The abc conjecture and correctly rounded reciprocal square roots
نویسندگان
چکیده
منابع مشابه
The abc conjecture and correctly rounded reciprocal square roots
The reciprocal square root calculation = 1= √ x is very common in scienti/c computations. Having a correctly rounded implementation of it is of great importance in producing numerically predictable code among today’s heterogenous computing environment. Existing results suggest that to get the correctly rounded in a 3oating point number system with p signi/cant bits, we may have to compute up to...
متن کاملTowards Correctly Rounded Transcendentals
The Table Maker’s Dilemma is the problem of always getting correctly rounded results when computing the elementary functions. After a brief presentation of this problem, we present new developments that have helped us to solve this problem for the double-precision exponential function in a small domain. These new results show that this problem can be solved, at least for the double-precision fo...
متن کاملRELAXATIONS OF THE ABC CONJECTURE USING INTEGER k ’TH ROOTS
Weakened forms of the ABC conjecture are defined in terms of the upper k’th root functions. These weakened forms, with quite small explicit values of their parameters, are shown to imply the asymptotic Fermat, Beale, general Fermat, and Catalan conjectures, that there exist an infinite number of non–Wieferich primes, that there exist only finitely many consecutive powerful numbers, Hall’s conje...
متن کاملFast and correctly rounded logarithms in double-precision
This article is a case study in the implementation of a portable, proven and efficient correctly rounded elementary function in double-precision. We describe the methodology used to achieve these goals in the crlibm library. There are two novel aspects to this approach. The first is the proof framework, and in general the techniques used to balance performance and provability. The second is the...
متن کاملAugmented precision square roots , 2 - D norms , and discussion on correctly rounding √ x 2 + y 2 .
Define an “augmented precision” algorithm as an algorithm that returns, in precision-p floating-point arithmetic, its result as the unevaluated sum of two floatingpoint numbers, with a relative error of the order of 2−2p. Assuming an FMA instruction is available, we perform a tight error analysis of an augmented precision algorithm for the square root, and introduce two slightly different augme...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: Theoretical Computer Science
سال: 2004
ISSN: 0304-3975
DOI: 10.1016/j.tcs.2004.01.013