# <QtMath> - Generic Math Functions

The <QtMath> header file provides various math functions. More...

## Functions

 auto qAcos(T v) auto qAsin(T v) auto qAtan2(T1 y, T2 x) auto qAtan(T v) int qCeil(T v) auto qCos(T v) float qDegreesToRadians(float degrees) double qDegreesToRadians(double degrees) long double qDegreesToRadians(long double degrees) auto qExp(T v) auto qFabs(T v) int qFloor(T v) auto qHypot(F first, Fs... rest) auto qHypot(Tx x, Ty y) auto qHypot(Tx x, Ty y, Tz z) auto qLn(T v) quint32 qNextPowerOfTwo(quint32 value) quint32 qNextPowerOfTwo(qint32 value) quint64 qNextPowerOfTwo(quint64 value) quint64 qNextPowerOfTwo(qint64 value) auto qPow(T1 x, T2 y) float qRadiansToDegrees(float radians) double qRadiansToDegrees(double radians) long double qRadiansToDegrees(long double radians) auto qSin(T v) auto qSqrt(T v) auto qTan(T v)

## Detailed Description

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 <math.h> on some platforms), are defined:

Constant Description
`M_E` The base of the natural logarithms, e = exp(1)
`M_LOG2E` The base-two logarithm of e
`M_LOG10E` The base-ten logarithm of e
`M_LN2` The natural logarithm of two
`M_LN10` The natural logarithm of ten
`M_PI` The ratio of a circle's circumference to diameter, π
`M_PI_2` Half M_PI, π / 2
`M_PI_4` Quarter M_PI, π / 4
`M_1_PI` The inverse of M_PI, 1 / π
`M_2_PI` Twice the inverse of M_PI, 2 / π
`M_2_SQRTPI` Two divided by the square root of pi, 2 / √π
`M_SQRT2` The square root of two, √2
`M_SQRT1_2` The square roof of half, 1 / √2

## Function Documentation

### template <typename T> autoqAcos(Tv)

Returns the arccosine of v as an angle in radians. Arccosine is the inverse operation of cosine.

### template <typename T> autoqAsin(Tv)

Returns the arcsine of v as an angle in radians. Arcsine is the inverse operation of sine.

### template <typename T1, typename T2> autoqAtan2(T1y, T2x)

Returns the arctangent of a point specified by the coordinates y and x. This function will return the angle (argument) of that point.

### template <typename T> autoqAtan(Tv)

Returns the arctangent of v as an angle in radians. Arctangent is the inverse operation of tangent.

### template <typename T> intqCeil(Tv)

Returns the ceiling of the value v.

The ceiling is the smallest integer that is not less than v. For example, if v is 41.2, then the ceiling is 42.

### template <typename T> autoqCos(Tv)

Returns the cosine of an angle v in radians.

### `[since 5.1]`floatqDegreesToRadians(floatdegrees)

This function converts the degrees in float to radians.

Example:

```float degrees = 180.0f

This function was introduced in Qt 5.1.

### `[since 5.1]`doubleqDegreesToRadians(doubledegrees)

This function converts the degrees in double to radians.

Example:

```double degrees = 180.0

This function was introduced in Qt 5.1.

### `[since 6.0]`longdoubleqDegreesToRadians(longdoubledegrees)

This function converts the degrees in double to radians.

This function was introduced in Qt 6.0.

### template <typename T> autoqExp(Tv)

Returns the exponential function of `e` to the power of v.

### template <typename T> autoqFabs(Tv)

Returns the absolute value of v.

### template <typename T> intqFloor(Tv)

Returns the floor of the value v.

The floor is the largest integer that is not greater than v. For example, if v is 41.2, then the floor is 41.

### `[since 6.1]` template <typename F, typename Fs> autoqHypot(Ffirst, 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 first and each of the 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.

This function was introduced in Qt 6.1.

### `[since 6.1]` template <typename Tx, typename Ty> autoqHypot(Txx, Tyy)

Returns the distance of a point (x, 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.

This function was introduced in Qt 6.1.

### `[since 6.1]` template <typename Tx, typename Ty, typename Tz> autoqHypot(Txx, Tyy, Tzz)

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.

This function was introduced in Qt 6.1.

### template <typename T> autoqLn(Tv)

Returns the natural logarithm of v. Natural logarithm uses base e.

### `[since 5.4]`quint32qNextPowerOfTwo(quint32value)

This function returns the nearest power of two greater than value. For 0 it returns 1, and for values larger than or equal to 2^31 the result is undefined.

This function was introduced in Qt 5.4.

### `[since 5.4]`quint32qNextPowerOfTwo(qint32value)

This function returns the nearest power of two greater than value. For negative values the result is undefined.

This function was introduced in Qt 5.4.

### `[since 5.4]`quint64qNextPowerOfTwo(quint64value)

This function returns the nearest power of two greater than value. For 0 it returns 1, and for values larger than or equal to 2^63 the result is undefined.

This function was introduced in Qt 5.4.

### `[since 5.4]`quint64qNextPowerOfTwo(qint64value)

This function returns the nearest power of two greater than value. For negative values the result is undefined.

This function was introduced in Qt 5.4.

### template <typename T1, typename T2> autoqPow(T1x, T2y)

Returns the value of x raised to the power of y. That is, x is the base and y is the exponent.

### `[since 5.1]`floatqRadiansToDegrees(floatradians)

This function converts the radians in float to degrees.

Example:

```float radians = float(M_PI)

This function was introduced in Qt 5.1.

### `[since 5.1]`doubleqRadiansToDegrees(doubleradians)

This function converts the radians in double to degrees.

Example:

```double radians = M_PI

This function was introduced in Qt 5.1.

### `[since 6.0]`longdoubleqRadiansToDegrees(longdoubleradians)

This function converts the radians in double to degrees.

This function was introduced in Qt 6.0.

### template <typename T> autoqSin(Tv)

Returns the sine of the angle v in radians.