The Thorium series

Half-lives shorter than 1h excluded from the decay chain:

In Python:

>>> from batemaneq import bateman_parent
>>> from math import log as ln
>>> d = 1./365  # Th-232 Ra-228 Ac-228 Th-228
>>> h = d/24    # Ra-224 Pb-212 Bi-212 (Pb-208)
>>> Thalf = [1.405e10, 5.75, 6.25*h, 1.9116, 3.6319*d, 10.64*h, 60.55/60*h]
>>> bateman_parent([ln(2)/x for x in Thalf], 100)  # 100 years
[0.9999999950665681, 4.0925028658312447e-10, 5.078051001187696e-14, 1.3605575316895603e-10, 7.082081172329036e-13, 8.64484883194704e-14, 8.199335787638167e-15]

In C++:

#include <cmath>
#include <iostream>
#include <iomanip>
#include <vector>
#include "bateman.hpp"

using vec_t = std::vector<double>;
double exp_cb(double arg){
    return std::exp(arg);
}

int main(){
   double one = 1;
   double d = one/365;
   double h = d/24;
   double ln2 = std::log(2);
   vec_t lmbd {{ ln2/1.405e10, ln2/5.75, ln2/(6.25*h),
       ln2/1.9116, ln2/(3.6319*d), ln2/(10.64*h), ln2/(60.55/60*h) }};
   auto p = bateman::bateman_parent(lmbd, 100.0, exp_cb);
   std::cout << std::setprecision(17);  // all significant digits
   for (auto v : p)
       std::cout << v << " ";
   std::cout << std::endl;
   return 0;
}

$ g++ -std=c++11 double.cpp -I../include
$ ./a.out
0.99999999506656811 4.0925028658312447e-10 5.0780510011876959e-14 1.3605575316895603e-10 7.0820811723290359e-13 8.6448488319470398e-14 8.1993357876381666e-15

In C++ using boost::multiprecision::cpp_dec_float_50:

#include <cmath>
#include <iostream>
#include <vector>
#include <boost/multiprecision/cpp_dec_float.hpp>
#include "bateman.hpp"

using Real_t = boost::multiprecision::cpp_dec_float_50;
using vec_t = std::vector<Real_t>;
Real_t exp_cb(Real_t arg){
    return boost::multiprecision::exp(arg);
}

int main(){
   Real_t one = 1;
   Real_t d = one/365;
   Real_t h = d/24;
   Real_t ln2 = boost::multiprecision::log(2*one);
   vec_t lmbd {{ ln2/1.405e10, ln2/5.75, ln2/(6.25*h),
       ln2/1.9116, ln2/(3.6319*d), ln2/(10.64*h), ln2/(60.55/60*h) }};
   auto p = bateman::bateman_parent(lmbd, static_cast<Real_t>(100), exp_cb);
   std::cout << std::setprecision(30);  // show 30 of our 50 digits
   for (auto v : p)
       std::cout << v << " ";
   std::cout << std::endl;
   return 0;
}

$ g++ -std=c++11 multi.cpp -I../include
$ ./a.out
0.999999995066568122063002778128 4.09250286583124398565537707859e-10 5.07805100118769662240802082504e-14 1.3605575316895606205575997585e-10 7.08208117232903695657287769184e-13 8.6448488319470425326824303941e-14 8.19933578763816849146541981927e-15

We see that the concentration of the final nuclide only varies in the 15th decimal place (we had no catastropic cancelation in this example).