\(\newcommand{\W}[1]{ \; #1 \; }\) \(\newcommand{\R}[1]{ {\rm #1} }\) \(\newcommand{\B}[1]{ {\bf #1} }\) \(\newcommand{\D}[2]{ \frac{\partial #1}{\partial #2} }\) \(\newcommand{\DD}[3]{ \frac{\partial^2 #1}{\partial #2 \partial #3} }\) \(\newcommand{\Dpow}[2]{ \frac{\partial^{#1}}{\partial {#2}^{#1}} }\) \(\newcommand{\dpow}[2]{ \frac{ {\rm d}^{#1}}{{\rm d}\, {#2}^{#1}} }\)

exp_eps_for1.cpp

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exp_eps: Verify First Order Forward Sweep

# include <cmath>                     // for fabs function
extern bool exp_eps_for0(double *v0); // computes zero order forward sweep
bool exp_eps_for1(double *v1)         // double v[8]
{  bool ok = true;
    double v0[8];

    // set the value of v0[j] for j = 1 , ... , 7
    ok &= exp_eps_for0(v0);

    v1[1] = 1.;                                      // v1 = x
    ok    &= std::fabs( v1[1] - 1. ) <= 1e-10;

    v1[2] = 1. * v1[1];                              // v2 = 1 * v1
    ok    &= std::fabs( v1[2] - 1. ) <= 1e-10;

    v1[3] = v1[2] / 1.;                              // v3 = v2 / 1
    ok    &= std::fabs( v1[3] - 1. ) <= 1e-10;

    v1[4] = v1[3];                                   // v4 = 1 + v3
    ok    &= std::fabs( v1[4] - 1. ) <= 1e-10;

    v1[5] = v1[3] * v0[1] + v0[3] * v1[1];           // v5 = v3 * v1
    ok    &= std::fabs( v1[5] - 1. ) <= 1e-10;

    v1[6] = v1[5] / 2.;                              // v6 = v5 / 2
    ok    &= std::fabs( v1[6] - 0.5 ) <= 1e-10;

    v1[7] = v1[4] + v1[6];                           // v7 = v4 + v6
    ok    &= std::fabs( v1[7] - 1.5 ) <= 1e-10;

    return ok;
}
bool exp_eps_for1(void)
{  double v1[8];
    return exp_eps_for1(v1);
}