/* $Id: chbevl.c,v 1.1 2003/04/15 03:20:17 cher Exp $ */

/* This file is taken from Cephes math library */

/*
  Cephes Math Library Release 2.0:  April, 1987
  Copyright 1985, 1987 by Stephen L. Moshier
  Direct inquiries to 30 Frost Street, Cambridge, MA 02140
*/

#include "cephes.h"
#include "mconf.h"
#include <math.h>

/*							chbevl.c
 *
 *	Evaluate Chebyshev series
 *
 *
 *
 * SYNOPSIS:
 *
 * int N;
 * double x, y, coef[N], chebevl();
 *
 * y = chbevl( x, coef, N );
 *
 *
 *
 * DESCRIPTION:
 *
 * Evaluates the series
 *
 *        N-1
 *         - '
 *  y  =   >   coef[i] T (x/2)
 *         -            i
 *        i=0
 *
 * of Chebyshev polynomials Ti at argument x/2.
 *
 * Coefficients are stored in reverse order, i.e. the zero
 * order term is last in the array.  Note N is the number of
 * coefficients, not the order.
 *
 * If coefficients are for the interval a to b, x must
 * have been transformed to x -> 2(2x - b - a)/(b-a) before
 * entering the routine.  This maps x from (a, b) to (-1, 1),
 * over which the Chebyshev polynomials are defined.
 *
 * If the coefficients are for the inverted interval, in
 * which (a, b) is mapped to (1/b, 1/a), the transformation
 * required is x -> 2(2ab/x - b - a)/(b-a).  If b is infinity,
 * this becomes x -> 4a/x - 1.
 *
 *
 *
 * SPEED:
 *
 * Taking advantage of the recurrence properties of the
 * Chebyshev polynomials, the routine requires one more
 * addition per loop than evaluating a nested polynomial of
 * the same degree.
 *
 */

double
cephes_chbevl(double x, double array[], int n)
{
  double b0, b1, b2, *p;
  int i;

  p = array;
  b0 = *p++;
  b1 = 0.0;
  i = n - 1;

  do {
    b2 = b1;
    b1 = b0;
    b0 = x * b1  -  b2  + *p++;
  } while( --i );

  return( 0.5*(b0-b2) );
}

/*
 * Local variables:
 *  compile-command: "make -C .."
 * End:
 */