How is floating point stored? When does it matter?

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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.)

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