emitted from intrinsic processing
1059	return MakeInvalidIntrinsic(std::move(funcRef));
1060	}
1061	ConstantSubscript maskElements{GetSize(mask->shape())};
1062	ConstantSubscript truths{0};
1063	ConstantSubscripts maskAt{mask->lbounds()};
1064	for (ConstantSubscript j{0}; j < maskElements;
1065	++j, mask->IncrementSubscripts(maskAt)) {
1066	if (mask->At(maskAt).IsTrue()) {
1067	++truths;
1068	}
1069	}
1070	if (truths > GetSize(vector->shape())) {
1071	context_.messages().Say(
1072	"Invalid 'vector=' argument in UNPACK: the 'mask=' argument has %jd true elements, but the vector has only %jd elements"_err_en_US,
1073	static_cast<std::intmax_t>(truths),
1074	static_cast<std::intmax_t>(GetSize(vector->shape())));
1075	return MakeInvalidIntrinsic(std::move(funcRef));
1076	}
1077	std::vector<Scalar<T>> resultElements;
1078	ConstantSubscripts vectorAt{vector->lbounds()};
1079	ConstantSubscripts fieldAt{field->lbounds()};
1080	for (ConstantSubscript j{0}; j < maskElements; ++j) {
1081	if (mask->At(maskAt).IsTrue()) {
1082	resultElements.push_back(vector->At(vectorAt));
1083	vector->IncrementSubscripts(vectorAt);
1084	} else {
1085	resultElements.push_back(field->At(fieldAt));
1086	}
1087	mask->IncrementSubscripts(maskAt);
1088	field->IncrementSubscripts(fieldAt);
1089	}
1090	return Expr<T>{
1091	PackageConstant<T>(std::move(resultElements), *vector, mask->shape())};
1092	}
1093
1094	std::optional<Expr<SomeType>> FoldTransfer(
1095	FoldingContext &, const ActualArguments &);
1096
1097	template <typename T> Expr<T> Folder<T>::TRANSFER(FunctionRef<T> &&funcRef) {
1098	if (auto folded{FoldTransfer(context_, funcRef.arguments())}) {
1099	return DEREF(UnwrapExpr<Expr<T>>(*folded));
1100	} else {
1101	return Expr<T>{std::move(funcRef)};
1102	}
1103	}
1104
1105	template <typename T>
1106	Expr<T> FoldMINorMAX(
1107	FoldingContext &context, FunctionRef<T> &&funcRef, Ordering order) {
1108	static_assert(T::category == TypeCategory::Integer ||
1109	T::category == TypeCategory::Unsigned ||
1110	T::category == TypeCategory::Real ||
1111	T::category == TypeCategory::Character);
1112	auto &args{funcRef.arguments()};
1113	bool ok{true};
1114	std::optional<Expr<T>> result;
1115	Folder<T> folder{context};
1116	for (std::optional<ActualArgument> &arg : args) {
1117	// Call Folding on all arguments to make operand promotion explicit.
1118	if (!folder.Folding(arg)) {
1119	// TODO: Lowering can't handle having every FunctionRef for max and min
1120	// being converted into Extremum<T>. That needs fixing. Until that
1121	// is corrected, however, it is important that max and min references
1122	// in module files be converted into Extremum<T> even when not constant;
1123	// the Extremum<SubscriptInteger> operations created to normalize the
1124	// values of array bounds are formatted as max operations in the
1125	// declarations in modules, and need to be read back in as such in
1126	// order for expression comparison to not produce false inequalities
1127	// when checking function results for procedure interface compatibility.
1128	if (!context.moduleFileName()) {
1129	ok = false;
1130	}
1131	}
1132	Expr<SomeType> *argExpr{arg ? arg->UnwrapExpr() : nullptr};
1133	if (argExpr) {
1134	*argExpr = Fold(context, std::move(*argExpr));
1135	}
1136	if (Expr<T> * tExpr{UnwrapExpr<Expr<T>>(argExpr)}) {
1137	if (result) {
1138	result = FoldOperation(
1139	context, Extremum<T>{order, std::move(*result), Expr<T>{*tExpr}});
1140	} else {
1141	result = Expr<T>{*tExpr};
1142	}
1143	} else {
1144	ok = false;
1145	}
1146	}
1147	return ok && result ? std::move(*result) : Expr<T>{std::move(funcRef)};
1148	}
1149
1150	// For AMAX0, AMIN0, AMAX1, AMIN1, DMAX1, DMIN1, MAX0, MIN0, MAX1, and MIN1
1151	// a special care has to be taken to insert the conversion on the result
1152	// of the MIN/MAX. This is made slightly more complex by the extension
1153	// supported by f18 that arguments may have different kinds. This implies
1154	// that the created MIN/MAX result type cannot be deduced from the standard but
1155	// has to be deduced from the arguments.
1156	// e.g. AMAX0(int8, int4) is rewritten to REAL(MAX(int8, INT(int4, 8)))).
1157	template <typename T>
1158	Expr<T> RewriteSpecificMINorMAX(
1159	FoldingContext &context, FunctionRef<T> &&funcRef) {
1160	ActualArguments &args{funcRef.arguments()};
1161	auto &intrinsic{DEREF(std::get_if<SpecificIntrinsic>(&funcRef.proc().u))};
1162	// Rewrite MAX1(args) to INT(MAX(args)) and fold. Same logic for MIN1.
1163	// Find result type for max/min based on the arguments.
1164	std::optional<DynamicType> resultType;
1165	ActualArgument *resultTypeArg{nullptr};
1166	for (auto j{args.size()}; j-- > 0;) {
1167	if (args[j]) {
1168	DynamicType type{args[j]->GetType().value()};
1169	// Handle mixed real/integer arguments: all the previous arguments were
1170	// integers and this one is real. The type of the MAX/MIN result will
1171	// be the one of the real argument.
1172	if (!resultType ||
1173	(type.category() == resultType->category() &&
1174	type.kind() > resultType->kind()) ||
1175	resultType->category() == TypeCategory::Integer) {
1176	resultType = type;
1177	resultTypeArg = &*args[j];
1178	}
1179	}
1180	}
1181	if (!resultType) { // error recovery
1182	return Expr<T>{std::move(funcRef)};
1183	}
1184	intrinsic.name =
1185	intrinsic.name.find("max") != std::string::npos ? "max"s : "min"s;
1186	intrinsic.characteristics.value().functionResult.value().SetType(*resultType);
1187	auto insertConversion{[&](const auto &x) -> Expr<T> {
1188	using TR = ResultType<decltype(x)>;
1189	FunctionRef<TR> maxRef{
1190	ProcedureDesignator{funcRef.proc()}, ActualArguments{args}};
1191	return Fold(context, ConvertToType<T>(AsCategoryExpr(std::move(maxRef))));
1192	}};
1193	if (auto *sx{UnwrapExpr<Expr<SomeReal>>(*resultTypeArg)}) {
1194	return common::visit(insertConversion, sx->u);
1195	} else if (auto *sx{UnwrapExpr<Expr<SomeInteger>>(*resultTypeArg)}) {
1196	return common::visit(insertConversion, sx->u);
1197	} else {
1198	return Expr<T>{std::move(funcRef)}; // error recovery
1199	}
1200	}
1201
1202	// FoldIntrinsicFunction()
1203	template <int KIND>
1204	Expr<Type<TypeCategory::Integer, KIND>> FoldIntrinsicFunction(
1205	FoldingContext &context, FunctionRef<Type<TypeCategory::Integer, KIND>> &&);
1206	template <int KIND>
1207	Expr<Type<TypeCategory::Unsigned, KIND>> FoldIntrinsicFunction(
1208	FoldingContext &context,
1209	FunctionRef<Type<TypeCategory::Unsigned, KIND>> &&);
1210	template <int KIND>
1211	Expr<Type<TypeCategory::Real, KIND>> FoldIntrinsicFunction(
1212	FoldingContext &context, FunctionRef<Type<TypeCategory::Real, KIND>> &&);
1213	template <int KIND>
1214	Expr<Type<TypeCategory::Complex, KIND>> FoldIntrinsicFunction(
1215	FoldingContext &context, FunctionRef<Type<TypeCategory::Complex, KIND>> &&);
1216	template <int KIND>
1217	Expr<Type<TypeCategory::Logical, KIND>> FoldIntrinsicFunction(
1218	FoldingContext &context, FunctionRef<Type<TypeCategory::Logical, KIND>> &&);
1219
1220	template <typename T>
1221	Expr<T> FoldOperation(FoldingContext &context, FunctionRef<T> &&funcRef) {
1222	ActualArguments &args{funcRef.arguments()};
1223	const auto *intrinsic{std::get_if<SpecificIntrinsic>(&funcRef.proc().u)};
1224	if (!intrinsic || intrinsic->name != "kind") {
1225	// Don't fold the argument to KIND(); it might be a TypeParamInquiry
1226	// with a forced result type that doesn't match the parameter.
1227	for (std::optional<ActualArgument> &arg : args) {
1228	if (auto *expr{UnwrapExpr<Expr<SomeType>>(arg)}) {
1229	*expr = Fold(context, std::move(*expr));
1230	}
1231	}
1232	}
1233	if (intrinsic) {
1234	const std::string name{intrinsic->name};
1235	if (name == "cshift") {
1236	return Folder<T>{context}.CSHIFT(std::move(funcRef));
1237	} else if (name == "eoshift") {
1238	return Folder<T>{context}.EOSHIFT(std::move(funcRef));
1239	} else if (name == "merge") {
1240	return Folder<T>{context}.MERGE(std::move(funcRef));
1241	} else if (name == "pack") {
1242	return Folder<T>{context}.PACK(std::move(funcRef));
1243	} else if (name == "reshape") {
1244	return Folder<T>{context}.RESHAPE(std::move(funcRef));
1245	} else if (name == "spread") {
1246	return Folder<T>{context}.SPREAD(std::move(funcRef));
1247	} else if (name == "transfer") {
1248	return Folder<T>{context}.TRANSFER(std::move(funcRef));
1249	} else if (name == "transpose") {
1250	return Folder<T>{context}.TRANSPOSE(std::move(funcRef));
1251	} else if (name == "unpack") {
1252	return Folder<T>{context}.UNPACK(std::move(funcRef));
1253	}
1254	// TODO: extends_type_of, same_type_as
1255	if constexpr (!std::is_same_v<T, SomeDerived>) {
1256	return FoldIntrinsicFunction(context, std::move(funcRef));
1257	}
1258	}
1259	return Expr<T>{std::move(funcRef)};
1260	}
1261
1262	Expr<ImpliedDoIndex::Result> FoldOperation(FoldingContext &, ImpliedDoIndex &&);
1263
1264	// Array constructor folding
1265	template <typename T> class ArrayConstructorFolder {
1266	public:
1267	explicit ArrayConstructorFolder(FoldingContext &c) : context_{c} {}
1268
1269	Expr<T> FoldArray(ArrayConstructor<T> &&array) {
1270	if constexpr (T::category == TypeCategory::Character) {
1271	if (const auto *len{array.LEN()}) {
1272	charLength_ = ToInt64(Fold(context_, common::Clone(*len)));
1273	knownCharLength_ = charLength_.has_value();
1274	}
1275	}
1276	// Calls FoldArray(const ArrayConstructorValues<T> &) below
1277	if (FoldArray(array)) {
1278	auto n{static_cast<ConstantSubscript>(elements_.size())};
1279	if constexpr (std::is_same_v<T, SomeDerived>) {
1280	return Expr<T>{Constant<T>{array.GetType().GetDerivedTypeSpec(),
1281	std::move(elements_), ConstantSubscripts{n}}};
1282	} else if constexpr (T::category == TypeCategory::Character) {
1283	if (charLength_) {
1284	return Expr<T>{Constant<T>{
1285	*charLength_, std::move(elements_), ConstantSubscripts{n}}};
1286	}
1287	} else {
1288	return Expr<T>{
1289	Constant<T>{std::move(elements_), ConstantSubscripts{n}}};
1290	}
1291	}
1292	return Expr<T>{std::move(array)};
1293	}
1294
1295	private:
1296	bool FoldArray(const Expr<T> &expr) {
1297	Expr<T> folded{Fold(context_, common::Clone(expr))};
1298	if (const auto *c{UnwrapConstantValue<T>(folded)}) {
1299	// Copy elements in Fortran array element order
1300	if (!c->empty()) {
1301	ConstantSubscripts index{c->lbounds()};
1302	do {
1303	elements_.emplace_back(c->At(index));
1304	} while (c->IncrementSubscripts(index));
1305	}
1306	if constexpr (T::category == TypeCategory::Character) {
1307	if (!knownCharLength_) {
1308	charLength_ = std::max(c->LEN(), charLength_.value_or(-1));
1309	}
1310	}
1311	return true;
1312	} else {
1313	return false;
1314	}
1315	}
1316	bool FoldArray(const common::CopyableIndirection<Expr<T>> &expr) {
1317	return FoldArray(expr.value());
1318	}
1319	bool FoldArray(const ImpliedDo<T> &iDo) {
1320	Expr<SubscriptInteger> lower{
1321	Fold(context_, Expr<SubscriptInteger>{iDo.lower()})};
1322	Expr<SubscriptInteger> upper{
1323	Fold(context_, Expr<SubscriptInteger>{iDo.upper()})};
1324	Expr<SubscriptInteger> stride{
1325	Fold(context_, Expr<SubscriptInteger>{iDo.stride()})};
1326	std::optional<ConstantSubscript> start{ToInt64(lower)}, end{ToInt64(upper)},
1327	step{ToInt64(stride)};
1328	if (start && end && step && *step != 0) {
1329	bool result{true};
1330	ConstantSubscript &j{context_.StartImpliedDo(iDo.name(), *start)};
1331	if (*step > 0) {
1332	for (; j <= *end; j += *step) {
1333	result &= FoldArray(iDo.values());
1334	}
1335	} else {
1336	for (; j >= *end; j += *step) {
1337	result &= FoldArray(iDo.values());
1338	}
1339	}
1340	context_.EndImpliedDo(iDo.name());
1341	return result;
1342	} else {
1343	return false;
1344	}
1345	}
1346	bool FoldArray(const ArrayConstructorValue<T> &x) {
1347	return common::visit([&](const auto &y) { return FoldArray(y); }, x.u);
1348	}
1349	bool FoldArray(const ArrayConstructorValues<T> &xs) {
1350	for (const auto &x : xs) {
1351	if (!FoldArray(x)) {
1352	return false;
1353	}
1354	}
1355	return true;
1356	}
1357
1358	FoldingContext &context_;
1359	std::vector<Scalar<T>> elements_;
1360	std::optional<ConstantSubscript> charLength_;
1361	bool knownCharLength_{false};
1362	};
1363
1364	template <typename T>
1365	Expr<T> FoldOperation(FoldingContext &context, ArrayConstructor<T> &&array) {
1366	return ArrayConstructorFolder<T>{context}.FoldArray(std::move(array));
1367	}
1368
1369	// Array operation elemental application: When all operands to an operation
1370	// are constant arrays, array constructors without any implied DO loops,
1371	// &/or expanded scalars, pull the operation "into" the array result by
1372	// applying it in an elementwise fashion. For example, [A,1]+[B,2]
1373	// is rewritten into [A+B,1+2] and then partially folded to [A+B,3].
1374
1375	// If possible, restructures an array expression into an array constructor
1376	// that comprises a "flat" ArrayConstructorValues with no implied DO loops.
1377	template <typename T>
1378	bool ArrayConstructorIsFlat(const ArrayConstructorValues<T> &values) {
1379	for (const ArrayConstructorValue<T> &x : values) {
1380	if (!std::holds_alternative<Expr<T>>(x.u)) {
1381	return false;
1382	}
1383	}
1384	return true;
1385	}
1386
1387	template <typename T>
1388	std::optional<Expr<T>> AsFlatArrayConstructor(const Expr<T> &expr) {
1389	if (const auto *c{UnwrapConstantValue<T>(expr)}) {
1390	ArrayConstructor<T> result{expr};
1391	if (!c->empty()) {
1392	ConstantSubscripts at{c->lbounds()};
1393	do {
1394	result.Push(Expr<T>{Constant<T>{c->At(at)}});
1395	} while (c->IncrementSubscripts(at));
1396	}
1397	return std::make_optional<Expr<T>>(std::move(result));
1398	} else if (const auto *a{UnwrapExpr<ArrayConstructor<T>>(expr)}) {
1399	if (ArrayConstructorIsFlat(*a)) {
1400	return std::make_optional<Expr<T>>(expr);
1401	}
1402	} else if (const auto *p{UnwrapExpr<Parentheses<T>>(expr)}) {
1403	return AsFlatArrayConstructor(Expr<T>{p->left()});
1404	}
1405	return std::nullopt;
1406	}
1407
1408	template <TypeCategory CAT>
1409	std::enable_if_t<CAT != TypeCategory::Derived,
1410	std::optional<Expr<SomeKind<CAT>>>>
1411	AsFlatArrayConstructor(const Expr<SomeKind<CAT>> &expr) {
1412	return common::visit(
1413	[&](const auto &kindExpr) -> std::optional<Expr<SomeKind<CAT>>> {
1414	if (auto flattened{AsFlatArrayConstructor(kindExpr)}) {
1415	return Expr<SomeKind<CAT>>{std::move(*flattened)};
1416	} else {
1417	return std::nullopt;
1418	}
1419	},
1420	expr.u);
1421	}
1422
1423	// FromArrayConstructor is a subroutine for MapOperation() below.
1424	// Given a flat ArrayConstructor<T> and a shape, it wraps the array
1425	// into an Expr<T>, folds it, and returns the resulting wrapped
1426	// array constructor or constant array value.
1427	template <typename T>
1428	std::optional<Expr<T>> FromArrayConstructor(
1429	FoldingContext &context, ArrayConstructor<T> &&values, const Shape &shape) {
1430	if (auto constShape{AsConstantExtents(context, shape)};
1431	constShape && !HasNegativeExtent(*constShape)) {
1432	Expr<T> result{Fold(context, Expr<T>{std::move(values)})};
1433	if (auto *constant{UnwrapConstantValue<T>(result)}) {
1434	// Elements and shape are both constant.
1435	return Expr<T>{constant->Reshape(std::move(*constShape))};
1436	}
1437	if (constShape->size() == 1) {
1438	if (auto elements{GetShape(context, result)}) {
1439	if (auto constElements{AsConstantExtents(context, *elements)}) {
1440	if (constElements->size() == 1 &&
1441	constElements->at(0) == constShape->at(0)) {
1442	// Elements are not constant, but array constructor has
1443	// the right known shape and can be simply returned as is.
1444	return std::move(result);
1445	}
1446	}
1447	}
1448	}
1449	}
1450	return std::nullopt;
1451	}
1452
1453	// MapOperation is a utility for various specializations of ApplyElementwise()
1454	// that follow. Given one or two flat ArrayConstructor<OPERAND> (wrapped in an
1455	// Expr<OPERAND>) for some specific operand type(s), apply a given function f
1456	// to each of their corresponding elements to produce a flat
1457	// ArrayConstructor<RESULT> (wrapped in an Expr<RESULT>).
1458	// Preserves shape.
1459
1460	// Unary case
1461	template <typename RESULT, typename OPERAND>
1462	std::optional<Expr<RESULT>> MapOperation(FoldingContext &context,
1463	std::function<Expr<RESULT>(Expr<OPERAND> &&)> &&f, const Shape &shape,
1464	[[maybe_unused]] std::optional<Expr<SubscriptInteger>> &&length,
1465	Expr<OPERAND> &&values) {
1466	ArrayConstructor<RESULT> result{values};
1467	if constexpr (common::HasMember<OPERAND, AllIntrinsicCategoryTypes>) {
1468	common::visit(
1469	[&](auto &&kindExpr) {
1470	using kindType = ResultType<decltype(kindExpr)>;
1471	auto &aConst{std::get<ArrayConstructor<kindType>>(kindExpr.u)};
1472	for (auto &acValue : aConst) {
1473	auto &scalar{std::get<Expr<kindType>>(acValue.u)};
1474	result.Push(Fold(context, f(Expr<OPERAND>{std::move(scalar)})));
1475	}
1476	},
1477	std::move(values.u));
1478	} else {
1479	auto &aConst{std::get<ArrayConstructor<OPERAND>>(values.u)};
1480	for (auto &acValue : aConst) {
1481	auto &scalar{std::get<Expr<OPERAND>>(acValue.u)};
1482	result.Push(Fold(context, f(std::move(scalar))));
1483	}
1484	}
1485	if constexpr (RESULT::category == TypeCategory::Character) {
1486	if (length) {
1487	result.set_LEN(std::move(*length));
1488	}
1489	}
1490	return FromArrayConstructor(context, std::move(result), shape);
1491	}
1492
1493	template <typename RESULT, typename A>
1494	ArrayConstructor<RESULT> ArrayConstructorFromMold(
1495	const A &prototype, std::optional<Expr<SubscriptInteger>> &&length) {
1496	ArrayConstructor<RESULT> result{prototype};
1497	if constexpr (RESULT::category == TypeCategory::Character) {
1498	if (length) {
1499	result.set_LEN(std::move(*length));
1500	}
1501	}
1502	return result;
1503	}
1504
1505	template <typename LEFT, typename RIGHT>
1506	bool ShapesMatch(FoldingContext &context,
1507	const ArrayConstructor<LEFT> &leftArrConst,
1508	const ArrayConstructor<RIGHT> &rightArrConst) {
1509	auto rightIter{rightArrConst.begin()};
1510	for (auto &leftValue : leftArrConst) {
1511	CHECK(rightIter != rightArrConst.end());
1512	auto &leftExpr{std::get<Expr<LEFT>>(leftValue.u)};
1513	auto &rightExpr{std::get<Expr<RIGHT>>(rightIter->u)};
1514	if (leftExpr.Rank() != rightExpr.Rank()) {
1515	return false;
1516	}
1517	std::optional<Shape> leftShape{GetShape(context, leftExpr)};
1518	std::optional<Shape> rightShape{GetShape(context, rightExpr)};
1519	if (!leftShape || !rightShape || *leftShape != *rightShape) {
1520	return false;
1521	}
1522	++rightIter;
1523	}
1524	return true;
1525	}
1526
1527	// array * array case
1528	template <typename RESULT, typename LEFT, typename RIGHT>
1529	auto MapOperation(FoldingContext &context,
1530	std::function<Expr<RESULT>(Expr<LEFT> &&, Expr<RIGHT> &&)> &&f,
1531	const Shape &shape, std::optional<Expr<SubscriptInteger>> &&length,
1532	Expr<LEFT> &&leftValues, Expr<RIGHT> &&rightValues)
1533	-> std::optional<Expr<RESULT>> {
1534	auto result{ArrayConstructorFromMold<RESULT>(leftValues, std::move(length))};
1535	auto &leftArrConst{std::get<ArrayConstructor<LEFT>>(leftValues.u)};
1536	if constexpr (common::HasMember<RIGHT, AllIntrinsicCategoryTypes>) {
1537	bool mapped{common::visit(
1538	[&](auto &&kindExpr) -> bool {
1539	using kindType = ResultType<decltype(kindExpr)>;
1540
1541	auto &rightArrConst{std::get<ArrayConstructor<kindType>>(kindExpr.u)};
1542	if (!ShapesMatch(context, leftArrConst, rightArrConst)) {
1543	return false;
1544	}
1545	auto rightIter{rightArrConst.begin()};
1546	for (auto &leftValue : leftArrConst) {
1547	CHECK(rightIter != rightArrConst.end());
1548	auto &leftScalar{std::get<Expr<LEFT>>(leftValue.u)};
1549	auto &rightScalar{std::get<Expr<kindType>>(rightIter->u)};
1550	result.Push(Fold(context,
1551	f(std::move(leftScalar), Expr<RIGHT>{std::move(rightScalar)})));
1552	++rightIter;
1553	}
1554	return true;
1555	},
1556	std::move(rightValues.u))};
1557	if (!mapped) {
1558	return std::nullopt;
1559	}
1560	} else {
1561	auto &rightArrConst{std::get<ArrayConstructor<RIGHT>>(rightValues.u)};
1562	if (!ShapesMatch(context, leftArrConst, rightArrConst)) {
1563	return std::nullopt;
1564	}
1565	auto rightIter{rightArrConst.begin()};
1566	for (auto &leftValue : leftArrConst) {
1567	CHECK(rightIter != rightArrConst.end());
1568	auto &leftScalar{std::get<Expr<LEFT>>(leftValue.u)};
1569	auto &rightScalar{std::get<Expr<RIGHT>>(rightIter->u)};
1570	result.Push(
1571	Fold(context, f(std::move(leftScalar), std::move(rightScalar))));
1572	++rightIter;
1573	}
1574	}
1575	return FromArrayConstructor(context, std::move(result), shape);
1576	}
1577
1578	// array * scalar case
1579	template <typename RESULT, typename LEFT, typename RIGHT>
1580	auto MapOperation(FoldingContext &context,
1581	std::function<Expr<RESULT>(Expr<LEFT> &&, Expr<RIGHT> &&)> &&f,
1582	const Shape &shape, std::optional<Expr<SubscriptInteger>> &&length,
1583	Expr<LEFT> &&leftValues, const Expr<RIGHT> &rightScalar)
1584	-> std::optional<Expr<RESULT>> {
1585	auto result{ArrayConstructorFromMold<RESULT>(leftValues, std::move(length))};
1586	auto &leftArrConst{std::get<ArrayConstructor<LEFT>>(leftValues.u)};
1587	for (auto &leftValue : leftArrConst) {
1588	auto &leftScalar{std::get<Expr<LEFT>>(leftValue.u)};
1589	result.Push(
1590	Fold(context, f(std::move(leftScalar), Expr<RIGHT>{rightScalar})));
1591	}
1592	return FromArrayConstructor(context, std::move(result), shape);
1593	}
1594
1595	// scalar * array case
1596	template <typename RESULT, typename LEFT, typename RIGHT>
1597	auto MapOperation(FoldingContext &context,
1598	std::function<Expr<RESULT>(Expr<LEFT> &&, Expr<RIGHT> &&)> &&f,
1599	const Shape &shape, std::optional<Expr<SubscriptInteger>> &&length,
1600	const Expr<LEFT> &leftScalar, Expr<RIGHT> &&rightValues)
1601	-> std::optional<Expr<RESULT>> {
1602	auto result{ArrayConstructorFromMold<RESULT>(leftScalar, std::move(length))};
1603	if constexpr (common::HasMember<RIGHT, AllIntrinsicCategoryTypes>) {
1604	common::visit(
1605	[&](auto &&kindExpr) {
1606	using kindType = ResultType<decltype(kindExpr)>;
1607	auto &rightArrConst{std::get<ArrayConstructor<kindType>>(kindExpr.u)};
1608	for (auto &rightValue : rightArrConst) {
1609	auto &rightScalar{std::get<Expr<kindType>>(rightValue.u)};
1610	result.Push(Fold(context,
1611	f(Expr<LEFT>{leftScalar},
1612	Expr<RIGHT>{std::move(rightScalar)})));
1613	}
1614	},
1615	std::move(rightValues.u));
1616	} else {
1617	auto &rightArrConst{std::get<ArrayConstructor<RIGHT>>(rightValues.u)};
1618	for (auto &rightValue : rightArrConst) {
1619	auto &rightScalar{std::get<Expr<RIGHT>>(rightValue.u)};
1620	result.Push(
1621	Fold(context, f(Expr<LEFT>{leftScalar}, std::move(rightScalar))));
1622	}
1623	}
1624	return FromArrayConstructor(context, std::move(result), shape);
1625	}
1626
1627	template <typename DERIVED, typename RESULT, typename... OPD>
1628	std::optional<Expr<SubscriptInteger>> ComputeResultLength(
1629	Operation<DERIVED, RESULT, OPD...> &operation) {
1630	if constexpr (RESULT::category == TypeCategory::Character) {
1631	return Expr<RESULT>{operation.derived()}.LEN();
1632	}
1633	return std::nullopt;
1634	}
1635
1636	// ApplyElementwise() recursively folds the operand expression(s) of an
1637	// operation, then attempts to apply the operation to the (corresponding)
1638	// scalar element(s) of those operands. Returns std::nullopt for scalars
1639	// or unlinearizable operands.
1640	template <typename DERIVED, typename RESULT, typename OPERAND>
1641	auto ApplyElementwise(FoldingContext &context,
1642	Operation<DERIVED, RESULT, OPERAND> &operation,
1643	std::function<Expr<RESULT>(Expr<OPERAND> &&)> &&f)
1644	-> std::optional<Expr<RESULT>> {
1645	auto &expr{operation.left()};
1646	expr = Fold(context, std::move(expr));
1647	if (expr.Rank() > 0) {
1648	if (std::optional<Shape> shape{GetShape(context, expr)}) {
1649	if (auto values{AsFlatArrayConstructor(expr)}) {
1650	return MapOperation(context, std::move(f), *shape,
1651	ComputeResultLength(operation), std::move(*values));
1652	}
1653	}
1654	}
1655	return std::nullopt;
1656	}
1657
1658	template <typename DERIVED, typename RESULT, typename OPERAND>
1659	auto ApplyElementwise(
1660	FoldingContext &context, Operation<DERIVED, RESULT, OPERAND> &operation)
1661	-> std::optional<Expr<RESULT>> {
1662	return ApplyElementwise(context, operation,
1663	std::function<Expr<RESULT>(Expr<OPERAND> &&)>{
1664	[](Expr<OPERAND> &&operand) {
1665	return Expr<RESULT>{DERIVED{std::move(operand)}};
1666	}});
1667	}
1668
1669	template <typename DERIVED, typename RESULT, typename LEFT, typename RIGHT>
1670	auto ApplyElementwise(FoldingContext &context,
1671	Operation<DERIVED, RESULT, LEFT, RIGHT> &operation,
1672	std::function<Expr<RESULT>(Expr<LEFT> &&, Expr<RIGHT> &&)> &&f)
1673	-> std::optional<Expr<RESULT>> {
1674	auto resultLength{ComputeResultLength(operation)};
1675	auto &leftExpr{operation.left()};
1676	auto &rightExpr{operation.right()};
1677	if (leftExpr.Rank() != rightExpr.Rank() && leftExpr.Rank() != 0 &&
1678	rightExpr.Rank() != 0) {
1679	return std::nullopt; // error recovery
1680	}
1681	leftExpr = Fold(context, std::move(leftExpr));
1682	rightExpr = Fold(context, std::move(rightExpr));
1683	if (leftExpr.Rank() > 0) {
1684	if (std::optional<Shape> leftShape{GetShape(context, leftExpr)}) {
1685	if (auto left{AsFlatArrayConstructor(leftExpr)}) {
1686	if (rightExpr.Rank() > 0) {
1687	if (std::optional<Shape> rightShape{GetShape(context, rightExpr)}) {
1688	if (auto right{AsFlatArrayConstructor(rightExpr)}) {
1689	if (CheckConformance(context.messages(), *leftShape, *rightShape,
1690	CheckConformanceFlags::EitherScalarExpandable)
1691	.value_or(false /*fail if not known now to conform*/)) {
1692	return MapOperation(context, std::move(f), *leftShape,
1693	std::move(resultLength), std::move(*left),
1694	std::move(*right));
1695	} else {
1696	return std::nullopt;
1697	}
1698	return MapOperation(context, std::move(f), *leftShape,
1699	std::move(resultLength), std::move(*left), std::move(*right));
1700	}
1701	}
1702	} else if (IsExpandableScalar(rightExpr, context, *leftShape)) {
1703	return MapOperation(context, std::move(f), *leftShape,
1704	std::move(resultLength), std::move(*left), rightExpr);
1705	}
1706	}
1707	}
1708	} else if (rightExpr.Rank() > 0) {
1709	if (std::optional<Shape> rightShape{GetShape(context, rightExpr)}) {
1710	if (IsExpandableScalar(leftExpr, context, *rightShape)) {
1711	if (auto right{AsFlatArrayConstructor(rightExpr)}) {
1712	return MapOperation(context, std::move(f), *rightShape,
1713	std::move(resultLength), leftExpr, std::move(*right));
1714	}
1715	}
1716	}
1717	}
1718	return std::nullopt;
1719	}
1720
1721	template <typename DERIVED, typename RESULT, typename LEFT, typename RIGHT>
1722	auto ApplyElementwise(
1723	FoldingContext &context, Operation<DERIVED, RESULT, LEFT, RIGHT> &operation)
1724	-> std::optional<Expr<RESULT>> {
1725	return ApplyElementwise(context, operation,
1726	std::function<Expr<RESULT>(Expr<LEFT> &&, Expr<RIGHT> &&)>{
1727	[](Expr<LEFT> &&left, Expr<RIGHT> &&right) {
1728	return Expr<RESULT>{DERIVED{std::move(left), std::move(right)}};
1729	}});
1730	}
1731
1732	// Unary operations
1733
1734	template <typename TO, typename FROM>
1735	common::IfNoLvalue<std::optional<TO>, FROM> ConvertString(FROM &&s) {
1736	if constexpr (std::is_same_v<TO, FROM>) {
1737	return std::make_optional<TO>(std::move(s));
1738	} else {
1739	// Fortran character conversion is well defined between distinct kinds
1740	// only when the actual characters are valid 7-bit ASCII.
1741	TO str;
1742	for (auto iter{s.cbegin()}; iter != s.cend(); ++iter) {
1743	if (static_cast<std::uint64_t>(*iter) > 127) {
1744	return std::nullopt;
1745	}
1746	str.push_back(*iter);
1747	}
1748	return std::make_optional<TO>(std::move(str));
1749	}
1750	}
1751
1752	template <typename TO, TypeCategory FROMCAT>
1753	Expr<TO> FoldOperation(
1754	FoldingContext &context, Convert<TO, FROMCAT> &&convert) {
1755	if (auto array{ApplyElementwise(context, convert)}) {
1756	return *array;
1757	}
1758	struct {
1759	FoldingContext &context;
1760	Convert<TO, FROMCAT> &convert;
1761	} msvcWorkaround{context, convert};
1762	return common::visit(
1763	[&msvcWorkaround](auto &kindExpr) -> Expr<TO> {
1764	using Operand = ResultType<decltype(kindExpr)>;
1765	// This variable is a workaround for msvc which emits an error when
1766	// using the FROMCAT template parameter below.
1767	TypeCategory constexpr FromCat{FROMCAT};
1768	static_assert(FromCat == Operand::category);
1769	auto &convert{msvcWorkaround.convert};
1770	if (auto value{GetScalarConstantValue<Operand>(kindExpr)}) {
1771	FoldingContext &ctx{msvcWorkaround.context};
1772	if constexpr (TO::category == TypeCategory::Integer) {
1773	if constexpr (FromCat == TypeCategory::Integer) {
1774	auto converted{Scalar<TO>::ConvertSigned(*value)};
1775	if (converted.overflow &&
1776	msvcWorkaround.context.languageFeatures().ShouldWarn(
1777	common::UsageWarning::FoldingException)) {
1778	ctx.messages().Say(common::UsageWarning::FoldingException,
1779	"conversion of %s_%d to INTEGER(%d) overflowed; result is %s"_warn_en_US,
1780	value->SignedDecimal(), Operand::kind, TO::kind,
1781	converted.value.SignedDecimal());
1782	}
1783	return ScalarConstantToExpr(std::move(converted.value));
1784	} else if constexpr (FromCat == TypeCategory::Unsigned) {
1785	auto converted{Scalar<TO>::ConvertUnsigned(*value)};
1786	if ((converted.overflow || converted.value.IsNegative()) &&
1787	msvcWorkaround.context.languageFeatures().ShouldWarn(
1788	common::UsageWarning::FoldingException)) {
1789	ctx.messages().Say(common::UsageWarning::FoldingException,
1790	"conversion of %s_U%d to INTEGER(%d) overflowed; result is %s"_warn_en_US,
1791	value->UnsignedDecimal(), Operand::kind, TO::kind,
1792	converted.value.SignedDecimal());
1793	}
1794	return ScalarConstantToExpr(std::move(converted.value));
1795	} else if constexpr (FromCat == TypeCategory::Real) {
1796	auto converted{value->template ToInteger<Scalar<TO>>()};
1797	if (msvcWorkaround.context.languageFeatures().ShouldWarn(
1798	common::UsageWarning::FoldingException)) {
1799	if (converted.flags.test(RealFlag::InvalidArgument)) {
1800	ctx.messages().Say(common::UsageWarning::FoldingException,
1801	"REAL(%d) to INTEGER(%d) conversion: invalid argument"_warn_en_US,
1802	Operand::kind, TO::kind);
1803	} else if (converted.flags.test(RealFlag::Overflow)) {
1804	ctx.messages().Say(
1805	"REAL(%d) to INTEGER(%d) conversion overflowed"_warn_en_US,
1806	Operand::kind, TO::kind);
1807	}
1808	}
1809	return ScalarConstantToExpr(std::move(converted.value));
1810	}
1811	} else if constexpr (TO::category == TypeCategory::Unsigned) {
1812	if constexpr (FromCat == TypeCategory::Integer ||
1813	FromCat == TypeCategory::Unsigned) {
1814	return Expr<TO>{
1815	Constant<TO>{Scalar<TO>::ConvertUnsigned(*value).value}};
1816	} else if constexpr (FromCat == TypeCategory::Real) {
1817	return Expr<TO>{
1818	Constant<TO>{value->template ToInteger<Scalar<TO>>().value}};
1819	}
1820	} else if constexpr (TO::category == TypeCategory::Real) {
1821	if constexpr (FromCat == TypeCategory::Integer ||
1822	FromCat == TypeCategory::Unsigned) {
1823	auto converted{Scalar<TO>::FromInteger(
1824	*value, FromCat == TypeCategory::Unsigned)};
1825	if (!converted.flags.empty()) {
1826	char buffer[64];
1827	std::snprintf(buffer, sizeof buffer,
1828	"INTEGER(%d) to REAL(%d) conversion", Operand::kind,
1829	TO::kind);
1830	RealFlagWarnings(ctx, converted.flags, buffer);
1831	}
1832	return ScalarConstantToExpr(std::move(converted.value));
1833	} else if constexpr (FromCat == TypeCategory::Real) {
1834	auto converted{Scalar<TO>::Convert(*value)};
1835	char buffer[64];
1836	if (!converted.flags.empty()) {
1837	std::snprintf(buffer, sizeof buffer,
1838	"REAL(%d) to REAL(%d) conversion", Operand::kind, TO::kind);
1839	RealFlagWarnings(ctx, converted.flags, buffer);
1840	}
1841	if (ctx.targetCharacteristics().areSubnormalsFlushedToZero()) {
1842	converted.value = converted.value.FlushSubnormalToZero();
1843	}
1844	return ScalarConstantToExpr(std::move(converted.value));
1845	}
1846	} else if constexpr (TO::category == TypeCategory::Complex) {
1847	if constexpr (FromCat == TypeCategory::Complex) {
1848	return FoldOperation(ctx,
1849	ComplexConstructor<TO::kind>{
1850	AsExpr(Convert<typename TO::Part>{AsCategoryExpr(
1851	Constant<typename Operand::Part>{value->REAL()})}),
1852	AsExpr(Convert<typename TO::Part>{AsCategoryExpr(
1853	Constant<typename Operand::Part>{value->AIMAG()})})});
1854	}
1855	} else if constexpr (TO::category == TypeCategory::Character &&
1856	FromCat == TypeCategory::Character) {
1857	if (auto converted{ConvertString<Scalar<TO>>(std::move(*value))}) {
1858	return ScalarConstantToExpr(std::move(*converted));
1859	}
1860	} else if constexpr (TO::category == TypeCategory::Logical &&
1861	FromCat == TypeCategory::Logical) {
1862	return Expr<TO>{value->IsTrue()};
1863	}
1864	} else if constexpr (TO::category == FromCat &&
1865	FromCat != TypeCategory::Character) {
1866	// Conversion of non-constant in same type category
1867	if constexpr (std::is_same_v<Operand, TO>) {
1868	return std::move(kindExpr); // remove needless conversion
1869	} else if constexpr (TO::category == TypeCategory::Logical ||
1870	TO::category == TypeCategory::Integer) {
1871	if (auto *innerConv{
1872	std::get_if<Convert<Operand, TO::category>>(&kindExpr.u)}) {
1873	// Conversion of conversion of same category & kind
1874	if (auto *x{std::get_if<Expr<TO>>(&innerConv->left().u)}) {
1875	if constexpr (TO::category == TypeCategory::Logical ||
1876	TO::kind <= Operand::kind) {
1877	return std::move(*x); // no-op Logical or Integer
1878	// widening/narrowing conversion pair
1879	} else if constexpr (std::is_same_v<TO,
1880	DescriptorInquiry::Result>) {
1881	if (std::holds_alternative<DescriptorInquiry>(x->u) ||
1882	std::holds_alternative<TypeParamInquiry>(x->u)) {
1883	// int(int(size(...),kind=k),kind=8) -> size(...)
1884	return std::move(*x);
1885	}
1886	}
1887	}
1888	}
1889	}
1890	}
1891	return Expr<TO>{std::move(convert)};
1892	},
1893	convert.left().u);
1894	}
1895
1896	template <typename T>
1897	Expr<T> FoldOperation(FoldingContext &context, Parentheses<T> &&x) {
1898	auto &operand{x.left()};
1899	operand = Fold(context, std::move(operand));
1900	if (auto value{GetScalarConstantValue<T>(operand)}) {
1901	// Preserve parentheses, even around constants.
1902	return Expr<T>{Parentheses<T>{Expr<T>{Constant<T>{*value}}}};
1903	} else if (std::holds_alternative<Parentheses<T>>(operand.u)) {
1904	// ((x)) -> (x)
1905	return std::move(operand);
1906	} else {
1907	return Expr<T>{Parentheses<T>{std::move(operand)}};
1908	}
1909	}
1910
1911	template <typename T>
1912	Expr<T> FoldOperation(FoldingContext &context, Negate<T> &&x) {
1913	if (auto array{ApplyElementwise(context, x)}) {
1914	return *array;
1915	}
1916	auto &operand{x.left()};
1917	if (auto *nn{std::get_if<Negate<T>>(&x.left().u)}) {
1918	// -(-x) -> (x)
1919	if (IsVariable(nn->left())) {
1920	return FoldOperation(context, Parentheses<T>{std::move(nn->left())});
1921	} else {
1922	return std::move(nn->left());
1923	}
1924	} else if (auto value{GetScalarConstantValue<T>(operand)}) {
1925	if constexpr (T::category == TypeCategory::Integer) {
1926	auto negated{value->Negate()};
1927	if (negated.overflow &&
1928	context.languageFeatures().ShouldWarn(
1929	common::UsageWarning::FoldingException)) {
1930	context.messages().Say(common::UsageWarning::FoldingException,
1931	"INTEGER(%d) negation overflowed"_warn_en_US, T::kind);
1932	}
1933	return Expr<T>{Constant<T>{std::move(negated.value)}};
1934	} else if constexpr (T::category == TypeCategory::Unsigned) {
1935	return Expr<T>{Constant<T>{std::move(value->Negate().value)}};
1936	} else {
1937	// REAL & COMPLEX negation: no exceptions possible
1938	return Expr<T>{Constant<T>{value->Negate()}};
1939	}
1940	}
1941	return Expr<T>{std::move(x)};
1942	}
1943
1944	// Binary (dyadic) operations
1945
1946	template <typename LEFT, typename RIGHT>
1947	std::optional<std::pair<Scalar<LEFT>, Scalar<RIGHT>>> OperandsAreConstants(
1948	const Expr<LEFT> &x, const Expr<RIGHT> &y) {
1949	if (auto xvalue{GetScalarConstantValue<LEFT>(x)}) {
1950	if (auto yvalue{GetScalarConstantValue<RIGHT>(y)}) {
1951	return {std::make_pair(*xvalue, *yvalue)};
1952	}
1953	}
1954	return std::nullopt;
1955	}
1956
1957	template <typename DERIVED, typename RESULT, typename LEFT, typename RIGHT>
1958	std::optional<std::pair<Scalar<LEFT>, Scalar<RIGHT>>> OperandsAreConstants(
1959	const Operation<DERIVED, RESULT, LEFT, RIGHT> &operation) {
1960	return OperandsAreConstants(operation.left(), operation.right());
1961	}
1962
1963	template <typename T>
1964	Expr<T> FoldOperation(FoldingContext &context, Add<T> &&x) {
1965	if (auto array{ApplyElementwise(context, x)}) {
1966	return *array;
1967	}
1968	if (auto folded{OperandsAreConstants(x)}) {
1969	if constexpr (T::category == TypeCategory::Integer) {
1970	auto sum{folded->first.AddSigned(folded->second)};
1971	if (sum.overflow &&
1972	context.languageFeatures().ShouldWarn(
1973	common::UsageWarning::FoldingException)) {
1974	context.messages().Say(common::UsageWarning::FoldingException,
1975	"INTEGER(%d) addition overflowed"_warn_en_US, T::kind);
1976	}
1977	return Expr<T>{Constant<T>{sum.value}};
1978	} else if constexpr (T::category == TypeCategory::Unsigned) {
1979	return Expr<T>{
1980	Constant<T>{folded->first.AddUnsigned(folded->second).value}};
1981	} else {
1982	auto sum{folded->first.Add(
1983	folded->second, context.targetCharacteristics().roundingMode())};
1984	RealFlagWarnings(context, sum.flags, "addition");
1985	if (context.targetCharacteristics().areSubnormalsFlushedToZero()) {
1986	sum.value = sum.value.FlushSubnormalToZero();
1987	}
1988	return Expr<T>{Constant<T>{sum.value}};
1989	}
1990	}
1991	return Expr<T>{std::move(x)};
1992	}
1993
1994	template <typename T>
1995	Expr<T> FoldOperation(FoldingContext &context, Subtract<T> &&x) {
1996	if (auto array{ApplyElementwise(context, x)}) {
1997	return *array;
1998	}
1999	if (auto folded{OperandsAreConstants(x)}) {
2000	if constexpr (T::category == TypeCategory::Integer) {
2001	auto difference{folded->first.SubtractSigned(folded->second)};
2002	if (difference.overflow &&
2003	context.languageFeatures().ShouldWarn(
2004	common::UsageWarning::FoldingException)) {
2005	context.messages().Say(common::UsageWarning::FoldingException,
2006	"INTEGER(%d) subtraction overflowed"_warn_en_US, T::kind);
2007	}
2008	return Expr<T>{Constant<T>{difference.value}};
2009	} else if constexpr (T::category == TypeCategory::Unsigned) {
2010	return Expr<T>{
2011	Constant<T>{folded->first.SubtractSigned(folded->second).value}};
2012	} else {
2013	auto difference{folded->first.Subtract(
2014	folded->second, context.targetCharacteristics().roundingMode())};
2015	RealFlagWarnings(context, difference.flags, "subtraction");
2016	if (context.targetCharacteristics().areSubnormalsFlushedToZero()) {
2017	difference.value = difference.value.FlushSubnormalToZero();
2018	}
2019	return Expr<T>{Constant<T>{difference.value}};
2020	}
2021	}
2022	return Expr<T>{std::move(x)};
2023	}
2024
2025	template <typename T>
2026	Expr<T> FoldOperation(FoldingContext &context, Multiply<T> &&x) {
2027	if (auto array{ApplyElementwise(context, x)}) {
2028	return *array;
2029	}
2030	if (auto folded{OperandsAreConstants(x)}) {
2031	if constexpr (T::category == TypeCategory::Integer) {
2032	auto product{folded->first.MultiplySigned(folded->second)};
2033	if (product.SignedMultiplicationOverflowed() &&
2034	context.languageFeatures().ShouldWarn(
2035	common::UsageWarning::FoldingException)) {
2036	context.messages().Say(common::UsageWarning::FoldingException,
2037	"INTEGER(%d) multiplication overflowed"_warn_en_US, T::kind);
2038	}
2039	return Expr<T>{Constant<T>{product.lower}};
2040	} else if constexpr (T::category == TypeCategory::Unsigned) {
2041	return Expr<T>{
2042	Constant<T>{folded->first.MultiplyUnsigned(folded->second).lower}};
2043	} else {
2044	auto product{folded->first.Multiply(
2045	folded->second, context.targetCharacteristics().roundingMode())};
2046	RealFlagWarnings(context, product.flags, "multiplication");
2047	if (context.targetCharacteristics().areSubnormalsFlushedToZero()) {
2048	product.value = product.value.FlushSubnormalToZero();
2049	}
2050	return Expr<T>{Constant<T>{product.value}};
2051	}
2052	} else if constexpr (T::category == TypeCategory::Integer) {
2053	if (auto c{GetScalarConstantValue<T>(x.right())}) {
2054	x.right() = std::move(x.left());
2055	x.left() = Expr<T>{std::move(*c)};
2056	}
2057	if (auto c{GetScalarConstantValue<T>(x.left())}) {
2058	if (c->IsZero() && x.right().Rank() == 0) {
2059	return std::move(x.left());
2060	} else if (c->CompareSigned(Scalar<T>{1}) == Ordering::Equal) {
2061	if (IsVariable(x.right())) {
2062	return FoldOperation(context, Parentheses<T>{std::move(x.right())});
2063	} else {
2064	return std::move(x.right());
2065	}
2066	} else if (c->CompareSigned(Scalar<T>{-1}) == Ordering::Equal) {
2067	return FoldOperation(context, Negate<T>{std::move(x.right())});
2068	}
2069	}
2070	}
2071	return Expr<T>{std::move(x)};
2072	}
2073
2074	template <typename T>
2075	Expr<T> FoldOperation(FoldingContext &context, Divide<T> &&x) {
2076	if (auto array{ApplyElementwise(context, x)}) {
2077	return *array;
2078	}
2079	if (auto folded{OperandsAreConstants(x)}) {
2080	if constexpr (T::category == TypeCategory::Integer) {
2081	auto quotAndRem{folded->first.DivideSigned(folded->second)};
2082	if (quotAndRem.divisionByZero) {
2083	if (context.languageFeatures().ShouldWarn(
2084	common::UsageWarning::FoldingException)) {
2085	context.messages().Say(common::UsageWarning::FoldingException,
2086	"INTEGER(%d) division by zero"_warn_en_US, T::kind);
2087	}
2088	return Expr<T>{std::move(x)};
2089	}
2090	if (quotAndRem.overflow &&
2091	context.languageFeatures().ShouldWarn(
2092	common::UsageWarning::FoldingException)) {
2093	context.messages().Say(common::UsageWarning::FoldingException,
2094	"INTEGER(%d) division overflowed"_warn_en_US, T::kind);
2095	}
2096	return Expr<T>{Constant<T>{quotAndRem.quotient}};
2097	} else if constexpr (T::category == TypeCategory::Unsigned) {
2098	auto quotAndRem{folded->first.DivideUnsigned(folded->second)};
2099	if (quotAndRem.divisionByZero) {
2100	if (context.languageFeatures().ShouldWarn(
2101	common::UsageWarning::FoldingException)) {
2102	context.messages().Say(common::UsageWarning::FoldingException,
2103	"UNSIGNED(%d) division by zero"_warn_en_US, T::kind);
2104	}
2105	return Expr<T>{std::move(x)};
2106	}
2107	return Expr<T>{Constant<T>{quotAndRem.quotient}};
2108	} else {
2109	auto quotient{folded->first.Divide(
2110	folded->second, context.targetCharacteristics().roundingMode())};
2111	// Don't warn about -1./0., 0./0., or 1./0. from a module file
2112	// they are interpreted as canonical Fortran representations of -Inf,
2113	// NaN, and Inf respectively.
2114	bool isCanonicalNaNOrInf{false};
2115	if constexpr (T::category == TypeCategory::Real) {
2116	if (folded->second.IsZero() && context.moduleFileName().has_value()) {
2117	using IntType = typename T::Scalar::Word;
2118	auto intNumerator{folded->first.template ToInteger<IntType>()};
2119	isCanonicalNaNOrInf = intNumerator.flags == RealFlags{} &&
2120	intNumerator.value >= IntType{-1} &&
2121	intNumerator.value <= IntType{1};
2122	}
2123	}
2124	if (!isCanonicalNaNOrInf) {
2125	RealFlagWarnings(context, quotient.flags, "division");
2126	}
2127	if (context.targetCharacteristics().areSubnormalsFlushedToZero()) {
2128	quotient.value = quotient.value.FlushSubnormalToZero();
2129	}
2130	return Expr<T>{Constant<T>{quotient.value}};
2131	}
2132	}
2133	return Expr<T>{std::move(x)};
2134	}
2135
2136	template <typename T>
2137	Expr<T> FoldOperation(FoldingContext &context, Power<T> &&x) {
2138	if (auto array{ApplyElementwise(context, x)}) {
2139	return *array;
2140	}
2141	if (auto folded{OperandsAreConstants(x)}) {
2142	if constexpr (T::category == TypeCategory::Integer) {
2143	auto power{folded->first.Power(folded->second)};
2144	if (context.languageFeatures().ShouldWarn(
2145	common::UsageWarning::FoldingException)) {
2146	if (power.divisionByZero) {
2147	context.messages().Say(common::UsageWarning::FoldingException,
2148	"INTEGER(%d) zero to negative power"_warn_en_US, T::kind);
2149	} else if (power.overflow) {
2150	context.messages().Say(common::UsageWarning::FoldingException,
2151	"INTEGER(%d) power overflowed"_warn_en_US, T::kind);
2152	} else if (power.zeroToZero) {
2153	context.messages().Say(common::UsageWarning::FoldingException,
2154	"INTEGER(%d) 0**0 is not defined"_warn_en_US, T::kind);
2155	}
2156	}
2157	return Expr<T>{Constant<T>{power.power}};
2158	} else {
2159	if (auto callable{GetHostRuntimeWrapper<T, T, T>("pow")}) {
2160	return Expr<T>{
2161	Constant<T>{(*callable)(context, folded->first, folded->second)}};
2162	} else if (context.languageFeatures().ShouldWarn(
2163	common::UsageWarning::FoldingFailure)) {
2164	context.messages().Say(common::UsageWarning::FoldingFailure,
2165	"Power for %s cannot be folded on host"_warn_en_US,
2166	T{}.AsFortran());
2167	}
2168	}
2169	}
2170	return Expr<T>{std::move(x)};
2171	}
2172
2173	template <typename T>
2174	Expr<T> FoldOperation(FoldingContext &context, RealToIntPower<T> &&x) {
2175	if (auto array{ApplyElementwise(context, x)}) {
2176	return *array;
2177	}
2178	return common::visit(
2179	[&](auto &y) -> Expr<T> {
2180	if (auto folded{OperandsAreConstants(x.left(), y)}) {
2181	auto power{evaluate::IntPower(folded->first, folded->second)};
2182	RealFlagWarnings(context, power.flags, "power with INTEGER exponent");
2183	if (context.targetCharacteristics().areSubnormalsFlushedToZero()) {
2184	power.value = power.value.FlushSubnormalToZero();
2185	}
2186	return Expr<T>{Constant<T>{power.value}};
2187	} else {
2188	return Expr<T>{std::move(x)};
2189	}
2190	},
2191	x.right().u);
2192	}
2193
2194	template <typename T>
2195	Expr<T> FoldOperation(FoldingContext &context, Extremum<T> &&x) {
2196	if (auto array{ApplyElementwise(context, x,
2197	std::function<Expr<T>(Expr<T> &&, Expr<T> &&)>{[=](Expr<T> &&l,
2198	Expr<T> &&r) {
2199	return Expr<T>{Extremum<T>{x.ordering, std::move(l), std::move(r)}};
2200	}})}) {
2201	return *array;
2202	}
2203	if (auto folded{OperandsAreConstants(x)}) {
2204	if constexpr (T::category == TypeCategory::Integer) {
2205	if (folded->first.CompareSigned(folded->second) == x.ordering) {
2206	return Expr<T>{Constant<T>{folded->first}};
2207	}
2208	} else if constexpr (T::category == TypeCategory::Unsigned) {
2209	if (folded->first.CompareUnsigned(folded->second) == x.ordering) {
2210	return Expr<T>{Constant<T>{folded->first}};
2211	}
2212	} else if constexpr (T::category == TypeCategory::Real) {
2213	if (folded->first.IsNotANumber() ||
2214	(folded->first.Compare(folded->second) == Relation::Less) ==
2215	(x.ordering == Ordering::Less)) {
2216	return Expr<T>{Constant<T>{folded->first}};
2217	}
2218	} else {
2219	static_assert(T::category == TypeCategory::Character);
2220	// Result of MIN and MAX on character has the length of
2221	// the longest argument.
2222	auto maxLen{std::max(folded->first.length(), folded->second.length())};
2223	bool isFirst{x.ordering == Compare(folded->first, folded->second)};
2224	auto res{isFirst ? std::move(folded->first) : std::move(folded->second)};
2225	res = res.length() == maxLen
2226	? std::move(res)
2227	: CharacterUtils<T::kind>::Resize(res, maxLen);
2228	return Expr<T>{Constant<T>{std::move(res)}};
2229	}
2230	return Expr<T>{Constant<T>{folded->second}};
2231	}
2232	return Expr<T>{std::move(x)};
2233	}
2234
2235	template <int KIND>
2236	Expr<Type<TypeCategory::Real, KIND>> ToReal(
2237	FoldingContext &context, Expr<SomeType> &&expr) {
2238	using Result = Type<TypeCategory::Real, KIND>;
2239	std::optional<Expr<Result>> result;
2240	common::visit(
2241	[&](auto &&x) {
2242	using From = std::decay_t<decltype(x)>;
2243	if constexpr (std::is_same_v<From, BOZLiteralConstant>) {
2244	// Move the bits without any integer->real conversion
2245	From original{x};
2246	result = ConvertToType<Result>(std::move(x));
2247	const auto *constant{UnwrapExpr<Constant<Result>>(*result)};
2248	CHECK(constant);
2249	Scalar<Result> real{constant->GetScalarValue().value()};
2250	From converted{From::ConvertUnsigned(real.RawBits()).value};
2251	if (original != converted &&
2252	context.languageFeatures().ShouldWarn(
2253	common::UsageWarning::FoldingValueChecks)) { // C1601
2254	context.messages().Say(common::UsageWarning::FoldingValueChecks,
2255	"Nonzero bits truncated from BOZ literal constant in REAL intrinsic"_warn_en_US);
2256	}
2257	} else if constexpr (IsNumericCategoryExpr<From>()) {
2258	result = Fold(context, ConvertToType<Result>(std::move(x)));
2259	} else {
2260	common::die("ToReal: bad argument expression");
2261	}
2262	},
2263	std::move(expr.u));
2264	return result.value();
2265	}
2266
2267	// REAL(z) and AIMAG(z)
2268	template <int KIND>
2269	Expr<Type<TypeCategory::Real, KIND>> FoldOperation(
2270	FoldingContext &context, ComplexComponent<KIND> &&x) {
2271	using Operand = Type<TypeCategory::Complex, KIND>;
2272	using Result = Type<TypeCategory::Real, KIND>;
2273	if (auto array{ApplyElementwise(context, x,
2274	std::function<Expr<Result>(Expr<Operand> &&)>{
2275	[=](Expr<Operand> &&operand) {
2276	return Expr<Result>{ComplexComponent<KIND>{
2277	x.isImaginaryPart, std::move(operand)}};
2278	}})}) {
2279	return *array;
2280	}
2281	auto &operand{x.left()};
2282	if (auto value{GetScalarConstantValue<Operand>(operand)}) {
2283	if (x.isImaginaryPart) {
2284	return Expr<Result>{Constant<Result>{value->AIMAG()}};
2285	} else {
2286	return Expr<Result>{Constant<Result>{value->REAL()}};
2287	}
2288	}
2289	return Expr<Result>{std::move(x)};
2290	}
2291
2292	template <typename T>
2293	Expr<T> ExpressionBase<T>::Rewrite(FoldingContext &context, Expr<T> &&expr) {
2294	return common::visit(
2295	[&](auto &&x) -> Expr<T> {
2296	if constexpr (IsSpecificIntrinsicType<T>) {
2297	return FoldOperation(context, std::move(x));
2298	} else if constexpr (std::is_same_v<T, SomeDerived>) {
2299	return FoldOperation(context, std::move(x));
2300	} else if constexpr (common::HasMember<decltype(x),
2301	TypelessExpression>) {
2302	return std::move(expr);
2303	} else {
2304	return Expr<T>{Fold(context, std::move(x))};
2305	}
2306	},
2307	std::move(expr.u));
2308	}
2309
2310	FOR_EACH_TYPE_AND_KIND(extern template class ExpressionBase, )
2311	} // namespace Fortran::evaluate
2312	#endif // FORTRAN_EVALUATE_FOLD_IMPLEMENTATION_H_
2313