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/* TwoPunctures: File "utilities.h"*/
#include <math.h>
#include "cctk.h"
#define Pi 3.14159265358979323846264338328
#define Pih 1.57079632679489661923132169164 /* Pi/2*/
#define Piq 0.78539816339744830961566084582 /* Pi/4*/
#define TINY 1.0e-20
#define SWAP(a,b) {temp=(a);(a)=(b);(b)=temp;}
#define nrerror TP_nrerror
#define ivector TP_ivector
#define dvector TP_dvector
#define imatrix TP_imatrix
#define dmatrix TP_dmatrix
#define d3tensor TP_d3tensor
#define free_ivector TP_free_ivector
#define free_dvector TP_free_dvector
#define free_imatrix TP_free_imatrix
#define free_dmatrix TP_free_dmatrix
#define free_d3tensor TP_free_d3tensor
void nrerror (char error_text[]);
int *ivector (long nl, long nh);
CCTK_REAL *dvector (long nl, long nh);
int **imatrix (long nrl, long nrh, long ncl, long nch);
CCTK_REAL **dmatrix (long nrl, long nrh, long ncl, long nch);
CCTK_REAL ***d3tensor (long nrl, long nrh, long ncl, long nch, long ndl,
long ndh);
void free_ivector (int *v, long nl, long nh);
void free_dvector (CCTK_REAL *v, long nl, long nh);
void free_imatrix (int **m, long nrl, long nrh, long ncl, long nch);
void free_dmatrix (CCTK_REAL **m, long nrl, long nrh, long ncl, long nch);
void free_d3tensor (CCTK_REAL ***t, long nrl, long nrh, long ncl, long nch,
long ndl, long ndh);
int minimum2 (int i, int j);
int minimum3 (int i, int j, int k);
int maximum2 (int i, int j);
int maximum3 (int i, int j, int k);
int pow_int (int mantisse, int exponent);
void chebft_Zeros (CCTK_REAL u[], int n, int inv);
void chebft_Extremes (CCTK_REAL u[], int n, int inv);
void chder (CCTK_REAL *c, CCTK_REAL *cder, int n);
CCTK_REAL chebev (CCTK_REAL a, CCTK_REAL b, CCTK_REAL c[], int m, CCTK_REAL x);
void fourft (CCTK_REAL *u, int N, int inv);
void fourder (CCTK_REAL u[], CCTK_REAL du[], int N);
void fourder2 (CCTK_REAL u[], CCTK_REAL d2u[], int N);
CCTK_REAL fourev (CCTK_REAL *u, int N, CCTK_REAL x);
CCTK_REAL norm1 (CCTK_REAL *v, int n);
CCTK_REAL norm2 (CCTK_REAL *v, int n);
CCTK_REAL scalarproduct (CCTK_REAL *v, CCTK_REAL *w, int n);
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