xref: /llvm-project-15.0.7/flang/lib/Lower/IntrinsicCall.cpp (revision ad4ee2d7)

//===-- IntrinsicCall.cpp -------------------------------------------------===//
//
// Part of the LLVM Project, under the Apache License v2.0 with LLVM Exceptions.
// See https://llvm.org/LICENSE.txt for license information.
// SPDX-License-Identifier: Apache-2.0 WITH LLVM-exception
//
//===----------------------------------------------------------------------===//
//
// Helper routines for constructing the FIR dialect of MLIR. As FIR is a
// dialect of MLIR, it makes extensive use of MLIR interfaces and MLIR's coding
// style (https://mlir.llvm.org/getting_started/DeveloperGuide/) is used in this
// module.
//
//===----------------------------------------------------------------------===//

#include "flang/Lower/IntrinsicCall.h"
#include "RTBuilder.h"
#include "flang/Common/static-multimap-view.h"
#include "flang/Lower/CharacterExpr.h"
#include "flang/Lower/ComplexExpr.h"
#include "flang/Lower/ConvertType.h"
#include "flang/Lower/Mangler.h"
#include "flang/Lower/Runtime.h"
#include "flang/Optimizer/Builder/FIRBuilder.h"
#include "llvm/Support/CommandLine.h"
#include "llvm/Support/ErrorHandling.h"
#include <algorithm>
#include <string_view>
#include <utility>

#define PGMATH_DECLARE
#include "flang/Evaluate/pgmath.h.inc"

/// This file implements lowering of Fortran intrinsic procedures.
/// Intrinsics are lowered to a mix of FIR and MLIR operations as
/// well as call to runtime functions or LLVM intrinsics.

/// Lowering of intrinsic procedure calls is based on a map that associates
/// Fortran intrinsic generic names to FIR generator functions.
/// All generator functions are member functions of the IntrinsicLibrary class
/// and have the same interface.
/// If no generator is given for an intrinsic name, a math runtime library
/// is searched for an implementation and, if a runtime function is found,
/// a call is generated for it. LLVM intrinsics are handled as a math
/// runtime library here.

/// Enums used to templatize and share lowering of MIN and MAX.
enum class Extremum { Min, Max };

// There are different ways to deal with NaNs in MIN and MAX.
// Known existing behaviors are listed below and can be selected for
// f18 MIN/MAX implementation.
enum class ExtremumBehavior {
  // Note: the Signaling/quiet aspect of NaNs in the behaviors below are
  // not described because there is no way to control/observe such aspect in
  // MLIR/LLVM yet. The IEEE behaviors come with requirements regarding this
  // aspect that are therefore currently not enforced. In the descriptions
  // below, NaNs can be signaling or quite. Returned NaNs may be signaling
  // if one of the input NaN was signaling but it cannot be guaranteed either.
  // Existing compilers using an IEEE behavior (gfortran) also do not fulfill
  // signaling/quiet requirements.
  IeeeMinMaximumNumber,
  // IEEE minimumNumber/maximumNumber behavior (754-2019, section 9.6):
  // If one of the argument is and number and the other is NaN, return the
  // number. If both arguements are NaN, return NaN.
  // Compilers: gfortran.
  IeeeMinMaximum,
  // IEEE minimum/maximum behavior (754-2019, section 9.6):
  // If one of the argument is NaN, return NaN.
  MinMaxss,
  // x86 minss/maxss behavior:
  // If the second argument is a number and the other is NaN, return the number.
  // In all other cases where at least one operand is NaN, return NaN.
  // Compilers: xlf (only for MAX), ifort, pgfortran -nollvm, and nagfor.
  PgfortranLlvm,
  // "Opposite of" x86 minss/maxss behavior:
  // If the first argument is a number and the other is NaN, return the
  // number.
  // In all other cases where at least one operand is NaN, return NaN.
  // Compilers: xlf (only for MIN), and pgfortran (with llvm).
  IeeeMinMaxNum
  // IEEE minNum/maxNum behavior (754-2008, section 5.3.1):
  // TODO: Not implemented.
  // It is the only behavior where the signaling/quiet aspect of a NaN argument
  // impacts if the result should be NaN or the argument that is a number.
  // LLVM/MLIR do not provide ways to observe this aspect, so it is not
  // possible to implement it without some target dependent runtime.
};

// TODO error handling -> return a code or directly emit messages ?
struct IntrinsicLibrary {

  // Constructors.
  explicit IntrinsicLibrary(fir::FirOpBuilder &builder, mlir::Location loc)
      : builder{builder}, loc{loc} {}
  IntrinsicLibrary() = delete;
  IntrinsicLibrary(const IntrinsicLibrary &) = delete;

  /// Generate FIR for call to Fortran intrinsic \p name with arguments \p arg
  /// and expected result type \p resultType.
  fir::ExtendedValue genIntrinsicCall(llvm::StringRef name,
                                      mlir::Type resultType,
                                      llvm::ArrayRef<fir::ExtendedValue> arg);

  /// Search a runtime function that is associated to the generic intrinsic name
  /// and whose signature matches the intrinsic arguments and result types.
  /// If no such runtime function is found but a runtime function associated
  /// with the Fortran generic exists and has the same number of arguments,
  /// conversions will be inserted before and/or after the call. This is to
  /// mainly to allow 16 bits float support even-though little or no math
  /// runtime is currently available for it.
  mlir::Value genRuntimeCall(llvm::StringRef name, mlir::Type,
                             llvm::ArrayRef<mlir::Value>);

  using RuntimeCallGenerator = std::function<mlir::Value(
      fir::FirOpBuilder &, mlir::Location, llvm::ArrayRef<mlir::Value>)>;
  RuntimeCallGenerator
  getRuntimeCallGenerator(llvm::StringRef name,
                          mlir::FunctionType soughtFuncType);

  mlir::Value genAbs(mlir::Type, llvm::ArrayRef<mlir::Value>);
  mlir::Value genAimag(mlir::Type, llvm::ArrayRef<mlir::Value>);
  mlir::Value genAint(mlir::Type, llvm::ArrayRef<mlir::Value>);
  mlir::Value genAnint(mlir::Type, llvm::ArrayRef<mlir::Value>);
  mlir::Value genCeiling(mlir::Type, llvm::ArrayRef<mlir::Value>);
  mlir::Value genConjg(mlir::Type, llvm::ArrayRef<mlir::Value>);
  mlir::Value genDim(mlir::Type, llvm::ArrayRef<mlir::Value>);
  mlir::Value genDprod(mlir::Type, llvm::ArrayRef<mlir::Value>);
  template <Extremum, ExtremumBehavior>
  mlir::Value genExtremum(mlir::Type, llvm::ArrayRef<mlir::Value>);
  mlir::Value genFloor(mlir::Type, llvm::ArrayRef<mlir::Value>);
  mlir::Value genIAnd(mlir::Type, llvm::ArrayRef<mlir::Value>);
  mlir::Value genIchar(mlir::Type, llvm::ArrayRef<mlir::Value>);
  mlir::Value genIEOr(mlir::Type, llvm::ArrayRef<mlir::Value>);
  mlir::Value genIOr(mlir::Type, llvm::ArrayRef<mlir::Value>);
  fir::ExtendedValue genLen(mlir::Type, llvm::ArrayRef<fir::ExtendedValue>);
  fir::ExtendedValue genLenTrim(mlir::Type, llvm::ArrayRef<fir::ExtendedValue>);
  mlir::Value genMerge(mlir::Type, llvm::ArrayRef<mlir::Value>);
  mlir::Value genMod(mlir::Type, llvm::ArrayRef<mlir::Value>);
  mlir::Value genNint(mlir::Type, llvm::ArrayRef<mlir::Value>);
  mlir::Value genSign(mlir::Type, llvm::ArrayRef<mlir::Value>);
  /// Implement all conversion functions like DBLE, the first argument is
  /// the value to convert. There may be an additional KIND arguments that
  /// is ignored because this is already reflected in the result type.
  mlir::Value genConversion(mlir::Type, llvm::ArrayRef<mlir::Value>);

  /// Define the different FIR generators that can be mapped to intrinsic to
  /// generate the related code.
  using ElementalGenerator = decltype(&IntrinsicLibrary::genAbs);
  using ExtendedGenerator = decltype(&IntrinsicLibrary::genLenTrim);
  using Generator = std::variant<ElementalGenerator, ExtendedGenerator>;

  /// All generators can be outlined. This will build a function named
  /// "fir."+ <generic name> + "." + <result type code> and generate the
  /// intrinsic implementation inside instead of at the intrinsic call sites.
  /// This can be used to keep the FIR more readable. Only one function will
  /// be generated for all the similar calls in a program.
  /// If the Generator is nullptr, the wrapper uses genRuntimeCall.
  template <typename GeneratorType>
  mlir::Value outlineInWrapper(GeneratorType, llvm::StringRef name,
                               mlir::Type resultType,
                               llvm::ArrayRef<mlir::Value> args);
  fir::ExtendedValue outlineInWrapper(ExtendedGenerator, llvm::StringRef name,
                                      mlir::Type resultType,
                                      llvm::ArrayRef<fir::ExtendedValue> args);

  template <typename GeneratorType>
  mlir::FuncOp getWrapper(GeneratorType, llvm::StringRef name,
                          mlir::FunctionType, bool loadRefArguments = false);

  /// Generate calls to ElementalGenerator, handling the elemental aspects
  template <typename GeneratorType>
  fir::ExtendedValue
  genElementalCall(GeneratorType, llvm::StringRef name, mlir::Type resultType,
                   llvm::ArrayRef<fir::ExtendedValue> args, bool outline);

  /// Helper to invoke code generator for the intrinsics given arguments.
  mlir::Value invokeGenerator(ElementalGenerator generator,
                              mlir::Type resultType,
                              llvm::ArrayRef<mlir::Value> args);
  mlir::Value invokeGenerator(RuntimeCallGenerator generator,
                              mlir::Type resultType,
                              llvm::ArrayRef<mlir::Value> args);
  mlir::Value invokeGenerator(ExtendedGenerator generator,
                              mlir::Type resultType,
                              llvm::ArrayRef<mlir::Value> args);

  /// Get pointer to unrestricted intrinsic. Generate the related unrestricted
  /// intrinsic if it is not defined yet.
  mlir::SymbolRefAttr
  getUnrestrictedIntrinsicSymbolRefAttr(llvm::StringRef name,
                                        mlir::FunctionType signature);

  fir::FirOpBuilder &builder;
  mlir::Location loc;
};

/// Table that drives the fir generation depending on the intrinsic.
/// one to one mapping with Fortran arguments. If no mapping is
/// defined here for a generic intrinsic, genRuntimeCall will be called
/// to look for a match in the runtime a emit a call.
struct IntrinsicHandler {
  const char *name;
  IntrinsicLibrary::Generator generator;
  bool isElemental = true;
  /// Code heavy intrinsic can be outlined to make FIR
  /// more readable.
  bool outline = false;
};
using I = IntrinsicLibrary;
static constexpr IntrinsicHandler handlers[]{
    {"abs", &I::genAbs},
    {"achar", &I::genConversion},
    {"aimag", &I::genAimag},
    {"aint", &I::genAint},
    {"anint", &I::genAnint},
    {"ceiling", &I::genCeiling},
    {"char", &I::genConversion},
    {"conjg", &I::genConjg},
    {"dim", &I::genDim},
    {"dble", &I::genConversion},
    {"dprod", &I::genDprod},
    {"floor", &I::genFloor},
    {"iand", &I::genIAnd},
    {"ichar", &I::genIchar},
    {"ieor", &I::genIEOr},
    {"ior", &I::genIOr},
    {"len", &I::genLen},
    {"len_trim", &I::genLenTrim},
    {"max", &I::genExtremum<Extremum::Max, ExtremumBehavior::MinMaxss>},
    {"min", &I::genExtremum<Extremum::Min, ExtremumBehavior::MinMaxss>},
    {"merge", &I::genMerge},
    {"mod", &I::genMod},
    {"nint", &I::genNint},
    {"sign", &I::genSign},
};

/// To make fir output more readable for debug, one can outline all intrinsic
/// implementation in wrappers (overrides the IntrinsicHandler::outline flag).
static llvm::cl::opt<bool> outlineAllIntrinsics(
    "outline-intrinsics",
    llvm::cl::desc(
        "Lower all intrinsic procedure implementation in their own functions"),
    llvm::cl::init(false));

//===----------------------------------------------------------------------===//
// Math runtime description and matching utility
//===----------------------------------------------------------------------===//

/// Command line option to modify math runtime version used to implement
/// intrinsics.
enum MathRuntimeVersion {
  fastVersion,
  relaxedVersion,
  preciseVersion,
  llvmOnly
};
llvm::cl::opt<MathRuntimeVersion> mathRuntimeVersion(
    "math-runtime", llvm::cl::desc("Select math runtime version:"),
    llvm::cl::values(
        clEnumValN(fastVersion, "fast", "use pgmath fast runtime"),
        clEnumValN(relaxedVersion, "relaxed", "use pgmath relaxed runtime"),
        clEnumValN(preciseVersion, "precise", "use pgmath precise runtime"),
        clEnumValN(llvmOnly, "llvm",
                   "only use LLVM intrinsics (may be incomplete)")),
    llvm::cl::init(fastVersion));

struct RuntimeFunction {
  // llvm::StringRef comparison operator are not constexpr, so use string_view.
  using Key = std::string_view;
  // Needed for implicit compare with keys.
  constexpr operator Key() const { return key; }
  Key key; // intrinsic name
  llvm::StringRef symbol;
  Fortran::lower::FuncTypeBuilderFunc typeGenerator;
};

#define RUNTIME_STATIC_DESCRIPTION(name, func)                                 \
  {#name, #func,                                                               \
   Fortran::lower::RuntimeTableKey<decltype(func)>::getTypeModel()},
static constexpr RuntimeFunction pgmathFast[] = {
#define PGMATH_FAST
#define PGMATH_USE_ALL_TYPES(name, func) RUNTIME_STATIC_DESCRIPTION(name, func)
#include "flang/Evaluate/pgmath.h.inc"
};
static constexpr RuntimeFunction pgmathRelaxed[] = {
#define PGMATH_RELAXED
#define PGMATH_USE_ALL_TYPES(name, func) RUNTIME_STATIC_DESCRIPTION(name, func)
#include "flang/Evaluate/pgmath.h.inc"
};
static constexpr RuntimeFunction pgmathPrecise[] = {
#define PGMATH_PRECISE
#define PGMATH_USE_ALL_TYPES(name, func) RUNTIME_STATIC_DESCRIPTION(name, func)
#include "flang/Evaluate/pgmath.h.inc"
};

static mlir::FunctionType genF32F32FuncType(mlir::MLIRContext *context) {
  auto t = mlir::FloatType::getF32(context);
  return mlir::FunctionType::get(context, {t}, {t});
}

static mlir::FunctionType genF64F64FuncType(mlir::MLIRContext *context) {
  auto t = mlir::FloatType::getF64(context);
  return mlir::FunctionType::get(context, {t}, {t});
}

template <int Bits>
static mlir::FunctionType genIntF64FuncType(mlir::MLIRContext *context) {
  auto t = mlir::FloatType::getF64(context);
  auto r = mlir::IntegerType::get(context, Bits);
  return mlir::FunctionType::get(context, {t}, {r});
}

template <int Bits>
static mlir::FunctionType genIntF32FuncType(mlir::MLIRContext *context) {
  auto t = mlir::FloatType::getF32(context);
  auto r = mlir::IntegerType::get(context, Bits);
  return mlir::FunctionType::get(context, {t}, {r});
}

// TODO : Fill-up this table with more intrinsic.
// Note: These are also defined as operations in LLVM dialect. See if this
// can be use and has advantages.
static constexpr RuntimeFunction llvmIntrinsics[] = {
    {"abs", "llvm.fabs.f32", genF32F32FuncType},
    {"abs", "llvm.fabs.f64", genF64F64FuncType},
    {"aint", "llvm.trunc.f32", genF32F32FuncType},
    {"aint", "llvm.trunc.f64", genF64F64FuncType},
    {"anint", "llvm.round.f32", genF32F32FuncType},
    {"anint", "llvm.round.f64", genF64F64FuncType},
    // ceil is used for CEILING but is different, it returns a real.
    {"ceil", "llvm.ceil.f32", genF32F32FuncType},
    {"ceil", "llvm.ceil.f64", genF64F64FuncType},
    {"cos", "llvm.cos.f32", genF32F32FuncType},
    {"cos", "llvm.cos.f64", genF64F64FuncType},
    // llvm.floor is used for FLOOR, but returns real.
    {"floor", "llvm.floor.f32", genF32F32FuncType},
    {"floor", "llvm.floor.f64", genF64F64FuncType},
    {"log", "llvm.log.f32", genF32F32FuncType},
    {"log", "llvm.log.f64", genF64F64FuncType},
    {"log10", "llvm.log10.f32", genF32F32FuncType},
    {"log10", "llvm.log10.f64", genF64F64FuncType},
    {"nint", "llvm.lround.i64.f64", genIntF64FuncType<64>},
    {"nint", "llvm.lround.i64.f32", genIntF32FuncType<64>},
    {"nint", "llvm.lround.i32.f64", genIntF64FuncType<32>},
    {"nint", "llvm.lround.i32.f32", genIntF32FuncType<32>},
    {"sin", "llvm.sin.f32", genF32F32FuncType},
    {"sin", "llvm.sin.f64", genF64F64FuncType},
    {"sqrt", "llvm.sqrt.f32", genF32F32FuncType},
    {"sqrt", "llvm.sqrt.f64", genF64F64FuncType},
};

// This helper class computes a "distance" between two function types.
// The distance measures how many narrowing conversions of actual arguments
// and result of "from" must be made in order to use "to" instead of "from".
// For instance, the distance between ACOS(REAL(10)) and ACOS(REAL(8)) is
// greater than the one between ACOS(REAL(10)) and ACOS(REAL(16)). This means
// if no implementation of ACOS(REAL(10)) is available, it is better to use
// ACOS(REAL(16)) with casts rather than ACOS(REAL(8)).
// Note that this is not a symmetric distance and the order of "from" and "to"
// arguments matters, d(foo, bar) may not be the same as d(bar, foo) because it
// may be safe to replace foo by bar, but not the opposite.
class FunctionDistance {
public:
  FunctionDistance() : infinite{true} {}

  FunctionDistance(mlir::FunctionType from, mlir::FunctionType to) {
    auto nInputs = from.getNumInputs();
    auto nResults = from.getNumResults();
    if (nResults != to.getNumResults() || nInputs != to.getNumInputs()) {
      infinite = true;
    } else {
      for (decltype(nInputs) i{0}; i < nInputs && !infinite; ++i)
        addArgumentDistance(from.getInput(i), to.getInput(i));
      for (decltype(nResults) i{0}; i < nResults && !infinite; ++i)
        addResultDistance(to.getResult(i), from.getResult(i));
    }
  }

  /// Beware both d1.isSmallerThan(d2) *and* d2.isSmallerThan(d1) may be
  /// false if both d1 and d2 are infinite. This implies that
  ///  d1.isSmallerThan(d2) is not equivalent to !d2.isSmallerThan(d1)
  bool isSmallerThan(const FunctionDistance &d) const {
    return !infinite &&
           (d.infinite || std::lexicographical_compare(
                              conversions.begin(), conversions.end(),
                              d.conversions.begin(), d.conversions.end()));
  }

  bool isLosingPrecision() const {
    return conversions[narrowingArg] != 0 || conversions[extendingResult] != 0;
  }

  bool isInfinite() const { return infinite; }

private:
  enum class Conversion { Forbidden, None, Narrow, Extend };

  void addArgumentDistance(mlir::Type from, mlir::Type to) {
    switch (conversionBetweenTypes(from, to)) {
    case Conversion::Forbidden:
      infinite = true;
      break;
    case Conversion::None:
      break;
    case Conversion::Narrow:
      conversions[narrowingArg]++;
      break;
    case Conversion::Extend:
      conversions[nonNarrowingArg]++;
      break;
    }
  }

  void addResultDistance(mlir::Type from, mlir::Type to) {
    switch (conversionBetweenTypes(from, to)) {
    case Conversion::Forbidden:
      infinite = true;
      break;
    case Conversion::None:
      break;
    case Conversion::Narrow:
      conversions[nonExtendingResult]++;
      break;
    case Conversion::Extend:
      conversions[extendingResult]++;
      break;
    }
  }

  // Floating point can be mlir::FloatType or fir::real
  static unsigned getFloatingPointWidth(mlir::Type t) {
    if (auto f{t.dyn_cast<mlir::FloatType>()})
      return f.getWidth();
    // FIXME: Get width another way for fir.real/complex
    // - use fir/KindMapping.h and llvm::Type
    // - or use evaluate/type.h
    if (auto r{t.dyn_cast<fir::RealType>()})
      return r.getFKind() * 4;
    if (auto cplx{t.dyn_cast<fir::ComplexType>()})
      return cplx.getFKind() * 4;
    llvm_unreachable("not a floating-point type");
  }

  static Conversion conversionBetweenTypes(mlir::Type from, mlir::Type to) {
    if (from == to) {
      return Conversion::None;
    }
    if (auto fromIntTy{from.dyn_cast<mlir::IntegerType>()}) {
      if (auto toIntTy{to.dyn_cast<mlir::IntegerType>()}) {
        return fromIntTy.getWidth() > toIntTy.getWidth() ? Conversion::Narrow
                                                         : Conversion::Extend;
      }
    }
    if (fir::isa_real(from) && fir::isa_real(to)) {
      return getFloatingPointWidth(from) > getFloatingPointWidth(to)
                 ? Conversion::Narrow
                 : Conversion::Extend;
    }
    if (auto fromCplxTy{from.dyn_cast<fir::ComplexType>()}) {
      if (auto toCplxTy{to.dyn_cast<fir::ComplexType>()}) {
        return getFloatingPointWidth(fromCplxTy) >
                       getFloatingPointWidth(toCplxTy)
                   ? Conversion::Narrow
                   : Conversion::Extend;
      }
    }
    // Notes:
    // - No conversion between character types, specialization of runtime
    // functions should be made instead.
    // - It is not clear there is a use case for automatic conversions
    // around Logical and it may damage hidden information in the physical
    // storage so do not do it.
    return Conversion::Forbidden;
  }

  // Below are indexes to access data in conversions.
  // The order in data does matter for lexicographical_compare
  enum {
    narrowingArg = 0,   // usually bad
    extendingResult,    // usually bad
    nonExtendingResult, // usually ok
    nonNarrowingArg,    // usually ok
    dataSize
  };

  std::array<int, dataSize> conversions{/* zero init*/};
  bool infinite{false}; // When forbidden conversion or wrong argument number
};

/// Build mlir::FuncOp from runtime symbol description and add
/// fir.runtime attribute.
static mlir::FuncOp getFuncOp(mlir::Location loc, fir::FirOpBuilder &builder,
                              const RuntimeFunction &runtime) {
  auto function = builder.addNamedFunction(
      loc, runtime.symbol, runtime.typeGenerator(builder.getContext()));
  function->setAttr("fir.runtime", builder.getUnitAttr());
  return function;
}

/// Select runtime function that has the smallest distance to the intrinsic
/// function type and that will not imply narrowing arguments or extending the
/// result.
/// If nothing is found, the mlir::FuncOp will contain a nullptr.
mlir::FuncOp searchFunctionInLibrary(
    mlir::Location loc, fir::FirOpBuilder &builder,
    const Fortran::common::StaticMultimapView<RuntimeFunction> &lib,
    llvm::StringRef name, mlir::FunctionType funcType,
    const RuntimeFunction **bestNearMatch,
    FunctionDistance &bestMatchDistance) {
  auto range = lib.equal_range(name);
  for (auto iter{range.first}; iter != range.second && iter; ++iter) {
    const auto &impl = *iter;
    auto implType = impl.typeGenerator(builder.getContext());
    if (funcType == implType) {
      return getFuncOp(loc, builder, impl); // exact match
    } else {
      FunctionDistance distance(funcType, implType);
      if (distance.isSmallerThan(bestMatchDistance)) {
        *bestNearMatch = &impl;
        bestMatchDistance = std::move(distance);
      }
    }
  }
  return {};
}

/// Search runtime for the best runtime function given an intrinsic name
/// and interface. The interface may not be a perfect match in which case
/// the caller is responsible to insert argument and return value conversions.
/// If nothing is found, the mlir::FuncOp will contain a nullptr.
static mlir::FuncOp getRuntimeFunction(mlir::Location loc,
                                       fir::FirOpBuilder &builder,
                                       llvm::StringRef name,
                                       mlir::FunctionType funcType) {
  const RuntimeFunction *bestNearMatch = nullptr;
  FunctionDistance bestMatchDistance{};
  mlir::FuncOp match;
  using RtMap = Fortran::common::StaticMultimapView<RuntimeFunction>;
  static constexpr RtMap pgmathF(pgmathFast);
  static_assert(pgmathF.Verify() && "map must be sorted");
  static constexpr RtMap pgmathR(pgmathRelaxed);
  static_assert(pgmathR.Verify() && "map must be sorted");
  static constexpr RtMap pgmathP(pgmathPrecise);
  static_assert(pgmathP.Verify() && "map must be sorted");
  if (mathRuntimeVersion == fastVersion) {
    match = searchFunctionInLibrary(loc, builder, pgmathF, name, funcType,
                                    &bestNearMatch, bestMatchDistance);
  } else if (mathRuntimeVersion == relaxedVersion) {
    match = searchFunctionInLibrary(loc, builder, pgmathR, name, funcType,
                                    &bestNearMatch, bestMatchDistance);
  } else if (mathRuntimeVersion == preciseVersion) {
    match = searchFunctionInLibrary(loc, builder, pgmathP, name, funcType,
                                    &bestNearMatch, bestMatchDistance);
  } else {
    assert(mathRuntimeVersion == llvmOnly && "unknown math runtime");
  }
  if (match)
    return match;

  // Go through llvm intrinsics if not exact match in libpgmath or if
  // mathRuntimeVersion == llvmOnly
  static constexpr RtMap llvmIntr(llvmIntrinsics);
  static_assert(llvmIntr.Verify() && "map must be sorted");
  if (auto exactMatch =
          searchFunctionInLibrary(loc, builder, llvmIntr, name, funcType,
                                  &bestNearMatch, bestMatchDistance))
    return exactMatch;

  if (bestNearMatch != nullptr) {
    assert(!bestMatchDistance.isLosingPrecision() &&
           "runtime selection loses precision");
    return getFuncOp(loc, builder, *bestNearMatch);
  }
  return {};
}

/// Helpers to get function type from arguments and result type.
static mlir::FunctionType getFunctionType(mlir::Type resultType,
                                          llvm::ArrayRef<mlir::Value> arguments,
                                          fir::FirOpBuilder &builder) {
  llvm::SmallVector<mlir::Type, 2> argumentTypes;
  for (auto &arg : arguments)
    argumentTypes.push_back(arg.getType());
  return mlir::FunctionType::get(builder.getModule().getContext(),
                                 argumentTypes, resultType);
}

/// fir::ExtendedValue to mlir::Value translation layer

fir::ExtendedValue toExtendedValue(mlir::Value val, fir::FirOpBuilder &builder,
                                   mlir::Location loc) {
  assert(val && "optional unhandled here");
  auto type = val.getType();
  auto base = val;
  auto indexType = builder.getIndexType();
  llvm::SmallVector<mlir::Value, 2> extents;

  Fortran::lower::CharacterExprHelper charHelper{builder, loc};
  if (charHelper.isCharacter(type))
    return charHelper.toExtendedValue(val);

  if (auto refType = type.dyn_cast<fir::ReferenceType>())
    type = refType.getEleTy();

  if (auto arrayType = type.dyn_cast<fir::SequenceType>()) {
    type = arrayType.getEleTy();
    for (auto extent : arrayType.getShape()) {
      if (extent == fir::SequenceType::getUnknownExtent())
        break;
      extents.emplace_back(
          builder.createIntegerConstant(loc, indexType, extent));
    }
    // Last extent might be missing in case of assumed-size. If more extents
    // could not be deduced from type, that's an error (a fir.box should
    // have been used in the interface).
    if (extents.size() + 1 < arrayType.getShape().size())
      mlir::emitError(loc, "cannot retrieve array extents from type");
  } else if (type.isa<fir::BoxType>() || type.isa<fir::RecordType>()) {
    mlir::emitError(loc, "descriptor or derived type not yet handled");
  }

  if (!extents.empty())
    return fir::ArrayBoxValue{base, extents};
  return base;
}

mlir::Value toValue(const fir::ExtendedValue &val, fir::FirOpBuilder &builder,
                    mlir::Location loc) {
  if (auto charBox = val.getCharBox()) {
    auto buffer = charBox->getBuffer();
    if (buffer.getType().isa<fir::BoxCharType>())
      return buffer;
    return Fortran::lower::CharacterExprHelper{builder, loc}.createEmboxChar(
        buffer, charBox->getLen());
  }

  // FIXME: need to access other ExtendedValue variants and handle them
  // properly.
  return fir::getBase(val);
}

//===----------------------------------------------------------------------===//
// IntrinsicLibrary
//===----------------------------------------------------------------------===//

template <typename GeneratorType>
fir::ExtendedValue IntrinsicLibrary::genElementalCall(
    GeneratorType generator, llvm::StringRef name, mlir::Type resultType,
    llvm::ArrayRef<fir::ExtendedValue> args, bool outline) {
  llvm::SmallVector<mlir::Value, 2> scalarArgs;
  for (const auto &arg : args) {
    if (arg.getUnboxed() || arg.getCharBox()) {
      scalarArgs.emplace_back(fir::getBase(arg));
    } else {
      // TODO: get the result shape and create the loop...
      mlir::emitError(loc, "array or descriptor not yet handled in elemental "
                           "intrinsic lowering");
      exit(1);
    }
  }
  if (outline)
    return outlineInWrapper(generator, name, resultType, scalarArgs);
  return invokeGenerator(generator, resultType, scalarArgs);
}

/// Some ExtendedGenerator operating on characters are also elemental
/// (e.g LEN_TRIM).
template <>
fir::ExtendedValue
IntrinsicLibrary::genElementalCall<IntrinsicLibrary::ExtendedGenerator>(
    ExtendedGenerator generator, llvm::StringRef name, mlir::Type resultType,
    llvm::ArrayRef<fir::ExtendedValue> args, bool outline) {
  for (const auto &arg : args)
    if (!arg.getUnboxed() && !arg.getCharBox()) {
      // TODO: get the result shape and create the loop...
      mlir::emitError(loc, "array or descriptor not yet handled in elemental "
                           "intrinsic lowering");
      exit(1);
    }
  if (outline)
    return outlineInWrapper(generator, name, resultType, args);
  return std::invoke(generator, *this, resultType, args);
}

fir::ExtendedValue
IntrinsicLibrary::genIntrinsicCall(llvm::StringRef name, mlir::Type resultType,
                                   llvm::ArrayRef<fir::ExtendedValue> args) {
  for (auto &handler : handlers)
    if (name == handler.name) {
      bool outline = handler.outline || outlineAllIntrinsics;
      if (const auto *elementalGenerator =
              std::get_if<ElementalGenerator>(&handler.generator))
        return genElementalCall(*elementalGenerator, name, resultType, args,
                                outline);
      const auto &generator = std::get<ExtendedGenerator>(handler.generator);
      if (handler.isElemental)
        return genElementalCall(generator, name, resultType, args, outline);
      if (outline)
        return outlineInWrapper(generator, name, resultType, args);
      return std::invoke(generator, *this, resultType, args);
    }

  // Try the runtime if no special handler was defined for the
  // intrinsic being called. Maths runtime only has numerical elemental.
  // No optional arguments are expected at this point, the code will
  // crash if it gets absent optional.

  // FIXME: using toValue to get the type won't work with array arguments.
  llvm::SmallVector<mlir::Value, 2> mlirArgs;
  for (const auto &extendedVal : args) {
    auto val = toValue(extendedVal, builder, loc);
    if (!val) {
      // If an absent optional gets there, most likely its handler has just
      // not yet been defined.
      mlir::emitError(loc,
                      "TODO: missing intrinsic lowering: " + llvm::Twine(name));
      exit(1);
    }
    mlirArgs.emplace_back(val);
  }
  mlir::FunctionType soughtFuncType =
      getFunctionType(resultType, mlirArgs, builder);

  auto runtimeCallGenerator = getRuntimeCallGenerator(name, soughtFuncType);
  return genElementalCall(runtimeCallGenerator, name, resultType, args,
                          /* outline */ true);
}

mlir::Value
IntrinsicLibrary::invokeGenerator(ElementalGenerator generator,
                                  mlir::Type resultType,
                                  llvm::ArrayRef<mlir::Value> args) {
  return std::invoke(generator, *this, resultType, args);
}

mlir::Value
IntrinsicLibrary::invokeGenerator(RuntimeCallGenerator generator,
                                  mlir::Type resultType,
                                  llvm::ArrayRef<mlir::Value> args) {
  return generator(builder, loc, args);
}

mlir::Value
IntrinsicLibrary::invokeGenerator(ExtendedGenerator generator,
                                  mlir::Type resultType,
                                  llvm::ArrayRef<mlir::Value> args) {
  llvm::SmallVector<fir::ExtendedValue, 2> extendedArgs;
  for (auto arg : args)
    extendedArgs.emplace_back(toExtendedValue(arg, builder, loc));
  auto extendedResult = std::invoke(generator, *this, resultType, extendedArgs);
  return toValue(extendedResult, builder, loc);
}

template <typename GeneratorType>
mlir::FuncOp IntrinsicLibrary::getWrapper(GeneratorType generator,
                                          llvm::StringRef name,
                                          mlir::FunctionType funcType,
                                          bool loadRefArguments) {
  assert(funcType.getNumResults() == 1 &&
         "expect one result for intrinsic functions");
  auto resultType = funcType.getResult(0);
  std::string wrapperName = fir::mangleIntrinsicProcedure(name, funcType);
  auto function = builder.getNamedFunction(wrapperName);
  if (!function) {
    // First time this wrapper is needed, build it.
    function = builder.createFunction(loc, wrapperName, funcType);
    function->setAttr("fir.intrinsic", builder.getUnitAttr());
    function.addEntryBlock();

    // Create local context to emit code into the newly created function
    // This new function is not linked to a source file location, only
    // its calls will be.
    auto localBuilder =
        std::make_unique<fir::FirOpBuilder>(function, builder.getKindMap());
    localBuilder->setInsertionPointToStart(&function.front());
    // Location of code inside wrapper of the wrapper is independent from
    // the location of the intrinsic call.
    auto localLoc = localBuilder->getUnknownLoc();
    llvm::SmallVector<mlir::Value, 2> localArguments;
    for (mlir::BlockArgument bArg : function.front().getArguments()) {
      auto refType = bArg.getType().dyn_cast<fir::ReferenceType>();
      if (loadRefArguments && refType) {
        auto loaded = localBuilder->create<fir::LoadOp>(localLoc, bArg);
        localArguments.push_back(loaded);
      } else {
        localArguments.push_back(bArg);
      }
    }

    IntrinsicLibrary localLib{*localBuilder, localLoc};
    auto result =
        localLib.invokeGenerator(generator, resultType, localArguments);
    localBuilder->create<mlir::ReturnOp>(localLoc, result);
  } else {
    // Wrapper was already built, ensure it has the sought type
    assert(function.getType() == funcType &&
           "conflict between intrinsic wrapper types");
  }
  return function;
}

/// Helpers to detect absent optional (not yet supported in outlining).
bool static hasAbsentOptional(llvm::ArrayRef<mlir::Value> args) {
  for (const auto &arg : args)
    if (!arg)
      return true;
  return false;
}
bool static hasAbsentOptional(llvm::ArrayRef<fir::ExtendedValue> args) {
  for (const auto &arg : args)
    if (!fir::getBase(arg))
      return true;
  return false;
}

template <typename GeneratorType>
mlir::Value
IntrinsicLibrary::outlineInWrapper(GeneratorType generator,
                                   llvm::StringRef name, mlir::Type resultType,
                                   llvm::ArrayRef<mlir::Value> args) {
  if (hasAbsentOptional(args)) {
    // TODO: absent optional in outlining is an issue: we cannot just ignore
    // them. Needs a better interface here. The issue is that we cannot easily
    // tell that a value is optional or not here if it is presents. And if it is
    // absent, we cannot tell what it type should be.
    mlir::emitError(loc, "todo: cannot outline call to intrinsic " +
                             llvm::Twine(name) +
                             " with absent optional argument");
    exit(1);
  }

  auto funcType = getFunctionType(resultType, args, builder);
  auto wrapper = getWrapper(generator, name, funcType);
  return builder.create<mlir::CallOp>(loc, wrapper, args).getResult(0);
}

fir::ExtendedValue
IntrinsicLibrary::outlineInWrapper(ExtendedGenerator generator,
                                   llvm::StringRef name, mlir::Type resultType,
                                   llvm::ArrayRef<fir::ExtendedValue> args) {
  if (hasAbsentOptional(args)) {
    // TODO
    mlir::emitError(loc, "todo: cannot outline call to intrinsic " +
                             llvm::Twine(name) +
                             " with absent optional argument");
    exit(1);
  }
  llvm::SmallVector<mlir::Value, 2> mlirArgs;
  for (const auto &extendedVal : args)
    mlirArgs.emplace_back(toValue(extendedVal, builder, loc));
  auto funcType = getFunctionType(resultType, mlirArgs, builder);
  auto wrapper = getWrapper(generator, name, funcType);
  auto mlirResult =
      builder.create<mlir::CallOp>(loc, wrapper, mlirArgs).getResult(0);
  return toExtendedValue(mlirResult, builder, loc);
}

IntrinsicLibrary::RuntimeCallGenerator
IntrinsicLibrary::getRuntimeCallGenerator(llvm::StringRef name,
                                          mlir::FunctionType soughtFuncType) {
  auto funcOp = getRuntimeFunction(loc, builder, name, soughtFuncType);
  if (!funcOp) {
    mlir::emitError(loc,
                    "TODO: missing intrinsic lowering: " + llvm::Twine(name));
    llvm::errs() << "requested type was: " << soughtFuncType << "\n";
    exit(1);
  }

  mlir::FunctionType actualFuncType = funcOp.getType();
  assert(actualFuncType.getNumResults() == soughtFuncType.getNumResults() &&
         actualFuncType.getNumInputs() == soughtFuncType.getNumInputs() &&
         actualFuncType.getNumResults() == 1 && "Bad intrinsic match");

  return [funcOp, actualFuncType,
          soughtFuncType](fir::FirOpBuilder &builder, mlir::Location loc,
                          llvm::ArrayRef<mlir::Value> args) {
    llvm::SmallVector<mlir::Value, 2> convertedArguments;
    for (const auto &pair : llvm::zip(actualFuncType.getInputs(), args))
      convertedArguments.push_back(
          builder.createConvert(loc, std::get<0>(pair), std::get<1>(pair)));
    auto call = builder.create<mlir::CallOp>(loc, funcOp, convertedArguments);
    mlir::Type soughtType = soughtFuncType.getResult(0);
    return builder.createConvert(loc, soughtType, call.getResult(0));
  };
}

mlir::SymbolRefAttr IntrinsicLibrary::getUnrestrictedIntrinsicSymbolRefAttr(
    llvm::StringRef name, mlir::FunctionType signature) {
  // Unrestricted intrinsics signature follows implicit rules: argument
  // are passed by references. But the runtime versions expect values.
  // So instead of duplicating the runtime, just have the wrappers loading
  // this before calling the code generators.
  bool loadRefArguments = true;
  mlir::FuncOp funcOp;
  for (auto &handler : handlers)
    if (name == handler.name)
      funcOp = std::visit(
          [&](auto generator) {
            return getWrapper(generator, name, signature, loadRefArguments);
          },
          handler.generator);

  if (!funcOp) {
    llvm::SmallVector<mlir::Type, 2> argTypes;
    for (auto type : signature.getInputs()) {
      if (auto refType = type.dyn_cast<fir::ReferenceType>())
        argTypes.push_back(refType.getEleTy());
      else
        argTypes.push_back(type);
    }
    auto soughtFuncType =
        builder.getFunctionType(signature.getResults(), argTypes);
    auto rtCallGenerator = getRuntimeCallGenerator(name, soughtFuncType);
    funcOp = getWrapper(rtCallGenerator, name, signature, loadRefArguments);
  }

  return SymbolRefAttr::get(funcOp);
}

//===----------------------------------------------------------------------===//
// Code generators for the intrinsic
//===----------------------------------------------------------------------===//

mlir::Value IntrinsicLibrary::genRuntimeCall(llvm::StringRef name,
                                             mlir::Type resultType,
                                             llvm::ArrayRef<mlir::Value> args) {
  mlir::FunctionType soughtFuncType =
      getFunctionType(resultType, args, builder);
  return getRuntimeCallGenerator(name, soughtFuncType)(builder, loc, args);
}

mlir::Value IntrinsicLibrary::genConversion(mlir::Type resultType,
                                            llvm::ArrayRef<mlir::Value> args) {
  // There can be an optional kind in second argument.
  assert(args.size() >= 1);
  return builder.convertWithSemantics(loc, resultType, args[0]);
}

// ABS
mlir::Value IntrinsicLibrary::genAbs(mlir::Type resultType,
                                     llvm::ArrayRef<mlir::Value> args) {
  assert(args.size() == 1);
  auto arg = args[0];
  auto type = arg.getType();
  if (fir::isa_real(type)) {
    // Runtime call to fp abs. An alternative would be to use mlir math::AbsOp
    // but it does not support all fir floating point types.
    return genRuntimeCall("abs", resultType, args);
  }
  if (auto intType = type.dyn_cast<mlir::IntegerType>()) {
    // At the time of this implementation there is no abs op in mlir.
    // So, implement abs here without branching.
    auto shift =
        builder.createIntegerConstant(loc, intType, intType.getWidth() - 1);
    auto mask = builder.create<mlir::arith::ShRSIOp>(loc, arg, shift);
    auto xored = builder.create<mlir::arith::XOrIOp>(loc, arg, mask);
    return builder.create<mlir::arith::SubIOp>(loc, xored, mask);
  }
  if (fir::isa_complex(type)) {
    // Use HYPOT to fulfill the no underflow/overflow requirement.
    auto parts =
        Fortran::lower::ComplexExprHelper{builder, loc}.extractParts(arg);
    llvm::SmallVector<mlir::Value, 2> args = {parts.first, parts.second};
    return genRuntimeCall("hypot", resultType, args);
  }
  llvm_unreachable("unexpected type in ABS argument");
}

// AIMAG
mlir::Value IntrinsicLibrary::genAimag(mlir::Type resultType,
                                       llvm::ArrayRef<mlir::Value> args) {
  assert(args.size() == 1);
  return Fortran::lower::ComplexExprHelper{builder, loc}.extractComplexPart(
      args[0], true /* isImagPart */);
}

// ANINT
mlir::Value IntrinsicLibrary::genAnint(mlir::Type resultType,
                                       llvm::ArrayRef<mlir::Value> args) {
  assert(args.size() >= 1);
  // Skip optional kind argument to search the runtime; it is already reflected
  // in result type.
  return genRuntimeCall("anint", resultType, {args[0]});
}

// AINT
mlir::Value IntrinsicLibrary::genAint(mlir::Type resultType,
                                      llvm::ArrayRef<mlir::Value> args) {
  assert(args.size() >= 1);
  // Skip optional kind argument to search the runtime; it is already reflected
  // in result type.
  return genRuntimeCall("aint", resultType, {args[0]});
}

// CEILING
mlir::Value IntrinsicLibrary::genCeiling(mlir::Type resultType,
                                         llvm::ArrayRef<mlir::Value> args) {
  // Optional KIND argument.
  assert(args.size() >= 1);
  auto arg = args[0];
  // Use ceil that is not an actual Fortran intrinsic but that is
  // an llvm intrinsic that does the same, but return a floating
  // point.
  auto ceil = genRuntimeCall("ceil", arg.getType(), {arg});
  return builder.createConvert(loc, resultType, ceil);
}

// CONJG
mlir::Value IntrinsicLibrary::genConjg(mlir::Type resultType,
                                       llvm::ArrayRef<mlir::Value> args) {
  assert(args.size() == 1);
  if (resultType != args[0].getType())
    llvm_unreachable("argument type mismatch");

  mlir::Value cplx = args[0];
  auto imag =
      Fortran::lower::ComplexExprHelper{builder, loc}.extractComplexPart(
          cplx, /*isImagPart=*/true);
  auto negImag = builder.create<mlir::arith::NegFOp>(loc, imag);
  return Fortran::lower::ComplexExprHelper{builder, loc}.insertComplexPart(
      cplx, negImag, /*isImagPart=*/true);
}

// DIM
mlir::Value IntrinsicLibrary::genDim(mlir::Type resultType,
                                     llvm::ArrayRef<mlir::Value> args) {
  assert(args.size() == 2);
  if (resultType.isa<mlir::IntegerType>()) {
    auto zero = builder.createIntegerConstant(loc, resultType, 0);
    auto diff = builder.create<mlir::arith::SubIOp>(loc, args[0], args[1]);
    auto cmp = builder.create<mlir::arith::CmpIOp>(
        loc, mlir::arith::CmpIPredicate::sgt, diff, zero);
    return builder.create<mlir::SelectOp>(loc, cmp, diff, zero);
  }
  assert(fir::isa_real(resultType) && "Only expects real and integer in DIM");
  auto zero = builder.createRealZeroConstant(loc, resultType);
  auto diff = builder.create<mlir::arith::SubFOp>(loc, args[0], args[1]);
  auto cmp = builder.create<mlir::arith::CmpFOp>(
      loc, mlir::arith::CmpFPredicate::OGT, diff, zero);
  return builder.create<mlir::SelectOp>(loc, cmp, diff, zero);
}

// DPROD
mlir::Value IntrinsicLibrary::genDprod(mlir::Type resultType,
                                       llvm::ArrayRef<mlir::Value> args) {
  assert(args.size() == 2);
  assert(fir::isa_real(resultType) &&
         "Result must be double precision in DPROD");
  auto a = builder.createConvert(loc, resultType, args[0]);
  auto b = builder.createConvert(loc, resultType, args[1]);
  return builder.create<mlir::arith::MulFOp>(loc, a, b);
}

// FLOOR
mlir::Value IntrinsicLibrary::genFloor(mlir::Type resultType,
                                       llvm::ArrayRef<mlir::Value> args) {
  // Optional KIND argument.
  assert(args.size() >= 1);
  auto arg = args[0];
  // Use LLVM floor that returns real.
  auto floor = genRuntimeCall("floor", arg.getType(), {arg});
  return builder.createConvert(loc, resultType, floor);
}

// IAND
mlir::Value IntrinsicLibrary::genIAnd(mlir::Type resultType,
                                      llvm::ArrayRef<mlir::Value> args) {
  assert(args.size() == 2);

  return builder.create<mlir::arith::AndIOp>(loc, args[0], args[1]);
}

// ICHAR
mlir::Value IntrinsicLibrary::genIchar(mlir::Type resultType,
                                       llvm::ArrayRef<mlir::Value> args) {
  // There can be an optional kind in second argument.
  assert(args.size() >= 1);

  auto arg = args[0];
  Fortran::lower::CharacterExprHelper helper{builder, loc};
  auto dataAndLen = helper.createUnboxChar(arg);
  auto charType = fir::CharacterType::get(
      builder.getContext(), helper.getCharacterKind(arg.getType()), 1);
  auto refType = builder.getRefType(charType);
  auto charAddr = builder.createConvert(loc, refType, dataAndLen.first);
  auto charVal = builder.create<fir::LoadOp>(loc, charType, charAddr);
  return builder.createConvert(loc, resultType, charVal);
}

// IEOR
mlir::Value IntrinsicLibrary::genIEOr(mlir::Type resultType,
                                      llvm::ArrayRef<mlir::Value> args) {
  assert(args.size() == 2);
  return builder.create<mlir::arith::XOrIOp>(loc, args[0], args[1]);
}

// IOR
mlir::Value IntrinsicLibrary::genIOr(mlir::Type resultType,
                                     llvm::ArrayRef<mlir::Value> args) {
  assert(args.size() == 2);
  return builder.create<mlir::arith::OrIOp>(loc, args[0], args[1]);
}

// LEN
// Note that this is only used for unrestricted intrinsic.
// Usage of LEN are otherwise rewritten as descriptor inquiries by the
// front-end.
fir::ExtendedValue
IntrinsicLibrary::genLen(mlir::Type resultType,
                         llvm::ArrayRef<fir::ExtendedValue> args) {
  // Optional KIND argument reflected in result type.
  assert(args.size() >= 1);
  mlir::Value len;
  if (const auto *charBox = args[0].getCharBox()) {
    len = charBox->getLen();
  } else if (const auto *charBoxArray = args[0].getCharBox()) {
    len = charBoxArray->getLen();
  } else {
    Fortran::lower::CharacterExprHelper helper{builder, loc};
    len = helper.createUnboxChar(fir::getBase(args[0])).second;
  }

  return builder.createConvert(loc, resultType, len);
}

// LEN_TRIM
fir::ExtendedValue
IntrinsicLibrary::genLenTrim(mlir::Type resultType,
                             llvm::ArrayRef<fir::ExtendedValue> args) {
  // Optional KIND argument reflected in result type.
  assert(args.size() >= 1);
  Fortran::lower::CharacterExprHelper helper{builder, loc};
  auto len = helper.createLenTrim(fir::getBase(args[0]));
  return builder.createConvert(loc, resultType, len);
}

// MERGE
mlir::Value IntrinsicLibrary::genMerge(mlir::Type,
                                       llvm::ArrayRef<mlir::Value> args) {
  assert(args.size() == 3);

  auto i1Type = mlir::IntegerType::get(builder.getContext(), 1);
  auto mask = builder.createConvert(loc, i1Type, args[2]);
  return builder.create<mlir::SelectOp>(loc, mask, args[0], args[1]);
}

// MOD
mlir::Value IntrinsicLibrary::genMod(mlir::Type resultType,
                                     llvm::ArrayRef<mlir::Value> args) {
  assert(args.size() == 2);
  if (resultType.isa<mlir::IntegerType>())
    return builder.create<mlir::arith::RemSIOp>(loc, args[0], args[1]);

  // Use runtime. Note that mlir::arith::RemFOp implements floating point
  // remainder, but it does not work with fir::Real type.
  // TODO: consider using mlir::arith::RemFOp when possible, that may help
  // folding and  optimizations.
  return genRuntimeCall("mod", resultType, args);
}

// NINT
mlir::Value IntrinsicLibrary::genNint(mlir::Type resultType,
                                      llvm::ArrayRef<mlir::Value> args) {
  assert(args.size() >= 1);
  // Skip optional kind argument to search the runtime; it is already reflected
  // in result type.
  return genRuntimeCall("nint", resultType, {args[0]});
}

// SIGN
mlir::Value IntrinsicLibrary::genSign(mlir::Type resultType,
                                      llvm::ArrayRef<mlir::Value> args) {
  assert(args.size() == 2);
  auto abs = genAbs(resultType, {args[0]});
  if (resultType.isa<mlir::IntegerType>()) {
    auto zero = builder.createIntegerConstant(loc, resultType, 0);
    auto neg = builder.create<mlir::arith::SubIOp>(loc, zero, abs);
    auto cmp = builder.create<mlir::arith::CmpIOp>(
        loc, mlir::arith::CmpIPredicate::slt, args[1], zero);
    return builder.create<mlir::SelectOp>(loc, cmp, neg, abs);
  }
  // TODO: Requirements when second argument is +0./0.
  auto zeroAttr = builder.getZeroAttr(resultType);
  auto zero =
      builder.create<mlir::arith::ConstantOp>(loc, resultType, zeroAttr);
  auto neg = builder.create<mlir::arith::NegFOp>(loc, abs);
  auto cmp = builder.create<mlir::arith::CmpFOp>(
      loc, mlir::arith::CmpFPredicate::OLT, args[1], zero);
  return builder.create<mlir::SelectOp>(loc, cmp, neg, abs);
}

// Compare two FIR values and return boolean result as i1.
template <Extremum extremum, ExtremumBehavior behavior>
static mlir::Value createExtremumCompare(mlir::Location loc,
                                         fir::FirOpBuilder &builder,
                                         mlir::Value left, mlir::Value right) {
  static constexpr auto integerPredicate =
      extremum == Extremum::Max ? mlir::arith::CmpIPredicate::sgt
                                : mlir::arith::CmpIPredicate::slt;
  static constexpr auto orderedCmp = extremum == Extremum::Max
                                         ? mlir::arith::CmpFPredicate::OGT
                                         : mlir::arith::CmpFPredicate::OLT;
  auto type = left.getType();
  mlir::Value result;
  if (fir::isa_real(type)) {
    // Note: the signaling/quit aspect of the result required by IEEE
    // cannot currently be obtained with LLVM without ad-hoc runtime.
    if constexpr (behavior == ExtremumBehavior::IeeeMinMaximumNumber) {
      // Return the number if one of the inputs is NaN and the other is
      // a number.
      auto leftIsResult =
          builder.create<mlir::arith::CmpFOp>(loc, orderedCmp, left, right);
      auto rightIsNan = builder.create<mlir::arith::CmpFOp>(
          loc, mlir::arith::CmpFPredicate::UNE, right, right);
      result =
          builder.create<mlir::arith::OrIOp>(loc, leftIsResult, rightIsNan);
    } else if constexpr (behavior == ExtremumBehavior::IeeeMinMaximum) {
      // Always return NaNs if one the input is NaNs
      auto leftIsResult =
          builder.create<mlir::arith::CmpFOp>(loc, orderedCmp, left, right);
      auto leftIsNan = builder.create<mlir::arith::CmpFOp>(
          loc, mlir::arith::CmpFPredicate::UNE, left, left);
      result = builder.create<mlir::arith::OrIOp>(loc, leftIsResult, leftIsNan);
    } else if constexpr (behavior == ExtremumBehavior::MinMaxss) {
      // If the left is a NaN, return the right whatever it is.
      result =
          builder.create<mlir::arith::CmpFOp>(loc, orderedCmp, left, right);
    } else if constexpr (behavior == ExtremumBehavior::PgfortranLlvm) {
      // If one of the operand is a NaN, return left whatever it is.
      static constexpr auto unorderedCmp =
          extremum == Extremum::Max ? mlir::arith::CmpFPredicate::UGT
                                    : mlir::arith::CmpFPredicate::ULT;
      result =
          builder.create<mlir::arith::CmpFOp>(loc, unorderedCmp, left, right);
    } else {
      // TODO: ieeeMinNum/ieeeMaxNum
      static_assert(behavior == ExtremumBehavior::IeeeMinMaxNum,
                    "ieeeMinNum/ieeeMaxNum behavior not implemented");
    }
  } else if (fir::isa_integer(type)) {
    result =
        builder.create<mlir::arith::CmpIOp>(loc, integerPredicate, left, right);
  } else if (type.isa<fir::CharacterType>()) {
    // TODO: ! character min and max is tricky because the result
    // length is the length of the longest argument!
    // So we may need a temp.
  }
  assert(result);
  return result;
}

// MIN and MAX
template <Extremum extremum, ExtremumBehavior behavior>
mlir::Value IntrinsicLibrary::genExtremum(mlir::Type,
                                          llvm::ArrayRef<mlir::Value> args) {
  assert(args.size() >= 1);
  mlir::Value result = args[0];
  for (auto arg : args.drop_front()) {
    auto mask =
        createExtremumCompare<extremum, behavior>(loc, builder, result, arg);
    result = builder.create<mlir::SelectOp>(loc, mask, result, arg);
  }
  return result;
}

//===----------------------------------------------------------------------===//
// Public intrinsic call helpers
//===----------------------------------------------------------------------===//

fir::ExtendedValue
Fortran::lower::genIntrinsicCall(fir::FirOpBuilder &builder, mlir::Location loc,
                                 llvm::StringRef name, mlir::Type resultType,
                                 llvm::ArrayRef<fir::ExtendedValue> args) {
  return IntrinsicLibrary{builder, loc}.genIntrinsicCall(name, resultType,
                                                         args);
}

mlir::Value Fortran::lower::genMax(fir::FirOpBuilder &builder,
                                   mlir::Location loc,
                                   llvm::ArrayRef<mlir::Value> args) {
  assert(args.size() > 0 && "max requires at least one argument");
  return IntrinsicLibrary{builder, loc}
      .genExtremum<Extremum::Max, ExtremumBehavior::MinMaxss>(args[0].getType(),
                                                              args);
}

mlir::Value Fortran::lower::genMin(fir::FirOpBuilder &builder,
                                   mlir::Location loc,
                                   llvm::ArrayRef<mlir::Value> args) {
  assert(args.size() > 0 && "min requires at least one argument");
  return IntrinsicLibrary{builder, loc}
      .genExtremum<Extremum::Min, ExtremumBehavior::MinMaxss>(args[0].getType(),
                                                              args);
}

mlir::Value Fortran::lower::genPow(fir::FirOpBuilder &builder,
                                   mlir::Location loc, mlir::Type type,
                                   mlir::Value x, mlir::Value y) {
  return IntrinsicLibrary{builder, loc}.genRuntimeCall("pow", type, {x, y});
}

mlir::SymbolRefAttr Fortran::lower::getUnrestrictedIntrinsicSymbolRefAttr(
    fir::FirOpBuilder &builder, mlir::Location loc, llvm::StringRef name,
    mlir::FunctionType signature) {
  return IntrinsicLibrary{builder, loc}.getUnrestrictedIntrinsicSymbolRefAttr(
      name, signature);
}