منابع مشابه
Ultimately Fast Accurate Summation
We present two new algorithms FastAccSum and FastPrecSum, one to compute a faithful rounding of the sum of floating-point numbers and the other for a result “as if” computed in K-fold precision. Faithful rounding means the computed result either is one of the immediate floating-point neighbors of the exact result or is equal to the exact sum if this is a floating-point number. The algorithms ar...
متن کاملAccurate floating point summation∗
We present and analyze several simple algorithms for accurately summing n floating point numbers S = ∑n i=1 si, independent of how much cancellation occurs in the sum. Let f be the number of significant bits in the si. We assume a register is available with F > f significant bits. Then assuming that (1) n ≤ b2F−f/(1 − 2−f )c + 1, (2) rounding is to nearest, (3) no overflow occurs, and (4) all u...
متن کاملAccurate Floating - Point Summation ∗
Given a vector of floating-point numbers with exact sum s, we present an algorithm for calculating a faithful rounding of s into the set of floating-point numbers, i.e. one of the immediate floating-point neighbors of s. If the s is a floating-point number, we prove that this is the result of our algorithm. The algorithm adapts to the condition number of the sum, i.e. it is very fast for mildly...
متن کاملFast Acceleration of Ultimately Periodic Relations
Computing transitive closures of integer relations is the key to finding precise invariants of integer programs. In this paper, we describe an efficient algorithm for computing the transitive closures of difference bounds, octagonal and finite monoid affine relations. On the theoretical side, this framework provides a common solution to the acceleration problem, for all these three classes of r...
متن کاملGosper’s Algorithm and Accurate Summation as Definite Summation Tools
Sufficient conditions are given for validity of the discrete Newton-Leibniz formula when the indefinite sum is obtained either by Gosper’s algorithm or by Accurate Summation algorithm. It is shown that sometimes a polynomial can be factored from the summand in such a way that the safe summation range is inreased.
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: SIAM Journal on Scientific Computing
سال: 2009
ISSN: 1064-8275,1095-7197
DOI: 10.1137/080738490