Miscellaneous Math

Miscellaneous math utility functions utilized within the API. More...

Collaboration diagram for Miscellaneous Math:

Macros
#define	INT_SQRT   0
#define	MAX(a, b)   ((a) > (b) ? (a) : (b))
	Calculates the maximum of two values.
#define	MIN(a, b)   ((a) < (b) ? (a) : (b))
	Calculates the minimum of two values.
#define	CLAMP(x, min, max)   (MIN(MAX((x), (min)), (max)))
	Clamps a value between a minimum and maximum boundary.

Functions
uint32_t	log2i (uint32_t x)
	Integer Base-2 Logarithm.
uint32_t	log2_round (uint32_t x)
	Integer Base-2 Logarithm with rounded result.
uint32_t	binary_round (uint32_t x)
	Finding the nearest power-of-two value.
uint32_t	popcount (uint32_t x)
	Counting bits set in a 32-bit unsigned integer.
uint32_t	ispowoftwo (uint32_t x)
	Determining if an integer is a power of 2.
uint32_t	absval (int32_t x)
	Calculates the absolute value.
uint32_t	floor2 (uint32_t x, uint_fast8_t n)
	Calculates the floor division by a factor of 2: floor(x / 2^n).
uint32_t	ceiling2 (uint32_t x, uint_fast8_t n)
	Calculates the ceildiv division by a factor of 2: ceildiv(x / 2^n).
uint32_t	ceildiv (uint32_t x, uint32_t y)
	Calculates the ceildiv division: ceildiv(x / y).

Detailed Description

Miscellaneous math utility functions utilized within the API.

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Modules overview:

• Integer Math: Mathematical functionality on integer values.
• Long integer multiplication (32bit x 32bit): double word integer multiplication algorithms.

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Macro Definition Documentation

CLAMP

#define CLAMP	(		x,
			min,
			max
	)		(MIN(MAX((x), (min)), (max)))

Clamps a value between a minimum and maximum boundary.

---

Clamps the values such that the condition min <= x <= max is true.

Note

The condition min <= max must hold!!!

Parameters

x	The input parameter to be clamped.
min	The minimum or lower boundary.
max	The maximum or upper boundary.

Returns

The clamped value of the input parameter within [min,max].

INT_SQRT

#define INT_SQRT   0

Enables the integer square root function.

MAX

#define MAX	(		a,
			b
	)		((a) > (b) ? (a) : (b))

Calculates the maximum of two values.

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Parameters

a	Input parameter.
b	Input parameter.

Returns

The maximum value of the input parameters.

MIN

#define MIN	(		a,
			b
	)		((a) < (b) ? (a) : (b))

Calculates the minimum of two values.

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Parameters

a	Input parameter.
b	Input parameter.

Returns

The minimum value of the input parameters.

Function Documentation

absval()

uint32_t absval ( int32_t  x )

inline

Calculates the absolute value.

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Parameters

x	Input parameter.

Returns

The absolute value of x.

binary_round()

uint32_t binary_round ( uint32_t  x )

inline

Finding the nearest power-of-two value.

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Implemented s.t. |x - 2^n| becomes minimum for all n. Special case 0: returns 0; Maximum input: 3037000499; higher number result in overflow! (returns 0)

Parameters

x	Input parameter.

Returns

Nearest power-of-two number, i.e. 2^n.

ceildiv()

uint32_t ceildiv ( uint32_t  x, uint32_t  y  )

inline

Calculates the ceildiv division: ceildiv(x / y).

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Parameters

x	Numerator
y	Denominator

Returns

The result of the ceildiv division ceildiv(x / y).

ceiling2()

uint32_t ceiling2 ( uint32_t  x, uint_fast8_t  n  )

inline

Calculates the ceildiv division by a factor of 2: ceildiv(x / 2^n).

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Parameters

x	Input parameter.
n	The shift value, maximum is 31.

Returns

The ceildiv division by 2^n result.

floor2()

uint32_t floor2 ( uint32_t  x, uint_fast8_t  n  )

inline

Calculates the floor division by a factor of 2: floor(x / 2^n).

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Parameters

x	Input parameter.
n	The shift value, maximum is 31.

Returns

The floor division by 2^n result.

ispowoftwo()

uint32_t ispowoftwo ( uint32_t  x )

inline

Determining if an integer is a power of 2.

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See also

http://graphics.stanford.edu/~seander/bithacks.html

Parameters

x	Input parameter.

Returns

True if integer is power of 2.

log2_round()

uint32_t log2_round ( uint32_t  x )

inline

Integer Base-2 Logarithm with rounded result.

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Calculates the base-2 logarithm for unsigned integer values and returns the rounded result. The result is the integer equivalent of round(log2(x)).

It is finding the nearest power-of-two value s.t. |x - 2^n| becomes minimum for all n.

Parameters

x	Input parameter.

Returns

The rounded value of the base-2 logarithm.

log2i()

uint32_t log2i ( uint32_t  x )

inline

Integer Base-2 Logarithm.

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Calculates the base-2 logarithm for unsigned integer values. The result is the integer equivalent of floor(log2(x)).

Parameters

x	Input parameter.

Returns

The floor of the base-2 logarithm.

popcount()

uint32_t popcount ( uint32_t  x )

inline

Counting bits set in a 32-bit unsigned integer.

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See also

http://graphics.stanford.edu/~seander/bithacks.html

Parameters

x	Input parameter.

Returns

Number of bits set in input value.