Towards Correctly Rounded Transcendentals
نویسندگان
چکیده
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 format, for the most usual functions.
منابع مشابه
Some notes for a proposal for elementary function implementation in floating-point arithmetic
In the present document, we present some aspects of what a standard for the implementation of the elementary functions could be. We do not claim that we always suggest the right choices, or that we have thought about all relevant issues. The mere goal of this paper is to raise questions and to launch the discussion towards a standard. 1 Introductory discussion We take the opportunity of the cur...
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 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 کاملCorrectly Rounded Binary-Decimal and Decimal-Binary Conversions
This note discusses the main issues in performing correctly rounded decimal-to-binary and binary-to-decimal conversions. It reviews recent work by Clinger and by Steele and White on these conversions and describes some efficiency enhancements. Computational experience with several kinds of arithmetic suggests that the average computational cost for correct rounding can be small for typical conv...
متن کاملPrinting Floating - Point
This paper presents a fast and accurate algorithm for printing oating-point numbers in both free-and xed-format modes. In free-format mode, the algorithm generates the shortest, correctly rounded output string that converts to the same number when read back in, accommodating whatever rounding mode the reader uses. In xed-format mode, the algorithm generates a correctly rounded output string usi...
متن کامل