xiiMath Namespace Reference

This namespace provides common math-functionality as functions. More...

Functions
template<typename TYPE>
constexpr TYPE	Pi ()
	Returns the natural constant Pi.
template<typename TYPE>
constexpr TYPE	e ()
	Returns the natural constant e.
template<typename TYPE>
constexpr TYPE	Phi ()
	Returns the constant Phi (a+b/a).
template<typename TYPE>
constexpr bool	SupportsNaN ()
	Returns whether the template type supports specialized values to represent NaN.
template<typename TYPE>
constexpr TYPE	NaN ()
	Returns the value for NaN as the template type. Returns zero, if the type does not support NaN.
template<typename TYPE>
constexpr bool	SupportsInfinity ()
	Returns whether the template type supports specialized values to represent Infinity.
template<typename TYPE>
constexpr TYPE	Infinity ()
	Returns the value for Infinity as the template type. Returns zero, if the type does not support Infinity.
template<typename TYPE>
constexpr TYPE	MaxValue ()
	Returns the largest possible positive value (that is not infinity).
template<typename TYPE>
constexpr TYPE	MinValue ()
	Returns the smallest possible value (that is not -infinity). Usually zero or -MaxValue(). For signed integers this will be -MaxValue() - 1.
template<typename TYPE>
constexpr TYPE	HighValue ()
	A very large value, that is slightly smaller than sqrt(MaxValue()).
template<typename TYPE>
constexpr TYPE	FloatEpsilon ()
	The difference between 1.0 and the next representable value for the given type.
template<typename TYPE>
constexpr TYPE	SmallEpsilon ()
template<typename TYPE>
constexpr TYPE	DefaultEpsilon ()
template<typename TYPE>
constexpr TYPE	LargeEpsilon ()
template<typename TYPE>
constexpr TYPE	HugeEpsilon ()
template<typename TYPE>
constexpr xiiUInt32	NumBits ()
	Returns the number of bits in the given type. Mostly useful for unsigned integer types.
double	EaseConstantZero (double t)
double	EaseConstantQuarter (double t)
double	EaseConstantHalf (double t)
double	EaseConstantThreeFourths (double t)
double	EaseConstantOne (double t)
double	EaseInLinear (double t)
double	EaseOutLinear (double t)
double	EaseInOutLinear (double t)
double	EaseInSine (double t)
double	EaseOutSine (double t)
double	EaseInOutSine (double t)
double	EaseInQuad (double t)
double	EaseOutQuad (double t)
double	EaseInOutQuad (double t)
double	EaseInCubic (double t)
double	EaseOutCubic (double t)
double	EaseInOutCubic (double t)
double	EaseInQuartic (double t)
double	EaseOutQuartic (double t)
double	EaseInOutQuartic (double t)
double	EaseInQuintic (double t)
double	EaseOutQuintic (double t)
double	EaseInOutQuintic (double t)
double	EaseInExpo (double t)
double	EaseOutExpo (double t)
double	EaseInOutExpo (double t)
double	EaseInCirc (double t)
double	EaseOutCirc (double t)
double	EaseInOutCirc (double t)
double	EaseInBack (double t)
double	EaseOutBack (double t)
double	EaseInOutBack (double t)
double	EaseInElastic (double t)
double	EaseOutElastic (double t)
double	EaseInOutElastic (double t)
double	EaseInBounce (double t)
double	EaseOutBounce (double t)
double	EaseInOutBounce (double t)
double	EaseConical (double t)
double	EaseFadeInHoldFadeOut (double t)
double	EaseFadeInFadeOut (double t)
double	EaseBell (double t)
template<>
constexpr float	Pi ()
template<>
constexpr double	Pi ()
template<>
constexpr float	Phi ()
template<>
constexpr double	Phi ()
template<>
constexpr float	e ()
template<>
constexpr double	e ()
template<>
constexpr bool	SupportsNaN< float > ()
template<>
constexpr bool	SupportsNaN< double > ()
template<>
constexpr float	NaN ()
template<>
constexpr double	NaN ()
template<>
constexpr bool	SupportsInfinity< float > ()
template<>
constexpr bool	SupportsInfinity< double > ()
template<>
constexpr float	Infinity ()
template<>
constexpr double	Infinity ()
template<>
constexpr xiiUInt8	MaxValue ()
template<>
constexpr xiiUInt16	MaxValue ()
template<>
constexpr xiiUInt32	MaxValue ()
template<>
constexpr xiiUInt64	MaxValue ()
template<>
constexpr xiiInt8	MaxValue ()
template<>
constexpr xiiInt16	MaxValue ()
template<>
constexpr xiiInt32	MaxValue ()
template<>
constexpr xiiInt64	MaxValue ()
template<>
constexpr float	MaxValue ()
template<>
constexpr double	MaxValue ()
template<>
constexpr xiiUInt8	MinValue ()
template<>
constexpr xiiUInt16	MinValue ()
template<>
constexpr xiiUInt32	MinValue ()
template<>
constexpr xiiUInt64	MinValue ()
template<>
constexpr xiiInt8	MinValue ()
template<>
constexpr xiiInt16	MinValue ()
template<>
constexpr xiiInt32	MinValue ()
template<>
constexpr xiiInt64	MinValue ()
template<>
constexpr float	MinValue ()
template<>
constexpr double	MinValue ()
template<>
constexpr float	HighValue ()
template<>
constexpr double	HighValue ()
template<>
constexpr float	FloatEpsilon ()
template<>
constexpr double	FloatEpsilon ()
template<>
constexpr xiiUInt32	NumBits< xiiUInt8 > ()
template<>
constexpr xiiUInt32	NumBits< xiiUInt16 > ()
template<>
constexpr xiiUInt32	NumBits< xiiUInt32 > ()
template<>
constexpr xiiUInt32	NumBits< xiiUInt64 > ()
template<>
constexpr xiiUInt32	NumBits< xiiInt8 > ()
template<>
constexpr xiiUInt32	NumBits< xiiInt16 > ()
template<>
constexpr xiiUInt32	NumBits< xiiInt32 > ()
template<>
constexpr xiiUInt32	NumBits< xiiInt64 > ()
template<>
constexpr xiiUInt32	NumBits< float > ()
template<>
constexpr xiiUInt32	NumBits< double > ()
template<typename T>
constexpr XII_ALWAYS_INLINE T	Square (T f)
	Returns f * f.
template<typename T>
constexpr XII_ALWAYS_INLINE T	Sign (T f)
	Returns the sign of f (i.e: -1, 1 or 0)
template<typename T>
constexpr XII_ALWAYS_INLINE T	Abs (T f)
	Returns the absolute value of f.
template<typename T>
constexpr XII_ALWAYS_INLINE T	Min (T f1, T f2)
	Returns the smaller value, f1 or f2.
template<typename T, typename... ARGS>
constexpr XII_ALWAYS_INLINE T	Min (T f1, T f2, ARGS... f)
	Returns the smaller value, f1 or f2 or ...
template<typename T>
constexpr XII_ALWAYS_INLINE T	Max (T f1, T f2)
	Returns the greater value, f1 or f2.
template<typename T, typename... ARGS>
constexpr XII_ALWAYS_INLINE T	Max (T f1, T f2, ARGS... f)
template<typename T>
constexpr XII_ALWAYS_INLINE T	Clamp (T value, T min_val, T max_val)
	Clamps "value" to the range [min; max]. Returns "value", if it is inside the range already.
template<typename T>
constexpr XII_ALWAYS_INLINE T	Saturate (T value)
	Clamps "value" to the range [0; 1]. Returns "value", if it is inside the range already.
template<typename Type>
constexpr Type	Invert (Type f)
	Returns 1 / f.
XII_ALWAYS_INLINE xiiUInt32	FirstBitLow (xiiUInt32 uiBitmask)
	Returns the index of the least significant bit set.
XII_ALWAYS_INLINE xiiUInt32	FirstBitLow (xiiUInt64 uiBitmask)
	Returns the index of the least significant bit set.
XII_ALWAYS_INLINE xiiUInt32	FirstBitHigh (xiiUInt32 uiBitmask)
	Returns the index of the most significant bit set.
XII_ALWAYS_INLINE xiiUInt32	FirstBitHigh (xiiUInt64 uiBitmask)
	Returns the index of the most significant bit set.
XII_ALWAYS_INLINE xiiUInt32	CountTrailingZeros (xiiUInt32 uiBitmask)
XII_ALWAYS_INLINE xiiUInt32	CountTrailingZeros (xiiUInt64 uiBitmask)
	64 bit overload for CountTrailingZeros()
XII_ALWAYS_INLINE xiiUInt32	CountLeadingZeros (xiiUInt32 uiBitmask)
XII_ALWAYS_INLINE xiiUInt32	CountBits (xiiUInt32 value)
	Returns the number of bits set.
XII_ALWAYS_INLINE xiiUInt32	CountBits (xiiUInt64 value)
	Returns the number of bits set.
template<typename Type>
XII_ALWAYS_INLINE constexpr Type	Bitmask_LowN (xiiUInt32 uiNumBitsToSet)
	Creates a bitmask in which the low N bits are set. For example for N=5, this would be '0000 ... 0001 1111'.
template<typename Type>
XII_ALWAYS_INLINE constexpr Type	Bitmask_HighN (xiiUInt32 uiNumBitsToSet)
	Creates a bitmask in which the high N bits are set. For example for N=5, this would be '1111 1000 ... 0000'.
template<typename T>
XII_ALWAYS_INLINE void	Swap (T &ref_f1, T &ref_f2)
	Swaps the values in the two variables f1 and f2.
template<typename T>
XII_FORCE_INLINE T	Lerp (T f1, T f2, float fFactor)
	Returns the linear interpolation of f1 and f2. factor is a value between 0 and 1.
template<typename T>
XII_FORCE_INLINE T	Lerp (T f1, T f2, double fFactor)
	Returns the linear interpolation of f1 and f2. factor is a value between 0 and 1.
template<typename T>
XII_FORCE_INLINE constexpr float	Unlerp (T fMin, T fMax, T fValue)
	Returns the interpolation factor such that Lerp(fMin, fMax, factor) == fValue.
template<typename T>
XII_FORCE_INLINE constexpr double	UnlerpDouble (T fMin, T fMax, T fValue)
	Returns the interpolation factor such that Lerp(fMin, fMax, factor) == fValue.
template<typename T>
constexpr XII_FORCE_INLINE T	Step (T value, T edge)
	Returns 0, if value < edge, and 1, if value >= edge.
constexpr XII_FORCE_INLINE bool	IsPowerOf2 (xiiInt32 value)
	Returns true, if there exists some x with 2^x == value.
constexpr XII_FORCE_INLINE bool	IsPowerOf2 (xiiUInt32 value)
	Returns true, if there exists some x with 2^x == value.
constexpr XII_FORCE_INLINE bool	IsPowerOf2 (xiiInt64 value)
	Returns true, if there exists some x with 2^x == value.
constexpr XII_FORCE_INLINE bool	IsPowerOf2 (xiiUInt64 value)
	Returns true, if there exists some x with 2^x == value.
template<typename Type>
constexpr bool	IsEqual (Type lhs, Type rhs, Type fEpsilon)
	Checks, whether fValue is in the range [fDesired - fMaxImprecision; fDesired + fMaxImprecision].
template<typename T>
constexpr bool	IsInRange (T value, T minVal, T maxVal)
	Checks whether the value of the first parameter lies between the value of the second and third.
template<typename Type>
bool	IsZero (Type f, Type fEpsilon)
	Checks whether the given number is close to zero.
template<typename Type>
XII_ALWAYS_INLINE Type	Trunc (Type f)
	Returns the integer-part of f (removes the fraction).
template<typename Type>
XII_ALWAYS_INLINE Type	Fraction (Type f)
	Returns the fraction-part of f.
template<typename Type>
Type	SmoothStep (Type value, Type edge1, Type edge2)
	Returns 0, if value is <= edge1, 1 if value >= edge2 and the hermite interpolation in between.
template<typename Type>
Type	SmootherStep (Type value, Type edge1, Type edge2)
	Returns 0, if value is <= edge1, 1 if value >= edge2 and the second order hermite interpolation in between.
template<xiiUInt32 BitCount>
xiiUInt32	ColorFloatToUnsignedInt (float value)
	Converts a color value from float [0;1] range to unsigned int with the given number of bits, with proper rounding.
xiiUInt8	ColorFloatToByte (float value)
	Converts a color value from float [0;1] range to unsigned byte [0;255] range, with proper rounding.
xiiUInt16	ColorFloatToShort (float value)
	Converts a color value from float [0;1] range to unsigned short [0;65535] range, with proper rounding.
xiiInt8	ColorFloatToSignedByte (float value)
	Converts a color value from float [-1;1] range to signed byte [-127;127] range, with proper rounding.
xiiInt16	ColorFloatToSignedShort (float value)
	Converts a color value from float [-1;1] range to signed short [-32767;32767] range, with proper rounding.
constexpr float	ColorByteToFloat (xiiUInt8 value)
	Converts a color value from unsigned byte [0;255] range to float [0;1] range, with proper rounding.
constexpr float	ColorShortToFloat (xiiUInt16 value)
	Converts a color value from unsigned short [0;65535] range to float [0;1] range, with proper rounding.
constexpr float	ColorSignedByteToFloat (xiiInt8 value)
	Converts a color value from signed byte [-128;127] range to float [-1;1] range, with proper rounding.
constexpr float	ColorSignedShortToFloat (xiiInt16 value)
	Converts a color value from signed short [-32768;32767] range to float [0;1] range, with proper rounding.
template<typename T, typename T2>
T	EvaluateBezierCurve (T2 t, const T &startPoint, const T &controlPoint1, const T &controlPoint2, const T &endPoint)
	Evaluates the cubic spline defined by four control points at time t and returns the interpolated result. Can be used with T as float, vec2, vec3 or vec4.
template<>
XII_ALWAYS_INLINE double	Sin (xiiAngleTemplate< double > a)
template<>
XII_ALWAYS_INLINE double	Cos (xiiAngleTemplate< double > a)
template<>
XII_ALWAYS_INLINE double	Tan (xiiAngleTemplate< double > a)
template<>
XII_ALWAYS_INLINE xiiAngleTemplate< double >	ASin (double f)
template<>
XII_ALWAYS_INLINE xiiAngleTemplate< double >	ACos (double f)
template<>
XII_ALWAYS_INLINE xiiAngleTemplate< double >	ATan (double f)
template<>
XII_ALWAYS_INLINE xiiAngleTemplate< double >	ATan2 (double y, double x)
XII_ALWAYS_INLINE bool	IsFinite (double value)
XII_ALWAYS_INLINE bool	IsNaN (double value)
XII_ALWAYS_INLINE double	Floor (double f)
	Returns the next smaller integer, closest to f. Also the SMALLER value, if f is negative.
XII_ALWAYS_INLINE double	Ceil (double f)
	Returns the next higher integer, closest to f. Also the HIGHER value, if f is negative.
XII_ALWAYS_INLINE double	Round (double f)
	Rounds f to the next integer.
double	RoundDown (double f, double fMultiple)
	Returns a multiple of fMultiple that is smaller than f.
double	RoundUp (double f, double fMultiple)
	Returns a multiple of fMultiple that is larger than f.
XII_ALWAYS_INLINE double	RoundToMultiple (double f, double fMultiple)
	Rounds f to the closest value of multiple.
XII_ALWAYS_INLINE double	Exp (double f)
	Returns e^f.
XII_ALWAYS_INLINE double	Ln (double f)
	Returns the logarithmus naturalis of f.
XII_ALWAYS_INLINE double	Log2 (double f)
	Returns log (f), to the base 2.
XII_ALWAYS_INLINE double	Log10 (double f)
	Returns log (f), to the base 10.
XII_ALWAYS_INLINE double	Log (double fBase, double f)
	Returns log (f), to the base fBase.
XII_ALWAYS_INLINE double	Pow2 (double f)
	Returns 2^f.
XII_ALWAYS_INLINE double	Pow (double fBase, double fExp)
	Returns base^exp.
XII_ALWAYS_INLINE double	Root (double f, double fNthRoot)
XII_ALWAYS_INLINE double	Sqrt (double f)
	Returns the square root of f.
XII_ALWAYS_INLINE double	Mod (double f, double fDiv)
	Returns "value mod div" for doubles. This also works with negative numbers, both for value and for div.
XII_ALWAYS_INLINE double	Hypot (double x, double y)
	Returns the hypotenuse of a given x and y term.
XII_ALWAYS_INLINE double	NormalizeToRange (double value, double fMin, double fMax)
	Calculates a value between 0 and 1, given the precondition that the value is between the min and the max. 0 means value = min and 1 means value = max.
template<>
XII_ALWAYS_INLINE float	Sin (xiiAngleTemplate< float > a)
template<>
XII_ALWAYS_INLINE float	Cos (xiiAngleTemplate< float > a)
template<>
XII_ALWAYS_INLINE float	Tan (xiiAngleTemplate< float > a)
template<>
XII_ALWAYS_INLINE xiiAngleTemplate< float >	ASin (float f)
template<>
XII_ALWAYS_INLINE xiiAngleTemplate< float >	ACos (float f)
template<>
XII_ALWAYS_INLINE xiiAngleTemplate< float >	ATan (float f)
template<>
XII_ALWAYS_INLINE xiiAngleTemplate< float >	ATan2 (float y, float x)
XII_ALWAYS_INLINE bool	IsFinite (float value)
XII_ALWAYS_INLINE bool	IsNaN (float value)
XII_ALWAYS_INLINE float	Floor (float f)
	Returns the next smaller integer, closest to f. Also the SMALLER value, if f is negative.
XII_ALWAYS_INLINE xiiInt32	FloorToInt (float f)
	Returns the next smaller integer, closest to f. Also the SMALLER value, if f is negative.
XII_ALWAYS_INLINE float	Ceil (float f)
	Returns the next higher integer, closest to f. Also the HIGHER value, if f is negative.
XII_ALWAYS_INLINE xiiInt32	CeilToInt (float f)
	Returns the next higher integer, closest to f. Also the HIGHER value, if f is negative.
XII_ALWAYS_INLINE float	Round (float f)
	Rounds f to the next integer.
XII_ALWAYS_INLINE xiiInt32	RoundToInt (float f)
	Rounds f to the next integer.
XII_ALWAYS_INLINE float	RoundToMultiple (float f, float fMultiple)
	Rounds f to the closest value of multiple.
float	RoundDown (float f, float fMultiple)
	Returns a multiple of fMultiple that is smaller than f.
float	RoundUp (float f, float fMultiple)
	Returns a multiple of fMultiple that is larger than f.
XII_ALWAYS_INLINE float	Exp (float f)
	Returns e^f.
XII_ALWAYS_INLINE float	Ln (float f)
	Returns the logarithmus naturalis of f.
XII_ALWAYS_INLINE float	Log2 (float f)
	Returns log (f), to the base 2.
XII_ALWAYS_INLINE float	Log10 (float f)
	Returns log (f), to the base 10.
XII_ALWAYS_INLINE float	Log (float fBase, float f)
	Returns log (f), to the base fBase.
XII_ALWAYS_INLINE float	Pow2 (float f)
	Returns 2^f.
XII_ALWAYS_INLINE float	Pow (float fBase, float fExp)
	Returns base^exp.
XII_ALWAYS_INLINE float	Root (float f, float fNthRoot)
	Returns the n-th root of f.
XII_ALWAYS_INLINE float	Sqrt (float f)
	Returns the square root of f.
XII_ALWAYS_INLINE float	Mod (float value, float fDiv)
	Returns "value mod div" for floats. This also works with negative numbers, both for value and for div.
XII_ALWAYS_INLINE float	Hypot (float x, float y)
	Returns the hypotenuse of a given x and y term.
XII_ALWAYS_INLINE float	NormalizeToRange (float value, float fMin, float fMax)
	Calculates a value between 0 and 1, given the precondition that the value is between the min and the max. 0 means value = min and 1 means value = max.
constexpr XII_ALWAYS_INLINE xiiInt32	RoundUp (xiiInt32 value, xiiUInt16 uiMultiple)
	Returns a multiple of the given multiple that is larger than or equal to value.
constexpr XII_ALWAYS_INLINE xiiInt32	RoundDown (xiiInt32 value, xiiUInt16 uiMultiple)
	Returns a multiple of the given multiple that is smaller than or equal to value.
constexpr XII_ALWAYS_INLINE xiiUInt32	RoundUp (xiiUInt32 value, xiiUInt16 uiMultiple)
	Returns a multiple of the given multiple that is greater than or equal to value.
constexpr XII_ALWAYS_INLINE xiiUInt32	RoundDown (xiiUInt32 value, xiiUInt16 uiMultiple)
	Returns a multiple of the given multiple that is smaller than or equal to value.
constexpr XII_ALWAYS_INLINE bool	IsOdd (xiiInt32 i)
	Returns true, if i is an odd number.
constexpr XII_ALWAYS_INLINE bool	IsEven (xiiInt32 i)
	Returns true, if i is an even number.
XII_ALWAYS_INLINE xiiUInt32	Log2i (xiiUInt32 uiVal)
	Returns the integral logarithm to the base 2, that comes closest to the given integer.
constexpr XII_ALWAYS_INLINE xiiInt32	Pow2 (xiiInt32 i)
	Returns 2^f.
xiiInt32	Pow (xiiInt32 iBase, xiiInt32 iExp)
	Returns base^exp.
template<typename Type>
Type	Sin (xiiAngleTemplate< Type > a)
	***** Trigonometric Functions *****
template<typename Type>
Type	Cos (xiiAngleTemplate< Type > a)
	Takes an angle, returns its cosine.
template<typename Type>
Type	Tan (xiiAngleTemplate< Type > a)
	Takes an angle, returns its tangent.
template<typename Type>
xiiAngleTemplate< Type >	ASin (Type f)
	Returns the arcus sinus of f.
template<typename Type>
xiiAngleTemplate< Type >	ACos (Type f)
	Returns the arcus cosinus of f.
template<typename Type>
xiiAngleTemplate< Type >	ATan (Type f)
	Returns the arcus tangent of f.
template<typename Type>
xiiAngleTemplate< Type >	ATan2 (Type y, Type x)
	Returns the atan2 of x and y.
template<typename T>
constexpr T	Square (T f)
	Returns f * f.
template<typename T>
constexpr T	Sign (T f)
	Returns the sign of f (i.e: -1, 1 or 0)
template<typename T>
constexpr T	Abs (T f)
	Returns the absolute value of f.
template<typename T>
constexpr T	Min (T f1, T f2)
	Returns the smaller value, f1 or f2.
template<typename T, typename... ARGS>
constexpr T	Min (T f1, T f2, ARGS... f)
	Returns the smaller value, f1 or f2 or ...
template<typename T>
constexpr T	Max (T f1, T f2)
	Returns the greater value, f1 or f2.
template<typename T>
constexpr T	Clamp (T value, T min_val, T max_val)
	Clamps "value" to the range [min; max]. Returns "value", if it is inside the range already.
constexpr xiiUInt32	WrapUInt (xiiUInt32 uiValue, xiiUInt32 uiExcludedMaxValue)
	Wraps uiValue around the maximum value, so that it stays within the range [0; uiExcludedMaxValue-1].
constexpr xiiInt32	WrapInt (xiiInt32 iValue, xiiUInt32 uiExcludedMaxValue)
	Wraps iValue around the maximum value, so that it stays within the range [0; uiExcludedMaxValue-1].
constexpr xiiInt32	WrapInt (xiiInt32 iValue, xiiInt32 iMinValue, xiiInt32 iExcludedMaxValue)
	Wraps iValue around the minimum and maximum value, so that it stays within the range [iMinValue; iExcludedMaxValue-1].
float	WrapFloat01 (float fValue)
	Wraps a float value around to stay within the [0; 1] range.
float	WrapFloat (float fValue, float fMinValue, float fMaxValue)
	Wraps a float value around to stay within the [min; max] range.
template<typename T>
constexpr T	Saturate (T value)
	Clamps "value" to the range [0; 1]. Returns "value", if it is inside the range already.
template<typename Type>
Type	Trunc (Type f)
	Returns the integer-part of f (removes the fraction).
constexpr xiiInt32	FloatToInt (float value)
	Casts the float to an integer, removes the fractional part.
constexpr xiiInt64	FloatToInt (double value)
	Casts the float to an integer, removes the fractional part.
template<typename Type>
Type	Fraction (Type f)
	Returns the fraction-part of f.
template<typename Type>
constexpr Type	Bitmask_LowN (xiiUInt32 uiNumBitsToSet)
	Creates a bitmask in which the low N bits are set. For example for N=5, this would be '0000 ... 0001 1111'.
template<typename Type>
constexpr Type	Bitmask_HighN (xiiUInt32 uiNumBitsToSet)
	Creates a bitmask in which the high N bits are set. For example for N=5, this would be '1111 1000 ... 0000'.
template<typename T>
void	Swap (T &ref_f1, T &ref_f2)
	Swaps the values in the two variables f1 and f2.
template<typename T>
T	Lerp (T f1, T f2, float fFactor)
	Returns the linear interpolation of f1 and f2. factor is a value between 0 and 1.
template<typename T>
T	Lerp (T f1, T f2, double fFactor)
	Returns the linear interpolation of f1 and f2. factor is a value between 0 and 1.
template<typename T>
constexpr float	Unlerp (T fMin, T fMax, T fValue)
	Returns the interpolation factor such that Lerp(fMin, fMax, factor) == fValue.
template<typename T>
constexpr double	UnlerpDouble (T fMin, T fMax, T fValue)
	Returns the interpolation factor such that Lerp(fMin, fMax, factor) == fValue.
template<typename T>
constexpr T	Step (T value, T edge)
	Returns 0, if value < edge, and 1, if value >= edge.
XII_FOUNDATION_DLL bool	IsPowerOf (xiiInt32 value, xiiInt32 iBase)
	Returns true, if there exists some x with base^x == value.
XII_FOUNDATION_DLL xiiUInt32	PowerOfTwo_Floor (xiiUInt32 value)
	Returns the next power-of-two that is <= value.
XII_FOUNDATION_DLL xiiUInt64	PowerOfTwo_Floor (xiiUInt64 value)
	Returns the next power-of-two that is <= value.
XII_FOUNDATION_DLL xiiUInt32	PowerOfTwo_Ceil (xiiUInt32 value)
	Returns the next power-of-two that is >= value.
XII_FOUNDATION_DLL xiiUInt64	PowerOfTwo_Ceil (xiiUInt64 value)
	Returns the next power-of-two that is >= value.
XII_FOUNDATION_DLL xiiUInt32	GreatestCommonDivisor (xiiUInt32 a, xiiUInt32 b)
	Returns the greatest common divisor.
XII_FOUNDATION_DLL xiiResult	TryMultiply32 (xiiUInt32 &out_uiResult, xiiUInt32 a, xiiUInt32 b, xiiUInt32 c=1, xiiUInt32 d=1)
	out_Result = a * b. If an overflow happens, XII_FAILURE is returned.
XII_FOUNDATION_DLL xiiUInt32	SafeMultiply32 (xiiUInt32 a, xiiUInt32 b, xiiUInt32 c=1, xiiUInt32 d=1)
	returns a * b. If an overflow happens, the program is terminated.
XII_FOUNDATION_DLL xiiResult	TryMultiply64 (xiiUInt64 &out_uiResult, xiiUInt64 a, xiiUInt64 b, xiiUInt64 c=1, xiiUInt64 d=1)
	out_Result = a * b. If an overflow happens, XII_FAILURE is returned.
XII_FOUNDATION_DLL xiiUInt64	SafeMultiply64 (xiiUInt64 a, xiiUInt64 b, xiiUInt64 c=1, xiiUInt64 d=1)
	returns a * b. If an overflow happens, the program is terminated.
xiiResult	TryConvertToSizeT (size_t &out_uiResult, xiiUInt64 uiValue)
	Checks whether the given 64bit value actually fits into size_t, If it doesn't XII_FAILURE is returned.
XII_FOUNDATION_DLL size_t	SafeConvertToSizeT (xiiUInt64 uiValue)
	Checks whether the given 64bit value actually fits into size_t, If it doesn't the program is terminated.
XII_FOUNDATION_DLL float	ReplaceNaN (float fValue, float fFallback)
	If 'value' is not-a-number (NaN) 'fallback' is returned, otherwise 'value' is passed through unmodified.
XII_FOUNDATION_DLL double	ReplaceNaN (double fValue, double fFallback)
	If 'value' is not-a-number (NaN) 'fallback' is returned, otherwise 'value' is passed through unmodified.
xiiVariant	Lerp (const xiiVariant &a, const xiiVariant &b, double fFactor)
	An overload of xiiMath::Lerp to interpolate variants. A and b must have the same type.

Detailed Description

This namespace provides common math-functionality as functions.

It is a namespace, instead of a static class, because that allows it to be extended at other locations, which is especially useful when adding custom types.

Function Documentation

Bitmask_HighN() [1/2]

template<typename Type>

XII_ALWAYS_INLINE constexpr Type xiiMath::Bitmask_HighN ( xiiUInt32 uiNumBitsToSet )

nodiscardconstexpr

Creates a bitmask in which the high N bits are set. For example for N=5, this would be '1111 1000 ... 0000'.

For N >= 32 all bits will be set.

Bitmask_HighN() [2/2]

template<typename Type>

Type xiiMath::Bitmask_HighN ( xiiUInt32 uiNumBitsToSet )

nodiscardconstexpr

Creates a bitmask in which the high N bits are set. For example for N=5, this would be '1111 1000 ... 0000'.

For N >= 32 all bits will be set.

Bitmask_LowN() [1/2]

template<typename Type>

XII_ALWAYS_INLINE constexpr Type xiiMath::Bitmask_LowN ( xiiUInt32 uiNumBitsToSet )

nodiscardconstexpr

Creates a bitmask in which the low N bits are set. For example for N=5, this would be '0000 ... 0001 1111'.

For N >= 32 all bits will be set.

Bitmask_LowN() [2/2]

template<typename Type>

Type xiiMath::Bitmask_LowN ( xiiUInt32 uiNumBitsToSet )

nodiscardconstexpr

Creates a bitmask in which the low N bits are set. For example for N=5, this would be '0000 ... 0001 1111'.

For N >= 32 all bits will be set.

CeilToInt()

xiiInt32 xiiMath::CeilToInt ( float f )

nodiscard

Returns the next higher integer, closest to f. Also the HIGHER value, if f is negative.

This function is identical to 'Ceil()' except that it already returns the result cast to an int.

CountLeadingZeros()

xiiUInt32 xiiMath::CountLeadingZeros ( xiiUInt32 uiBitmask )

nodiscard

Returns the number of zeros at the start (most significant part) of a bitmask.

E.g. 0b0111 -> 29 0b0011 -> 30 0b0001 -> 31 0b0000 -> 32 Returns 32 when the input is 0

CountTrailingZeros()

xiiUInt32 xiiMath::CountTrailingZeros ( xiiUInt32 uiBitmask )

nodiscard

Returns the number of zeros at the end (least significant part) of a bitmask.

E.g. 0b0111 -> 0 0b0110 -> 1 0b0100 -> 2 Returns 32 when the input is 0

FirstBitHigh() [1/2]

xiiUInt32 xiiMath::FirstBitHigh ( xiiUInt32 uiBitmask )

nodiscard

Returns the index of the most significant bit set.

Asserts that bitmask is not 0.

FirstBitHigh() [2/2]

xiiUInt32 xiiMath::FirstBitHigh ( xiiUInt64 uiBitmask )

nodiscard

Returns the index of the most significant bit set.

Asserts that bitmask is not 0.

FirstBitLow() [1/2]

xiiUInt32 xiiMath::FirstBitLow ( xiiUInt32 uiBitmask )

nodiscard

Returns the index of the least significant bit set.

Asserts that bitmask is not 0.

FirstBitLow() [2/2]

xiiUInt32 xiiMath::FirstBitLow ( xiiUInt64 uiBitmask )

nodiscard

Returns the index of the least significant bit set.

Asserts that bitmask is not 0.

FloatToInt() [1/2]

XII_FORCE_INLINE xiiInt64 xiiMath::FloatToInt ( double value )

nodiscardconstexpr

Casts the float to an integer, removes the fractional part.

See also

Trunc, Round, Floor, Ceil

FloatToInt() [2/2]

XII_FORCE_INLINE xiiInt32 xiiMath::FloatToInt ( float value )

nodiscardconstexpr

Casts the float to an integer, removes the fractional part.

See also

Trunc, Round, Floor, Ceil

FloorToInt()

xiiInt32 xiiMath::FloorToInt ( float f )

nodiscard

Returns the next smaller integer, closest to f. Also the SMALLER value, if f is negative.

This function is identical to 'Floor()' except that it already returns the result cast to an int.

HighValue()

template<typename TYPE>

TYPE xiiMath::HighValue ( )

constexpr

A very large value, that is slightly smaller than sqrt(MaxValue()).

Useful to default initialize values, that may get squared in subsequent operations.

Lerp()

XII_FOUNDATION_DLL xiiVariant xiiMath::Lerp	(	const xiiVariant &	a,
		const xiiVariant &	b,
		double	fFactor )

An overload of xiiMath::Lerp to interpolate variants. A and b must have the same type.

If the type can't be interpolated like e.g. strings, a is returned for a fFactor less than 0.5, b is returned for a fFactor greater or equal to 0.5.

NaN()

template<typename TYPE>

TYPE xiiMath::NaN ( )

constexpr

Returns the value for NaN as the template type. Returns zero, if the type does not support NaN.

Do not use this for comparisons, it will fail. Use it to initialize data (e.g. in debug builds), to detect uninitialized variables. Use the function IsNaN() to check whether a value is not a number.

Round() [1/2]

double xiiMath::Round ( double f )

nodiscard

Rounds f to the next integer.

If f is positive 0.5 is rounded UP (i.e. to 1), if f is negative, -0.5 is rounded DOWN (i.e. to -1).

Round() [2/2]

float xiiMath::Round ( float f )

nodiscard

Rounds f to the next integer.

If f is positive 0.5 is rounded UP (i.e. to 1), if f is negative, -0.5 is rounded DOWN (i.e. to -1).

RoundToInt()

xiiInt32 xiiMath::RoundToInt ( float f )

nodiscard

Rounds f to the next integer.

If f is positive 0.5 is rounded UP (i.e. to 1), if f is negative, -0.5 is rounded DOWN (i.e. to -1).

This function is identical to 'Round()' except that it already returns the result cast to an int.

Sin()

template<typename Type>

Type xiiMath::Sin ( xiiAngleTemplate< Type > a )

nodiscard

***** Trigonometric Functions *****

Takes an angle, returns its sine.

WrapFloat()

XII_ALWAYS_INLINE float xiiMath::WrapFloat ( float fValue, float fMinValue, float fMaxValue )

nodiscard

Wraps a float value around to stay within the [min; max] range.

Both fMinValue and fMaxValue are inclusive. Both values may be negative, but fMinValue has to be strictly smaller than fMaxValue.

WrapFloat01()

XII_ALWAYS_INLINE float xiiMath::WrapFloat01 ( float fValue )

nodiscard

Wraps a float value around to stay within the [0; 1] range.

Wrapping happens in both positive and negative direction. Ie -0.1f will be wrapped to 0.9f and 1.1f will be wrapped to 0.1f. Note that here the value 1.0f is included in the range. Only values larger than 1.0f get wrapped back to zero. Therefore it is different to what 'Fraction' would return.

WrapInt() [1/2]

XII_ALWAYS_INLINE constexpr xiiInt32 xiiMath::WrapInt ( xiiInt32 iValue, xiiInt32 iMinValue, xiiInt32 iExcludedMaxValue )

nodiscardconstexpr

Wraps iValue around the minimum and maximum value, so that it stays within the range [iMinValue; iExcludedMaxValue-1].

Ie a value of iExcludedMaxValue would be wrapped to iMinValue, and (iExcludedMaxValue+1) to (iMinValue+1), etc. Values below iMinValue are wrapped back around to a large value, ie (iMinValue-1) would be wrapped to (iExcludedMaxValue-1).

Both iMinValue and iExcludedMaxValue can be negative, but iMinValue has to be strictly smaller than iExcludedMaxValue.

WrapInt() [2/2]

XII_ALWAYS_INLINE constexpr xiiInt32 xiiMath::WrapInt ( xiiInt32 iValue, xiiUInt32 uiExcludedMaxValue )

nodiscardconstexpr

Wraps iValue around the maximum value, so that it stays within the range [0; uiExcludedMaxValue-1].

Ie a value of uiExcludedMaxValue would be wrapped to 0, and (uiExcludedMaxValue+1) to 1, etc. Negative values are wrapped back around to a large value, ie -1 would be wrapped to (uiExcludedMaxValue-1). A value of 0 for uiExcludedMaxValue is invalid and results in a division by zero error.

WrapUInt()

XII_ALWAYS_INLINE constexpr xiiUInt32 xiiMath::WrapUInt ( xiiUInt32 uiValue, xiiUInt32 uiExcludedMaxValue )

nodiscardconstexpr

Wraps uiValue around the maximum value, so that it stays within the range [0; uiExcludedMaxValue-1].

Ie a value of uiExcludedMaxValue would be wrapped to 0, and (uiExcludedMaxValue+1) to 1, etc. A value of 0 for uiExcludedMaxValue is invalid and results in a division by zero error.