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//
// GENERATED FILE
//
use super::*;
use crate::SpiceContext;
use f2rust_std::*;
/// Value of a Chebyshev polynomial expansion
///
/// Return the value of a polynomial evaluated at the input X using
/// the coefficients for the Chebyshev expansion of the polynomial.
///
/// # Brief I/O
///
/// ```text
/// VARIABLE I/O DESCRIPTION
/// -------- --- --------------------------------------------------
/// CP I DEGP+1 Chebyshev polynomial coefficients.
/// DEGP I Degree of polynomial.
/// X2S I Transformation parameters of polynomial.
/// X I Value for which the polynomial is to be evaluated.
/// P O Value of the polynomial at X.
/// ```
///
/// # Detailed Input
///
/// ```text
/// CP is an array of coefficients a polynomial with respect
/// to the Chebyshev basis. The polynomial to be
/// evaluated is assumed to be of the form:
///
/// CP(DEGP+1)*T(DEGP,S) + CP(DEGP)*T(DEGP-1,S) + ...
///
/// + CP(2)*T(1,S) + CP(1)*T(0,S)
///
/// where T(I,S) is the I'th Chebyshev polynomial
/// evaluated at a number S whose double precision
/// value lies between -1 and 1. The value of S is
/// computed from the input variables X2S(1), X2S(2)
/// and X.
///
/// DEGP is the degree of the Chebyshev polynomial to be
/// evaluated.
///
/// X2S is an array of two parameters. These parameters are
/// used to transform the domain of the input variable X
/// into the standard domain of the Chebyshev polynomial.
/// X2S(1) should be a reference point in the domain of X;
/// X2S(2) should be the radius by which points are
/// allowed to deviate from the reference point and while
/// remaining within the domain of X. The value of
/// X is transformed into the value S given by
///
/// S = ( X - X2S(1) ) / X2S(2)
///
/// Typically X2S(1) is the midpoint of the interval over
/// which X is allowed to vary and X2S(2) is the radius of
/// the interval.
///
/// The main reason for doing this is that a Chebyshev
/// expansion is usually fit to data over a span
/// from A to B where A and B are not -1 and 1
/// respectively. Thus to get the "best fit" the
/// data was transformed to the interval [-1,1] and
/// coefficients generated. These coefficients are
/// not rescaled to the interval of the data so that
/// the numerical "robustness" of the Chebyshev fit will
/// not be lost. Consequently, when the "best fitting"
/// polynomial needs to be evaluated at an intermediate
/// point, the point of evaluation must be transformed
/// in the same way that the generating points were
/// transformed.
///
/// X is the value for which the polynomial is to be
/// evaluated.
/// ```
///
/// # Detailed Output
///
/// ```text
/// P is the value of the polynomial to be evaluated. It
/// is given by
///
/// CP(DEGP+1)*T(DEGP,S) + CP(DEGP)*T(DEGP-1,S) + ...
///
/// + CP(2)*T(1,S) + CP(1)*T(0,S)
///
/// where T(I,S) is the I'th Chebyshev polynomial
/// evaluated at a number S = ( X - X2S(1) )/X2S(2)
/// ```
///
/// # Exceptions
///
/// ```text
/// Error free.
///
/// 1) No tests are performed for exceptional values (DEGP negative,
/// etc.). This routine is expected to be used at a low level in
/// ephemeris evaluations. For that reason it has been elected as
/// a routine that will not participate in error handling.
/// ```
///
/// # Particulars
///
/// ```text
/// This routine computes the value P given by
///
/// CP(DEGP+1)*T(DEGP,S) + CP(DEGP)*T(DEGP-1,S) + ...
///
/// + CP(2)*T(1,S) + CP(1)*T(0,S)
///
/// where
///
/// S = ( X - X2S(1) ) / X2S(2)
///
/// and
///
/// T(I,S) is the I'th Chebyshev polynomial of the first kind
/// evaluated at S.
/// ```
///
/// # Examples
///
/// ```text
/// The numerical results shown for this example may differ across
/// platforms. The results depend on the SPICE kernels used as
/// input, the compiler and supporting libraries, and the machine
/// specific arithmetic implementation.
///
/// 1) Depending upon the user's needs, there are 3 routines
/// available for evaluating Chebyshev polynomials.
///
/// CHBVAL for evaluating a Chebyshev polynomial when no
/// derivatives are desired.
///
/// CHBINT for evaluating a Chebyshev polynomial and its
/// first derivative.
///
/// CHBDER for evaluating a Chebyshev polynomial and a user
/// or application dependent number of derivatives.
///
/// Of these 3 the one most commonly employed by SPICE software
/// is CHBINT as it is used to interpolate ephemeris state
/// vectors; this requires the evaluation of a polynomial
/// and its derivative. When no derivatives are desired one
/// should use CHBVAL, or when more than one or an unknown
/// number of derivatives are desired one should use CHBDER.
///
/// The code example below illustrates how this routine might
/// be used to obtain points for plotting a polynomial.
///
///
/// Example code begins here.
///
///
/// PROGRAM CHBVAL_EX1
/// IMPLICIT NONE
///
/// C
/// C Local variables.
/// C
/// DOUBLE PRECISION CP (7)
/// DOUBLE PRECISION X
/// DOUBLE PRECISION P
/// DOUBLE PRECISION X2S (2)
///
/// INTEGER DEGP
/// INTEGER I
///
/// C
/// C Set the coefficients of the polynomial and its
/// C transformation parameters
/// C
/// DATA CP / 1.D0, 3.D0, 0.5D0,
/// . 1.D0, 0.5D0, -1.D0,
/// . 1.D0 /
/// DATA X2S / 0.5D0, 3.D0 /
///
/// DEGP = 6
/// X = 1.D0
///
/// CALL CHBVAL ( CP, DEGP, X2S, X, P )
///
/// WRITE(*,'(A,F10.6)')
/// . 'Value of the polynomial at X=1: ', P
///
/// END
///
///
/// When this program was executed on a Mac/Intel/gfortran/64-bit
/// platform, the output was:
///
///
/// Value of the polynomial at X=1: -0.340878
/// ```
///
/// # Restrictions
///
/// ```text
/// 1) One needs to be careful that the value
///
/// (X-X2S(1)) / X2S(2)
///
/// lies between -1 and 1. Otherwise, the routine may fail
/// spectacularly (for example with a floating point overflow).
/// ```
///
/// # Literature References
///
/// ```text
/// [1] W. Press, B. Flannery, S. Teukolsky and W. Vetterling,
/// "Numerical Recipes -- The Art of Scientific Computing,"
/// chapter 5.4, "Recurrence Relations and Clenshaw's Recurrence
/// Formula," p 161, Cambridge University Press, 1986.
///
/// [2] T. Rivlin, "The Chebyshev Polynomials," Wisley, 1974.
///
/// [3] R. Weast and S. Selby, "CRC Handbook of Tables for
/// Mathematics," 4th Edition, CRC Press, 1976.
/// ```
///
/// # Author and Institution
///
/// ```text
/// J. Diaz del Rio (ODC Space)
/// W.M. Owen (JPL)
/// W.L. Taber (JPL)
/// ```
///
/// # Version
///
/// ```text
/// - SPICELIB Version 1.1.0, 16-JUL-2021 (JDR)
///
/// Added IMPLICIT NONE statement.
///
/// Updated the header to comply with NAIF standard. Added
/// full code example.
///
/// - SPICELIB Version 1.0.1, 10-MAR-1992 (WLT)
///
/// Comment section for permuted index source lines was added
/// following the header.
///
/// - SPICELIB Version 1.0.0, 31-JAN-1990 (WMO) (WLT)
/// ```
///
/// # Revisions
///
/// ```text
/// - Beta Version 1.0.1, 30-DEC-1988 (WLT)
///
/// The Error free specification was added to the routine as
/// well as an explanation for this designation. Examples added.
/// ```
pub fn chbval(cp: &[f64], degp: i32, x2s: &[f64; 2], x: f64, p: &mut f64) {
CHBVAL(cp, degp, x2s, x, p);
}
//$Procedure CHBVAL ( Value of a Chebyshev polynomial expansion )
pub fn CHBVAL(CP: &[f64], DEGP: i32, X2S: &[f64], X: f64, P: &mut f64) {
let CP = DummyArray::new(CP, 1..);
let X2S = DummyArray::new(X2S, 1..=2);
let mut J: i32 = 0;
let mut W = StackArray::<f64, 3>::new(1..=3);
let mut S: f64 = 0.0;
let mut S2: f64 = 0.0;
//
// Local variables
//
//
// Transform X to S and initialize temporary variables.
//
S = ((X - X2S[1]) / X2S[2]);
S2 = (2.0 * S);
J = (DEGP + 1);
W[1] = 0.0;
W[2] = 0.0;
//
// Evaluate the polynomial using recursion.
//
while (J > 1) {
W[3] = W[2];
W[2] = W[1];
W[1] = (CP[J] + ((S2 * W[2]) - W[3]));
J = (J - 1);
}
*P = (((S * W[1]) - W[2]) + CP[1]);
}