A dividing method utilizing the best multiplication in affine arithmetic
نویسندگان
چکیده
منابع مشابه
Affine Arithmetic
We give a formalization of affine forms [1, 2] as abstract representations of zonotopes. We provide affine operations as well as overapproximations of some non-affine operations like multiplication and division. Expressions involving those operations can automatically be turned into (executable) functions approximating the original expression in affine arithmetic. Moreover we give a verified im...
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In this paper we give mathematical proofs of two new results relevant to evaluating algebraic functions over a box-shaped region: (i) using interval arithmetic in centered form is always more accurate than standard affine arithmetic, and (ii) modified affine arithmetic is always more accurate than interval arithmetic in centered form. Test results show that modified affine arithmetic is not onl...
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Affine arithmetic (AA) is widely used in range analysis in word-length optimization of hardware designs. To reduce the uncertainty in the AA and achieve efficient and accurate range analysis of multiplication, this paper presents a novel refined affine approximation method, Approximation Affine based on Space Extreme Estimation (AASEE). The affine form of multiplication is divided into two part...
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We present a new RNS modular multiplication for very large operands. The algorithm is based on Montgomery's method adapted to residue arithmetic. By choosing the moduli of the RNS system reasonably large, an eeect corresponding to a redundant high-radix implementation is achieved, due to the carry-free nature of residue arithmetic. The actual computation in the multiplication takes place in con...
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Affine arithmetic (AA) is a model for self-validated computation which, like standard interval arithmetic (IA), produces guaranteed enclosures for computed quantities, taking into account any uncertainties in the input data as well as all internal truncation and roundoff errors. Unlike standard IA, the quantity representations used by AA are first-order approximations, whose error is generally ...
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ژورنال
عنوان ژورنال: IEICE Electronics Express
سال: 2004
ISSN: 1349-2543
DOI: 10.1587/elex.1.176