Modular Integer Arithmetic
نویسندگان
چکیده
منابع مشابه
Lecture 1 & 2 : Integer and Modular Arithmetic
Efficient recipes for performing integer arithmetic are indispensable as they are widely used in several algorithms in diverse areas such as cryptology, computer graphics and other engineering areas. Hence our first object of study would be the most basic integer operations namely addition, subtraction, multiplication and division. We will start off with algorithms that are typically referred t...
متن کاملModular Integer Arithmetic 1 Christoph Schwarzweller Institute of Computer
In this article we show the correctness of integer arithmetic based on Chinese Remainder theorem as described e.g. in [11]: Integers are transformed to finite sequences of modular integers, on which the arithmetic operations are performed. Retransformation of the results to the integers is then accomplished by means of the Chinese Remainder theorem. The method presented is a typical example for...
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This paper investigates performance and energy characteristics of software algorithms for long integer arithmetic. We analyze and compare the number of RISC-like processor instructions (e.g. singleprecision multiplication, addition, load, and store instructions) required for the execution of different algorithms such as Schoolbook multiplication, Karatsuba and Comba multiplication, as well as M...
متن کاملModular arithmetic
Since congruence modulo m is an equivalence relation, it partitions the universe of integers into equivalence classes, which we’ll call congruence classes modulo m. Within any one of these classes, all of the members are congruent to all of the other members; but congruence modulo m never holds between members of different equivalence classes. For instance, there are two congruence classes modu...
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Some codes require computations to use fewer bits of precision than are normal for the target machine. For example, Java requires 32-bit arithmetic even on a 64-bit target. To run narrow codes on a wide target machine, we present a widening transformation. Almost every narrow operation can be widened by signor zero-extending the operands and using a target-machine instruction at its natural wid...
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ژورنال
عنوان ژورنال: Formalized Mathematics
سال: 2008
ISSN: 1898-9934,1426-2630
DOI: 10.2478/v10037-008-0029-8