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_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;
}
bool exp_eps_rev1(void)
{ bool ok = true;
// set the value of v0[j] for j = 1 , ... , 7
double v0[8];
ok &= exp_eps_for0(v0);
// initial all partial derivatives as zero
double f_v[8];
size_t j;
for(j = 0; j < 8; j++)
f_v[j] = 0.;
// set partial derivative for f7
f_v[7] = 1.;
ok &= std::fabs( f_v[7] - 1. ) <= 1e-10; // f7_v7
// f6( v1 , v2 , v3 , v4 , v5 , v6 )
f_v[4] += f_v[7] * 1.;
f_v[6] += f_v[7] * 1.;
ok &= std::fabs( f_v[4] - 1. ) <= 1e-10; // f6_v4
ok &= std::fabs( f_v[6] - 1. ) <= 1e-10; // f6_v6
// f5( v1 , v2 , v3 , v4 , v5 )
f_v[5] += f_v[6] / 2.;
ok &= std::fabs( f_v[5] - 0.5 ) <= 1e-10; // f5_v5
// f4( v1 , v2 , v3 , v4 )
f_v[1] += f_v[5] * v0[3];
f_v[3] += f_v[5] * v0[1];
ok &= std::fabs( f_v[1] - 0.25) <= 1e-10; // f4_v1
ok &= std::fabs( f_v[3] - 0.25) <= 1e-10; // f4_v3
// f3( v1 , v2 , v3 )
f_v[3] += f_v[4] * 1.;
ok &= std::fabs( f_v[3] - 1.25) <= 1e-10; // f3_v3
// f2( v1 , v2 )
f_v[2] += f_v[3] / 1.;
ok &= std::fabs( f_v[2] - 1.25) <= 1e-10; // f2_v2
// f1( v1 )
f_v[1] += f_v[2] * 1.;
ok &= std::fabs( f_v[1] - 1.5 ) <= 1e-10; // f1_v2
return ok;
}
bool exp_eps_rev2(void)
{ bool ok = true;
// set the value of v0[j], v1[j] for j = 1 , ... , 7
double v0[8], v1[8];
ok &= exp_eps_for0(v0);
ok &= exp_eps_for1(v1);
// initial all partial derivatives as zero
double f_v0[8], f_v1[8];
size_t j;
for(j = 0; j < 8; j++)
{ f_v0[j] = 0.;
f_v1[j] = 0.;
}
// set partial derivative for f_7
f_v1[7] = 1.;
ok &= std::fabs( f_v1[7] - 1. ) <= 1e-10; // partial f_7 w.r.t. v_7^1
// f_6 = f_7( v_1^0 , ... , v_6^1 , v_4^0 + v_6^0, v_4^1 , v_6^1 )
f_v0[4] += f_v0[7];
f_v0[6] += f_v0[7];
f_v1[4] += f_v1[7];
f_v1[6] += f_v1[7];
ok &= std::fabs( f_v0[4] - 0. ) <= 1e-10; // partial f_6 w.r.t. v_4^0
ok &= std::fabs( f_v0[6] - 0. ) <= 1e-10; // partial f_6 w.r.t. v_6^0
ok &= std::fabs( f_v1[4] - 1. ) <= 1e-10; // partial f_6 w.r.t. v_4^1
ok &= std::fabs( f_v1[6] - 1. ) <= 1e-10; // partial f_6 w.r.t. v_6^1
// f_5 = f_6( v_1^0 , ... , v_5^1 , v_5^0 / 2 , v_5^1 / 2 )
f_v0[5] += f_v0[6] / 2.;
f_v1[5] += f_v1[6] / 2.;
ok &= std::fabs( f_v0[5] - 0. ) <= 1e-10; // partial f_5 w.r.t. v_5^0
ok &= std::fabs( f_v1[5] - 0.5 ) <= 1e-10; // partial f_5 w.r.t. v_5^1
// f_4 = f_5( v_1^0 , ... , v_4^1 , v_3^0 * v_1^0 ,
// v_3^1 * v_1^0 + v_3^0 * v_1^1 )
f_v0[1] += f_v0[5] * v0[3] + f_v1[5] * v1[3];
f_v0[3] += f_v0[5] * v0[1] + f_v1[5] * v1[1];
f_v1[1] += f_v1[5] * v0[3];
f_v1[3] += f_v1[5] * v0[1];
ok &= std::fabs( f_v0[1] - 0.5 ) <= 1e-10; // partial f_4 w.r.t. v_1^0
ok &= std::fabs( f_v0[3] - 0.5 ) <= 1e-10; // partial f_4 w.r.t. v_3^0
ok &= std::fabs( f_v1[1] - 0.25 ) <= 1e-10; // partial f_4 w.r.t. v_1^1
ok &= std::fabs( f_v1[3] - 0.25 ) <= 1e-10; // partial f_4 w.r.t. v_3^1
// f_3 = f_4( v_1^0 , ... , v_3^1 , 1 + v_3^0 , v_3^1 )
f_v0[3] += f_v0[4];
f_v1[3] += f_v1[4];
ok &= std::fabs( f_v0[3] - 0.5 ) <= 1e-10; // partial f_3 w.r.t. v_3^0
ok &= std::fabs( f_v1[3] - 1.25) <= 1e-10; // partial f_3 w.r.t. v_3^1
// f_2 = f_3( v_1^0 , ... , v_2^1 , v_2^0 , v_2^1 )
f_v0[2] += f_v0[3];
f_v1[2] += f_v1[3];
ok &= std::fabs( f_v0[2] - 0.5 ) <= 1e-10; // partial f_2 w.r.t. v_2^0
ok &= std::fabs( f_v1[2] - 1.25) <= 1e-10; // partial f_2 w.r.t. v_2^1
// f_1 = f_2 ( v_1^0 , v_2^0 , v_1^0 , v_2^0 )
f_v0[1] += f_v0[2];
f_v1[1] += f_v1[2];
ok &= std::fabs( f_v0[1] - 1. ) <= 1e-10; // partial f_1 w.r.t. v_1^0
ok &= std::fabs( f_v1[1] - 1.5 ) <= 1e-10; // partial f_1 w.r.t. v_1^1
return ok;
}