Hash function for floats

Question

I'm currently implementing a hash table in C++ and I'm trying to make a hash function for floats...

I was going to treat floats as integers by padding the decimal numbers, but then I realized that I would probably reach the overflow with big numbers...

Is there a good way to hash floats?

You don't have to give me the function directly, but I'd like to see/understand different concepts...

Notes:

1. I don't need it to be really fast, just evenly distributed if possible.

2. I've read that floats should not be hashed because of the speed of computation, can someone confirm/explain this and give me other reasons why floats should not be hashed? I don't really understand why (besides the speed)

Answer 1

It depends on the application but most of time floats should not be hashed because hashing is used for fast lookup for exact matches and most floats are the result of calculations that produce a float which is only an approximation to the correct answer. The usually way to check for floating equality is to check if it is within some delta (in absolute value) of the correct answer. This type of check does not lend itself to hashed lookup tables.

EDIT:

Normally, because of rounding errors and inherent limitations of floating point arithmetic, if you expect that floating point numbers a and b should be equal to each other because the math says so, you need to pick some relatively small delta > 0, and then you declare a and b to be equal if abs(a-b) < delta, where abs is the absolute value function. For more detail, see this article.

Here is a small example that demonstrates the problem:

float x = 1.0f;
x = x / 41;
x = x * 41;
if (x != 1.0f)
{
    std::cout << "ooops...\n";
}

Depending on your platform, compiler and optimization levels, this may print ooops... to your screen, meaning that the mathematical equation x / y * y = x does not necessarily hold on your computer.

There are cases where floating point arithmetic produces exact results, e.g. reasonably sized integers and rationals with power-of-2 denominators.