double flin ( int n, int j, double l, double f ( double x[], int n ), 
  double x[], int *nf, double v[], double q0[], double q1[], double *qd0, 
  double *qd1, double *qa, double *qb, double *qc );
void minfit ( int n, double tol, double a[], double q[] );
void minny ( int n, int j, int nits, double *d2, double *x1, double *f1, 
  int fk, double f ( double x[], int n ), double x[], double t, double h, 
  double v[], double q0[], double q1[], int *nl, int *nf, double dmin, 
  double ldt, double *fx, double *qa, double *qb, double *qc, double *qd0, 
  double *qd1 );
double praxis ( double t0, double h0, int n, int prin, double x[], 
  double f ( double x[], int n ) );
void print2 ( int n, double x[], int prin, double fx, int nf, int nl );
void quad ( int n, double f ( double x[], int n ), double x[], double t, 
  double h, double v[], double q0[], double q1[], int *nl, int *nf, double dmin, 
  double ldt, double *fx, double *qf1, double *qa, double *qb, double *qc, 
  double *qd0, double *qd1 );
double r8_epsilon ( );
double r8_hypot ( double x, double y );
double r8_max ( double x, double y );
double r8_min ( double x, double y );
double r8_uniform_01 ( int *seed );
void r8mat_print ( int m, int n, double a[], char *title );
void r8mat_print_some ( int m, int n, double a[], int ilo, int jlo, int ihi,
  int jhi, char *title );
void r8mat_transpose_in_place ( int n, double a[] );
void r8vec_copy ( int n, double a1[], double a2[] );
double r8vec_max ( int n, double r8vec[] );
double r8vec_min ( int n, double r8vec[] );
double r8vec_norm ( int n, double a[] );
void r8vec_print ( int n, double a[], char *title );
void svsort ( int n, double d[], double v[] ) ;
void timestamp ( );