Despite the mathematical elegance of Knuth's floored division and Euclidean division, it is usually a great deal more common to find a truncated division-based modulo in programming languages.
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In nearly all computing techniques, the quotient q and the rest r of a divided by n fulfill the following situations:
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Quotient and remainder making use of rounded division Typical Lisp and IEEE 754 use rounded division, for which the quotient is defined by
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