Correctly Rounded Arbitrary-Precision Floating-Point Summation
نویسندگان
چکیده
منابع مشابه
Algorithms for arbitrary precision floating point arithmetic
We present techniques which may be used to perform computations of very high accuracy using only straightforward oating point arithmetic operations of limited precision, and we prove the validity of these techniques under very general hypotheses satissed by most implementations of oating point arithmetic. To illustrate the application of these techniques, we present an algorithm which computes ...
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• If m > n, the exact quotient of two n-bit numbers cannot be an m-bit number. • Let x, y ∈ Mn. x = y ⇒ |x/y − 1| ≥ 2−n. We call a breakpoint a value z where the rounding changes, that is, if t1 and t2 are real numbers satisfying t1 < z < t2 and ◦t is the rounding mode, then ◦t(t1) < ◦t(t2). For “directed” rounding modes (i.e., towards +∞, −∞ or 0), the breakpoints are the FP numbers. For round...
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ژورنال
عنوان ژورنال: IEEE Transactions on Computers
سال: 2017
ISSN: 0018-9340
DOI: 10.1109/tc.2017.2690632