Arithmetic Supplements

Module Description

Some additional useful arithmetic functions, f.ex. map().

Note

Due to many "modern" compiler's lack of support for FPU 80 bit "long double",
the "real number" functions (e.g. _root()) may suffer truncation errors due to the
lack of precision in "double", and You need to account for that in Your programming.

Macros
#define	min(a, b)   ((a)<(b)?(a):(b))
#define	max(a, b)   ((a)>(b)?(a):(b))

Functions
long	map (long x, long xMin, long xMax, long toMin, long toMax)
long	constrain (long x, long lo, long hi)
short	random (short iMin, short iMax)
void	randomize ()
long	runningAvg (long Avg, long X, unsigned int Period)
ulong	ipow2 (ushort expo)
uint64	ipow2x (ushort expo)
ushort	ilog2 (ulong X)
ushort	ilog2x (uint64 X)
ushort	ilog10 (ulong X)
ushort	ilog10x (uint64 X)
long double	_root (long double base, long double X)
long double	_log (long double base, long double X)
double	_round (double x, unsigned char ndecimals)
bool	_isprime (unsigned long X)
long double	EngUnits (long double Value, int *pExpo)
template<typename T >
T	map_ (T x, T xMin, T xMax, T toMin, T toMax)
template<typename T >
T	constrain_ (T x, T lo, T hi)
template<typename T >
T	min_ (T a, T b)
template<typename T >
T	max_ (T a, T b)
template<typename T >
T	runningAvg_ (T Avg, T X, unsigned int Period)
template<typename T >
T	mulDiv_ (const T X, const T Mu, const T Dv)

Macro Definition Documentation

min

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

Definition at line 933 of file Common.h.

max

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

Definition at line 936 of file Common.h.

Function Documentation

map()

long map	(	long	x,
		long	xMin,
		long	xMax,
		long	toMin,
		long	toMax
	)

Convert one integer range to another.
Inversions are also possible.

Definition at line 145 of file Common.cpp.

constrain()

long constrain	(	long	x,
		long	lo,
		long	hi
	)

Limit a value to an inclusive range.

Definition at line 151 of file Common.cpp.

random()

short random	(	short	iMin,
		short	iMax
	)

Return a range inclusive random number. Negatives also possible.

Definition at line 156 of file Common.cpp.

randomize()

void randomize

(

)

Randomize the internal random seed.

Definition at line 167 of file Common.cpp.

runningAvg()

long runningAvg	(	long	Avg,
		long	X,
		unsigned int	Period
	)

Return the running average of Avg and X over Period.
Example:

Avg = runningAvg( Avg, In, 4 ); 

Definition at line 176 of file Common.cpp.

ipow2()

ulong ipow2

(

ushort

expo

)

Compute the integer 2^expo (by left shift).

Definition at line 183 of file Common.cpp.

ipow2x()

uint64 ipow2x

(

ushort

expo

)

Compute the 64bit integer 2^expo (by left shift).

Definition at line 189 of file Common.cpp.

ilog2()

ushort ilog2

(

ulong

X

)

Compute the integer log2 of X (by right shift).

Definition at line 208 of file Common.cpp.

ilog2x()

ushort ilog2x

(

uint64

X

)

See ilog2( ulong ).

Definition at line 241 of file Common.cpp.

ilog10()

ushort ilog10

(

ulong

X

)

Compute the integer log10 of an integer.
ilog10() is computed by the relationship log10(v) = log2(v) / log2(10).
Note: The return value is an integer approximation, not the true log10().

Definition at line 247 of file Common.cpp.

ilog10x()

ushort ilog10x

(

uint64

X

)

See ilog10( ulong ).

Definition at line 271 of file Common.cpp.

_root()

long double _root	(	long double	base,
		long double	X
	)

Compute the N'th root of x, e.g. root( 2,x ) == sqrt( x ).
Calculated with the inverse power method, _root( b,x ) = x^(1/b).

Definition at line 296 of file Common.cpp.

_log()

long double _log	(	long double	base,
		long double	X
	)

Compute the base n logartithm of x.
Calculated by the relationship logB(x) = log(x) / log(B).

Definition at line 303 of file Common.cpp.

_round()

double _round	(	double	x,
		unsigned char	ndecimals
	)

Round a floating point number to arbitrary precision.

Note

Due to the limited internal math precision of many "modern" compilers,
the the result of _round() is itself subject to rounding errors [sic],
which may produce an aberration in the last decimal.
Hence, Your programming may need to account for this.

Definition at line 343 of file Common.cpp.

_isprime()

bool _isprime

(

unsigned long

x

)

_isprime() returns true if x is a prime number, using an allocation-free "Sieve of Erathostenes". Credits to an unknown Borland programmer!

_isprime() returns true if x is a prime number.
Thus is a port of an old "set-less" Borland Pascal implementation of the
"Sieve of Erathostenes". While this may be slower than using a bit array
to tick off values already checked (due to having to re-mod the cases)
it does not need any allocation, hence can be used "on the fly".

Definition at line 373 of file Common.cpp.

EngUnits()

long double EngUnits	(	long double	Value,
		int *	pExpo
	)

Eng[ineering]Units returns a value as a multiple of 10^3, and it's exponent.
Note: MSVC silently trucates long double to a measly double.

Definition at line 180 of file UtilFunc.cpp.

map_()

template<typename T >

T map_	(	T	x,
		T	xMin,
		T	xMax,
		T	toMin,
		T	toMax
	)

See map()

float Y = map_<float>( X, 0, 255, -1.0f, 1.0f ); 

Note: The templated map_ might overflow in the intermediate product!

Definition at line 891 of file Common.h.

constrain_()

template<typename T >

T constrain_	(	T	x,
		T	lo,
		T	hi
	)

See constrain()

Definition at line 901 of file Common.h.

min_()

template<typename T >

T min_	(	T	a,
		T	b
	)

Definition at line 906 of file Common.h.

max_()

template<typename T >

T max_	(	T	a,
		T	b
	)

Definition at line 907 of file Common.h.

runningAvg_()

template<typename T >

T runningAvg_	(	T	Avg,
		T	X,
		unsigned int	Period
	)

See runningAvg()

Definition at line 912 of file Common.h.

mulDiv_()

template<typename T >

T mulDiv_	(	const T	X,
		const T	Mu,
		const T	Dv
	)

The muldiv ratio concept is sometimes useful even for non-integers.

Definition at line 920 of file Common.h.