include/QtCore/qfloat16.h

0001 // Copyright (C) 2022 The Qt Company Ltd.
0002 // Copyright (C) 2016 by Southwest Research Institute (R)
0003 // SPDX-License-Identifier: LicenseRef-Qt-Commercial OR LGPL-3.0-only OR GPL-2.0-only OR GPL-3.0-only
0004
0005 #ifndef QFLOAT16_H
0006 #define QFLOAT16_H
0007
0008 #include <QtCore/qcompare.h>
0009 #include <QtCore/qglobal.h>
0010 #include <QtCore/qhashfunctions.h>
0011 #include <QtCore/qmath.h>
0012 #include <QtCore/qnamespace.h>
0013 #include <QtCore/qtconfigmacros.h>
0014 #include <QtCore/qtformat_impl.h>
0015 #include <QtCore/qtypes.h>
0016
0017 #include <limits>
0018 #include <string.h>
0019 #include <type_traits>
0020
0021 #if defined(QT_COMPILER_SUPPORTS_F16C) && defined(__AVX2__) && !defined(__F16C__)
0022 // All processors that support AVX2 do support F16C too, so we could enable the
0023 // feature unconditionally if __AVX2__ is defined. However, all currently
0024 // supported compilers except Microsoft's are able to define __F16C__ on their
0025 // own when the user enables the feature, so we'll trust them.
0026 #  if defined(Q_CC_MSVC) && !defined(Q_CC_CLANG)
0027 #    define __F16C__        1
0028 #  endif
0029 #endif
0030
0031 #if defined(QT_COMPILER_SUPPORTS_F16C) && defined(__F16C__)
0032 #include <immintrin.h>
0033 #endif
0034
0035 QT_BEGIN_NAMESPACE
0036
0037 #if 0
0038 #pragma qt_class(QFloat16)
0039 #pragma qt_no_master_include
0040 #endif
0041
0042 #ifndef QT_NO_DATASTREAM
0043 class QDataStream;
0044 #endif
0045 class QTextStream;
0046
0047 class qfloat16
0048 {
0049     struct Wrap
0050     {
0051         // To let our private constructor work, without other code seeing
0052         // ambiguity when constructing from int, double &c.
0053         quint16 b16;
0054         constexpr inline explicit Wrap(int value) : b16(quint16(value)) {}
0055     };
0056
0057     template <typename T>
0058     using if_type_is_integral = std::enable_if_t<std::is_integral_v<std::remove_reference_t<T>>, bool>;
0059
0060 public:
0061     using NativeType = QtPrivate::NativeFloat16Type;
0062
0063     static constexpr bool IsNative = QFLOAT16_IS_NATIVE;
0064     using NearestFloat = std::conditional_t<IsNative, NativeType, float>;
0065
0066     constexpr inline qfloat16() noexcept : b16(0) {}
0067     explicit qfloat16(Qt::Initialization) noexcept { }
0068
0069 #if QFLOAT16_IS_NATIVE
0070     constexpr inline qfloat16(NativeType f) : nf(f) {}
0071     constexpr operator NativeType() const noexcept { return nf; }
0072 #else
0073     inline qfloat16(float f) noexcept;
0074     inline operator float() const noexcept;
0075 #endif
0076     template <typename T, typename = std::enable_if_t<std::is_arithmetic_v<T> && !std::is_same_v<T, NearestFloat>>>
0077     constexpr explicit qfloat16(T value) noexcept : qfloat16(NearestFloat(value)) {}
0078
0079     // Support for qIs{Inf,NaN,Finite}:
0080     bool isInf() const noexcept { return (b16 & 0x7fff) == 0x7c00; }
0081     bool isNaN() const noexcept { return (b16 & 0x7fff) > 0x7c00; }
0082     bool isFinite() const noexcept { return (b16 & 0x7fff) < 0x7c00; }
0083     Q_CORE_EXPORT int fpClassify() const noexcept;
0084     // Can't specialize std::copysign() for qfloat16
0085     qfloat16 copySign(qfloat16 sign) const noexcept
0086     { return qfloat16(Wrap((sign.b16 & 0x8000) | (b16 & 0x7fff))); }
0087     // Support for std::numeric_limits<qfloat16>
0088
0089 #ifdef __STDCPP_FLOAT16_T__
0090 private:
0091     using Bounds = std::numeric_limits<NativeType>;
0092 public:
0093     static constexpr qfloat16 _limit_epsilon()    noexcept { return Bounds::epsilon(); }
0094     static constexpr qfloat16 _limit_min()        noexcept { return Bounds::min(); }
0095     static constexpr qfloat16 _limit_denorm_min() noexcept { return Bounds::denorm_min(); }
0096     static constexpr qfloat16 _limit_max()        noexcept { return Bounds::max(); }
0097     static constexpr qfloat16 _limit_lowest()     noexcept { return Bounds::lowest(); }
0098     static constexpr qfloat16 _limit_infinity()   noexcept { return Bounds::infinity(); }
0099     static constexpr qfloat16 _limit_quiet_NaN()  noexcept { return Bounds::quiet_NaN(); }
0100 #if QT_CONFIG(signaling_nan)
0101     static constexpr qfloat16 _limit_signaling_NaN() noexcept { return Bounds::signaling_NaN(); }
0102 #endif
0103 #else
0104     static constexpr qfloat16 _limit_epsilon()    noexcept { return qfloat16(Wrap(0x1400)); }
0105     static constexpr qfloat16 _limit_min()        noexcept { return qfloat16(Wrap(0x400)); }
0106     static constexpr qfloat16 _limit_denorm_min() noexcept { return qfloat16(Wrap(1)); }
0107     static constexpr qfloat16 _limit_max()        noexcept { return qfloat16(Wrap(0x7bff)); }
0108     static constexpr qfloat16 _limit_lowest()     noexcept { return qfloat16(Wrap(0xfbff)); }
0109     static constexpr qfloat16 _limit_infinity()   noexcept { return qfloat16(Wrap(0x7c00)); }
0110     static constexpr qfloat16 _limit_quiet_NaN()  noexcept { return qfloat16(Wrap(0x7e00)); }
0111 #if QT_CONFIG(signaling_nan)
0112     static constexpr qfloat16 _limit_signaling_NaN() noexcept { return qfloat16(Wrap(0x7d00)); }
0113 #endif
0114 #endif
0115     inline constexpr bool isNormal() const noexcept
0116     { return (b16 & 0x7c00) && (b16 & 0x7c00) != 0x7c00; }
0117 private:
0118     // ABI note: Qt 6's qfloat16 began with just a quint16 member so it ended
0119     // up passed in general purpose registers in any function call taking
0120     // qfloat16 by value (it has trivial copy constructors). This means the
0121     // integer member in the anonymous union below must remain until a
0122     // binary-incompatible version of Qt. If you remove it, on platforms using
0123     // the System V ABI for C, the native type is passed in FP registers.
0124     union {
0125         quint16 b16;
0126 #if QFLOAT16_IS_NATIVE
0127         NativeType nf;
0128 #endif
0129     };
0130     constexpr inline explicit qfloat16(Wrap nibble) noexcept :
0131 #if QFLOAT16_IS_NATIVE && defined(__cpp_lib_bit_cast)
0132         nf(std::bit_cast<NativeType>(nibble.b16))
0133 #else
0134         b16(nibble.b16)
0135 #endif
0136     {}
0137
0138     Q_CORE_EXPORT static const quint32 mantissatable[];
0139     Q_CORE_EXPORT static const quint32 exponenttable[];
0140     Q_CORE_EXPORT static const quint32 offsettable[];
0141     Q_CORE_EXPORT static const quint16 basetable[];
0142     Q_CORE_EXPORT static const quint16 shifttable[];
0143     Q_CORE_EXPORT static const quint32 roundtable[];
0144
0145     friend bool qIsNull(qfloat16 f) noexcept;
0146
0147     friend inline qfloat16 operator-(qfloat16 a) noexcept
0148     {
0149         qfloat16 f;
0150         f.b16 = a.b16 ^ quint16(0x8000);
0151         return f;
0152     }
0153
0154     friend inline qfloat16 operator+(qfloat16 a, qfloat16 b) noexcept { return qfloat16(static_cast<NearestFloat>(a) + static_cast<NearestFloat>(b)); }
0155     friend inline qfloat16 operator-(qfloat16 a, qfloat16 b) noexcept { return qfloat16(static_cast<NearestFloat>(a) - static_cast<NearestFloat>(b)); }
0156     friend inline qfloat16 operator*(qfloat16 a, qfloat16 b) noexcept { return qfloat16(static_cast<NearestFloat>(a) * static_cast<NearestFloat>(b)); }
0157     friend inline qfloat16 operator/(qfloat16 a, qfloat16 b) noexcept { return qfloat16(static_cast<NearestFloat>(a) / static_cast<NearestFloat>(b)); }
0158
0159     friend size_t qHash(qfloat16 key, size_t seed = 0) noexcept
0160     { return qHash(float(key), seed); } // 6.4 algorithm, so keep using it; ### Qt 7: fix QTBUG-116077
0161
0162 QT_WARNING_PUSH
0163 QT_WARNING_DISABLE_GCC("-Wfloat-conversion")
0164
0165 #define QF16_MAKE_ARITH_OP_FP(FP, OP) \
0166     friend inline FP operator OP(qfloat16 lhs, FP rhs) noexcept { return static_cast<FP>(lhs) OP rhs; } \
0167     friend inline FP operator OP(FP lhs, qfloat16 rhs) noexcept { return lhs OP static_cast<FP>(rhs); }
0168 #define QF16_MAKE_ARITH_OP_EQ_FP(FP, OP_EQ, OP) \
0169     friend inline qfloat16& operator OP_EQ(qfloat16& lhs, FP rhs) noexcept \
0170     { lhs = qfloat16(NearestFloat(static_cast<FP>(lhs) OP rhs)); return lhs; }
0171 #define QF16_MAKE_ARITH_OP(FP) \
0172     QF16_MAKE_ARITH_OP_FP(FP, +) \
0173     QF16_MAKE_ARITH_OP_FP(FP, -) \
0174     QF16_MAKE_ARITH_OP_FP(FP, *) \
0175     QF16_MAKE_ARITH_OP_FP(FP, /) \
0176     QF16_MAKE_ARITH_OP_EQ_FP(FP, +=, +) \
0177     QF16_MAKE_ARITH_OP_EQ_FP(FP, -=, -) \
0178     QF16_MAKE_ARITH_OP_EQ_FP(FP, *=, *) \
0179     QF16_MAKE_ARITH_OP_EQ_FP(FP, /=, /)
0180
0181     QF16_MAKE_ARITH_OP(long double)
0182     QF16_MAKE_ARITH_OP(double)
0183     QF16_MAKE_ARITH_OP(float)
0184 #if QFLOAT16_IS_NATIVE
0185     QF16_MAKE_ARITH_OP(NativeType)
0186 #endif
0187 #undef QF16_MAKE_ARITH_OP
0188 #undef QF16_MAKE_ARITH_OP_FP
0189
0190 #define QF16_MAKE_ARITH_OP_INT(OP) \
0191     friend inline double operator OP(qfloat16 lhs, int rhs) noexcept { return static_cast<double>(lhs) OP rhs; } \
0192     friend inline double operator OP(int lhs, qfloat16 rhs) noexcept { return lhs OP static_cast<double>(rhs); }
0193
0194     QF16_MAKE_ARITH_OP_INT(+)
0195     QF16_MAKE_ARITH_OP_INT(-)
0196     QF16_MAKE_ARITH_OP_INT(*)
0197     QF16_MAKE_ARITH_OP_INT(/)
0198 #undef QF16_MAKE_ARITH_OP_INT
0199
0200 QT_WARNING_DISABLE_FLOAT_COMPARE
0201
0202 #if QFLOAT16_IS_NATIVE
0203 #  define QF16_CONSTEXPR constexpr
0204 #  define QF16_PARTIALLY_ORDERED Q_DECLARE_PARTIALLY_ORDERED_LITERAL_TYPE
0205 #else
0206 #  define QF16_CONSTEXPR
0207 #  define QF16_PARTIALLY_ORDERED Q_DECLARE_PARTIALLY_ORDERED
0208 #endif
0209
0210     friend QF16_CONSTEXPR bool comparesEqual(const qfloat16 &lhs, const qfloat16 &rhs) noexcept
0211     { return static_cast<NearestFloat>(lhs) == static_cast<NearestFloat>(rhs); }
0212     friend QF16_CONSTEXPR
0213     Qt::partial_ordering compareThreeWay(const qfloat16 &lhs, const qfloat16 &rhs) noexcept
0214     { return Qt::compareThreeWay(static_cast<NearestFloat>(lhs), static_cast<NearestFloat>(rhs)); }
0215     QF16_PARTIALLY_ORDERED(qfloat16)
0216
0217 #define QF16_MAKE_ORDER_OP_FP(FP) \
0218     friend QF16_CONSTEXPR bool comparesEqual(const qfloat16 &lhs, FP rhs) noexcept \
0219     { return static_cast<FP>(lhs) == rhs; } \
0220     friend QF16_CONSTEXPR \
0221     Qt::partial_ordering compareThreeWay(const qfloat16 &lhs, FP rhs) noexcept \
0222     { return Qt::compareThreeWay(static_cast<FP>(lhs), rhs); } \
0223     QF16_PARTIALLY_ORDERED(qfloat16, FP)
0224
0225     QF16_MAKE_ORDER_OP_FP(long double)
0226     QF16_MAKE_ORDER_OP_FP(double)
0227     QF16_MAKE_ORDER_OP_FP(float)
0228 #if QFLOAT16_IS_NATIVE
0229     QF16_MAKE_ORDER_OP_FP(qfloat16::NativeType)
0230 #endif
0231 #undef QF16_MAKE_ORDER_OP_FP
0232
0233     template <typename T, if_type_is_integral<T> = true>
0234     friend QF16_CONSTEXPR bool comparesEqual(const qfloat16 &lhs, T rhs) noexcept
0235     { return static_cast<NearestFloat>(lhs) == static_cast<NearestFloat>(rhs); }
0236     template <typename T, if_type_is_integral<T> = true>
0237     friend QF16_CONSTEXPR Qt::partial_ordering compareThreeWay(const qfloat16 &lhs, T rhs) noexcept
0238     { return Qt::compareThreeWay(static_cast<NearestFloat>(lhs), static_cast<NearestFloat>(rhs)); }
0239
0240     QF16_PARTIALLY_ORDERED(qfloat16, qint8)
0241     QF16_PARTIALLY_ORDERED(qfloat16, quint8)
0242     QF16_PARTIALLY_ORDERED(qfloat16, qint16)
0243     QF16_PARTIALLY_ORDERED(qfloat16, quint16)
0244     QF16_PARTIALLY_ORDERED(qfloat16, qint32)
0245     QF16_PARTIALLY_ORDERED(qfloat16, quint32)
0246     QF16_PARTIALLY_ORDERED(qfloat16, long)
0247     QF16_PARTIALLY_ORDERED(qfloat16, unsigned long)
0248     QF16_PARTIALLY_ORDERED(qfloat16, qint64)
0249     QF16_PARTIALLY_ORDERED(qfloat16, quint64)
0250 #ifdef QT_SUPPORTS_INT128
0251     QF16_PARTIALLY_ORDERED(qfloat16, qint128)
0252     QF16_PARTIALLY_ORDERED(qfloat16, quint128)
0253 #endif
0254
0255 #undef QF16_PARTIALLY_ORDERED
0256 #undef QF16_CONSTEXPR
0257
0258 QT_WARNING_POP
0259
0260 #ifndef QT_NO_DATASTREAM
0261     friend Q_CORE_EXPORT QDataStream &operator<<(QDataStream &ds, qfloat16 f);
0262     friend Q_CORE_EXPORT QDataStream &operator>>(QDataStream &ds, qfloat16 &f);
0263 #endif
0264     friend Q_CORE_EXPORT QTextStream &operator<<(QTextStream &ts, qfloat16 f);
0265     friend Q_CORE_EXPORT QTextStream &operator>>(QTextStream &ts, qfloat16 &f);
0266 };
0267
0268 Q_DECLARE_TYPEINFO(qfloat16, Q_PRIMITIVE_TYPE);
0269
0270 Q_CORE_EXPORT void qFloatToFloat16(qfloat16 *, const float *, qsizetype length) noexcept;
0271 Q_CORE_EXPORT void qFloatFromFloat16(float *, const qfloat16 *, qsizetype length) noexcept;
0272
0273 // Complement qnumeric.h:
0274 [[nodiscard]] inline bool qIsInf(qfloat16 f) noexcept { return f.isInf(); }
0275 [[nodiscard]] inline bool qIsNaN(qfloat16 f) noexcept { return f.isNaN(); }
0276 [[nodiscard]] inline bool qIsFinite(qfloat16 f) noexcept { return f.isFinite(); }
0277 [[nodiscard]] inline int qFpClassify(qfloat16 f) noexcept { return f.fpClassify(); }
0278 // [[nodiscard]] quint32 qFloatDistance(qfloat16 a, qfloat16 b);
0279
0280 [[nodiscard]] inline qfloat16 qSqrt(qfloat16 f)
0281 {
0282 #if defined(__cpp_lib_extended_float) && defined(__STDCPP_FLOAT16_T__) && 0
0283     // https://wg21.link/p1467 - disabled until tested
0284     using namespace std;
0285     return sqrt(f);
0286 #elif QFLOAT16_IS_NATIVE && defined(__HAVE_FLOAT16) && __HAVE_FLOAT16
0287     // This C library (glibc) has sqrtf16().
0288     return sqrtf16(f);
0289 #else
0290     bool mathUpdatesErrno = true;
0291 #  if defined(__NO_MATH_ERRNO__) || defined(_M_FP_FAST)
0292     mathUpdatesErrno = false;
0293 #  elif defined(math_errhandling)
0294     mathUpdatesErrno = (math_errhandling & MATH_ERRNO);
0295 #  endif
0296
0297     // We don't need to set errno to EDOM if (f >= 0 && f != -0 && !isnan(f))
0298     // (or if we don't care about errno in the first place). We can merge the
0299     // NaN check with by negating and inverting: !(0 > f), and leaving zero to
0300     // sqrtf().
0301     if (!mathUpdatesErrno || !(0 > f)) {
0302 #  if defined(__AVX512FP16__)
0303         __m128h v = _mm_set_sh(f);
0304         v = _mm_sqrt_sh(v, v);
0305         return _mm_cvtsh_h(v);
0306 #  endif
0307     }
0308
0309     // WG14's N2601 does not provide a way to tell which types an
0310     // implementation supports, so we assume it doesn't and fall back to FP32
0311     float f32 = float(f);
0312     f32 = sqrtf(f32);
0313     return qfloat16::NearestFloat(f32);
0314 #endif
0315 }
0316
0317 // The remainder of these utility functions complement qglobal.h
0318 [[nodiscard]] inline int qRound(qfloat16 d) noexcept
0319 { return qRound(static_cast<float>(d)); }
0320
0321 [[nodiscard]] inline qint64 qRound64(qfloat16 d) noexcept
0322 { return qRound64(static_cast<float>(d)); }
0323
0324 [[nodiscard]] inline bool qFuzzyCompare(qfloat16 p1, qfloat16 p2) noexcept
0325 {
0326     qfloat16::NearestFloat f1 = static_cast<qfloat16::NearestFloat>(p1);
0327     qfloat16::NearestFloat f2 = static_cast<qfloat16::NearestFloat>(p2);
0328     // The significand precision for IEEE754 half precision is
0329     // 11 bits (10 explicitly stored), or approximately 3 decimal
0330     // digits.  In selecting the fuzzy comparison factor of 102.5f
0331     // (that is, (2^10+1)/10) below, we effectively select a
0332     // window of about 1 (least significant) decimal digit about
0333     // which the two operands can vary and still return true.
0334     return (qAbs(f1 - f2) * 102.5f <= qMin(qAbs(f1), qAbs(f2)));
0335 }
0336
0337 /*!
0338   \internal
0339 */
0340 [[nodiscard]] inline bool qFuzzyIsNull(qfloat16 f) noexcept
0341 {
0342     return qAbs(f) < 0.00976f; // 1/102.5 to 3 significant digits; see qFuzzyCompare()
0343 }
0344
0345 [[nodiscard]] inline bool qIsNull(qfloat16 f) noexcept
0346 {
0347     return (f.b16 & static_cast<quint16>(0x7fff)) == 0;
0348 }
0349
0350 inline int qIntCast(qfloat16 f) noexcept
0351 { return int(static_cast<qfloat16::NearestFloat>(f)); }
0352
0353 #if !defined(Q_QDOC) && !QFLOAT16_IS_NATIVE
0354 QT_WARNING_PUSH
0355 QT_WARNING_DISABLE_CLANG("-Wc99-extensions")
0356 QT_WARNING_DISABLE_GCC("-Wold-style-cast")
0357 inline qfloat16::qfloat16(float f) noexcept
0358 {
0359 #if defined(QT_COMPILER_SUPPORTS_F16C) && defined(__F16C__)
0360     __m128 packsingle = _mm_set_ss(f);
0361     __m128i packhalf = _mm_cvtps_ph(packsingle, 0);
0362     b16 = _mm_extract_epi16(packhalf, 0);
0363 #elif defined (__ARM_FP16_FORMAT_IEEE)
0364     __fp16 f16 = __fp16(f);
0365     memcpy(&b16, &f16, sizeof(quint16));
0366 #else
0367     quint32 u;
0368     memcpy(&u, &f, sizeof(quint32));
0369     const quint32 signAndExp = u >> 23;
0370     const quint16 base = basetable[signAndExp];
0371     const quint16 shift = shifttable[signAndExp];
0372     const quint32 round = roundtable[signAndExp];
0373     quint32 mantissa = (u & 0x007fffff);
0374     if ((signAndExp & 0xff) == 0xff) {
0375         if (mantissa) // keep nan from truncating to inf
0376             mantissa = qMax(1U << shift, mantissa);
0377     } else {
0378         // Round half to even. First round up by adding one in the most
0379         // significant bit we'll be discarding:
0380         mantissa += round;
0381         // If the last bit we'll be keeping is now set, but all later bits are
0382         // clear, we were at half and shouldn't have rounded up; decrement will
0383         // clear this last kept bit. Any later set bit hides the decrement.
0384         if (mantissa & (1 << shift))
0385             --mantissa;
0386     }
0387
0388     // We use add as the mantissa may overflow causing
0389     // the exp part to shift exactly one value.
0390     b16 = quint16(base + (mantissa >> shift));
0391 #endif
0392 }
0393 QT_WARNING_POP
0394
0395 inline qfloat16::operator float() const noexcept
0396 {
0397 #if defined(QT_COMPILER_SUPPORTS_F16C) && defined(__F16C__)
0398     __m128i packhalf = _mm_cvtsi32_si128(b16);
0399     __m128 packsingle = _mm_cvtph_ps(packhalf);
0400     return _mm_cvtss_f32(packsingle);
0401 #elif defined (__ARM_FP16_FORMAT_IEEE)
0402     __fp16 f16;
0403     memcpy(&f16, &b16, sizeof(quint16));
0404     return float(f16);
0405 #else
0406     quint32 u = mantissatable[offsettable[b16 >> 10] + (b16 & 0x3ff)]
0407                 + exponenttable[b16 >> 10];
0408     float f;
0409     memcpy(&f, &u, sizeof(quint32));
0410     return f;
0411 #endif
0412 }
0413 #endif // Q_QDOC and non-native
0414
0415 /*
0416   qHypot compatibility; see ../kernel/qmath.h
0417 */
0418 namespace QtPrivate {
0419 template <> struct QHypotType<qfloat16, qfloat16>
0420 {
0421     using type = qfloat16;
0422 };
0423 template <typename R> struct QHypotType<R, qfloat16>
0424 {
0425     using type = std::conditional_t<std::is_floating_point_v<R>, R, double>;
0426 };
0427 template <typename R> struct QHypotType<qfloat16, R> : QHypotType<R, qfloat16>
0428 {
0429 };
0430 }
0431
0432 // Avoid passing qfloat16 to std::hypot(), while ensuring return types
0433 // consistent with the above:
0434 inline auto qHypot(qfloat16 x, qfloat16 y)
0435 {
0436 #if defined(QT_COMPILER_SUPPORTS_F16C) && defined(__F16C__) || QFLOAT16_IS_NATIVE
0437     return QtPrivate::QHypotHelper<qfloat16>(x).add(y).result();
0438 #else
0439     return qfloat16(qHypot(float(x), float(y)));
0440 #endif
0441 }
0442
0443 // in ../kernel/qmath.h
0444 template<typename F, typename ...Fs> auto qHypot(F first, Fs... rest);
0445
0446 template <typename T> typename QtPrivate::QHypotType<T, qfloat16>::type
0447 qHypot(T x, qfloat16 y)
0448 {
0449     if constexpr (std::is_floating_point_v<T>)
0450         return qHypot(x, float(y));
0451     else
0452         return qHypot(qfloat16(x), y);
0453 }
0454 template <typename T> auto qHypot(qfloat16 x, T y)
0455 {
0456     return qHypot(y, x);
0457 }
0458
0459 #if defined(__cpp_lib_hypot) && __cpp_lib_hypot >= 201603L // Expected to be true
0460 // If any are not qfloat16, convert each qfloat16 to float:
0461 /* (The following splits the some-but-not-all-qfloat16 cases up, using
0462    (X|Y|Z)&~(X&Y&Z) = X ? ~(Y&Z) : Y|Z = X&~(Y&Z) | ~X&Y | ~X&~Y&Z,
0463    into non-overlapping cases, to avoid ambiguity.) */
0464 template <typename Ty, typename Tz,
0465           typename std::enable_if<
0466               // Ty, Tz aren't both qfloat16:
0467               !(std::is_same_v<qfloat16, Ty> && std::is_same_v<qfloat16, Tz>), int>::type = 0>
0468 auto qHypot(qfloat16 x, Ty y, Tz z) { return qHypot(qfloat16::NearestFloat(x), y, z); }
0469 template <typename Tx, typename Tz,
0470           typename std::enable_if<
0471               // Tx isn't qfloat16:
0472               !std::is_same_v<qfloat16, Tx>, int>::type = 0>
0473 auto qHypot(Tx x, qfloat16 y, Tz z) { return qHypot(x, qfloat16::NearestFloat(y), z); }
0474 template <typename Tx, typename Ty,
0475           typename std::enable_if<
0476               // Neither Tx nor Ty is qfloat16:
0477               !std::is_same_v<qfloat16, Tx> && !std::is_same_v<qfloat16, Ty>, int>::type = 0>
0478 auto qHypot(Tx x, Ty y, qfloat16 z) { return qHypot(x, y, qfloat16::NearestFloat(z)); }
0479
0480 // If all are qfloat16, stay with qfloat16 (albeit via float, if no native support):
0481 inline auto qHypot(qfloat16 x, qfloat16 y, qfloat16 z)
0482 {
0483 #if (defined(QT_COMPILER_SUPPORTS_F16C) && defined(__F16C__)) || QFLOAT16_IS_NATIVE
0484     return QtPrivate::QHypotHelper<qfloat16>(x).add(y).add(z).result();
0485 #else
0486     return qfloat16(qHypot(float(x), float(y), float(z)));
0487 #endif
0488 }
0489 #endif // 3-arg std::hypot() is available
0490
0491 QT_END_NAMESPACE
0492
0493 namespace std {
0494 template<>
0495 class numeric_limits<QT_PREPEND_NAMESPACE(qfloat16)> : public numeric_limits<float>
0496 {
0497 public:
0498     /*
0499       Treat quint16 b16 as if it were:
0500       uint S: 1; // b16 >> 15 (sign); can be set for zero
0501       uint E: 5; // (b16 >> 10) & 0x1f (offset exponent)
0502       uint M: 10; // b16 & 0x3ff (adjusted mantissa)
0503
0504       for E == 0: magnitude is M / 2.^{24}
0505       for 0 < E < 31: magnitude is (1. + M / 2.^{10}) * 2.^{E - 15)
0506       for E == 31: not finite
0507      */
0508     static constexpr int digits = 11;
0509     static constexpr int min_exponent = -13;
0510     static constexpr int max_exponent = 16;
0511
0512     static constexpr int digits10 = 3;
0513     static constexpr int max_digits10 = 5;
0514     static constexpr int min_exponent10 = -4;
0515     static constexpr int max_exponent10 = 4;
0516
0517     static constexpr QT_PREPEND_NAMESPACE(qfloat16) epsilon()
0518     { return QT_PREPEND_NAMESPACE(qfloat16)::_limit_epsilon(); }
0519     static constexpr QT_PREPEND_NAMESPACE(qfloat16) (min)()
0520     { return QT_PREPEND_NAMESPACE(qfloat16)::_limit_min(); }
0521     static constexpr QT_PREPEND_NAMESPACE(qfloat16) denorm_min()
0522     { return QT_PREPEND_NAMESPACE(qfloat16)::_limit_denorm_min(); }
0523     static constexpr QT_PREPEND_NAMESPACE(qfloat16) (max)()
0524     { return QT_PREPEND_NAMESPACE(qfloat16)::_limit_max(); }
0525     static constexpr QT_PREPEND_NAMESPACE(qfloat16) lowest()
0526     { return QT_PREPEND_NAMESPACE(qfloat16)::_limit_lowest(); }
0527     static constexpr QT_PREPEND_NAMESPACE(qfloat16) infinity()
0528     { return QT_PREPEND_NAMESPACE(qfloat16)::_limit_infinity(); }
0529     static constexpr QT_PREPEND_NAMESPACE(qfloat16) quiet_NaN()
0530     { return QT_PREPEND_NAMESPACE(qfloat16)::_limit_quiet_NaN(); }
0531 #if QT_CONFIG(signaling_nan)
0532     static constexpr QT_PREPEND_NAMESPACE(qfloat16) signaling_NaN()
0533     { return QT_PREPEND_NAMESPACE(qfloat16)::_limit_signaling_NaN(); }
0534 #else
0535     static constexpr bool has_signaling_NaN = false;
0536 #endif
0537 };
0538
0539 template<> class numeric_limits<const QT_PREPEND_NAMESPACE(qfloat16)>
0540     : public numeric_limits<QT_PREPEND_NAMESPACE(qfloat16)> {};
0541 template<> class numeric_limits<volatile QT_PREPEND_NAMESPACE(qfloat16)>
0542     : public numeric_limits<QT_PREPEND_NAMESPACE(qfloat16)> {};
0543 template<> class numeric_limits<const volatile QT_PREPEND_NAMESPACE(qfloat16)>
0544     : public numeric_limits<QT_PREPEND_NAMESPACE(qfloat16)> {};
0545
0546 // Adding overloads to std isn't allowed, so we can't extend this to support
0547 // for fpclassify(), isnormal() &c. (which, furthermore, are macros on MinGW).
0548 } // namespace std
0549
0550 // std::format support
0551 #ifdef QT_SUPPORTS_STD_FORMAT
0552
0553 QT_BEGIN_NAMESPACE
0554
0555 namespace QtPrivate {
0556
0557 // [format.formatter.spec] / 5
0558 template <typename T, typename CharT>
0559 constexpr bool FormatterDoesNotExist =
0560         std::negation_v<
0561                 std::disjunction<
0562                         std::is_default_constructible<std::formatter<T, CharT>>,
0563                         std::is_copy_constructible<std::formatter<T, CharT>>,
0564                         std::is_move_constructible<std::formatter<T, CharT>>,
0565                         std::is_copy_assignable<std::formatter<T, CharT>>,
0566                         std::is_move_assignable<std::formatter<T, CharT>>
0567                         >
0568                 >;
0569
0570 template <typename CharT>
0571 using QFloat16FormatterBaseType =
0572         std::conditional_t<FormatterDoesNotExist<qfloat16::NearestFloat, CharT>,
0573                            float,
0574                            qfloat16::NearestFloat>;
0575
0576 } // namespace QtPrivate
0577
0578 QT_END_NAMESPACE
0579
0580 namespace std {
0581 template <typename CharT>
0582 struct formatter<QT_PREPEND_NAMESPACE(qfloat16), CharT>
0583     : std::formatter<QT_PREPEND_NAMESPACE(QtPrivate::QFloat16FormatterBaseType<CharT>), CharT>
0584 {
0585     template <typename FormatContext>
0586     auto format(QT_PREPEND_NAMESPACE(qfloat16) val, FormatContext &ctx) const
0587     {
0588         using FloatType = QT_PREPEND_NAMESPACE(QtPrivate::QFloat16FormatterBaseType<CharT>);
0589         return std::formatter<FloatType, CharT>::format(FloatType(val), ctx);
0590     }
0591 };
0592 } // namespace std
0593
0594 #endif // QT_SUPPORTS_STD_FORMAT
0595
0596 #endif // QFLOAT16_H