Saturation Arithmetic
Saturation arithmetic is a version of arithmetic in which all operations such as addition and multiplication are limited to a fixed range between a minimum and maximum value. If the result of an operation is greater than the maximum it is set (“clamped”) to the maximum, while if it is below the minimum it is clamped to the minimum. The name comes from how the value becomes “saturated” once it reaches the extreme values; further additions to a maximum or subtractions from a minimum will not change the result.
Typically, early computer microprocessors did not implement integer arithmetic operations using saturation arithmetic; instead, they used the easier-to-implement modular arithmetic, in which values exceeding the maximum value “wrap around” to the minimum value, like the hours on a clock passing from 12 to 1. In hardware, modular arithmetic with a minimum of zero and a maximum of 2n can be implemented by simply discarding all but the lowest n bits.
However, although more difficult to implement, saturation arithmetic has numerous practical advantages. The result is as numerically close to the true answer as possible; it’s considerably less surprising to get an answer of 127 instead of 130 than to get an answer of −126 instead of 130. It also enables overflow of additions and multiplications to be detected consistently without an overflow bit or excessive computation by simple comparison with the maximum or minimum value (provided the datum is not permitted to take on these values).
Additionally, saturation arithmetic enables efficient algorithms for many problems, particularly in digital signal processing. For example, adjusting the volume level of a sound signal can result in overflow, and saturation causes significantly less distortion to the sound than wrap-around.
via Saturation arithmetic – Wikipedia, the free encyclopedia.