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$\newcommand{\W}[1]{ \; #1 \; } \newcommand{\R}[1]{ {\rm #1} } \newcommand{\B}[1]{ {\bf #1} } \newcommand{\D}[2]{ \frac{\partial #1}{\partial #2} } \newcommand{\DD}[3]{ \frac{\partial^2 #1}{\partial #2 \partial #3} } \newcommand{\Dpow}[2]{ \frac{\partial^{#1}}{\partial {#2}^{#1}} } \newcommand{\dpow}[2]{ \frac{ {\rm d}^{#1}}{{\rm d}\, {#2}^{#1}} }$
exp_eps: Verify Second Order Forward Sweep
# include <cmath>                     // for fabs function
extern bool exp_eps_for0(double *v0); // computes zero order forward sweep
extern bool exp_eps_for1(double *v1); // computes first order forward sweep
bool exp_eps_for2(void)
{     bool ok = true;
double v0[8], v1[8], v2[8];

// set the value of v0[j], v1[j] for j = 1 , ... , 7
ok &= exp_eps_for0(v0);
ok &= exp_eps_for1(v1);

v2[1] = 0.;                                      // v1 = x
ok    &= std::fabs( v2[1] - 0. ) <= 1e-10;

v2[2] = 1. * v2[1];                              // v2 = 1 * v1
ok    &= std::fabs( v2[2] - 0. ) <= 1e-10;

v2[3] = v2[2] / 1.;                              // v3 = v2 / 1
ok    &= std::fabs( v2[3] - 0. ) <= 1e-10;

v2[4] = v2[3];                                   // v4 = 1 + v3
ok    &= std::fabs( v2[4] - 0. ) <= 1e-10;

v2[5] = v2[3] * v0[1] + 2. * v1[3] * v1[1]       // v5 = v3 * v1
+ v0[3] * v2[1];
ok    &= std::fabs( v2[5] - 2. ) <= 1e-10;

v2[6] = v2[5] / 2.;                              // v6 = v5 / 2
ok    &= std::fabs( v2[6] - 1. ) <= 1e-10;

v2[7] = v2[4] + v2[6];                           // v7 = v4 + v6
ok    &= std::fabs( v2[7] - 1. ) <= 1e-10;

return ok;
}

Input File: introduction/exp_eps_for2.cpp