qnumeric_p.h

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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
 
#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>
 
#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 {
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(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).
        // [1] https://en.wikipedia.org/wiki/Floating-point_arithmetic#Exception_handling
        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.
    // See https://github.com/llvm/llvm-project/issues/83661.
    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) > (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
 
/*
    Safely narrows \a x to \c{To}. Let \c L be
    \c{std::numeric_limit<To>::min()} and \c H be \c{std::numeric_limit<To>::max()}.
 
    If \a x is less than L, returns L. If \a x is greater than H,
    returns H. Otherwise, returns \c{To(x)}.
*/
template <typename To, typename From>
static constexpr auto qt_saturate(From x)
{
    static_assert(std::is_integral_v<To>);
    static_assert(std::is_integral_v<From>);
 
    [[maybe_unused]]
    constexpr auto Lo = (std::numeric_limits<To>::min)();
    constexpr auto Hi = (std::numeric_limits<To>::max)();
 
    if constexpr (std::is_signed_v<From> == std::is_signed_v<To>) {
        // same signedness, we can accept regular integer conversion rules
        return x < Lo  ? Lo :
               x > Hi  ? Hi :
               /*else*/  To(x);
    } else {
        if constexpr (std::is_signed_v<From>) { // ie. !is_signed_v<To>
            if (x < From{0})
                return To{0};
        }
 
        // from here on, x >= 0
        using FromU = std::make_unsigned_t<From>;
        using ToU = std::make_unsigned_t<To>;
        return FromU(x) > ToU(Hi) ? Hi : To(x); // assumes Hi >= 0
    }
}
 
QT_END_NAMESPACE
 
#endif // QNUMERIC_P_H