Floating Point/Rounding

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IEEE 754 specified four distinct rounding modes. We will talk about those modes, and their effects in this chapter. Also, rounding can play an important role in the accuracy of a floating-point computation, so we will discuss those effects here as well.

Rounding Modes[edit]

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Rounding Errors[edit]

Relative Error[edit]

Relative error is one measure of error commonly used with floating point numbers. If \tilde x is an approximation to x, then the relative error, r, is defined as

  r = {{|x - \tilde x|} \over x}