# <QtMath> - Generic Math Functions

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

Header: | #include <QtMath> |

## 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> auto qAcos(T *v*)

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

**See also **qAtan(), qAsin(), and qCos().

### template <typename T> auto qAsin(T *v*)

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

**See also **qSin(), qAtan(), and qAcos().

### template <typename T1, typename T2> auto qAtan2(T1 *y*, T2 *x*)

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

**See also **qAtan() and qHypot().

### template <typename T> auto qAtan(T *v*)

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

**See also **qTan(), qAcos(), and qAsin().

### template <typename T> int qCeil(T *v*)

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.

**See also **qFloor().

### template <typename T> auto qCos(T *v*)

Returns the cosine of an angle *v* in radians.

`[constexpr] `

float qDegreesToRadians(float *degrees*)

This function converts the *degrees* in float to radians.

Example:

float degrees = 180.0f float radians = qDegreesToRadians(degrees)

**See also **qRadiansToDegrees().

`[constexpr] `

double qDegreesToRadians(double *degrees*)

This function converts the *degrees* in double to radians.

Example:

double degrees = 180.0 double radians = qDegreesToRadians(degrees)

**See also **qRadiansToDegrees().

`[constexpr, since 6.0] `

long double qDegreesToRadians(long double *degrees*)

This function converts the *degrees* in double to radians.

This function was introduced in Qt 6.0.

**See also **qRadiansToDegrees().

### template <typename T> auto qExp(T *v*)

Returns the exponential function of `e`

to the power of *v*.

**See also **qLn().

### template <typename T> auto qFabs(T *v*)

Returns the absolute value of *v*.

### template <typename T> int qFloor(T *v*)

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.

**See also **qCeil().

`[since 6.1] `

template <typename F, typename Fs> 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 *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.

**See also **qSqrt().

`[since 6.1] `

template <typename Tx, typename Ty> auto qHypot(Tx *x*, Ty *y*)

This is an overloaded function.

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.

**See also **qSqrt() and qAtan2().

`[since 6.1] `

template <typename Tx, typename Ty, typename Tz> auto qHypot(Tx *x*, Ty *y*, Tz *z*)

This is an overloaded function.

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.

**See also **qSqrt().

### template <typename T> auto qLn(T *v*)

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

**See also **qExp().

`[constexpr] `

quint32 qNextPowerOfTwo(quint32 *value*)

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.

`[constexpr] `

quint32 qNextPowerOfTwo(qint32 *value*)

This is an overloaded function.

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

`[constexpr] `

quint64 qNextPowerOfTwo(quint64 *value*)

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.

`[constexpr] `

quint64 qNextPowerOfTwo(qint64 *value*)

This is an overloaded function.

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

### template <typename T1, typename T2> auto qPow(T1 *x*, T2 *y*)

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

**See also **qSqrt().

`[constexpr] `

float qRadiansToDegrees(float *radians*)

This function converts the *radians* in float to degrees.

Example:

float radians = float(M_PI) float degrees = qRadiansToDegrees(radians)

**See also **qDegreesToRadians().

`[constexpr] `

double qRadiansToDegrees(double *radians*)

This function converts the *radians* in double to degrees.

Example:

double radians = M_PI double degrees = qRadiansToDegrees(radians)

**See also **qDegreesToRadians().

`[constexpr, since 6.0] `

long double qRadiansToDegrees(long double *radians*)

This function converts the *radians* in double to degrees.

This function was introduced in Qt 6.0.

**See also **qDegreesToRadians().

### template <typename T> auto qSin(T *v*)

Returns the sine of the angle *v* in radians.

### template <typename T> auto qSqrt(T *v*)

Returns the square root of *v*. This function returns a NaN if *v* is a negative number.

### template <typename T> auto qTan(T *v*)

Returns the tangent of an angle *v* in radians.

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