Inverting Frexp With Ldexp

If I understand the documentation correctly, we should be able to use ldexp to recover a floating point number decomposed into a signed mantissa and an exponent by frexp. I have be

Solution 1:

Modify your C++ program by including the typeinfo header and inserting the following lines right before the calls to compare in your test_ldexp function.

std::cout << "types:" << std::endl;
std::cout << "  x         : " << typeid(x).name() << std::endl;
std::cout << "  mantissa  : " << typeid(frexp(x, &exponent)).name()
          << std::endl;
std::cout << "  ldexp(...): " << typeid(ldexp(x, 0)).name() << std::endl;
std::cout << "  ldexp(...): " << typeid(ldexp(mantissa, exponent)).name()
          << std::endl;

The output is now:

max=3.402823466385288598117042e+38, max_exp=128, max_10_exp=38,
min=1.175494350822287507968737e-38, min_exp=-125, min_10_exp=-37, dig=6,
mant_dig=24, epsilon=1.1920928955078125e-07, radix=2, rounds=1
types:
  x         : f
  mantissa  : d
  ldexp(...): d
  ldexp(...): d
1.000000119209289550781251.00000011920928955078125 (equal)
1.000000119209289550781251.00000011920928955078125 (equal)

max=1.797693134862315708145274e+308, max_exp=1024, max_10_exp=308,
min=2.225073858507201383090233e-308, min_exp=-1021, min_10_exp=-307, dig=15,
mant_dig=53, epsilon=2.220446049250313080847263e-16, radix=2, rounds=1
types:
  x         : d
  mantissa  : d
  ldexp(...): d
  ldexp(...): d
1.0000000000000002220446051.000000000000000222044605 (equal)
1.0000000000000002220446051.000000000000000222044605 (equal)

max=1.189731495357231765021264e+4932, max_exp=16384, max_10_exp=4932,
min=3.362103143112093506262678e-4932, min_exp=-16381, min_10_exp=-4931, dig=18,
mant_dig=64, epsilon=1.084202172485504434007453e-19, radix=2, rounds=1
types:
  x         : e
  mantissa  : d
  ldexp(...): d
  ldexp(...): d
1.000000000000000000108421 (unequal)
1.000000000000000000108421 (unequal)

frexpr and ldexpr are returning doubles no matter what type you put in! It appears that you are using the functions defined in math.h (see here and here) instead those defined in cmath. Replace your calls to frexpr and ldexpr with calls to std::frexpr and std::ldexpr and your code will work as you expect.