path: root/src/corelib/global/qnumeric_p.h

// Copyright (C) 2020 The Qt Company Ltd.// Copyright (C) 2021 Intel Corporation.// SPDX-License-Identifier: LicenseRef-Qt-Commercial OR LGPL-3.0-only OR GPL-2.0-only OR GPL-3.0-only#ifndef QNUMERIC_P_H#define QNUMERIC_P_H//// W A R N I N G// -------------//// This file is not part of the Qt API. It exists purely as an// implementation detail. This header file may change from version to// version without notice, or even be removed.//// We mean it.//#include"QtCore/private/qglobal_p.h"#include"QtCore/qnumeric.h"#include"QtCore/qsimd.h"#include <cmath>#include <limits>#include <type_traits>#include <QtCore/q26numeric.h>// temporarily, for saturate_cast#ifndef __has_extension# define __has_extension(X) 0#endif#if !defined(Q_CC_MSVC) && defined(Q_OS_QNX)# include <math.h># ifdef isnan# define QT_MATH_H_DEFINES_MACROS QT_BEGIN_NAMESPACE namespace qnumeric_std_wrapper {// the 'using namespace std' below is cases where the stdlib already put the math.h functions in the std namespace and undefined the macros. Q_DECL_CONST_FUNCTION staticinlineboolmath_h_isnan(double d) {using namespace std;returnisnan(d); } Q_DECL_CONST_FUNCTION staticinlineboolmath_h_isinf(double d) {using namespace std;returnisinf(d); } Q_DECL_CONST_FUNCTION staticinlineboolmath_h_isfinite(double d) {using namespace std;returnisfinite(d); } Q_DECL_CONST_FUNCTION staticinlineintmath_h_fpclassify(double d) {using namespace std;returnfpclassify(d); } Q_DECL_CONST_FUNCTION staticinlineboolmath_h_isnan(float f) {using namespace std;returnisnan(f); } Q_DECL_CONST_FUNCTION staticinlineboolmath_h_isinf(float f) {using namespace std;returnisinf(f); } Q_DECL_CONST_FUNCTION staticinlineboolmath_h_isfinite(float f) {using namespace std;returnisfinite(f); } Q_DECL_CONST_FUNCTION staticinlineintmath_h_fpclassify(float f) {using namespace std;returnfpclassify(f); }} QT_END_NAMESPACE // These macros from math.h conflict with the real functions in the std namespace.# undef signbit# undef isnan# undef isinf# undef isfinite# undef fpclassify# endif// defined(isnan)#endif QT_BEGIN_NAMESPACE class qfloat16;namespace qnumeric_std_wrapper {#if defined(QT_MATH_H_DEFINES_MACROS)# undef QT_MATH_H_DEFINES_MACROS Q_DECL_CONST_FUNCTION staticinlineboolisnan(double d) {returnmath_h_isnan(d); } Q_DECL_CONST_FUNCTION staticinlineboolisinf(double d) {returnmath_h_isinf(d); } Q_DECL_CONST_FUNCTION staticinlineboolisfinite(double d) {returnmath_h_isfinite(d); } Q_DECL_CONST_FUNCTION staticinlineintfpclassify(double d) {returnmath_h_fpclassify(d); } Q_DECL_CONST_FUNCTION staticinlineboolisnan(float f) {returnmath_h_isnan(f); } Q_DECL_CONST_FUNCTION staticinlineboolisinf(float f) {returnmath_h_isinf(f); } Q_DECL_CONST_FUNCTION staticinlineboolisfinite(float f) {returnmath_h_isfinite(f); } Q_DECL_CONST_FUNCTION staticinlineintfpclassify(float f) {returnmath_h_fpclassify(f); }#else Q_DECL_CONST_FUNCTION staticinlineboolisnan(double d) {returnstd::isnan(d); } Q_DECL_CONST_FUNCTION staticinlineboolisinf(double d) {returnstd::isinf(d); } Q_DECL_CONST_FUNCTION staticinlineboolisfinite(double d) {returnstd::isfinite(d); } Q_DECL_CONST_FUNCTION staticinlineintfpclassify(double d) {returnstd::fpclassify(d); } Q_DECL_CONST_FUNCTION staticinlineboolisnan(float f) {returnstd::isnan(f); } Q_DECL_CONST_FUNCTION staticinlineboolisinf(float f) {returnstd::isinf(f); } Q_DECL_CONST_FUNCTION staticinlineboolisfinite(float f) {returnstd::isfinite(f); } Q_DECL_CONST_FUNCTION staticinlineintfpclassify(float f) {returnstd::fpclassify(f); }#endif}constexpr Q_DECL_CONST_FUNCTION staticinlinedoubleqt_inf() noexcept {static_assert(std::numeric_limits<double>::has_infinity,"platform has no definition for infinity for type double");returnstd::numeric_limits<double>::infinity();}#if QT_CONFIG(signaling_nan)constexpr Q_DECL_CONST_FUNCTION staticinlinedoubleqt_snan() noexcept {static_assert(std::numeric_limits<double>::has_signaling_NaN,"platform has no definition for signaling NaN for type double");returnstd::numeric_limits<double>::signaling_NaN();}#endif// Quiet NaNconstexpr Q_DECL_CONST_FUNCTION staticinlinedoubleqt_qnan() noexcept {static_assert(std::numeric_limits<double>::has_quiet_NaN,"platform has no definition for quiet NaN for type double");returnstd::numeric_limits<double>::quiet_NaN();} Q_DECL_CONST_FUNCTION staticinlineboolqt_is_inf(double d){returnqnumeric_std_wrapper::isinf(d);} Q_DECL_CONST_FUNCTION staticinlineboolqt_is_nan(double d){returnqnumeric_std_wrapper::isnan(d);} Q_DECL_CONST_FUNCTION staticinlineboolqt_is_finite(double d){returnqnumeric_std_wrapper::isfinite(d);} Q_DECL_CONST_FUNCTION staticinlineintqt_fpclassify(double d){returnqnumeric_std_wrapper::fpclassify(d);} Q_DECL_CONST_FUNCTION staticinlineboolqt_is_inf(float f){returnqnumeric_std_wrapper::isinf(f);} Q_DECL_CONST_FUNCTION staticinlineboolqt_is_nan(float f){returnqnumeric_std_wrapper::isnan(f);} Q_DECL_CONST_FUNCTION staticinlineboolqt_is_finite(float f){returnqnumeric_std_wrapper::isfinite(f);} Q_DECL_CONST_FUNCTION staticinlineintqt_fpclassify(float f){returnqnumeric_std_wrapper::fpclassify(f);}#ifndef Q_QDOCnamespace{/*! Returns true if the double \a v can be converted to type \c T, false if it's out of range. If the conversion is successful, the converted value is stored in \a value; if it was not successful, \a value will contain the minimum or maximum of T, depending on the sign of \a d. If \c T is unsigned, then \a value contains the absolute value of \a v. If \c T is \c float, an underflow is also signalled by returning false and setting \a value to zero. This function works for v containing infinities, but not NaN. It's the caller's responsibility to exclude that possibility before calling it.*/template<typename T>staticinline std::enable_if_t<std::is_integral_v<T>,bool>convertDoubleTo(double v, T *value,bool allow_precision_upgrade =true){static_assert(std::is_integral_v<T>);constexprbool TypeIsLarger =std::numeric_limits<T>::digits >std::numeric_limits<double>::digits;ifconstexpr(TypeIsLarger) {using S =std::make_signed_t<T>;constexpr S max_mantissa =S(1) <<std::numeric_limits<double>::digits;// T has more bits than double's mantissa, so don't allow "upgrading"// to T (makes it look like the number had more precision than really// was transmitted)if(!allow_precision_upgrade && !(v <=double(max_mantissa) && v >=double(-max_mantissa -1)))return false;}constexpr T Tmin = (std::numeric_limits<T>::min)();constexpr T Tmax = (std::numeric_limits<T>::max)();// The [conv.fpint] (7.10 Floating-integral conversions) section of the C++// standard says only exact conversions are guaranteed. Converting// integrals to floating-point with loss of precision has implementation-// defined behavior whether the next higher or next lower is returned;// converting FP to integral is UB if it can't be represented.//// That means we can't write UINT64_MAX+1. Writing ldexp(1, 64) would be// correct, but Clang, ICC and MSVC don't realize that it's a constant and// the math call stays in the compiled code.#if defined(Q_PROCESSOR_X86_64) && defined(__SSE2__)// Of course, UB doesn't apply if we use intrinsics, in which case we are// allowed to dpeend on exactly the processor's behavior. This// implementation uses the truncating conversions from Scalar Double to// integral types (CVTTSD2SI and VCVTTSD2USI), which is documented to// return the "indefinite integer value" if the range of the target type is// exceeded. (only implemented for x86-64 to avoid having to deal with the// non-existence of the 64-bit intrinsics on i386)if(std::numeric_limits<T>::is_signed) { __m128d mv =_mm_set_sd(v);# ifdef __AVX512F__// use explicit round control and suppress exceptionsif(sizeof(T) >4)*value =T(_mm_cvtt_roundsd_i64(mv, _MM_FROUND_TO_NEAREST_INT | _MM_FROUND_NO_EXC));else*value =_mm_cvtt_roundsd_i32(mv, _MM_FROUND_TO_NEAREST_INT | _MM_FROUND_NO_EXC);# else*value =sizeof(T) >4?T(_mm_cvttsd_si64(mv)) :_mm_cvttsd_si32(mv);# endif// if *value is the "indefinite integer value", check if the original// variable \a v is the same value (Tmin is an exact representation)if(*value == Tmin && !_mm_ucomieq_sd(mv,_mm_set_sd(Tmin))) {// v != Tmin, so it was out of rangeif(v >0)*value = Tmax;return false;}// convert the integer back to double and compare for equality with v,// to determine if we've lost any precision __m128d mi =_mm_setzero_pd(); mi =sizeof(T) >4?_mm_cvtsi64_sd(mv, *value) :_mm_cvtsi32_sd(mv, *value);return_mm_ucomieq_sd(mv, mi);}# ifdef __AVX512F__if(!std::numeric_limits<T>::is_signed) {// Same thing as above, but this function operates on absolute values// and the "indefinite integer value" for the 64-bit unsigned// conversion (Tmax) is not representable in double, so it can never be// the result of an in-range conversion. This is implemented for AVX512// and later because of the unsigned conversion instruction. Converting// to unsigned without losing an extra bit of precision prior to AVX512// is left to the compiler below. v =fabs(v); __m128d mv =_mm_set_sd(v);// use explicit round control and suppress exceptionsif(sizeof(T) >4)*value =T(_mm_cvtt_roundsd_u64(mv, _MM_FROUND_TO_NEAREST_INT | _MM_FROUND_NO_EXC));else*value =_mm_cvtt_roundsd_u32(mv, _MM_FROUND_TO_NEAREST_INT | _MM_FROUND_NO_EXC);if(*value == Tmax) {// no double can have an exact value of quint64(-1), but they can// quint32(-1), so we need to compare for thatif(TypeIsLarger ||_mm_ucomieq_sd(mv,_mm_set_sd(Tmax)))return false;}// return true if it was an exact conversion __m128d mi =_mm_setzero_pd(); mi =sizeof(T) >4?_mm_cvtu64_sd(mv, *value) :_mm_cvtu32_sd(mv, *value);return_mm_ucomieq_sd(mv, mi);}# endif#endifdouble supremum;if(std::numeric_limits<T>::is_signed) { supremum = -1.0* Tmin;// -1 * (-2^63) = 2^63, exact (for T = qint64)*value = Tmin;if(v < Tmin)return false;}else{using ST = typename std::make_signed<T>::type; supremum = -2.0* (std::numeric_limits<ST>::min)();// -2 * (-2^63) = 2^64, exact (for T = quint64) v =fabs(v);}*value = Tmax;if(v >= supremum)return false;// Now we can convert, these two conversions cannot be UB*value =T(v); QT_WARNING_PUSH QT_WARNING_DISABLE_FLOAT_COMPARE return*value == v; QT_WARNING_POP }template<typename T>staticstd::enable_if_t<std::is_floating_point_v<T> ||std::is_same_v<T, qfloat16>,bool>convertDoubleTo(double v, T *value,bool allow_precision_upgrade =true){Q_UNUSED(allow_precision_upgrade);constexpr T Huge =std::numeric_limits<T>::infinity();ifconstexpr(std::numeric_limits<double>::max_exponent <=std::numeric_limits<T>::max_exponent) {// no UB can happen*value =T(v);return true;}#if defined(__SSE2__) && (defined(Q_CC_GNU) || __has_extension(gnu_asm))// The x86 CVTSD2SH instruction from SSE2 does what we want:// - converts out-of-range doubles to ±infinity and sets #O// - converts underflows to zero and sets #U// We need to clear any previously-stored exceptions from it before the// operation (3-cycle cost) and obtain the new state afterwards (1 cycle).unsigned csr = _MM_MASK_MASK;// clear stored exception indicatorsauto sse_check_result = [&](auto result) {if((csr & (_MM_EXCEPT_UNDERFLOW | _MM_EXCEPT_OVERFLOW)) ==0)return true;if(csr & _MM_EXCEPT_OVERFLOW)return false;// According to IEEE 754[1], #U is also set when the result is tiny and// inexact, but still non-zero, so detect that (this won't generate// good code for types without hardware support).// [1] https://en.wikipedia.org/wiki/Floating-point_arithmetic#Exception_handlingreturn result !=0;};// Written directly in assembly because both Clang and GCC have been// observed to reorder the STMXCSR instruction above the conversion// operation. MSVC generates horrid code when using the intrinsics anyway,// so it's not a loss.// See https://github.com/llvm/llvm-project/issues/83661.ifconstexpr(std::is_same_v<T,float>) {# ifdef __AVX__asm("vldmxcsr %[csr]\n\t""vcvtsd2ss %[in], %[in], %[out]\n\t""vstmxcsr %[csr]": [csr]"+m"(csr), [out]"=v"(*value) : [in]"v"(v));# elseasm("ldmxcsr %[csr]\n\t""cvtsd2ss %[in], %[out]\n\t""stmxcsr %[csr]": [csr]"+m"(csr), [out]"=v"(*value) : [in]"v"(v));# endifreturnsse_check_result(*value);}# if defined(__F16C__) || defined(__AVX512FP16__)ifconstexpr(sizeof(T) ==2&&std::numeric_limits<T>::max_exponent ==16) {// qfloat16 or std::float16_t, but not std::bfloat16_t or std::bfloat8_tauto doConvert = [&](auto*out) {asm("vldmxcsr %[csr]\n\t"# ifdef __AVX512FP16__// AVX512FP16 & AVX10 have an instruction for this"vcvtsd2sh %[in], %[in], %[out]\n\t"# else"vcvtsd2ss %[in], %[in], %[out]\n\t"// sets DEST[MAXVL-1:128] := 0"vcvtps2ph %[rc], %[out], %[out]\n\t"# endif"vstmxcsr %[csr]": [csr]"+m"(csr), [out]"=v"(*out): [in]"v"(v), [rc]"i"(_MM_FROUND_CUR_DIRECTION));returnsse_check_result(out);};ifconstexpr(std::is_same_v<T, qfloat16> && !std::is_void_v<typename T::NativeType>) { typename T::NativeType tmp;bool b =doConvert(&tmp);*value = tmp;return b;}else{# ifndef Q_CC_CLANG// Clang can only implement this if it has a native FP16 typereturndoConvert(value);# endif}}# endif#endif// __SSE2__ && inline assemblyif(!qt_is_finite(v) &&std::numeric_limits<T>::has_infinity) {// infinity (or NaN)*value =T(v);return true;}// Check for in-range value to ensure the conversion is not UB (see the// comment above for Standard language).if(std::fabs(v) >double{(std::numeric_limits<T>::max)()}) {*value = v <0? -Huge : Huge;return false;}*value =T(v);if(v !=0&& *value ==0) {// Underflow through loss of precisionreturn false;}return true;}template<typename T>inlinebooladd_overflow(T v1, T v2, T *r) {returnqAddOverflow(v1, v2, r); }template<typename T>inlineboolsub_overflow(T v1, T v2, T *r) {returnqSubOverflow(v1, v2, r); }template<typename T>inlineboolmul_overflow(T v1, T v2, T *r) {returnqMulOverflow(v1, v2, r); }template<typename T, T V2>booladd_overflow(T v1,std::integral_constant<T, V2>, T *r){return qAddOverflow<T, V2>(v1,std::integral_constant<T, V2>{}, r);}template<auto V2, typename T>booladd_overflow(T v1, T *r){return qAddOverflow<V2, T>(v1, r);}template<typename T, T V2>boolsub_overflow(T v1,std::integral_constant<T, V2>, T *r){return qSubOverflow<T, V2>(v1,std::integral_constant<T, V2>{}, r);}template<auto V2, typename T>boolsub_overflow(T v1, T *r){return qSubOverflow<V2, T>(v1, r);}template<typename T, T V2>boolmul_overflow(T v1,std::integral_constant<T, V2>, T *r){return qMulOverflow<T, V2>(v1,std::integral_constant<T, V2>{}, r);}template<auto V2, typename T>boolmul_overflow(T v1, T *r){return qMulOverflow<V2, T>(v1, r);}}#endif// Q_QDOCtemplate<typename To, typename From>staticconstexpr autoqt_saturate(From x){returnq26::saturate_cast<To>(x);} QT_END_NAMESPACE #endif// QNUMERIC_P_H