Explain an IEEE754 single-/double-precision floating point number

ieee754_explain.cpp

#include <bitset>
#include <iomanip>
#include <iostream>
#include <string.h>

namespace {
template <typename Floating, typename Integral, int expBits>
void explain(Floating x) {
  static_assert(sizeof(Floating) == sizeof(Integral),
                "types not the same size");
  Integral l;
  memcpy(&l, &x, sizeof l);
  int constexpr totalBits = 8 * sizeof l;
  int constexpr fracBits = totalBits - 1 - expBits;
  Integral sign = l >> (totalBits - 1);
  Integral exp = (l >> fracBits) & (((Integral) 1 << expBits) - 1);
  Integral frac = l & (((Integral) 1 << fracBits) - 1);
  bool is_normal = exp;
  Integral bias = ((Integral) 1 << (expBits - 1)) - 1;
  Integral actual_exp = is_normal ? exp - bias : 1 - bias;
  std::cout << "Number:    " << std::setprecision(30) << x << '\n'
            << "           " << std::hexfloat << x << std::defaultfloat << '\n'
            << "Sign bit:  " << std::bitset<1>(sign) << '\n'
            << "Exp bits:  " << std::bitset<expBits>(exp) << '\n'
            << "Frac bits: " << std::bitset<fracBits>(frac) << '\n';

  if (exp != ((Integral) 1 << expBits) - 1)
    std::cout << "Actual exponent: " << actual_exp << '\n'
              << "Mathematical value: " << (sign ? "-" : "") << "2^("
              << actual_exp << ") * (" << (int) is_normal << " + " << frac << " / 2^" << fracBits << ")\n\n";
  else std::cout << "\n";
}
}

void explain_double(double x) {
  explain<double, long, 11>(x);
}

void explain_float(float x) {
  explain<float, int, 8>(x);
}


int main(void) {
  for (int i = 0; i < 20; ++i) {
    explain_float((float) i / 10.0f);
    explain_double(i / 10.0);
  }

  explain_double(4.9406564584124654418e-324); // Smallest (positive) denormal
  explain_double(2.2250738585072008890e-308); // Biggest denormal
  explain_double(2.2250738585072013831e-308); // Smallest (positive) normal
  explain_double(1.7976931348623157081e+308); // Biggest normal

  explain_double(1.0 / 0.0);
  explain_double(0.0 / 0.0);
}