Getting to the Bits in C++

Getting to the Bits in C++

The basic 32-bit floating-point number in C++ is a float with a size of 4 bytes. How can you manipulate the bits in a floating-point value, using the 32-bit float type? You cannot use any of the C++ bitwise operators on floating-point numbers, as they only work for integers.

The trick is to convert it to an unsigned integer (32-bit) with the same bits, and then use the integer bitwise operations. The obvious way to convert a float to unsigned is casting:

    float f = 3.14f;
    unsigned int u = (unsigned)f;  // Fail!

Nope. That doesn't get to the bits, because it does a proper conversion between floating-point numbers and integers, which is usually what you want when you aren't thinking about bits (i.e. all normal people).

To get to the bits in C++, we have to trick the compiler into thinking that it's already got an unsigned integer with pointer type casts:

    unsigned int u = *(unsigned int*)(&f);  // Tricky!

That's a bit old-school for type casting. Here's the modern way with reinterpret_cast:

    unsigned int u = *reinterpret_cast<unsigned int*>(&f);

Once we have the bits, then we can twiddle the bits of our unsigned integer to our heart's content. When we're finished, we can do the same trick in reverse to re-create a floating-point number:

    f = *(float *)(&u);   // Floating again...
    f = *reinterpret_cast<float*> (&u);  // Trendy version

And here's a timely reminder that it's important to use an “unsigned” type in C++ for the bit faking code, because the “>>” right-shift operator has undefined behavior on negatives.

Other Methods: Type casts aren't the only way in C++. There's also a trick involving “union” structures, and you can also directly copy the bits to a differently typed variable using “memcpy” or “bcopy”.

It seems to me that this type cast trick should be the fastest way, because a good compiler should convert the address-of, reinterpret_cast and indirection sequence into a simple variable copy, especially with the “reinterpret_cast” hint. However, I haven't actually benchmarked the speed of the different methods.

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