FPBits.h

//===-- Abstract class for bit manipulation of float numbers. ---*- 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
//
//===----------------------------------------------------------------------===//

// -----------------------------------------------------------------------------
//                               **** WARNING ****
// This file is shared with libc++. You should also be careful when adding
// dependencies to this file, since it needs to build for all libc++ targets.
// -----------------------------------------------------------------------------

#ifndef LLVM_LIBC_SRC___SUPPORT_FPUTIL_FPBITS_H
#define LLVM_LIBC_SRC___SUPPORT_FPUTIL_FPBITS_H

#include "src/__support/CPP/bit.h"
#include "src/__support/CPP/type_traits.h"
#include "src/__support/common.h"
#include "src/__support/libc_assert.h"       // LIBC_ASSERT
#include "src/__support/macros/attributes.h" // LIBC_INLINE, LIBC_INLINE_VAR
#include "src/__support/macros/config.h"
#include "src/__support/macros/properties/types.h" // LIBC_TYPES_HAS_FLOAT128
#include "src/__support/math_extras.h"             // mask_trailing_ones
#include "src/__support/sign.h"                    // Sign
#include "src/__support/uint128.h"

#include <stdint.h>

namespace LIBC_NAMESPACE_DECL {
namespace fputil {

// The supported floating point types.
enum class FPType {
  IEEE754_Binary16,
  IEEE754_Binary32,
  IEEE754_Binary64,
  IEEE754_Binary128,
  X86_Binary80,
  BFloat16
};

// The classes hierarchy is as follows:
//
//             ┌───────────────────┐
//             │ FPLayout<FPType>  │
//             └─────────▲─────────┘
//                       │
//             ┌─────────┴─────────┐
//             │ FPStorage<FPType> │
//             └─────────▲─────────┘
//                       │
//          ┌────────────┴─────────────┐
//          │                          │
// ┌────────┴─────────┐ ┌──────────────┴──────────────────┐
// │ FPRepSem<FPType> │ │  FPRepSem<FPType::X86_Binary80  │
// └────────▲─────────┘ └──────────────▲──────────────────┘
//          │                          │
//          └────────────┬─────────────┘
//                       │
//               ┌───────┴───────┐
//               │  FPRepImpl<T> │
//               └───────▲───────┘
//                       │
//              ┌────────┴────────┐
//        ┌─────┴─────┐     ┌─────┴─────┐
//        │  FPRep<T> │     │ FPBits<T> │
//        └───────────┘     └───────────┘
//
// - 'FPLayout' defines only a few constants, namely the 'StorageType' and
//   length of the sign, the exponent, fraction and significand parts.
// - 'FPStorage' builds more constants on top of those from 'FPLayout' like
//   exponent bias and masks. It also holds the bit representation of the
//   floating point as a 'StorageType' type and defines tools to assemble or
//   test these parts.
// - 'FPRepSem' defines functions to interact semantically with the floating
//   point representation. The default implementation is the one for 'IEEE754',
//   a specialization is provided for X86 Extended Precision.
// - 'FPRepImpl' derives from 'FPRepSem' and adds functions that are common to
//   all implementations or build on the ones in 'FPRepSem'.
// - 'FPRep' exposes all functions from 'FPRepImpl' and returns 'FPRep'
//   instances when using Builders (static functions to create values).
// - 'FPBits' exposes all the functions from 'FPRepImpl' but operates on the
//   native C++ floating point type instead of 'FPType'. An additional 'get_val'
//   function allows getting the C++ floating point type value back. Builders
//   called from 'FPBits' return 'FPBits' instances.

namespace internal {

// Defines the layout (sign, exponent, significand) of a floating point type in
// memory. It also defines its associated StorageType, i.e., the unsigned
// integer type used to manipulate its representation.
// Additionally we provide the fractional part length, i.e., the number of bits
// after the decimal dot when the number is in normal form.
template <FPType> struct FPLayout {};

template <> struct FPLayout<FPType::IEEE754_Binary16> {
  using StorageType = uint16_t;
  LIBC_INLINE_VAR static constexpr int SIGN_LEN = 1;
  LIBC_INLINE_VAR static constexpr int EXP_LEN = 5;
  LIBC_INLINE_VAR static constexpr int SIG_LEN = 10;
  LIBC_INLINE_VAR static constexpr int FRACTION_LEN = SIG_LEN;
};

template <> struct FPLayout<FPType::IEEE754_Binary32> {
  using StorageType = uint32_t;
  LIBC_INLINE_VAR static constexpr int SIGN_LEN = 1;
  LIBC_INLINE_VAR static constexpr int EXP_LEN = 8;
  LIBC_INLINE_VAR static constexpr int SIG_LEN = 23;
  LIBC_INLINE_VAR static constexpr int FRACTION_LEN = SIG_LEN;
};

template <> struct FPLayout<FPType::IEEE754_Binary64> {
  using StorageType = uint64_t;
  LIBC_INLINE_VAR static constexpr int SIGN_LEN = 1;
  LIBC_INLINE_VAR static constexpr int EXP_LEN = 11;
  LIBC_INLINE_VAR static constexpr int SIG_LEN = 52;
  LIBC_INLINE_VAR static constexpr int FRACTION_LEN = SIG_LEN;
};

template <> struct FPLayout<FPType::IEEE754_Binary128> {
  using StorageType = UInt128;
  LIBC_INLINE_VAR static constexpr int SIGN_LEN = 1;
  LIBC_INLINE_VAR static constexpr int EXP_LEN = 15;
  LIBC_INLINE_VAR static constexpr int SIG_LEN = 112;
  LIBC_INLINE_VAR static constexpr int FRACTION_LEN = SIG_LEN;
};

template <> struct FPLayout<FPType::X86_Binary80> {
#if __SIZEOF_LONG_DOUBLE__ == 12
  using StorageType = UInt<__SIZEOF_LONG_DOUBLE__ * CHAR_BIT>;
#else
  using StorageType = UInt128;
#endif
  LIBC_INLINE_VAR static constexpr int SIGN_LEN = 1;
  LIBC_INLINE_VAR static constexpr int EXP_LEN = 15;
  LIBC_INLINE_VAR static constexpr int SIG_LEN = 64;
  LIBC_INLINE_VAR static constexpr int FRACTION_LEN = SIG_LEN - 1;
};

template <> struct FPLayout<FPType::BFloat16> {
  using StorageType = uint16_t;
  LIBC_INLINE_VAR static constexpr int SIGN_LEN = 1;
  LIBC_INLINE_VAR static constexpr int EXP_LEN = 8;
  LIBC_INLINE_VAR static constexpr int SIG_LEN = 7;
  LIBC_INLINE_VAR static constexpr int FRACTION_LEN = SIG_LEN;
};

// FPStorage derives useful constants from the FPLayout above.
template <FPType fp_type> struct FPStorage : public FPLayout<fp_type> {
  using UP = FPLayout<fp_type>;

  using UP::EXP_LEN;  // The number of bits for the *exponent* part
  using UP::SIG_LEN;  // The number of bits for the *significand* part
  using UP::SIGN_LEN; // The number of bits for the *sign* part
  // For convenience, the sum of `SIG_LEN`, `EXP_LEN`, and `SIGN_LEN`.
  LIBC_INLINE_VAR static constexpr int TOTAL_LEN = SIGN_LEN + EXP_LEN + SIG_LEN;

  // The number of bits after the decimal dot when the number is in normal form.
  using UP::FRACTION_LEN;

  // An unsigned integer that is wide enough to contain all of the floating
  // point bits.
  using StorageType = typename UP::StorageType;

  // The number of bits in StorageType.
  LIBC_INLINE_VAR static constexpr int STORAGE_LEN =
      sizeof(StorageType) * CHAR_BIT;
  static_assert(STORAGE_LEN >= TOTAL_LEN);

  // The exponent bias. Always positive.
  LIBC_INLINE_VAR static constexpr int32_t EXP_BIAS =
      (1U << (EXP_LEN - 1U)) - 1U;
  static_assert(EXP_BIAS > 0);

  // The bit pattern that keeps only the *significand* part.
  LIBC_INLINE_VAR static constexpr StorageType SIG_MASK =
      mask_trailing_ones<StorageType, SIG_LEN>();
  // The bit pattern that keeps only the *exponent* part.
  LIBC_INLINE_VAR static constexpr StorageType EXP_MASK =
      mask_trailing_ones<StorageType, EXP_LEN>() << SIG_LEN;
  // The bit pattern that keeps only the *sign* part.
  LIBC_INLINE_VAR static constexpr StorageType SIGN_MASK =
      mask_trailing_ones<StorageType, SIGN_LEN>() << (EXP_LEN + SIG_LEN);
  // The bit pattern that keeps only the *exponent + significand* part.
  LIBC_INLINE_VAR static constexpr StorageType EXP_SIG_MASK =
      mask_trailing_ones<StorageType, EXP_LEN + SIG_LEN>();
  // The bit pattern that keeps only the *sign + exponent + significand* part.
  LIBC_INLINE_VAR static constexpr StorageType FP_MASK =
      mask_trailing_ones<StorageType, TOTAL_LEN>();
  // The bit pattern that keeps only the *fraction* part.
  // i.e., the *significand* without the leading one.
  LIBC_INLINE_VAR static constexpr StorageType FRACTION_MASK =
      mask_trailing_ones<StorageType, FRACTION_LEN>();

  static_assert((SIG_MASK & EXP_MASK & SIGN_MASK) == 0, "masks disjoint");
  static_assert((SIG_MASK | EXP_MASK | SIGN_MASK) == FP_MASK, "masks cover");

protected:
  // Merge bits from 'a' and 'b' values according to 'mask'.
  // Use 'a' bits when corresponding 'mask' bits are zeroes and 'b' bits when
  // corresponding bits are ones.
  LIBC_INLINE static constexpr StorageType merge(StorageType a, StorageType b,
                                                 StorageType mask) {
    // https://graphics.stanford.edu/~seander/bithacks.html#MaskedMerge
    return a ^ ((a ^ b) & mask);
  }

  // A stongly typed integer that prevents mixing and matching integers with
  // different semantics.
  template <typename T> struct TypedInt {
    using value_type = T;
    LIBC_INLINE constexpr explicit TypedInt(T value) : value(value) {}
    LIBC_INLINE constexpr TypedInt(const TypedInt &value) = default;
    LIBC_INLINE constexpr TypedInt &operator=(const TypedInt &value) = default;

    LIBC_INLINE constexpr explicit operator T() const { return value; }

    LIBC_INLINE constexpr StorageType to_storage_type() const {
      return StorageType(value);
    }

    LIBC_INLINE friend constexpr bool operator==(TypedInt a, TypedInt b) {
      return a.value == b.value;
    }
    LIBC_INLINE friend constexpr bool operator!=(TypedInt a, TypedInt b) {
      return a.value != b.value;
    }

  protected:
    T value;
  };

  // An opaque type to store a floating point exponent.
  // We define special values but it is valid to create arbitrary values as long
  // as they are in the range [min, max].
  struct Exponent : public TypedInt<int32_t> {
    using UP = TypedInt<int32_t>;
    using UP::UP;
    LIBC_INLINE static constexpr auto subnormal() {
      return Exponent(-EXP_BIAS);
    }
    LIBC_INLINE static constexpr auto min() { return Exponent(1 - EXP_BIAS); }
    LIBC_INLINE static constexpr auto zero() { return Exponent(0); }
    LIBC_INLINE static constexpr auto max() { return Exponent(EXP_BIAS); }
    LIBC_INLINE static constexpr auto inf() { return Exponent(EXP_BIAS + 1); }
  };

  // An opaque type to store a floating point biased exponent.
  // We define special values but it is valid to create arbitrary values as long
  // as they are in the range [zero, bits_all_ones].
  // Values greater than bits_all_ones are truncated.
  struct BiasedExponent : public TypedInt<uint32_t> {
    using UP = TypedInt<uint32_t>;
    using UP::UP;

    LIBC_INLINE constexpr BiasedExponent(Exponent exp)
        : UP(static_cast<uint32_t>(static_cast<int32_t>(exp) + EXP_BIAS)) {}

    // Cast operator to get convert from BiasedExponent to Exponent.
    LIBC_INLINE constexpr operator Exponent() const {
      return Exponent(static_cast<int32_t>(UP::value - EXP_BIAS));
    }

    LIBC_INLINE constexpr BiasedExponent &operator++() {
      LIBC_ASSERT(*this != BiasedExponent(Exponent::inf()));
      ++UP::value;
      return *this;
    }

    LIBC_INLINE constexpr BiasedExponent &operator--() {
      LIBC_ASSERT(*this != BiasedExponent(Exponent::subnormal()));
      --UP::value;
      return *this;
    }
  };

  // An opaque type to store a floating point significand.
  // We define special values but it is valid to create arbitrary values as long
  // as they are in the range [zero, bits_all_ones].
  // Note that the semantics of the Significand are implementation dependent.
  // Values greater than bits_all_ones are truncated.
  struct Significand : public TypedInt<StorageType> {
    using UP = TypedInt<StorageType>;
    using UP::UP;

    LIBC_INLINE friend constexpr Significand operator|(const Significand a,
                                                       const Significand b) {
      return Significand(
          StorageType(a.to_storage_type() | b.to_storage_type()));
    }
    LIBC_INLINE friend constexpr Significand operator^(const Significand a,
                                                       const Significand b) {
      return Significand(
          StorageType(a.to_storage_type() ^ b.to_storage_type()));
    }
    LIBC_INLINE friend constexpr Significand operator>>(const Significand a,
                                                        int shift) {
      return Significand(StorageType(a.to_storage_type() >> shift));
    }

    LIBC_INLINE static constexpr auto zero() {
      return Significand(StorageType(0));
    }
    LIBC_INLINE static constexpr auto lsb() {
      return Significand(StorageType(1));
    }
    LIBC_INLINE static constexpr auto msb() {
      return Significand(StorageType(1) << (SIG_LEN - 1));
    }
    LIBC_INLINE static constexpr auto bits_all_ones() {
      return Significand(SIG_MASK);
    }
  };

  LIBC_INLINE static constexpr StorageType encode(BiasedExponent exp) {
    return (exp.to_storage_type() << SIG_LEN) & EXP_MASK;
  }

  LIBC_INLINE static constexpr StorageType encode(Significand value) {
    return value.to_storage_type() & SIG_MASK;
  }

  LIBC_INLINE static constexpr StorageType encode(BiasedExponent exp,
                                                  Significand sig) {
    return encode(exp) | encode(sig);
  }

  LIBC_INLINE static constexpr StorageType encode(Sign sign, BiasedExponent exp,
                                                  Significand sig) {
    if (sign.is_neg())
      return SIGN_MASK | encode(exp, sig);
    return encode(exp, sig);
  }

  // The floating point number representation as an unsigned integer.
  StorageType bits{};

  LIBC_INLINE constexpr FPStorage() : bits(0) {}
  LIBC_INLINE constexpr FPStorage(StorageType value) : bits(value) {}

  // Observers
  LIBC_INLINE constexpr StorageType exp_bits() const { return bits & EXP_MASK; }
  LIBC_INLINE constexpr StorageType sig_bits() const { return bits & SIG_MASK; }
  LIBC_INLINE constexpr StorageType exp_sig_bits() const {
    return bits & EXP_SIG_MASK;
  }

  // Parts
  LIBC_INLINE constexpr BiasedExponent biased_exponent() const {
    return BiasedExponent(static_cast<uint32_t>(exp_bits() >> SIG_LEN));
  }
  LIBC_INLINE constexpr void set_biased_exponent(BiasedExponent biased) {
    bits = merge(bits, encode(biased), EXP_MASK);
  }

public:
  LIBC_INLINE constexpr Sign sign() const {
    return (bits & SIGN_MASK) ? Sign::NEG : Sign::POS;
  }
  LIBC_INLINE constexpr void set_sign(Sign signVal) {
    if (sign() != signVal)
      bits ^= SIGN_MASK;
  }
};

// This layer defines all functions that are specific to how the the floating
// point type is encoded. It enables constructions, modification and observation
// of values manipulated as 'StorageType'.
template <FPType fp_type, typename RetT>
struct FPRepSem : public FPStorage<fp_type> {
  using UP = FPStorage<fp_type>;
  using typename UP::StorageType;
  using UP::FRACTION_LEN;
  using UP::FRACTION_MASK;

protected:
  using typename UP::Exponent;
  using typename UP::Significand;
  using UP::bits;
  using UP::encode;
  using UP::exp_bits;
  using UP::exp_sig_bits;
  using UP::sig_bits;
  using UP::UP;

public:
  // Builders
  LIBC_INLINE static constexpr RetT zero(Sign sign = Sign::POS) {
    return RetT(encode(sign, Exponent::subnormal(), Significand::zero()));
  }
  LIBC_INLINE static constexpr RetT one(Sign sign = Sign::POS) {
    return RetT(encode(sign, Exponent::zero(), Significand::zero()));
  }
  LIBC_INLINE static constexpr RetT min_subnormal(Sign sign = Sign::POS) {
    return RetT(encode(sign, Exponent::subnormal(), Significand::lsb()));
  }
  LIBC_INLINE static constexpr RetT max_subnormal(Sign sign = Sign::POS) {
    return RetT(
        encode(sign, Exponent::subnormal(), Significand::bits_all_ones()));
  }
  LIBC_INLINE static constexpr RetT min_normal(Sign sign = Sign::POS) {
    return RetT(encode(sign, Exponent::min(), Significand::zero()));
  }
  LIBC_INLINE static constexpr RetT max_normal(Sign sign = Sign::POS) {
    return RetT(encode(sign, Exponent::max(), Significand::bits_all_ones()));
  }
  LIBC_INLINE static constexpr RetT inf(Sign sign = Sign::POS) {
    return RetT(encode(sign, Exponent::inf(), Significand::zero()));
  }
  LIBC_INLINE static constexpr RetT signaling_nan(Sign sign = Sign::POS,
                                                  StorageType v = 0) {
    return RetT(encode(sign, Exponent::inf(),
                       (v ? Significand(v) : (Significand::msb() >> 1))));
  }
  LIBC_INLINE static constexpr RetT quiet_nan(Sign sign = Sign::POS,
                                              StorageType v = 0) {
    return RetT(
        encode(sign, Exponent::inf(), Significand::msb() | Significand(v)));
  }

  // Observers
  LIBC_INLINE constexpr bool is_zero() const { return exp_sig_bits() == 0; }
  LIBC_INLINE constexpr bool is_nan() const {
    return exp_sig_bits() > encode(Exponent::inf(), Significand::zero());
  }
  LIBC_INLINE constexpr bool is_quiet_nan() const {
    return exp_sig_bits() >= encode(Exponent::inf(), Significand::msb());
  }
  LIBC_INLINE constexpr bool is_signaling_nan() const {
    return is_nan() && !is_quiet_nan();
  }
  LIBC_INLINE constexpr bool is_inf() const {
    return exp_sig_bits() == encode(Exponent::inf(), Significand::zero());
  }
  LIBC_INLINE constexpr bool is_finite() const {
    return exp_bits() != encode(Exponent::inf());
  }
  LIBC_INLINE
  constexpr bool is_subnormal() const {
    return exp_bits() == encode(Exponent::subnormal());
  }
  LIBC_INLINE constexpr bool is_normal() const {
    return is_finite() && !is_subnormal();
  }
  LIBC_INLINE constexpr RetT next_toward_inf() const {
    if (is_finite())
      return RetT(bits + StorageType(1));
    return RetT(bits);
  }

  // Returns the mantissa with the implicit bit set iff the current
  // value is a valid normal number.
  LIBC_INLINE constexpr StorageType get_explicit_mantissa() const {
    if (is_subnormal())
      return sig_bits();
    return (StorageType(1) << UP::SIG_LEN) | sig_bits();
  }
};

// Specialization for the X86 Extended Precision type.
template <typename RetT>
struct FPRepSem<FPType::X86_Binary80, RetT>
    : public FPStorage<FPType::X86_Binary80> {
  using UP = FPStorage<FPType::X86_Binary80>;
  using typename UP::StorageType;
  using UP::FRACTION_LEN;
  using UP::FRACTION_MASK;

  // The x86 80 bit float represents the leading digit of the mantissa
  // explicitly. This is the mask for that bit.
  static constexpr StorageType EXPLICIT_BIT_MASK = StorageType(1)
                                                   << FRACTION_LEN;
  // The X80 significand is made of an explicit bit and the fractional part.
  static_assert((EXPLICIT_BIT_MASK & FRACTION_MASK) == 0,
                "the explicit bit and the fractional part should not overlap");
  static_assert((EXPLICIT_BIT_MASK | FRACTION_MASK) == SIG_MASK,
                "the explicit bit and the fractional part should cover the "
                "whole significand");

protected:
  using typename UP::Exponent;
  using typename UP::Significand;
  using UP::encode;
  using UP::UP;

public:
  // Builders
  LIBC_INLINE static constexpr RetT zero(Sign sign = Sign::POS) {
    return RetT(encode(sign, Exponent::subnormal(), Significand::zero()));
  }
  LIBC_INLINE static constexpr RetT one(Sign sign = Sign::POS) {
    return RetT(encode(sign, Exponent::zero(), Significand::msb()));
  }
  LIBC_INLINE static constexpr RetT min_subnormal(Sign sign = Sign::POS) {
    return RetT(encode(sign, Exponent::subnormal(), Significand::lsb()));
  }
  LIBC_INLINE static constexpr RetT max_subnormal(Sign sign = Sign::POS) {
    return RetT(encode(sign, Exponent::subnormal(),
                       Significand::bits_all_ones() ^ Significand::msb()));
  }
  LIBC_INLINE static constexpr RetT min_normal(Sign sign = Sign::POS) {
    return RetT(encode(sign, Exponent::min(), Significand::msb()));
  }
  LIBC_INLINE static constexpr RetT max_normal(Sign sign = Sign::POS) {
    return RetT(encode(sign, Exponent::max(), Significand::bits_all_ones()));
  }
  LIBC_INLINE static constexpr RetT inf(Sign sign = Sign::POS) {
    return RetT(encode(sign, Exponent::inf(), Significand::msb()));
  }
  LIBC_INLINE static constexpr RetT signaling_nan(Sign sign = Sign::POS,
                                                  StorageType v = 0) {
    return RetT(encode(sign, Exponent::inf(),
                       Significand::msb() |
                           (v ? Significand(v) : (Significand::msb() >> 2))));
  }
  LIBC_INLINE static constexpr RetT quiet_nan(Sign sign = Sign::POS,
                                              StorageType v = 0) {
    return RetT(encode(sign, Exponent::inf(),
                       Significand::msb() | (Significand::msb() >> 1) |
                           Significand(v)));
  }

  // Observers
  LIBC_INLINE constexpr bool is_zero() const { return exp_sig_bits() == 0; }
  LIBC_INLINE constexpr bool is_nan() const {
    // Most encoding forms from the table found in
    // https://en.wikipedia.org/wiki/Extended_precision#x86_extended_precision_format
    // are interpreted as NaN.
    // More precisely :
    // - Pseudo-Infinity
    // - Pseudo Not a Number
    // - Signalling Not a Number
    // - Floating-point Indefinite
    // - Quiet Not a Number
    // - Unnormal
    // This can be reduced to the following logic:
    if (exp_bits() == encode(Exponent::inf()))
      return !is_inf();
    if (exp_bits() != encode(Exponent::subnormal()))
      return (sig_bits() & encode(Significand::msb())) == 0;
    return false;
  }
  LIBC_INLINE constexpr bool is_quiet_nan() const {
    return exp_sig_bits() >=
           encode(Exponent::inf(),
                  Significand::msb() | (Significand::msb() >> 1));
  }
  LIBC_INLINE constexpr bool is_signaling_nan() const {
    return is_nan() && !is_quiet_nan();
  }
  LIBC_INLINE constexpr bool is_inf() const {
    return exp_sig_bits() == encode(Exponent::inf(), Significand::msb());
  }
  LIBC_INLINE constexpr bool is_finite() const {
    return !is_inf() && !is_nan();
  }
  LIBC_INLINE
  constexpr bool is_subnormal() const {
    return exp_bits() == encode(Exponent::subnormal());
  }
  LIBC_INLINE constexpr bool is_normal() const {
    const auto exp = exp_bits();
    if (exp == encode(Exponent::subnormal()) || exp == encode(Exponent::inf()))
      return false;
    return get_implicit_bit();
  }
  LIBC_INLINE constexpr RetT next_toward_inf() const {
    if (is_finite()) {
      if (exp_sig_bits() == max_normal().uintval()) {
        return inf(sign());
      } else if (exp_sig_bits() == max_subnormal().uintval()) {
        return min_normal(sign());
      } else if (sig_bits() == SIG_MASK) {
        return RetT(encode(sign(), ++biased_exponent(), Significand::zero()));
      } else {
        return RetT(bits + StorageType(1));
      }
    }
    return RetT(bits);
  }

  LIBC_INLINE constexpr StorageType get_explicit_mantissa() const {
    return sig_bits();
  }

  // This functions is specific to FPRepSem<FPType::X86_Binary80>.
  // TODO: Remove if possible.
  LIBC_INLINE constexpr bool get_implicit_bit() const {
    return static_cast<bool>(bits & EXPLICIT_BIT_MASK);
  }

  // This functions is specific to FPRepSem<FPType::X86_Binary80>.
  // TODO: Remove if possible.
  LIBC_INLINE constexpr void set_implicit_bit(bool implicitVal) {
    if (get_implicit_bit() != implicitVal)
      bits ^= EXPLICIT_BIT_MASK;
  }
};

// 'FPRepImpl' is the bottom of the class hierarchy that only deals with
// 'FPType'. The operations dealing with specific float semantics are
// implemented by 'FPRepSem' above and specialized when needed.
//
// The 'RetT' type is being propagated up to 'FPRepSem' so that the functions
// creating new values (Builders) can return the appropriate type. That is, when
// creating a value through 'FPBits' below the builder will return an 'FPBits'
// value.
// FPBits<float>::zero(); // returns an FPBits<>
//
// When we don't care about specific C++ floating point type we can use
// 'FPRep' and specify the 'FPType' directly.
// FPRep<FPType::IEEE754_Binary32:>::zero() // returns an FPRep<>
template <FPType fp_type, typename RetT>
struct FPRepImpl : public FPRepSem<fp_type, RetT> {
  using UP = FPRepSem<fp_type, RetT>;
  using StorageType = typename UP::StorageType;

protected:
  using UP::bits;
  using UP::encode;
  using UP::exp_bits;
  using UP::exp_sig_bits;

  using typename UP::BiasedExponent;
  using typename UP::Exponent;
  using typename UP::Significand;

  using UP::FP_MASK;

public:
  // Constants.
  using UP::EXP_BIAS;
  using UP::EXP_MASK;
  using UP::FRACTION_MASK;
  using UP::SIG_LEN;
  using UP::SIG_MASK;
  using UP::SIGN_MASK;
  LIBC_INLINE_VAR static constexpr int MAX_BIASED_EXPONENT =
      (1 << UP::EXP_LEN) - 1;

  // CTors
  LIBC_INLINE constexpr FPRepImpl() = default;
  LIBC_INLINE constexpr explicit FPRepImpl(StorageType x) : UP(x) {}

  // Comparison
  LIBC_INLINE constexpr friend bool operator==(FPRepImpl a, FPRepImpl b) {
    return a.uintval() == b.uintval();
  }
  LIBC_INLINE constexpr friend bool operator!=(FPRepImpl a, FPRepImpl b) {
    return a.uintval() != b.uintval();
  }

  // Representation
  LIBC_INLINE constexpr StorageType uintval() const { return bits & FP_MASK; }
  LIBC_INLINE constexpr void set_uintval(StorageType value) {
    bits = (value & FP_MASK);
  }

  // Builders
  using UP::inf;
  using UP::max_normal;
  using UP::max_subnormal;
  using UP::min_normal;
  using UP::min_subnormal;
  using UP::one;
  using UP::quiet_nan;
  using UP::signaling_nan;
  using UP::zero;

  // Modifiers
  LIBC_INLINE constexpr RetT abs() const {
    return RetT(static_cast<StorageType>(bits & UP::EXP_SIG_MASK));
  }

  // Observers
  using UP::get_explicit_mantissa;
  using UP::is_finite;
  using UP::is_inf;
  using UP::is_nan;
  using UP::is_normal;
  using UP::is_quiet_nan;
  using UP::is_signaling_nan;
  using UP::is_subnormal;
  using UP::is_zero;
  using UP::next_toward_inf;
  using UP::sign;
  LIBC_INLINE constexpr bool is_inf_or_nan() const { return !is_finite(); }
  LIBC_INLINE constexpr bool is_neg() const { return sign().is_neg(); }
  LIBC_INLINE constexpr bool is_pos() const { return sign().is_pos(); }

  LIBC_INLINE constexpr uint16_t get_biased_exponent() const {
    return static_cast<uint16_t>(static_cast<uint32_t>(UP::biased_exponent()));
  }

  LIBC_INLINE constexpr void set_biased_exponent(StorageType biased) {
    UP::set_biased_exponent(BiasedExponent(static_cast<uint32_t>(biased)));
  }

  LIBC_INLINE constexpr int get_exponent() const {
    return static_cast<int32_t>(Exponent(UP::biased_exponent()));
  }

  // If the number is subnormal, the exponent is treated as if it were the
  // minimum exponent for a normal number. This is to keep continuity between
  // the normal and subnormal ranges, but it causes problems for functions where
  // values are calculated from the exponent, since just subtracting the bias
  // will give a slightly incorrect result. Additionally, zero has an exponent
  // of zero, and that should actually be treated as zero.
  LIBC_INLINE constexpr int get_explicit_exponent() const {
    Exponent exponent(UP::biased_exponent());
    if (is_zero())
      exponent = Exponent::zero();
    if (exponent == Exponent::subnormal())
      exponent = Exponent::min();
    return static_cast<int32_t>(exponent);
  }

  LIBC_INLINE constexpr StorageType get_mantissa() const {
    return bits & FRACTION_MASK;
  }

  LIBC_INLINE constexpr void set_mantissa(StorageType mantVal) {
    bits = UP::merge(bits, mantVal, FRACTION_MASK);
  }

  LIBC_INLINE constexpr void set_significand(StorageType sigVal) {
    bits = UP::merge(bits, sigVal, SIG_MASK);
  }
  // Unsafe function to create a floating point representation.
  // It simply packs the sign, biased exponent and mantissa values without
  // checking bound nor normalization.
  //
  // WARNING: For X86 Extended Precision, implicit bit needs to be set correctly
  // in the 'mantissa' by the caller.  This function will not check for its
  // validity.
  //
  // FIXME: Use an uint32_t for 'biased_exp'.
  LIBC_INLINE static constexpr RetT
  create_value(Sign sign, StorageType biased_exp, StorageType mantissa) {
    return RetT(encode(sign, BiasedExponent(static_cast<uint32_t>(biased_exp)),
                       Significand(mantissa)));
  }

  // The function converts integer number and unbiased exponent to proper
  // float T type:
  //   Result = number * 2^(ep+1 - exponent_bias)
  // Be careful!
  //   1) "ep" is the raw exponent value.
  //   2) The function adds +1 to ep for seamless normalized to denormalized
  //      transition.
  //   3) The function does not check exponent high limit.
  //   4) "number" zero value is not processed correctly.
  //   5) Number is unsigned, so the result can be only positive.
  LIBC_INLINE static constexpr RetT make_value(StorageType number, int ep) {
    FPRepImpl result(0);
    int lz =
        UP::FRACTION_LEN + 1 - (UP::STORAGE_LEN - cpp::countl_zero(number));

    number <<= lz;
    ep -= lz;

    if (LIBC_LIKELY(ep >= 0)) {
      // Implicit number bit will be removed by mask
      result.set_significand(number);
      result.set_biased_exponent(static_cast<StorageType>(ep + 1));
    } else {
      result.set_significand(number >> static_cast<unsigned>(-ep));
    }
    return RetT(result.uintval());
  }
};

// A generic class to manipulate floating point formats.
// It derives its functionality to FPRepImpl above.
template <FPType fp_type>
struct FPRep : public FPRepImpl<fp_type, FPRep<fp_type>> {
  using UP = FPRepImpl<fp_type, FPRep<fp_type>>;
  using StorageType = typename UP::StorageType;
  using UP::UP;

  LIBC_INLINE constexpr explicit operator StorageType() const {
    return UP::uintval();
  }
};

} // namespace internal

// Returns the FPType corresponding to C++ type T on the host.
template <typename T> LIBC_INLINE static constexpr FPType get_fp_type() {
  using UnqualT = cpp::remove_cv_t<T>;
  if constexpr (cpp::is_same_v<UnqualT, float> && __FLT_MANT_DIG__ == 24)
    return FPType::IEEE754_Binary32;
  else if constexpr (cpp::is_same_v<UnqualT, double> && __DBL_MANT_DIG__ == 53)
    return FPType::IEEE754_Binary64;
  else if constexpr (cpp::is_same_v<UnqualT, long double>) {
    if constexpr (__LDBL_MANT_DIG__ == 53)
      return FPType::IEEE754_Binary64;
    else if constexpr (__LDBL_MANT_DIG__ == 64)
      return FPType::X86_Binary80;
    else if constexpr (__LDBL_MANT_DIG__ == 113)
      return FPType::IEEE754_Binary128;
  }
#if defined(LIBC_TYPES_HAS_FLOAT16)
  else if constexpr (cpp::is_same_v<UnqualT, float16>)
    return FPType::IEEE754_Binary16;
#endif
#if defined(LIBC_TYPES_HAS_FLOAT128)
  else if constexpr (cpp::is_same_v<UnqualT, float128>)
    return FPType::IEEE754_Binary128;
#endif
  else if constexpr (cpp::is_same_v<UnqualT, bfloat16>)
    return FPType::BFloat16;
  else
    static_assert(cpp::always_false<UnqualT>, "Unsupported type");
}

// -----------------------------------------------------------------------------
//                               **** WARNING ****
// This interface is shared with libc++, if you change this interface you need
// to update it in both libc and libc++. You should also be careful when adding
// dependencies to this file, since it needs to build for all libc++ targets.
// -----------------------------------------------------------------------------
// A generic class to manipulate C++ floating point formats.
// It derives its functionality to FPRepImpl above.
template <typename T>
struct FPBits final : public internal::FPRepImpl<get_fp_type<T>(), FPBits<T>> {
  static_assert(cpp::is_floating_point_v<T>,
                "FPBits instantiated with invalid type.");
  using UP = internal::FPRepImpl<get_fp_type<T>(), FPBits<T>>;
  using StorageType = typename UP::StorageType;

  // Constructors.
  LIBC_INLINE constexpr FPBits() = default;

  template <typename XType> LIBC_INLINE constexpr explicit FPBits(XType x) {
    using Unqual = typename cpp::remove_cv_t<XType>;
    if constexpr (cpp::is_same_v<Unqual, T>) {
      UP::bits = cpp::bit_cast<StorageType>(x);
    } else if constexpr (cpp::is_same_v<Unqual, StorageType>) {
      UP::bits = x;
    } else {
      // We don't want accidental type promotions/conversions, so we require
      // exact type match.
      static_assert(cpp::always_false<XType>);
    }
  }

  // Floating-point conversions.
  LIBC_INLINE constexpr T get_val() const { return cpp::bit_cast<T>(UP::bits); }
};

} // namespace fputil
} // namespace LIBC_NAMESPACE_DECL

#endif // LLVM_LIBC_SRC___SUPPORT_FPUTIL_FPBITS_H