Finite Precision Rational Arithmetic: An Arithmetic Unit
Copyright policy )Finite Precision Rational Arithmetic: An Arithmetic Unit
The foundations of an arithmetic unit performing the add, subtract, multiply, and divide operations on rational operands are developed. The unit uses the classical Euclidean algorithm as one unified algorithm for all the arithmetic operations, including rounding. Binary implementations are discussed, based on techniques known from SRT division, and utilizing ripple-free borrow-save and carry-save addition. Average time behavior is investigated.
- Aarhus University Denmark
- Southern Methodist University United States
Farey approximations, Continued fractions and generalizations, continued fraction expansion, Analysis of algorithms and problem complexity, Continued fractions, Interval and finite arithmetic, finite arithmetic, complexity analysis, rational numbers, mediant rounding, exact rational arithmetic, Euclidean algorithm
Farey approximations, Continued fractions and generalizations, continued fraction expansion, Analysis of algorithms and problem complexity, Continued fractions, Interval and finite arithmetic, finite arithmetic, complexity analysis, rational numbers, mediant rounding, exact rational arithmetic, Euclidean algorithm
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