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BaseDefinitions.h File Reference

#include <stdio.h>
#include <fstream.h>

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Defines
#define	Zahl   double
#define	min(a, b)   (a<b)?a:b
#define	epsilon   0.0000000001
#define	M_SQRTPI   1.772453850905516027298167483341145182798
#define	M_1SQRT2PI   0.398942280401432677939946059934
#define	Free(ptr)   delete[] ptr;ptr=NULL;
#define	lfloor(f)   (long)floor(f)
#define	min(x, y)   (x<y)?x:y
#define	max(x, y)   (x>y)?x:y
Functions
Zahl	AsymErfc (Zahl zsq)
void	WriteDoubleArray (ofstream &str, long len, double *vals, char *endchar, long dim)
long	power (long m, long n)
double	power (double m, long n)
long	binom (long i, long k)
double	vectabs (double a1, double a2, double a3)
double	Phi (long base, long x)
long	LongToCoeff (long nr, long base, long *cfs, long cflen)
double	CoeffToDoubleModified (long base, long *cfs, long cflen, long modfact)
double	CoeffToDouble (long base, long *cfs, long cflen)
bool	IsPrimitiveRoot (long proot, long base)
long	CalcDeterminant (long *A, long dim, long i)
Variables
long	ERFCMAXREK

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Define Documentation

#define Free( ptr )   delete[] ptr;ptr=NULL;

Frees the array-pointer ptr and sets it to NULL afterwards.

#define M_1SQRT2PI   0.398942280401432677939946059934

#define M_SQRTPI   1.772453850905516027298167483341145182798

approximate value for the square root of pi.

#define Zahl   double

We want to use double, but who knows, maybe sometimes we need long double or just float. By using our own type we only have to change this here and then to recompile

#define epsilon   0.0000000001

#define lfloor( f )   (long)floor(f)

#define max( x, y )   (x>y)?x:y

Macro, returns the maximum of two given values.

#define min( x, y )   (x<y)?x:y

Macro, returns the minimum of two given values.

#define min( a, b )   (a<b)?a:b

Macro, returns the minimum of two given values.

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Function Documentation

Zahl AsymErfc ( Zahl zsq )

Calculates the Erfc by means of its asymptotic expansion. Parameters: zsq   The variable z^2 in the expansion.

long CalcDeterminant ( long * A, long dim, long dimtocalc )

calculates the determinant of the (upper left) i*i submatrix of the dim*dim Matrix A. This is really slow, but never mind... flag the rows used so that we don't need another array for the cofactor. This saves a lot of mem...

double CoeffToDouble ( long base, long * cfs, long cflen )

returns the double-representation of the cofficients in base "base" given in cfs. E.g. cfs={1,2,1,2,1}, base=3 => returns 1/3 + 2/9 + 1/27 + 2/81 + 1/243

double CoeffToDoubleModified ( long base, long * cfs, long cflen, long modfact )

returns the double-representation of the cofficients in base "base" given in cfs. E.g. cfs={1,2,1,2,1}, base=3 => returns 1/3 + 2/9 + 1/27 + 2/81 + 1/243 This is the modified version, needed by Atanassov's sequence. (Not quite implemented yet ...)

bool IsPrimitiveRoot ( long proot, long base )

Checks if proot is a primitive root modulo base.

long LongToCoeff ( long nr, long base, long * cfs, long cflen )

Expands n in base "base". Parameters: nr   the number to develop in base base   Which base to use for the expansion cfs   long-array where the coefficients should be stored cflen   length of the buffer cfs Returns: Returns the number of coefficients (lowest n s.t. nr<base^n) or cflen, depending in which one is smaller

double Phi ( long base, long x )

The digit inversion function. This inverts x (written down in base "base") at the comma. E.g. Phi(3, 25): 25=2*9+2*3+1=221_3 => 0.112_3=1/3 + 1/9 + 2/27

void WriteDoubleArray ( ofstream & str, long len, double * vals, char * endchar, long dim )

Writes the "dim"-dimensional array vals in Mathematica-List format to the file str. Parameters: endchar   defines a string which should be written out after the list, e.g. ";" or "//MatrixForm" len   vals   The dim-dimensional array of double-Values endchar   String that is appended to the file after the List is written out. dim

long binom ( long i, long k )

Returns the binomial coefficient (i k).

double power ( double m, long n )

Returns m^n where n and m are double variable. The result is of type double, too.

long power ( long m, long n )

Returns m^n, where n and m are long variables. The result, of course, is also of type long.

double vectabs ( double a1, double a2, double a3 )

Returns the length of the 3-dimensional vector (a1, a2, a3) (just sqrt(a1*a1 + a2*a2 + a3*a3) ).

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Variable Documentation

long ERFCMAXREK

Defines how many term in the asymptotic expansion of erfc=1-erf should be used for the calculation.

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