erroneous Visual C float / double conversion?

Question

In Visual C++ i wrote the following sample in a C++ program:

float f1 = 42.48f;
double d1 = 42.48;
double d2 = f1;

I compiled the program with Visual Studio 2005. In the debugger i see the following values:

f1  42.480000   float
d1  42.479999999999997  double
d2  42.479999542236328  double

d1 by my knowledege is OK, but d2 is wrong.

The problem occurs as well with /fp=precise as with /fp=strict as with /fp=fast.

Whats the problem here? Any hint how to avoid this Problem? This leads to serious numerical problems.

Answer 1

This isn't an issue with VC++ or anything like that - it's a fundamental issue with how floating point numbers are stored on the computer. For more information, see IEEE-754.

The issue is that a conversion from float to double is done such that converting back from double to float results in exactly the same float value that you started with. I'm not aware of any way around the loss of precision, except to use only doubles when you need the longer precision. It may be that trying to round the converted float to two decimal places will set it to the correct value, but I'm not sure of that.