Math wrappers. More...

#include <system/kzs_types.h>
#include <system/debug/kzs_error.h>
#include <system/kzs_header.h>
#include <math.h>
#include <float.h>
#include <limits.h>
#include <stdlib.h>

Classes
union	KZ_FLOAT_UNION_TYPE
	Used for keeping strict aliasing when interpreting kzU32 as kzFloat. More...

Macros
#define	KZS_PI
	Mathematical constant pi. More...

#define	KZS_E
	Mathematical constant e. More...

#define	KZS_LN_2
	Natural logarithm of 2. More...

#define	KZ_FLOAT_MAXIMUM
	Largest value for a floating point number. More...

#define	KZ_FLOAT_MINIMUM
	Most negative value for a floating point number. More...

#define	KZ_FLOAT_SMALLEST_POSITIVE
	Smallest normalized value larger than positive zero. More...

#define	KZ_FLOAT_EPSILON
	Smallest float such that 1.0f + KZ_FLOAT_EPSILON != 1.0f. More...

#define	KZ_INT_MAXIMUM
	Largest value for integer. More...

#define	KZ_INT_MINIMUM
	Smallest value for integer. More...

#define	KZ_UINT_MAXIMUM
	Largest value for unsigned integer. More...

#define	KZ_UINT_MINIMUM
	Smallest value for unsigned integer. More...

#define	KZ_UINT32_MAXIMUM
	Largest value for 32-bit unsigned integer. More...

#define	KZ_UINT32_MINIMUM
	Smallest value for 32-bit unsigned integer. More...

#define	KZ_UINT64_MAXIMUM
	Largest value for 64-bit unsigned integer. More...

#define	KZ_UINT64_MINIMUM
	Smallest value for 64-bit unsigned integer. More...

#define	KZS_NAN
	Floating point value for Not a Number. More...

#define	KZS_INFINITY
	Floating point value for positive infinity. More...

Functions
KZ_INLINE kzBool	kzsIsNan (kzFloat x)
	Returns KZ_TRUE if x is NaN. More...

KZ_INLINE kzBool	kzsIsPositiveInfinity (kzFloat x)
	Returns KZ_TRUE if x is positive infinity. More...

KZ_INLINE kzBool	kzsIsNegativeInfinity (kzFloat x)
	Returns KZ_TRUE if x is negative infinity. More...

KZ_INLINE kzBool	kzsIsInfinity (kzFloat x)
	Returns KZ_TRUE if x is an infinity. More...

KZ_INLINE kzBool	kzsIsIEEENegativeInfinity (kzFloat x)
	Returns KZ_TRUE if x is the specific IEEE floating point negative infinity constant. More...

KZ_INLINE kzBool	kzsIsIEEEPositiveInfinity (kzFloat x)
	Returns KZ_TRUE if x is the specific IEEE floating point positive infinity constant. More...

KZ_INLINE kzFloat	kzsSinf (kzFloat angleInRadians)
	Returns sine of given angle. More...

KZ_INLINE kzFloat	kzsCosf (kzFloat angleInRadians)
	Returns cosine of given angle. More...

KZ_INLINE kzFloat	kzsAsinf (kzFloat x)
	Returns inverse sine from floating point number between -1 and 1. More...

KZ_INLINE kzFloat	kzsAcosf (kzFloat x)
	Returns inverse cosine from floating point number between -1 and 1. More...

KZ_INLINE kzFloat	kzsTanf (kzFloat angleInRadians)
	Returns tangent of given angle. More...

KZ_INLINE kzFloat	kzsAtanf (kzFloat x)
	Returns atan from floating point number. More...

KZ_INLINE kzFloat	kzsAtan2f (kzFloat y, kzFloat x)
	Returns atan2 from floating point number. More...

KZ_INLINE kzFloat	kzsSqrtf (kzFloat value)
	Returns square root of given value. More...

KZ_INLINE kzFloat	kzsSignf (kzFloat value)
	Returns the signum of given value. More...

KZ_INLINE kzFloat	kzsFmod (kzFloat value, kzFloat divisor)
	Floating point remainder of value divided by divisor. More...

KZ_INLINE kzFloat	kzsModf (kzFloat value, kzFloat *intPart)
	Breaks floating point number to integral and fractional part. More...

KZ_INLINE kzUint	kzsRemainder (kzInt dividend, kzUint divisor)
	Returns modulo dividend % divisor for signed numbers in a way that negative numbers are treated as an extension instead of mirroring compared to positive numbers. More...

KZ_INLINE kzFloat	kzsRemainderf (kzFloat dividend, kzFloat divisor)
	Same as kzsRemainder, but for floating point numbers. More...

KZ_INLINE kzFloat	kzsPowf (kzFloat value, kzFloat exponent)
	Raises 'value' to the power of 'exponent'. More...

KZ_INLINE kzFloat	kzsExpf (kzFloat value)
	Raises e (base of natural logarithm) to the power of 'value'. More...

KZ_INLINE kzFloat	kzsLog10f (kzFloat value)
	Returns base 10 logarithm of given floating point value. More...

KZ_INLINE kzDouble	kzsLogE (kzDouble value)
	Returns natural logarithm of given double value. More...

KZ_INLINE kzFloat	kzsLogEf (kzFloat value)
	Returns natural logarithm of given floating point value. More...

KZ_INLINE kzFloat	kzsFloorf (kzFloat value)
	Returns the largest integer not greater than value as float. More...

KZ_INLINE kzInt	kzsIFloorf (kzFloat value)
	Returns the largest integer not greater than value as integer. More...

KZ_INLINE kzFloat	kzsRoundf (kzFloat value)
	Returns the floating point value rounded as per normal rounding rules. More...

KZ_INLINE kzFloat	kzsCeilf (kzFloat value)
	Returns the smallest integer no less than value in float. More...

KZ_INLINE kzInt	kzsICeilf (kzFloat value)
	Returns the smallest integer no less than value in integer. More...

KZ_INLINE kzUint	kzsAbs (kzInt value)
	Returns absolute value from integer value. More...

KZ_INLINE kzFloat	kzsFabsf (kzFloat value)
	Returns absolute value from floating point number. More...

KZ_INLINE kzFloat	kzsClampf (kzFloat value, kzFloat minimum, kzFloat maximum)
	Clamps float value to given range. More...

KZ_INLINE kzInt	kzsClampi (kzInt value, kzInt minimum, kzInt maximum)
	Clamps integer value to given range. More...

KZ_INLINE kzUint	kzsClampui (kzUint value, kzUint minimum, kzUint maximum)
	Clamps unsigned integer value to given range. More...

KZ_INLINE kzFloat	kzsLerpf (kzFloat minimum, kzFloat maximum, kzFloat t)
	Linearly interpolate between [a,b] where t should be in range [0,1]. More...

KZ_INLINE kzFloat	kzsDegreesToRadians (kzFloat angleInDegrees)
	Converts degrees to radians. More...

KZ_INLINE kzFloat	kzsRadiansToDegrees (kzFloat angleInRadians)
	Converts radians to degrees. More...

KZ_INLINE kzBool	kzsIsInClosedInterval (kzFloat value, kzFloat minimum, kzFloat maximum)
	Check whether value is in [min, max] (an interval inclusive of the limit points) More...

KZ_INLINE kzBool	kzsFloatIsEqual (kzFloat valueA, kzFloat valueB)
	Check if two floats are equal. More...

KZ_INLINE kzBool	kzsFloatIsAlmostEqualUlps (kzFloat valueA, kzFloat valueB, kzUint maxUlps)
	Check if two IEEE 754 binary32 floats are equal up to a given number of ulps. More...

KZ_INLINE kzBool	kzsFloatIsAlmostEqualAbsolute (kzFloat valueA, kzFloat valueB, kzFloat maxAbsoluteDifference)
	Check if two floats are equal up to a given difference. More...

KZ_INLINE kzBool	kzsFloatIsAlmostEqualRelative (kzFloat valueA, kzFloat valueB, kzFloat maxRelativeDifference)
	Check if two floats are equal up to a given difference scaled by the larger value. More...

KZ_INLINE kzBool	kzsFloatIsAlmostEqual (kzFloat valueA, kzFloat valueB)
	Check if two floats are approximately equal. More...

KZ_INLINE kzBool	kzsIsInOpenInterval (kzFloat value, kzFloat minimum, kzFloat maximum)
	Check whether value in (min, max) (an interval range exclusive of the limit points) More...

KZ_INLINE kzInt	kzsMin (kzInt a, kzInt b)
	Returns the smaller of two integers. More...

KZ_INLINE kzInt	kzsMax (kzInt a, kzInt b)
	Returns the greater of two integers. More...

KZ_INLINE kzUint	kzsMinU (kzUint a, kzUint b)
	Returns the smaller of two unsigned integers. More...

KZ_INLINE kzUint	kzsMaxU (kzUint a, kzUint b)
	Returns the greater of two unsigned integers. More...

KZ_INLINE kzFloat	kzsMinf (kzFloat a, kzFloat b)
	Returns the smaller of two floats. More...

KZ_INLINE kzFloat	kzsMaxf (kzFloat a, kzFloat b)
	Returns the greater of two floats. More...

KZ_INLINE kzInt	kzsStep (kzInt a, kzInt b)
	Returns the step function of two integers. More...

KZ_INLINE kzUint	kzsStepU (kzUint a, kzUint b)
	Returns the step function of two unsigned integers. More...

KZ_INLINE kzFloat	kzsStepf (kzFloat a, kzFloat b)
	Returns the step function of two floats. More...

KZ_INLINE void	kzsQsort (void buffer, kzUint itemCount, kzUint itemSize, kzInt(comparator)(const void left, const void right))
	Sorts values in buffer using quick sort. More...

KZ_INLINE kzUint	kzsFloatToUint (kzFloat value)
	Casts a float to unsigned int. More...

KZ_INLINE kzFloat	kzsUintToFloat (kzUint value)
	Casts an unsigned int to float. More...

KZ_INLINE kzInt	kzsFloatRoundToInt (kzFloat value)
	Rounds a float to the nearest integer. More...

KZ_INLINE kzUint	kzsFloatRoundToUint (kzFloat value)
	Rounds a float to the nearest unsigned integer. More...

KZ_INLINE void	kzsSwap (void element1, void element2, kzUint elementSize)
	Swaps two arbitrary elements of arbitrary size. More...

Variables
KANZI_API const union KZ_FLOAT_UNION_TYPE	KZS_NAN_PRIVATE

KANZI_API const union KZ_FLOAT_UNION_TYPE	KZS_INFINITY_PRIVATE

Detailed Description

Math wrappers.

Macro Definition Documentation

#define KZS_PI

Mathematical constant pi.

#define KZS_E

Mathematical constant e.

#define KZS_LN_2

Natural logarithm of 2.

#define KZ_FLOAT_MAXIMUM

Largest value for a floating point number.

#define KZ_FLOAT_MINIMUM

Most negative value for a floating point number.

#define KZ_FLOAT_SMALLEST_POSITIVE

Smallest normalized value larger than positive zero.

#define KZ_FLOAT_EPSILON

Smallest float such that 1.0f + KZ_FLOAT_EPSILON != 1.0f.

#define KZ_INT_MAXIMUM

Largest value for integer.

#define KZ_INT_MINIMUM

Smallest value for integer.

#define KZ_UINT_MAXIMUM

Largest value for unsigned integer.

#define KZ_UINT_MINIMUM

Smallest value for unsigned integer.

#define KZ_UINT32_MAXIMUM

Largest value for 32-bit unsigned integer.

#define KZ_UINT32_MINIMUM

Smallest value for 32-bit unsigned integer.

#define KZ_UINT64_MAXIMUM

Largest value for 64-bit unsigned integer.

#define KZ_UINT64_MINIMUM

Smallest value for 64-bit unsigned integer.

#define KZS_NAN

Floating point value for Not a Number.

#define KZS_INFINITY

Floating point value for positive infinity.

Negative infinity is -KZS_INFINITY.

Function Documentation

KZ_INLINE kzBool kzsIsNan ( kzFloat x )

Returns KZ_TRUE if x is NaN.

KZ_INLINE kzBool kzsIsPositiveInfinity ( kzFloat x )

Returns KZ_TRUE if x is positive infinity.

KZ_INLINE kzBool kzsIsNegativeInfinity ( kzFloat x )

Returns KZ_TRUE if x is negative infinity.

KZ_INLINE kzBool kzsIsInfinity ( kzFloat x )

Returns KZ_TRUE if x is an infinity.

KZ_INLINE kzBool kzsIsIEEENegativeInfinity ( kzFloat x )

Returns KZ_TRUE if x is the specific IEEE floating point negative infinity constant.

KZ_INLINE kzBool kzsIsIEEEPositiveInfinity ( kzFloat x )

Returns KZ_TRUE if x is the specific IEEE floating point positive infinity constant.

KZ_INLINE kzFloat kzsSinf ( kzFloat angleInRadians )

Returns sine of given angle.

KZ_INLINE kzFloat kzsCosf ( kzFloat angleInRadians )

Returns cosine of given angle.

KZ_INLINE kzFloat kzsAsinf ( kzFloat x )

Returns inverse sine from floating point number between -1 and 1.

KZ_INLINE kzFloat kzsAcosf ( kzFloat x )

Returns inverse cosine from floating point number between -1 and 1.

KZ_INLINE kzFloat kzsTanf ( kzFloat angleInRadians )

Returns tangent of given angle.

KZ_INLINE kzFloat kzsAtanf ( kzFloat x )

Returns atan from floating point number.

KZ_INLINE kzFloat kzsAtan2f	(	kzFloat	y,
		kzFloat	x
	)

Returns atan2 from floating point number.

KZ_INLINE kzFloat kzsSqrtf ( kzFloat value )

Returns square root of given value.

KZ_INLINE kzFloat kzsSignf ( kzFloat value )

Returns the signum of given value.

KZ_INLINE kzFloat kzsFmod	(	kzFloat	value,
		kzFloat	divisor
	)

Floating point remainder of value divided by divisor.

The result may be negative for negative values.

KZ_INLINE kzFloat kzsModf	(	kzFloat	value,
		kzFloat *	intPart
	)

Breaks floating point number to integral and fractional part.

Returns fractional part as return value and sets intPart to integral part.

KZ_INLINE kzUint kzsRemainder	(	kzInt	dividend,
		kzUint	divisor
	)

Returns modulo dividend % divisor for signed numbers in a way that negative numbers are treated as an extension instead of mirroring compared to positive numbers.

For example kzsRemainder(-16, 5) = 4

KZ_INLINE kzFloat kzsRemainderf	(	kzFloat	dividend,
		kzFloat	divisor
	)

Same as kzsRemainder, but for floating point numbers.

Results are undefined if divisor is not greater than zero.

KZ_INLINE kzFloat kzsPowf	(	kzFloat	value,
		kzFloat	exponent
	)

Raises 'value' to the power of 'exponent'.

KZ_INLINE kzFloat kzsExpf ( kzFloat value )

Raises e (base of natural logarithm) to the power of 'value'.

KZ_INLINE kzFloat kzsLog10f ( kzFloat value )

Returns base 10 logarithm of given floating point value.

KZ_INLINE kzDouble kzsLogE ( kzDouble value )

Returns natural logarithm of given double value.

KZ_INLINE kzFloat kzsLogEf ( kzFloat value )

Returns natural logarithm of given floating point value.

KZ_INLINE kzFloat kzsFloorf ( kzFloat value )

Returns the largest integer not greater than value as float.

KZ_INLINE kzInt kzsIFloorf ( kzFloat value )

Returns the largest integer not greater than value as integer.

KZ_INLINE kzFloat kzsRoundf ( kzFloat value )

Returns the floating point value rounded as per normal rounding rules.

KZ_INLINE kzFloat kzsCeilf ( kzFloat value )

Returns the smallest integer no less than value in float.

KZ_INLINE kzInt kzsICeilf ( kzFloat value )

Returns the smallest integer no less than value in integer.

KZ_INLINE kzUint kzsAbs ( kzInt value )

Returns absolute value from integer value.

KZ_INLINE kzFloat kzsFabsf ( kzFloat value )

Returns absolute value from floating point number.

KZ_INLINE kzFloat kzsClampf	(	kzFloat	value,
		kzFloat	minimum,
		kzFloat	maximum
	)

Clamps float value to given range.

KZ_INLINE kzInt kzsClampi	(	kzInt	value,
		kzInt	minimum,
		kzInt	maximum
	)

Clamps integer value to given range.

KZ_INLINE kzUint kzsClampui	(	kzUint	value,
		kzUint	minimum,
		kzUint	maximum
	)

Clamps unsigned integer value to given range.

KZ_INLINE kzFloat kzsLerpf	(	kzFloat	minimum,
		kzFloat	maximum,
		kzFloat	t
	)

Linearly interpolate between [a,b] where t should be in range [0,1].

KZ_INLINE kzFloat kzsDegreesToRadians ( kzFloat angleInDegrees )

Converts degrees to radians.

KZ_INLINE kzFloat kzsRadiansToDegrees ( kzFloat angleInRadians )

Converts radians to degrees.

KZ_INLINE kzBool kzsIsInClosedInterval	(	kzFloat	value,
		kzFloat	minimum,
		kzFloat	maximum
	)

Check whether value is in [min, max] (an interval inclusive of the limit points)

KZ_INLINE kzBool kzsFloatIsEqual	(	kzFloat	valueA,
		kzFloat	valueB
	)

Check if two floats are equal.

KZ_INLINE kzBool kzsFloatIsAlmostEqualUlps	(	kzFloat	valueA,
		kzFloat	valueB,
		kzUint	maxUlps
	)

Check if two IEEE 754 binary32 floats are equal up to a given number of ulps.

KZ_INLINE kzBool kzsFloatIsAlmostEqualAbsolute	(	kzFloat	valueA,
		kzFloat	valueB,
		kzFloat	maxAbsoluteDifference
	)

Check if two floats are equal up to a given difference.

KZ_INLINE kzBool kzsFloatIsAlmostEqualRelative	(	kzFloat	valueA,
		kzFloat	valueB,
		kzFloat	maxRelativeDifference
	)

Check if two floats are equal up to a given difference scaled by the larger value.

KZ_INLINE kzBool kzsFloatIsAlmostEqual	(	kzFloat	valueA,
		kzFloat	valueB
	)

Check if two floats are approximately equal.

KZ_INLINE kzBool kzsIsInOpenInterval	(	kzFloat	value,
		kzFloat	minimum,
		kzFloat	maximum
	)

Check whether value in (min, max) (an interval range exclusive of the limit points)

KZ_INLINE kzInt kzsMin	(	kzInt	a,
		kzInt	b
	)

Returns the smaller of two integers.

KZ_INLINE kzInt kzsMax	(	kzInt	a,
		kzInt	b
	)

Returns the greater of two integers.

KZ_INLINE kzUint kzsMinU	(	kzUint	a,
		kzUint	b
	)

Returns the smaller of two unsigned integers.

KZ_INLINE kzUint kzsMaxU	(	kzUint	a,
		kzUint	b
	)

Returns the greater of two unsigned integers.

KZ_INLINE kzFloat kzsMinf	(	kzFloat	a,
		kzFloat	b
	)

Returns the smaller of two floats.

KZ_INLINE kzFloat kzsMaxf	(	kzFloat	a,
		kzFloat	b
	)

Returns the greater of two floats.

KZ_INLINE kzInt kzsStep	(	kzInt	a,
		kzInt	b
	)

Returns the step function of two integers.

Returns: 1 if b >= a, 0 otherwise.

KZ_INLINE kzUint kzsStepU	(	kzUint	a,
		kzUint	b
	)

Returns the step function of two unsigned integers.

Returns: 1 if b >= a, 0 otherwise.

KZ_INLINE kzFloat kzsStepf	(	kzFloat	a,
		kzFloat	b
	)

Returns the step function of two floats.

Returns: 1.0f if b >= a, 0.0f otherwise.

KZ_INLINE void kzsQsort	(	void *	buffer,
		kzUint	itemCount,
		kzUint	itemSize,
		kzInt()(const void left, const void *right)	comparator
	)

Sorts values in buffer using quick sort.

KZ_INLINE kzUint kzsFloatToUint ( kzFloat value )

Casts a float to unsigned int.

KZ_INLINE kzFloat kzsUintToFloat ( kzUint value )

Casts an unsigned int to float.

KZ_INLINE kzInt kzsFloatRoundToInt ( kzFloat value )

Rounds a float to the nearest integer.

KZ_INLINE kzUint kzsFloatRoundToUint ( kzFloat value )

Rounds a float to the nearest unsigned integer.

KZ_INLINE void kzsSwap	(	void *	element1,
		void *	element2,
		kzUint	elementSize
	)

Swaps two arbitrary elements of arbitrary size.

Variable Documentation

KANZI_API const union KZ_FLOAT_UNION_TYPE KZS_NAN_PRIVATE

See also: KZS_NAN

KANZI_API const union KZ_FLOAT_UNION_TYPE KZS_INFINITY_PRIVATE

See also: KZS_INFINITY

Classes

Macros

Functions

Variables

Detailed Description

Macro Definition Documentation

Function Documentation

Variable Documentation