creating full range of random floats using std::random - c++

Question

I'm attempting to test a mathematical class I've created using random numbers from the full range of representable positivefloats, but I find that I seem to be having a problem with my use of std::random. This program
#include <random>
#include <iostream>
#include <functional>
template <typename T>
class Rand {
public:
Rand(T lo=std::numeric_limits<T>::min(),
T hi=std::numeric_limits<T>::max()) :
r(bind(std::uniform_real_distribution<>(lo, hi),std::mt19937_64{})) {}
T operator()() const { return r(); }
private:
std::function<T()> r;
};
int main()
{
Rand<float> f{};
const int samples = 1000000;
float min = std::numeric_limits<float>::max();
float max = std::numeric_limits<float>::min();
std::cout << "range min = " << max
<< ", max = " << min << '\n';
for (int i=0; i < samples; ++i) {
float r = f();
if (r < min) min = r;
if (r > max) max = r;
}
std::cout << "for n = " << samples
<< "\nsample min = " << min
<< ", max = " << max << std::endl;
}
produces this output
range min = 1.17549e-38, max = 3.40282e+38
for n = 1000000
sample min = 8.14884e+31, max = 3.40281e+38
Clearly the range is extremely skewed toward larger numbers. How do I generate the desired range of floats with a uniform distribution?

Answer 1

In addition to the statistics you have printed out, I've computed both the theoretical and actual mean, variance, skew and kurtosis of this distribution. Here is my code, and the results:
#include <random>
#include <iostream>
#include <functional>
#include <vector>
#include <numeric>
#include <cmath>
template <typename T>
class Rand {
public:
Rand(T lo=std::numeric_limits<T>::min(),
T hi=std::numeric_limits<T>::max()) :
r(bind(std::uniform_real_distribution<>(lo, hi),std::mt19937_64{})) {}
T operator()() const { return r(); }
private:
std::function<T()> r;
};
template <class T>
inline
T
sqr(T x)
{
return x * x;
}
int main()
{
Rand<float> f{};
const int samples = 1000000;
float min = std::numeric_limits<float>::max();
float max = std::numeric_limits<float>::min();
std::vector<float> u;
std::cout << "range min = " << max
<< ", max = " << min << '\n';
for (int i=0; i < samples; ++i) {
float r = f();
if (r < min) min = r;
if (r > max) max = r;
u.push_back(r);
}
std::cout << "for n = " << samples
<< "\nsample min = " << min
<< ", max = " << max << std::endl;
double mean = std::accumulate(u.begin(), u.end(),
double(0)) / u.size();
double var = 0;
double skew = 0;
double kurtosis = 0;
for (int i = 0; i < u.size(); ++i)
{
double d = (u[i] - mean);
double d2 = sqr(d);
var += d2;
skew += d * d2;
kurtosis += d2 * d2;
}
var /= u.size();
double dev = std::sqrt(var);
skew /= u.size() * dev * var;
kurtosis /= u.size() * var * var;
kurtosis -= 3;
double x_mean = ((double)min + max) / 2;
double x_var = sqr((double)max - min) / 12;
double x_skew = 0;
double x_kurtosis = -6./5;
std::cout << std::scientific << '\n';
std::cout << " expected actual\n";
std::cout << "mean " << x_mean << " " << mean << "\n";
std::cout << "variance " << x_var << " " << var << "\n";
std::cout << "skew " << x_skew << " " << skew << "\n";
std::cout << "kurtosis " << x_kurtosis << " " << kurtosis << "\n";
}
And here are the results:
range min = 1.17549e-38, max = 3.40282e+38
for n = 1000000
sample min = 8.14884e+31, max = 3.40281e+38
expected actual
mean 1.701407e+38 1.700724e+38
variance 9.649275e+75 9.645774e+75
skew 0.000000e+00 7.401975e-04
kurtosis -1.200000e+00 -1.199432e+00
Everything is looking pretty good to me.

Answer 2

The biggest point you are missing is that you are not generating numbers between (-max_value,max_value) , but between ( 0 ,max_value).
There are about pow(10,32) numbers between 0 and 8.14884e+31, but there are about pow(10,37) numbers between 8.14884e+31 and 3.40281e+38. Hence the result is obvious.