numeric-templates.h

//===-- runtime/numeric-templates.h -----------------------------*- C++ -*-===//
//
// 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
//
//===----------------------------------------------------------------------===//
 
// Generic class and function templates used for implementing
// various numeric intrinsics (EXPONENT, FRACTION, etc.).
//
// This header file also defines generic templates for "basic"
// math operations like abs, isnan, etc. The Float128Math
// library provides specializations for these templates
// for the data type corresponding to CppTypeFor<TypeCategory::Real, 16>
// on the target.
 
#ifndef FORTRAN_RUNTIME_NUMERIC_TEMPLATES_H_
#define FORTRAN_RUNTIME_NUMERIC_TEMPLATES_H_
 
#include "terminator.h"
#include "tools.h"
#include "flang/Common/api-attrs.h"
#include "flang/Common/erfc-scaled.h"
#include "flang/Common/float128.h"
#include <cstdint>
#include <limits>
 
namespace Fortran::runtime {
 
// MAX/MIN/LOWEST values for different data types.
 
// MaxOrMinIdentity returns MAX or LOWEST value of the given type.
template <TypeCategory CAT, int KIND, bool IS_MAXVAL, typename Enable = void>
struct MaxOrMinIdentity {
  using Type = CppTypeFor<CAT, KIND>;
  static constexpr RT_API_ATTRS Type Value() {
    return IS_MAXVAL ? std::numeric_limits<Type>::lowest()
                     : std::numeric_limits<Type>::max();
  }
};
 
// std::numeric_limits<> may not know int128_t
template <bool IS_MAXVAL>
struct MaxOrMinIdentity<TypeCategory::Integer, 16, IS_MAXVAL> {
  using Type = CppTypeFor<TypeCategory::Integer, 16>;
  static constexpr RT_API_ATTRS Type Value() {
    return IS_MAXVAL ? Type{1} << 127 : ~Type{0} >> 1;
  }
};
 
#if HAS_FLOAT128
// std::numeric_limits<> may not support __float128.
//
// Usage of GCC quadmath.h's FLT128_MAX is complicated by the fact that
// even GCC complains about 'Q' literal suffix under -Wpedantic.
// We just recreate FLT128_MAX ourselves.
//
// This specialization must engage only when
// CppTypeFor<TypeCategory::Real, 16> is __float128.
template <bool IS_MAXVAL>
struct MaxOrMinIdentity<TypeCategory::Real, 16, IS_MAXVAL,
    typename std::enable_if_t<
        std::is_same_v<CppTypeFor<TypeCategory::Real, 16>, __float128>>> {
  using Type = __float128;
  static RT_API_ATTRS Type Value() {
    // Create a buffer to store binary representation of __float128 constant.
    constexpr std::size_t alignment =
        std::max(alignof(Type), alignof(std::uint64_t));
    alignas(alignment) char data[sizeof(Type)];
 
    // First, verify that our interpretation of __float128 format is correct,
    // e.g. by checking at least one known constant.
    *reinterpret_cast<Type *>(data) = Type(1.0);
    if (*reinterpret_cast<std::uint64_t *>(data) != 0 ||
        *(reinterpret_cast<std::uint64_t *>(data) + 1) != 0x3FFF000000000000) {
      Terminator terminator{__FILE__, __LINE__};
      terminator.Crash("not yet implemented: no full support for __float128");
    }
 
    // Recreate FLT128_MAX.
    *reinterpret_cast<std::uint64_t *>(data) = 0xFFFFFFFFFFFFFFFF;
    *(reinterpret_cast<std::uint64_t *>(data) + 1) = 0x7FFEFFFFFFFFFFFF;
    Type max = *reinterpret_cast<Type *>(data);
    return IS_MAXVAL ? -max : max;
  }
};
#endif // HAS_FLOAT128
 
// Minimum finite representable value.
// For floating-point types, returns minimum positive normalized value.
template <int PREC, typename T> struct MinValue {
  static RT_API_ATTRS T get() { return std::numeric_limits<T>::min(); }
};
template <typename T> struct MinValue<11, T> {
  // TINY(0._2)
  static constexpr RT_API_ATTRS T get() { return 0.00006103515625E-04; }
};
 
#if HAS_FLOAT128
template <> struct MinValue<113, CppTypeFor<TypeCategory::Real, 16>> {
  using Type = CppTypeFor<TypeCategory::Real, 16>;
  static RT_API_ATTRS Type get() {
    // Create a buffer to store binary representation of __float128 constant.
    constexpr std::size_t alignment =
        std::max(alignof(Type), alignof(std::uint64_t));
    alignas(alignment) char data[sizeof(Type)];
 
    // First, verify that our interpretation of __float128 format is correct,
    // e.g. by checking at least one known constant.
    *reinterpret_cast<Type *>(data) = Type(1.0);
    if (*reinterpret_cast<std::uint64_t *>(data) != 0 ||
        *(reinterpret_cast<std::uint64_t *>(data) + 1) != 0x3FFF000000000000) {
      Terminator terminator{__FILE__, __LINE__};
      terminator.Crash("not yet implemented: no full support for __float128");
    }
 
    // Recreate FLT128_MIN.
    *reinterpret_cast<std::uint64_t *>(data) = 0;
    *(reinterpret_cast<std::uint64_t *>(data) + 1) = 0x1000000000000;
    return *reinterpret_cast<Type *>(data);
  }
};
#endif // HAS_FLOAT128
 
template <typename T> struct ABSTy {
  static constexpr RT_API_ATTRS T compute(T x) { return std::abs(x); }
};
 
// Suppress the warnings about calling __host__-only
// 'long double' std::frexp, from __device__ code.
RT_DIAG_PUSH
RT_DIAG_DISABLE_CALL_HOST_FROM_DEVICE_WARN
 
template <typename T> struct FREXPTy {
  static constexpr RT_API_ATTRS T compute(T x, int *e) {
    return std::frexp(x, e);
  }
};
 
RT_DIAG_POP
 
template <typename T> struct ILOGBTy {
  static constexpr RT_API_ATTRS int compute(T x) { return std::ilogb(x); }
};
 
template <typename T> struct ISINFTy {
  static constexpr RT_API_ATTRS bool compute(T x) { return std::isinf(x); }
};
 
template <typename T> struct ISNANTy {
  static constexpr RT_API_ATTRS bool compute(T x) { return std::isnan(x); }
};
 
template <typename T> struct LDEXPTy {
  template <typename ET> static constexpr RT_API_ATTRS T compute(T x, ET e) {
    return std::ldexp(x, e);
  }
};
 
template <typename T> struct MAXTy {
  static constexpr RT_API_ATTRS T compute() {
    return std::numeric_limits<T>::max();
  }
};
 
#if HAS_LDBL128 || HAS_FLOAT128
template <> struct MAXTy<CppTypeFor<TypeCategory::Real, 16>> {
  static CppTypeFor<TypeCategory::Real, 16> compute() {
    return MaxOrMinIdentity<TypeCategory::Real, 16, true>::Value();
  }
};
#endif
 
template <int PREC, typename T> struct MINTy {
  static constexpr RT_API_ATTRS T compute() { return MinValue<PREC, T>::get(); }
};
 
template <typename T> struct QNANTy {
  static constexpr RT_API_ATTRS T compute() {
    return std::numeric_limits<T>::quiet_NaN();
  }
};
 
template <typename T> struct SQRTTy {
  static constexpr RT_API_ATTRS T compute(T x) { return std::sqrt(x); }
};
 
// EXPONENT (16.9.75)
template <typename RESULT, typename ARG>
inline RT_API_ATTRS RESULT Exponent(ARG x) {
  if (ISINFTy<ARG>::compute(x) || ISNANTy<ARG>::compute(x)) {
    return MAXTy<RESULT>::compute(); // +/-Inf, NaN -> HUGE(0)
  } else if (x == 0) {
    return 0; // 0 -> 0
  } else {
    return ILOGBTy<ARG>::compute(x) + 1;
  }
}
 
// FRACTION (16.9.80)
template <typename T> inline RT_API_ATTRS T Fraction(T x) {
  if (ISNANTy<T>::compute(x)) {
    return x; // NaN -> same NaN
  } else if (ISINFTy<T>::compute(x)) {
    return QNANTy<T>::compute(); // +/-Inf -> NaN
  } else if (x == 0) {
    return x; // 0 -> same 0
  } else {
    int ignoredExp;
    return FREXPTy<T>::compute(x, &ignoredExp);
  }
}
 
// SET_EXPONENT (16.9.171)
template <typename T> inline RT_API_ATTRS T SetExponent(T x, std::int64_t p) {
  if (ISNANTy<T>::compute(x)) {
    return x; // NaN -> same NaN
  } else if (ISINFTy<T>::compute(x)) {
    return QNANTy<T>::compute(); // +/-Inf -> NaN
  } else if (x == 0) {
    return x; // return negative zero if x is negative zero
  } else {
    int expo{ILOGBTy<T>::compute(x) + 1};
    auto ip{static_cast<int>(p - expo)};
    if (ip != p - expo) {
      ip = p < 0 ? std::numeric_limits<int>::min()
                 : std::numeric_limits<int>::max();
    }
    return LDEXPTy<T>::compute(x, ip); // x*2**(p-e)
  }
}
 
// MOD & MODULO (16.9.135, .136)
template <bool IS_MODULO, typename T>
inline RT_API_ATTRS T RealMod(
    T a, T p, const char *sourceFile, int sourceLine) {
  if (p == 0) {
    Terminator{sourceFile, sourceLine}.Crash(
        IS_MODULO ? "MODULO with P==0" : "MOD with P==0");
  }
  if (ISNANTy<T>::compute(a) || ISNANTy<T>::compute(p) ||
      ISINFTy<T>::compute(a)) {
    return QNANTy<T>::compute();
  } else if (IS_MODULO && ISINFTy<T>::compute(p)) {
    // Other compilers behave consistently for MOD(x, +/-INF)
    // and always return x. This is probably related to
    // implementation of std::fmod(). Stick to this behavior
    // for MOD, but return NaN for MODULO(x, +/-INF).
    return QNANTy<T>::compute();
  }
  T aAbs{ABSTy<T>::compute(a)};
  T pAbs{ABSTy<T>::compute(p)};
  if (aAbs <= static_cast<T>(std::numeric_limits<std::int64_t>::max()) &&
      pAbs <= static_cast<T>(std::numeric_limits<std::int64_t>::max())) {
    if (auto aInt{static_cast<std::int64_t>(a)}; a == aInt) {
      if (auto pInt{static_cast<std::int64_t>(p)}; p == pInt) {
        // Fast exact case for integer operands
        auto mod{aInt - (aInt / pInt) * pInt};
        if constexpr (IS_MODULO) {
          if (mod == 0) {
            // Return properly signed zero.
            return pInt > 0 ? T{0} : -T{0};
          }
          if ((aInt > 0) != (pInt > 0)) {
            mod += pInt;
          }
        } else {
          if (mod == 0) {
            // Return properly signed zero.
            return aInt > 0 ? T{0} : -T{0};
          }
        }
        return static_cast<T>(mod);
      }
    }
  }
  if constexpr (std::is_same_v<T, float> || std::is_same_v<T, double> ||
      std::is_same_v<T, long double>) {
    // std::fmod() semantics on signed operands seems to match
    // the requirements of MOD().  MODULO() needs adjustment.
    T result{std::fmod(a, p)};
    if constexpr (IS_MODULO) {
      if ((a < 0) != (p < 0)) {
        if (result == 0.) {
          result = -result;
        } else {
          result += p;
        }
      }
    }
    return result;
  } else {
    // The standard defines MOD(a,p)=a-AINT(a/p)*p and
    // MODULO(a,p)=a-FLOOR(a/p)*p, but those definitions lose
    // precision badly due to cancellation when ABS(a) is
    // much larger than ABS(p).
    // Insights:
    //  - MOD(a,p)=MOD(a-n*p,p) when a>0, p>0, integer n>0, and a>=n*p
    //  - when n is a power of two, n*p is exact
    //  - as a>=n*p, a-n*p does not round.
    // So repeatedly reduce a by all n*p in decreasing order of n;
    // what's left is the desired remainder.  This is basically
    // the same algorithm as arbitrary precision binary long division,
    // discarding the quotient.
    T tmp{aAbs};
    for (T adj{SetExponent(pAbs, Exponent<int>(aAbs))}; tmp >= pAbs; adj /= 2) {
      if (tmp >= adj) {
        tmp -= adj;
        if (tmp == 0) {
          break;
        }
      }
    }
    if (a < 0) {
      tmp = -tmp;
    }
    if constexpr (IS_MODULO) {
      if ((a < 0) != (p < 0)) {
        if (tmp == 0.) {
          tmp = -tmp;
        } else {
          tmp += p;
        }
      }
    }
    return tmp;
  }
}
 
// RRSPACING (16.9.164)
template <int PREC, typename T> inline RT_API_ATTRS T RRSpacing(T x) {
  if (ISNANTy<T>::compute(x)) {
    return x; // NaN -> same NaN
  } else if (ISINFTy<T>::compute(x)) {
    return QNANTy<T>::compute(); // +/-Inf -> NaN
  } else if (x == 0) {
    return 0; // 0 -> 0
  } else {
    return LDEXPTy<T>::compute(
        ABSTy<T>::compute(x), PREC - (ILOGBTy<T>::compute(x) + 1));
  }
}
 
// SPACING (16.9.180)
template <int PREC, typename T> inline RT_API_ATTRS T Spacing(T x) {
  T tiny{MINTy<PREC, T>::compute()};
  if (ISNANTy<T>::compute(x)) {
    return x; // NaN -> same NaN
  } else if (ISINFTy<T>::compute(x)) {
    return QNANTy<T>::compute(); // +/-Inf -> NaN
  } else if (x == 0) { // 0 -> TINY(x)
    return tiny;
  } else {
    T result{LDEXPTy<T>::compute(
        static_cast<T>(1.0), ILOGBTy<T>::compute(x) + 1 - PREC)}; // 2**(e-p)
    // All compilers return TINY(x) for |x| <= TINY(x), but differ over whether
    // SPACING(x) can be < TINY(x) for |x| > TINY(x).  The most common precedent
    // is to never return a value < TINY(x).
    return result <= tiny ? tiny : result;
  }
}
 
// ERFC_SCALED (16.9.71)
template <typename T> inline RT_API_ATTRS T ErfcScaled(T arg) {
  return common::ErfcScaled(arg);
}
 
} // namespace Fortran::runtime
 
#endif // FORTRAN_RUNTIME_NUMERIC_TEMPLATES_H_