void   chfact(double **A, int p);
void cprod(double **A, double *b, int m, int n, double *x);
double f_max(double *x, int n);
double f_min(double *x, int n);
void freemem(int ndim, ...);
void ifreemem(int ndim, ...);
int    fwhich_min(double *x, int n);
double inprod(double *v1, double *v2, int d);
double int_simp(double *f, double h, int n);
double int_romberg(double *f);
double int_trape(double *f);
double ldexgam(double x,double shape,double scale);
double norm2(double *vec, int len);
double pexgam(double x,double shape,double scale);
double qexgam(double p,double shape,double scale);
void quadsolve(double a, double b, double c, double *x, int get_both);
int    rdisc(int n,double *prob,int islog);
void r_simple_dirichlet(double *x, int k, double *shape);
double rexgam(double shape, double scale);
void   rperm(int size, int *samp, int n);
void   Rprintvec(char *a, double *x, int len);
void   Rprintveci(char *a, int *x, int len);
void   Rprintmat(char *a, double **m, int d1, int d2, int iscol);
void   Rprintmati(char *a, int **m, int d1, int d2, int iscol);
void *setmem(int ndim, ...);
void *isetmem(int ndim, ...);
double sigmoid(double x);
double sigmoid2(double x);
double sum(double *x, int n);
double sumlog(double *x, int n);
void swap(double *x, int i, int j);
double ss(double *vec, int len);
void transpose(double **A, int m, int n, double **B);
void Uprod(double **A, int n, double *x, double *b, int transpose);
void   Usolve(double **A, int p, double *b, double *x, int transpose);
double trace(double **a, int n, int is_log);
double fracf(double x);
double fold(double x);
double logadd(double lx, double ly);

int order, *twopow, grid_len;
double grid_incr;