path: root/src/corelib/global/qnumeric.cpp

// Copyright (C) 2019 The Qt Company Ltd.// SPDX-License-Identifier: LicenseRef-Qt-Commercial OR LGPL-3.0-only OR GPL-2.0-only OR GPL-3.0-only#include"qnumeric.h"#include"qnumeric_p.h"#include <string.h> QT_BEGIN_NAMESPACE /*! \headerfile <QtNumeric> \inmodule QtCore \title Qt Numeric Functions \brief The <QtNumeric> header file provides common numeric functions. The <QtNumeric> header file contains various numeric functions for comparing and adjusting a numeric value.*//*! Returns \c true if the double \a {d} is equivalent to infinity. \relates <QtNumeric> \sa qInf()*/ Q_CORE_EXPORT boolqIsInf(double d) {returnqt_is_inf(d); }/*! Returns \c true if the double \a {d} is not a number (NaN). \relates <QtNumeric>*/ Q_CORE_EXPORT boolqIsNaN(double d) {returnqt_is_nan(d); }/*! Returns \c true if the double \a {d} is a finite number. \relates <QtNumeric>*/ Q_CORE_EXPORT boolqIsFinite(double d) {returnqt_is_finite(d); }/*! Returns \c true if the float \a {f} is equivalent to infinity. \relates <QtNumeric> \sa qInf()*/ Q_CORE_EXPORT boolqIsInf(float f) {returnqt_is_inf(f); }/*! Returns \c true if the float \a {f} is not a number (NaN). \relates <QtNumeric>*/ Q_CORE_EXPORT boolqIsNaN(float f) {returnqt_is_nan(f); }/*! Returns \c true if the float \a {f} is a finite number. \relates <QtNumeric>*/ Q_CORE_EXPORT boolqIsFinite(float f) {returnqt_is_finite(f); }#if QT_CONFIG(signaling_nan)/*! Returns the bit pattern of a signalling NaN as a double. \relates <QtNumeric>*/ Q_CORE_EXPORT doubleqSNaN() {returnqt_snan(); }#endif/*! Returns the bit pattern of a quiet NaN as a double. \relates <QtNumeric> \sa qIsNaN()*/ Q_CORE_EXPORT doubleqQNaN() {returnqt_qnan(); }/*! Returns the bit pattern for an infinite number as a double. \relates <QtNumeric> \sa qIsInf()*/ Q_CORE_EXPORT doubleqInf() {returnqt_inf(); }/*! \fn int qFpClassify(double val) \fn int qFpClassify(float val) \relates <QtNumeric> Classifies a floating-point value. The return values are defined in \c{<cmath>}: returns one of the following, determined by the floating-point class of \a val: \list \li FP_NAN not a number \li FP_INFINITE infinities (positive or negative) \li FP_ZERO zero (positive or negative) \li FP_NORMAL finite with a full mantissa \li FP_SUBNORMAL finite with a reduced mantissa \endlist*/ Q_CORE_EXPORT intqFpClassify(double val) {returnqt_fpclassify(val); } Q_CORE_EXPORT intqFpClassify(float val) {returnqt_fpclassify(val); }/*! \internal */staticinline quint32 f2i(float f){ quint32 i;memcpy(&i, &f,sizeof(f));return i;}/*! Returns the number of representable floating-point numbers between \a a and \a b. This function provides an alternative way of doing approximated comparisons of floating-point numbers similar to qFuzzyCompare(). However, it returns the distance between two numbers, which gives the caller a possibility to choose the accepted error. Errors are relative, so for instance the distance between 1.0E-5 and 1.00001E-5 will give 110, while the distance between 1.0E36 and 1.00001E36 will give 127. This function is useful if a floating point comparison requires a certain precision. Therefore, if \a a and \a b are equal it will return 0. The maximum value it will return for 32-bit floating point numbers is 4,278,190,078. This is the distance between \c{-FLT_MAX} and \c{+FLT_MAX}. The function does not give meaningful results if any of the arguments are \c Infinite or \c NaN. You can check for this by calling qIsFinite(). The return value can be considered as the "error", so if you for instance want to compare two 32-bit floating point numbers and all you need is an approximated 24-bit precision, you can use this function like this: \snippet code/src_corelib_global_qnumeric.cpp 0 \sa qFuzzyCompare() \since 5.2 \relates <QtNumeric>*/ Q_CORE_EXPORT quint32 qFloatDistance(float a,float b){static const quint32 smallestPositiveFloatAsBits =0x00000001;// denormalized, (SMALLEST), (1.4E-45)/* Assumes: * IEE754 format. * Integers and floats have the same endian */static_assert(sizeof(quint32) ==sizeof(float));Q_ASSERT(qIsFinite(a) &&qIsFinite(b));if(a == b)return0;if((a <0) != (b <0)) {// if they have different signsif(a <0) a = -a;else/*if (b < 0)*/ b = -b;returnqFloatDistance(0.0F, a) +qFloatDistance(0.0F, b);}if(a <0) { a = -a; b = -b;}// at this point a and b should not be negative// 0 is specialif(!a)returnf2i(b) - smallestPositiveFloatAsBits +1;if(!b)returnf2i(a) - smallestPositiveFloatAsBits +1;// finally do the common integer subtractionreturn a > b ?f2i(a) -f2i(b) :f2i(b) -f2i(a);}/*! \internal */staticinline quint64 d2i(double d){ quint64 i;memcpy(&i, &d,sizeof(d));return i;}/*! Returns the number of representable floating-point numbers between \a a and \a b. This function serves the same purpose as \c{qFloatDistance(float, float)}, but returns the distance between two \c double numbers. Since the range is larger than for two \c float numbers (\c{[-DBL_MAX,DBL_MAX]}), the return type is quint64. \sa qFuzzyCompare() \since 5.2 \relates <QtNumeric>*/ Q_CORE_EXPORT quint64 qFloatDistance(double a,double b){static const quint64 smallestPositiveFloatAsBits =0x1;// denormalized, (SMALLEST)/* Assumes: * IEE754 format double precision * Integers and floats have the same endian */static_assert(sizeof(quint64) ==sizeof(double));Q_ASSERT(qIsFinite(a) &&qIsFinite(b));if(a == b)return0;if((a <0) != (b <0)) {// if they have different signsif(a <0) a = -a;else/*if (b < 0)*/ b = -b;returnqFloatDistance(0.0, a) +qFloatDistance(0.0, b);}if(a <0) { a = -a; b = -b;}// at this point a and b should not be negative// 0 is specialif(!a)returnd2i(b) - smallestPositiveFloatAsBits +1;if(!b)returnd2i(a) - smallestPositiveFloatAsBits +1;// finally do the common integer subtractionreturn a > b ?d2i(a) -d2i(b) :d2i(b) -d2i(a);}/*! \fn template<typename T> bool qAddOverflow(T v1, T v2, T *result) \relates <QtNumeric> \since 6.1 Adds two values \a v1 and \a v2, of a numeric type \c T and records the value in \a result. If the addition overflows the valid range for type \c T, returns \c true, otherwise returns \c false. An implementation is guaranteed to be available for 8-, 16-, and 32-bit integer types, as well as integer types of the size of a pointer. Overflow math for other types, if available, is considered private API.*//*! \fn template <typename T, T V2> bool qAddOverflow(T v1, std::integral_constant<T, V2>, T *r) \since 6.1 \internal Equivalent to qAddOverflow(v1, v2, r) with \a v1 as first argument, the compile time constant \c V2 as second argument, and \a r as third argument.*//*! \fn template <auto V2, typename T> bool qAddOverflow(T v1, T *r) \since 6.1 \internal Equivalent to qAddOverflow(v1, v2, r) with \a v1 as first argument, the compile time constant \c V2 as second argument, and \a r as third argument.*//*! \fn template<typename T> bool qSubOverflow(T v1, T v2, T *result) \relates <QtNumeric> \since 6.1 Subtracts \a v2 from \a v1 and records the resulting value in \a result. If the subtraction overflows the valid range for type \c T, returns \c true, otherwise returns \c false. An implementation is guaranteed to be available for 8-, 16-, and 32-bit integer types, as well as integer types of the size of a pointer. Overflow math for other types, if available, is considered private API.*//*! \fn template <typename T, T V2> bool qSubOverflow(T v1, std::integral_constant<T, V2>, T *r) \since 6.1 \internal Equivalent to qSubOverflow(v1, v2, r) with \a v1 as first argument, the compile time constant \c V2 as second argument, and \a r as third argument.*//*! \fn template <auto V2, typename T> bool qSubOverflow(T v1, T *r) \since 6.1 \internal Equivalent to qSubOverflow(v1, v2, r) with \a v1 as first argument, the compile time constant \c V2 as second argument, and \a r as third argument.*//*! \fn template<typename T> bool qMulOverflow(T v1, T v2, T *result) \relates <QtNumeric> \since 6.1 Multiplies \a v1 and \a v2, and records the resulting value in \a result. If the multiplication overflows the valid range for type \c T, returns \c true, otherwise returns \c false. An implementation is guaranteed to be available for 8-, 16-, and 32-bit integer types, as well as integer types of the size of a pointer. Overflow math for other types, if available, is considered private API.*//*! \fn template <typename T, T V2> bool qMulOverflow(T v1, std::integral_constant<T, V2>, T *r) \since 6.1 \internal Equivalent to qMulOverflow(v1, v2, r) with \a v1 as first argument, the compile time constant \c V2 as second argument, and \a r as third argument. This can be faster than calling the version with only variable arguments.*//*! \fn template <auto V2, typename T> bool qMulOverflow(T v1, T *r) \since 6.1 \internal Equivalent to qMulOverflow(v1, v2, r) with \a v1 as first argument, the compile time constant \c V2 as second argument, and \a r as third argument. This can be faster than calling the version with only variable arguments.*//*! \fn template <typename T> T qAbs(const T &t) \relates <QtNumeric> Compares \a t to the 0 of type T and returns the absolute value. Thus if T is \e {double}, then \a t is compared to \e{(double) 0}. Example: \snippet code/src_corelib_global_qglobal.cpp 10*//*! \fn int qRound(double d) \relates <QtNumeric> Rounds \a d to the nearest integer. Rounds half away from zero (e.g. 0.5 -> 1, -0.5 -> -1). \note This function does not guarantee correctness for high precisions. Example: \snippet code/src_corelib_global_qglobal.cpp 11A \note If the value \a d is outside the range of \c int, the behavior is undefined.*//*! \fn int qRound(float d) \relates <QtNumeric> Rounds \a d to the nearest integer. Rounds half away from zero (e.g. 0.5f -> 1, -0.5f -> -1). \note This function does not guarantee correctness for high precisions. Example: \snippet code/src_corelib_global_qglobal.cpp 11B \note If the value \a d is outside the range of \c int, the behavior is undefined.*//*! \fn qint64 qRound64(double d) \relates <QtNumeric> Rounds \a d to the nearest 64-bit integer. Rounds half away from zero (e.g. 0.5 -> 1, -0.5 -> -1). \note This function does not guarantee correctness for high precisions. Example: \snippet code/src_corelib_global_qglobal.cpp 12A \note If the value \a d is outside the range of \c qint64, the behavior is undefined.*//*! \fn qint64 qRound64(float d) \relates <QtNumeric> Rounds \a d to the nearest 64-bit integer. Rounds half away from zero (e.g. 0.5f -> 1, -0.5f -> -1). \note This function does not guarantee correctness for high precisions. Example: \snippet code/src_corelib_global_qglobal.cpp 12B \note If the value \a d is outside the range of \c qint64, the behavior is undefined.*//*! \fn bool qFuzzyCompare(double p1, double p2) \relates <QtNumeric> \since 4.4 \threadsafe Compares the floating point value \a p1 and \a p2 and returns \c true if they are considered equal, otherwise \c false. Note that comparing values where either \a p1 or \a p2 is 0.0 will not work, nor does comparing values where one of the values is NaN or infinity. If one of the values is always 0.0, use qFuzzyIsNull instead. If one of the values is likely to be 0.0, one solution is to add 1.0 to both values. \snippet code/src_corelib_global_qglobal.cpp 46 The two numbers are compared in a relative way, where the exactness is stronger the smaller the numbers are.*//*! \fn bool qFuzzyCompare(float p1, float p2) \relates <QtNumeric> \since 4.4 \threadsafe Compares the floating point value \a p1 and \a p2 and returns \c true if they are considered equal, otherwise \c false. The two numbers are compared in a relative way, where the exactness is stronger the smaller the numbers are.*//*! \fn bool qFuzzyIsNull(double d) \relates <QtNumeric> \since 4.4 \threadsafe Returns true if the absolute value of \a d is within 0.000000000001 of 0.0.*//*! \fn bool qFuzzyIsNull(float f) \relates <QtNumeric> \since 4.4 \threadsafe Returns true if the absolute value of \a f is within 0.00001f of 0.0.*/ QT_END_NAMESPACE