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Suppose . We can represent it as by simply discarding (``chopping'') the digits which do not fit the mantissa format (here the remaining digits are 625). We see that the FP representation is precisely , and we have . Now, if was negative, , the chopped representation would be , but now this is . Note that in this situation . In consequence, with chopping, we choose if and is . In both situations the floating point number is closer to 0 than the real number , so chopping is also called rounding toward 0.

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Chopping has the advantage of being very simple to implement in hardware. The roundoff error for chopping satisfies

For example:


Adrian Sandu 2001-08-26