595 changes: 313 additions & 282 deletions libc/src/__support/FPUtil/FPBits.h
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Original file line number Diff line number Diff line change
Expand Up @@ -64,90 +64,101 @@ LIBC_INLINE_VAR constexpr Sign Sign::POS = Sign(false);
// └─────────▲─────────┘
// │
// ┌─────────┴─────────┐
// │ FPRepBase<FPType> │
// │ FPStorage<FPType> │
// └─────────▲─────────┘
// │
// ┌────────────┴─────────────┐
// │ │
// ┌────────┴──────┐ ┌─────────────┴──────────────┐
// │ FPRep<FPType> │ │ FPRep<FPType::X86_Binary80 │
// └────────▲──────┘ └─────────────▲──────────────┘
// ┌────────┴─────────┐ ┌──────────────┴──────────────────┐
// │ FPRepSem<FPType> │ │ FPRepSem<FPType::X86_Binary80 │
// └────────▲─────────┘ └──────────────▲──────────────────┘
// │ │
// └────────────┬─────────────┘
// │
// ┌─────┴─────┐
// │ FPRep<T> │
// └───────────┘
// │
// ┌─────┴─────┐
// │ FPBits<T> │
// └───────────┘
//
// - 'FPLayout' defines only a few constants, namely the 'StorageType' and the
// length of the sign, the exponent and significand parts.
// - 'FPRepBase' builds more constants on top of those from 'FPLayout' like
// exponent bias, shifts and masks. It also defines tools to assemble or test
// - '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.
// - 'FPRep' defines functions to interact with the floating point
// representation. The default implementation is the one for 'IEEE754', a
// specialization is provided for X86 Extended Precision that has a different
// encoding.
// - 'FPBits' is templated on the platform floating point types. Contrary to
// 'FPRep' that is platform agnostic 'FPBits' is architecture dependent.
// - '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.
// - 'FPRep' derives from 'FPRepSem' and adds functions that are common to all
// implementations.
// - 'FPBits' exposes all functions from 'FPRep' but operates on the native C++
// floating point type instead of 'FPType'.

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> {
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 = 64;
LIBC_INLINE_VAR static constexpr int FRACTION_LEN = SIG_LEN - 1;
};

} // namespace internal

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

public:
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;
Expand All @@ -162,41 +173,30 @@ struct FPRepBase : public internal::FPLayout<fp_type> {
(1U << (EXP_LEN - 1U)) - 1U;
static_assert(EXP_BIAS > 0);

protected:
// The shift amount to get the *significand* part to the least significant
// bit. Always `0` but kept for consistency.
LIBC_INLINE_VAR static constexpr int SIG_MASK_SHIFT = 0;
// The shift amount to get the *exponent* part to the least significant bit.
LIBC_INLINE_VAR static constexpr int EXP_MASK_SHIFT = SIG_LEN;
// The shift amount to get the *sign* part to the least significant bit.
LIBC_INLINE_VAR static constexpr int SIGN_MASK_SHIFT = SIG_LEN + EXP_LEN;

// The bit pattern that keeps only the *significand* part.
LIBC_INLINE_VAR static constexpr StorageType SIG_MASK =
mask_trailing_ones<StorageType, SIG_LEN>() << SIG_MASK_SHIFT;

public:
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>() << EXP_MASK_SHIFT;
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>() << SIGN_MASK_SHIFT;
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:
LIBC_INLINE static constexpr StorageType bit_at(int position) {
return StorageType(1) << position;
}

// A stongly typed integer that prevents mixing and matching integers with
// different semantics.
template <typename T> struct TypedInt {
Expand Down Expand Up @@ -248,7 +248,7 @@ struct FPRepBase : public internal::FPLayout<fp_type> {

// 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 [BITS_ALL_ZEROES, BITS_ALL_ONES].
// 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> {
Expand Down Expand Up @@ -277,10 +277,8 @@ struct FPRepBase : public internal::FPLayout<fp_type> {
return Significand(StorageType(1));
}
LIBC_INLINE static constexpr auto MSB() {
return Significand(StorageType(bit_at(SIG_LEN - 1)));
return Significand(StorageType(1) << (SIG_LEN - 1));
}
// Aliases
LIBC_INLINE static constexpr auto BITS_ALL_ZEROES() { return ZERO(); }
LIBC_INLINE static constexpr auto BITS_ALL_ONES() {
return Significand(SIG_MASK);
}
Expand All @@ -306,204 +304,112 @@ struct FPRepBase : public internal::FPLayout<fp_type> {
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;
}

private:
// 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);
}

protected:
// The number of bits after the decimal dot when the number is in normal form.
LIBC_INLINE_VAR static constexpr int FRACTION_LEN =
fp_type == FPType::X86_Binary80 ? SIG_LEN - 1 : SIG_LEN;
LIBC_INLINE_VAR static constexpr uint32_t MANTISSA_PRECISION =
FRACTION_LEN + 1;
LIBC_INLINE_VAR static constexpr StorageType FRACTION_MASK =
mask_trailing_ones<StorageType, FRACTION_LEN>();

// The floating point number representation as an unsigned integer.
StorageType bits = 0;

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;
}

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

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

LIBC_INLINE constexpr uint16_t get_biased_exponent() const {
return uint16_t((bits & EXP_MASK) >> EXP_MASK_SHIFT);
}

LIBC_INLINE constexpr void set_biased_exponent(StorageType biased) {
bits = merge(bits, biased << EXP_MASK_SHIFT, EXP_MASK);
}

LIBC_INLINE constexpr int get_exponent() const {
return int(get_biased_exponent()) - EXP_BIAS;
}

// 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 {
const int biased_exp = int(get_biased_exponent());
if (is_zero()) {
return 0;
} else if (biased_exp == 0) {
return 1 - EXP_BIAS;
} else {
return biased_exp - EXP_BIAS;
}
}

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

LIBC_INLINE constexpr bool is_zero() const { return exp_sig_bits() == 0; }

LIBC_INLINE
constexpr bool is_subnormal() const {
return exp_bits() == encode(BiasedExponent::BITS_ALL_ZEROES());
}

LIBC_INLINE constexpr bool is_neg() const { return sign().is_neg(); }
LIBC_INLINE constexpr bool is_pos() const { return sign().is_pos(); }
};

namespace internal {

// Manipulates the representation of a floating point number defined by its
// FPType. This layer is architecture agnostic and does not handle C++ floating
// point types directly ('float', 'double' and 'long double'). Use the FPBits
// below if needed.
//
// TODO: Specialize this class for FPType::X86_Binary80 and remove ad-hoc logic
// from FPRepBase.
template <FPType fp_type> struct FPRep : public FPRepBase<fp_type> {
using UP = FPRepBase<fp_type>;
// 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;
using UP::MANTISSA_PRECISION;

protected:
using typename UP::BiasedExponent;
using typename UP::Exponent;
using typename UP::Significand;
using BiasedExp = typename UP::BiasedExponent;
using Exp = typename UP::Exponent;
using Sig = typename UP::Significand;
using UP::encode;
using UP::exp_bits;
using UP::exp_sig_bits;
using UP::sig_bits;
using UP::UP;

public:
LIBC_INLINE constexpr bool is_nan() const {
return exp_sig_bits() >
encode(BiasedExponent::BITS_ALL_ONES(), Significand::ZERO());
// Builders
LIBC_INLINE static constexpr RetT one(Sign sign = Sign::POS) {
return RetT(encode(sign, Exp::ZERO(), Sig::ZERO()));
}
LIBC_INLINE constexpr bool is_quiet_nan() const {
return exp_sig_bits() >=
encode(BiasedExponent::BITS_ALL_ONES(), Significand::MSB());
LIBC_INLINE static constexpr RetT min_subnormal(Sign sign = Sign::POS) {
return RetT(encode(sign, BiasedExp::BITS_ALL_ZEROES(), Sig::LSB()));
}
LIBC_INLINE constexpr bool is_signaling_nan() const {
return is_nan() && !is_quiet_nan();
LIBC_INLINE static constexpr RetT max_subnormal(Sign sign = Sign::POS) {
return RetT(
encode(sign, BiasedExp::BITS_ALL_ZEROES(), Sig::BITS_ALL_ONES()));
}
LIBC_INLINE constexpr bool is_inf() const {
return exp_sig_bits() ==
encode(BiasedExponent::BITS_ALL_ONES(), Significand::ZERO());
LIBC_INLINE static constexpr RetT min_normal(Sign sign = Sign::POS) {
return RetT(encode(sign, Exp::MIN(), Sig::ZERO()));
}
LIBC_INLINE constexpr bool is_finite() const {
return exp_bits() != encode(BiasedExponent::BITS_ALL_ONES());
LIBC_INLINE static constexpr RetT max_normal(Sign sign = Sign::POS) {
return RetT(encode(sign, Exp::MAX(), Sig::BITS_ALL_ONES()));
}
LIBC_INLINE constexpr bool is_normal() const {
return is_finite() && !UP::is_subnormal();
LIBC_INLINE static constexpr RetT inf(Sign sign = Sign::POS) {
return RetT(encode(sign, BiasedExp::BITS_ALL_ONES(), Sig::ZERO()));
}

LIBC_INLINE static constexpr StorageType zero(Sign sign = Sign::POS) {
return encode(sign, BiasedExponent::BITS_ALL_ZEROES(), Significand::ZERO());
LIBC_INLINE static constexpr RetT build_nan(Sign sign = Sign::POS,
StorageType v = 0) {
return RetT(encode(sign, BiasedExp::BITS_ALL_ONES(),
(v ? Sig(v) : (Sig::MSB() >> 1))));
}
LIBC_INLINE static constexpr StorageType one(Sign sign = Sign::POS) {
return encode(sign, Exponent::ZERO(), Significand::ZERO());
LIBC_INLINE static constexpr RetT build_quiet_nan(Sign sign = Sign::POS,
StorageType v = 0) {
return RetT(encode(sign, BiasedExp::BITS_ALL_ONES(), Sig::MSB() | Sig(v)));
}
LIBC_INLINE static constexpr StorageType
min_subnormal(Sign sign = Sign::POS) {
return encode(sign, BiasedExponent::BITS_ALL_ZEROES(), Significand::LSB());

// Observers
LIBC_INLINE constexpr bool is_nan() const {
return exp_sig_bits() > encode(BiasedExp::BITS_ALL_ONES(), Sig::ZERO());
}
LIBC_INLINE static constexpr StorageType
max_subnormal(Sign sign = Sign::POS) {
return encode(sign, BiasedExponent::BITS_ALL_ZEROES(),
Significand::BITS_ALL_ONES());
LIBC_INLINE constexpr bool is_quiet_nan() const {
return exp_sig_bits() >= encode(BiasedExp::BITS_ALL_ONES(), Sig::MSB());
}
LIBC_INLINE static constexpr StorageType min_normal(Sign sign = Sign::POS) {
return encode(sign, Exponent::MIN(), Significand::ZERO());
LIBC_INLINE constexpr bool is_signaling_nan() const {
return is_nan() && !is_quiet_nan();
}
LIBC_INLINE static constexpr StorageType max_normal(Sign sign = Sign::POS) {
return encode(sign, Exponent::MAX(), Significand::BITS_ALL_ONES());
LIBC_INLINE constexpr bool is_inf() const {
return exp_sig_bits() == encode(BiasedExp::BITS_ALL_ONES(), Sig::ZERO());
}
LIBC_INLINE static constexpr StorageType inf(Sign sign = Sign::POS) {
return encode(sign, BiasedExponent::BITS_ALL_ONES(), Significand::ZERO());
LIBC_INLINE constexpr bool is_finite() const {
return exp_bits() != encode(BiasedExp::BITS_ALL_ONES());
}
LIBC_INLINE static constexpr StorageType build_nan(Sign sign = Sign::POS,
StorageType v = 0) {
return encode(sign, BiasedExponent::BITS_ALL_ONES(),
(v ? Significand(v) : (Significand::MSB() >> 1)));
LIBC_INLINE
constexpr bool is_subnormal() const {
return exp_bits() == encode(BiasedExp::BITS_ALL_ZEROES());
}
LIBC_INLINE static constexpr StorageType
build_quiet_nan(Sign sign = Sign::POS, StorageType v = 0) {
return encode(sign, BiasedExponent::BITS_ALL_ONES(),
Significand::MSB() | Significand(v));
LIBC_INLINE constexpr bool is_normal() const {
return is_finite() && !UP::is_subnormal();
}

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

// Specialization for the X86 Extended Precision type.
template <>
struct FPRep<FPType::X86_Binary80> : public FPRepBase<FPType::X86_Binary80> {
using UP = FPRepBase<FPType::X86_Binary80>;
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;
using UP::MANTISSA_PRECISION;

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

public:
// 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)
Expand All @@ -515,6 +421,45 @@ struct FPRep<FPType::X86_Binary80> : public FPRepBase<FPType::X86_Binary80> {
"the explicit bit and the fractional part should cover the "
"whole significand");

protected:
using BiasedExp = typename UP::BiasedExponent;
using Sig = typename UP::Significand;
using UP::encode;
using UP::UP;

public:
// Builders
LIBC_INLINE static constexpr RetT one(Sign sign = Sign::POS) {
return RetT(encode(sign, Exponent::ZERO(), Sig::MSB()));
}
LIBC_INLINE static constexpr RetT min_subnormal(Sign sign = Sign::POS) {
return RetT(encode(sign, BiasedExp::BITS_ALL_ZEROES(), Sig::LSB()));
}
LIBC_INLINE static constexpr RetT max_subnormal(Sign sign = Sign::POS) {
return RetT(encode(sign, BiasedExp::BITS_ALL_ZEROES(),
Sig::BITS_ALL_ONES() ^ Sig::MSB()));
}
LIBC_INLINE static constexpr RetT min_normal(Sign sign = Sign::POS) {
return RetT(encode(sign, Exponent::MIN(), Sig::MSB()));
}
LIBC_INLINE static constexpr RetT max_normal(Sign sign = Sign::POS) {
return RetT(encode(sign, Exponent::MAX(), Sig::BITS_ALL_ONES()));
}
LIBC_INLINE static constexpr RetT inf(Sign sign = Sign::POS) {
return RetT(encode(sign, BiasedExp::BITS_ALL_ONES(), Sig::MSB()));
}
LIBC_INLINE static constexpr RetT build_nan(Sign sign = Sign::POS,
StorageType v = 0) {
return RetT(encode(sign, BiasedExp::BITS_ALL_ONES(),
Sig::MSB() | (v ? Sig(v) : (Sig::MSB() >> 2))));
}
LIBC_INLINE static constexpr RetT build_quiet_nan(Sign sign = Sign::POS,
StorageType v = 0) {
return RetT(encode(sign, BiasedExp::BITS_ALL_ONES(),
Sig::MSB() | (Sig::MSB() >> 1) | Sig(v)));
}

// Observers
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
Expand All @@ -527,85 +472,183 @@ struct FPRep<FPType::X86_Binary80> : public FPRepBase<FPType::X86_Binary80> {
// - Quiet Not a Number
// - Unnormal
// This can be reduced to the following logic:
if (exp_bits() == encode(BiasedExponent::BITS_ALL_ONES()))
if (exp_bits() == encode(BiasedExp::BITS_ALL_ONES()))
return !is_inf();
if (exp_bits() != encode(BiasedExponent::BITS_ALL_ZEROES()))
return (sig_bits() & encode(Significand::MSB())) == 0;
if (exp_bits() != encode(BiasedExp::BITS_ALL_ZEROES()))
return (sig_bits() & encode(Sig::MSB())) == 0;
return false;
}
LIBC_INLINE constexpr bool is_quiet_nan() const {
return exp_sig_bits() >=
encode(BiasedExponent::BITS_ALL_ONES(),
Significand::MSB() | (Significand::MSB() >> 1));
encode(BiasedExp::BITS_ALL_ONES(), Sig::MSB() | (Sig::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(BiasedExponent::BITS_ALL_ONES(), Significand::MSB());
return exp_sig_bits() == encode(BiasedExp::BITS_ALL_ONES(), Sig::MSB());
}
LIBC_INLINE constexpr bool is_finite() const {
return !is_inf() && !is_nan();
}
LIBC_INLINE
constexpr bool is_subnormal() const {
return exp_bits() == encode(BiasedExp::BITS_ALL_ZEROES());
}
LIBC_INLINE constexpr bool is_normal() const {
const auto exp = exp_bits();
if (exp == encode(BiasedExponent::BITS_ALL_ZEROES()) ||
exp == encode(BiasedExponent::BITS_ALL_ONES()))
if (exp == encode(BiasedExp::BITS_ALL_ZEROES()) ||
exp == encode(BiasedExp::BITS_ALL_ONES()))
return false;
return get_implicit_bit();
}
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;
}
};

// 'FPRep' 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:
// i.e., FPBits<float>::zero() // returns an FPBits<float>
// When we don't care about specific C++ floating point type we can use 'FPRep'
// directly and 'RetT' defaults to 'StorageType':
// i.e., FPRep<FPType:IEEE754_Binary32:>::zero() // returns an 'uint32_t'
template <FPType fp_type,
typename RetT = typename FPLayout<fp_type>::StorageType>
struct FPRep : 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 BiasedExp = typename UP::BiasedExponent;
using Sig = typename UP::Significand;

LIBC_INLINE static constexpr StorageType zero(Sign sign = Sign::POS) {
return encode(sign, BiasedExponent::BITS_ALL_ZEROES(), Significand::ZERO());
using UP::FP_MASK;
using UP::SIG_LEN;

public:
using UP::EXP_BIAS;
using UP::EXP_MASK;
using UP::FRACTION_MASK;
using UP::SIGN_MASK;

// Representation
LIBC_INLINE constexpr StorageType uintval() const { return bits & FP_MASK; }
LIBC_INLINE constexpr void set_uintval(StorageType value) {
bits = (value & FP_MASK);
}
LIBC_INLINE static constexpr StorageType one(Sign sign = Sign::POS) {
return encode(sign, Exponent::ZERO(), Significand::MSB());

// Builders
LIBC_INLINE static constexpr RetT zero(Sign sign = Sign::POS) {
return RetT(encode(sign, BiasedExp::BITS_ALL_ZEROES(), Sig::ZERO()));
}
LIBC_INLINE static constexpr StorageType
min_subnormal(Sign sign = Sign::POS) {
return encode(sign, BiasedExponent::BITS_ALL_ZEROES(), Significand::LSB());
using UP::build_nan;
using UP::build_quiet_nan;
using UP::inf;
using UP::max_normal;
using UP::max_subnormal;
using UP::min_normal;
using UP::min_subnormal;
using UP::one;

// Modifiers
LIBC_INLINE constexpr RetT abs() const {
return RetT(bits & UP::EXP_SIG_MASK);
}
LIBC_INLINE static constexpr StorageType
max_subnormal(Sign sign = Sign::POS) {
return encode(sign, BiasedExponent::BITS_ALL_ZEROES(),
Significand::BITS_ALL_ONES() ^ Significand::MSB());

// Observers
using UP::get_explicit_mantissa;
LIBC_INLINE constexpr bool is_zero() const { return exp_sig_bits() == 0; }
LIBC_INLINE constexpr bool is_inf_or_nan() const { return !is_finite(); }
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;
LIBC_INLINE constexpr bool is_neg() const { return sign().is_neg(); }
LIBC_INLINE constexpr bool is_pos() const { return sign().is_pos(); }

// Parts
LIBC_INLINE constexpr Sign sign() const {
return (bits & SIGN_MASK) ? Sign::NEG : Sign::POS;
}
LIBC_INLINE static constexpr StorageType min_normal(Sign sign = Sign::POS) {
return encode(sign, Exponent::MIN(), Significand::MSB());

LIBC_INLINE constexpr void set_sign(Sign signVal) {
if (sign() != signVal)
bits ^= SIGN_MASK;
}
LIBC_INLINE static constexpr StorageType max_normal(Sign sign = Sign::POS) {
return encode(sign, Exponent::MAX(), Significand::BITS_ALL_ONES());

LIBC_INLINE constexpr uint16_t get_biased_exponent() const {
return uint16_t((bits & UP::EXP_MASK) >> UP::SIG_LEN);
}
LIBC_INLINE static constexpr StorageType inf(Sign sign = Sign::POS) {
return encode(sign, BiasedExponent::BITS_ALL_ONES(), Significand::MSB());

LIBC_INLINE constexpr void set_biased_exponent(StorageType biased) {
bits = merge(bits, biased << SIG_LEN, EXP_MASK);
}
LIBC_INLINE static constexpr StorageType build_nan(Sign sign = Sign::POS,
StorageType v = 0) {
return encode(sign, BiasedExponent::BITS_ALL_ONES(),
Significand::MSB() |
(v ? Significand(v) : (Significand::MSB() >> 2)));

LIBC_INLINE constexpr int get_exponent() const {
return int(get_biased_exponent()) - EXP_BIAS;
}
LIBC_INLINE static constexpr StorageType
build_quiet_nan(Sign sign = Sign::POS, StorageType v = 0) {
return encode(sign, BiasedExponent::BITS_ALL_ONES(),
Significand::MSB() | (Significand::MSB() >> 1) |
Significand(v));

// 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 {
const int biased_exp = int(get_biased_exponent());
if (is_zero()) {
return 0;
} else if (biased_exp == 0) {
return 1 - EXP_BIAS;
} else {
return biased_exp - EXP_BIAS;
}
}

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

// The following functions are specific to FPRep<FPType::X86_Binary80>.
// TODO: Remove if possible.
LIBC_INLINE constexpr bool get_implicit_bit() const {
return static_cast<bool>(bits & EXPLICIT_BIT_MASK);
LIBC_INLINE constexpr void set_mantissa(StorageType mantVal) {
bits = merge(bits, mantVal, FRACTION_MASK);
}

LIBC_INLINE constexpr void set_implicit_bit(bool implicitVal) {
if (get_implicit_bit() != implicitVal)
bits ^= EXPLICIT_BIT_MASK;
private:
// 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);
}
};

Expand Down Expand Up @@ -642,29 +685,31 @@ template <typename T> LIBC_INLINE static constexpr FPType get_fp_type() {
static_assert(cpp::always_false<UnqualT>, "Unsupported type");
}

// A generic class to represent floating point formats.
// On most platforms, the 'float' type corresponds to single precision
// floating point numbers, the 'double' type corresponds to double precision
// floating point numers, and the 'long double' type corresponds to the quad
// precision floating numbers. On x86 platforms however, the 'long double'
// type maps to an x87 floating point format.
template <typename T> struct FPBits : public internal::FPRep<get_fp_type<T>()> {
// A generic class to manipulate floating point formats.
// It derives most of its functionality to FPRep above.
template <typename T>
struct FPBits final : public internal::FPRep<get_fp_type<T>(), FPBits<T>> {
static_assert(cpp::is_floating_point_v<T>,
"FPBits instantiated with invalid type.");
using UP = internal::FPRep<get_fp_type<T>()>;
using UP = internal::FPRep<get_fp_type<T>(), FPBits<T>>;
using Rep = UP;
using StorageType = typename UP::StorageType;

using UP::bits;
using UP::EXP_LEN;
using UP::UP;

// Constants.
static constexpr int MAX_BIASED_EXPONENT = (1 << EXP_LEN) - 1;
static constexpr StorageType MIN_NORMAL = UP::min_normal(Sign::POS);
static constexpr StorageType MAX_NORMAL = UP::max_normal(Sign::POS);
static constexpr StorageType MIN_SUBNORMAL = UP::min_subnormal(Sign::POS);
static constexpr StorageType MAX_SUBNORMAL = UP::max_subnormal(Sign::POS);
LIBC_INLINE_VAR static constexpr uint32_t MANTISSA_PRECISION =
UP::FRACTION_LEN + 1;
LIBC_INLINE_VAR static constexpr StorageType MIN_NORMAL =
UP::min_normal(Sign::POS).uintval();
LIBC_INLINE_VAR static constexpr StorageType MAX_NORMAL =
UP::max_normal(Sign::POS).uintval();
LIBC_INLINE_VAR static constexpr StorageType MIN_SUBNORMAL =
UP::min_subnormal(Sign::POS).uintval();
LIBC_INLINE_VAR static constexpr StorageType MAX_SUBNORMAL =
UP::max_subnormal(Sign::POS).uintval();
LIBC_INLINE_VAR static constexpr int MAX_BIASED_EXPONENT =
(1 << UP::EXP_LEN) - 1;

// Constructors.
LIBC_INLINE constexpr FPBits() = default;
Expand All @@ -686,49 +731,35 @@ template <typename T> struct FPBits : public internal::FPRep<get_fp_type<T>()> {

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

LIBC_INLINE constexpr bool is_inf_or_nan() const { return !UP::is_finite(); }

LIBC_INLINE constexpr FPBits abs() const {
return FPBits(bits & UP::EXP_SIG_MASK);
}

// Methods below this are used by tests.

// TODO: inline and remove.
LIBC_INLINE static constexpr T one(Sign sign = Sign::POS) {
return FPBits(UP::one(sign)).get_val();
return T(UP::one(sign));
}

LIBC_INLINE static constexpr T zero(Sign sign = Sign::POS) {
return FPBits(UP::zero(sign)).get_val();
return T(UP::zero(sign));
}

LIBC_INLINE static constexpr T inf(Sign sign = Sign::POS) {
return FPBits(UP::inf(sign)).get_val();
return T(UP::inf(sign));
}

LIBC_INLINE static constexpr T min_normal() {
return FPBits(UP::min_normal(Sign::POS)).get_val();
return T(UP::min_normal(Sign::POS));
}

LIBC_INLINE static constexpr T max_normal() {
return FPBits(UP::max_normal(Sign::POS)).get_val();
return T(UP::max_normal(Sign::POS));
}

LIBC_INLINE static constexpr T min_denormal() {
return FPBits(UP::min_subnormal(Sign::POS)).get_val();
return T(UP::min_subnormal(Sign::POS));
}

LIBC_INLINE static constexpr T max_denormal() {
return FPBits(UP::max_subnormal(Sign::POS)).get_val();
return T(UP::max_subnormal(Sign::POS));
}

LIBC_INLINE static constexpr T build_nan(StorageType v) {
return FPBits(UP::build_nan(Sign::POS, v)).get_val();
return T(UP::build_nan(Sign::POS, v));
}

LIBC_INLINE static constexpr T build_quiet_nan(StorageType v,
Sign sign = Sign::POS) {
return FPBits(UP::build_quiet_nan(sign, v)).get_val();
return T(UP::build_quiet_nan(sign, v));
}

// TODO: Use an uint32_t for 'biased_exp'.
Expand Down Expand Up @@ -757,7 +788,7 @@ template <typename T> struct FPBits : public internal::FPRep<get_fp_type<T>()> {
"This function is not tested for X86 Extended Precision");
FPBits<T> result;
// offset: +1 for sign, but -1 for implicit first bit
int lz = cpp::countl_zero(number) - EXP_LEN;
int lz = cpp::countl_zero(number) - UP::EXP_LEN;
number <<= lz;
ep -= lz;

Expand Down
171 changes: 87 additions & 84 deletions libc/test/src/__support/FPUtil/fpbits_test.cpp
View file
Original file line number Diff line number Diff line change
Expand Up @@ -17,69 +17,72 @@ TEST(LlvmLibcFPBitsTest, FPType_IEEE754_Binary16) {
using LIBC_NAMESPACE::fputil::FPType;
using LIBC_NAMESPACE::fputil::internal::FPRep;
using Rep = FPRep<FPType::IEEE754_Binary16>;
using u16 = uint16_t;

EXPECT_EQ(u16(0b0'00000'0000000000), Rep::zero());
EXPECT_EQ(u16(0b0'01111'0000000000), Rep::one());
EXPECT_EQ(u16(0b0'00000'0000000001), Rep::min_subnormal());
EXPECT_EQ(u16(0b0'00000'1111111111), Rep::max_subnormal());
EXPECT_EQ(u16(0b0'00001'0000000000), Rep::min_normal());
EXPECT_EQ(u16(0b0'11110'1111111111), Rep::max_normal());
EXPECT_EQ(u16(0b0'11111'0000000000), Rep::inf());
EXPECT_EQ(u16(0b0'11111'0100000000), Rep::build_nan());
EXPECT_EQ(u16(0b0'11111'1000000000), Rep::build_quiet_nan());
using u16 = typename Rep::StorageType;

EXPECT_EQ(u16(0b0'00000'0000000000), u16(Rep::zero()));
EXPECT_EQ(u16(0b0'01111'0000000000), u16(Rep::one()));
EXPECT_EQ(u16(0b0'00000'0000000001), u16(Rep::min_subnormal()));
EXPECT_EQ(u16(0b0'00000'1111111111), u16(Rep::max_subnormal()));
EXPECT_EQ(u16(0b0'00001'0000000000), u16(Rep::min_normal()));
EXPECT_EQ(u16(0b0'11110'1111111111), u16(Rep::max_normal()));
EXPECT_EQ(u16(0b0'11111'0000000000), u16(Rep::inf()));
EXPECT_EQ(u16(0b0'11111'0100000000), u16(Rep::build_nan()));
EXPECT_EQ(u16(0b0'11111'1000000000), u16(Rep::build_quiet_nan()));
}

TEST(LlvmLibcFPBitsTest, FPType_IEEE754_Binary32) {
using LIBC_NAMESPACE::fputil::FPType;
using LIBC_NAMESPACE::fputil::internal::FPRep;
using Rep = FPRep<FPType::IEEE754_Binary32>;
using u32 = uint32_t;

EXPECT_EQ(u32(0b0'00000000'00000000000000000000000), Rep::zero());
EXPECT_EQ(u32(0b0'01111111'00000000000000000000000), Rep::one());
EXPECT_EQ(u32(0b0'00000000'00000000000000000000001), Rep::min_subnormal());
EXPECT_EQ(u32(0b0'00000000'11111111111111111111111), Rep::max_subnormal());
EXPECT_EQ(u32(0b0'00000001'00000000000000000000000), Rep::min_normal());
EXPECT_EQ(u32(0b0'11111110'11111111111111111111111), Rep::max_normal());
EXPECT_EQ(u32(0b0'11111111'00000000000000000000000), Rep::inf());
EXPECT_EQ(u32(0b0'11111111'01000000000000000000000), Rep::build_nan());
EXPECT_EQ(u32(0b0'11111111'10000000000000000000000), Rep::build_quiet_nan());
using u32 = typename Rep::StorageType;

EXPECT_EQ(u32(0b0'00000000'00000000000000000000000), u32(Rep::zero()));
EXPECT_EQ(u32(0b0'01111111'00000000000000000000000), u32(Rep::one()));
EXPECT_EQ(u32(0b0'00000000'00000000000000000000001),
u32(Rep::min_subnormal()));
EXPECT_EQ(u32(0b0'00000000'11111111111111111111111),
u32(Rep::max_subnormal()));
EXPECT_EQ(u32(0b0'00000001'00000000000000000000000), u32(Rep::min_normal()));
EXPECT_EQ(u32(0b0'11111110'11111111111111111111111), u32(Rep::max_normal()));
EXPECT_EQ(u32(0b0'11111111'00000000000000000000000), u32(Rep::inf()));
EXPECT_EQ(u32(0b0'11111111'01000000000000000000000), u32(Rep::build_nan()));
EXPECT_EQ(u32(0b0'11111111'10000000000000000000000),
u32(Rep::build_quiet_nan()));
}

TEST(LlvmLibcFPBitsTest, FPType_IEEE754_Binary64) {
using LIBC_NAMESPACE::fputil::FPType;
using LIBC_NAMESPACE::fputil::internal::FPRep;
using Rep = FPRep<FPType::IEEE754_Binary64>;
using u64 = uint64_t;
using u64 = typename Rep::StorageType;

EXPECT_EQ(
u64(0b0'00000000000'0000000000000000000000000000000000000000000000000000),
Rep::zero());
u64(Rep::zero()));
EXPECT_EQ(
u64(0b0'01111111111'0000000000000000000000000000000000000000000000000000),
Rep::one());
u64(Rep::one()));
EXPECT_EQ(
u64(0b0'00000000000'0000000000000000000000000000000000000000000000000001),
Rep::min_subnormal());
u64(Rep::min_subnormal()));
EXPECT_EQ(
u64(0b0'00000000000'1111111111111111111111111111111111111111111111111111),
Rep::max_subnormal());
u64(Rep::max_subnormal()));
EXPECT_EQ(
u64(0b0'00000000001'0000000000000000000000000000000000000000000000000000),
Rep::min_normal());
u64(Rep::min_normal()));
EXPECT_EQ(
u64(0b0'11111111110'1111111111111111111111111111111111111111111111111111),
Rep::max_normal());
u64(Rep::max_normal()));
EXPECT_EQ(
u64(0b0'11111111111'0000000000000000000000000000000000000000000000000000),
Rep::inf());
u64(Rep::inf()));
EXPECT_EQ(
u64(0b0'11111111111'0100000000000000000000000000000000000000000000000000),
Rep::build_nan());
u64(Rep::build_nan()));
EXPECT_EQ(
u64(0b0'11111111111'1000000000000000000000000000000000000000000000000000),
Rep::build_quiet_nan());
u64(Rep::build_quiet_nan()));
}

static constexpr UInt128 u128(uint64_t hi, uint64_t lo) {
Expand All @@ -90,6 +93,49 @@ static constexpr UInt128 u128(uint64_t hi, uint64_t lo) {
#endif
}

TEST(LlvmLibcFPBitsTest, FPType_IEEE754_Binary128) {
using LIBC_NAMESPACE::fputil::FPType;
using LIBC_NAMESPACE::fputil::internal::FPRep;
using Rep = FPRep<FPType::IEEE754_Binary128>;

EXPECT_EQ(
u128(0b0'000000000000000'000000000000000000000000000000000000000000000000,
0b0000000000000000000000000000000000000000000000000000000000000000),
UInt128(Rep::zero()));
EXPECT_EQ(
u128(0b0'011111111111111'000000000000000000000000000000000000000000000000,
0b0000000000000000000000000000000000000000000000000000000000000000),
UInt128(Rep::one()));
EXPECT_EQ(
u128(0b0'000000000000000'000000000000000000000000000000000000000000000000,
0b0000000000000000000000000000000000000000000000000000000000000001),
UInt128(Rep::min_subnormal()));
EXPECT_EQ(
u128(0b0'000000000000000'111111111111111111111111111111111111111111111111,
0b1111111111111111111111111111111111111111111111111111111111111111),
UInt128(Rep::max_subnormal()));
EXPECT_EQ(
u128(0b0'000000000000001'000000000000000000000000000000000000000000000000,
0b0000000000000000000000000000000000000000000000000000000000000000),
UInt128(Rep::min_normal()));
EXPECT_EQ(
u128(0b0'111111111111110'111111111111111111111111111111111111111111111111,
0b1111111111111111111111111111111111111111111111111111111111111111),
UInt128(Rep::max_normal()));
EXPECT_EQ(
u128(0b0'111111111111111'000000000000000000000000000000000000000000000000,
0b0000000000000000000000000000000000000000000000000000000000000000),
UInt128(Rep::inf()));
EXPECT_EQ(
u128(0b0'111111111111111'010000000000000000000000000000000000000000000000,
0b0000000000000000000000000000000000000000000000000000000000000000),
UInt128(Rep::build_nan()));
EXPECT_EQ(
u128(0b0'111111111111111'100000000000000000000000000000000000000000000000,
0b0000000000000000000000000000000000000000000000000000000000000000),
UInt128(Rep::build_quiet_nan()));
}

TEST(LlvmLibcFPBitsTest, FPType_X86_Binary80) {
using LIBC_NAMESPACE::fputil::FPType;
using LIBC_NAMESPACE::fputil::internal::FPRep;
Expand All @@ -98,39 +144,39 @@ TEST(LlvmLibcFPBitsTest, FPType_X86_Binary80) {
EXPECT_EQ(
u128(0b0'000000000000000,
0b0000000000000000000000000000000000000000000000000000000000000000),
Rep::zero());
UInt128(Rep::zero()));
EXPECT_EQ(
u128(0b0'011111111111111,
0b1000000000000000000000000000000000000000000000000000000000000000),
Rep::one());
UInt128(Rep::one()));
EXPECT_EQ(
u128(0b0'000000000000000,
0b0000000000000000000000000000000000000000000000000000000000000001),
Rep::min_subnormal());
UInt128(Rep::min_subnormal()));
EXPECT_EQ(
u128(0b0'000000000000000,
0b0111111111111111111111111111111111111111111111111111111111111111),
Rep::max_subnormal());
UInt128(Rep::max_subnormal()));
EXPECT_EQ(
u128(0b0'000000000000001,
0b1000000000000000000000000000000000000000000000000000000000000000),
Rep::min_normal());
UInt128(Rep::min_normal()));
EXPECT_EQ(
u128(0b0'111111111111110,
0b1111111111111111111111111111111111111111111111111111111111111111),
Rep::max_normal());
UInt128(Rep::max_normal()));
EXPECT_EQ(
u128(0b0'111111111111111,
0b1000000000000000000000000000000000000000000000000000000000000000),
Rep::inf());
UInt128(Rep::inf()));
EXPECT_EQ(
u128(0b0'111111111111111,
0b1010000000000000000000000000000000000000000000000000000000000000),
Rep::build_nan());
UInt128(Rep::build_nan()));
EXPECT_EQ(
u128(0b0'111111111111111,
0b1100000000000000000000000000000000000000000000000000000000000000),
Rep::build_quiet_nan());
UInt128(Rep::build_quiet_nan()));
}

TEST(LlvmLibcFPBitsTest, FPType_X86_Binary80_IsNan) {
Expand Down Expand Up @@ -183,49 +229,6 @@ TEST(LlvmLibcFPBitsTest, FPType_X86_Binary80_IsNan) {
0b1000000000000000000000000000000000000000000000000000000000000000));
}

TEST(LlvmLibcFPBitsTest, FPType_IEEE754_Binary128) {
using LIBC_NAMESPACE::fputil::FPType;
using LIBC_NAMESPACE::fputil::internal::FPRep;
using Rep = FPRep<FPType::IEEE754_Binary128>;

EXPECT_EQ(
u128(0b0'000000000000000'000000000000000000000000000000000000000000000000,
0b0000000000000000000000000000000000000000000000000000000000000000),
Rep::zero());
EXPECT_EQ(
u128(0b0'011111111111111'000000000000000000000000000000000000000000000000,
0b0000000000000000000000000000000000000000000000000000000000000000),
Rep::one());
EXPECT_EQ(
u128(0b0'000000000000000'000000000000000000000000000000000000000000000000,
0b0000000000000000000000000000000000000000000000000000000000000001),
Rep::min_subnormal());
EXPECT_EQ(
u128(0b0'000000000000000'111111111111111111111111111111111111111111111111,
0b1111111111111111111111111111111111111111111111111111111111111111),
Rep::max_subnormal());
EXPECT_EQ(
u128(0b0'000000000000001'000000000000000000000000000000000000000000000000,
0b0000000000000000000000000000000000000000000000000000000000000000),
Rep::min_normal());
EXPECT_EQ(
u128(0b0'111111111111110'111111111111111111111111111111111111111111111111,
0b1111111111111111111111111111111111111111111111111111111111111111),
Rep::max_normal());
EXPECT_EQ(
u128(0b0'111111111111111'000000000000000000000000000000000000000000000000,
0b0000000000000000000000000000000000000000000000000000000000000000),
Rep::inf());
EXPECT_EQ(
u128(0b0'111111111111111'010000000000000000000000000000000000000000000000,
0b0000000000000000000000000000000000000000000000000000000000000000),
Rep::build_nan());
EXPECT_EQ(
u128(0b0'111111111111111'100000000000000000000000000000000000000000000000,
0b0000000000000000000000000000000000000000000000000000000000000000),
Rep::build_quiet_nan());
}

TEST(LlvmLibcFPBitsTest, FloatType) {
using FloatBits = FPBits<float>;

Expand Down