// Copyright (C) 2020 The Qt Company Ltd. // SPDX-License-Identifier: LicenseRef-Qt-Commercial OR GFDL-1.3-no-invariants-only /*! \headerfile \inmodule QtCore \title Generic Math Functions \ingroup funclists \brief The header file provides various math functions. These functions are partly convenience definitions for basic math operations not available in the C or Standard Template Libraries. The header also ensures some constants specified in POSIX, but not present in C++ standards (so absent from on some platforms), are defined: \value M_E The base of the natural logarithms, e = exp(1) \value M_LOG2E The base-two logarithm of e \value M_LOG10E The base-ten logarithm of e \value M_LN2 The natural logarithm of two \value M_LN10 The natural logarithm of ten \value M_PI The ratio of a circle's circumference to diameter, \unicode{0x3C0} \value M_PI_2 Half M_PI, \unicode{0x3C0} / 2 \value M_PI_4 Quarter M_PI, \unicode{0x3C0} / 4 \value M_1_PI The inverse of M_PI, 1 / \unicode{0x3C0} \value M_2_PI Twice the inverse of M_PI, 2 / \unicode{0x3C0} \value M_2_SQRTPI Two divided by the square root of pi, 2 / \unicode{0x221A}\unicode{0x3C0} \value M_SQRT2 The square root of two, \unicode{0x221A}2 \value M_SQRT1_2 The square roof of half, 1 / \unicode{0x221A}2 */ /*! \fn template int qCeil(T v) Returns the ceiling of the value \a v. The ceiling is the smallest integer that is not less than \a v. For example, if \a v is 41.2, then the ceiling is 42. \relates \sa qFloor() */ /*! \fn template int qFloor(T v) Returns the floor of the value \a v. The floor is the largest integer that is not greater than \a v. For example, if \a v is 41.2, then the floor is 41. \relates \sa qCeil() */ /*! \fn template auto qFabs(T v) Returns the absolute value of \a v. \relates */ /*! \fn template auto qSin(T v) Returns the sine of the angle \a v in radians. \relates \sa qCos(), qTan() */ /*! \fn template auto qCos(T v) Returns the cosine of an angle \a v in radians. \relates \sa qSin(), qTan() */ /*! \fn template auto qTan(T v) Returns the tangent of an angle \a v in radians. \relates \sa qSin(), qCos() */ /*! \fn template auto qAcos(T v) Returns the arccosine of \a v as an angle in radians. Arccosine is the inverse operation of cosine. \relates \sa qAtan(), qAsin(), qCos() */ /*! \fn template auto qAsin(T v) Returns the arcsine of \a v as an angle in radians. Arcsine is the inverse operation of sine. \relates \sa qSin(), qAtan(), qAcos() */ /*! \fn template auto qAtan(T v) Returns the arctangent of \a v as an angle in radians. Arctangent is the inverse operation of tangent. \relates \sa qTan(), qAcos(), qAsin() */ /*! \fn template auto qAtan2(T1 y, T2 x) Returns the arctangent of a point specified by the coordinates \a y and \a x. This function will return the angle (argument) of that point. \relates \sa qAtan(), qHypot() */ /*! \fn template auto qSqrt(T v) Returns the square root of \a v. This function returns a NaN if \a v is a negative number. \relates \sa qPow(), qHypot() */ /*! \since 6.1 \overload \fn template auto qHypot(Tx x, Ty y) Returns the distance of a point (\a x, \a y) from the origin (0, 0). This is qSqrt(x * x + y * y), optimized. In particular, underflow and overflow may be avoided. Accepts any mix of numeric types, returning the same floating-point type as std::hypot(). If either parameter is infinite, so is the result; otherwise, if either is a NaN, so is the result. \relates \sa qSqrt(), qAtan2() */ /*! \since 6.1 \overload \fn template auto qHypot(Tx x, Ty y, Tz z) Returns the distance of a point (x, y, z) from the origin (0, 0, 0). This is qSqrt(x * x + y * y + z * z), optimized where supported. In particular, underflow and overflow may be avoided. Accepts any mix of numeric types, returning the same floating-point type as std::hypot(). If any parameter is infinite, so is the result; otherwise, if any is NaN, so is the result. \relates \sa qSqrt() */ /*! \since 6.1 \fn template auto qHypot(F first, Fs... rest) Returns the distance from origin in arbitrarily many dimensions This is as for the two-argument and three-argument forms, supported by std::hypot(), but with as many numeric parameters as you care to pass to it. Uses \a first and each of the \a rest as coordinates, performing a calculation equivalent to squaring each, summing and returning the square root, save that underflow and overflow are avoided as far as possible. \relates \sa qSqrt() */ /*! \fn template auto qLn(T v) Returns the natural logarithm of \a v. Natural logarithm uses base e. \relates \sa qExp() */ /*! \fn template auto qExp(T v) Returns the exponential function of \c e to the power of \a v. \relates \sa qLn() */ /*! \fn template auto qPow(T1 x, T2 y) Returns the value of \a x raised to the power of \a y. That is, \a x is the base and \a y is the exponent. \relates \sa qSqrt() */ /*! \fn float qDegreesToRadians(float degrees) \relates \since 5.1 This function converts the \a degrees in float to radians. Example: \snippet code/src_corelib_kernel_qmath.cpp 0 \sa qRadiansToDegrees() */ /*! \fn double qDegreesToRadians(double degrees) \relates \since 5.1 This function converts the \a degrees in double to radians. Example: \snippet code/src_corelib_kernel_qmath.cpp 1 \sa qRadiansToDegrees() */ /*! \fn long double qDegreesToRadians(long double degrees) \relates \since 6.0 This function converts the \a degrees in double to radians. \sa qRadiansToDegrees() */ /*! \fn template double qDegreesToRadians(Integral degrees) \relates \since 6.0 This function converts the \a degrees in double to radians; the angle is casted to a double before the conversion. This function participates in overload resolution if and only if \c Integral is an integral type. \sa qRadiansToDegrees() */ /*! \fn float qRadiansToDegrees(float radians) \relates \since 5.1 This function converts the \a radians in float to degrees. Example: \snippet code/src_corelib_kernel_qmath.cpp 2 \sa qDegreesToRadians() */ /*! \fn double qRadiansToDegrees(double radians) \relates \since 5.1 This function converts the \a radians in double to degrees. Example: \snippet code/src_corelib_kernel_qmath.cpp 3 \sa qDegreesToRadians() */ /*! \fn long double qRadiansToDegrees(long double radians) \relates \since 6.0 This function converts the \a radians in double to degrees. \sa qDegreesToRadians() */ /*! \fn quint32 qNextPowerOfTwo(quint32 value) \relates \since 5.4 This function returns the nearest power of two greater than \a value. For 0 it returns 1, and for values larger than or equal to 2^31 the result is undefined. */ /*! \fn quint32 qNextPowerOfTwo(qint32 value) \relates \since 5.4 \overload This function returns the nearest power of two greater than \a value. For negative values the result is undefined. */ /*! \fn quint64 qNextPowerOfTwo(quint64 value) \relates \since 5.4 This function returns the nearest power of two greater than \a value. For 0 it returns 1, and for values larger than or equal to 2^63 the result is undefined. */ /*! \fn quint64 qNextPowerOfTwo(qint64 value) \relates \since 5.4 \overload This function returns the nearest power of two greater than \a value. For negative values the result is undefined. */