How is floating point stored? When does it matter?

Solution 1:

As mentioned, the Wikipedia article on IEEE 754 does a good job of showing how floating point numbers are stored on most systems.

Now, here are some common gotchas:

• The biggest is that you almost never want to compare two floating point numbers for equality (or inequality). You'll want to use greater than/less than comparisons instead.
• The more operations you do on a floating point number, the more significant rounding errors can become.
• Precision is limited by the size of the fraction, so you may not be able to correctly add numbers that are separated by several orders of magnitude. (For example, you won't be able to add 1E-30 to 1E30.)

Solution 2:

The standard is IEEE 754.

Of course, there are other means to store numbers when IEE754 isn't good enough. Libraries like Java's BigDecimal are available for most platforms and map well to SQL's number type. Symbols can be used for irrational numbers, and ratios that can't be accurately represented in binary or decimal floating point can be stored as a ratio.

Solution 3:

As to the second part of your question, unless performance and efficiency are important for your project, then I suggest you transfer the floating point data as a string over TCP/IP. This lets you avoid issues such as byte alignment and will ease debugging.

Solution 4:

Basically what you need to worry about in floating point numbers is that there is a limited number of digits of precision. This can cause problems when testing for equality, or if your program actually needs more digits of precision than what that data type give you.

In C++, a good rule of thumb is to think that a float gives you 7 digits of precision, while a double gives you 15. Also, if you are interested in knowing how to test for equality, you can look at this question thread.