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// 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
// Qt-Security score:significant reason:default
#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 saturating_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 static inline bool math_h_isnan(double d) { using namespace std; return isnan(d); }
Q_DECL_CONST_FUNCTION static inline bool math_h_isinf(double d) { using namespace std; return isinf(d); }
Q_DECL_CONST_FUNCTION static inline bool math_h_isfinite(double d) { using namespace std; return isfinite(d); }
Q_DECL_CONST_FUNCTION static inline int math_h_fpclassify(double d) { using namespace std; return fpclassify(d); }
Q_DECL_CONST_FUNCTION static inline bool math_h_isnan(float f) { using namespace std; return isnan(f); }
Q_DECL_CONST_FUNCTION static inline bool math_h_isinf(float f) { using namespace std; return isinf(f); }
Q_DECL_CONST_FUNCTION static inline bool math_h_isfinite(float f) { using namespace std; return isfinite(f); }
Q_DECL_CONST_FUNCTION static inline int math_h_fpclassify(float f) { using namespace std; return fpclassify(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 static inline bool isnan(double d) { return math_h_isnan(d); }
Q_DECL_CONST_FUNCTION static inline bool isinf(double d) { return math_h_isinf(d); }
Q_DECL_CONST_FUNCTION static inline bool isfinite(double d) { return math_h_isfinite(d); }
Q_DECL_CONST_FUNCTION static inline int fpclassify(double d) { return math_h_fpclassify(d); }
Q_DECL_CONST_FUNCTION static inline bool isnan(float f) { return math_h_isnan(f); }
Q_DECL_CONST_FUNCTION static inline bool isinf(float f) { return math_h_isinf(f); }
Q_DECL_CONST_FUNCTION static inline bool isfinite(float f) { return math_h_isfinite(f); }
Q_DECL_CONST_FUNCTION static inline int fpclassify(float f) { return math_h_fpclassify(f); }
#else
Q_DECL_CONST_FUNCTION static inline bool isnan(double d) { return std::isnan(d); }
Q_DECL_CONST_FUNCTION static inline bool isinf(double d) { return std::isinf(d); }
Q_DECL_CONST_FUNCTION static inline bool isfinite(double d) { return std::isfinite(d); }
Q_DECL_CONST_FUNCTION static inline int fpclassify(double d) { return std::fpclassify(d); }
Q_DECL_CONST_FUNCTION static inline bool isnan(float f) { return std::isnan(f); }
Q_DECL_CONST_FUNCTION static inline bool isinf(float f) { return std::isinf(f); }
Q_DECL_CONST_FUNCTION static inline bool isfinite(float f) { return std::isfinite(f); }
Q_DECL_CONST_FUNCTION static inline int fpclassify(float f) { return std::fpclassify(f); }
#endif
}
constexpr Q_DECL_CONST_FUNCTION static inline double qt_inf() noexcept
{
static_assert(std::numeric_limits<double>::has_infinity,
"platform has no definition for infinity for type double");
return std::numeric_limits<double>::infinity();
}
#if QT_CONFIG(signaling_nan)
constexpr Q_DECL_CONST_FUNCTION static inline double qt_snan() noexcept
{
static_assert(std::numeric_limits<double>::has_signaling_NaN,
"platform has no definition for signaling NaN for type double");
return std::numeric_limits<double>::signaling_NaN();
}
#endif
// Quiet NaN
constexpr Q_DECL_CONST_FUNCTION static inline double qt_qnan() noexcept
{
static_assert(std::numeric_limits<double>::has_quiet_NaN,
"platform has no definition for quiet NaN for type double");
return std::numeric_limits<double>::quiet_NaN();
}
Q_DECL_CONST_FUNCTION static inline bool qt_is_inf(double d)
{
return qnumeric_std_wrapper::isinf(d);
}
Q_DECL_CONST_FUNCTION static inline bool qt_is_nan(double d)
{
return qnumeric_std_wrapper::isnan(d);
}
Q_DECL_CONST_FUNCTION static inline bool qt_is_finite(double d)
{
return qnumeric_std_wrapper::isfinite(d);
}
Q_DECL_CONST_FUNCTION static inline int qt_fpclassify(double d)
{
return qnumeric_std_wrapper::fpclassify(d);
}
Q_DECL_CONST_FUNCTION static inline bool qt_is_inf(float f)
{
return qnumeric_std_wrapper::isinf(f);
}
Q_DECL_CONST_FUNCTION static inline bool qt_is_nan(float f)
{
return qnumeric_std_wrapper::isnan(f);
}
Q_DECL_CONST_FUNCTION static inline bool qt_is_finite(float f)
{
return qnumeric_std_wrapper::isfinite(f);
}
Q_DECL_CONST_FUNCTION static inline int qt_fpclassify(float f)
{
return qnumeric_std_wrapper::fpclassify(f);
}
#ifndef Q_QDOC
namespace {
/*!
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> static inline 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>);
constexpr bool TypeIsLarger = std::numeric_limits<T>::digits > std::numeric_limits<double>::digits;
if constexpr (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 exceptions
if (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 range
if (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 exceptions
if (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 that
if (TypeIsLarger || _mm_ucomieq_sd(mv, _mm_set_sd(double(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
#endif
double 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> static
std::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();
if constexpr (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 indicators
auto 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).
return 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.
if constexpr (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));
# else
asm ("ldmxcsr %[csr]\n\t"
"cvtsd2ss %[in], %[out]\n\t"
"stmxcsr %[csr]"
: [csr] "+m" (csr), [out] "=v" (*value) : [in] "v" (v));
# endif
return sse_check_result(*value);
}
# if defined(__F16C__) || defined(__AVX512FP16__)
if constexpr (sizeof(T) == 2 && std::numeric_limits<T>::max_exponent == 16) {
// qfloat16 or std::float16_t, but not std::bfloat16_t or std::bfloat8_t
auto 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)
);
return sse_check_result(out);
};
if constexpr (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 type
return doConvert(value);
# endif
}
}
# endif
#endif // __SSE2__ && inline assembly
if (!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 precision
return false;
}
return true;
}
template <typename T> inline bool add_overflow(T v1, T v2, T *r) { return qAddOverflow(v1, v2, r); }
template <typename T> inline bool sub_overflow(T v1, T v2, T *r) { return qSubOverflow(v1, v2, r); }
template <typename T> inline bool mul_overflow(T v1, T v2, T *r) { return qMulOverflow(v1, v2, r); }
template <typename T, T V2> bool add_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> bool add_overflow(T v1, T *r)
{
return qAddOverflow<V2, T>(v1, r);
}
template <typename T, T V2> bool sub_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> bool sub_overflow(T v1, T *r)
{
return qSubOverflow<V2, T>(v1, r);
}
template <typename T, T V2> bool mul_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> bool mul_overflow(T v1, T *r)
{
return qMulOverflow<V2, T>(v1, r);
}
}
#endif // Q_QDOC
template <typename To, typename From>
static constexpr auto qt_saturate(From x)
{
return q26::saturating_cast<To>(x);
}
QT_END_NAMESPACE
#endif // QNUMERIC_P_H