mirror of
https://github.com/saitohirga/WSJT-X.git
synced 2024-11-15 16:42:12 -05:00
219 lines
6.1 KiB
C++
219 lines
6.1 KiB
C++
// (C) Copyright John Maddock 2006.
|
|
// Use, modification and distribution are subject to the
|
|
// Boost Software License, Version 1.0. (See accompanying file
|
|
// LICENSE_1_0.txt or copy at http://www.boost.org/LICENSE_1_0.txt)
|
|
|
|
#include <boost/math/special_functions/gamma.hpp>
|
|
#include <boost/math/special_functions/erf.hpp> // for inverses
|
|
#include <boost/math/constants/constants.hpp>
|
|
#include <fstream>
|
|
#include <boost/math/tools/test_data.hpp>
|
|
#include "mp_t.hpp"
|
|
|
|
using namespace boost::math::tools;
|
|
using namespace std;
|
|
|
|
float external_f;
|
|
float force_truncate(const float* f)
|
|
{
|
|
external_f = *f;
|
|
return external_f;
|
|
}
|
|
|
|
float truncate_to_float(mp_t r)
|
|
{
|
|
float f = boost::math::tools::real_cast<float>(r);
|
|
return force_truncate(&f);
|
|
}
|
|
|
|
struct erf_data_generator
|
|
{
|
|
boost::math::tuple<mp_t, mp_t> operator()(mp_t z)
|
|
{
|
|
// very naively calculate spots using the gamma function at high precision:
|
|
int sign = 1;
|
|
if(z < 0)
|
|
{
|
|
sign = -1;
|
|
z = -z;
|
|
}
|
|
mp_t g1, g2;
|
|
g1 = boost::math::tgamma_lower(mp_t(0.5), z * z);
|
|
g1 /= sqrt(boost::math::constants::pi<mp_t>());
|
|
g1 *= sign;
|
|
|
|
if(z < 0.5)
|
|
{
|
|
g2 = 1 - (sign * g1);
|
|
}
|
|
else
|
|
{
|
|
g2 = boost::math::tgamma(mp_t(0.5), z * z);
|
|
g2 /= sqrt(boost::math::constants::pi<mp_t>());
|
|
}
|
|
if(sign < 1)
|
|
g2 = 2 - g2;
|
|
return boost::math::make_tuple(g1, g2);
|
|
}
|
|
};
|
|
|
|
double double_factorial(int N)
|
|
{
|
|
double result = 1;
|
|
while(N > 2)
|
|
{
|
|
N -= 2;
|
|
result *= N;
|
|
}
|
|
return result;
|
|
}
|
|
|
|
void asymptotic_limit(int Bits)
|
|
{
|
|
//
|
|
// The following block of code estimates how large z has
|
|
// to be before we can use the asymptotic expansion for
|
|
// erf/erfc and still get convergence: the series becomes
|
|
// divergent eventually so we have to be careful!
|
|
//
|
|
double result = (std::numeric_limits<double>::max)();
|
|
int terms = 0;
|
|
for(int n = 1; n < 15; ++n)
|
|
{
|
|
double lim = (Bits-n) * log(2.0) - log(sqrt(3.14)) + log(double_factorial(2*n+1));
|
|
double x = 1;
|
|
while(x*x + (2*n+1)*log(x) <= lim)
|
|
x += 0.1;
|
|
if(x < result)
|
|
{
|
|
result = x;
|
|
terms = n;
|
|
}
|
|
}
|
|
|
|
std::cout << "Erf asymptotic limit for "
|
|
<< Bits << " bit numbers is "
|
|
<< result << " after approximately "
|
|
<< terms << " terms." << std::endl;
|
|
|
|
result = (std::numeric_limits<double>::max)();
|
|
terms = 0;
|
|
for(int n = 1; n < 30; ++n)
|
|
{
|
|
double x = pow(double_factorial(2*n+1)/pow(2.0, n-Bits), 1 / (2.0*n));
|
|
if(x < result)
|
|
{
|
|
result = x;
|
|
terms = n;
|
|
}
|
|
}
|
|
|
|
std::cout << "Erfc asymptotic limit for "
|
|
<< Bits << " bit numbers is "
|
|
<< result << " after approximately "
|
|
<< terms << " terms." << std::endl;
|
|
}
|
|
|
|
boost::math::tuple<mp_t, mp_t> erfc_inv(mp_t r)
|
|
{
|
|
mp_t x = exp(-r * r);
|
|
x = x.convert_to<double>();
|
|
std::cout << x << " ";
|
|
mp_t result = boost::math::erfc_inv(x);
|
|
std::cout << result << std::endl;
|
|
return boost::math::make_tuple(x, result);
|
|
}
|
|
|
|
|
|
int main(int argc, char*argv [])
|
|
{
|
|
parameter_info<mp_t> arg1;
|
|
test_data<mp_t> data;
|
|
|
|
bool cont;
|
|
std::string line;
|
|
|
|
if(argc >= 2)
|
|
{
|
|
if(strcmp(argv[1], "--limits") == 0)
|
|
{
|
|
asymptotic_limit(24);
|
|
asymptotic_limit(53);
|
|
asymptotic_limit(64);
|
|
asymptotic_limit(106);
|
|
asymptotic_limit(113);
|
|
return 0;
|
|
}
|
|
else if(strcmp(argv[1], "--erf_inv") == 0)
|
|
{
|
|
mp_t (*f)(mp_t);
|
|
f = boost::math::erf_inv;
|
|
std::cout << "Welcome.\n"
|
|
"This program will generate spot tests for the inverse erf function:\n";
|
|
std::cout << "Enter the number of data points: ";
|
|
int points;
|
|
std::cin >> points;
|
|
data.insert(f, make_random_param(mp_t(-1), mp_t(1), points));
|
|
}
|
|
else if(strcmp(argv[1], "--erfc_inv") == 0)
|
|
{
|
|
boost::math::tuple<mp_t, mp_t> (*f)(mp_t);
|
|
f = erfc_inv;
|
|
std::cout << "Welcome.\n"
|
|
"This program will generate spot tests for the inverse erfc function:\n";
|
|
std::cout << "Enter the maximum *result* expected from erfc_inv: ";
|
|
double max_val;
|
|
std::cin >> max_val;
|
|
std::cout << "Enter the number of data points: ";
|
|
int points;
|
|
std::cin >> points;
|
|
parameter_info<mp_t> arg = make_random_param(mp_t(0), mp_t(max_val), points);
|
|
arg.type |= dummy_param;
|
|
data.insert(f, arg);
|
|
}
|
|
}
|
|
else
|
|
{
|
|
std::cout << "Welcome.\n"
|
|
"This program will generate spot tests for the erf and erfc functions:\n"
|
|
" erf(z) and erfc(z)\n\n";
|
|
|
|
do{
|
|
if(0 == get_user_parameter_info(arg1, "a"))
|
|
return 1;
|
|
data.insert(erf_data_generator(), arg1);
|
|
|
|
std::cout << "Any more data [y/n]?";
|
|
std::getline(std::cin, line);
|
|
boost::algorithm::trim(line);
|
|
cont = (line == "y");
|
|
}while(cont);
|
|
}
|
|
|
|
std::cout << "Enter name of test data file [default=erf_data.ipp]";
|
|
std::getline(std::cin, line);
|
|
boost::algorithm::trim(line);
|
|
if(line == "")
|
|
line = "erf_data.ipp";
|
|
std::ofstream ofs(line.c_str());
|
|
ofs << std::scientific << std::setprecision(40);
|
|
write_code(ofs, data, "erf_data");
|
|
|
|
return 0;
|
|
}
|
|
|
|
/* Output for asymptotic limits:
|
|
|
|
Erf asymptotic limit for 24 bit numbers is 2.8 after approximately 6 terms.
|
|
Erfc asymptotic limit for 24 bit numbers is 4.12064 after approximately 17 terms.
|
|
Erf asymptotic limit for 53 bit numbers is 4.3 after approximately 11 terms.
|
|
Erfc asymptotic limit for 53 bit numbers is 6.19035 after approximately 29 terms.
|
|
Erf asymptotic limit for 64 bit numbers is 4.8 after approximately 12 terms.
|
|
Erfc asymptotic limit for 64 bit numbers is 7.06004 after approximately 29 terms.
|
|
Erf asymptotic limit for 106 bit numbers is 6.5 after approximately 14 terms.
|
|
Erfc asymptotic limit for 106 bit numbers is 11.6626 after approximately 29 terms.
|
|
Erf asymptotic limit for 113 bit numbers is 6.8 after approximately 14 terms.
|
|
Erfc asymptotic limit for 113 bit numbers is 12.6802 after approximately 29 terms.
|
|
*/
|
|
|