Exponential Sums and Correctly-Rounded Functions
نویسندگان
چکیده
منابع مشابه
Towards 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 کاملParallel Hardware Designs for Correctly Rounded Elementary Functions
This paper presents an algorithm for evaluating the functions of reciprocal, square root, 2, and log2(x) with special purpose hardware. For these functions, the algorithm produces correctly rounded results, according to a specified rounding mode. This algorithm can be used to implement directed rounding which is essential for interval arithmetic, or exact rounding which minimizes the maximum er...
متن کاملBilinear Sums with Exponential Functions
Let g = 0,±1 be a fixed integer. Given two sequences of complex numbers (φm) ∞ m=1 and (ψn) ∞ n=1 and two sufficiently large integers M and N , we estimate the exponential sums ∑ p≤M gcd(ag,p)=1 ∑ 1≤n≤N φpψnep (ag ) , a ∈ Z, where the outer summation is taken over all primes p ≤ M with gcd(ag, p) = 1.
متن کاملEmulation of FMA and correctly-rounded sums: proved algorithms using rounding to odd
Rounding to odd is a non-standard rounding on floating-point numbers. By using it for some intermediate values instead of rounding to nearest, correctly rounded results can be obtained at the end of computations. We present an algorithm for emulating the fused multiply-and-add operator. We also present an iterative algorithm for computing the correctly rounded sum of a set floating-point number...
متن کاملOn Approximation of Functions by Exponential Sums
We introduce a new approach, and associated algorithms, for the efficient approximation of functions and sequences by short linear combinations of exponential functions with complex-valued exponents and coefficients. These approximations are obtained for a finite but arbitrary accuracy and typically have significantly fewer terms than Fourier representations. We present several examples of thes...
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: IEEE Transactions on Computers
سال: 2017
ISSN: 0018-9340
DOI: 10.1109/tc.2017.2690850