module lmdz_coefpoly

  IMPLICIT NONE

contains

  SUBROUTINE coefpoly(xf1, xf2, xprim1, xprim2, xtild1, xtild2, a0, a1, a2, a3)

    ! From LMDZ4/libf/dyn3d/coefpoly.F, version 1.1.1.1 2004/05/19 12:53:05

    ! Author: P. Le Van

    ! Calcul des coefficients a0, a1, a2, a3 du polynôme de degré 3 qui
    ! satisfait aux 4 équations suivantes :

    ! a0 + a1 * xtild1 + a2 * xtild1**2 + a3 * xtild1**3 = Xf1
    ! a0 + a1 * xtild2 + a2 * xtild2**2 + a3 * xtild2**3 = Xf2
    ! a1 + 2. * a2 * xtild1 + 3. * a3 * xtild1**2 = Xprim1
    ! a1 + 2. * a2 * xtild2 + 3. * a3 * xtild2**2 = Xprim2

    ! (passe par les points (Xf(it), xtild(it)) et (Xf(it + 1),
    ! xtild(it + 1))

    ! On en revient à resoudre un système de 4 équations à 4 inconnues
    ! a0, a1, a2, a3.

    use nrtype, only: k8

    REAL(K8), intent(in) :: xf1, xf2, xprim1, xprim2, xtild1, xtild2
    REAL(K8), intent(out) :: a0, a1, a2, a3

    ! Local:
    REAL(K8) xtil1car, xtil2car, derr, x1x2car

    !------------------------------------------------------------

    xtil1car = xtild1 * xtild1
    xtil2car = xtild2 * xtild2

    derr = 2. * (xf2 - xf1) / (xtild1 - xtild2)

    x1x2car = (xtild1 - xtild2) * (xtild1 - xtild2)

    a3 = (derr + xprim1 + xprim2) / x1x2car
    a2 = (xprim1 - xprim2 + 3. * a3 * (xtil2car - xtil1car)) / (2. * (xtild1 - xtild2))

    a1 = xprim1 - 3. * a3 * xtil1car - 2. * a2 * xtild1
    a0 = xf1 - a3 * xtild1 * xtil1car - a2 * xtil1car - a1 * xtild1

  END SUBROUTINE coefpoly

end module lmdz_coefpoly