1 //===-- lib/Evaluate/fold-integer.cpp -------------------------------------===//
2 //
3 // Part of the LLVM Project, under the Apache License v2.0 with LLVM Exceptions.
4 // See https://llvm.org/LICENSE.txt for license information.
5 // SPDX-License-Identifier: Apache-2.0 WITH LLVM-exception
6 //
7 //===----------------------------------------------------------------------===//
8 
9 #include "fold-implementation.h"
10 #include "fold-reduction.h"
11 #include "flang/Evaluate/check-expression.h"
12 
13 namespace Fortran::evaluate {
14 
15 // Class to retrieve the constant lower bound of an expression which is an
16 // array that devolves to a type of Constant<T>
17 class GetConstantArrayLboundHelper {
18 public:
19   GetConstantArrayLboundHelper(ConstantSubscript dim) : dim_{dim} {}
20 
21   template <typename T> ConstantSubscript GetLbound(const T &) {
22     // The method is needed for template expansion, but we should never get
23     // here in practice.
24     CHECK(false);
25     return 0;
26   }
27 
28   template <typename T> ConstantSubscript GetLbound(const Constant<T> &x) {
29     // Return the lower bound
30     return x.lbounds()[dim_];
31   }
32 
33   template <typename T> ConstantSubscript GetLbound(const Parentheses<T> &x) {
34     // Strip off the parentheses
35     return GetLbound(x.left());
36   }
37 
38   template <typename T> ConstantSubscript GetLbound(const Expr<T> &x) {
39     // recurse through Expr<T>'a until we hit a constant
40     return std::visit([&](const auto &inner) { return GetLbound(inner); },
41         //      [&](const auto &) { return 0; },
42         x.u);
43   }
44 
45 private:
46   ConstantSubscript dim_;
47 };
48 
49 template <int KIND>
50 Expr<Type<TypeCategory::Integer, KIND>> LBOUND(FoldingContext &context,
51     FunctionRef<Type<TypeCategory::Integer, KIND>> &&funcRef) {
52   using T = Type<TypeCategory::Integer, KIND>;
53   ActualArguments &args{funcRef.arguments()};
54   if (const auto *array{UnwrapExpr<Expr<SomeType>>(args[0])}) {
55     if (int rank{array->Rank()}; rank > 0) {
56       std::optional<int> dim;
57       if (funcRef.Rank() == 0) {
58         // Optional DIM= argument is present: result is scalar.
59         if (auto dim64{GetInt64Arg(args[1])}) {
60           if (*dim64 < 1 || *dim64 > rank) {
61             context.messages().Say("DIM=%jd dimension is out of range for "
62                                    "rank-%d array"_err_en_US,
63                 *dim64, rank);
64             return MakeInvalidIntrinsic<T>(std::move(funcRef));
65           } else {
66             dim = *dim64 - 1; // 1-based to 0-based
67           }
68         } else {
69           // DIM= is present but not constant
70           return Expr<T>{std::move(funcRef)};
71         }
72       }
73       bool lowerBoundsAreOne{true};
74       if (auto named{ExtractNamedEntity(*array)}) {
75         const Symbol &symbol{named->GetLastSymbol()};
76         if (symbol.Rank() == rank) {
77           lowerBoundsAreOne = false;
78           if (dim) {
79             return Fold(context,
80                 ConvertToType<T>(GetLowerBound(context, *named, *dim)));
81           } else if (auto extents{
82                          AsExtentArrayExpr(GetLowerBounds(context, *named))}) {
83             return Fold(context,
84                 ConvertToType<T>(Expr<ExtentType>{std::move(*extents)}));
85           }
86         } else {
87           lowerBoundsAreOne = symbol.Rank() == 0; // LBOUND(array%component)
88         }
89       }
90       if (IsActuallyConstant(*array)) {
91         return Expr<T>{GetConstantArrayLboundHelper{*dim}.GetLbound(*array)};
92       }
93       if (lowerBoundsAreOne) {
94         if (dim) {
95           return Expr<T>{1};
96         } else {
97           std::vector<Scalar<T>> ones(rank, Scalar<T>{1});
98           return Expr<T>{
99               Constant<T>{std::move(ones), ConstantSubscripts{rank}}};
100         }
101       }
102     }
103   }
104   return Expr<T>{std::move(funcRef)};
105 }
106 
107 template <int KIND>
108 Expr<Type<TypeCategory::Integer, KIND>> UBOUND(FoldingContext &context,
109     FunctionRef<Type<TypeCategory::Integer, KIND>> &&funcRef) {
110   using T = Type<TypeCategory::Integer, KIND>;
111   ActualArguments &args{funcRef.arguments()};
112   if (auto *array{UnwrapExpr<Expr<SomeType>>(args[0])}) {
113     if (int rank{array->Rank()}; rank > 0) {
114       std::optional<int> dim;
115       if (funcRef.Rank() == 0) {
116         // Optional DIM= argument is present: result is scalar.
117         if (auto dim64{GetInt64Arg(args[1])}) {
118           if (*dim64 < 1 || *dim64 > rank) {
119             context.messages().Say("DIM=%jd dimension is out of range for "
120                                    "rank-%d array"_err_en_US,
121                 *dim64, rank);
122             return MakeInvalidIntrinsic<T>(std::move(funcRef));
123           } else {
124             dim = *dim64 - 1; // 1-based to 0-based
125           }
126         } else {
127           // DIM= is present but not constant
128           return Expr<T>{std::move(funcRef)};
129         }
130       }
131       bool takeBoundsFromShape{true};
132       if (auto named{ExtractNamedEntity(*array)}) {
133         const Symbol &symbol{named->GetLastSymbol()};
134         if (symbol.Rank() == rank) {
135           takeBoundsFromShape = false;
136           if (dim) {
137             if (semantics::IsAssumedSizeArray(symbol) && *dim == rank - 1) {
138               context.messages().Say("DIM=%jd dimension is out of range for "
139                                      "rank-%d assumed-size array"_err_en_US,
140                   rank, rank);
141               return MakeInvalidIntrinsic<T>(std::move(funcRef));
142             } else if (auto ub{GetUpperBound(context, *named, *dim)}) {
143               return Fold(context, ConvertToType<T>(std::move(*ub)));
144             }
145           } else {
146             Shape ubounds{GetUpperBounds(context, *named)};
147             if (semantics::IsAssumedSizeArray(symbol)) {
148               CHECK(!ubounds.back());
149               ubounds.back() = ExtentExpr{-1};
150             }
151             if (auto extents{AsExtentArrayExpr(ubounds)}) {
152               return Fold(context,
153                   ConvertToType<T>(Expr<ExtentType>{std::move(*extents)}));
154             }
155           }
156         } else {
157           takeBoundsFromShape = symbol.Rank() == 0; // UBOUND(array%component)
158         }
159       }
160       if (takeBoundsFromShape) {
161         if (auto shape{GetShape(context, *array)}) {
162           if (dim) {
163             if (auto &dimSize{shape->at(*dim)}) {
164               return Fold(context,
165                   ConvertToType<T>(Expr<ExtentType>{std::move(*dimSize)}));
166             }
167           } else if (auto shapeExpr{AsExtentArrayExpr(*shape)}) {
168             return Fold(context, ConvertToType<T>(std::move(*shapeExpr)));
169           }
170         }
171       }
172     }
173   }
174   return Expr<T>{std::move(funcRef)};
175 }
176 
177 // COUNT()
178 template <typename T>
179 static Expr<T> FoldCount(FoldingContext &context, FunctionRef<T> &&ref) {
180   static_assert(T::category == TypeCategory::Integer);
181   ActualArguments &arg{ref.arguments()};
182   if (const Constant<LogicalResult> *mask{arg.empty()
183               ? nullptr
184               : Folder<LogicalResult>{context}.Folding(arg[0])}) {
185     std::optional<int> dim;
186     if (CheckReductionDIM(dim, context, arg, 1, mask->Rank())) {
187       auto accumulator{[&](Scalar<T> &element, const ConstantSubscripts &at) {
188         if (mask->At(at).IsTrue()) {
189           element = element.AddSigned(Scalar<T>{1}).value;
190         }
191       }};
192       return Expr<T>{DoReduction<T>(*mask, dim, Scalar<T>{}, accumulator)};
193     }
194   }
195   return Expr<T>{std::move(ref)};
196 }
197 
198 // FINDLOC(), MAXLOC(), & MINLOC()
199 enum class WhichLocation { Findloc, Maxloc, Minloc };
200 template <WhichLocation WHICH> class LocationHelper {
201 public:
202   LocationHelper(
203       DynamicType &&type, ActualArguments &arg, FoldingContext &context)
204       : type_{type}, arg_{arg}, context_{context} {}
205   using Result = std::optional<Constant<SubscriptInteger>>;
206   using Types = std::conditional_t<WHICH == WhichLocation::Findloc,
207       AllIntrinsicTypes, RelationalTypes>;
208 
209   template <typename T> Result Test() const {
210     if (T::category != type_.category() || T::kind != type_.kind()) {
211       return std::nullopt;
212     }
213     CHECK(arg_.size() == (WHICH == WhichLocation::Findloc ? 6 : 5));
214     Folder<T> folder{context_};
215     Constant<T> *array{folder.Folding(arg_[0])};
216     if (!array) {
217       return std::nullopt;
218     }
219     std::optional<Constant<T>> value;
220     if constexpr (WHICH == WhichLocation::Findloc) {
221       if (const Constant<T> *p{folder.Folding(arg_[1])}) {
222         value.emplace(*p);
223       } else {
224         return std::nullopt;
225       }
226     }
227     std::optional<int> dim;
228     Constant<LogicalResult> *mask{
229         GetReductionMASK(arg_[maskArg], array->shape(), context_)};
230     if ((!mask && arg_[maskArg]) ||
231         !CheckReductionDIM(dim, context_, arg_, dimArg, array->Rank())) {
232       return std::nullopt;
233     }
234     bool back{false};
235     if (arg_[backArg]) {
236       const auto *backConst{
237           Folder<LogicalResult>{context_}.Folding(arg_[backArg])};
238       if (backConst) {
239         back = backConst->GetScalarValue().value().IsTrue();
240       } else {
241         return std::nullopt;
242       }
243     }
244     const RelationalOperator relation{WHICH == WhichLocation::Findloc
245             ? RelationalOperator::EQ
246             : WHICH == WhichLocation::Maxloc
247             ? (back ? RelationalOperator::GE : RelationalOperator::GT)
248             : back ? RelationalOperator::LE
249                    : RelationalOperator::LT};
250     // Use lower bounds of 1 exclusively.
251     array->SetLowerBoundsToOne();
252     ConstantSubscripts at{array->lbounds()}, maskAt, resultIndices, resultShape;
253     if (mask) {
254       mask->SetLowerBoundsToOne();
255       maskAt = mask->lbounds();
256     }
257     if (dim) { // DIM=
258       if (*dim < 1 || *dim > array->Rank()) {
259         context_.messages().Say(
260             "FINDLOC(DIM=%d) is out of range"_err_en_US, *dim);
261         return std::nullopt;
262       }
263       int zbDim{*dim - 1};
264       resultShape = array->shape();
265       resultShape.erase(
266           resultShape.begin() + zbDim); // scalar if array is vector
267       ConstantSubscript dimLength{array->shape()[zbDim]};
268       ConstantSubscript n{GetSize(resultShape)};
269       for (ConstantSubscript j{0}; j < n; ++j) {
270         ConstantSubscript hit{array->lbounds()[zbDim] - 1};
271         value.reset();
272         for (ConstantSubscript k{0}; k < dimLength;
273              ++k, ++at[zbDim], mask && ++maskAt[zbDim]) {
274           if ((!mask || mask->At(maskAt).IsTrue()) &&
275               IsHit(array->At(at), value, relation)) {
276             hit = at[zbDim];
277             if (!back) {
278               break;
279             }
280           }
281         }
282         resultIndices.emplace_back(hit);
283         at[zbDim] = array->lbounds()[zbDim] + dimLength - 1;
284         array->IncrementSubscripts(at);
285         at[zbDim] = array->lbounds()[zbDim];
286         if (mask) {
287           maskAt[zbDim] = mask->lbounds()[zbDim] + dimLength - 1;
288           mask->IncrementSubscripts(maskAt);
289           maskAt[zbDim] = mask->lbounds()[zbDim];
290         }
291       }
292     } else { // no DIM=
293       resultShape = ConstantSubscripts{array->Rank()}; // always a vector
294       ConstantSubscript n{GetSize(array->shape())};
295       resultIndices = ConstantSubscripts(array->Rank(), 0);
296       for (ConstantSubscript j{0}; j < n; ++j, array->IncrementSubscripts(at),
297            mask && mask->IncrementSubscripts(maskAt)) {
298         if ((!mask || mask->At(maskAt).IsTrue()) &&
299             IsHit(array->At(at), value, relation)) {
300           resultIndices = at;
301           if (!back) {
302             break;
303           }
304         }
305       }
306     }
307     std::vector<Scalar<SubscriptInteger>> resultElements;
308     for (ConstantSubscript j : resultIndices) {
309       resultElements.emplace_back(j);
310     }
311     return Constant<SubscriptInteger>{
312         std::move(resultElements), std::move(resultShape)};
313   }
314 
315 private:
316   template <typename T>
317   bool IsHit(typename Constant<T>::Element element,
318       std::optional<Constant<T>> &value,
319       [[maybe_unused]] RelationalOperator relation) const {
320     std::optional<Expr<LogicalResult>> cmp;
321     if (value) {
322       if constexpr (T::category == TypeCategory::Logical) {
323         // array(at) .EQV. value?
324         static_assert(WHICH == WhichLocation::Findloc);
325         cmp.emplace(
326             ConvertToType<LogicalResult>(Expr<T>{LogicalOperation<T::kind>{
327                 LogicalOperator::Eqv, Expr<T>{Constant<T>{std::move(element)}},
328                 Expr<T>{Constant<T>{*value}}}}));
329       } else { // compare array(at) to value
330         cmp.emplace(
331             PackageRelation(relation, Expr<T>{Constant<T>{std::move(element)}},
332                 Expr<T>{Constant<T>{*value}}));
333       }
334       Expr<LogicalResult> folded{Fold(context_, std::move(*cmp))};
335       return GetScalarConstantValue<LogicalResult>(folded).value().IsTrue();
336     } else { // first unmasked element seen for MAXLOC/MINLOC
337       value.emplace(std::move(element));
338       return true;
339     }
340   }
341 
342   static constexpr int dimArg{WHICH == WhichLocation::Findloc ? 2 : 1};
343   static constexpr int maskArg{dimArg + 1};
344   static constexpr int backArg{maskArg + 2};
345 
346   DynamicType type_;
347   ActualArguments &arg_;
348   FoldingContext &context_;
349 };
350 
351 template <WhichLocation which>
352 static std::optional<Constant<SubscriptInteger>> FoldLocationCall(
353     ActualArguments &arg, FoldingContext &context) {
354   if (arg[0]) {
355     if (auto type{arg[0]->GetType()}) {
356       return common::SearchTypes(
357           LocationHelper<which>{std::move(*type), arg, context});
358     }
359   }
360   return std::nullopt;
361 }
362 
363 template <WhichLocation which, typename T>
364 static Expr<T> FoldLocation(FoldingContext &context, FunctionRef<T> &&ref) {
365   static_assert(T::category == TypeCategory::Integer);
366   if (std::optional<Constant<SubscriptInteger>> found{
367           FoldLocationCall<which>(ref.arguments(), context)}) {
368     return Expr<T>{Fold(
369         context, ConvertToType<T>(Expr<SubscriptInteger>{std::move(*found)}))};
370   } else {
371     return Expr<T>{std::move(ref)};
372   }
373 }
374 
375 // for IALL, IANY, & IPARITY
376 template <typename T>
377 static Expr<T> FoldBitReduction(FoldingContext &context, FunctionRef<T> &&ref,
378     Scalar<T> (Scalar<T>::*operation)(const Scalar<T> &) const,
379     Scalar<T> identity) {
380   static_assert(T::category == TypeCategory::Integer);
381   std::optional<int> dim;
382   if (std::optional<Constant<T>> array{
383           ProcessReductionArgs<T>(context, ref.arguments(), dim, identity,
384               /*ARRAY=*/0, /*DIM=*/1, /*MASK=*/2)}) {
385     auto accumulator{[&](Scalar<T> &element, const ConstantSubscripts &at) {
386       element = (element.*operation)(array->At(at));
387     }};
388     return Expr<T>{DoReduction<T>(*array, dim, identity, accumulator)};
389   }
390   return Expr<T>{std::move(ref)};
391 }
392 
393 template <int KIND>
394 Expr<Type<TypeCategory::Integer, KIND>> FoldIntrinsicFunction(
395     FoldingContext &context,
396     FunctionRef<Type<TypeCategory::Integer, KIND>> &&funcRef) {
397   using T = Type<TypeCategory::Integer, KIND>;
398   using Int4 = Type<TypeCategory::Integer, 4>;
399   ActualArguments &args{funcRef.arguments()};
400   auto *intrinsic{std::get_if<SpecificIntrinsic>(&funcRef.proc().u)};
401   CHECK(intrinsic);
402   std::string name{intrinsic->name};
403   if (name == "abs") {
404     return FoldElementalIntrinsic<T, T>(context, std::move(funcRef),
405         ScalarFunc<T, T>([&context](const Scalar<T> &i) -> Scalar<T> {
406           typename Scalar<T>::ValueWithOverflow j{i.ABS()};
407           if (j.overflow) {
408             context.messages().Say(
409                 "abs(integer(kind=%d)) folding overflowed"_en_US, KIND);
410           }
411           return j.value;
412         }));
413   } else if (name == "bit_size") {
414     return Expr<T>{Scalar<T>::bits};
415   } else if (name == "ceiling" || name == "floor" || name == "nint") {
416     if (const auto *cx{UnwrapExpr<Expr<SomeReal>>(args[0])}) {
417       // NINT rounds ties away from zero, not to even
418       common::RoundingMode mode{name == "ceiling" ? common::RoundingMode::Up
419               : name == "floor"                   ? common::RoundingMode::Down
420                                 : common::RoundingMode::TiesAwayFromZero};
421       return std::visit(
422           [&](const auto &kx) {
423             using TR = ResultType<decltype(kx)>;
424             return FoldElementalIntrinsic<T, TR>(context, std::move(funcRef),
425                 ScalarFunc<T, TR>([&](const Scalar<TR> &x) {
426                   auto y{x.template ToInteger<Scalar<T>>(mode)};
427                   if (y.flags.test(RealFlag::Overflow)) {
428                     context.messages().Say(
429                         "%s intrinsic folding overflow"_en_US, name);
430                   }
431                   return y.value;
432                 }));
433           },
434           cx->u);
435     }
436   } else if (name == "count") {
437     return FoldCount<T>(context, std::move(funcRef));
438   } else if (name == "digits") {
439     if (const auto *cx{UnwrapExpr<Expr<SomeInteger>>(args[0])}) {
440       return Expr<T>{std::visit(
441           [](const auto &kx) {
442             return Scalar<ResultType<decltype(kx)>>::DIGITS;
443           },
444           cx->u)};
445     } else if (const auto *cx{UnwrapExpr<Expr<SomeReal>>(args[0])}) {
446       return Expr<T>{std::visit(
447           [](const auto &kx) {
448             return Scalar<ResultType<decltype(kx)>>::DIGITS;
449           },
450           cx->u)};
451     } else if (const auto *cx{UnwrapExpr<Expr<SomeComplex>>(args[0])}) {
452       return Expr<T>{std::visit(
453           [](const auto &kx) {
454             return Scalar<typename ResultType<decltype(kx)>::Part>::DIGITS;
455           },
456           cx->u)};
457     }
458   } else if (name == "dim") {
459     return FoldElementalIntrinsic<T, T, T>(
460         context, std::move(funcRef), &Scalar<T>::DIM);
461   } else if (name == "dshiftl" || name == "dshiftr") {
462     const auto fptr{
463         name == "dshiftl" ? &Scalar<T>::DSHIFTL : &Scalar<T>::DSHIFTR};
464     // Third argument can be of any kind. However, it must be smaller or equal
465     // than BIT_SIZE. It can be converted to Int4 to simplify.
466     return FoldElementalIntrinsic<T, T, T, Int4>(context, std::move(funcRef),
467         ScalarFunc<T, T, T, Int4>(
468             [&fptr](const Scalar<T> &i, const Scalar<T> &j,
469                 const Scalar<Int4> &shift) -> Scalar<T> {
470               return std::invoke(fptr, i, j, static_cast<int>(shift.ToInt64()));
471             }));
472   } else if (name == "exponent") {
473     if (auto *sx{UnwrapExpr<Expr<SomeReal>>(args[0])}) {
474       return std::visit(
475           [&funcRef, &context](const auto &x) -> Expr<T> {
476             using TR = typename std::decay_t<decltype(x)>::Result;
477             return FoldElementalIntrinsic<T, TR>(context, std::move(funcRef),
478                 &Scalar<TR>::template EXPONENT<Scalar<T>>);
479           },
480           sx->u);
481     } else {
482       DIE("exponent argument must be real");
483     }
484   } else if (name == "findloc") {
485     return FoldLocation<WhichLocation::Findloc, T>(context, std::move(funcRef));
486   } else if (name == "huge") {
487     return Expr<T>{Scalar<T>::HUGE()};
488   } else if (name == "iachar" || name == "ichar") {
489     auto *someChar{UnwrapExpr<Expr<SomeCharacter>>(args[0])};
490     CHECK(someChar);
491     if (auto len{ToInt64(someChar->LEN())}) {
492       if (len.value() != 1) {
493         // Do not die, this was not checked before
494         context.messages().Say(
495             "Character in intrinsic function %s must have length one"_en_US,
496             name);
497       } else {
498         return std::visit(
499             [&funcRef, &context](const auto &str) -> Expr<T> {
500               using Char = typename std::decay_t<decltype(str)>::Result;
501               return FoldElementalIntrinsic<T, Char>(context,
502                   std::move(funcRef),
503                   ScalarFunc<T, Char>([](const Scalar<Char> &c) {
504                     return Scalar<T>{CharacterUtils<Char::kind>::ICHAR(c)};
505                   }));
506             },
507             someChar->u);
508       }
509     }
510   } else if (name == "iand" || name == "ior" || name == "ieor") {
511     auto fptr{&Scalar<T>::IAND};
512     if (name == "iand") { // done in fptr declaration
513     } else if (name == "ior") {
514       fptr = &Scalar<T>::IOR;
515     } else if (name == "ieor") {
516       fptr = &Scalar<T>::IEOR;
517     } else {
518       common::die("missing case to fold intrinsic function %s", name.c_str());
519     }
520     return FoldElementalIntrinsic<T, T, T>(
521         context, std::move(funcRef), ScalarFunc<T, T, T>(fptr));
522   } else if (name == "iall") {
523     return FoldBitReduction(
524         context, std::move(funcRef), &Scalar<T>::IAND, Scalar<T>{}.NOT());
525   } else if (name == "iany") {
526     return FoldBitReduction(
527         context, std::move(funcRef), &Scalar<T>::IOR, Scalar<T>{});
528   } else if (name == "ibclr" || name == "ibset") {
529     // Second argument can be of any kind. However, it must be smaller
530     // than BIT_SIZE. It can be converted to Int4 to simplify.
531     auto fptr{&Scalar<T>::IBCLR};
532     if (name == "ibclr") { // done in fptr definition
533     } else if (name == "ibset") {
534       fptr = &Scalar<T>::IBSET;
535     } else {
536       common::die("missing case to fold intrinsic function %s", name.c_str());
537     }
538     return FoldElementalIntrinsic<T, T, Int4>(context, std::move(funcRef),
539         ScalarFunc<T, T, Int4>([&](const Scalar<T> &i,
540                                    const Scalar<Int4> &pos) -> Scalar<T> {
541           auto posVal{static_cast<int>(pos.ToInt64())};
542           if (posVal < 0) {
543             context.messages().Say(
544                 "bit position for %s (%d) is negative"_err_en_US, name, posVal);
545           } else if (posVal >= i.bits) {
546             context.messages().Say(
547                 "bit position for %s (%d) is not less than %d"_err_en_US, name,
548                 posVal, i.bits);
549           }
550           return std::invoke(fptr, i, posVal);
551         }));
552   } else if (name == "index" || name == "scan" || name == "verify") {
553     if (auto *charExpr{UnwrapExpr<Expr<SomeCharacter>>(args[0])}) {
554       return std::visit(
555           [&](const auto &kch) -> Expr<T> {
556             using TC = typename std::decay_t<decltype(kch)>::Result;
557             if (UnwrapExpr<Expr<SomeLogical>>(args[2])) { // BACK=
558               return FoldElementalIntrinsic<T, TC, TC, LogicalResult>(context,
559                   std::move(funcRef),
560                   ScalarFunc<T, TC, TC, LogicalResult>{
561                       [&name](const Scalar<TC> &str, const Scalar<TC> &other,
562                           const Scalar<LogicalResult> &back) -> Scalar<T> {
563                         return name == "index"
564                             ? CharacterUtils<TC::kind>::INDEX(
565                                   str, other, back.IsTrue())
566                             : name == "scan" ? CharacterUtils<TC::kind>::SCAN(
567                                                    str, other, back.IsTrue())
568                                              : CharacterUtils<TC::kind>::VERIFY(
569                                                    str, other, back.IsTrue());
570                       }});
571             } else {
572               return FoldElementalIntrinsic<T, TC, TC>(context,
573                   std::move(funcRef),
574                   ScalarFunc<T, TC, TC>{
575                       [&name](const Scalar<TC> &str,
576                           const Scalar<TC> &other) -> Scalar<T> {
577                         return name == "index"
578                             ? CharacterUtils<TC::kind>::INDEX(str, other)
579                             : name == "scan"
580                             ? CharacterUtils<TC::kind>::SCAN(str, other)
581                             : CharacterUtils<TC::kind>::VERIFY(str, other);
582                       }});
583             }
584           },
585           charExpr->u);
586     } else {
587       DIE("first argument must be CHARACTER");
588     }
589   } else if (name == "int") {
590     if (auto *expr{UnwrapExpr<Expr<SomeType>>(args[0])}) {
591       return std::visit(
592           [&](auto &&x) -> Expr<T> {
593             using From = std::decay_t<decltype(x)>;
594             if constexpr (std::is_same_v<From, BOZLiteralConstant> ||
595                 IsNumericCategoryExpr<From>()) {
596               return Fold(context, ConvertToType<T>(std::move(x)));
597             }
598             DIE("int() argument type not valid");
599           },
600           std::move(expr->u));
601     }
602   } else if (name == "int_ptr_kind") {
603     return Expr<T>{8};
604   } else if (name == "kind") {
605     if constexpr (common::HasMember<T, IntegerTypes>) {
606       return Expr<T>{args[0].value().GetType()->kind()};
607     } else {
608       DIE("kind() result not integral");
609     }
610   } else if (name == "iparity") {
611     return FoldBitReduction(
612         context, std::move(funcRef), &Scalar<T>::IEOR, Scalar<T>{});
613   } else if (name == "ishft") {
614     return FoldElementalIntrinsic<T, T, Int4>(context, std::move(funcRef),
615         ScalarFunc<T, T, Int4>([&](const Scalar<T> &i,
616                                    const Scalar<Int4> &pos) -> Scalar<T> {
617           auto posVal{static_cast<int>(pos.ToInt64())};
618           if (posVal < -i.bits) {
619             context.messages().Say(
620                 "SHIFT=%d count for ishft is less than %d"_err_en_US, posVal,
621                 -i.bits);
622           } else if (posVal > i.bits) {
623             context.messages().Say(
624                 "SHIFT=%d count for ishft is greater than %d"_err_en_US, posVal,
625                 i.bits);
626           }
627           return i.ISHFT(posVal);
628         }));
629   } else if (name == "lbound") {
630     return LBOUND(context, std::move(funcRef));
631   } else if (name == "leadz" || name == "trailz" || name == "poppar" ||
632       name == "popcnt") {
633     if (auto *sn{UnwrapExpr<Expr<SomeInteger>>(args[0])}) {
634       return std::visit(
635           [&funcRef, &context, &name](const auto &n) -> Expr<T> {
636             using TI = typename std::decay_t<decltype(n)>::Result;
637             if (name == "poppar") {
638               return FoldElementalIntrinsic<T, TI>(context, std::move(funcRef),
639                   ScalarFunc<T, TI>([](const Scalar<TI> &i) -> Scalar<T> {
640                     return Scalar<T>{i.POPPAR() ? 1 : 0};
641                   }));
642             }
643             auto fptr{&Scalar<TI>::LEADZ};
644             if (name == "leadz") { // done in fptr definition
645             } else if (name == "trailz") {
646               fptr = &Scalar<TI>::TRAILZ;
647             } else if (name == "popcnt") {
648               fptr = &Scalar<TI>::POPCNT;
649             } else {
650               common::die(
651                   "missing case to fold intrinsic function %s", name.c_str());
652             }
653             return FoldElementalIntrinsic<T, TI>(context, std::move(funcRef),
654                 ScalarFunc<T, TI>([&fptr](const Scalar<TI> &i) -> Scalar<T> {
655                   return Scalar<T>{std::invoke(fptr, i)};
656                 }));
657           },
658           sn->u);
659     } else {
660       DIE("leadz argument must be integer");
661     }
662   } else if (name == "len") {
663     if (auto *charExpr{UnwrapExpr<Expr<SomeCharacter>>(args[0])}) {
664       return std::visit(
665           [&](auto &kx) {
666             if (auto len{kx.LEN()}) {
667               return Fold(context, ConvertToType<T>(*std::move(len)));
668             } else {
669               return Expr<T>{std::move(funcRef)};
670             }
671           },
672           charExpr->u);
673     } else {
674       DIE("len() argument must be of character type");
675     }
676   } else if (name == "len_trim") {
677     if (auto *charExpr{UnwrapExpr<Expr<SomeCharacter>>(args[0])}) {
678       return std::visit(
679           [&](const auto &kch) -> Expr<T> {
680             using TC = typename std::decay_t<decltype(kch)>::Result;
681             return FoldElementalIntrinsic<T, TC>(context, std::move(funcRef),
682                 ScalarFunc<T, TC>{[](const Scalar<TC> &str) -> Scalar<T> {
683                   return CharacterUtils<TC::kind>::LEN_TRIM(str);
684                 }});
685           },
686           charExpr->u);
687     } else {
688       DIE("len_trim() argument must be of character type");
689     }
690   } else if (name == "maskl" || name == "maskr") {
691     // Argument can be of any kind but value has to be smaller than BIT_SIZE.
692     // It can be safely converted to Int4 to simplify.
693     const auto fptr{name == "maskl" ? &Scalar<T>::MASKL : &Scalar<T>::MASKR};
694     return FoldElementalIntrinsic<T, Int4>(context, std::move(funcRef),
695         ScalarFunc<T, Int4>([&fptr](const Scalar<Int4> &places) -> Scalar<T> {
696           return fptr(static_cast<int>(places.ToInt64()));
697         }));
698   } else if (name == "max") {
699     return FoldMINorMAX(context, std::move(funcRef), Ordering::Greater);
700   } else if (name == "max0" || name == "max1") {
701     return RewriteSpecificMINorMAX(context, std::move(funcRef));
702   } else if (name == "maxexponent") {
703     if (auto *sx{UnwrapExpr<Expr<SomeReal>>(args[0])}) {
704       return std::visit(
705           [](const auto &x) {
706             using TR = typename std::decay_t<decltype(x)>::Result;
707             return Expr<T>{Scalar<TR>::MAXEXPONENT};
708           },
709           sx->u);
710     }
711   } else if (name == "maxloc") {
712     return FoldLocation<WhichLocation::Maxloc, T>(context, std::move(funcRef));
713   } else if (name == "maxval") {
714     return FoldMaxvalMinval<T>(context, std::move(funcRef),
715         RelationalOperator::GT, T::Scalar::Least());
716   } else if (name == "merge") {
717     return FoldMerge<T>(context, std::move(funcRef));
718   } else if (name == "merge_bits") {
719     return FoldElementalIntrinsic<T, T, T, T>(
720         context, std::move(funcRef), &Scalar<T>::MERGE_BITS);
721   } else if (name == "min") {
722     return FoldMINorMAX(context, std::move(funcRef), Ordering::Less);
723   } else if (name == "min0" || name == "min1") {
724     return RewriteSpecificMINorMAX(context, std::move(funcRef));
725   } else if (name == "minexponent") {
726     if (auto *sx{UnwrapExpr<Expr<SomeReal>>(args[0])}) {
727       return std::visit(
728           [](const auto &x) {
729             using TR = typename std::decay_t<decltype(x)>::Result;
730             return Expr<T>{Scalar<TR>::MINEXPONENT};
731           },
732           sx->u);
733     }
734   } else if (name == "minloc") {
735     return FoldLocation<WhichLocation::Minloc, T>(context, std::move(funcRef));
736   } else if (name == "minval") {
737     return FoldMaxvalMinval<T>(
738         context, std::move(funcRef), RelationalOperator::LT, T::Scalar::HUGE());
739   } else if (name == "mod") {
740     return FoldElementalIntrinsic<T, T, T>(context, std::move(funcRef),
741         ScalarFuncWithContext<T, T, T>(
742             [](FoldingContext &context, const Scalar<T> &x,
743                 const Scalar<T> &y) -> Scalar<T> {
744               auto quotRem{x.DivideSigned(y)};
745               if (quotRem.divisionByZero) {
746                 context.messages().Say("mod() by zero"_en_US);
747               } else if (quotRem.overflow) {
748                 context.messages().Say("mod() folding overflowed"_en_US);
749               }
750               return quotRem.remainder;
751             }));
752   } else if (name == "modulo") {
753     return FoldElementalIntrinsic<T, T, T>(context, std::move(funcRef),
754         ScalarFuncWithContext<T, T, T>(
755             [](FoldingContext &context, const Scalar<T> &x,
756                 const Scalar<T> &y) -> Scalar<T> {
757               auto result{x.MODULO(y)};
758               if (result.overflow) {
759                 context.messages().Say("modulo() folding overflowed"_en_US);
760               }
761               return result.value;
762             }));
763   } else if (name == "not") {
764     return FoldElementalIntrinsic<T, T>(
765         context, std::move(funcRef), &Scalar<T>::NOT);
766   } else if (name == "precision") {
767     if (const auto *cx{UnwrapExpr<Expr<SomeReal>>(args[0])}) {
768       return Expr<T>{std::visit(
769           [](const auto &kx) {
770             return Scalar<ResultType<decltype(kx)>>::PRECISION;
771           },
772           cx->u)};
773     } else if (const auto *cx{UnwrapExpr<Expr<SomeComplex>>(args[0])}) {
774       return Expr<T>{std::visit(
775           [](const auto &kx) {
776             return Scalar<typename ResultType<decltype(kx)>::Part>::PRECISION;
777           },
778           cx->u)};
779     }
780   } else if (name == "product") {
781     return FoldProduct<T>(context, std::move(funcRef), Scalar<T>{1});
782   } else if (name == "radix") {
783     return Expr<T>{2};
784   } else if (name == "range") {
785     if (const auto *cx{UnwrapExpr<Expr<SomeInteger>>(args[0])}) {
786       return Expr<T>{std::visit(
787           [](const auto &kx) {
788             return Scalar<ResultType<decltype(kx)>>::RANGE;
789           },
790           cx->u)};
791     } else if (const auto *cx{UnwrapExpr<Expr<SomeReal>>(args[0])}) {
792       return Expr<T>{std::visit(
793           [](const auto &kx) {
794             return Scalar<ResultType<decltype(kx)>>::RANGE;
795           },
796           cx->u)};
797     } else if (const auto *cx{UnwrapExpr<Expr<SomeComplex>>(args[0])}) {
798       return Expr<T>{std::visit(
799           [](const auto &kx) {
800             return Scalar<typename ResultType<decltype(kx)>::Part>::RANGE;
801           },
802           cx->u)};
803     }
804   } else if (name == "rank") {
805     if (const auto *array{UnwrapExpr<Expr<SomeType>>(args[0])}) {
806       if (auto named{ExtractNamedEntity(*array)}) {
807         const Symbol &symbol{named->GetLastSymbol()};
808         if (IsAssumedRank(symbol)) {
809           // DescriptorInquiry can only be placed in expression of kind
810           // DescriptorInquiry::Result::kind.
811           return ConvertToType<T>(Expr<
812               Type<TypeCategory::Integer, DescriptorInquiry::Result::kind>>{
813               DescriptorInquiry{*named, DescriptorInquiry::Field::Rank}});
814         }
815       }
816       return Expr<T>{args[0].value().Rank()};
817     }
818     return Expr<T>{args[0].value().Rank()};
819   } else if (name == "selected_char_kind") {
820     if (const auto *chCon{UnwrapExpr<Constant<TypeOf<std::string>>>(args[0])}) {
821       if (std::optional<std::string> value{chCon->GetScalarValue()}) {
822         int defaultKind{
823             context.defaults().GetDefaultKind(TypeCategory::Character)};
824         return Expr<T>{SelectedCharKind(*value, defaultKind)};
825       }
826     }
827   } else if (name == "selected_int_kind") {
828     if (auto p{GetInt64Arg(args[0])}) {
829       return Expr<T>{SelectedIntKind(*p)};
830     }
831   } else if (name == "selected_real_kind" ||
832       name == "__builtin_ieee_selected_real_kind") {
833     if (auto p{GetInt64ArgOr(args[0], 0)}) {
834       if (auto r{GetInt64ArgOr(args[1], 0)}) {
835         if (auto radix{GetInt64ArgOr(args[2], 2)}) {
836           return Expr<T>{SelectedRealKind(*p, *r, *radix)};
837         }
838       }
839     }
840   } else if (name == "shape") {
841     if (auto shape{GetShape(context, args[0])}) {
842       if (auto shapeExpr{AsExtentArrayExpr(*shape)}) {
843         return Fold(context, ConvertToType<T>(std::move(*shapeExpr)));
844       }
845     }
846   } else if (name == "shifta" || name == "shiftr" || name == "shiftl") {
847     // Second argument can be of any kind. However, it must be smaller or
848     // equal than BIT_SIZE. It can be converted to Int4 to simplify.
849     auto fptr{&Scalar<T>::SHIFTA};
850     if (name == "shifta") { // done in fptr definition
851     } else if (name == "shiftr") {
852       fptr = &Scalar<T>::SHIFTR;
853     } else if (name == "shiftl") {
854       fptr = &Scalar<T>::SHIFTL;
855     } else {
856       common::die("missing case to fold intrinsic function %s", name.c_str());
857     }
858     return FoldElementalIntrinsic<T, T, Int4>(context, std::move(funcRef),
859         ScalarFunc<T, T, Int4>([&](const Scalar<T> &i,
860                                    const Scalar<Int4> &pos) -> Scalar<T> {
861           auto posVal{static_cast<int>(pos.ToInt64())};
862           if (posVal < 0) {
863             context.messages().Say(
864                 "SHIFT=%d count for %s is negative"_err_en_US, posVal, name);
865           } else if (posVal > i.bits) {
866             context.messages().Say(
867                 "SHIFT=%d count for %s is greater than %d"_err_en_US, posVal,
868                 name, i.bits);
869           }
870           return std::invoke(fptr, i, posVal);
871         }));
872   } else if (name == "sign") {
873     return FoldElementalIntrinsic<T, T, T>(context, std::move(funcRef),
874         ScalarFunc<T, T, T>(
875             [&context](const Scalar<T> &j, const Scalar<T> &k) -> Scalar<T> {
876               typename Scalar<T>::ValueWithOverflow result{j.SIGN(k)};
877               if (result.overflow) {
878                 context.messages().Say(
879                     "sign(integer(kind=%d)) folding overflowed"_en_US, KIND);
880               }
881               return result.value;
882             }));
883   } else if (name == "size") {
884     if (auto shape{GetShape(context, args[0])}) {
885       if (auto &dimArg{args[1]}) { // DIM= is present, get one extent
886         if (auto dim{GetInt64Arg(args[1])}) {
887           int rank{GetRank(*shape)};
888           if (*dim >= 1 && *dim <= rank) {
889             const Symbol *symbol{UnwrapWholeSymbolDataRef(args[0])};
890             if (symbol && IsAssumedSizeArray(*symbol) && *dim == rank) {
891               context.messages().Say(
892                   "size(array,dim=%jd) of last dimension is not available for rank-%d assumed-size array dummy argument"_err_en_US,
893                   *dim, rank);
894               return MakeInvalidIntrinsic<T>(std::move(funcRef));
895             } else if (auto &extent{shape->at(*dim - 1)}) {
896               return Fold(context, ConvertToType<T>(std::move(*extent)));
897             }
898           } else {
899             context.messages().Say(
900                 "size(array,dim=%jd) dimension is out of range for rank-%d array"_en_US,
901                 *dim, rank);
902           }
903         }
904       } else if (auto extents{common::AllElementsPresent(std::move(*shape))}) {
905         // DIM= is absent; compute PRODUCT(SHAPE())
906         ExtentExpr product{1};
907         for (auto &&extent : std::move(*extents)) {
908           product = std::move(product) * std::move(extent);
909         }
910         return Expr<T>{ConvertToType<T>(Fold(context, std::move(product)))};
911       }
912     }
913   } else if (name == "sizeof") { // in bytes; extension
914     if (auto info{
915             characteristics::TypeAndShape::Characterize(args[0], context)}) {
916       if (auto bytes{info->MeasureSizeInBytes(context)}) {
917         return Expr<T>{Fold(context, ConvertToType<T>(std::move(*bytes)))};
918       }
919     }
920   } else if (name == "storage_size") { // in bits
921     if (auto info{
922             characteristics::TypeAndShape::Characterize(args[0], context)}) {
923       if (auto bytes{info->MeasureElementSizeInBytes(context, true)}) {
924         return Expr<T>{
925             Fold(context, Expr<T>{8} * ConvertToType<T>(std::move(*bytes)))};
926       }
927     }
928   } else if (name == "sum") {
929     return FoldSum<T>(context, std::move(funcRef));
930   } else if (name == "ubound") {
931     return UBOUND(context, std::move(funcRef));
932   }
933   // TODO: dot_product, ibits, ishftc, matmul, sign, transfer
934   return Expr<T>{std::move(funcRef)};
935 }
936 
937 // Substitutes a bare type parameter reference with its value if it has one now
938 // in an instantiation.  Bare LEN type parameters are substituted only when
939 // the known value is constant.
940 Expr<TypeParamInquiry::Result> FoldOperation(
941     FoldingContext &context, TypeParamInquiry &&inquiry) {
942   std::optional<NamedEntity> base{inquiry.base()};
943   parser::CharBlock parameterName{inquiry.parameter().name()};
944   if (base) {
945     // Handling "designator%typeParam".  Get the value of the type parameter
946     // from the instantiation of the base
947     if (const semantics::DeclTypeSpec *
948         declType{base->GetLastSymbol().GetType()}) {
949       if (const semantics::ParamValue *
950           paramValue{
951               declType->derivedTypeSpec().FindParameter(parameterName)}) {
952         const semantics::MaybeIntExpr &paramExpr{paramValue->GetExplicit()};
953         if (paramExpr && IsConstantExpr(*paramExpr)) {
954           Expr<SomeInteger> intExpr{*paramExpr};
955           return Fold(context,
956               ConvertToType<TypeParamInquiry::Result>(std::move(intExpr)));
957         }
958       }
959     }
960   } else {
961     // A "bare" type parameter: replace with its value, if that's now known
962     // in a current derived type instantiation, for KIND type parameters.
963     if (const auto *pdt{context.pdtInstance()}) {
964       bool isLen{false};
965       if (const semantics::Scope * scope{context.pdtInstance()->scope()}) {
966         auto iter{scope->find(parameterName)};
967         if (iter != scope->end()) {
968           const Symbol &symbol{*iter->second};
969           const auto *details{symbol.detailsIf<semantics::TypeParamDetails>()};
970           if (details) {
971             isLen = details->attr() == common::TypeParamAttr::Len;
972             const semantics::MaybeIntExpr &initExpr{details->init()};
973             if (initExpr && IsConstantExpr(*initExpr) &&
974                 (!isLen || ToInt64(*initExpr))) {
975               Expr<SomeInteger> expr{*initExpr};
976               return Fold(context,
977                   ConvertToType<TypeParamInquiry::Result>(std::move(expr)));
978             }
979           }
980         }
981       }
982       if (const auto *value{pdt->FindParameter(parameterName)}) {
983         if (value->isExplicit()) {
984           auto folded{Fold(context,
985               AsExpr(ConvertToType<TypeParamInquiry::Result>(
986                   Expr<SomeInteger>{value->GetExplicit().value()})))};
987           if (!isLen || ToInt64(folded)) {
988             return folded;
989           }
990         }
991       }
992     }
993   }
994   return AsExpr(std::move(inquiry));
995 }
996 
997 std::optional<std::int64_t> ToInt64(const Expr<SomeInteger> &expr) {
998   return std::visit(
999       [](const auto &kindExpr) { return ToInt64(kindExpr); }, expr.u);
1000 }
1001 
1002 std::optional<std::int64_t> ToInt64(const Expr<SomeType> &expr) {
1003   if (const auto *intExpr{UnwrapExpr<Expr<SomeInteger>>(expr)}) {
1004     return ToInt64(*intExpr);
1005   } else {
1006     return std::nullopt;
1007   }
1008 }
1009 
1010 FOR_EACH_INTEGER_KIND(template class ExpressionBase, )
1011 template class ExpressionBase<SomeInteger>;
1012 } // namespace Fortran::evaluate
1013