Common Mathematical Functions For Fixed Types. More...

Namespaces
	playrho::detail
	Name space for internal/detail related PlayRho names.

Functions
template<typename BT , unsigned int FB, int N = 5>
constexpr Fixed< BT, FB >	playrho::abs (Fixed< BT, FB > arg)
	Computes the absolute value. More...

template<typename BT , unsigned int FB>
constexpr Fixed< BT, FB >	playrho::pow (Fixed< BT, FB > value, int n)
	Computes the value of the given number raised to the given power. More...

template<typename BT , unsigned int FB>
constexpr Fixed< BT, FB >	playrho::trunc (Fixed< BT, FB > arg)
	Truncates the given value. More...

template<typename BT , unsigned int FB>
Fixed< BT, FB >	playrho::nextafter (Fixed< BT, FB > from, Fixed< BT, FB > to) noexcept
	Next after function for Fixed types. More...

template<typename BT , unsigned int FB>
Fixed< BT, FB >	playrho::fmod (Fixed< BT, FB > dividend, Fixed< BT, FB > divisor) noexcept
	Computes the remainder of the division of the given dividend by the given divisor. More...

template<typename BT , unsigned int FB>
auto	playrho::sqrt (Fixed< BT, FB > arg)
	Square root's the given value. More...

template<typename BT , unsigned int FB>
bool	playrho::isnormal (Fixed< BT, FB > arg)
	Gets whether the given value is normal - i.e. not 0 nor infinite. More...

template<typename BT , unsigned int FB>
Fixed< BT, FB >	playrho::sin (Fixed< BT, FB > arg)
	Computes the sine of the argument for Fixed types. More...

template<typename BT , unsigned int FB>
Fixed< BT, FB >	playrho::cos (Fixed< BT, FB > arg)
	Computes the cosine of the argument for Fixed types. More...

template<typename BT , unsigned int FB>
Fixed< BT, FB >	playrho::atan (Fixed< BT, FB > arg)
	Computes the arc tangent. More...

template<typename BT , unsigned int FB>
Fixed< BT, FB >	playrho::atan2 (Fixed< BT, FB > y, Fixed< BT, FB > x)
	Computes the multi-valued inverse tangent. More...

template<typename BT , unsigned int FB>
Fixed< BT, FB >	playrho::log (Fixed< BT, FB > arg)
	Computes the natural logarithm of the given argument. More...

template<typename BT , unsigned int FB>
Fixed< BT, FB >	playrho::exp (Fixed< BT, FB > arg)
	Computes the Euler number raised to the power of the given argument. More...

template<typename BT , unsigned int FB>
Fixed< BT, FB >	playrho::pow (Fixed< BT, FB > base, Fixed< BT, FB > exponent)
	Computes the value of the base number raised to the power of the exponent. More...

template<typename BT , unsigned int FB>
Fixed< BT, FB >	playrho::hypot (Fixed< BT, FB > x, Fixed< BT, FB > y)
	Computes the square root of the sum of the squares. More...

template<typename BT , unsigned int FB>
Fixed< BT, FB >	playrho::round (Fixed< BT, FB > value) noexcept
	Rounds the given value. More...

template<typename BT , unsigned int FB>
bool	playrho::signbit (Fixed< BT, FB > value) noexcept
	Determines whether the given value is negative. More...

template<typename BT , unsigned int FB>
constexpr bool	playrho::isnan (Fixed< BT, FB > value) noexcept
	Gets whether the given value is not-a-number. More...

template<typename BT , unsigned int FB>
bool	playrho::isfinite (Fixed< BT, FB > value) noexcept
	Gets whether the given value is finite. More...

Detailed Description

Common Mathematical Functions For Fixed Types.

Note: These functions directly compute their respective results. They don't convert their inputs to a floating point type to use the standard math functions and then convert those results back to the fixed point type. This has pros and cons. Some pros are that: this won't suffer from the "non-determinism" inherent with different hardware platforms potentially having different floating point or math library implementations; this implementation won't suffer any overhead of converting between the underlying type and a floating point type. On the con side however: this implementation is unlikely to be anywhere near as tested as standard C++ math library functions likely are; this implementation is unlikely to have anywhere near as much performance tuning as standard library functions have had.

See also: Fixed; https://en.cppreference.com/w/cpp/numeric/math

Function Documentation

◆ abs()

template<typename BT , unsigned int FB, int N = 5>

constexpr Fixed<BT, FB> playrho::abs ( Fixed< BT, FB > arg )

constexpr

Computes the absolute value.

See also: https://en.cppreference.com/w/cpp/numeric/math/fabs

Examples: DistanceJoint.cpp.

Referenced by playrho::abs(), playrho::d2::UnitVec::Absolute(), playrho::AlmostEqual(), playrho::AlmostZero(), playrho::detail::atan(), playrho::d2::Cap(), playrho::GetAreaOfPolygon(), playrho::d2::GetToiViaSat(), playrho::d2::InitVelocity(), playrho::d2::RayCast(), playrho::d2::SolvePosition(), and playrho::d2::WorldImpl::Update().

◆ atan()

template<typename BT , unsigned int FB>

Fixed<BT, FB> playrho::atan ( Fixed< BT, FB > arg )

inline

Computes the arc tangent.

See also: https://en.cppreference.com/w/cpp/numeric/math/atan

Returns: Value between -Pi / 2 and Pi / 2.

Referenced by playrho::atan2().

◆ atan2()

template<typename BT , unsigned int FB>

Fixed<BT, FB> playrho::atan2	(	Fixed< BT, FB >	y,
		Fixed< BT, FB >	x
	)

inline

Computes the multi-valued inverse tangent.

See also: https://en.cppreference.com/w/cpp/numeric/math/atan2

Returns: Value between -Pi and +Pi inclusive.

Referenced by playrho::Atan2().

◆ cos()

template<typename BT , unsigned int FB>

Fixed<BT, FB> playrho::cos ( Fixed< BT, FB > arg )

inline

Computes the cosine of the argument for Fixed types.

See also: https://en.cppreference.com/w/cpp/numeric/math/cos

Examples: World.cpp.

Referenced by playrho::d2::UnitVec::Get(), playrho::GetCircleVertices(), and playrho::d2::RotateAboutWorldPoint().

◆ exp()

template<typename BT , unsigned int FB>

Fixed<BT, FB> playrho::exp ( Fixed< BT, FB > arg )

inline

Computes the Euler number raised to the power of the given argument.

See also: https://en.cppreference.com/w/cpp/numeric/math/exp

Referenced by playrho::pow().

◆ fmod()

template<typename BT , unsigned int FB>

Fixed<BT, FB> playrho::fmod	(	Fixed< BT, FB >	dividend,
		Fixed< BT, FB >	divisor
	)

inlinenoexcept

Computes the remainder of the division of the given dividend by the given divisor.

See also: https://en.cppreference.com/w/cpp/numeric/math/fmod

Referenced by playrho::detail::AngularNormalize(), and playrho::ModuloViaFmod().

◆ hypot()

template<typename BT , unsigned int FB>

Fixed<BT, FB> playrho::hypot	(	Fixed< BT, FB >	x,
		Fixed< BT, FB >	y
	)

inline

Computes the square root of the sum of the squares.

See also: https://en.cppreference.com/w/cpp/numeric/math/hypot

Referenced by playrho::d2::UnitVec::Get().

◆ isfinite()

template<typename BT , unsigned int FB>

bool playrho::isfinite ( Fixed< BT, FB > value )

inlinenoexcept

Gets whether the given value is finite.

See also: https://en.cppreference.com/w/cpp/numeric/math/isfinite

Referenced by playrho::Cross(), and playrho::d2::GetToiViaSat().

◆ isnan()

template<typename BT , unsigned int FB>

constexpr bool playrho::isnan ( Fixed< BT, FB > value )

constexprnoexcept

Gets whether the given value is not-a-number.

See also: https://en.cppreference.com/w/cpp/numeric/math/isnan

◆ isnormal()

template<typename BT , unsigned int FB>

bool playrho::isnormal ( Fixed< BT, FB > arg )

inline

Gets whether the given value is normal - i.e. not 0 nor infinite.

See also: https://en.cppreference.com/w/cpp/numeric/math/isnormal

Referenced by playrho::d2::UnitVec::Get().

◆ log()

template<typename BT , unsigned int FB>

Fixed<BT, FB> playrho::log ( Fixed< BT, FB > arg )

inline

Computes the natural logarithm of the given argument.

See also: https://en.cppreference.com/w/cpp/numeric/math/log

Referenced by playrho::pow().

◆ nextafter()

template<typename BT , unsigned int FB>

Fixed<BT, FB> playrho::nextafter	(	Fixed< BT, FB >	from,
		Fixed< BT, FB >	to
	)

inlinenoexcept

Next after function for Fixed types.

See also: https://en.cppreference.com/w/cpp/numeric/math/nextafter

Examples: World.cpp.

Referenced by playrho::d2::WorldImpl::GetSoonestContact(), playrho::d2::GetToiViaSat(), playrho::IsMaxTranslationWithinTolerance(), and playrho::d2::RayCast().

◆ pow() [1/2]

template<typename BT , unsigned int FB>

Fixed<BT, FB> playrho::pow	(	Fixed< BT, FB >	base,
		Fixed< BT, FB >	exponent
	)

inline

Computes the value of the base number raised to the power of the exponent.

See also: https://en.cppreference.com/w/cpp/numeric/math/pow

◆ pow() [2/2]

template<typename BT , unsigned int FB>

constexpr Fixed<BT, FB> playrho::pow	(	Fixed< BT, FB >	value,
		int	n
	)

constexpr

Computes the value of the given number raised to the given power.

Note: This implementation is for raising a given value to an integer power. This may have significantly different performance than raising a value to a non-integer power.

See also: https://en.cppreference.com/w/cpp/numeric/math/pow

Referenced by playrho::pow().

◆ round()

template<typename BT , unsigned int FB>

Fixed<BT, FB> playrho::round ( Fixed< BT, FB > value )

inlinenoexcept

Rounds the given value.

See also: https://en.cppreference.com/w/cpp/numeric/math/round

Referenced by playrho::RoundOff().

◆ signbit()

template<typename BT , unsigned int FB>

bool playrho::signbit ( Fixed< BT, FB > value )

inlinenoexcept

Determines whether the given value is negative.

See also: https://en.cppreference.com/w/cpp/numeric/math/signbit

Referenced by playrho::d2::ClipSegmentToLine(), and playrho::d2::Body::SetAcceleration().

◆ sin()

template<typename BT , unsigned int FB>

Fixed<BT, FB> playrho::sin ( Fixed< BT, FB > arg )

inline

Computes the sine of the argument for Fixed types.

See also: https://en.cppreference.com/w/cpp/numeric/math/sin

Examples: World.cpp.

Referenced by playrho::d2::UnitVec::Get(), playrho::GetCircleVertices(), and playrho::d2::RotateAboutWorldPoint().

◆ sqrt()

template<typename BT , unsigned int FB>

auto playrho::sqrt ( Fixed< BT, FB > arg )

inline

Square root's the given value.

Note: This implementation isn't meant to be fast, only correct enough.; The IEEE standard (presumably IEC 60559), requires std::sqrt to be exact to within half of a ULP for floating-point types (float, double). That sets a precedence that puts a high expectation on this implementation for fixed-point types.; "Domain error" occurs if arg is less than zero.

Returns: Mathematical square root value of the given value or the NaN value.

See also: https://en.cppreference.com/w/cpp/numeric/math/sqrt

Referenced by playrho::d2::Cap(), playrho::d2::UnitVec::Get(), playrho::d2::VertexSet::GetDefaultMinSeparationSquared(), playrho::GetMagnitude(), playrho::hypot(), playrho::MixFriction(), and playrho::d2::RayCast().

◆ trunc()

template<typename BT , unsigned int FB>

constexpr Fixed<BT, FB> playrho::trunc ( Fixed< BT, FB > arg )

constexpr

Truncates the given value.

See also: https://en.cppreference.com/w/c/numeric/math/trunc

Referenced by playrho::fmod(), and playrho::ModuloViaTrunc().

Namespaces

Functions

Detailed Description

Function Documentation

◆ abs()

◆ atan()

◆ atan2()

◆ cos()

◆ exp()

◆ fmod()

◆ hypot()

◆ isfinite()

◆ isnan()

◆ isnormal()

◆ log()

◆ nextafter()

◆ pow() [1/2]

◆ pow() [2/2]

◆ round()

◆ signbit()

◆ sin()

◆ sqrt()

◆ trunc()