1// Copyright (C) 2022 The Qt Company Ltd.
2// Copyright (C) 2016 by Southwest Research Institute (R)
3// SPDX-License-Identifier: LicenseRef-Qt-Commercial OR LGPL-3.0-only OR GPL-2.0-only OR GPL-3.0-only
4
5#ifndef QFLOAT16_H
6#define QFLOAT16_H
7
8#include <QtCore/qcompare.h>
9#include <QtCore/qglobal.h>
10#include <QtCore/qhashfunctions.h>
11#include <QtCore/qmath.h>
12#include <QtCore/qnamespace.h>
13#include <QtCore/qtconfigmacros.h>
14#include <QtCore/qtypes.h>
15
16#include <limits>
17#include <string.h>
18#include <type_traits>
19
20#if defined(QT_COMPILER_SUPPORTS_F16C) && defined(__AVX2__) && !defined(__F16C__)
21// All processors that support AVX2 do support F16C too, so we could enable the
22// feature unconditionally if __AVX2__ is defined. However, all currently
23// supported compilers except Microsoft's are able to define __F16C__ on their
24// own when the user enables the feature, so we'll trust them.
25# if defined(Q_CC_MSVC) && !defined(Q_CC_CLANG)
26# define __F16C__ 1
27# endif
28#endif
29
30#if defined(QT_COMPILER_SUPPORTS_F16C) && defined(__F16C__)
31#include <immintrin.h>
32#endif
33
34QT_BEGIN_NAMESPACE
35
36#if 0
37#pragma qt_class(QFloat16)
38#pragma qt_no_master_include
39#endif
40
41#ifndef QT_NO_DATASTREAM
42class QDataStream;
43#endif
44class QTextStream;
45
46class qfloat16
47{
48 struct Wrap
49 {
50 // To let our private constructor work, without other code seeing
51 // ambiguity when constructing from int, double &c.
52 quint16 b16;
53 constexpr inline explicit Wrap(int value) : b16(quint16(value)) {}
54 };
55
56 template <typename T>
57 using if_type_is_integral = std::enable_if_t<std::is_integral_v<std::remove_reference_t<T>>, bool>;
58
59public:
60 using NativeType = QtPrivate::NativeFloat16Type;
61
62 static constexpr bool IsNative = QFLOAT16_IS_NATIVE;
63 using NearestFloat = std::conditional_t<IsNative, NativeType, float>;
64
65 constexpr inline qfloat16() noexcept : b16(0) {}
66 explicit qfloat16(Qt::Initialization) noexcept { }
67
68#if QFLOAT16_IS_NATIVE
69 constexpr inline qfloat16(NativeType f) : nf(f) {}
70 constexpr operator NativeType() const noexcept { return nf; }
71#else
72 inline qfloat16(float f) noexcept;
73 inline operator float() const noexcept;
74#endif
75 template <typename T, typename = std::enable_if_t<std::is_arithmetic_v<T> && !std::is_same_v<T, NearestFloat>>>
76 constexpr explicit qfloat16(T value) noexcept : qfloat16(NearestFloat(value)) {}
77
78 // Support for qIs{Inf,NaN,Finite}:
79 bool isInf() const noexcept { return (b16 & 0x7fff) == 0x7c00; }
80 bool isNaN() const noexcept { return (b16 & 0x7fff) > 0x7c00; }
81 bool isFinite() const noexcept { return (b16 & 0x7fff) < 0x7c00; }
82 Q_CORE_EXPORT int fpClassify() const noexcept;
83 // Can't specialize std::copysign() for qfloat16
84 qfloat16 copySign(qfloat16 sign) const noexcept
85 { return qfloat16(Wrap((sign.b16 & 0x8000) | (b16 & 0x7fff))); }
86 // Support for std::numeric_limits<qfloat16>
87
88#ifdef __STDCPP_FLOAT16_T__
89private:
90 using Bounds = std::numeric_limits<NativeType>;
91public:
92 static constexpr qfloat16 _limit_epsilon() noexcept { return Bounds::epsilon(); }
93 static constexpr qfloat16 _limit_min() noexcept { return Bounds::min(); }
94 static constexpr qfloat16 _limit_denorm_min() noexcept { return Bounds::denorm_min(); }
95 static constexpr qfloat16 _limit_max() noexcept { return Bounds::max(); }
96 static constexpr qfloat16 _limit_lowest() noexcept { return Bounds::lowest(); }
97 static constexpr qfloat16 _limit_infinity() noexcept { return Bounds::infinity(); }
98 static constexpr qfloat16 _limit_quiet_NaN() noexcept { return Bounds::quiet_NaN(); }
99#if QT_CONFIG(signaling_nan)
100 static constexpr qfloat16 _limit_signaling_NaN() noexcept { return Bounds::signaling_NaN(); }
101#endif
102#else
103 static constexpr qfloat16 _limit_epsilon() noexcept { return qfloat16(Wrap(0x1400)); }
104 static constexpr qfloat16 _limit_min() noexcept { return qfloat16(Wrap(0x400)); }
105 static constexpr qfloat16 _limit_denorm_min() noexcept { return qfloat16(Wrap(1)); }
106 static constexpr qfloat16 _limit_max() noexcept { return qfloat16(Wrap(0x7bff)); }
107 static constexpr qfloat16 _limit_lowest() noexcept { return qfloat16(Wrap(0xfbff)); }
108 static constexpr qfloat16 _limit_infinity() noexcept { return qfloat16(Wrap(0x7c00)); }
109 static constexpr qfloat16 _limit_quiet_NaN() noexcept { return qfloat16(Wrap(0x7e00)); }
110#if QT_CONFIG(signaling_nan)
111 static constexpr qfloat16 _limit_signaling_NaN() noexcept { return qfloat16(Wrap(0x7d00)); }
112#endif
113#endif
114 inline constexpr bool isNormal() const noexcept
115 { return (b16 & 0x7c00) && (b16 & 0x7c00) != 0x7c00; }
116private:
117 // ABI note: Qt 6's qfloat16 began with just a quint16 member so it ended
118 // up passed in general purpose registers in any function call taking
119 // qfloat16 by value (it has trivial copy constructors). This means the
120 // integer member in the anonymous union below must remain until a
121 // binary-incompatible version of Qt. If you remove it, on platforms using
122 // the System V ABI for C, the native type is passed in FP registers.
123 union {
124 quint16 b16;
125#if QFLOAT16_IS_NATIVE
126 NativeType nf;
127#endif
128 };
129 constexpr inline explicit qfloat16(Wrap nibble) noexcept :
130#if QFLOAT16_IS_NATIVE && defined(__cpp_lib_bit_cast)
131 nf(std::bit_cast<NativeType>(nibble.b16))
132#else
133 b16(nibble.b16)
134#endif
135 {}
136
137 Q_CORE_EXPORT static const quint32 mantissatable[];
138 Q_CORE_EXPORT static const quint32 exponenttable[];
139 Q_CORE_EXPORT static const quint32 offsettable[];
140 Q_CORE_EXPORT static const quint16 basetable[];
141 Q_CORE_EXPORT static const quint16 shifttable[];
142 Q_CORE_EXPORT static const quint32 roundtable[];
143
144 friend bool qIsNull(qfloat16 f) noexcept;
145
146 friend inline qfloat16 operator-(qfloat16 a) noexcept
147 {
148 qfloat16 f;
149 f.b16 = a.b16 ^ quint16(0x8000);
150 return f;
151 }
152
153 friend inline qfloat16 operator+(qfloat16 a, qfloat16 b) noexcept { return qfloat16(static_cast<NearestFloat>(a) + static_cast<NearestFloat>(b)); }
154 friend inline qfloat16 operator-(qfloat16 a, qfloat16 b) noexcept { return qfloat16(static_cast<NearestFloat>(a) - static_cast<NearestFloat>(b)); }
155 friend inline qfloat16 operator*(qfloat16 a, qfloat16 b) noexcept { return qfloat16(static_cast<NearestFloat>(a) * static_cast<NearestFloat>(b)); }
156 friend inline qfloat16 operator/(qfloat16 a, qfloat16 b) noexcept { return qfloat16(static_cast<NearestFloat>(a) / static_cast<NearestFloat>(b)); }
157
158 friend size_t qHash(qfloat16 key, size_t seed = 0) noexcept
159 { return qHash(key: float(key), seed); } // 6.4 algorithm, so keep using it; ### Qt 7: fix QTBUG-116077
160
161QT_WARNING_PUSH
162QT_WARNING_DISABLE_GCC("-Wfloat-conversion")
163
164#define QF16_MAKE_ARITH_OP_FP(FP, OP) \
165 friend inline FP operator OP(qfloat16 lhs, FP rhs) noexcept { return static_cast<FP>(lhs) OP rhs; } \
166 friend inline FP operator OP(FP lhs, qfloat16 rhs) noexcept { return lhs OP static_cast<FP>(rhs); }
167#define QF16_MAKE_ARITH_OP_EQ_FP(FP, OP_EQ, OP) \
168 friend inline qfloat16& operator OP_EQ(qfloat16& lhs, FP rhs) noexcept \
169 { lhs = qfloat16(NearestFloat(static_cast<FP>(lhs) OP rhs)); return lhs; }
170#define QF16_MAKE_ARITH_OP(FP) \
171 QF16_MAKE_ARITH_OP_FP(FP, +) \
172 QF16_MAKE_ARITH_OP_FP(FP, -) \
173 QF16_MAKE_ARITH_OP_FP(FP, *) \
174 QF16_MAKE_ARITH_OP_FP(FP, /) \
175 QF16_MAKE_ARITH_OP_EQ_FP(FP, +=, +) \
176 QF16_MAKE_ARITH_OP_EQ_FP(FP, -=, -) \
177 QF16_MAKE_ARITH_OP_EQ_FP(FP, *=, *) \
178 QF16_MAKE_ARITH_OP_EQ_FP(FP, /=, /)
179
180 QF16_MAKE_ARITH_OP(long double)
181 QF16_MAKE_ARITH_OP(double)
182 QF16_MAKE_ARITH_OP(float)
183#if QFLOAT16_IS_NATIVE
184 QF16_MAKE_ARITH_OP(NativeType)
185#endif
186#undef QF16_MAKE_ARITH_OP
187#undef QF16_MAKE_ARITH_OP_FP
188
189#define QF16_MAKE_ARITH_OP_INT(OP) \
190 friend inline double operator OP(qfloat16 lhs, int rhs) noexcept { return static_cast<double>(lhs) OP rhs; } \
191 friend inline double operator OP(int lhs, qfloat16 rhs) noexcept { return lhs OP static_cast<double>(rhs); }
192
193 QF16_MAKE_ARITH_OP_INT(+)
194 QF16_MAKE_ARITH_OP_INT(-)
195 QF16_MAKE_ARITH_OP_INT(*)
196 QF16_MAKE_ARITH_OP_INT(/)
197#undef QF16_MAKE_ARITH_OP_INT
198
199QT_WARNING_DISABLE_FLOAT_COMPARE
200
201#if QFLOAT16_IS_NATIVE
202# define QF16_CONSTEXPR constexpr
203# define QF16_PARTIALLY_ORDERED Q_DECLARE_PARTIALLY_ORDERED_LITERAL_TYPE
204#else
205# define QF16_CONSTEXPR
206# define QF16_PARTIALLY_ORDERED Q_DECLARE_PARTIALLY_ORDERED
207#endif
208
209 friend QF16_CONSTEXPR bool comparesEqual(const qfloat16 &lhs, const qfloat16 &rhs) noexcept
210 { return static_cast<NearestFloat>(lhs) == static_cast<NearestFloat>(rhs); }
211 friend QF16_CONSTEXPR
212 Qt::partial_ordering compareThreeWay(const qfloat16 &lhs, const qfloat16 &rhs) noexcept
213 { return Qt::compareThreeWay(lhs: static_cast<NearestFloat>(lhs), rhs: static_cast<NearestFloat>(rhs)); }
214 QF16_PARTIALLY_ORDERED(qfloat16)
215
216#define QF16_MAKE_ORDER_OP_FP(FP) \
217 friend QF16_CONSTEXPR bool comparesEqual(const qfloat16 &lhs, FP rhs) noexcept \
218 { return static_cast<FP>(lhs) == rhs; } \
219 friend QF16_CONSTEXPR \
220 Qt::partial_ordering compareThreeWay(const qfloat16 &lhs, FP rhs) noexcept \
221 { return Qt::compareThreeWay(static_cast<FP>(lhs), rhs); } \
222 QF16_PARTIALLY_ORDERED(qfloat16, FP)
223
224 QF16_MAKE_ORDER_OP_FP(long double)
225 QF16_MAKE_ORDER_OP_FP(double)
226 QF16_MAKE_ORDER_OP_FP(float)
227#if QFLOAT16_IS_NATIVE
228 QF16_MAKE_ORDER_OP_FP(qfloat16::NativeType)
229#endif
230#undef QF16_MAKE_ORDER_OP_FP
231
232 template <typename T, if_type_is_integral<T> = true>
233 friend QF16_CONSTEXPR bool comparesEqual(const qfloat16 &lhs, T rhs) noexcept
234 { return static_cast<NearestFloat>(lhs) == static_cast<NearestFloat>(rhs); }
235 template <typename T, if_type_is_integral<T> = true>
236 friend QF16_CONSTEXPR Qt::partial_ordering compareThreeWay(const qfloat16 &lhs, T rhs) noexcept
237 { return Qt::compareThreeWay(lhs: static_cast<NearestFloat>(lhs), rhs: static_cast<NearestFloat>(rhs)); }
238
239 QF16_PARTIALLY_ORDERED(qfloat16, qint8)
240 QF16_PARTIALLY_ORDERED(qfloat16, quint8)
241 QF16_PARTIALLY_ORDERED(qfloat16, qint16)
242 QF16_PARTIALLY_ORDERED(qfloat16, quint16)
243 QF16_PARTIALLY_ORDERED(qfloat16, qint32)
244 QF16_PARTIALLY_ORDERED(qfloat16, quint32)
245 QF16_PARTIALLY_ORDERED(qfloat16, long)
246 QF16_PARTIALLY_ORDERED(qfloat16, unsigned long)
247 QF16_PARTIALLY_ORDERED(qfloat16, qint64)
248 QF16_PARTIALLY_ORDERED(qfloat16, quint64)
249#ifdef QT_SUPPORTS_INT128
250 QF16_PARTIALLY_ORDERED(qfloat16, qint128)
251 QF16_PARTIALLY_ORDERED(qfloat16, quint128)
252#endif
253
254#undef QF16_PARTIALLY_ORDERED
255#undef QF16_CONSTEXPR
256
257QT_WARNING_POP
258
259#ifndef QT_NO_DATASTREAM
260 friend Q_CORE_EXPORT QDataStream &operator<<(QDataStream &ds, qfloat16 f);
261 friend Q_CORE_EXPORT QDataStream &operator>>(QDataStream &ds, qfloat16 &f);
262#endif
263 friend Q_CORE_EXPORT QTextStream &operator<<(QTextStream &ts, qfloat16 f);
264 friend Q_CORE_EXPORT QTextStream &operator>>(QTextStream &ts, qfloat16 &f);
265};
266
267Q_DECLARE_TYPEINFO(qfloat16, Q_PRIMITIVE_TYPE);
268
269Q_CORE_EXPORT void qFloatToFloat16(qfloat16 *, const float *, qsizetype length) noexcept;
270Q_CORE_EXPORT void qFloatFromFloat16(float *, const qfloat16 *, qsizetype length) noexcept;
271
272// Complement qnumeric.h:
273[[nodiscard]] inline bool qIsInf(qfloat16 f) noexcept { return f.isInf(); }
274[[nodiscard]] inline bool qIsNaN(qfloat16 f) noexcept { return f.isNaN(); }
275[[nodiscard]] inline bool qIsFinite(qfloat16 f) noexcept { return f.isFinite(); }
276[[nodiscard]] inline int qFpClassify(qfloat16 f) noexcept { return f.fpClassify(); }
277// [[nodiscard]] quint32 qFloatDistance(qfloat16 a, qfloat16 b);
278
279[[nodiscard]] inline qfloat16 qSqrt(qfloat16 f)
280{
281#if defined(__cpp_lib_extended_float) && defined(__STDCPP_FLOAT16_T__) && 0
282 // https://wg21.link/p1467 - disabled until tested
283 using namespace std;
284 return sqrt(f);
285#elif QFLOAT16_IS_NATIVE && defined(__HAVE_FLOAT16) && __HAVE_FLOAT16
286 // This C library (glibc) has sqrtf16().
287 return sqrtf16(f);
288#else
289 bool mathUpdatesErrno = true;
290# if defined(__NO_MATH_ERRNO__) || defined(_M_FP_FAST)
291 mathUpdatesErrno = false;
292# elif defined(math_errhandling)
293 mathUpdatesErrno = (math_errhandling & MATH_ERRNO);
294# endif
295
296 // We don't need to set errno to EDOM if (f >= 0 && f != -0 && !isnan(f))
297 // (or if we don't care about errno in the first place). We can merge the
298 // NaN check with by negating and inverting: !(0 > f), and leaving zero to
299 // sqrtf().
300 if (!mathUpdatesErrno || !(0 > f)) {
301# if defined(__AVX512FP16__)
302 __m128h v = _mm_set_sh(f);
303 v = _mm_sqrt_sh(v, v);
304 return _mm_cvtsh_h(v);
305# endif
306 }
307
308 // WG14's N2601 does not provide a way to tell which types an
309 // implementation supports, so we assume it doesn't and fall back to FP32
310 float f32 = float(f);
311 f32 = sqrtf(x: f32);
312 return qfloat16::NearestFloat(f32);
313#endif
314}
315
316// The remainder of these utility functions complement qglobal.h
317[[nodiscard]] inline int qRound(qfloat16 d) noexcept
318{ return qRound(f: static_cast<float>(d)); }
319
320[[nodiscard]] inline qint64 qRound64(qfloat16 d) noexcept
321{ return qRound64(f: static_cast<float>(d)); }
322
323[[nodiscard]] inline bool qFuzzyCompare(qfloat16 p1, qfloat16 p2) noexcept
324{
325 qfloat16::NearestFloat f1 = static_cast<qfloat16::NearestFloat>(p1);
326 qfloat16::NearestFloat f2 = static_cast<qfloat16::NearestFloat>(p2);
327 // The significand precision for IEEE754 half precision is
328 // 11 bits (10 explicitly stored), or approximately 3 decimal
329 // digits. In selecting the fuzzy comparison factor of 102.5f
330 // (that is, (2^10+1)/10) below, we effectively select a
331 // window of about 1 (least significant) decimal digit about
332 // which the two operands can vary and still return true.
333 return (qAbs(t: f1 - f2) * 102.5f <= qMin(a: qAbs(t: f1), b: qAbs(t: f2)));
334}
335
336/*!
337 \internal
338*/
339[[nodiscard]] inline bool qFuzzyIsNull(qfloat16 f) noexcept
340{
341 return qAbs(t: f) < 0.00976f; // 1/102.5 to 3 significant digits; see qFuzzyCompare()
342}
343
344[[nodiscard]] inline bool qIsNull(qfloat16 f) noexcept
345{
346 return (f.b16 & static_cast<quint16>(0x7fff)) == 0;
347}
348
349inline int qIntCast(qfloat16 f) noexcept
350{ return int(static_cast<qfloat16::NearestFloat>(f)); }
351
352#if !defined(Q_QDOC) && !QFLOAT16_IS_NATIVE
353QT_WARNING_PUSH
354QT_WARNING_DISABLE_CLANG("-Wc99-extensions")
355QT_WARNING_DISABLE_GCC("-Wold-style-cast")
356inline qfloat16::qfloat16(float f) noexcept
357{
358#if defined(QT_COMPILER_SUPPORTS_F16C) && defined(__F16C__)
359 __m128 packsingle = _mm_set_ss(f);
360 __m128i packhalf = _mm_cvtps_ph(packsingle, 0);
361 b16 = _mm_extract_epi16(packhalf, 0);
362#elif defined (__ARM_FP16_FORMAT_IEEE)
363 __fp16 f16 = __fp16(f);
364 memcpy(&b16, &f16, sizeof(quint16));
365#else
366 quint32 u;
367 memcpy(dest: &u, src: &f, n: sizeof(quint32));
368 const quint32 signAndExp = u >> 23;
369 const quint16 base = basetable[signAndExp];
370 const quint16 shift = shifttable[signAndExp];
371 const quint32 round = roundtable[signAndExp];
372 quint32 mantissa = (u & 0x007fffff);
373 if ((signAndExp & 0xff) == 0xff) {
374 if (mantissa) // keep nan from truncating to inf
375 mantissa = qMax(a: 1U << shift, b: mantissa);
376 } else {
377 // Round half to even. First round up by adding one in the most
378 // significant bit we'll be discarding:
379 mantissa += round;
380 // If the last bit we'll be keeping is now set, but all later bits are
381 // clear, we were at half and shouldn't have rounded up; decrement will
382 // clear this last kept bit. Any later set bit hides the decrement.
383 if (mantissa & (1 << shift))
384 --mantissa;
385 }
386
387 // We use add as the mantissa may overflow causing
388 // the exp part to shift exactly one value.
389 b16 = quint16(base + (mantissa >> shift));
390#endif
391}
392QT_WARNING_POP
393
394inline qfloat16::operator float() const noexcept
395{
396#if defined(QT_COMPILER_SUPPORTS_F16C) && defined(__F16C__)
397 __m128i packhalf = _mm_cvtsi32_si128(b16);
398 __m128 packsingle = _mm_cvtph_ps(packhalf);
399 return _mm_cvtss_f32(packsingle);
400#elif defined (__ARM_FP16_FORMAT_IEEE)
401 __fp16 f16;
402 memcpy(&f16, &b16, sizeof(quint16));
403 return float(f16);
404#else
405 quint32 u = mantissatable[offsettable[b16 >> 10] + (b16 & 0x3ff)]
406 + exponenttable[b16 >> 10];
407 float f;
408 memcpy(dest: &f, src: &u, n: sizeof(quint32));
409 return f;
410#endif
411}
412#endif // Q_QDOC and non-native
413
414/*
415 qHypot compatibility; see ../kernel/qmath.h
416*/
417namespace QtPrivate {
418template <> struct QHypotType<qfloat16, qfloat16>
419{
420 using type = qfloat16;
421};
422template <typename R> struct QHypotType<R, qfloat16>
423{
424 using type = std::conditional_t<std::is_floating_point_v<R>, R, double>;
425};
426template <typename R> struct QHypotType<qfloat16, R> : QHypotType<R, qfloat16>
427{
428};
429}
430
431// Avoid passing qfloat16 to std::hypot(), while ensuring return types
432// consistent with the above:
433inline auto qHypot(qfloat16 x, qfloat16 y)
434{
435#if defined(QT_COMPILER_SUPPORTS_F16C) && defined(__F16C__) || QFLOAT16_IS_NATIVE
436 return QtPrivate::QHypotHelper<qfloat16>(x).add(y).result();
437#else
438 return qfloat16(qHypot(x: float(x), y: float(y)));
439#endif
440}
441
442// in ../kernel/qmath.h
443template<typename F, typename ...Fs> auto qHypot(F first, Fs... rest);
444
445template <typename T> typename QtPrivate::QHypotType<T, qfloat16>::type
446qHypot(T x, qfloat16 y)
447{
448 if constexpr (std::is_floating_point_v<T>)
449 return qHypot(x, float(y));
450 else
451 return qHypot(x: qfloat16(x), y);
452}
453template <typename T> auto qHypot(qfloat16 x, T y)
454{
455 return qHypot(y, x);
456}
457
458#if defined(__cpp_lib_hypot) && __cpp_lib_hypot >= 201603L // Expected to be true
459// If any are not qfloat16, convert each qfloat16 to float:
460/* (The following splits the some-but-not-all-qfloat16 cases up, using
461 (X|Y|Z)&~(X&Y&Z) = X ? ~(Y&Z) : Y|Z = X&~(Y&Z) | ~X&Y | ~X&~Y&Z,
462 into non-overlapping cases, to avoid ambiguity.) */
463template <typename Ty, typename Tz,
464 typename std::enable_if<
465 // Ty, Tz aren't both qfloat16:
466 !(std::is_same_v<qfloat16, Ty> && std::is_same_v<qfloat16, Tz>), int>::type = 0>
467auto qHypot(qfloat16 x, Ty y, Tz z) { return qHypot(qfloat16::NearestFloat(x), y, z); }
468template <typename Tx, typename Tz,
469 typename std::enable_if<
470 // Tx isn't qfloat16:
471 !std::is_same_v<qfloat16, Tx>, int>::type = 0>
472auto qHypot(Tx x, qfloat16 y, Tz z) { return qHypot(x, qfloat16::NearestFloat(y), z); }
473template <typename Tx, typename Ty,
474 typename std::enable_if<
475 // Neither Tx nor Ty is qfloat16:
476 !std::is_same_v<qfloat16, Tx> && !std::is_same_v<qfloat16, Ty>, int>::type = 0>
477auto qHypot(Tx x, Ty y, qfloat16 z) { return qHypot(x, y, qfloat16::NearestFloat(z)); }
478
479// If all are qfloat16, stay with qfloat16 (albeit via float, if no native support):
480inline auto qHypot(qfloat16 x, qfloat16 y, qfloat16 z)
481{
482#if (defined(QT_COMPILER_SUPPORTS_F16C) && defined(__F16C__)) || QFLOAT16_IS_NATIVE
483 return QtPrivate::QHypotHelper<qfloat16>(x).add(y).add(z).result();
484#else
485 return qfloat16(qHypot(x: float(x), y: float(y), z: float(z)));
486#endif
487}
488#endif // 3-arg std::hypot() is available
489
490QT_END_NAMESPACE
491
492namespace std {
493template<>
494class numeric_limits<QT_PREPEND_NAMESPACE(qfloat16)> : public numeric_limits<float>
495{
496public:
497 /*
498 Treat quint16 b16 as if it were:
499 uint S: 1; // b16 >> 15 (sign); can be set for zero
500 uint E: 5; // (b16 >> 10) & 0x1f (offset exponent)
501 uint M: 10; // b16 & 0x3ff (adjusted mantissa)
502
503 for E == 0: magnitude is M / 2.^{24}
504 for 0 < E < 31: magnitude is (1. + M / 2.^{10}) * 2.^{E - 15)
505 for E == 31: not finite
506 */
507 static constexpr int digits = 11;
508 static constexpr int min_exponent = -13;
509 static constexpr int max_exponent = 16;
510
511 static constexpr int digits10 = 3;
512 static constexpr int max_digits10 = 5;
513 static constexpr int min_exponent10 = -4;
514 static constexpr int max_exponent10 = 4;
515
516 static constexpr QT_PREPEND_NAMESPACE(qfloat16) epsilon()
517 { return QT_PREPEND_NAMESPACE(qfloat16)::_limit_epsilon(); }
518 static constexpr QT_PREPEND_NAMESPACE(qfloat16) (min)()
519 { return QT_PREPEND_NAMESPACE(qfloat16)::_limit_min(); }
520 static constexpr QT_PREPEND_NAMESPACE(qfloat16) denorm_min()
521 { return QT_PREPEND_NAMESPACE(qfloat16)::_limit_denorm_min(); }
522 static constexpr QT_PREPEND_NAMESPACE(qfloat16) (max)()
523 { return QT_PREPEND_NAMESPACE(qfloat16)::_limit_max(); }
524 static constexpr QT_PREPEND_NAMESPACE(qfloat16) lowest()
525 { return QT_PREPEND_NAMESPACE(qfloat16)::_limit_lowest(); }
526 static constexpr QT_PREPEND_NAMESPACE(qfloat16) infinity()
527 { return QT_PREPEND_NAMESPACE(qfloat16)::_limit_infinity(); }
528 static constexpr QT_PREPEND_NAMESPACE(qfloat16) quiet_NaN()
529 { return QT_PREPEND_NAMESPACE(qfloat16)::_limit_quiet_NaN(); }
530#if QT_CONFIG(signaling_nan)
531 static constexpr QT_PREPEND_NAMESPACE(qfloat16) signaling_NaN()
532 { return QT_PREPEND_NAMESPACE(qfloat16)::_limit_signaling_NaN(); }
533#else
534 static constexpr bool has_signaling_NaN = false;
535#endif
536};
537
538template<> class numeric_limits<const QT_PREPEND_NAMESPACE(qfloat16)>
539 : public numeric_limits<QT_PREPEND_NAMESPACE(qfloat16)> {};
540template<> class numeric_limits<volatile QT_PREPEND_NAMESPACE(qfloat16)>
541 : public numeric_limits<QT_PREPEND_NAMESPACE(qfloat16)> {};
542template<> class numeric_limits<const volatile QT_PREPEND_NAMESPACE(qfloat16)>
543 : public numeric_limits<QT_PREPEND_NAMESPACE(qfloat16)> {};
544
545// Adding overloads to std isn't allowed, so we can't extend this to support
546// for fpclassify(), isnormal() &c. (which, furthermore, are macros on MinGW).
547} // namespace std
548
549#endif // QFLOAT16_H
550

source code of qtbase/src/corelib/global/qfloat16.h